diff --git a/qpms/qpms_c.pyx b/qpms/qpms_c.pyx
index 5635d20..e09d0d5 100644
--- a/qpms/qpms_c.pyx
+++ b/qpms/qpms_c.pyx
@@ -6,6 +6,10 @@ import cmath
 from qpms_cdefs cimport *
 cimport cython
 from cython.parallel cimport parallel, prange
+#import enum
+
+# Here will be enum and dtype definitions; maybe move these to a separate file
+
 
 import math # for copysign in crep methods
 #import re # TODO for crep methods?
@@ -650,17 +654,26 @@ cdef class BaseSpec:
 
     def __cinit__(self, *args, **kwargs):
         cdef const qpms_uvswfi_t[:] ilist_memview
-        if len(args) > 0:
+        if len(args) == 0:
+            if 'lMax' in kwargs.keys(): # if only lMax is specified, create the 'usual' definition in ('E','M') order
+                lMax = kwargs['lMax']
+                my, ny = get_mn_y(lMax)
+                nelem = len(my)
+                tlist = nelem * (QPMS_VSWF_ELECTRIC,) + nelem * (QPMS_VSWF_MAGNETIC,)
+                mlist = 2*list(my)
+                llist = 2*list(ny)
+                ilist = tlm2uvswfi(tlist,llist,mlist)
+            else:
+                raise ValueError
+        else: # len(args) > 0:
             ilist = args[0]
             #self.__ilist = np.array(args[0], dtype=qpms_uvswfi_t, order='C', copy=True) # FIXME define the dtypes at qpms_cdef.pxd level
-            self.__ilist = np.array(args[0], dtype=np.ulonglong, order='C', copy=True)
-            self.__ilist.setflags(write=False)
-            ilist_memview = self.__ilist
-            self.s.ilist = &ilist_memview[0]
-            self.s.n = len(self.__ilist)
-            self.s.capacity = 0 # is this the best way?
-        else:
-            raise ValueError
+        self.__ilist = np.array(ilist, dtype=np.ulonglong, order='C', copy=True)
+        self.__ilist.setflags(write=False)
+        ilist_memview = self.__ilist
+        self.s.ilist = &ilist_memview[0]
+        self.s.n = len(self.__ilist)
+        self.s.capacity = 0 # is this the best way?
         if 'norm' in kwargs.keys():
             self.s.norm = kwargs['norm']
         else:
@@ -936,7 +949,7 @@ cdef class IRot3:
 
     def __mul__(IRot3 self, IRot3 other):
         res = IRot3(CQuat(1,0,0,0), 1) 
-        res.qd = qpms_IRot3_mult(self.qd, other.qd)
+        res.qd = qpms_irot3_mult(self.qd, other.qd)
         return res
 
     def __pow__(IRot3 self, n, _):
@@ -946,7 +959,7 @@ cdef class IRot3:
         else:
             raise ValueError("The exponent of an IRot3 has to have an integer value.")
         res = IRot3(CQuat(1,0,0,0), 1)
-        res.qd = qpms_IRot3_pow(self.qd, n)
+        res.qd = qpms_irot3_pow(self.qd, n)
         return res
 
     def isclose(IRot3 self, IRot3 other, rtol=1e-5, atol=1e-8):
@@ -1011,14 +1024,14 @@ cdef class IRot3:
         r.rot = CQuat(math.cos(math.pi/n),0,0,math.sin(math.pi/n))
         return r
 
-    def as_uvswf_matrix(IRot3 self, basespec bspec):
+    def as_uvswf_matrix(IRot3 self, BaseSpec bspec):
         '''
         Returns the uvswf representation of the current transform as a numpy array
         '''
         cdef ssize_t sz = len(bspec)
         cdef np.ndarray m = np.empty((sz, sz), dtype=complex, order='C') # FIXME explicit dtype
         cdef cdouble[:, ::1] view = m
-        qpms_IRot3_uvswfi_dense(&view[0,0], bspec.rawpointer(), self.qd)
+        qpms_irot3_uvswfi_dense(&view[0,0], bspec.rawpointer(), self.qd)
         return m
 
 cdef class TMatrixInterpolator:
@@ -1045,10 +1058,20 @@ cdef class TMatrix:
         self.t.spec = spec.rawpointer();
         # The following will raise an exception if shape is wrong
         self.m = np.array(matrix, dtype=complex, copy=True, order='C').reshape((len(spec), len(spec)))
+        #self.m.setflags(write=False) # checkme
         cdef cdouble[:,::1] m_memview = self.m
         self.t.m = &(m_memview[0,0])
         self.t.owns_m = False # Memory in self.t.m is "owned" by self.m, not by self.t...
 
+    cdef qpms_tmatrix_t *rawpointer(TMatrix self):
+        '''Pointer to the qpms_tmatrix_t structure.
+        Don't forget to reference the BaseSpec object itself when storing the pointer anywhere!!!
+        '''
+        return &(self.t)
+
+    def as_array(TMatrix self):
+        return np.array(self.m, copy=True)
+
 cdef class FinitePointGroup:
     '''
     Wrapper over the qpms_finite_group_t structure.
@@ -1059,7 +1082,7 @@ cdef class Particle:
     '''
     Wrapper over the qpms_particle_t structure.
     '''
-    cdef readonly qpms_particle_t p
+    cdef qpms_particle_t p
     cdef readonly TMatrix t # We hold the reference to the T-matrix to ensure correct reference counting
 
     def __cinit__(Particle self, position, TMatrix t):
@@ -1074,7 +1097,8 @@ cdef class ScatteringSystem:
     pass
 
 def tlm2uvswfi(t, l, m):
-    ''' TODO doc 
+    ''' TODO doc
+    And TODO this should rather be an ufunc.
     '''
     # Very low-priority TODO: add some types / cythonize
     if isinstance(t, int) and isinstance(l, int) and isinstance(m, int): 
@@ -1082,16 +1106,19 @@ def tlm2uvswfi(t, l, m):
     elif len(t) == len(l) and len(t) == len(m):
         u = list()
         for i in range(len(t)):
-            if not (isinstance(t[i], int) and isinstance(l[i], int) and isinstance(m[i], int)): # not the best check possible, though
+            if not (t[i] % 1 == 0 and l[i] % 1 == 0 and m[i] % 1 == 0): # maybe not the best check possible, though
                 raise ValueError # TODO error message
             u.append(qpms_tmn2uvswfi(t[i],m[i],l[i]))
         return u
     else:
-        raise ValueError # TODO error message
+        print(len(t), len(l), len(m))
+        raise ValueError("Lengths of the t,l,m arrays must be equal, but they are %d, %d, %d." 
+                % (len(t), len(l), len(m)))
 
 
 def uvswfi2tlm(u):
     ''' TODO doc
+    and TODO this should rather be an ufunc.
     '''
     cdef qpms_vswf_type_t t
     cdef qpms_l_t l