Basic properties
| Modulus: | \(2646\) | |
| Conductor: | \(1323\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(63\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1323}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2646.cc
\(\chi_{2646}(43,\cdot)\) \(\chi_{2646}(85,\cdot)\) \(\chi_{2646}(169,\cdot)\) \(\chi_{2646}(211,\cdot)\) \(\chi_{2646}(337,\cdot)\) \(\chi_{2646}(421,\cdot)\) \(\chi_{2646}(463,\cdot)\) \(\chi_{2646}(547,\cdot)\) \(\chi_{2646}(673,\cdot)\) \(\chi_{2646}(715,\cdot)\) \(\chi_{2646}(799,\cdot)\) \(\chi_{2646}(841,\cdot)\) \(\chi_{2646}(925,\cdot)\) \(\chi_{2646}(967,\cdot)\) \(\chi_{2646}(1051,\cdot)\) \(\chi_{2646}(1093,\cdot)\) \(\chi_{2646}(1219,\cdot)\) \(\chi_{2646}(1303,\cdot)\) \(\chi_{2646}(1345,\cdot)\) \(\chi_{2646}(1429,\cdot)\) \(\chi_{2646}(1555,\cdot)\) \(\chi_{2646}(1597,\cdot)\) \(\chi_{2646}(1681,\cdot)\) \(\chi_{2646}(1723,\cdot)\) \(\chi_{2646}(1807,\cdot)\) \(\chi_{2646}(1849,\cdot)\) \(\chi_{2646}(1933,\cdot)\) \(\chi_{2646}(1975,\cdot)\) \(\chi_{2646}(2101,\cdot)\) \(\chi_{2646}(2185,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((785,1081)\) → \((e\left(\frac{2}{9}\right),e\left(\frac{1}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 2646 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{38}{63}\right)\) | \(e\left(\frac{31}{63}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{50}{63}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{19}{21}\right)\) |