Basic properties
| Modulus: | \(4034\) | |
| Conductor: | \(2017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(168\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2017}(65,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4034.bb
\(\chi_{4034}(65,\cdot)\) \(\chi_{4034}(447,\cdot)\) \(\chi_{4034}(663,\cdot)\) \(\chi_{4034}(727,\cdot)\) \(\chi_{4034}(729,\cdot)\) \(\chi_{4034}(841,\cdot)\) \(\chi_{4034}(957,\cdot)\) \(\chi_{4034}(961,\cdot)\) \(\chi_{4034}(993,\cdot)\) \(\chi_{4034}(1043,\cdot)\) \(\chi_{4034}(1089,\cdot)\) \(\chi_{4034}(1101,\cdot)\) \(\chi_{4034}(1115,\cdot)\) \(\chi_{4034}(1193,\cdot)\) \(\chi_{4034}(1251,\cdot)\) \(\chi_{4034}(1257,\cdot)\) \(\chi_{4034}(1317,\cdot)\) \(\chi_{4034}(1439,\cdot)\) \(\chi_{4034}(1465,\cdot)\) \(\chi_{4034}(1493,\cdot)\) \(\chi_{4034}(1513,\cdot)\) \(\chi_{4034}(1547,\cdot)\) \(\chi_{4034}(1801,\cdot)\) \(\chi_{4034}(2013,\cdot)\) \(\chi_{4034}(2021,\cdot)\) \(\chi_{4034}(2233,\cdot)\) \(\chi_{4034}(2487,\cdot)\) \(\chi_{4034}(2521,\cdot)\) \(\chi_{4034}(2541,\cdot)\) \(\chi_{4034}(2569,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{168})$ |
| Fixed field: | Number field defined by a degree 168 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{59}{168}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 4034 }(65, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{59}{168}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{13}{168}\right)\) | \(e\left(\frac{11}{56}\right)\) | \(e\left(\frac{163}{168}\right)\) | \(e\left(\frac{25}{42}\right)\) |