Basic properties
| Modulus: | \(7581\) | |
| Conductor: | \(2527\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2527}(94,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7581.de
\(\chi_{7581}(94,\cdot)\) \(\chi_{7581}(208,\cdot)\) \(\chi_{7581}(493,\cdot)\) \(\chi_{7581}(607,\cdot)\) \(\chi_{7581}(892,\cdot)\) \(\chi_{7581}(1006,\cdot)\) \(\chi_{7581}(1291,\cdot)\) \(\chi_{7581}(1405,\cdot)\) \(\chi_{7581}(1690,\cdot)\) \(\chi_{7581}(2089,\cdot)\) \(\chi_{7581}(2203,\cdot)\) \(\chi_{7581}(2488,\cdot)\) \(\chi_{7581}(2602,\cdot)\) \(\chi_{7581}(3001,\cdot)\) \(\chi_{7581}(3286,\cdot)\) \(\chi_{7581}(3400,\cdot)\) \(\chi_{7581}(3685,\cdot)\) \(\chi_{7581}(3799,\cdot)\) \(\chi_{7581}(4084,\cdot)\) \(\chi_{7581}(4198,\cdot)\) \(\chi_{7581}(4483,\cdot)\) \(\chi_{7581}(4597,\cdot)\) \(\chi_{7581}(4882,\cdot)\) \(\chi_{7581}(4996,\cdot)\) \(\chi_{7581}(5281,\cdot)\) \(\chi_{7581}(5395,\cdot)\) \(\chi_{7581}(5680,\cdot)\) \(\chi_{7581}(5794,\cdot)\) \(\chi_{7581}(6079,\cdot)\) \(\chi_{7581}(6193,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((2528,6499,1807)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{3}{38}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(20\) |
| \( \chi_{ 7581 }(94, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{114}\right)\) | \(e\left(\frac{47}{57}\right)\) | \(e\left(\frac{17}{114}\right)\) | \(e\left(\frac{9}{38}\right)\) | \(e\left(\frac{32}{57}\right)\) | \(e\left(\frac{41}{57}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{1}{114}\right)\) | \(e\left(\frac{37}{38}\right)\) |