Basic properties
| Modulus: | \(7581\) | |
| Conductor: | \(7581\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7581.cz
\(\chi_{7581}(107,\cdot)\) \(\chi_{7581}(179,\cdot)\) \(\chi_{7581}(506,\cdot)\) \(\chi_{7581}(578,\cdot)\) \(\chi_{7581}(905,\cdot)\) \(\chi_{7581}(977,\cdot)\) \(\chi_{7581}(1304,\cdot)\) \(\chi_{7581}(1703,\cdot)\) \(\chi_{7581}(1775,\cdot)\) \(\chi_{7581}(2102,\cdot)\) \(\chi_{7581}(2174,\cdot)\) \(\chi_{7581}(2501,\cdot)\) \(\chi_{7581}(2573,\cdot)\) \(\chi_{7581}(2900,\cdot)\) \(\chi_{7581}(2972,\cdot)\) \(\chi_{7581}(3299,\cdot)\) \(\chi_{7581}(3371,\cdot)\) \(\chi_{7581}(3698,\cdot)\) \(\chi_{7581}(3770,\cdot)\) \(\chi_{7581}(4097,\cdot)\) \(\chi_{7581}(4169,\cdot)\) \(\chi_{7581}(4496,\cdot)\) \(\chi_{7581}(4568,\cdot)\) \(\chi_{7581}(4895,\cdot)\) \(\chi_{7581}(4967,\cdot)\) \(\chi_{7581}(5294,\cdot)\) \(\chi_{7581}(5366,\cdot)\) \(\chi_{7581}(5693,\cdot)\) \(\chi_{7581}(5765,\cdot)\) \(\chi_{7581}(6092,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((2528,6499,1807)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{61}{114}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(20\) |
| \( \chi_{ 7581 }(4568, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{37}{38}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{13}{38}\right)\) | \(e\left(\frac{85}{114}\right)\) | \(e\left(\frac{5}{114}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{11}{114}\right)\) | \(e\left(\frac{27}{38}\right)\) |