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 \(\chi_{2527}(46,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7581.dx
\(\chi_{7581}(46,\cdot)\) \(\chi_{7581}(373,\cdot)\) \(\chi_{7581}(445,\cdot)\) \(\chi_{7581}(772,\cdot)\) \(\chi_{7581}(844,\cdot)\) \(\chi_{7581}(1171,\cdot)\) \(\chi_{7581}(1243,\cdot)\) \(\chi_{7581}(1570,\cdot)\) \(\chi_{7581}(1642,\cdot)\) \(\chi_{7581}(1969,\cdot)\) \(\chi_{7581}(2041,\cdot)\) \(\chi_{7581}(2368,\cdot)\) \(\chi_{7581}(2440,\cdot)\) \(\chi_{7581}(2767,\cdot)\) \(\chi_{7581}(2839,\cdot)\) \(\chi_{7581}(3166,\cdot)\) \(\chi_{7581}(3238,\cdot)\) \(\chi_{7581}(3565,\cdot)\) \(\chi_{7581}(3637,\cdot)\) \(\chi_{7581}(3964,\cdot)\) \(\chi_{7581}(4036,\cdot)\) \(\chi_{7581}(4363,\cdot)\) \(\chi_{7581}(4435,\cdot)\) \(\chi_{7581}(4834,\cdot)\) \(\chi_{7581}(5161,\cdot)\) \(\chi_{7581}(5233,\cdot)\) \(\chi_{7581}(5560,\cdot)\) \(\chi_{7581}(5632,\cdot)\) \(\chi_{7581}(5959,\cdot)\) \(\chi_{7581}(6031,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((2528,6499,1807)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{49}{114}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(20\) |
| \( \chi_{ 7581 }(46, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{38}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{11}{38}\right)\) | \(e\left(\frac{31}{38}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{47}{114}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{46}{57}\right)\) | \(e\left(\frac{11}{19}\right)\) |