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 \(\chi_{2527}(160,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7581.db
\(\chi_{7581}(160,\cdot)\) \(\chi_{7581}(202,\cdot)\) \(\chi_{7581}(559,\cdot)\) \(\chi_{7581}(601,\cdot)\) \(\chi_{7581}(958,\cdot)\) \(\chi_{7581}(1000,\cdot)\) \(\chi_{7581}(1357,\cdot)\) \(\chi_{7581}(1399,\cdot)\) \(\chi_{7581}(1756,\cdot)\) \(\chi_{7581}(1798,\cdot)\) \(\chi_{7581}(2155,\cdot)\) \(\chi_{7581}(2197,\cdot)\) \(\chi_{7581}(2554,\cdot)\) \(\chi_{7581}(2953,\cdot)\) \(\chi_{7581}(2995,\cdot)\) \(\chi_{7581}(3352,\cdot)\) \(\chi_{7581}(3394,\cdot)\) \(\chi_{7581}(3751,\cdot)\) \(\chi_{7581}(3793,\cdot)\) \(\chi_{7581}(4150,\cdot)\) \(\chi_{7581}(4192,\cdot)\) \(\chi_{7581}(4549,\cdot)\) \(\chi_{7581}(4591,\cdot)\) \(\chi_{7581}(4948,\cdot)\) \(\chi_{7581}(4990,\cdot)\) \(\chi_{7581}(5389,\cdot)\) \(\chi_{7581}(5746,\cdot)\) \(\chi_{7581}(5788,\cdot)\) \(\chi_{7581}(6145,\cdot)\) \(\chi_{7581}(6187,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((2528,6499,1807)\) → \((1,-1,e\left(\frac{79}{114}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(20\) |
| \( \chi_{ 7581 }(160, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{114}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{31}{114}\right)\) | \(e\left(\frac{3}{38}\right)\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{28}{57}\right)\) | \(e\left(\frac{44}{57}\right)\) | \(e\left(\frac{13}{114}\right)\) | \(e\left(\frac{25}{38}\right)\) |