Basic properties
| Modulus: | \(916\) | |
| Conductor: | \(916\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(228\) | 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 916.w
\(\chi_{916}(7,\cdot)\) \(\chi_{916}(23,\cdot)\) \(\chi_{916}(31,\cdot)\) \(\chi_{916}(35,\cdot)\) \(\chi_{916}(39,\cdot)\) \(\chi_{916}(47,\cdot)\) \(\chi_{916}(59,\cdot)\) \(\chi_{916}(63,\cdot)\) \(\chi_{916}(67,\cdot)\) \(\chi_{916}(79,\cdot)\) \(\chi_{916}(87,\cdot)\) \(\chi_{916}(119,\cdot)\) \(\chi_{916}(127,\cdot)\) \(\chi_{916}(131,\cdot)\) \(\chi_{916}(139,\cdot)\) \(\chi_{916}(155,\cdot)\) \(\chi_{916}(163,\cdot)\) \(\chi_{916}(179,\cdot)\) \(\chi_{916}(191,\cdot)\) \(\chi_{916}(219,\cdot)\) \(\chi_{916}(223,\cdot)\) \(\chi_{916}(235,\cdot)\) \(\chi_{916}(239,\cdot)\) \(\chi_{916}(267,\cdot)\) \(\chi_{916}(279,\cdot)\) \(\chi_{916}(295,\cdot)\) \(\chi_{916}(303,\cdot)\) \(\chi_{916}(319,\cdot)\) \(\chi_{916}(327,\cdot)\) \(\chi_{916}(331,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{228})$ |
| Fixed field: | Number field defined by a degree 228 polynomial (not computed) |
Values on generators
\((459,693)\) → \((-1,e\left(\frac{65}{228}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 916 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{91}{114}\right)\) | \(e\left(\frac{107}{114}\right)\) | \(e\left(\frac{1}{228}\right)\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{27}{76}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{83}{114}\right)\) | \(e\left(\frac{61}{76}\right)\) |