Basic properties
| Modulus: | \(12675\) | |
| Conductor: | \(12675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(260\) | 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 12675.fd
\(\chi_{12675}(44,\cdot)\) \(\chi_{12675}(164,\cdot)\) \(\chi_{12675}(359,\cdot)\) \(\chi_{12675}(434,\cdot)\) \(\chi_{12675}(554,\cdot)\) \(\chi_{12675}(629,\cdot)\) \(\chi_{12675}(1019,\cdot)\) \(\chi_{12675}(1139,\cdot)\) \(\chi_{12675}(1214,\cdot)\) \(\chi_{12675}(1334,\cdot)\) \(\chi_{12675}(1409,\cdot)\) \(\chi_{12675}(1529,\cdot)\) \(\chi_{12675}(1604,\cdot)\) \(\chi_{12675}(1919,\cdot)\) \(\chi_{12675}(1994,\cdot)\) \(\chi_{12675}(2114,\cdot)\) \(\chi_{12675}(2189,\cdot)\) \(\chi_{12675}(2309,\cdot)\) \(\chi_{12675}(2384,\cdot)\) \(\chi_{12675}(2504,\cdot)\) \(\chi_{12675}(2579,\cdot)\) \(\chi_{12675}(2894,\cdot)\) \(\chi_{12675}(2969,\cdot)\) \(\chi_{12675}(3089,\cdot)\) \(\chi_{12675}(3164,\cdot)\) \(\chi_{12675}(3284,\cdot)\) \(\chi_{12675}(3359,\cdot)\) \(\chi_{12675}(3554,\cdot)\) \(\chi_{12675}(3869,\cdot)\) \(\chi_{12675}(3944,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{260})$ |
| Fixed field: | Number field defined by a degree 260 polynomial (not computed) |
Values on generators
\((4226,9127,12001)\) → \((-1,e\left(\frac{1}{10}\right),e\left(\frac{37}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(14\) | \(16\) | \(17\) | \(19\) | \(22\) |
| \( \chi_{ 12675 }(7379, a) \) | \(1\) | \(1\) | \(e\left(\frac{81}{260}\right)\) | \(e\left(\frac{81}{130}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{243}{260}\right)\) | \(e\left(\frac{101}{260}\right)\) | \(e\left(\frac{123}{130}\right)\) | \(e\left(\frac{16}{65}\right)\) | \(e\left(\frac{89}{130}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) |