Basic properties
| Modulus: | \(79350\) | |
| Conductor: | \(13225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(230\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{13225}(12511,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 79350.cn
\(\chi_{79350}(91,\cdot)\) \(\chi_{79350}(781,\cdot)\) \(\chi_{79350}(1471,\cdot)\) \(\chi_{79350}(2161,\cdot)\) \(\chi_{79350}(3541,\cdot)\) \(\chi_{79350}(4921,\cdot)\) \(\chi_{79350}(5611,\cdot)\) \(\chi_{79350}(6991,\cdot)\) \(\chi_{79350}(7681,\cdot)\) \(\chi_{79350}(8371,\cdot)\) \(\chi_{79350}(9061,\cdot)\) \(\chi_{79350}(10441,\cdot)\) \(\chi_{79350}(11131,\cdot)\) \(\chi_{79350}(11821,\cdot)\) \(\chi_{79350}(12511,\cdot)\) \(\chi_{79350}(13891,\cdot)\) \(\chi_{79350}(14581,\cdot)\) \(\chi_{79350}(15271,\cdot)\) \(\chi_{79350}(15961,\cdot)\) \(\chi_{79350}(17341,\cdot)\) \(\chi_{79350}(18031,\cdot)\) \(\chi_{79350}(18721,\cdot)\) \(\chi_{79350}(19411,\cdot)\) \(\chi_{79350}(20791,\cdot)\) \(\chi_{79350}(21481,\cdot)\) \(\chi_{79350}(22171,\cdot)\) \(\chi_{79350}(22861,\cdot)\) \(\chi_{79350}(24241,\cdot)\) \(\chi_{79350}(24931,\cdot)\) \(\chi_{79350}(25621,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{115})$ |
| Fixed field: | Number field defined by a degree 230 polynomial (not computed) |
Values on generators
\((52901,76177,39151)\) → \((1,e\left(\frac{4}{5}\right),e\left(\frac{11}{46}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 79350 }(12511, a) \) | \(-1\) | \(1\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{39}{230}\right)\) | \(e\left(\frac{73}{115}\right)\) | \(e\left(\frac{77}{230}\right)\) | \(e\left(\frac{167}{230}\right)\) | \(e\left(\frac{54}{115}\right)\) | \(e\left(\frac{91}{115}\right)\) | \(e\left(\frac{91}{230}\right)\) | \(e\left(\frac{48}{115}\right)\) | \(e\left(\frac{21}{46}\right)\) |