Basic properties
| Modulus: | \(259200\) | |
| Conductor: | \(129600\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2160\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{129600}(58259,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 259200.bab
\(\chi_{259200}(119,\cdot)\) \(\chi_{259200}(839,\cdot)\) \(\chi_{259200}(1319,\cdot)\) \(\chi_{259200}(1559,\cdot)\) \(\chi_{259200}(2039,\cdot)\) \(\chi_{259200}(2279,\cdot)\) \(\chi_{259200}(2759,\cdot)\) \(\chi_{259200}(3479,\cdot)\) \(\chi_{259200}(3719,\cdot)\) \(\chi_{259200}(4439,\cdot)\) \(\chi_{259200}(4919,\cdot)\) \(\chi_{259200}(5159,\cdot)\) \(\chi_{259200}(5639,\cdot)\) \(\chi_{259200}(5879,\cdot)\) \(\chi_{259200}(6359,\cdot)\) \(\chi_{259200}(7079,\cdot)\) \(\chi_{259200}(7319,\cdot)\) \(\chi_{259200}(8039,\cdot)\) \(\chi_{259200}(8519,\cdot)\) \(\chi_{259200}(8759,\cdot)\) \(\chi_{259200}(9239,\cdot)\) \(\chi_{259200}(9479,\cdot)\) \(\chi_{259200}(9959,\cdot)\) \(\chi_{259200}(10679,\cdot)\) \(\chi_{259200}(10919,\cdot)\) \(\chi_{259200}(11639,\cdot)\) \(\chi_{259200}(12119,\cdot)\) \(\chi_{259200}(12359,\cdot)\) \(\chi_{259200}(12839,\cdot)\) \(\chi_{259200}(13079,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{2160})$ |
| Fixed field: | Number field defined by a degree 2160 polynomial (not computed) |
Values on generators
\((157951,202501,6401,72577)\) → \((-1,e\left(\frac{7}{16}\right),e\left(\frac{25}{54}\right),e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 259200 }(1559, a) \) | \(1\) | \(1\) | \(e\left(\frac{169}{216}\right)\) | \(e\left(\frac{1957}{2160}\right)\) | \(e\left(\frac{1223}{2160}\right)\) | \(e\left(\frac{113}{180}\right)\) | \(e\left(\frac{277}{720}\right)\) | \(e\left(\frac{451}{1080}\right)\) | \(e\left(\frac{739}{2160}\right)\) | \(e\left(\frac{116}{135}\right)\) | \(e\left(\frac{491}{720}\right)\) | \(e\left(\frac{499}{1080}\right)\) |