Basic properties
| Modulus: | \(374790\) | |
| Conductor: | \(37479\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1860\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{37479}(431,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 374790.bdm
\(\chi_{374790}(71,\cdot)\) \(\chi_{374790}(431,\cdot)\) \(\chi_{374790}(1931,\cdot)\) \(\chi_{374790}(1991,\cdot)\) \(\chi_{374790}(5081,\cdot)\) \(\chi_{374790}(5501,\cdot)\) \(\chi_{374790}(6281,\cdot)\) \(\chi_{374790}(6311,\cdot)\) \(\chi_{374790}(6641,\cdot)\) \(\chi_{374790}(7481,\cdot)\) \(\chi_{374790}(8171,\cdot)\) \(\chi_{374790}(9041,\cdot)\) \(\chi_{374790}(9341,\cdot)\) \(\chi_{374790}(10151,\cdot)\) \(\chi_{374790}(10901,\cdot)\) \(\chi_{374790}(10931,\cdot)\) \(\chi_{374790}(12161,\cdot)\) \(\chi_{374790}(12521,\cdot)\) \(\chi_{374790}(14021,\cdot)\) \(\chi_{374790}(14081,\cdot)\) \(\chi_{374790}(17171,\cdot)\) \(\chi_{374790}(17591,\cdot)\) \(\chi_{374790}(18371,\cdot)\) \(\chi_{374790}(18401,\cdot)\) \(\chi_{374790}(18731,\cdot)\) \(\chi_{374790}(19571,\cdot)\) \(\chi_{374790}(20261,\cdot)\) \(\chi_{374790}(21131,\cdot)\) \(\chi_{374790}(21431,\cdot)\) \(\chi_{374790}(22241,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1860})$ |
| Fixed field: | Number field defined by a degree 1860 polynomial (not computed) |
Values on generators
\((124931,149917,86491,26911)\) → \((-1,1,e\left(\frac{1}{12}\right),e\left(\frac{83}{465}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(29\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 374790 }(431, a) \) | \(1\) | \(1\) | \(e\left(\frac{227}{620}\right)\) | \(e\left(\frac{457}{620}\right)\) | \(e\left(\frac{67}{155}\right)\) | \(e\left(\frac{381}{620}\right)\) | \(e\left(\frac{401}{465}\right)\) | \(e\left(\frac{709}{930}\right)\) | \(e\left(\frac{233}{372}\right)\) | \(e\left(\frac{491}{620}\right)\) | \(e\left(\frac{263}{310}\right)\) | \(e\left(\frac{49}{620}\right)\) |