Basic properties
| Modulus: | \(6145\) | |
| Conductor: | \(6145\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(614\) | 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 6145.n
\(\chi_{6145}(34,\cdot)\) \(\chi_{6145}(49,\cdot)\) \(\chi_{6145}(69,\cdot)\) \(\chi_{6145}(79,\cdot)\) \(\chi_{6145}(89,\cdot)\) \(\chi_{6145}(139,\cdot)\) \(\chi_{6145}(149,\cdot)\) \(\chi_{6145}(154,\cdot)\) \(\chi_{6145}(164,\cdot)\) \(\chi_{6145}(179,\cdot)\) \(\chi_{6145}(184,\cdot)\) \(\chi_{6145}(204,\cdot)\) \(\chi_{6145}(209,\cdot)\) \(\chi_{6145}(239,\cdot)\) \(\chi_{6145}(254,\cdot)\) \(\chi_{6145}(294,\cdot)\) \(\chi_{6145}(299,\cdot)\) \(\chi_{6145}(309,\cdot)\) \(\chi_{6145}(334,\cdot)\) \(\chi_{6145}(369,\cdot)\) \(\chi_{6145}(389,\cdot)\) \(\chi_{6145}(399,\cdot)\) \(\chi_{6145}(409,\cdot)\) \(\chi_{6145}(414,\cdot)\) \(\chi_{6145}(449,\cdot)\) \(\chi_{6145}(459,\cdot)\) \(\chi_{6145}(474,\cdot)\) \(\chi_{6145}(479,\cdot)\) \(\chi_{6145}(484,\cdot)\) \(\chi_{6145}(514,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{307})$ |
| Fixed field: | Number field defined by a degree 614 polynomial (not computed) |
Values on generators
\((4917,1231)\) → \((-1,e\left(\frac{194}{307}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 6145 }(1049, a) \) | \(1\) | \(1\) | \(e\left(\frac{81}{614}\right)\) | \(e\left(\frac{337}{614}\right)\) | \(e\left(\frac{81}{307}\right)\) | \(e\left(\frac{209}{307}\right)\) | \(e\left(\frac{75}{614}\right)\) | \(e\left(\frac{243}{614}\right)\) | \(e\left(\frac{30}{307}\right)\) | \(e\left(\frac{276}{307}\right)\) | \(e\left(\frac{499}{614}\right)\) | \(e\left(\frac{449}{614}\right)\) |