Basic properties
| Modulus: | \(6034\) | |
| Conductor: | \(3017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1290\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3017}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6034.be
\(\chi_{6034}(17,\cdot)\) \(\chi_{6034}(31,\cdot)\) \(\chi_{6034}(73,\cdot)\) \(\chi_{6034}(89,\cdot)\) \(\chi_{6034}(103,\cdot)\) \(\chi_{6034}(117,\cdot)\) \(\chi_{6034}(129,\cdot)\) \(\chi_{6034}(131,\cdot)\) \(\chi_{6034}(185,\cdot)\) \(\chi_{6034}(187,\cdot)\) \(\chi_{6034}(199,\cdot)\) \(\chi_{6034}(201,\cdot)\) \(\chi_{6034}(213,\cdot)\) \(\chi_{6034}(241,\cdot)\) \(\chi_{6034}(255,\cdot)\) \(\chi_{6034}(257,\cdot)\) \(\chi_{6034}(271,\cdot)\) \(\chi_{6034}(299,\cdot)\) \(\chi_{6034}(311,\cdot)\) \(\chi_{6034}(313,\cdot)\) \(\chi_{6034}(325,\cdot)\) \(\chi_{6034}(339,\cdot)\) \(\chi_{6034}(341,\cdot)\) \(\chi_{6034}(355,\cdot)\) \(\chi_{6034}(381,\cdot)\) \(\chi_{6034}(409,\cdot)\) \(\chi_{6034}(411,\cdot)\) \(\chi_{6034}(465,\cdot)\) \(\chi_{6034}(493,\cdot)\) \(\chi_{6034}(509,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{645})$ |
| Fixed field: | Number field defined by a degree 1290 polynomial (not computed) |
Values on generators
\((1725,869)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{59}{430}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 6034 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{151}{258}\right)\) | \(e\left(\frac{979}{1290}\right)\) | \(e\left(\frac{22}{129}\right)\) | \(e\left(\frac{13}{645}\right)\) | \(e\left(\frac{89}{215}\right)\) | \(e\left(\frac{74}{215}\right)\) | \(e\left(\frac{271}{645}\right)\) | \(e\left(\frac{913}{1290}\right)\) | \(e\left(\frac{41}{645}\right)\) | \(e\left(\frac{334}{645}\right)\) |