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 \(\chi_{3017}(39,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6034.bf
\(\chi_{6034}(37,\cdot)\) \(\chi_{6034}(39,\cdot)\) \(\chi_{6034}(51,\cdot)\) \(\chi_{6034}(65,\cdot)\) \(\chi_{6034}(67,\cdot)\) \(\chi_{6034}(79,\cdot)\) \(\chi_{6034}(93,\cdot)\) \(\chi_{6034}(137,\cdot)\) \(\chi_{6034}(191,\cdot)\) \(\chi_{6034}(193,\cdot)\) \(\chi_{6034}(219,\cdot)\) \(\chi_{6034}(233,\cdot)\) \(\chi_{6034}(235,\cdot)\) \(\chi_{6034}(247,\cdot)\) \(\chi_{6034}(249,\cdot)\) \(\chi_{6034}(317,\cdot)\) \(\chi_{6034}(331,\cdot)\) \(\chi_{6034}(333,\cdot)\) \(\chi_{6034}(373,\cdot)\) \(\chi_{6034}(387,\cdot)\) \(\chi_{6034}(401,\cdot)\) \(\chi_{6034}(445,\cdot)\) \(\chi_{6034}(459,\cdot)\) \(\chi_{6034}(473,\cdot)\) \(\chi_{6034}(487,\cdot)\) \(\chi_{6034}(499,\cdot)\) \(\chi_{6034}(501,\cdot)\) \(\chi_{6034}(515,\cdot)\) \(\chi_{6034}(543,\cdot)\) \(\chi_{6034}(555,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{645})$ |
| Fixed field: | Number field defined by a degree 1290 polynomial (not computed) |
Values on generators
\((1725,869)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{17}{430}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 6034 }(39, a) \) | \(-1\) | \(1\) | \(e\left(\frac{95}{129}\right)\) | \(e\left(\frac{551}{645}\right)\) | \(e\left(\frac{61}{129}\right)\) | \(e\left(\frac{124}{645}\right)\) | \(e\left(\frac{259}{430}\right)\) | \(e\left(\frac{127}{215}\right)\) | \(e\left(\frac{1151}{1290}\right)\) | \(e\left(\frac{137}{645}\right)\) | \(e\left(\frac{143}{645}\right)\) | \(e\left(\frac{457}{645}\right)\) |