Basic properties
| Modulus: | \(8024\) | |
| Conductor: | \(8024\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(464\) | 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 8024.cw
\(\chi_{8024}(37,\cdot)\) \(\chi_{8024}(61,\cdot)\) \(\chi_{8024}(109,\cdot)\) \(\chi_{8024}(141,\cdot)\) \(\chi_{8024}(165,\cdot)\) \(\chi_{8024}(173,\cdot)\) \(\chi_{8024}(269,\cdot)\) \(\chi_{8024}(301,\cdot)\) \(\chi_{8024}(309,\cdot)\) \(\chi_{8024}(333,\cdot)\) \(\chi_{8024}(397,\cdot)\) \(\chi_{8024}(437,\cdot)\) \(\chi_{8024}(445,\cdot)\) \(\chi_{8024}(453,\cdot)\) \(\chi_{8024}(469,\cdot)\) \(\chi_{8024}(533,\cdot)\) \(\chi_{8024}(541,\cdot)\) \(\chi_{8024}(549,\cdot)\) \(\chi_{8024}(573,\cdot)\) \(\chi_{8024}(581,\cdot)\) \(\chi_{8024}(741,\cdot)\) \(\chi_{8024}(805,\cdot)\) \(\chi_{8024}(821,\cdot)\) \(\chi_{8024}(925,\cdot)\) \(\chi_{8024}(941,\cdot)\) \(\chi_{8024}(957,\cdot)\) \(\chi_{8024}(981,\cdot)\) \(\chi_{8024}(1013,\cdot)\) \(\chi_{8024}(1085,\cdot)\) \(\chi_{8024}(1093,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{464})$ |
| Fixed field: | Number field defined by a degree 464 polynomial (not computed) |
Values on generators
\((2007,4013,3777,3129)\) → \((1,-1,e\left(\frac{1}{16}\right),e\left(\frac{55}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 8024 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{453}{464}\right)\) | \(e\left(\frac{233}{464}\right)\) | \(e\left(\frac{351}{464}\right)\) | \(e\left(\frac{221}{232}\right)\) | \(e\left(\frac{299}{464}\right)\) | \(e\left(\frac{49}{116}\right)\) | \(e\left(\frac{111}{232}\right)\) | \(e\left(\frac{95}{232}\right)\) | \(e\left(\frac{85}{116}\right)\) | \(e\left(\frac{75}{464}\right)\) |