Basic properties
| Modulus: | \(8024\) | |
| Conductor: | \(1003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(464\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1003}(249,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8024.cv
\(\chi_{8024}(65,\cdot)\) \(\chi_{8024}(73,\cdot)\) \(\chi_{8024}(97,\cdot)\) \(\chi_{8024}(113,\cdot)\) \(\chi_{8024}(129,\cdot)\) \(\chi_{8024}(201,\cdot)\) \(\chi_{8024}(209,\cdot)\) \(\chi_{8024}(233,\cdot)\) \(\chi_{8024}(249,\cdot)\) \(\chi_{8024}(313,\cdot)\) \(\chi_{8024}(329,\cdot)\) \(\chi_{8024}(337,\cdot)\) \(\chi_{8024}(345,\cdot)\) \(\chi_{8024}(377,\cdot)\) \(\chi_{8024}(385,\cdot)\) \(\chi_{8024}(401,\cdot)\) \(\chi_{8024}(465,\cdot)\) \(\chi_{8024}(505,\cdot)\) \(\chi_{8024}(537,\cdot)\) \(\chi_{8024}(585,\cdot)\) \(\chi_{8024}(601,\cdot)\) \(\chi_{8024}(657,\cdot)\) \(\chi_{8024}(673,\cdot)\) \(\chi_{8024}(721,\cdot)\) \(\chi_{8024}(745,\cdot)\) \(\chi_{8024}(777,\cdot)\) \(\chi_{8024}(785,\cdot)\) \(\chi_{8024}(809,\cdot)\) \(\chi_{8024}(857,\cdot)\) \(\chi_{8024}(873,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{464})$ |
| Fixed field: | Number field defined by a degree 464 polynomial (not computed) |
Values on generators
\((2007,4013,3777,3129)\) → \((1,1,e\left(\frac{7}{16}\right),e\left(\frac{45}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 8024 }(249, a) \) | \(1\) | \(1\) | \(e\left(\frac{107}{464}\right)\) | \(e\left(\frac{391}{464}\right)\) | \(e\left(\frac{361}{464}\right)\) | \(e\left(\frac{107}{232}\right)\) | \(e\left(\frac{213}{464}\right)\) | \(e\left(\frac{77}{116}\right)\) | \(e\left(\frac{17}{232}\right)\) | \(e\left(\frac{141}{232}\right)\) | \(e\left(\frac{1}{116}\right)\) | \(e\left(\frac{93}{464}\right)\) |