Basic properties
| Modulus: | \(8024\) | |
| Conductor: | \(4012\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(464\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4012}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8024.da
\(\chi_{8024}(7,\cdot)\) \(\chi_{8024}(63,\cdot)\) \(\chi_{8024}(71,\cdot)\) \(\chi_{8024}(79,\cdot)\) \(\chi_{8024}(95,\cdot)\) \(\chi_{8024}(143,\cdot)\) \(\chi_{8024}(159,\cdot)\) \(\chi_{8024}(167,\cdot)\) \(\chi_{8024}(175,\cdot)\) \(\chi_{8024}(199,\cdot)\) \(\chi_{8024}(311,\cdot)\) \(\chi_{8024}(343,\cdot)\) \(\chi_{8024}(439,\cdot)\) \(\chi_{8024}(479,\cdot)\) \(\chi_{8024}(487,\cdot)\) \(\chi_{8024}(551,\cdot)\) \(\chi_{8024}(567,\cdot)\) \(\chi_{8024}(607,\cdot)\) \(\chi_{8024}(615,\cdot)\) \(\chi_{8024}(639,\cdot)\) \(\chi_{8024}(711,\cdot)\) \(\chi_{8024}(743,\cdot)\) \(\chi_{8024}(759,\cdot)\) \(\chi_{8024}(847,\cdot)\) \(\chi_{8024}(855,\cdot)\) \(\chi_{8024}(879,\cdot)\) \(\chi_{8024}(911,\cdot)\) \(\chi_{8024}(959,\cdot)\) \(\chi_{8024}(1015,\cdot)\) \(\chi_{8024}(1023,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{464})$ |
| Fixed field: | Number field defined by a degree 464 polynomial (not computed) |
Values on generators
\((2007,4013,3777,3129)\) → \((-1,1,e\left(\frac{11}{16}\right),e\left(\frac{9}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 8024 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{327}{464}\right)\) | \(e\left(\frac{139}{464}\right)\) | \(e\left(\frac{301}{464}\right)\) | \(e\left(\frac{95}{232}\right)\) | \(e\left(\frac{33}{464}\right)\) | \(e\left(\frac{83}{116}\right)\) | \(e\left(\frac{1}{232}\right)\) | \(e\left(\frac{213}{232}\right)\) | \(e\left(\frac{41}{116}\right)\) | \(e\left(\frac{217}{464}\right)\) |