Basic properties
| Modulus: | \(87362\) | |
| Conductor: | \(3971\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(570\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3971}(27,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 87362.cq
\(\chi_{87362}(27,\cdot)\) \(\chi_{87362}(487,\cdot)\) \(\chi_{87362}(753,\cdot)\) \(\chi_{87362}(977,\cdot)\) \(\chi_{87362}(1703,\cdot)\) \(\chi_{87362}(1775,\cdot)\) \(\chi_{87362}(2501,\cdot)\) \(\chi_{87362}(4359,\cdot)\) \(\chi_{87362}(5085,\cdot)\) \(\chi_{87362}(5351,\cdot)\) \(\chi_{87362}(5575,\cdot)\) \(\chi_{87362}(6301,\cdot)\) \(\chi_{87362}(6373,\cdot)\) \(\chi_{87362}(7099,\cdot)\) \(\chi_{87362}(9223,\cdot)\) \(\chi_{87362}(9683,\cdot)\) \(\chi_{87362}(9949,\cdot)\) \(\chi_{87362}(10173,\cdot)\) \(\chi_{87362}(10971,\cdot)\) \(\chi_{87362}(11697,\cdot)\) \(\chi_{87362}(13555,\cdot)\) \(\chi_{87362}(13821,\cdot)\) \(\chi_{87362}(14281,\cdot)\) \(\chi_{87362}(14547,\cdot)\) \(\chi_{87362}(14771,\cdot)\) \(\chi_{87362}(15497,\cdot)\) \(\chi_{87362}(15569,\cdot)\) \(\chi_{87362}(16295,\cdot)\) \(\chi_{87362}(18153,\cdot)\) \(\chi_{87362}(18419,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{285})$ |
| Fixed field: | Number field defined by a degree 570 polynomial (not computed) |
Values on generators
\((21661,22023)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{25}{114}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 87362 }(27, a) \) | \(-1\) | \(1\) | \(e\left(\frac{389}{570}\right)\) | \(e\left(\frac{136}{285}\right)\) | \(e\left(\frac{66}{95}\right)\) | \(e\left(\frac{104}{285}\right)\) | \(e\left(\frac{313}{570}\right)\) | \(e\left(\frac{91}{570}\right)\) | \(e\left(\frac{46}{285}\right)\) | \(e\left(\frac{43}{114}\right)\) | \(e\left(\frac{1}{57}\right)\) | \(e\left(\frac{272}{285}\right)\) |