Basic properties
| Modulus: | \(100315\) | |
| Conductor: | \(100315\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(40124\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 100315.w
\(\chi_{100315}(3,\cdot)\) \(\chi_{100315}(12,\cdot)\) \(\chi_{100315}(13,\cdot)\) \(\chi_{100315}(18,\cdot)\) \(\chi_{100315}(22,\cdot)\) \(\chi_{100315}(23,\cdot)\) \(\chi_{100315}(27,\cdot)\) \(\chi_{100315}(33,\cdot)\) \(\chi_{100315}(37,\cdot)\) \(\chi_{100315}(38,\cdot)\) \(\chi_{100315}(48,\cdot)\) \(\chi_{100315}(52,\cdot)\) \(\chi_{100315}(53,\cdot)\) \(\chi_{100315}(57,\cdot)\) \(\chi_{100315}(58,\cdot)\) \(\chi_{100315}(62,\cdot)\) \(\chi_{100315}(67,\cdot)\) \(\chi_{100315}(72,\cdot)\) \(\chi_{100315}(78,\cdot)\) \(\chi_{100315}(83,\cdot)\) \(\chi_{100315}(88,\cdot)\) \(\chi_{100315}(92,\cdot)\) \(\chi_{100315}(93,\cdot)\) \(\chi_{100315}(97,\cdot)\) \(\chi_{100315}(98,\cdot)\) \(\chi_{100315}(107,\cdot)\) \(\chi_{100315}(108,\cdot)\) \(\chi_{100315}(113,\cdot)\) \(\chi_{100315}(117,\cdot)\) \(\chi_{100315}(132,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{40124})$ |
| Fixed field: | Number field defined by a degree 40124 polynomial (not computed) |
Values on generators
\((40127,40131)\) → \((-i,e\left(\frac{8637}{10031}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 100315 }(78, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1431}{5732}\right)\) | \(e\left(\frac{25379}{40124}\right)\) | \(e\left(\frac{1431}{2866}\right)\) | \(e\left(\frac{8849}{10031}\right)\) | \(e\left(\frac{37209}{40124}\right)\) | \(e\left(\frac{4293}{5732}\right)\) | \(e\left(\frac{5317}{20062}\right)\) | \(e\left(\frac{5386}{10031}\right)\) | \(e\left(\frac{5289}{40124}\right)\) | \(e\left(\frac{32659}{40124}\right)\) |