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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 100315.x
\(\chi_{100315}(7,\cdot)\) \(\chi_{100315}(17,\cdot)\) \(\chi_{100315}(28,\cdot)\) \(\chi_{100315}(42,\cdot)\) \(\chi_{100315}(43,\cdot)\) \(\chi_{100315}(63,\cdot)\) \(\chi_{100315}(68,\cdot)\) \(\chi_{100315}(82,\cdot)\) \(\chi_{100315}(102,\cdot)\) \(\chi_{100315}(103,\cdot)\) \(\chi_{100315}(112,\cdot)\) \(\chi_{100315}(118,\cdot)\) \(\chi_{100315}(123,\cdot)\) \(\chi_{100315}(127,\cdot)\) \(\chi_{100315}(133,\cdot)\) \(\chi_{100315}(158,\cdot)\) \(\chi_{100315}(163,\cdot)\) \(\chi_{100315}(168,\cdot)\) \(\chi_{100315}(172,\cdot)\) \(\chi_{100315}(177,\cdot)\) \(\chi_{100315}(178,\cdot)\) \(\chi_{100315}(182,\cdot)\) \(\chi_{100315}(183,\cdot)\) \(\chi_{100315}(187,\cdot)\) \(\chi_{100315}(197,\cdot)\) \(\chi_{100315}(217,\cdot)\) \(\chi_{100315}(227,\cdot)\) \(\chi_{100315}(237,\cdot)\) \(\chi_{100315}(252,\cdot)\) \(\chi_{100315}(258,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{40124})$ |
| Fixed field: | Number field defined by a degree 40124 polynomial (not computed) |
Values on generators
\((40127,40131)\) → \((-i,e\left(\frac{15441}{20062}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 100315 }(28, a) \) | \(1\) | \(1\) | \(e\left(\frac{2911}{5732}\right)\) | \(e\left(\frac{23}{40124}\right)\) | \(e\left(\frac{45}{2866}\right)\) | \(e\left(\frac{5100}{10031}\right)\) | \(e\left(\frac{24747}{40124}\right)\) | \(e\left(\frac{3001}{5732}\right)\) | \(e\left(\frac{23}{20062}\right)\) | \(e\left(\frac{4919}{10031}\right)\) | \(e\left(\frac{653}{40124}\right)\) | \(e\left(\frac{36843}{40124}\right)\) |