Basic properties
| Modulus: | \(10015\) | |
| Conductor: | \(10015\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(4004\) | 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 10015.bu
\(\chi_{10015}(7,\cdot)\) \(\chi_{10015}(18,\cdot)\) \(\chi_{10015}(28,\cdot)\) \(\chi_{10015}(33,\cdot)\) \(\chi_{10015}(37,\cdot)\) \(\chi_{10015}(38,\cdot)\) \(\chi_{10015}(43,\cdot)\) \(\chi_{10015}(63,\cdot)\) \(\chi_{10015}(68,\cdot)\) \(\chi_{10015}(72,\cdot)\) \(\chi_{10015}(78,\cdot)\) \(\chi_{10015}(83,\cdot)\) \(\chi_{10015}(93,\cdot)\) \(\chi_{10015}(97,\cdot)\) \(\chi_{10015}(98,\cdot)\) \(\chi_{10015}(103,\cdot)\) \(\chi_{10015}(112,\cdot)\) \(\chi_{10015}(118,\cdot)\) \(\chi_{10015}(123,\cdot)\) \(\chi_{10015}(127,\cdot)\) \(\chi_{10015}(133,\cdot)\) \(\chi_{10015}(137,\cdot)\) \(\chi_{10015}(143,\cdot)\) \(\chi_{10015}(148,\cdot)\) \(\chi_{10015}(152,\cdot)\) \(\chi_{10015}(153,\cdot)\) \(\chi_{10015}(157,\cdot)\) \(\chi_{10015}(158,\cdot)\) \(\chi_{10015}(162,\cdot)\) \(\chi_{10015}(163,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{4004})$ |
| Fixed field: | Number field defined by a degree 4004 polynomial (not computed) |
Values on generators
\((4007,4011)\) → \((i,e\left(\frac{123}{2002}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 10015 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{225}{572}\right)\) | \(e\left(\frac{31}{4004}\right)\) | \(e\left(\frac{225}{286}\right)\) | \(e\left(\frac{73}{182}\right)\) | \(e\left(\frac{3231}{4004}\right)\) | \(e\left(\frac{103}{572}\right)\) | \(e\left(\frac{31}{2002}\right)\) | \(e\left(\frac{3}{286}\right)\) | \(e\left(\frac{3181}{4004}\right)\) | \(e\left(\frac{2159}{4004}\right)\) |