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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 10015.bv
\(\chi_{10015}(3,\cdot)\) \(\chi_{10015}(12,\cdot)\) \(\chi_{10015}(13,\cdot)\) \(\chi_{10015}(27,\cdot)\) \(\chi_{10015}(47,\cdot)\) \(\chi_{10015}(52,\cdot)\) \(\chi_{10015}(58,\cdot)\) \(\chi_{10015}(62,\cdot)\) \(\chi_{10015}(73,\cdot)\) \(\chi_{10015}(77,\cdot)\) \(\chi_{10015}(82,\cdot)\) \(\chi_{10015}(107,\cdot)\) \(\chi_{10015}(108,\cdot)\) \(\chi_{10015}(117,\cdot)\) \(\chi_{10015}(122,\cdot)\) \(\chi_{10015}(138,\cdot)\) \(\chi_{10015}(147,\cdot)\) \(\chi_{10015}(167,\cdot)\) \(\chi_{10015}(173,\cdot)\) \(\chi_{10015}(177,\cdot)\) \(\chi_{10015}(187,\cdot)\) \(\chi_{10015}(188,\cdot)\) \(\chi_{10015}(192,\cdot)\) \(\chi_{10015}(197,\cdot)\) \(\chi_{10015}(198,\cdot)\) \(\chi_{10015}(203,\cdot)\) \(\chi_{10015}(212,\cdot)\) \(\chi_{10015}(217,\cdot)\) \(\chi_{10015}(218,\cdot)\) \(\chi_{10015}(222,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{4004})$ |
| Fixed field: | Number field defined by a degree 4004 polynomial (not computed) |
Values on generators
\((4007,4011)\) → \((-i,e\left(\frac{173}{1001}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 10015 }(3, a) \) | \(-1\) | \(1\) | \(e\left(\frac{469}{572}\right)\) | \(e\left(\frac{193}{4004}\right)\) | \(e\left(\frac{183}{286}\right)\) | \(e\left(\frac{79}{91}\right)\) | \(e\left(\frac{31}{4004}\right)\) | \(e\left(\frac{263}{572}\right)\) | \(e\left(\frac{193}{2002}\right)\) | \(e\left(\frac{67}{143}\right)\) | \(e\left(\frac{2755}{4004}\right)\) | \(e\left(\frac{1817}{4004}\right)\) |