Basic properties
| Modulus: | \(10015\) | |
| Conductor: | \(10015\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2002\) | 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.bs
\(\chi_{10015}(9,\cdot)\) \(\chi_{10015}(14,\cdot)\) \(\chi_{10015}(19,\cdot)\) \(\chi_{10015}(39,\cdot)\) \(\chi_{10015}(49,\cdot)\) \(\chi_{10015}(59,\cdot)\) \(\chi_{10015}(74,\cdot)\) \(\chi_{10015}(119,\cdot)\) \(\chi_{10015}(144,\cdot)\) \(\chi_{10015}(159,\cdot)\) \(\chi_{10015}(169,\cdot)\) \(\chi_{10015}(179,\cdot)\) \(\chi_{10015}(194,\cdot)\) \(\chi_{10015}(224,\cdot)\) \(\chi_{10015}(229,\cdot)\) \(\chi_{10015}(254,\cdot)\) \(\chi_{10015}(259,\cdot)\) \(\chi_{10015}(264,\cdot)\) \(\chi_{10015}(274,\cdot)\) \(\chi_{10015}(304,\cdot)\) \(\chi_{10015}(314,\cdot)\) \(\chi_{10015}(324,\cdot)\) \(\chi_{10015}(339,\cdot)\) \(\chi_{10015}(344,\cdot)\) \(\chi_{10015}(359,\cdot)\) \(\chi_{10015}(379,\cdot)\) \(\chi_{10015}(404,\cdot)\) \(\chi_{10015}(419,\cdot)\) \(\chi_{10015}(449,\cdot)\) \(\chi_{10015}(469,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1001})$ |
| Fixed field: | Number field defined by a degree 2002 polynomial (not computed) |
Values on generators
\((4007,4011)\) → \((-1,e\left(\frac{346}{1001}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 10015 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{183}{286}\right)\) | \(e\left(\frac{193}{2002}\right)\) | \(e\left(\frac{40}{143}\right)\) | \(e\left(\frac{67}{91}\right)\) | \(e\left(\frac{31}{2002}\right)\) | \(e\left(\frac{263}{286}\right)\) | \(e\left(\frac{193}{1001}\right)\) | \(e\left(\frac{134}{143}\right)\) | \(e\left(\frac{753}{2002}\right)\) | \(e\left(\frac{1817}{2002}\right)\) |