Basic properties
| Modulus: | \(3013\) | |
| Conductor: | \(3013\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1430\) | 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 3013.be
\(\chi_{3013}(2,\cdot)\) \(\chi_{3013}(6,\cdot)\) \(\chi_{3013}(8,\cdot)\) \(\chi_{3013}(26,\cdot)\) \(\chi_{3013}(29,\cdot)\) \(\chi_{3013}(31,\cdot)\) \(\chi_{3013}(50,\cdot)\) \(\chi_{3013}(54,\cdot)\) \(\chi_{3013}(72,\cdot)\) \(\chi_{3013}(82,\cdot)\) \(\chi_{3013}(85,\cdot)\) \(\chi_{3013}(87,\cdot)\) \(\chi_{3013}(95,\cdot)\) \(\chi_{3013}(96,\cdot)\) \(\chi_{3013}(98,\cdot)\) \(\chi_{3013}(104,\cdot)\) \(\chi_{3013}(110,\cdot)\) \(\chi_{3013}(118,\cdot)\) \(\chi_{3013}(119,\cdot)\) \(\chi_{3013}(124,\cdot)\) \(\chi_{3013}(127,\cdot)\) \(\chi_{3013}(128,\cdot)\) \(\chi_{3013}(133,\cdot)\) \(\chi_{3013}(141,\cdot)\) \(\chi_{3013}(154,\cdot)\) \(\chi_{3013}(187,\cdot)\) \(\chi_{3013}(188,\cdot)\) \(\chi_{3013}(197,\cdot)\) \(\chi_{3013}(213,\cdot)\) \(\chi_{3013}(216,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{715})$ |
| Fixed field: | Number field defined by a degree 1430 polynomial (not computed) |
Values on generators
\((787,1312)\) → \((e\left(\frac{10}{11}\right),e\left(\frac{99}{130}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 3013 }(449, a) \) | \(-1\) | \(1\) | \(e\left(\frac{829}{1430}\right)\) | \(e\left(\frac{269}{715}\right)\) | \(e\left(\frac{114}{715}\right)\) | \(e\left(\frac{672}{715}\right)\) | \(e\left(\frac{1367}{1430}\right)\) | \(e\left(\frac{272}{715}\right)\) | \(e\left(\frac{1057}{1430}\right)\) | \(e\left(\frac{538}{715}\right)\) | \(e\left(\frac{743}{1430}\right)\) | \(e\left(\frac{592}{715}\right)\) |