Basic properties
| Modulus: | \(8035\) | |
| Conductor: | \(8035\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(3212\) | 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 8035.w
\(\chi_{8035}(7,\cdot)\) \(\chi_{8035}(13,\cdot)\) \(\chi_{8035}(22,\cdot)\) \(\chi_{8035}(28,\cdot)\) \(\chi_{8035}(33,\cdot)\) \(\chi_{8035}(42,\cdot)\) \(\chi_{8035}(43,\cdot)\) \(\chi_{8035}(47,\cdot)\) \(\chi_{8035}(57,\cdot)\) \(\chi_{8035}(58,\cdot)\) \(\chi_{8035}(63,\cdot)\) \(\chi_{8035}(78,\cdot)\) \(\chi_{8035}(83,\cdot)\) \(\chi_{8035}(87,\cdot)\) \(\chi_{8035}(88,\cdot)\) \(\chi_{8035}(97,\cdot)\) \(\chi_{8035}(112,\cdot)\) \(\chi_{8035}(117,\cdot)\) \(\chi_{8035}(122,\cdot)\) \(\chi_{8035}(132,\cdot)\) \(\chi_{8035}(142,\cdot)\) \(\chi_{8035}(152,\cdot)\) \(\chi_{8035}(168,\cdot)\) \(\chi_{8035}(172,\cdot)\) \(\chi_{8035}(173,\cdot)\) \(\chi_{8035}(183,\cdot)\) \(\chi_{8035}(188,\cdot)\) \(\chi_{8035}(197,\cdot)\) \(\chi_{8035}(198,\cdot)\) \(\chi_{8035}(208,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{3212})$ |
| Fixed field: | Number field defined by a degree 3212 polynomial (not computed) |
Values on generators
\((4822,4826)\) → \((i,e\left(\frac{617}{1606}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 8035 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{2823}{3212}\right)\) | \(e\left(\frac{537}{3212}\right)\) | \(e\left(\frac{1217}{1606}\right)\) | \(e\left(\frac{37}{803}\right)\) | \(e\left(\frac{937}{3212}\right)\) | \(e\left(\frac{2045}{3212}\right)\) | \(e\left(\frac{537}{1606}\right)\) | \(e\left(\frac{823}{1606}\right)\) | \(e\left(\frac{2971}{3212}\right)\) | \(e\left(\frac{195}{3212}\right)\) |