Basic properties
| Modulus: | \(1682\) | |
| Conductor: | \(841\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(406\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{841}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1682.k
\(\chi_{1682}(5,\cdot)\) \(\chi_{1682}(9,\cdot)\) \(\chi_{1682}(13,\cdot)\) \(\chi_{1682}(33,\cdot)\) \(\chi_{1682}(35,\cdot)\) \(\chi_{1682}(51,\cdot)\) \(\chi_{1682}(67,\cdot)\) \(\chi_{1682}(71,\cdot)\) \(\chi_{1682}(91,\cdot)\) \(\chi_{1682}(93,\cdot)\) \(\chi_{1682}(109,\cdot)\) \(\chi_{1682}(121,\cdot)\) \(\chi_{1682}(125,\cdot)\) \(\chi_{1682}(129,\cdot)\) \(\chi_{1682}(149,\cdot)\) \(\chi_{1682}(151,\cdot)\) \(\chi_{1682}(167,\cdot)\) \(\chi_{1682}(179,\cdot)\) \(\chi_{1682}(183,\cdot)\) \(\chi_{1682}(187,\cdot)\) \(\chi_{1682}(207,\cdot)\) \(\chi_{1682}(209,\cdot)\) \(\chi_{1682}(225,\cdot)\) \(\chi_{1682}(237,\cdot)\) \(\chi_{1682}(241,\cdot)\) \(\chi_{1682}(245,\cdot)\) \(\chi_{1682}(265,\cdot)\) \(\chi_{1682}(283,\cdot)\) \(\chi_{1682}(295,\cdot)\) \(\chi_{1682}(299,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{203})$ |
| Fixed field: | Number field defined by a degree 406 polynomial (not computed) |
Values on generators
\(843\) → \(e\left(\frac{151}{406}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1682 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{293}{406}\right)\) | \(e\left(\frac{65}{203}\right)\) | \(e\left(\frac{171}{203}\right)\) | \(e\left(\frac{90}{203}\right)\) | \(e\left(\frac{51}{406}\right)\) | \(e\left(\frac{43}{203}\right)\) | \(e\left(\frac{17}{406}\right)\) | \(e\left(\frac{25}{58}\right)\) | \(e\left(\frac{183}{406}\right)\) | \(e\left(\frac{229}{406}\right)\) |