Basic properties
| Modulus: | \(1682\) | |
| Conductor: | \(841\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(203\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{841}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1682.j
\(\chi_{1682}(7,\cdot)\) \(\chi_{1682}(23,\cdot)\) \(\chi_{1682}(25,\cdot)\) \(\chi_{1682}(45,\cdot)\) \(\chi_{1682}(49,\cdot)\) \(\chi_{1682}(53,\cdot)\) \(\chi_{1682}(65,\cdot)\) \(\chi_{1682}(81,\cdot)\) \(\chi_{1682}(83,\cdot)\) \(\chi_{1682}(103,\cdot)\) \(\chi_{1682}(107,\cdot)\) \(\chi_{1682}(111,\cdot)\) \(\chi_{1682}(123,\cdot)\) \(\chi_{1682}(139,\cdot)\) \(\chi_{1682}(141,\cdot)\) \(\chi_{1682}(161,\cdot)\) \(\chi_{1682}(165,\cdot)\) \(\chi_{1682}(169,\cdot)\) \(\chi_{1682}(181,\cdot)\) \(\chi_{1682}(197,\cdot)\) \(\chi_{1682}(199,\cdot)\) \(\chi_{1682}(219,\cdot)\) \(\chi_{1682}(223,\cdot)\) \(\chi_{1682}(227,\cdot)\) \(\chi_{1682}(239,\cdot)\) \(\chi_{1682}(255,\cdot)\) \(\chi_{1682}(257,\cdot)\) \(\chi_{1682}(277,\cdot)\) \(\chi_{1682}(281,\cdot)\) \(\chi_{1682}(285,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{203})$ |
| Fixed field: | Number field defined by a degree 203 polynomial (not computed) |
Values on generators
\(843\) → \(e\left(\frac{94}{203}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1682 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{134}{203}\right)\) | \(e\left(\frac{171}{203}\right)\) | \(e\left(\frac{22}{203}\right)\) | \(e\left(\frac{65}{203}\right)\) | \(e\left(\frac{103}{203}\right)\) | \(e\left(\frac{110}{203}\right)\) | \(e\left(\frac{102}{203}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{83}{203}\right)\) | \(e\left(\frac{156}{203}\right)\) |