Basic properties
| Modulus: | \(1077\) | |
| Conductor: | \(1077\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(358\) | 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 1077.h
\(\chi_{1077}(14,\cdot)\) \(\chi_{1077}(26,\cdot)\) \(\chi_{1077}(29,\cdot)\) \(\chi_{1077}(35,\cdot)\) \(\chi_{1077}(38,\cdot)\) \(\chi_{1077}(53,\cdot)\) \(\chi_{1077}(56,\cdot)\) \(\chi_{1077}(59,\cdot)\) \(\chi_{1077}(62,\cdot)\) \(\chi_{1077}(65,\cdot)\) \(\chi_{1077}(71,\cdot)\) \(\chi_{1077}(77,\cdot)\) \(\chi_{1077}(83,\cdot)\) \(\chi_{1077}(86,\cdot)\) \(\chi_{1077}(89,\cdot)\) \(\chi_{1077}(95,\cdot)\) \(\chi_{1077}(104,\cdot)\) \(\chi_{1077}(113,\cdot)\) \(\chi_{1077}(116,\cdot)\) \(\chi_{1077}(119,\cdot)\) \(\chi_{1077}(122,\cdot)\) \(\chi_{1077}(134,\cdot)\) \(\chi_{1077}(137,\cdot)\) \(\chi_{1077}(140,\cdot)\) \(\chi_{1077}(143,\cdot)\) \(\chi_{1077}(152,\cdot)\) \(\chi_{1077}(155,\cdot)\) \(\chi_{1077}(161,\cdot)\) \(\chi_{1077}(167,\cdot)\) \(\chi_{1077}(179,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{179})$ |
| Fixed field: | Number field defined by a degree 358 polynomial (not computed) |
Values on generators
\((719,7)\) → \((-1,e\left(\frac{123}{358}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 1077 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{137}{358}\right)\) | \(e\left(\frac{137}{179}\right)\) | \(e\left(\frac{15}{358}\right)\) | \(e\left(\frac{123}{358}\right)\) | \(e\left(\frac{53}{358}\right)\) | \(e\left(\frac{76}{179}\right)\) | \(e\left(\frac{333}{358}\right)\) | \(e\left(\frac{155}{358}\right)\) | \(e\left(\frac{130}{179}\right)\) | \(e\left(\frac{95}{179}\right)\) |