Basic properties
| Modulus: | \(961\) | |
| Conductor: | \(961\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(186\) | 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 961.m
\(\chi_{961}(6,\cdot)\) \(\chi_{961}(26,\cdot)\) \(\chi_{961}(37,\cdot)\) \(\chi_{961}(57,\cdot)\) \(\chi_{961}(68,\cdot)\) \(\chi_{961}(88,\cdot)\) \(\chi_{961}(99,\cdot)\) \(\chi_{961}(119,\cdot)\) \(\chi_{961}(130,\cdot)\) \(\chi_{961}(150,\cdot)\) \(\chi_{961}(161,\cdot)\) \(\chi_{961}(181,\cdot)\) \(\chi_{961}(192,\cdot)\) \(\chi_{961}(212,\cdot)\) \(\chi_{961}(223,\cdot)\) \(\chi_{961}(243,\cdot)\) \(\chi_{961}(254,\cdot)\) \(\chi_{961}(274,\cdot)\) \(\chi_{961}(285,\cdot)\) \(\chi_{961}(305,\cdot)\) \(\chi_{961}(316,\cdot)\) \(\chi_{961}(336,\cdot)\) \(\chi_{961}(347,\cdot)\) \(\chi_{961}(367,\cdot)\) \(\chi_{961}(378,\cdot)\) \(\chi_{961}(398,\cdot)\) \(\chi_{961}(409,\cdot)\) \(\chi_{961}(429,\cdot)\) \(\chi_{961}(460,\cdot)\) \(\chi_{961}(471,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{93})$ |
| Fixed field: | Number field defined by a degree 186 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{49}{186}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 961 }(305, a) \) | \(-1\) | \(1\) | \(e\left(\frac{12}{31}\right)\) | \(e\left(\frac{49}{186}\right)\) | \(e\left(\frac{24}{31}\right)\) | \(e\left(\frac{85}{93}\right)\) | \(e\left(\frac{121}{186}\right)\) | \(e\left(\frac{32}{93}\right)\) | \(e\left(\frac{5}{31}\right)\) | \(e\left(\frac{49}{93}\right)\) | \(e\left(\frac{28}{93}\right)\) | \(e\left(\frac{17}{186}\right)\) |