Basic properties
| Modulus: | \(961\) | |
| Conductor: | \(961\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(930\) | 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.p
\(\chi_{961}(3,\cdot)\) \(\chi_{961}(11,\cdot)\) \(\chi_{961}(12,\cdot)\) \(\chi_{961}(13,\cdot)\) \(\chi_{961}(17,\cdot)\) \(\chi_{961}(21,\cdot)\) \(\chi_{961}(22,\cdot)\) \(\chi_{961}(24,\cdot)\) \(\chi_{961}(34,\cdot)\) \(\chi_{961}(42,\cdot)\) \(\chi_{961}(43,\cdot)\) \(\chi_{961}(44,\cdot)\) \(\chi_{961}(48,\cdot)\) \(\chi_{961}(52,\cdot)\) \(\chi_{961}(53,\cdot)\) \(\chi_{961}(55,\cdot)\) \(\chi_{961}(65,\cdot)\) \(\chi_{961}(73,\cdot)\) \(\chi_{961}(74,\cdot)\) \(\chi_{961}(75,\cdot)\) \(\chi_{961}(79,\cdot)\) \(\chi_{961}(83,\cdot)\) \(\chi_{961}(84,\cdot)\) \(\chi_{961}(86,\cdot)\) \(\chi_{961}(96,\cdot)\) \(\chi_{961}(104,\cdot)\) \(\chi_{961}(105,\cdot)\) \(\chi_{961}(106,\cdot)\) \(\chi_{961}(110,\cdot)\) \(\chi_{961}(114,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{465})$ |
| Fixed field: | Number field defined by a degree 930 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{319}{930}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 961 }(12, a) \) | \(-1\) | \(1\) | \(e\left(\frac{6}{155}\right)\) | \(e\left(\frac{319}{930}\right)\) | \(e\left(\frac{12}{155}\right)\) | \(e\left(\frac{86}{93}\right)\) | \(e\left(\frac{71}{186}\right)\) | \(e\left(\frac{326}{465}\right)\) | \(e\left(\frac{18}{155}\right)\) | \(e\left(\frac{319}{465}\right)\) | \(e\left(\frac{448}{465}\right)\) | \(e\left(\frac{737}{930}\right)\) |