Basic properties
| Modulus: | \(1175\) | |
| Conductor: | \(1175\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(230\) | 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 1175.u
\(\chi_{1175}(4,\cdot)\) \(\chi_{1175}(9,\cdot)\) \(\chi_{1175}(14,\cdot)\) \(\chi_{1175}(34,\cdot)\) \(\chi_{1175}(54,\cdot)\) \(\chi_{1175}(59,\cdot)\) \(\chi_{1175}(64,\cdot)\) \(\chi_{1175}(79,\cdot)\) \(\chi_{1175}(84,\cdot)\) \(\chi_{1175}(89,\cdot)\) \(\chi_{1175}(119,\cdot)\) \(\chi_{1175}(144,\cdot)\) \(\chi_{1175}(159,\cdot)\) \(\chi_{1175}(169,\cdot)\) \(\chi_{1175}(194,\cdot)\) \(\chi_{1175}(204,\cdot)\) \(\chi_{1175}(209,\cdot)\) \(\chi_{1175}(239,\cdot)\) \(\chi_{1175}(244,\cdot)\) \(\chi_{1175}(259,\cdot)\) \(\chi_{1175}(269,\cdot)\) \(\chi_{1175}(284,\cdot)\) \(\chi_{1175}(289,\cdot)\) \(\chi_{1175}(294,\cdot)\) \(\chi_{1175}(309,\cdot)\) \(\chi_{1175}(314,\cdot)\) \(\chi_{1175}(319,\cdot)\) \(\chi_{1175}(354,\cdot)\) \(\chi_{1175}(379,\cdot)\) \(\chi_{1175}(384,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{115})$ |
| Fixed field: | Number field defined by a degree 230 polynomial (not computed) |
Values on generators
\((377,851)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{18}{23}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 1175 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{230}\right)\) | \(e\left(\frac{81}{230}\right)\) | \(e\left(\frac{43}{115}\right)\) | \(e\left(\frac{62}{115}\right)\) | \(e\left(\frac{25}{46}\right)\) | \(e\left(\frac{129}{230}\right)\) | \(e\left(\frac{81}{115}\right)\) | \(e\left(\frac{9}{115}\right)\) | \(e\left(\frac{167}{230}\right)\) | \(e\left(\frac{117}{230}\right)\) |