Basic properties
| Modulus: | \(1169\) | |
| Conductor: | \(167\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{167}(15,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1169.j
\(\chi_{1169}(15,\cdot)\) \(\chi_{1169}(43,\cdot)\) \(\chi_{1169}(71,\cdot)\) \(\chi_{1169}(78,\cdot)\) \(\chi_{1169}(92,\cdot)\) \(\chi_{1169}(106,\cdot)\) \(\chi_{1169}(113,\cdot)\) \(\chi_{1169}(120,\cdot)\) \(\chi_{1169}(134,\cdot)\) \(\chi_{1169}(148,\cdot)\) \(\chi_{1169}(155,\cdot)\) \(\chi_{1169}(190,\cdot)\) \(\chi_{1169}(197,\cdot)\) \(\chi_{1169}(204,\cdot)\) \(\chi_{1169}(218,\cdot)\) \(\chi_{1169}(246,\cdot)\) \(\chi_{1169}(253,\cdot)\) \(\chi_{1169}(302,\cdot)\) \(\chi_{1169}(309,\cdot)\) \(\chi_{1169}(316,\cdot)\) \(\chi_{1169}(323,\cdot)\) \(\chi_{1169}(330,\cdot)\) \(\chi_{1169}(344,\cdot)\) \(\chi_{1169}(351,\cdot)\) \(\chi_{1169}(379,\cdot)\) \(\chi_{1169}(386,\cdot)\) \(\chi_{1169}(393,\cdot)\) \(\chi_{1169}(407,\cdot)\) \(\chi_{1169}(414,\cdot)\) \(\chi_{1169}(435,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((836,673)\) → \((1,e\left(\frac{95}{166}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1169 }(15, a) \) | \(-1\) | \(1\) | \(e\left(\frac{74}{83}\right)\) | \(e\left(\frac{66}{83}\right)\) | \(e\left(\frac{65}{83}\right)\) | \(e\left(\frac{95}{166}\right)\) | \(e\left(\frac{57}{83}\right)\) | \(e\left(\frac{56}{83}\right)\) | \(e\left(\frac{49}{83}\right)\) | \(e\left(\frac{77}{166}\right)\) | \(e\left(\frac{2}{83}\right)\) | \(e\left(\frac{48}{83}\right)\) |