Basic properties
| Modulus: | \(1169\) | |
| Conductor: | \(1169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(166\) | 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 1169.k
\(\chi_{1169}(13,\cdot)\) \(\chi_{1169}(20,\cdot)\) \(\chi_{1169}(34,\cdot)\) \(\chi_{1169}(41,\cdot)\) \(\chi_{1169}(55,\cdot)\) \(\chi_{1169}(69,\cdot)\) \(\chi_{1169}(83,\cdot)\) \(\chi_{1169}(90,\cdot)\) \(\chi_{1169}(104,\cdot)\) \(\chi_{1169}(111,\cdot)\) \(\chi_{1169}(118,\cdot)\) \(\chi_{1169}(125,\cdot)\) \(\chi_{1169}(139,\cdot)\) \(\chi_{1169}(146,\cdot)\) \(\chi_{1169}(153,\cdot)\) \(\chi_{1169}(160,\cdot)\) \(\chi_{1169}(202,\cdot)\) \(\chi_{1169}(237,\cdot)\) \(\chi_{1169}(258,\cdot)\) \(\chi_{1169}(272,\cdot)\) \(\chi_{1169}(286,\cdot)\) \(\chi_{1169}(307,\cdot)\) \(\chi_{1169}(328,\cdot)\) \(\chi_{1169}(349,\cdot)\) \(\chi_{1169}(377,\cdot)\) \(\chi_{1169}(405,\cdot)\) \(\chi_{1169}(412,\cdot)\) \(\chi_{1169}(426,\cdot)\) \(\chi_{1169}(440,\cdot)\) \(\chi_{1169}(447,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{83})$ |
| Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((836,673)\) → \((-1,e\left(\frac{81}{166}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 1169 }(20, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{83}\right)\) | \(e\left(\frac{61}{166}\right)\) | \(e\left(\frac{3}{83}\right)\) | \(e\left(\frac{82}{83}\right)\) | \(e\left(\frac{147}{166}\right)\) | \(e\left(\frac{46}{83}\right)\) | \(e\left(\frac{61}{83}\right)\) | \(e\left(\frac{42}{83}\right)\) | \(e\left(\frac{55}{83}\right)\) | \(e\left(\frac{67}{166}\right)\) |