Basic properties
| Modulus: | \(2166\) | |
| Conductor: | \(1083\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(342\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1083}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2166.v
\(\chi_{2166}(29,\cdot)\) \(\chi_{2166}(41,\cdot)\) \(\chi_{2166}(53,\cdot)\) \(\chi_{2166}(59,\cdot)\) \(\chi_{2166}(71,\cdot)\) \(\chi_{2166}(89,\cdot)\) \(\chi_{2166}(143,\cdot)\) \(\chi_{2166}(155,\cdot)\) \(\chi_{2166}(167,\cdot)\) \(\chi_{2166}(173,\cdot)\) \(\chi_{2166}(185,\cdot)\) \(\chi_{2166}(203,\cdot)\) \(\chi_{2166}(257,\cdot)\) \(\chi_{2166}(269,\cdot)\) \(\chi_{2166}(281,\cdot)\) \(\chi_{2166}(287,\cdot)\) \(\chi_{2166}(317,\cdot)\) \(\chi_{2166}(371,\cdot)\) \(\chi_{2166}(383,\cdot)\) \(\chi_{2166}(395,\cdot)\) \(\chi_{2166}(401,\cdot)\) \(\chi_{2166}(413,\cdot)\) \(\chi_{2166}(431,\cdot)\) \(\chi_{2166}(485,\cdot)\) \(\chi_{2166}(497,\cdot)\) \(\chi_{2166}(509,\cdot)\) \(\chi_{2166}(515,\cdot)\) \(\chi_{2166}(527,\cdot)\) \(\chi_{2166}(545,\cdot)\) \(\chi_{2166}(599,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((1445,1807)\) → \((-1,e\left(\frac{17}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 2166 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{342}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{65}{114}\right)\) | \(e\left(\frac{121}{342}\right)\) | \(e\left(\frac{251}{342}\right)\) | \(e\left(\frac{259}{342}\right)\) | \(e\left(\frac{11}{171}\right)\) | \(e\left(\frac{59}{171}\right)\) | \(e\left(\frac{7}{114}\right)\) | \(e\left(\frac{167}{342}\right)\) |