Basic properties
| Modulus: | \(1316\) | |
| Conductor: | \(329\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(138\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{329}(73,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1316.bb
\(\chi_{1316}(5,\cdot)\) \(\chi_{1316}(33,\cdot)\) \(\chi_{1316}(45,\cdot)\) \(\chi_{1316}(73,\cdot)\) \(\chi_{1316}(117,\cdot)\) \(\chi_{1316}(129,\cdot)\) \(\chi_{1316}(185,\cdot)\) \(\chi_{1316}(201,\cdot)\) \(\chi_{1316}(229,\cdot)\) \(\chi_{1316}(257,\cdot)\) \(\chi_{1316}(297,\cdot)\) \(\chi_{1316}(313,\cdot)\) \(\chi_{1316}(325,\cdot)\) \(\chi_{1316}(369,\cdot)\) \(\chi_{1316}(381,\cdot)\) \(\chi_{1316}(409,\cdot)\) \(\chi_{1316}(453,\cdot)\) \(\chi_{1316}(481,\cdot)\) \(\chi_{1316}(493,\cdot)\) \(\chi_{1316}(509,\cdot)\) \(\chi_{1316}(537,\cdot)\) \(\chi_{1316}(577,\cdot)\) \(\chi_{1316}(593,\cdot)\) \(\chi_{1316}(605,\cdot)\) \(\chi_{1316}(621,\cdot)\) \(\chi_{1316}(633,\cdot)\) \(\chi_{1316}(649,\cdot)\) \(\chi_{1316}(677,\cdot)\) \(\chi_{1316}(689,\cdot)\) \(\chi_{1316}(745,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{69})$ |
| Fixed field: | Number field defined by a degree 138 polynomial (not computed) |
Values on generators
\((659,941,757)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{29}{46}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 1316 }(73, a) \) | \(1\) | \(1\) | \(e\left(\frac{107}{138}\right)\) | \(e\left(\frac{32}{69}\right)\) | \(e\left(\frac{38}{69}\right)\) | \(e\left(\frac{11}{138}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{11}{46}\right)\) | \(e\left(\frac{35}{138}\right)\) | \(e\left(\frac{14}{69}\right)\) | \(e\left(\frac{67}{138}\right)\) | \(e\left(\frac{64}{69}\right)\) |