Basic properties
| Modulus: | \(2888\) | |
| Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{361}(65,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2888.bj
\(\chi_{2888}(65,\cdot)\) \(\chi_{2888}(145,\cdot)\) \(\chi_{2888}(217,\cdot)\) \(\chi_{2888}(297,\cdot)\) \(\chi_{2888}(369,\cdot)\) \(\chi_{2888}(449,\cdot)\) \(\chi_{2888}(521,\cdot)\) \(\chi_{2888}(601,\cdot)\) \(\chi_{2888}(673,\cdot)\) \(\chi_{2888}(753,\cdot)\) \(\chi_{2888}(825,\cdot)\) \(\chi_{2888}(905,\cdot)\) \(\chi_{2888}(977,\cdot)\) \(\chi_{2888}(1057,\cdot)\) \(\chi_{2888}(1129,\cdot)\) \(\chi_{2888}(1209,\cdot)\) \(\chi_{2888}(1281,\cdot)\) \(\chi_{2888}(1361,\cdot)\) \(\chi_{2888}(1433,\cdot)\) \(\chi_{2888}(1585,\cdot)\) \(\chi_{2888}(1665,\cdot)\) \(\chi_{2888}(1817,\cdot)\) \(\chi_{2888}(1889,\cdot)\) \(\chi_{2888}(1969,\cdot)\) \(\chi_{2888}(2041,\cdot)\) \(\chi_{2888}(2121,\cdot)\) \(\chi_{2888}(2193,\cdot)\) \(\chi_{2888}(2273,\cdot)\) \(\chi_{2888}(2345,\cdot)\) \(\chi_{2888}(2425,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((2167,1445,2529)\) → \((1,1,e\left(\frac{73}{114}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 2888 }(65, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{114}\right)\) | \(e\left(\frac{32}{57}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{1}{57}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{77}{114}\right)\) | \(e\left(\frac{65}{114}\right)\) | \(e\left(\frac{41}{57}\right)\) | \(e\left(\frac{7}{114}\right)\) | \(e\left(\frac{28}{57}\right)\) |