Basic properties
| Modulus: | \(2151\) | |
| Conductor: | \(717\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(238\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{717}(8,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2151.ba
\(\chi_{2151}(8,\cdot)\) \(\chi_{2151}(17,\cdot)\) \(\chi_{2151}(62,\cdot)\) \(\chi_{2151}(80,\cdot)\) \(\chi_{2151}(116,\cdot)\) \(\chi_{2151}(125,\cdot)\) \(\chi_{2151}(134,\cdot)\) \(\chi_{2151}(161,\cdot)\) \(\chi_{2151}(170,\cdot)\) \(\chi_{2151}(197,\cdot)\) \(\chi_{2151}(242,\cdot)\) \(\chi_{2151}(251,\cdot)\) \(\chi_{2151}(269,\cdot)\) \(\chi_{2151}(287,\cdot)\) \(\chi_{2151}(305,\cdot)\) \(\chi_{2151}(332,\cdot)\) \(\chi_{2151}(341,\cdot)\) \(\chi_{2151}(359,\cdot)\) \(\chi_{2151}(386,\cdot)\) \(\chi_{2151}(404,\cdot)\) \(\chi_{2151}(413,\cdot)\) \(\chi_{2151}(422,\cdot)\) \(\chi_{2151}(431,\cdot)\) \(\chi_{2151}(494,\cdot)\) \(\chi_{2151}(503,\cdot)\) \(\chi_{2151}(512,\cdot)\) \(\chi_{2151}(539,\cdot)\) \(\chi_{2151}(566,\cdot)\) \(\chi_{2151}(602,\cdot)\) \(\chi_{2151}(611,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{119})$ |
| Fixed field: | Number field defined by a degree 238 polynomial (not computed) |
Values on generators
\((479,1441)\) → \((-1,e\left(\frac{99}{119}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2151 }(8, a) \) | \(-1\) | \(1\) | \(e\left(\frac{97}{238}\right)\) | \(e\left(\frac{97}{119}\right)\) | \(e\left(\frac{73}{238}\right)\) | \(e\left(\frac{99}{119}\right)\) | \(e\left(\frac{53}{238}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{197}{238}\right)\) | \(e\left(\frac{92}{119}\right)\) | \(e\left(\frac{57}{238}\right)\) | \(e\left(\frac{75}{119}\right)\) |