Basic properties
| Modulus: | \(2151\) | |
| Conductor: | \(239\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(238\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{239}(46,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2151.bb
\(\chi_{2151}(19,\cdot)\) \(\chi_{2151}(37,\cdot)\) \(\chi_{2151}(46,\cdot)\) \(\chi_{2151}(82,\cdot)\) \(\chi_{2151}(118,\cdot)\) \(\chi_{2151}(154,\cdot)\) \(\chi_{2151}(181,\cdot)\) \(\chi_{2151}(190,\cdot)\) \(\chi_{2151}(208,\cdot)\) \(\chi_{2151}(235,\cdot)\) \(\chi_{2151}(253,\cdot)\) \(\chi_{2151}(280,\cdot)\) \(\chi_{2151}(298,\cdot)\) \(\chi_{2151}(316,\cdot)\) \(\chi_{2151}(325,\cdot)\) \(\chi_{2151}(334,\cdot)\) \(\chi_{2151}(343,\cdot)\) \(\chi_{2151}(370,\cdot)\) \(\chi_{2151}(379,\cdot)\) \(\chi_{2151}(388,\cdot)\) \(\chi_{2151}(397,\cdot)\) \(\chi_{2151}(406,\cdot)\) \(\chi_{2151}(424,\cdot)\) \(\chi_{2151}(433,\cdot)\) \(\chi_{2151}(451,\cdot)\) \(\chi_{2151}(460,\cdot)\) \(\chi_{2151}(469,\cdot)\) \(\chi_{2151}(541,\cdot)\) \(\chi_{2151}(595,\cdot)\) \(\chi_{2151}(604,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{119})$ |
| Fixed field: | Number field defined by a degree 238 polynomial (not computed) |
Values on generators
\((479,1441)\) → \((1,e\left(\frac{129}{238}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2151 }(46, a) \) | \(-1\) | \(1\) | \(e\left(\frac{92}{119}\right)\) | \(e\left(\frac{65}{119}\right)\) | \(e\left(\frac{95}{119}\right)\) | \(e\left(\frac{129}{238}\right)\) | \(e\left(\frac{38}{119}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{20}{119}\right)\) | \(e\left(\frac{73}{238}\right)\) | \(e\left(\frac{75}{238}\right)\) | \(e\left(\frac{11}{119}\right)\) |