Basic properties
| Modulus: | \(338130\) | |
| Conductor: | \(169065\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(204\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169065}(47,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 338130.bmn
\(\chi_{338130}(47,\cdot)\) \(\chi_{338130}(11003,\cdot)\) \(\chi_{338130}(13307,\cdot)\) \(\chi_{338130}(17633,\cdot)\) \(\chi_{338130}(19937,\cdot)\) \(\chi_{338130}(30893,\cdot)\) \(\chi_{338130}(37523,\cdot)\) \(\chi_{338130}(39827,\cdot)\) \(\chi_{338130}(50783,\cdot)\) \(\chi_{338130}(53087,\cdot)\) \(\chi_{338130}(57413,\cdot)\) \(\chi_{338130}(59717,\cdot)\) \(\chi_{338130}(70673,\cdot)\) \(\chi_{338130}(72977,\cdot)\) \(\chi_{338130}(77303,\cdot)\) \(\chi_{338130}(79607,\cdot)\) \(\chi_{338130}(90563,\cdot)\) \(\chi_{338130}(92867,\cdot)\) \(\chi_{338130}(97193,\cdot)\) \(\chi_{338130}(99497,\cdot)\) \(\chi_{338130}(110453,\cdot)\) \(\chi_{338130}(112757,\cdot)\) \(\chi_{338130}(119387,\cdot)\) \(\chi_{338130}(130343,\cdot)\) \(\chi_{338130}(132647,\cdot)\) \(\chi_{338130}(136973,\cdot)\) \(\chi_{338130}(139277,\cdot)\) \(\chi_{338130}(150233,\cdot)\) \(\chi_{338130}(152537,\cdot)\) \(\chi_{338130}(156863,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{204})$ |
| Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((262991,67627,104041,145081)\) → \((e\left(\frac{1}{6}\right),i,i,e\left(\frac{25}{68}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 338130 }(47, a) \) | \(-1\) | \(1\) | \(e\left(\frac{133}{204}\right)\) | \(e\left(\frac{19}{51}\right)\) | \(e\left(\frac{61}{68}\right)\) | \(e\left(\frac{7}{102}\right)\) | \(e\left(\frac{127}{204}\right)\) | \(e\left(\frac{91}{102}\right)\) | \(e\left(\frac{29}{68}\right)\) | \(e\left(\frac{97}{102}\right)\) | \(e\left(\frac{1}{204}\right)\) | \(e\left(\frac{95}{102}\right)\) |