Basic properties
| Modulus: | \(283920\) | |
| Conductor: | \(5915\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{5915}(97,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 283920.dlp
\(\chi_{283920}(97,\cdot)\) \(\chi_{283920}(2113,\cdot)\) \(\chi_{283920}(5137,\cdot)\) \(\chi_{283920}(18913,\cdot)\) \(\chi_{283920}(21937,\cdot)\) \(\chi_{283920}(23953,\cdot)\) \(\chi_{283920}(26977,\cdot)\) \(\chi_{283920}(40753,\cdot)\) \(\chi_{283920}(43777,\cdot)\) \(\chi_{283920}(45793,\cdot)\) \(\chi_{283920}(48817,\cdot)\) \(\chi_{283920}(62593,\cdot)\) \(\chi_{283920}(65617,\cdot)\) \(\chi_{283920}(67633,\cdot)\) \(\chi_{283920}(70657,\cdot)\) \(\chi_{283920}(84433,\cdot)\) \(\chi_{283920}(87457,\cdot)\) \(\chi_{283920}(89473,\cdot)\) \(\chi_{283920}(92497,\cdot)\) \(\chi_{283920}(106273,\cdot)\) \(\chi_{283920}(109297,\cdot)\) \(\chi_{283920}(111313,\cdot)\) \(\chi_{283920}(114337,\cdot)\) \(\chi_{283920}(128113,\cdot)\) \(\chi_{283920}(131137,\cdot)\) \(\chi_{283920}(136177,\cdot)\) \(\chi_{283920}(149953,\cdot)\) \(\chi_{283920}(152977,\cdot)\) \(\chi_{283920}(154993,\cdot)\) \(\chi_{283920}(158017,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((248431,70981,189281,227137,40561,255361)\) → \((1,1,1,i,-1,e\left(\frac{17}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 283920 }(97, a) \) | \(-1\) | \(1\) | \(e\left(\frac{35}{156}\right)\) | \(e\left(\frac{103}{156}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{119}{156}\right)\) | \(e\left(\frac{7}{156}\right)\) | \(e\left(\frac{8}{13}\right)\) |