Basic properties
| Modulus: | \(338130\) | |
| Conductor: | \(56355\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(816\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{56355}(107,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 338130.bvo
\(\chi_{338130}(107,\cdot)\) \(\chi_{338130}(1043,\cdot)\) \(\chi_{338130}(1673,\cdot)\) \(\chi_{338130}(1907,\cdot)\) \(\chi_{338130}(4247,\cdot)\) \(\chi_{338130}(5723,\cdot)\) \(\chi_{338130}(7757,\cdot)\) \(\chi_{338130}(8693,\cdot)\) \(\chi_{338130}(10637,\cdot)\) \(\chi_{338130}(12743,\cdot)\) \(\chi_{338130}(13373,\cdot)\) \(\chi_{338130}(13913,\cdot)\) \(\chi_{338130}(14147,\cdot)\) \(\chi_{338130}(16487,\cdot)\) \(\chi_{338130}(18287,\cdot)\) \(\chi_{338130}(19997,\cdot)\) \(\chi_{338130}(20393,\cdot)\) \(\chi_{338130}(20933,\cdot)\) \(\chi_{338130}(21563,\cdot)\) \(\chi_{338130}(21797,\cdot)\) \(\chi_{338130}(24137,\cdot)\) \(\chi_{338130}(25613,\cdot)\) \(\chi_{338130}(27647,\cdot)\) \(\chi_{338130}(28583,\cdot)\) \(\chi_{338130}(30527,\cdot)\) \(\chi_{338130}(32633,\cdot)\) \(\chi_{338130}(33263,\cdot)\) \(\chi_{338130}(33803,\cdot)\) \(\chi_{338130}(36377,\cdot)\) \(\chi_{338130}(38177,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{816})$ |
| Fixed field: | Number field defined by a degree 816 polynomial (not computed) |
Values on generators
\((262991,67627,104041,145081)\) → \((-1,i,e\left(\frac{1}{3}\right),e\left(\frac{133}{272}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 338130 }(107, a) \) | \(-1\) | \(1\) | \(e\left(\frac{577}{816}\right)\) | \(e\left(\frac{65}{816}\right)\) | \(e\left(\frac{5}{408}\right)\) | \(e\left(\frac{509}{816}\right)\) | \(e\left(\frac{371}{816}\right)\) | \(e\left(\frac{109}{272}\right)\) | \(e\left(\frac{539}{816}\right)\) | \(e\left(\frac{365}{816}\right)\) | \(e\left(\frac{377}{408}\right)\) | \(e\left(\frac{11}{17}\right)\) |