Basic properties
| Modulus: | \(338130\) | |
| Conductor: | \(169065\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(408\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169065}(49,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 338130.bsn
\(\chi_{338130}(49,\cdot)\) \(\chi_{338130}(2389,\cdot)\) \(\chi_{338130}(5659,\cdot)\) \(\chi_{338130}(7999,\cdot)\) \(\chi_{338130}(9409,\cdot)\) \(\chi_{338130}(11749,\cdot)\) \(\chi_{338130}(15019,\cdot)\) \(\chi_{338130}(17359,\cdot)\) \(\chi_{338130}(19939,\cdot)\) \(\chi_{338130}(22279,\cdot)\) \(\chi_{338130}(25549,\cdot)\) \(\chi_{338130}(27889,\cdot)\) \(\chi_{338130}(31639,\cdot)\) \(\chi_{338130}(34909,\cdot)\) \(\chi_{338130}(37249,\cdot)\) \(\chi_{338130}(39829,\cdot)\) \(\chi_{338130}(42169,\cdot)\) \(\chi_{338130}(45439,\cdot)\) \(\chi_{338130}(47779,\cdot)\) \(\chi_{338130}(49189,\cdot)\) \(\chi_{338130}(51529,\cdot)\) \(\chi_{338130}(54799,\cdot)\) \(\chi_{338130}(57139,\cdot)\) \(\chi_{338130}(59719,\cdot)\) \(\chi_{338130}(62059,\cdot)\) \(\chi_{338130}(65329,\cdot)\) \(\chi_{338130}(67669,\cdot)\) \(\chi_{338130}(69079,\cdot)\) \(\chi_{338130}(71419,\cdot)\) \(\chi_{338130}(74689,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{408})$ |
| Fixed field: | Number field defined by a degree 408 polynomial (not computed) |
Values on generators
\((262991,67627,104041,145081)\) → \((e\left(\frac{1}{3}\right),-1,e\left(\frac{5}{6}\right),e\left(\frac{19}{136}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 338130 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{89}{136}\right)\) | \(e\left(\frac{155}{408}\right)\) | \(e\left(\frac{25}{204}\right)\) | \(e\left(\frac{89}{136}\right)\) | \(e\left(\frac{53}{408}\right)\) | \(e\left(\frac{173}{408}\right)\) | \(e\left(\frac{145}{408}\right)\) | \(e\left(\frac{53}{136}\right)\) | \(e\left(\frac{5}{68}\right)\) | \(e\left(\frac{31}{102}\right)\) |