Basic properties
| Modulus: | \(338130\) | |
| Conductor: | \(18785\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(408\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{18785}(127,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 338130.bty
\(\chi_{338130}(127,\cdot)\) \(\chi_{338130}(2773,\cdot)\) \(\chi_{338130}(5347,\cdot)\) \(\chi_{338130}(10423,\cdot)\) \(\chi_{338130}(10963,\cdot)\) \(\chi_{338130}(12367,\cdot)\) \(\chi_{338130}(12997,\cdot)\) \(\chi_{338130}(18613,\cdot)\) \(\chi_{338130}(20017,\cdot)\) \(\chi_{338130}(22663,\cdot)\) \(\chi_{338130}(25237,\cdot)\) \(\chi_{338130}(30313,\cdot)\) \(\chi_{338130}(30853,\cdot)\) \(\chi_{338130}(32257,\cdot)\) \(\chi_{338130}(32887,\cdot)\) \(\chi_{338130}(38503,\cdot)\) \(\chi_{338130}(39907,\cdot)\) \(\chi_{338130}(42553,\cdot)\) \(\chi_{338130}(45127,\cdot)\) \(\chi_{338130}(50203,\cdot)\) \(\chi_{338130}(50743,\cdot)\) \(\chi_{338130}(52147,\cdot)\) \(\chi_{338130}(58393,\cdot)\) \(\chi_{338130}(59797,\cdot)\) \(\chi_{338130}(62443,\cdot)\) \(\chi_{338130}(65017,\cdot)\) \(\chi_{338130}(70633,\cdot)\) \(\chi_{338130}(72037,\cdot)\) \(\chi_{338130}(72667,\cdot)\) \(\chi_{338130}(78283,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{408})$ |
| Fixed field: | Number field defined by a degree 408 polynomial (not computed) |
Values on generators
\((262991,67627,104041,145081)\) → \((1,i,e\left(\frac{5}{6}\right),e\left(\frac{29}{136}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 338130 }(127, a) \) | \(-1\) | \(1\) | \(e\left(\frac{191}{408}\right)\) | \(e\left(\frac{301}{408}\right)\) | \(e\left(\frac{133}{204}\right)\) | \(e\left(\frac{259}{408}\right)\) | \(e\left(\frac{199}{408}\right)\) | \(e\left(\frac{57}{136}\right)\) | \(e\left(\frac{241}{408}\right)\) | \(e\left(\frac{121}{408}\right)\) | \(e\left(\frac{31}{51}\right)\) | \(e\left(\frac{5}{68}\right)\) |