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 \(\chi_{169065}(77,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 338130.btq
\(\chi_{338130}(77,\cdot)\) \(\chi_{338130}(4133,\cdot)\) \(\chi_{338130}(5693,\cdot)\) \(\chi_{338130}(6707,\cdot)\) \(\chi_{338130}(7097,\cdot)\) \(\chi_{338130}(12323,\cdot)\) \(\chi_{338130}(13727,\cdot)\) \(\chi_{338130}(17393,\cdot)\) \(\chi_{338130}(19967,\cdot)\) \(\chi_{338130}(24023,\cdot)\) \(\chi_{338130}(25583,\cdot)\) \(\chi_{338130}(26597,\cdot)\) \(\chi_{338130}(33617,\cdot)\) \(\chi_{338130}(37283,\cdot)\) \(\chi_{338130}(39857,\cdot)\) \(\chi_{338130}(43913,\cdot)\) \(\chi_{338130}(45473,\cdot)\) \(\chi_{338130}(46487,\cdot)\) \(\chi_{338130}(46877,\cdot)\) \(\chi_{338130}(52103,\cdot)\) \(\chi_{338130}(53507,\cdot)\) \(\chi_{338130}(57173,\cdot)\) \(\chi_{338130}(59747,\cdot)\) \(\chi_{338130}(63803,\cdot)\) \(\chi_{338130}(65363,\cdot)\) \(\chi_{338130}(66377,\cdot)\) \(\chi_{338130}(66767,\cdot)\) \(\chi_{338130}(71993,\cdot)\) \(\chi_{338130}(73397,\cdot)\) \(\chi_{338130}(77063,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{408})$ |
| Fixed field: | Number field defined by a degree 408 polynomial (not computed) |
Values on generators
\((262991,67627,104041,145081)\) → \((e\left(\frac{5}{6}\right),i,-1,e\left(\frac{89}{136}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 338130 }(77, a) \) | \(1\) | \(1\) | \(e\left(\frac{211}{408}\right)\) | \(e\left(\frac{157}{408}\right)\) | \(e\left(\frac{11}{68}\right)\) | \(e\left(\frac{347}{408}\right)\) | \(e\left(\frac{55}{408}\right)\) | \(e\left(\frac{23}{408}\right)\) | \(e\left(\frac{23}{136}\right)\) | \(e\left(\frac{233}{408}\right)\) | \(e\left(\frac{50}{51}\right)\) | \(e\left(\frac{5}{204}\right)\) |