Basic properties
| Modulus: | \(338130\) | |
| Conductor: | \(18785\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(272\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{18785}(109,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 338130.bqk
\(\chi_{338130}(109,\cdot)\) \(\chi_{338130}(2179,\cdot)\) \(\chi_{338130}(4519,\cdot)\) \(\chi_{338130}(7129,\cdot)\) \(\chi_{338130}(8029,\cdot)\) \(\chi_{338130}(18559,\cdot)\) \(\chi_{338130}(18829,\cdot)\) \(\chi_{338130}(19999,\cdot)\) \(\chi_{338130}(22069,\cdot)\) \(\chi_{338130}(24409,\cdot)\) \(\chi_{338130}(27019,\cdot)\) \(\chi_{338130}(27919,\cdot)\) \(\chi_{338130}(31699,\cdot)\) \(\chi_{338130}(38449,\cdot)\) \(\chi_{338130}(38719,\cdot)\) \(\chi_{338130}(39889,\cdot)\) \(\chi_{338130}(41959,\cdot)\) \(\chi_{338130}(44299,\cdot)\) \(\chi_{338130}(46909,\cdot)\) \(\chi_{338130}(47809,\cdot)\) \(\chi_{338130}(51589,\cdot)\) \(\chi_{338130}(58339,\cdot)\) \(\chi_{338130}(58609,\cdot)\) \(\chi_{338130}(59779,\cdot)\) \(\chi_{338130}(61849,\cdot)\) \(\chi_{338130}(64189,\cdot)\) \(\chi_{338130}(67699,\cdot)\) \(\chi_{338130}(71479,\cdot)\) \(\chi_{338130}(78229,\cdot)\) \(\chi_{338130}(78499,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{272})$ |
| Fixed field: | Number field defined by a degree 272 polynomial (not computed) |
Values on generators
\((262991,67627,104041,145081)\) → \((1,-1,-i,e\left(\frac{203}{272}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 338130 }(109, a) \) | \(1\) | \(1\) | \(e\left(\frac{117}{272}\right)\) | \(e\left(\frac{113}{272}\right)\) | \(e\left(\frac{27}{136}\right)\) | \(e\left(\frac{117}{272}\right)\) | \(e\left(\frac{79}{272}\right)\) | \(e\left(\frac{127}{272}\right)\) | \(e\left(\frac{7}{272}\right)\) | \(e\left(\frac{101}{272}\right)\) | \(e\left(\frac{91}{136}\right)\) | \(e\left(\frac{13}{34}\right)\) |