Basic properties
Modulus: | \(1078\) | |
Conductor: | \(539\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{539}(171,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1078.bf
\(\chi_{1078}(17,\cdot)\) \(\chi_{1078}(61,\cdot)\) \(\chi_{1078}(73,\cdot)\) \(\chi_{1078}(101,\cdot)\) \(\chi_{1078}(145,\cdot)\) \(\chi_{1078}(171,\cdot)\) \(\chi_{1078}(173,\cdot)\) \(\chi_{1078}(255,\cdot)\) \(\chi_{1078}(271,\cdot)\) \(\chi_{1078}(283,\cdot)\) \(\chi_{1078}(299,\cdot)\) \(\chi_{1078}(327,\cdot)\) \(\chi_{1078}(369,\cdot)\) \(\chi_{1078}(381,\cdot)\) \(\chi_{1078}(409,\cdot)\) \(\chi_{1078}(425,\cdot)\) \(\chi_{1078}(437,\cdot)\) \(\chi_{1078}(453,\cdot)\) \(\chi_{1078}(479,\cdot)\) \(\chi_{1078}(481,\cdot)\) \(\chi_{1078}(523,\cdot)\) \(\chi_{1078}(535,\cdot)\) \(\chi_{1078}(563,\cdot)\) \(\chi_{1078}(579,\cdot)\) \(\chi_{1078}(591,\cdot)\) \(\chi_{1078}(633,\cdot)\) \(\chi_{1078}(635,\cdot)\) \(\chi_{1078}(677,\cdot)\) \(\chi_{1078}(689,\cdot)\) \(\chi_{1078}(733,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((199,981)\) → \((e\left(\frac{37}{42}\right),e\left(\frac{9}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 1078 }(171, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{210}\right)\) | \(e\left(\frac{31}{210}\right)\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{13}{105}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{31}{105}\right)\) | \(e\left(\frac{17}{70}\right)\) |