Basic properties
| Modulus: | \(3234\) | |
| Conductor: | \(1617\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1617}(101,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3234.ch
\(\chi_{3234}(17,\cdot)\) \(\chi_{3234}(101,\cdot)\) \(\chi_{3234}(173,\cdot)\) \(\chi_{3234}(299,\cdot)\) \(\chi_{3234}(425,\cdot)\) \(\chi_{3234}(437,\cdot)\) \(\chi_{3234}(479,\cdot)\) \(\chi_{3234}(563,\cdot)\) \(\chi_{3234}(635,\cdot)\) \(\chi_{3234}(677,\cdot)\) \(\chi_{3234}(689,\cdot)\) \(\chi_{3234}(761,\cdot)\) \(\chi_{3234}(887,\cdot)\) \(\chi_{3234}(899,\cdot)\) \(\chi_{3234}(941,\cdot)\) \(\chi_{3234}(1025,\cdot)\) \(\chi_{3234}(1139,\cdot)\) \(\chi_{3234}(1151,\cdot)\) \(\chi_{3234}(1223,\cdot)\) \(\chi_{3234}(1349,\cdot)\) \(\chi_{3234}(1361,\cdot)\) \(\chi_{3234}(1487,\cdot)\) \(\chi_{3234}(1559,\cdot)\) \(\chi_{3234}(1601,\cdot)\) \(\chi_{3234}(1613,\cdot)\) \(\chi_{3234}(1811,\cdot)\) \(\chi_{3234}(1823,\cdot)\) \(\chi_{3234}(1865,\cdot)\) \(\chi_{3234}(1949,\cdot)\) \(\chi_{3234}(2021,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1079,199,2059)\) → \((-1,e\left(\frac{1}{42}\right),e\left(\frac{1}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 3234 }(101, a) \) | \(-1\) | \(1\) | \(e\left(\frac{62}{105}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{209}{210}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{19}{105}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{101}{105}\right)\) | \(e\left(\frac{11}{70}\right)\) |