Basic properties
Modulus: | \(3234\) | |
Conductor: | \(1617\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1617}(149,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3234.ci
\(\chi_{3234}(95,\cdot)\) \(\chi_{3234}(107,\cdot)\) \(\chi_{3234}(149,\cdot)\) \(\chi_{3234}(233,\cdot)\) \(\chi_{3234}(305,\cdot)\) \(\chi_{3234}(347,\cdot)\) \(\chi_{3234}(359,\cdot)\) \(\chi_{3234}(431,\cdot)\) \(\chi_{3234}(611,\cdot)\) \(\chi_{3234}(695,\cdot)\) \(\chi_{3234}(767,\cdot)\) \(\chi_{3234}(809,\cdot)\) \(\chi_{3234}(821,\cdot)\) \(\chi_{3234}(893,\cdot)\) \(\chi_{3234}(1019,\cdot)\) \(\chi_{3234}(1031,\cdot)\) \(\chi_{3234}(1073,\cdot)\) \(\chi_{3234}(1229,\cdot)\) \(\chi_{3234}(1271,\cdot)\) \(\chi_{3234}(1283,\cdot)\) \(\chi_{3234}(1355,\cdot)\) \(\chi_{3234}(1481,\cdot)\) \(\chi_{3234}(1493,\cdot)\) \(\chi_{3234}(1535,\cdot)\) \(\chi_{3234}(1619,\cdot)\) \(\chi_{3234}(1691,\cdot)\) \(\chi_{3234}(1817,\cdot)\) \(\chi_{3234}(1943,\cdot)\) \(\chi_{3234}(1955,\cdot)\) \(\chi_{3234}(1997,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1079,199,2059)\) → \((-1,e\left(\frac{13}{21}\right),e\left(\frac{9}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 3234 }(149, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{210}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{8}{105}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{11}{105}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{64}{105}\right)\) | \(e\left(\frac{17}{35}\right)\) |