Basic properties
Modulus: | \(3234\) | |
Conductor: | \(539\) | 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 \(\chi_{539}(255,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3234.ck
\(\chi_{3234}(61,\cdot)\) \(\chi_{3234}(73,\cdot)\) \(\chi_{3234}(145,\cdot)\) \(\chi_{3234}(271,\cdot)\) \(\chi_{3234}(283,\cdot)\) \(\chi_{3234}(409,\cdot)\) \(\chi_{3234}(481,\cdot)\) \(\chi_{3234}(523,\cdot)\) \(\chi_{3234}(535,\cdot)\) \(\chi_{3234}(733,\cdot)\) \(\chi_{3234}(745,\cdot)\) \(\chi_{3234}(787,\cdot)\) \(\chi_{3234}(871,\cdot)\) \(\chi_{3234}(943,\cdot)\) \(\chi_{3234}(985,\cdot)\) \(\chi_{3234}(997,\cdot)\) \(\chi_{3234}(1069,\cdot)\) \(\chi_{3234}(1249,\cdot)\) \(\chi_{3234}(1333,\cdot)\) \(\chi_{3234}(1405,\cdot)\) \(\chi_{3234}(1447,\cdot)\) \(\chi_{3234}(1459,\cdot)\) \(\chi_{3234}(1531,\cdot)\) \(\chi_{3234}(1657,\cdot)\) \(\chi_{3234}(1669,\cdot)\) \(\chi_{3234}(1711,\cdot)\) \(\chi_{3234}(1867,\cdot)\) \(\chi_{3234}(1909,\cdot)\) \(\chi_{3234}(1921,\cdot)\) \(\chi_{3234}(1993,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((1079,199,2059)\) → \((1,e\left(\frac{13}{42}\right),e\left(\frac{1}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 3234 }(1333, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{210}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{67}{105}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{11}{105}\right)\) | \(e\left(\frac{33}{35}\right)\) |