Basic properties
Modulus: | \(6030\) | |
Conductor: | \(3015\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{3015}(247,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6030.ef
\(\chi_{6030}(247,\cdot)\) \(\chi_{6030}(727,\cdot)\) \(\chi_{6030}(733,\cdot)\) \(\chi_{6030}(817,\cdot)\) \(\chi_{6030}(1033,\cdot)\) \(\chi_{6030}(1123,\cdot)\) \(\chi_{6030}(1237,\cdot)\) \(\chi_{6030}(1267,\cdot)\) \(\chi_{6030}(1453,\cdot)\) \(\chi_{6030}(1687,\cdot)\) \(\chi_{6030}(1933,\cdot)\) \(\chi_{6030}(1987,\cdot)\) \(\chi_{6030}(2023,\cdot)\) \(\chi_{6030}(2347,\cdot)\) \(\chi_{6030}(2443,\cdot)\) \(\chi_{6030}(2473,\cdot)\) \(\chi_{6030}(2527,\cdot)\) \(\chi_{6030}(2587,\cdot)\) \(\chi_{6030}(2767,\cdot)\) \(\chi_{6030}(2797,\cdot)\) \(\chi_{6030}(2893,\cdot)\) \(\chi_{6030}(3193,\cdot)\) \(\chi_{6030}(3553,\cdot)\) \(\chi_{6030}(3733,\cdot)\) \(\chi_{6030}(3793,\cdot)\) \(\chi_{6030}(3973,\cdot)\) \(\chi_{6030}(4003,\cdot)\) \(\chi_{6030}(4027,\cdot)\) \(\chi_{6030}(4387,\cdot)\) \(\chi_{6030}(4507,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((4691,1207,3151)\) → \((e\left(\frac{1}{3}\right),i,e\left(\frac{29}{66}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 6030 }(247, a) \) | \(1\) | \(1\) | \(e\left(\frac{91}{132}\right)\) | \(e\left(\frac{17}{66}\right)\) | \(e\left(\frac{101}{132}\right)\) | \(e\left(\frac{49}{132}\right)\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{95}{132}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{21}{22}\right)\) |