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 \(\chi_{3015}(23,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6030.ep
\(\chi_{6030}(23,\cdot)\) \(\chi_{6030}(47,\cdot)\) \(\chi_{6030}(77,\cdot)\) \(\chi_{6030}(227,\cdot)\) \(\chi_{6030}(743,\cdot)\) \(\chi_{6030}(887,\cdot)\) \(\chi_{6030}(977,\cdot)\) \(\chi_{6030}(1127,\cdot)\) \(\chi_{6030}(1193,\cdot)\) \(\chi_{6030}(1253,\cdot)\) \(\chi_{6030}(1283,\cdot)\) \(\chi_{6030}(1433,\cdot)\) \(\chi_{6030}(1577,\cdot)\) \(\chi_{6030}(2093,\cdot)\) \(\chi_{6030}(2183,\cdot)\) \(\chi_{6030}(2327,\cdot)\) \(\chi_{6030}(2333,\cdot)\) \(\chi_{6030}(2567,\cdot)\) \(\chi_{6030}(2783,\cdot)\) \(\chi_{6030}(3287,\cdot)\) \(\chi_{6030}(3533,\cdot)\) \(\chi_{6030}(3773,\cdot)\) \(\chi_{6030}(4037,\cdot)\) \(\chi_{6030}(4187,\cdot)\) \(\chi_{6030}(4277,\cdot)\) \(\chi_{6030}(4307,\cdot)\) \(\chi_{6030}(4457,\cdot)\) \(\chi_{6030}(4487,\cdot)\) \(\chi_{6030}(4493,\cdot)\) \(\chi_{6030}(4817,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((4691,1207,3151)\) → \((e\left(\frac{5}{6}\right),-i,e\left(\frac{14}{33}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 6030 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{53}{132}\right)\) | \(e\left(\frac{49}{66}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(1\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{43}{66}\right)\) |