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 \(\chi_{3015}(2153,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6030.eg
\(\chi_{6030}(263,\cdot)\) \(\chi_{6030}(293,\cdot)\) \(\chi_{6030}(533,\cdot)\) \(\chi_{6030}(617,\cdot)\) \(\chi_{6030}(893,\cdot)\) \(\chi_{6030}(947,\cdot)\) \(\chi_{6030}(1067,\cdot)\) \(\chi_{6030}(1163,\cdot)\) \(\chi_{6030}(1337,\cdot)\) \(\chi_{6030}(1667,\cdot)\) \(\chi_{6030}(1697,\cdot)\) \(\chi_{6030}(1757,\cdot)\) \(\chi_{6030}(1823,\cdot)\) \(\chi_{6030}(1967,\cdot)\) \(\chi_{6030}(2117,\cdot)\) \(\chi_{6030}(2153,\cdot)\) \(\chi_{6030}(2273,\cdot)\) \(\chi_{6030}(2543,\cdot)\) \(\chi_{6030}(2873,\cdot)\) \(\chi_{6030}(2903,\cdot)\) \(\chi_{6030}(2957,\cdot)\) \(\chi_{6030}(2963,\cdot)\) \(\chi_{6030}(3107,\cdot)\) \(\chi_{6030}(3173,\cdot)\) \(\chi_{6030}(3323,\cdot)\) \(\chi_{6030}(3677,\cdot)\) \(\chi_{6030}(3767,\cdot)\) \(\chi_{6030}(4127,\cdot)\) \(\chi_{6030}(4163,\cdot)\) \(\chi_{6030}(4313,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((4691,1207,3151)\) → \((e\left(\frac{1}{6}\right),-i,e\left(\frac{2}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 6030 }(2153, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{132}\right)\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{5}{132}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{23}{132}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(-i\) | \(e\left(\frac{31}{66}\right)\) |