Basic properties
| Modulus: | \(6030\) | |
| Conductor: | \(3015\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3015}(83,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6030.ec
\(\chi_{6030}(83,\cdot)\) \(\chi_{6030}(167,\cdot)\) \(\chi_{6030}(173,\cdot)\) \(\chi_{6030}(257,\cdot)\) \(\chi_{6030}(317,\cdot)\) \(\chi_{6030}(437,\cdot)\) \(\chi_{6030}(473,\cdot)\) \(\chi_{6030}(797,\cdot)\) \(\chi_{6030}(1373,\cdot)\) \(\chi_{6030}(1463,\cdot)\) \(\chi_{6030}(1523,\cdot)\) \(\chi_{6030}(1643,\cdot)\) \(\chi_{6030}(2003,\cdot)\) \(\chi_{6030}(2027,\cdot)\) \(\chi_{6030}(2057,\cdot)\) \(\chi_{6030}(2237,\cdot)\) \(\chi_{6030}(2297,\cdot)\) \(\chi_{6030}(2477,\cdot)\) \(\chi_{6030}(2837,\cdot)\) \(\chi_{6030}(3137,\cdot)\) \(\chi_{6030}(3233,\cdot)\) \(\chi_{6030}(3263,\cdot)\) \(\chi_{6030}(3443,\cdot)\) \(\chi_{6030}(3503,\cdot)\) \(\chi_{6030}(3557,\cdot)\) \(\chi_{6030}(3587,\cdot)\) \(\chi_{6030}(3683,\cdot)\) \(\chi_{6030}(4007,\cdot)\) \(\chi_{6030}(4043,\cdot)\) \(\chi_{6030}(4097,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((4691,1207,3151)\) → \((e\left(\frac{1}{6}\right),-i,e\left(\frac{2}{33}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 6030 }(83, a) \) | \(1\) | \(1\) | \(e\left(\frac{107}{132}\right)\) | \(e\left(\frac{49}{66}\right)\) | \(e\left(\frac{97}{132}\right)\) | \(e\left(\frac{17}{132}\right)\) | \(e\left(\frac{7}{66}\right)\) | \(e\left(\frac{103}{132}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{22}\right)\) |