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 \(\chi_{3015}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6030.eo
\(\chi_{6030}(7,\cdot)\) \(\chi_{6030}(13,\cdot)\) \(\chi_{6030}(337,\cdot)\) \(\chi_{6030}(367,\cdot)\) \(\chi_{6030}(463,\cdot)\) \(\chi_{6030}(517,\cdot)\) \(\chi_{6030}(547,\cdot)\) \(\chi_{6030}(637,\cdot)\) \(\chi_{6030}(787,\cdot)\) \(\chi_{6030}(1183,\cdot)\) \(\chi_{6030}(1213,\cdot)\) \(\chi_{6030}(1537,\cdot)\) \(\chi_{6030}(1543,\cdot)\) \(\chi_{6030}(1573,\cdot)\) \(\chi_{6030}(1723,\cdot)\) \(\chi_{6030}(1753,\cdot)\) \(\chi_{6030}(1843,\cdot)\) \(\chi_{6030}(1993,\cdot)\) \(\chi_{6030}(2257,\cdot)\) \(\chi_{6030}(2497,\cdot)\) \(\chi_{6030}(2743,\cdot)\) \(\chi_{6030}(3247,\cdot)\) \(\chi_{6030}(3463,\cdot)\) \(\chi_{6030}(3697,\cdot)\) \(\chi_{6030}(3703,\cdot)\) \(\chi_{6030}(3847,\cdot)\) \(\chi_{6030}(3937,\cdot)\) \(\chi_{6030}(4453,\cdot)\) \(\chi_{6030}(4597,\cdot)\) \(\chi_{6030}(4747,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((4691,1207,3151)\) → \((e\left(\frac{2}{3}\right),i,e\left(\frac{23}{66}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 6030 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{73}{132}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(-1\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{53}{66}\right)\) |