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 \(\chi_{3015}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6030.eh
\(\chi_{6030}(43,\cdot)\) \(\chi_{6030}(187,\cdot)\) \(\chi_{6030}(313,\cdot)\) \(\chi_{6030}(673,\cdot)\) \(\chi_{6030}(697,\cdot)\) \(\chi_{6030}(913,\cdot)\) \(\chi_{6030}(943,\cdot)\) \(\chi_{6030}(1057,\cdot)\) \(\chi_{6030}(1147,\cdot)\) \(\chi_{6030}(1393,\cdot)\) \(\chi_{6030}(1717,\cdot)\) \(\chi_{6030}(1867,\cdot)\) \(\chi_{6030}(1903,\cdot)\) \(\chi_{6030}(2263,\cdot)\) \(\chi_{6030}(2353,\cdot)\) \(\chi_{6030}(2707,\cdot)\) \(\chi_{6030}(2857,\cdot)\) \(\chi_{6030}(2923,\cdot)\) \(\chi_{6030}(3067,\cdot)\) \(\chi_{6030}(3073,\cdot)\) \(\chi_{6030}(3127,\cdot)\) \(\chi_{6030}(3157,\cdot)\) \(\chi_{6030}(3487,\cdot)\) \(\chi_{6030}(3757,\cdot)\) \(\chi_{6030}(3877,\cdot)\) \(\chi_{6030}(3913,\cdot)\) \(\chi_{6030}(4063,\cdot)\) \(\chi_{6030}(4207,\cdot)\) \(\chi_{6030}(4273,\cdot)\) \(\chi_{6030}(4333,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((4691,1207,3151)\) → \((e\left(\frac{2}{3}\right),-i,e\left(\frac{3}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 6030 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{132}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{23}{132}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{53}{132}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{49}{66}\right)\) | \(-i\) | \(e\left(\frac{37}{66}\right)\) |