Basic properties
| Modulus: | \(76230\) | |
| Conductor: | \(5445\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(660\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{5445}(3557,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 76230.rg
\(\chi_{76230}(113,\cdot)\) \(\chi_{76230}(533,\cdot)\) \(\chi_{76230}(1037,\cdot)\) \(\chi_{76230}(1247,\cdot)\) \(\chi_{76230}(1373,\cdot)\) \(\chi_{76230}(2297,\cdot)\) \(\chi_{76230}(2633,\cdot)\) \(\chi_{76230}(3557,\cdot)\) \(\chi_{76230}(3683,\cdot)\) \(\chi_{76230}(3767,\cdot)\) \(\chi_{76230}(4943,\cdot)\) \(\chi_{76230}(5153,\cdot)\) \(\chi_{76230}(5657,\cdot)\) \(\chi_{76230}(6917,\cdot)\) \(\chi_{76230}(7043,\cdot)\) \(\chi_{76230}(7463,\cdot)\) \(\chi_{76230}(7967,\cdot)\) \(\chi_{76230}(8177,\cdot)\) \(\chi_{76230}(8303,\cdot)\) \(\chi_{76230}(9227,\cdot)\) \(\chi_{76230}(9353,\cdot)\) \(\chi_{76230}(9563,\cdot)\) \(\chi_{76230}(10613,\cdot)\) \(\chi_{76230}(10697,\cdot)\) \(\chi_{76230}(11873,\cdot)\) \(\chi_{76230}(12083,\cdot)\) \(\chi_{76230}(13007,\cdot)\) \(\chi_{76230}(13847,\cdot)\) \(\chi_{76230}(13973,\cdot)\) \(\chi_{76230}(14393,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{660})$ |
| Fixed field: | Number field defined by a degree 660 polynomial (not computed) |
Values on generators
\((8471,15247,65341,57961)\) → \((e\left(\frac{1}{6}\right),i,1,e\left(\frac{46}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 76230 }(3557, a) \) | \(1\) | \(1\) | \(e\left(\frac{367}{660}\right)\) | \(e\left(\frac{161}{220}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{17}{132}\right)\) | \(e\left(\frac{146}{165}\right)\) | \(e\left(\frac{43}{165}\right)\) | \(e\left(\frac{83}{220}\right)\) | \(e\left(\frac{23}{330}\right)\) | \(e\left(\frac{43}{132}\right)\) | \(e\left(\frac{251}{660}\right)\) |