Basic properties
| Modulus: | \(86190\) | |
| Conductor: | \(8619\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(208\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{8619}(4772,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 86190.ry
\(\chi_{86190}(131,\cdot)\) \(\chi_{86190}(521,\cdot)\) \(\chi_{86190}(911,\cdot)\) \(\chi_{86190}(2081,\cdot)\) \(\chi_{86190}(2471,\cdot)\) \(\chi_{86190}(2861,\cdot)\) \(\chi_{86190}(3641,\cdot)\) \(\chi_{86190}(5981,\cdot)\) \(\chi_{86190}(7151,\cdot)\) \(\chi_{86190}(7541,\cdot)\) \(\chi_{86190}(8711,\cdot)\) \(\chi_{86190}(9101,\cdot)\) \(\chi_{86190}(9491,\cdot)\) \(\chi_{86190}(10271,\cdot)\) \(\chi_{86190}(12611,\cdot)\) \(\chi_{86190}(13391,\cdot)\) \(\chi_{86190}(13781,\cdot)\) \(\chi_{86190}(14171,\cdot)\) \(\chi_{86190}(15341,\cdot)\) \(\chi_{86190}(15731,\cdot)\) \(\chi_{86190}(16121,\cdot)\) \(\chi_{86190}(19241,\cdot)\) \(\chi_{86190}(20021,\cdot)\) \(\chi_{86190}(20411,\cdot)\) \(\chi_{86190}(20801,\cdot)\) \(\chi_{86190}(22361,\cdot)\) \(\chi_{86190}(22751,\cdot)\) \(\chi_{86190}(23531,\cdot)\) \(\chi_{86190}(25871,\cdot)\) \(\chi_{86190}(26651,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{208})$ |
| Fixed field: | Number field defined by a degree 208 polynomial (not computed) |
Values on generators
\((57461,34477,57631,45631)\) → \((-1,1,e\left(\frac{1}{13}\right),e\left(\frac{13}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 86190 }(13391, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{208}\right)\) | \(e\left(\frac{23}{208}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{29}{208}\right)\) | \(e\left(\frac{193}{208}\right)\) | \(e\left(\frac{89}{208}\right)\) | \(e\left(\frac{203}{208}\right)\) | \(e\left(\frac{1}{104}\right)\) | \(e\left(\frac{31}{52}\right)\) |