Basic properties
| Modulus: | \(86190\) | |
| Conductor: | \(14365\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(624\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{14365}(7027,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 86190.up
\(\chi_{86190}(7,\cdot)\) \(\chi_{86190}(397,\cdot)\) \(\chi_{86190}(643,\cdot)\) \(\chi_{86190}(1423,\cdot)\) \(\chi_{86190}(2173,\cdot)\) \(\chi_{86190}(3547,\cdot)\) \(\chi_{86190}(3937,\cdot)\) \(\chi_{86190}(4153,\cdot)\) \(\chi_{86190}(4933,\cdot)\) \(\chi_{86190}(5077,\cdot)\) \(\chi_{86190}(5107,\cdot)\) \(\chi_{86190}(5467,\cdot)\) \(\chi_{86190}(5683,\cdot)\) \(\chi_{86190}(6463,\cdot)\) \(\chi_{86190}(6637,\cdot)\) \(\chi_{86190}(7027,\cdot)\) \(\chi_{86190}(7273,\cdot)\) \(\chi_{86190}(8053,\cdot)\) \(\chi_{86190}(8803,\cdot)\) \(\chi_{86190}(9583,\cdot)\) \(\chi_{86190}(10177,\cdot)\) \(\chi_{86190}(10783,\cdot)\) \(\chi_{86190}(11563,\cdot)\) \(\chi_{86190}(11707,\cdot)\) \(\chi_{86190}(11737,\cdot)\) \(\chi_{86190}(12097,\cdot)\) \(\chi_{86190}(12127,\cdot)\) \(\chi_{86190}(12313,\cdot)\) \(\chi_{86190}(13267,\cdot)\) \(\chi_{86190}(13657,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{624})$ |
| Fixed field: | Number field defined by a degree 624 polynomial (not computed) |
Values on generators
\((57461,34477,57631,45631)\) → \((1,i,e\left(\frac{59}{156}\right),e\left(\frac{15}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 86190 }(7027, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{624}\right)\) | \(e\left(\frac{323}{624}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{47}{48}\right)\) | \(e\left(\frac{509}{624}\right)\) | \(e\left(\frac{79}{208}\right)\) | \(e\left(\frac{185}{624}\right)\) | \(e\left(\frac{287}{624}\right)\) | \(e\left(\frac{239}{312}\right)\) | \(e\left(\frac{43}{52}\right)\) |