Basic properties
Modulus: | \(8624\) | |
Conductor: | \(784\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{784}(45,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8624.fx
\(\chi_{8624}(45,\cdot)\) \(\chi_{8624}(397,\cdot)\) \(\chi_{8624}(661,\cdot)\) \(\chi_{8624}(1013,\cdot)\) \(\chi_{8624}(1277,\cdot)\) \(\chi_{8624}(1629,\cdot)\) \(\chi_{8624}(2245,\cdot)\) \(\chi_{8624}(2509,\cdot)\) \(\chi_{8624}(3125,\cdot)\) \(\chi_{8624}(3477,\cdot)\) \(\chi_{8624}(3741,\cdot)\) \(\chi_{8624}(4093,\cdot)\) \(\chi_{8624}(4357,\cdot)\) \(\chi_{8624}(4709,\cdot)\) \(\chi_{8624}(4973,\cdot)\) \(\chi_{8624}(5325,\cdot)\) \(\chi_{8624}(5589,\cdot)\) \(\chi_{8624}(5941,\cdot)\) \(\chi_{8624}(6557,\cdot)\) \(\chi_{8624}(6821,\cdot)\) \(\chi_{8624}(7437,\cdot)\) \(\chi_{8624}(7789,\cdot)\) \(\chi_{8624}(8053,\cdot)\) \(\chi_{8624}(8405,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((5391,6469,7745,3137)\) → \((1,-i,e\left(\frac{31}{42}\right),1)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 8624 }(45, a) \) | \(-1\) | \(1\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{27}{28}\right)\) |