Basic properties
Modulus: | \(8041\) | |
Conductor: | \(731\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(112\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{731}(419,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8041.eh
\(\chi_{8041}(45,\cdot)\) \(\chi_{8041}(199,\cdot)\) \(\chi_{8041}(309,\cdot)\) \(\chi_{8041}(419,\cdot)\) \(\chi_{8041}(452,\cdot)\) \(\chi_{8041}(925,\cdot)\) \(\chi_{8041}(991,\cdot)\) \(\chi_{8041}(1145,\cdot)\) \(\chi_{8041}(1200,\cdot)\) \(\chi_{8041}(1255,\cdot)\) \(\chi_{8041}(1365,\cdot)\) \(\chi_{8041}(1618,\cdot)\) \(\chi_{8041}(1673,\cdot)\) \(\chi_{8041}(1728,\cdot)\) \(\chi_{8041}(2564,\cdot)\) \(\chi_{8041}(2674,\cdot)\) \(\chi_{8041}(2817,\cdot)\) \(\chi_{8041}(2883,\cdot)\) \(\chi_{8041}(3037,\cdot)\) \(\chi_{8041}(3257,\cdot)\) \(\chi_{8041}(3356,\cdot)\) \(\chi_{8041}(3565,\cdot)\) \(\chi_{8041}(3730,\cdot)\) \(\chi_{8041}(3763,\cdot)\) \(\chi_{8041}(3983,\cdot)\) \(\chi_{8041}(4236,\cdot)\) \(\chi_{8041}(4511,\cdot)\) \(\chi_{8041}(4566,\cdot)\) \(\chi_{8041}(4984,\cdot)\) \(\chi_{8041}(5039,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{112})$ |
Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((1,e\left(\frac{7}{16}\right),e\left(\frac{3}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(419, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{56}\right)\) | \(e\left(\frac{73}{112}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{61}{112}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{41}{56}\right)\) | \(e\left(\frac{17}{56}\right)\) | \(e\left(\frac{51}{112}\right)\) | \(e\left(\frac{53}{112}\right)\) |