Basic properties
Modulus: | \(8041\) | |
Conductor: | \(731\) | 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 \(\chi_{731}(225,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8041.ed
\(\chi_{8041}(353,\cdot)\) \(\chi_{8041}(540,\cdot)\) \(\chi_{8041}(1475,\cdot)\) \(\chi_{8041}(1772,\cdot)\) \(\chi_{8041}(1959,\cdot)\) \(\chi_{8041}(2036,\cdot)\) \(\chi_{8041}(2597,\cdot)\) \(\chi_{8041}(2894,\cdot)\) \(\chi_{8041}(3455,\cdot)\) \(\chi_{8041}(4016,\cdot)\) \(\chi_{8041}(4280,\cdot)\) \(\chi_{8041}(4467,\cdot)\) \(\chi_{8041}(4654,\cdot)\) \(\chi_{8041}(4841,\cdot)\) \(\chi_{8041}(5028,\cdot)\) \(\chi_{8041}(5699,\cdot)\) \(\chi_{8041}(5776,\cdot)\) \(\chi_{8041}(5886,\cdot)\) \(\chi_{8041}(6073,\cdot)\) \(\chi_{8041}(6260,\cdot)\) \(\chi_{8041}(6447,\cdot)\) \(\chi_{8041}(6524,\cdot)\) \(\chi_{8041}(7195,\cdot)\) \(\chi_{8041}(7943,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{84})$ |
Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((6580,2366,562)\) → \((1,-i,e\left(\frac{5}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(6073, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{71}{84}\right)\) |