Basic properties
Modulus: | \(8041\) | |
Conductor: | \(731\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(168\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{731}(529,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8041.es
\(\chi_{8041}(100,\cdot)\) \(\chi_{8041}(111,\cdot)\) \(\chi_{8041}(144,\cdot)\) \(\chi_{8041}(298,\cdot)\) \(\chi_{8041}(529,\cdot)\) \(\chi_{8041}(705,\cdot)\) \(\chi_{8041}(848,\cdot)\) \(\chi_{8041}(1046,\cdot)\) \(\chi_{8041}(1090,\cdot)\) \(\chi_{8041}(1651,\cdot)\) \(\chi_{8041}(1794,\cdot)\) \(\chi_{8041}(2388,\cdot)\) \(\chi_{8041}(2575,\cdot)\) \(\chi_{8041}(2718,\cdot)\) \(\chi_{8041}(2762,\cdot)\) \(\chi_{8041}(2905,\cdot)\) \(\chi_{8041}(2949,\cdot)\) \(\chi_{8041}(3136,\cdot)\) \(\chi_{8041}(3334,\cdot)\) \(\chi_{8041}(3521,\cdot)\) \(\chi_{8041}(3664,\cdot)\) \(\chi_{8041}(3708,\cdot)\) \(\chi_{8041}(3840,\cdot)\) \(\chi_{8041}(3851,\cdot)\) \(\chi_{8041}(3884,\cdot)\) \(\chi_{8041}(3895,\cdot)\) \(\chi_{8041}(4082,\cdot)\) \(\chi_{8041}(4401,\cdot)\) \(\chi_{8041}(4632,\cdot)\) \(\chi_{8041}(4786,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{168})$ |
Fixed field: | Number field defined by a degree 168 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{16}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(529, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{107}{168}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{71}{168}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{41}{168}\right)\) | \(e\left(\frac{47}{168}\right)\) |