Basic properties
Modulus: | \(8041\) | |
Conductor: | \(473\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(105\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{473}(53,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8041.ee
\(\chi_{8041}(103,\cdot)\) \(\chi_{8041}(273,\cdot)\) \(\chi_{8041}(324,\cdot)\) \(\chi_{8041}(443,\cdot)\) \(\chi_{8041}(511,\cdot)\) \(\chi_{8041}(698,\cdot)\) \(\chi_{8041}(834,\cdot)\) \(\chi_{8041}(885,\cdot)\) \(\chi_{8041}(1004,\cdot)\) \(\chi_{8041}(1072,\cdot)\) \(\chi_{8041}(1565,\cdot)\) \(\chi_{8041}(1786,\cdot)\) \(\chi_{8041}(1820,\cdot)\) \(\chi_{8041}(1973,\cdot)\) \(\chi_{8041}(2160,\cdot)\) \(\chi_{8041}(2347,\cdot)\) \(\chi_{8041}(2517,\cdot)\) \(\chi_{8041}(2534,\cdot)\) \(\chi_{8041}(2568,\cdot)\) \(\chi_{8041}(2704,\cdot)\) \(\chi_{8041}(2891,\cdot)\) \(\chi_{8041}(3078,\cdot)\) \(\chi_{8041}(3248,\cdot)\) \(\chi_{8041}(3265,\cdot)\) \(\chi_{8041}(3282,\cdot)\) \(\chi_{8041}(3435,\cdot)\) \(\chi_{8041}(3622,\cdot)\) \(\chi_{8041}(3809,\cdot)\) \(\chi_{8041}(3996,\cdot)\) \(\chi_{8041}(4013,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{3}{5}\right),1,e\left(\frac{5}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(2891, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{4}{105}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{37}{105}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{8}{105}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{2}{21}\right)\) |