Basic properties
Modulus: | \(8041\) | |
Conductor: | \(8041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8041.ek
\(\chi_{8041}(36,\cdot)\) \(\chi_{8041}(49,\cdot)\) \(\chi_{8041}(423,\cdot)\) \(\chi_{8041}(995,\cdot)\) \(\chi_{8041}(1369,\cdot)\) \(\chi_{8041}(1511,\cdot)\) \(\chi_{8041}(1885,\cdot)\) \(\chi_{8041}(2242,\cdot)\) \(\chi_{8041}(2457,\cdot)\) \(\chi_{8041}(2616,\cdot)\) \(\chi_{8041}(2831,\cdot)\) \(\chi_{8041}(2973,\cdot)\) \(\chi_{8041}(3188,\cdot)\) \(\chi_{8041}(3347,\cdot)\) \(\chi_{8041}(3562,\cdot)\) \(\chi_{8041}(3833,\cdot)\) \(\chi_{8041}(3919,\cdot)\) \(\chi_{8041}(4207,\cdot)\) \(\chi_{8041}(4293,\cdot)\) \(\chi_{8041}(4779,\cdot)\) \(\chi_{8041}(5153,\cdot)\) \(\chi_{8041}(5295,\cdot)\) \(\chi_{8041}(5669,\cdot)\) \(\chi_{8041}(6026,\cdot)\) \(\chi_{8041}(6241,\cdot)\) \(\chi_{8041}(6400,\cdot)\) \(\chi_{8041}(6615,\cdot)\) \(\chi_{8041}(6757,\cdot)\) \(\chi_{8041}(6972,\cdot)\) \(\chi_{8041}(7131,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{1}{8}\right),e\left(\frac{2}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(2457, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{47}{120}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{11}{120}\right)\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{7}{24}\right)\) |