Basic properties
Modulus: | \(2601\) | |
Conductor: | \(2601\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(204\) | 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
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2601.bg
\(\chi_{2601}(4,\cdot)\) \(\chi_{2601}(13,\cdot)\) \(\chi_{2601}(106,\cdot)\) \(\chi_{2601}(115,\cdot)\) \(\chi_{2601}(157,\cdot)\) \(\chi_{2601}(166,\cdot)\) \(\chi_{2601}(259,\cdot)\) \(\chi_{2601}(268,\cdot)\) \(\chi_{2601}(310,\cdot)\) \(\chi_{2601}(319,\cdot)\) \(\chi_{2601}(412,\cdot)\) \(\chi_{2601}(421,\cdot)\) \(\chi_{2601}(463,\cdot)\) \(\chi_{2601}(472,\cdot)\) \(\chi_{2601}(565,\cdot)\) \(\chi_{2601}(574,\cdot)\) \(\chi_{2601}(625,\cdot)\) \(\chi_{2601}(718,\cdot)\) \(\chi_{2601}(727,\cdot)\) \(\chi_{2601}(769,\cdot)\) \(\chi_{2601}(778,\cdot)\) \(\chi_{2601}(871,\cdot)\) \(\chi_{2601}(880,\cdot)\) \(\chi_{2601}(922,\cdot)\) \(\chi_{2601}(931,\cdot)\) \(\chi_{2601}(1024,\cdot)\) \(\chi_{2601}(1033,\cdot)\) \(\chi_{2601}(1075,\cdot)\) \(\chi_{2601}(1084,\cdot)\) \(\chi_{2601}(1177,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{204})$ |
Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((290,2026)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{35}{68}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 2601 }(1075, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{102}\right)\) | \(e\left(\frac{13}{51}\right)\) | \(e\left(\frac{109}{204}\right)\) | \(e\left(\frac{23}{204}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{45}{68}\right)\) | \(e\left(\frac{35}{204}\right)\) | \(e\left(\frac{28}{51}\right)\) | \(e\left(\frac{49}{204}\right)\) | \(e\left(\frac{26}{51}\right)\) |