Basic properties
Modulus: | \(2601\) | |
Conductor: | \(2601\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(102\) | 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.bd
\(\chi_{2601}(16,\cdot)\) \(\chi_{2601}(67,\cdot)\) \(\chi_{2601}(169,\cdot)\) \(\chi_{2601}(220,\cdot)\) \(\chi_{2601}(322,\cdot)\) \(\chi_{2601}(373,\cdot)\) \(\chi_{2601}(475,\cdot)\) \(\chi_{2601}(526,\cdot)\) \(\chi_{2601}(628,\cdot)\) \(\chi_{2601}(679,\cdot)\) \(\chi_{2601}(781,\cdot)\) \(\chi_{2601}(832,\cdot)\) \(\chi_{2601}(934,\cdot)\) \(\chi_{2601}(985,\cdot)\) \(\chi_{2601}(1087,\cdot)\) \(\chi_{2601}(1138,\cdot)\) \(\chi_{2601}(1240,\cdot)\) \(\chi_{2601}(1291,\cdot)\) \(\chi_{2601}(1393,\cdot)\) \(\chi_{2601}(1546,\cdot)\) \(\chi_{2601}(1597,\cdot)\) \(\chi_{2601}(1699,\cdot)\) \(\chi_{2601}(1750,\cdot)\) \(\chi_{2601}(1852,\cdot)\) \(\chi_{2601}(1903,\cdot)\) \(\chi_{2601}(2005,\cdot)\) \(\chi_{2601}(2056,\cdot)\) \(\chi_{2601}(2158,\cdot)\) \(\chi_{2601}(2209,\cdot)\) \(\chi_{2601}(2362,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((290,2026)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{11}{34}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 2601 }(220, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{51}\right)\) | \(e\left(\frac{31}{51}\right)\) | \(e\left(\frac{77}{102}\right)\) | \(e\left(\frac{49}{102}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{79}{102}\right)\) | \(e\left(\frac{4}{51}\right)\) | \(e\left(\frac{29}{102}\right)\) | \(e\left(\frac{11}{51}\right)\) |