Basic properties
Modulus: | \(2601\) | |
Conductor: | \(2601\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(816\) | 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 2601.bn
\(\chi_{2601}(5,\cdot)\) \(\chi_{2601}(11,\cdot)\) \(\chi_{2601}(14,\cdot)\) \(\chi_{2601}(20,\cdot)\) \(\chi_{2601}(23,\cdot)\) \(\chi_{2601}(29,\cdot)\) \(\chi_{2601}(41,\cdot)\) \(\chi_{2601}(56,\cdot)\) \(\chi_{2601}(74,\cdot)\) \(\chi_{2601}(92,\cdot)\) \(\chi_{2601}(95,\cdot)\) \(\chi_{2601}(113,\cdot)\) \(\chi_{2601}(122,\cdot)\) \(\chi_{2601}(146,\cdot)\) \(\chi_{2601}(164,\cdot)\) \(\chi_{2601}(167,\cdot)\) \(\chi_{2601}(173,\cdot)\) \(\chi_{2601}(176,\cdot)\) \(\chi_{2601}(182,\cdot)\) \(\chi_{2601}(194,\cdot)\) \(\chi_{2601}(209,\cdot)\) \(\chi_{2601}(218,\cdot)\) \(\chi_{2601}(227,\cdot)\) \(\chi_{2601}(245,\cdot)\) \(\chi_{2601}(248,\cdot)\) \(\chi_{2601}(266,\cdot)\) \(\chi_{2601}(275,\cdot)\) \(\chi_{2601}(284,\cdot)\) \(\chi_{2601}(299,\cdot)\) \(\chi_{2601}(311,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{816})$ |
Fixed field: | Number field defined by a degree 816 polynomial (not computed) |
Values on generators
\((290,2026)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{93}{272}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 2601 }(284, a) \) | \(1\) | \(1\) | \(e\left(\frac{325}{408}\right)\) | \(e\left(\frac{121}{204}\right)\) | \(e\left(\frac{379}{816}\right)\) | \(e\left(\frac{269}{816}\right)\) | \(e\left(\frac{53}{136}\right)\) | \(e\left(\frac{71}{272}\right)\) | \(e\left(\frac{569}{816}\right)\) | \(e\left(\frac{139}{204}\right)\) | \(e\left(\frac{103}{816}\right)\) | \(e\left(\frac{19}{102}\right)\) |