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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2601.bm
\(\chi_{2601}(7,\cdot)\) \(\chi_{2601}(22,\cdot)\) \(\chi_{2601}(31,\cdot)\) \(\chi_{2601}(58,\cdot)\) \(\chi_{2601}(61,\cdot)\) \(\chi_{2601}(79,\cdot)\) \(\chi_{2601}(88,\cdot)\) \(\chi_{2601}(97,\cdot)\) \(\chi_{2601}(112,\cdot)\) \(\chi_{2601}(124,\cdot)\) \(\chi_{2601}(130,\cdot)\) \(\chi_{2601}(133,\cdot)\) \(\chi_{2601}(139,\cdot)\) \(\chi_{2601}(142,\cdot)\) \(\chi_{2601}(148,\cdot)\) \(\chi_{2601}(160,\cdot)\) \(\chi_{2601}(175,\cdot)\) \(\chi_{2601}(184,\cdot)\) \(\chi_{2601}(193,\cdot)\) \(\chi_{2601}(211,\cdot)\) \(\chi_{2601}(232,\cdot)\) \(\chi_{2601}(241,\cdot)\) \(\chi_{2601}(250,\cdot)\) \(\chi_{2601}(265,\cdot)\) \(\chi_{2601}(277,\cdot)\) \(\chi_{2601}(283,\cdot)\) \(\chi_{2601}(286,\cdot)\) \(\chi_{2601}(292,\cdot)\) \(\chi_{2601}(295,\cdot)\) \(\chi_{2601}(301,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{816})$ |
Fixed field: | Number field defined by a degree 816 polynomial (not computed) |
Values on generators
\((290,2026)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{9}{272}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 2601 }(31, a) \) | \(-1\) | \(1\) | \(e\left(\frac{253}{408}\right)\) | \(e\left(\frac{49}{204}\right)\) | \(e\left(\frac{199}{816}\right)\) | \(e\left(\frac{377}{816}\right)\) | \(e\left(\frac{117}{136}\right)\) | \(e\left(\frac{235}{272}\right)\) | \(e\left(\frac{77}{816}\right)\) | \(e\left(\frac{31}{204}\right)\) | \(e\left(\frac{67}{816}\right)\) | \(e\left(\frac{49}{102}\right)\) |