Basic properties
Modulus: | \(1117\) | |
Conductor: | \(1117\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(1116\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1117.r
\(\chi_{1117}(2,\cdot)\) \(\chi_{1117}(6,\cdot)\) \(\chi_{1117}(14,\cdot)\) \(\chi_{1117}(17,\cdot)\) \(\chi_{1117}(18,\cdot)\) \(\chi_{1117}(20,\cdot)\) \(\chi_{1117}(26,\cdot)\) \(\chi_{1117}(29,\cdot)\) \(\chi_{1117}(32,\cdot)\) \(\chi_{1117}(35,\cdot)\) \(\chi_{1117}(42,\cdot)\) \(\chi_{1117}(43,\cdot)\) \(\chi_{1117}(44,\cdot)\) \(\chi_{1117}(50,\cdot)\) \(\chi_{1117}(51,\cdot)\) \(\chi_{1117}(54,\cdot)\) \(\chi_{1117}(56,\cdot)\) \(\chi_{1117}(59,\cdot)\) \(\chi_{1117}(60,\cdot)\) \(\chi_{1117}(62,\cdot)\) \(\chi_{1117}(67,\cdot)\) \(\chi_{1117}(68,\cdot)\) \(\chi_{1117}(71,\cdot)\) \(\chi_{1117}(73,\cdot)\) \(\chi_{1117}(74,\cdot)\) \(\chi_{1117}(76,\cdot)\) \(\chi_{1117}(77,\cdot)\) \(\chi_{1117}(78,\cdot)\) \(\chi_{1117}(80,\cdot)\) \(\chi_{1117}(82,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1116})$ |
Fixed field: | Number field defined by a degree 1116 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{1}{1116}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1117 }(2, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{1116}\right)\) | \(e\left(\frac{92}{93}\right)\) | \(e\left(\frac{1}{558}\right)\) | \(e\left(\frac{251}{372}\right)\) | \(e\left(\frac{1105}{1116}\right)\) | \(e\left(\frac{173}{558}\right)\) | \(e\left(\frac{1}{372}\right)\) | \(e\left(\frac{91}{93}\right)\) | \(e\left(\frac{377}{558}\right)\) | \(e\left(\frac{5}{12}\right)\) |