Basic properties
Modulus: | \(1003\) | |
Conductor: | \(1003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(232\) | 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)
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Galois orbit 1003.r
\(\chi_{1003}(9,\cdot)\) \(\chi_{1003}(15,\cdot)\) \(\chi_{1003}(19,\cdot)\) \(\chi_{1003}(25,\cdot)\) \(\chi_{1003}(26,\cdot)\) \(\chi_{1003}(36,\cdot)\) \(\chi_{1003}(49,\cdot)\) \(\chi_{1003}(53,\cdot)\) \(\chi_{1003}(66,\cdot)\) \(\chi_{1003}(76,\cdot)\) \(\chi_{1003}(87,\cdot)\) \(\chi_{1003}(94,\cdot)\) \(\chi_{1003}(100,\cdot)\) \(\chi_{1003}(104,\cdot)\) \(\chi_{1003}(110,\cdot)\) \(\chi_{1003}(121,\cdot)\) \(\chi_{1003}(127,\cdot)\) \(\chi_{1003}(134,\cdot)\) \(\chi_{1003}(138,\cdot)\) \(\chi_{1003}(144,\cdot)\) \(\chi_{1003}(145,\cdot)\) \(\chi_{1003}(189,\cdot)\) \(\chi_{1003}(196,\cdot)\) \(\chi_{1003}(202,\cdot)\) \(\chi_{1003}(206,\cdot)\) \(\chi_{1003}(212,\cdot)\) \(\chi_{1003}(213,\cdot)\) \(\chi_{1003}(223,\cdot)\) \(\chi_{1003}(230,\cdot)\) \(\chi_{1003}(240,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{232})$ |
Fixed field: | Number field defined by a degree 232 polynomial (not computed) |
Values on generators
\((768,120)\) → \((e\left(\frac{3}{8}\right),e\left(\frac{7}{29}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1003 }(100, a) \) | \(1\) | \(1\) | \(e\left(\frac{57}{116}\right)\) | \(e\left(\frac{103}{232}\right)\) | \(e\left(\frac{57}{58}\right)\) | \(e\left(\frac{75}{232}\right)\) | \(e\left(\frac{217}{232}\right)\) | \(e\left(\frac{109}{232}\right)\) | \(e\left(\frac{55}{116}\right)\) | \(e\left(\frac{103}{116}\right)\) | \(e\left(\frac{189}{232}\right)\) | \(e\left(\frac{153}{232}\right)\) |