Basic properties
Modulus: | \(1003\) | |
Conductor: | \(1003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(464\) | 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)
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Galois orbit 1003.s
\(\chi_{1003}(3,\cdot)\) \(\chi_{1003}(5,\cdot)\) \(\chi_{1003}(7,\cdot)\) \(\chi_{1003}(12,\cdot)\) \(\chi_{1003}(20,\cdot)\) \(\chi_{1003}(22,\cdot)\) \(\chi_{1003}(27,\cdot)\) \(\chi_{1003}(28,\cdot)\) \(\chi_{1003}(29,\cdot)\) \(\chi_{1003}(41,\cdot)\) \(\chi_{1003}(45,\cdot)\) \(\chi_{1003}(46,\cdot)\) \(\chi_{1003}(48,\cdot)\) \(\chi_{1003}(57,\cdot)\) \(\chi_{1003}(62,\cdot)\) \(\chi_{1003}(63,\cdot)\) \(\chi_{1003}(71,\cdot)\) \(\chi_{1003}(74,\cdot)\) \(\chi_{1003}(75,\cdot)\) \(\chi_{1003}(78,\cdot)\) \(\chi_{1003}(79,\cdot)\) \(\chi_{1003}(80,\cdot)\) \(\chi_{1003}(88,\cdot)\) \(\chi_{1003}(95,\cdot)\) \(\chi_{1003}(105,\cdot)\) \(\chi_{1003}(107,\cdot)\) \(\chi_{1003}(108,\cdot)\) \(\chi_{1003}(112,\cdot)\) \(\chi_{1003}(116,\cdot)\) \(\chi_{1003}(122,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{464})$ |
Fixed field: | Number field defined by a degree 464 polynomial (not computed) |
Values on generators
\((768,120)\) → \((e\left(\frac{1}{16}\right),e\left(\frac{8}{29}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1003 }(105, a) \) | \(-1\) | \(1\) | \(e\left(\frac{35}{232}\right)\) | \(e\left(\frac{397}{464}\right)\) | \(e\left(\frac{35}{116}\right)\) | \(e\left(\frac{449}{464}\right)\) | \(e\left(\frac{3}{464}\right)\) | \(e\left(\frac{303}{464}\right)\) | \(e\left(\frac{105}{232}\right)\) | \(e\left(\frac{165}{232}\right)\) | \(e\left(\frac{55}{464}\right)\) | \(e\left(\frac{155}{464}\right)\) |