Basic properties
Modulus: | \(1003\) | |
Conductor: | \(1003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1003.t
\(\chi_{1003}(6,\cdot)\) \(\chi_{1003}(10,\cdot)\) \(\chi_{1003}(11,\cdot)\) \(\chi_{1003}(14,\cdot)\) \(\chi_{1003}(23,\cdot)\) \(\chi_{1003}(24,\cdot)\) \(\chi_{1003}(31,\cdot)\) \(\chi_{1003}(37,\cdot)\) \(\chi_{1003}(39,\cdot)\) \(\chi_{1003}(40,\cdot)\) \(\chi_{1003}(44,\cdot)\) \(\chi_{1003}(54,\cdot)\) \(\chi_{1003}(56,\cdot)\) \(\chi_{1003}(61,\cdot)\) \(\chi_{1003}(65,\cdot)\) \(\chi_{1003}(73,\cdot)\) \(\chi_{1003}(82,\cdot)\) \(\chi_{1003}(90,\cdot)\) \(\chi_{1003}(91,\cdot)\) \(\chi_{1003}(92,\cdot)\) \(\chi_{1003}(96,\cdot)\) \(\chi_{1003}(97,\cdot)\) \(\chi_{1003}(99,\cdot)\) \(\chi_{1003}(109,\cdot)\) \(\chi_{1003}(113,\cdot)\) \(\chi_{1003}(114,\cdot)\) \(\chi_{1003}(124,\cdot)\) \(\chi_{1003}(126,\cdot)\) \(\chi_{1003}(129,\cdot)\) \(\chi_{1003}(131,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{464})$ |
Fixed field: | Number field defined by a degree 464 polynomial (not computed) |
Values on generators
\((768,120)\) → \((e\left(\frac{3}{16}\right),e\left(\frac{7}{58}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1003 }(10, a) \) | \(1\) | \(1\) | \(e\left(\frac{173}{232}\right)\) | \(e\left(\frac{103}{464}\right)\) | \(e\left(\frac{57}{116}\right)\) | \(e\left(\frac{307}{464}\right)\) | \(e\left(\frac{449}{464}\right)\) | \(e\left(\frac{109}{464}\right)\) | \(e\left(\frac{55}{232}\right)\) | \(e\left(\frac{103}{232}\right)\) | \(e\left(\frac{189}{464}\right)\) | \(e\left(\frac{153}{464}\right)\) |