Basic properties
Modulus: | \(8026\) | |
Conductor: | \(4013\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1003\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4013}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8026.j
\(\chi_{8026}(7,\cdot)\) \(\chi_{8026}(11,\cdot)\) \(\chi_{8026}(19,\cdot)\) \(\chi_{8026}(41,\cdot)\) \(\chi_{8026}(43,\cdot)\) \(\chi_{8026}(49,\cdot)\) \(\chi_{8026}(61,\cdot)\) \(\chi_{8026}(67,\cdot)\) \(\chi_{8026}(73,\cdot)\) \(\chi_{8026}(77,\cdot)\) \(\chi_{8026}(81,\cdot)\) \(\chi_{8026}(83,\cdot)\) \(\chi_{8026}(87,\cdot)\) \(\chi_{8026}(109,\cdot)\) \(\chi_{8026}(111,\cdot)\) \(\chi_{8026}(117,\cdot)\) \(\chi_{8026}(121,\cdot)\) \(\chi_{8026}(133,\cdot)\) \(\chi_{8026}(135,\cdot)\) \(\chi_{8026}(139,\cdot)\) \(\chi_{8026}(145,\cdot)\) \(\chi_{8026}(153,\cdot)\) \(\chi_{8026}(169,\cdot)\) \(\chi_{8026}(173,\cdot)\) \(\chi_{8026}(179,\cdot)\) \(\chi_{8026}(185,\cdot)\) \(\chi_{8026}(195,\cdot)\) \(\chi_{8026}(199,\cdot)\) \(\chi_{8026}(209,\cdot)\) \(\chi_{8026}(211,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1003})$ |
Fixed field: | Number field defined by a degree 1003 polynomial (not computed) |
Values on generators
\(4015\) → \(e\left(\frac{653}{1003}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 8026 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{77}{1003}\right)\) | \(e\left(\frac{999}{1003}\right)\) | \(e\left(\frac{536}{1003}\right)\) | \(e\left(\frac{154}{1003}\right)\) | \(e\left(\frac{74}{1003}\right)\) | \(e\left(\frac{244}{1003}\right)\) | \(e\left(\frac{73}{1003}\right)\) | \(e\left(\frac{484}{1003}\right)\) | \(e\left(\frac{596}{1003}\right)\) | \(e\left(\frac{613}{1003}\right)\) |