Basic properties
Modulus: | \(8026\) | |
Conductor: | \(4013\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(2006\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4013}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8026.k
\(\chi_{8026}(9,\cdot)\) \(\chi_{8026}(13,\cdot)\) \(\chi_{8026}(15,\cdot)\) \(\chi_{8026}(17,\cdot)\) \(\chi_{8026}(25,\cdot)\) \(\chi_{8026}(31,\cdot)\) \(\chi_{8026}(47,\cdot)\) \(\chi_{8026}(59,\cdot)\) \(\chi_{8026}(63,\cdot)\) \(\chi_{8026}(69,\cdot)\) \(\chi_{8026}(71,\cdot)\) \(\chi_{8026}(89,\cdot)\) \(\chi_{8026}(91,\cdot)\) \(\chi_{8026}(97,\cdot)\) \(\chi_{8026}(99,\cdot)\) \(\chi_{8026}(105,\cdot)\) \(\chi_{8026}(115,\cdot)\) \(\chi_{8026}(127,\cdot)\) \(\chi_{8026}(143,\cdot)\) \(\chi_{8026}(165,\cdot)\) \(\chi_{8026}(171,\cdot)\) \(\chi_{8026}(175,\cdot)\) \(\chi_{8026}(187,\cdot)\) \(\chi_{8026}(191,\cdot)\) \(\chi_{8026}(217,\cdot)\) \(\chi_{8026}(237,\cdot)\) \(\chi_{8026}(247,\cdot)\) \(\chi_{8026}(257,\cdot)\) \(\chi_{8026}(271,\cdot)\) \(\chi_{8026}(275,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1003})$ |
Fixed field: | Number field defined by a degree 2006 polynomial (not computed) |
Values on generators
\(4015\) → \(e\left(\frac{1745}{2006}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 8026 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{1923}{2006}\right)\) | \(e\left(\frac{851}{2006}\right)\) | \(e\left(\frac{154}{1003}\right)\) | \(e\left(\frac{920}{1003}\right)\) | \(e\left(\frac{403}{1003}\right)\) | \(e\left(\frac{624}{1003}\right)\) | \(e\left(\frac{384}{1003}\right)\) | \(e\left(\frac{169}{1003}\right)\) | \(e\left(\frac{291}{1003}\right)\) | \(e\left(\frac{225}{2006}\right)\) |