Basic properties
Modulus: | \(8044\) | |
Conductor: | \(8044\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(670\) | 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
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8044.bb
\(\chi_{8044}(27,\cdot)\) \(\chi_{8044}(47,\cdot)\) \(\chi_{8044}(55,\cdot)\) \(\chi_{8044}(59,\cdot)\) \(\chi_{8044}(75,\cdot)\) \(\chi_{8044}(95,\cdot)\) \(\chi_{8044}(267,\cdot)\) \(\chi_{8044}(335,\cdot)\) \(\chi_{8044}(343,\cdot)\) \(\chi_{8044}(351,\cdot)\) \(\chi_{8044}(391,\cdot)\) \(\chi_{8044}(439,\cdot)\) \(\chi_{8044}(463,\cdot)\) \(\chi_{8044}(535,\cdot)\) \(\chi_{8044}(623,\cdot)\) \(\chi_{8044}(711,\cdot)\) \(\chi_{8044}(715,\cdot)\) \(\chi_{8044}(819,\cdot)\) \(\chi_{8044}(891,\cdot)\) \(\chi_{8044}(919,\cdot)\) \(\chi_{8044}(971,\cdot)\) \(\chi_{8044}(975,\cdot)\) \(\chi_{8044}(1107,\cdot)\) \(\chi_{8044}(1115,\cdot)\) \(\chi_{8044}(1135,\cdot)\) \(\chi_{8044}(1179,\cdot)\) \(\chi_{8044}(1199,\cdot)\) \(\chi_{8044}(1215,\cdot)\) \(\chi_{8044}(1251,\cdot)\) \(\chi_{8044}(1331,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{335})$ |
Fixed field: | Number field defined by a degree 670 polynomial (not computed) |
Values on generators
\((4023,4025)\) → \((-1,e\left(\frac{549}{670}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 8044 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{107}{335}\right)\) | \(e\left(\frac{23}{335}\right)\) | \(e\left(\frac{54}{335}\right)\) | \(e\left(\frac{214}{335}\right)\) | \(e\left(\frac{74}{335}\right)\) | \(e\left(\frac{1}{335}\right)\) | \(e\left(\frac{26}{67}\right)\) | \(e\left(\frac{223}{670}\right)\) | \(e\left(\frac{156}{335}\right)\) | \(e\left(\frac{161}{335}\right)\) |