Basic properties
Modulus: | \(7744\) | |
Conductor: | \(7744\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(880\) | 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 7744.db
\(\chi_{7744}(19,\cdot)\) \(\chi_{7744}(35,\cdot)\) \(\chi_{7744}(51,\cdot)\) \(\chi_{7744}(83,\cdot)\) \(\chi_{7744}(107,\cdot)\) \(\chi_{7744}(123,\cdot)\) \(\chi_{7744}(139,\cdot)\) \(\chi_{7744}(171,\cdot)\) \(\chi_{7744}(195,\cdot)\) \(\chi_{7744}(211,\cdot)\) \(\chi_{7744}(227,\cdot)\) \(\chi_{7744}(259,\cdot)\) \(\chi_{7744}(283,\cdot)\) \(\chi_{7744}(299,\cdot)\) \(\chi_{7744}(315,\cdot)\) \(\chi_{7744}(347,\cdot)\) \(\chi_{7744}(371,\cdot)\) \(\chi_{7744}(387,\cdot)\) \(\chi_{7744}(435,\cdot)\) \(\chi_{7744}(459,\cdot)\) \(\chi_{7744}(491,\cdot)\) \(\chi_{7744}(523,\cdot)\) \(\chi_{7744}(547,\cdot)\) \(\chi_{7744}(563,\cdot)\) \(\chi_{7744}(579,\cdot)\) \(\chi_{7744}(611,\cdot)\) \(\chi_{7744}(635,\cdot)\) \(\chi_{7744}(651,\cdot)\) \(\chi_{7744}(667,\cdot)\) \(\chi_{7744}(739,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{880})$ |
Fixed field: | Number field defined by a degree 880 polynomial (not computed) |
Values on generators
\((5567,4357,6657)\) → \((-1,e\left(\frac{7}{16}\right),e\left(\frac{83}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 7744 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{80}\right)\) | \(e\left(\frac{241}{880}\right)\) | \(e\left(\frac{69}{440}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{679}{880}\right)\) | \(e\left(\frac{107}{220}\right)\) | \(e\left(\frac{49}{220}\right)\) | \(e\left(\frac{167}{880}\right)\) | \(e\left(\frac{65}{176}\right)\) | \(e\left(\frac{39}{88}\right)\) |