Basic properties
Modulus: | \(3968\) | |
Conductor: | \(3968\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(160\) | 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 3968.di
\(\chi_{3968}(27,\cdot)\) \(\chi_{3968}(91,\cdot)\) \(\chi_{3968}(139,\cdot)\) \(\chi_{3968}(147,\cdot)\) \(\chi_{3968}(275,\cdot)\) \(\chi_{3968}(339,\cdot)\) \(\chi_{3968}(387,\cdot)\) \(\chi_{3968}(395,\cdot)\) \(\chi_{3968}(523,\cdot)\) \(\chi_{3968}(587,\cdot)\) \(\chi_{3968}(635,\cdot)\) \(\chi_{3968}(643,\cdot)\) \(\chi_{3968}(771,\cdot)\) \(\chi_{3968}(835,\cdot)\) \(\chi_{3968}(883,\cdot)\) \(\chi_{3968}(891,\cdot)\) \(\chi_{3968}(1019,\cdot)\) \(\chi_{3968}(1083,\cdot)\) \(\chi_{3968}(1131,\cdot)\) \(\chi_{3968}(1139,\cdot)\) \(\chi_{3968}(1267,\cdot)\) \(\chi_{3968}(1331,\cdot)\) \(\chi_{3968}(1379,\cdot)\) \(\chi_{3968}(1387,\cdot)\) \(\chi_{3968}(1515,\cdot)\) \(\chi_{3968}(1579,\cdot)\) \(\chi_{3968}(1627,\cdot)\) \(\chi_{3968}(1635,\cdot)\) \(\chi_{3968}(1763,\cdot)\) \(\chi_{3968}(1827,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{160})$ |
Fixed field: | Number field defined by a degree 160 polynomial (not computed) |
Values on generators
\((2047,3845,2049)\) → \((-1,e\left(\frac{15}{32}\right),e\left(\frac{1}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 3968 }(1267, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{160}\right)\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{1}{80}\right)\) | \(e\left(\frac{103}{160}\right)\) | \(e\left(\frac{21}{160}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{109}{160}\right)\) | \(e\left(\frac{159}{160}\right)\) |