Basic properties
Modulus: | \(3200\) | |
Conductor: | \(3200\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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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
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Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Galois orbit 3200.dg
\(\chi_{3200}(19,\cdot)\) \(\chi_{3200}(59,\cdot)\) \(\chi_{3200}(139,\cdot)\) \(\chi_{3200}(179,\cdot)\) \(\chi_{3200}(219,\cdot)\) \(\chi_{3200}(259,\cdot)\) \(\chi_{3200}(339,\cdot)\) \(\chi_{3200}(379,\cdot)\) \(\chi_{3200}(419,\cdot)\) \(\chi_{3200}(459,\cdot)\) \(\chi_{3200}(539,\cdot)\) \(\chi_{3200}(579,\cdot)\) \(\chi_{3200}(619,\cdot)\) \(\chi_{3200}(659,\cdot)\) \(\chi_{3200}(739,\cdot)\) \(\chi_{3200}(779,\cdot)\) \(\chi_{3200}(819,\cdot)\) \(\chi_{3200}(859,\cdot)\) \(\chi_{3200}(939,\cdot)\) \(\chi_{3200}(979,\cdot)\) \(\chi_{3200}(1019,\cdot)\) \(\chi_{3200}(1059,\cdot)\) \(\chi_{3200}(1139,\cdot)\) \(\chi_{3200}(1179,\cdot)\) \(\chi_{3200}(1219,\cdot)\) \(\chi_{3200}(1259,\cdot)\) \(\chi_{3200}(1339,\cdot)\) \(\chi_{3200}(1379,\cdot)\) \(\chi_{3200}(1419,\cdot)\) \(\chi_{3200}(1459,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{160})$ |
Fixed field: | Number field defined by a degree 160 polynomial (not computed) |
Values on generators
\((1151,901,2177)\) → \((-1,e\left(\frac{23}{32}\right),e\left(\frac{9}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 3200 }(19, a) \) | \(-1\) | \(1\) | \(e\left(\frac{153}{160}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{159}{160}\right)\) | \(e\left(\frac{141}{160}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{37}{160}\right)\) | \(e\left(\frac{23}{160}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{139}{160}\right)\) |