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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Galois orbit 3200.dc
\(\chi_{3200}(67,\cdot)\) \(\chi_{3200}(123,\cdot)\) \(\chi_{3200}(147,\cdot)\) \(\chi_{3200}(203,\cdot)\) \(\chi_{3200}(227,\cdot)\) \(\chi_{3200}(283,\cdot)\) \(\chi_{3200}(363,\cdot)\) \(\chi_{3200}(387,\cdot)\) \(\chi_{3200}(467,\cdot)\) \(\chi_{3200}(523,\cdot)\) \(\chi_{3200}(547,\cdot)\) \(\chi_{3200}(603,\cdot)\) \(\chi_{3200}(627,\cdot)\) \(\chi_{3200}(683,\cdot)\) \(\chi_{3200}(763,\cdot)\) \(\chi_{3200}(787,\cdot)\) \(\chi_{3200}(867,\cdot)\) \(\chi_{3200}(923,\cdot)\) \(\chi_{3200}(947,\cdot)\) \(\chi_{3200}(1003,\cdot)\) \(\chi_{3200}(1027,\cdot)\) \(\chi_{3200}(1083,\cdot)\) \(\chi_{3200}(1163,\cdot)\) \(\chi_{3200}(1187,\cdot)\) \(\chi_{3200}(1267,\cdot)\) \(\chi_{3200}(1323,\cdot)\) \(\chi_{3200}(1347,\cdot)\) \(\chi_{3200}(1403,\cdot)\) \(\chi_{3200}(1427,\cdot)\) \(\chi_{3200}(1483,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{160})$ |
Fixed field: | Number field defined by a degree 160 polynomial (not computed) |
Values on generators
\((1151,901,2177)\) → \((-1,e\left(\frac{19}{32}\right),e\left(\frac{13}{20}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 3200 }(67, a) \) | \(1\) | \(1\) | \(e\left(\frac{133}{160}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{59}{160}\right)\) | \(e\left(\frac{41}{160}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{137}{160}\right)\) | \(e\left(\frac{83}{160}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{79}{160}\right)\) |