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.di
\(\chi_{3200}(3,\cdot)\) \(\chi_{3200}(27,\cdot)\) \(\chi_{3200}(83,\cdot)\) \(\chi_{3200}(163,\cdot)\) \(\chi_{3200}(187,\cdot)\) \(\chi_{3200}(267,\cdot)\) \(\chi_{3200}(323,\cdot)\) \(\chi_{3200}(347,\cdot)\) \(\chi_{3200}(403,\cdot)\) \(\chi_{3200}(427,\cdot)\) \(\chi_{3200}(483,\cdot)\) \(\chi_{3200}(563,\cdot)\) \(\chi_{3200}(587,\cdot)\) \(\chi_{3200}(667,\cdot)\) \(\chi_{3200}(723,\cdot)\) \(\chi_{3200}(747,\cdot)\) \(\chi_{3200}(803,\cdot)\) \(\chi_{3200}(827,\cdot)\) \(\chi_{3200}(883,\cdot)\) \(\chi_{3200}(963,\cdot)\) \(\chi_{3200}(987,\cdot)\) \(\chi_{3200}(1067,\cdot)\) \(\chi_{3200}(1123,\cdot)\) \(\chi_{3200}(1147,\cdot)\) \(\chi_{3200}(1203,\cdot)\) \(\chi_{3200}(1227,\cdot)\) \(\chi_{3200}(1283,\cdot)\) \(\chi_{3200}(1363,\cdot)\) \(\chi_{3200}(1387,\cdot)\) \(\chi_{3200}(1467,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{160})$ |
Fixed field: | Number field defined by a degree 160 polynomial (not computed) |
Values on generators
\((1151,901,2177)\) → \((-1,e\left(\frac{1}{32}\right),e\left(\frac{17}{20}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 3200 }(1147, a) \) | \(1\) | \(1\) | \(e\left(\frac{87}{160}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{121}{160}\right)\) | \(e\left(\frac{99}{160}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{83}{160}\right)\) | \(e\left(\frac{97}{160}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{101}{160}\right)\) |