Basic properties
Modulus: | \(8002\) | |
Conductor: | \(4001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(250\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4001}(1763,\cdot)\) | 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)
|
Galois orbit 8002.r
\(\chi_{8002}(65,\cdot)\) \(\chi_{8002}(95,\cdot)\) \(\chi_{8002}(107,\cdot)\) \(\chi_{8002}(211,\cdot)\) \(\chi_{8002}(279,\cdot)\) \(\chi_{8002}(557,\cdot)\) \(\chi_{8002}(737,\cdot)\) \(\chi_{8002}(967,\cdot)\) \(\chi_{8002}(1047,\cdot)\) \(\chi_{8002}(1145,\cdot)\) \(\chi_{8002}(1161,\cdot)\) \(\chi_{8002}(1275,\cdot)\) \(\chi_{8002}(1303,\cdot)\) \(\chi_{8002}(1409,\cdot)\) \(\chi_{8002}(1485,\cdot)\) \(\chi_{8002}(1669,\cdot)\) \(\chi_{8002}(1685,\cdot)\) \(\chi_{8002}(1733,\cdot)\) \(\chi_{8002}(1763,\cdot)\) \(\chi_{8002}(1789,\cdot)\) \(\chi_{8002}(1827,\cdot)\) \(\chi_{8002}(1829,\cdot)\) \(\chi_{8002}(1837,\cdot)\) \(\chi_{8002}(2003,\cdot)\) \(\chi_{8002}(2155,\cdot)\) \(\chi_{8002}(2179,\cdot)\) \(\chi_{8002}(2255,\cdot)\) \(\chi_{8002}(2275,\cdot)\) \(\chi_{8002}(2289,\cdot)\) \(\chi_{8002}(2319,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{125})$ |
Fixed field: | Number field defined by a degree 250 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{137}{250}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 8002 }(1763, a) \) | \(1\) | \(1\) | \(e\left(\frac{137}{250}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{118}{125}\right)\) | \(e\left(\frac{12}{125}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{109}{125}\right)\) | \(e\left(\frac{47}{250}\right)\) | \(e\left(\frac{47}{250}\right)\) | \(e\left(\frac{44}{125}\right)\) | \(e\left(\frac{123}{250}\right)\) |