Basic properties
Modulus: | \(8002\) | |
Conductor: | \(4001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(500\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4001}(1297,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8002.t
\(\chi_{8002}(49,\cdot)\) \(\chi_{8002}(51,\cdot)\) \(\chi_{8002}(91,\cdot)\) \(\chi_{8002}(133,\cdot)\) \(\chi_{8002}(159,\cdot)\) \(\chi_{8002}(169,\cdot)\) \(\chi_{8002}(187,\cdot)\) \(\chi_{8002}(247,\cdot)\) \(\chi_{8002}(361,\cdot)\) \(\chi_{8002}(393,\cdot)\) \(\chi_{8002}(541,\cdot)\) \(\chi_{8002}(543,\cdot)\) \(\chi_{8002}(553,\cdot)\) \(\chi_{8002}(567,\cdot)\) \(\chi_{8002}(629,\cdot)\) \(\chi_{8002}(643,\cdot)\) \(\chi_{8002}(747,\cdot)\) \(\chi_{8002}(861,\cdot)\) \(\chi_{8002}(875,\cdot)\) \(\chi_{8002}(1009,\cdot)\) \(\chi_{8002}(1027,\cdot)\) \(\chi_{8002}(1053,\cdot)\) \(\chi_{8002}(1099,\cdot)\) \(\chi_{8002}(1211,\cdot)\) \(\chi_{8002}(1297,\cdot)\) \(\chi_{8002}(1319,\cdot)\) \(\chi_{8002}(1383,\cdot)\) \(\chi_{8002}(1441,\cdot)\) \(\chi_{8002}(1457,\cdot)\) \(\chi_{8002}(1501,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{500})$ |
Fixed field: | Number field defined by a degree 500 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{337}{500}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 8002 }(1297, a) \) | \(1\) | \(1\) | \(e\left(\frac{337}{500}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{84}{125}\right)\) | \(e\left(\frac{87}{250}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{67}{125}\right)\) | \(e\left(\frac{497}{500}\right)\) | \(e\left(\frac{247}{500}\right)\) | \(e\left(\frac{97}{125}\right)\) | \(e\left(\frac{173}{500}\right)\) |