Basic properties
Modulus: | \(8002\) | |
Conductor: | \(4001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(1000\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4001}(423,\cdot)\) | 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)
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Galois orbit 8002.v
\(\chi_{8002}(7,\cdot)\) \(\chi_{8002}(13,\cdot)\) \(\chi_{8002}(19,\cdot)\) \(\chi_{8002}(81,\cdot)\) \(\chi_{8002}(123,\cdot)\) \(\chi_{8002}(157,\cdot)\) \(\chi_{8002}(173,\cdot)\) \(\chi_{8002}(175,\cdot)\) \(\chi_{8002}(219,\cdot)\) \(\chi_{8002}(229,\cdot)\) \(\chi_{8002}(245,\cdot)\) \(\chi_{8002}(255,\cdot)\) \(\chi_{8002}(277,\cdot)\) \(\chi_{8002}(297,\cdot)\) \(\chi_{8002}(307,\cdot)\) \(\chi_{8002}(309,\cdot)\) \(\chi_{8002}(325,\cdot)\) \(\chi_{8002}(327,\cdot)\) \(\chi_{8002}(337,\cdot)\) \(\chi_{8002}(343,\cdot)\) \(\chi_{8002}(355,\cdot)\) \(\chi_{8002}(423,\cdot)\) \(\chi_{8002}(431,\cdot)\) \(\chi_{8002}(451,\cdot)\) \(\chi_{8002}(455,\cdot)\) \(\chi_{8002}(475,\cdot)\) \(\chi_{8002}(479,\cdot)\) \(\chi_{8002}(497,\cdot)\) \(\chi_{8002}(531,\cdot)\) \(\chi_{8002}(535,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1000})$ |
Fixed field: | Number field defined by a degree 1000 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{371}{1000}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 8002 }(423, a) \) | \(1\) | \(1\) | \(e\left(\frac{371}{1000}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{147}{250}\right)\) | \(e\left(\frac{371}{500}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{211}{250}\right)\) | \(e\left(\frac{151}{1000}\right)\) | \(e\left(\frac{901}{1000}\right)\) | \(e\left(\frac{201}{250}\right)\) | \(e\left(\frac{959}{1000}\right)\) |