Basic properties
Modulus: | \(8002\) | |
Conductor: | \(4001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(2000\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4001}(83,\cdot)\) | 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.w
\(\chi_{8002}(9,\cdot)\) \(\chi_{8002}(29,\cdot)\) \(\chi_{8002}(31,\cdot)\) \(\chi_{8002}(33,\cdot)\) \(\chi_{8002}(45,\cdot)\) \(\chi_{8002}(47,\cdot)\) \(\chi_{8002}(61,\cdot)\) \(\chi_{8002}(83,\cdot)\) \(\chi_{8002}(89,\cdot)\) \(\chi_{8002}(97,\cdot)\) \(\chi_{8002}(111,\cdot)\) \(\chi_{8002}(117,\cdot)\) \(\chi_{8002}(137,\cdot)\) \(\chi_{8002}(145,\cdot)\) \(\chi_{8002}(149,\cdot)\) \(\chi_{8002}(155,\cdot)\) \(\chi_{8002}(165,\cdot)\) \(\chi_{8002}(171,\cdot)\) \(\chi_{8002}(197,\cdot)\) \(\chi_{8002}(203,\cdot)\) \(\chi_{8002}(225,\cdot)\) \(\chi_{8002}(231,\cdot)\) \(\chi_{8002}(235,\cdot)\) \(\chi_{8002}(253,\cdot)\) \(\chi_{8002}(257,\cdot)\) \(\chi_{8002}(269,\cdot)\) \(\chi_{8002}(289,\cdot)\) \(\chi_{8002}(305,\cdot)\) \(\chi_{8002}(339,\cdot)\) \(\chi_{8002}(377,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{2000})$ |
Fixed field: | Number field defined by a degree 2000 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{1531}{2000}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 8002 }(83, a) \) | \(1\) | \(1\) | \(e\left(\frac{1531}{2000}\right)\) | \(e\left(\frac{29}{100}\right)\) | \(e\left(\frac{267}{500}\right)\) | \(e\left(\frac{531}{1000}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{271}{500}\right)\) | \(e\left(\frac{111}{2000}\right)\) | \(e\left(\frac{861}{2000}\right)\) | \(e\left(\frac{411}{500}\right)\) | \(e\left(\frac{599}{2000}\right)\) |