Basic properties
Modulus: | \(8002\) | |
Conductor: | \(4001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(400\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4001}(129,\cdot)\) | 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.s
\(\chi_{8002}(59,\cdot)\) \(\chi_{8002}(63,\cdot)\) \(\chi_{8002}(69,\cdot)\) \(\chi_{8002}(127,\cdot)\) \(\chi_{8002}(129,\cdot)\) \(\chi_{8002}(217,\cdot)\) \(\chi_{8002}(223,\cdot)\) \(\chi_{8002}(241,\cdot)\) \(\chi_{8002}(295,\cdot)\) \(\chi_{8002}(303,\cdot)\) \(\chi_{8002}(315,\cdot)\) \(\chi_{8002}(329,\cdot)\) \(\chi_{8002}(345,\cdot)\) \(\chi_{8002}(397,\cdot)\) \(\chi_{8002}(401,\cdot)\) \(\chi_{8002}(409,\cdot)\) \(\chi_{8002}(427,\cdot)\) \(\chi_{8002}(429,\cdot)\) \(\chi_{8002}(581,\cdot)\) \(\chi_{8002}(605,\cdot)\) \(\chi_{8002}(607,\cdot)\) \(\chi_{8002}(623,\cdot)\) \(\chi_{8002}(645,\cdot)\) \(\chi_{8002}(701,\cdot)\) \(\chi_{8002}(829,\cdot)\) \(\chi_{8002}(879,\cdot)\) \(\chi_{8002}(937,\cdot)\) \(\chi_{8002}(963,\cdot)\) \(\chi_{8002}(1085,\cdot)\) \(\chi_{8002}(1139,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{400})$ |
Fixed field: | Number field defined by a degree 400 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{331}{400}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 8002 }(129, a) \) | \(1\) | \(1\) | \(e\left(\frac{331}{400}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{67}{100}\right)\) | \(e\left(\frac{131}{200}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{71}{100}\right)\) | \(e\left(\frac{111}{400}\right)\) | \(e\left(\frac{61}{400}\right)\) | \(e\left(\frac{11}{100}\right)\) | \(e\left(\frac{199}{400}\right)\) |