Basic properties
Modulus: | \(8002\) | |
Conductor: | \(4001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(200\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{4001}(997,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8002.q
\(\chi_{8002}(5,\cdot)\) \(\chi_{8002}(79,\cdot)\) \(\chi_{8002}(125,\cdot)\) \(\chi_{8002}(261,\cdot)\) \(\chi_{8002}(347,\cdot)\) \(\chi_{8002}(357,\cdot)\) \(\chi_{8002}(509,\cdot)\) \(\chi_{8002}(637,\cdot)\) \(\chi_{8002}(731,\cdot)\) \(\chi_{8002}(761,\cdot)\) \(\chi_{8002}(803,\cdot)\) \(\chi_{8002}(821,\cdot)\) \(\chi_{8002}(857,\cdot)\) \(\chi_{8002}(863,\cdot)\) \(\chi_{8002}(919,\cdot)\) \(\chi_{8002}(923,\cdot)\) \(\chi_{8002}(931,\cdot)\) \(\chi_{8002}(997,\cdot)\) \(\chi_{8002}(1005,\cdot)\) \(\chi_{8002}(1349,\cdot)\) \(\chi_{8002}(1477,\cdot)\) \(\chi_{8002}(1717,\cdot)\) \(\chi_{8002}(1769,\cdot)\) \(\chi_{8002}(1895,\cdot)\) \(\chi_{8002}(1975,\cdot)\) \(\chi_{8002}(2067,\cdot)\) \(\chi_{8002}(2251,\cdot)\) \(\chi_{8002}(2431,\cdot)\) \(\chi_{8002}(2581,\cdot)\) \(\chi_{8002}(3021,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{200})$ |
Fixed field: | Number field defined by a degree 200 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{199}{200}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 8002 }(997, a) \) | \(1\) | \(1\) | \(e\left(\frac{199}{200}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{43}{50}\right)\) | \(e\left(\frac{99}{100}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{9}{50}\right)\) | \(e\left(\frac{19}{200}\right)\) | \(e\left(\frac{169}{200}\right)\) | \(e\left(\frac{19}{50}\right)\) | \(e\left(\frac{171}{200}\right)\) |