Basic properties
| Modulus: | \(6002\) | |
| Conductor: | \(3001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(375\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3001}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6002.z
\(\chi_{6002}(17,\cdot)\) \(\chi_{6002}(31,\cdot)\) \(\chi_{6002}(91,\cdot)\) \(\chi_{6002}(187,\cdot)\) \(\chi_{6002}(213,\cdot)\) \(\chi_{6002}(289,\cdot)\) \(\chi_{6002}(295,\cdot)\) \(\chi_{6002}(305,\cdot)\) \(\chi_{6002}(309,\cdot)\) \(\chi_{6002}(341,\cdot)\) \(\chi_{6002}(425,\cdot)\) \(\chi_{6002}(469,\cdot)\) \(\chi_{6002}(501,\cdot)\) \(\chi_{6002}(531,\cdot)\) \(\chi_{6002}(565,\cdot)\) \(\chi_{6002}(597,\cdot)\) \(\chi_{6002}(601,\cdot)\) \(\chi_{6002}(609,\cdot)\) \(\chi_{6002}(629,\cdot)\) \(\chi_{6002}(633,\cdot)\) \(\chi_{6002}(665,\cdot)\) \(\chi_{6002}(697,\cdot)\) \(\chi_{6002}(739,\cdot)\) \(\chi_{6002}(765,\cdot)\) \(\chi_{6002}(775,\cdot)\) \(\chi_{6002}(789,\cdot)\) \(\chi_{6002}(805,\cdot)\) \(\chi_{6002}(893,\cdot)\) \(\chi_{6002}(897,\cdot)\) \(\chi_{6002}(917,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{375})$ |
| Fixed field: | Number field defined by a degree 375 polynomial (not computed) |
Values on generators
\(3015\) → \(e\left(\frac{181}{375}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 6002 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{125}\right)\) | \(e\left(\frac{89}{125}\right)\) | \(e\left(\frac{9}{125}\right)\) | \(e\left(\frac{33}{125}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{74}{75}\right)\) | \(e\left(\frac{43}{125}\right)\) | \(e\left(\frac{338}{375}\right)\) | \(e\left(\frac{64}{75}\right)\) | \(e\left(\frac{88}{125}\right)\) |