Basic properties
Modulus: | \(6002\) | |
Conductor: | \(3001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(375\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{3001}(597,\cdot)\) | 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
\(3015\) → \(e\left(\frac{188}{375}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 6002 }(597, a) \) | \(1\) | \(1\) | \(e\left(\frac{42}{125}\right)\) | \(e\left(\frac{22}{125}\right)\) | \(e\left(\frac{57}{125}\right)\) | \(e\left(\frac{84}{125}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{52}{75}\right)\) | \(e\left(\frac{64}{125}\right)\) | \(e\left(\frac{349}{375}\right)\) | \(e\left(\frac{47}{75}\right)\) | \(e\left(\frac{99}{125}\right)\) |