Basic properties
Modulus: | \(6012\) | |
Conductor: | \(1503\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(498\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1503}(605,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6012.bf
\(\chi_{6012}(5,\cdot)\) \(\chi_{6012}(41,\cdot)\) \(\chi_{6012}(101,\cdot)\) \(\chi_{6012}(113,\cdot)\) \(\chi_{6012}(149,\cdot)\) \(\chi_{6012}(245,\cdot)\) \(\chi_{6012}(257,\cdot)\) \(\chi_{6012}(389,\cdot)\) \(\chi_{6012}(401,\cdot)\) \(\chi_{6012}(425,\cdot)\) \(\chi_{6012}(437,\cdot)\) \(\chi_{6012}(473,\cdot)\) \(\chi_{6012}(497,\cdot)\) \(\chi_{6012}(569,\cdot)\) \(\chi_{6012}(581,\cdot)\) \(\chi_{6012}(605,\cdot)\) \(\chi_{6012}(641,\cdot)\) \(\chi_{6012}(713,\cdot)\) \(\chi_{6012}(785,\cdot)\) \(\chi_{6012}(797,\cdot)\) \(\chi_{6012}(821,\cdot)\) \(\chi_{6012}(833,\cdot)\) \(\chi_{6012}(869,\cdot)\) \(\chi_{6012}(905,\cdot)\) \(\chi_{6012}(941,\cdot)\) \(\chi_{6012}(977,\cdot)\) \(\chi_{6012}(1037,\cdot)\) \(\chi_{6012}(1073,\cdot)\) \(\chi_{6012}(1085,\cdot)\) \(\chi_{6012}(1121,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{249})$ |
Fixed field: | Number field defined by a degree 498 polynomial (not computed) |
Values on generators
\((3007,3341,4681)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{57}{166}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 6012 }(605, a) \) | \(1\) | \(1\) | \(e\left(\frac{44}{249}\right)\) | \(e\left(\frac{46}{249}\right)\) | \(e\left(\frac{389}{498}\right)\) | \(e\left(\frac{349}{498}\right)\) | \(e\left(\frac{58}{83}\right)\) | \(e\left(\frac{76}{83}\right)\) | \(e\left(\frac{206}{249}\right)\) | \(e\left(\frac{88}{249}\right)\) | \(e\left(\frac{335}{498}\right)\) | \(e\left(\frac{59}{249}\right)\) |