Basic properties
Modulus: | \(6004\) | |
Conductor: | \(1501\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(117\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1501}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6004.ea
\(\chi_{6004}(5,\cdot)\) \(\chi_{6004}(25,\cdot)\) \(\chi_{6004}(73,\cdot)\) \(\chi_{6004}(169,\cdot)\) \(\chi_{6004}(253,\cdot)\) \(\chi_{6004}(309,\cdot)\) \(\chi_{6004}(313,\cdot)\) \(\chi_{6004}(321,\cdot)\) \(\chi_{6004}(329,\cdot)\) \(\chi_{6004}(365,\cdot)\) \(\chi_{6004}(625,\cdot)\) \(\chi_{6004}(909,\cdot)\) \(\chi_{6004}(973,\cdot)\) \(\chi_{6004}(997,\cdot)\) \(\chi_{6004}(1137,\cdot)\) \(\chi_{6004}(1201,\cdot)\) \(\chi_{6004}(1277,\cdot)\) \(\chi_{6004}(1441,\cdot)\) \(\chi_{6004}(1545,\cdot)\) \(\chi_{6004}(1605,\cdot)\) \(\chi_{6004}(1821,\cdot)\) \(\chi_{6004}(1833,\cdot)\) \(\chi_{6004}(1905,\cdot)\) \(\chi_{6004}(1909,\cdot)\) \(\chi_{6004}(2153,\cdot)\) \(\chi_{6004}(2221,\cdot)\) \(\chi_{6004}(2285,\cdot)\) \(\chi_{6004}(2493,\cdot)\) \(\chi_{6004}(2601,\cdot)\) \(\chi_{6004}(2609,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{117})$ |
Fixed field: | Number field defined by a degree 117 polynomial (not computed) |
Values on generators
\((3003,2529,3953)\) → \((1,e\left(\frac{8}{9}\right),e\left(\frac{31}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 6004 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{117}\right)\) | \(e\left(\frac{59}{117}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{82}{117}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{55}{117}\right)\) | \(e\left(\frac{100}{117}\right)\) | \(e\left(\frac{68}{117}\right)\) | \(e\left(\frac{95}{117}\right)\) | \(e\left(\frac{4}{9}\right)\) |