Basic properties
Modulus: | \(6004\) | |
Conductor: | \(6004\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(234\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Galois orbit 6004.ev
\(\chi_{6004}(51,\cdot)\) \(\chi_{6004}(203,\cdot)\) \(\chi_{6004}(231,\cdot)\) \(\chi_{6004}(279,\cdot)\) \(\chi_{6004}(287,\cdot)\) \(\chi_{6004}(431,\cdot)\) \(\chi_{6004}(471,\cdot)\) \(\chi_{6004}(523,\cdot)\) \(\chi_{6004}(603,\cdot)\) \(\chi_{6004}(743,\cdot)\) \(\chi_{6004}(895,\cdot)\) \(\chi_{6004}(1059,\cdot)\) \(\chi_{6004}(1067,\cdot)\) \(\chi_{6004}(1131,\cdot)\) \(\chi_{6004}(1155,\cdot)\) \(\chi_{6004}(1211,\cdot)\) \(\chi_{6004}(1275,\cdot)\) \(\chi_{6004}(1295,\cdot)\) \(\chi_{6004}(1359,\cdot)\) \(\chi_{6004}(1419,\cdot)\) \(\chi_{6004}(1427,\cdot)\) \(\chi_{6004}(1435,\cdot)\) \(\chi_{6004}(1591,\cdot)\) \(\chi_{6004}(1599,\cdot)\) \(\chi_{6004}(1731,\cdot)\) \(\chi_{6004}(1743,\cdot)\) \(\chi_{6004}(1763,\cdot)\) \(\chi_{6004}(1979,\cdot)\) \(\chi_{6004}(1991,\cdot)\) \(\chi_{6004}(2047,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{117})$ |
Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((3003,2529,3953)\) → \((-1,e\left(\frac{5}{18}\right),e\left(\frac{11}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 6004 }(51, a) \) | \(1\) | \(1\) | \(e\left(\frac{46}{117}\right)\) | \(e\left(\frac{109}{117}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{92}{117}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{229}{234}\right)\) | \(e\left(\frac{38}{117}\right)\) | \(e\left(\frac{82}{117}\right)\) | \(e\left(\frac{119}{234}\right)\) | \(e\left(\frac{7}{18}\right)\) |