Basic properties
Modulus: | \(6004\) | |
Conductor: | \(6004\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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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.eq
\(\chi_{6004}(175,\cdot)\) \(\chi_{6004}(199,\cdot)\) \(\chi_{6004}(215,\cdot)\) \(\chi_{6004}(251,\cdot)\) \(\chi_{6004}(491,\cdot)\) \(\chi_{6004}(567,\cdot)\) \(\chi_{6004}(807,\cdot)\) \(\chi_{6004}(823,\cdot)\) \(\chi_{6004}(859,\cdot)\) \(\chi_{6004}(883,\cdot)\) \(\chi_{6004}(975,\cdot)\) \(\chi_{6004}(1163,\cdot)\) \(\chi_{6004}(1175,\cdot)\) \(\chi_{6004}(1279,\cdot)\) \(\chi_{6004}(1335,\cdot)\) \(\chi_{6004}(1355,\cdot)\) \(\chi_{6004}(1479,\cdot)\) \(\chi_{6004}(1491,\cdot)\) \(\chi_{6004}(1651,\cdot)\) \(\chi_{6004}(1771,\cdot)\) \(\chi_{6004}(1795,\cdot)\) \(\chi_{6004}(1923,\cdot)\) \(\chi_{6004}(2087,\cdot)\) \(\chi_{6004}(2095,\cdot)\) \(\chi_{6004}(2115,\cdot)\) \(\chi_{6004}(2191,\cdot)\) \(\chi_{6004}(2227,\cdot)\) \(\chi_{6004}(2239,\cdot)\) \(\chi_{6004}(2303,\cdot)\) \(\chi_{6004}(2403,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{117})$ |
Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((3003,2529,3953)\) → \((-1,e\left(\frac{1}{9}\right),e\left(\frac{7}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 6004 }(175, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{117}\right)\) | \(e\left(\frac{55}{117}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{50}{117}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{83}{117}\right)\) | \(e\left(\frac{80}{117}\right)\) | \(e\left(\frac{179}{234}\right)\) | \(e\left(\frac{76}{117}\right)\) | \(e\left(\frac{13}{18}\right)\) |