Basic properties
Modulus: | \(6018\) | |
Conductor: | \(1003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(232\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1003}(637,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6018.bg
\(\chi_{6018}(43,\cdot)\) \(\chi_{6018}(151,\cdot)\) \(\chi_{6018}(229,\cdot)\) \(\chi_{6018}(247,\cdot)\) \(\chi_{6018}(325,\cdot)\) \(\chi_{6018}(349,\cdot)\) \(\chi_{6018}(427,\cdot)\) \(\chi_{6018}(451,\cdot)\) \(\chi_{6018}(457,\cdot)\) \(\chi_{6018}(637,\cdot)\) \(\chi_{6018}(655,\cdot)\) \(\chi_{6018}(739,\cdot)\) \(\chi_{6018}(763,\cdot)\) \(\chi_{6018}(859,\cdot)\) \(\chi_{6018}(865,\cdot)\) \(\chi_{6018}(937,\cdot)\) \(\chi_{6018}(967,\cdot)\) \(\chi_{6018}(1045,\cdot)\) \(\chi_{6018}(1165,\cdot)\) \(\chi_{6018}(1171,\cdot)\) \(\chi_{6018}(1249,\cdot)\) \(\chi_{6018}(1273,\cdot)\) \(\chi_{6018}(1345,\cdot)\) \(\chi_{6018}(1375,\cdot)\) \(\chi_{6018}(1447,\cdot)\) \(\chi_{6018}(1453,\cdot)\) \(\chi_{6018}(1471,\cdot)\) \(\chi_{6018}(1477,\cdot)\) \(\chi_{6018}(1573,\cdot)\) \(\chi_{6018}(1675,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{232})$ |
Fixed field: | Number field defined by a degree 232 polynomial (not computed) |
Values on generators
\((4013,1771,1123)\) → \((1,e\left(\frac{5}{8}\right),e\left(\frac{23}{58}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6018 }(637, a) \) | \(-1\) | \(1\) | \(e\left(\frac{117}{232}\right)\) | \(e\left(\frac{3}{232}\right)\) | \(e\left(\frac{67}{232}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{95}{116}\right)\) | \(e\left(\frac{75}{232}\right)\) | \(e\left(\frac{1}{116}\right)\) | \(e\left(\frac{53}{232}\right)\) | \(e\left(\frac{13}{232}\right)\) | \(e\left(\frac{15}{29}\right)\) |