Basic properties
Modulus: | \(6018\) | |
Conductor: | \(3009\) | 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 \(\chi_{3009}(1589,\cdot)\) | 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)
|
Galois orbit 6018.bh
\(\chi_{6018}(77,\cdot)\) \(\chi_{6018}(83,\cdot)\) \(\chi_{6018}(155,\cdot)\) \(\chi_{6018}(161,\cdot)\) \(\chi_{6018}(179,\cdot)\) \(\chi_{6018}(185,\cdot)\) \(\chi_{6018}(365,\cdot)\) \(\chi_{6018}(467,\cdot)\) \(\chi_{6018}(485,\cdot)\) \(\chi_{6018}(563,\cdot)\) \(\chi_{6018}(569,\cdot)\) \(\chi_{6018}(587,\cdot)\) \(\chi_{6018}(689,\cdot)\) \(\chi_{6018}(773,\cdot)\) \(\chi_{6018}(791,\cdot)\) \(\chi_{6018}(797,\cdot)\) \(\chi_{6018}(869,\cdot)\) \(\chi_{6018}(893,\cdot)\) \(\chi_{6018}(899,\cdot)\) \(\chi_{6018}(977,\cdot)\) \(\chi_{6018}(1073,\cdot)\) \(\chi_{6018}(1175,\cdot)\) \(\chi_{6018}(1277,\cdot)\) \(\chi_{6018}(1283,\cdot)\) \(\chi_{6018}(1409,\cdot)\) \(\chi_{6018}(1481,\cdot)\) \(\chi_{6018}(1505,\cdot)\) \(\chi_{6018}(1589,\cdot)\) \(\chi_{6018}(1607,\cdot)\) \(\chi_{6018}(1685,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{232})$ |
Fixed field: | Number field defined by a degree 232 polynomial (not computed) |
Values on generators
\((4013,1771,1123)\) → \((-1,e\left(\frac{5}{8}\right),e\left(\frac{31}{58}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6018 }(1589, a) \) | \(1\) | \(1\) | \(e\left(\frac{193}{232}\right)\) | \(e\left(\frac{115}{232}\right)\) | \(e\left(\frac{55}{232}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{7}{116}\right)\) | \(e\left(\frac{207}{232}\right)\) | \(e\left(\frac{77}{116}\right)\) | \(e\left(\frac{137}{232}\right)\) | \(e\left(\frac{189}{232}\right)\) | \(e\left(\frac{19}{58}\right)\) |