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 \(\chi_{1003}(661,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6018.bi
\(\chi_{6018}(19,\cdot)\) \(\chi_{6018}(25,\cdot)\) \(\chi_{6018}(49,\cdot)\) \(\chi_{6018}(121,\cdot)\) \(\chi_{6018}(127,\cdot)\) \(\chi_{6018}(145,\cdot)\) \(\chi_{6018}(223,\cdot)\) \(\chi_{6018}(253,\cdot)\) \(\chi_{6018}(331,\cdot)\) \(\chi_{6018}(433,\cdot)\) \(\chi_{6018}(529,\cdot)\) \(\chi_{6018}(535,\cdot)\) \(\chi_{6018}(553,\cdot)\) \(\chi_{6018}(559,\cdot)\) \(\chi_{6018}(631,\cdot)\) \(\chi_{6018}(661,\cdot)\) \(\chi_{6018}(733,\cdot)\) \(\chi_{6018}(757,\cdot)\) \(\chi_{6018}(835,\cdot)\) \(\chi_{6018}(841,\cdot)\) \(\chi_{6018}(961,\cdot)\) \(\chi_{6018}(1039,\cdot)\) \(\chi_{6018}(1069,\cdot)\) \(\chi_{6018}(1141,\cdot)\) \(\chi_{6018}(1147,\cdot)\) \(\chi_{6018}(1243,\cdot)\) \(\chi_{6018}(1267,\cdot)\) \(\chi_{6018}(1351,\cdot)\) \(\chi_{6018}(1369,\cdot)\) \(\chi_{6018}(1549,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{232})$ |
Fixed field: | Number field defined by a degree 232 polynomial (not computed) |
Values on generators
\((4013,1771,1123)\) → \((1,e\left(\frac{3}{8}\right),e\left(\frac{26}{29}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6018 }(661, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{232}\right)\) | \(e\left(\frac{61}{232}\right)\) | \(e\left(\frac{9}{232}\right)\) | \(e\left(\frac{49}{58}\right)\) | \(e\left(\frac{37}{116}\right)\) | \(e\left(\frac{17}{232}\right)\) | \(e\left(\frac{59}{116}\right)\) | \(e\left(\frac{227}{232}\right)\) | \(e\left(\frac{71}{232}\right)\) | \(e\left(\frac{15}{29}\right)\) |