Basic properties
Modulus: | \(3525\) | |
Conductor: | \(1175\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(230\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1175}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3525.bp
\(\chi_{3525}(31,\cdot)\) \(\chi_{3525}(91,\cdot)\) \(\chi_{3525}(181,\cdot)\) \(\chi_{3525}(211,\cdot)\) \(\chi_{3525}(391,\cdot)\) \(\chi_{3525}(406,\cdot)\) \(\chi_{3525}(421,\cdot)\) \(\chi_{3525}(436,\cdot)\) \(\chi_{3525}(466,\cdot)\) \(\chi_{3525}(481,\cdot)\) \(\chi_{3525}(496,\cdot)\) \(\chi_{3525}(511,\cdot)\) \(\chi_{3525}(556,\cdot)\) \(\chi_{3525}(586,\cdot)\) \(\chi_{3525}(616,\cdot)\) \(\chi_{3525}(631,\cdot)\) \(\chi_{3525}(646,\cdot)\) \(\chi_{3525}(691,\cdot)\) \(\chi_{3525}(736,\cdot)\) \(\chi_{3525}(781,\cdot)\) \(\chi_{3525}(796,\cdot)\) \(\chi_{3525}(856,\cdot)\) \(\chi_{3525}(886,\cdot)\) \(\chi_{3525}(916,\cdot)\) \(\chi_{3525}(931,\cdot)\) \(\chi_{3525}(1006,\cdot)\) \(\chi_{3525}(1096,\cdot)\) \(\chi_{3525}(1111,\cdot)\) \(\chi_{3525}(1141,\cdot)\) \(\chi_{3525}(1171,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{115})$ |
Fixed field: | Number field defined by a degree 230 polynomial (not computed) |
Values on generators
\((2351,1552,2026)\) → \((1,e\left(\frac{2}{5}\right),e\left(\frac{3}{46}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3525 }(31, a) \) | \(-1\) | \(1\) | \(e\left(\frac{66}{115}\right)\) | \(e\left(\frac{17}{115}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{83}{115}\right)\) | \(e\left(\frac{197}{230}\right)\) | \(e\left(\frac{73}{230}\right)\) | \(e\left(\frac{76}{115}\right)\) | \(e\left(\frac{34}{115}\right)\) | \(e\left(\frac{28}{115}\right)\) | \(e\left(\frac{31}{230}\right)\) |