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 \(\chi_{1175}(4,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3525.bo
\(\chi_{3525}(4,\cdot)\) \(\chi_{3525}(34,\cdot)\) \(\chi_{3525}(64,\cdot)\) \(\chi_{3525}(79,\cdot)\) \(\chi_{3525}(169,\cdot)\) \(\chi_{3525}(244,\cdot)\) \(\chi_{3525}(259,\cdot)\) \(\chi_{3525}(289,\cdot)\) \(\chi_{3525}(319,\cdot)\) \(\chi_{3525}(379,\cdot)\) \(\chi_{3525}(394,\cdot)\) \(\chi_{3525}(439,\cdot)\) \(\chi_{3525}(484,\cdot)\) \(\chi_{3525}(529,\cdot)\) \(\chi_{3525}(544,\cdot)\) \(\chi_{3525}(559,\cdot)\) \(\chi_{3525}(589,\cdot)\) \(\chi_{3525}(619,\cdot)\) \(\chi_{3525}(664,\cdot)\) \(\chi_{3525}(679,\cdot)\) \(\chi_{3525}(694,\cdot)\) \(\chi_{3525}(709,\cdot)\) \(\chi_{3525}(739,\cdot)\) \(\chi_{3525}(754,\cdot)\) \(\chi_{3525}(769,\cdot)\) \(\chi_{3525}(784,\cdot)\) \(\chi_{3525}(964,\cdot)\) \(\chi_{3525}(994,\cdot)\) \(\chi_{3525}(1084,\cdot)\) \(\chi_{3525}(1144,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{115})$ |
Fixed field: | Number field defined by a degree 230 polynomial (not computed) |
Values on generators
\((2351,1552,2026)\) → \((1,e\left(\frac{1}{10}\right),e\left(\frac{18}{23}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3525 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{230}\right)\) | \(e\left(\frac{43}{115}\right)\) | \(e\left(\frac{25}{46}\right)\) | \(e\left(\frac{129}{230}\right)\) | \(e\left(\frac{9}{115}\right)\) | \(e\left(\frac{117}{230}\right)\) | \(e\left(\frac{84}{115}\right)\) | \(e\left(\frac{86}{115}\right)\) | \(e\left(\frac{189}{230}\right)\) | \(e\left(\frac{2}{115}\right)\) |