Basic properties
Modulus: | \(3525\) | |
Conductor: | \(1175\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(460\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1175}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3525.bu
\(\chi_{3525}(28,\cdot)\) \(\chi_{3525}(37,\cdot)\) \(\chi_{3525}(97,\cdot)\) \(\chi_{3525}(103,\cdot)\) \(\chi_{3525}(112,\cdot)\) \(\chi_{3525}(148,\cdot)\) \(\chi_{3525}(178,\cdot)\) \(\chi_{3525}(202,\cdot)\) \(\chi_{3525}(238,\cdot)\) \(\chi_{3525}(247,\cdot)\) \(\chi_{3525}(253,\cdot)\) \(\chi_{3525}(262,\cdot)\) \(\chi_{3525}(277,\cdot)\) \(\chi_{3525}(298,\cdot)\) \(\chi_{3525}(337,\cdot)\) \(\chi_{3525}(388,\cdot)\) \(\chi_{3525}(397,\cdot)\) \(\chi_{3525}(403,\cdot)\) \(\chi_{3525}(412,\cdot)\) \(\chi_{3525}(427,\cdot)\) \(\chi_{3525}(448,\cdot)\) \(\chi_{3525}(472,\cdot)\) \(\chi_{3525}(478,\cdot)\) \(\chi_{3525}(487,\cdot)\) \(\chi_{3525}(502,\cdot)\) \(\chi_{3525}(523,\cdot)\) \(\chi_{3525}(538,\cdot)\) \(\chi_{3525}(553,\cdot)\) \(\chi_{3525}(592,\cdot)\) \(\chi_{3525}(598,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{460})$ |
Fixed field: | Number field defined by a degree 460 polynomial (not computed) |
Values on generators
\((2351,1552,2026)\) → \((1,e\left(\frac{9}{20}\right),e\left(\frac{21}{23}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3525 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{407}{460}\right)\) | \(e\left(\frac{177}{230}\right)\) | \(e\left(\frac{43}{92}\right)\) | \(e\left(\frac{301}{460}\right)\) | \(e\left(\frac{68}{115}\right)\) | \(e\left(\frac{273}{460}\right)\) | \(e\left(\frac{81}{230}\right)\) | \(e\left(\frac{62}{115}\right)\) | \(e\left(\frac{211}{460}\right)\) | \(e\left(\frac{43}{230}\right)\) |