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 \(\chi_{1175}(58,\cdot)\) | 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 3525.bs
\(\chi_{3525}(13,\cdot)\) \(\chi_{3525}(22,\cdot)\) \(\chi_{3525}(52,\cdot)\) \(\chi_{3525}(58,\cdot)\) \(\chi_{3525}(67,\cdot)\) \(\chi_{3525}(73,\cdot)\) \(\chi_{3525}(88,\cdot)\) \(\chi_{3525}(127,\cdot)\) \(\chi_{3525}(133,\cdot)\) \(\chi_{3525}(163,\cdot)\) \(\chi_{3525}(172,\cdot)\) \(\chi_{3525}(208,\cdot)\) \(\chi_{3525}(217,\cdot)\) \(\chi_{3525}(223,\cdot)\) \(\chi_{3525}(292,\cdot)\) \(\chi_{3525}(313,\cdot)\) \(\chi_{3525}(322,\cdot)\) \(\chi_{3525}(352,\cdot)\) \(\chi_{3525}(358,\cdot)\) \(\chi_{3525}(367,\cdot)\) \(\chi_{3525}(373,\cdot)\) \(\chi_{3525}(433,\cdot)\) \(\chi_{3525}(442,\cdot)\) \(\chi_{3525}(463,\cdot)\) \(\chi_{3525}(508,\cdot)\) \(\chi_{3525}(547,\cdot)\) \(\chi_{3525}(562,\cdot)\) \(\chi_{3525}(577,\cdot)\) \(\chi_{3525}(583,\cdot)\) \(\chi_{3525}(622,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{460})$ |
Fixed field: | Number field defined by a degree 460 polynomial (not computed) |
Values on generators
\((2351,1552,2026)\) → \((1,e\left(\frac{3}{20}\right),e\left(\frac{7}{46}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3525 }(58, a) \) | \(1\) | \(1\) | \(e\left(\frac{409}{460}\right)\) | \(e\left(\frac{179}{230}\right)\) | \(e\left(\frac{57}{92}\right)\) | \(e\left(\frac{307}{460}\right)\) | \(e\left(\frac{107}{230}\right)\) | \(e\left(\frac{241}{460}\right)\) | \(e\left(\frac{117}{230}\right)\) | \(e\left(\frac{64}{115}\right)\) | \(e\left(\frac{177}{460}\right)\) | \(e\left(\frac{63}{115}\right)\) |