Basic properties
Modulus: | \(3525\) | |
Conductor: | \(3525\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(460\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3525.bt
\(\chi_{3525}(2,\cdot)\) \(\chi_{3525}(8,\cdot)\) \(\chi_{3525}(17,\cdot)\) \(\chi_{3525}(53,\cdot)\) \(\chi_{3525}(83,\cdot)\) \(\chi_{3525}(98,\cdot)\) \(\chi_{3525}(122,\cdot)\) \(\chi_{3525}(128,\cdot)\) \(\chi_{3525}(158,\cdot)\) \(\chi_{3525}(173,\cdot)\) \(\chi_{3525}(197,\cdot)\) \(\chi_{3525}(212,\cdot)\) \(\chi_{3525}(242,\cdot)\) \(\chi_{3525}(263,\cdot)\) \(\chi_{3525}(272,\cdot)\) \(\chi_{3525}(338,\cdot)\) \(\chi_{3525}(347,\cdot)\) \(\chi_{3525}(353,\cdot)\) \(\chi_{3525}(383,\cdot)\) \(\chi_{3525}(392,\cdot)\) \(\chi_{3525}(413,\cdot)\) \(\chi_{3525}(437,\cdot)\) \(\chi_{3525}(473,\cdot)\) \(\chi_{3525}(488,\cdot)\) \(\chi_{3525}(497,\cdot)\) \(\chi_{3525}(512,\cdot)\) \(\chi_{3525}(533,\cdot)\) \(\chi_{3525}(542,\cdot)\) \(\chi_{3525}(572,\cdot)\) \(\chi_{3525}(578,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{460})$ |
Fixed field: | Number field defined by a degree 460 polynomial (not computed) |
Values on generators
\((2351,1552,2026)\) → \((-1,e\left(\frac{7}{20}\right),e\left(\frac{19}{23}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3525 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{331}{460}\right)\) | \(e\left(\frac{101}{230}\right)\) | \(e\left(\frac{17}{92}\right)\) | \(e\left(\frac{73}{460}\right)\) | \(e\left(\frac{203}{230}\right)\) | \(e\left(\frac{339}{460}\right)\) | \(e\left(\frac{104}{115}\right)\) | \(e\left(\frac{101}{115}\right)\) | \(e\left(\frac{123}{460}\right)\) | \(e\left(\frac{109}{230}\right)\) |