Basic properties
Modulus: | \(3525\) | |
Conductor: | \(3525\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(230\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
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.br
\(\chi_{3525}(29,\cdot)\) \(\chi_{3525}(44,\cdot)\) \(\chi_{3525}(104,\cdot)\) \(\chi_{3525}(134,\cdot)\) \(\chi_{3525}(164,\cdot)\) \(\chi_{3525}(179,\cdot)\) \(\chi_{3525}(254,\cdot)\) \(\chi_{3525}(344,\cdot)\) \(\chi_{3525}(359,\cdot)\) \(\chi_{3525}(389,\cdot)\) \(\chi_{3525}(419,\cdot)\) \(\chi_{3525}(434,\cdot)\) \(\chi_{3525}(464,\cdot)\) \(\chi_{3525}(509,\cdot)\) \(\chi_{3525}(539,\cdot)\) \(\chi_{3525}(569,\cdot)\) \(\chi_{3525}(584,\cdot)\) \(\chi_{3525}(644,\cdot)\) \(\chi_{3525}(689,\cdot)\) \(\chi_{3525}(734,\cdot)\) \(\chi_{3525}(809,\cdot)\) \(\chi_{3525}(839,\cdot)\) \(\chi_{3525}(869,\cdot)\) \(\chi_{3525}(884,\cdot)\) \(\chi_{3525}(959,\cdot)\) \(\chi_{3525}(1064,\cdot)\) \(\chi_{3525}(1079,\cdot)\) \(\chi_{3525}(1094,\cdot)\) \(\chi_{3525}(1139,\cdot)\) \(\chi_{3525}(1154,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{115})$ |
Fixed field: | Number field defined by a degree 230 polynomial (not computed) |
Values on generators
\((2351,1552,2026)\) → \((-1,e\left(\frac{1}{10}\right),e\left(\frac{35}{46}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3525 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{34}{115}\right)\) | \(e\left(\frac{68}{115}\right)\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{102}{115}\right)\) | \(e\left(\frac{49}{115}\right)\) | \(e\left(\frac{31}{115}\right)\) | \(e\left(\frac{33}{230}\right)\) | \(e\left(\frac{21}{115}\right)\) | \(e\left(\frac{112}{115}\right)\) | \(e\left(\frac{9}{230}\right)\) |