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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3525.bq
\(\chi_{3525}(14,\cdot)\) \(\chi_{3525}(59,\cdot)\) \(\chi_{3525}(89,\cdot)\) \(\chi_{3525}(119,\cdot)\) \(\chi_{3525}(194,\cdot)\) \(\chi_{3525}(209,\cdot)\) \(\chi_{3525}(239,\cdot)\) \(\chi_{3525}(269,\cdot)\) \(\chi_{3525}(284,\cdot)\) \(\chi_{3525}(314,\cdot)\) \(\chi_{3525}(404,\cdot)\) \(\chi_{3525}(479,\cdot)\) \(\chi_{3525}(494,\cdot)\) \(\chi_{3525}(554,\cdot)\) \(\chi_{3525}(614,\cdot)\) \(\chi_{3525}(629,\cdot)\) \(\chi_{3525}(719,\cdot)\) \(\chi_{3525}(764,\cdot)\) \(\chi_{3525}(779,\cdot)\) \(\chi_{3525}(794,\cdot)\) \(\chi_{3525}(854,\cdot)\) \(\chi_{3525}(914,\cdot)\) \(\chi_{3525}(929,\cdot)\) \(\chi_{3525}(944,\cdot)\) \(\chi_{3525}(989,\cdot)\) \(\chi_{3525}(1004,\cdot)\) \(\chi_{3525}(1019,\cdot)\) \(\chi_{3525}(1109,\cdot)\) \(\chi_{3525}(1184,\cdot)\) \(\chi_{3525}(1229,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{115})$ |
Fixed field: | Number field defined by a degree 230 polynomial (not computed) |
Values on generators
\((2351,1552,2026)\) → \((-1,e\left(\frac{3}{10}\right),e\left(\frac{2}{23}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3525 }(14, a) \) | \(-1\) | \(1\) | \(e\left(\frac{42}{115}\right)\) | \(e\left(\frac{84}{115}\right)\) | \(e\left(\frac{13}{46}\right)\) | \(e\left(\frac{11}{115}\right)\) | \(e\left(\frac{209}{230}\right)\) | \(e\left(\frac{151}{230}\right)\) | \(e\left(\frac{149}{230}\right)\) | \(e\left(\frac{53}{115}\right)\) | \(e\left(\frac{91}{115}\right)\) | \(e\left(\frac{36}{115}\right)\) |