Basic properties
| Modulus: | \(3525\) | |
| Conductor: | \(1175\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(115\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1175}(16,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3525.bk
\(\chi_{3525}(16,\cdot)\) \(\chi_{3525}(61,\cdot)\) \(\chi_{3525}(106,\cdot)\) \(\chi_{3525}(121,\cdot)\) \(\chi_{3525}(136,\cdot)\) \(\chi_{3525}(166,\cdot)\) \(\chi_{3525}(196,\cdot)\) \(\chi_{3525}(241,\cdot)\) \(\chi_{3525}(256,\cdot)\) \(\chi_{3525}(271,\cdot)\) \(\chi_{3525}(286,\cdot)\) \(\chi_{3525}(316,\cdot)\) \(\chi_{3525}(331,\cdot)\) \(\chi_{3525}(346,\cdot)\) \(\chi_{3525}(361,\cdot)\) \(\chi_{3525}(541,\cdot)\) \(\chi_{3525}(571,\cdot)\) \(\chi_{3525}(661,\cdot)\) \(\chi_{3525}(721,\cdot)\) \(\chi_{3525}(766,\cdot)\) \(\chi_{3525}(811,\cdot)\) \(\chi_{3525}(841,\cdot)\) \(\chi_{3525}(871,\cdot)\) \(\chi_{3525}(946,\cdot)\) \(\chi_{3525}(961,\cdot)\) \(\chi_{3525}(991,\cdot)\) \(\chi_{3525}(1021,\cdot)\) \(\chi_{3525}(1036,\cdot)\) \(\chi_{3525}(1066,\cdot)\) \(\chi_{3525}(1156,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{115})$ |
| Fixed field: | Number field defined by a degree 115 polynomial (not computed) |
Values on generators
\((2351,1552,2026)\) → \((1,e\left(\frac{1}{5}\right),e\left(\frac{13}{23}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 3525 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{115}\right)\) | \(e\left(\frac{86}{115}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{14}{115}\right)\) | \(e\left(\frac{18}{115}\right)\) | \(e\left(\frac{2}{115}\right)\) | \(e\left(\frac{53}{115}\right)\) | \(e\left(\frac{57}{115}\right)\) | \(e\left(\frac{74}{115}\right)\) | \(e\left(\frac{4}{115}\right)\) |