Basic properties
Modulus: | \(3525\) | |
Conductor: | \(235\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(92\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{235}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3525.bj
\(\chi_{3525}(43,\cdot)\) \(\chi_{3525}(82,\cdot)\) \(\chi_{3525}(193,\cdot)\) \(\chi_{3525}(232,\cdot)\) \(\chi_{3525}(268,\cdot)\) \(\chi_{3525}(493,\cdot)\) \(\chi_{3525}(532,\cdot)\) \(\chi_{3525}(607,\cdot)\) \(\chi_{3525}(718,\cdot)\) \(\chi_{3525}(757,\cdot)\) \(\chi_{3525}(793,\cdot)\) \(\chi_{3525}(832,\cdot)\) \(\chi_{3525}(868,\cdot)\) \(\chi_{3525}(1018,\cdot)\) \(\chi_{3525}(1057,\cdot)\) \(\chi_{3525}(1168,\cdot)\) \(\chi_{3525}(1282,\cdot)\) \(\chi_{3525}(1357,\cdot)\) \(\chi_{3525}(1393,\cdot)\) \(\chi_{3525}(1432,\cdot)\) \(\chi_{3525}(1468,\cdot)\) \(\chi_{3525}(1543,\cdot)\) \(\chi_{3525}(1582,\cdot)\) \(\chi_{3525}(1618,\cdot)\) \(\chi_{3525}(1732,\cdot)\) \(\chi_{3525}(1768,\cdot)\) \(\chi_{3525}(1843,\cdot)\) \(\chi_{3525}(1918,\cdot)\) \(\chi_{3525}(1957,\cdot)\) \(\chi_{3525}(1993,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{92})$ |
Fixed field: | Number field defined by a degree 92 polynomial |
Values on generators
\((2351,1552,2026)\) → \((1,-i,e\left(\frac{13}{46}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3525 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{77}{92}\right)\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{73}{92}\right)\) | \(e\left(\frac{47}{92}\right)\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{33}{92}\right)\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{25}{92}\right)\) | \(e\left(\frac{5}{23}\right)\) |