Basic properties
Modulus: | \(3525\) | |
Conductor: | \(705\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(92\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{705}(107,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3525.bg
\(\chi_{3525}(107,\cdot)\) \(\chi_{3525}(182,\cdot)\) \(\chi_{3525}(218,\cdot)\) \(\chi_{3525}(257,\cdot)\) \(\chi_{3525}(293,\cdot)\) \(\chi_{3525}(368,\cdot)\) \(\chi_{3525}(407,\cdot)\) \(\chi_{3525}(443,\cdot)\) \(\chi_{3525}(557,\cdot)\) \(\chi_{3525}(593,\cdot)\) \(\chi_{3525}(668,\cdot)\) \(\chi_{3525}(743,\cdot)\) \(\chi_{3525}(782,\cdot)\) \(\chi_{3525}(818,\cdot)\) \(\chi_{3525}(857,\cdot)\) \(\chi_{3525}(932,\cdot)\) \(\chi_{3525}(1007,\cdot)\) \(\chi_{3525}(1157,\cdot)\) \(\chi_{3525}(1232,\cdot)\) \(\chi_{3525}(1307,\cdot)\) \(\chi_{3525}(1382,\cdot)\) \(\chi_{3525}(1643,\cdot)\) \(\chi_{3525}(1718,\cdot)\) \(\chi_{3525}(1868,\cdot)\) \(\chi_{3525}(2018,\cdot)\) \(\chi_{3525}(2207,\cdot)\) \(\chi_{3525}(2282,\cdot)\) \(\chi_{3525}(2318,\cdot)\) \(\chi_{3525}(2393,\cdot)\) \(\chi_{3525}(2432,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{92})$ |
Fixed field: | Number field defined by a degree 92 polynomial |
Values on generators
\((2351,1552,2026)\) → \((-1,i,e\left(\frac{11}{46}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3525 }(107, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{92}\right)\) | \(e\left(\frac{5}{46}\right)\) | \(e\left(\frac{83}{92}\right)\) | \(e\left(\frac{15}{92}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{35}{92}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{53}{92}\right)\) | \(e\left(\frac{6}{23}\right)\) |