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 \(\chi_{705}(32,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3525.bi
\(\chi_{3525}(32,\cdot)\) \(\chi_{3525}(68,\cdot)\) \(\chi_{3525}(143,\cdot)\) \(\chi_{3525}(332,\cdot)\) \(\chi_{3525}(482,\cdot)\) \(\chi_{3525}(632,\cdot)\) \(\chi_{3525}(707,\cdot)\) \(\chi_{3525}(968,\cdot)\) \(\chi_{3525}(1043,\cdot)\) \(\chi_{3525}(1118,\cdot)\) \(\chi_{3525}(1193,\cdot)\) \(\chi_{3525}(1343,\cdot)\) \(\chi_{3525}(1418,\cdot)\) \(\chi_{3525}(1493,\cdot)\) \(\chi_{3525}(1532,\cdot)\) \(\chi_{3525}(1568,\cdot)\) \(\chi_{3525}(1607,\cdot)\) \(\chi_{3525}(1682,\cdot)\) \(\chi_{3525}(1757,\cdot)\) \(\chi_{3525}(1793,\cdot)\) \(\chi_{3525}(1907,\cdot)\) \(\chi_{3525}(1943,\cdot)\) \(\chi_{3525}(1982,\cdot)\) \(\chi_{3525}(2057,\cdot)\) \(\chi_{3525}(2093,\cdot)\) \(\chi_{3525}(2132,\cdot)\) \(\chi_{3525}(2168,\cdot)\) \(\chi_{3525}(2243,\cdot)\) \(\chi_{3525}(2357,\cdot)\) \(\chi_{3525}(2468,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{92})$ |
Fixed field: | Number field defined by a degree 92 polynomial |
Values on generators
\((2351,1552,2026)\) → \((-1,i,e\left(\frac{22}{23}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3525 }(32, a) \) | \(1\) | \(1\) | \(e\left(\frac{89}{92}\right)\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{79}{92}\right)\) | \(e\left(\frac{83}{92}\right)\) | \(e\left(\frac{9}{46}\right)\) | \(e\left(\frac{25}{92}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{5}{92}\right)\) | \(e\left(\frac{25}{46}\right)\) |