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 \(\chi_{235}(157,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3525.bh
\(\chi_{3525}(7,\cdot)\) \(\chi_{3525}(118,\cdot)\) \(\chi_{3525}(157,\cdot)\) \(\chi_{3525}(307,\cdot)\) \(\chi_{3525}(343,\cdot)\) \(\chi_{3525}(382,\cdot)\) \(\chi_{3525}(418,\cdot)\) \(\chi_{3525}(457,\cdot)\) \(\chi_{3525}(568,\cdot)\) \(\chi_{3525}(643,\cdot)\) \(\chi_{3525}(682,\cdot)\) \(\chi_{3525}(907,\cdot)\) \(\chi_{3525}(943,\cdot)\) \(\chi_{3525}(982,\cdot)\) \(\chi_{3525}(1093,\cdot)\) \(\chi_{3525}(1132,\cdot)\) \(\chi_{3525}(1207,\cdot)\) \(\chi_{3525}(1243,\cdot)\) \(\chi_{3525}(1318,\cdot)\) \(\chi_{3525}(1507,\cdot)\) \(\chi_{3525}(1657,\cdot)\) \(\chi_{3525}(1807,\cdot)\) \(\chi_{3525}(1882,\cdot)\) \(\chi_{3525}(2143,\cdot)\) \(\chi_{3525}(2218,\cdot)\) \(\chi_{3525}(2293,\cdot)\) \(\chi_{3525}(2368,\cdot)\) \(\chi_{3525}(2518,\cdot)\) \(\chi_{3525}(2593,\cdot)\) \(\chi_{3525}(2668,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{92})$ |
Fixed field: | Number field defined by a degree 92 polynomial |
Values on generators
\((2351,1552,2026)\) → \((1,i,e\left(\frac{13}{23}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3525 }(157, a) \) | \(-1\) | \(1\) | \(e\left(\frac{39}{92}\right)\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{31}{92}\right)\) | \(e\left(\frac{25}{92}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{89}{92}\right)\) | \(e\left(\frac{35}{46}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{27}{92}\right)\) | \(e\left(\frac{43}{46}\right)\) |