Basic properties
Modulus: | \(3525\) | |
Conductor: | \(235\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(46\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{235}(49,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3525.be
\(\chi_{3525}(49,\cdot)\) \(\chi_{3525}(874,\cdot)\) \(\chi_{3525}(949,\cdot)\) \(\chi_{3525}(1024,\cdot)\) \(\chi_{3525}(1099,\cdot)\) \(\chi_{3525}(1249,\cdot)\) \(\chi_{3525}(1324,\cdot)\) \(\chi_{3525}(1399,\cdot)\) \(\chi_{3525}(1474,\cdot)\) \(\chi_{3525}(1699,\cdot)\) \(\chi_{3525}(1849,\cdot)\) \(\chi_{3525}(1999,\cdot)\) \(\chi_{3525}(2074,\cdot)\) \(\chi_{3525}(2149,\cdot)\) \(\chi_{3525}(2374,\cdot)\) \(\chi_{3525}(2599,\cdot)\) \(\chi_{3525}(2674,\cdot)\) \(\chi_{3525}(2824,\cdot)\) \(\chi_{3525}(2899,\cdot)\) \(\chi_{3525}(3199,\cdot)\) \(\chi_{3525}(3349,\cdot)\) \(\chi_{3525}(3499,\cdot)\)
Related number fields
Field of values: | \(\Q(\zeta_{23})\) |
Fixed field: | 46.46.445262221645814097378614331350194306504897709623466822770698795048558574688434600830078125.1 |
Values on generators
\((2351,1552,2026)\) → \((1,-1,e\left(\frac{9}{23}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3525 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{46}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{17}{23}\right)\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{35}{46}\right)\) | \(e\left(\frac{14}{23}\right)\) |