Basic properties
Modulus: | \(3525\) | |
Conductor: | \(141\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(46\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{141}(26,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3525.bc
\(\chi_{3525}(26,\cdot)\) \(\chi_{3525}(176,\cdot)\) \(\chi_{3525}(326,\cdot)\) \(\chi_{3525}(626,\cdot)\) \(\chi_{3525}(701,\cdot)\) \(\chi_{3525}(851,\cdot)\) \(\chi_{3525}(926,\cdot)\) \(\chi_{3525}(1151,\cdot)\) \(\chi_{3525}(1376,\cdot)\) \(\chi_{3525}(1451,\cdot)\) \(\chi_{3525}(1526,\cdot)\) \(\chi_{3525}(1676,\cdot)\) \(\chi_{3525}(1826,\cdot)\) \(\chi_{3525}(2051,\cdot)\) \(\chi_{3525}(2126,\cdot)\) \(\chi_{3525}(2201,\cdot)\) \(\chi_{3525}(2276,\cdot)\) \(\chi_{3525}(2426,\cdot)\) \(\chi_{3525}(2501,\cdot)\) \(\chi_{3525}(2576,\cdot)\) \(\chi_{3525}(2651,\cdot)\) \(\chi_{3525}(3476,\cdot)\)
Related number fields
Field of values: | \(\Q(\zeta_{23})\) |
Fixed field: | \(\Q(\zeta_{141})^+\) |
Values on generators
\((2351,1552,2026)\) → \((-1,1,e\left(\frac{29}{46}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3525 }(26, a) \) | \(1\) | \(1\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{25}{46}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{1}{46}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{27}{46}\right)\) | \(e\left(\frac{17}{46}\right)\) |