Basic properties
Modulus: | \(3525\) | |
Conductor: | \(47\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(46\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{47}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3525.z
\(\chi_{3525}(76,\cdot)\) \(\chi_{3525}(151,\cdot)\) \(\chi_{3525}(226,\cdot)\) \(\chi_{3525}(301,\cdot)\) \(\chi_{3525}(1126,\cdot)\) \(\chi_{3525}(1201,\cdot)\) \(\chi_{3525}(1351,\cdot)\) \(\chi_{3525}(1501,\cdot)\) \(\chi_{3525}(1801,\cdot)\) \(\chi_{3525}(1876,\cdot)\) \(\chi_{3525}(2026,\cdot)\) \(\chi_{3525}(2101,\cdot)\) \(\chi_{3525}(2326,\cdot)\) \(\chi_{3525}(2551,\cdot)\) \(\chi_{3525}(2626,\cdot)\) \(\chi_{3525}(2701,\cdot)\) \(\chi_{3525}(2851,\cdot)\) \(\chi_{3525}(3001,\cdot)\) \(\chi_{3525}(3226,\cdot)\) \(\chi_{3525}(3301,\cdot)\) \(\chi_{3525}(3376,\cdot)\) \(\chi_{3525}(3451,\cdot)\)
Related number fields
Field of values: | \(\Q(\zeta_{23})\) |
Fixed field: | Number field defined by a degree 46 polynomial |
Values on generators
\((2351,1552,2026)\) → \((1,1,e\left(\frac{1}{46}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 3525 }(2026, a) \) | \(-1\) | \(1\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{18}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{7}{46}\right)\) | \(e\left(\frac{11}{46}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{45}{46}\right)\) |