Basic properties
| Modulus: | \(3525\) | |
| Conductor: | \(47\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(23\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{47}(28,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3525.y
\(\chi_{3525}(451,\cdot)\) \(\chi_{3525}(526,\cdot)\) \(\chi_{3525}(601,\cdot)\) \(\chi_{3525}(676,\cdot)\) \(\chi_{3525}(826,\cdot)\) \(\chi_{3525}(901,\cdot)\) \(\chi_{3525}(976,\cdot)\) \(\chi_{3525}(1051,\cdot)\) \(\chi_{3525}(1276,\cdot)\) \(\chi_{3525}(1426,\cdot)\) \(\chi_{3525}(1576,\cdot)\) \(\chi_{3525}(1651,\cdot)\) \(\chi_{3525}(1726,\cdot)\) \(\chi_{3525}(1951,\cdot)\) \(\chi_{3525}(2176,\cdot)\) \(\chi_{3525}(2251,\cdot)\) \(\chi_{3525}(2401,\cdot)\) \(\chi_{3525}(2476,\cdot)\) \(\chi_{3525}(2776,\cdot)\) \(\chi_{3525}(2926,\cdot)\) \(\chi_{3525}(3076,\cdot)\) \(\chi_{3525}(3151,\cdot)\)
Related number fields
| Field of values: | \(\Q(\zeta_{23})\) |
| Fixed field: | Number field defined by a degree 23 polynomial |
Values on generators
\((2351,1552,2026)\) → \((1,1,e\left(\frac{11}{23}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 3525 }(451, a) \) | \(1\) | \(1\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{7}{23}\right)\) | \(e\left(\frac{19}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) |