Basic properties
Modulus: | \(2850\) | |
Conductor: | \(475\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{475}(91,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2850.cl
\(\chi_{2850}(91,\cdot)\) \(\chi_{2850}(181,\cdot)\) \(\chi_{2850}(211,\cdot)\) \(\chi_{2850}(241,\cdot)\) \(\chi_{2850}(421,\cdot)\) \(\chi_{2850}(661,\cdot)\) \(\chi_{2850}(781,\cdot)\) \(\chi_{2850}(811,\cdot)\) \(\chi_{2850}(991,\cdot)\) \(\chi_{2850}(1021,\cdot)\) \(\chi_{2850}(1231,\cdot)\) \(\chi_{2850}(1321,\cdot)\) \(\chi_{2850}(1381,\cdot)\) \(\chi_{2850}(1561,\cdot)\) \(\chi_{2850}(1591,\cdot)\) \(\chi_{2850}(1891,\cdot)\) \(\chi_{2850}(1921,\cdot)\) \(\chi_{2850}(2131,\cdot)\) \(\chi_{2850}(2161,\cdot)\) \(\chi_{2850}(2371,\cdot)\) \(\chi_{2850}(2461,\cdot)\) \(\chi_{2850}(2491,\cdot)\) \(\chi_{2850}(2521,\cdot)\) \(\chi_{2850}(2731,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((1901,1027,1351)\) → \((1,e\left(\frac{1}{5}\right),e\left(\frac{11}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 2850 }(91, a) \) | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{7}{9}\right)\) |