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 \(\chi_{475}(79,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2850.co
\(\chi_{2850}(79,\cdot)\) \(\chi_{2850}(109,\cdot)\) \(\chi_{2850}(319,\cdot)\) \(\chi_{2850}(409,\cdot)\) \(\chi_{2850}(439,\cdot)\) \(\chi_{2850}(469,\cdot)\) \(\chi_{2850}(679,\cdot)\) \(\chi_{2850}(889,\cdot)\) \(\chi_{2850}(979,\cdot)\) \(\chi_{2850}(1009,\cdot)\) \(\chi_{2850}(1039,\cdot)\) \(\chi_{2850}(1219,\cdot)\) \(\chi_{2850}(1459,\cdot)\) \(\chi_{2850}(1579,\cdot)\) \(\chi_{2850}(1609,\cdot)\) \(\chi_{2850}(1789,\cdot)\) \(\chi_{2850}(1819,\cdot)\) \(\chi_{2850}(2029,\cdot)\) \(\chi_{2850}(2119,\cdot)\) \(\chi_{2850}(2179,\cdot)\) \(\chi_{2850}(2359,\cdot)\) \(\chi_{2850}(2389,\cdot)\) \(\chi_{2850}(2689,\cdot)\) \(\chi_{2850}(2719,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((1901,1027,1351)\) → \((1,e\left(\frac{1}{10}\right),e\left(\frac{13}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 2850 }(79, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{1}{18}\right)\) |