Basic properties
| Modulus: | \(2850\) | |
| Conductor: | \(1425\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1425}(941,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2850.cj
\(\chi_{2850}(41,\cdot)\) \(\chi_{2850}(71,\cdot)\) \(\chi_{2850}(281,\cdot)\) \(\chi_{2850}(371,\cdot)\) \(\chi_{2850}(431,\cdot)\) \(\chi_{2850}(611,\cdot)\) \(\chi_{2850}(641,\cdot)\) \(\chi_{2850}(941,\cdot)\) \(\chi_{2850}(971,\cdot)\) \(\chi_{2850}(1181,\cdot)\) \(\chi_{2850}(1211,\cdot)\) \(\chi_{2850}(1421,\cdot)\) \(\chi_{2850}(1511,\cdot)\) \(\chi_{2850}(1541,\cdot)\) \(\chi_{2850}(1571,\cdot)\) \(\chi_{2850}(1781,\cdot)\) \(\chi_{2850}(1991,\cdot)\) \(\chi_{2850}(2081,\cdot)\) \(\chi_{2850}(2111,\cdot)\) \(\chi_{2850}(2141,\cdot)\) \(\chi_{2850}(2321,\cdot)\) \(\chi_{2850}(2561,\cdot)\) \(\chi_{2850}(2681,\cdot)\) \(\chi_{2850}(2711,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((1901,1027,1351)\) → \((-1,e\left(\frac{1}{5}\right),e\left(\frac{17}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 2850 }(941, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{1}{9}\right)\) |