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 \(\chi_{1425}(344,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2850.cm
\(\chi_{2850}(29,\cdot)\) \(\chi_{2850}(59,\cdot)\) \(\chi_{2850}(89,\cdot)\) \(\chi_{2850}(269,\cdot)\) \(\chi_{2850}(509,\cdot)\) \(\chi_{2850}(629,\cdot)\) \(\chi_{2850}(659,\cdot)\) \(\chi_{2850}(839,\cdot)\) \(\chi_{2850}(869,\cdot)\) \(\chi_{2850}(1079,\cdot)\) \(\chi_{2850}(1169,\cdot)\) \(\chi_{2850}(1229,\cdot)\) \(\chi_{2850}(1409,\cdot)\) \(\chi_{2850}(1439,\cdot)\) \(\chi_{2850}(1739,\cdot)\) \(\chi_{2850}(1769,\cdot)\) \(\chi_{2850}(1979,\cdot)\) \(\chi_{2850}(2009,\cdot)\) \(\chi_{2850}(2219,\cdot)\) \(\chi_{2850}(2309,\cdot)\) \(\chi_{2850}(2339,\cdot)\) \(\chi_{2850}(2369,\cdot)\) \(\chi_{2850}(2579,\cdot)\) \(\chi_{2850}(2789,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((1901,1027,1351)\) → \((-1,e\left(\frac{9}{10}\right),e\left(\frac{1}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 2850 }(1769, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{7}{18}\right)\) |