Basic properties
| Modulus: | \(5550\) | |
| Conductor: | \(925\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{925}(229,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5550.ec
\(\chi_{5550}(229,\cdot)\) \(\chi_{5550}(379,\cdot)\) \(\chi_{5550}(589,\cdot)\) \(\chi_{5550}(1069,\cdot)\) \(\chi_{5550}(1159,\cdot)\) \(\chi_{5550}(1339,\cdot)\) \(\chi_{5550}(1459,\cdot)\) \(\chi_{5550}(1489,\cdot)\) \(\chi_{5550}(2179,\cdot)\) \(\chi_{5550}(2269,\cdot)\) \(\chi_{5550}(2569,\cdot)\) \(\chi_{5550}(2809,\cdot)\) \(\chi_{5550}(3289,\cdot)\) \(\chi_{5550}(3379,\cdot)\) \(\chi_{5550}(3559,\cdot)\) \(\chi_{5550}(3679,\cdot)\) \(\chi_{5550}(3709,\cdot)\) \(\chi_{5550}(3919,\cdot)\) \(\chi_{5550}(4489,\cdot)\) \(\chi_{5550}(4669,\cdot)\) \(\chi_{5550}(4789,\cdot)\) \(\chi_{5550}(4819,\cdot)\) \(\chi_{5550}(5029,\cdot)\) \(\chi_{5550}(5509,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((3701,1777,2851)\) → \((1,e\left(\frac{1}{10}\right),e\left(\frac{8}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(41\) | \(43\) |
| \( \chi_{ 5550 }(229, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(-1\) |