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 \(\chi_{925}(139,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5550.ed
\(\chi_{5550}(139,\cdot)\) \(\chi_{5550}(169,\cdot)\) \(\chi_{5550}(289,\cdot)\) \(\chi_{5550}(469,\cdot)\) \(\chi_{5550}(559,\cdot)\) \(\chi_{5550}(1039,\cdot)\) \(\chi_{5550}(1279,\cdot)\) \(\chi_{5550}(1579,\cdot)\) \(\chi_{5550}(1669,\cdot)\) \(\chi_{5550}(2359,\cdot)\) \(\chi_{5550}(2389,\cdot)\) \(\chi_{5550}(2509,\cdot)\) \(\chi_{5550}(2689,\cdot)\) \(\chi_{5550}(2779,\cdot)\) \(\chi_{5550}(3259,\cdot)\) \(\chi_{5550}(3469,\cdot)\) \(\chi_{5550}(3619,\cdot)\) \(\chi_{5550}(3889,\cdot)\) \(\chi_{5550}(4369,\cdot)\) \(\chi_{5550}(4579,\cdot)\) \(\chi_{5550}(4609,\cdot)\) \(\chi_{5550}(4729,\cdot)\) \(\chi_{5550}(4909,\cdot)\) \(\chi_{5550}(5479,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((3701,1777,2851)\) → \((1,e\left(\frac{3}{10}\right),e\left(\frac{17}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(41\) | \(43\) |
| \( \chi_{ 5550 }(139, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{41}{90}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(1\) |