Basic properties
| Modulus: | \(8550\) | |
| Conductor: | \(475\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(45\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{475}(271,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8550.fl
\(\chi_{8550}(271,\cdot)\) \(\chi_{8550}(541,\cdot)\) \(\chi_{8550}(631,\cdot)\) \(\chi_{8550}(1081,\cdot)\) \(\chi_{8550}(1441,\cdot)\) \(\chi_{8550}(1621,\cdot)\) \(\chi_{8550}(1981,\cdot)\) \(\chi_{8550}(2341,\cdot)\) \(\chi_{8550}(2791,\cdot)\) \(\chi_{8550}(3331,\cdot)\) \(\chi_{8550}(3691,\cdot)\) \(\chi_{8550}(3961,\cdot)\) \(\chi_{8550}(4861,\cdot)\) \(\chi_{8550}(5041,\cdot)\) \(\chi_{8550}(5671,\cdot)\) \(\chi_{8550}(5761,\cdot)\) \(\chi_{8550}(6211,\cdot)\) \(\chi_{8550}(6571,\cdot)\) \(\chi_{8550}(7111,\cdot)\) \(\chi_{8550}(7381,\cdot)\) \(\chi_{8550}(7471,\cdot)\) \(\chi_{8550}(7921,\cdot)\) \(\chi_{8550}(8281,\cdot)\) \(\chi_{8550}(8461,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((1901,1027,1351)\) → \((1,e\left(\frac{3}{5}\right),e\left(\frac{8}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8550 }(271, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{2}{9}\right)\) |