Basic properties
| Modulus: | \(8550\) | |
| Conductor: | \(475\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{475}(127,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8550.hf
\(\chi_{8550}(127,\cdot)\) \(\chi_{8550}(433,\cdot)\) \(\chi_{8550}(523,\cdot)\) \(\chi_{8550}(667,\cdot)\) \(\chi_{8550}(1117,\cdot)\) \(\chi_{8550}(1153,\cdot)\) \(\chi_{8550}(1333,\cdot)\) \(\chi_{8550}(1477,\cdot)\) \(\chi_{8550}(1837,\cdot)\) \(\chi_{8550}(2017,\cdot)\) \(\chi_{8550}(2233,\cdot)\) \(\chi_{8550}(2377,\cdot)\) \(\chi_{8550}(2503,\cdot)\) \(\chi_{8550}(2827,\cdot)\) \(\chi_{8550}(2863,\cdot)\) \(\chi_{8550}(2917,\cdot)\) \(\chi_{8550}(3187,\cdot)\) \(\chi_{8550}(3403,\cdot)\) \(\chi_{8550}(3547,\cdot)\) \(\chi_{8550}(3727,\cdot)\) \(\chi_{8550}(3853,\cdot)\) \(\chi_{8550}(4087,\cdot)\) \(\chi_{8550}(4213,\cdot)\) \(\chi_{8550}(4537,\cdot)\) \(\chi_{8550}(4573,\cdot)\) \(\chi_{8550}(4627,\cdot)\) \(\chi_{8550}(4753,\cdot)\) \(\chi_{8550}(4897,\cdot)\) \(\chi_{8550}(5113,\cdot)\) \(\chi_{8550}(5437,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((1901,1027,1351)\) → \((1,e\left(\frac{1}{20}\right),e\left(\frac{5}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8550 }(127, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{61}{180}\right)\) | \(e\left(\frac{77}{180}\right)\) | \(e\left(\frac{19}{180}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{7}{36}\right)\) |