Basic properties
| Modulus: | \(8550\) | |
| Conductor: | \(4275\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4275}(148,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8550.he
\(\chi_{8550}(13,\cdot)\) \(\chi_{8550}(67,\cdot)\) \(\chi_{8550}(97,\cdot)\) \(\chi_{8550}(223,\cdot)\) \(\chi_{8550}(697,\cdot)\) \(\chi_{8550}(763,\cdot)\) \(\chi_{8550}(1003,\cdot)\) \(\chi_{8550}(1123,\cdot)\) \(\chi_{8550}(1447,\cdot)\) \(\chi_{8550}(1687,\cdot)\) \(\chi_{8550}(1723,\cdot)\) \(\chi_{8550}(1777,\cdot)\) \(\chi_{8550}(1933,\cdot)\) \(\chi_{8550}(2473,\cdot)\) \(\chi_{8550}(2617,\cdot)\) \(\chi_{8550}(2713,\cdot)\) \(\chi_{8550}(2803,\cdot)\) \(\chi_{8550}(2833,\cdot)\) \(\chi_{8550}(3397,\cdot)\) \(\chi_{8550}(3433,\cdot)\) \(\chi_{8550}(3487,\cdot)\) \(\chi_{8550}(3517,\cdot)\) \(\chi_{8550}(4117,\cdot)\) \(\chi_{8550}(4183,\cdot)\) \(\chi_{8550}(4327,\cdot)\) \(\chi_{8550}(4423,\cdot)\) \(\chi_{8550}(4513,\cdot)\) \(\chi_{8550}(4867,\cdot)\) \(\chi_{8550}(5197,\cdot)\) \(\chi_{8550}(5227,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((1901,1027,1351)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{11}{20}\right),e\left(\frac{11}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8550 }(4423, a) \) | \(1\) | \(1\) | \(-i\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{31}{180}\right)\) | \(e\left(\frac{47}{180}\right)\) | \(e\left(\frac{169}{180}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{13}{36}\right)\) |