Basic properties
| Modulus: | \(5550\) | |
| Conductor: | \(2775\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2775}(59,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5550.en
\(\chi_{5550}(59,\cdot)\) \(\chi_{5550}(89,\cdot)\) \(\chi_{5550}(209,\cdot)\) \(\chi_{5550}(239,\cdot)\) \(\chi_{5550}(389,\cdot)\) \(\chi_{5550}(479,\cdot)\) \(\chi_{5550}(779,\cdot)\) \(\chi_{5550}(809,\cdot)\) \(\chi_{5550}(869,\cdot)\) \(\chi_{5550}(1019,\cdot)\) \(\chi_{5550}(1169,\cdot)\) \(\chi_{5550}(1319,\cdot)\) \(\chi_{5550}(1559,\cdot)\) \(\chi_{5550}(1589,\cdot)\) \(\chi_{5550}(1889,\cdot)\) \(\chi_{5550}(1919,\cdot)\) \(\chi_{5550}(1979,\cdot)\) \(\chi_{5550}(2129,\cdot)\) \(\chi_{5550}(2159,\cdot)\) \(\chi_{5550}(2279,\cdot)\) \(\chi_{5550}(2309,\cdot)\) \(\chi_{5550}(2429,\cdot)\) \(\chi_{5550}(2459,\cdot)\) \(\chi_{5550}(2609,\cdot)\) \(\chi_{5550}(2669,\cdot)\) \(\chi_{5550}(3029,\cdot)\) \(\chi_{5550}(3089,\cdot)\) \(\chi_{5550}(3239,\cdot)\) \(\chi_{5550}(3269,\cdot)\) \(\chi_{5550}(3389,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((3701,1777,2851)\) → \((-1,e\left(\frac{7}{10}\right),e\left(\frac{31}{36}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(41\) | \(43\) |
| \( \chi_{ 5550 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{139}{180}\right)\) | \(e\left(\frac{113}{180}\right)\) | \(e\left(\frac{133}{180}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(-i\) |