Basic properties
| Modulus: | \(3630\) | |
| Conductor: | \(605\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{605}(19,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3630.br
\(\chi_{3630}(19,\cdot)\) \(\chi_{3630}(79,\cdot)\) \(\chi_{3630}(139,\cdot)\) \(\chi_{3630}(259,\cdot)\) \(\chi_{3630}(349,\cdot)\) \(\chi_{3630}(409,\cdot)\) \(\chi_{3630}(469,\cdot)\) \(\chi_{3630}(589,\cdot)\) \(\chi_{3630}(679,\cdot)\) \(\chi_{3630}(739,\cdot)\) \(\chi_{3630}(799,\cdot)\) \(\chi_{3630}(919,\cdot)\) \(\chi_{3630}(1009,\cdot)\) \(\chi_{3630}(1069,\cdot)\) \(\chi_{3630}(1249,\cdot)\) \(\chi_{3630}(1339,\cdot)\) \(\chi_{3630}(1399,\cdot)\) \(\chi_{3630}(1459,\cdot)\) \(\chi_{3630}(1579,\cdot)\) \(\chi_{3630}(1669,\cdot)\) \(\chi_{3630}(1729,\cdot)\) \(\chi_{3630}(1789,\cdot)\) \(\chi_{3630}(1999,\cdot)\) \(\chi_{3630}(2059,\cdot)\) \(\chi_{3630}(2119,\cdot)\) \(\chi_{3630}(2239,\cdot)\) \(\chi_{3630}(2329,\cdot)\) \(\chi_{3630}(2389,\cdot)\) \(\chi_{3630}(2449,\cdot)\) \(\chi_{3630}(2569,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1211,727,3511)\) → \((1,-1,e\left(\frac{83}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 3630 }(19, a) \) | \(-1\) | \(1\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{91}{110}\right)\) | \(e\left(\frac{49}{55}\right)\) | \(e\left(\frac{21}{110}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{4}{11}\right)\) |