Basic properties
| Modulus: | \(3630\) | |
| Conductor: | \(1815\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1815}(119,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3630.bo
\(\chi_{3630}(59,\cdot)\) \(\chi_{3630}(119,\cdot)\) \(\chi_{3630}(179,\cdot)\) \(\chi_{3630}(389,\cdot)\) \(\chi_{3630}(449,\cdot)\) \(\chi_{3630}(509,\cdot)\) \(\chi_{3630}(599,\cdot)\) \(\chi_{3630}(719,\cdot)\) \(\chi_{3630}(779,\cdot)\) \(\chi_{3630}(839,\cdot)\) \(\chi_{3630}(929,\cdot)\) \(\chi_{3630}(1109,\cdot)\) \(\chi_{3630}(1169,\cdot)\) \(\chi_{3630}(1259,\cdot)\) \(\chi_{3630}(1379,\cdot)\) \(\chi_{3630}(1439,\cdot)\) \(\chi_{3630}(1499,\cdot)\) \(\chi_{3630}(1589,\cdot)\) \(\chi_{3630}(1709,\cdot)\) \(\chi_{3630}(1769,\cdot)\) \(\chi_{3630}(1829,\cdot)\) \(\chi_{3630}(1919,\cdot)\) \(\chi_{3630}(2039,\cdot)\) \(\chi_{3630}(2099,\cdot)\) \(\chi_{3630}(2159,\cdot)\) \(\chi_{3630}(2249,\cdot)\) \(\chi_{3630}(2369,\cdot)\) \(\chi_{3630}(2489,\cdot)\) \(\chi_{3630}(2579,\cdot)\) \(\chi_{3630}(2699,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1211,727,3511)\) → \((-1,-1,e\left(\frac{28}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 3630 }(119, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{110}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{52}{55}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{17}{110}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{97}{110}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{5}{22}\right)\) |