Basic properties
Modulus: | \(3630\) | |
Conductor: | \(363\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{363}(248,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3630.bn
\(\chi_{3630}(41,\cdot)\) \(\chi_{3630}(101,\cdot)\) \(\chi_{3630}(281,\cdot)\) \(\chi_{3630}(371,\cdot)\) \(\chi_{3630}(431,\cdot)\) \(\chi_{3630}(491,\cdot)\) \(\chi_{3630}(611,\cdot)\) \(\chi_{3630}(701,\cdot)\) \(\chi_{3630}(761,\cdot)\) \(\chi_{3630}(821,\cdot)\) \(\chi_{3630}(1031,\cdot)\) \(\chi_{3630}(1091,\cdot)\) \(\chi_{3630}(1151,\cdot)\) \(\chi_{3630}(1271,\cdot)\) \(\chi_{3630}(1361,\cdot)\) \(\chi_{3630}(1421,\cdot)\) \(\chi_{3630}(1481,\cdot)\) \(\chi_{3630}(1601,\cdot)\) \(\chi_{3630}(1751,\cdot)\) \(\chi_{3630}(1811,\cdot)\) \(\chi_{3630}(1931,\cdot)\) \(\chi_{3630}(2021,\cdot)\) \(\chi_{3630}(2081,\cdot)\) \(\chi_{3630}(2141,\cdot)\) \(\chi_{3630}(2261,\cdot)\) \(\chi_{3630}(2351,\cdot)\) \(\chi_{3630}(2471,\cdot)\) \(\chi_{3630}(2591,\cdot)\) \(\chi_{3630}(2681,\cdot)\) \(\chi_{3630}(2741,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1211,727,3511)\) → \((-1,1,e\left(\frac{89}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 3630 }(611, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{17}{110}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{5}{22}\right)\) |