Basic properties
Modulus: | \(3630\) | |
Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(55\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{121}(16,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3630.bk
\(\chi_{3630}(31,\cdot)\) \(\chi_{3630}(91,\cdot)\) \(\chi_{3630}(181,\cdot)\) \(\chi_{3630}(301,\cdot)\) \(\chi_{3630}(361,\cdot)\) \(\chi_{3630}(421,\cdot)\) \(\chi_{3630}(631,\cdot)\) \(\chi_{3630}(691,\cdot)\) \(\chi_{3630}(751,\cdot)\) \(\chi_{3630}(841,\cdot)\) \(\chi_{3630}(961,\cdot)\) \(\chi_{3630}(1021,\cdot)\) \(\chi_{3630}(1081,\cdot)\) \(\chi_{3630}(1171,\cdot)\) \(\chi_{3630}(1351,\cdot)\) \(\chi_{3630}(1411,\cdot)\) \(\chi_{3630}(1501,\cdot)\) \(\chi_{3630}(1621,\cdot)\) \(\chi_{3630}(1681,\cdot)\) \(\chi_{3630}(1741,\cdot)\) \(\chi_{3630}(1831,\cdot)\) \(\chi_{3630}(1951,\cdot)\) \(\chi_{3630}(2011,\cdot)\) \(\chi_{3630}(2071,\cdot)\) \(\chi_{3630}(2161,\cdot)\) \(\chi_{3630}(2281,\cdot)\) \(\chi_{3630}(2341,\cdot)\) \(\chi_{3630}(2401,\cdot)\) \(\chi_{3630}(2491,\cdot)\) \(\chi_{3630}(2611,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((1211,727,3511)\) → \((1,1,e\left(\frac{2}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 3630 }(1831, a) \) | \(1\) | \(1\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{29}{55}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{10}{11}\right)\) |