Basic properties
Modulus: | \(3630\) | |
Conductor: | \(605\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{605}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3630.bs
\(\chi_{3630}(37,\cdot)\) \(\chi_{3630}(97,\cdot)\) \(\chi_{3630}(103,\cdot)\) \(\chi_{3630}(157,\cdot)\) \(\chi_{3630}(163,\cdot)\) \(\chi_{3630}(223,\cdot)\) \(\chi_{3630}(247,\cdot)\) \(\chi_{3630}(313,\cdot)\) \(\chi_{3630}(367,\cdot)\) \(\chi_{3630}(427,\cdot)\) \(\chi_{3630}(433,\cdot)\) \(\chi_{3630}(553,\cdot)\) \(\chi_{3630}(577,\cdot)\) \(\chi_{3630}(643,\cdot)\) \(\chi_{3630}(697,\cdot)\) \(\chi_{3630}(757,\cdot)\) \(\chi_{3630}(763,\cdot)\) \(\chi_{3630}(817,\cdot)\) \(\chi_{3630}(823,\cdot)\) \(\chi_{3630}(883,\cdot)\) \(\chi_{3630}(907,\cdot)\) \(\chi_{3630}(973,\cdot)\) \(\chi_{3630}(1027,\cdot)\) \(\chi_{3630}(1087,\cdot)\) \(\chi_{3630}(1093,\cdot)\) \(\chi_{3630}(1147,\cdot)\) \(\chi_{3630}(1153,\cdot)\) \(\chi_{3630}(1303,\cdot)\) \(\chi_{3630}(1357,\cdot)\) \(\chi_{3630}(1417,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{220})$ |
Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((1211,727,3511)\) → \((1,i,e\left(\frac{21}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 3630 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{203}{220}\right)\) | \(e\left(\frac{69}{220}\right)\) | \(e\left(\frac{211}{220}\right)\) | \(e\left(\frac{21}{110}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{109}{110}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{63}{220}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{13}{44}\right)\) |