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 \(\chi_{605}(159,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3630.bm
\(\chi_{3630}(49,\cdot)\) \(\chi_{3630}(169,\cdot)\) \(\chi_{3630}(229,\cdot)\) \(\chi_{3630}(289,\cdot)\) \(\chi_{3630}(379,\cdot)\) \(\chi_{3630}(499,\cdot)\) \(\chi_{3630}(559,\cdot)\) \(\chi_{3630}(619,\cdot)\) \(\chi_{3630}(709,\cdot)\) \(\chi_{3630}(829,\cdot)\) \(\chi_{3630}(889,\cdot)\) \(\chi_{3630}(949,\cdot)\) \(\chi_{3630}(1039,\cdot)\) \(\chi_{3630}(1159,\cdot)\) \(\chi_{3630}(1279,\cdot)\) \(\chi_{3630}(1369,\cdot)\) \(\chi_{3630}(1489,\cdot)\) \(\chi_{3630}(1549,\cdot)\) \(\chi_{3630}(1609,\cdot)\) \(\chi_{3630}(1699,\cdot)\) \(\chi_{3630}(1819,\cdot)\) \(\chi_{3630}(1879,\cdot)\) \(\chi_{3630}(2029,\cdot)\) \(\chi_{3630}(2149,\cdot)\) \(\chi_{3630}(2209,\cdot)\) \(\chi_{3630}(2269,\cdot)\) \(\chi_{3630}(2359,\cdot)\) \(\chi_{3630}(2479,\cdot)\) \(\chi_{3630}(2539,\cdot)\) \(\chi_{3630}(2599,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1211,727,3511)\) → \((1,-1,e\left(\frac{42}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 3630 }(1369, a) \) | \(1\) | \(1\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{63}{110}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{13}{22}\right)\) |