Basic properties
| Modulus: | \(3630\) | |
| Conductor: | \(1815\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1815}(107,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3630.bu
\(\chi_{3630}(17,\cdot)\) \(\chi_{3630}(83,\cdot)\) \(\chi_{3630}(107,\cdot)\) \(\chi_{3630}(167,\cdot)\) \(\chi_{3630}(173,\cdot)\) \(\chi_{3630}(227,\cdot)\) \(\chi_{3630}(293,\cdot)\) \(\chi_{3630}(347,\cdot)\) \(\chi_{3630}(413,\cdot)\) \(\chi_{3630}(437,\cdot)\) \(\chi_{3630}(497,\cdot)\) \(\chi_{3630}(503,\cdot)\) \(\chi_{3630}(557,\cdot)\) \(\chi_{3630}(563,\cdot)\) \(\chi_{3630}(623,\cdot)\) \(\chi_{3630}(677,\cdot)\) \(\chi_{3630}(743,\cdot)\) \(\chi_{3630}(767,\cdot)\) \(\chi_{3630}(827,\cdot)\) \(\chi_{3630}(833,\cdot)\) \(\chi_{3630}(893,\cdot)\) \(\chi_{3630}(953,\cdot)\) \(\chi_{3630}(1007,\cdot)\) \(\chi_{3630}(1073,\cdot)\) \(\chi_{3630}(1097,\cdot)\) \(\chi_{3630}(1157,\cdot)\) \(\chi_{3630}(1163,\cdot)\) \(\chi_{3630}(1217,\cdot)\) \(\chi_{3630}(1223,\cdot)\) \(\chi_{3630}(1283,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((1211,727,3511)\) → \((-1,i,e\left(\frac{63}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 3630 }(107, a) \) | \(-1\) | \(1\) | \(e\left(\frac{57}{220}\right)\) | \(e\left(\frac{131}{220}\right)\) | \(e\left(\frac{179}{220}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{67}{220}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{3}{44}\right)\) |