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 \(\chi_{605}(73,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3630.bv
\(\chi_{3630}(7,\cdot)\) \(\chi_{3630}(13,\cdot)\) \(\chi_{3630}(73,\cdot)\) \(\chi_{3630}(127,\cdot)\) \(\chi_{3630}(193,\cdot)\) \(\chi_{3630}(217,\cdot)\) \(\chi_{3630}(277,\cdot)\) \(\chi_{3630}(283,\cdot)\) \(\chi_{3630}(337,\cdot)\) \(\chi_{3630}(343,\cdot)\) \(\chi_{3630}(523,\cdot)\) \(\chi_{3630}(547,\cdot)\) \(\chi_{3630}(607,\cdot)\) \(\chi_{3630}(613,\cdot)\) \(\chi_{3630}(667,\cdot)\) \(\chi_{3630}(673,\cdot)\) \(\chi_{3630}(733,\cdot)\) \(\chi_{3630}(787,\cdot)\) \(\chi_{3630}(853,\cdot)\) \(\chi_{3630}(877,\cdot)\) \(\chi_{3630}(937,\cdot)\) \(\chi_{3630}(943,\cdot)\) \(\chi_{3630}(997,\cdot)\) \(\chi_{3630}(1003,\cdot)\) \(\chi_{3630}(1063,\cdot)\) \(\chi_{3630}(1117,\cdot)\) \(\chi_{3630}(1267,\cdot)\) \(\chi_{3630}(1273,\cdot)\) \(\chi_{3630}(1327,\cdot)\) \(\chi_{3630}(1333,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((1211,727,3511)\) → \((1,-i,e\left(\frac{37}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 3630 }(73, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{220}\right)\) | \(e\left(\frac{49}{220}\right)\) | \(e\left(\frac{51}{220}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{193}{220}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{29}{44}\right)\) |