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 \(\chi_{1815}(203,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3630.bt
\(\chi_{3630}(47,\cdot)\) \(\chi_{3630}(53,\cdot)\) \(\chi_{3630}(113,\cdot)\) \(\chi_{3630}(137,\cdot)\) \(\chi_{3630}(203,\cdot)\) \(\chi_{3630}(257,\cdot)\) \(\chi_{3630}(317,\cdot)\) \(\chi_{3630}(377,\cdot)\) \(\chi_{3630}(383,\cdot)\) \(\chi_{3630}(443,\cdot)\) \(\chi_{3630}(467,\cdot)\) \(\chi_{3630}(533,\cdot)\) \(\chi_{3630}(587,\cdot)\) \(\chi_{3630}(647,\cdot)\) \(\chi_{3630}(653,\cdot)\) \(\chi_{3630}(707,\cdot)\) \(\chi_{3630}(713,\cdot)\) \(\chi_{3630}(773,\cdot)\) \(\chi_{3630}(797,\cdot)\) \(\chi_{3630}(863,\cdot)\) \(\chi_{3630}(917,\cdot)\) \(\chi_{3630}(983,\cdot)\) \(\chi_{3630}(1037,\cdot)\) \(\chi_{3630}(1043,\cdot)\) \(\chi_{3630}(1103,\cdot)\) \(\chi_{3630}(1127,\cdot)\) \(\chi_{3630}(1193,\cdot)\) \(\chi_{3630}(1247,\cdot)\) \(\chi_{3630}(1307,\cdot)\) \(\chi_{3630}(1313,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((1211,727,3511)\) → \((-1,-i,e\left(\frac{12}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 3630 }(203, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{220}\right)\) | \(e\left(\frac{63}{220}\right)\) | \(e\left(\frac{207}{220}\right)\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{201}{220}\right)\) | \(e\left(\frac{57}{110}\right)\) | \(e\left(\frac{31}{44}\right)\) |