Basic properties
| Modulus: | \(3630\) | |
| Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{121}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3630.bl
\(\chi_{3630}(61,\cdot)\) \(\chi_{3630}(151,\cdot)\) \(\chi_{3630}(211,\cdot)\) \(\chi_{3630}(271,\cdot)\) \(\chi_{3630}(391,\cdot)\) \(\chi_{3630}(541,\cdot)\) \(\chi_{3630}(601,\cdot)\) \(\chi_{3630}(721,\cdot)\) \(\chi_{3630}(811,\cdot)\) \(\chi_{3630}(871,\cdot)\) \(\chi_{3630}(931,\cdot)\) \(\chi_{3630}(1051,\cdot)\) \(\chi_{3630}(1141,\cdot)\) \(\chi_{3630}(1261,\cdot)\) \(\chi_{3630}(1381,\cdot)\) \(\chi_{3630}(1471,\cdot)\) \(\chi_{3630}(1531,\cdot)\) \(\chi_{3630}(1591,\cdot)\) \(\chi_{3630}(1711,\cdot)\) \(\chi_{3630}(1801,\cdot)\) \(\chi_{3630}(1861,\cdot)\) \(\chi_{3630}(1921,\cdot)\) \(\chi_{3630}(2041,\cdot)\) \(\chi_{3630}(2131,\cdot)\) \(\chi_{3630}(2191,\cdot)\) \(\chi_{3630}(2251,\cdot)\) \(\chi_{3630}(2371,\cdot)\) \(\chi_{3630}(2461,\cdot)\) \(\chi_{3630}(2521,\cdot)\) \(\chi_{3630}(2701,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1211,727,3511)\) → \((1,1,e\left(\frac{109}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 3630 }(61, a) \) | \(-1\) | \(1\) | \(e\left(\frac{103}{110}\right)\) | \(e\left(\frac{9}{110}\right)\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{27}{110}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{87}{110}\right)\) | \(e\left(\frac{17}{22}\right)\) |