Basic properties
Modulus: | \(3800\) | |
Conductor: | \(1900\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1900}(23,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3800.fg
\(\chi_{3800}(23,\cdot)\) \(\chi_{3800}(47,\cdot)\) \(\chi_{3800}(63,\cdot)\) \(\chi_{3800}(263,\cdot)\) \(\chi_{3800}(327,\cdot)\) \(\chi_{3800}(367,\cdot)\) \(\chi_{3800}(423,\cdot)\) \(\chi_{3800}(503,\cdot)\) \(\chi_{3800}(567,\cdot)\) \(\chi_{3800}(663,\cdot)\) \(\chi_{3800}(727,\cdot)\) \(\chi_{3800}(783,\cdot)\) \(\chi_{3800}(823,\cdot)\) \(\chi_{3800}(967,\cdot)\) \(\chi_{3800}(1023,\cdot)\) \(\chi_{3800}(1087,\cdot)\) \(\chi_{3800}(1127,\cdot)\) \(\chi_{3800}(1183,\cdot)\) \(\chi_{3800}(1263,\cdot)\) \(\chi_{3800}(1327,\cdot)\) \(\chi_{3800}(1423,\cdot)\) \(\chi_{3800}(1487,\cdot)\) \(\chi_{3800}(1567,\cdot)\) \(\chi_{3800}(1583,\cdot)\) \(\chi_{3800}(1727,\cdot)\) \(\chi_{3800}(1783,\cdot)\) \(\chi_{3800}(1847,\cdot)\) \(\chi_{3800}(1887,\cdot)\) \(\chi_{3800}(2023,\cdot)\) \(\chi_{3800}(2087,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{180})$ |
Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((951,1901,1977,401)\) → \((-1,1,e\left(\frac{11}{20}\right),e\left(\frac{1}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 3800 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{143}{180}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{1}{180}\right)\) | \(e\left(\frac{47}{180}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{139}{180}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{89}{90}\right)\) |