Basic properties
| Modulus: | \(3800\) | |
| Conductor: | \(3800\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3800.fh
\(\chi_{3800}(13,\cdot)\) \(\chi_{3800}(53,\cdot)\) \(\chi_{3800}(117,\cdot)\) \(\chi_{3800}(173,\cdot)\) \(\chi_{3800}(317,\cdot)\) \(\chi_{3800}(333,\cdot)\) \(\chi_{3800}(413,\cdot)\) \(\chi_{3800}(477,\cdot)\) \(\chi_{3800}(573,\cdot)\) \(\chi_{3800}(637,\cdot)\) \(\chi_{3800}(717,\cdot)\) \(\chi_{3800}(773,\cdot)\) \(\chi_{3800}(813,\cdot)\) \(\chi_{3800}(877,\cdot)\) \(\chi_{3800}(933,\cdot)\) \(\chi_{3800}(1077,\cdot)\) \(\chi_{3800}(1117,\cdot)\) \(\chi_{3800}(1173,\cdot)\) \(\chi_{3800}(1237,\cdot)\) \(\chi_{3800}(1333,\cdot)\) \(\chi_{3800}(1397,\cdot)\) \(\chi_{3800}(1477,\cdot)\) \(\chi_{3800}(1533,\cdot)\) \(\chi_{3800}(1573,\cdot)\) \(\chi_{3800}(1637,\cdot)\) \(\chi_{3800}(1837,\cdot)\) \(\chi_{3800}(1853,\cdot)\) \(\chi_{3800}(1877,\cdot)\) \(\chi_{3800}(1933,\cdot)\) \(\chi_{3800}(1997,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((951,1901,1977,401)\) → \((1,-1,e\left(\frac{19}{20}\right),e\left(\frac{5}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3800 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{137}{180}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{169}{180}\right)\) | \(e\left(\frac{23}{180}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{1}{180}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{11}{90}\right)\) |