Basic properties
| Modulus: | \(3800\) | |
| Conductor: | \(475\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{475}(302,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3800.fn
\(\chi_{3800}(17,\cdot)\) \(\chi_{3800}(73,\cdot)\) \(\chi_{3800}(137,\cdot)\) \(\chi_{3800}(177,\cdot)\) \(\chi_{3800}(233,\cdot)\) \(\chi_{3800}(313,\cdot)\) \(\chi_{3800}(377,\cdot)\) \(\chi_{3800}(473,\cdot)\) \(\chi_{3800}(537,\cdot)\) \(\chi_{3800}(617,\cdot)\) \(\chi_{3800}(633,\cdot)\) \(\chi_{3800}(777,\cdot)\) \(\chi_{3800}(833,\cdot)\) \(\chi_{3800}(897,\cdot)\) \(\chi_{3800}(937,\cdot)\) \(\chi_{3800}(1073,\cdot)\) \(\chi_{3800}(1137,\cdot)\) \(\chi_{3800}(1233,\cdot)\) \(\chi_{3800}(1297,\cdot)\) \(\chi_{3800}(1353,\cdot)\) \(\chi_{3800}(1377,\cdot)\) \(\chi_{3800}(1537,\cdot)\) \(\chi_{3800}(1697,\cdot)\) \(\chi_{3800}(1753,\cdot)\) \(\chi_{3800}(1833,\cdot)\) \(\chi_{3800}(1897,\cdot)\) \(\chi_{3800}(2113,\cdot)\) \(\chi_{3800}(2137,\cdot)\) \(\chi_{3800}(2153,\cdot)\) \(\chi_{3800}(2297,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((951,1901,1977,401)\) → \((1,1,e\left(\frac{1}{20}\right),e\left(\frac{5}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3800 }(777, a) \) | \(-1\) | \(1\) | \(e\left(\frac{103}{180}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{13}{90}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{131}{180}\right)\) | \(e\left(\frac{37}{180}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{119}{180}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{49}{90}\right)\) |