Basic properties
| Modulus: | \(3800\) | |
| Conductor: | \(475\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{475}(44,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3800.fd
\(\chi_{3800}(9,\cdot)\) \(\chi_{3800}(169,\cdot)\) \(\chi_{3800}(289,\cdot)\) \(\chi_{3800}(329,\cdot)\) \(\chi_{3800}(529,\cdot)\) \(\chi_{3800}(689,\cdot)\) \(\chi_{3800}(769,\cdot)\) \(\chi_{3800}(929,\cdot)\) \(\chi_{3800}(1089,\cdot)\) \(\chi_{3800}(1289,\cdot)\) \(\chi_{3800}(1529,\cdot)\) \(\chi_{3800}(1689,\cdot)\) \(\chi_{3800}(1809,\cdot)\) \(\chi_{3800}(2209,\cdot)\) \(\chi_{3800}(2289,\cdot)\) \(\chi_{3800}(2569,\cdot)\) \(\chi_{3800}(2609,\cdot)\) \(\chi_{3800}(2809,\cdot)\) \(\chi_{3800}(2969,\cdot)\) \(\chi_{3800}(3209,\cdot)\) \(\chi_{3800}(3329,\cdot)\) \(\chi_{3800}(3369,\cdot)\) \(\chi_{3800}(3569,\cdot)\) \(\chi_{3800}(3729,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((951,1901,1977,401)\) → \((1,1,e\left(\frac{9}{10}\right),e\left(\frac{7}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3800 }(3369, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{41}{90}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{1}{45}\right)\) |