Basic properties
| Modulus: | \(4275\) | |
| 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 \(\chi_{475}(244,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4275.gp
\(\chi_{4275}(244,\cdot)\) \(\chi_{4275}(289,\cdot)\) \(\chi_{4275}(739,\cdot)\) \(\chi_{4275}(784,\cdot)\) \(\chi_{4275}(1054,\cdot)\) \(\chi_{4275}(1144,\cdot)\) \(\chi_{4275}(1279,\cdot)\) \(\chi_{4275}(1594,\cdot)\) \(\chi_{4275}(1639,\cdot)\) \(\chi_{4275}(1909,\cdot)\) \(\chi_{4275}(1954,\cdot)\) \(\chi_{4275}(2134,\cdot)\) \(\chi_{4275}(2494,\cdot)\) \(\chi_{4275}(2764,\cdot)\) \(\chi_{4275}(2809,\cdot)\) \(\chi_{4275}(2854,\cdot)\) \(\chi_{4275}(2989,\cdot)\) \(\chi_{4275}(3304,\cdot)\) \(\chi_{4275}(3619,\cdot)\) \(\chi_{4275}(3664,\cdot)\) \(\chi_{4275}(3709,\cdot)\) \(\chi_{4275}(3844,\cdot)\) \(\chi_{4275}(4159,\cdot)\) \(\chi_{4275}(4204,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((1901,1027,1351)\) → \((1,e\left(\frac{9}{10}\right),e\left(\frac{2}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
| \( \chi_{ 4275 }(244, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{17}{90}\right)\) |