Basic properties
Modulus: | \(4275\) | |
Conductor: | \(4275\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(90\) | 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 4275.gn
\(\chi_{4275}(454,\cdot)\) \(\chi_{4275}(484,\cdot)\) \(\chi_{4275}(709,\cdot)\) \(\chi_{4275}(814,\cdot)\) \(\chi_{4275}(1309,\cdot)\) \(\chi_{4275}(1339,\cdot)\) \(\chi_{4275}(1354,\cdot)\) \(\chi_{4275}(1429,\cdot)\) \(\chi_{4275}(1564,\cdot)\) \(\chi_{4275}(1669,\cdot)\) \(\chi_{4275}(2164,\cdot)\) \(\chi_{4275}(2194,\cdot)\) \(\chi_{4275}(2209,\cdot)\) \(\chi_{4275}(2284,\cdot)\) \(\chi_{4275}(2419,\cdot)\) \(\chi_{4275}(3019,\cdot)\) \(\chi_{4275}(3064,\cdot)\) \(\chi_{4275}(3139,\cdot)\) \(\chi_{4275}(3379,\cdot)\) \(\chi_{4275}(3904,\cdot)\) \(\chi_{4275}(3919,\cdot)\) \(\chi_{4275}(3994,\cdot)\) \(\chi_{4275}(4129,\cdot)\) \(\chi_{4275}(4234,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((1901,1027,1351)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{1}{10}\right),e\left(\frac{5}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
\( \chi_{ 4275 }(454, a) \) | \(1\) | \(1\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{53}{90}\right)\) |