Basic properties
Modulus: | \(9450\) | |
Conductor: | \(4725\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{4725}(4279,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9450.gu
\(\chi_{9450}(529,\cdot)\) \(\chi_{9450}(1129,\cdot)\) \(\chi_{9450}(1159,\cdot)\) \(\chi_{9450}(1759,\cdot)\) \(\chi_{9450}(1789,\cdot)\) \(\chi_{9450}(2389,\cdot)\) \(\chi_{9450}(2419,\cdot)\) \(\chi_{9450}(3019,\cdot)\) \(\chi_{9450}(3679,\cdot)\) \(\chi_{9450}(4279,\cdot)\) \(\chi_{9450}(4309,\cdot)\) \(\chi_{9450}(4909,\cdot)\) \(\chi_{9450}(4939,\cdot)\) \(\chi_{9450}(5539,\cdot)\) \(\chi_{9450}(5569,\cdot)\) \(\chi_{9450}(6169,\cdot)\) \(\chi_{9450}(6829,\cdot)\) \(\chi_{9450}(7429,\cdot)\) \(\chi_{9450}(7459,\cdot)\) \(\chi_{9450}(8059,\cdot)\) \(\chi_{9450}(8089,\cdot)\) \(\chi_{9450}(8689,\cdot)\) \(\chi_{9450}(8719,\cdot)\) \(\chi_{9450}(9319,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((9101,6427,6751)\) → \((e\left(\frac{4}{9}\right),e\left(\frac{1}{10}\right),e\left(\frac{1}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 9450 }(4279, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{41}{90}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{59}{90}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{5}{18}\right)\) |