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 \(\chi_{4725}(11,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9450.gv
\(\chi_{9450}(11,\cdot)\) \(\chi_{9450}(641,\cdot)\) \(\chi_{9450}(1031,\cdot)\) \(\chi_{9450}(1271,\cdot)\) \(\chi_{9450}(1661,\cdot)\) \(\chi_{9450}(2291,\cdot)\) \(\chi_{9450}(2531,\cdot)\) \(\chi_{9450}(2921,\cdot)\) \(\chi_{9450}(3161,\cdot)\) \(\chi_{9450}(3791,\cdot)\) \(\chi_{9450}(4181,\cdot)\) \(\chi_{9450}(4421,\cdot)\) \(\chi_{9450}(4811,\cdot)\) \(\chi_{9450}(5441,\cdot)\) \(\chi_{9450}(5681,\cdot)\) \(\chi_{9450}(6071,\cdot)\) \(\chi_{9450}(6311,\cdot)\) \(\chi_{9450}(6941,\cdot)\) \(\chi_{9450}(7331,\cdot)\) \(\chi_{9450}(7571,\cdot)\) \(\chi_{9450}(7961,\cdot)\) \(\chi_{9450}(8591,\cdot)\) \(\chi_{9450}(8831,\cdot)\) \(\chi_{9450}(9221,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((9101,6427,6751)\) → \((e\left(\frac{13}{18}\right),e\left(\frac{4}{5}\right),e\left(\frac{2}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 9450 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{8}{9}\right)\) |