Basic properties
Modulus: | \(9450\) | |
Conductor: | \(4725\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4725}(4646,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9450.go
\(\chi_{9450}(311,\cdot)\) \(\chi_{9450}(941,\cdot)\) \(\chi_{9450}(1181,\cdot)\) \(\chi_{9450}(1571,\cdot)\) \(\chi_{9450}(1811,\cdot)\) \(\chi_{9450}(2441,\cdot)\) \(\chi_{9450}(2831,\cdot)\) \(\chi_{9450}(3071,\cdot)\) \(\chi_{9450}(3461,\cdot)\) \(\chi_{9450}(4091,\cdot)\) \(\chi_{9450}(4331,\cdot)\) \(\chi_{9450}(4721,\cdot)\) \(\chi_{9450}(4961,\cdot)\) \(\chi_{9450}(5591,\cdot)\) \(\chi_{9450}(5981,\cdot)\) \(\chi_{9450}(6221,\cdot)\) \(\chi_{9450}(6611,\cdot)\) \(\chi_{9450}(7241,\cdot)\) \(\chi_{9450}(7481,\cdot)\) \(\chi_{9450}(7871,\cdot)\) \(\chi_{9450}(8111,\cdot)\) \(\chi_{9450}(8741,\cdot)\) \(\chi_{9450}(9131,\cdot)\) \(\chi_{9450}(9371,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((9101,6427,6751)\) → \((e\left(\frac{1}{18}\right),e\left(\frac{3}{5}\right),e\left(\frac{5}{6}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 9450 }(9371, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{90}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{2}{9}\right)\) |