Basic properties
Modulus: | \(5225\) | |
Conductor: | \(475\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(45\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{475}(111,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5225.ga
\(\chi_{5225}(111,\cdot)\) \(\chi_{5225}(386,\cdot)\) \(\chi_{5225}(441,\cdot)\) \(\chi_{5225}(606,\cdot)\) \(\chi_{5225}(936,\cdot)\) \(\chi_{5225}(1156,\cdot)\) \(\chi_{5225}(1431,\cdot)\) \(\chi_{5225}(1486,\cdot)\) \(\chi_{5225}(1871,\cdot)\) \(\chi_{5225}(1981,\cdot)\) \(\chi_{5225}(2531,\cdot)\) \(\chi_{5225}(2696,\cdot)\) \(\chi_{5225}(2916,\cdot)\) \(\chi_{5225}(3246,\cdot)\) \(\chi_{5225}(3521,\cdot)\) \(\chi_{5225}(3741,\cdot)\) \(\chi_{5225}(3961,\cdot)\) \(\chi_{5225}(4071,\cdot)\) \(\chi_{5225}(4291,\cdot)\) \(\chi_{5225}(4566,\cdot)\) \(\chi_{5225}(4621,\cdot)\) \(\chi_{5225}(4786,\cdot)\) \(\chi_{5225}(5006,\cdot)\) \(\chi_{5225}(5116,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((2927,2851,4676)\) → \((e\left(\frac{4}{5}\right),1,e\left(\frac{2}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
\( \chi_{ 5225 }(111, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{16}{45}\right)\) |