Basic properties
Modulus: | \(5225\) | |
Conductor: | \(5225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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 5225.is
\(\chi_{5225}(21,\cdot)\) \(\chi_{5225}(186,\cdot)\) \(\chi_{5225}(241,\cdot)\) \(\chi_{5225}(516,\cdot)\) \(\chi_{5225}(736,\cdot)\) \(\chi_{5225}(846,\cdot)\) \(\chi_{5225}(1066,\cdot)\) \(\chi_{5225}(1231,\cdot)\) \(\chi_{5225}(1286,\cdot)\) \(\chi_{5225}(1561,\cdot)\) \(\chi_{5225}(1781,\cdot)\) \(\chi_{5225}(1891,\cdot)\) \(\chi_{5225}(2111,\cdot)\) \(\chi_{5225}(2331,\cdot)\) \(\chi_{5225}(2606,\cdot)\) \(\chi_{5225}(2936,\cdot)\) \(\chi_{5225}(3156,\cdot)\) \(\chi_{5225}(3321,\cdot)\) \(\chi_{5225}(3871,\cdot)\) \(\chi_{5225}(3981,\cdot)\) \(\chi_{5225}(4366,\cdot)\) \(\chi_{5225}(4421,\cdot)\) \(\chi_{5225}(4696,\cdot)\) \(\chi_{5225}(4916,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((2927,2851,4676)\) → \((e\left(\frac{3}{5}\right),-1,e\left(\frac{1}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
\( \chi_{ 5225 }(21, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{89}{90}\right)\) |