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.hu
\(\chi_{5225}(261,\cdot)\) \(\chi_{5225}(281,\cdot)\) \(\chi_{5225}(811,\cdot)\) \(\chi_{5225}(831,\cdot)\) \(\chi_{5225}(1041,\cdot)\) \(\chi_{5225}(1086,\cdot)\) \(\chi_{5225}(1381,\cdot)\) \(\chi_{5225}(1421,\cdot)\) \(\chi_{5225}(1591,\cdot)\) \(\chi_{5225}(1636,\cdot)\) \(\chi_{5225}(1656,\cdot)\) \(\chi_{5225}(1971,\cdot)\) \(\chi_{5225}(2141,\cdot)\) \(\chi_{5225}(2206,\cdot)\) \(\chi_{5225}(2416,\cdot)\) \(\chi_{5225}(2461,\cdot)\) \(\chi_{5225}(2521,\cdot)\) \(\chi_{5225}(2796,\cdot)\) \(\chi_{5225}(2966,\cdot)\) \(\chi_{5225}(3031,\cdot)\) \(\chi_{5225}(3346,\cdot)\) \(\chi_{5225}(3791,\cdot)\) \(\chi_{5225}(4171,\cdot)\) \(\chi_{5225}(4936,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((2927,2851,4676)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{9}{10}\right),e\left(\frac{7}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
\( \chi_{ 5225 }(831, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{29}{90}\right)\) |