Basic properties
| Modulus: | \(5225\) | |
| Conductor: | \(475\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{475}(67,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5225.iv
\(\chi_{5225}(67,\cdot)\) \(\chi_{5225}(78,\cdot)\) \(\chi_{5225}(287,\cdot)\) \(\chi_{5225}(298,\cdot)\) \(\chi_{5225}(452,\cdot)\) \(\chi_{5225}(573,\cdot)\) \(\chi_{5225}(903,\cdot)\) \(\chi_{5225}(1002,\cdot)\) \(\chi_{5225}(1112,\cdot)\) \(\chi_{5225}(1123,\cdot)\) \(\chi_{5225}(1288,\cdot)\) \(\chi_{5225}(1497,\cdot)\) \(\chi_{5225}(1552,\cdot)\) \(\chi_{5225}(1827,\cdot)\) \(\chi_{5225}(1838,\cdot)\) \(\chi_{5225}(1948,\cdot)\) \(\chi_{5225}(2047,\cdot)\) \(\chi_{5225}(2333,\cdot)\) \(\chi_{5225}(2377,\cdot)\) \(\chi_{5225}(2388,\cdot)\) \(\chi_{5225}(2542,\cdot)\) \(\chi_{5225}(2597,\cdot)\) \(\chi_{5225}(2663,\cdot)\) \(\chi_{5225}(2872,\cdot)\) \(\chi_{5225}(2883,\cdot)\) \(\chi_{5225}(3092,\cdot)\) \(\chi_{5225}(3202,\cdot)\) \(\chi_{5225}(3213,\cdot)\) \(\chi_{5225}(3378,\cdot)\) \(\chi_{5225}(3422,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((2927,2851,4676)\) → \((e\left(\frac{13}{20}\right),1,e\left(\frac{17}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 5225 }(67, a) \) | \(1\) | \(1\) | \(e\left(\frac{107}{180}\right)\) | \(e\left(\frac{149}{180}\right)\) | \(e\left(\frac{17}{90}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{59}{90}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{13}{180}\right)\) | \(e\left(\frac{23}{45}\right)\) |