Basic properties
| Modulus: | \(5225\) | |
| Conductor: | \(209\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(45\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{209}(42,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5225.gc
\(\chi_{5225}(251,\cdot)\) \(\chi_{5225}(301,\cdot)\) \(\chi_{5225}(576,\cdot)\) \(\chi_{5225}(1126,\cdot)\) \(\chi_{5225}(1301,\cdot)\) \(\chi_{5225}(1676,\cdot)\) \(\chi_{5225}(1776,\cdot)\) \(\chi_{5225}(2126,\cdot)\) \(\chi_{5225}(2601,\cdot)\) \(\chi_{5225}(2676,\cdot)\) \(\chi_{5225}(2726,\cdot)\) \(\chi_{5225}(2951,\cdot)\) \(\chi_{5225}(3151,\cdot)\) \(\chi_{5225}(3426,\cdot)\) \(\chi_{5225}(3501,\cdot)\) \(\chi_{5225}(3551,\cdot)\) \(\chi_{5225}(3976,\cdot)\) \(\chi_{5225}(4051,\cdot)\) \(\chi_{5225}(4101,\cdot)\) \(\chi_{5225}(4151,\cdot)\) \(\chi_{5225}(4376,\cdot)\) \(\chi_{5225}(4526,\cdot)\) \(\chi_{5225}(4926,\cdot)\) \(\chi_{5225}(4976,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | 45.45.43679806300610465846484971330073185012597520004657724600953543350870941304329239684756561.1 |
Values on generators
\((2927,2851,4676)\) → \((1,e\left(\frac{3}{5}\right),e\left(\frac{1}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 5225 }(251, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{26}{45}\right)\) |