Basic properties
| Modulus: | \(5225\) | |
| Conductor: | \(5225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(45\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| 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.ge
\(\chi_{5225}(16,\cdot)\) \(\chi_{5225}(256,\cdot)\) \(\chi_{5225}(291,\cdot)\) \(\chi_{5225}(636,\cdot)\) \(\chi_{5225}(796,\cdot)\) \(\chi_{5225}(841,\cdot)\) \(\chi_{5225}(1081,\cdot)\) \(\chi_{5225}(1346,\cdot)\) \(\chi_{5225}(1391,\cdot)\) \(\chi_{5225}(1461,\cdot)\) \(\chi_{5225}(1621,\cdot)\) \(\chi_{5225}(1631,\cdot)\) \(\chi_{5225}(1906,\cdot)\) \(\chi_{5225}(2011,\cdot)\) \(\chi_{5225}(2171,\cdot)\) \(\chi_{5225}(2286,\cdot)\) \(\chi_{5225}(2456,\cdot)\) \(\chi_{5225}(2721,\cdot)\) \(\chi_{5225}(2836,\cdot)\) \(\chi_{5225}(3006,\cdot)\) \(\chi_{5225}(3386,\cdot)\) \(\chi_{5225}(3866,\cdot)\) \(\chi_{5225}(4691,\cdot)\) \(\chi_{5225}(5196,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((2927,2851,4676)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{2}{5}\right),e\left(\frac{2}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 5225 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{43}{45}\right)\) |