Basic properties
| Modulus: | \(2805\) | |
| Conductor: | \(2805\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | 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 2805.fl
\(\chi_{2805}(107,\cdot)\) \(\chi_{2805}(167,\cdot)\) \(\chi_{2805}(182,\cdot)\) \(\chi_{2805}(248,\cdot)\) \(\chi_{2805}(398,\cdot)\) \(\chi_{2805}(437,\cdot)\) \(\chi_{2805}(503,\cdot)\) \(\chi_{2805}(623,\cdot)\) \(\chi_{2805}(677,\cdot)\) \(\chi_{2805}(788,\cdot)\) \(\chi_{2805}(887,\cdot)\) \(\chi_{2805}(908,\cdot)\) \(\chi_{2805}(932,\cdot)\) \(\chi_{2805}(1163,\cdot)\) \(\chi_{2805}(1382,\cdot)\) \(\chi_{2805}(1388,\cdot)\) \(\chi_{2805}(1553,\cdot)\) \(\chi_{2805}(1652,\cdot)\) \(\chi_{2805}(1712,\cdot)\) \(\chi_{2805}(1778,\cdot)\) \(\chi_{2805}(1898,\cdot)\) \(\chi_{2805}(2063,\cdot)\) \(\chi_{2805}(2147,\cdot)\) \(\chi_{2805}(2153,\cdot)\) \(\chi_{2805}(2162,\cdot)\) \(\chi_{2805}(2207,\cdot)\) \(\chi_{2805}(2318,\cdot)\) \(\chi_{2805}(2417,\cdot)\) \(\chi_{2805}(2438,\cdot)\) \(\chi_{2805}(2477,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1871,562,1531,496)\) → \((-1,-i,e\left(\frac{9}{10}\right),e\left(\frac{15}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(19\) | \(23\) | \(26\) |
| \( \chi_{ 2805 }(2063, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{7}{40}\right)\) |