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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2805.ez
\(\chi_{2805}(113,\cdot)\) \(\chi_{2805}(278,\cdot)\) \(\chi_{2805}(368,\cdot)\) \(\chi_{2805}(377,\cdot)\) \(\chi_{2805}(422,\cdot)\) \(\chi_{2805}(533,\cdot)\) \(\chi_{2805}(632,\cdot)\) \(\chi_{2805}(653,\cdot)\) \(\chi_{2805}(872,\cdot)\) \(\chi_{2805}(878,\cdot)\) \(\chi_{2805}(1043,\cdot)\) \(\chi_{2805}(1127,\cdot)\) \(\chi_{2805}(1142,\cdot)\) \(\chi_{2805}(1202,\cdot)\) \(\chi_{2805}(1268,\cdot)\) \(\chi_{2805}(1457,\cdot)\) \(\chi_{2805}(1523,\cdot)\) \(\chi_{2805}(1637,\cdot)\) \(\chi_{2805}(1643,\cdot)\) \(\chi_{2805}(1697,\cdot)\) \(\chi_{2805}(1808,\cdot)\) \(\chi_{2805}(1907,\cdot)\) \(\chi_{2805}(1928,\cdot)\) \(\chi_{2805}(1952,\cdot)\) \(\chi_{2805}(1967,\cdot)\) \(\chi_{2805}(2033,\cdot)\) \(\chi_{2805}(2183,\cdot)\) \(\chi_{2805}(2402,\cdot)\) \(\chi_{2805}(2462,\cdot)\) \(\chi_{2805}(2693,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1871,562,1531,496)\) → \((-1,i,e\left(\frac{3}{5}\right),e\left(\frac{5}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(19\) | \(23\) | \(26\) |
| \( \chi_{ 2805 }(1637, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{71}{80}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{13}{40}\right)\) |