Basic properties
| Modulus: | \(1870\) | |
| Conductor: | \(935\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{935}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1870.cn
\(\chi_{1870}(37,\cdot)\) \(\chi_{1870}(97,\cdot)\) \(\chi_{1870}(113,\cdot)\) \(\chi_{1870}(163,\cdot)\) \(\chi_{1870}(207,\cdot)\) \(\chi_{1870}(267,\cdot)\) \(\chi_{1870}(313,\cdot)\) \(\chi_{1870}(333,\cdot)\) \(\chi_{1870}(377,\cdot)\) \(\chi_{1870}(533,\cdot)\) \(\chi_{1870}(653,\cdot)\) \(\chi_{1870}(823,\cdot)\) \(\chi_{1870}(873,\cdot)\) \(\chi_{1870}(993,\cdot)\) \(\chi_{1870}(1017,\cdot)\) \(\chi_{1870}(1043,\cdot)\) \(\chi_{1870}(1127,\cdot)\) \(\chi_{1870}(1213,\cdot)\) \(\chi_{1870}(1303,\cdot)\) \(\chi_{1870}(1357,\cdot)\) \(\chi_{1870}(1457,\cdot)\) \(\chi_{1870}(1467,\cdot)\) \(\chi_{1870}(1523,\cdot)\) \(\chi_{1870}(1527,\cdot)\) \(\chi_{1870}(1567,\cdot)\) \(\chi_{1870}(1637,\cdot)\) \(\chi_{1870}(1643,\cdot)\) \(\chi_{1870}(1697,\cdot)\) \(\chi_{1870}(1797,\cdot)\) \(\chi_{1870}(1807,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1497,1531,1431)\) → \((i,e\left(\frac{1}{5}\right),e\left(\frac{1}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 1870 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{80}\right)\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(-i\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{19}{80}\right)\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{61}{80}\right)\) |