Basic properties
| Modulus: | \(1870\) | |
| Conductor: | \(187\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{187}(40,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1870.co
\(\chi_{1870}(41,\cdot)\) \(\chi_{1870}(61,\cdot)\) \(\chi_{1870}(211,\cdot)\) \(\chi_{1870}(261,\cdot)\) \(\chi_{1870}(371,\cdot)\) \(\chi_{1870}(381,\cdot)\) \(\chi_{1870}(431,\cdot)\) \(\chi_{1870}(481,\cdot)\) \(\chi_{1870}(541,\cdot)\) \(\chi_{1870}(601,\cdot)\) \(\chi_{1870}(651,\cdot)\) \(\chi_{1870}(711,\cdot)\) \(\chi_{1870}(721,\cdot)\) \(\chi_{1870}(811,\cdot)\) \(\chi_{1870}(821,\cdot)\) \(\chi_{1870}(921,\cdot)\) \(\chi_{1870}(941,\cdot)\) \(\chi_{1870}(981,\cdot)\) \(\chi_{1870}(1031,\cdot)\) \(\chi_{1870}(1051,\cdot)\) \(\chi_{1870}(1091,\cdot)\) \(\chi_{1870}(1151,\cdot)\) \(\chi_{1870}(1161,\cdot)\) \(\chi_{1870}(1201,\cdot)\) \(\chi_{1870}(1251,\cdot)\) \(\chi_{1870}(1261,\cdot)\) \(\chi_{1870}(1371,\cdot)\) \(\chi_{1870}(1421,\cdot)\) \(\chi_{1870}(1491,\cdot)\) \(\chi_{1870}(1591,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1497,1531,1431)\) → \((1,e\left(\frac{7}{10}\right),e\left(\frac{15}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 1870 }(601, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{17}{80}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(-i\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{51}{80}\right)\) |