Basic properties
| Modulus: | \(1700\) | |
| Conductor: | \(1700\) | 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 1700.cp
\(\chi_{1700}(39,\cdot)\) \(\chi_{1700}(79,\cdot)\) \(\chi_{1700}(139,\cdot)\) \(\chi_{1700}(159,\cdot)\) \(\chi_{1700}(279,\cdot)\) \(\chi_{1700}(379,\cdot)\) \(\chi_{1700}(419,\cdot)\) \(\chi_{1700}(439,\cdot)\) \(\chi_{1700}(479,\cdot)\) \(\chi_{1700}(539,\cdot)\) \(\chi_{1700}(619,\cdot)\) \(\chi_{1700}(639,\cdot)\) \(\chi_{1700}(719,\cdot)\) \(\chi_{1700}(759,\cdot)\) \(\chi_{1700}(779,\cdot)\) \(\chi_{1700}(819,\cdot)\) \(\chi_{1700}(839,\cdot)\) \(\chi_{1700}(879,\cdot)\) \(\chi_{1700}(959,\cdot)\) \(\chi_{1700}(979,\cdot)\) \(\chi_{1700}(1059,\cdot)\) \(\chi_{1700}(1119,\cdot)\) \(\chi_{1700}(1159,\cdot)\) \(\chi_{1700}(1179,\cdot)\) \(\chi_{1700}(1219,\cdot)\) \(\chi_{1700}(1319,\cdot)\) \(\chi_{1700}(1439,\cdot)\) \(\chi_{1700}(1459,\cdot)\) \(\chi_{1700}(1519,\cdot)\) \(\chi_{1700}(1559,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((851,477,1601)\) → \((-1,e\left(\frac{1}{10}\right),e\left(\frac{9}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 1700 }(779, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{3}{80}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{3}{80}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{41}{80}\right)\) |