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.cq
\(\chi_{1700}(11,\cdot)\) \(\chi_{1700}(31,\cdot)\) \(\chi_{1700}(71,\cdot)\) \(\chi_{1700}(91,\cdot)\) \(\chi_{1700}(131,\cdot)\) \(\chi_{1700}(211,\cdot)\) \(\chi_{1700}(231,\cdot)\) \(\chi_{1700}(311,\cdot)\) \(\chi_{1700}(371,\cdot)\) \(\chi_{1700}(411,\cdot)\) \(\chi_{1700}(431,\cdot)\) \(\chi_{1700}(471,\cdot)\) \(\chi_{1700}(571,\cdot)\) \(\chi_{1700}(691,\cdot)\) \(\chi_{1700}(711,\cdot)\) \(\chi_{1700}(771,\cdot)\) \(\chi_{1700}(811,\cdot)\) \(\chi_{1700}(891,\cdot)\) \(\chi_{1700}(911,\cdot)\) \(\chi_{1700}(991,\cdot)\) \(\chi_{1700}(1031,\cdot)\) \(\chi_{1700}(1091,\cdot)\) \(\chi_{1700}(1111,\cdot)\) \(\chi_{1700}(1231,\cdot)\) \(\chi_{1700}(1331,\cdot)\) \(\chi_{1700}(1371,\cdot)\) \(\chi_{1700}(1391,\cdot)\) \(\chi_{1700}(1431,\cdot)\) \(\chi_{1700}(1491,\cdot)\) \(\chi_{1700}(1571,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((851,477,1601)\) → \((-1,e\left(\frac{2}{5}\right),e\left(\frac{9}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 1700 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{69}{80}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{47}{80}\right)\) | \(e\left(\frac{9}{80}\right)\) |