Basic properties
| Modulus: | \(6534\) | |
| Conductor: | \(3267\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(990\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3267}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6534.bt
\(\chi_{6534}(29,\cdot)\) \(\chi_{6534}(41,\cdot)\) \(\chi_{6534}(83,\cdot)\) \(\chi_{6534}(95,\cdot)\) \(\chi_{6534}(101,\cdot)\) \(\chi_{6534}(149,\cdot)\) \(\chi_{6534}(167,\cdot)\) \(\chi_{6534}(173,\cdot)\) \(\chi_{6534}(227,\cdot)\) \(\chi_{6534}(281,\cdot)\) \(\chi_{6534}(293,\cdot)\) \(\chi_{6534}(299,\cdot)\) \(\chi_{6534}(347,\cdot)\) \(\chi_{6534}(365,\cdot)\) \(\chi_{6534}(371,\cdot)\) \(\chi_{6534}(425,\cdot)\) \(\chi_{6534}(437,\cdot)\) \(\chi_{6534}(479,\cdot)\) \(\chi_{6534}(491,\cdot)\) \(\chi_{6534}(497,\cdot)\) \(\chi_{6534}(545,\cdot)\) \(\chi_{6534}(563,\cdot)\) \(\chi_{6534}(569,\cdot)\) \(\chi_{6534}(623,\cdot)\) \(\chi_{6534}(635,\cdot)\) \(\chi_{6534}(677,\cdot)\) \(\chi_{6534}(689,\cdot)\) \(\chi_{6534}(695,\cdot)\) \(\chi_{6534}(743,\cdot)\) \(\chi_{6534}(761,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{495})$ |
| Fixed field: | Number field defined by a degree 990 polynomial (not computed) |
Values on generators
\((6293,3511)\) → \((e\left(\frac{1}{18}\right),e\left(\frac{17}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 6534 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{707}{990}\right)\) | \(e\left(\frac{961}{990}\right)\) | \(e\left(\frac{53}{990}\right)\) | \(e\left(\frac{67}{165}\right)\) | \(e\left(\frac{163}{330}\right)\) | \(e\left(\frac{85}{198}\right)\) | \(e\left(\frac{212}{495}\right)\) | \(e\left(\frac{338}{495}\right)\) | \(e\left(\frac{199}{495}\right)\) | \(e\left(\frac{113}{165}\right)\) |