Basic properties
Modulus: | \(8281\) | |
Conductor: | \(8281\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(273\) | 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 8281.dr
\(\chi_{8281}(29,\cdot)\) \(\chi_{8281}(113,\cdot)\) \(\chi_{8281}(120,\cdot)\) \(\chi_{8281}(204,\cdot)\) \(\chi_{8281}(211,\cdot)\) \(\chi_{8281}(302,\cdot)\) \(\chi_{8281}(386,\cdot)\) \(\chi_{8281}(477,\cdot)\) \(\chi_{8281}(568,\cdot)\) \(\chi_{8281}(575,\cdot)\) \(\chi_{8281}(659,\cdot)\) \(\chi_{8281}(666,\cdot)\) \(\chi_{8281}(750,\cdot)\) \(\chi_{8281}(757,\cdot)\) \(\chi_{8281}(841,\cdot)\) \(\chi_{8281}(848,\cdot)\) \(\chi_{8281}(939,\cdot)\) \(\chi_{8281}(1023,\cdot)\) \(\chi_{8281}(1114,\cdot)\) \(\chi_{8281}(1121,\cdot)\) \(\chi_{8281}(1212,\cdot)\) \(\chi_{8281}(1296,\cdot)\) \(\chi_{8281}(1303,\cdot)\) \(\chi_{8281}(1387,\cdot)\) \(\chi_{8281}(1394,\cdot)\) \(\chi_{8281}(1478,\cdot)\) \(\chi_{8281}(1485,\cdot)\) \(\chi_{8281}(1576,\cdot)\) \(\chi_{8281}(1660,\cdot)\) \(\chi_{8281}(1751,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{273})$ |
Fixed field: | Number field defined by a degree 273 polynomial (not computed) |
Values on generators
\((1522,3382)\) → \((e\left(\frac{3}{7}\right),e\left(\frac{10}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 8281 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{109}{273}\right)\) | \(e\left(\frac{61}{273}\right)\) | \(e\left(\frac{218}{273}\right)\) | \(e\left(\frac{67}{91}\right)\) | \(e\left(\frac{170}{273}\right)\) | \(e\left(\frac{18}{91}\right)\) | \(e\left(\frac{122}{273}\right)\) | \(e\left(\frac{37}{273}\right)\) | \(e\left(\frac{151}{273}\right)\) | \(e\left(\frac{2}{91}\right)\) |