Basic properties
Modulus: | \(779\) | |
Conductor: | \(779\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(45\) | 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 779.bi
\(\chi_{779}(16,\cdot)\) \(\chi_{779}(92,\cdot)\) \(\chi_{779}(100,\cdot)\) \(\chi_{779}(119,\cdot)\) \(\chi_{779}(139,\cdot)\) \(\chi_{779}(180,\cdot)\) \(\chi_{779}(215,\cdot)\) \(\chi_{779}(256,\cdot)\) \(\chi_{779}(264,\cdot)\) \(\chi_{779}(283,\cdot)\) \(\chi_{779}(346,\cdot)\) \(\chi_{779}(365,\cdot)\) \(\chi_{779}(385,\cdot)\) \(\chi_{779}(461,\cdot)\) \(\chi_{779}(510,\cdot)\) \(\chi_{779}(529,\cdot)\) \(\chi_{779}(549,\cdot)\) \(\chi_{779}(625,\cdot)\) \(\chi_{779}(631,\cdot)\) \(\chi_{779}(633,\cdot)\) \(\chi_{779}(652,\cdot)\) \(\chi_{779}(674,\cdot)\) \(\chi_{779}(693,\cdot)\) \(\chi_{779}(707,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((534,457)\) → \((e\left(\frac{1}{9}\right),e\left(\frac{4}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 779 }(365, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{11}{15}\right)\) |