Basic properties
Modulus: | \(803\) | |
Conductor: | \(803\) | 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 803.bi
\(\chi_{803}(4,\cdot)\) \(\chi_{803}(16,\cdot)\) \(\chi_{803}(37,\cdot)\) \(\chi_{803}(75,\cdot)\) \(\chi_{803}(148,\cdot)\) \(\chi_{803}(201,\cdot)\) \(\chi_{803}(223,\cdot)\) \(\chi_{803}(235,\cdot)\) \(\chi_{803}(251,\cdot)\) \(\chi_{803}(256,\cdot)\) \(\chi_{803}(324,\cdot)\) \(\chi_{803}(367,\cdot)\) \(\chi_{803}(454,\cdot)\) \(\chi_{803}(493,\cdot)\) \(\chi_{803}(515,\cdot)\) \(\chi_{803}(543,\cdot)\) \(\chi_{803}(548,\cdot)\) \(\chi_{803}(566,\cdot)\) \(\chi_{803}(586,\cdot)\) \(\chi_{803}(588,\cdot)\) \(\chi_{803}(621,\cdot)\) \(\chi_{803}(746,\cdot)\) \(\chi_{803}(762,\cdot)\) \(\chi_{803}(785,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((585,78)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{1}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 803 }(586, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(1\) | \(e\left(\frac{4}{9}\right)\) |