Basic properties
Modulus: | \(837\) | |
Conductor: | \(837\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(90\) | 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 837.cf
\(\chi_{837}(11,\cdot)\) \(\chi_{837}(83,\cdot)\) \(\chi_{837}(86,\cdot)\) \(\chi_{837}(137,\cdot)\) \(\chi_{837}(146,\cdot)\) \(\chi_{837}(158,\cdot)\) \(\chi_{837}(167,\cdot)\) \(\chi_{837}(203,\cdot)\) \(\chi_{837}(290,\cdot)\) \(\chi_{837}(362,\cdot)\) \(\chi_{837}(365,\cdot)\) \(\chi_{837}(416,\cdot)\) \(\chi_{837}(425,\cdot)\) \(\chi_{837}(437,\cdot)\) \(\chi_{837}(446,\cdot)\) \(\chi_{837}(482,\cdot)\) \(\chi_{837}(569,\cdot)\) \(\chi_{837}(641,\cdot)\) \(\chi_{837}(644,\cdot)\) \(\chi_{837}(695,\cdot)\) \(\chi_{837}(704,\cdot)\) \(\chi_{837}(716,\cdot)\) \(\chi_{837}(725,\cdot)\) \(\chi_{837}(761,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((218,406)\) → \((e\left(\frac{13}{18}\right),e\left(\frac{17}{30}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 837 }(146, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{13}{45}\right)\) |