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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 837.cg
\(\chi_{837}(2,\cdot)\) \(\chi_{837}(47,\cdot)\) \(\chi_{837}(95,\cdot)\) \(\chi_{837}(101,\cdot)\) \(\chi_{837}(128,\cdot)\) \(\chi_{837}(140,\cdot)\) \(\chi_{837}(194,\cdot)\) \(\chi_{837}(221,\cdot)\) \(\chi_{837}(281,\cdot)\) \(\chi_{837}(326,\cdot)\) \(\chi_{837}(374,\cdot)\) \(\chi_{837}(380,\cdot)\) \(\chi_{837}(407,\cdot)\) \(\chi_{837}(419,\cdot)\) \(\chi_{837}(473,\cdot)\) \(\chi_{837}(500,\cdot)\) \(\chi_{837}(560,\cdot)\) \(\chi_{837}(605,\cdot)\) \(\chi_{837}(653,\cdot)\) \(\chi_{837}(659,\cdot)\) \(\chi_{837}(686,\cdot)\) \(\chi_{837}(698,\cdot)\) \(\chi_{837}(752,\cdot)\) \(\chi_{837}(779,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((218,406)\) → \((e\left(\frac{17}{18}\right),e\left(\frac{3}{5}\right))\)
Values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 837 }(500, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{17}{45}\right)\) |