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.ce
\(\chi_{837}(65,\cdot)\) \(\chi_{837}(74,\cdot)\) \(\chi_{837}(104,\cdot)\) \(\chi_{837}(110,\cdot)\) \(\chi_{837}(176,\cdot)\) \(\chi_{837}(230,\cdot)\) \(\chi_{837}(239,\cdot)\) \(\chi_{837}(272,\cdot)\) \(\chi_{837}(344,\cdot)\) \(\chi_{837}(353,\cdot)\) \(\chi_{837}(383,\cdot)\) \(\chi_{837}(389,\cdot)\) \(\chi_{837}(455,\cdot)\) \(\chi_{837}(509,\cdot)\) \(\chi_{837}(518,\cdot)\) \(\chi_{837}(551,\cdot)\) \(\chi_{837}(623,\cdot)\) \(\chi_{837}(632,\cdot)\) \(\chi_{837}(662,\cdot)\) \(\chi_{837}(668,\cdot)\) \(\chi_{837}(734,\cdot)\) \(\chi_{837}(788,\cdot)\) \(\chi_{837}(797,\cdot)\) \(\chi_{837}(830,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((218,406)\) → \((e\left(\frac{17}{18}\right),e\left(\frac{23}{30}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 837 }(662, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{17}{45}\right)\) |