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.cd
\(\chi_{837}(38,\cdot)\) \(\chi_{837}(41,\cdot)\) \(\chi_{837}(113,\cdot)\) \(\chi_{837}(200,\cdot)\) \(\chi_{837}(236,\cdot)\) \(\chi_{837}(245,\cdot)\) \(\chi_{837}(257,\cdot)\) \(\chi_{837}(266,\cdot)\) \(\chi_{837}(317,\cdot)\) \(\chi_{837}(320,\cdot)\) \(\chi_{837}(392,\cdot)\) \(\chi_{837}(479,\cdot)\) \(\chi_{837}(515,\cdot)\) \(\chi_{837}(524,\cdot)\) \(\chi_{837}(536,\cdot)\) \(\chi_{837}(545,\cdot)\) \(\chi_{837}(596,\cdot)\) \(\chi_{837}(599,\cdot)\) \(\chi_{837}(671,\cdot)\) \(\chi_{837}(758,\cdot)\) \(\chi_{837}(794,\cdot)\) \(\chi_{837}(803,\cdot)\) \(\chi_{837}(815,\cdot)\) \(\chi_{837}(824,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((218,406)\) → \((e\left(\frac{11}{18}\right),e\left(\frac{13}{15}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 837 }(266, a) \) | \(-1\) | \(1\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{41}{90}\right)\) | \(e\left(\frac{29}{45}\right)\) |