Basic properties
Modulus: | \(1216\) | |
Conductor: | \(608\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{608}(517,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1216.ca
\(\chi_{1216}(9,\cdot)\) \(\chi_{1216}(25,\cdot)\) \(\chi_{1216}(73,\cdot)\) \(\chi_{1216}(137,\cdot)\) \(\chi_{1216}(169,\cdot)\) \(\chi_{1216}(233,\cdot)\) \(\chi_{1216}(313,\cdot)\) \(\chi_{1216}(329,\cdot)\) \(\chi_{1216}(377,\cdot)\) \(\chi_{1216}(441,\cdot)\) \(\chi_{1216}(473,\cdot)\) \(\chi_{1216}(537,\cdot)\) \(\chi_{1216}(617,\cdot)\) \(\chi_{1216}(633,\cdot)\) \(\chi_{1216}(681,\cdot)\) \(\chi_{1216}(745,\cdot)\) \(\chi_{1216}(777,\cdot)\) \(\chi_{1216}(841,\cdot)\) \(\chi_{1216}(921,\cdot)\) \(\chi_{1216}(937,\cdot)\) \(\chi_{1216}(985,\cdot)\) \(\chi_{1216}(1049,\cdot)\) \(\chi_{1216}(1081,\cdot)\) \(\chi_{1216}(1145,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{72})$ |
Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((191,837,705)\) → \((1,e\left(\frac{1}{8}\right),e\left(\frac{1}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 1216 }(1049, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{72}\right)\) | \(e\left(\frac{65}{72}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{31}{72}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{53}{72}\right)\) | \(e\left(\frac{35}{36}\right)\) |