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 \(\chi_{608}(403,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1216.cc
\(\chi_{1216}(23,\cdot)\) \(\chi_{1216}(55,\cdot)\) \(\chi_{1216}(119,\cdot)\) \(\chi_{1216}(199,\cdot)\) \(\chi_{1216}(215,\cdot)\) \(\chi_{1216}(263,\cdot)\) \(\chi_{1216}(327,\cdot)\) \(\chi_{1216}(359,\cdot)\) \(\chi_{1216}(423,\cdot)\) \(\chi_{1216}(503,\cdot)\) \(\chi_{1216}(519,\cdot)\) \(\chi_{1216}(567,\cdot)\) \(\chi_{1216}(631,\cdot)\) \(\chi_{1216}(663,\cdot)\) \(\chi_{1216}(727,\cdot)\) \(\chi_{1216}(807,\cdot)\) \(\chi_{1216}(823,\cdot)\) \(\chi_{1216}(871,\cdot)\) \(\chi_{1216}(935,\cdot)\) \(\chi_{1216}(967,\cdot)\) \(\chi_{1216}(1031,\cdot)\) \(\chi_{1216}(1111,\cdot)\) \(\chi_{1216}(1127,\cdot)\) \(\chi_{1216}(1175,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((191,837,705)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{1}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 1216 }(23, a) \) | \(-1\) | \(1\) | \(e\left(\frac{41}{72}\right)\) | \(e\left(\frac{47}{72}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{49}{72}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{35}{72}\right)\) | \(e\left(\frac{35}{36}\right)\) |