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 \(\chi_{608}(269,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1216.cd
\(\chi_{1216}(41,\cdot)\) \(\chi_{1216}(89,\cdot)\) \(\chi_{1216}(105,\cdot)\) \(\chi_{1216}(185,\cdot)\) \(\chi_{1216}(249,\cdot)\) \(\chi_{1216}(281,\cdot)\) \(\chi_{1216}(345,\cdot)\) \(\chi_{1216}(393,\cdot)\) \(\chi_{1216}(409,\cdot)\) \(\chi_{1216}(489,\cdot)\) \(\chi_{1216}(553,\cdot)\) \(\chi_{1216}(585,\cdot)\) \(\chi_{1216}(649,\cdot)\) \(\chi_{1216}(697,\cdot)\) \(\chi_{1216}(713,\cdot)\) \(\chi_{1216}(793,\cdot)\) \(\chi_{1216}(857,\cdot)\) \(\chi_{1216}(889,\cdot)\) \(\chi_{1216}(953,\cdot)\) \(\chi_{1216}(1001,\cdot)\) \(\chi_{1216}(1017,\cdot)\) \(\chi_{1216}(1097,\cdot)\) \(\chi_{1216}(1161,\cdot)\) \(\chi_{1216}(1193,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((191,837,705)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{13}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 1216 }(41, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{72}\right)\) | \(e\left(\frac{31}{72}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{53}{72}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{7}{72}\right)\) | \(e\left(\frac{25}{36}\right)\) |