Basic properties
| Modulus: | \(4335\) | |
| Conductor: | \(867\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(272\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{867}(311,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4335.cp
\(\chi_{4335}(11,\cdot)\) \(\chi_{4335}(41,\cdot)\) \(\chi_{4335}(56,\cdot)\) \(\chi_{4335}(71,\cdot)\) \(\chi_{4335}(116,\cdot)\) \(\chi_{4335}(146,\cdot)\) \(\chi_{4335}(176,\cdot)\) \(\chi_{4335}(266,\cdot)\) \(\chi_{4335}(296,\cdot)\) \(\chi_{4335}(311,\cdot)\) \(\chi_{4335}(326,\cdot)\) \(\chi_{4335}(371,\cdot)\) \(\chi_{4335}(386,\cdot)\) \(\chi_{4335}(401,\cdot)\) \(\chi_{4335}(431,\cdot)\) \(\chi_{4335}(521,\cdot)\) \(\chi_{4335}(551,\cdot)\) \(\chi_{4335}(566,\cdot)\) \(\chi_{4335}(581,\cdot)\) \(\chi_{4335}(626,\cdot)\) \(\chi_{4335}(641,\cdot)\) \(\chi_{4335}(656,\cdot)\) \(\chi_{4335}(686,\cdot)\) \(\chi_{4335}(776,\cdot)\) \(\chi_{4335}(806,\cdot)\) \(\chi_{4335}(821,\cdot)\) \(\chi_{4335}(836,\cdot)\) \(\chi_{4335}(881,\cdot)\) \(\chi_{4335}(896,\cdot)\) \(\chi_{4335}(911,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{272})$ |
| Fixed field: | Number field defined by a degree 272 polynomial (not computed) |
Values on generators
\((2891,2602,2026)\) → \((-1,1,e\left(\frac{213}{272}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(19\) | \(22\) |
| \( \chi_{ 4335 }(311, a) \) | \(1\) | \(1\) | \(e\left(\frac{39}{136}\right)\) | \(e\left(\frac{39}{68}\right)\) | \(e\left(\frac{103}{272}\right)\) | \(e\left(\frac{117}{136}\right)\) | \(e\left(\frac{139}{272}\right)\) | \(e\left(\frac{33}{68}\right)\) | \(e\left(\frac{181}{272}\right)\) | \(e\left(\frac{5}{34}\right)\) | \(e\left(\frac{131}{136}\right)\) | \(e\left(\frac{217}{272}\right)\) |