Basic properties
| Modulus: | \(4335\) | |
| Conductor: | \(4335\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(272\) | 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 4335.cn
\(\chi_{4335}(23,\cdot)\) \(\chi_{4335}(107,\cdot)\) \(\chi_{4335}(113,\cdot)\) \(\chi_{4335}(122,\cdot)\) \(\chi_{4335}(143,\cdot)\) \(\chi_{4335}(167,\cdot)\) \(\chi_{4335}(182,\cdot)\) \(\chi_{4335}(248,\cdot)\) \(\chi_{4335}(278,\cdot)\) \(\chi_{4335}(362,\cdot)\) \(\chi_{4335}(368,\cdot)\) \(\chi_{4335}(377,\cdot)\) \(\chi_{4335}(398,\cdot)\) \(\chi_{4335}(422,\cdot)\) \(\chi_{4335}(437,\cdot)\) \(\chi_{4335}(533,\cdot)\) \(\chi_{4335}(617,\cdot)\) \(\chi_{4335}(623,\cdot)\) \(\chi_{4335}(632,\cdot)\) \(\chi_{4335}(677,\cdot)\) \(\chi_{4335}(692,\cdot)\) \(\chi_{4335}(758,\cdot)\) \(\chi_{4335}(788,\cdot)\) \(\chi_{4335}(872,\cdot)\) \(\chi_{4335}(878,\cdot)\) \(\chi_{4335}(887,\cdot)\) \(\chi_{4335}(908,\cdot)\) \(\chi_{4335}(947,\cdot)\) \(\chi_{4335}(1013,\cdot)\) \(\chi_{4335}(1043,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{272})$ |
| Fixed field: | Number field defined by a degree 272 polynomial (not computed) |
Values on generators
\((2891,2602,2026)\) → \((-1,-i,e\left(\frac{43}{272}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(19\) | \(22\) |
| \( \chi_{ 4335 }(2948, a) \) | \(-1\) | \(1\) | \(e\left(\frac{39}{136}\right)\) | \(e\left(\frac{39}{68}\right)\) | \(e\left(\frac{69}{272}\right)\) | \(e\left(\frac{117}{136}\right)\) | \(e\left(\frac{37}{272}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{147}{272}\right)\) | \(e\left(\frac{5}{34}\right)\) | \(e\left(\frac{97}{136}\right)\) | \(e\left(\frac{115}{272}\right)\) |