Basic properties
| Modulus: | \(4011\) | |
| Conductor: | \(4011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(570\) | 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 4011.ci
\(\chi_{4011}(2,\cdot)\) \(\chi_{4011}(23,\cdot)\) \(\chi_{4011}(65,\cdot)\) \(\chi_{4011}(86,\cdot)\) \(\chi_{4011}(128,\cdot)\) \(\chi_{4011}(149,\cdot)\) \(\chi_{4011}(158,\cdot)\) \(\chi_{4011}(170,\cdot)\) \(\chi_{4011}(200,\cdot)\) \(\chi_{4011}(242,\cdot)\) \(\chi_{4011}(263,\cdot)\) \(\chi_{4011}(326,\cdot)\) \(\chi_{4011}(338,\cdot)\) \(\chi_{4011}(347,\cdot)\) \(\chi_{4011}(422,\cdot)\) \(\chi_{4011}(485,\cdot)\) \(\chi_{4011}(515,\cdot)\) \(\chi_{4011}(590,\cdot)\) \(\chi_{4011}(599,\cdot)\) \(\chi_{4011}(632,\cdot)\) \(\chi_{4011}(641,\cdot)\) \(\chi_{4011}(653,\cdot)\) \(\chi_{4011}(767,\cdot)\) \(\chi_{4011}(779,\cdot)\) \(\chi_{4011}(788,\cdot)\) \(\chi_{4011}(809,\cdot)\) \(\chi_{4011}(842,\cdot)\) \(\chi_{4011}(872,\cdot)\) \(\chi_{4011}(884,\cdot)\) \(\chi_{4011}(893,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{285})$ |
| Fixed field: | Number field defined by a degree 570 polynomial (not computed) |
Values on generators
\((2675,2866,2311)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{86}{95}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 4011 }(515, a) \) | \(-1\) | \(1\) | \(e\left(\frac{379}{570}\right)\) | \(e\left(\frac{94}{285}\right)\) | \(e\left(\frac{11}{114}\right)\) | \(e\left(\frac{189}{190}\right)\) | \(e\left(\frac{217}{285}\right)\) | \(e\left(\frac{13}{114}\right)\) | \(e\left(\frac{37}{95}\right)\) | \(e\left(\frac{188}{285}\right)\) | \(e\left(\frac{503}{570}\right)\) | \(e\left(\frac{68}{285}\right)\) |