Basic properties
| Modulus: | \(4851\) | |
| Conductor: | \(1617\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1617}(125,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4851.eu
\(\chi_{4851}(125,\cdot)\) \(\chi_{4851}(251,\cdot)\) \(\chi_{4851}(377,\cdot)\) \(\chi_{4851}(566,\cdot)\) \(\chi_{4851}(818,\cdot)\) \(\chi_{4851}(944,\cdot)\) \(\chi_{4851}(1070,\cdot)\) \(\chi_{4851}(1259,\cdot)\) \(\chi_{4851}(1511,\cdot)\) \(\chi_{4851}(1637,\cdot)\) \(\chi_{4851}(1952,\cdot)\) \(\chi_{4851}(2330,\cdot)\) \(\chi_{4851}(2456,\cdot)\) \(\chi_{4851}(2897,\cdot)\) \(\chi_{4851}(3023,\cdot)\) \(\chi_{4851}(3149,\cdot)\) \(\chi_{4851}(3338,\cdot)\) \(\chi_{4851}(3590,\cdot)\) \(\chi_{4851}(3716,\cdot)\) \(\chi_{4851}(3842,\cdot)\) \(\chi_{4851}(4031,\cdot)\) \(\chi_{4851}(4283,\cdot)\) \(\chi_{4851}(4535,\cdot)\) \(\chi_{4851}(4724,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((4313,199,442)\) → \((-1,e\left(\frac{1}{14}\right),e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 4851 }(125, a) \) | \(1\) | \(1\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{17}{35}\right)\) |