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 \(\chi_{1617}(8,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4851.ew
\(\chi_{4851}(8,\cdot)\) \(\chi_{4851}(134,\cdot)\) \(\chi_{4851}(260,\cdot)\) \(\chi_{4851}(512,\cdot)\) \(\chi_{4851}(701,\cdot)\) \(\chi_{4851}(827,\cdot)\) \(\chi_{4851}(953,\cdot)\) \(\chi_{4851}(1205,\cdot)\) \(\chi_{4851}(1394,\cdot)\) \(\chi_{4851}(1646,\cdot)\) \(\chi_{4851}(1898,\cdot)\) \(\chi_{4851}(2087,\cdot)\) \(\chi_{4851}(2213,\cdot)\) \(\chi_{4851}(2339,\cdot)\) \(\chi_{4851}(2591,\cdot)\) \(\chi_{4851}(2780,\cdot)\) \(\chi_{4851}(2906,\cdot)\) \(\chi_{4851}(3032,\cdot)\) \(\chi_{4851}(3473,\cdot)\) \(\chi_{4851}(3599,\cdot)\) \(\chi_{4851}(3977,\cdot)\) \(\chi_{4851}(4292,\cdot)\) \(\chi_{4851}(4418,\cdot)\) \(\chi_{4851}(4670,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((4313,199,442)\) → \((-1,e\left(\frac{6}{7}\right),e\left(\frac{3}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 4851 }(8, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{51}{70}\right)\) |