Basic properties
Modulus: | \(5776\) | |
Conductor: | \(5776\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(76\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5776.bv
\(\chi_{5776}(77,\cdot)\) \(\chi_{5776}(229,\cdot)\) \(\chi_{5776}(381,\cdot)\) \(\chi_{5776}(533,\cdot)\) \(\chi_{5776}(685,\cdot)\) \(\chi_{5776}(837,\cdot)\) \(\chi_{5776}(989,\cdot)\) \(\chi_{5776}(1141,\cdot)\) \(\chi_{5776}(1293,\cdot)\) \(\chi_{5776}(1597,\cdot)\) \(\chi_{5776}(1749,\cdot)\) \(\chi_{5776}(1901,\cdot)\) \(\chi_{5776}(2053,\cdot)\) \(\chi_{5776}(2205,\cdot)\) \(\chi_{5776}(2357,\cdot)\) \(\chi_{5776}(2509,\cdot)\) \(\chi_{5776}(2661,\cdot)\) \(\chi_{5776}(2813,\cdot)\) \(\chi_{5776}(2965,\cdot)\) \(\chi_{5776}(3117,\cdot)\) \(\chi_{5776}(3269,\cdot)\) \(\chi_{5776}(3421,\cdot)\) \(\chi_{5776}(3573,\cdot)\) \(\chi_{5776}(3725,\cdot)\) \(\chi_{5776}(3877,\cdot)\) \(\chi_{5776}(4029,\cdot)\) \(\chi_{5776}(4181,\cdot)\) \(\chi_{5776}(4485,\cdot)\) \(\chi_{5776}(4637,\cdot)\) \(\chi_{5776}(4789,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{76})$ |
Fixed field: | Number field defined by a degree 76 polynomial |
Values on generators
\((5055,1445,2529)\) → \((1,-i,e\left(\frac{14}{19}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 5776 }(77, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{76}\right)\) | \(e\left(\frac{53}{76}\right)\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{13}{38}\right)\) | \(e\left(\frac{69}{76}\right)\) | \(e\left(\frac{51}{76}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{53}{76}\right)\) | \(e\left(\frac{3}{38}\right)\) |