Basic properties
Modulus: | \(5776\) | |
Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(171\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{361}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5776.ce
\(\chi_{5776}(17,\cdot)\) \(\chi_{5776}(81,\cdot)\) \(\chi_{5776}(161,\cdot)\) \(\chi_{5776}(177,\cdot)\) \(\chi_{5776}(225,\cdot)\) \(\chi_{5776}(289,\cdot)\) \(\chi_{5776}(321,\cdot)\) \(\chi_{5776}(385,\cdot)\) \(\chi_{5776}(465,\cdot)\) \(\chi_{5776}(481,\cdot)\) \(\chi_{5776}(529,\cdot)\) \(\chi_{5776}(593,\cdot)\) \(\chi_{5776}(625,\cdot)\) \(\chi_{5776}(689,\cdot)\) \(\chi_{5776}(769,\cdot)\) \(\chi_{5776}(785,\cdot)\) \(\chi_{5776}(833,\cdot)\) \(\chi_{5776}(897,\cdot)\) \(\chi_{5776}(929,\cdot)\) \(\chi_{5776}(993,\cdot)\) \(\chi_{5776}(1073,\cdot)\) \(\chi_{5776}(1089,\cdot)\) \(\chi_{5776}(1201,\cdot)\) \(\chi_{5776}(1233,\cdot)\) \(\chi_{5776}(1297,\cdot)\) \(\chi_{5776}(1377,\cdot)\) \(\chi_{5776}(1393,\cdot)\) \(\chi_{5776}(1441,\cdot)\) \(\chi_{5776}(1505,\cdot)\) \(\chi_{5776}(1537,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{171})$ |
Fixed field: | Number field defined by a degree 171 polynomial (not computed) |
Values on generators
\((5055,1445,2529)\) → \((1,1,e\left(\frac{113}{171}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 5776 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{146}{171}\right)\) | \(e\left(\frac{53}{171}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{121}{171}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{70}{171}\right)\) | \(e\left(\frac{28}{171}\right)\) | \(e\left(\frac{59}{171}\right)\) | \(e\left(\frac{167}{171}\right)\) | \(e\left(\frac{82}{171}\right)\) |