Basic properties
| Modulus: | \(4624\) | |
| Conductor: | \(289\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(136\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{289}(111,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4624.ck
\(\chi_{4624}(49,\cdot)\) \(\chi_{4624}(145,\cdot)\) \(\chi_{4624}(161,\cdot)\) \(\chi_{4624}(257,\cdot)\) \(\chi_{4624}(321,\cdot)\) \(\chi_{4624}(417,\cdot)\) \(\chi_{4624}(433,\cdot)\) \(\chi_{4624}(529,\cdot)\) \(\chi_{4624}(593,\cdot)\) \(\chi_{4624}(689,\cdot)\) \(\chi_{4624}(705,\cdot)\) \(\chi_{4624}(801,\cdot)\) \(\chi_{4624}(865,\cdot)\) \(\chi_{4624}(961,\cdot)\) \(\chi_{4624}(1073,\cdot)\) \(\chi_{4624}(1137,\cdot)\) \(\chi_{4624}(1233,\cdot)\) \(\chi_{4624}(1249,\cdot)\) \(\chi_{4624}(1345,\cdot)\) \(\chi_{4624}(1409,\cdot)\) \(\chi_{4624}(1505,\cdot)\) \(\chi_{4624}(1521,\cdot)\) \(\chi_{4624}(1617,\cdot)\) \(\chi_{4624}(1681,\cdot)\) \(\chi_{4624}(1777,\cdot)\) \(\chi_{4624}(1793,\cdot)\) \(\chi_{4624}(1953,\cdot)\) \(\chi_{4624}(2049,\cdot)\) \(\chi_{4624}(2065,\cdot)\) \(\chi_{4624}(2161,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{136})$ |
| Fixed field: | Number field defined by a degree 136 polynomial (not computed) |
Values on generators
\((4047,1157,4049)\) → \((1,1,e\left(\frac{65}{136}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 4624 }(689, a) \) | \(1\) | \(1\) | \(e\left(\frac{65}{136}\right)\) | \(e\left(\frac{61}{136}\right)\) | \(e\left(\frac{11}{136}\right)\) | \(e\left(\frac{65}{68}\right)\) | \(e\left(\frac{135}{136}\right)\) | \(e\left(\frac{23}{34}\right)\) | \(e\left(\frac{63}{68}\right)\) | \(e\left(\frac{47}{68}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{79}{136}\right)\) |