Basic properties
Modulus: | \(1648\) | |
Conductor: | \(103\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(102\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{103}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1648.bo
\(\chi_{1648}(65,\cdot)\) \(\chi_{1648}(177,\cdot)\) \(\chi_{1648}(241,\cdot)\) \(\chi_{1648}(257,\cdot)\) \(\chi_{1648}(273,\cdot)\) \(\chi_{1648}(305,\cdot)\) \(\chi_{1648}(321,\cdot)\) \(\chi_{1648}(353,\cdot)\) \(\chi_{1648}(417,\cdot)\) \(\chi_{1648}(433,\cdot)\) \(\chi_{1648}(465,\cdot)\) \(\chi_{1648}(497,\cdot)\) \(\chi_{1648}(513,\cdot)\) \(\chi_{1648}(577,\cdot)\) \(\chi_{1648}(593,\cdot)\) \(\chi_{1648}(689,\cdot)\) \(\chi_{1648}(705,\cdot)\) \(\chi_{1648}(769,\cdot)\) \(\chi_{1648}(817,\cdot)\) \(\chi_{1648}(1041,\cdot)\) \(\chi_{1648}(1073,\cdot)\) \(\chi_{1648}(1105,\cdot)\) \(\chi_{1648}(1153,\cdot)\) \(\chi_{1648}(1217,\cdot)\) \(\chi_{1648}(1281,\cdot)\) \(\chi_{1648}(1313,\cdot)\) \(\chi_{1648}(1345,\cdot)\) \(\chi_{1648}(1393,\cdot)\) \(\chi_{1648}(1409,\cdot)\) \(\chi_{1648}(1425,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{51})$ |
Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((207,1237,417)\) → \((1,1,e\left(\frac{1}{102}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 1648 }(417, a) \) | \(-1\) | \(1\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{1}{102}\right)\) | \(e\left(\frac{2}{51}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{61}{102}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{20}{51}\right)\) | \(e\left(\frac{35}{51}\right)\) | \(e\left(\frac{40}{51}\right)\) | \(e\left(\frac{43}{102}\right)\) |