Basic properties
Modulus: | \(1792\) | |
Conductor: | \(896\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(96\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{896}(205,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1792.by
\(\chi_{1792}(9,\cdot)\) \(\chi_{1792}(25,\cdot)\) \(\chi_{1792}(121,\cdot)\) \(\chi_{1792}(137,\cdot)\) \(\chi_{1792}(233,\cdot)\) \(\chi_{1792}(249,\cdot)\) \(\chi_{1792}(345,\cdot)\) \(\chi_{1792}(361,\cdot)\) \(\chi_{1792}(457,\cdot)\) \(\chi_{1792}(473,\cdot)\) \(\chi_{1792}(569,\cdot)\) \(\chi_{1792}(585,\cdot)\) \(\chi_{1792}(681,\cdot)\) \(\chi_{1792}(697,\cdot)\) \(\chi_{1792}(793,\cdot)\) \(\chi_{1792}(809,\cdot)\) \(\chi_{1792}(905,\cdot)\) \(\chi_{1792}(921,\cdot)\) \(\chi_{1792}(1017,\cdot)\) \(\chi_{1792}(1033,\cdot)\) \(\chi_{1792}(1129,\cdot)\) \(\chi_{1792}(1145,\cdot)\) \(\chi_{1792}(1241,\cdot)\) \(\chi_{1792}(1257,\cdot)\) \(\chi_{1792}(1353,\cdot)\) \(\chi_{1792}(1369,\cdot)\) \(\chi_{1792}(1465,\cdot)\) \(\chi_{1792}(1481,\cdot)\) \(\chi_{1792}(1577,\cdot)\) \(\chi_{1792}(1593,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{96})$ |
Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((1023,1541,1025)\) → \((1,e\left(\frac{31}{32}\right),e\left(\frac{1}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 1792 }(1577, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{96}\right)\) | \(e\left(\frac{61}{96}\right)\) | \(e\left(\frac{23}{48}\right)\) | \(e\left(\frac{65}{96}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{91}{96}\right)\) | \(e\left(\frac{11}{48}\right)\) | \(e\left(\frac{13}{48}\right)\) |