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 \(\chi_{896}(395,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1792.bx
\(\chi_{1792}(87,\cdot)\) \(\chi_{1792}(103,\cdot)\) \(\chi_{1792}(199,\cdot)\) \(\chi_{1792}(215,\cdot)\) \(\chi_{1792}(311,\cdot)\) \(\chi_{1792}(327,\cdot)\) \(\chi_{1792}(423,\cdot)\) \(\chi_{1792}(439,\cdot)\) \(\chi_{1792}(535,\cdot)\) \(\chi_{1792}(551,\cdot)\) \(\chi_{1792}(647,\cdot)\) \(\chi_{1792}(663,\cdot)\) \(\chi_{1792}(759,\cdot)\) \(\chi_{1792}(775,\cdot)\) \(\chi_{1792}(871,\cdot)\) \(\chi_{1792}(887,\cdot)\) \(\chi_{1792}(983,\cdot)\) \(\chi_{1792}(999,\cdot)\) \(\chi_{1792}(1095,\cdot)\) \(\chi_{1792}(1111,\cdot)\) \(\chi_{1792}(1207,\cdot)\) \(\chi_{1792}(1223,\cdot)\) \(\chi_{1792}(1319,\cdot)\) \(\chi_{1792}(1335,\cdot)\) \(\chi_{1792}(1431,\cdot)\) \(\chi_{1792}(1447,\cdot)\) \(\chi_{1792}(1543,\cdot)\) \(\chi_{1792}(1559,\cdot)\) \(\chi_{1792}(1655,\cdot)\) \(\chi_{1792}(1671,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{96})$ |
Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((1023,1541,1025)\) → \((-1,e\left(\frac{21}{32}\right),e\left(\frac{1}{6}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 1792 }(647, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{96}\right)\) | \(e\left(\frac{47}{96}\right)\) | \(e\left(\frac{13}{48}\right)\) | \(e\left(\frac{91}{96}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{41}{96}\right)\) | \(e\left(\frac{1}{48}\right)\) | \(e\left(\frac{47}{48}\right)\) |