Basic properties
| Modulus: | \(3072\) | |
| Conductor: | \(512\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(128\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{512}(163,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3072.bc
\(\chi_{3072}(7,\cdot)\) \(\chi_{3072}(55,\cdot)\) \(\chi_{3072}(103,\cdot)\) \(\chi_{3072}(151,\cdot)\) \(\chi_{3072}(199,\cdot)\) \(\chi_{3072}(247,\cdot)\) \(\chi_{3072}(295,\cdot)\) \(\chi_{3072}(343,\cdot)\) \(\chi_{3072}(391,\cdot)\) \(\chi_{3072}(439,\cdot)\) \(\chi_{3072}(487,\cdot)\) \(\chi_{3072}(535,\cdot)\) \(\chi_{3072}(583,\cdot)\) \(\chi_{3072}(631,\cdot)\) \(\chi_{3072}(679,\cdot)\) \(\chi_{3072}(727,\cdot)\) \(\chi_{3072}(775,\cdot)\) \(\chi_{3072}(823,\cdot)\) \(\chi_{3072}(871,\cdot)\) \(\chi_{3072}(919,\cdot)\) \(\chi_{3072}(967,\cdot)\) \(\chi_{3072}(1015,\cdot)\) \(\chi_{3072}(1063,\cdot)\) \(\chi_{3072}(1111,\cdot)\) \(\chi_{3072}(1159,\cdot)\) \(\chi_{3072}(1207,\cdot)\) \(\chi_{3072}(1255,\cdot)\) \(\chi_{3072}(1303,\cdot)\) \(\chi_{3072}(1351,\cdot)\) \(\chi_{3072}(1399,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{128})$ |
| Fixed field: | Number field defined by a degree 128 polynomial (not computed) |
Values on generators
\((2047,2053,1025)\) → \((-1,e\left(\frac{107}{128}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 3072 }(55, a) \) | \(-1\) | \(1\) | \(e\left(\frac{107}{128}\right)\) | \(e\left(\frac{23}{64}\right)\) | \(e\left(\frac{71}{128}\right)\) | \(e\left(\frac{101}{128}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{93}{128}\right)\) | \(e\left(\frac{13}{64}\right)\) | \(e\left(\frac{43}{64}\right)\) | \(e\left(\frac{105}{128}\right)\) | \(e\left(\frac{3}{16}\right)\) |