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 \(\chi_{512}(157,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3072.bd
\(\chi_{3072}(25,\cdot)\) \(\chi_{3072}(73,\cdot)\) \(\chi_{3072}(121,\cdot)\) \(\chi_{3072}(169,\cdot)\) \(\chi_{3072}(217,\cdot)\) \(\chi_{3072}(265,\cdot)\) \(\chi_{3072}(313,\cdot)\) \(\chi_{3072}(361,\cdot)\) \(\chi_{3072}(409,\cdot)\) \(\chi_{3072}(457,\cdot)\) \(\chi_{3072}(505,\cdot)\) \(\chi_{3072}(553,\cdot)\) \(\chi_{3072}(601,\cdot)\) \(\chi_{3072}(649,\cdot)\) \(\chi_{3072}(697,\cdot)\) \(\chi_{3072}(745,\cdot)\) \(\chi_{3072}(793,\cdot)\) \(\chi_{3072}(841,\cdot)\) \(\chi_{3072}(889,\cdot)\) \(\chi_{3072}(937,\cdot)\) \(\chi_{3072}(985,\cdot)\) \(\chi_{3072}(1033,\cdot)\) \(\chi_{3072}(1081,\cdot)\) \(\chi_{3072}(1129,\cdot)\) \(\chi_{3072}(1177,\cdot)\) \(\chi_{3072}(1225,\cdot)\) \(\chi_{3072}(1273,\cdot)\) \(\chi_{3072}(1321,\cdot)\) \(\chi_{3072}(1369,\cdot)\) \(\chi_{3072}(1417,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{128})$ |
Fixed field: | Number field defined by a degree 128 polynomial (not computed) |
Values on generators
\((2047,2053,1025)\) → \((1,e\left(\frac{91}{128}\right),1)\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 3072 }(73, a) \) | \(1\) | \(1\) | \(e\left(\frac{91}{128}\right)\) | \(e\left(\frac{39}{64}\right)\) | \(e\left(\frac{55}{128}\right)\) | \(e\left(\frac{117}{128}\right)\) | \(e\left(\frac{29}{32}\right)\) | \(e\left(\frac{45}{128}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{27}{64}\right)\) | \(e\left(\frac{57}{128}\right)\) | \(e\left(\frac{11}{16}\right)\) |