Basic properties
Modulus: | \(3072\) | |
Conductor: | \(1536\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(128\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1536}(467,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3072.be
\(\chi_{3072}(23,\cdot)\) \(\chi_{3072}(71,\cdot)\) \(\chi_{3072}(119,\cdot)\) \(\chi_{3072}(167,\cdot)\) \(\chi_{3072}(215,\cdot)\) \(\chi_{3072}(263,\cdot)\) \(\chi_{3072}(311,\cdot)\) \(\chi_{3072}(359,\cdot)\) \(\chi_{3072}(407,\cdot)\) \(\chi_{3072}(455,\cdot)\) \(\chi_{3072}(503,\cdot)\) \(\chi_{3072}(551,\cdot)\) \(\chi_{3072}(599,\cdot)\) \(\chi_{3072}(647,\cdot)\) \(\chi_{3072}(695,\cdot)\) \(\chi_{3072}(743,\cdot)\) \(\chi_{3072}(791,\cdot)\) \(\chi_{3072}(839,\cdot)\) \(\chi_{3072}(887,\cdot)\) \(\chi_{3072}(935,\cdot)\) \(\chi_{3072}(983,\cdot)\) \(\chi_{3072}(1031,\cdot)\) \(\chi_{3072}(1079,\cdot)\) \(\chi_{3072}(1127,\cdot)\) \(\chi_{3072}(1175,\cdot)\) \(\chi_{3072}(1223,\cdot)\) \(\chi_{3072}(1271,\cdot)\) \(\chi_{3072}(1319,\cdot)\) \(\chi_{3072}(1367,\cdot)\) \(\chi_{3072}(1415,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{128})$ |
Fixed field: | Number field defined by a degree 128 polynomial (not computed) |
Values on generators
\((2047,2053,1025)\) → \((-1,e\left(\frac{71}{128}\right),-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 3072 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{128}\right)\) | \(e\left(\frac{35}{64}\right)\) | \(e\left(\frac{19}{128}\right)\) | \(e\left(\frac{73}{128}\right)\) | \(e\left(\frac{1}{32}\right)\) | \(e\left(\frac{33}{128}\right)\) | \(e\left(\frac{49}{64}\right)\) | \(e\left(\frac{7}{64}\right)\) | \(e\left(\frac{93}{128}\right)\) | \(e\left(\frac{15}{16}\right)\) |