Basic properties
Modulus: | \(3072\) | |
Conductor: | \(768\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(64\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{768}(419,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3072.ba
\(\chi_{3072}(47,\cdot)\) \(\chi_{3072}(143,\cdot)\) \(\chi_{3072}(239,\cdot)\) \(\chi_{3072}(335,\cdot)\) \(\chi_{3072}(431,\cdot)\) \(\chi_{3072}(527,\cdot)\) \(\chi_{3072}(623,\cdot)\) \(\chi_{3072}(719,\cdot)\) \(\chi_{3072}(815,\cdot)\) \(\chi_{3072}(911,\cdot)\) \(\chi_{3072}(1007,\cdot)\) \(\chi_{3072}(1103,\cdot)\) \(\chi_{3072}(1199,\cdot)\) \(\chi_{3072}(1295,\cdot)\) \(\chi_{3072}(1391,\cdot)\) \(\chi_{3072}(1487,\cdot)\) \(\chi_{3072}(1583,\cdot)\) \(\chi_{3072}(1679,\cdot)\) \(\chi_{3072}(1775,\cdot)\) \(\chi_{3072}(1871,\cdot)\) \(\chi_{3072}(1967,\cdot)\) \(\chi_{3072}(2063,\cdot)\) \(\chi_{3072}(2159,\cdot)\) \(\chi_{3072}(2255,\cdot)\) \(\chi_{3072}(2351,\cdot)\) \(\chi_{3072}(2447,\cdot)\) \(\chi_{3072}(2543,\cdot)\) \(\chi_{3072}(2639,\cdot)\) \(\chi_{3072}(2735,\cdot)\) \(\chi_{3072}(2831,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{64})$ |
Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((2047,2053,1025)\) → \((-1,e\left(\frac{43}{64}\right),-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 3072 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{64}\right)\) | \(e\left(\frac{7}{32}\right)\) | \(e\left(\frac{7}{64}\right)\) | \(e\left(\frac{37}{64}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{9}{64}\right)\) | \(e\left(\frac{7}{8}\right)\) |