Basic properties
Modulus: | \(1024\) | |
Conductor: | \(256\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(64\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{256}(163,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1024.n
\(\chi_{1024}(15,\cdot)\) \(\chi_{1024}(47,\cdot)\) \(\chi_{1024}(79,\cdot)\) \(\chi_{1024}(111,\cdot)\) \(\chi_{1024}(143,\cdot)\) \(\chi_{1024}(175,\cdot)\) \(\chi_{1024}(207,\cdot)\) \(\chi_{1024}(239,\cdot)\) \(\chi_{1024}(271,\cdot)\) \(\chi_{1024}(303,\cdot)\) \(\chi_{1024}(335,\cdot)\) \(\chi_{1024}(367,\cdot)\) \(\chi_{1024}(399,\cdot)\) \(\chi_{1024}(431,\cdot)\) \(\chi_{1024}(463,\cdot)\) \(\chi_{1024}(495,\cdot)\) \(\chi_{1024}(527,\cdot)\) \(\chi_{1024}(559,\cdot)\) \(\chi_{1024}(591,\cdot)\) \(\chi_{1024}(623,\cdot)\) \(\chi_{1024}(655,\cdot)\) \(\chi_{1024}(687,\cdot)\) \(\chi_{1024}(719,\cdot)\) \(\chi_{1024}(751,\cdot)\) \(\chi_{1024}(783,\cdot)\) \(\chi_{1024}(815,\cdot)\) \(\chi_{1024}(847,\cdot)\) \(\chi_{1024}(879,\cdot)\) \(\chi_{1024}(911,\cdot)\) \(\chi_{1024}(943,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{64})$ |
Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((1023,5)\) → \((-1,e\left(\frac{43}{64}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 1024 }(47, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{64}\right)\) | \(e\left(\frac{43}{64}\right)\) | \(e\left(\frac{7}{32}\right)\) | \(e\left(\frac{1}{32}\right)\) | \(e\left(\frac{39}{64}\right)\) | \(e\left(\frac{37}{64}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{15}{64}\right)\) |