Basic properties
| Modulus: | \(3072\) | |
| 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 \(\chi_{256}(235,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3072.bb
\(\chi_{3072}(79,\cdot)\) \(\chi_{3072}(175,\cdot)\) \(\chi_{3072}(271,\cdot)\) \(\chi_{3072}(367,\cdot)\) \(\chi_{3072}(463,\cdot)\) \(\chi_{3072}(559,\cdot)\) \(\chi_{3072}(655,\cdot)\) \(\chi_{3072}(751,\cdot)\) \(\chi_{3072}(847,\cdot)\) \(\chi_{3072}(943,\cdot)\) \(\chi_{3072}(1039,\cdot)\) \(\chi_{3072}(1135,\cdot)\) \(\chi_{3072}(1231,\cdot)\) \(\chi_{3072}(1327,\cdot)\) \(\chi_{3072}(1423,\cdot)\) \(\chi_{3072}(1519,\cdot)\) \(\chi_{3072}(1615,\cdot)\) \(\chi_{3072}(1711,\cdot)\) \(\chi_{3072}(1807,\cdot)\) \(\chi_{3072}(1903,\cdot)\) \(\chi_{3072}(1999,\cdot)\) \(\chi_{3072}(2095,\cdot)\) \(\chi_{3072}(2191,\cdot)\) \(\chi_{3072}(2287,\cdot)\) \(\chi_{3072}(2383,\cdot)\) \(\chi_{3072}(2479,\cdot)\) \(\chi_{3072}(2575,\cdot)\) \(\chi_{3072}(2671,\cdot)\) \(\chi_{3072}(2767,\cdot)\) \(\chi_{3072}(2863,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((2047,2053,1025)\) → \((-1,e\left(\frac{45}{64}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 3072 }(79, a) \) | \(-1\) | \(1\) | \(e\left(\frac{45}{64}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{17}{64}\right)\) | \(e\left(\frac{3}{64}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{43}{64}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{31}{64}\right)\) | \(e\left(\frac{1}{8}\right)\) |