Basic properties
Modulus: | \(4608\) | |
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 \(\chi_{768}(491,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4608.bu
\(\chi_{4608}(71,\cdot)\) \(\chi_{4608}(215,\cdot)\) \(\chi_{4608}(359,\cdot)\) \(\chi_{4608}(503,\cdot)\) \(\chi_{4608}(647,\cdot)\) \(\chi_{4608}(791,\cdot)\) \(\chi_{4608}(935,\cdot)\) \(\chi_{4608}(1079,\cdot)\) \(\chi_{4608}(1223,\cdot)\) \(\chi_{4608}(1367,\cdot)\) \(\chi_{4608}(1511,\cdot)\) \(\chi_{4608}(1655,\cdot)\) \(\chi_{4608}(1799,\cdot)\) \(\chi_{4608}(1943,\cdot)\) \(\chi_{4608}(2087,\cdot)\) \(\chi_{4608}(2231,\cdot)\) \(\chi_{4608}(2375,\cdot)\) \(\chi_{4608}(2519,\cdot)\) \(\chi_{4608}(2663,\cdot)\) \(\chi_{4608}(2807,\cdot)\) \(\chi_{4608}(2951,\cdot)\) \(\chi_{4608}(3095,\cdot)\) \(\chi_{4608}(3239,\cdot)\) \(\chi_{4608}(3383,\cdot)\) \(\chi_{4608}(3527,\cdot)\) \(\chi_{4608}(3671,\cdot)\) \(\chi_{4608}(3815,\cdot)\) \(\chi_{4608}(3959,\cdot)\) \(\chi_{4608}(4103,\cdot)\) \(\chi_{4608}(4247,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{64})$ |
Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((3583,2053,4097)\) → \((-1,e\left(\frac{45}{64}\right),-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 4608 }(71, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{64}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{49}{64}\right)\) | \(e\left(\frac{3}{64}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{43}{64}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{63}{64}\right)\) | \(e\left(\frac{1}{8}\right)\) |