Basic properties
| Modulus: | \(7168\) | |
| 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 \(\chi_{256}(133,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7168.bs
\(\chi_{7168}(113,\cdot)\) \(\chi_{7168}(337,\cdot)\) \(\chi_{7168}(561,\cdot)\) \(\chi_{7168}(785,\cdot)\) \(\chi_{7168}(1009,\cdot)\) \(\chi_{7168}(1233,\cdot)\) \(\chi_{7168}(1457,\cdot)\) \(\chi_{7168}(1681,\cdot)\) \(\chi_{7168}(1905,\cdot)\) \(\chi_{7168}(2129,\cdot)\) \(\chi_{7168}(2353,\cdot)\) \(\chi_{7168}(2577,\cdot)\) \(\chi_{7168}(2801,\cdot)\) \(\chi_{7168}(3025,\cdot)\) \(\chi_{7168}(3249,\cdot)\) \(\chi_{7168}(3473,\cdot)\) \(\chi_{7168}(3697,\cdot)\) \(\chi_{7168}(3921,\cdot)\) \(\chi_{7168}(4145,\cdot)\) \(\chi_{7168}(4369,\cdot)\) \(\chi_{7168}(4593,\cdot)\) \(\chi_{7168}(4817,\cdot)\) \(\chi_{7168}(5041,\cdot)\) \(\chi_{7168}(5265,\cdot)\) \(\chi_{7168}(5489,\cdot)\) \(\chi_{7168}(5713,\cdot)\) \(\chi_{7168}(5937,\cdot)\) \(\chi_{7168}(6161,\cdot)\) \(\chi_{7168}(6385,\cdot)\) \(\chi_{7168}(6609,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((1023,5125,1025)\) → \((1,e\left(\frac{33}{64}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 7168 }(113, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{64}\right)\) | \(e\left(\frac{33}{64}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{53}{64}\right)\) | \(e\left(\frac{15}{64}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{55}{64}\right)\) | \(e\left(\frac{7}{32}\right)\) | \(e\left(\frac{1}{32}\right)\) |