Basic properties
| Modulus: | \(7168\) | |
| Conductor: | \(7168\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(256\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7168.ci
\(\chi_{7168}(27,\cdot)\) \(\chi_{7168}(83,\cdot)\) \(\chi_{7168}(139,\cdot)\) \(\chi_{7168}(195,\cdot)\) \(\chi_{7168}(251,\cdot)\) \(\chi_{7168}(307,\cdot)\) \(\chi_{7168}(363,\cdot)\) \(\chi_{7168}(419,\cdot)\) \(\chi_{7168}(475,\cdot)\) \(\chi_{7168}(531,\cdot)\) \(\chi_{7168}(587,\cdot)\) \(\chi_{7168}(643,\cdot)\) \(\chi_{7168}(699,\cdot)\) \(\chi_{7168}(755,\cdot)\) \(\chi_{7168}(811,\cdot)\) \(\chi_{7168}(867,\cdot)\) \(\chi_{7168}(923,\cdot)\) \(\chi_{7168}(979,\cdot)\) \(\chi_{7168}(1035,\cdot)\) \(\chi_{7168}(1091,\cdot)\) \(\chi_{7168}(1147,\cdot)\) \(\chi_{7168}(1203,\cdot)\) \(\chi_{7168}(1259,\cdot)\) \(\chi_{7168}(1315,\cdot)\) \(\chi_{7168}(1371,\cdot)\) \(\chi_{7168}(1427,\cdot)\) \(\chi_{7168}(1483,\cdot)\) \(\chi_{7168}(1539,\cdot)\) \(\chi_{7168}(1595,\cdot)\) \(\chi_{7168}(1651,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{256})$ |
| Fixed field: | Number field defined by a degree 256 polynomial (not computed) |
Values on generators
\((1023,5125,1025)\) → \((-1,e\left(\frac{233}{256}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 7168 }(27, a) \) | \(1\) | \(1\) | \(e\left(\frac{91}{256}\right)\) | \(e\left(\frac{105}{256}\right)\) | \(e\left(\frac{91}{128}\right)\) | \(e\left(\frac{93}{256}\right)\) | \(e\left(\frac{7}{256}\right)\) | \(e\left(\frac{49}{64}\right)\) | \(e\left(\frac{31}{64}\right)\) | \(e\left(\frac{111}{256}\right)\) | \(e\left(\frac{95}{128}\right)\) | \(e\left(\frac{105}{128}\right)\) |