Basic properties
| Modulus: | \(7168\) | |
| Conductor: | \(3584\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(128\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3584}(2211,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7168.cb
\(\chi_{7168}(55,\cdot)\) \(\chi_{7168}(167,\cdot)\) \(\chi_{7168}(279,\cdot)\) \(\chi_{7168}(391,\cdot)\) \(\chi_{7168}(503,\cdot)\) \(\chi_{7168}(615,\cdot)\) \(\chi_{7168}(727,\cdot)\) \(\chi_{7168}(839,\cdot)\) \(\chi_{7168}(951,\cdot)\) \(\chi_{7168}(1063,\cdot)\) \(\chi_{7168}(1175,\cdot)\) \(\chi_{7168}(1287,\cdot)\) \(\chi_{7168}(1399,\cdot)\) \(\chi_{7168}(1511,\cdot)\) \(\chi_{7168}(1623,\cdot)\) \(\chi_{7168}(1735,\cdot)\) \(\chi_{7168}(1847,\cdot)\) \(\chi_{7168}(1959,\cdot)\) \(\chi_{7168}(2071,\cdot)\) \(\chi_{7168}(2183,\cdot)\) \(\chi_{7168}(2295,\cdot)\) \(\chi_{7168}(2407,\cdot)\) \(\chi_{7168}(2519,\cdot)\) \(\chi_{7168}(2631,\cdot)\) \(\chi_{7168}(2743,\cdot)\) \(\chi_{7168}(2855,\cdot)\) \(\chi_{7168}(2967,\cdot)\) \(\chi_{7168}(3079,\cdot)\) \(\chi_{7168}(3191,\cdot)\) \(\chi_{7168}(3303,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{128})$ |
| Fixed field: | Number field defined by a degree 128 polynomial (not computed) |
Values on generators
\((1023,5125,1025)\) → \((-1,e\left(\frac{107}{128}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 7168 }(55, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{128}\right)\) | \(e\left(\frac{43}{128}\right)\) | \(e\left(\frac{33}{64}\right)\) | \(e\left(\frac{71}{128}\right)\) | \(e\left(\frac{37}{128}\right)\) | \(e\left(\frac{19}{32}\right)\) | \(e\left(\frac{29}{32}\right)\) | \(e\left(\frac{29}{128}\right)\) | \(e\left(\frac{13}{64}\right)\) | \(e\left(\frac{43}{64}\right)\) |