Basic properties
| Modulus: | \(7168\) | |
| Conductor: | \(896\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(96\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{896}(429,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7168.by
\(\chi_{7168}(289,\cdot)\) \(\chi_{7168}(417,\cdot)\) \(\chi_{7168}(737,\cdot)\) \(\chi_{7168}(865,\cdot)\) \(\chi_{7168}(1185,\cdot)\) \(\chi_{7168}(1313,\cdot)\) \(\chi_{7168}(1633,\cdot)\) \(\chi_{7168}(1761,\cdot)\) \(\chi_{7168}(2081,\cdot)\) \(\chi_{7168}(2209,\cdot)\) \(\chi_{7168}(2529,\cdot)\) \(\chi_{7168}(2657,\cdot)\) \(\chi_{7168}(2977,\cdot)\) \(\chi_{7168}(3105,\cdot)\) \(\chi_{7168}(3425,\cdot)\) \(\chi_{7168}(3553,\cdot)\) \(\chi_{7168}(3873,\cdot)\) \(\chi_{7168}(4001,\cdot)\) \(\chi_{7168}(4321,\cdot)\) \(\chi_{7168}(4449,\cdot)\) \(\chi_{7168}(4769,\cdot)\) \(\chi_{7168}(4897,\cdot)\) \(\chi_{7168}(5217,\cdot)\) \(\chi_{7168}(5345,\cdot)\) \(\chi_{7168}(5665,\cdot)\) \(\chi_{7168}(5793,\cdot)\) \(\chi_{7168}(6113,\cdot)\) \(\chi_{7168}(6241,\cdot)\) \(\chi_{7168}(6561,\cdot)\) \(\chi_{7168}(6689,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{96})$ |
| Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((1023,5125,1025)\) → \((1,e\left(\frac{7}{32}\right),e\left(\frac{1}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 7168 }(289, a) \) | \(1\) | \(1\) | \(e\left(\frac{95}{96}\right)\) | \(e\left(\frac{85}{96}\right)\) | \(e\left(\frac{47}{48}\right)\) | \(e\left(\frac{89}{96}\right)\) | \(e\left(\frac{9}{32}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{67}{96}\right)\) | \(e\left(\frac{35}{48}\right)\) | \(e\left(\frac{37}{48}\right)\) |