Basic properties
Modulus: | \(7168\) | |
Conductor: | \(1024\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(256\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1024}(981,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7168.cl
\(\chi_{7168}(29,\cdot)\) \(\chi_{7168}(85,\cdot)\) \(\chi_{7168}(141,\cdot)\) \(\chi_{7168}(197,\cdot)\) \(\chi_{7168}(253,\cdot)\) \(\chi_{7168}(309,\cdot)\) \(\chi_{7168}(365,\cdot)\) \(\chi_{7168}(421,\cdot)\) \(\chi_{7168}(477,\cdot)\) \(\chi_{7168}(533,\cdot)\) \(\chi_{7168}(589,\cdot)\) \(\chi_{7168}(645,\cdot)\) \(\chi_{7168}(701,\cdot)\) \(\chi_{7168}(757,\cdot)\) \(\chi_{7168}(813,\cdot)\) \(\chi_{7168}(869,\cdot)\) \(\chi_{7168}(925,\cdot)\) \(\chi_{7168}(981,\cdot)\) \(\chi_{7168}(1037,\cdot)\) \(\chi_{7168}(1093,\cdot)\) \(\chi_{7168}(1149,\cdot)\) \(\chi_{7168}(1205,\cdot)\) \(\chi_{7168}(1261,\cdot)\) \(\chi_{7168}(1317,\cdot)\) \(\chi_{7168}(1373,\cdot)\) \(\chi_{7168}(1429,\cdot)\) \(\chi_{7168}(1485,\cdot)\) \(\chi_{7168}(1541,\cdot)\) \(\chi_{7168}(1597,\cdot)\) \(\chi_{7168}(1653,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{256})$ |
Fixed field: | Number field defined by a degree 256 polynomial (not computed) |
Values on generators
\((1023,5125,1025)\) → \((1,e\left(\frac{61}{256}\right),1)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 7168 }(981, a) \) | \(1\) | \(1\) | \(e\left(\frac{215}{256}\right)\) | \(e\left(\frac{61}{256}\right)\) | \(e\left(\frac{87}{128}\right)\) | \(e\left(\frac{193}{256}\right)\) | \(e\left(\frac{243}{256}\right)\) | \(e\left(\frac{5}{64}\right)\) | \(e\left(\frac{11}{64}\right)\) | \(e\left(\frac{251}{256}\right)\) | \(e\left(\frac{107}{128}\right)\) | \(e\left(\frac{61}{128}\right)\) |