Basic properties
Modulus: | \(1792\) | |
Conductor: | \(256\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(64\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{256}(221,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1792.bs
\(\chi_{1792}(29,\cdot)\) \(\chi_{1792}(85,\cdot)\) \(\chi_{1792}(141,\cdot)\) \(\chi_{1792}(197,\cdot)\) \(\chi_{1792}(253,\cdot)\) \(\chi_{1792}(309,\cdot)\) \(\chi_{1792}(365,\cdot)\) \(\chi_{1792}(421,\cdot)\) \(\chi_{1792}(477,\cdot)\) \(\chi_{1792}(533,\cdot)\) \(\chi_{1792}(589,\cdot)\) \(\chi_{1792}(645,\cdot)\) \(\chi_{1792}(701,\cdot)\) \(\chi_{1792}(757,\cdot)\) \(\chi_{1792}(813,\cdot)\) \(\chi_{1792}(869,\cdot)\) \(\chi_{1792}(925,\cdot)\) \(\chi_{1792}(981,\cdot)\) \(\chi_{1792}(1037,\cdot)\) \(\chi_{1792}(1093,\cdot)\) \(\chi_{1792}(1149,\cdot)\) \(\chi_{1792}(1205,\cdot)\) \(\chi_{1792}(1261,\cdot)\) \(\chi_{1792}(1317,\cdot)\) \(\chi_{1792}(1373,\cdot)\) \(\chi_{1792}(1429,\cdot)\) \(\chi_{1792}(1485,\cdot)\) \(\chi_{1792}(1541,\cdot)\) \(\chi_{1792}(1597,\cdot)\) \(\chi_{1792}(1653,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{64})$ |
Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((1023,1541,1025)\) → \((1,e\left(\frac{11}{64}\right),1)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 1792 }(477, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{64}\right)\) | \(e\left(\frac{11}{64}\right)\) | \(e\left(\frac{1}{32}\right)\) | \(e\left(\frac{39}{64}\right)\) | \(e\left(\frac{5}{64}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{11}{32}\right)\) |