Basic properties
Modulus: | \(1792\) | |
Conductor: | \(1792\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(64\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1792.bt
\(\chi_{1792}(13,\cdot)\) \(\chi_{1792}(69,\cdot)\) \(\chi_{1792}(125,\cdot)\) \(\chi_{1792}(181,\cdot)\) \(\chi_{1792}(237,\cdot)\) \(\chi_{1792}(293,\cdot)\) \(\chi_{1792}(349,\cdot)\) \(\chi_{1792}(405,\cdot)\) \(\chi_{1792}(461,\cdot)\) \(\chi_{1792}(517,\cdot)\) \(\chi_{1792}(573,\cdot)\) \(\chi_{1792}(629,\cdot)\) \(\chi_{1792}(685,\cdot)\) \(\chi_{1792}(741,\cdot)\) \(\chi_{1792}(797,\cdot)\) \(\chi_{1792}(853,\cdot)\) \(\chi_{1792}(909,\cdot)\) \(\chi_{1792}(965,\cdot)\) \(\chi_{1792}(1021,\cdot)\) \(\chi_{1792}(1077,\cdot)\) \(\chi_{1792}(1133,\cdot)\) \(\chi_{1792}(1189,\cdot)\) \(\chi_{1792}(1245,\cdot)\) \(\chi_{1792}(1301,\cdot)\) \(\chi_{1792}(1357,\cdot)\) \(\chi_{1792}(1413,\cdot)\) \(\chi_{1792}(1469,\cdot)\) \(\chi_{1792}(1525,\cdot)\) \(\chi_{1792}(1581,\cdot)\) \(\chi_{1792}(1637,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{64})$ |
Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((1023,1541,1025)\) → \((1,e\left(\frac{29}{64}\right),-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 1792 }(853, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{64}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{33}{64}\right)\) | \(e\left(\frac{51}{64}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{59}{64}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{29}{32}\right)\) |