Basic properties
Modulus: | \(1280\) | |
Conductor: | \(1280\) | 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
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1280.bz
\(\chi_{1280}(13,\cdot)\) \(\chi_{1280}(37,\cdot)\) \(\chi_{1280}(93,\cdot)\) \(\chi_{1280}(117,\cdot)\) \(\chi_{1280}(173,\cdot)\) \(\chi_{1280}(197,\cdot)\) \(\chi_{1280}(253,\cdot)\) \(\chi_{1280}(277,\cdot)\) \(\chi_{1280}(333,\cdot)\) \(\chi_{1280}(357,\cdot)\) \(\chi_{1280}(413,\cdot)\) \(\chi_{1280}(437,\cdot)\) \(\chi_{1280}(493,\cdot)\) \(\chi_{1280}(517,\cdot)\) \(\chi_{1280}(573,\cdot)\) \(\chi_{1280}(597,\cdot)\) \(\chi_{1280}(653,\cdot)\) \(\chi_{1280}(677,\cdot)\) \(\chi_{1280}(733,\cdot)\) \(\chi_{1280}(757,\cdot)\) \(\chi_{1280}(813,\cdot)\) \(\chi_{1280}(837,\cdot)\) \(\chi_{1280}(893,\cdot)\) \(\chi_{1280}(917,\cdot)\) \(\chi_{1280}(973,\cdot)\) \(\chi_{1280}(997,\cdot)\) \(\chi_{1280}(1053,\cdot)\) \(\chi_{1280}(1077,\cdot)\) \(\chi_{1280}(1133,\cdot)\) \(\chi_{1280}(1157,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{64})$ |
Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((511,261,257)\) → \((1,e\left(\frac{25}{64}\right),i)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 1280 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{27}{64}\right)\) | \(e\left(\frac{5}{32}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{13}{64}\right)\) | \(e\left(\frac{7}{64}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{31}{64}\right)\) | \(e\left(\frac{37}{64}\right)\) | \(e\left(\frac{7}{32}\right)\) | \(e\left(\frac{17}{64}\right)\) |