Basic properties
Modulus: | \(3072\) | |
Conductor: | \(3072\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(256\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3072.bi
\(\chi_{3072}(11,\cdot)\) \(\chi_{3072}(35,\cdot)\) \(\chi_{3072}(59,\cdot)\) \(\chi_{3072}(83,\cdot)\) \(\chi_{3072}(107,\cdot)\) \(\chi_{3072}(131,\cdot)\) \(\chi_{3072}(155,\cdot)\) \(\chi_{3072}(179,\cdot)\) \(\chi_{3072}(203,\cdot)\) \(\chi_{3072}(227,\cdot)\) \(\chi_{3072}(251,\cdot)\) \(\chi_{3072}(275,\cdot)\) \(\chi_{3072}(299,\cdot)\) \(\chi_{3072}(323,\cdot)\) \(\chi_{3072}(347,\cdot)\) \(\chi_{3072}(371,\cdot)\) \(\chi_{3072}(395,\cdot)\) \(\chi_{3072}(419,\cdot)\) \(\chi_{3072}(443,\cdot)\) \(\chi_{3072}(467,\cdot)\) \(\chi_{3072}(491,\cdot)\) \(\chi_{3072}(515,\cdot)\) \(\chi_{3072}(539,\cdot)\) \(\chi_{3072}(563,\cdot)\) \(\chi_{3072}(587,\cdot)\) \(\chi_{3072}(611,\cdot)\) \(\chi_{3072}(635,\cdot)\) \(\chi_{3072}(659,\cdot)\) \(\chi_{3072}(683,\cdot)\) \(\chi_{3072}(707,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{256})$ |
Fixed field: | Number field defined by a degree 256 polynomial (not computed) |
Values on generators
\((2047,2053,1025)\) → \((-1,e\left(\frac{209}{256}\right),-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 3072 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{81}{256}\right)\) | \(e\left(\frac{53}{128}\right)\) | \(e\left(\frac{229}{256}\right)\) | \(e\left(\frac{31}{256}\right)\) | \(e\left(\frac{55}{64}\right)\) | \(e\left(\frac{199}{256}\right)\) | \(e\left(\frac{119}{128}\right)\) | \(e\left(\frac{81}{128}\right)\) | \(e\left(\frac{235}{256}\right)\) | \(e\left(\frac{17}{32}\right)\) |