Basic properties
Modulus: | \(9216\) | |
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: | no, induced from \(\chi_{3072}(35,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9216.ck
\(\chi_{9216}(35,\cdot)\) \(\chi_{9216}(107,\cdot)\) \(\chi_{9216}(179,\cdot)\) \(\chi_{9216}(251,\cdot)\) \(\chi_{9216}(323,\cdot)\) \(\chi_{9216}(395,\cdot)\) \(\chi_{9216}(467,\cdot)\) \(\chi_{9216}(539,\cdot)\) \(\chi_{9216}(611,\cdot)\) \(\chi_{9216}(683,\cdot)\) \(\chi_{9216}(755,\cdot)\) \(\chi_{9216}(827,\cdot)\) \(\chi_{9216}(899,\cdot)\) \(\chi_{9216}(971,\cdot)\) \(\chi_{9216}(1043,\cdot)\) \(\chi_{9216}(1115,\cdot)\) \(\chi_{9216}(1187,\cdot)\) \(\chi_{9216}(1259,\cdot)\) \(\chi_{9216}(1331,\cdot)\) \(\chi_{9216}(1403,\cdot)\) \(\chi_{9216}(1475,\cdot)\) \(\chi_{9216}(1547,\cdot)\) \(\chi_{9216}(1619,\cdot)\) \(\chi_{9216}(1691,\cdot)\) \(\chi_{9216}(1763,\cdot)\) \(\chi_{9216}(1835,\cdot)\) \(\chi_{9216}(1907,\cdot)\) \(\chi_{9216}(1979,\cdot)\) \(\chi_{9216}(2051,\cdot)\) \(\chi_{9216}(2123,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{256})$ |
Fixed field: | Number field defined by a degree 256 polynomial (not computed) |
Values on generators
\((8191,2053,4097)\) → \((-1,e\left(\frac{203}{256}\right),-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 9216 }(35, a) \) | \(1\) | \(1\) | \(e\left(\frac{75}{256}\right)\) | \(e\left(\frac{87}{128}\right)\) | \(e\left(\frac{231}{256}\right)\) | \(e\left(\frac{133}{256}\right)\) | \(e\left(\frac{13}{64}\right)\) | \(e\left(\frac{61}{256}\right)\) | \(e\left(\frac{77}{128}\right)\) | \(e\left(\frac{75}{128}\right)\) | \(e\left(\frac{9}{256}\right)\) | \(e\left(\frac{11}{32}\right)\) |