Basic properties
Modulus: | \(1011\) | |
Conductor: | \(1011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(336\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1011.bm
\(\chi_{1011}(20,\cdot)\) \(\chi_{1011}(23,\cdot)\) \(\chi_{1011}(29,\cdot)\) \(\chi_{1011}(44,\cdot)\) \(\chi_{1011}(53,\cdot)\) \(\chi_{1011}(68,\cdot)\) \(\chi_{1011}(71,\cdot)\) \(\chi_{1011}(80,\cdot)\) \(\chi_{1011}(83,\cdot)\) \(\chi_{1011}(89,\cdot)\) \(\chi_{1011}(101,\cdot)\) \(\chi_{1011}(116,\cdot)\) \(\chi_{1011}(134,\cdot)\) \(\chi_{1011}(143,\cdot)\) \(\chi_{1011}(152,\cdot)\) \(\chi_{1011}(161,\cdot)\) \(\chi_{1011}(176,\cdot)\) \(\chi_{1011}(185,\cdot)\) \(\chi_{1011}(194,\cdot)\) \(\chi_{1011}(203,\cdot)\) \(\chi_{1011}(221,\cdot)\) \(\chi_{1011}(236,\cdot)\) \(\chi_{1011}(248,\cdot)\) \(\chi_{1011}(254,\cdot)\) \(\chi_{1011}(257,\cdot)\) \(\chi_{1011}(266,\cdot)\) \(\chi_{1011}(269,\cdot)\) \(\chi_{1011}(284,\cdot)\) \(\chi_{1011}(293,\cdot)\) \(\chi_{1011}(308,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{336})$ |
Fixed field: | Number field defined by a degree 336 polynomial (not computed) |
Values on generators
\((338,10)\) → \((-1,e\left(\frac{169}{336}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 1011 }(1001, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{11}{112}\right)\) | \(e\left(\frac{53}{56}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{169}{336}\right)\) | \(e\left(\frac{57}{112}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{59}{168}\right)\) | \(e\left(\frac{13}{21}\right)\) |