Basic properties
Modulus: | \(1011\) | |
Conductor: | \(1011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(112\) | 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 1011.bj
\(\chi_{1011}(5,\cdot)\) \(\chi_{1011}(11,\cdot)\) \(\chi_{1011}(17,\cdot)\) \(\chi_{1011}(35,\cdot)\) \(\chi_{1011}(62,\cdot)\) \(\chi_{1011}(77,\cdot)\) \(\chi_{1011}(92,\cdot)\) \(\chi_{1011}(119,\cdot)\) \(\chi_{1011}(122,\cdot)\) \(\chi_{1011}(125,\cdot)\) \(\chi_{1011}(212,\cdot)\) \(\chi_{1011}(215,\cdot)\) \(\chi_{1011}(218,\cdot)\) \(\chi_{1011}(245,\cdot)\) \(\chi_{1011}(260,\cdot)\) \(\chi_{1011}(275,\cdot)\) \(\chi_{1011}(302,\cdot)\) \(\chi_{1011}(320,\cdot)\) \(\chi_{1011}(326,\cdot)\) \(\chi_{1011}(332,\cdot)\) \(\chi_{1011}(395,\cdot)\) \(\chi_{1011}(413,\cdot)\) \(\chi_{1011}(425,\cdot)\) \(\chi_{1011}(434,\cdot)\) \(\chi_{1011}(464,\cdot)\) \(\chi_{1011}(473,\cdot)\) \(\chi_{1011}(479,\cdot)\) \(\chi_{1011}(494,\cdot)\) \(\chi_{1011}(515,\cdot)\) \(\chi_{1011}(539,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{112})$ |
Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\((338,10)\) → \((-1,e\left(\frac{11}{112}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 1011 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{83}{112}\right)\) | \(e\left(\frac{13}{56}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{11}{112}\right)\) | \(e\left(\frac{33}{112}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{33}{56}\right)\) | \(e\left(\frac{3}{7}\right)\) |