Basic properties
Modulus: | \(1183\) | |
Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(52\) | 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 1183.bn
\(\chi_{1183}(34,\cdot)\) \(\chi_{1183}(83,\cdot)\) \(\chi_{1183}(125,\cdot)\) \(\chi_{1183}(174,\cdot)\) \(\chi_{1183}(216,\cdot)\) \(\chi_{1183}(265,\cdot)\) \(\chi_{1183}(307,\cdot)\) \(\chi_{1183}(356,\cdot)\) \(\chi_{1183}(398,\cdot)\) \(\chi_{1183}(447,\cdot)\) \(\chi_{1183}(489,\cdot)\) \(\chi_{1183}(538,\cdot)\) \(\chi_{1183}(580,\cdot)\) \(\chi_{1183}(629,\cdot)\) \(\chi_{1183}(671,\cdot)\) \(\chi_{1183}(720,\cdot)\) \(\chi_{1183}(762,\cdot)\) \(\chi_{1183}(811,\cdot)\) \(\chi_{1183}(853,\cdot)\) \(\chi_{1183}(902,\cdot)\) \(\chi_{1183}(993,\cdot)\) \(\chi_{1183}(1035,\cdot)\) \(\chi_{1183}(1126,\cdot)\) \(\chi_{1183}(1175,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{52})$ |
Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((339,1016)\) → \((-1,e\left(\frac{35}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 1183 }(720, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{33}{52}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{4}{13}\right)\) |