Basic properties
Modulus: | \(1157\) | |
Conductor: | \(1157\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(132\) | 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 1157.bu
\(\chi_{1157}(10,\cdot)\) \(\chi_{1157}(17,\cdot)\) \(\chi_{1157}(36,\cdot)\) \(\chi_{1157}(49,\cdot)\) \(\chi_{1157}(69,\cdot)\) \(\chi_{1157}(160,\cdot)\) \(\chi_{1157}(173,\cdot)\) \(\chi_{1157}(199,\cdot)\) \(\chi_{1157}(218,\cdot)\) \(\chi_{1157}(225,\cdot)\) \(\chi_{1157}(231,\cdot)\) \(\chi_{1157}(257,\cdot)\) \(\chi_{1157}(277,\cdot)\) \(\chi_{1157}(303,\cdot)\) \(\chi_{1157}(309,\cdot)\) \(\chi_{1157}(316,\cdot)\) \(\chi_{1157}(335,\cdot)\) \(\chi_{1157}(361,\cdot)\) \(\chi_{1157}(374,\cdot)\) \(\chi_{1157}(465,\cdot)\) \(\chi_{1157}(485,\cdot)\) \(\chi_{1157}(498,\cdot)\) \(\chi_{1157}(517,\cdot)\) \(\chi_{1157}(524,\cdot)\) \(\chi_{1157}(543,\cdot)\) \(\chi_{1157}(576,\cdot)\) \(\chi_{1157}(602,\cdot)\) \(\chi_{1157}(628,\cdot)\) \(\chi_{1157}(641,\cdot)\) \(\chi_{1157}(732,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((535,92)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{7}{44}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1157 }(732, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{109}{132}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{71}{132}\right)\) | \(e\left(\frac{95}{132}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{23}{66}\right)\) | \(e\left(\frac{35}{66}\right)\) |