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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1157.by
\(\chi_{1157}(2,\cdot)\) \(\chi_{1157}(32,\cdot)\) \(\chi_{1157}(45,\cdot)\) \(\chi_{1157}(67,\cdot)\) \(\chi_{1157}(93,\cdot)\) \(\chi_{1157}(97,\cdot)\) \(\chi_{1157}(128,\cdot)\) \(\chi_{1157}(167,\cdot)\) \(\chi_{1157}(180,\cdot)\) \(\chi_{1157}(210,\cdot)\) \(\chi_{1157}(223,\cdot)\) \(\chi_{1157}(245,\cdot)\) \(\chi_{1157}(271,\cdot)\) \(\chi_{1157}(275,\cdot)\) \(\chi_{1157}(306,\cdot)\) \(\chi_{1157}(331,\cdot)\) \(\chi_{1157}(345,\cdot)\) \(\chi_{1157}(358,\cdot)\) \(\chi_{1157}(388,\cdot)\) \(\chi_{1157}(401,\cdot)\) \(\chi_{1157}(423,\cdot)\) \(\chi_{1157}(449,\cdot)\) \(\chi_{1157}(453,\cdot)\) \(\chi_{1157}(461,\cdot)\) \(\chi_{1157}(509,\cdot)\) \(\chi_{1157}(566,\cdot)\) \(\chi_{1157}(579,\cdot)\) \(\chi_{1157}(631,\cdot)\) \(\chi_{1157}(639,\cdot)\) \(\chi_{1157}(687,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((535,92)\) → \((e\left(\frac{1}{12}\right),e\left(\frac{8}{11}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1157 }(639, a) \) | \(-1\) | \(1\) | \(e\left(\frac{95}{132}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{103}{132}\right)\) | \(e\left(\frac{109}{132}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{89}{132}\right)\) |