Basic properties
Modulus: | \(1007\) | |
Conductor: | \(1007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(39\) | 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 1007.w
\(\chi_{1007}(49,\cdot)\) \(\chi_{1007}(68,\cdot)\) \(\chi_{1007}(102,\cdot)\) \(\chi_{1007}(121,\cdot)\) \(\chi_{1007}(201,\cdot)\) \(\chi_{1007}(254,\cdot)\) \(\chi_{1007}(258,\cdot)\) \(\chi_{1007}(311,\cdot)\) \(\chi_{1007}(334,\cdot)\) \(\chi_{1007}(387,\cdot)\) \(\chi_{1007}(448,\cdot)\) \(\chi_{1007}(501,\cdot)\) \(\chi_{1007}(505,\cdot)\) \(\chi_{1007}(524,\cdot)\) \(\chi_{1007}(543,\cdot)\) \(\chi_{1007}(558,\cdot)\) \(\chi_{1007}(577,\cdot)\) \(\chi_{1007}(596,\cdot)\) \(\chi_{1007}(619,\cdot)\) \(\chi_{1007}(672,\cdot)\) \(\chi_{1007}(733,\cdot)\) \(\chi_{1007}(752,\cdot)\) \(\chi_{1007}(786,\cdot)\) \(\chi_{1007}(805,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((743,267)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{6}{13}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1007 }(596, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{10}{13}\right)\) |