Basic properties
Modulus: | \(709\) | |
Conductor: | \(709\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(59\) | 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 709.g
\(\chi_{709}(20,\cdot)\) \(\chi_{709}(27,\cdot)\) \(\chi_{709}(44,\cdot)\) \(\chi_{709}(59,\cdot)\) \(\chi_{709}(63,\cdot)\) \(\chi_{709}(75,\cdot)\) \(\chi_{709}(82,\cdot)\) \(\chi_{709}(87,\cdot)\) \(\chi_{709}(104,\cdot)\) \(\chi_{709}(138,\cdot)\) \(\chi_{709}(144,\cdot)\) \(\chi_{709}(147,\cdot)\) \(\chi_{709}(149,\cdot)\) \(\chi_{709}(163,\cdot)\) \(\chi_{709}(165,\cdot)\) \(\chi_{709}(170,\cdot)\) \(\chi_{709}(171,\cdot)\) \(\chi_{709}(172,\cdot)\) \(\chi_{709}(175,\cdot)\) \(\chi_{709}(181,\cdot)\) \(\chi_{709}(186,\cdot)\) \(\chi_{709}(201,\cdot)\) \(\chi_{709}(203,\cdot)\) \(\chi_{709}(222,\cdot)\) \(\chi_{709}(283,\cdot)\) \(\chi_{709}(322,\cdot)\) \(\chi_{709}(336,\cdot)\) \(\chi_{709}(339,\cdot)\) \(\chi_{709}(343,\cdot)\) \(\chi_{709}(363,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{59})$ |
Fixed field: | Number field defined by a degree 59 polynomial |
Values on generators
\(2\) → \(e\left(\frac{44}{59}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 709 }(697, a) \) | \(1\) | \(1\) | \(e\left(\frac{44}{59}\right)\) | \(e\left(\frac{16}{59}\right)\) | \(e\left(\frac{29}{59}\right)\) | \(e\left(\frac{8}{59}\right)\) | \(e\left(\frac{1}{59}\right)\) | \(e\left(\frac{46}{59}\right)\) | \(e\left(\frac{14}{59}\right)\) | \(e\left(\frac{32}{59}\right)\) | \(e\left(\frac{52}{59}\right)\) | \(e\left(\frac{39}{59}\right)\) |