Basic properties
Modulus: | \(709\) | |
Conductor: | \(709\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(118\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
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.h
\(\chi_{709}(12,\cdot)\) \(\chi_{709}(28,\cdot)\) \(\chi_{709}(45,\cdot)\) \(\chi_{709}(47,\cdot)\) \(\chi_{709}(64,\cdot)\) \(\chi_{709}(76,\cdot)\) \(\chi_{709}(99,\cdot)\) \(\chi_{709}(102,\cdot)\) \(\chi_{709}(105,\cdot)\) \(\chi_{709}(125,\cdot)\) \(\chi_{709}(145,\cdot)\) \(\chi_{709}(158,\cdot)\) \(\chi_{709}(169,\cdot)\) \(\chi_{709}(191,\cdot)\) \(\chi_{709}(194,\cdot)\) \(\chi_{709}(230,\cdot)\) \(\chi_{709}(231,\cdot)\) \(\chi_{709}(234,\cdot)\) \(\chi_{709}(238,\cdot)\) \(\chi_{709}(240,\cdot)\) \(\chi_{709}(245,\cdot)\) \(\chi_{709}(275,\cdot)\) \(\chi_{709}(285,\cdot)\) \(\chi_{709}(309,\cdot)\) \(\chi_{709}(310,\cdot)\) \(\chi_{709}(319,\cdot)\) \(\chi_{709}(324,\cdot)\) \(\chi_{709}(335,\cdot)\) \(\chi_{709}(346,\cdot)\) \(\chi_{709}(366,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{59})$ |
Fixed field: | Number field defined by a degree 118 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{29}{118}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 709 }(12, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{118}\right)\) | \(e\left(\frac{16}{59}\right)\) | \(e\left(\frac{29}{59}\right)\) | \(e\left(\frac{8}{59}\right)\) | \(e\left(\frac{61}{118}\right)\) | \(e\left(\frac{46}{59}\right)\) | \(e\left(\frac{87}{118}\right)\) | \(e\left(\frac{32}{59}\right)\) | \(e\left(\frac{45}{118}\right)\) | \(e\left(\frac{39}{59}\right)\) |