Basic properties
Modulus: | \(709\) | |
Conductor: | \(709\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(236\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
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 709.j
\(\chi_{709}(8,\cdot)\) \(\chi_{709}(13,\cdot)\) \(\chi_{709}(18,\cdot)\) \(\chi_{709}(30,\cdot)\) \(\chi_{709}(42,\cdot)\) \(\chi_{709}(50,\cdot)\) \(\chi_{709}(53,\cdot)\) \(\chi_{709}(58,\cdot)\) \(\chi_{709}(66,\cdot)\) \(\chi_{709}(68,\cdot)\) \(\chi_{709}(70,\cdot)\) \(\chi_{709}(73,\cdot)\) \(\chi_{709}(83,\cdot)\) \(\chi_{709}(92,\cdot)\) \(\chi_{709}(98,\cdot)\) \(\chi_{709}(101,\cdot)\) \(\chi_{709}(107,\cdot)\) \(\chi_{709}(109,\cdot)\) \(\chi_{709}(110,\cdot)\) \(\chi_{709}(114,\cdot)\) \(\chi_{709}(123,\cdot)\) \(\chi_{709}(124,\cdot)\) \(\chi_{709}(131,\cdot)\) \(\chi_{709}(134,\cdot)\) \(\chi_{709}(137,\cdot)\) \(\chi_{709}(148,\cdot)\) \(\chi_{709}(153,\cdot)\) \(\chi_{709}(154,\cdot)\) \(\chi_{709}(156,\cdot)\) \(\chi_{709}(160,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{236})$ |
Fixed field: | Number field defined by a degree 236 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{75}{236}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 709 }(42, a) \) | \(-1\) | \(1\) | \(e\left(\frac{75}{236}\right)\) | \(e\left(\frac{39}{59}\right)\) | \(e\left(\frac{75}{118}\right)\) | \(e\left(\frac{39}{118}\right)\) | \(e\left(\frac{231}{236}\right)\) | \(e\left(\frac{31}{59}\right)\) | \(e\left(\frac{225}{236}\right)\) | \(e\left(\frac{19}{59}\right)\) | \(e\left(\frac{153}{236}\right)\) | \(e\left(\frac{109}{118}\right)\) |