Basic properties
Modulus: | \(709\) | |
Conductor: | \(709\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(354\) | 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.k
\(\chi_{709}(4,\cdot)\) \(\chi_{709}(5,\cdot)\) \(\chi_{709}(11,\cdot)\) \(\chi_{709}(15,\cdot)\) \(\chi_{709}(26,\cdot)\) \(\chi_{709}(33,\cdot)\) \(\chi_{709}(34,\cdot)\) \(\chi_{709}(35,\cdot)\) \(\chi_{709}(36,\cdot)\) \(\chi_{709}(43,\cdot)\) \(\chi_{709}(77,\cdot)\) \(\chi_{709}(78,\cdot)\) \(\chi_{709}(80,\cdot)\) \(\chi_{709}(84,\cdot)\) \(\chi_{709}(95,\cdot)\) \(\chi_{709}(100,\cdot)\) \(\chi_{709}(103,\cdot)\) \(\chi_{709}(106,\cdot)\) \(\chi_{709}(108,\cdot)\) \(\chi_{709}(116,\cdot)\) \(\chi_{709}(122,\cdot)\) \(\chi_{709}(129,\cdot)\) \(\chi_{709}(135,\cdot)\) \(\chi_{709}(141,\cdot)\) \(\chi_{709}(142,\cdot)\) \(\chi_{709}(146,\cdot)\) \(\chi_{709}(151,\cdot)\) \(\chi_{709}(166,\cdot)\) \(\chi_{709}(176,\cdot)\) \(\chi_{709}(178,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{177})$ |
Fixed field: | Number field defined by a degree 354 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{247}{354}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 709 }(15, a) \) | \(1\) | \(1\) | \(e\left(\frac{247}{354}\right)\) | \(e\left(\frac{2}{177}\right)\) | \(e\left(\frac{70}{177}\right)\) | \(e\left(\frac{119}{177}\right)\) | \(e\left(\frac{251}{354}\right)\) | \(e\left(\frac{50}{177}\right)\) | \(e\left(\frac{11}{118}\right)\) | \(e\left(\frac{4}{177}\right)\) | \(e\left(\frac{131}{354}\right)\) | \(e\left(\frac{86}{177}\right)\) |