Basic properties
| Modulus: | \(709\) | |
| Conductor: | \(709\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(177\) | 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.i
\(\chi_{709}(3,\cdot)\) \(\chi_{709}(7,\cdot)\) \(\chi_{709}(9,\cdot)\) \(\chi_{709}(16,\cdot)\) \(\chi_{709}(19,\cdot)\) \(\chi_{709}(21,\cdot)\) \(\chi_{709}(25,\cdot)\) \(\chi_{709}(29,\cdot)\) \(\chi_{709}(46,\cdot)\) \(\chi_{709}(48,\cdot)\) \(\chi_{709}(49,\cdot)\) \(\chi_{709}(55,\cdot)\) \(\chi_{709}(57,\cdot)\) \(\chi_{709}(60,\cdot)\) \(\chi_{709}(62,\cdot)\) \(\chi_{709}(67,\cdot)\) \(\chi_{709}(74,\cdot)\) \(\chi_{709}(81,\cdot)\) \(\chi_{709}(112,\cdot)\) \(\chi_{709}(113,\cdot)\) \(\chi_{709}(121,\cdot)\) \(\chi_{709}(127,\cdot)\) \(\chi_{709}(130,\cdot)\) \(\chi_{709}(132,\cdot)\) \(\chi_{709}(133,\cdot)\) \(\chi_{709}(136,\cdot)\) \(\chi_{709}(140,\cdot)\) \(\chi_{709}(157,\cdot)\) \(\chi_{709}(177,\cdot)\) \(\chi_{709}(180,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{177})$ |
| Fixed field: | Number field defined by a degree 177 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{23}{177}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 709 }(67, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{177}\right)\) | \(e\left(\frac{62}{177}\right)\) | \(e\left(\frac{46}{177}\right)\) | \(e\left(\frac{149}{177}\right)\) | \(e\left(\frac{85}{177}\right)\) | \(e\left(\frac{134}{177}\right)\) | \(e\left(\frac{23}{59}\right)\) | \(e\left(\frac{124}{177}\right)\) | \(e\left(\frac{172}{177}\right)\) | \(e\left(\frac{11}{177}\right)\) |