Basic properties
Modulus: | \(709\) | |
Conductor: | \(709\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(177\) | 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.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
\(2\) → \(e\left(\frac{167}{177}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 709 }(180, a) \) | \(1\) | \(1\) | \(e\left(\frac{167}{177}\right)\) | \(e\left(\frac{50}{177}\right)\) | \(e\left(\frac{157}{177}\right)\) | \(e\left(\frac{143}{177}\right)\) | \(e\left(\frac{40}{177}\right)\) | \(e\left(\frac{11}{177}\right)\) | \(e\left(\frac{49}{59}\right)\) | \(e\left(\frac{100}{177}\right)\) | \(e\left(\frac{133}{177}\right)\) | \(e\left(\frac{26}{177}\right)\) |