Basic properties
Modulus: | \(569\) | |
Conductor: | \(569\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(142\) | 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 569.f
\(\chi_{569}(4,\cdot)\) \(\chi_{569}(14,\cdot)\) \(\chi_{569}(20,\cdot)\) \(\chi_{569}(26,\cdot)\) \(\chi_{569}(34,\cdot)\) \(\chi_{569}(41,\cdot)\) \(\chi_{569}(43,\cdot)\) \(\chi_{569}(49,\cdot)\) \(\chi_{569}(64,\cdot)\) \(\chi_{569}(70,\cdot)\) \(\chi_{569}(72,\cdot)\) \(\chi_{569}(81,\cdot)\) \(\chi_{569}(87,\cdot)\) \(\chi_{569}(91,\cdot)\) \(\chi_{569}(93,\cdot)\) \(\chi_{569}(100,\cdot)\) \(\chi_{569}(119,\cdot)\) \(\chi_{569}(122,\cdot)\) \(\chi_{569}(130,\cdot)\) \(\chi_{569}(132,\cdot)\) \(\chi_{569}(158,\cdot)\) \(\chi_{569}(169,\cdot)\) \(\chi_{569}(170,\cdot)\) \(\chi_{569}(197,\cdot)\) \(\chi_{569}(205,\cdot)\) \(\chi_{569}(215,\cdot)\) \(\chi_{569}(221,\cdot)\) \(\chi_{569}(224,\cdot)\) \(\chi_{569}(242,\cdot)\) \(\chi_{569}(245,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{71})$ |
Fixed field: | Number field defined by a degree 142 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{45}{142}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 569 }(20, a) \) | \(1\) | \(1\) | \(e\left(\frac{44}{71}\right)\) | \(e\left(\frac{45}{142}\right)\) | \(e\left(\frac{17}{71}\right)\) | \(e\left(\frac{57}{71}\right)\) | \(e\left(\frac{133}{142}\right)\) | \(e\left(\frac{25}{71}\right)\) | \(e\left(\frac{61}{71}\right)\) | \(e\left(\frac{45}{71}\right)\) | \(e\left(\frac{30}{71}\right)\) | \(e\left(\frac{5}{142}\right)\) |