Basic properties
Modulus: | \(517\) | |
Conductor: | \(517\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(230\) | 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 517.p
\(\chi_{517}(5,\cdot)\) \(\chi_{517}(15,\cdot)\) \(\chi_{517}(20,\cdot)\) \(\chi_{517}(26,\cdot)\) \(\chi_{517}(31,\cdot)\) \(\chi_{517}(38,\cdot)\) \(\chi_{517}(58,\cdot)\) \(\chi_{517}(60,\cdot)\) \(\chi_{517}(69,\cdot)\) \(\chi_{517}(70,\cdot)\) \(\chi_{517}(80,\cdot)\) \(\chi_{517}(82,\cdot)\) \(\chi_{517}(86,\cdot)\) \(\chi_{517}(91,\cdot)\) \(\chi_{517}(92,\cdot)\) \(\chi_{517}(104,\cdot)\) \(\chi_{517}(113,\cdot)\) \(\chi_{517}(114,\cdot)\) \(\chi_{517}(124,\cdot)\) \(\chi_{517}(125,\cdot)\) \(\chi_{517}(135,\cdot)\) \(\chi_{517}(137,\cdot)\) \(\chi_{517}(146,\cdot)\) \(\chi_{517}(152,\cdot)\) \(\chi_{517}(163,\cdot)\) \(\chi_{517}(170,\cdot)\) \(\chi_{517}(174,\cdot)\) \(\chi_{517}(179,\cdot)\) \(\chi_{517}(180,\cdot)\) \(\chi_{517}(181,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{115})$ |
Fixed field: | Number field defined by a degree 230 polynomial (not computed) |
Values on generators
\((189,287)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{37}{46}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 517 }(20, a) \) | \(-1\) | \(1\) | \(e\left(\frac{9}{115}\right)\) | \(e\left(\frac{102}{115}\right)\) | \(e\left(\frac{18}{115}\right)\) | \(e\left(\frac{47}{230}\right)\) | \(e\left(\frac{111}{115}\right)\) | \(e\left(\frac{108}{115}\right)\) | \(e\left(\frac{27}{115}\right)\) | \(e\left(\frac{89}{115}\right)\) | \(e\left(\frac{13}{46}\right)\) | \(e\left(\frac{1}{23}\right)\) |