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.o
\(\chi_{517}(2,\cdot)\) \(\chi_{517}(6,\cdot)\) \(\chi_{517}(7,\cdot)\) \(\chi_{517}(8,\cdot)\) \(\chi_{517}(17,\cdot)\) \(\chi_{517}(18,\cdot)\) \(\chi_{517}(24,\cdot)\) \(\chi_{517}(28,\cdot)\) \(\chi_{517}(50,\cdot)\) \(\chi_{517}(51,\cdot)\) \(\chi_{517}(61,\cdot)\) \(\chi_{517}(63,\cdot)\) \(\chi_{517}(68,\cdot)\) \(\chi_{517}(72,\cdot)\) \(\chi_{517}(74,\cdot)\) \(\chi_{517}(79,\cdot)\) \(\chi_{517}(83,\cdot)\) \(\chi_{517}(84,\cdot)\) \(\chi_{517}(96,\cdot)\) \(\chi_{517}(101,\cdot)\) \(\chi_{517}(106,\cdot)\) \(\chi_{517}(112,\cdot)\) \(\chi_{517}(118,\cdot)\) \(\chi_{517}(128,\cdot)\) \(\chi_{517}(145,\cdot)\) \(\chi_{517}(149,\cdot)\) \(\chi_{517}(150,\cdot)\) \(\chi_{517}(162,\cdot)\) \(\chi_{517}(173,\cdot)\) \(\chi_{517}(178,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{115})$ |
Fixed field: | Number field defined by a degree 230 polynomial (not computed) |
Values on generators
\((189,287)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{1}{23}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 517 }(72, a) \) | \(-1\) | \(1\) | \(e\left(\frac{157}{230}\right)\) | \(e\left(\frac{8}{115}\right)\) | \(e\left(\frac{42}{115}\right)\) | \(e\left(\frac{74}{115}\right)\) | \(e\left(\frac{173}{230}\right)\) | \(e\left(\frac{159}{230}\right)\) | \(e\left(\frac{11}{230}\right)\) | \(e\left(\frac{16}{115}\right)\) | \(e\left(\frac{15}{46}\right)\) | \(e\left(\frac{10}{23}\right)\) |