Basic properties
Modulus: | \(517\) | |
Conductor: | \(517\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(115\) | 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 517.m
\(\chi_{517}(3,\cdot)\) \(\chi_{517}(4,\cdot)\) \(\chi_{517}(9,\cdot)\) \(\chi_{517}(14,\cdot)\) \(\chi_{517}(16,\cdot)\) \(\chi_{517}(25,\cdot)\) \(\chi_{517}(27,\cdot)\) \(\chi_{517}(36,\cdot)\) \(\chi_{517}(37,\cdot)\) \(\chi_{517}(42,\cdot)\) \(\chi_{517}(49,\cdot)\) \(\chi_{517}(53,\cdot)\) \(\chi_{517}(59,\cdot)\) \(\chi_{517}(64,\cdot)\) \(\chi_{517}(71,\cdot)\) \(\chi_{517}(75,\cdot)\) \(\chi_{517}(81,\cdot)\) \(\chi_{517}(97,\cdot)\) \(\chi_{517}(102,\cdot)\) \(\chi_{517}(103,\cdot)\) \(\chi_{517}(108,\cdot)\) \(\chi_{517}(115,\cdot)\) \(\chi_{517}(119,\cdot)\) \(\chi_{517}(126,\cdot)\) \(\chi_{517}(130,\cdot)\) \(\chi_{517}(136,\cdot)\) \(\chi_{517}(147,\cdot)\) \(\chi_{517}(148,\cdot)\) \(\chi_{517}(157,\cdot)\) \(\chi_{517}(158,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{115})$ |
Fixed field: | Number field defined by a degree 115 polynomial (not computed) |
Values on generators
\((189,287)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{15}{23}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 517 }(130, a) \) | \(1\) | \(1\) | \(e\left(\frac{39}{115}\right)\) | \(e\left(\frac{97}{115}\right)\) | \(e\left(\frac{78}{115}\right)\) | \(e\left(\frac{6}{115}\right)\) | \(e\left(\frac{21}{115}\right)\) | \(e\left(\frac{8}{115}\right)\) | \(e\left(\frac{2}{115}\right)\) | \(e\left(\frac{79}{115}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) |