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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 517.n
\(\chi_{517}(13,\cdot)\) \(\chi_{517}(19,\cdot)\) \(\chi_{517}(29,\cdot)\) \(\chi_{517}(30,\cdot)\) \(\chi_{517}(35,\cdot)\) \(\chi_{517}(39,\cdot)\) \(\chi_{517}(40,\cdot)\) \(\chi_{517}(41,\cdot)\) \(\chi_{517}(52,\cdot)\) \(\chi_{517}(57,\cdot)\) \(\chi_{517}(62,\cdot)\) \(\chi_{517}(73,\cdot)\) \(\chi_{517}(85,\cdot)\) \(\chi_{517}(90,\cdot)\) \(\chi_{517}(105,\cdot)\) \(\chi_{517}(107,\cdot)\) \(\chi_{517}(116,\cdot)\) \(\chi_{517}(117,\cdot)\) \(\chi_{517}(123,\cdot)\) \(\chi_{517}(127,\cdot)\) \(\chi_{517}(129,\cdot)\) \(\chi_{517}(134,\cdot)\) \(\chi_{517}(138,\cdot)\) \(\chi_{517}(139,\cdot)\) \(\chi_{517}(151,\cdot)\) \(\chi_{517}(156,\cdot)\) \(\chi_{517}(160,\cdot)\) \(\chi_{517}(161,\cdot)\) \(\chi_{517}(167,\cdot)\) \(\chi_{517}(171,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{115})$ |
Fixed field: | Number field defined by a degree 230 polynomial (not computed) |
Values on generators
\((189,287)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{43}{46}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 517 }(138, a) \) | \(1\) | \(1\) | \(e\left(\frac{167}{230}\right)\) | \(e\left(\frac{103}{115}\right)\) | \(e\left(\frac{52}{115}\right)\) | \(e\left(\frac{123}{230}\right)\) | \(e\left(\frac{143}{230}\right)\) | \(e\left(\frac{49}{230}\right)\) | \(e\left(\frac{41}{230}\right)\) | \(e\left(\frac{91}{115}\right)\) | \(e\left(\frac{6}{23}\right)\) | \(e\left(\frac{8}{23}\right)\) |