Basic properties
Modulus: | \(500\) | |
Conductor: | \(500\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(100\) | 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 500.r
\(\chi_{500}(3,\cdot)\) \(\chi_{500}(23,\cdot)\) \(\chi_{500}(27,\cdot)\) \(\chi_{500}(47,\cdot)\) \(\chi_{500}(63,\cdot)\) \(\chi_{500}(67,\cdot)\) \(\chi_{500}(83,\cdot)\) \(\chi_{500}(87,\cdot)\) \(\chi_{500}(103,\cdot)\) \(\chi_{500}(123,\cdot)\) \(\chi_{500}(127,\cdot)\) \(\chi_{500}(147,\cdot)\) \(\chi_{500}(163,\cdot)\) \(\chi_{500}(167,\cdot)\) \(\chi_{500}(183,\cdot)\) \(\chi_{500}(187,\cdot)\) \(\chi_{500}(203,\cdot)\) \(\chi_{500}(223,\cdot)\) \(\chi_{500}(227,\cdot)\) \(\chi_{500}(247,\cdot)\) \(\chi_{500}(263,\cdot)\) \(\chi_{500}(267,\cdot)\) \(\chi_{500}(283,\cdot)\) \(\chi_{500}(287,\cdot)\) \(\chi_{500}(303,\cdot)\) \(\chi_{500}(323,\cdot)\) \(\chi_{500}(327,\cdot)\) \(\chi_{500}(347,\cdot)\) \(\chi_{500}(363,\cdot)\) \(\chi_{500}(367,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{100})$ |
Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((251,377)\) → \((-1,e\left(\frac{73}{100}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 500 }(267, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{100}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{11}{50}\right)\) | \(e\left(\frac{49}{50}\right)\) | \(e\left(\frac{47}{100}\right)\) | \(e\left(\frac{29}{100}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{13}{100}\right)\) | \(e\left(\frac{83}{100}\right)\) |