Basic properties
Modulus: | \(1000\) | |
Conductor: | \(1000\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1000.bj
\(\chi_{1000}(13,\cdot)\) \(\chi_{1000}(37,\cdot)\) \(\chi_{1000}(53,\cdot)\) \(\chi_{1000}(77,\cdot)\) \(\chi_{1000}(117,\cdot)\) \(\chi_{1000}(133,\cdot)\) \(\chi_{1000}(173,\cdot)\) \(\chi_{1000}(197,\cdot)\) \(\chi_{1000}(213,\cdot)\) \(\chi_{1000}(237,\cdot)\) \(\chi_{1000}(253,\cdot)\) \(\chi_{1000}(277,\cdot)\) \(\chi_{1000}(317,\cdot)\) \(\chi_{1000}(333,\cdot)\) \(\chi_{1000}(373,\cdot)\) \(\chi_{1000}(397,\cdot)\) \(\chi_{1000}(413,\cdot)\) \(\chi_{1000}(437,\cdot)\) \(\chi_{1000}(453,\cdot)\) \(\chi_{1000}(477,\cdot)\) \(\chi_{1000}(517,\cdot)\) \(\chi_{1000}(533,\cdot)\) \(\chi_{1000}(573,\cdot)\) \(\chi_{1000}(597,\cdot)\) \(\chi_{1000}(613,\cdot)\) \(\chi_{1000}(637,\cdot)\) \(\chi_{1000}(653,\cdot)\) \(\chi_{1000}(677,\cdot)\) \(\chi_{1000}(717,\cdot)\) \(\chi_{1000}(733,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{100})$ |
Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((751,501,377)\) → \((1,-1,e\left(\frac{73}{100}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 1000 }(517, a) \) | \(-1\) | \(1\) | \(e\left(\frac{61}{100}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{11}{50}\right)\) | \(e\left(\frac{49}{50}\right)\) | \(e\left(\frac{97}{100}\right)\) | \(e\left(\frac{29}{100}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{33}{50}\right)\) | \(e\left(\frac{63}{100}\right)\) | \(e\left(\frac{83}{100}\right)\) |