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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1000.bh
\(\chi_{1000}(3,\cdot)\) \(\chi_{1000}(27,\cdot)\) \(\chi_{1000}(67,\cdot)\) \(\chi_{1000}(83,\cdot)\) \(\chi_{1000}(123,\cdot)\) \(\chi_{1000}(147,\cdot)\) \(\chi_{1000}(163,\cdot)\) \(\chi_{1000}(187,\cdot)\) \(\chi_{1000}(203,\cdot)\) \(\chi_{1000}(227,\cdot)\) \(\chi_{1000}(267,\cdot)\) \(\chi_{1000}(283,\cdot)\) \(\chi_{1000}(323,\cdot)\) \(\chi_{1000}(347,\cdot)\) \(\chi_{1000}(363,\cdot)\) \(\chi_{1000}(387,\cdot)\) \(\chi_{1000}(403,\cdot)\) \(\chi_{1000}(427,\cdot)\) \(\chi_{1000}(467,\cdot)\) \(\chi_{1000}(483,\cdot)\) \(\chi_{1000}(523,\cdot)\) \(\chi_{1000}(547,\cdot)\) \(\chi_{1000}(563,\cdot)\) \(\chi_{1000}(587,\cdot)\) \(\chi_{1000}(603,\cdot)\) \(\chi_{1000}(627,\cdot)\) \(\chi_{1000}(667,\cdot)\) \(\chi_{1000}(683,\cdot)\) \(\chi_{1000}(723,\cdot)\) \(\chi_{1000}(747,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{100})$ |
Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((751,501,377)\) → \((-1,-1,e\left(\frac{93}{100}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 1000 }(667, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{100}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{1}{50}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{77}{100}\right)\) | \(e\left(\frac{89}{100}\right)\) | \(e\left(\frac{37}{50}\right)\) | \(e\left(\frac{3}{50}\right)\) | \(e\left(\frac{33}{100}\right)\) | \(e\left(\frac{53}{100}\right)\) |