Basic properties
| Modulus: | \(2000\) | |
| Conductor: | \(2000\) | 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 2000.cg
\(\chi_{2000}(21,\cdot)\) \(\chi_{2000}(61,\cdot)\) \(\chi_{2000}(141,\cdot)\) \(\chi_{2000}(181,\cdot)\) \(\chi_{2000}(221,\cdot)\) \(\chi_{2000}(261,\cdot)\) \(\chi_{2000}(341,\cdot)\) \(\chi_{2000}(381,\cdot)\) \(\chi_{2000}(421,\cdot)\) \(\chi_{2000}(461,\cdot)\) \(\chi_{2000}(541,\cdot)\) \(\chi_{2000}(581,\cdot)\) \(\chi_{2000}(621,\cdot)\) \(\chi_{2000}(661,\cdot)\) \(\chi_{2000}(741,\cdot)\) \(\chi_{2000}(781,\cdot)\) \(\chi_{2000}(821,\cdot)\) \(\chi_{2000}(861,\cdot)\) \(\chi_{2000}(941,\cdot)\) \(\chi_{2000}(981,\cdot)\) \(\chi_{2000}(1021,\cdot)\) \(\chi_{2000}(1061,\cdot)\) \(\chi_{2000}(1141,\cdot)\) \(\chi_{2000}(1181,\cdot)\) \(\chi_{2000}(1221,\cdot)\) \(\chi_{2000}(1261,\cdot)\) \(\chi_{2000}(1341,\cdot)\) \(\chi_{2000}(1381,\cdot)\) \(\chi_{2000}(1421,\cdot)\) \(\chi_{2000}(1461,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((751,501,1377)\) → \((1,-i,e\left(\frac{14}{25}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 2000 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{100}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{17}{50}\right)\) | \(e\left(\frac{31}{100}\right)\) | \(e\left(\frac{9}{100}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{33}{100}\right)\) | \(e\left(\frac{27}{100}\right)\) | \(e\left(\frac{43}{50}\right)\) | \(e\left(\frac{51}{100}\right)\) |