Basic properties
| Modulus: | \(2500\) | |
| Conductor: | \(500\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(100\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{500}(47,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2500.r
\(\chi_{2500}(7,\cdot)\) \(\chi_{2500}(43,\cdot)\) \(\chi_{2500}(107,\cdot)\) \(\chi_{2500}(143,\cdot)\) \(\chi_{2500}(207,\cdot)\) \(\chi_{2500}(243,\cdot)\) \(\chi_{2500}(343,\cdot)\) \(\chi_{2500}(407,\cdot)\) \(\chi_{2500}(507,\cdot)\) \(\chi_{2500}(543,\cdot)\) \(\chi_{2500}(607,\cdot)\) \(\chi_{2500}(643,\cdot)\) \(\chi_{2500}(707,\cdot)\) \(\chi_{2500}(743,\cdot)\) \(\chi_{2500}(843,\cdot)\) \(\chi_{2500}(907,\cdot)\) \(\chi_{2500}(1007,\cdot)\) \(\chi_{2500}(1043,\cdot)\) \(\chi_{2500}(1107,\cdot)\) \(\chi_{2500}(1143,\cdot)\) \(\chi_{2500}(1207,\cdot)\) \(\chi_{2500}(1243,\cdot)\) \(\chi_{2500}(1343,\cdot)\) \(\chi_{2500}(1407,\cdot)\) \(\chi_{2500}(1507,\cdot)\) \(\chi_{2500}(1543,\cdot)\) \(\chi_{2500}(1607,\cdot)\) \(\chi_{2500}(1643,\cdot)\) \(\chi_{2500}(1707,\cdot)\) \(\chi_{2500}(1743,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((1251,1877)\) → \((-1,e\left(\frac{97}{100}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 2500 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{100}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{11}{50}\right)\) | \(e\left(\frac{83}{100}\right)\) | \(e\left(\frac{81}{100}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{57}{100}\right)\) | \(e\left(\frac{87}{100}\right)\) |