Basic properties
| Modulus: | \(10000\) | |
| Conductor: | \(2000\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(100\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2000}(1067,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 10000.cf
\(\chi_{10000}(107,\cdot)\) \(\chi_{10000}(243,\cdot)\) \(\chi_{10000}(507,\cdot)\) \(\chi_{10000}(643,\cdot)\) \(\chi_{10000}(907,\cdot)\) \(\chi_{10000}(1043,\cdot)\) \(\chi_{10000}(1707,\cdot)\) \(\chi_{10000}(1843,\cdot)\) \(\chi_{10000}(2107,\cdot)\) \(\chi_{10000}(2243,\cdot)\) \(\chi_{10000}(2507,\cdot)\) \(\chi_{10000}(2643,\cdot)\) \(\chi_{10000}(2907,\cdot)\) \(\chi_{10000}(3043,\cdot)\) \(\chi_{10000}(3707,\cdot)\) \(\chi_{10000}(3843,\cdot)\) \(\chi_{10000}(4107,\cdot)\) \(\chi_{10000}(4243,\cdot)\) \(\chi_{10000}(4507,\cdot)\) \(\chi_{10000}(4643,\cdot)\) \(\chi_{10000}(4907,\cdot)\) \(\chi_{10000}(5043,\cdot)\) \(\chi_{10000}(5707,\cdot)\) \(\chi_{10000}(5843,\cdot)\) \(\chi_{10000}(6107,\cdot)\) \(\chi_{10000}(6243,\cdot)\) \(\chi_{10000}(6507,\cdot)\) \(\chi_{10000}(6643,\cdot)\) \(\chi_{10000}(6907,\cdot)\) \(\chi_{10000}(7043,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((8751,2501,9377)\) → \((-1,i,e\left(\frac{13}{100}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 10000 }(107, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{63}{100}\right)\) | \(e\left(\frac{41}{50}\right)\) | \(e\left(\frac{49}{100}\right)\) | \(e\left(\frac{59}{100}\right)\) | \(e\left(\frac{21}{100}\right)\) | \(e\left(\frac{3}{100}\right)\) | \(e\left(\frac{12}{25}\right)\) |