The database currently contains 21,045,332 Galois orbits of Dirichlet characters of modulus up to 100,000. This comprises 3,039,650,754 Dirichlet characters. The tables below show counts of Galois orbits.
Distribution of conductors
conductor | 1-10 | 11-100 | 101-1000 | 1001-10000 |
---|---|---|---|---|
count | 288410 | 736315 | 2044830 | 5544321 |
proportion | 3.35% | 8.55% | 23.74% | 64.36% |
Distribution of order by modulus
modulus | ||||||
---|---|---|---|---|---|---|
1-10 | 11-100 | 101-1000 | 1001-10000 | Total | ||
order
|
1-10 | 26 | 695 | 13681 | 236212 | 250614 |
100.00% | 80.25% | 52.70% | 31.85% | 32.61% | ||
11-100 | 171 | 10719 | 362601 | 373491 | ||
19.75% | 41.29% | 48.89% | 48.60% | |||
101-1000 | 1560 | 129250 | 130810 | |||
6.01% | 17.43% | 17.02% | ||||
1001-10000 | 13597 | 13597 | ||||
1.83% | 1.77% | |||||
Total | 26 | 866 | 25960 | 741660 | 768512 | |
0.00% | 0.11% | 3.38% | 96.51% |
Distribution of primitivity by modulus
modulus | ||||||
---|---|---|---|---|---|---|
1-10 | 11-100 | 101-1000 | 1001-10000 | Total | ||
primitive
|
no | 14 | 517 | 16485 | 480433 | 497449 |
53.85% | 59.70% | 63.50% | 64.78% | 64.73% | ||
yes | 12 | 349 | 9475 | 261227 | 271063 | |
46.15% | 40.30% | 36.50% | 35.22% | 35.27% | ||
Total | 26 | 866 | 25960 | 741660 | 768512 | |
0.00% | 0.11% | 3.38% | 96.51% |
Distribution of real characters by modulus
modulus | ||||||
---|---|---|---|---|---|---|
1-10 | 11-100 | 101-1000 | 1001-10000 | Total | ||
real
|
no | 6 | 548 | 21522 | 684672 | 706748 |
23.08% | 63.28% | 82.90% | 92.32% | 91.96% | ||
yes | 20 | 318 | 4438 | 56988 | 61764 | |
76.92% | 36.72% | 17.10% | 7.68% | 8.04% | ||
Total | 26 | 866 | 25960 | 741660 | 768512 | |
0.00% | 0.11% | 3.38% | 96.51% |
Distribution of minimality by modulus
modulus | ||||||
---|---|---|---|---|---|---|
1-10 | 11-100 | 101-1000 | 1001-10000 | Total | ||
minimal
|
no | 2 | 101 | 3719 | 116996 | 120818 |
7.69% | 11.66% | 14.33% | 15.77% | 15.72% | ||
yes | 24 | 765 | 22241 | 624664 | 647694 | |
92.31% | 88.34% | 85.67% | 84.23% | 84.28% | ||
Total | 26 | 866 | 25960 | 741660 | 768512 | |
0.00% | 0.11% | 3.38% | 96.51% |