The database currently contains 30,397,486 Dirichlet characters of modulus up to 10,000, lying in 768,512 Galois orbits. The tables below show counts of Galois orbits.
Distribution of conductors
conductor | 1-10 | 11-100 | 101-1000 | 1001-10000 |
---|---|---|---|---|
count | 28839 | 73467 | 200366 | 465840 |
proportion | 3.75% | 9.56% | 26.07% | 60.62% |
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 | 1 | 71 | 2807 | 90797 | 93676 |
3.85% | 8.20% | 10.81% | 12.24% | 12.19% | ||
yes | 25 | 795 | 23153 | 650863 | 674836 | |
96.15% | 91.80% | 89.19% | 87.76% | 87.81% | ||
Total | 26 | 866 | 25960 | 741660 | 768512 | |
0.00% | 0.11% | 3.38% | 96.51% |