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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%