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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%