LMFDB - Classical modular forms: Statistics

The database currently contains $1{,}141{,}510$ (Galois orbits of) newforms in $62{,}273$ newspaces, and $14{,}417{,}694$ of their embeddings into the complex numbers. In addition to the statistics below, you can also create your own.

See the completeness knowl for a description of the set of newforms that are included in these statistics.

Distribution of levels and weights

		weight
		1	2	3	4	5-8	9-16	17-32	33-64	65-316	Total
level	1						2	8	16	126	152
	1						0.02%	0.16%	0.86%	8.58%	0.01%
	2-10			4	10	58	154	333	675	1343	2577
	2-10			0.03%	0.04%	0.26%	1.27%	6.86%	36.43%	91.42%	0.23%
	11-100	29	634	570	864	3056	5125	4315	1162		15755
	11-100	0.15%	0.06%	4.48%	3.04%	13.47%	42.41%	88.88%	62.71%		1.38%
	101-1000	2101	32977	8561	12307	18156	6804	199			81105
	101-1000	10.88%	3.18%	67.34%	43.23%	80.00%	56.30%	4.10%			7.11%
	1001-5000	17176	68539	3578	15285	1425					106003
	1001-5000	88.97%	6.60%	28.14%	53.70%	6.28%					9.29%
	5001-10000		76373								76373
	5001-10000		7.36%								6.69%
	10001-50000		702640								702640
	10001-50000		67.69%								61.55%
	50001-100000		9836								9836
	50001-100000		0.95%								0.86%
	100001-1000000		147069								147069
	100001-1000000		14.17%								12.88%
	Total	19306	1038068	12713	28466	22695	12085	4855	1853	1469	1141510
	Total	1.69%	90.94%	1.11%	2.49%	1.99%	1.06%	0.43%	0.16%	0.13%

Distribution of levels and absolute dimension

		abs. dimension
		1	2	3	4	5	6-10	11-20	21-100	101-1000	1001-10000	10001-100000	Total
level	1	6	6	6	6	6	30	60	32				152
	1	3.95%	3.95%	3.95%	3.95%	3.95%	19.74%	39.47%	21.05%				0.01%
	2-10	349	184	150	182	138	491	346	616	121			2577
	2-10	13.54%	7.14%	5.82%	7.06%	5.36%	19.05%	13.43%	23.90%	4.70%			0.23%
	11-100	1700	1955	609	1286	336	2083	2077	4197	1454	58		15755
	11-100	10.79%	12.41%	3.87%	8.16%	2.13%	13.22%	13.18%	26.64%	9.23%	0.37%		1.38%
	101-1000	6691	10792	2213	8562	1307	11147	10481	19004	8898	1918	92	81105
	101-1000	8.25%	13.31%	2.73%	10.56%	1.61%	13.74%	12.92%	23.43%	10.97%	2.36%	0.11%	7.11%
	1001-5000	19217	19386	5011	11643	2516	15772	12956	17804	1698			106003
	1001-5000	18.13%	18.29%	4.73%	10.98%	2.37%	14.88%	12.22%	16.80%	1.60%			9.29%
	5001-10000	20728	9505	4288	3923	2009	7757	8302	15430	4431			76373
	5001-10000	27.14%	12.45%	5.61%	5.14%	2.63%	10.16%	10.87%	20.20%	5.80%			6.69%
	10001-50000	176159	61554	24293	19793	11096	45754	57059	170903	130702	5327		702640
	10001-50000	25.07%	8.76%	3.46%	2.82%	1.58%	6.51%	8.12%	24.32%	18.60%	0.76%		61.55%
	50001-100000	670	229	17	1	1					8918		9836
	50001-100000	6.81%	2.33%	0.17%	0.01%	0.01%					90.67%		0.86%
	100001-1000000	7486	1675	92	3		1				23265	114547	147069
	100001-1000000	5.09%	1.14%	0.06%	0.00%		0.00%				15.82%	77.89%	12.88%
	Total	233006	105286	36679	45399	17409	83035	91281	227986	147304	39486	114639	1141510
	Total	20.41%	9.22%	3.21%	3.98%	1.53%	7.27%	8.00%	19.97%	12.90%	3.46%	10.04%

Distribution of character orders and relative dimension

		rel. dimension
		1	2	3	4	5	6-10	11-20	21-100	101-1000	Total
character order	1	229267	84954	35946	29430	17199	66735	76829	201290	137076	878726
	1	26.09%	9.67%	4.09%	3.35%	1.96%	7.59%	8.74%	22.91%	15.60%	88.81%
	2	3739	10551	733	6877	210	7120	6403	11172	117	46922
	2	7.97%	22.49%	1.56%	14.66%	0.45%	15.17%	13.65%	23.81%	0.25%	4.74%
	3	4023	1547	926	743	454	1684	1303	1032	11	11723
	3	34.32%	13.20%	7.90%	6.34%	3.87%	14.36%	11.11%	8.80%	0.09%	1.18%
	4	2218	2058	175	1105	79	1544	1461	1979	102	10721
	4	20.69%	19.20%	1.63%	10.31%	0.74%	14.40%	13.63%	18.46%	0.95%	1.08%
	5	551	256	117	141	82	295	252	218		1912
	5	28.82%	13.39%	6.12%	7.37%	4.29%	15.43%	13.18%	11.40%		0.19%
	6-10	4991	3645	494	1667	240	2459	2395	4493	259	20643
	6-10	24.18%	17.66%	2.39%	8.08%	1.16%	11.91%	11.60%	21.77%	1.25%	2.09%
	11-20	2534	878	215	373	152	940	1172	2413	254	8931
	11-20	28.37%	9.83%	2.41%	4.18%	1.70%	10.53%	13.12%	27.02%	2.84%	0.90%
	21-100	2498	375	77	146	105	703	1107	3047	267	8325
	21-100	30.01%	4.50%	0.92%	1.75%	1.26%	8.44%	13.30%	36.60%	3.21%	0.84%
	101-1000	595	12	3			18	148	729	45	1550
	101-1000	38.39%	0.77%	0.19%			1.16%	9.55%	47.03%	2.90%	0.16%
	Total	250416	104276	38686	40482	18521	81498	91070	226373	138131	989453
	Total	25.31%	10.54%	3.91%	4.09%	1.87%	8.24%	9.20%	22.88%	13.96%

Distribution of analytic ranks

analytic rank	Unknown	0	1	2	3	$\mathrm{avg}\ 0.33$
count	859625	192245	87073	2566	1	281885
proportion	304.96%	68.20%	30.89%	0.91%	0.00%	100.00%

Distribution of projective images for weight 1 forms

projective image	$A_{4}$	$S_{4}$	$A_{5}$	$D_{2}$	$D_{3}$	$D_{4}$	$D_{5}$	$D_{6}$	$D_{7}$	$D_{8}$
count	458	1033	202	1311	2924	1648	1126	1940	581	536
proportion	2.37%	5.35%	1.05%	6.79%	15.15%	8.54%	5.83%	10.05%	3.01%	2.78%
projective image	$D_{9}$	$D_{10}$	$D_{11}$	$D_{12}$	$D_{13}$	$D_{14}$	$D_{15}$	$D_{16}$	$D_{17}$	$D_{18}$
count	733	639	267	764	154	258	452	204	75	402
proportion	3.80%	3.31%	1.38%	3.96%	0.80%	1.34%	2.34%	1.06%	0.39%	2.08%
projective image	$D_{19}$	$D_{20}$	$D_{21}$	$D_{22}$	$D_{23}$	$D_{24}$	$D_{25}$	$D_{26}$	$D_{27}$	$D_{28}$
count	50	234	185	122	59	153	65	87	95	115
proportion	0.26%	1.21%	0.96%	0.63%	0.31%	0.79%	0.34%	0.45%	0.49%	0.60%
projective image	$D_{29}$	$D_{30}$	$D_{31}$	$D_{32}$	$D_{33}$	$D_{34}$	$D_{35}$	$D_{36}$	$D_{37}$	$D_{38}$
count	42	259	17	49	74	25	60	165	13	18
proportion	0.22%	1.34%	0.09%	0.25%	0.38%	0.13%	0.31%	0.85%	0.07%	0.09%
projective image	$D_{39}$	$D_{40}$	$D_{41}$	$D_{42}$	$D_{43}$	$D_{44}$	$D_{45}$	$D_{46}$	$D_{47}$	$D_{48}$
count	55	78	26	101	10	42	58	23	5	59
proportion	0.28%	0.40%	0.13%	0.52%	0.05%	0.22%	0.30%	0.12%	0.03%	0.31%
projective image	$D_{49}$	$D_{50}$	$D_{51}$	$D_{52}$	$D_{53}$	$D_{54}$	$D_{55}$	$D_{56}$	$D_{57}$	$D_{58}$
count	13	33	23	55	12	37	25	24	17	16
proportion	0.07%	0.17%	0.12%	0.28%	0.06%	0.19%	0.13%	0.12%	0.09%	0.08%

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projective image	$A_{4}$	$S_{4}$	$A_{5}$	$D_{2}$	$D_{3}$	$D_{4}$	$D_{5}$	$D_{6}$	$D_{7}$	$D_{8}$
count	458	1033	202	1311	2924	1648	1126	1940	581	536
proportion	2.37%	5.35%	1.05%	6.79%	15.15%	8.54%	5.83%	10.05%	3.01%	2.78%
projective image	$D_{9}$	$D_{10}$	$D_{11}$	$D_{12}$	$D_{13}$	$D_{14}$	$D_{15}$	$D_{16}$	$D_{17}$	$D_{18}$
count	733	639	267	764	154	258	452	204	75	402
proportion	3.80%	3.31%	1.38%	3.96%	0.80%	1.34%	2.34%	1.06%	0.39%	2.08%
projective image	$D_{19}$	$D_{20}$	$D_{21}$	$D_{22}$	$D_{23}$	$D_{24}$	$D_{25}$	$D_{26}$	$D_{27}$	$D_{28}$
count	50	234	185	122	59	153	65	87	95	115
proportion	0.26%	1.21%	0.96%	0.63%	0.31%	0.79%	0.34%	0.45%	0.49%	0.60%
projective image	$D_{29}$	$D_{30}$	$D_{31}$	$D_{32}$	$D_{33}$	$D_{34}$	$D_{35}$	$D_{36}$	$D_{37}$	$D_{38}$
count	42	259	17	49	74	25	60	165	13	18
proportion	0.22%	1.34%	0.09%	0.25%	0.38%	0.13%	0.31%	0.85%	0.07%	0.09%
projective image	$D_{39}$	$D_{40}$	$D_{41}$	$D_{42}$	$D_{43}$	$D_{44}$	$D_{45}$	$D_{46}$	$D_{47}$	$D_{48}$
count	55	78	26	101	10	42	58	23	5	59
proportion	0.28%	0.40%	0.13%	0.52%	0.05%	0.22%	0.30%	0.12%	0.03%	0.31%
projective image	$D_{49}$	$D_{50}$	$D_{51}$	$D_{52}$	$D_{53}$	$D_{54}$	$D_{55}$	$D_{56}$	$D_{57}$	$D_{58}$
count	13	33	23	55	12	37	25	24	17	16
proportion	0.07%	0.17%	0.12%	0.28%	0.06%	0.19%	0.13%	0.12%	0.09%	0.08%
projective image	$D_{59}$	$D_{60}$	$D_{61}$	$D_{62}$	$D_{63}$	$D_{64}$	$D_{65}$	$D_{66}$	$D_{67}$	$D_{68}$
count	5	83	5	4	27	12	11	42	3	12
proportion	0.03%	0.43%	0.03%	0.02%	0.14%	0.06%	0.06%	0.22%	0.02%	0.06%
projective image	$D_{69}$	$D_{70}$	$D_{71}$	$D_{72}$	$D_{73}$	$D_{74}$	$D_{75}$	$D_{76}$	$D_{77}$	$D_{78}$
count	21	36	5	34	5	9	22	4	3	42
proportion	0.11%	0.19%	0.03%	0.18%	0.03%	0.05%	0.11%	0.02%	0.02%	0.22%
projective image	$D_{79}$	$D_{80}$	$D_{81}$	$D_{82}$	$D_{83}$	$D_{84}$	$D_{85}$	$D_{86}$	$D_{87}$	$D_{88}$
count	3	17	19	5	11	19	1	6	5	13
proportion	0.02%	0.09%	0.10%	0.03%	0.06%	0.10%	0.01%	0.03%	0.03%	0.07%
projective image	$D_{89}$	$D_{90}$	$D_{91}$	$D_{92}$	$D_{93}$	$D_{94}$	$D_{95}$	$D_{96}$	$D_{97}$	$D_{98}$
count	4	32	3	3	3	2	7	28	2	8
proportion	0.02%	0.17%	0.02%	0.02%	0.02%	0.01%	0.04%	0.15%	0.01%	0.04%
projective image	$D_{99}$	$D_{100}$	$D_{101}$	$D_{102}$	$D_{103}$	$D_{104}$	$D_{105}$	$D_{106}$	$D_{107}$	$D_{108}$
count	10	10	3	10	2	5	18	4	2	16
proportion	0.05%	0.05%	0.02%	0.05%	0.01%	0.03%	0.09%	0.02%	0.01%	0.08%
projective image	$D_{110}$	$D_{111}$	$D_{112}$	$D_{113}$	$D_{114}$	$D_{115}$	$D_{116}$	$D_{117}$	$D_{118}$	$D_{119}$
count	10	2	16	3	9	2	8	2	1	2
proportion	0.05%	0.01%	0.08%	0.02%	0.05%	0.01%	0.04%	0.01%	0.01%	0.01%
projective image	$D_{120}$	$D_{121}$	$D_{122}$	$D_{123}$	$D_{124}$	$D_{125}$	$D_{126}$	$D_{127}$	$D_{128}$	$D_{129}$
count	13	1	3	1	1	4	12	1	5	1
proportion	0.07%	0.01%	0.02%	0.01%	0.01%	0.02%	0.06%	0.01%	0.03%	0.01%
projective image	$D_{130}$	$D_{131}$	$D_{132}$	$D_{134}$	$D_{135}$	$D_{136}$	$D_{137}$	$D_{138}$	$D_{139}$	$D_{140}$
count	4	4	6	1	5	8	1	10	2	9
proportion	0.02%	0.02%	0.03%	0.01%	0.03%	0.04%	0.01%	0.05%	0.01%	0.05%
projective image	$D_{141}$	$D_{142}$	$D_{143}$	$D_{144}$	$D_{145}$	$D_{146}$	$D_{147}$	$D_{148}$	$D_{150}$	$D_{151}$
count	2	3	1	8	1	2	2	3	7	1
proportion	0.01%	0.02%	0.01%	0.04%	0.01%	0.01%	0.01%	0.02%	0.04%	0.01%
projective image	$D_{153}$	$D_{154}$	$D_{155}$	$D_{156}$	$D_{158}$	$D_{159}$	$D_{160}$	$D_{161}$	$D_{162}$	$D_{163}$
count	5	1	2	16	2	1	1	1	5	1
proportion	0.03%	0.01%	0.01%	0.08%	0.01%	0.01%	0.01%	0.01%	0.03%	0.01%
projective image	$D_{165}$	$D_{166}$	$D_{168}$	$D_{169}$	$D_{170}$	$D_{171}$	$D_{172}$	$D_{173}$	$D_{175}$	$D_{176}$
count	6	1	5	1	1	1	3	3	3	2
proportion	0.03%	0.01%	0.03%	0.01%	0.01%	0.01%	0.02%	0.02%	0.02%	0.01%
projective image	$D_{177}$	$D_{178}$	$D_{179}$	$D_{180}$	$D_{181}$	$D_{182}$	$D_{183}$	$D_{186}$	$D_{187}$	$D_{188}$
count	2	1	1	12	1	1	1	2	1	1
proportion	0.01%	0.01%	0.01%	0.06%	0.01%	0.01%	0.01%	0.01%	0.01%	0.01%
projective image	$D_{189}$	$D_{190}$	$D_{192}$	$D_{193}$	$D_{194}$	$D_{195}$	$D_{196}$	$D_{198}$	$D_{199}$	$D_{200}$
count	4	1	4	1	1	3	2	2	1	3
proportion	0.02%	0.01%	0.02%	0.01%	0.01%	0.02%	0.01%	0.01%	0.01%	0.02%
projective image	$D_{202}$	$D_{203}$	$D_{204}$	$D_{205}$	$D_{206}$	$D_{207}$	$D_{208}$	$D_{209}$	$D_{210}$	$D_{213}$
count	2	1	1	3	1	2	3	1	7	2
proportion	0.01%	0.01%	0.01%	0.02%	0.01%	0.01%	0.02%	0.01%	0.04%	0.01%
projective image	$D_{214}$	$D_{215}$	$D_{216}$	$D_{217}$	$D_{219}$	$D_{220}$	$D_{221}$	$D_{224}$	$D_{228}$	$D_{231}$
count	1	2	2	1	1	2	3	2	2	1
proportion	0.01%	0.01%	0.01%	0.01%	0.01%	0.01%	0.02%	0.01%	0.01%	0.01%
projective image	$D_{232}$	$D_{233}$	$D_{234}$	$D_{235}$	$D_{238}$	$D_{243}$	$D_{244}$	$D_{245}$	$D_{249}$	$D_{253}$
count	1	1	2	1	1	1	1	2	4	1
proportion	0.01%	0.01%	0.01%	0.01%	0.01%	0.01%	0.01%	0.01%	0.02%	0.01%
projective image	$D_{258}$	$D_{270}$	$D_{273}$	$D_{278}$	$D_{284}$	$D_{285}$
count	1	1	1	1	1	1
proportion	0.01%	0.01%	0.01%	0.01%	0.01%	0.01%

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Distribution of number of newforms in $S_k(N, \chi)$

newforms	Unknown	0	1	2	3	4	5	6	7	8
count	558562	860189	23501	13877	3718	5962	2574	1906	990	1877
proportion	60.55%	93.25%	2.55%	1.50%	0.40%	0.65%	0.28%	0.21%	0.11%	0.20%
newforms	9	10	11	12	13	14	15	16	17	18
count	961	901	602	637	460	425	317	344	248	298
proportion	0.10%	0.10%	0.07%	0.07%	0.05%	0.05%	0.03%	0.04%	0.03%	0.03%
newforms	19	20	21	22	23	24	25	26	27	28
count	201	220	129	187	113	158	95	128	85	107
proportion	0.02%	0.02%	0.01%	0.02%	0.01%	0.02%	0.01%	0.01%	0.01%	0.01%
newforms	29	30	31	32	33	34	35	36	37	38
count	81	92	64	81	50	58	57	65	41	62
proportion	0.01%	0.01%	0.01%	0.01%	0.01%	0.01%	0.01%	0.01%	0.00%	0.01%
newforms	39	40	41	42	43	44	45	46	47	48
count	34	43	28	31	27	29	22	30	18	35
proportion	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%
newforms	49	50	51	52	53	54	55	56	57	58
count	18	23	11	17	17	16	7	18	7	17
proportion	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%

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newforms	Unknown	0	1	2	3	4	5	6	7	8
count	558562	860189	23501	13877	3718	5962	2574	1906	990	1877
proportion	60.55%	93.25%	2.55%	1.50%	0.40%	0.65%	0.28%	0.21%	0.11%	0.20%
newforms	9	10	11	12	13	14	15	16	17	18
count	961	901	602	637	460	425	317	344	248	298
proportion	0.10%	0.10%	0.07%	0.07%	0.05%	0.05%	0.03%	0.04%	0.03%	0.03%
newforms	19	20	21	22	23	24	25	26	27	28
count	201	220	129	187	113	158	95	128	85	107
proportion	0.02%	0.02%	0.01%	0.02%	0.01%	0.02%	0.01%	0.01%	0.01%	0.01%
newforms	29	30	31	32	33	34	35	36	37	38
count	81	92	64	81	50	58	57	65	41	62
proportion	0.01%	0.01%	0.01%	0.01%	0.01%	0.01%	0.01%	0.01%	0.00%	0.01%
newforms	39	40	41	42	43	44	45	46	47	48
count	34	43	28	31	27	29	22	30	18	35
proportion	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%
newforms	49	50	51	52	53	54	55	56	57	58
count	18	23	11	17	17	16	7	18	7	17
proportion	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%
newforms	59	60	61	62	63	64	65	66	67	68
count	13	8	5	8	8	13	4	7	4	11
proportion	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%
newforms	69	70	71	72	73	74	75	76	77	78
count	3	5	1	4	3	7	3	6	3	1
proportion	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%
newforms	79	80	81	82	83	84	85	86	88	90
count	2	6	3	1	3	3	2	1	3	1
proportion	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%
newforms	92	94	96	99	100	101	105	107	118	128
count	2	1	1	1	1	1	1	1	1	1
proportion	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%

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Distribution of inner twists

inner twists	Unknown	1	2	4	6	8	10	12	16	20
count	416944	607636	72068	38059	30	6263	6	58	392	6
proportion	36.53%	53.23%	6.31%	3.33%	0.00%	0.55%	0.00%	0.01%	0.03%	0.00%
inner twists	24	32	40	44	56
count	14	24	7	1	2
proportion	0.00%	0.00%	0.00%	0.00%	0.00%

Distribution of self twist types by weights

		weight
		1	2	3	4	5-8	9-16	17-32	33-64	65-316	Total
self twist type	neither	1693	1016809	11173	27903	21484	11303	4492	1690	1367	1097914
	neither	8.77%	99.70%	87.89%	98.02%	94.66%	93.53%	92.52%	91.20%	93.06%	97.74%
	CM only	15841	3105	1540	563	1211	782	363	163	102	23670
	CM only	82.05%	0.30%	12.11%	1.98%	5.34%	6.47%	7.48%	8.80%	6.94%	2.11%
	RM only	461									461
	RM only	2.39%									0.04%
	both	1311									1311
	both	6.79%									0.12%

Distribution of complex multiplication

CM disc	-3	-4	-7	-8	-11	-15	-19	-20	-23	-24
count	4361	3030	1498	1530	1114	857	574	703	514	589
proportion	16.59%	11.52%	5.70%	5.82%	4.24%	3.26%	2.18%	2.67%	1.95%	2.24%
CM disc	-31	-35	-39	-40	-43	-47	-51	-52	-55	-56
count	382	374	312	308	121	242	230	173	211	258
proportion	1.45%	1.42%	1.19%	1.17%	0.46%	0.92%	0.87%	0.66%	0.80%	0.98%
CM disc	-59	-67	-68	-71	-79	-83	-84	-87	-88	-91
count	205	54	170	122	98	118	169	149	71	88
proportion	0.78%	0.21%	0.65%	0.46%	0.37%	0.45%	0.64%	0.57%	0.27%	0.33%
CM disc	-95	-103	-104	-107	-111	-115	-116	-119	-120	-123
count	115	70	127	69	113	58	105	102	99	52
proportion	0.44%	0.27%	0.48%	0.26%	0.43%	0.22%	0.40%	0.39%	0.38%	0.20%
CM disc	-127	-131	-132	-136	-139	-143	-148	-151	-152	-155
count	52	63	87	62	45	90	28	41	71	63
proportion	0.20%	0.24%	0.33%	0.24%	0.17%	0.34%	0.11%	0.16%	0.27%	0.24%
CM disc	-159	-163	-164	-167	-168	-179	-183	-184	-187	-191
count	70	13	57	34	39	44	51	36	18	41
proportion	0.27%	0.05%	0.22%	0.13%	0.15%	0.17%	0.19%	0.14%	0.07%	0.16%

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CM disc	-3	-4	-7	-8	-11	-15	-19	-20	-23	-24
count	4361	3030	1498	1530	1114	857	574	703	514	589
proportion	16.59%	11.52%	5.70%	5.82%	4.24%	3.26%	2.18%	2.67%	1.95%	2.24%
CM disc	-31	-35	-39	-40	-43	-47	-51	-52	-55	-56
count	382	374	312	308	121	242	230	173	211	258
proportion	1.45%	1.42%	1.19%	1.17%	0.46%	0.92%	0.87%	0.66%	0.80%	0.98%
CM disc	-59	-67	-68	-71	-79	-83	-84	-87	-88	-91
count	205	54	170	122	98	118	169	149	71	88
proportion	0.78%	0.21%	0.65%	0.46%	0.37%	0.45%	0.64%	0.57%	0.27%	0.33%
CM disc	-95	-103	-104	-107	-111	-115	-116	-119	-120	-123
count	115	70	127	69	113	58	105	102	99	52
proportion	0.44%	0.27%	0.48%	0.26%	0.43%	0.22%	0.40%	0.39%	0.38%	0.20%
CM disc	-127	-131	-132	-136	-139	-143	-148	-151	-152	-155
count	52	63	87	62	45	90	28	41	71	63
proportion	0.20%	0.24%	0.33%	0.24%	0.17%	0.34%	0.11%	0.16%	0.27%	0.24%
CM disc	-159	-163	-164	-167	-168	-179	-183	-184	-187	-191
count	70	13	57	34	39	44	51	36	18	41
proportion	0.27%	0.05%	0.22%	0.13%	0.15%	0.17%	0.19%	0.14%	0.07%	0.16%
CM disc	-195	-199	-203	-211	-212	-215	-219	-223	-227	-228
count	40	37	35	25	40	35	40	21	18	22
proportion	0.15%	0.14%	0.13%	0.10%	0.15%	0.13%	0.15%	0.08%	0.07%	0.08%
CM disc	-231	-232	-235	-239	-244	-247	-248	-251	-255	-259
count	56	9	20	45	31	24	32	26	37	29
proportion	0.21%	0.03%	0.08%	0.17%	0.12%	0.09%	0.12%	0.10%	0.14%	0.11%
CM disc	-260	-263	-264	-267	-271	-276	-280	-283	-287	-291
count	36	21	47	10	15	39	13	21	29	16
proportion	0.14%	0.08%	0.18%	0.04%	0.06%	0.15%	0.05%	0.08%	0.11%	0.06%
CM disc	-292	-295	-296	-299	-303	-307	-308	-311	-312	-319
count	17	17	28	32	27	12	24	16	10	20
proportion	0.06%	0.06%	0.11%	0.12%	0.10%	0.05%	0.09%	0.06%	0.04%	0.08%
CM disc	-323	-327	-328	-331	-335	-339	-340	-344	-347	-355
count	13	33	13	9	19	20	14	17	9	15
proportion	0.05%	0.13%	0.05%	0.03%	0.07%	0.08%	0.05%	0.06%	0.03%	0.06%
CM disc	-356	-359	-367	-371	-372	-376	-379	-383	-388	-391
count	24	11	12	19	12	18	9	9	14	20
proportion	0.09%	0.04%	0.05%	0.07%	0.05%	0.07%	0.03%	0.03%	0.05%	0.08%
CM disc	-395	-399	-403	-404	-407	-408	-411	-415	-419	-420
count	22	29	8	18	14	10	16	13	16	20
proportion	0.08%	0.11%	0.03%	0.07%	0.05%	0.04%	0.06%	0.05%	0.06%	0.08%
CM disc	-424	-427	-431	-435	-436	-439	-440	-443	-447	-451
count	14	8	17	15	14	25	26	8	11	18
proportion	0.05%	0.03%	0.06%	0.06%	0.05%	0.10%	0.10%	0.03%	0.04%	0.07%
CM disc	-452	-455	-456	-463	-467	-471	-472	-479	-483	-487
count	3	14	10	4	7	6	6	12	6	4
proportion	0.01%	0.05%	0.04%	0.02%	0.03%	0.02%	0.02%	0.05%	0.02%	0.02%
CM disc	-488	-491	-499	-503	-511	-515	-516	-519	-523	-527
count	8	8	6	6	8	5	16	8	7	6
proportion	0.03%	0.03%	0.02%	0.02%	0.03%	0.02%	0.06%	0.03%	0.03%	0.02%
CM disc	-532	-535	-536	-543	-547	-548	-551	-552	-555	-559
count	2	7	6	5	6	3	12	10	6	9
proportion	0.01%	0.03%	0.02%	0.02%	0.02%	0.01%	0.05%	0.04%	0.02%	0.03%
CM disc	-563	-564	-568	-571	-579	-580	-583	-584	-587	-591
count	6	8	2	7	10	7	2	7	5	5
proportion	0.02%	0.03%	0.01%	0.03%	0.04%	0.03%	0.01%	0.03%	0.02%	0.02%
CM disc	-595	-596	-599	-607	-611	-615	-616	-619	-623	-627
count	4	6	6	1	8	6	8	5	2	6
proportion	0.02%	0.02%	0.02%	0.00%	0.03%	0.02%	0.03%	0.02%	0.01%	0.02%
CM disc	-628	-631	-632	-635	-643	-644	-647	-651	-655	-659
count	4	3	4	7	2	8	1	10	7	5
proportion	0.02%	0.01%	0.02%	0.03%	0.01%	0.03%	0.00%	0.04%	0.03%	0.02%
CM disc	-660	-663	-664	-667	-671	-679	-680	-683	-687	-691
count	4	4	6	4	14	7	10	3	5	5
proportion	0.02%	0.02%	0.02%	0.02%	0.05%	0.03%	0.04%	0.01%	0.02%	0.02%
CM disc	-692	-695	-696	-699	-703	-707	-708	-712	-715	-719
count	4	11	12	10	2	4	2	4	4	3
proportion	0.02%	0.04%	0.05%	0.04%	0.01%	0.02%	0.01%	0.02%	0.02%	0.01%
CM disc	-723	-724	-727	-728	-731	-739	-740	-743	-744	-751
count	5	6	1	8	9	5	8	3	12	7
proportion	0.02%	0.02%	0.00%	0.03%	0.03%	0.02%	0.03%	0.01%	0.05%	0.03%
CM disc	-755	-759	-763	-767	-771	-772	-776	-779	-787	-788
count	16	12	4	2	6	2	10	10	3	4
proportion	0.06%	0.05%	0.02%	0.01%	0.02%	0.01%	0.04%	0.04%	0.01%	0.02%
CM disc	-791	-795	-799	-803	-804	-807	-808	-811	-815	-820
count	5	4	4	6	8	2	4	3	6	6
proportion	0.02%	0.02%	0.02%	0.02%	0.03%	0.01%	0.02%	0.01%	0.02%	0.02%
CM disc	-823	-824	-827	-831	-835	-836	-839	-843	-851	-852
count	2	8	3	4	4	8	3	4	6	4
proportion	0.01%	0.03%	0.01%	0.02%	0.02%	0.03%	0.01%	0.02%	0.02%	0.02%
CM disc	-856	-859	-863	-868	-871	-872	-879	-883	-884	-887
count	4	3	3	4	2	4	2	2	10	1
proportion	0.02%	0.01%	0.01%	0.02%	0.01%	0.02%	0.01%	0.01%	0.04%	0.00%
CM disc	-888	-895	-899	-903	-904	-907	-911	-915	-916	-919
count	8	3	6	4	4	2	1	8	4	1
proportion	0.03%	0.01%	0.02%	0.02%	0.02%	0.01%	0.00%	0.03%	0.02%	0.00%
CM disc	-920	-923	-932	-935	-939	-943	-947	-948	-951	-952
count	8	6	6	4	6	3	3	8	2	4
proportion	0.03%	0.02%	0.02%	0.02%	0.02%	0.01%	0.01%	0.03%	0.01%	0.02%
CM disc	-955	-959	-964	-967	-971	-979	-983	-984	-987	-991
count	4	7	6	1	5	6	3	8	8	1
proportion	0.02%	0.03%	0.02%	0.00%	0.02%	0.02%	0.01%	0.03%	0.03%	0.00%
CM disc	-995	-996	-1003	-1007	-1011	-1015	-1016	-1019	-1023	-1027
count	6	8	1	6	4	4	3	1	4	1
proportion	0.02%	0.03%	0.00%	0.02%	0.02%	0.02%	0.01%	0.00%	0.02%	0.00%
CM disc	-1028	-1031	-1032	-1039	-1043	-1047	-1048	-1051	-1055	-1059
count	3	3	2	1	2	3	2	1	7	2
proportion	0.01%	0.01%	0.01%	0.00%	0.01%	0.01%	0.01%	0.00%	0.03%	0.01%
CM disc	-1060	-1063	-1064	-1067	-1076	-1079	-1087	-1091	-1095	-1096
count	2	1	4	4	2	2	2	1	4	4
proportion	0.01%	0.00%	0.02%	0.02%	0.01%	0.01%	0.01%	0.00%	0.02%	0.02%
CM disc	-1099	-1103	-1108	-1111	-1112	-1115	-1119	-1123	-1124	-1128
count	2	1	2	2	2	2	4	1	4	2
proportion	0.01%	0.00%	0.01%	0.01%	0.01%	0.01%	0.02%	0.00%	0.02%	0.01%
CM disc	-1131	-1135	-1139	-1140	-1144	-1147	-1151	-1159	-1160	-1163
count	2	4	3	4	4	2	1	3	4	1
proportion	0.01%	0.02%	0.01%	0.02%	0.02%	0.01%	0.00%	0.01%	0.02%	0.00%
CM disc	-1167	-1171	-1172	-1187	-1191	-1192	-1195	-1199	-1203	-1204
count	2	1	4	2	6	2	2	2	2	2
proportion	0.01%	0.00%	0.02%	0.01%	0.02%	0.01%	0.01%	0.01%	0.01%	0.01%
CM disc	-1207	-1208	-1211	-1219	-1220	-1223	-1227	-1231	-1235	-1236
count	4	4	2	2	4	3	1	3	4	4
proportion	0.02%	0.02%	0.01%	0.01%	0.02%	0.01%	0.00%	0.01%	0.02%	0.02%
CM disc	-1239	-1240	-1243	-1247	-1252	-1255	-1256	-1259	-1263	-1267
count	6	2	1	2	2	4	2	3	4	2
proportion	0.02%	0.01%	0.00%	0.01%	0.01%	0.02%	0.01%	0.01%	0.02%	0.01%
CM disc	-1268	-1271	-1272	-1279	-1283	-1284	-1288	-1291	-1295	-1299
count	2	6	4	1	1	4	2	2	8	2
proportion	0.01%	0.02%	0.02%	0.00%	0.00%	0.02%	0.01%	0.01%	0.03%	0.01%
CM disc	-1303	-1304	-1307	-1311	-1315	-1316	-1319	-1327	-1335	-1336
count	1	2	1	4	2	8	5	3	4	4
proportion	0.00%	0.01%	0.00%	0.02%	0.01%	0.03%	0.02%	0.01%	0.02%	0.02%
CM disc	-1339	-1343	-1347	-1348	-1351	-1355	-1363	-1364	-1367	-1371
count	2	2	2	2	6	4	2	4	2	4
proportion	0.01%	0.01%	0.01%	0.01%	0.02%	0.02%	0.01%	0.02%	0.01%	0.02%
CM disc	-1379	-1383	-1384	-1387	-1391	-1396	-1399	-1403	-1407	-1411
count	3	4	2	1	4	2	3	2	8	1
proportion	0.01%	0.02%	0.01%	0.00%	0.02%	0.01%	0.01%	0.01%	0.03%	0.00%
CM disc	-1412	-1415	-1416	-1419	-1423	-1427	-1432	-1439	-1443	-1447
count	3	2	4	4	2	3	2	3	2	1
proportion	0.01%	0.01%	0.02%	0.02%	0.01%	0.01%	0.01%	0.01%	0.01%	0.00%
CM disc	-1448	-1451	-1455	-1459	-1460	-1463	-1464	-1471	-1479	-1480
count	4	1	4	1	4	6	4	1	4	4
proportion	0.02%	0.00%	0.02%	0.00%	0.02%	0.02%	0.02%	0.00%	0.02%	0.02%
CM disc	-1483	-1487	-1491	-1492	-1495	-1496	-1499	-1507	-1508	-1511
count	1	1	4	2	4	4	1	1	4	2
proportion	0.00%	0.00%	0.02%	0.01%	0.02%	0.02%	0.00%	0.00%	0.02%	0.01%
CM disc	-1515	-1523	-1524	-1527	-1528	-1531	-1535	-1543	-1544	-1547
count	4	1	4	2	2	1	2	1	4	4
proportion	0.02%	0.00%	0.02%	0.01%	0.01%	0.00%	0.01%	0.00%	0.02%	0.02%
CM disc	-1551	-1555	-1556	-1559	-1560	-1563	-1567	-1571	-1572	-1576
count	6	1	2	3	4	2	3	1	4	2
proportion	0.02%	0.00%	0.01%	0.01%	0.02%	0.01%	0.01%	0.00%	0.02%	0.01%
CM disc	-1579	-1583	-1588	-1591	-1592	-1595	-1599	-1603	-1604	-1607
count	2	3	2	2	4	4	8	2	4	3
proportion	0.01%	0.01%	0.01%	0.01%	0.02%	0.02%	0.03%	0.01%	0.02%	0.01%
CM disc	-1608	-1615	-1619	-1623	-1624	-1627	-1631	-1635	-1636	-1639
count	4	8	3	4	4	1	4	2	3	2
proportion	0.02%	0.03%	0.01%	0.02%	0.02%	0.00%	0.02%	0.01%	0.01%	0.01%
CM disc	-1640	-1643	-1651	-1652	-1655	-1659	-1663	-1667	-1668	-1671
count	4	2	2	4	4	2	1	1	4	2
proportion	0.02%	0.01%	0.01%	0.02%	0.02%	0.01%	0.00%	0.00%	0.02%	0.01%
CM disc	-1672	-1679	-1684	-1687	-1688	-1691	-1695	-1699	-1703	-1704
count	2	4	2	4	2	4	4	1	4	8
proportion	0.01%	0.02%	0.01%	0.02%	0.01%	0.02%	0.02%	0.00%	0.02%	0.03%
CM disc	-1707	-1711	-1716	-1720	-1723	-1727	-1731	-1732	-1735	-1736
count	2	4	4	4	1	7	2	4	2	8
proportion	0.01%	0.02%	0.02%	0.02%	0.00%	0.03%	0.01%	0.02%	0.01%	0.03%
CM disc	-1739	-1743	-1747	-1748	-1751	-1752	-1759	-1763	-1767	-1768
count	4	8	1	4	8	2	3	4	6	2
proportion	0.02%	0.03%	0.00%	0.02%	0.03%	0.01%	0.01%	0.02%	0.02%	0.01%
CM disc	-1771	-1779	-1780	-1783	-1784	-1787	-1795	-1796	-1799	-1803
count	2	2	2	1	4	1	2	4	4	2
proportion	0.01%	0.01%	0.01%	0.00%	0.02%	0.00%	0.01%	0.02%	0.02%	0.01%
CM disc	-1807	-1811	-1812	-1816	-1819	-1823	-1828	-1831	-1832	-1835
count	4	1	4	2	2	5	2	1	2	2
proportion	0.02%	0.00%	0.02%	0.01%	0.01%	0.02%	0.01%	0.00%	0.01%	0.01%
CM disc	-1839	-1843	-1844	-1847	-1851	-1855	-1860	-1864	-1867	-1871
count	6	2	6	1	2	4	4	2	1	5
proportion	0.02%	0.01%	0.02%	0.00%	0.01%	0.02%	0.02%	0.01%	0.00%	0.02%
CM disc	-1876	-1879	-1880	-1883	-1887	-1891	-1892	-1895	-1896	-1903
count	4	3	4	2	4	2	4	8	4	2
proportion	0.02%	0.01%	0.02%	0.01%	0.02%	0.01%	0.02%	0.03%	0.02%	0.01%
CM disc	-1907	-1912	-1915	-1919	-1923	-1924	-1927	-1928	-1931	-1939
count	1	2	2	4	2	4	4	4	3	2
proportion	0.00%	0.01%	0.01%	0.02%	0.01%	0.02%	0.02%	0.02%	0.01%	0.01%
CM disc	-1940	-1943	-1947	-1951	-1955	-1956	-1959	-1963	-1967	-1972
count	4	4	2	3	4	4	6	2	7	4
proportion	0.02%	0.02%	0.01%	0.01%	0.02%	0.02%	0.02%	0.01%	0.03%	0.02%
CM disc	-1976	-1979	-1983	-1987	-1988	-1991	-1992	-1999	-2003	-2004
count	4	1	3	1	8	6	2	3	2	4
proportion	0.02%	0.00%	0.01%	0.00%	0.03%	0.02%	0.01%	0.01%	0.01%	0.02%
CM disc	-2008	-2011	-2015	-2019	-2020	-2024	-2027	-2031	-2035	-2036
count	2	1	4	3	2	4	1	2	2	6
proportion	0.01%	0.00%	0.02%	0.01%	0.01%	0.02%	0.00%	0.01%	0.01%	0.02%
CM disc	-2039	-2040	-2047	-2051	-2055	-2056	-2059	-2063	-2067	-2068
count	5	4	4	4	4	3	2	5	2	4
proportion	0.02%	0.02%	0.02%	0.02%	0.02%	0.01%	0.01%	0.02%	0.01%	0.02%
CM disc	-2071	-2072	-2083	-2084	-2087	-2091	-2095	-2099	-2103	-2104
count	6	4	1	4	3	4	3	1	2	4
proportion	0.02%	0.02%	0.00%	0.02%	0.01%	0.02%	0.01%	0.00%	0.01%	0.02%
CM disc	-2111	-2119	-2120	-2123	-2127	-2131	-2132	-2135	-2136	-2139
count	2	2	4	2	4	1	4	4	4	2
proportion	0.01%	0.01%	0.02%	0.01%	0.02%	0.00%	0.02%	0.02%	0.02%	0.01%
CM disc	-2143	-2147	-2148	-2152	-2155	-2159	-2163	-2164	-2167	-2168
count	1	2	4	2	4	10	2	2	4	6
proportion	0.00%	0.01%	0.02%	0.01%	0.02%	0.04%	0.01%	0.01%	0.02%	0.02%
CM disc	-2171	-2179	-2180	-2183	-2184	-2191	-2195	-2199	-2203	-2207
count	2	1	6	6	8	6	3	7	1	3
proportion	0.01%	0.00%	0.02%	0.02%	0.03%	0.02%	0.01%	0.03%	0.00%	0.01%
CM disc	-2211	-2212	-2215	-2216	-2219	-2227	-2228	-2231	-2235	-2239
count	4	2	2	2	6	2	4	2	4	3
proportion	0.02%	0.01%	0.01%	0.01%	0.02%	0.01%	0.02%	0.01%	0.02%	0.01%
CM disc	-2243	-2244	-2247	-2248	-2251	-2255	-2260	-2263	-2264	-2267
count	3	4	4	2	1	8	4	2	6	1
proportion	0.01%	0.02%	0.02%	0.01%	0.00%	0.03%	0.02%	0.01%	0.02%	0.00%
CM disc	-2271	-2276	-2279	-2280	-2283	-2287	-2291	-2292	-2296	-2307
count	4	4	6	4	2	1	4	4	4	2
proportion	0.02%	0.02%	0.02%	0.02%	0.01%	0.00%	0.02%	0.02%	0.02%	0.01%
CM disc	-2308	-2311	-2315	-2319	-2323	-2324	-2327	-2328	-2335	-2339
count	2	1	4	6	2	4	8	4	2	1
proportion	0.01%	0.00%	0.02%	0.02%	0.01%	0.02%	0.03%	0.02%	0.01%	0.00%
CM disc	-2343	-2344	-2347	-2351	-2355	-2356	-2359	-2360	-2363	-2371
count	6	4	1	5	4	4	4	4	2	1
proportion	0.02%	0.02%	0.00%	0.02%	0.02%	0.02%	0.02%	0.02%	0.01%	0.00%
CM disc	-2372	-2379	-2383	-2387	-2388	-2391	-2392	-2395	-2399	-2404
count	6	6	1	4	4	2	2	2	1	4
proportion	0.02%	0.02%	0.00%	0.02%	0.02%	0.01%	0.01%	0.01%	0.00%	0.02%
CM disc	-2407	-2408	-2411	-2415	-2419	-2423	-2424	-2427	-2431	-2435
count	4	8	1	8	2	3	4	2	4	2
proportion	0.02%	0.03%	0.00%	0.03%	0.01%	0.01%	0.02%	0.01%	0.02%	0.01%
CM disc	-2436	-2440	-2443	-2447	-2451	-2452	-2455	-2456	-2459	-2463
count	4	4	2	1	2	2	4	2	1	2
proportion	0.02%	0.02%	0.01%	0.00%	0.01%	0.01%	0.02%	0.01%	0.00%	0.01%
CM disc	-2467	-2468	-2471	-2472	-2479	-2483	-2487	-2488	-2491	-2495
count	1	4	2	4	6	4	4	4	4	6
proportion	0.00%	0.02%	0.01%	0.02%	0.02%	0.02%	0.02%	0.02%	0.02%	0.02%
CM disc	-2503	-2504	-2507	-2515	-2516	-2519	-2531	-2532	-2536	-2539
count	3	7	2	2	8	5	1	4	2	1
proportion	0.01%	0.03%	0.01%	0.01%	0.03%	0.02%	0.00%	0.02%	0.01%	0.00%
CM disc	-2543	-2551	-2552	-2555	-2559	-2563	-2564	-2567	-2568	-2571
count	3	1	4	4	6	2	4	4	4	2
proportion	0.01%	0.00%	0.02%	0.02%	0.02%	0.01%	0.02%	0.02%	0.02%	0.01%
CM disc	-2579	-2580	-2584	-2587	-2591	-2595	-2596	-2599	-2603	-2607
count	3	4	4	2	3	4	4	6	4	4
proportion	0.01%	0.02%	0.02%	0.01%	0.01%	0.02%	0.02%	0.02%	0.02%	0.02%
CM disc	-2611	-2612	-2615	-2616	-2623	-2627	-2631	-2632	-2635	-2639
count	2	2	2	4	2	4	8	2	4	8
proportion	0.01%	0.01%	0.01%	0.02%	0.01%	0.02%	0.03%	0.01%	0.02%	0.03%
CM disc	-2643	-2644	-2647	-2648	-2651	-2659	-2660	-2663	-2667	-2671
count	2	4	3	2	2	1	8	1	2	1
proportion	0.01%	0.02%	0.01%	0.01%	0.01%	0.00%	0.03%	0.00%	0.01%	0.00%
CM disc	-2676	-2679	-2680	-2683	-2687	-2692	-2696	-2699	-2703	-2707
count	4	4	4	1	3	4	6	3	4	1
proportion	0.02%	0.02%	0.02%	0.00%	0.01%	0.02%	0.02%	0.01%	0.02%	0.00%
CM disc	-2708	-2711	-2712	-2715	-2719	-2723	-2724	-2728	-2731	-2735
count	6	1	4	2	1	4	4	4	1	2
proportion	0.02%	0.00%	0.02%	0.01%	0.00%	0.02%	0.02%	0.02%	0.00%	0.01%
CM disc	-2739	-2740	-2743	-2747	-2751	-2755	-2756	-2759	-2760	-2767
count	4	4	4	4	8	2	8	6	4	3
proportion	0.02%	0.02%	0.02%	0.02%	0.03%	0.01%	0.03%	0.02%	0.02%	0.01%
CM disc	-2771	-2776	-2779	-2787	-2788	-2791	-2792	-2795	-2803	-2804
count	2	2	2	2	2	3	2	4	2	2
proportion	0.01%	0.01%	0.01%	0.01%	0.01%	0.01%	0.01%	0.02%	0.01%	0.01%
CM disc	-2807	-2811	-2815	-2819	-2820	-2823	-2824	-2827	-2831	-2836
count	4	3	2	3	8	2	6	2	4	2
proportion	0.02%	0.01%	0.01%	0.01%	0.03%	0.01%	0.02%	0.01%	0.02%	0.01%
CM disc	-2839	-2840	-2843	-2847	-2851	-2852	-2855	-2856	-2859	-2863
count	2	6	3	6	1	8	10	8	4	2
proportion	0.01%	0.02%	0.01%	0.02%	0.00%	0.03%	0.04%	0.03%	0.02%	0.01%
CM disc	-2867	-2868	-2872	-2879	-2884	-2887	-2895	-2899	-2903	-2911
count	4	4	4	3	4	2	8	2	1	6
proportion	0.02%	0.02%	0.02%	0.01%	0.02%	0.01%	0.03%	0.01%	0.00%	0.02%
CM disc	-2915	-2919	-2920	-2923	-2927	-2931	-2932	-2935	-2936	-2939
count	8	8	4	2	1	2	2	2	6	1
proportion	0.03%	0.03%	0.02%	0.01%	0.00%	0.01%	0.01%	0.01%	0.02%	0.00%
CM disc	-2947	-2948	-2951	-2955	-2959	-2963	-2964	-2967	-2968	-2971
count	2	4	6	4	6	1	8	4	2	1
proportion	0.01%	0.02%	0.02%	0.02%	0.02%	0.00%	0.03%	0.02%	0.01%	0.00%
CM disc	-2980	-2983	-2984	-2987	-2991	-2995	-2996	-2999	-3007	-3011
count	4	4	2	4	8	2	6	1	4	3
proportion	0.02%	0.02%	0.01%	0.02%	0.03%	0.01%	0.02%	0.00%	0.02%	0.01%
CM disc	-3012	-3016	-3019	-3023	-3027	-3028	-3031	-3032	-3035	-3039
count	4	4	1	1	4	2	2	2	4	6
proportion	0.02%	0.02%	0.00%	0.00%	0.02%	0.01%	0.01%	0.01%	0.02%	0.02%
CM disc	-3043	-3044	-3047	-3048	-3055	-3059	-3063	-3064	-3067	-3071
count	4	6	2	4	8	8	3	6	1	4
proportion	0.02%	0.02%	0.01%	0.02%	0.03%	0.03%	0.01%	0.02%	0.00%	0.02%
CM disc	-3076	-3079	-3080	-3083	-3091	-3092	-3095	-3099	-3103	-3107
count	4	1	8	1	2	2	8	4	4	4
proportion	0.02%	0.00%	0.03%	0.00%	0.01%	0.01%	0.03%	0.02%	0.02%	0.02%
CM disc	-3108	-3111	-3112	-3115	-3119	-3124	-3127	-3128	-3131	-3135
count	4	4	2	4	3	4	6	8	4	8
proportion	0.02%	0.02%	0.01%	0.02%	0.01%	0.02%	0.02%	0.03%	0.02%	0.03%
CM disc	-3139	-3140	-3143	-3144	-3147	-3151	-3155	-3156	-3160	-3163
count	2	4	6	4	2	2	4	6	4	2
proportion	0.01%	0.02%	0.02%	0.02%	0.01%	0.01%	0.02%	0.02%	0.02%	0.01%
CM disc	-3167	-3171	-3172	-3176	-3183	-3187	-3188	-3191	-3192	-3199
count	1	4	2	6	2	1	6	3	4	4
proportion	0.00%	0.02%	0.01%	0.02%	0.01%	0.00%	0.02%	0.01%	0.02%	0.02%
CM disc	-3203	-3207	-3208	-3215	-3219	-3220	-3223	-3224	-3227	-3235
count	1	4	4	4	4	4	6	4	2	2
proportion	0.00%	0.02%	0.02%	0.02%	0.02%	0.02%	0.02%	0.02%	0.01%	0.01%
CM disc	-3236	-3239	-3243	-3247	-3251	-3252	-3255	-3256	-3259	-3263
count	4	6	2	4	1	4	8	4	2	8
proportion	0.02%	0.02%	0.01%	0.02%	0.00%	0.02%	0.03%	0.02%	0.01%	0.03%
CM disc	-3268	-3271	-3272	-3279	-3284	-3287	-3288	-3291	-3295	-3299
count	4	3	4	4	6	2	4	2	4	7
proportion	0.02%	0.01%	0.02%	0.02%	0.02%	0.01%	0.02%	0.01%	0.02%	0.03%
CM disc	-3304	-3307	-3311	-3316	-3319	-3320	-3323	-3327	-3331	-3335
count	4	2	14	2	1	4	1	2	3	8
proportion	0.02%	0.01%	0.05%	0.01%	0.00%	0.02%	0.00%	0.01%	0.01%	0.03%
CM disc	-3336	-3343	-3347	-3351	-3352	-3355	-3359	-3363	-3367	-3368
count	4	1	1	10	2	2	3	4	4	2
proportion	0.02%	0.00%	0.00%	0.04%	0.01%	0.01%	0.01%	0.02%	0.02%	0.01%
CM disc	-3371	-3379	-3383	-3387	-3391	-3395	-3396	-3399	-3403	-3407
count	3	3	2	4	1	4	4	8	2	3
proportion	0.01%	0.01%	0.01%	0.02%	0.00%	0.02%	0.02%	0.03%	0.01%	0.01%
CM disc	-3412	-3415	-3416	-3419	-3423	-3427	-3428	-3431	-3432	-3435
count	2	2	4	4	8	2	4	6	4	4
proportion	0.01%	0.01%	0.02%	0.02%	0.03%	0.01%	0.02%	0.02%	0.02%	0.02%
CM disc	-3439	-3443	-3444	-3448	-3451	-3455	-3459	-3460	-3463	-3464
count	6	3	8	2	4	4	4	4	1	4
proportion	0.02%	0.01%	0.03%	0.01%	0.02%	0.02%	0.02%	0.02%	0.00%	0.02%
CM disc	-3467	-3471	-3476	-3480	-3487	-3491	-3495	-3496	-3499	-3503
count	1	12	6	4	4	1	8	4	1	4
proportion	0.00%	0.05%	0.02%	0.02%	0.02%	0.00%	0.03%	0.02%	0.00%	0.02%
CM disc	-3507	-3508	-3511	-3512	-3515	-3523	-3524	-3527	-3531	-3535
count	2	2	1	4	4	2	6	3	4	4
proportion	0.01%	0.01%	0.00%	0.02%	0.02%	0.01%	0.02%	0.01%	0.02%	0.02%
CM disc	-3539	-3540	-3543	-3544	-3547	-3551	-3556	-3559	-3560	-3563
count	1	8	4	4	2	2	4	5	8	2
proportion	0.00%	0.03%	0.02%	0.02%	0.01%	0.01%	0.02%	0.02%	0.03%	0.01%
CM disc	-3567	-3571	-3572	-3576	-3579	-3583	-3587	-3588	-3592	-3595
count	4	3	4	4	2	1	2	4	4	2
proportion	0.02%	0.01%	0.02%	0.02%	0.01%	0.00%	0.01%	0.02%	0.02%	0.01%
CM disc	-3599	-3603	-3604	-3607	-3608	-3611	-3615	-3619	-3620	-3623
count	6	3	8	1	4	2	12	4	8	5
proportion	0.02%	0.01%	0.03%	0.00%	0.02%	0.01%	0.05%	0.02%	0.03%	0.02%
CM disc	-3624	-3631	-3635	-3639	-3640	-3643	-3647	-3651	-3652	-3655
count	4	1	2	10	4	2	6	4	4	4
proportion	0.02%	0.00%	0.01%	0.04%	0.02%	0.01%	0.02%	0.02%	0.02%	0.02%
CM disc	-3656	-3659	-3667	-3668	-3671	-3679	-3683	-3684	-3687	-3688
count	7	1	2	4	4	4	2	4	6	4
proportion	0.03%	0.00%	0.01%	0.02%	0.02%	0.02%	0.01%	0.02%	0.02%	0.02%
CM disc	-3691	-3695	-3704	-3707	-3711	-3715	-3716	-3719	-3720	-3723
count	1	10	6	2	7	2	7	1	8	4
proportion	0.00%	0.04%	0.02%	0.01%	0.03%	0.01%	0.03%	0.00%	0.03%	0.02%
CM disc	-3727	-3731	-3732	-3736	-3739	-3743	-3747	-3748	-3752	-3755
count	1	4	4	2	1	6	4	4	4	4
proportion	0.00%	0.02%	0.02%	0.01%	0.00%	0.02%	0.02%	0.02%	0.02%	0.02%
CM disc	-3759	-3763	-3764	-3767	-3768	-3779	-3783	-3784	-3787	-3791
count	4	2	2	3	4	1	12	4	2	4
proportion	0.02%	0.01%	0.01%	0.01%	0.02%	0.00%	0.05%	0.02%	0.01%	0.02%
CM disc	-3795	-3796	-3799	-3803	-3811	-3812	-3815	-3819	-3823	-3827
count	4	4	2	3	2	4	8	4	1	2
proportion	0.02%	0.02%	0.01%	0.01%	0.01%	0.02%	0.03%	0.02%	0.00%	0.01%
CM disc	-3828	-3831	-3832	-3835	-3839	-3847	-3848	-3851	-3855	-3859
count	4	6	3	4	2	1	4	2	4	2
proportion	0.02%	0.02%	0.01%	0.02%	0.01%	0.00%	0.02%	0.01%	0.02%	0.01%
CM disc	-3860	-3863	-3864	-3867	-3876	-3880	-3883	-3891	-3892	-3895
count	4	1	8	2	8	4	2	6	4	6
proportion	0.02%	0.00%	0.03%	0.01%	0.03%	0.02%	0.01%	0.02%	0.02%	0.02%
CM disc	-3896	-3899	-3903	-3907	-3908	-3911	-3912	-3919	-3923	-3927
count	13	6	2	1	4	1	8	3	1	8
proportion	0.05%	0.02%	0.01%	0.00%	0.02%	0.00%	0.03%	0.01%	0.00%	0.03%
CM disc	-3928	-3931	-3935	-3939	-3940	-3943	-3944	-3947	-3955	-3956
count	2	1	6	4	8	3	4	1	4	8
proportion	0.01%	0.00%	0.02%	0.02%	0.03%	0.01%	0.02%	0.00%	0.02%	0.03%
CM disc	-3959	-3963	-3967	-3972	-3976	-3979	-3983	-3988	-3991	-3992
count	4	2	3	4	4	4	4	2	6	2
proportion	0.02%	0.01%	0.01%	0.02%	0.02%	0.02%	0.02%	0.01%	0.02%	0.01%
CM disc	-3995	-3999
count	4	12
proportion	0.02%	0.05%

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Distribution of real multiplication

RM disc	5	8	12	13	17	21	24	28	29	33
count	168	95	66	78	57	48	40	33	39	30
proportion	9.48%	5.36%	3.72%	4.40%	3.22%	2.71%	2.26%	1.86%	2.20%	1.69%
RM disc	37	40	41	44	53	56	57	60	61	65
count	29	34	24	27	16	20	21	20	22	26
proportion	1.64%	1.92%	1.35%	1.52%	0.90%	1.13%	1.19%	1.13%	1.24%	1.47%
RM disc	69	73	76	77	85	88	89	92	93	97
count	14	10	18	7	17	16	14	4	10	10
proportion	0.79%	0.56%	1.02%	0.40%	0.96%	0.90%	0.79%	0.23%	0.56%	0.56%
RM disc	101	104	105	109	113	120	124	129	133	136
count	10	10	14	13	7	8	12	8	7	10
proportion	0.56%	0.56%	0.79%	0.73%	0.40%	0.45%	0.68%	0.45%	0.40%	0.56%
RM disc	137	140	141	145	149	152	156	157	161	165
count	6	5	6	15	4	3	9	5	8	6
proportion	0.34%	0.28%	0.34%	0.85%	0.23%	0.17%	0.51%	0.28%	0.45%	0.34%
RM disc	168	172	173	177	181	184	185	193	197	201
count	7	4	4	4	7	6	8	4	5	5
proportion	0.40%	0.23%	0.23%	0.23%	0.40%	0.34%	0.45%	0.23%	0.28%	0.28%

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RM disc	5	8	12	13	17	21	24	28	29	33
count	168	95	66	78	57	48	40	33	39	30
proportion	9.48%	5.36%	3.72%	4.40%	3.22%	2.71%	2.26%	1.86%	2.20%	1.69%
RM disc	37	40	41	44	53	56	57	60	61	65
count	29	34	24	27	16	20	21	20	22	26
proportion	1.64%	1.92%	1.35%	1.52%	0.90%	1.13%	1.19%	1.13%	1.24%	1.47%
RM disc	69	73	76	77	85	88	89	92	93	97
count	14	10	18	7	17	16	14	4	10	10
proportion	0.79%	0.56%	1.02%	0.40%	0.96%	0.90%	0.79%	0.23%	0.56%	0.56%
RM disc	101	104	105	109	113	120	124	129	133	136
count	10	10	14	13	7	8	12	8	7	10
proportion	0.56%	0.56%	0.79%	0.73%	0.40%	0.45%	0.68%	0.45%	0.40%	0.56%
RM disc	137	140	141	145	149	152	156	157	161	165
count	6	5	6	15	4	3	9	5	8	6
proportion	0.34%	0.28%	0.34%	0.85%	0.23%	0.17%	0.51%	0.28%	0.45%	0.34%
RM disc	168	172	173	177	181	184	185	193	197	201
count	7	4	4	4	7	6	8	4	5	5
proportion	0.40%	0.23%	0.23%	0.23%	0.40%	0.34%	0.45%	0.23%	0.28%	0.28%
RM disc	204	205	209	213	217	220	221	229	232	233
count	9	3	7	2	4	4	7	12	9	5
proportion	0.51%	0.17%	0.40%	0.11%	0.23%	0.23%	0.40%	0.68%	0.51%	0.28%
RM disc	237	241	249	253	257	264	265	268	269	273
count	3	5	4	4	8	4	10	4	1	8
proportion	0.17%	0.28%	0.23%	0.23%	0.45%	0.23%	0.56%	0.23%	0.06%	0.45%
RM disc	277	280	281	284	285	296	301	305	309	312
count	4	3	3	4	2	2	4	3	3	4
proportion	0.23%	0.17%	0.17%	0.23%	0.11%	0.11%	0.23%	0.17%	0.17%	0.23%
RM disc	313	316	317	321	328	329	332	337	341	344
count	4	8	2	4	4	1	1	5	4	4
proportion	0.23%	0.45%	0.11%	0.23%	0.23%	0.06%	0.06%	0.28%	0.23%	0.23%
RM disc	345	348	349	353	365	373	377	381	385	389
count	7	2	2	3	1	2	3	1	5	1
proportion	0.40%	0.11%	0.11%	0.17%	0.06%	0.11%	0.17%	0.06%	0.28%	0.06%
RM disc	393	397	401	408	409	417	421	424	428	433
count	2	2	8	4	3	4	2	5	2	3
proportion	0.11%	0.11%	0.45%	0.23%	0.17%	0.23%	0.11%	0.28%	0.11%	0.17%
RM disc	440	444	445	449	453	456	457	460	461	465
count	3	1	3	3	1	4	4	3	1	2
proportion	0.17%	0.06%	0.17%	0.17%	0.06%	0.23%	0.23%	0.17%	0.06%	0.11%
RM disc	469	472	473	476	481	485	489	492	493	497
count	9	1	8	2	6	1	3	2	1	2
proportion	0.51%	0.06%	0.45%	0.11%	0.34%	0.06%	0.17%	0.11%	0.06%	0.11%
RM disc	505	508	509	520	521	533	536	541	545	553
count	4	2	1	4	2	1	2	3	5	4
proportion	0.23%	0.11%	0.06%	0.23%	0.11%	0.06%	0.11%	0.17%	0.28%	0.23%
RM disc	557	561	565	568	569	577	589	593	597	601
count	1	2	1	4	3	4	4	1	1	2
proportion	0.06%	0.11%	0.06%	0.23%	0.17%	0.23%	0.23%	0.06%	0.06%	0.11%
RM disc	609	613	616	617	629	633	636	641	645	661
count	1	1	2	1	1	1	1	1	1	1
proportion	0.06%	0.06%	0.11%	0.06%	0.06%	0.06%	0.06%	0.06%	0.06%	0.06%
RM disc	669	673	685	689	696	697	705	709	721	732
count	1	2	1	4	2	6	3	2	2	1
proportion	0.06%	0.11%	0.06%	0.23%	0.11%	0.34%	0.17%	0.11%	0.11%	0.06%
RM disc	733	741	744	745	757	760	761	769	777	785
count	2	2	3	5	1	3	4	3	3	4
proportion	0.11%	0.11%	0.17%	0.28%	0.06%	0.17%	0.23%	0.17%	0.17%	0.23%
RM disc	793	808	809	813	817	829	849	853	857	865
count	8	1	1	1	4	1	1	1	1	3
proportion	0.45%	0.06%	0.06%	0.06%	0.23%	0.06%	0.06%	0.06%	0.06%	0.17%
RM disc	877	881	889	901	904	905	921	924	929	937
count	1	1	2	1	1	4	1	2	1	2
proportion	0.06%	0.06%	0.11%	0.06%	0.06%	0.23%	0.06%	0.11%	0.06%	0.11%
RM disc	940	949	953	969	973	977	985	993	997	1009
count	4	2	1	1	2	1	6	2	1	2
proportion	0.23%	0.11%	0.06%	0.06%	0.11%	0.06%	0.34%	0.11%	0.06%	0.11%
RM disc	1020	1021	1033	1036	1057	1069	1093	1096	1101	1105
count	2	1	1	2	2	1	2	1	2	2
proportion	0.11%	0.06%	0.06%	0.11%	0.11%	0.06%	0.11%	0.06%	0.11%	0.11%
RM disc	1113	1117	1129	1137	1141	1144	1153	1165	1185	1189
count	1	1	3	1	2	2	1	1	1	1
proportion	0.06%	0.06%	0.17%	0.06%	0.11%	0.11%	0.06%	0.06%	0.06%	0.06%
RM disc	1192	1201	1209	1212	1213	1221	1237	1240	1249	1261
count	1	1	2	1	1	1	1	2	1	2
proportion	0.06%	0.06%	0.11%	0.06%	0.06%	0.06%	0.06%	0.11%	0.06%	0.11%
RM disc	1273	1276	1281	1285	1297	1308	1317	1320	1321	1333
count	2	2	2	1	2	1	1	2	1	2
proportion	0.11%	0.11%	0.11%	0.06%	0.11%	0.06%	0.06%	0.11%	0.06%	0.11%

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Distribution of levels and weights

Distribution of levels and absolute dimension

Distribution of character orders and relative dimension

Distribution of analytic ranks

Distribution of projective images for weight 1 forms

Distribution of number of newforms in \(S_k(N, \chi)\)

Distribution of inner twists

Distribution of self twist types by weights

Distribution of complex multiplication

Distribution of real multiplication

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

analytic rank	Unknown	0	1	2	3	\(\mathrm{avg}\ 0.33\)
count	859625	192245	87073	2566	1	281885
proportion	304.96%	68.20%	30.89%	0.91%	0.00%	100.00%

projective image	\(A_{4}\)	\(S_{4}\)	\(A_{5}\)	\(D_{2}\)	\(D_{3}\)	\(D_{4}\)	\(D_{5}\)	\(D_{6}\)	\(D_{7}\)	\(D_{8}\)
count	458	1033	202	1311	2924	1648	1126	1940	581	536
proportion	2.37%	5.35%	1.05%	6.79%	15.15%	8.54%	5.83%	10.05%	3.01%	2.78%
projective image	\(D_{9}\)	\(D_{10}\)	\(D_{11}\)	\(D_{12}\)	\(D_{13}\)	\(D_{14}\)	\(D_{15}\)	\(D_{16}\)	\(D_{17}\)	\(D_{18}\)
count	733	639	267	764	154	258	452	204	75	402
proportion	3.80%	3.31%	1.38%	3.96%	0.80%	1.34%	2.34%	1.06%	0.39%	2.08%
projective image	\(D_{19}\)	\(D_{20}\)	\(D_{21}\)	\(D_{22}\)	\(D_{23}\)	\(D_{24}\)	\(D_{25}\)	\(D_{26}\)	\(D_{27}\)	\(D_{28}\)
count	50	234	185	122	59	153	65	87	95	115
proportion	0.26%	1.21%	0.96%	0.63%	0.31%	0.79%	0.34%	0.45%	0.49%	0.60%
projective image	\(D_{29}\)	\(D_{30}\)	\(D_{31}\)	\(D_{32}\)	\(D_{33}\)	\(D_{34}\)	\(D_{35}\)	\(D_{36}\)	\(D_{37}\)	\(D_{38}\)
count	42	259	17	49	74	25	60	165	13	18
proportion	0.22%	1.34%	0.09%	0.25%	0.38%	0.13%	0.31%	0.85%	0.07%	0.09%
projective image	\(D_{39}\)	\(D_{40}\)	\(D_{41}\)	\(D_{42}\)	\(D_{43}\)	\(D_{44}\)	\(D_{45}\)	\(D_{46}\)	\(D_{47}\)	\(D_{48}\)
count	55	78	26	101	10	42	58	23	5	59
proportion	0.28%	0.40%	0.13%	0.52%	0.05%	0.22%	0.30%	0.12%	0.03%	0.31%
projective image	\(D_{49}\)	\(D_{50}\)	\(D_{51}\)	\(D_{52}\)	\(D_{53}\)	\(D_{54}\)	\(D_{55}\)	\(D_{56}\)	\(D_{57}\)	\(D_{58}\)
count	13	33	23	55	12	37	25	24	17	16
proportion	0.07%	0.17%	0.12%	0.28%	0.06%	0.19%	0.13%	0.12%	0.09%	0.08%