LMFDB - Embedded newform 784.4.a.r.1.1

Newspace parameters

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	784.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$46.2574974445$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 7)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	784.1

$q$-expansion

$f(q)$

$=$

$q+7.00000 q^{3} -7.00000 q^{5} +22.0000 q^{9} +O(q^{10})$

$q+7.00000 q^{3} -7.00000 q^{5} +22.0000 q^{9} +5.00000 q^{11} +14.0000 q^{13} -49.0000 q^{15} +21.0000 q^{17} +49.0000 q^{19} +159.000 q^{23} -76.0000 q^{25} -35.0000 q^{27} +58.0000 q^{29} +147.000 q^{31} +35.0000 q^{33} +219.000 q^{37} +98.0000 q^{39} -350.000 q^{41} +124.000 q^{43} -154.000 q^{45} +525.000 q^{47} +147.000 q^{51} +303.000 q^{53} -35.0000 q^{55} +343.000 q^{57} -105.000 q^{59} +413.000 q^{61} -98.0000 q^{65} -415.000 q^{67} +1113.00 q^{69} +432.000 q^{71} +1113.00 q^{73} -532.000 q^{75} +103.000 q^{79} -839.000 q^{81} +1092.00 q^{83} -147.000 q^{85} +406.000 q^{87} +329.000 q^{89} +1029.00 q^{93} -343.000 q^{95} +882.000 q^{97} +110.000 q^{99} +O(q^{100})$

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0	0
$2$	0	0
$3$	7.00000	1.34715	0.673575	−	0.739119i	$-0.264758\pi$
$3$	7.00000	1.34715	0.673575	+	0.739119i	$0.264758\pi$
$4$	0	0
$5$	−7.00000	−0.626099	−0.313050	−	0.949737i	$-0.601351\pi$
$5$	−7.00000	−0.626099	−0.313050	+	0.949737i	$0.601351\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	22.0000	0.814815
$10$	0	0
$11$	5.00000	0.137051	0.0685253	−	0.997649i	$-0.478171\pi$
$11$	5.00000	0.137051	0.0685253	+	0.997649i	$0.478171\pi$
$12$	0	0
$13$	14.0000	0.298685	0.149342	−	0.988786i	$-0.452284\pi$
$13$	14.0000	0.298685	0.149342	+	0.988786i	$0.452284\pi$
$14$	0	0
$15$	−49.0000	−0.843450
$16$	0	0
$17$	21.0000	0.299603	0.149801	−	0.988716i	$-0.452137\pi$
$17$	21.0000	0.299603	0.149801	+	0.988716i	$0.452137\pi$
$18$	0	0
$19$	49.0000	0.591651	0.295826	−	0.955242i	$-0.404405\pi$
$19$	49.0000	0.591651	0.295826	+	0.955242i	$0.404405\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	159.000	1.44147	0.720735	−	0.693211i	$-0.243805\pi$
$23$	159.000	1.44147	0.720735	+	0.693211i	$0.243805\pi$
$24$	0	0
$25$	−76.0000	−0.608000
$26$	0	0
$27$	−35.0000	−0.249472
$28$	0	0
$29$	58.0000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	58.0000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	0	0
$31$	147.000	0.851677	0.425838	−	0.904799i	$-0.359979\pi$
$31$	147.000	0.851677	0.425838	+	0.904799i	$0.359979\pi$
$32$	0	0
$33$	35.0000	0.184628
$34$	0	0
$35$	0	0
$36$	0	0
$37$	219.000	0.973064	0.486532	−	0.873663i	$-0.338262\pi$
$37$	219.000	0.973064	0.486532	+	0.873663i	$0.338262\pi$
$38$	0	0
$39$	98.0000	0.402373
$40$	0	0
$41$	−350.000	−1.33319	−0.666595	−	0.745420i	$-0.732249\pi$
$41$	−350.000	−1.33319	−0.666595	+	0.745420i	$0.732249\pi$
$42$	0	0
$43$	124.000	0.439763	0.219882	−	0.975527i	$-0.429433\pi$
$43$	124.000	0.439763	0.219882	+	0.975527i	$0.429433\pi$
$44$	0	0
$45$	−154.000	−0.510155
$46$	0	0
$47$	525.000	1.62934	0.814671	−	0.579923i	$-0.196917\pi$
$47$	525.000	1.62934	0.814671	+	0.579923i	$0.196917\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	147.000	0.403610
$52$	0	0
$53$	303.000	0.785288	0.392644	−	0.919691i	$-0.371561\pi$
$53$	303.000	0.785288	0.392644	+	0.919691i	$0.371561\pi$
$54$	0	0
$55$	−35.0000	−0.0858073
$56$	0	0
$57$	343.000	0.797043
$58$	0	0
$59$	−105.000	−0.231692	−0.115846	−	0.993267i	$-0.536958\pi$
$59$	−105.000	−0.231692	−0.115846	+	0.993267i	$0.536958\pi$
$60$	0	0
$61$	413.000	0.866873	0.433436	−	0.901184i	$-0.357301\pi$
$61$	413.000	0.866873	0.433436	+	0.901184i	$0.357301\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	−98.0000	−0.187006
$66$	0	0
$67$	−415.000	−0.756721	−0.378361	−	0.925658i	$-0.623512\pi$
$67$	−415.000	−0.756721	−0.378361	+	0.925658i	$0.623512\pi$
$68$	0	0
$69$	1113.00	1.94188
$70$	0	0
$71$	432.000	0.722098	0.361049	−	0.932547i	$-0.382419\pi$
$71$	432.000	0.722098	0.361049	+	0.932547i	$0.382419\pi$
$72$	0	0
$73$	1113.00	1.78448	0.892238	−	0.451565i	$-0.149134\pi$
$73$	1113.00	1.78448	0.892238	+	0.451565i	$0.149134\pi$
$74$	0	0
$75$	−532.000	−0.819068
$76$	0	0
$77$	0	0
$78$	0	0
$79$	103.000	0.146689	0.0733443	−	0.997307i	$-0.476633\pi$
$79$	103.000	0.146689	0.0733443	+	0.997307i	$0.476633\pi$
$80$	0	0
$81$	−839.000	−1.15089
$82$	0	0
$83$	1092.00	1.44413	0.722064	−	0.691827i	$-0.243194\pi$
$83$	1092.00	1.44413	0.722064	+	0.691827i	$0.243194\pi$
$84$	0	0
$85$	−147.000	−0.187581
$86$	0	0
$87$	406.000	0.500319
$88$	0	0
$89$	329.000	0.391842	0.195921	−	0.980620i	$-0.437230\pi$
$89$	329.000	0.391842	0.195921	+	0.980620i	$0.437230\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	1029.00	1.14734
$94$	0	0
$95$	−343.000	−0.370432
$96$	0	0
$97$	882.000	0.923232	0.461616	−	0.887080i	$-0.347270\pi$
$97$	882.000	0.923232	0.461616	+	0.887080i	$0.347270\pi$
$98$	0	0
$99$	110.000	0.111671
$100$	0	0
$101$	−1379.00	−1.35857	−0.679285	−	0.733874i	$-0.737710\pi$
$101$	−1379.00	−1.35857	−0.679285	+	0.733874i	$0.737710\pi$
$102$	0	0
$103$	−679.000	−0.649552	−0.324776	−	0.945791i	$-0.605289\pi$
$103$	−679.000	−0.649552	−0.324776	+	0.945791i	$0.605289\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−457.000	−0.412896	−0.206448	−	0.978458i	$-0.566190\pi$
$107$	−457.000	−0.412896	−0.206448	+	0.978458i	$0.566190\pi$
$108$	0	0
$109$	−1125.00	−0.988582	−0.494291	−	0.869296i	$-0.664572\pi$
$109$	−1125.00	−0.988582	−0.494291	+	0.869296i	$0.664572\pi$
$110$	0	0
$111$	1533.00	1.31086
$112$	0	0
$113$	−1538.00	−1.28038	−0.640190	−	0.768217i	$-0.721144\pi$
$113$	−1538.00	−1.28038	−0.640190	+	0.768217i	$0.721144\pi$
$114$	0	0
$115$	−1113.00	−0.902502
$116$	0	0
$117$	308.000	0.243373
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−1306.00	−0.981217
$122$	0	0
$123$	−2450.00	−1.79601
$124$	0	0
$125$	1407.00	1.00677
$126$	0	0
$127$	−72.0000	−0.0503068	−0.0251534	−	0.999684i	$-0.508007\pi$
$127$	−72.0000	−0.0503068	−0.0251534	+	0.999684i	$0.508007\pi$
$128$	0	0
$129$	868.000	0.592427
$130$	0	0
$131$	2149.00	1.43327	0.716637	−	0.697446i	$-0.245680\pi$
$131$	2149.00	1.43327	0.716637	+	0.697446i	$0.245680\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	245.000	0.156194
$136$	0	0
$137$	−1125.00	−0.701571	−0.350786	−	0.936456i	$-0.614085\pi$
$137$	−1125.00	−0.701571	−0.350786	+	0.936456i	$0.614085\pi$
$138$	0	0
$139$	252.000	0.153772	0.0768862	−	0.997040i	$-0.475502\pi$
$139$	252.000	0.153772	0.0768862	+	0.997040i	$0.475502\pi$
$140$	0	0
$141$	3675.00	2.19497
$142$	0	0
$143$	70.0000	0.0409349
$144$	0	0
$145$	−406.000	−0.232527
$146$	0	0
$147$	0	0
$148$	0	0
$149$	−201.000	−0.110514	−0.0552569	−	0.998472i	$-0.517598\pi$
$149$	−201.000	−0.110514	−0.0552569	+	0.998472i	$0.517598\pi$
$150$	0	0
$151$	−1619.00	−0.872532	−0.436266	−	0.899818i	$-0.643699\pi$
$151$	−1619.00	−0.872532	−0.436266	+	0.899818i	$0.643699\pi$
$152$	0	0
$153$	462.000	0.244121
$154$	0	0
$155$	−1029.00	−0.533234
$156$	0	0
$157$	−679.000	−0.345160	−0.172580	−	0.984996i	$-0.555210\pi$
$157$	−679.000	−0.345160	−0.172580	+	0.984996i	$0.555210\pi$
$158$	0	0
$159$	2121.00	1.05790
$160$	0	0
$161$	0	0
$162$	0	0
$163$	467.000	0.224407	0.112203	−	0.993685i	$-0.464209\pi$
$163$	467.000	0.224407	0.112203	+	0.993685i	$0.464209\pi$
$164$	0	0
$165$	−245.000	−0.115595
$166$	0	0
$167$	1204.00	0.557894	0.278947	−	0.960306i	$-0.410015\pi$
$167$	1204.00	0.557894	0.278947	+	0.960306i	$0.410015\pi$
$168$	0	0
$169$	−2001.00	−0.910787
$170$	0	0
$171$	1078.00	0.482086
$172$	0	0
$173$	2821.00	1.23975	0.619875	−	0.784701i	$-0.287183\pi$
$173$	2821.00	1.23975	0.619875	+	0.784701i	$0.287183\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−735.000	−0.312124
$178$	0	0
$179$	3253.00	1.35833	0.679164	−	0.733987i	$-0.262343\pi$
$179$	3253.00	1.35833	0.679164	+	0.733987i	$0.262343\pi$
$180$	0	0
$181$	−1582.00	−0.649664	−0.324832	−	0.945772i	$-0.605308\pi$
$181$	−1582.00	−0.649664	−0.324832	+	0.945772i	$0.605308\pi$
$182$	0	0
$183$	2891.00	1.16781
$184$	0	0
$185$	−1533.00	−0.609235
$186$	0	0
$187$	105.000	0.0410608
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−2557.00	−0.968681	−0.484340	−	0.874880i	$-0.660940\pi$
$191$	−2557.00	−0.968681	−0.484340	+	0.874880i	$0.660940\pi$
$192$	0	0
$193$	−397.000	−0.148066	−0.0740329	−	0.997256i	$-0.523587\pi$
$193$	−397.000	−0.148066	−0.0740329	+	0.997256i	$0.523587\pi$
$194$	0	0
$195$	−686.000	−0.251926
$196$	0	0
$197$	2914.00	1.05388	0.526939	−	0.849903i	$-0.323340\pi$
$197$	2914.00	1.05388	0.526939	+	0.849903i	$0.323340\pi$
$198$	0	0
$199$	3339.00	1.18942	0.594712	−	0.803939i	$-0.297266\pi$
$199$	3339.00	1.18942	0.594712	+	0.803939i	$0.297266\pi$
$200$	0	0
$201$	−2905.00	−1.01942
$202$	0	0
$203$	0	0
$204$	0	0
$205$	2450.00	0.834709
$206$	0	0
$207$	3498.00	1.17453
$208$	0	0
$209$	245.000	0.0810861
$210$	0	0
$211$	−1780.00	−0.580759	−0.290380	−	0.956911i	$-0.593782\pi$
$211$	−1780.00	−0.580759	−0.290380	+	0.956911i	$0.593782\pi$
$212$	0	0
$213$	3024.00	0.972775
$214$	0	0
$215$	−868.000	−0.275335
$216$	0	0
$217$	0	0
$218$	0	0
$219$	7791.00	2.40396
$220$	0	0
$221$	294.000	0.0894868
$222$	0	0
$223$	−1400.00	−0.420408	−0.210204	−	0.977658i	$-0.567413\pi$
$223$	−1400.00	−0.420408	−0.210204	+	0.977658i	$0.567413\pi$
$224$	0	0
$225$	−1672.00	−0.495407
$226$	0	0
$227$	−2205.00	−0.644718	−0.322359	−	0.946617i	$-0.604476\pi$
$227$	−2205.00	−0.644718	−0.322359	+	0.946617i	$0.604476\pi$
$228$	0	0
$229$	−287.000	−0.0828188	−0.0414094	−	0.999142i	$-0.513185\pi$
$229$	−287.000	−0.0828188	−0.0414094	+	0.999142i	$0.513185\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	4587.00	1.28972	0.644859	−	0.764301i	$-0.276916\pi$
$233$	4587.00	1.28972	0.644859	+	0.764301i	$0.276916\pi$
$234$	0	0
$235$	−3675.00	−1.02013
$236$	0	0
$237$	721.000	0.197612
$238$	0	0
$239$	−1668.00	−0.451439	−0.225720	−	0.974192i	$-0.572473\pi$
$239$	−1668.00	−0.451439	−0.225720	+	0.974192i	$0.572473\pi$
$240$	0	0
$241$	3409.00	0.911174	0.455587	−	0.890191i	$-0.349429\pi$
$241$	3409.00	0.911174	0.455587	+	0.890191i	$0.349429\pi$
$242$	0	0
$243$	−4928.00	−1.30095
$244$	0	0
$245$	0	0
$246$	0	0
$247$	686.000	0.176717
$248$	0	0
$249$	7644.00	1.94546
$250$	0	0
$251$	−4760.00	−1.19701	−0.598503	−	0.801121i	$-0.704238\pi$
$251$	−4760.00	−1.19701	−0.598503	+	0.801121i	$0.704238\pi$
$252$	0	0
$253$	795.000	0.197554
$254$	0	0
$255$	−1029.00	−0.252700
$256$	0	0
$257$	805.000	0.195387	0.0976936	−	0.995217i	$-0.468853\pi$
$257$	805.000	0.195387	0.0976936	+	0.995217i	$0.468853\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	1276.00	0.302615
$262$	0	0
$263$	257.000	0.0602559	0.0301279	−	0.999546i	$-0.490409\pi$
$263$	257.000	0.0602559	0.0301279	+	0.999546i	$0.490409\pi$
$264$	0	0
$265$	−2121.00	−0.491668
$266$	0	0
$267$	2303.00	0.527870
$268$	0	0
$269$	−3591.00	−0.813930	−0.406965	−	0.913444i	$-0.633413\pi$
$269$	−3591.00	−0.813930	−0.406965	+	0.913444i	$0.633413\pi$
$270$	0	0
$271$	1393.00	0.312246	0.156123	−	0.987738i	$-0.450100\pi$
$271$	1393.00	0.312246	0.156123	+	0.987738i	$0.450100\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	−380.000	−0.0833268
$276$	0	0
$277$	415.000	0.0900178	0.0450089	−	0.998987i	$-0.485668\pi$
$277$	415.000	0.0900178	0.0450089	+	0.998987i	$0.485668\pi$
$278$	0	0
$279$	3234.00	0.693959
$280$	0	0
$281$	−4954.00	−1.05171	−0.525856	−	0.850574i	$-0.676255\pi$
$281$	−4954.00	−1.05171	−0.525856	+	0.850574i	$0.676255\pi$
$282$	0	0
$283$	−4277.00	−0.898379	−0.449190	−	0.893437i	$-0.648287\pi$
$283$	−4277.00	−0.898379	−0.449190	+	0.893437i	$0.648287\pi$
$284$	0	0
$285$	−2401.00	−0.499028
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−4472.00	−0.910238
$290$	0	0
$291$	6174.00	1.24373
$292$	0	0
$293$	−7742.00	−1.54366	−0.771830	−	0.635829i	$-0.780658\pi$
$293$	−7742.00	−1.54366	−0.771830	+	0.635829i	$0.780658\pi$
$294$	0	0
$295$	735.000	0.145062
$296$	0	0
$297$	−175.000	−0.0341903
$298$	0	0
$299$	2226.00	0.430545
$300$	0	0
$301$	0	0
$302$	0	0
$303$	−9653.00	−1.83020
$304$	0	0
$305$	−2891.00	−0.542748
$306$	0	0
$307$	−7364.00	−1.36901	−0.684504	−	0.729009i	$-0.739981\pi$
$307$	−7364.00	−1.36901	−0.684504	+	0.729009i	$0.739981\pi$
$308$	0	0
$309$	−4753.00	−0.875044
$310$	0	0
$311$	9975.00	1.81875	0.909374	−	0.415980i	$-0.136562\pi$
$311$	9975.00	1.81875	0.909374	+	0.415980i	$0.136562\pi$
$312$	0	0
$313$	4753.00	0.858324	0.429162	−	0.903228i	$-0.358809\pi$
$313$	4753.00	0.858324	0.429162	+	0.903228i	$0.358809\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−3477.00	−0.616050	−0.308025	−	0.951378i	$-0.599668\pi$
$317$	−3477.00	−0.616050	−0.308025	+	0.951378i	$0.599668\pi$
$318$	0	0
$319$	290.000	0.0508993
$320$	0	0
$321$	−3199.00	−0.556233
$322$	0	0
$323$	1029.00	0.177260
$324$	0	0
$325$	−1064.00	−0.181600
$326$	0	0
$327$	−7875.00	−1.33177
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−3341.00	−0.554797	−0.277399	−	0.960755i	$-0.589472\pi$
$331$	−3341.00	−0.554797	−0.277399	+	0.960755i	$0.589472\pi$
$332$	0	0
$333$	4818.00	0.792867
$334$	0	0
$335$	2905.00	0.473782
$336$	0	0
$337$	7366.00	1.19066	0.595329	−	0.803482i	$-0.297022\pi$
$337$	7366.00	1.19066	0.595329	+	0.803482i	$0.297022\pi$
$338$	0	0
$339$	−10766.0	−1.72486
$340$	0	0
$341$	735.000	0.116723
$342$	0	0
$343$	0	0
$344$	0	0
$345$	−7791.00	−1.21581
$346$	0	0
$347$	−7415.00	−1.14714	−0.573571	−	0.819156i	$-0.694442\pi$
$347$	−7415.00	−1.14714	−0.573571	+	0.819156i	$0.694442\pi$
$348$	0	0
$349$	3878.00	0.594798	0.297399	−	0.954753i	$-0.403881\pi$
$349$	3878.00	0.594798	0.297399	+	0.954753i	$0.403881\pi$
$350$	0	0
$351$	−490.000	−0.0745136
$352$	0	0
$353$	−1267.00	−0.191036	−0.0955179	−	0.995428i	$-0.530451\pi$
$353$	−1267.00	−0.191036	−0.0955179	+	0.995428i	$0.530451\pi$
$354$	0	0
$355$	−3024.00	−0.452105
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−4685.00	−0.688760	−0.344380	−	0.938830i	$-0.611911\pi$
$359$	−4685.00	−0.688760	−0.344380	+	0.938830i	$0.611911\pi$
$360$	0	0
$361$	−4458.00	−0.649949
$362$	0	0
$363$	−9142.00	−1.32185
$364$	0	0
$365$	−7791.00	−1.11726
$366$	0	0
$367$	−4641.00	−0.660104	−0.330052	−	0.943963i	$-0.607066\pi$
$367$	−4641.00	−0.660104	−0.330052	+	0.943963i	$0.607066\pi$
$368$	0	0
$369$	−7700.00	−1.08630
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−8797.00	−1.22116	−0.610578	−	0.791956i	$-0.709063\pi$
$373$	−8797.00	−1.22116	−0.610578	+	0.791956i	$0.709063\pi$
$374$	0	0
$375$	9849.00	1.35627
$376$	0	0
$377$	812.000	0.110929
$378$	0	0
$379$	−13680.0	−1.85407	−0.927037	−	0.374969i	$-0.877653\pi$
$379$	−13680.0	−1.85407	−0.927037	+	0.374969i	$0.877653\pi$
$380$	0	0
$381$	−504.000	−0.0677709
$382$	0	0
$383$	9765.00	1.30279	0.651395	−	0.758739i	$-0.274184\pi$
$383$	9765.00	1.30279	0.651395	+	0.758739i	$0.274184\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	2728.00	0.358326
$388$	0	0
$389$	1731.00	0.225617	0.112809	−	0.993617i	$-0.464015\pi$
$389$	1731.00	0.225617	0.112809	+	0.993617i	$0.464015\pi$
$390$	0	0
$391$	3339.00	0.431868
$392$	0	0
$393$	15043.0	1.93084
$394$	0	0
$395$	−721.000	−0.0918416
$396$	0	0
$397$	−10983.0	−1.38847	−0.694233	−	0.719750i	$-0.744256\pi$
$397$	−10983.0	−1.38847	−0.694233	+	0.719750i	$0.744256\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	6603.00	0.822289	0.411145	−	0.911570i	$-0.365129\pi$
$401$	6603.00	0.822289	0.411145	+	0.911570i	$0.365129\pi$
$402$	0	0
$403$	2058.00	0.254383
$404$	0	0
$405$	5873.00	0.720572
$406$	0	0
$407$	1095.00	0.133359
$408$	0	0
$409$	−10955.0	−1.32443	−0.662213	−	0.749316i	$-0.730382\pi$
$409$	−10955.0	−1.32443	−0.662213	+	0.749316i	$0.730382\pi$
$410$	0	0
$411$	−7875.00	−0.945122
$412$	0	0
$413$	0	0
$414$	0	0
$415$	−7644.00	−0.904167
$416$	0	0
$417$	1764.00	0.207155
$418$	0	0
$419$	6636.00	0.773723	0.386861	−	0.922138i	$-0.373559\pi$
$419$	6636.00	0.773723	0.386861	+	0.922138i	$0.373559\pi$
$420$	0	0
$421$	−16630.0	−1.92517	−0.962585	−	0.270980i	$-0.912652\pi$
$421$	−16630.0	−1.92517	−0.962585	+	0.270980i	$0.912652\pi$
$422$	0	0
$423$	11550.0	1.32761
$424$	0	0
$425$	−1596.00	−0.182159
$426$	0	0
$427$	0	0
$428$	0	0
$429$	490.000	0.0551455
$430$	0	0
$431$	−4923.00	−0.550192	−0.275096	−	0.961417i	$-0.588710\pi$
$431$	−4923.00	−0.550192	−0.275096	+	0.961417i	$0.588710\pi$
$432$	0	0
$433$	−8974.00	−0.995988	−0.497994	−	0.867180i	$-0.665930\pi$
$433$	−8974.00	−0.995988	−0.497994	+	0.867180i	$0.665930\pi$
$434$	0	0
$435$	−2842.00	−0.313249
$436$	0	0
$437$	7791.00	0.852847
$438$	0	0
$439$	−4179.00	−0.454334	−0.227167	−	0.973856i	$-0.572946\pi$
$439$	−4179.00	−0.454334	−0.227167	+	0.973856i	$0.572946\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	12927.0	1.38641	0.693206	−	0.720740i	$-0.256198\pi$
$443$	12927.0	1.38641	0.693206	+	0.720740i	$0.256198\pi$
$444$	0	0
$445$	−2303.00	−0.245332
$446$	0	0
$447$	−1407.00	−0.148879
$448$	0	0
$449$	−2826.00	−0.297032	−0.148516	−	0.988910i	$-0.547450\pi$
$449$	−2826.00	−0.297032	−0.148516	+	0.988910i	$0.547450\pi$
$450$	0	0
$451$	−1750.00	−0.182715
$452$	0	0
$453$	−11333.0	−1.17543
$454$	0	0
$455$	0	0
$456$	0	0
$457$	8479.00	0.867901	0.433951	−	0.900937i	$-0.357119\pi$
$457$	8479.00	0.867901	0.433951	+	0.900937i	$0.357119\pi$
$458$	0	0
$459$	−735.000	−0.0747426
$460$	0	0
$461$	−9338.00	−0.943414	−0.471707	−	0.881755i	$-0.656362\pi$
$461$	−9338.00	−0.943414	−0.471707	+	0.881755i	$0.656362\pi$
$462$	0	0
$463$	4016.00	0.403109	0.201554	−	0.979477i	$-0.435401\pi$
$463$	4016.00	0.403109	0.201554	+	0.979477i	$0.435401\pi$
$464$	0	0
$465$	−7203.00	−0.718347
$466$	0	0
$467$	−5859.00	−0.580561	−0.290281	−	0.956942i	$-0.593749\pi$
$467$	−5859.00	−0.580561	−0.290281	+	0.956942i	$0.593749\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	−4753.00	−0.464982
$472$	0	0
$473$	620.000	0.0602698
$474$	0	0
$475$	−3724.00	−0.359724
$476$	0	0
$477$	6666.00	0.639864
$478$	0	0
$479$	6503.00	0.620312	0.310156	−	0.950686i	$-0.399619\pi$
$479$	6503.00	0.620312	0.310156	+	0.950686i	$0.399619\pi$
$480$	0	0
$481$	3066.00	0.290639
$482$	0	0
$483$	0	0
$484$	0	0
$485$	−6174.00	−0.578035
$486$	0	0
$487$	16049.0	1.49333	0.746663	−	0.665203i	$-0.231655\pi$
$487$	16049.0	1.49333	0.746663	+	0.665203i	$0.231655\pi$
$488$	0	0
$489$	3269.00	0.302309
$490$	0	0
$491$	−8864.00	−0.814718	−0.407359	−	0.913268i	$-0.633550\pi$
$491$	−8864.00	−0.814718	−0.407359	+	0.913268i	$0.633550\pi$
$492$	0	0
$493$	1218.00	0.111270
$494$	0	0
$495$	−770.000	−0.0699170
$496$	0	0
$497$	0	0
$498$	0	0
$499$	10211.0	0.916046	0.458023	−	0.888940i	$-0.348558\pi$
$499$	10211.0	0.916046	0.458023	+	0.888940i	$0.348558\pi$
$500$	0	0
$501$	8428.00	0.751567
$502$	0	0
$503$	−1680.00	−0.148921	−0.0744607	−	0.997224i	$-0.523724\pi$
$503$	−1680.00	−0.148921	−0.0744607	+	0.997224i	$0.523724\pi$
$504$	0	0
$505$	9653.00	0.850600
$506$	0	0
$507$	−14007.0	−1.22697
$508$	0	0
$509$	9457.00	0.823525	0.411762	−	0.911291i	$-0.364913\pi$
$509$	9457.00	0.823525	0.411762	+	0.911291i	$0.364913\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	−1715.00	−0.147601
$514$	0	0
$515$	4753.00	0.406684
$516$	0	0
$517$	2625.00	0.223302
$518$	0	0
$519$	19747.0	1.67013
$520$	0	0
$521$	18081.0	1.52043	0.760214	−	0.649673i	$-0.225094\pi$
$521$	18081.0	1.52043	0.760214	+	0.649673i	$0.225094\pi$
$522$	0	0
$523$	20377.0	1.70368	0.851839	−	0.523803i	$-0.175487\pi$
$523$	20377.0	1.70368	0.851839	+	0.523803i	$0.175487\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	3087.00	0.255165
$528$	0	0
$529$	13114.0	1.07783
$530$	0	0
$531$	−2310.00	−0.188786
$532$	0	0
$533$	−4900.00	−0.398204
$534$	0	0
$535$	3199.00	0.258514
$536$	0	0
$537$	22771.0	1.82987
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−6193.00	−0.492159	−0.246079	−	0.969250i	$-0.579142\pi$
$541$	−6193.00	−0.492159	−0.246079	+	0.969250i	$0.579142\pi$
$542$	0	0
$543$	−11074.0	−0.875195
$544$	0	0
$545$	7875.00	0.618950
$546$	0	0
$547$	18464.0	1.44326	0.721630	−	0.692279i	$-0.243393\pi$
$547$	18464.0	1.44326	0.721630	+	0.692279i	$0.243393\pi$
$548$	0	0
$549$	9086.00	0.706341
$550$	0	0
$551$	2842.00	0.219734
$552$	0	0
$553$	0	0
$554$	0	0
$555$	−10731.0	−0.820731
$556$	0	0
$557$	−9413.00	−0.716053	−0.358027	−	0.933711i	$-0.616550\pi$
$557$	−9413.00	−0.716053	−0.358027	+	0.933711i	$0.616550\pi$
$558$	0	0
$559$	1736.00	0.131351
$560$	0	0
$561$	735.000	0.0553150
$562$	0	0
$563$	3199.00	0.239470	0.119735	−	0.992806i	$-0.461795\pi$
$563$	3199.00	0.239470	0.119735	+	0.992806i	$0.461795\pi$
$564$	0	0
$565$	10766.0	0.801644
$566$	0	0
$567$	0	0
$568$	0	0
$569$	21583.0	1.59017	0.795085	−	0.606498i	$-0.207426\pi$
$569$	21583.0	1.59017	0.795085	+	0.606498i	$0.207426\pi$
$570$	0	0
$571$	−20267.0	−1.48537	−0.742686	−	0.669640i	$-0.766449\pi$
$571$	−20267.0	−1.48537	−0.742686	+	0.669640i	$0.766449\pi$
$572$	0	0
$573$	−17899.0	−1.30496
$574$	0	0
$575$	−12084.0	−0.876413
$576$	0	0
$577$	−13951.0	−1.00656	−0.503282	−	0.864122i	$-0.667874\pi$
$577$	−13951.0	−1.00656	−0.503282	+	0.864122i	$0.667874\pi$
$578$	0	0
$579$	−2779.00	−0.199467
$580$	0	0
$581$	0	0
$582$	0	0
$583$	1515.00	0.107624
$584$	0	0
$585$	−2156.00	−0.152375
$586$	0	0
$587$	−20972.0	−1.47463	−0.737314	−	0.675550i	$-0.763906\pi$
$587$	−20972.0	−1.47463	−0.737314	+	0.675550i	$0.763906\pi$
$588$	0	0
$589$	7203.00	0.503895
$590$	0	0
$591$	20398.0	1.41973
$592$	0	0
$593$	189.000	0.0130882	0.00654410	−	0.999979i	$-0.497917\pi$
$593$	189.000	0.0130882	0.00654410	+	0.999979i	$0.497917\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	23373.0	1.60233
$598$	0	0
$599$	10281.0	0.701286	0.350643	−	0.936509i	$-0.385963\pi$
$599$	10281.0	0.701286	0.350643	+	0.936509i	$0.385963\pi$
$600$	0	0
$601$	6090.00	0.413338	0.206669	−	0.978411i	$-0.433738\pi$
$601$	6090.00	0.413338	0.206669	+	0.978411i	$0.433738\pi$
$602$	0	0
$603$	−9130.00	−0.616588
$604$	0	0
$605$	9142.00	0.614339
$606$	0	0
$607$	4949.00	0.330929	0.165464	−	0.986216i	$-0.447088\pi$
$607$	4949.00	0.330929	0.165464	+	0.986216i	$0.447088\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	7350.00	0.486660
$612$	0	0
$613$	−15797.0	−1.04084	−0.520420	−	0.853910i	$-0.674225\pi$
$613$	−15797.0	−1.04084	−0.520420	+	0.853910i	$0.674225\pi$
$614$	0	0
$615$	17150.0	1.12448
$616$	0	0
$617$	−9378.00	−0.611903	−0.305951	−	0.952047i	$-0.598975\pi$
$617$	−9378.00	−0.611903	−0.305951	+	0.952047i	$0.598975\pi$
$618$	0	0
$619$	−24353.0	−1.58131	−0.790654	−	0.612263i	$-0.790259\pi$
$619$	−24353.0	−1.58131	−0.790654	+	0.612263i	$0.790259\pi$
$620$	0	0
$621$	−5565.00	−0.359607
$622$	0	0
$623$	0	0
$624$	0	0
$625$	−349.000	−0.0223360
$626$	0	0
$627$	1715.00	0.109235
$628$	0	0
$629$	4599.00	0.291533
$630$	0	0
$631$	12640.0	0.797449	0.398725	−	0.917071i	$-0.369453\pi$
$631$	12640.0	0.797449	0.398725	+	0.917071i	$0.369453\pi$
$632$	0	0
$633$	−12460.0	−0.782371
$634$	0	0
$635$	504.000	0.0314971
$636$	0	0
$637$	0	0
$638$	0	0
$639$	9504.00	0.588376
$640$	0	0
$641$	−1041.00	−0.0641451	−0.0320726	−	0.999486i	$-0.510211\pi$
$641$	−1041.00	−0.0641451	−0.0320726	+	0.999486i	$0.510211\pi$
$642$	0	0
$643$	9548.00	0.585593	0.292797	−	0.956175i	$-0.405414\pi$
$643$	9548.00	0.585593	0.292797	+	0.956175i	$0.405414\pi$
$644$	0	0
$645$	−6076.00	−0.370918
$646$	0	0
$647$	−3241.00	−0.196935	−0.0984674	−	0.995140i	$-0.531394\pi$
$647$	−3241.00	−0.196935	−0.0984674	+	0.995140i	$0.531394\pi$
$648$	0	0
$649$	−525.000	−0.0317535
$650$	0	0
$651$	0	0
$652$	0	0
$653$	−8853.00	−0.530543	−0.265272	−	0.964174i	$-0.585462\pi$
$653$	−8853.00	−0.530543	−0.265272	+	0.964174i	$0.585462\pi$
$654$	0	0
$655$	−15043.0	−0.897372
$656$	0	0
$657$	24486.0	1.45402
$658$	0	0
$659$	−7044.00	−0.416381	−0.208191	−	0.978088i	$-0.566757\pi$
$659$	−7044.00	−0.416381	−0.208191	+	0.978088i	$0.566757\pi$
$660$	0	0
$661$	12089.0	0.711358	0.355679	−	0.934608i	$-0.384250\pi$
$661$	12089.0	0.711358	0.355679	+	0.934608i	$0.384250\pi$
$662$	0	0
$663$	2058.00	0.120552
$664$	0	0
$665$	0	0
$666$	0	0
$667$	9222.00	0.535348
$668$	0	0
$669$	−9800.00	−0.566353
$670$	0	0
$671$	2065.00	0.118805
$672$	0	0
$673$	982.000	0.0562456	0.0281228	−	0.999604i	$-0.491047\pi$
$673$	982.000	0.0562456	0.0281228	+	0.999604i	$0.491047\pi$
$674$	0	0
$675$	2660.00	0.151679
$676$	0	0
$677$	30513.0	1.73222	0.866108	−	0.499857i	$-0.166614\pi$
$677$	30513.0	1.73222	0.866108	+	0.499857i	$0.166614\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	−15435.0	−0.868532
$682$	0	0
$683$	−11475.0	−0.642868	−0.321434	−	0.946932i	$-0.604165\pi$
$683$	−11475.0	−0.642868	−0.321434	+	0.946932i	$0.604165\pi$
$684$	0	0
$685$	7875.00	0.439253
$686$	0	0
$687$	−2009.00	−0.111569
$688$	0	0
$689$	4242.00	0.234553
$690$	0	0
$691$	−28315.0	−1.55883	−0.779416	−	0.626506i	$-0.784484\pi$
$691$	−28315.0	−1.55883	−0.779416	+	0.626506i	$0.784484\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	−1764.00	−0.0962767
$696$	0	0
$697$	−7350.00	−0.399428
$698$	0	0
$699$	32109.0	1.73744
$700$	0	0
$701$	10614.0	0.571876	0.285938	−	0.958248i	$-0.407695\pi$
$701$	10614.0	0.571876	0.285938	+	0.958248i	$0.407695\pi$
$702$	0	0
$703$	10731.0	0.575715
$704$	0	0
$705$	−25725.0	−1.37427
$706$	0	0
$707$	0	0
$708$	0	0
$709$	10299.0	0.545539	0.272769	−	0.962079i	$-0.412060\pi$
$709$	10299.0	0.545539	0.272769	+	0.962079i	$0.412060\pi$
$710$	0	0
$711$	2266.00	0.119524
$712$	0	0
$713$	23373.0	1.22767
$714$	0	0
$715$	−490.000	−0.0256293
$716$	0	0
$717$	−11676.0	−0.608156
$718$	0	0
$719$	32529.0	1.68724	0.843621	−	0.536939i	$-0.180420\pi$
$719$	32529.0	1.68724	0.843621	+	0.536939i	$0.180420\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	23863.0	1.22749
$724$	0	0
$725$	−4408.00	−0.225806
$726$	0	0
$727$	29456.0	1.50270	0.751350	−	0.659904i	$-0.229403\pi$
$727$	29456.0	1.50270	0.751350	+	0.659904i	$0.229403\pi$
$728$	0	0
$729$	−11843.0	−0.601687
$730$	0	0
$731$	2604.00	0.131754
$732$	0	0
$733$	−27867.0	−1.40422	−0.702109	−	0.712070i	$-0.747758\pi$
$733$	−27867.0	−1.40422	−0.702109	+	0.712070i	$0.747758\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−2075.00	−0.103709
$738$	0	0
$739$	−19539.0	−0.972603	−0.486302	−	0.873791i	$-0.661654\pi$
$739$	−19539.0	−0.972603	−0.486302	+	0.873791i	$0.661654\pi$
$740$	0	0
$741$	4802.00	0.238065
$742$	0	0
$743$	−1248.00	−0.0616214	−0.0308107	−	0.999525i	$-0.509809\pi$
$743$	−1248.00	−0.0616214	−0.0308107	+	0.999525i	$0.509809\pi$
$744$	0	0
$745$	1407.00	0.0691926
$746$	0	0
$747$	24024.0	1.17670
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−28093.0	−1.36502	−0.682509	−	0.730877i	$-0.739111\pi$
$751$	−28093.0	−1.36502	−0.682509	+	0.730877i	$0.739111\pi$
$752$	0	0
$753$	−33320.0	−1.61255
$754$	0	0
$755$	11333.0	0.546292
$756$	0	0
$757$	35954.0	1.72625	0.863124	−	0.504991i	$-0.168504\pi$
$757$	35954.0	1.72625	0.863124	+	0.504991i	$0.168504\pi$
$758$	0	0
$759$	5565.00	0.266135
$760$	0	0
$761$	861.000	0.0410134	0.0205067	−	0.999790i	$-0.493472\pi$
$761$	861.000	0.0410134	0.0205067	+	0.999790i	$0.493472\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	−3234.00	−0.152844
$766$	0	0
$767$	−1470.00	−0.0692029
$768$	0	0
$769$	−24710.0	−1.15873	−0.579366	−	0.815067i	$-0.696700\pi$
$769$	−24710.0	−1.15873	−0.579366	+	0.815067i	$0.696700\pi$
$770$	0	0
$771$	5635.00	0.263216
$772$	0	0
$773$	−16499.0	−0.767694	−0.383847	−	0.923397i	$-0.625401\pi$
$773$	−16499.0	−0.767694	−0.383847	+	0.923397i	$0.625401\pi$
$774$	0	0
$775$	−11172.0	−0.517819
$776$	0	0
$777$	0	0
$778$	0	0
$779$	−17150.0	−0.788784
$780$	0	0
$781$	2160.00	0.0989640
$782$	0	0
$783$	−2030.00	−0.0926517
$784$	0	0
$785$	4753.00	0.216104
$786$	0	0
$787$	16471.0	0.746033	0.373016	−	0.927825i	$-0.378324\pi$
$787$	16471.0	0.746033	0.373016	+	0.927825i	$0.378324\pi$
$788$	0	0
$789$	1799.00	0.0811738
$790$	0	0
$791$	0	0
$792$	0	0
$793$	5782.00	0.258922
$794$	0	0
$795$	−14847.0	−0.662351
$796$	0	0
$797$	36470.0	1.62087	0.810435	−	0.585828i	$-0.199231\pi$
$797$	36470.0	1.62087	0.810435	+	0.585828i	$0.199231\pi$
$798$	0	0
$799$	11025.0	0.488156
$800$	0	0
$801$	7238.00	0.319279
$802$	0	0
$803$	5565.00	0.244564
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−25137.0	−1.09649
$808$	0	0
$809$	35751.0	1.55369	0.776847	−	0.629690i	$-0.216818\pi$
$809$	35751.0	1.55369	0.776847	+	0.629690i	$0.216818\pi$
$810$	0	0
$811$	−16492.0	−0.714072	−0.357036	−	0.934091i	$-0.616213\pi$
$811$	−16492.0	−0.714072	−0.357036	+	0.934091i	$0.616213\pi$
$812$	0	0
$813$	9751.00	0.420643
$814$	0	0
$815$	−3269.00	−0.140501
$816$	0	0
$817$	6076.00	0.260186
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−41473.0	−1.76299	−0.881497	−	0.472190i	$-0.843464\pi$
$821$	−41473.0	−1.76299	−0.881497	+	0.472190i	$0.843464\pi$
$822$	0	0
$823$	25065.0	1.06162	0.530809	−	0.847492i	$-0.321888\pi$
$823$	25065.0	1.06162	0.530809	+	0.847492i	$0.321888\pi$
$824$	0	0
$825$	−2660.00	−0.112254
$826$	0	0
$827$	−9732.00	−0.409208	−0.204604	−	0.978845i	$-0.565591\pi$
$827$	−9732.00	−0.409208	−0.204604	+	0.978845i	$0.565591\pi$
$828$	0	0
$829$	−27755.0	−1.16281	−0.581406	−	0.813614i	$-0.697497\pi$
$829$	−27755.0	−1.16281	−0.581406	+	0.813614i	$0.697497\pi$
$830$	0	0
$831$	2905.00	0.121268
$832$	0	0
$833$	0	0
$834$	0	0
$835$	−8428.00	−0.349297
$836$	0	0
$837$	−5145.00	−0.212470
$838$	0	0
$839$	21112.0	0.868733	0.434367	−	0.900736i	$-0.356972\pi$
$839$	21112.0	0.868733	0.434367	+	0.900736i	$0.356972\pi$
$840$	0	0
$841$	−21025.0	−0.862069
$842$	0	0
$843$	−34678.0	−1.41681
$844$	0	0
$845$	14007.0	0.570243
$846$	0	0
$847$	0	0
$848$	0	0
$849$	−29939.0	−1.21025
$850$	0	0
$851$	34821.0	1.40264
$852$	0	0
$853$	21238.0	0.852492	0.426246	−	0.904607i	$-0.359836\pi$
$853$	21238.0	0.852492	0.426246	+	0.904607i	$0.359836\pi$
$854$	0	0
$855$	−7546.00	−0.301834
$856$	0	0
$857$	35609.0	1.41935	0.709673	−	0.704531i	$-0.248842\pi$
$857$	35609.0	1.41935	0.709673	+	0.704531i	$0.248842\pi$
$858$	0	0
$859$	2177.00	0.0864706	0.0432353	−	0.999065i	$-0.486233\pi$
$859$	2177.00	0.0864706	0.0432353	+	0.999065i	$0.486233\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	32247.0	1.27196	0.635980	−	0.771706i	$-0.280596\pi$
$863$	32247.0	1.27196	0.635980	+	0.771706i	$0.280596\pi$
$864$	0	0
$865$	−19747.0	−0.776206
$866$	0	0
$867$	−31304.0	−1.22623
$868$	0	0
$869$	515.000	0.0201038
$870$	0	0
$871$	−5810.00	−0.226021
$872$	0	0
$873$	19404.0	0.752263
$874$	0	0
$875$	0	0
$876$	0	0
$877$	27631.0	1.06389	0.531946	−	0.846779i	$-0.321461\pi$
$877$	27631.0	1.06389	0.531946	+	0.846779i	$0.321461\pi$
$878$	0	0
$879$	−54194.0	−2.07954
$880$	0	0
$881$	−24402.0	−0.933172	−0.466586	−	0.884476i	$-0.654516\pi$
$881$	−24402.0	−0.933172	−0.466586	+	0.884476i	$0.654516\pi$
$882$	0	0
$883$	19612.0	0.747448	0.373724	−	0.927540i	$-0.378081\pi$
$883$	19612.0	0.747448	0.373724	+	0.927540i	$0.378081\pi$
$884$	0	0
$885$	5145.00	0.195421
$886$	0	0
$887$	2261.00	0.0855884	0.0427942	−	0.999084i	$-0.486374\pi$
$887$	2261.00	0.0855884	0.0427942	+	0.999084i	$0.486374\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−4195.00	−0.157730
$892$	0	0
$893$	25725.0	0.964003
$894$	0	0
$895$	−22771.0	−0.850448
$896$	0	0
$897$	15582.0	0.580009
$898$	0	0
$899$	8526.00	0.316305
$900$	0	0
$901$	6363.00	0.235274
$902$	0	0
$903$	0	0
$904$	0	0
$905$	11074.0	0.406754
$906$	0	0
$907$	23833.0	0.872505	0.436252	−	0.899824i	$-0.356305\pi$
$907$	23833.0	0.872505	0.436252	+	0.899824i	$0.356305\pi$
$908$	0	0
$909$	−30338.0	−1.10698
$910$	0	0
$911$	−31824.0	−1.15738	−0.578692	−	0.815546i	$-0.696437\pi$
$911$	−31824.0	−1.15738	−0.578692	+	0.815546i	$0.696437\pi$
$912$	0	0
$913$	5460.00	0.197919
$914$	0	0
$915$	−20237.0	−0.731163
$916$	0	0
$917$	0	0
$918$	0	0
$919$	16819.0	0.603708	0.301854	−	0.953354i	$-0.402394\pi$
$919$	16819.0	0.603708	0.301854	+	0.953354i	$0.402394\pi$
$920$	0	0
$921$	−51548.0	−1.84426
$922$	0	0
$923$	6048.00	0.215680
$924$	0	0
$925$	−16644.0	−0.591623
$926$	0	0
$927$	−14938.0	−0.529265
$928$	0	0
$929$	−1799.00	−0.0635342	−0.0317671	−	0.999495i	$-0.510113\pi$
$929$	−1799.00	−0.0635342	−0.0317671	+	0.999495i	$0.510113\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	69825.0	2.45013
$934$	0	0
$935$	−735.000	−0.0257081
$936$	0	0
$937$	−14154.0	−0.493480	−0.246740	−	0.969082i	$-0.579359\pi$
$937$	−14154.0	−0.493480	−0.246740	+	0.969082i	$0.579359\pi$
$938$	0	0
$939$	33271.0	1.15629
$940$	0	0
$941$	−12047.0	−0.417344	−0.208672	−	0.977986i	$-0.566914\pi$
$941$	−12047.0	−0.417344	−0.208672	+	0.977986i	$0.566914\pi$
$942$	0	0
$943$	−55650.0	−1.92175
$944$	0	0
$945$	0	0
$946$	0	0
$947$	24379.0	0.836548	0.418274	−	0.908321i	$-0.362635\pi$
$947$	24379.0	0.836548	0.418274	+	0.908321i	$0.362635\pi$
$948$	0	0
$949$	15582.0	0.532996
$950$	0	0
$951$	−24339.0	−0.829912
$952$	0	0
$953$	−52330.0	−1.77874	−0.889368	−	0.457192i	$-0.848855\pi$
$953$	−52330.0	−1.77874	−0.889368	+	0.457192i	$0.848855\pi$
$954$	0	0
$955$	17899.0	0.606490
$956$	0	0
$957$	2030.00	0.0685690
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−8182.00	−0.274647
$962$	0	0
$963$	−10054.0	−0.336434
$964$	0	0
$965$	2779.00	0.0927038
$966$	0	0
$967$	12416.0	0.412897	0.206449	−	0.978457i	$-0.433809\pi$
$967$	12416.0	0.412897	0.206449	+	0.978457i	$0.433809\pi$
$968$	0	0
$969$	7203.00	0.238796
$970$	0	0
$971$	36813.0	1.21667	0.608334	−	0.793681i	$-0.291838\pi$
$971$	36813.0	1.21667	0.608334	+	0.793681i	$0.291838\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	−7448.00	−0.244643
$976$	0	0
$977$	34995.0	1.14595	0.572973	−	0.819574i	$-0.305790\pi$
$977$	34995.0	1.14595	0.572973	+	0.819574i	$0.305790\pi$
$978$	0	0
$979$	1645.00	0.0537022
$980$	0	0
$981$	−24750.0	−0.805511
$982$	0	0
$983$	−14301.0	−0.464019	−0.232010	−	0.972713i	$-0.574530\pi$
$983$	−14301.0	−0.464019	−0.232010	+	0.972713i	$0.574530\pi$
$984$	0	0
$985$	−20398.0	−0.659832
$986$	0	0
$987$	0	0
$988$	0	0
$989$	19716.0	0.633905
$990$	0	0
$991$	2665.00	0.0854253	0.0427127	−	0.999087i	$-0.486400\pi$
$991$	2665.00	0.0854253	0.0427127	+	0.999087i	$0.486400\pi$
$992$	0	0
$993$	−23387.0	−0.747396
$994$	0	0
$995$	−23373.0	−0.744697
$996$	0	0
$997$	−24871.0	−0.790043	−0.395021	−	0.918672i	$-0.629263\pi$
$997$	−24871.0	−0.790043	−0.395021	+	0.918672i	$0.629263\pi$
$998$	0	0
$999$	−7665.00	−0.242753

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.4.a.r.1.1		1
4.3	odd	2		49.4.a.c.1.1		1
7.3	odd	6		112.4.i.c.65.1		2
7.5	odd	6		112.4.i.c.81.1		2
7.6	odd	2		784.4.a.b.1.1		1
12.11	even	2		441.4.a.e.1.1		1
20.19	odd	2		1225.4.a.d.1.1		1
28.3	even	6		7.4.c.a.2.1	✓	2
28.11	odd	6		49.4.c.a.30.1		2
28.19	even	6		7.4.c.a.4.1	yes	2
28.23	odd	6		49.4.c.a.18.1		2
28.27	even	2		49.4.a.d.1.1		1
56.3	even	6		448.4.i.f.65.1		2
56.5	odd	6		448.4.i.a.193.1		2
56.19	even	6		448.4.i.f.193.1		2
56.45	odd	6		448.4.i.a.65.1		2
84.11	even	6		441.4.e.k.226.1		2
84.23	even	6		441.4.e.k.361.1		2
84.47	odd	6		63.4.e.b.46.1		2
84.59	odd	6		63.4.e.b.37.1		2
84.83	odd	2		441.4.a.d.1.1		1
140.3	odd	12		175.4.k.a.149.2		4
140.19	even	6		175.4.e.a.151.1		2
140.47	odd	12		175.4.k.a.74.2		4
140.59	even	6		175.4.e.a.51.1		2
140.87	odd	12		175.4.k.a.149.1		4
140.103	odd	12		175.4.k.a.74.1		4
140.139	even	2		1225.4.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.4.c.a.2.1	✓	2	28.3	even	6
7.4.c.a.4.1	yes	2	28.19	even	6
49.4.a.c.1.1		1	4.3	odd	2
49.4.a.d.1.1		1	28.27	even	2
49.4.c.a.18.1		2	28.23	odd	6
49.4.c.a.30.1		2	28.11	odd	6
63.4.e.b.37.1		2	84.59	odd	6
63.4.e.b.46.1		2	84.47	odd	6
112.4.i.c.65.1		2	7.3	odd	6
112.4.i.c.81.1		2	7.5	odd	6
175.4.e.a.51.1		2	140.59	even	6
175.4.e.a.151.1		2	140.19	even	6
175.4.k.a.74.1		4	140.103	odd	12
175.4.k.a.74.2		4	140.47	odd	12
175.4.k.a.149.1		4	140.87	odd	12
175.4.k.a.149.2		4	140.3	odd	12
441.4.a.d.1.1		1	84.83	odd	2
441.4.a.e.1.1		1	12.11	even	2
441.4.e.k.226.1		2	84.11	even	6
441.4.e.k.361.1		2	84.23	even	6
448.4.i.a.65.1		2	56.45	odd	6
448.4.i.a.193.1		2	56.5	odd	6
448.4.i.f.65.1		2	56.3	even	6
448.4.i.f.193.1		2	56.19	even	6
784.4.a.b.1.1		1	7.6	odd	2
784.4.a.r.1.1		1	1.1	even	1	trivial
1225.4.a.c.1.1		1	140.139	even	2
1225.4.a.d.1.1		1	20.19	odd	2

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	784.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

Downloads

Learn more about