LMFDB - Embedded newform 49.4.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,4,Mod(1,49)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("49.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	49.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$2.89109359028$
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	$\chi$	$=$	49.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$

$=$

\(q+2.00000 q^{2} +7.00000 q^{3} -4.00000 q^{4} +7.00000 q^{5} +14.0000 q^{6} -24.0000 q^{8} +22.0000 q^{9} +14.0000 q^{10} -5.00000 q^{11} -28.0000 q^{12} -14.0000 q^{13} +49.0000 q^{15} -16.0000 q^{16} -21.0000 q^{17} +44.0000 q^{18} +49.0000 q^{19} -28.0000 q^{20} -10.0000 q^{22} -159.000 q^{23} -168.000 q^{24} -76.0000 q^{25} -28.0000 q^{26} -35.0000 q^{27} +58.0000 q^{29} +98.0000 q^{30} +147.000 q^{31} +160.000 q^{32} -35.0000 q^{33} -42.0000 q^{34} -88.0000 q^{36} +219.000 q^{37} +98.0000 q^{38} -98.0000 q^{39} -168.000 q^{40} +350.000 q^{41} -124.000 q^{43} +20.0000 q^{44} +154.000 q^{45} -318.000 q^{46} +525.000 q^{47} -112.000 q^{48} -152.000 q^{50} -147.000 q^{51} +56.0000 q^{52} +303.000 q^{53} -70.0000 q^{54} -35.0000 q^{55} +343.000 q^{57} +116.000 q^{58} -105.000 q^{59} -196.000 q^{60} -413.000 q^{61} +294.000 q^{62} +448.000 q^{64} -98.0000 q^{65} -70.0000 q^{66} +415.000 q^{67} +84.0000 q^{68} -1113.00 q^{69} -432.000 q^{71} -528.000 q^{72} -1113.00 q^{73} +438.000 q^{74} -532.000 q^{75} -196.000 q^{76} -196.000 q^{78} -103.000 q^{79} -112.000 q^{80} -839.000 q^{81} +700.000 q^{82} +1092.00 q^{83} -147.000 q^{85} -248.000 q^{86} +406.000 q^{87} +120.000 q^{88} -329.000 q^{89} +308.000 q^{90} +636.000 q^{92} +1029.00 q^{93} +1050.00 q^{94} +343.000 q^{95} +1120.00 q^{96} -882.000 q^{97} -110.000 q^{99} +O(q^{100})\)

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 $

$2$	2.00000	0.707107	0.353553	−	0.935414i	$-0.384973\pi$
$2$	2.00000	0.707107	0.353553	+	0.935414i	$0.384973\pi$
$3$	7.00000	1.34715	0.673575	−	0.739119i	$-0.264758\pi$
$3$	7.00000	1.34715	0.673575	+	0.739119i	$0.264758\pi$
$4$	−4.00000	−0.500000
$5$	7.00000	0.626099	0.313050	−	0.949737i	$-0.398649\pi$
$5$	7.00000	0.626099	0.313050	+	0.949737i	$0.398649\pi$
$6$	14.0000	0.952579
$7$	0	0
$7$	0	0
$8$	−24.0000	−1.06066
$9$	22.0000	0.814815
$10$	14.0000	0.442719
$11$	−5.00000	−0.137051	−0.0685253	−	0.997649i	$-0.521829\pi$
$11$	−5.00000	−0.137051	−0.0685253	+	0.997649i	$0.521829\pi$
$12$	−28.0000	−0.673575
$13$	−14.0000	−0.298685	−0.149342	−	0.988786i	$-0.547716\pi$
$13$	−14.0000	−0.298685	−0.149342	+	0.988786i	$0.547716\pi$
$14$	0	0
$15$	49.0000	0.843450
$16$	−16.0000	−0.250000
$17$	−21.0000	−0.299603	−0.149801	−	0.988716i	$-0.547863\pi$
$17$	−21.0000	−0.299603	−0.149801	+	0.988716i	$0.547863\pi$
$18$	44.0000	0.576161
$19$	49.0000	0.591651	0.295826	−	0.955242i	$-0.404405\pi$
$19$	49.0000	0.591651	0.295826	+	0.955242i	$0.404405\pi$
$20$	−28.0000	−0.313050
$21$	0	0
$22$	−10.0000	−0.0969094
$23$	−159.000	−1.44147	−0.720735	−	0.693211i	$-0.756195\pi$
$23$	−159.000	−1.44147	−0.720735	+	0.693211i	$0.756195\pi$
$24$	−168.000	−1.42887
$25$	−76.0000	−0.608000
$26$	−28.0000	−0.211202
$27$	−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	$0.440546\pi$
$30$	98.0000	0.596409
$31$	147.000	0.851677	0.425838	−	0.904799i	$-0.359979\pi$
$31$	147.000	0.851677	0.425838	+	0.904799i	$0.359979\pi$
$32$	160.000	0.883883
$33$	−35.0000	−0.184628
$34$	−42.0000	−0.211851
$35$	0	0
$36$	−88.0000	−0.407407
$37$	219.000	0.973064	0.486532	−	0.873663i	$-0.338262\pi$
$37$	219.000	0.973064	0.486532	+	0.873663i	$0.338262\pi$
$38$	98.0000	0.418361
$39$	−98.0000	−0.402373
$40$	−168.000	−0.664078
$41$	350.000	1.33319	0.666595	−	0.745420i	$-0.267751\pi$
$41$	350.000	1.33319	0.666595	+	0.745420i	$0.267751\pi$
$42$	0	0
$43$	−124.000	−0.439763	−0.219882	−	0.975527i	$-0.570567\pi$
$43$	−124.000	−0.439763	−0.219882	+	0.975527i	$0.570567\pi$
$44$	20.0000	0.0685253
$45$	154.000	0.510155
$46$	−318.000	−1.01927
$47$	525.000	1.62934	0.814671	−	0.579923i	$-0.196917\pi$
$47$	525.000	1.62934	0.814671	+	0.579923i	$0.196917\pi$
$48$	−112.000	−0.336788
$49$	0	0
$50$	−152.000	−0.429921
$51$	−147.000	−0.403610
$52$	56.0000	0.149342
$53$	303.000	0.785288	0.392644	−	0.919691i	$-0.371561\pi$
$53$	303.000	0.785288	0.392644	+	0.919691i	$0.371561\pi$
$54$	−70.0000	−0.176404
$55$	−35.0000	−0.0858073
$56$	0	0
$57$	343.000	0.797043
$58$	116.000	0.262613
$59$	−105.000	−0.231692	−0.115846	−	0.993267i	$-0.536958\pi$
$59$	−105.000	−0.231692	−0.115846	+	0.993267i	$0.536958\pi$
$60$	−196.000	−0.421725
$61$	−413.000	−0.866873	−0.433436	−	0.901184i	$-0.642699\pi$
$61$	−413.000	−0.866873	−0.433436	+	0.901184i	$0.642699\pi$
$62$	294.000	0.602226
$63$	0	0
$64$	448.000	0.875000
$65$	−98.0000	−0.187006
$66$	−70.0000	−0.130552
$67$	415.000	0.756721	0.378361	−	0.925658i	$-0.376488\pi$
$67$	415.000	0.756721	0.378361	+	0.925658i	$0.376488\pi$
$68$	84.0000	0.149801
$69$	−1113.00	−1.94188
$70$	0	0
$71$	−432.000	−0.722098	−0.361049	−	0.932547i	$-0.617581\pi$
$71$	−432.000	−0.722098	−0.361049	+	0.932547i	$0.617581\pi$
$72$	−528.000	−0.864242
$73$	−1113.00	−1.78448	−0.892238	−	0.451565i	$-0.850866\pi$
$73$	−1113.00	−1.78448	−0.892238	+	0.451565i	$0.850866\pi$
$74$	438.000	0.688060
$75$	−532.000	−0.819068
$76$	−196.000	−0.295826
$77$	0	0
$78$	−196.000	−0.284521
$79$	−103.000	−0.146689	−0.0733443	−	0.997307i	$-0.523367\pi$
$79$	−103.000	−0.146689	−0.0733443	+	0.997307i	$0.523367\pi$
$80$	−112.000	−0.156525
$81$	−839.000	−1.15089
$82$	700.000	0.942708
$83$	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
$86$	−248.000	−0.310960
$87$	406.000	0.500319
$88$	120.000	0.145364
$89$	−329.000	−0.391842	−0.195921	−	0.980620i	$-0.562770\pi$
$89$	−329.000	−0.391842	−0.195921	+	0.980620i	$0.562770\pi$
$90$	308.000	0.360734
$91$	0	0
$92$	636.000	0.720735
$93$	1029.00	1.14734
$94$	1050.00	1.15212
$95$	343.000	0.370432
$96$	1120.00	1.19072
$97$	−882.000	−0.923232	−0.461616	−	0.887080i	$-0.652730\pi$
$97$	−882.000	−0.923232	−0.461616	+	0.887080i	$0.652730\pi$
$98$	0	0
$99$	−110.000	−0.111671
$100$	304.000	0.304000
$101$	1379.00	1.35857	0.679285	−	0.733874i	$-0.262290\pi$
$101$	1379.00	1.35857	0.679285	+	0.733874i	$0.262290\pi$
$102$	−294.000	−0.285395
$103$	−679.000	−0.649552	−0.324776	−	0.945791i	$-0.605289\pi$
$103$	−679.000	−0.649552	−0.324776	+	0.945791i	$0.605289\pi$
$104$	336.000	0.316803
$105$	0	0
$106$	606.000	0.555282
$107$	457.000	0.412896	0.206448	−	0.978458i	$-0.433810\pi$
$107$	457.000	0.412896	0.206448	+	0.978458i	$0.433810\pi$
$108$	140.000	0.124736
$109$	−1125.00	−0.988582	−0.494291	−	0.869296i	$-0.664572\pi$
$109$	−1125.00	−0.988582	−0.494291	+	0.869296i	$0.664572\pi$
$110$	−70.0000	−0.0606749
$111$	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	$0.721144\pi$
$114$	686.000	0.563595
$115$	−1113.00	−0.902502
$116$	−232.000	−0.185695
$117$	−308.000	−0.243373
$118$	−210.000	−0.163831
$119$	0	0
$120$	−1176.00	−0.894614
$121$	−1306.00	−0.981217
$122$	−826.000	−0.612972
$123$	2450.00	1.79601
$124$	−588.000	−0.425838
$125$	−1407.00	−1.00677
$126$	0	0
$127$	72.0000	0.0503068	0.0251534	−	0.999684i	$-0.491993\pi$
$127$	72.0000	0.0503068	0.0251534	+	0.999684i	$0.491993\pi$
$128$	−384.000	−0.265165
$129$	−868.000	−0.592427
$130$	−196.000	−0.132233
$131$	2149.00	1.43327	0.716637	−	0.697446i	$-0.245680\pi$
$131$	2149.00	1.43327	0.716637	+	0.697446i	$0.245680\pi$
$132$	140.000	0.0923139
$133$	0	0
$134$	830.000	0.535083
$135$	−245.000	−0.156194
$136$	504.000	0.317777
$137$	−1125.00	−0.701571	−0.350786	−	0.936456i	$-0.614085\pi$
$137$	−1125.00	−0.701571	−0.350786	+	0.936456i	$0.614085\pi$
$138$	−2226.00	−1.37311
$139$	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
$142$	−864.000	−0.510600
$143$	70.0000	0.0409349
$144$	−352.000	−0.203704
$145$	406.000	0.232527
$146$	−2226.00	−1.26182
$147$	0	0
$148$	−876.000	−0.486532
$149$	−201.000	−0.110514	−0.0552569	−	0.998472i	$-0.517598\pi$
$149$	−201.000	−0.110514	−0.0552569	+	0.998472i	$0.517598\pi$
$150$	−1064.00	−0.579168
$151$	1619.00	0.872532	0.436266	−	0.899818i	$-0.356301\pi$
$151$	1619.00	0.872532	0.436266	+	0.899818i	$0.356301\pi$
$152$	−1176.00	−0.627541
$153$	−462.000	−0.244121
$154$	0	0
$155$	1029.00	0.533234
$156$	392.000	0.201187
$157$	679.000	0.345160	0.172580	−	0.984996i	$-0.444790\pi$
$157$	679.000	0.345160	0.172580	+	0.984996i	$0.444790\pi$
$158$	−206.000	−0.103725
$159$	2121.00	1.05790
$160$	1120.00	0.553399
$161$	0	0
$162$	−1678.00	−0.813803
$163$	−467.000	−0.224407	−0.112203	−	0.993685i	$-0.535791\pi$
$163$	−467.000	−0.224407	−0.112203	+	0.993685i	$0.535791\pi$
$164$	−1400.00	−0.666595
$165$	−245.000	−0.115595
$166$	2184.00	1.02115
$167$	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
$170$	−294.000	−0.132640
$171$	1078.00	0.482086
$172$	496.000	0.219882
$173$	−2821.00	−1.23975	−0.619875	−	0.784701i	$-0.712817\pi$
$173$	−2821.00	−1.23975	−0.619875	+	0.784701i	$0.712817\pi$
$174$	812.000	0.353779
$175$	0	0
$176$	80.0000	0.0342627
$177$	−735.000	−0.312124
$178$	−658.000	−0.277074
$179$	−3253.00	−1.35833	−0.679164	−	0.733987i	$-0.737657\pi$
$179$	−3253.00	−1.35833	−0.679164	+	0.733987i	$0.737657\pi$
$180$	−616.000	−0.255077
$181$	1582.00	0.649664	0.324832	−	0.945772i	$-0.394692\pi$
$181$	1582.00	0.649664	0.324832	+	0.945772i	$0.394692\pi$
$182$	0	0
$183$	−2891.00	−1.16781
$184$	3816.00	1.52891
$185$	1533.00	0.609235
$186$	2058.00	0.811290
$187$	105.000	0.0410608
$188$	−2100.00	−0.814671
$189$	0	0
$190$	686.000	0.261935
$191$	2557.00	0.968681	0.484340	−	0.874880i	$-0.339060\pi$
$191$	2557.00	0.968681	0.484340	+	0.874880i	$0.339060\pi$
$192$	3136.00	1.17876
$193$	−397.000	−0.148066	−0.0740329	−	0.997256i	$-0.523587\pi$
$193$	−397.000	−0.148066	−0.0740329	+	0.997256i	$0.523587\pi$
$194$	−1764.00	−0.652824
$195$	−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	$0.323340\pi$
$198$	−220.000	−0.0789632
$199$	3339.00	1.18942	0.594712	−	0.803939i	$-0.297266\pi$
$199$	3339.00	1.18942	0.594712	+	0.803939i	$0.297266\pi$
$200$	1824.00	0.644881
$201$	2905.00	1.01942
$202$	2758.00	0.960654
$203$	0	0
$204$	588.000	0.201805
$205$	2450.00	0.834709
$206$	−1358.00	−0.459303
$207$	−3498.00	−1.17453
$208$	224.000	0.0746712
$209$	−245.000	−0.0810861
$210$	0	0
$211$	1780.00	0.580759	0.290380	−	0.956911i	$-0.406218\pi$
$211$	1780.00	0.580759	0.290380	+	0.956911i	$0.406218\pi$
$212$	−1212.00	−0.392644
$213$	−3024.00	−0.972775
$214$	914.000	0.291961
$215$	−868.000	−0.275335
$216$	840.000	0.264605
$217$	0	0
$218$	−2250.00	−0.699033
$219$	−7791.00	−2.40396
$220$	140.000	0.0429036
$221$	294.000	0.0894868
$222$	3066.00	0.926921
$223$	−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
$226$	−3076.00	−0.905365
$227$	−2205.00	−0.644718	−0.322359	−	0.946617i	$-0.604476\pi$
$227$	−2205.00	−0.644718	−0.322359	+	0.946617i	$0.604476\pi$
$228$	−1372.00	−0.398522
$229$	287.000	0.0828188	0.0414094	−	0.999142i	$-0.486815\pi$
$229$	287.000	0.0828188	0.0414094	+	0.999142i	$0.486815\pi$
$230$	−2226.00	−0.638166
$231$	0	0
$232$	−1392.00	−0.393919
$233$	4587.00	1.28972	0.644859	−	0.764301i	$-0.276916\pi$
$233$	4587.00	1.28972	0.644859	+	0.764301i	$0.276916\pi$
$234$	−616.000	−0.172091
$235$	3675.00	1.02013
$236$	420.000	0.115846
$237$	−721.000	−0.197612
$238$	0	0
$239$	1668.00	0.451439	0.225720	−	0.974192i	$-0.427527\pi$
$239$	1668.00	0.451439	0.225720	+	0.974192i	$0.427527\pi$
$240$	−784.000	−0.210862
$241$	−3409.00	−0.911174	−0.455587	−	0.890191i	$-0.650571\pi$
$241$	−3409.00	−0.911174	−0.455587	+	0.890191i	$0.650571\pi$
$242$	−2612.00	−0.693825
$243$	−4928.00	−1.30095
$244$	1652.00	0.433436
$245$	0	0
$246$	4900.00	1.26997
$247$	−686.000	−0.176717
$248$	−3528.00	−0.903340
$249$	7644.00	1.94546
$250$	−2814.00	−0.711892
$251$	−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
$254$	144.000	0.0355723
$255$	−1029.00	−0.252700
$256$	−4352.00	−1.06250
$257$	−805.000	−0.195387	−0.0976936	−	0.995217i	$-0.531147\pi$
$257$	−805.000	−0.195387	−0.0976936	+	0.995217i	$0.531147\pi$
$258$	−1736.00	−0.418909
$259$	0	0
$260$	392.000	0.0935031
$261$	1276.00	0.302615
$262$	4298.00	1.01348
$263$	−257.000	−0.0602559	−0.0301279	−	0.999546i	$-0.509591\pi$
$263$	−257.000	−0.0602559	−0.0301279	+	0.999546i	$0.509591\pi$
$264$	840.000	0.195827
$265$	2121.00	0.491668
$266$	0	0
$267$	−2303.00	−0.527870
$268$	−1660.00	−0.378361
$269$	3591.00	0.813930	0.406965	−	0.913444i	$-0.366587\pi$
$269$	3591.00	0.813930	0.406965	+	0.913444i	$0.366587\pi$
$270$	−490.000	−0.110446
$271$	1393.00	0.312246	0.156123	−	0.987738i	$-0.450100\pi$
$271$	1393.00	0.312246	0.156123	+	0.987738i	$0.450100\pi$
$272$	336.000	0.0749007
$273$	0	0
$274$	−2250.00	−0.496086
$275$	380.000	0.0833268
$276$	4452.00	0.970938
$277$	415.000	0.0900178	0.0450089	−	0.998987i	$-0.485668\pi$
$277$	415.000	0.0900178	0.0450089	+	0.998987i	$0.485668\pi$
$278$	504.000	0.108733
$279$	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	$0.676255\pi$
$282$	7350.00	1.55208
$283$	−4277.00	−0.898379	−0.449190	−	0.893437i	$-0.648287\pi$
$283$	−4277.00	−0.898379	−0.449190	+	0.893437i	$0.648287\pi$
$284$	1728.00	0.361049
$285$	2401.00	0.499028
$286$	140.000	0.0289454
$287$	0	0
$288$	3520.00	0.720201
$289$	−4472.00	−0.910238
$290$	812.000	0.164422
$291$	−6174.00	−1.24373
$292$	4452.00	0.892238
$293$	7742.00	1.54366	0.771830	−	0.635829i	$-0.219342\pi$
$293$	7742.00	1.54366	0.771830	+	0.635829i	$0.219342\pi$
$294$	0	0
$295$	−735.000	−0.145062
$296$	−5256.00	−1.03209
$297$	175.000	0.0341903
$298$	−402.000	−0.0781451
$299$	2226.00	0.430545
$300$	2128.00	0.409534
$301$	0	0
$302$	3238.00	0.616973
$303$	9653.00	1.83020
$304$	−784.000	−0.147913
$305$	−2891.00	−0.542748
$306$	−924.000	−0.172619
$307$	−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
$310$	2058.00	0.377053
$311$	9975.00	1.81875	0.909374	−	0.415980i	$-0.136562\pi$
$311$	9975.00	1.81875	0.909374	+	0.415980i	$0.136562\pi$
$312$	2352.00	0.426781
$313$	−4753.00	−0.858324	−0.429162	−	0.903228i	$-0.641191\pi$
$313$	−4753.00	−0.858324	−0.429162	+	0.903228i	$0.641191\pi$
$314$	1358.00	0.244065
$315$	0	0
$316$	412.000	0.0733443
$317$	−3477.00	−0.616050	−0.308025	−	0.951378i	$-0.599668\pi$
$317$	−3477.00	−0.616050	−0.308025	+	0.951378i	$0.599668\pi$
$318$	4242.00	0.748049
$319$	−290.000	−0.0508993
$320$	3136.00	0.547837
$321$	3199.00	0.556233
$322$	0	0
$323$	−1029.00	−0.177260
$324$	3356.00	0.575446
$325$	1064.00	0.181600
$326$	−934.000	−0.158679
$327$	−7875.00	−1.33177
$328$	−8400.00	−1.41406
$329$	0	0
$330$	−490.000	−0.0817382
$331$	3341.00	0.554797	0.277399	−	0.960755i	$-0.410528\pi$
$331$	3341.00	0.554797	0.277399	+	0.960755i	$0.410528\pi$
$332$	−4368.00	−0.722064
$333$	4818.00	0.792867
$334$	2408.00	0.394491
$335$	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	$0.297022\pi$
$338$	−4002.00	−0.644024
$339$	−10766.0	−1.72486
$340$	588.000	0.0937905
$341$	−735.000	−0.116723
$342$	2156.00	0.340886
$343$	0	0
$344$	2976.00	0.466439
$345$	−7791.00	−1.21581
$346$	−5642.00	−0.876635
$347$	7415.00	1.14714	0.573571	−	0.819156i	$-0.305558\pi$
$347$	7415.00	1.14714	0.573571	+	0.819156i	$0.305558\pi$
$348$	−1624.00	−0.250160
$349$	−3878.00	−0.594798	−0.297399	−	0.954753i	$-0.596119\pi$
$349$	−3878.00	−0.594798	−0.297399	+	0.954753i	$0.596119\pi$
$350$	0	0
$351$	490.000	0.0745136
$352$	−800.000	−0.121137
$353$	1267.00	0.191036	0.0955179	−	0.995428i	$-0.469549\pi$
$353$	1267.00	0.191036	0.0955179	+	0.995428i	$0.469549\pi$
$354$	−1470.00	−0.220705
$355$	−3024.00	−0.452105
$356$	1316.00	0.195921
$357$	0	0
$358$	−6506.00	−0.960483
$359$	4685.00	0.688760	0.344380	−	0.938830i	$-0.388089\pi$
$359$	4685.00	0.688760	0.344380	+	0.938830i	$0.388089\pi$
$360$	−3696.00	−0.541101
$361$	−4458.00	−0.649949
$362$	3164.00	0.459382
$363$	−9142.00	−1.32185
$364$	0	0
$365$	−7791.00	−1.11726
$366$	−5782.00	−0.825765
$367$	−4641.00	−0.660104	−0.330052	−	0.943963i	$-0.607066\pi$
$367$	−4641.00	−0.660104	−0.330052	+	0.943963i	$0.607066\pi$
$368$	2544.00	0.360367
$369$	7700.00	1.08630
$370$	3066.00	0.430794
$371$	0	0
$372$	−4116.00	−0.573668
$373$	−8797.00	−1.22116	−0.610578	−	0.791956i	$-0.709063\pi$
$373$	−8797.00	−1.22116	−0.610578	+	0.791956i	$0.709063\pi$
$374$	210.000	0.0290343
$375$	−9849.00	−1.35627
$376$	−12600.0	−1.72818
$377$	−812.000	−0.110929
$378$	0	0
$379$	13680.0	1.85407	0.927037	−	0.374969i	$-0.122347\pi$
$379$	13680.0	1.85407	0.927037	+	0.374969i	$0.122347\pi$
$380$	−1372.00	−0.185216
$381$	504.000	0.0677709
$382$	5114.00	0.684961
$383$	9765.00	1.30279	0.651395	−	0.758739i	$-0.274184\pi$
$383$	9765.00	1.30279	0.651395	+	0.758739i	$0.274184\pi$
$384$	−2688.00	−0.357217
$385$	0	0
$386$	−794.000	−0.104698
$387$	−2728.00	−0.358326
$388$	3528.00	0.461616
$389$	1731.00	0.225617	0.112809	−	0.993617i	$-0.464015\pi$
$389$	1731.00	0.225617	0.112809	+	0.993617i	$0.464015\pi$
$390$	−1372.00	−0.178138
$391$	3339.00	0.431868
$392$	0	0
$393$	15043.0	1.93084
$394$	5828.00	0.745204
$395$	−721.000	−0.0918416
$396$	440.000	0.0558354
$397$	10983.0	1.38847	0.694233	−	0.719750i	$-0.255744\pi$
$397$	10983.0	1.38847	0.694233	+	0.719750i	$0.255744\pi$
$398$	6678.00	0.841050
$399$	0	0
$400$	1216.00	0.152000
$401$	6603.00	0.822289	0.411145	−	0.911570i	$-0.365129\pi$
$401$	6603.00	0.822289	0.411145	+	0.911570i	$0.365129\pi$
$402$	5810.00	0.720837
$403$	−2058.00	−0.254383
$404$	−5516.00	−0.679285
$405$	−5873.00	−0.720572
$406$	0	0
$407$	−1095.00	−0.133359
$408$	3528.00	0.428093
$409$	10955.0	1.32443	0.662213	−	0.749316i	$-0.269618\pi$
$409$	10955.0	1.32443	0.662213	+	0.749316i	$0.269618\pi$
$410$	4900.00	0.590229
$411$	−7875.00	−0.945122
$412$	2716.00	0.324776
$413$	0	0
$414$	−6996.00	−0.830518
$415$	7644.00	0.904167
$416$	−2240.00	−0.264002
$417$	1764.00	0.207155
$418$	−490.000	−0.0573366
$419$	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	$0.912652\pi$
$422$	3560.00	0.410659
$423$	11550.0	1.32761
$424$	−7272.00	−0.832923
$425$	1596.00	0.182159
$426$	−6048.00	−0.687856
$427$	0	0
$428$	−1828.00	−0.206448
$429$	490.000	0.0551455
$430$	−1736.00	−0.194692
$431$	4923.00	0.550192	0.275096	−	0.961417i	$-0.411290\pi$
$431$	4923.00	0.550192	0.275096	+	0.961417i	$0.411290\pi$
$432$	560.000	0.0623681
$433$	8974.00	0.995988	0.497994	−	0.867180i	$-0.334070\pi$
$433$	8974.00	0.995988	0.497994	+	0.867180i	$0.334070\pi$
$434$	0	0
$435$	2842.00	0.313249
$436$	4500.00	0.494291
$437$	−7791.00	−0.852847
$438$	−15582.0	−1.69986
$439$	−4179.00	−0.454334	−0.227167	−	0.973856i	$-0.572946\pi$
$439$	−4179.00	−0.454334	−0.227167	+	0.973856i	$0.572946\pi$
$440$	840.000	0.0910123
$441$	0	0
$442$	588.000	0.0632767
$443$	−12927.0	−1.38641	−0.693206	−	0.720740i	$-0.743802\pi$
$443$	−12927.0	−1.38641	−0.693206	+	0.720740i	$0.743802\pi$
$444$	−6132.00	−0.655432
$445$	−2303.00	−0.245332
$446$	−2800.00	−0.297273
$447$	−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	$0.547450\pi$
$450$	−3344.00	−0.350306
$451$	−1750.00	−0.182715
$452$	6152.00	0.640190
$453$	11333.0	1.17543
$454$	−4410.00	−0.455884
$455$	0	0
$456$	−8232.00	−0.845392
$457$	8479.00	0.867901	0.433951	−	0.900937i	$-0.357119\pi$
$457$	8479.00	0.867901	0.433951	+	0.900937i	$0.357119\pi$
$458$	574.000	0.0585617
$459$	735.000	0.0747426
$460$	4452.00	0.451251
$461$	9338.00	0.943414	0.471707	−	0.881755i	$-0.343638\pi$
$461$	9338.00	0.943414	0.471707	+	0.881755i	$0.343638\pi$
$462$	0	0
$463$	−4016.00	−0.403109	−0.201554	−	0.979477i	$-0.564599\pi$
$463$	−4016.00	−0.403109	−0.201554	+	0.979477i	$0.564599\pi$
$464$	−928.000	−0.0928477
$465$	7203.00	0.718347
$466$	9174.00	0.911969
$467$	−5859.00	−0.580561	−0.290281	−	0.956942i	$-0.593749\pi$
$467$	−5859.00	−0.580561	−0.290281	+	0.956942i	$0.593749\pi$
$468$	1232.00	0.121686
$469$	0	0
$470$	7350.00	0.721341
$471$	4753.00	0.464982
$472$	2520.00	0.245747
$473$	620.000	0.0602698
$474$	−1442.00	−0.139733
$475$	−3724.00	−0.359724
$476$	0	0
$477$	6666.00	0.639864
$478$	3336.00	0.319216
$479$	6503.00	0.620312	0.310156	−	0.950686i	$-0.399619\pi$
$479$	6503.00	0.620312	0.310156	+	0.950686i	$0.399619\pi$
$480$	7840.00	0.745511
$481$	−3066.00	−0.290639
$482$	−6818.00	−0.644297
$483$	0	0
$484$	5224.00	0.490609
$485$	−6174.00	−0.578035
$486$	−9856.00	−0.919912
$487$	−16049.0	−1.49333	−0.746663	−	0.665203i	$-0.768345\pi$
$487$	−16049.0	−1.49333	−0.746663	+	0.665203i	$0.768345\pi$
$488$	9912.00	0.919457
$489$	−3269.00	−0.302309
$490$	0	0
$491$	8864.00	0.814718	0.407359	−	0.913268i	$-0.366450\pi$
$491$	8864.00	0.814718	0.407359	+	0.913268i	$0.366450\pi$
$492$	−9800.00	−0.898004
$493$	−1218.00	−0.111270
$494$	−1372.00	−0.124958
$495$	−770.000	−0.0699170
$496$	−2352.00	−0.212919
$497$	0	0
$498$	15288.0	1.37565
$499$	−10211.0	−0.916046	−0.458023	−	0.888940i	$-0.651442\pi$
$499$	−10211.0	−0.916046	−0.458023	+	0.888940i	$0.651442\pi$
$500$	5628.00	0.503384
$501$	8428.00	0.751567
$502$	−9520.00	−0.846411
$503$	−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
$506$	1590.00	0.139692
$507$	−14007.0	−1.22697
$508$	−288.000	−0.0251534
$509$	−9457.00	−0.823525	−0.411762	−	0.911291i	$-0.635087\pi$
$509$	−9457.00	−0.823525	−0.411762	+	0.911291i	$0.635087\pi$
$510$	−2058.00	−0.178686
$511$	0	0
$512$	−5632.00	−0.486136
$513$	−1715.00	−0.147601
$514$	−1610.00	−0.138160
$515$	−4753.00	−0.406684
$516$	3472.00	0.296214
$517$	−2625.00	−0.223302
$518$	0	0
$519$	−19747.0	−1.67013
$520$	2352.00	0.198350
$521$	−18081.0	−1.52043	−0.760214	−	0.649673i	$-0.774906\pi$
$521$	−18081.0	−1.52043	−0.760214	+	0.649673i	$0.774906\pi$
$522$	2552.00	0.213981
$523$	20377.0	1.70368	0.851839	−	0.523803i	$-0.175487\pi$
$523$	20377.0	1.70368	0.851839	+	0.523803i	$0.175487\pi$
$524$	−8596.00	−0.716637
$525$	0	0
$526$	−514.000	−0.0426073
$527$	−3087.00	−0.255165
$528$	560.000	0.0461570
$529$	13114.0	1.07783
$530$	4242.00	0.347662
$531$	−2310.00	−0.188786
$532$	0	0
$533$	−4900.00	−0.398204
$534$	−4606.00	−0.373261
$535$	3199.00	0.258514
$536$	−9960.00	−0.802624
$537$	−22771.0	−1.82987
$538$	7182.00	0.575535
$539$	0	0
$540$	980.000	0.0780972
$541$	−6193.00	−0.492159	−0.246079	−	0.969250i	$-0.579142\pi$
$541$	−6193.00	−0.492159	−0.246079	+	0.969250i	$0.579142\pi$
$542$	2786.00	0.220791
$543$	11074.0	0.875195
$544$	−3360.00	−0.264814
$545$	−7875.00	−0.618950
$546$	0	0
$547$	−18464.0	−1.44326	−0.721630	−	0.692279i	$-0.756607\pi$
$547$	−18464.0	−1.44326	−0.721630	+	0.692279i	$0.756607\pi$
$548$	4500.00	0.350786
$549$	−9086.00	−0.706341
$550$	760.000	0.0589209
$551$	2842.00	0.219734
$552$	26712.0	2.05967
$553$	0	0
$554$	830.000	0.0636522
$555$	10731.0	0.820731
$556$	−1008.00	−0.0768862
$557$	−9413.00	−0.716053	−0.358027	−	0.933711i	$-0.616550\pi$
$557$	−9413.00	−0.716053	−0.358027	+	0.933711i	$0.616550\pi$
$558$	6468.00	0.490703
$559$	1736.00	0.131351
$560$	0	0
$561$	735.000	0.0553150
$562$	−9908.00	−0.743672
$563$	3199.00	0.239470	0.119735	−	0.992806i	$-0.461795\pi$
$563$	3199.00	0.239470	0.119735	+	0.992806i	$0.461795\pi$
$564$	−14700.0	−1.09749
$565$	−10766.0	−0.801644
$566$	−8554.00	−0.635250
$567$	0	0
$568$	10368.0	0.765901
$569$	21583.0	1.59017	0.795085	−	0.606498i	$-0.207426\pi$
$569$	21583.0	1.59017	0.795085	+	0.606498i	$0.207426\pi$
$570$	4802.00	0.352866
$571$	20267.0	1.48537	0.742686	−	0.669640i	$-0.233551\pi$
$571$	20267.0	1.48537	0.742686	+	0.669640i	$0.233551\pi$
$572$	−280.000	−0.0204675
$573$	17899.0	1.30496
$574$	0	0
$575$	12084.0	0.876413
$576$	9856.00	0.712963
$577$	13951.0	1.00656	0.503282	−	0.864122i	$-0.332126\pi$
$577$	13951.0	1.00656	0.503282	+	0.864122i	$0.332126\pi$
$578$	−8944.00	−0.643636
$579$	−2779.00	−0.199467
$580$	−1624.00	−0.116264
$581$	0	0
$582$	−12348.0	−0.879452
$583$	−1515.00	−0.107624
$584$	26712.0	1.89272
$585$	−2156.00	−0.152375
$586$	15484.0	1.09153
$587$	−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
$590$	−1470.00	−0.102574
$591$	20398.0	1.41973
$592$	−3504.00	−0.243266
$593$	−189.000	−0.0130882	−0.00654410	−	0.999979i	$-0.502083\pi$
$593$	−189.000	−0.0130882	−0.00654410	+	0.999979i	$0.502083\pi$
$594$	350.000	0.0241762
$595$	0	0
$596$	804.000	0.0552569
$597$	23373.0	1.60233
$598$	4452.00	0.304441
$599$	−10281.0	−0.701286	−0.350643	−	0.936509i	$-0.614037\pi$
$599$	−10281.0	−0.701286	−0.350643	+	0.936509i	$0.614037\pi$
$600$	12768.0	0.868752
$601$	−6090.00	−0.413338	−0.206669	−	0.978411i	$-0.566262\pi$
$601$	−6090.00	−0.413338	−0.206669	+	0.978411i	$0.566262\pi$
$602$	0	0
$603$	9130.00	0.616588
$604$	−6476.00	−0.436266
$605$	−9142.00	−0.614339
$606$	19306.0	1.29415
$607$	4949.00	0.330929	0.165464	−	0.986216i	$-0.447088\pi$
$607$	4949.00	0.330929	0.165464	+	0.986216i	$0.447088\pi$
$608$	7840.00	0.522951
$609$	0	0
$610$	−5782.00	−0.383781
$611$	−7350.00	−0.486660
$612$	1848.00	0.122060
$613$	−15797.0	−1.04084	−0.520420	−	0.853910i	$-0.674225\pi$
$613$	−15797.0	−1.04084	−0.520420	+	0.853910i	$0.674225\pi$
$614$	−14728.0	−0.968035
$615$	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	$0.598975\pi$
$618$	−9506.00	−0.618750
$619$	−24353.0	−1.58131	−0.790654	−	0.612263i	$-0.790259\pi$
$619$	−24353.0	−1.58131	−0.790654	+	0.612263i	$0.790259\pi$
$620$	−4116.00	−0.266617
$621$	5565.00	0.359607
$622$	19950.0	1.28605
$623$	0	0
$624$	1568.00	0.100593
$625$	−349.000	−0.0223360
$626$	−9506.00	−0.606927
$627$	−1715.00	−0.109235
$628$	−2716.00	−0.172580
$629$	−4599.00	−0.291533
$630$	0	0
$631$	−12640.0	−0.797449	−0.398725	−	0.917071i	$-0.630547\pi$
$631$	−12640.0	−0.797449	−0.398725	+	0.917071i	$0.630547\pi$
$632$	2472.00	0.155587
$633$	12460.0	0.782371
$634$	−6954.00	−0.435613
$635$	504.000	0.0314971
$636$	−8484.00	−0.528950
$637$	0	0
$638$	−580.000	−0.0359913
$639$	−9504.00	−0.588376
$640$	−2688.00	−0.166020
$641$	−1041.00	−0.0641451	−0.0320726	−	0.999486i	$-0.510211\pi$
$641$	−1041.00	−0.0641451	−0.0320726	+	0.999486i	$0.510211\pi$
$642$	6398.00	0.393316
$643$	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
$646$	−2058.00	−0.125342
$647$	−3241.00	−0.196935	−0.0984674	−	0.995140i	$-0.531394\pi$
$647$	−3241.00	−0.196935	−0.0984674	+	0.995140i	$0.531394\pi$
$648$	20136.0	1.22070
$649$	525.000	0.0317535
$650$	2128.00	0.128411
$651$	0	0
$652$	1868.00	0.112203
$653$	−8853.00	−0.530543	−0.265272	−	0.964174i	$-0.585462\pi$
$653$	−8853.00	−0.530543	−0.265272	+	0.964174i	$0.585462\pi$
$654$	−15750.0	−0.941703
$655$	15043.0	0.897372
$656$	−5600.00	−0.333298
$657$	−24486.0	−1.45402
$658$	0	0
$659$	7044.00	0.416381	0.208191	−	0.978088i	$-0.433243\pi$
$659$	7044.00	0.416381	0.208191	+	0.978088i	$0.433243\pi$
$660$	980.000	0.0577976
$661$	−12089.0	−0.711358	−0.355679	−	0.934608i	$-0.615750\pi$
$661$	−12089.0	−0.711358	−0.355679	+	0.934608i	$0.615750\pi$
$662$	6682.00	0.392301
$663$	2058.00	0.120552
$664$	−26208.0	−1.53173
$665$	0	0
$666$	9636.00	0.560642
$667$	−9222.00	−0.535348
$668$	−4816.00	−0.278947
$669$	−9800.00	−0.566353
$670$	5810.00	0.335015
$671$	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	$0.491047\pi$
$674$	14732.0	0.841922
$675$	2660.00	0.151679
$676$	8004.00	0.455394
$677$	−30513.0	−1.73222	−0.866108	−	0.499857i	$-0.833386\pi$
$677$	−30513.0	−1.73222	−0.866108	+	0.499857i	$0.833386\pi$
$678$	−21532.0	−1.21966
$679$	0	0
$680$	3528.00	0.198960
$681$	−15435.0	−0.868532
$682$	−1470.00	−0.0825355
$683$	11475.0	0.642868	0.321434	−	0.946932i	$-0.395835\pi$
$683$	11475.0	0.642868	0.321434	+	0.946932i	$0.395835\pi$
$684$	−4312.00	−0.241043
$685$	−7875.00	−0.439253
$686$	0	0
$687$	2009.00	0.111569
$688$	1984.00	0.109941
$689$	−4242.00	−0.234553
$690$	−15582.0	−0.859705
$691$	−28315.0	−1.55883	−0.779416	−	0.626506i	$-0.784484\pi$
$691$	−28315.0	−1.55883	−0.779416	+	0.626506i	$0.784484\pi$
$692$	11284.0	0.619875
$693$	0	0
$694$	14830.0	0.811151
$695$	1764.00	0.0962767
$696$	−9744.00	−0.530669
$697$	−7350.00	−0.399428
$698$	−7756.00	−0.420586
$699$	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	$0.407695\pi$
$702$	980.000	0.0526891
$703$	10731.0	0.575715
$704$	−2240.00	−0.119919
$705$	25725.0	1.37427
$706$	2534.00	0.135083
$707$	0	0
$708$	2940.00	0.156062
$709$	10299.0	0.545539	0.272769	−	0.962079i	$-0.412060\pi$
$709$	10299.0	0.545539	0.272769	+	0.962079i	$0.412060\pi$
$710$	−6048.00	−0.319686
$711$	−2266.00	−0.119524
$712$	7896.00	0.415611
$713$	−23373.0	−1.22767
$714$	0	0
$715$	490.000	0.0256293
$716$	13012.0	0.679164
$717$	11676.0	0.608156
$718$	9370.00	0.487027
$719$	32529.0	1.68724	0.843621	−	0.536939i	$-0.180420\pi$
$719$	32529.0	1.68724	0.843621	+	0.536939i	$0.180420\pi$
$720$	−2464.00	−0.127539
$721$	0	0
$722$	−8916.00	−0.459583
$723$	−23863.0	−1.22749
$724$	−6328.00	−0.324832
$725$	−4408.00	−0.225806
$726$	−18284.0	−0.934687
$727$	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
$730$	−15582.0	−0.790021
$731$	2604.00	0.131754
$732$	11564.0	0.583904
$733$	27867.0	1.40422	0.702109	−	0.712070i	$-0.252242\pi$
$733$	27867.0	1.40422	0.702109	+	0.712070i	$0.252242\pi$
$734$	−9282.00	−0.466764
$735$	0	0
$736$	−25440.0	−1.27409
$737$	−2075.00	−0.103709
$738$	15400.0	0.768133
$739$	19539.0	0.972603	0.486302	−	0.873791i	$-0.338346\pi$
$739$	19539.0	0.972603	0.486302	+	0.873791i	$0.338346\pi$
$740$	−6132.00	−0.304617
$741$	−4802.00	−0.238065
$742$	0	0
$743$	1248.00	0.0616214	0.0308107	−	0.999525i	$-0.490191\pi$
$743$	1248.00	0.0616214	0.0308107	+	0.999525i	$0.490191\pi$
$744$	−24696.0	−1.21693
$745$	−1407.00	−0.0691926
$746$	−17594.0	−0.863488
$747$	24024.0	1.17670
$748$	−420.000	−0.0205304
$749$	0	0
$750$	−19698.0	−0.959026
$751$	28093.0	1.36502	0.682509	−	0.730877i	$-0.260889\pi$
$751$	28093.0	1.36502	0.682509	+	0.730877i	$0.260889\pi$
$752$	−8400.00	−0.407336
$753$	−33320.0	−1.61255
$754$	−1624.00	−0.0784385
$755$	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	$0.168504\pi$
$758$	27360.0	1.31103
$759$	5565.00	0.266135
$760$	−8232.00	−0.392903
$761$	−861.000	−0.0410134	−0.0205067	−	0.999790i	$-0.506528\pi$
$761$	−861.000	−0.0410134	−0.0205067	+	0.999790i	$0.506528\pi$
$762$	1008.00	0.0479212
$763$	0	0
$764$	−10228.0	−0.484340
$765$	−3234.00	−0.152844
$766$	19530.0	0.921211
$767$	1470.00	0.0692029
$768$	−30464.0	−1.43135
$769$	24710.0	1.15873	0.579366	−	0.815067i	$-0.303300\pi$
$769$	24710.0	1.15873	0.579366	+	0.815067i	$0.303300\pi$
$770$	0	0
$771$	−5635.00	−0.263216
$772$	1588.00	0.0740329
$773$	16499.0	0.767694	0.383847	−	0.923397i	$-0.374599\pi$
$773$	16499.0	0.767694	0.383847	+	0.923397i	$0.374599\pi$
$774$	−5456.00	−0.253375
$775$	−11172.0	−0.517819
$776$	21168.0	0.979236
$777$	0	0
$778$	3462.00	0.159536
$779$	17150.0	0.788784
$780$	2744.00	0.125963
$781$	2160.00	0.0989640
$782$	6678.00	0.305377
$783$	−2030.00	−0.0926517
$784$	0	0
$785$	4753.00	0.216104
$786$	30086.0	1.36531
$787$	16471.0	0.746033	0.373016	−	0.927825i	$-0.378324\pi$
$787$	16471.0	0.746033	0.373016	+	0.927825i	$0.378324\pi$
$788$	−11656.0	−0.526939
$789$	−1799.00	−0.0811738
$790$	−1442.00	−0.0649418
$791$	0	0
$792$	2640.00	0.118445
$793$	5782.00	0.258922
$794$	21966.0	0.981794
$795$	14847.0	0.662351
$796$	−13356.0	−0.594712
$797$	−36470.0	−1.62087	−0.810435	−	0.585828i	$-0.800769\pi$
$797$	−36470.0	−1.62087	−0.810435	+	0.585828i	$0.800769\pi$
$798$	0	0
$799$	−11025.0	−0.488156
$800$	−12160.0	−0.537401
$801$	−7238.00	−0.319279
$802$	13206.0	0.581446
$803$	5565.00	0.244564
$804$	−11620.0	−0.509709
$805$	0	0
$806$	−4116.00	−0.179876
$807$	25137.0	1.09649
$808$	−33096.0	−1.44098
$809$	35751.0	1.55369	0.776847	−	0.629690i	$-0.216818\pi$
$809$	35751.0	1.55369	0.776847	+	0.629690i	$0.216818\pi$
$810$	−11746.0	−0.509521
$811$	−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
$814$	−2190.00	−0.0942991
$815$	−3269.00	−0.140501
$816$	2352.00	0.100903
$817$	−6076.00	−0.260186
$818$	21910.0	0.936510
$819$	0	0
$820$	−9800.00	−0.417355
$821$	−41473.0	−1.76299	−0.881497	−	0.472190i	$-0.843464\pi$
$821$	−41473.0	−1.76299	−0.881497	+	0.472190i	$0.843464\pi$
$822$	−15750.0	−0.668302
$823$	−25065.0	−1.06162	−0.530809	−	0.847492i	$-0.678112\pi$
$823$	−25065.0	−1.06162	−0.530809	+	0.847492i	$0.678112\pi$
$824$	16296.0	0.688954
$825$	2660.00	0.112254
$826$	0	0
$827$	9732.00	0.409208	0.204604	−	0.978845i	$-0.434409\pi$
$827$	9732.00	0.409208	0.204604	+	0.978845i	$0.434409\pi$
$828$	13992.0	0.587265
$829$	27755.0	1.16281	0.581406	−	0.813614i	$-0.302503\pi$
$829$	27755.0	1.16281	0.581406	+	0.813614i	$0.302503\pi$
$830$	15288.0	0.639342
$831$	2905.00	0.121268
$832$	−6272.00	−0.261349
$833$	0	0
$834$	3528.00	0.146480
$835$	8428.00	0.349297
$836$	980.000	0.0405431
$837$	−5145.00	−0.212470
$838$	13272.0	0.547105
$839$	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
$842$	−33260.0	−1.36130
$843$	−34678.0	−1.41681
$844$	−7120.00	−0.290380
$845$	−14007.0	−0.570243
$846$	23100.0	0.938764
$847$	0	0
$848$	−4848.00	−0.196322
$849$	−29939.0	−1.21025
$850$	3192.00	0.128806
$851$	−34821.0	−1.40264
$852$	12096.0	0.486387
$853$	−21238.0	−0.852492	−0.426246	−	0.904607i	$-0.640164\pi$
$853$	−21238.0	−0.852492	−0.426246	+	0.904607i	$0.640164\pi$
$854$	0	0
$855$	7546.00	0.301834
$856$	−10968.0	−0.437942
$857$	−35609.0	−1.41935	−0.709673	−	0.704531i	$-0.751158\pi$
$857$	−35609.0	−1.41935	−0.709673	+	0.704531i	$0.751158\pi$
$858$	980.000	0.0389938
$859$	2177.00	0.0864706	0.0432353	−	0.999065i	$-0.486233\pi$
$859$	2177.00	0.0864706	0.0432353	+	0.999065i	$0.486233\pi$
$860$	3472.00	0.137668
$861$	0	0
$862$	9846.00	0.389044
$863$	−32247.0	−1.27196	−0.635980	−	0.771706i	$-0.719404\pi$
$863$	−32247.0	−1.27196	−0.635980	+	0.771706i	$0.719404\pi$
$864$	−5600.00	−0.220504
$865$	−19747.0	−0.776206
$866$	17948.0	0.704270
$867$	−31304.0	−1.22623
$868$	0	0
$869$	515.000	0.0201038
$870$	5684.00	0.221501
$871$	−5810.00	−0.226021
$872$	27000.0	1.04855
$873$	−19404.0	−0.752263
$874$	−15582.0	−0.603054
$875$	0	0
$876$	31164.0	1.20198
$877$	27631.0	1.06389	0.531946	−	0.846779i	$-0.321461\pi$
$877$	27631.0	1.06389	0.531946	+	0.846779i	$0.321461\pi$
$878$	−8358.00	−0.321263
$879$	54194.0	2.07954
$880$	560.000	0.0214518
$881$	24402.0	0.933172	0.466586	−	0.884476i	$-0.345484\pi$
$881$	24402.0	0.933172	0.466586	+	0.884476i	$0.345484\pi$
$882$	0	0
$883$	−19612.0	−0.747448	−0.373724	−	0.927540i	$-0.621919\pi$
$883$	−19612.0	−0.747448	−0.373724	+	0.927540i	$0.621919\pi$
$884$	−1176.00	−0.0447434
$885$	−5145.00	−0.195421
$886$	−25854.0	−0.980341
$887$	2261.00	0.0855884	0.0427942	−	0.999084i	$-0.486374\pi$
$887$	2261.00	0.0855884	0.0427942	+	0.999084i	$0.486374\pi$
$888$	−36792.0	−1.39038
$889$	0	0
$890$	−4606.00	−0.173476
$891$	4195.00	0.157730
$892$	5600.00	0.210204
$893$	25725.0	0.964003
$894$	−2814.00	−0.105273
$895$	−22771.0	−0.850448
$896$	0	0
$897$	15582.0	0.580009
$898$	−5652.00	−0.210033
$899$	8526.00	0.316305
$900$	6688.00	0.247704
$901$	−6363.00	−0.235274
$902$	−3500.00	−0.129199
$903$	0	0
$904$	36912.0	1.35805
$905$	11074.0	0.406754
$906$	22666.0	0.831156
$907$	−23833.0	−0.872505	−0.436252	−	0.899824i	$-0.643695\pi$
$907$	−23833.0	−0.872505	−0.436252	+	0.899824i	$0.643695\pi$
$908$	8820.00	0.322359
$909$	30338.0	1.10698
$910$	0	0
$911$	31824.0	1.15738	0.578692	−	0.815546i	$-0.303563\pi$
$911$	31824.0	1.15738	0.578692	+	0.815546i	$0.303563\pi$
$912$	−5488.00	−0.199261
$913$	−5460.00	−0.197919
$914$	16958.0	0.613699
$915$	−20237.0	−0.731163
$916$	−1148.00	−0.0414094
$917$	0	0
$918$	1470.00	0.0528510
$919$	−16819.0	−0.603708	−0.301854	−	0.953354i	$-0.597606\pi$
$919$	−16819.0	−0.603708	−0.301854	+	0.953354i	$0.597606\pi$
$920$	26712.0	0.957248
$921$	−51548.0	−1.84426
$922$	18676.0	0.667095
$923$	6048.00	0.215680
$924$	0	0
$925$	−16644.0	−0.591623
$926$	−8032.00	−0.285041
$927$	−14938.0	−0.529265
$928$	9280.00	0.328266
$929$	1799.00	0.0635342	0.0317671	−	0.999495i	$-0.489887\pi$
$929$	1799.00	0.0635342	0.0317671	+	0.999495i	$0.489887\pi$
$930$	14406.0	0.507948
$931$	0	0
$932$	−18348.0	−0.644859
$933$	69825.0	2.45013
$934$	−11718.0	−0.410519
$935$	735.000	0.0257081
$936$	7392.00	0.258136
$937$	14154.0	0.493480	0.246740	−	0.969082i	$-0.420641\pi$
$937$	14154.0	0.493480	0.246740	+	0.969082i	$0.420641\pi$
$938$	0	0
$939$	−33271.0	−1.15629
$940$	−14700.0	−0.510065
$941$	12047.0	0.417344	0.208672	−	0.977986i	$-0.433086\pi$
$941$	12047.0	0.417344	0.208672	+	0.977986i	$0.433086\pi$
$942$	9506.00	0.328792
$943$	−55650.0	−1.92175
$944$	1680.00	0.0579230
$945$	0	0
$946$	1240.00	0.0426172
$947$	−24379.0	−0.836548	−0.418274	−	0.908321i	$-0.637365\pi$
$947$	−24379.0	−0.836548	−0.418274	+	0.908321i	$0.637365\pi$
$948$	2884.00	0.0988059
$949$	15582.0	0.532996
$950$	−7448.00	−0.254363
$951$	−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	$0.848855\pi$
$954$	13332.0	0.452452
$955$	17899.0	0.606490
$956$	−6672.00	−0.225720
$957$	−2030.00	−0.0685690
$958$	13006.0	0.438627
$959$	0	0
$960$	21952.0	0.738018
$961$	−8182.00	−0.274647
$962$	−6132.00	−0.205513
$963$	10054.0	0.336434
$964$	13636.0	0.455587
$965$	−2779.00	−0.0927038
$966$	0	0
$967$	−12416.0	−0.412897	−0.206449	−	0.978457i	$-0.566191\pi$
$967$	−12416.0	−0.412897	−0.206449	+	0.978457i	$0.566191\pi$
$968$	31344.0	1.04074
$969$	−7203.00	−0.238796
$970$	−12348.0	−0.408732
$971$	36813.0	1.21667	0.608334	−	0.793681i	$-0.291838\pi$
$971$	36813.0	1.21667	0.608334	+	0.793681i	$0.291838\pi$
$972$	19712.0	0.650476
$973$	0	0
$974$	−32098.0	−1.05594
$975$	7448.00	0.244643
$976$	6608.00	0.216718
$977$	34995.0	1.14595	0.572973	−	0.819574i	$-0.305790\pi$
$977$	34995.0	1.14595	0.572973	+	0.819574i	$0.305790\pi$
$978$	−6538.00	−0.213765
$979$	1645.00	0.0537022
$980$	0	0
$981$	−24750.0	−0.805511
$982$	17728.0	0.576093
$983$	−14301.0	−0.464019	−0.232010	−	0.972713i	$-0.574530\pi$
$983$	−14301.0	−0.464019	−0.232010	+	0.972713i	$0.574530\pi$
$984$	−58800.0	−1.90495
$985$	20398.0	0.659832
$986$	−2436.00	−0.0786796
$987$	0	0
$988$	2744.00	0.0883586
$989$	19716.0	0.633905
$990$	−1540.00	−0.0494388
$991$	−2665.00	−0.0854253	−0.0427127	−	0.999087i	$-0.513600\pi$
$991$	−2665.00	−0.0854253	−0.0427127	+	0.999087i	$0.513600\pi$
$992$	23520.0	0.752783
$993$	23387.0	0.747396
$994$	0	0
$995$	23373.0	0.744697
$996$	−30576.0	−0.972729
$997$	24871.0	0.790043	0.395021	−	0.918672i	$-0.370737\pi$
$997$	24871.0	0.790043	0.395021	+	0.918672i	$0.370737\pi$
$998$	−20422.0	−0.647743
$999$	−7665.00	−0.242753

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.4.a.d.1.1		1
3.2	odd	2		441.4.a.d.1.1		1
4.3	odd	2		784.4.a.b.1.1		1
5.4	even	2		1225.4.a.c.1.1		1
7.2	even	3		7.4.c.a.4.1	yes	2
7.3	odd	6		49.4.c.a.30.1		2
7.4	even	3		7.4.c.a.2.1	✓	2
7.5	odd	6		49.4.c.a.18.1		2
7.6	odd	2		49.4.a.c.1.1		1
21.2	odd	6		63.4.e.b.46.1		2
21.5	even	6		441.4.e.k.361.1		2
21.11	odd	6		63.4.e.b.37.1		2
21.17	even	6		441.4.e.k.226.1		2
21.20	even	2		441.4.a.e.1.1		1
28.11	odd	6		112.4.i.c.65.1		2
28.23	odd	6		112.4.i.c.81.1		2
28.27	even	2		784.4.a.r.1.1		1
35.2	odd	12		175.4.k.a.74.2		4
35.4	even	6		175.4.e.a.51.1		2
35.9	even	6		175.4.e.a.151.1		2
35.18	odd	12		175.4.k.a.149.2		4
35.23	odd	12		175.4.k.a.74.1		4
35.32	odd	12		175.4.k.a.149.1		4
35.34	odd	2		1225.4.a.d.1.1		1
56.11	odd	6		448.4.i.a.65.1		2
56.37	even	6		448.4.i.f.193.1		2
56.51	odd	6		448.4.i.a.193.1		2
56.53	even	6		448.4.i.f.65.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.4.c.a.2.1	✓	2	7.4	even	3
7.4.c.a.4.1	yes	2	7.2	even	3
49.4.a.c.1.1		1	7.6	odd	2
49.4.a.d.1.1		1	1.1	even	1	trivial
49.4.c.a.18.1		2	7.5	odd	6
49.4.c.a.30.1		2	7.3	odd	6
63.4.e.b.37.1		2	21.11	odd	6
63.4.e.b.46.1		2	21.2	odd	6
112.4.i.c.65.1		2	28.11	odd	6
112.4.i.c.81.1		2	28.23	odd	6
175.4.e.a.51.1		2	35.4	even	6
175.4.e.a.151.1		2	35.9	even	6
175.4.k.a.74.1		4	35.23	odd	12
175.4.k.a.74.2		4	35.2	odd	12
175.4.k.a.149.1		4	35.32	odd	12
175.4.k.a.149.2		4	35.18	odd	12
441.4.a.d.1.1		1	3.2	odd	2
441.4.a.e.1.1		1	21.20	even	2
441.4.e.k.226.1		2	21.17	even	6
441.4.e.k.361.1		2	21.5	even	6
448.4.i.a.65.1		2	56.11	odd	6
448.4.i.a.193.1		2	56.51	odd	6
448.4.i.f.65.1		2	56.53	even	6
448.4.i.f.193.1		2	56.37	even	6
784.4.a.b.1.1		1	4.3	odd	2
784.4.a.r.1.1		1	28.27	even	2
1225.4.a.c.1.1		1	5.4	even	2
1225.4.a.d.1.1		1	35.34	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	49.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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