LMFDB - Embedded newform 4830.2.a.l.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [4830,2,Mod(1,4830)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4830, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("4830.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	4830.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,-1,1,1,-1,-1,1,-1,1,1,0,1,-4,-1,-1,1,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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

Self dual:	yes
Analytic conductor:	$38.5677441763$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4830.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

f(q)

=

q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{12} -4.00000 q^{13} -1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{18} +2.00000 q^{19} -1.00000 q^{20} +1.00000 q^{21} +1.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} +4.00000 q^{26} +1.00000 q^{27} +1.00000 q^{28} +6.00000 q^{29} +1.00000 q^{30} +2.00000 q^{31} -1.00000 q^{32} -1.00000 q^{35} +1.00000 q^{36} -10.0000 q^{37} -2.00000 q^{38} -4.00000 q^{39} +1.00000 q^{40} +6.00000 q^{41} -1.00000 q^{42} -4.00000 q^{43} -1.00000 q^{45} -1.00000 q^{46} +6.00000 q^{47} +1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} -4.00000 q^{52} -6.00000 q^{53} -1.00000 q^{54} -1.00000 q^{56} +2.00000 q^{57} -6.00000 q^{58} +12.0000 q^{59} -1.00000 q^{60} -10.0000 q^{61} -2.00000 q^{62} +1.00000 q^{63} +1.00000 q^{64} +4.00000 q^{65} -4.00000 q^{67} +1.00000 q^{69} +1.00000 q^{70} -1.00000 q^{72} +14.0000 q^{73} +10.0000 q^{74} +1.00000 q^{75} +2.00000 q^{76} +4.00000 q^{78} +8.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} -6.00000 q^{82} +6.00000 q^{83} +1.00000 q^{84} +4.00000 q^{86} +6.00000 q^{87} +1.00000 q^{90} -4.00000 q^{91} +1.00000 q^{92} +2.00000 q^{93} -6.00000 q^{94} -2.00000 q^{95} -1.00000 q^{96} +8.00000 q^{97} -1.00000 q^{98} +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

)

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	1.00000	0.288675
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	−1.00000	−0.267261
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	−1.00000	−0.235702
$19$	2.00000	0.458831	0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000	0.458831	0.229416	+	0.973329i	$0.426318\pi$
$20$	−1.00000	−0.223607
$21$	1.00000	0.218218
$22$	0	0
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	4.00000	0.784465
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	1.00000	0.182574
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	0	0
$35$	−1.00000	−0.169031
$36$	1.00000	0.166667
$37$	−10.0000	−1.64399	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−10.0000	−1.64399	−0.821995	+	0.569495i	$0.807139\pi$
$38$	−2.00000	−0.324443
$39$	−4.00000	−0.640513
$40$	1.00000	0.158114
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	−1.00000	−0.154303
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	−1.00000	−0.147442
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	0	0
$52$	−4.00000	−0.554700
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−1.00000	−0.133631
$57$	2.00000	0.264906
$58$	−6.00000	−0.787839
$59$	12.0000	1.56227	0.781133	−	0.624364i	$-0.214642\pi$
$59$	12.0000	1.56227	0.781133	+	0.624364i	$0.214642\pi$
$60$	−1.00000	−0.129099
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	−2.00000	−0.254000
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	4.00000	0.496139
$66$	0	0
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	0	0
$69$	1.00000	0.120386
$70$	1.00000	0.119523
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	−1.00000	−0.117851
$73$	14.0000	1.63858	0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000	1.63858	0.819288	+	0.573382i	$0.194369\pi$
$74$	10.0000	1.16248
$75$	1.00000	0.115470
$76$	2.00000	0.229416
$77$	0	0
$78$	4.00000	0.452911
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−6.00000	−0.662589
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	1.00000	0.109109
$85$	0	0
$86$	4.00000	0.431331
$87$	6.00000	0.643268
$88$	0	0
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	1.00000	0.105409
$91$	−4.00000	−0.419314
$92$	1.00000	0.104257
$93$	2.00000	0.207390
$94$	−6.00000	−0.618853
$95$	−2.00000	−0.205196
$96$	−1.00000	−0.102062
$97$	8.00000	0.812277	0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000	0.812277	0.406138	+	0.913812i	$0.366875\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	0	0
$103$	−4.00000	−0.394132	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000	−0.394132	−0.197066	+	0.980390i	$0.563141\pi$
$104$	4.00000	0.392232
$105$	−1.00000	−0.0975900
$106$	6.00000	0.582772
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	1.00000	0.0962250
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	0	0
$111$	−10.0000	−0.949158
$112$	1.00000	0.0944911
$113$	18.0000	1.69330	0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000	1.69330	0.846649	+	0.532152i	$0.178617\pi$
$114$	−2.00000	−0.187317
$115$	−1.00000	−0.0932505
$116$	6.00000	0.557086
$117$	−4.00000	−0.369800
$118$	−12.0000	−1.10469
$119$	0	0
$120$	1.00000	0.0912871
$121$	−11.0000	−1.00000
$122$	10.0000	0.905357
$123$	6.00000	0.541002
$124$	2.00000	0.179605
$125$	−1.00000	−0.0894427
$126$	−1.00000	−0.0890871
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	−1.00000	−0.0883883
$129$	−4.00000	−0.352180
$130$	−4.00000	−0.350823
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	0	0
$133$	2.00000	0.173422
$134$	4.00000	0.345547
$135$	−1.00000	−0.0860663
$136$	0	0
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	−1.00000	−0.0851257
$139$	−16.0000	−1.35710	−0.678551	−	0.734553i	$-0.737392\pi$
$139$	−16.0000	−1.35710	−0.678551	+	0.734553i	$0.737392\pi$
$140$	−1.00000	−0.0845154
$141$	6.00000	0.505291
$142$	0	0
$143$	0	0
$144$	1.00000	0.0833333
$145$	−6.00000	−0.498273
$146$	−14.0000	−1.15865
$147$	1.00000	0.0824786
$148$	−10.0000	−0.821995
$149$	−18.0000	−1.47462	−0.737309	−	0.675556i	$-0.763904\pi$
$149$	−18.0000	−1.47462	−0.737309	+	0.675556i	$0.763904\pi$
$150$	−1.00000	−0.0816497
$151$	20.0000	1.62758	0.813788	−	0.581161i	$-0.197401\pi$
$151$	20.0000	1.62758	0.813788	+	0.581161i	$0.197401\pi$
$152$	−2.00000	−0.162221
$153$	0	0
$154$	0	0
$155$	−2.00000	−0.160644
$156$	−4.00000	−0.320256
$157$	2.00000	0.159617	0.0798087	−	0.996810i	$-0.474569\pi$
$157$	2.00000	0.159617	0.0798087	+	0.996810i	$0.474569\pi$
$158$	−8.00000	−0.636446
$159$	−6.00000	−0.475831
$160$	1.00000	0.0790569
$161$	1.00000	0.0788110
$162$	−1.00000	−0.0785674
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	6.00000	0.468521
$165$	0	0
$166$	−6.00000	−0.465690
$167$	−6.00000	−0.464294	−0.232147	−	0.972681i	$-0.574575\pi$
$167$	−6.00000	−0.464294	−0.232147	+	0.972681i	$0.574575\pi$
$168$	−1.00000	−0.0771517
$169$	3.00000	0.230769
$170$	0	0
$171$	2.00000	0.152944
$172$	−4.00000	−0.304997
$173$	−12.0000	−0.912343	−0.456172	−	0.889892i	$-0.650780\pi$
$173$	−12.0000	−0.912343	−0.456172	+	0.889892i	$0.650780\pi$
$174$	−6.00000	−0.454859
$175$	1.00000	0.0755929
$176$	0	0
$177$	12.0000	0.901975
$178$	0	0
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	−1.00000	−0.0745356
$181$	14.0000	1.04061	0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000	1.04061	0.520306	+	0.853980i	$0.325818\pi$
$182$	4.00000	0.296500
$183$	−10.0000	−0.739221
$184$	−1.00000	−0.0737210
$185$	10.0000	0.735215
$186$	−2.00000	−0.146647
$187$	0	0
$188$	6.00000	0.437595
$189$	1.00000	0.0727393
$190$	2.00000	0.145095
$191$	24.0000	1.73658	0.868290	−	0.496058i	$-0.165220\pi$
$191$	24.0000	1.73658	0.868290	+	0.496058i	$0.165220\pi$
$192$	1.00000	0.0721688
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	−8.00000	−0.574367
$195$	4.00000	0.286446
$196$	1.00000	0.0714286
$197$	−18.0000	−1.28245	−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000	−1.28245	−0.641223	+	0.767354i	$0.721573\pi$
$198$	0	0
$199$	−4.00000	−0.283552	−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000	−0.283552	−0.141776	+	0.989899i	$0.545281\pi$
$200$	−1.00000	−0.0707107
$201$	−4.00000	−0.282138
$202$	0	0
$203$	6.00000	0.421117
$204$	0	0
$205$	−6.00000	−0.419058
$206$	4.00000	0.278693
$207$	1.00000	0.0695048
$208$	−4.00000	−0.277350
$209$	0	0
$210$	1.00000	0.0690066
$211$	20.0000	1.37686	0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000	1.37686	0.688428	+	0.725304i	$0.258301\pi$
$212$	−6.00000	−0.412082
$213$	0	0
$214$	−12.0000	−0.820303
$215$	4.00000	0.272798
$216$	−1.00000	−0.0680414
$217$	2.00000	0.135769
$218$	−2.00000	−0.135457
$219$	14.0000	0.946032
$220$	0	0
$221$	0	0
$222$	10.0000	0.671156
$223$	−22.0000	−1.47323	−0.736614	−	0.676313i	$-0.763577\pi$
$223$	−22.0000	−1.47323	−0.736614	+	0.676313i	$0.763577\pi$
$224$	−1.00000	−0.0668153
$225$	1.00000	0.0666667
$226$	−18.0000	−1.19734
$227$	−30.0000	−1.99117	−0.995585	−	0.0938647i	$-0.970078\pi$
$227$	−30.0000	−1.99117	−0.995585	+	0.0938647i	$0.970078\pi$
$228$	2.00000	0.132453
$229$	14.0000	0.925146	0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000	0.925146	0.462573	+	0.886581i	$0.346926\pi$
$230$	1.00000	0.0659380
$231$	0	0
$232$	−6.00000	−0.393919
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	4.00000	0.261488
$235$	−6.00000	−0.391397
$236$	12.0000	0.781133
$237$	8.00000	0.519656
$238$	0	0
$239$	24.0000	1.55243	0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000	1.55243	0.776215	+	0.630468i	$0.217137\pi$
$240$	−1.00000	−0.0645497
$241$	−16.0000	−1.03065	−0.515325	−	0.856995i	$-0.672329\pi$
$241$	−16.0000	−1.03065	−0.515325	+	0.856995i	$0.672329\pi$
$242$	11.0000	0.707107
$243$	1.00000	0.0641500
$244$	−10.0000	−0.640184
$245$	−1.00000	−0.0638877
$246$	−6.00000	−0.382546
$247$	−8.00000	−0.509028
$248$	−2.00000	−0.127000
$249$	6.00000	0.380235
$250$	1.00000	0.0632456
$251$	−6.00000	−0.378717	−0.189358	−	0.981908i	$-0.560641\pi$
$251$	−6.00000	−0.378717	−0.189358	+	0.981908i	$0.560641\pi$
$252$	1.00000	0.0629941
$253$	0	0
$254$	−8.00000	−0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	18.0000	1.12281	0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000	1.12281	0.561405	+	0.827541i	$0.310261\pi$
$258$	4.00000	0.249029
$259$	−10.0000	−0.621370
$260$	4.00000	0.248069
$261$	6.00000	0.371391
$262$	−12.0000	−0.741362
$263$	24.0000	1.47990	0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000	1.47990	0.739952	+	0.672660i	$0.234848\pi$
$264$	0	0
$265$	6.00000	0.368577
$266$	−2.00000	−0.122628
$267$	0	0
$268$	−4.00000	−0.244339
$269$	24.0000	1.46331	0.731653	−	0.681677i	$-0.238749\pi$
$269$	24.0000	1.46331	0.731653	+	0.681677i	$0.238749\pi$
$270$	1.00000	0.0608581
$271$	2.00000	0.121491	0.0607457	−	0.998153i	$-0.480652\pi$
$271$	2.00000	0.121491	0.0607457	+	0.998153i	$0.480652\pi$
$272$	0	0
$273$	−4.00000	−0.242091
$274$	−6.00000	−0.362473
$275$	0	0
$276$	1.00000	0.0601929
$277$	26.0000	1.56219	0.781094	−	0.624413i	$-0.214662\pi$
$277$	26.0000	1.56219	0.781094	+	0.624413i	$0.214662\pi$
$278$	16.0000	0.959616
$279$	2.00000	0.119737
$280$	1.00000	0.0597614
$281$	−6.00000	−0.357930	−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000	−0.357930	−0.178965	+	0.983855i	$0.557275\pi$
$282$	−6.00000	−0.357295
$283$	14.0000	0.832214	0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000	0.832214	0.416107	+	0.909316i	$0.363394\pi$
$284$	0	0
$285$	−2.00000	−0.118470
$286$	0	0
$287$	6.00000	0.354169
$288$	−1.00000	−0.0589256
$289$	−17.0000	−1.00000
$290$	6.00000	0.352332
$291$	8.00000	0.468968
$292$	14.0000	0.819288
$293$	−6.00000	−0.350524	−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000	−0.350524	−0.175262	+	0.984522i	$0.556077\pi$
$294$	−1.00000	−0.0583212
$295$	−12.0000	−0.698667
$296$	10.0000	0.581238
$297$	0	0
$298$	18.0000	1.04271
$299$	−4.00000	−0.231326
$300$	1.00000	0.0577350
$301$	−4.00000	−0.230556
$302$	−20.0000	−1.15087
$303$	0	0
$304$	2.00000	0.114708
$305$	10.0000	0.572598
$306$	0	0
$307$	8.00000	0.456584	0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000	0.456584	0.228292	+	0.973593i	$0.426686\pi$
$308$	0	0
$309$	−4.00000	−0.227552
$310$	2.00000	0.113592
$311$	18.0000	1.02069	0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000	1.02069	0.510343	+	0.859971i	$0.329518\pi$
$312$	4.00000	0.226455
$313$	−4.00000	−0.226093	−0.113047	−	0.993590i	$-0.536061\pi$
$313$	−4.00000	−0.226093	−0.113047	+	0.993590i	$0.536061\pi$
$314$	−2.00000	−0.112867
$315$	−1.00000	−0.0563436
$316$	8.00000	0.450035
$317$	−18.0000	−1.01098	−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000	−1.01098	−0.505490	+	0.862832i	$0.668688\pi$
$318$	6.00000	0.336463
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	12.0000	0.669775
$322$	−1.00000	−0.0557278
$323$	0	0
$324$	1.00000	0.0555556
$325$	−4.00000	−0.221880
$326$	4.00000	0.221540
$327$	2.00000	0.110600
$328$	−6.00000	−0.331295
$329$	6.00000	0.330791
$330$	0	0
$331$	20.0000	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$332$	6.00000	0.329293
$333$	−10.0000	−0.547997
$334$	6.00000	0.328305
$335$	4.00000	0.218543
$336$	1.00000	0.0545545
$337$	−22.0000	−1.19842	−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000	−1.19842	−0.599208	+	0.800593i	$0.704518\pi$
$338$	−3.00000	−0.163178
$339$	18.0000	0.977626
$340$	0	0
$341$	0	0
$342$	−2.00000	−0.108148
$343$	1.00000	0.0539949
$344$	4.00000	0.215666
$345$	−1.00000	−0.0538382
$346$	12.0000	0.645124
$347$	−12.0000	−0.644194	−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000	−0.644194	−0.322097	+	0.946707i	$0.604388\pi$
$348$	6.00000	0.321634
$349$	−28.0000	−1.49881	−0.749403	−	0.662114i	$-0.769659\pi$
$349$	−28.0000	−1.49881	−0.749403	+	0.662114i	$0.769659\pi$
$350$	−1.00000	−0.0534522
$351$	−4.00000	−0.213504
$352$	0	0
$353$	30.0000	1.59674	0.798369	−	0.602168i	$-0.205696\pi$
$353$	30.0000	1.59674	0.798369	+	0.602168i	$0.205696\pi$
$354$	−12.0000	−0.637793
$355$	0	0
$356$	0	0
$357$	0	0
$358$	−12.0000	−0.634220
$359$	24.0000	1.26667	0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000	1.26667	0.633336	+	0.773877i	$0.281685\pi$
$360$	1.00000	0.0527046
$361$	−15.0000	−0.789474
$362$	−14.0000	−0.735824
$363$	−11.0000	−0.577350
$364$	−4.00000	−0.209657
$365$	−14.0000	−0.732793
$366$	10.0000	0.522708
$367$	−4.00000	−0.208798	−0.104399	−	0.994535i	$-0.533292\pi$
$367$	−4.00000	−0.208798	−0.104399	+	0.994535i	$0.533292\pi$
$368$	1.00000	0.0521286
$369$	6.00000	0.312348
$370$	−10.0000	−0.519875
$371$	−6.00000	−0.311504
$372$	2.00000	0.103695
$373$	14.0000	0.724893	0.362446	−	0.932005i	$-0.381942\pi$
$373$	14.0000	0.724893	0.362446	+	0.932005i	$0.381942\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	−6.00000	−0.309426
$377$	−24.0000	−1.23606
$378$	−1.00000	−0.0514344
$379$	20.0000	1.02733	0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000	1.02733	0.513665	+	0.857991i	$0.328287\pi$
$380$	−2.00000	−0.102598
$381$	8.00000	0.409852
$382$	−24.0000	−1.22795
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−14.0000	−0.712581
$387$	−4.00000	−0.203331
$388$	8.00000	0.406138
$389$	−30.0000	−1.52106	−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000	−1.52106	−0.760530	+	0.649303i	$0.775061\pi$
$390$	−4.00000	−0.202548
$391$	0	0
$392$	−1.00000	−0.0505076
$393$	12.0000	0.605320
$394$	18.0000	0.906827
$395$	−8.00000	−0.402524
$396$	0	0
$397$	−4.00000	−0.200754	−0.100377	−	0.994949i	$-0.532005\pi$
$397$	−4.00000	−0.200754	−0.100377	+	0.994949i	$0.532005\pi$
$398$	4.00000	0.200502
$399$	2.00000	0.100125
$400$	1.00000	0.0500000
$401$	18.0000	0.898877	0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000	0.898877	0.449439	+	0.893311i	$0.351624\pi$
$402$	4.00000	0.199502
$403$	−8.00000	−0.398508
$404$	0	0
$405$	−1.00000	−0.0496904
$406$	−6.00000	−0.297775
$407$	0	0
$408$	0	0
$409$	−22.0000	−1.08783	−0.543915	−	0.839140i	$-0.683059\pi$
$409$	−22.0000	−1.08783	−0.543915	+	0.839140i	$0.683059\pi$
$410$	6.00000	0.296319
$411$	6.00000	0.295958
$412$	−4.00000	−0.197066
$413$	12.0000	0.590481
$414$	−1.00000	−0.0491473
$415$	−6.00000	−0.294528
$416$	4.00000	0.196116
$417$	−16.0000	−0.783523
$418$	0	0
$419$	−30.0000	−1.46560	−0.732798	−	0.680446i	$-0.761786\pi$
$419$	−30.0000	−1.46560	−0.732798	+	0.680446i	$0.761786\pi$
$420$	−1.00000	−0.0487950
$421$	26.0000	1.26716	0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000	1.26716	0.633581	+	0.773676i	$0.281584\pi$
$422$	−20.0000	−0.973585
$423$	6.00000	0.291730
$424$	6.00000	0.291386
$425$	0	0
$426$	0	0
$427$	−10.0000	−0.483934
$428$	12.0000	0.580042
$429$	0	0
$430$	−4.00000	−0.192897
$431$	−24.0000	−1.15604	−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000	−1.15604	−0.578020	+	0.816023i	$0.696174\pi$
$432$	1.00000	0.0481125
$433$	−16.0000	−0.768911	−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000	−0.768911	−0.384455	+	0.923144i	$0.625611\pi$
$434$	−2.00000	−0.0960031
$435$	−6.00000	−0.287678
$436$	2.00000	0.0957826
$437$	2.00000	0.0956730
$438$	−14.0000	−0.668946
$439$	−34.0000	−1.62273	−0.811366	−	0.584539i	$-0.801275\pi$
$439$	−34.0000	−1.62273	−0.811366	+	0.584539i	$0.801275\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	0	0
$443$	36.0000	1.71041	0.855206	−	0.518289i	$-0.173431\pi$
$443$	36.0000	1.71041	0.855206	+	0.518289i	$0.173431\pi$
$444$	−10.0000	−0.474579
$445$	0	0
$446$	22.0000	1.04173
$447$	−18.0000	−0.851371
$448$	1.00000	0.0472456
$449$	−18.0000	−0.849473	−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000	−0.849473	−0.424736	+	0.905317i	$0.639633\pi$
$450$	−1.00000	−0.0471405
$451$	0	0
$452$	18.0000	0.846649
$453$	20.0000	0.939682
$454$	30.0000	1.40797
$455$	4.00000	0.187523
$456$	−2.00000	−0.0936586
$457$	38.0000	1.77757	0.888783	−	0.458329i	$-0.151552\pi$
$457$	38.0000	1.77757	0.888783	+	0.458329i	$0.151552\pi$
$458$	−14.0000	−0.654177
$459$	0	0
$460$	−1.00000	−0.0466252
$461$	24.0000	1.11779	0.558896	−	0.829238i	$-0.311225\pi$
$461$	24.0000	1.11779	0.558896	+	0.829238i	$0.311225\pi$
$462$	0	0
$463$	20.0000	0.929479	0.464739	−	0.885448i	$-0.346148\pi$
$463$	20.0000	0.929479	0.464739	+	0.885448i	$0.346148\pi$
$464$	6.00000	0.278543
$465$	−2.00000	−0.0927478
$466$	−6.00000	−0.277945
$467$	−6.00000	−0.277647	−0.138823	−	0.990317i	$-0.544332\pi$
$467$	−6.00000	−0.277647	−0.138823	+	0.990317i	$0.544332\pi$
$468$	−4.00000	−0.184900
$469$	−4.00000	−0.184703
$470$	6.00000	0.276759
$471$	2.00000	0.0921551
$472$	−12.0000	−0.552345
$473$	0	0
$474$	−8.00000	−0.367452
$475$	2.00000	0.0917663
$476$	0	0
$477$	−6.00000	−0.274721
$478$	−24.0000	−1.09773
$479$	36.0000	1.64488	0.822441	−	0.568850i	$-0.192612\pi$
$479$	36.0000	1.64488	0.822441	+	0.568850i	$0.192612\pi$
$480$	1.00000	0.0456435
$481$	40.0000	1.82384
$482$	16.0000	0.728780
$483$	1.00000	0.0455016
$484$	−11.0000	−0.500000
$485$	−8.00000	−0.363261
$486$	−1.00000	−0.0453609
$487$	−28.0000	−1.26880	−0.634401	−	0.773004i	$-0.718753\pi$
$487$	−28.0000	−1.26880	−0.634401	+	0.773004i	$0.718753\pi$
$488$	10.0000	0.452679
$489$	−4.00000	−0.180886
$490$	1.00000	0.0451754
$491$	36.0000	1.62466	0.812329	−	0.583200i	$-0.198200\pi$
$491$	36.0000	1.62466	0.812329	+	0.583200i	$0.198200\pi$
$492$	6.00000	0.270501
$493$	0	0
$494$	8.00000	0.359937
$495$	0	0
$496$	2.00000	0.0898027
$497$	0	0
$498$	−6.00000	−0.268866
$499$	−4.00000	−0.179065	−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000	−0.179065	−0.0895323	+	0.995984i	$0.528537\pi$
$500$	−1.00000	−0.0447214
$501$	−6.00000	−0.268060
$502$	6.00000	0.267793
$503$	−24.0000	−1.07011	−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000	−1.07011	−0.535054	+	0.844818i	$0.679709\pi$
$504$	−1.00000	−0.0445435
$505$	0	0
$506$	0	0
$507$	3.00000	0.133235
$508$	8.00000	0.354943
$509$	24.0000	1.06378	0.531891	−	0.846813i	$-0.321482\pi$
$509$	24.0000	1.06378	0.531891	+	0.846813i	$0.321482\pi$
$510$	0	0
$511$	14.0000	0.619324
$512$	−1.00000	−0.0441942
$513$	2.00000	0.0883022
$514$	−18.0000	−0.793946
$515$	4.00000	0.176261
$516$	−4.00000	−0.176090
$517$	0	0
$518$	10.0000	0.439375
$519$	−12.0000	−0.526742
$520$	−4.00000	−0.175412
$521$	0	0		−	1.00000i	$-0.5\pi$
$521$	0	0			1.00000i	$0.5\pi$
$522$	−6.00000	−0.262613
$523$	14.0000	0.612177	0.306089	−	0.952003i	$-0.400980\pi$
$523$	14.0000	0.612177	0.306089	+	0.952003i	$0.400980\pi$
$524$	12.0000	0.524222
$525$	1.00000	0.0436436
$526$	−24.0000	−1.04645
$527$	0	0
$528$	0	0
$529$	1.00000	0.0434783
$530$	−6.00000	−0.260623
$531$	12.0000	0.520756
$532$	2.00000	0.0867110
$533$	−24.0000	−1.03956
$534$	0	0
$535$	−12.0000	−0.518805
$536$	4.00000	0.172774
$537$	12.0000	0.517838
$538$	−24.0000	−1.03471
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	38.0000	1.63375	0.816874	−	0.576816i	$-0.195705\pi$
$541$	38.0000	1.63375	0.816874	+	0.576816i	$0.195705\pi$
$542$	−2.00000	−0.0859074
$543$	14.0000	0.600798
$544$	0	0
$545$	−2.00000	−0.0856706
$546$	4.00000	0.171184
$547$	−28.0000	−1.19719	−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000	−1.19719	−0.598597	+	0.801050i	$0.704275\pi$
$548$	6.00000	0.256307
$549$	−10.0000	−0.426790
$550$	0	0
$551$	12.0000	0.511217
$552$	−1.00000	−0.0425628
$553$	8.00000	0.340195
$554$	−26.0000	−1.10463
$555$	10.0000	0.424476
$556$	−16.0000	−0.678551
$557$	−18.0000	−0.762684	−0.381342	−	0.924434i	$-0.624538\pi$
$557$	−18.0000	−0.762684	−0.381342	+	0.924434i	$0.624538\pi$
$558$	−2.00000	−0.0846668
$559$	16.0000	0.676728
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	6.00000	0.253095
$563$	6.00000	0.252870	0.126435	−	0.991975i	$-0.459647\pi$
$563$	6.00000	0.252870	0.126435	+	0.991975i	$0.459647\pi$
$564$	6.00000	0.252646
$565$	−18.0000	−0.757266
$566$	−14.0000	−0.588464
$567$	1.00000	0.0419961
$568$	0	0
$569$	−6.00000	−0.251533	−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000	−0.251533	−0.125767	+	0.992060i	$0.540139\pi$
$570$	2.00000	0.0837708
$571$	32.0000	1.33916	0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000	1.33916	0.669579	+	0.742741i	$0.266474\pi$
$572$	0	0
$573$	24.0000	1.00261
$574$	−6.00000	−0.250435
$575$	1.00000	0.0417029
$576$	1.00000	0.0416667
$577$	14.0000	0.582828	0.291414	−	0.956597i	$-0.405874\pi$
$577$	14.0000	0.582828	0.291414	+	0.956597i	$0.405874\pi$
$578$	17.0000	0.707107
$579$	14.0000	0.581820
$580$	−6.00000	−0.249136
$581$	6.00000	0.248922
$582$	−8.00000	−0.331611
$583$	0	0
$584$	−14.0000	−0.579324
$585$	4.00000	0.165380
$586$	6.00000	0.247858
$587$	−48.0000	−1.98117	−0.990586	−	0.136892i	$-0.956289\pi$
$587$	−48.0000	−1.98117	−0.990586	+	0.136892i	$0.956289\pi$
$588$	1.00000	0.0412393
$589$	4.00000	0.164817
$590$	12.0000	0.494032
$591$	−18.0000	−0.740421
$592$	−10.0000	−0.410997
$593$	−30.0000	−1.23195	−0.615976	−	0.787765i	$-0.711238\pi$
$593$	−30.0000	−1.23195	−0.615976	+	0.787765i	$0.711238\pi$
$594$	0	0
$595$	0	0
$596$	−18.0000	−0.737309
$597$	−4.00000	−0.163709
$598$	4.00000	0.163572
$599$	−12.0000	−0.490307	−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000	−0.490307	−0.245153	+	0.969484i	$0.578838\pi$
$600$	−1.00000	−0.0408248
$601$	−10.0000	−0.407909	−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000	−0.407909	−0.203954	+	0.978980i	$0.565379\pi$
$602$	4.00000	0.163028
$603$	−4.00000	−0.162893
$604$	20.0000	0.813788
$605$	11.0000	0.447214
$606$	0	0
$607$	14.0000	0.568242	0.284121	−	0.958788i	$-0.408298\pi$
$607$	14.0000	0.568242	0.284121	+	0.958788i	$0.408298\pi$
$608$	−2.00000	−0.0811107
$609$	6.00000	0.243132
$610$	−10.0000	−0.404888
$611$	−24.0000	−0.970936
$612$	0	0
$613$	2.00000	0.0807792	0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000	0.0807792	0.0403896	+	0.999184i	$0.487140\pi$
$614$	−8.00000	−0.322854
$615$	−6.00000	−0.241943
$616$	0	0
$617$	30.0000	1.20775	0.603877	−	0.797077i	$-0.293622\pi$
$617$	30.0000	1.20775	0.603877	+	0.797077i	$0.293622\pi$
$618$	4.00000	0.160904
$619$	14.0000	0.562708	0.281354	−	0.959604i	$-0.409217\pi$
$619$	14.0000	0.562708	0.281354	+	0.959604i	$0.409217\pi$
$620$	−2.00000	−0.0803219
$621$	1.00000	0.0401286
$622$	−18.0000	−0.721734
$623$	0	0
$624$	−4.00000	−0.160128
$625$	1.00000	0.0400000
$626$	4.00000	0.159872
$627$	0	0
$628$	2.00000	0.0798087
$629$	0	0
$630$	1.00000	0.0398410
$631$	−16.0000	−0.636950	−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000	−0.636950	−0.318475	+	0.947931i	$0.603171\pi$
$632$	−8.00000	−0.318223
$633$	20.0000	0.794929
$634$	18.0000	0.714871
$635$	−8.00000	−0.317470
$636$	−6.00000	−0.237915
$637$	−4.00000	−0.158486
$638$	0	0
$639$	0	0
$640$	1.00000	0.0395285
$641$	18.0000	0.710957	0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000	0.710957	0.355479	+	0.934684i	$0.384318\pi$
$642$	−12.0000	−0.473602
$643$	2.00000	0.0788723	0.0394362	−	0.999222i	$-0.487444\pi$
$643$	2.00000	0.0788723	0.0394362	+	0.999222i	$0.487444\pi$
$644$	1.00000	0.0394055
$645$	4.00000	0.157500
$646$	0	0
$647$	18.0000	0.707653	0.353827	−	0.935311i	$-0.384880\pi$
$647$	18.0000	0.707653	0.353827	+	0.935311i	$0.384880\pi$
$648$	−1.00000	−0.0392837
$649$	0	0
$650$	4.00000	0.156893
$651$	2.00000	0.0783862
$652$	−4.00000	−0.156652
$653$	18.0000	0.704394	0.352197	−	0.935926i	$-0.385435\pi$
$653$	18.0000	0.704394	0.352197	+	0.935926i	$0.385435\pi$
$654$	−2.00000	−0.0782062
$655$	−12.0000	−0.468879
$656$	6.00000	0.234261
$657$	14.0000	0.546192
$658$	−6.00000	−0.233904
$659$	−12.0000	−0.467454	−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000	−0.467454	−0.233727	+	0.972302i	$0.575092\pi$
$660$	0	0
$661$	−10.0000	−0.388955	−0.194477	−	0.980907i	$-0.562301\pi$
$661$	−10.0000	−0.388955	−0.194477	+	0.980907i	$0.562301\pi$
$662$	−20.0000	−0.777322
$663$	0	0
$664$	−6.00000	−0.232845
$665$	−2.00000	−0.0775567
$666$	10.0000	0.387492
$667$	6.00000	0.232321
$668$	−6.00000	−0.232147
$669$	−22.0000	−0.850569
$670$	−4.00000	−0.154533
$671$	0	0
$672$	−1.00000	−0.0385758
$673$	14.0000	0.539660	0.269830	−	0.962908i	$-0.413032\pi$
$673$	14.0000	0.539660	0.269830	+	0.962908i	$0.413032\pi$
$674$	22.0000	0.847408
$675$	1.00000	0.0384900
$676$	3.00000	0.115385
$677$	18.0000	0.691796	0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000	0.691796	0.345898	+	0.938272i	$0.387574\pi$
$678$	−18.0000	−0.691286
$679$	8.00000	0.307012
$680$	0	0
$681$	−30.0000	−1.14960
$682$	0	0
$683$	−36.0000	−1.37750	−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000	−1.37750	−0.688751	+	0.724998i	$0.741841\pi$
$684$	2.00000	0.0764719
$685$	−6.00000	−0.229248
$686$	−1.00000	−0.0381802
$687$	14.0000	0.534133
$688$	−4.00000	−0.152499
$689$	24.0000	0.914327
$690$	1.00000	0.0380693
$691$	8.00000	0.304334	0.152167	−	0.988355i	$-0.451375\pi$
$691$	8.00000	0.304334	0.152167	+	0.988355i	$0.451375\pi$
$692$	−12.0000	−0.456172
$693$	0	0
$694$	12.0000	0.455514
$695$	16.0000	0.606915
$696$	−6.00000	−0.227429
$697$	0	0
$698$	28.0000	1.05982
$699$	6.00000	0.226941
$700$	1.00000	0.0377964
$701$	30.0000	1.13308	0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000	1.13308	0.566542	+	0.824033i	$0.308281\pi$
$702$	4.00000	0.150970
$703$	−20.0000	−0.754314
$704$	0	0
$705$	−6.00000	−0.225973
$706$	−30.0000	−1.12906
$707$	0	0
$708$	12.0000	0.450988
$709$	14.0000	0.525781	0.262891	−	0.964826i	$-0.415324\pi$
$709$	14.0000	0.525781	0.262891	+	0.964826i	$0.415324\pi$
$710$	0	0
$711$	8.00000	0.300023
$712$	0	0
$713$	2.00000	0.0749006
$714$	0	0
$715$	0	0
$716$	12.0000	0.448461
$717$	24.0000	0.896296
$718$	−24.0000	−0.895672
$719$	−42.0000	−1.56634	−0.783168	−	0.621810i	$-0.786397\pi$
$719$	−42.0000	−1.56634	−0.783168	+	0.621810i	$0.786397\pi$
$720$	−1.00000	−0.0372678
$721$	−4.00000	−0.148968
$722$	15.0000	0.558242
$723$	−16.0000	−0.595046
$724$	14.0000	0.520306
$725$	6.00000	0.222834
$726$	11.0000	0.408248
$727$	−28.0000	−1.03846	−0.519231	−	0.854634i	$-0.673782\pi$
$727$	−28.0000	−1.03846	−0.519231	+	0.854634i	$0.673782\pi$
$728$	4.00000	0.148250
$729$	1.00000	0.0370370
$730$	14.0000	0.518163
$731$	0	0
$732$	−10.0000	−0.369611
$733$	2.00000	0.0738717	0.0369358	−	0.999318i	$-0.488240\pi$
$733$	2.00000	0.0738717	0.0369358	+	0.999318i	$0.488240\pi$
$734$	4.00000	0.147643
$735$	−1.00000	−0.0368856
$736$	−1.00000	−0.0368605
$737$	0	0
$738$	−6.00000	−0.220863
$739$	44.0000	1.61857	0.809283	−	0.587419i	$-0.199856\pi$
$739$	44.0000	1.61857	0.809283	+	0.587419i	$0.199856\pi$
$740$	10.0000	0.367607
$741$	−8.00000	−0.293887
$742$	6.00000	0.220267
$743$	0	0		−	1.00000i	$-0.5\pi$
$743$	0	0			1.00000i	$0.5\pi$
$744$	−2.00000	−0.0733236
$745$	18.0000	0.659469
$746$	−14.0000	−0.512576
$747$	6.00000	0.219529
$748$	0	0
$749$	12.0000	0.438470
$750$	1.00000	0.0365148
$751$	−16.0000	−0.583848	−0.291924	−	0.956441i	$-0.594295\pi$
$751$	−16.0000	−0.583848	−0.291924	+	0.956441i	$0.594295\pi$
$752$	6.00000	0.218797
$753$	−6.00000	−0.218652
$754$	24.0000	0.874028
$755$	−20.0000	−0.727875
$756$	1.00000	0.0363696
$757$	−46.0000	−1.67190	−0.835949	−	0.548807i	$-0.815082\pi$
$757$	−46.0000	−1.67190	−0.835949	+	0.548807i	$0.815082\pi$
$758$	−20.0000	−0.726433
$759$	0	0
$760$	2.00000	0.0725476
$761$	−30.0000	−1.08750	−0.543750	−	0.839248i	$-0.682996\pi$
$761$	−30.0000	−1.08750	−0.543750	+	0.839248i	$0.682996\pi$
$762$	−8.00000	−0.289809
$763$	2.00000	0.0724049
$764$	24.0000	0.868290
$765$	0	0
$766$	0	0
$767$	−48.0000	−1.73318
$768$	1.00000	0.0360844
$769$	−16.0000	−0.576975	−0.288487	−	0.957484i	$-0.593152\pi$
$769$	−16.0000	−0.576975	−0.288487	+	0.957484i	$0.593152\pi$
$770$	0	0
$771$	18.0000	0.648254
$772$	14.0000	0.503871
$773$	54.0000	1.94225	0.971123	−	0.238581i	$-0.0766824\pi$
$773$	54.0000	1.94225	0.971123	+	0.238581i	$0.0766824\pi$
$774$	4.00000	0.143777
$775$	2.00000	0.0718421
$776$	−8.00000	−0.287183
$777$	−10.0000	−0.358748
$778$	30.0000	1.07555
$779$	12.0000	0.429945
$780$	4.00000	0.143223
$781$	0	0
$782$	0	0
$783$	6.00000	0.214423
$784$	1.00000	0.0357143
$785$	−2.00000	−0.0713831
$786$	−12.0000	−0.428026
$787$	2.00000	0.0712923	0.0356462	−	0.999364i	$-0.488651\pi$
$787$	2.00000	0.0712923	0.0356462	+	0.999364i	$0.488651\pi$
$788$	−18.0000	−0.641223
$789$	24.0000	0.854423
$790$	8.00000	0.284627
$791$	18.0000	0.640006
$792$	0	0
$793$	40.0000	1.42044
$794$	4.00000	0.141955
$795$	6.00000	0.212798
$796$	−4.00000	−0.141776
$797$	−18.0000	−0.637593	−0.318796	−	0.947823i	$-0.603279\pi$
$797$	−18.0000	−0.637593	−0.318796	+	0.947823i	$0.603279\pi$
$798$	−2.00000	−0.0707992
$799$	0	0
$800$	−1.00000	−0.0353553
$801$	0	0
$802$	−18.0000	−0.635602
$803$	0	0
$804$	−4.00000	−0.141069
$805$	−1.00000	−0.0352454
$806$	8.00000	0.281788
$807$	24.0000	0.844840
$808$	0	0
$809$	54.0000	1.89854	0.949269	−	0.314464i	$-0.101825\pi$
$809$	54.0000	1.89854	0.949269	+	0.314464i	$0.101825\pi$
$810$	1.00000	0.0351364
$811$	20.0000	0.702295	0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000	0.702295	0.351147	+	0.936320i	$0.385792\pi$
$812$	6.00000	0.210559
$813$	2.00000	0.0701431
$814$	0	0
$815$	4.00000	0.140114
$816$	0	0
$817$	−8.00000	−0.279885
$818$	22.0000	0.769212
$819$	−4.00000	−0.139771
$820$	−6.00000	−0.209529
$821$	−6.00000	−0.209401	−0.104701	−	0.994504i	$-0.533388\pi$
$821$	−6.00000	−0.209401	−0.104701	+	0.994504i	$0.533388\pi$
$822$	−6.00000	−0.209274
$823$	32.0000	1.11545	0.557725	−	0.830026i	$-0.311674\pi$
$823$	32.0000	1.11545	0.557725	+	0.830026i	$0.311674\pi$
$824$	4.00000	0.139347
$825$	0	0
$826$	−12.0000	−0.417533
$827$	−12.0000	−0.417281	−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000	−0.417281	−0.208640	+	0.977992i	$0.566904\pi$
$828$	1.00000	0.0347524
$829$	−16.0000	−0.555703	−0.277851	−	0.960624i	$-0.589622\pi$
$829$	−16.0000	−0.555703	−0.277851	+	0.960624i	$0.589622\pi$
$830$	6.00000	0.208263
$831$	26.0000	0.901930
$832$	−4.00000	−0.138675
$833$	0	0
$834$	16.0000	0.554035
$835$	6.00000	0.207639
$836$	0	0
$837$	2.00000	0.0691301
$838$	30.0000	1.03633
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	1.00000	0.0345033
$841$	7.00000	0.241379
$842$	−26.0000	−0.896019
$843$	−6.00000	−0.206651
$844$	20.0000	0.688428
$845$	−3.00000	−0.103203
$846$	−6.00000	−0.206284
$847$	−11.0000	−0.377964
$848$	−6.00000	−0.206041
$849$	14.0000	0.480479
$850$	0	0
$851$	−10.0000	−0.342796
$852$	0	0
$853$	−52.0000	−1.78045	−0.890223	−	0.455525i	$-0.849452\pi$
$853$	−52.0000	−1.78045	−0.890223	+	0.455525i	$0.849452\pi$
$854$	10.0000	0.342193
$855$	−2.00000	−0.0683986
$856$	−12.0000	−0.410152
$857$	−42.0000	−1.43469	−0.717346	−	0.696717i	$-0.754643\pi$
$857$	−42.0000	−1.43469	−0.717346	+	0.696717i	$0.754643\pi$
$858$	0	0
$859$	−40.0000	−1.36478	−0.682391	−	0.730987i	$-0.739060\pi$
$859$	−40.0000	−1.36478	−0.682391	+	0.730987i	$0.739060\pi$
$860$	4.00000	0.136399
$861$	6.00000	0.204479
$862$	24.0000	0.817443
$863$	12.0000	0.408485	0.204242	−	0.978920i	$-0.434527\pi$
$863$	12.0000	0.408485	0.204242	+	0.978920i	$0.434527\pi$
$864$	−1.00000	−0.0340207
$865$	12.0000	0.408012
$866$	16.0000	0.543702
$867$	−17.0000	−0.577350
$868$	2.00000	0.0678844
$869$	0	0
$870$	6.00000	0.203419
$871$	16.0000	0.542139
$872$	−2.00000	−0.0677285
$873$	8.00000	0.270759
$874$	−2.00000	−0.0676510
$875$	−1.00000	−0.0338062
$876$	14.0000	0.473016
$877$	−10.0000	−0.337676	−0.168838	−	0.985644i	$-0.554001\pi$
$877$	−10.0000	−0.337676	−0.168838	+	0.985644i	$0.554001\pi$
$878$	34.0000	1.14744
$879$	−6.00000	−0.202375
$880$	0	0
$881$	12.0000	0.404290	0.202145	−	0.979356i	$-0.435209\pi$
$881$	12.0000	0.404290	0.202145	+	0.979356i	$0.435209\pi$
$882$	−1.00000	−0.0336718
$883$	20.0000	0.673054	0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000	0.673054	0.336527	+	0.941674i	$0.390748\pi$
$884$	0	0
$885$	−12.0000	−0.403376
$886$	−36.0000	−1.20944
$887$	−6.00000	−0.201460	−0.100730	−	0.994914i	$-0.532118\pi$
$887$	−6.00000	−0.201460	−0.100730	+	0.994914i	$0.532118\pi$
$888$	10.0000	0.335578
$889$	8.00000	0.268311
$890$	0	0
$891$	0	0
$892$	−22.0000	−0.736614
$893$	12.0000	0.401565
$894$	18.0000	0.602010
$895$	−12.0000	−0.401116
$896$	−1.00000	−0.0334077
$897$	−4.00000	−0.133556
$898$	18.0000	0.600668
$899$	12.0000	0.400222
$900$	1.00000	0.0333333
$901$	0	0
$902$	0	0
$903$	−4.00000	−0.133112
$904$	−18.0000	−0.598671
$905$	−14.0000	−0.465376
$906$	−20.0000	−0.664455
$907$	−16.0000	−0.531271	−0.265636	−	0.964073i	$-0.585582\pi$
$907$	−16.0000	−0.531271	−0.265636	+	0.964073i	$0.585582\pi$
$908$	−30.0000	−0.995585
$909$	0	0
$910$	−4.00000	−0.132599
$911$	−24.0000	−0.795155	−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000	−0.795155	−0.397578	+	0.917568i	$0.630149\pi$
$912$	2.00000	0.0662266
$913$	0	0
$914$	−38.0000	−1.25693
$915$	10.0000	0.330590
$916$	14.0000	0.462573
$917$	12.0000	0.396275
$918$	0	0
$919$	8.00000	0.263896	0.131948	−	0.991257i	$-0.457877\pi$
$919$	8.00000	0.263896	0.131948	+	0.991257i	$0.457877\pi$
$920$	1.00000	0.0329690
$921$	8.00000	0.263609
$922$	−24.0000	−0.790398
$923$	0	0
$924$	0	0
$925$	−10.0000	−0.328798
$926$	−20.0000	−0.657241
$927$	−4.00000	−0.131377
$928$	−6.00000	−0.196960
$929$	−18.0000	−0.590561	−0.295280	−	0.955411i	$-0.595413\pi$
$929$	−18.0000	−0.590561	−0.295280	+	0.955411i	$0.595413\pi$
$930$	2.00000	0.0655826
$931$	2.00000	0.0655474
$932$	6.00000	0.196537
$933$	18.0000	0.589294
$934$	6.00000	0.196326
$935$	0	0
$936$	4.00000	0.130744
$937$	−4.00000	−0.130674	−0.0653372	−	0.997863i	$-0.520812\pi$
$937$	−4.00000	−0.130674	−0.0653372	+	0.997863i	$0.520812\pi$
$938$	4.00000	0.130605
$939$	−4.00000	−0.130535
$940$	−6.00000	−0.195698
$941$	18.0000	0.586783	0.293392	−	0.955992i	$-0.405216\pi$
$941$	18.0000	0.586783	0.293392	+	0.955992i	$0.405216\pi$
$942$	−2.00000	−0.0651635
$943$	6.00000	0.195387
$944$	12.0000	0.390567
$945$	−1.00000	−0.0325300
$946$	0	0
$947$	−36.0000	−1.16984	−0.584921	−	0.811090i	$-0.698875\pi$
$947$	−36.0000	−1.16984	−0.584921	+	0.811090i	$0.698875\pi$
$948$	8.00000	0.259828
$949$	−56.0000	−1.81784
$950$	−2.00000	−0.0648886
$951$	−18.0000	−0.583690
$952$	0	0
$953$	−54.0000	−1.74923	−0.874616	−	0.484817i	$-0.838886\pi$
$953$	−54.0000	−1.74923	−0.874616	+	0.484817i	$0.838886\pi$
$954$	6.00000	0.194257
$955$	−24.0000	−0.776622
$956$	24.0000	0.776215
$957$	0	0
$958$	−36.0000	−1.16311
$959$	6.00000	0.193750
$960$	−1.00000	−0.0322749
$961$	−27.0000	−0.870968
$962$	−40.0000	−1.28965
$963$	12.0000	0.386695
$964$	−16.0000	−0.515325
$965$	−14.0000	−0.450676
$966$	−1.00000	−0.0321745
$967$	−4.00000	−0.128631	−0.0643157	−	0.997930i	$-0.520486\pi$
$967$	−4.00000	−0.128631	−0.0643157	+	0.997930i	$0.520486\pi$
$968$	11.0000	0.353553
$969$	0	0
$970$	8.00000	0.256865
$971$	42.0000	1.34784	0.673922	−	0.738802i	$-0.264608\pi$
$971$	42.0000	1.34784	0.673922	+	0.738802i	$0.264608\pi$
$972$	1.00000	0.0320750
$973$	−16.0000	−0.512936
$974$	28.0000	0.897178
$975$	−4.00000	−0.128103
$976$	−10.0000	−0.320092
$977$	−18.0000	−0.575871	−0.287936	−	0.957650i	$-0.592969\pi$
$977$	−18.0000	−0.575871	−0.287936	+	0.957650i	$0.592969\pi$
$978$	4.00000	0.127906
$979$	0	0
$980$	−1.00000	−0.0319438
$981$	2.00000	0.0638551
$982$	−36.0000	−1.14881
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	−6.00000	−0.191273
$985$	18.0000	0.573528
$986$	0	0
$987$	6.00000	0.190982
$988$	−8.00000	−0.254514
$989$	−4.00000	−0.127193
$990$	0	0
$991$	−4.00000	−0.127064	−0.0635321	−	0.997980i	$-0.520237\pi$
$991$	−4.00000	−0.127064	−0.0635321	+	0.997980i	$0.520237\pi$
$992$	−2.00000	−0.0635001
$993$	20.0000	0.634681
$994$	0	0
$995$	4.00000	0.126809
$996$	6.00000	0.190117
$997$	−4.00000	−0.126681	−0.0633406	−	0.997992i	$-0.520175\pi$
$997$	−4.00000	−0.126681	−0.0633406	+	0.997992i	$0.520175\pi$
$998$	4.00000	0.126618
$999$	−10.0000	−0.316386

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4830.2.a.l.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4830.2.a.l.1.1	✓	1	1.1	even	1	trivial

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

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Newspace parameters

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Embedding invariants

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Twists

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

Label	4830.2.a.l.1.1

Level	$4830$
Weight	$2$
Character	4830.1
Self dual	yes
Analytic conductor	$38.568$
Analytic rank	$0$
Dimension	$1$
CM	no
Inner twists	$1$