LMFDB - Embedded newform 7220.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7220,2,Mod(1,7220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7220, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("7220.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7220 = 2^{2} \cdot 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7220.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:	$57.6519902594$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 20)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	7220.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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
$3$	2.00000	1.15470	0.577350	−	0.816497i	$-0.304087\pi$
$3$	2.00000	1.15470	0.577350	+	0.816497i	$0.304087\pi$
$4$	0	0
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	2.00000	0.755929	0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000	0.755929	0.377964	+	0.925820i	$0.376624\pi$
$8$	0	0
$9$	1.00000	0.333333
$10$	0	0
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	0	0
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	0	0
$15$	−2.00000	−0.516398
$16$	0	0
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	0	0
$19$	0	0
$19$	0	0
$20$	0	0
$21$	4.00000	0.872872
$22$	0	0
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	−4.00000	−0.769800
$28$	0	0
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	0	0
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	−2.00000	−0.338062
$36$	0	0
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	0	0
$39$	−4.00000	−0.640513
$40$	0	0
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	0	0
$43$	−10.0000	−1.52499	−0.762493	−	0.646997i	$-0.776025\pi$
$43$	−10.0000	−1.52499	−0.762493	+	0.646997i	$0.776025\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	0	0
$47$	−6.00000	−0.875190	−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000	−0.875190	−0.437595	+	0.899172i	$0.644170\pi$
$48$	0	0
$49$	−3.00000	−0.428571
$50$	0	0
$51$	−12.0000	−1.68034
$52$	0	0
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	0	0
$59$	−12.0000	−1.56227	−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000	−1.56227	−0.781133	+	0.624364i	$0.785358\pi$
$60$	0	0
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	0	0
$63$	2.00000	0.251976
$64$	0	0
$65$	2.00000	0.248069
$66$	0	0
$67$	−2.00000	−0.244339	−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000	−0.244339	−0.122169	+	0.992509i	$0.538985\pi$
$68$	0	0
$69$	12.0000	1.44463
$70$	0	0
$71$	12.0000	1.42414	0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000	1.42414	0.712069	+	0.702109i	$0.247758\pi$
$72$	0	0
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	0	0
$75$	2.00000	0.230940
$76$	0	0
$77$	0	0
$78$	0	0
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	0	0
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	0	0
$85$	6.00000	0.650791
$86$	0	0
$87$	−12.0000	−1.28654
$88$	0	0
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	0	0
$91$	−4.00000	−0.419314
$92$	0	0
$93$	8.00000	0.829561
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	0	0
$103$	−14.0000	−1.37946	−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000	−1.37946	−0.689730	+	0.724066i	$0.742271\pi$
$104$	0	0
$105$	−4.00000	−0.390360
$106$	0	0
$107$	6.00000	0.580042	0.290021	−	0.957020i	$-0.406338\pi$
$107$	6.00000	0.580042	0.290021	+	0.957020i	$0.406338\pi$
$108$	0	0
$109$	−2.00000	−0.191565	−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000	−0.191565	−0.0957826	+	0.995402i	$0.530535\pi$
$110$	0	0
$111$	−4.00000	−0.379663
$112$	0	0
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	0	0
$115$	−6.00000	−0.559503
$116$	0	0
$117$	−2.00000	−0.184900
$118$	0	0
$119$	−12.0000	−1.10004
$120$	0	0
$121$	−11.0000	−1.00000
$122$	0	0
$123$	−12.0000	−1.08200
$124$	0	0
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−2.00000	−0.177471	−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000	−0.177471	−0.0887357	+	0.996055i	$0.528283\pi$
$128$	0	0
$129$	−20.0000	−1.76090
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	4.00000	0.344265
$136$	0	0
$137$	18.0000	1.53784	0.768922	−	0.639343i	$-0.220793\pi$
$137$	18.0000	1.53784	0.768922	+	0.639343i	$0.220793\pi$
$138$	0	0
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	0	0
$141$	−12.0000	−1.01058
$142$	0	0
$143$	0	0
$144$	0	0
$145$	6.00000	0.498273
$146$	0	0
$147$	−6.00000	−0.494872
$148$	0	0
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	0	0
$151$	−20.0000	−1.62758	−0.813788	−	0.581161i	$-0.802599\pi$
$151$	−20.0000	−1.62758	−0.813788	+	0.581161i	$0.802599\pi$
$152$	0	0
$153$	−6.00000	−0.485071
$154$	0	0
$155$	−4.00000	−0.321288
$156$	0	0
$157$	−22.0000	−1.75579	−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000	−1.75579	−0.877896	+	0.478852i	$0.841053\pi$
$158$	0	0
$159$	12.0000	0.951662
$160$	0	0
$161$	12.0000	0.945732
$162$	0	0
$163$	−10.0000	−0.783260	−0.391630	−	0.920123i	$-0.628089\pi$
$163$	−10.0000	−0.783260	−0.391630	+	0.920123i	$0.628089\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−18.0000	−1.39288	−0.696441	−	0.717614i	$-0.745234\pi$
$167$	−18.0000	−1.39288	−0.696441	+	0.717614i	$0.745234\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	0	0
$171$	0	0
$172$	0	0
$173$	6.00000	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	0	0
$175$	2.00000	0.151186
$176$	0	0
$177$	−24.0000	−1.80395
$178$	0	0
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	0	0
$181$	10.0000	0.743294	0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000	0.743294	0.371647	+	0.928374i	$0.378793\pi$
$182$	0	0
$183$	4.00000	0.295689
$184$	0	0
$185$	2.00000	0.147043
$186$	0	0
$187$	0	0
$188$	0	0
$189$	−8.00000	−0.581914
$190$	0	0
$191$	−12.0000	−0.868290	−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000	−0.868290	−0.434145	+	0.900843i	$0.642949\pi$
$192$	0	0
$193$	−26.0000	−1.87152	−0.935760	−	0.352636i	$-0.885285\pi$
$193$	−26.0000	−1.87152	−0.935760	+	0.352636i	$0.885285\pi$
$194$	0	0
$195$	4.00000	0.286446
$196$	0	0
$197$	18.0000	1.28245	0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000	1.28245	0.641223	+	0.767354i	$0.278427\pi$
$198$	0	0
$199$	8.00000	0.567105	0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000	0.567105	0.283552	+	0.958957i	$0.408487\pi$
$200$	0	0
$201$	−4.00000	−0.282138
$202$	0	0
$203$	−12.0000	−0.842235
$204$	0	0
$205$	6.00000	0.419058
$206$	0	0
$207$	6.00000	0.417029
$208$	0	0
$209$	0	0
$210$	0	0
$211$	16.0000	1.10149	0.550743	−	0.834675i	$-0.314345\pi$
$211$	16.0000	1.10149	0.550743	+	0.834675i	$0.314345\pi$
$212$	0	0
$213$	24.0000	1.64445
$214$	0	0
$215$	10.0000	0.681994
$216$	0	0
$217$	8.00000	0.543075
$218$	0	0
$219$	4.00000	0.270295
$220$	0	0
$221$	12.0000	0.807207
$222$	0	0
$223$	10.0000	0.669650	0.334825	−	0.942280i	$-0.391323\pi$
$223$	10.0000	0.669650	0.334825	+	0.942280i	$0.391323\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	0	0
$227$	6.00000	0.398234	0.199117	−	0.979976i	$-0.436193\pi$
$227$	6.00000	0.398234	0.199117	+	0.979976i	$0.436193\pi$
$228$	0	0
$229$	14.0000	0.925146	0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000	0.925146	0.462573	+	0.886581i	$0.346926\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	0	0
$235$	6.00000	0.391397
$236$	0	0
$237$	−16.0000	−1.03931
$238$	0	0
$239$	−24.0000	−1.55243	−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000	−1.55243	−0.776215	+	0.630468i	$0.782863\pi$
$240$	0	0
$241$	−14.0000	−0.901819	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000	−0.901819	−0.450910	+	0.892570i	$0.648900\pi$
$242$	0	0
$243$	−10.0000	−0.641500
$244$	0	0
$245$	3.00000	0.191663
$246$	0	0
$247$	0	0
$248$	0	0
$249$	12.0000	0.760469
$250$	0	0
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	12.0000	0.751469
$256$	0	0
$257$	6.00000	0.374270	0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000	0.374270	0.187135	+	0.982334i	$0.440080\pi$
$258$	0	0
$259$	−4.00000	−0.248548
$260$	0	0
$261$	−6.00000	−0.371391
$262$	0	0
$263$	−18.0000	−1.10993	−0.554964	−	0.831875i	$-0.687268\pi$
$263$	−18.0000	−1.10993	−0.554964	+	0.831875i	$0.687268\pi$
$264$	0	0
$265$	−6.00000	−0.368577
$266$	0	0
$267$	12.0000	0.734388
$268$	0	0
$269$	−18.0000	−1.09748	−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000	−1.09748	−0.548740	+	0.835993i	$0.684892\pi$
$270$	0	0
$271$	20.0000	1.21491	0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000	1.21491	0.607457	+	0.794353i	$0.292190\pi$
$272$	0	0
$273$	−8.00000	−0.484182
$274$	0	0
$275$	0	0
$276$	0	0
$277$	26.0000	1.56219	0.781094	−	0.624413i	$-0.214662\pi$
$277$	26.0000	1.56219	0.781094	+	0.624413i	$0.214662\pi$
$278$	0	0
$279$	4.00000	0.239474
$280$	0	0
$281$	−6.00000	−0.357930	−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000	−0.357930	−0.178965	+	0.983855i	$0.557275\pi$
$282$	0	0
$283$	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
$285$	0	0
$286$	0	0
$287$	−12.0000	−0.708338
$288$	0	0
$289$	19.0000	1.11765
$290$	0	0
$291$	−4.00000	−0.234484
$292$	0	0
$293$	30.0000	1.75262	0.876309	−	0.481749i	$-0.159998\pi$
$293$	30.0000	1.75262	0.876309	+	0.481749i	$0.159998\pi$
$294$	0	0
$295$	12.0000	0.698667
$296$	0	0
$297$	0	0
$298$	0	0
$299$	−12.0000	−0.693978
$300$	0	0
$301$	−20.0000	−1.15278
$302$	0	0
$303$	12.0000	0.689382
$304$	0	0
$305$	−2.00000	−0.114520
$306$	0	0
$307$	−2.00000	−0.114146	−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000	−0.114146	−0.0570730	+	0.998370i	$0.518177\pi$
$308$	0	0
$309$	−28.0000	−1.59286
$310$	0	0
$311$	12.0000	0.680458	0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000	0.680458	0.340229	+	0.940343i	$0.389495\pi$
$312$	0	0
$313$	−22.0000	−1.24351	−0.621757	−	0.783210i	$-0.713581\pi$
$313$	−22.0000	−1.24351	−0.621757	+	0.783210i	$0.713581\pi$
$314$	0	0
$315$	−2.00000	−0.112687
$316$	0	0
$317$	6.00000	0.336994	0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000	0.336994	0.168497	+	0.985702i	$0.446109\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	12.0000	0.669775
$322$	0	0
$323$	0	0
$324$	0	0
$325$	−2.00000	−0.110940
$326$	0	0
$327$	−4.00000	−0.221201
$328$	0	0
$329$	−12.0000	−0.661581
$330$	0	0
$331$	−8.00000	−0.439720	−0.219860	−	0.975531i	$-0.570560\pi$
$331$	−8.00000	−0.439720	−0.219860	+	0.975531i	$0.570560\pi$
$332$	0	0
$333$	−2.00000	−0.109599
$334$	0	0
$335$	2.00000	0.109272
$336$	0	0
$337$	−2.00000	−0.108947	−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000	−0.108947	−0.0544735	+	0.998515i	$0.517348\pi$
$338$	0	0
$339$	12.0000	0.651751
$340$	0	0
$341$	0	0
$342$	0	0
$343$	−20.0000	−1.07990
$344$	0	0
$345$	−12.0000	−0.646058
$346$	0	0
$347$	−30.0000	−1.61048	−0.805242	−	0.592946i	$-0.797965\pi$
$347$	−30.0000	−1.61048	−0.805242	+	0.592946i	$0.797965\pi$
$348$	0	0
$349$	−10.0000	−0.535288	−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000	−0.535288	−0.267644	+	0.963518i	$0.586245\pi$
$350$	0	0
$351$	8.00000	0.427008
$352$	0	0
$353$	18.0000	0.958043	0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000	0.958043	0.479022	+	0.877803i	$0.340992\pi$
$354$	0	0
$355$	−12.0000	−0.636894
$356$	0	0
$357$	−24.0000	−1.27021
$358$	0	0
$359$	24.0000	1.26667	0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000	1.26667	0.633336	+	0.773877i	$0.281685\pi$
$360$	0	0
$361$	0	0
$362$	0	0
$363$	−22.0000	−1.15470
$364$	0	0
$365$	−2.00000	−0.104685
$366$	0	0
$367$	−22.0000	−1.14839	−0.574195	−	0.818718i	$-0.694685\pi$
$367$	−22.0000	−1.14839	−0.574195	+	0.818718i	$0.694685\pi$
$368$	0	0
$369$	−6.00000	−0.312348
$370$	0	0
$371$	12.0000	0.623009
$372$	0	0
$373$	−26.0000	−1.34623	−0.673114	−	0.739538i	$-0.735044\pi$
$373$	−26.0000	−1.34623	−0.673114	+	0.739538i	$0.735044\pi$
$374$	0	0
$375$	−2.00000	−0.103280
$376$	0	0
$377$	12.0000	0.618031
$378$	0	0
$379$	28.0000	1.43826	0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000	1.43826	0.719132	+	0.694874i	$0.244540\pi$
$380$	0	0
$381$	−4.00000	−0.204926
$382$	0	0
$383$	−6.00000	−0.306586	−0.153293	−	0.988181i	$-0.548988\pi$
$383$	−6.00000	−0.306586	−0.153293	+	0.988181i	$0.548988\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−10.0000	−0.508329
$388$	0	0
$389$	−6.00000	−0.304212	−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000	−0.304212	−0.152106	+	0.988364i	$0.548606\pi$
$390$	0	0
$391$	−36.0000	−1.82060
$392$	0	0
$393$	0	0
$394$	0	0
$395$	8.00000	0.402524
$396$	0	0
$397$	2.00000	0.100377	0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000	0.100377	0.0501886	+	0.998740i	$0.484018\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	30.0000	1.49813	0.749064	−	0.662497i	$-0.230503\pi$
$401$	30.0000	1.49813	0.749064	+	0.662497i	$0.230503\pi$
$402$	0	0
$403$	−8.00000	−0.398508
$404$	0	0
$405$	11.0000	0.546594
$406$	0	0
$407$	0	0
$408$	0	0
$409$	34.0000	1.68119	0.840596	−	0.541663i	$-0.182205\pi$
$409$	34.0000	1.68119	0.840596	+	0.541663i	$0.182205\pi$
$410$	0	0
$411$	36.0000	1.77575
$412$	0	0
$413$	−24.0000	−1.18096
$414$	0	0
$415$	−6.00000	−0.294528
$416$	0	0
$417$	−8.00000	−0.391762
$418$	0	0
$419$	36.0000	1.75872	0.879358	−	0.476162i	$-0.157972\pi$
$419$	36.0000	1.75872	0.879358	+	0.476162i	$0.157972\pi$
$420$	0	0
$421$	−26.0000	−1.26716	−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000	−1.26716	−0.633581	+	0.773676i	$0.718416\pi$
$422$	0	0
$423$	−6.00000	−0.291730
$424$	0	0
$425$	−6.00000	−0.291043
$426$	0	0
$427$	4.00000	0.193574
$428$	0	0
$429$	0	0
$430$	0	0
$431$	−36.0000	−1.73406	−0.867029	−	0.498257i	$-0.833974\pi$
$431$	−36.0000	−1.73406	−0.867029	+	0.498257i	$0.833974\pi$
$432$	0	0
$433$	−2.00000	−0.0961139	−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000	−0.0961139	−0.0480569	+	0.998845i	$0.515303\pi$
$434$	0	0
$435$	12.0000	0.575356
$436$	0	0
$437$	0	0
$438$	0	0
$439$	−8.00000	−0.381819	−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000	−0.381819	−0.190910	+	0.981608i	$0.561144\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	0	0
$443$	6.00000	0.285069	0.142534	−	0.989790i	$-0.454475\pi$
$443$	6.00000	0.285069	0.142534	+	0.989790i	$0.454475\pi$
$444$	0	0
$445$	−6.00000	−0.284427
$446$	0	0
$447$	−12.0000	−0.567581
$448$	0	0
$449$	−6.00000	−0.283158	−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000	−0.283158	−0.141579	+	0.989927i	$0.545218\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	−40.0000	−1.87936
$454$	0	0
$455$	4.00000	0.187523
$456$	0	0
$457$	26.0000	1.21623	0.608114	−	0.793849i	$-0.291926\pi$
$457$	26.0000	1.21623	0.608114	+	0.793849i	$0.291926\pi$
$458$	0	0
$459$	24.0000	1.12022
$460$	0	0
$461$	30.0000	1.39724	0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000	1.39724	0.698620	+	0.715493i	$0.253798\pi$
$462$	0	0
$463$	14.0000	0.650635	0.325318	−	0.945605i	$-0.394529\pi$
$463$	14.0000	0.650635	0.325318	+	0.945605i	$0.394529\pi$
$464$	0	0
$465$	−8.00000	−0.370991
$466$	0	0
$467$	−30.0000	−1.38823	−0.694117	−	0.719862i	$-0.744205\pi$
$467$	−30.0000	−1.38823	−0.694117	+	0.719862i	$0.744205\pi$
$468$	0	0
$469$	−4.00000	−0.184703
$470$	0	0
$471$	−44.0000	−2.02741
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	0	0
$477$	6.00000	0.274721
$478$	0	0
$479$	−24.0000	−1.09659	−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000	−1.09659	−0.548294	+	0.836286i	$0.684723\pi$
$480$	0	0
$481$	4.00000	0.182384
$482$	0	0
$483$	24.0000	1.09204
$484$	0	0
$485$	2.00000	0.0908153
$486$	0	0
$487$	−26.0000	−1.17817	−0.589086	−	0.808070i	$-0.700512\pi$
$487$	−26.0000	−1.17817	−0.589086	+	0.808070i	$0.700512\pi$
$488$	0	0
$489$	−20.0000	−0.904431
$490$	0	0
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	0	0
$493$	36.0000	1.62136
$494$	0	0
$495$	0	0
$496$	0	0
$497$	24.0000	1.07655
$498$	0	0
$499$	−4.00000	−0.179065	−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000	−0.179065	−0.0895323	+	0.995984i	$0.528537\pi$
$500$	0	0
$501$	−36.0000	−1.60836
$502$	0	0
$503$	−18.0000	−0.802580	−0.401290	−	0.915951i	$-0.631438\pi$
$503$	−18.0000	−0.802580	−0.401290	+	0.915951i	$0.631438\pi$
$504$	0	0
$505$	−6.00000	−0.266996
$506$	0	0
$507$	−18.0000	−0.799408
$508$	0	0
$509$	−6.00000	−0.265945	−0.132973	−	0.991120i	$-0.542452\pi$
$509$	−6.00000	−0.265945	−0.132973	+	0.991120i	$0.542452\pi$
$510$	0	0
$511$	4.00000	0.176950
$512$	0	0
$513$	0	0
$514$	0	0
$515$	14.0000	0.616914
$516$	0	0
$517$	0	0
$518$	0	0
$519$	12.0000	0.526742
$520$	0	0
$521$	6.00000	0.262865	0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000	0.262865	0.131432	+	0.991325i	$0.458042\pi$
$522$	0	0
$523$	−14.0000	−0.612177	−0.306089	−	0.952003i	$-0.599020\pi$
$523$	−14.0000	−0.612177	−0.306089	+	0.952003i	$0.599020\pi$
$524$	0	0
$525$	4.00000	0.174574
$526$	0	0
$527$	−24.0000	−1.04546
$528$	0	0
$529$	13.0000	0.565217
$530$	0	0
$531$	−12.0000	−0.520756
$532$	0	0
$533$	12.0000	0.519778
$534$	0	0
$535$	−6.00000	−0.259403
$536$	0	0
$537$	24.0000	1.03568
$538$	0	0
$539$	0	0
$540$	0	0
$541$	14.0000	0.601907	0.300954	−	0.953639i	$-0.402695\pi$
$541$	14.0000	0.601907	0.300954	+	0.953639i	$0.402695\pi$
$542$	0	0
$543$	20.0000	0.858282
$544$	0	0
$545$	2.00000	0.0856706
$546$	0	0
$547$	−26.0000	−1.11168	−0.555840	−	0.831289i	$-0.687603\pi$
$547$	−26.0000	−1.11168	−0.555840	+	0.831289i	$0.687603\pi$
$548$	0	0
$549$	2.00000	0.0853579
$550$	0	0
$551$	0	0
$552$	0	0
$553$	−16.0000	−0.680389
$554$	0	0
$555$	4.00000	0.169791
$556$	0	0
$557$	−30.0000	−1.27114	−0.635570	−	0.772043i	$-0.719235\pi$
$557$	−30.0000	−1.27114	−0.635570	+	0.772043i	$0.719235\pi$
$558$	0	0
$559$	20.0000	0.845910
$560$	0	0
$561$	0	0
$562$	0	0
$563$	18.0000	0.758610	0.379305	−	0.925272i	$-0.376163\pi$
$563$	18.0000	0.758610	0.379305	+	0.925272i	$0.376163\pi$
$564$	0	0
$565$	−6.00000	−0.252422
$566$	0	0
$567$	−22.0000	−0.923913
$568$	0	0
$569$	−30.0000	−1.25767	−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000	−1.25767	−0.628833	+	0.777541i	$0.716467\pi$
$570$	0	0
$571$	8.00000	0.334790	0.167395	−	0.985890i	$-0.446465\pi$
$571$	8.00000	0.334790	0.167395	+	0.985890i	$0.446465\pi$
$572$	0	0
$573$	−24.0000	−1.00261
$574$	0	0
$575$	6.00000	0.250217
$576$	0	0
$577$	−22.0000	−0.915872	−0.457936	−	0.888985i	$-0.651411\pi$
$577$	−22.0000	−0.915872	−0.457936	+	0.888985i	$0.651411\pi$
$578$	0	0
$579$	−52.0000	−2.16105
$580$	0	0
$581$	12.0000	0.497844
$582$	0	0
$583$	0	0
$584$	0	0
$585$	2.00000	0.0826898
$586$	0	0
$587$	−6.00000	−0.247647	−0.123823	−	0.992304i	$-0.539516\pi$
$587$	−6.00000	−0.247647	−0.123823	+	0.992304i	$0.539516\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	36.0000	1.48084
$592$	0	0
$593$	18.0000	0.739171	0.369586	−	0.929197i	$-0.379500\pi$
$593$	18.0000	0.739171	0.369586	+	0.929197i	$0.379500\pi$
$594$	0	0
$595$	12.0000	0.491952
$596$	0	0
$597$	16.0000	0.654836
$598$	0	0
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	0	0
$601$	10.0000	0.407909	0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000	0.407909	0.203954	+	0.978980i	$0.434621\pi$
$602$	0	0
$603$	−2.00000	−0.0814463
$604$	0	0
$605$	11.0000	0.447214
$606$	0	0
$607$	22.0000	0.892952	0.446476	−	0.894795i	$-0.352679\pi$
$607$	22.0000	0.892952	0.446476	+	0.894795i	$0.352679\pi$
$608$	0	0
$609$	−24.0000	−0.972529
$610$	0	0
$611$	12.0000	0.485468
$612$	0	0
$613$	2.00000	0.0807792	0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000	0.0807792	0.0403896	+	0.999184i	$0.487140\pi$
$614$	0	0
$615$	12.0000	0.483887
$616$	0	0
$617$	−6.00000	−0.241551	−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000	−0.241551	−0.120775	+	0.992680i	$0.538538\pi$
$618$	0	0
$619$	20.0000	0.803868	0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000	0.803868	0.401934	+	0.915669i	$0.368338\pi$
$620$	0	0
$621$	−24.0000	−0.963087
$622$	0	0
$623$	12.0000	0.480770
$624$	0	0
$625$	1.00000	0.0400000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	12.0000	0.478471
$630$	0	0
$631$	−28.0000	−1.11466	−0.557331	−	0.830290i	$-0.688175\pi$
$631$	−28.0000	−1.11466	−0.557331	+	0.830290i	$0.688175\pi$
$632$	0	0
$633$	32.0000	1.27189
$634$	0	0
$635$	2.00000	0.0793676
$636$	0	0
$637$	6.00000	0.237729
$638$	0	0
$639$	12.0000	0.474713
$640$	0	0
$641$	18.0000	0.710957	0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000	0.710957	0.355479	+	0.934684i	$0.384318\pi$
$642$	0	0
$643$	14.0000	0.552106	0.276053	−	0.961142i	$-0.410973\pi$
$643$	14.0000	0.552106	0.276053	+	0.961142i	$0.410973\pi$
$644$	0	0
$645$	20.0000	0.787499
$646$	0	0
$647$	42.0000	1.65119	0.825595	−	0.564263i	$-0.190840\pi$
$647$	42.0000	1.65119	0.825595	+	0.564263i	$0.190840\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	16.0000	0.627089
$652$	0	0
$653$	42.0000	1.64359	0.821794	−	0.569785i	$-0.192974\pi$
$653$	42.0000	1.64359	0.821794	+	0.569785i	$0.192974\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	2.00000	0.0780274
$658$	0	0
$659$	−36.0000	−1.40236	−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000	−1.40236	−0.701180	+	0.712984i	$0.747343\pi$
$660$	0	0
$661$	22.0000	0.855701	0.427850	−	0.903850i	$-0.359271\pi$
$661$	22.0000	0.855701	0.427850	+	0.903850i	$0.359271\pi$
$662$	0	0
$663$	24.0000	0.932083
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−36.0000	−1.39393
$668$	0	0
$669$	20.0000	0.773245
$670$	0	0
$671$	0	0
$672$	0	0
$673$	46.0000	1.77317	0.886585	−	0.462566i	$-0.153071\pi$
$673$	46.0000	1.77317	0.886585	+	0.462566i	$0.153071\pi$
$674$	0	0
$675$	−4.00000	−0.153960
$676$	0	0
$677$	−18.0000	−0.691796	−0.345898	−	0.938272i	$-0.612426\pi$
$677$	−18.0000	−0.691796	−0.345898	+	0.938272i	$0.612426\pi$
$678$	0	0
$679$	−4.00000	−0.153506
$680$	0	0
$681$	12.0000	0.459841
$682$	0	0
$683$	42.0000	1.60709	0.803543	−	0.595247i	$-0.202946\pi$
$683$	42.0000	1.60709	0.803543	+	0.595247i	$0.202946\pi$
$684$	0	0
$685$	−18.0000	−0.687745
$686$	0	0
$687$	28.0000	1.06827
$688$	0	0
$689$	−12.0000	−0.457164
$690$	0	0
$691$	8.00000	0.304334	0.152167	−	0.988355i	$-0.451375\pi$
$691$	8.00000	0.304334	0.152167	+	0.988355i	$0.451375\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	4.00000	0.151729
$696$	0	0
$697$	36.0000	1.36360
$698$	0	0
$699$	−12.0000	−0.453882
$700$	0	0
$701$	−30.0000	−1.13308	−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000	−1.13308	−0.566542	+	0.824033i	$0.691719\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	12.0000	0.451946
$706$	0	0
$707$	12.0000	0.451306
$708$	0	0
$709$	−34.0000	−1.27690	−0.638448	−	0.769665i	$-0.720423\pi$
$709$	−34.0000	−1.27690	−0.638448	+	0.769665i	$0.720423\pi$
$710$	0	0
$711$	−8.00000	−0.300023
$712$	0	0
$713$	24.0000	0.898807
$714$	0	0
$715$	0	0
$716$	0	0
$717$	−48.0000	−1.79259
$718$	0	0
$719$	−24.0000	−0.895049	−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000	−0.895049	−0.447524	+	0.894272i	$0.647694\pi$
$720$	0	0
$721$	−28.0000	−1.04277
$722$	0	0
$723$	−28.0000	−1.04133
$724$	0	0
$725$	−6.00000	−0.222834
$726$	0	0
$727$	−46.0000	−1.70605	−0.853023	−	0.521874i	$-0.825233\pi$
$727$	−46.0000	−1.70605	−0.853023	+	0.521874i	$0.825233\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	60.0000	2.21918
$732$	0	0
$733$	−22.0000	−0.812589	−0.406294	−	0.913742i	$-0.633179\pi$
$733$	−22.0000	−0.812589	−0.406294	+	0.913742i	$0.633179\pi$
$734$	0	0
$735$	6.00000	0.221313
$736$	0	0
$737$	0	0
$738$	0	0
$739$	20.0000	0.735712	0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000	0.735712	0.367856	+	0.929883i	$0.380092\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	−6.00000	−0.220119	−0.110059	−	0.993925i	$-0.535104\pi$
$743$	−6.00000	−0.220119	−0.110059	+	0.993925i	$0.535104\pi$
$744$	0	0
$745$	6.00000	0.219823
$746$	0	0
$747$	6.00000	0.219529
$748$	0	0
$749$	12.0000	0.438470
$750$	0	0
$751$	4.00000	0.145962	0.0729810	−	0.997333i	$-0.476749\pi$
$751$	4.00000	0.145962	0.0729810	+	0.997333i	$0.476749\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	20.0000	0.727875
$756$	0	0
$757$	−22.0000	−0.799604	−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000	−0.799604	−0.399802	+	0.916602i	$0.630921\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	42.0000	1.52250	0.761249	−	0.648459i	$-0.224586\pi$
$761$	42.0000	1.52250	0.761249	+	0.648459i	$0.224586\pi$
$762$	0	0
$763$	−4.00000	−0.144810
$764$	0	0
$765$	6.00000	0.216930
$766$	0	0
$767$	24.0000	0.866590
$768$	0	0
$769$	2.00000	0.0721218	0.0360609	−	0.999350i	$-0.488519\pi$
$769$	2.00000	0.0721218	0.0360609	+	0.999350i	$0.488519\pi$
$770$	0	0
$771$	12.0000	0.432169
$772$	0	0
$773$	30.0000	1.07903	0.539513	−	0.841978i	$-0.318609\pi$
$773$	30.0000	1.07903	0.539513	+	0.841978i	$0.318609\pi$
$774$	0	0
$775$	4.00000	0.143684
$776$	0	0
$777$	−8.00000	−0.286998
$778$	0	0
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	24.0000	0.857690
$784$	0	0
$785$	22.0000	0.785214
$786$	0	0
$787$	−26.0000	−0.926800	−0.463400	−	0.886149i	$-0.653371\pi$
$787$	−26.0000	−0.926800	−0.463400	+	0.886149i	$0.653371\pi$
$788$	0	0
$789$	−36.0000	−1.28163
$790$	0	0
$791$	12.0000	0.426671
$792$	0	0
$793$	−4.00000	−0.142044
$794$	0	0
$795$	−12.0000	−0.425596
$796$	0	0
$797$	−42.0000	−1.48772	−0.743858	−	0.668338i	$-0.767006\pi$
$797$	−42.0000	−1.48772	−0.743858	+	0.668338i	$0.767006\pi$
$798$	0	0
$799$	36.0000	1.27359
$800$	0	0
$801$	6.00000	0.212000
$802$	0	0
$803$	0	0
$804$	0	0
$805$	−12.0000	−0.422944
$806$	0	0
$807$	−36.0000	−1.26726
$808$	0	0
$809$	−6.00000	−0.210949	−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000	−0.210949	−0.105474	+	0.994422i	$0.533636\pi$
$810$	0	0
$811$	16.0000	0.561836	0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000	0.561836	0.280918	+	0.959732i	$0.409361\pi$
$812$	0	0
$813$	40.0000	1.40286
$814$	0	0
$815$	10.0000	0.350285
$816$	0	0
$817$	0	0
$818$	0	0
$819$	−4.00000	−0.139771
$820$	0	0
$821$	−54.0000	−1.88461	−0.942306	−	0.334751i	$-0.891348\pi$
$821$	−54.0000	−1.88461	−0.942306	+	0.334751i	$0.891348\pi$
$822$	0	0
$823$	38.0000	1.32460	0.662298	−	0.749240i	$-0.269581\pi$
$823$	38.0000	1.32460	0.662298	+	0.749240i	$0.269581\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	30.0000	1.04320	0.521601	−	0.853189i	$-0.325335\pi$
$827$	30.0000	1.04320	0.521601	+	0.853189i	$0.325335\pi$
$828$	0	0
$829$	−2.00000	−0.0694629	−0.0347314	−	0.999397i	$-0.511058\pi$
$829$	−2.00000	−0.0694629	−0.0347314	+	0.999397i	$0.511058\pi$
$830$	0	0
$831$	52.0000	1.80386
$832$	0	0
$833$	18.0000	0.623663
$834$	0	0
$835$	18.0000	0.622916
$836$	0	0
$837$	−16.0000	−0.553041
$838$	0	0
$839$	48.0000	1.65714	0.828572	−	0.559883i	$-0.189154\pi$
$839$	48.0000	1.65714	0.828572	+	0.559883i	$0.189154\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	0	0
$843$	−12.0000	−0.413302
$844$	0	0
$845$	9.00000	0.309609
$846$	0	0
$847$	−22.0000	−0.755929
$848$	0	0
$849$	28.0000	0.960958
$850$	0	0
$851$	−12.0000	−0.411355
$852$	0	0
$853$	50.0000	1.71197	0.855984	−	0.517003i	$-0.172952\pi$
$853$	50.0000	1.71197	0.855984	+	0.517003i	$0.172952\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−18.0000	−0.614868	−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000	−0.614868	−0.307434	+	0.951569i	$0.599470\pi$
$858$	0	0
$859$	−4.00000	−0.136478	−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000	−0.136478	−0.0682391	+	0.997669i	$0.521738\pi$
$860$	0	0
$861$	−24.0000	−0.817918
$862$	0	0
$863$	−6.00000	−0.204242	−0.102121	−	0.994772i	$-0.532563\pi$
$863$	−6.00000	−0.204242	−0.102121	+	0.994772i	$0.532563\pi$
$864$	0	0
$865$	−6.00000	−0.204006
$866$	0	0
$867$	38.0000	1.29055
$868$	0	0
$869$	0	0
$870$	0	0
$871$	4.00000	0.135535
$872$	0	0
$873$	−2.00000	−0.0676897
$874$	0	0
$875$	−2.00000	−0.0676123
$876$	0	0
$877$	−26.0000	−0.877958	−0.438979	−	0.898497i	$-0.644660\pi$
$877$	−26.0000	−0.877958	−0.438979	+	0.898497i	$0.644660\pi$
$878$	0	0
$879$	60.0000	2.02375
$880$	0	0
$881$	−18.0000	−0.606435	−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000	−0.606435	−0.303218	+	0.952921i	$0.598061\pi$
$882$	0	0
$883$	14.0000	0.471138	0.235569	−	0.971858i	$-0.424305\pi$
$883$	14.0000	0.471138	0.235569	+	0.971858i	$0.424305\pi$
$884$	0	0
$885$	24.0000	0.806751
$886$	0	0
$887$	−18.0000	−0.604381	−0.302190	−	0.953248i	$-0.597718\pi$
$887$	−18.0000	−0.604381	−0.302190	+	0.953248i	$0.597718\pi$
$888$	0	0
$889$	−4.00000	−0.134156
$890$	0	0
$891$	0	0
$892$	0	0
$893$	0	0
$894$	0	0
$895$	−12.0000	−0.401116
$896$	0	0
$897$	−24.0000	−0.801337
$898$	0	0
$899$	−24.0000	−0.800445
$900$	0	0
$901$	−36.0000	−1.19933
$902$	0	0
$903$	−40.0000	−1.33112
$904$	0	0
$905$	−10.0000	−0.332411
$906$	0	0
$907$	46.0000	1.52740	0.763702	−	0.645568i	$-0.223379\pi$
$907$	46.0000	1.52740	0.763702	+	0.645568i	$0.223379\pi$
$908$	0	0
$909$	6.00000	0.199007
$910$	0	0
$911$	−12.0000	−0.397578	−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000	−0.397578	−0.198789	+	0.980042i	$0.563701\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	−4.00000	−0.132236
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−16.0000	−0.527791	−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000	−0.527791	−0.263896	+	0.964551i	$0.585007\pi$
$920$	0	0
$921$	−4.00000	−0.131804
$922$	0	0
$923$	−24.0000	−0.789970
$924$	0	0
$925$	−2.00000	−0.0657596
$926$	0	0
$927$	−14.0000	−0.459820
$928$	0	0
$929$	−42.0000	−1.37798	−0.688988	−	0.724773i	$-0.741945\pi$
$929$	−42.0000	−1.37798	−0.688988	+	0.724773i	$0.741945\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	24.0000	0.785725
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−22.0000	−0.718709	−0.359354	−	0.933201i	$-0.617003\pi$
$937$	−22.0000	−0.718709	−0.359354	+	0.933201i	$0.617003\pi$
$938$	0	0
$939$	−44.0000	−1.43589
$940$	0	0
$941$	18.0000	0.586783	0.293392	−	0.955992i	$-0.405216\pi$
$941$	18.0000	0.586783	0.293392	+	0.955992i	$0.405216\pi$
$942$	0	0
$943$	−36.0000	−1.17232
$944$	0	0
$945$	8.00000	0.260240
$946$	0	0
$947$	18.0000	0.584921	0.292461	−	0.956278i	$-0.405526\pi$
$947$	18.0000	0.584921	0.292461	+	0.956278i	$0.405526\pi$
$948$	0	0
$949$	−4.00000	−0.129845
$950$	0	0
$951$	12.0000	0.389127
$952$	0	0
$953$	6.00000	0.194359	0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000	0.194359	0.0971795	+	0.995267i	$0.469018\pi$
$954$	0	0
$955$	12.0000	0.388311
$956$	0	0
$957$	0	0
$958$	0	0
$959$	36.0000	1.16250
$960$	0	0
$961$	−15.0000	−0.483871
$962$	0	0
$963$	6.00000	0.193347
$964$	0	0
$965$	26.0000	0.836970
$966$	0	0
$967$	−22.0000	−0.707472	−0.353736	−	0.935345i	$-0.615089\pi$
$967$	−22.0000	−0.707472	−0.353736	+	0.935345i	$0.615089\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	24.0000	0.770197	0.385098	−	0.922876i	$-0.374168\pi$
$971$	24.0000	0.770197	0.385098	+	0.922876i	$0.374168\pi$
$972$	0	0
$973$	−8.00000	−0.256468
$974$	0	0
$975$	−4.00000	−0.128103
$976$	0	0
$977$	−18.0000	−0.575871	−0.287936	−	0.957650i	$-0.592969\pi$
$977$	−18.0000	−0.575871	−0.287936	+	0.957650i	$0.592969\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	−2.00000	−0.0638551
$982$	0	0
$983$	18.0000	0.574111	0.287055	−	0.957914i	$-0.407324\pi$
$983$	18.0000	0.574111	0.287055	+	0.957914i	$0.407324\pi$
$984$	0	0
$985$	−18.0000	−0.573528
$986$	0	0
$987$	−24.0000	−0.763928
$988$	0	0
$989$	−60.0000	−1.90789
$990$	0	0
$991$	4.00000	0.127064	0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000	0.127064	0.0635321	+	0.997980i	$0.479763\pi$
$992$	0	0
$993$	−16.0000	−0.507745
$994$	0	0
$995$	−8.00000	−0.253617
$996$	0	0
$997$	26.0000	0.823428	0.411714	−	0.911313i	$-0.364930\pi$
$997$	26.0000	0.823428	0.411714	+	0.911313i	$0.364930\pi$
$998$	0	0
$999$	8.00000	0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7220.2.a.f.1.1		1
19.18	odd	2		20.2.a.a.1.1	✓	1
57.56	even	2		180.2.a.a.1.1		1
76.75	even	2		80.2.a.b.1.1		1
95.18	even	4		100.2.c.a.49.1		2
95.37	even	4		100.2.c.a.49.2		2
95.94	odd	2		100.2.a.a.1.1		1
133.18	odd	6		980.2.i.i.961.1		2
133.37	odd	6		980.2.i.i.361.1		2
133.75	even	6		980.2.i.c.361.1		2
133.94	even	6		980.2.i.c.961.1		2
133.132	even	2		980.2.a.h.1.1		1
152.37	odd	2		320.2.a.f.1.1		1
152.75	even	2		320.2.a.a.1.1		1
171.56	even	6		1620.2.i.b.1081.1		2
171.94	odd	6		1620.2.i.h.541.1		2
171.113	even	6		1620.2.i.b.541.1		2
171.151	odd	6		1620.2.i.h.1081.1		2
209.208	even	2		2420.2.a.a.1.1		1
228.227	odd	2		720.2.a.h.1.1		1
247.18	even	4		3380.2.f.b.3041.2		2
247.151	even	4		3380.2.f.b.3041.1		2
247.246	odd	2		3380.2.a.c.1.1		1
285.113	odd	4		900.2.d.c.649.1		2
285.227	odd	4		900.2.d.c.649.2		2
285.284	even	2		900.2.a.b.1.1		1
304.37	odd	4		1280.2.d.c.641.2		2
304.75	even	4		1280.2.d.g.641.1		2
304.189	odd	4		1280.2.d.c.641.1		2
304.227	even	4		1280.2.d.g.641.2		2
323.132	odd	4		5780.2.c.a.5201.1		2
323.208	odd	4		5780.2.c.a.5201.2		2
323.322	odd	2		5780.2.a.f.1.1		1
380.227	odd	4		400.2.c.b.49.1		2
380.303	odd	4		400.2.c.b.49.2		2
380.379	even	2		400.2.a.c.1.1		1
399.398	odd	2		8820.2.a.g.1.1		1
456.227	odd	2		2880.2.a.f.1.1		1
456.341	even	2		2880.2.a.m.1.1		1
532.531	odd	2		3920.2.a.h.1.1		1
665.132	odd	4		4900.2.e.f.2549.1		2
665.398	odd	4		4900.2.e.f.2549.2		2
665.664	even	2		4900.2.a.e.1.1		1
760.37	even	4		1600.2.c.d.449.1		2
760.189	odd	2		1600.2.a.c.1.1		1
760.227	odd	4		1600.2.c.e.449.2		2
760.379	even	2		1600.2.a.w.1.1		1
760.493	even	4		1600.2.c.d.449.2		2
760.683	odd	4		1600.2.c.e.449.1		2
836.835	odd	2		9680.2.a.ba.1.1		1
1140.227	even	4		3600.2.f.j.2449.1		2
1140.683	even	4		3600.2.f.j.2449.2		2
1140.1139	odd	2		3600.2.a.be.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.2.a.a.1.1	✓	1	19.18	odd	2
80.2.a.b.1.1		1	76.75	even	2
100.2.a.a.1.1		1	95.94	odd	2
100.2.c.a.49.1		2	95.18	even	4
100.2.c.a.49.2		2	95.37	even	4
180.2.a.a.1.1		1	57.56	even	2
320.2.a.a.1.1		1	152.75	even	2
320.2.a.f.1.1		1	152.37	odd	2
400.2.a.c.1.1		1	380.379	even	2
400.2.c.b.49.1		2	380.227	odd	4
400.2.c.b.49.2		2	380.303	odd	4
720.2.a.h.1.1		1	228.227	odd	2
900.2.a.b.1.1		1	285.284	even	2
900.2.d.c.649.1		2	285.113	odd	4
900.2.d.c.649.2		2	285.227	odd	4
980.2.a.h.1.1		1	133.132	even	2
980.2.i.c.361.1		2	133.75	even	6
980.2.i.c.961.1		2	133.94	even	6
980.2.i.i.361.1		2	133.37	odd	6
980.2.i.i.961.1		2	133.18	odd	6
1280.2.d.c.641.1		2	304.189	odd	4
1280.2.d.c.641.2		2	304.37	odd	4
1280.2.d.g.641.1		2	304.75	even	4
1280.2.d.g.641.2		2	304.227	even	4
1600.2.a.c.1.1		1	760.189	odd	2
1600.2.a.w.1.1		1	760.379	even	2
1600.2.c.d.449.1		2	760.37	even	4
1600.2.c.d.449.2		2	760.493	even	4
1600.2.c.e.449.1		2	760.683	odd	4
1600.2.c.e.449.2		2	760.227	odd	4
1620.2.i.b.541.1		2	171.113	even	6
1620.2.i.b.1081.1		2	171.56	even	6
1620.2.i.h.541.1		2	171.94	odd	6
1620.2.i.h.1081.1		2	171.151	odd	6
2420.2.a.a.1.1		1	209.208	even	2
2880.2.a.f.1.1		1	456.227	odd	2
2880.2.a.m.1.1		1	456.341	even	2
3380.2.a.c.1.1		1	247.246	odd	2
3380.2.f.b.3041.1		2	247.151	even	4
3380.2.f.b.3041.2		2	247.18	even	4
3600.2.a.be.1.1		1	1140.1139	odd	2
3600.2.f.j.2449.1		2	1140.227	even	4
3600.2.f.j.2449.2		2	1140.683	even	4
3920.2.a.h.1.1		1	532.531	odd	2
4900.2.a.e.1.1		1	665.664	even	2
4900.2.e.f.2549.1		2	665.132	odd	4
4900.2.e.f.2549.2		2	665.398	odd	4
5780.2.a.f.1.1		1	323.322	odd	2
5780.2.c.a.5201.1		2	323.132	odd	4
5780.2.c.a.5201.2		2	323.208	odd	4
7220.2.a.f.1.1		1	1.1	even	1	trivial
8820.2.a.g.1.1		1	399.398	odd	2
9680.2.a.ba.1.1		1	836.835	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:	\( N \)	\(=\)	\( 7220 = 2^{2} \cdot 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7220.a (trivial)

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