LMFDB - Embedded newform 3776.2.a.z.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3776,2,Mod(1,3776)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3776.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3776, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 3776 = 2^{6} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3776.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,0,3,0,3,0,-3,0,6,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	yes
Analytic conductor:	$30.1515118032$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 472)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	3776.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

$q+3.00000 q^{3} +3.00000 q^{5} -3.00000 q^{7} +6.00000 q^{9} +6.00000 q^{11} +6.00000 q^{13} +9.00000 q^{15} -2.00000 q^{17} -1.00000 q^{19} -9.00000 q^{21} -8.00000 q^{23} +4.00000 q^{25} +9.00000 q^{27} +1.00000 q^{29} +2.00000 q^{31} +18.0000 q^{33} -9.00000 q^{35} +4.00000 q^{37} +18.0000 q^{39} -1.00000 q^{41} -10.0000 q^{43} +18.0000 q^{45} -6.00000 q^{47} +2.00000 q^{49} -6.00000 q^{51} -5.00000 q^{53} +18.0000 q^{55} -3.00000 q^{57} -1.00000 q^{59} +8.00000 q^{61} -18.0000 q^{63} +18.0000 q^{65} +2.00000 q^{67} -24.0000 q^{69} +4.00000 q^{71} -8.00000 q^{73} +12.0000 q^{75} -18.0000 q^{77} +11.0000 q^{79} +9.00000 q^{81} -10.0000 q^{83} -6.00000 q^{85} +3.00000 q^{87} -16.0000 q^{89} -18.0000 q^{91} +6.00000 q^{93} -3.00000 q^{95} -4.00000 q^{97} +36.0000 q^{99} +O(q^{100})$

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 $

$2$	0	0
$2$	0	0
$3$	3.00000	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$3$	3.00000	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$4$	0	0
$5$	3.00000	1.34164	0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000	1.34164	0.670820	+	0.741620i	$0.265942\pi$
$6$	0	0
$7$	−3.00000	−1.13389	−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000	−1.13389	−0.566947	+	0.823754i	$0.691875\pi$
$8$	0	0
$9$	6.00000	2.00000
$10$	0	0
$11$	6.00000	1.80907	0.904534	−	0.426401i	$-0.140219\pi$
$11$	6.00000	1.80907	0.904534	+	0.426401i	$0.140219\pi$
$12$	0	0
$13$	6.00000	1.66410	0.832050	−	0.554700i	$-0.187167\pi$
$13$	6.00000	1.66410	0.832050	+	0.554700i	$0.187167\pi$
$14$	0	0
$15$	9.00000	2.32379
$16$	0	0
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	0	0
$19$	−1.00000	−0.229416	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000	−0.229416	−0.114708	+	0.993399i	$0.536593\pi$
$20$	0	0
$21$	−9.00000	−1.96396
$22$	0	0
$23$	−8.00000	−1.66812	−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000	−1.66812	−0.834058	+	0.551677i	$0.813988\pi$
$24$	0	0
$25$	4.00000	0.800000
$26$	0	0
$27$	9.00000	1.73205
$28$	0	0
$29$	1.00000	0.185695	0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000	0.185695	0.0928477	+	0.995680i	$0.470403\pi$
$30$	0	0
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	0	0
$33$	18.0000	3.13340
$34$	0	0
$35$	−9.00000	−1.52128
$36$	0	0
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	0	0
$39$	18.0000	2.88231
$40$	0	0
$41$	−1.00000	−0.156174	−0.0780869	−	0.996947i	$-0.524881\pi$
$41$	−1.00000	−0.156174	−0.0780869	+	0.996947i	$0.524881\pi$
$42$	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
$45$	18.0000	2.68328
$46$	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
$49$	2.00000	0.285714
$50$	0	0
$51$	−6.00000	−0.840168
$52$	0	0
$53$	−5.00000	−0.686803	−0.343401	−	0.939189i	$-0.611579\pi$
$53$	−5.00000	−0.686803	−0.343401	+	0.939189i	$0.611579\pi$
$54$	0	0
$55$	18.0000	2.42712
$56$	0	0
$57$	−3.00000	−0.397360
$58$	0	0
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	0	0
$61$	8.00000	1.02430	0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000	1.02430	0.512148	+	0.858898i	$0.328850\pi$
$62$	0	0
$63$	−18.0000	−2.26779
$64$	0	0
$65$	18.0000	2.23263
$66$	0	0
$67$	2.00000	0.244339	0.122169	−	0.992509i	$-0.461015\pi$
$67$	2.00000	0.244339	0.122169	+	0.992509i	$0.461015\pi$
$68$	0	0
$69$	−24.0000	−2.88926
$70$	0	0
$71$	4.00000	0.474713	0.237356	−	0.971423i	$-0.423719\pi$
$71$	4.00000	0.474713	0.237356	+	0.971423i	$0.423719\pi$
$72$	0	0
$73$	−8.00000	−0.936329	−0.468165	−	0.883641i	$-0.655085\pi$
$73$	−8.00000	−0.936329	−0.468165	+	0.883641i	$0.655085\pi$
$74$	0	0
$75$	12.0000	1.38564
$76$	0	0
$77$	−18.0000	−2.05129
$78$	0	0
$79$	11.0000	1.23760	0.618798	−	0.785550i	$-0.287620\pi$
$79$	11.0000	1.23760	0.618798	+	0.785550i	$0.287620\pi$
$80$	0	0
$81$	9.00000	1.00000
$82$	0	0
$83$	−10.0000	−1.09764	−0.548821	−	0.835940i	$-0.684923\pi$
$83$	−10.0000	−1.09764	−0.548821	+	0.835940i	$0.684923\pi$
$84$	0	0
$85$	−6.00000	−0.650791
$86$	0	0
$87$	3.00000	0.321634
$88$	0	0
$89$	−16.0000	−1.69600	−0.847998	−	0.529999i	$-0.822192\pi$
$89$	−16.0000	−1.69600	−0.847998	+	0.529999i	$0.822192\pi$
$90$	0	0
$91$	−18.0000	−1.88691
$92$	0	0
$93$	6.00000	0.622171
$94$	0	0
$95$	−3.00000	−0.307794
$96$	0	0
$97$	−4.00000	−0.406138	−0.203069	−	0.979164i	$-0.565092\pi$
$97$	−4.00000	−0.406138	−0.203069	+	0.979164i	$0.565092\pi$
$98$	0	0
$99$	36.0000	3.61814
$100$	0	0
$101$	10.0000	0.995037	0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000	0.995037	0.497519	+	0.867453i	$0.334245\pi$
$102$	0	0
$103$	−20.0000	−1.97066	−0.985329	−	0.170664i	$-0.945409\pi$
$103$	−20.0000	−1.97066	−0.985329	+	0.170664i	$0.945409\pi$
$104$	0	0
$105$	−27.0000	−2.63493
$106$	0	0
$107$	15.0000	1.45010	0.725052	−	0.688694i	$-0.241816\pi$
$107$	15.0000	1.45010	0.725052	+	0.688694i	$0.241816\pi$
$108$	0	0
$109$	−8.00000	−0.766261	−0.383131	−	0.923694i	$-0.625154\pi$
$109$	−8.00000	−0.766261	−0.383131	+	0.923694i	$0.625154\pi$
$110$	0	0
$111$	12.0000	1.13899
$112$	0	0
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	0	0
$115$	−24.0000	−2.23801
$116$	0	0
$117$	36.0000	3.32820
$118$	0	0
$119$	6.00000	0.550019
$120$	0	0
$121$	25.0000	2.27273
$122$	0	0
$123$	−3.00000	−0.270501
$124$	0	0
$125$	−3.00000	−0.268328
$126$	0	0
$127$	−13.0000	−1.15356	−0.576782	−	0.816898i	$-0.695692\pi$
$127$	−13.0000	−1.15356	−0.576782	+	0.816898i	$0.695692\pi$
$128$	0	0
$129$	−30.0000	−2.64135
$130$	0	0
$131$	22.0000	1.92215	0.961074	−	0.276289i	$-0.0891049\pi$
$131$	22.0000	1.92215	0.961074	+	0.276289i	$0.0891049\pi$
$132$	0	0
$133$	3.00000	0.260133
$134$	0	0
$135$	27.0000	2.32379
$136$	0	0
$137$	3.00000	0.256307	0.128154	−	0.991754i	$-0.459095\pi$
$137$	3.00000	0.256307	0.128154	+	0.991754i	$0.459095\pi$
$138$	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
$141$	−18.0000	−1.51587
$142$	0	0
$143$	36.0000	3.01047
$144$	0	0
$145$	3.00000	0.249136
$146$	0	0
$147$	6.00000	0.494872
$148$	0	0
$149$	18.0000	1.47462	0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000	1.47462	0.737309	+	0.675556i	$0.236096\pi$
$150$	0	0
$151$	−2.00000	−0.162758	−0.0813788	−	0.996683i	$-0.525932\pi$
$151$	−2.00000	−0.162758	−0.0813788	+	0.996683i	$0.525932\pi$
$152$	0	0
$153$	−12.0000	−0.970143
$154$	0	0
$155$	6.00000	0.481932
$156$	0	0
$157$	12.0000	0.957704	0.478852	−	0.877896i	$-0.341053\pi$
$157$	12.0000	0.957704	0.478852	+	0.877896i	$0.341053\pi$
$158$	0	0
$159$	−15.0000	−1.18958
$160$	0	0
$161$	24.0000	1.89146
$162$	0	0
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	0	0
$165$	54.0000	4.20389
$166$	0	0
$167$	−3.00000	−0.232147	−0.116073	−	0.993241i	$-0.537031\pi$
$167$	−3.00000	−0.232147	−0.116073	+	0.993241i	$0.537031\pi$
$168$	0	0
$169$	23.0000	1.76923
$170$	0	0
$171$	−6.00000	−0.458831
$172$	0	0
$173$	8.00000	0.608229	0.304114	−	0.952636i	$-0.401639\pi$
$173$	8.00000	0.608229	0.304114	+	0.952636i	$0.401639\pi$
$174$	0	0
$175$	−12.0000	−0.907115
$176$	0	0
$177$	−3.00000	−0.225494
$178$	0	0
$179$	−4.00000	−0.298974	−0.149487	−	0.988764i	$-0.547762\pi$
$179$	−4.00000	−0.298974	−0.149487	+	0.988764i	$0.547762\pi$
$180$	0	0
$181$	−7.00000	−0.520306	−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000	−0.520306	−0.260153	+	0.965567i	$0.583773\pi$
$182$	0	0
$183$	24.0000	1.77413
$184$	0	0
$185$	12.0000	0.882258
$186$	0	0
$187$	−12.0000	−0.877527
$188$	0	0
$189$	−27.0000	−1.96396
$190$	0	0
$191$	2.00000	0.144715	0.0723575	−	0.997379i	$-0.476948\pi$
$191$	2.00000	0.144715	0.0723575	+	0.997379i	$0.476948\pi$
$192$	0	0
$193$	11.0000	0.791797	0.395899	−	0.918294i	$-0.370433\pi$
$193$	11.0000	0.791797	0.395899	+	0.918294i	$0.370433\pi$
$194$	0	0
$195$	54.0000	3.86702
$196$	0	0
$197$	6.00000	0.427482	0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000	0.427482	0.213741	+	0.976890i	$0.431435\pi$
$198$	0	0
$199$	−11.0000	−0.779769	−0.389885	−	0.920864i	$-0.627485\pi$
$199$	−11.0000	−0.779769	−0.389885	+	0.920864i	$0.627485\pi$
$200$	0	0
$201$	6.00000	0.423207
$202$	0	0
$203$	−3.00000	−0.210559
$204$	0	0
$205$	−3.00000	−0.209529
$206$	0	0
$207$	−48.0000	−3.33623
$208$	0	0
$209$	−6.00000	−0.415029
$210$	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
$213$	12.0000	0.822226
$214$	0	0
$215$	−30.0000	−2.04598
$216$	0	0
$217$	−6.00000	−0.407307
$218$	0	0
$219$	−24.0000	−1.62177
$220$	0	0
$221$	−12.0000	−0.807207
$222$	0	0
$223$	8.00000	0.535720	0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000	0.535720	0.267860	+	0.963458i	$0.413684\pi$
$224$	0	0
$225$	24.0000	1.60000
$226$	0	0
$227$	8.00000	0.530979	0.265489	−	0.964114i	$-0.414466\pi$
$227$	8.00000	0.530979	0.265489	+	0.964114i	$0.414466\pi$
$228$	0	0
$229$	−2.00000	−0.132164	−0.0660819	−	0.997814i	$-0.521050\pi$
$229$	−2.00000	−0.132164	−0.0660819	+	0.997814i	$0.521050\pi$
$230$	0	0
$231$	−54.0000	−3.55294
$232$	0	0
$233$	−14.0000	−0.917170	−0.458585	−	0.888650i	$-0.651644\pi$
$233$	−14.0000	−0.917170	−0.458585	+	0.888650i	$0.651644\pi$
$234$	0	0
$235$	−18.0000	−1.17419
$236$	0	0
$237$	33.0000	2.14358
$238$	0	0
$239$	−15.0000	−0.970269	−0.485135	−	0.874439i	$-0.661229\pi$
$239$	−15.0000	−0.970269	−0.485135	+	0.874439i	$0.661229\pi$
$240$	0	0
$241$	25.0000	1.61039	0.805196	−	0.593009i	$-0.202060\pi$
$241$	25.0000	1.61039	0.805196	+	0.593009i	$0.202060\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	6.00000	0.383326
$246$	0	0
$247$	−6.00000	−0.381771
$248$	0	0
$249$	−30.0000	−1.90117
$250$	0	0
$251$	5.00000	0.315597	0.157799	−	0.987471i	$-0.449560\pi$
$251$	5.00000	0.315597	0.157799	+	0.987471i	$0.449560\pi$
$252$	0	0
$253$	−48.0000	−3.01773
$254$	0	0
$255$	−18.0000	−1.12720
$256$	0	0
$257$	21.0000	1.30994	0.654972	−	0.755653i	$-0.272680\pi$
$257$	21.0000	1.30994	0.654972	+	0.755653i	$0.272680\pi$
$258$	0	0
$259$	−12.0000	−0.745644
$260$	0	0
$261$	6.00000	0.371391
$262$	0	0
$263$	−19.0000	−1.17159	−0.585795	−	0.810459i	$-0.699218\pi$
$263$	−19.0000	−1.17159	−0.585795	+	0.810459i	$0.699218\pi$
$264$	0	0
$265$	−15.0000	−0.921443
$266$	0	0
$267$	−48.0000	−2.93755
$268$	0	0
$269$	6.00000	0.365826	0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000	0.365826	0.182913	+	0.983129i	$0.441447\pi$
$270$	0	0
$271$	−1.00000	−0.0607457	−0.0303728	−	0.999539i	$-0.509669\pi$
$271$	−1.00000	−0.0607457	−0.0303728	+	0.999539i	$0.509669\pi$
$272$	0	0
$273$	−54.0000	−3.26823
$274$	0	0
$275$	24.0000	1.44725
$276$	0	0
$277$	−9.00000	−0.540758	−0.270379	−	0.962754i	$-0.587149\pi$
$277$	−9.00000	−0.540758	−0.270379	+	0.962754i	$0.587149\pi$
$278$	0	0
$279$	12.0000	0.718421
$280$	0	0
$281$	3.00000	0.178965	0.0894825	−	0.995988i	$-0.471479\pi$
$281$	3.00000	0.178965	0.0894825	+	0.995988i	$0.471479\pi$
$282$	0	0
$283$	8.00000	0.475551	0.237775	−	0.971320i	$-0.423582\pi$
$283$	8.00000	0.475551	0.237775	+	0.971320i	$0.423582\pi$
$284$	0	0
$285$	−9.00000	−0.533114
$286$	0	0
$287$	3.00000	0.177084
$288$	0	0
$289$	−13.0000	−0.764706
$290$	0	0
$291$	−12.0000	−0.703452
$292$	0	0
$293$	1.00000	0.0584206	0.0292103	−	0.999573i	$-0.490701\pi$
$293$	1.00000	0.0584206	0.0292103	+	0.999573i	$0.490701\pi$
$294$	0	0
$295$	−3.00000	−0.174667
$296$	0	0
$297$	54.0000	3.13340
$298$	0	0
$299$	−48.0000	−2.77591
$300$	0	0
$301$	30.0000	1.72917
$302$	0	0
$303$	30.0000	1.72345
$304$	0	0
$305$	24.0000	1.37424
$306$	0	0
$307$	−23.0000	−1.31268	−0.656340	−	0.754466i	$-0.727896\pi$
$307$	−23.0000	−1.31268	−0.656340	+	0.754466i	$0.727896\pi$
$308$	0	0
$309$	−60.0000	−3.41328
$310$	0	0
$311$	−31.0000	−1.75785	−0.878924	−	0.476961i	$-0.841738\pi$
$311$	−31.0000	−1.75785	−0.878924	+	0.476961i	$0.841738\pi$
$312$	0	0
$313$	0	0		−	1.00000i	$-0.5\pi$
$313$	0	0			1.00000i	$0.5\pi$
$314$	0	0
$315$	−54.0000	−3.04256
$316$	0	0
$317$	−30.0000	−1.68497	−0.842484	−	0.538721i	$-0.818908\pi$
$317$	−30.0000	−1.68497	−0.842484	+	0.538721i	$0.818908\pi$
$318$	0	0
$319$	6.00000	0.335936
$320$	0	0
$321$	45.0000	2.51166
$322$	0	0
$323$	2.00000	0.111283
$324$	0	0
$325$	24.0000	1.33128
$326$	0	0
$327$	−24.0000	−1.32720
$328$	0	0
$329$	18.0000	0.992372
$330$	0	0
$331$	−17.0000	−0.934405	−0.467202	−	0.884150i	$-0.654738\pi$
$331$	−17.0000	−0.934405	−0.467202	+	0.884150i	$0.654738\pi$
$332$	0	0
$333$	24.0000	1.31519
$334$	0	0
$335$	6.00000	0.327815
$336$	0	0
$337$	20.0000	1.08947	0.544735	−	0.838608i	$-0.316630\pi$
$337$	20.0000	1.08947	0.544735	+	0.838608i	$0.316630\pi$
$338$	0	0
$339$	−18.0000	−0.977626
$340$	0	0
$341$	12.0000	0.649836
$342$	0	0
$343$	15.0000	0.809924
$344$	0	0
$345$	−72.0000	−3.87635
$346$	0	0
$347$	18.0000	0.966291	0.483145	−	0.875540i	$-0.339494\pi$
$347$	18.0000	0.966291	0.483145	+	0.875540i	$0.339494\pi$
$348$	0	0
$349$	18.0000	0.963518	0.481759	−	0.876304i	$-0.339998\pi$
$349$	18.0000	0.963518	0.481759	+	0.876304i	$0.339998\pi$
$350$	0	0
$351$	54.0000	2.88231
$352$	0	0
$353$	0	0		−	1.00000i	$-0.5\pi$
$353$	0	0			1.00000i	$0.5\pi$
$354$	0	0
$355$	12.0000	0.636894
$356$	0	0
$357$	18.0000	0.952661
$358$	0	0
$359$	23.0000	1.21389	0.606947	−	0.794742i	$-0.292394\pi$
$359$	23.0000	1.21389	0.606947	+	0.794742i	$0.292394\pi$
$360$	0	0
$361$	−18.0000	−0.947368
$362$	0	0
$363$	75.0000	3.93648
$364$	0	0
$365$	−24.0000	−1.25622
$366$	0	0
$367$	−14.0000	−0.730794	−0.365397	−	0.930852i	$-0.619067\pi$
$367$	−14.0000	−0.730794	−0.365397	+	0.930852i	$0.619067\pi$
$368$	0	0
$369$	−6.00000	−0.312348
$370$	0	0
$371$	15.0000	0.778761
$372$	0	0
$373$	2.00000	0.103556	0.0517780	−	0.998659i	$-0.483511\pi$
$373$	2.00000	0.103556	0.0517780	+	0.998659i	$0.483511\pi$
$374$	0	0
$375$	−9.00000	−0.464758
$376$	0	0
$377$	6.00000	0.309016
$378$	0	0
$379$	1.00000	0.0513665	0.0256833	−	0.999670i	$-0.491824\pi$
$379$	1.00000	0.0513665	0.0256833	+	0.999670i	$0.491824\pi$
$380$	0	0
$381$	−39.0000	−1.99803
$382$	0	0
$383$	−16.0000	−0.817562	−0.408781	−	0.912633i	$-0.634046\pi$
$383$	−16.0000	−0.817562	−0.408781	+	0.912633i	$0.634046\pi$
$384$	0	0
$385$	−54.0000	−2.75209
$386$	0	0
$387$	−60.0000	−3.04997
$388$	0	0
$389$	18.0000	0.912636	0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000	0.912636	0.456318	+	0.889817i	$0.349168\pi$
$390$	0	0
$391$	16.0000	0.809155
$392$	0	0
$393$	66.0000	3.32926
$394$	0	0
$395$	33.0000	1.66041
$396$	0	0
$397$	−2.00000	−0.100377	−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000	−0.100377	−0.0501886	+	0.998740i	$0.515982\pi$
$398$	0	0
$399$	9.00000	0.450564
$400$	0	0
$401$	24.0000	1.19850	0.599251	−	0.800561i	$-0.295465\pi$
$401$	24.0000	1.19850	0.599251	+	0.800561i	$0.295465\pi$
$402$	0	0
$403$	12.0000	0.597763
$404$	0	0
$405$	27.0000	1.34164
$406$	0	0
$407$	24.0000	1.18964
$408$	0	0
$409$	−32.0000	−1.58230	−0.791149	−	0.611623i	$-0.790517\pi$
$409$	−32.0000	−1.58230	−0.791149	+	0.611623i	$0.790517\pi$
$410$	0	0
$411$	9.00000	0.443937
$412$	0	0
$413$	3.00000	0.147620
$414$	0	0
$415$	−30.0000	−1.47264
$416$	0	0
$417$	−12.0000	−0.587643
$418$	0	0
$419$	12.0000	0.586238	0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000	0.586238	0.293119	+	0.956076i	$0.405307\pi$
$420$	0	0
$421$	16.0000	0.779792	0.389896	−	0.920859i	$-0.372511\pi$
$421$	16.0000	0.779792	0.389896	+	0.920859i	$0.372511\pi$
$422$	0	0
$423$	−36.0000	−1.75038
$424$	0	0
$425$	−8.00000	−0.388057
$426$	0	0
$427$	−24.0000	−1.16144
$428$	0	0
$429$	108.000	5.21429
$430$	0	0
$431$	30.0000	1.44505	0.722525	−	0.691345i	$-0.242982\pi$
$431$	30.0000	1.44505	0.722525	+	0.691345i	$0.242982\pi$
$432$	0	0
$433$	35.0000	1.68199	0.840996	−	0.541041i	$-0.181970\pi$
$433$	35.0000	1.68199	0.840996	+	0.541041i	$0.181970\pi$
$434$	0	0
$435$	9.00000	0.431517
$436$	0	0
$437$	8.00000	0.382692
$438$	0	0
$439$	−4.00000	−0.190910	−0.0954548	−	0.995434i	$-0.530431\pi$
$439$	−4.00000	−0.190910	−0.0954548	+	0.995434i	$0.530431\pi$
$440$	0	0
$441$	12.0000	0.571429
$442$	0	0
$443$	−8.00000	−0.380091	−0.190046	−	0.981775i	$-0.560864\pi$
$443$	−8.00000	−0.380091	−0.190046	+	0.981775i	$0.560864\pi$
$444$	0	0
$445$	−48.0000	−2.27542
$446$	0	0
$447$	54.0000	2.55411
$448$	0	0
$449$	5.00000	0.235965	0.117982	−	0.993016i	$-0.462357\pi$
$449$	5.00000	0.235965	0.117982	+	0.993016i	$0.462357\pi$
$450$	0	0
$451$	−6.00000	−0.282529
$452$	0	0
$453$	−6.00000	−0.281905
$454$	0	0
$455$	−54.0000	−2.53156
$456$	0	0
$457$	2.00000	0.0935561	0.0467780	−	0.998905i	$-0.485105\pi$
$457$	2.00000	0.0935561	0.0467780	+	0.998905i	$0.485105\pi$
$458$	0	0
$459$	−18.0000	−0.840168
$460$	0	0
$461$	−22.0000	−1.02464	−0.512321	−	0.858794i	$-0.671214\pi$
$461$	−22.0000	−1.02464	−0.512321	+	0.858794i	$0.671214\pi$
$462$	0	0
$463$	24.0000	1.11537	0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000	1.11537	0.557687	+	0.830051i	$0.311689\pi$
$464$	0	0
$465$	18.0000	0.834730
$466$	0	0
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	0	0
$469$	−6.00000	−0.277054
$470$	0	0
$471$	36.0000	1.65879
$472$	0	0
$473$	−60.0000	−2.75880
$474$	0	0
$475$	−4.00000	−0.183533
$476$	0	0
$477$	−30.0000	−1.37361
$478$	0	0
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	0	0
$481$	24.0000	1.09431
$482$	0	0
$483$	72.0000	3.27611
$484$	0	0
$485$	−12.0000	−0.544892
$486$	0	0
$487$	−23.0000	−1.04223	−0.521115	−	0.853487i	$-0.674484\pi$
$487$	−23.0000	−1.04223	−0.521115	+	0.853487i	$0.674484\pi$
$488$	0	0
$489$	−12.0000	−0.542659
$490$	0	0
$491$	−15.0000	−0.676941	−0.338470	−	0.940977i	$-0.609909\pi$
$491$	−15.0000	−0.676941	−0.338470	+	0.940977i	$0.609909\pi$
$492$	0	0
$493$	−2.00000	−0.0900755
$494$	0	0
$495$	108.000	4.85424
$496$	0	0
$497$	−12.0000	−0.538274
$498$	0	0
$499$	−21.0000	−0.940089	−0.470045	−	0.882643i	$-0.655762\pi$
$499$	−21.0000	−0.940089	−0.470045	+	0.882643i	$0.655762\pi$
$500$	0	0
$501$	−9.00000	−0.402090
$502$	0	0
$503$	−28.0000	−1.24846	−0.624229	−	0.781241i	$-0.714587\pi$
$503$	−28.0000	−1.24846	−0.624229	+	0.781241i	$0.714587\pi$
$504$	0	0
$505$	30.0000	1.33498
$506$	0	0
$507$	69.0000	3.06440
$508$	0	0
$509$	8.00000	0.354594	0.177297	−	0.984157i	$-0.443265\pi$
$509$	8.00000	0.354594	0.177297	+	0.984157i	$0.443265\pi$
$510$	0	0
$511$	24.0000	1.06170
$512$	0	0
$513$	−9.00000	−0.397360
$514$	0	0
$515$	−60.0000	−2.64392
$516$	0	0
$517$	−36.0000	−1.58328
$518$	0	0
$519$	24.0000	1.05348
$520$	0	0
$521$	−18.0000	−0.788594	−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000	−0.788594	−0.394297	+	0.918983i	$0.629012\pi$
$522$	0	0
$523$	1.00000	0.0437269	0.0218635	−	0.999761i	$-0.493040\pi$
$523$	1.00000	0.0437269	0.0218635	+	0.999761i	$0.493040\pi$
$524$	0	0
$525$	−36.0000	−1.57117
$526$	0	0
$527$	−4.00000	−0.174243
$528$	0	0
$529$	41.0000	1.78261
$530$	0	0
$531$	−6.00000	−0.260378
$532$	0	0
$533$	−6.00000	−0.259889
$534$	0	0
$535$	45.0000	1.94552
$536$	0	0
$537$	−12.0000	−0.517838
$538$	0	0
$539$	12.0000	0.516877
$540$	0	0
$541$	−20.0000	−0.859867	−0.429934	−	0.902861i	$-0.641463\pi$
$541$	−20.0000	−0.859867	−0.429934	+	0.902861i	$0.641463\pi$
$542$	0	0
$543$	−21.0000	−0.901196
$544$	0	0
$545$	−24.0000	−1.02805
$546$	0	0
$547$	28.0000	1.19719	0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000	1.19719	0.598597	+	0.801050i	$0.295725\pi$
$548$	0	0
$549$	48.0000	2.04859
$550$	0	0
$551$	−1.00000	−0.0426014
$552$	0	0
$553$	−33.0000	−1.40330
$554$	0	0
$555$	36.0000	1.52811
$556$	0	0
$557$	3.00000	0.127114	0.0635570	−	0.997978i	$-0.479756\pi$
$557$	3.00000	0.127114	0.0635570	+	0.997978i	$0.479756\pi$
$558$	0	0
$559$	−60.0000	−2.53773
$560$	0	0
$561$	−36.0000	−1.51992
$562$	0	0
$563$	−24.0000	−1.01148	−0.505740	−	0.862686i	$-0.668780\pi$
$563$	−24.0000	−1.01148	−0.505740	+	0.862686i	$0.668780\pi$
$564$	0	0
$565$	−18.0000	−0.757266
$566$	0	0
$567$	−27.0000	−1.13389
$568$	0	0
$569$	6.00000	0.251533	0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000	0.251533	0.125767	+	0.992060i	$0.459861\pi$
$570$	0	0
$571$	−26.0000	−1.08807	−0.544033	−	0.839064i	$-0.683103\pi$
$571$	−26.0000	−1.08807	−0.544033	+	0.839064i	$0.683103\pi$
$572$	0	0
$573$	6.00000	0.250654
$574$	0	0
$575$	−32.0000	−1.33449
$576$	0	0
$577$	−31.0000	−1.29055	−0.645273	−	0.763952i	$-0.723257\pi$
$577$	−31.0000	−1.29055	−0.645273	+	0.763952i	$0.723257\pi$
$578$	0	0
$579$	33.0000	1.37143
$580$	0	0
$581$	30.0000	1.24461
$582$	0	0
$583$	−30.0000	−1.24247
$584$	0	0
$585$	108.000	4.46525
$586$	0	0
$587$	−28.0000	−1.15568	−0.577842	−	0.816149i	$-0.696105\pi$
$587$	−28.0000	−1.15568	−0.577842	+	0.816149i	$0.696105\pi$
$588$	0	0
$589$	−2.00000	−0.0824086
$590$	0	0
$591$	18.0000	0.740421
$592$	0	0
$593$	−27.0000	−1.10876	−0.554379	−	0.832265i	$-0.687044\pi$
$593$	−27.0000	−1.10876	−0.554379	+	0.832265i	$0.687044\pi$
$594$	0	0
$595$	18.0000	0.737928
$596$	0	0
$597$	−33.0000	−1.35060
$598$	0	0
$599$	−9.00000	−0.367730	−0.183865	−	0.982952i	$-0.558861\pi$
$599$	−9.00000	−0.367730	−0.183865	+	0.982952i	$0.558861\pi$
$600$	0	0
$601$	−8.00000	−0.326327	−0.163163	−	0.986599i	$-0.552170\pi$
$601$	−8.00000	−0.326327	−0.163163	+	0.986599i	$0.552170\pi$
$602$	0	0
$603$	12.0000	0.488678
$604$	0	0
$605$	75.0000	3.04918
$606$	0	0
$607$	−3.00000	−0.121766	−0.0608831	−	0.998145i	$-0.519392\pi$
$607$	−3.00000	−0.121766	−0.0608831	+	0.998145i	$0.519392\pi$
$608$	0	0
$609$	−9.00000	−0.364698
$610$	0	0
$611$	−36.0000	−1.45640
$612$	0	0
$613$	32.0000	1.29247	0.646234	−	0.763139i	$-0.276343\pi$
$613$	32.0000	1.29247	0.646234	+	0.763139i	$0.276343\pi$
$614$	0	0
$615$	−9.00000	−0.362915
$616$	0	0
$617$	−23.0000	−0.925945	−0.462973	−	0.886373i	$-0.653217\pi$
$617$	−23.0000	−0.925945	−0.462973	+	0.886373i	$0.653217\pi$
$618$	0	0
$619$	−7.00000	−0.281354	−0.140677	−	0.990056i	$-0.544928\pi$
$619$	−7.00000	−0.281354	−0.140677	+	0.990056i	$0.544928\pi$
$620$	0	0
$621$	−72.0000	−2.88926
$622$	0	0
$623$	48.0000	1.92308
$624$	0	0
$625$	−29.0000	−1.16000
$626$	0	0
$627$	−18.0000	−0.718851
$628$	0	0
$629$	−8.00000	−0.318981
$630$	0	0
$631$	40.0000	1.59237	0.796187	−	0.605050i	$-0.206847\pi$
$631$	40.0000	1.59237	0.796187	+	0.605050i	$0.206847\pi$
$632$	0	0
$633$	48.0000	1.90783
$634$	0	0
$635$	−39.0000	−1.54767
$636$	0	0
$637$	12.0000	0.475457
$638$	0	0
$639$	24.0000	0.949425
$640$	0	0
$641$	42.0000	1.65890	0.829450	−	0.558581i	$-0.188654\pi$
$641$	42.0000	1.65890	0.829450	+	0.558581i	$0.188654\pi$
$642$	0	0
$643$	47.0000	1.85350	0.926750	−	0.375680i	$-0.122591\pi$
$643$	47.0000	1.85350	0.926750	+	0.375680i	$0.122591\pi$
$644$	0	0
$645$	−90.0000	−3.54375
$646$	0	0
$647$	9.00000	0.353827	0.176913	−	0.984226i	$-0.443389\pi$
$647$	9.00000	0.353827	0.176913	+	0.984226i	$0.443389\pi$
$648$	0	0
$649$	−6.00000	−0.235521
$650$	0	0
$651$	−18.0000	−0.705476
$652$	0	0
$653$	27.0000	1.05659	0.528296	−	0.849060i	$-0.322831\pi$
$653$	27.0000	1.05659	0.528296	+	0.849060i	$0.322831\pi$
$654$	0	0
$655$	66.0000	2.57883
$656$	0	0
$657$	−48.0000	−1.87266
$658$	0	0
$659$	36.0000	1.40236	0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000	1.40236	0.701180	+	0.712984i	$0.252657\pi$
$660$	0	0
$661$	11.0000	0.427850	0.213925	−	0.976850i	$-0.431375\pi$
$661$	11.0000	0.427850	0.213925	+	0.976850i	$0.431375\pi$
$662$	0	0
$663$	−36.0000	−1.39812
$664$	0	0
$665$	9.00000	0.349005
$666$	0	0
$667$	−8.00000	−0.309761
$668$	0	0
$669$	24.0000	0.927894
$670$	0	0
$671$	48.0000	1.85302
$672$	0	0
$673$	−36.0000	−1.38770	−0.693849	−	0.720121i	$-0.744086\pi$
$673$	−36.0000	−1.38770	−0.693849	+	0.720121i	$0.744086\pi$
$674$	0	0
$675$	36.0000	1.38564
$676$	0	0
$677$	−34.0000	−1.30673	−0.653363	−	0.757045i	$-0.726642\pi$
$677$	−34.0000	−1.30673	−0.653363	+	0.757045i	$0.726642\pi$
$678$	0	0
$679$	12.0000	0.460518
$680$	0	0
$681$	24.0000	0.919682
$682$	0	0
$683$	46.0000	1.76014	0.880071	−	0.474843i	$-0.157495\pi$
$683$	46.0000	1.76014	0.880071	+	0.474843i	$0.157495\pi$
$684$	0	0
$685$	9.00000	0.343872
$686$	0	0
$687$	−6.00000	−0.228914
$688$	0	0
$689$	−30.0000	−1.14291
$690$	0	0
$691$	20.0000	0.760836	0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000	0.760836	0.380418	+	0.924815i	$0.375780\pi$
$692$	0	0
$693$	−108.000	−4.10258
$694$	0	0
$695$	−12.0000	−0.455186
$696$	0	0
$697$	2.00000	0.0757554
$698$	0	0
$699$	−42.0000	−1.58859
$700$	0	0
$701$	36.0000	1.35970	0.679851	−	0.733351i	$-0.262045\pi$
$701$	36.0000	1.35970	0.679851	+	0.733351i	$0.262045\pi$
$702$	0	0
$703$	−4.00000	−0.150863
$704$	0	0
$705$	−54.0000	−2.03376
$706$	0	0
$707$	−30.0000	−1.12827
$708$	0	0
$709$	25.0000	0.938895	0.469447	−	0.882960i	$-0.344453\pi$
$709$	25.0000	0.938895	0.469447	+	0.882960i	$0.344453\pi$
$710$	0	0
$711$	66.0000	2.47519
$712$	0	0
$713$	−16.0000	−0.599205
$714$	0	0
$715$	108.000	4.03897
$716$	0	0
$717$	−45.0000	−1.68056
$718$	0	0
$719$	−8.00000	−0.298350	−0.149175	−	0.988811i	$-0.547662\pi$
$719$	−8.00000	−0.298350	−0.149175	+	0.988811i	$0.547662\pi$
$720$	0	0
$721$	60.0000	2.23452
$722$	0	0
$723$	75.0000	2.78928
$724$	0	0
$725$	4.00000	0.148556
$726$	0	0
$727$	32.0000	1.18681	0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000	1.18681	0.593407	+	0.804902i	$0.297782\pi$
$728$	0	0
$729$	−27.0000	−1.00000
$730$	0	0
$731$	20.0000	0.739727
$732$	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
$735$	18.0000	0.663940
$736$	0	0
$737$	12.0000	0.442026
$738$	0	0
$739$	−16.0000	−0.588570	−0.294285	−	0.955718i	$-0.595081\pi$
$739$	−16.0000	−0.588570	−0.294285	+	0.955718i	$0.595081\pi$
$740$	0	0
$741$	−18.0000	−0.661247
$742$	0	0
$743$	−40.0000	−1.46746	−0.733729	−	0.679442i	$-0.762222\pi$
$743$	−40.0000	−1.46746	−0.733729	+	0.679442i	$0.762222\pi$
$744$	0	0
$745$	54.0000	1.97841
$746$	0	0
$747$	−60.0000	−2.19529
$748$	0	0
$749$	−45.0000	−1.64426
$750$	0	0
$751$	−22.0000	−0.802791	−0.401396	−	0.915905i	$-0.631475\pi$
$751$	−22.0000	−0.802791	−0.401396	+	0.915905i	$0.631475\pi$
$752$	0	0
$753$	15.0000	0.546630
$754$	0	0
$755$	−6.00000	−0.218362
$756$	0	0
$757$	−19.0000	−0.690567	−0.345283	−	0.938498i	$-0.612217\pi$
$757$	−19.0000	−0.690567	−0.345283	+	0.938498i	$0.612217\pi$
$758$	0	0
$759$	−144.000	−5.22687
$760$	0	0
$761$	−3.00000	−0.108750	−0.0543750	−	0.998521i	$-0.517317\pi$
$761$	−3.00000	−0.108750	−0.0543750	+	0.998521i	$0.517317\pi$
$762$	0	0
$763$	24.0000	0.868858
$764$	0	0
$765$	−36.0000	−1.30158
$766$	0	0
$767$	−6.00000	−0.216647
$768$	0	0
$769$	−14.0000	−0.504853	−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000	−0.504853	−0.252426	+	0.967616i	$0.581229\pi$
$770$	0	0
$771$	63.0000	2.26889
$772$	0	0
$773$	−48.0000	−1.72644	−0.863220	−	0.504828i	$-0.831556\pi$
$773$	−48.0000	−1.72644	−0.863220	+	0.504828i	$0.831556\pi$
$774$	0	0
$775$	8.00000	0.287368
$776$	0	0
$777$	−36.0000	−1.29149
$778$	0	0
$779$	1.00000	0.0358287
$780$	0	0
$781$	24.0000	0.858788
$782$	0	0
$783$	9.00000	0.321634
$784$	0	0
$785$	36.0000	1.28490
$786$	0	0
$787$	12.0000	0.427754	0.213877	−	0.976861i	$-0.431391\pi$
$787$	12.0000	0.427754	0.213877	+	0.976861i	$0.431391\pi$
$788$	0	0
$789$	−57.0000	−2.02925
$790$	0	0
$791$	18.0000	0.640006
$792$	0	0
$793$	48.0000	1.70453
$794$	0	0
$795$	−45.0000	−1.59599
$796$	0	0
$797$	−28.0000	−0.991811	−0.495905	−	0.868377i	$-0.665164\pi$
$797$	−28.0000	−0.991811	−0.495905	+	0.868377i	$0.665164\pi$
$798$	0	0
$799$	12.0000	0.424529
$800$	0	0
$801$	−96.0000	−3.39199
$802$	0	0
$803$	−48.0000	−1.69388
$804$	0	0
$805$	72.0000	2.53767
$806$	0	0
$807$	18.0000	0.633630
$808$	0	0
$809$	−54.0000	−1.89854	−0.949269	−	0.314464i	$-0.898175\pi$
$809$	−54.0000	−1.89854	−0.949269	+	0.314464i	$0.898175\pi$
$810$	0	0
$811$	−54.0000	−1.89620	−0.948098	−	0.317978i	$-0.896996\pi$
$811$	−54.0000	−1.89620	−0.948098	+	0.317978i	$0.896996\pi$
$812$	0	0
$813$	−3.00000	−0.105215
$814$	0	0
$815$	−12.0000	−0.420342
$816$	0	0
$817$	10.0000	0.349856
$818$	0	0
$819$	−108.000	−3.77383
$820$	0	0
$821$	8.00000	0.279202	0.139601	−	0.990208i	$-0.455418\pi$
$821$	8.00000	0.279202	0.139601	+	0.990208i	$0.455418\pi$
$822$	0	0
$823$	−4.00000	−0.139431	−0.0697156	−	0.997567i	$-0.522209\pi$
$823$	−4.00000	−0.139431	−0.0697156	+	0.997567i	$0.522209\pi$
$824$	0	0
$825$	72.0000	2.50672
$826$	0	0
$827$	4.00000	0.139094	0.0695468	−	0.997579i	$-0.477845\pi$
$827$	4.00000	0.139094	0.0695468	+	0.997579i	$0.477845\pi$
$828$	0	0
$829$	1.00000	0.0347314	0.0173657	−	0.999849i	$-0.494472\pi$
$829$	1.00000	0.0347314	0.0173657	+	0.999849i	$0.494472\pi$
$830$	0	0
$831$	−27.0000	−0.936620
$832$	0	0
$833$	−4.00000	−0.138592
$834$	0	0
$835$	−9.00000	−0.311458
$836$	0	0
$837$	18.0000	0.622171
$838$	0	0
$839$	−56.0000	−1.93333	−0.966667	−	0.256036i	$-0.917584\pi$
$839$	−56.0000	−1.93333	−0.966667	+	0.256036i	$0.917584\pi$
$840$	0	0
$841$	−28.0000	−0.965517
$842$	0	0
$843$	9.00000	0.309976
$844$	0	0
$845$	69.0000	2.37367
$846$	0	0
$847$	−75.0000	−2.57703
$848$	0	0
$849$	24.0000	0.823678
$850$	0	0
$851$	−32.0000	−1.09695
$852$	0	0
$853$	1.00000	0.0342393	0.0171197	−	0.999853i	$-0.494550\pi$
$853$	1.00000	0.0342393	0.0171197	+	0.999853i	$0.494550\pi$
$854$	0	0
$855$	−18.0000	−0.615587
$856$	0	0
$857$	32.0000	1.09310	0.546550	−	0.837427i	$-0.315941\pi$
$857$	32.0000	1.09310	0.546550	+	0.837427i	$0.315941\pi$
$858$	0	0
$859$	40.0000	1.36478	0.682391	−	0.730987i	$-0.260940\pi$
$859$	40.0000	1.36478	0.682391	+	0.730987i	$0.260940\pi$
$860$	0	0
$861$	9.00000	0.306719
$862$	0	0
$863$	−24.0000	−0.816970	−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000	−0.816970	−0.408485	+	0.912765i	$0.633943\pi$
$864$	0	0
$865$	24.0000	0.816024
$866$	0	0
$867$	−39.0000	−1.32451
$868$	0	0
$869$	66.0000	2.23890
$870$	0	0
$871$	12.0000	0.406604
$872$	0	0
$873$	−24.0000	−0.812277
$874$	0	0
$875$	9.00000	0.304256
$876$	0	0
$877$	17.0000	0.574049	0.287025	−	0.957923i	$-0.407334\pi$
$877$	17.0000	0.574049	0.287025	+	0.957923i	$0.407334\pi$
$878$	0	0
$879$	3.00000	0.101187
$880$	0	0
$881$	50.0000	1.68454	0.842271	−	0.539054i	$-0.181218\pi$
$881$	50.0000	1.68454	0.842271	+	0.539054i	$0.181218\pi$
$882$	0	0
$883$	−15.0000	−0.504790	−0.252395	−	0.967624i	$-0.581218\pi$
$883$	−15.0000	−0.504790	−0.252395	+	0.967624i	$0.581218\pi$
$884$	0	0
$885$	−9.00000	−0.302532
$886$	0	0
$887$	20.0000	0.671534	0.335767	−	0.941945i	$-0.391004\pi$
$887$	20.0000	0.671534	0.335767	+	0.941945i	$0.391004\pi$
$888$	0	0
$889$	39.0000	1.30802
$890$	0	0
$891$	54.0000	1.80907
$892$	0	0
$893$	6.00000	0.200782
$894$	0	0
$895$	−12.0000	−0.401116
$896$	0	0
$897$	−144.000	−4.80802
$898$	0	0
$899$	2.00000	0.0667037
$900$	0	0
$901$	10.0000	0.333148
$902$	0	0
$903$	90.0000	2.99501
$904$	0	0
$905$	−21.0000	−0.698064
$906$	0	0
$907$	31.0000	1.02934	0.514669	−	0.857389i	$-0.327915\pi$
$907$	31.0000	1.02934	0.514669	+	0.857389i	$0.327915\pi$
$908$	0	0
$909$	60.0000	1.99007
$910$	0	0
$911$	5.00000	0.165657	0.0828287	−	0.996564i	$-0.473605\pi$
$911$	5.00000	0.165657	0.0828287	+	0.996564i	$0.473605\pi$
$912$	0	0
$913$	−60.0000	−1.98571
$914$	0	0
$915$	72.0000	2.38025
$916$	0	0
$917$	−66.0000	−2.17951
$918$	0	0
$919$	−22.0000	−0.725713	−0.362857	−	0.931845i	$-0.618198\pi$
$919$	−22.0000	−0.725713	−0.362857	+	0.931845i	$0.618198\pi$
$920$	0	0
$921$	−69.0000	−2.27363
$922$	0	0
$923$	24.0000	0.789970
$924$	0	0
$925$	16.0000	0.526077
$926$	0	0
$927$	−120.000	−3.94132
$928$	0	0
$929$	−34.0000	−1.11550	−0.557752	−	0.830008i	$-0.688336\pi$
$929$	−34.0000	−1.11550	−0.557752	+	0.830008i	$0.688336\pi$
$930$	0	0
$931$	−2.00000	−0.0655474
$932$	0	0
$933$	−93.0000	−3.04468
$934$	0	0
$935$	−36.0000	−1.17733
$936$	0	0
$937$	−10.0000	−0.326686	−0.163343	−	0.986569i	$-0.552228\pi$
$937$	−10.0000	−0.326686	−0.163343	+	0.986569i	$0.552228\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	−20.0000	−0.651981	−0.325991	−	0.945373i	$-0.605698\pi$
$941$	−20.0000	−0.651981	−0.325991	+	0.945373i	$0.605698\pi$
$942$	0	0
$943$	8.00000	0.260516
$944$	0	0
$945$	−81.0000	−2.63493
$946$	0	0
$947$	−25.0000	−0.812391	−0.406195	−	0.913786i	$-0.633145\pi$
$947$	−25.0000	−0.812391	−0.406195	+	0.913786i	$0.633145\pi$
$948$	0	0
$949$	−48.0000	−1.55815
$950$	0	0
$951$	−90.0000	−2.91845
$952$	0	0
$953$	−54.0000	−1.74923	−0.874616	−	0.484817i	$-0.838886\pi$
$953$	−54.0000	−1.74923	−0.874616	+	0.484817i	$0.838886\pi$
$954$	0	0
$955$	6.00000	0.194155
$956$	0	0
$957$	18.0000	0.581857
$958$	0	0
$959$	−9.00000	−0.290625
$960$	0	0
$961$	−27.0000	−0.870968
$962$	0	0
$963$	90.0000	2.90021
$964$	0	0
$965$	33.0000	1.06231
$966$	0	0
$967$	54.0000	1.73652	0.868261	−	0.496107i	$-0.165238\pi$
$967$	54.0000	1.73652	0.868261	+	0.496107i	$0.165238\pi$
$968$	0	0
$969$	6.00000	0.192748
$970$	0	0
$971$	33.0000	1.05902	0.529510	−	0.848304i	$-0.322376\pi$
$971$	33.0000	1.05902	0.529510	+	0.848304i	$0.322376\pi$
$972$	0	0
$973$	12.0000	0.384702
$974$	0	0
$975$	72.0000	2.30585
$976$	0	0
$977$	−58.0000	−1.85558	−0.927792	−	0.373097i	$-0.878296\pi$
$977$	−58.0000	−1.85558	−0.927792	+	0.373097i	$0.878296\pi$
$978$	0	0
$979$	−96.0000	−3.06817
$980$	0	0
$981$	−48.0000	−1.53252
$982$	0	0
$983$	54.0000	1.72233	0.861166	−	0.508323i	$-0.169735\pi$
$983$	54.0000	1.72233	0.861166	+	0.508323i	$0.169735\pi$
$984$	0	0
$985$	18.0000	0.573528
$986$	0	0
$987$	54.0000	1.71884
$988$	0	0
$989$	80.0000	2.54385
$990$	0	0
$991$	−30.0000	−0.952981	−0.476491	−	0.879180i	$-0.658091\pi$
$991$	−30.0000	−0.952981	−0.476491	+	0.879180i	$0.658091\pi$
$992$	0	0
$993$	−51.0000	−1.61844
$994$	0	0
$995$	−33.0000	−1.04617
$996$	0	0
$997$	37.0000	1.17180	0.585901	−	0.810383i	$-0.300741\pi$
$997$	37.0000	1.17180	0.585901	+	0.810383i	$0.300741\pi$
$998$	0	0
$999$	36.0000	1.13899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3776.2.a.z.1.1		1
4.3	odd	2		3776.2.a.c.1.1		1
8.3	odd	2		472.2.a.e.1.1	✓	1
8.5	even	2		944.2.a.a.1.1		1
24.5	odd	2		8496.2.a.u.1.1		1
24.11	even	2		4248.2.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
472.2.a.e.1.1	✓	1	8.3	odd	2
944.2.a.a.1.1		1	8.5	even	2
3776.2.a.c.1.1		1	4.3	odd	2
3776.2.a.z.1.1		1	1.1	even	1	trivial
4248.2.a.h.1.1		1	24.11	even	2
8496.2.a.u.1.1		1	24.5	odd	2

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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:	\( N \)	\(=\)	\( 3776 = 2^{6} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3776.a (trivial)

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