LMFDB - Embedded newform 117.2.x.a.11.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,2,Mod(2,117)] 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("117.2"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.x (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.5
Character	$\chi$	$=$	117.11
Dual form			117.2.x.a.32.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.662754 + 0.662754i) q^{2} +(1.56154 + 0.749386i) q^{3} +1.12151i q^{4} +(0.101414 + 0.0271738i) q^{5} +(-1.53158 + 0.538261i) q^{6} +(-0.353095 - 0.0946115i) q^{7} +(-2.06880 - 2.06880i) q^{8} +(1.87684 + 2.34040i) q^{9} +(-0.0852221 + 0.0492030i) q^{10} +(-2.25143 - 2.25143i) q^{11} +(-0.840447 + 1.75129i) q^{12} +(3.51083 + 0.821016i) q^{13} +(0.296719 - 0.171311i) q^{14} +(0.137999 + 0.118431i) q^{15} +0.499177 q^{16} +(-0.713952 + 1.23660i) q^{17} +(-2.79499 - 0.307224i) q^{18} +(2.92701 - 0.784289i) q^{19} +(-0.0304758 + 0.113737i) q^{20} +(-0.480473 - 0.412345i) q^{21} +2.98429 q^{22} +(1.83687 - 3.18155i) q^{23} +(-1.68019 - 4.78084i) q^{24} +(-4.32058 - 2.49449i) q^{25} +(-2.87095 + 1.78269i) q^{26} +(1.17691 + 5.06111i) q^{27} +(0.106108 - 0.396001i) q^{28} -5.17142i q^{29} +(-0.169950 + 0.0129684i) q^{30} +(1.46476 - 5.46656i) q^{31} +(3.80676 - 3.80676i) q^{32} +(-1.82852 - 5.20290i) q^{33} +(-0.346388 - 1.29274i) q^{34} +(-0.0332378 - 0.0191899i) q^{35} +(-2.62479 + 2.10490i) q^{36} +(-4.32627 - 1.15922i) q^{37} +(-1.42009 + 2.45967i) q^{38} +(4.86706 + 3.91302i) q^{39} +(-0.153588 - 0.266022i) q^{40} +(1.76108 + 6.57243i) q^{41} +(0.591718 - 0.0451524i) q^{42} +(1.94536 - 1.12315i) q^{43} +(2.52501 - 2.52501i) q^{44} +(0.126741 + 0.288350i) q^{45} +(0.891194 + 3.32598i) q^{46} +(-4.42009 + 1.18436i) q^{47} +(0.779487 + 0.374076i) q^{48} +(-5.94645 - 3.43319i) q^{49} +(4.51671 - 1.21025i) q^{50} +(-2.04156 + 1.39598i) q^{51} +(-0.920781 + 3.93745i) q^{52} +13.0901i q^{53} +(-4.13428 - 2.57427i) q^{54} +(-0.167147 - 0.289507i) q^{55} +(0.534750 + 0.926214i) q^{56} +(5.15838 + 0.968755i) q^{57} +(3.42738 + 3.42738i) q^{58} +(2.44633 + 2.44633i) q^{59} +(-0.132822 + 0.154768i) q^{60} +(3.12378 + 5.41055i) q^{61} +(2.65221 + 4.59376i) q^{62} +(-0.441275 - 1.00395i) q^{63} +6.04425i q^{64} +(0.333737 + 0.178665i) q^{65} +(4.66010 + 2.23639i) q^{66} +(-14.8055 + 3.96713i) q^{67} +(-1.38687 - 0.800708i) q^{68} +(5.25257 - 3.59161i) q^{69} +(0.0347467 - 0.00931034i) q^{70} +(1.56835 + 5.85317i) q^{71} +(0.959005 - 8.72461i) q^{72} +(-4.13084 + 4.13084i) q^{73} +(3.63553 - 2.09897i) q^{74} +(-4.87744 - 7.13304i) q^{75} +(0.879591 + 3.28268i) q^{76} +(0.581958 + 1.00798i) q^{77} +(-5.81903 + 0.632294i) q^{78} +(8.15587 - 14.1264i) q^{79} +(0.0506235 + 0.0135645i) q^{80} +(-1.95493 + 8.78511i) q^{81} +(-5.52307 - 3.18874i) q^{82} +(-4.29512 - 16.0296i) q^{83} +(0.462450 - 0.538857i) q^{84} +(-0.106008 + 0.106008i) q^{85} +(-0.544920 + 2.03367i) q^{86} +(3.87539 - 8.07541i) q^{87} +9.31551i q^{88} +(0.630472 - 2.35295i) q^{89} +(-0.275103 - 0.107107i) q^{90} +(-1.16198 - 0.622062i) q^{91} +(3.56816 + 2.06008i) q^{92} +(6.38385 - 7.43860i) q^{93} +(2.14449 - 3.71437i) q^{94} +0.318151 q^{95} +(8.79716 - 3.09169i) q^{96} +(-3.20249 + 11.9519i) q^{97} +(6.21639 - 1.66568i) q^{98} +(1.04367 - 9.49483i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9} - 12 q^{10} - 6 q^{11} + 18 q^{12} - 2 q^{13} - 12 q^{14} - 26 q^{15} - 28 q^{16} - 14 q^{18} - 4 q^{19} - 18 q^{20} - 8 q^{21}+ \cdots - 8 q^{99}+O(q^{100}) $ 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^5 - 8 * q^6 - 4 * q^7 + 30 * q^8 - 2 * q^9 - 12 * q^10 - 6 * q^11 + 18 * q^12 - 2 * q^13 - 12 * q^14 - 26 * q^15 - 28 * q^16 - 14 * q^18 - 4 * q^19 - 18 * q^20 - 8 * q^21 - 4 * q^22 - 6 * q^23 + 6 * q^24 - 48 * q^26 - 32 * q^27 + 42 * q^30 - 18 * q^31 + 54 * q^32 + 28 * q^33 + 6 * q^34 + 6 * q^35 + 24 * q^36 - 6 * q^37 + 36 * q^38 + 10 * q^39 - 12 * q^40 + 18 * q^41 - 70 * q^42 - 30 * q^43 + 12 * q^44 + 40 * q^45 - 12 * q^46 - 36 * q^47 - 14 * q^48 - 6 * q^49 - 60 * q^50 + 56 * q^52 + 34 * q^54 - 4 * q^55 - 6 * q^56 - 56 * q^57 + 50 * q^58 - 6 * q^59 + 44 * q^60 + 2 * q^61 + 18 * q^62 + 22 * q^63 + 72 * q^65 + 32 * q^66 + 26 * q^67 + 42 * q^68 + 30 * q^69 - 16 * q^70 - 48 * q^71 + 30 * q^72 - 22 * q^73 + 30 * q^74 - 24 * q^75 + 6 * q^76 + 72 * q^77 - 20 * q^78 + 8 * q^79 - 54 * q^80 + 82 * q^81 - 12 * q^82 + 54 * q^83 - 38 * q^84 - 24 * q^85 - 54 * q^86 + 2 * q^87 - 114 * q^90 - 16 * q^91 + 120 * q^92 + 52 * q^93 + 26 * q^94 - 12 * q^95 + 94 * q^96 - 24 * q^97 + 36 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.662754	+	0.662754i	−0.468638	+	0.468638i	−0.901473	−	0.432835i	$-0.857513\pi$
$2$	−0.662754	+	0.662754i	−0.468638	+	0.468638i	0.432835	+	0.901473i	$0.357513\pi$
$3$	1.56154	+	0.749386i	0.901558	+	0.432658i
$3$	1.56154	+	0.749386i	0.901558	+	0.432658i
$4$			1.12151i			0.560757i
$5$	0.101414	+	0.0271738i	0.0453537	+	0.0121525i	0.281425	−	0.959583i	$-0.409193\pi$
$5$	0.101414	+	0.0271738i	0.0453537	+	0.0121525i	−0.236071	+	0.971736i	$0.575860\pi$
$6$	−1.53158	+	0.538261i	−0.625264	+	0.219744i
$7$	−0.353095	−	0.0946115i	−0.133457	−	0.0357598i	0.191472	−	0.981498i	$-0.438674\pi$
$7$	−0.353095	−	0.0946115i	−0.133457	−	0.0357598i	−0.324929	+	0.945738i	$0.605341\pi$
$8$	−2.06880	−	2.06880i	−0.731430	−	0.731430i
$9$	1.87684	+	2.34040i	0.625614	+	0.780133i
$10$	−0.0852221	+	0.0492030i	−0.0269496	+	0.0155594i
$11$	−2.25143	−	2.25143i	−0.678833	−	0.678833i	0.280903	−	0.959736i	$-0.409366\pi$
$11$	−2.25143	−	2.25143i	−0.678833	−	0.678833i	−0.959736	+	0.280903i	$0.909366\pi$
$12$	−0.840447	+	1.75129i	−0.242616	+	0.505555i
$13$	3.51083	+	0.821016i	0.973729	+	0.227709i
$13$	3.51083	+	0.821016i	0.973729	+	0.227709i
$14$	0.296719	−	0.171311i	0.0793016	−	0.0457848i
$15$	0.137999	+	0.118431i	0.0356311	+	0.0305788i
$16$	0.499177			0.124794
$17$	−0.713952	+	1.23660i	−0.173159	+	0.299920i	−0.939523	−	0.342487i	$-0.888731\pi$
$17$	−0.713952	+	1.23660i	−0.173159	+	0.299920i	0.766364	+	0.642407i	$0.222064\pi$
$18$	−2.79499	−	0.307224i	−0.658786	−	0.0724134i
$19$	2.92701	−	0.784289i	0.671501	−	0.179928i	0.0930701	−	0.995660i	$-0.470332\pi$
$19$	2.92701	−	0.784289i	0.671501	−	0.179928i	0.578431	+	0.815731i	$0.303665\pi$
$20$	−0.0304758	+	0.113737i	−0.00681460	+	0.0254324i
$21$	−0.480473	−	0.412345i	−0.104848	−	0.0899810i
$22$	2.98429			0.636253
$23$	1.83687	−	3.18155i	0.383014	−	0.663400i	−0.608477	−	0.793571i	$-0.708219\pi$
$23$	1.83687	−	3.18155i	0.383014	−	0.663400i	0.991492	+	0.130171i	$0.0415527\pi$
$24$	−1.68019	−	4.78084i	−0.342967	−	0.975886i
$25$	−4.32058	−	2.49449i	−0.864116	−	0.498898i
$26$	−2.87095	+	1.78269i	−0.563039	+	0.349613i
$27$	1.17691	+	5.06111i	0.226496	+	0.974012i
$28$	0.106108	−	0.396001i	0.0200526	−	0.0748372i
$29$		−	5.17142i		−	0.960309i	−0.877184	−	0.480155i	$-0.840581\pi$
$29$		−	5.17142i		−	0.960309i	0.877184	−	0.480155i	$-0.159419\pi$
$30$	−0.169950	+	0.0129684i	−0.0310285	+	0.00236770i
$31$	1.46476	−	5.46656i	0.263079	−	0.981823i	−0.700337	−	0.713812i	$-0.746967\pi$
$31$	1.46476	−	5.46656i	0.263079	−	0.981823i	0.963416	−	0.268011i	$-0.0863663\pi$
$32$	3.80676	−	3.80676i	0.672947	−	0.672947i
$33$	−1.82852	−	5.20290i	−0.318305	−	0.905709i
$34$	−0.346388	−	1.29274i	−0.0594050	−	0.221703i
$35$	−0.0332378	−	0.0191899i	−0.00561822	−	0.00324368i
$36$	−2.62479	+	2.10490i	−0.437465	+	0.350817i
$37$	−4.32627	−	1.15922i	−0.711234	−	0.190575i	−0.114977	−	0.993368i	$-0.536679\pi$
$37$	−4.32627	−	1.15922i	−0.711234	−	0.190575i	−0.596257	+	0.802793i	$0.703346\pi$
$38$	−1.42009	+	2.45967i	−0.230370	+	0.399012i
$39$	4.86706	+	3.91302i	0.779353	+	0.626585i
$40$	−0.153588	−	0.266022i	−0.0242844	−	0.0420618i
$41$	1.76108	+	6.57243i	0.275034	+	1.02644i	0.955818	+	0.293958i	$0.0949724\pi$
$41$	1.76108	+	6.57243i	0.275034	+	1.02644i	−0.680784	+	0.732484i	$0.738361\pi$
$42$	0.591718	−	0.0451524i	0.0913041	−	0.00696717i
$43$	1.94536	−	1.12315i	0.296665	−	0.171279i	−0.344279	−	0.938867i	$-0.611877\pi$
$43$	1.94536	−	1.12315i	0.296665	−	0.171279i	0.640944	+	0.767588i	$0.278543\pi$
$44$	2.52501	−	2.52501i	0.380660	−	0.380660i
$45$	0.126741	+	0.288350i	0.0188934	+	0.0429847i
$46$	0.891194	+	3.32598i	0.131399	+	0.490389i
$47$	−4.42009	+	1.18436i	−0.644736	+	0.172756i	−0.566348	−	0.824166i	$-0.691644\pi$
$47$	−4.42009	+	1.18436i	−0.644736	+	0.172756i	−0.0783882	+	0.996923i	$0.524977\pi$
$48$	0.779487	+	0.374076i	0.112509	+	0.0539933i
$49$	−5.94645	−	3.43319i	−0.849493	−	0.490455i
$50$	4.51671	−	1.21025i	0.638760	−	0.171155i
$51$	−2.04156	+	1.39598i	−0.285876	+	0.195477i
$52$	−0.920781	+	3.93745i	−0.127689	+	0.546026i
$53$			13.0901i			1.79807i	0.437881	+	0.899033i	$0.355729\pi$
$53$			13.0901i			1.79807i	−0.437881	+	0.899033i	$0.644271\pi$
$54$	−4.13428	−	2.57427i	−0.562604	−	0.350314i
$55$	−0.167147	−	0.289507i	−0.0225381	−	0.0390371i
$56$	0.534750	+	0.926214i	0.0714589	+	0.123771i
$57$	5.15838	+	0.968755i	0.683245	+	0.128315i
$58$	3.42738	+	3.42738i	0.450037	+	0.450037i
$59$	2.44633	+	2.44633i	0.318485	+	0.318485i	0.848185	−	0.529700i	$-0.177696\pi$
$59$	2.44633	+	2.44633i	0.318485	+	0.318485i	−0.529700	+	0.848185i	$0.677696\pi$
$60$	−0.132822	+	0.154768i	−0.0171473	+	0.0199804i
$61$	3.12378	+	5.41055i	0.399959	+	0.692750i	0.993720	−	0.111892i	$-0.0356909\pi$
$61$	3.12378	+	5.41055i	0.399959	+	0.692750i	−0.593761	+	0.804641i	$0.702358\pi$
$62$	2.65221	+	4.59376i	0.336831	+	0.583408i
$63$	−0.441275	−	1.00395i	−0.0555954	−	0.126486i
$64$			6.04425i			0.755531i
$65$	0.333737	+	0.178665i	0.0413950	+	0.0221607i
$66$	4.66010	+	2.23639i	0.573619	+	0.275280i
$67$	−14.8055	+	3.96713i	−1.80878	+	0.484662i	−0.995292	−	0.0969186i	$-0.969101\pi$
$67$	−14.8055	+	3.96713i	−1.80878	+	0.484662i	−0.813489	+	0.581580i	$0.802435\pi$
$68$	−1.38687	−	0.800708i	−0.168182	−	0.0971001i
$69$	5.25257	−	3.59161i	0.632335	−	0.432379i
$70$	0.0347467	−	0.00931034i	0.00415302	−	0.00111280i
$71$	1.56835	+	5.85317i	0.186129	+	0.694643i	0.994386	+	0.105813i	$0.0337445\pi$
$71$	1.56835	+	5.85317i	0.186129	+	0.694643i	−0.808257	+	0.588830i	$0.799589\pi$
$72$	0.959005	−	8.72461i	0.113020	−	1.02821i
$73$	−4.13084	+	4.13084i	−0.483478	+	0.483478i	−0.906241	−	0.422763i	$-0.861060\pi$
$73$	−4.13084	+	4.13084i	−0.483478	+	0.483478i	0.422763	+	0.906241i	$0.361060\pi$
$74$	3.63553	−	2.09897i	0.422622	−	0.244001i
$75$	−4.87744	−	7.13304i	−0.563199	−	0.823652i
$76$	0.879591	+	3.28268i	0.100896	+	0.376549i
$77$	0.581958	+	1.00798i	0.0663203	+	0.114870i
$78$	−5.81903	+	0.632294i	−0.658876	+	0.0715932i
$79$	8.15587	−	14.1264i	0.917607	−	1.58934i	0.114569	−	0.993415i	$-0.463451\pi$
$79$	8.15587	−	14.1264i	0.917607	−	1.58934i	0.803039	−	0.595927i	$-0.203215\pi$
$80$	0.0506235	+	0.0135645i	0.00565988	+	0.00151656i
$81$	−1.95493	+	8.78511i	−0.217215	+	0.976124i
$82$	−5.52307	−	3.18874i	−0.609921	−	0.352138i
$83$	−4.29512	−	16.0296i	−0.471450	−	1.75948i	−0.634565	−	0.772870i	$-0.718821\pi$
$83$	−4.29512	−	16.0296i	−0.471450	−	1.75948i	0.163114	−	0.986607i	$-0.447846\pi$
$84$	0.462450	−	0.538857i	0.0504575	−	0.0587942i
$85$	−0.106008	+	0.106008i	−0.0114982	+	0.0114982i
$86$	−0.544920	+	2.03367i	−0.0587603	+	0.219296i
$87$	3.87539	−	8.07541i	0.415486	−	0.865775i
$88$			9.31551i			0.993037i
$89$	0.630472	−	2.35295i	0.0668298	−	0.249412i	−0.924427	−	0.381359i	$-0.875456\pi$
$89$	0.630472	−	2.35295i	0.0668298	−	0.249412i	0.991257	+	0.131947i	$0.0421228\pi$
$90$	−0.275103	−	0.107107i	−0.0289984	−	0.0112901i
$91$	−1.16198	−	0.622062i	−0.121809	−	0.0652098i
$92$	3.56816	+	2.06008i	0.372006	+	0.214778i
$93$	6.38385	−	7.43860i	0.661974	−	0.771347i
$94$	2.14449	−	3.71437i	0.221187	−	0.383108i
$95$	0.318151			0.0326416
$96$	8.79716	−	3.09169i	0.897856	−	0.315545i
$97$	−3.20249	+	11.9519i	−0.325164	+	1.21353i	0.588983	+	0.808145i	$0.299529\pi$
$97$	−3.20249	+	11.9519i	−0.325164	+	1.21353i	−0.914147	+	0.405383i	$0.867138\pi$
$98$	6.21639	−	1.66568i	0.627951	−	0.168259i
$99$	1.04367	−	9.49483i	0.104893	−	0.954267i
$100$	2.79760	−	4.84559i	0.279760	−	0.484559i
$101$	3.80275			0.378388			0.189194	−	0.981940i	$-0.439413\pi$
$101$	3.80275			0.378388			0.189194	+	0.981940i	$0.439413\pi$
$102$	0.427859	−	2.27824i	0.0423643	−	0.225580i
$103$	−5.80875	+	3.35368i	−0.572353	+	0.330448i	−0.758089	−	0.652152i	$-0.773867\pi$
$103$	−5.80875	+	3.35368i	−0.572353	+	0.330448i	0.185736	+	0.982600i	$0.440533\pi$
$104$	−5.56468	−	8.96171i	−0.545662	−	0.878768i
$105$	−0.0375217	−	0.0548738i	−0.00366175	−	0.00535513i
$106$	−8.67553	−	8.67553i	−0.842642	−	0.842642i
$107$	−10.4912	+	6.05707i	−1.01422	+	0.585559i	−0.912424	−	0.409246i	$-0.865792\pi$
$107$	−10.4912	+	6.05707i	−1.01422	+	0.585559i	−0.101795	+	0.994805i	$0.532458\pi$
$108$	−5.67611	+	1.31992i	−0.546184	+	0.127009i
$109$	−0.643264	−	0.643264i	−0.0616135	−	0.0616135i	0.675629	−	0.737242i	$-0.263872\pi$
$109$	−0.643264	−	0.643264i	−0.0616135	−	0.0616135i	−0.737242	+	0.675629i	$0.763872\pi$
$110$	0.302649	+	0.0810946i	0.0288565	+	0.00773206i
$111$	−5.88696	−	5.05222i	−0.558765	−	0.479535i
$112$	−0.176257	−	0.0472279i	−0.0166547	−	0.00446262i
$113$			3.07587i			0.289354i	0.989479	+	0.144677i	$0.0462143\pi$
$113$			3.07587i			0.289354i	−0.989479	+	0.144677i	$0.953786\pi$
$114$	−4.06079	+	2.77669i	−0.380327	+	0.260061i
$115$	0.272739	−	0.272739i	0.0254331	−	0.0254331i
$116$	5.79983			0.538500
$117$	4.66777	+	9.75766i	0.431535	+	0.902096i
$118$	−3.24263			−0.298508
$119$	0.369090	−	0.369090i	0.0338344	−	0.0338344i
$120$	−0.0404811	−	0.530502i	−0.00369541	−	0.0484280i
$121$		−	0.862100i		−	0.0783727i
$122$	−5.65616	−	1.51556i	−0.512085	−	0.137213i
$123$	−2.17529	+	11.5829i	−0.196139	+	1.04439i
$124$	6.13082	+	1.64275i	0.550564	+	0.147523i
$125$	−0.741584	−	0.741584i	−0.0663293	−	0.0663293i
$126$	0.957831	+	0.372918i	0.0853304	+	0.0332222i
$127$	11.1811	−	6.45543i	0.992165	−	0.572827i	0.0862440	−	0.996274i	$-0.472514\pi$
$127$	11.1811	−	6.45543i	0.992165	−	0.572827i	0.905921	+	0.423448i	$0.139180\pi$
$128$	3.60767	+	3.60767i	0.318876	+	0.318876i
$129$	3.87944	−	0.296030i	0.341566	−	0.0260640i
$130$	−0.339597	+	0.102775i	−0.0297846	+	0.00901393i
$131$	−13.4537	+	7.76749i	−1.17545	+	0.678649i	−0.954958	−	0.296739i	$-0.904101\pi$
$131$	−13.4537	+	7.76749i	−1.17545	+	0.678649i	−0.220495	+	0.975388i	$0.570767\pi$
$132$	5.83513	−	2.05071i	0.507883	−	0.178492i
$133$	−1.10771			−0.0960510
$134$	7.18319	−	12.4416i	0.620533	−	1.07479i
$135$	−0.0181746	+	0.545249i	−0.00156422	+	0.0469276i
$136$	4.03530	−	1.08125i	0.346024	−	0.0927168i
$137$	−4.77136	+	17.8070i	−0.407645	+	1.52135i	0.391480	+	0.920187i	$0.371963\pi$
$137$	−4.77136	+	17.8070i	−0.407645	+	1.52135i	−0.799125	+	0.601165i	$0.794703\pi$
$138$	−1.10080	+	5.86152i	−0.0937067	+	0.498965i
$139$	9.08265			0.770381			0.385190	−	0.922837i	$-0.374136\pi$
$139$	9.08265			0.770381			0.385190	+	0.922837i	$0.374136\pi$
$140$	0.0215217	−	0.0372767i	0.00181892	−	0.00315046i
$141$	−7.78970	−	1.46292i	−0.656011	−	0.123200i
$142$	−4.91864	−	2.83978i	−0.412763	−	0.238309i
$143$	−6.05594	−	9.75286i	−0.506423	−	0.815575i
$144$	0.936876	+	1.16827i	0.0780730	+	0.0973561i
$145$	0.140527	−	0.524455i	0.0116702	−	0.0435536i
$146$		−	5.47546i		−	0.453152i
$147$	−6.71287	−	9.81726i	−0.553668	−	0.809714i
$148$	1.30008	−	4.85197i	0.106866	−	0.398830i
$149$	8.51487	−	8.51487i	0.697565	−	0.697565i	−0.266319	−	0.963885i	$-0.585808\pi$
$149$	8.51487	−	8.51487i	0.697565	−	0.697565i	0.963885	+	0.266319i	$0.0858076\pi$
$150$	7.95999	+	1.49490i	0.649931	+	0.122058i
$151$	−0.0109208	−	0.0407571i	−0.000888724	−	0.00331676i	0.965480	−	0.260477i	$-0.0838798\pi$
$151$	−0.0109208	−	0.0407571i	−0.000888724	−	0.00331676i	−0.966369	+	0.257160i	$0.917213\pi$
$152$	−7.67791	−	4.43284i	−0.622761	−	0.359551i
$153$	−4.23412	+	0.649972i	−0.342308	+	0.0525472i
$154$	−1.05374	−	0.282348i	−0.0849127	−	0.0227523i
$155$	0.297094	−	0.514583i	0.0238632	−	0.0413323i
$156$	−4.38851	+	5.45848i	−0.351362	+	0.437028i
$157$	−6.95508	−	12.0466i	−0.555076	−	0.961420i	−0.997898	−	0.0648102i	$-0.979356\pi$
$157$	−6.95508	−	12.0466i	−0.555076	−	0.961420i	0.442822	−	0.896610i	$-0.353978\pi$
$158$	3.95698	+	14.7677i	0.314801	+	1.17485i
$159$	−9.80955	+	20.4408i	−0.777948	+	1.62106i
$160$	0.489503	−	0.282615i	0.0386986	−	0.0223427i
$161$	−0.949602	+	0.949602i	−0.0748391	+	0.0748391i
$162$	−4.52673	−	7.11801i	−0.355654	−	0.559244i
$163$	0.208136	+	0.776776i	0.0163025	+	0.0608418i	0.973598	−	0.228270i	$-0.0733068\pi$
$163$	0.208136	+	0.776776i	0.0163025	+	0.0608418i	−0.957295	+	0.289112i	$0.906640\pi$
$164$	−7.37108	+	1.97507i	−0.575584	+	0.154227i
$165$	−0.0440549	−	0.577335i	−0.00342967	−	0.0449455i
$166$	13.4703	+	7.77707i	1.04550	+	0.603618i
$167$	14.9871	−	4.01578i	1.15974	−	0.310750i	0.372875	−	0.927881i	$-0.378372\pi$
$167$	14.9871	−	4.01578i	1.15974	−	0.310750i	0.786860	+	0.617131i	$0.211705\pi$
$168$	0.140944	+	1.84706i	0.0108741	+	0.142504i
$169$	11.6519	+	5.76490i	0.896297	+	0.443454i
$170$		−	0.140514i		−	0.0107770i
$171$	7.32907	+	5.37837i	0.560468	+	0.411294i
$172$	1.25963	+	2.18175i	0.0960462	+	0.166357i
$173$	7.66869	+	13.2826i	0.583039	+	1.00985i	0.995117	+	0.0987051i	$0.0314700\pi$
$173$	7.66869	+	13.2826i	0.583039	+	1.00985i	−0.412077	+	0.911149i	$0.635197\pi$
$174$	2.78358	+	7.92044i	0.211022	+	0.600447i
$175$	1.28957	+	1.28957i	0.0974822	+	0.0974822i
$176$	−1.12386	−	1.12386i	−0.0847144	−	0.0847144i
$177$	1.98681	+	5.65330i	0.149338	+	0.424928i
$178$	1.14158	+	1.97728i	0.0855651	+	0.148203i
$179$	−9.33636	−	16.1710i	−0.697832	−	1.20868i	−0.969217	−	0.246209i	$-0.920815\pi$
$179$	−9.33636	−	16.1710i	−0.697832	−	1.20868i	0.271385	−	0.962471i	$-0.412518\pi$
$180$	−0.323389	+	0.142141i	−0.0241040	+	0.0105946i
$181$		−	14.2199i		−	1.05695i	−0.848947	−	0.528477i	$-0.822763\pi$
$181$		−	14.2199i		−	1.05695i	0.848947	−	0.528477i	$-0.177237\pi$
$182$	1.18238	−	0.357832i	0.0876439	−	0.0265243i
$183$	0.823335	+	10.7897i	0.0608627	+	0.797600i
$184$	−10.3821	+	2.78188i	−0.765378	+	0.205083i
$185$	−0.407244	−	0.235122i	−0.0299412	−	0.0172865i
$186$	0.699042	+	9.16089i	0.0512563	+	0.671709i
$187$	4.39154	−	1.17671i	0.321141	−	0.0860495i
$188$	−1.32827	−	4.95719i	−0.0968744	−	0.361540i
$189$	0.0632788	−	1.89840i	0.00460286	−	0.138089i
$190$	−0.210856	+	0.210856i	−0.0152971	+	0.0152971i
$191$	6.35291	−	3.66785i	0.459680	−	0.265397i	−0.252229	−	0.967667i	$-0.581164\pi$
$191$	6.35291	−	3.66785i	0.459680	−	0.265397i	0.711910	+	0.702271i	$0.247830\pi$
$192$	−4.52947	+	9.43836i	−0.326886	+	0.681155i
$193$	5.53999	+	20.6755i	0.398777	+	1.48826i	0.815250	+	0.579109i	$0.196599\pi$
$193$	5.53999	+	20.6755i	0.398777	+	1.48826i	−0.416473	+	0.909148i	$0.636734\pi$
$194$	−5.79868	−	10.0436i	−0.416321	−	0.721090i
$195$	0.387256	+	0.529092i	0.0277320	+	0.0378890i
$196$	3.85037	−	6.66903i	0.275026	−	0.476359i
$197$	3.74628	+	1.00381i	0.266911	+	0.0715186i	0.389792	−	0.920903i	$-0.372547\pi$
$197$	3.74628	+	1.00381i	0.266911	+	0.0715186i	−0.122881	+	0.992421i	$0.539213\pi$
$198$	5.60104	+	6.98443i	0.398049	+	0.496362i
$199$	8.87017	+	5.12119i	0.628790	+	0.363032i	0.780283	−	0.625426i	$-0.215075\pi$
$199$	8.87017	+	5.12119i	0.628790	+	0.363032i	−0.151494	+	0.988458i	$0.548408\pi$
$200$	3.77781	+	14.0990i	0.267132	+	0.996949i
$201$	−26.0924	−	4.90020i	−1.84041	−	0.345633i
$202$	−2.52029	+	2.52029i	−0.177327	+	0.177327i
$203$	−0.489276	+	1.82600i	−0.0343405	+	0.128160i
$204$	−1.56561	−	2.28964i	−0.109615	−	0.160307i
$205$			0.714392i			0.0498953i
$206$	1.62710	−	6.07244i	0.113366	−	0.423087i
$207$	10.8936	−	1.67226i	0.757159	−	0.116230i
$208$	1.75253	+	0.409832i	0.121516	+	0.0284168i
$209$	−8.35573	−	4.82418i	−0.577978	−	0.333696i
$210$	0.0612355	+	0.0115002i	0.00422565	+	0.000793586i
$211$	9.03550	−	15.6500i	0.622030	−	1.07739i	−0.367078	−	0.930190i	$-0.619642\pi$
$211$	9.03550	−	15.6500i	0.622030	−	1.07739i	0.989107	−	0.147197i	$-0.0470250\pi$
$212$	−14.6808			−1.00828
$213$	−1.93723	+	10.3153i	−0.132737	+	0.706791i
$214$	2.93871	−	10.9674i	0.200886	−	0.749717i
$215$	0.227807	−	0.0610407i	0.0155363	−	0.00416294i
$216$	8.03563	−	12.9052i	0.546755	−	0.878088i
$217$	−1.03440	+	1.79163i	−0.0702196	+	0.121624i
$218$	0.852651			0.0577488
$219$	−9.54608	+	3.35490i	−0.645064	+	0.226703i
$220$	0.324686	−	0.187458i	0.0218903	−	0.0126384i
$221$	−3.52183	+	3.75533i	−0.236904	+	0.252611i
$222$	7.24998	−	0.553227i	0.486587	−	0.0371301i
$223$	2.26872	+	2.26872i	0.151925	+	0.151925i	0.778977	−	0.627052i	$-0.215739\pi$
$223$	2.26872	+	2.26872i	0.151925	+	0.151925i	−0.627052	+	0.778977i	$0.715739\pi$
$224$	−1.70431	+	0.983985i	−0.113874	+	0.0657453i
$225$	−2.27095	−	14.7936i	−0.151397	−	0.986243i
$226$	−2.03855	−	2.03855i	−0.135602	−	0.135602i
$227$	−3.66821	−	0.982895i	−0.243468	−	0.0652370i	0.135021	−	0.990843i	$-0.456890\pi$
$227$	−3.66821	−	0.982895i	−0.243468	−	0.0652370i	−0.378489	+	0.925606i	$0.623556\pi$
$228$	−1.08647	+	5.78520i	−0.0719534	+	0.383134i
$229$	16.9464	+	4.54078i	1.11985	+	0.300063i	0.770823	−	0.637050i	$-0.219845\pi$
$229$	16.9464	+	4.54078i	1.11985	+	0.300063i	0.349027	+	0.937113i	$0.386512\pi$
$230$			0.361518i			0.0238378i
$231$	0.153387	+	2.01012i	0.0100921	+	0.132256i
$232$	−10.6986	+	10.6986i	−0.702399	+	0.702399i
$233$	14.4728			0.948143			0.474072	−	0.880486i	$-0.342784\pi$
$233$	14.4728			0.948143			0.474072	+	0.880486i	$0.342784\pi$
$234$	−9.56051	−	3.37335i	−0.624990	−	0.220523i
$235$	−0.480442			−0.0313406
$236$	−2.74359	+	2.74359i	−0.178593	+	0.178593i
$237$	23.3219	−	15.9471i	1.51492	−	1.03587i
$238$			0.489231i			0.0317122i
$239$	−19.7813	−	5.30038i	−1.27955	−	0.342853i	−0.445865	−	0.895100i	$-0.647104\pi$
$239$	−19.7813	−	5.30038i	−1.27955	−	0.342853i	−0.833681	+	0.552247i	$0.813771\pi$
$240$	0.0688858	+	0.0591182i	0.00444656	+	0.00381606i
$241$	−23.3290	−	6.25098i	−1.50275	−	0.402661i	−0.588732	−	0.808329i	$-0.700372\pi$
$241$	−23.3290	−	6.25098i	−1.50275	−	0.402661i	−0.914021	+	0.405667i	$0.867039\pi$
$242$	0.571360	+	0.571360i	0.0367284	+	0.0367284i
$243$	−9.63615	+	12.2533i	−0.618159	+	0.786053i
$244$	−6.06801	+	3.50337i	−0.388464	+	0.224280i
$245$	−0.509761	−	0.509761i	−0.0325674	−	0.0325674i
$246$	−6.23491	−	9.11827i	−0.397524	−	0.581360i
$247$	10.9201	−	0.350386i	0.694831	−	0.0222945i
$248$	−14.3395	+	8.27891i	−0.910558	+	0.525711i
$249$	5.30534	−	28.2496i	0.336212	−	1.79025i
$250$	0.982975			0.0621688
$251$	3.92544	−	6.79906i	0.247772	−	0.429153i	−0.715136	−	0.698986i	$-0.753635\pi$
$251$	3.92544	−	6.79906i	0.247772	−	0.429153i	0.962907	+	0.269833i	$0.0869684\pi$
$252$	1.12595	−	0.494896i	0.0709281	−	0.0311755i
$253$	−11.2986	+	3.02746i	−0.710340	+	0.190335i
$254$	−3.13198	+	11.6887i	−0.196518	+	0.733414i
$255$	−0.244977	+	0.0860952i	−0.0153410	+	0.00539149i
$256$	−16.8705			−1.05441
$257$	13.1768	−	22.8229i	0.821947	−	1.42365i	−0.0822831	−	0.996609i	$-0.526221\pi$
$257$	13.1768	−	22.8229i	0.821947	−	1.42365i	0.904230	−	0.427045i	$-0.140446\pi$
$258$	−2.37492	+	2.76731i	−0.147856	+	0.172285i
$259$	1.41791	+	0.818630i	0.0881046	+	0.0508672i
$260$	−0.200376	+	0.374291i	−0.0124268	+	0.0232126i
$261$	12.1032	−	9.70595i	0.749169	−	0.600783i
$262$	3.76855	−	14.0644i	0.232822	−	0.868903i
$263$		−	21.1195i		−	1.30229i	−0.758955	−	0.651143i	$-0.774290\pi$
$263$		−	21.1195i		−	1.30229i	0.758955	−	0.651143i	$-0.225710\pi$
$264$	−6.98091	+	14.5466i	−0.429645	+	0.895280i
$265$	−0.355708	+	1.32752i	−0.0218510	+	0.0815490i
$266$	0.734142	−	0.734142i	0.0450131	−	0.0450131i
$267$	2.74778	−	3.20177i	0.168161	−	0.195945i
$268$	−4.44919	−	16.6046i	−0.271777	−	1.01429i
$269$	−3.78449	−	2.18498i	−0.230744	−	0.133220i	0.380171	−	0.924916i	$-0.375865\pi$
$269$	−3.78449	−	2.18498i	−0.230744	−	0.133220i	−0.610915	+	0.791696i	$0.709198\pi$
$270$	−0.349321	−	0.373411i	−0.0212590	−	0.0227251i
$271$	13.6523	+	3.65813i	0.829320	+	0.222216i	0.648417	−	0.761285i	$-0.275431\pi$
$271$	13.6523	+	3.65813i	0.829320	+	0.222216i	0.180903	+	0.983501i	$0.442098\pi$
$272$	−0.356389	+	0.617283i	−0.0216092	+	0.0374283i
$273$	−1.34832	−	1.84215i	−0.0816039	−	0.111492i
$274$	−8.63940	−	14.9639i	−0.521925	−	0.904001i
$275$	4.11132	+	15.3437i	0.247922	+	0.925258i
$276$	4.02805	+	5.89083i	0.242460	+	0.354586i
$277$	−21.2996	+	12.2973i	−1.27977	+	0.738874i	−0.976805	−	0.214129i	$-0.931309\pi$
$277$	−21.2996	+	12.2973i	−1.27977	+	0.738874i	−0.302961	+	0.953003i	$0.597975\pi$
$278$	−6.01957	+	6.01957i	−0.361030	+	0.361030i
$279$	15.5430	−	6.83174i	0.930538	−	0.409006i
$280$	0.0290624	+	0.108462i	0.00173681	+	0.00648186i
$281$	20.3630	−	5.45626i	1.21476	−	0.325493i	0.406131	−	0.913815i	$-0.366878\pi$
$281$	20.3630	−	5.45626i	1.21476	−	0.325493i	0.808627	+	0.588322i	$0.200211\pi$
$282$	6.13221	−	4.19310i	0.365168	−	0.249695i
$283$	3.49027	+	2.01511i	0.207475	+	0.119786i	0.600137	−	0.799897i	$-0.295113\pi$
$283$	3.49027	+	2.01511i	0.207475	+	0.119786i	−0.392662	+	0.919683i	$0.628446\pi$
$284$	−6.56441	+	1.75893i	−0.389526	+	0.104373i
$285$	0.496808	+	0.238418i	0.0294283	+	0.0141227i
$286$	10.4773	+	2.45015i	0.619538	+	0.144881i
$287$		−	2.48731i		−	0.146821i
$288$	16.0540	+	1.76465i	0.945992	+	0.103983i
$289$	7.48054	+	12.9567i	0.440032	+	0.762158i
$290$	0.254450	+	0.440720i	0.0149418	+	0.0258799i
$291$	−13.9574	+	16.2635i	−0.818197	+	0.953382i
$292$	−4.63279	−	4.63279i	−0.271114	−	0.271114i
$293$	−8.16540	−	8.16540i	−0.477028	−	0.477028i	0.427152	−	0.904180i	$-0.359517\pi$
$293$	−8.16540	−	8.16540i	−0.477028	−	0.477028i	−0.904180	+	0.427152i	$0.859517\pi$
$294$	10.9554	+	2.05745i	0.638932	+	0.119993i
$295$	0.181616	+	0.314568i	0.0105741	+	0.0183149i
$296$	6.55198	+	11.3484i	0.380826	+	0.659610i
$297$	8.74503	−	14.0445i	0.507438	−	0.814944i
$298$			11.2865i			0.653811i
$299$	9.06105	−	9.66180i	0.524014	−	0.558756i
$300$	7.99980	−	5.47012i	0.461869	−	0.315818i
$301$	−0.793160	+	0.212527i	−0.0457170	+	0.0122498i
$302$	0.0342497	+	0.0197741i	0.00197085	+	0.00113787i
$303$	5.93816	+	2.84973i	0.341138	+	0.163713i
$304$	1.46109	−	0.391499i	0.0837995	−	0.0224540i
$305$	0.169770	+	0.633591i	0.00972101	+	0.0362793i
$306$	2.37540	−	3.23695i	0.135793	−	0.185044i
$307$	−17.9190	+	17.9190i	−1.02269	+	1.02269i	−0.0229527	+	0.999737i	$0.507307\pi$
$307$	−17.9190	+	17.9190i	−1.02269	+	1.02269i	−0.999737	+	0.0229527i	$0.992693\pi$
$308$	−1.13047	+	0.652675i	−0.0644143	+	0.0371896i
$309$	−11.5838	+	0.883930i	−0.658980	+	0.0502850i
$310$	0.144141	+	0.537942i	0.00818667	+	0.0305531i
$311$	11.1301	+	19.2779i	0.631129	+	1.09315i	0.987321	+	0.158735i	$0.0507415\pi$
$311$	11.1301	+	19.2779i	0.631129	+	1.09315i	−0.356192	+	0.934413i	$0.615925\pi$
$312$	−1.97371	−	18.1642i	−0.111740	−	1.02835i
$313$	4.30058	−	7.44883i	0.243083	−	0.421033i	−0.718508	−	0.695519i	$-0.755175\pi$
$313$	4.30058	−	7.44883i	0.243083	−	0.421033i	0.961591	+	0.274486i	$0.0885078\pi$
$314$	12.5934	+	3.37439i	0.710687	+	0.190428i
$315$	−0.0174702	−	0.113806i	−0.000984334	−	0.00641225i
$316$	15.8429	+	9.14693i	0.891235	+	0.514555i
$317$	8.15039	+	30.4177i	0.457771	+	1.70843i	0.679810	+	0.733388i	$0.262062\pi$
$317$	8.15039	+	30.4177i	0.457771	+	1.70843i	−0.222039	+	0.975038i	$0.571271\pi$
$318$	−7.04590	−	20.0485i	−0.395115	−	1.12427i
$319$	−11.6431	+	11.6431i	−0.651889	+	0.651889i
$320$	−0.164245	+	0.612971i	−0.00918158	+	0.0342661i
$321$	−20.9215	+	1.59646i	−1.16772	+	0.0891059i
$322$		−	1.25870i		−	0.0701449i
$323$	−1.11989	+	4.17948i	−0.0623123	+	0.232553i
$324$	−9.85263	−	2.19248i	−0.547368	−	0.121805i
$325$	−13.1208	−	12.3050i	−0.727812	−	0.682558i
$326$	−0.652755	−	0.376868i	−0.0361527	−	0.0208728i
$327$	−0.522432	−	1.48654i	−0.0288906	−	0.0822057i
$328$	9.95371	−	17.2403i	0.549602	−	0.951938i
$329$	1.67276			0.0922225
$330$	0.411829	+	0.353434i	0.0226704	+	0.0194559i
$331$	−4.04974	+	15.1138i	−0.222594	+	0.830732i	0.760760	+	0.649033i	$0.224826\pi$
$331$	−4.04974	+	15.1138i	−0.222594	+	0.830732i	−0.983354	+	0.181699i	$0.941840\pi$
$332$	17.9774	−	4.81704i	0.986639	−	0.264369i
$333$	−5.40668	−	12.3009i	−0.296284	−	0.674083i
$334$	−7.27128	+	12.5942i	−0.397867	+	0.689125i
$335$	−1.60929			−0.0879248
$336$	−0.239841	−	0.205833i	−0.0130844	−	0.0112291i
$337$	5.42515	−	3.13221i	0.295527	−	0.170622i	−0.344905	−	0.938638i	$-0.612089\pi$
$337$	5.42515	−	3.13221i	0.295527	−	0.170622i	0.640432	+	0.768015i	$0.278756\pi$
$338$	−11.5430	+	3.90161i	−0.627858	+	0.212220i
$339$	−2.30502	+	4.80311i	−0.125191	+	0.260869i
$340$	−0.118889	−	0.118889i	−0.00644768	−	0.00644768i
$341$	−15.6054	+	9.00978i	−0.845080	+	0.487907i
$342$	−8.42191	+	1.29283i	−0.455405	+	0.0699085i
$343$	3.58423	+	3.58423i	0.193530	+	0.193530i
$344$	−6.34813	−	1.70098i	−0.342268	−	0.0917105i
$345$	0.630282	−	0.221508i	0.0339332	−	0.0119256i
$346$	−13.8855	−	3.72061i	−0.746490	−	0.200021i
$347$			18.2400i			0.979176i	0.871954	+	0.489588i	$0.162853\pi$
$347$			18.2400i			0.979176i	−0.871954	+	0.489588i	$0.837147\pi$
$348$	9.05669	+	4.34631i	0.485489	+	0.232987i
$349$	5.66873	−	5.66873i	0.303440	−	0.303440i	−0.538918	−	0.842358i	$-0.681167\pi$
$349$	5.66873	−	5.66873i	0.303440	−	0.303440i	0.842358	+	0.538918i	$0.181167\pi$
$350$	−1.70933			−0.0913677
$351$	−0.0233262	+	18.7350i	−0.00124506	+	0.999999i
$352$	−17.1413			−0.913636
$353$	12.2134	−	12.2134i	0.650052	−	0.650052i	−0.302954	−	0.953005i	$-0.597973\pi$
$353$	12.2134	−	12.2134i	0.650052	−	0.650052i	0.953005	+	0.302954i	$0.0979727\pi$
$354$	−5.06351	−	2.42998i	−0.269123	−	0.129152i
$355$			0.636211i			0.0337666i
$356$	2.63887	+	0.707083i	0.139860	+	0.0374753i
$357$	0.852941	−	0.299759i	0.0451424	−	0.0158649i
$358$	16.9051	+	4.52972i	0.893464	+	0.239403i
$359$	21.8853	+	21.8853i	1.15506	+	1.15506i	0.985523	+	0.169540i	$0.0542283\pi$
$359$	21.8853	+	21.8853i	1.15506	+	1.15506i	0.169540	+	0.985523i	$0.445772\pi$
$360$	0.334337	−	0.858738i	0.0176211	−	0.0452595i
$361$	−8.50223	+	4.90877i	−0.447486	+	0.258356i
$362$	9.42428	+	9.42428i	0.495329	+	0.495329i
$363$	0.646045	−	1.34621i	0.0339086	−	0.0706576i
$364$	0.697651	−	1.30318i	0.0365669	−	0.0683050i
$365$	−0.531175	+	0.306674i	−0.0278030	+	0.0160521i
$366$	−7.69661	−	6.60527i	−0.402308	−	0.345263i
$367$	−1.31076			−0.0684213			−0.0342106	−	0.999415i	$-0.510892\pi$
$367$	−1.31076			−0.0684213			−0.0342106	+	0.999415i	$0.510892\pi$
$368$	0.916924	−	1.58816i	0.0477980	−	0.0827885i
$369$	−12.0768	+	16.4570i	−0.628696	+	0.856719i
$370$	0.425731	−	0.114074i	0.0221327	−	0.00593044i
$371$	1.23848	−	4.62206i	0.0642985	−	0.239965i
$372$	8.34250	+	7.15958i	0.432538	+	0.371207i
$373$	−28.8214			−1.49231			−0.746157	−	0.665770i	$-0.768103\pi$
$373$	−28.8214			−1.49231			−0.746157	+	0.665770i	$0.768103\pi$
$374$	−2.13064	+	3.69038i	−0.110173	+	0.190825i
$375$	−0.602284	−	1.71375i	−0.0311018	−	0.0884976i
$376$	11.5945	+	6.69406i	0.597938	+	0.345220i
$377$	4.24582	−	18.1560i	0.218671	−	0.935081i
$378$	1.21624	+	1.30011i	0.0625565	+	0.0668706i
$379$	−4.45400	+	16.6226i	−0.228787	+	0.853843i	0.752065	+	0.659088i	$0.229058\pi$
$379$	−4.45400	+	16.6226i	−0.228787	+	0.853843i	−0.980852	+	0.194755i	$0.937609\pi$
$380$			0.356811i			0.0183040i
$381$	22.2974	−	1.70146i	1.14233	−	0.0871683i
$382$	−1.77953	+	6.64130i	−0.0910487	+	0.339798i
$383$	22.6717	−	22.6717i	1.15847	−	1.15847i	0.173666	−	0.984805i	$-0.444439\pi$
$383$	22.6717	−	22.6717i	1.15847	−	1.15847i	0.984805	−	0.173666i	$-0.0555615\pi$
$384$	2.93000	+	8.33708i	0.149521	+	0.425450i
$385$	0.0316280	+	0.118037i	0.00161191	+	0.00601575i
$386$	−17.3744	−	10.0311i	−0.884336	−	0.510571i
$387$	6.27976	+	2.44494i	0.319218	+	0.124283i
$388$	−13.4042	−	3.59164i	−0.680495	−	0.182338i
$389$	−8.01814	+	13.8878i	−0.406536	+	0.704141i	−0.994499	−	0.104747i	$-0.966597\pi$
$389$	−8.01814	+	13.8878i	−0.406536	+	0.704141i	0.587963	+	0.808888i	$0.299930\pi$
$390$	−0.607313	−	0.0940018i	−0.0307525	−	0.00475997i
$391$	2.62288	+	4.54295i	0.132645	+	0.229747i
$392$	5.19944	+	19.4046i	0.262611	+	0.980078i
$393$	−26.8294	+	2.04728i	−1.35336	+	0.103271i
$394$	−3.14814	+	1.81758i	−0.158601	+	0.0915684i
$395$	1.21099	−	1.21099i	0.0609314	−	0.0609314i
$396$	10.6486	+	1.17049i	0.535112	+	0.0588192i
$397$	−7.81599	−	29.1697i	−0.392273	−	1.46398i	−0.826375	−	0.563120i	$-0.809601\pi$
$397$	−7.81599	−	29.1697i	−0.392273	−	1.46398i	0.434102	−	0.900864i	$-0.357066\pi$
$398$	−9.27283	+	2.48465i	−0.464805	+	0.124544i
$399$	−1.72974	−	0.830105i	−0.0865955	−	0.0415572i
$400$	−2.15673	−	1.24519i	−0.107837	−	0.0622596i
$401$	10.9633	−	2.93761i	0.547482	−	0.146697i	0.0255329	−	0.999674i	$-0.491872\pi$
$401$	10.9633	−	2.93761i	0.547482	−	0.146697i	0.521949	+	0.852977i	$0.325205\pi$
$402$	20.5405	−	14.0452i	1.02446	−	0.700511i
$403$	9.63066	−	17.9896i	0.479737	−	0.896124i
$404$			4.26484i			0.212184i
$405$	−0.436982	+	0.837811i	−0.0217138	+	0.0416312i
$406$	−0.885922	−	1.53446i	−0.0439676	−	0.0761541i
$407$	7.13040	+	12.3502i	0.353441	+	0.612177i
$408$	7.11157	+	1.33557i	0.352075	+	0.0661205i
$409$	8.33215	+	8.33215i	0.411998	+	0.411998i	0.882434	−	0.470436i	$-0.155903\pi$
$409$	8.33215	+	8.33215i	0.411998	+	0.411998i	−0.470436	+	0.882434i	$0.655903\pi$
$410$	−0.473466	−	0.473466i	−0.0233828	−	0.0233828i
$411$	−20.7950	+	24.2308i	−1.02574	+	1.19522i
$412$	−3.76120	−	6.51459i	−0.185301	−	0.320951i
$413$	−0.632336	−	1.09524i	−0.0311152	−	0.0538931i
$414$	−6.11149	+	8.32809i	−0.300363	+	0.409303i
$415$		−	1.74234i		−	0.0855281i
$416$	16.4903	−	10.2395i	0.808504	−	0.502032i
$417$	14.1830	+	6.80641i	0.694543	+	0.333311i
$418$	8.73504	−	2.34055i	0.427245	−	0.114480i
$419$	−2.49796	−	1.44220i	−0.122033	−	0.0704561i	0.437741	−	0.899101i	$-0.355779\pi$
$419$	−2.49796	−	1.44220i	−0.122033	−	0.0704561i	−0.559774	+	0.828645i	$0.689112\pi$
$420$	0.0615417	−	0.0420812i	0.00300293	−	0.00205335i
$421$	2.42199	−	0.648970i	0.118040	−	0.0316288i	−0.199315	−	0.979935i	$-0.563872\pi$
$421$	2.42199	−	0.648970i	0.118040	−	0.0316288i	0.317356	+	0.948307i	$0.397205\pi$
$422$	4.38375	+	16.3604i	0.213398	+	0.796411i
$423$	−11.0677	−	8.12191i	−0.538129	−	0.394901i
$424$	27.0808	−	27.0808i	1.31516	−	1.31516i
$425$	6.16938	−	3.56189i	0.299259	−	0.172777i
$426$	−5.55258	−	8.12040i	−0.269024	−	0.393435i
$427$	−0.591092	−	2.20598i	−0.0286049	−	0.106755i
$428$	−6.79309	−	11.7660i	−0.328357	−	0.568730i
$429$	−2.14796	−	19.7678i	−0.103704	−	0.954397i
$430$	−0.110525	+	0.191435i	−0.00532999	+	0.00923182i
$431$	−14.9429	−	4.00393i	−0.719773	−	0.192863i	−0.119703	−	0.992810i	$-0.538194\pi$
$431$	−14.9429	−	4.00393i	−0.719773	−	0.192863i	−0.600071	+	0.799947i	$0.704861\pi$
$432$	0.587486	+	2.52639i	0.0282655	+	0.121551i
$433$	4.53654	+	2.61917i	0.218012	+	0.125869i	0.605029	−	0.796203i	$-0.293161\pi$
$433$	4.53654	+	2.61917i	0.218012	+	0.125869i	−0.387017	+	0.922072i	$0.626495\pi$
$434$	−0.501859	−	1.87296i	−0.0240900	−	0.0899051i
$435$	0.612459	−	0.713650i	0.0293651	−	0.0342169i
$436$	0.721429	−	0.721429i	0.0345502	−	0.0345502i
$437$	2.88127	−	10.7531i	0.137830	−	0.514389i
$438$	4.10323	−	8.55017i	0.196060	−	0.408543i
$439$			15.7759i			0.752941i	0.926429	+	0.376470i	$0.122862\pi$
$439$			15.7759i			0.752941i	−0.926429	+	0.376470i	$0.877138\pi$
$440$	−0.253138	+	0.944723i	−0.0120679	+	0.0450379i
$441$	−3.12553	−	20.3606i	−0.148835	−	0.969553i
$442$	−0.154751	−	4.82297i	−0.00736076	−	0.229405i
$443$	−22.7538	−	13.1369i	−1.08107	−	0.624155i	−0.149884	−	0.988704i	$-0.547890\pi$
$443$	−22.7538	−	13.1369i	−1.08107	−	0.624155i	−0.931184	+	0.364549i	$0.881223\pi$
$444$	5.66614	−	6.60231i	0.268903	−	0.313332i
$445$	0.127877	−	0.221490i	0.00606196	−	0.0104996i
$446$	−3.00721			−0.142395
$447$	19.6773	−	6.91543i	0.930703	−	0.327088i
$448$	0.571855	−	2.13419i	0.0270176	−	0.100831i
$449$	12.2297	−	3.27694i	0.577156	−	0.154648i	0.0415795	−	0.999135i	$-0.486761\pi$
$449$	12.2297	−	3.27694i	0.577156	−	0.154648i	0.535576	+	0.844487i	$0.320094\pi$
$450$	11.3096	+	8.29946i	0.533141	+	0.391240i
$451$	10.8324	−	18.7623i	0.510080	−	0.883484i
$452$	−3.44964			−0.162257
$453$	0.0134894	−	0.0718279i	0.000633788	−	0.00337477i
$454$	3.08254	−	1.77971i	0.144671	−	0.0835258i
$455$	−0.100937	−	0.0946612i	−0.00473201	−	0.00443778i
$456$	−8.66749	−	12.6758i	−0.405892	−	0.593599i
$457$	−9.27033	−	9.27033i	−0.433648	−	0.433648i	0.456219	−	0.889867i	$-0.349203\pi$
$457$	−9.27033	−	9.27033i	−0.433648	−	0.433648i	−0.889867	+	0.456219i	$0.849203\pi$
$458$	−14.2407	+	8.22188i	−0.665425	+	0.384183i
$459$	−7.09884	−	2.15803i	−0.331345	−	0.100728i
$460$	0.305881	+	0.305881i	0.0142618	+	0.0142618i
$461$	−32.3624	−	8.67148i	−1.50727	−	0.403871i	−0.591741	−	0.806128i	$-0.701559\pi$
$461$	−32.3624	−	8.67148i	−1.50727	−	0.403871i	−0.915527	+	0.402257i	$0.868226\pi$
$462$	−1.43387	−	1.23056i	−0.0667098	−	0.0572507i
$463$	14.9116	+	3.99555i	0.693000	+	0.185689i	0.588093	−	0.808793i	$-0.299879\pi$
$463$	14.9116	+	3.99555i	0.693000	+	0.185689i	0.104907	+	0.994482i	$0.466545\pi$
$464$		−	2.58146i		−	0.119841i
$465$	0.849547	−	0.580905i	0.0393968	−	0.0269388i
$466$	−9.59189	+	9.59189i	−0.444336	+	0.444336i
$467$	−20.9252			−0.968302			−0.484151	−	0.874985i	$-0.660871\pi$
$467$	−20.9252			−0.968302			−0.484151	+	0.874985i	$0.660871\pi$
$468$	−10.9434	+	5.23497i	−0.505857	+	0.241987i
$469$	5.60309			0.258727
$470$	0.318415	−	0.318415i	0.0146874	−	0.0146874i
$471$	−1.83315	−	24.0233i	−0.0844671	−	1.10693i
$472$		−	10.1219i		−	0.465899i
$473$	−6.90855	−	1.85114i	−0.317656	−	0.0851156i
$474$	−4.88767	+	26.0257i	−0.224498	+	1.19540i
$475$	−14.6028	−	3.91280i	−0.670021	−	0.179531i
$476$	0.413939	+	0.413939i	0.0189729	+	0.0189729i
$477$	−30.6361	+	24.5681i	−1.40273	+	1.12489i
$478$	16.6230	−	9.59729i	0.760318	−	0.438970i
$479$	−16.0406	−	16.0406i	−0.732914	−	0.732914i	0.238282	−	0.971196i	$-0.423416\pi$
$479$	−16.0406	−	16.0406i	−0.732914	−	0.732914i	−0.971196	+	0.238282i	$0.923416\pi$
$480$	0.976168	−	0.0744887i	0.0445558	−	0.00339993i
$481$	−14.2371	−	7.62176i	−0.649154	−	0.347523i
$482$	19.6042	−	11.3185i	0.892949	−	0.515544i
$483$	−2.19446	+	0.771227i	−0.0998516	+	0.0350921i
$484$	0.966857			0.0439481
$485$	−0.649556	+	1.12506i	−0.0294948	+	0.0510865i
$486$	−1.73456	−	14.5074i	−0.0786811	−	0.658067i
$487$	6.17114	−	1.65355i	0.279641	−	0.0749295i	−0.116273	−	0.993217i	$-0.537095\pi$
$487$	6.17114	−	1.65355i	0.279641	−	0.0749295i	0.395914	+	0.918288i	$0.370428\pi$
$488$	4.73085	−	17.6558i	0.214156	−	0.799240i
$489$	−0.257091	+	1.36894i	−0.0116260	+	0.0619058i
$490$	0.675692			0.0305247
$491$	−6.90407	+	11.9582i	−0.311576	+	0.539666i	−0.978704	−	0.205278i	$-0.934190\pi$
$491$	−6.90407	+	11.9582i	−0.311576	+	0.539666i	0.667128	+	0.744943i	$0.267524\pi$
$492$	−12.9904	−	2.43961i	−0.585650	−	0.109986i
$493$	6.39499	+	3.69215i	0.288016	+	0.166286i
$494$	−7.00514	+	7.46958i	−0.315176	+	0.336072i
$495$	0.363853	−	0.934549i	0.0163540	−	0.0420048i
$496$	0.731175	−	2.72878i	0.0328307	−	0.122526i
$497$		−	2.21511i		−	0.0993612i
$498$	15.2064	+	22.2387i	0.681416	+	0.996539i
$499$	−1.01763	+	3.79783i	−0.0455552	+	0.170014i	−0.984956	−	0.172808i	$-0.944716\pi$
$499$	−1.01763	+	3.79783i	−0.0455552	+	0.170014i	0.939400	+	0.342822i	$0.111383\pi$
$500$	0.831697	−	0.831697i	0.0371946	−	0.0371946i
$501$	26.4124	+	4.96030i	1.18002	+	0.221610i
$502$	1.90450	+	7.10771i	0.0850022	+	0.317232i
$503$	−9.04338	−	5.22120i	−0.403224	−	0.232802i	0.284650	−	0.958632i	$-0.408123\pi$
$503$	−9.04338	−	5.22120i	−0.403224	−	0.232802i	−0.687874	+	0.725830i	$0.741456\pi$
$504$	−1.16407	+	2.98988i	−0.0518517	+	0.133180i
$505$	0.385652	+	0.103335i	0.0171613	+	0.00459835i
$506$	5.48176	−	9.49469i	0.243694	−	0.422090i
$507$	13.8748	+	17.7339i	0.616200	+	0.787590i
$508$	7.23985	+	12.5398i	0.321217	+	0.556363i
$509$	−8.12088	−	30.3075i	−0.359952	−	1.34336i	−0.874137	−	0.485679i	$-0.838572\pi$
$509$	−8.12088	−	30.3075i	−0.359952	−	1.34336i	0.514186	−	0.857679i	$-0.328094\pi$
$510$	0.105299	−	0.219419i	0.00466274	−	0.00971605i
$511$	1.84940	−	1.06775i	0.0818128	−	0.0472346i
$512$	3.96564	−	3.96564i	0.175258	−	0.175258i
$513$	7.41420	+	13.8909i	0.327345	+	0.613297i
$514$	6.39299	+	23.8590i	0.281983	+	1.05237i
$515$	−0.680221	+	0.182265i	−0.0299741	+	0.00803154i
$516$	0.332002	+	4.35085i	0.0146156	+	0.191536i
$517$	12.6180	+	7.28502i	0.554940	+	0.320395i
$518$	−1.48227	+	0.397174i	−0.0651274	+	0.0174508i
$519$	2.02124	+	26.4881i	0.0887224	+	1.16270i
$520$	−0.320813	−	1.06006i	−0.0140686	−	0.0464865i
$521$		−	22.8205i		−	0.999785i	−0.866087	−	0.499893i	$-0.833373\pi$
$521$		−	22.8205i		−	0.999785i	0.866087	−	0.499893i	$-0.166627\pi$
$522$	−1.58879	+	14.4541i	−0.0695393	+	0.632639i
$523$	−1.54860	−	2.68225i	−0.0677156	−	0.117287i	0.830180	−	0.557496i	$-0.188238\pi$
$523$	−1.54860	−	2.68225i	−0.0677156	−	0.117287i	−0.897895	+	0.440209i	$0.854904\pi$
$524$	−8.71135	−	15.0885i	−0.380557	−	0.659144i
$525$	1.04733	+	2.98010i	0.0457094	+	0.130062i
$526$	13.9970	+	13.9970i	0.610300	+	0.610300i
$527$	5.71419	+	5.71419i	0.248914	+	0.248914i
$528$	−0.912755	−	2.59717i	−0.0397226	−	0.113027i
$529$	4.75181	+	8.23037i	0.206600	+	0.357842i
$530$	−0.644073	−	1.11557i	−0.0279767	−	0.0484571i
$531$	−1.13401	+	10.3168i	−0.0492120	+	0.447709i
$532$		−	1.24232i		−	0.0538613i
$533$	0.786773	+	24.5206i	0.0340789	+	1.06210i
$534$	0.300886	+	3.94309i	0.0130206	+	0.170634i
$535$	−1.22854	+	0.329187i	−0.0531146	+	0.0142320i
$536$	38.8368	+	22.4224i	1.67749	+	0.968501i
$537$	−2.46078	−	32.2483i	−0.106191	−	1.39162i
$538$	3.95629	−	1.06008i	0.170568	−	0.0457035i
$539$	5.65845	+	21.1176i	0.243727	+	0.909601i
$540$	−0.611505	−	0.0203831i	−0.0263150	−	0.000877147i
$541$	−5.55366	+	5.55366i	−0.238771	+	0.238771i	−0.816341	−	0.577570i	$-0.804001\pi$
$541$	−5.55366	+	5.55366i	−0.238771	+	0.238771i	0.577570	+	0.816341i	$0.304001\pi$
$542$	−11.4726	+	6.62369i	−0.492789	+	0.284512i
$543$	10.6562	−	22.2050i	0.457300	−	0.952906i
$544$	1.98960	+	7.42529i	0.0853034	+	0.318357i
$545$	−0.0477560	−	0.0827159i	−0.00204564	−	0.00354316i
$546$	2.11449	+	0.327288i	0.0904920	+	0.0140066i
$547$	−8.77561	+	15.1998i	−0.375218	+	0.649897i	−0.990360	−	0.138520i	$-0.955766\pi$
$547$	−8.77561	+	15.1998i	−0.375218	+	0.649897i	0.615142	+	0.788417i	$0.289099\pi$
$548$	−19.9708	−	5.35115i	−0.853109	−	0.228590i
$549$	−6.80000	+	17.4656i	−0.290217	+	0.745415i
$550$	−12.8939	−	7.44428i	−0.549797	−	0.317425i
$551$	−4.05589	−	15.1368i	−0.172787	−	0.644849i
$552$	−18.2968	−	3.43618i	−0.778764	−	0.146253i
$553$	−4.21632	+	4.21632i	−0.179296	+	0.179296i
$554$	5.96628	−	22.2665i	0.253483	−	0.946011i
$555$	−0.459732	−	0.672337i	−0.0195145	−	0.0285391i
$556$			10.1863i			0.431996i
$557$	−4.44615	+	16.5933i	−0.188390	+	0.703079i	0.805490	+	0.592609i	$0.201902\pi$
$557$	−4.44615	+	16.5933i	−0.188390	+	0.703079i	−0.993879	+	0.110470i	$0.964764\pi$
$558$	−5.77345	+	14.8290i	−0.244410	+	0.627761i
$559$	7.75196	−	2.34603i	0.327873	−	0.0992266i
$560$	−0.0165916	−	0.00957914i	−0.000701121	−	0.000404793i
$561$	7.73939	+	1.45347i	0.326757	+	0.0613657i
$562$	−9.87953	+	17.1119i	−0.416743	+	0.721820i
$563$	9.32207			0.392879			0.196439	−	0.980516i	$-0.437062\pi$
$563$	9.32207			0.392879			0.196439	+	0.980516i	$0.437062\pi$
$564$	1.64069	−	8.73626i	0.0690854	−	0.367863i
$565$	−0.0835832	+	0.311937i	−0.00351637	+	0.0131233i
$566$	−3.64871	+	0.977668i	−0.153367	+	0.0410945i
$567$	1.52145	−	2.91702i	0.0638949	−	0.122503i
$568$	8.86441	−	15.3536i	0.371942	−	0.644223i
$569$	−26.0138			−1.09056			−0.545278	−	0.838255i	$-0.683576\pi$
$569$	−26.0138			−1.09056			−0.545278	+	0.838255i	$0.683576\pi$
$570$	−0.487274	+	0.171249i	−0.0204097	+	0.00717281i
$571$	−2.90676	+	1.67822i	−0.121644	+	0.0702313i	−0.559587	−	0.828771i	$-0.689040\pi$
$571$	−2.90676	+	1.67822i	−0.121644	+	0.0702313i	0.437943	+	0.899003i	$0.355707\pi$
$572$	10.9380	−	6.79182i	0.457340	−	0.283980i
$573$	12.6690	−	0.966736i	0.529255	−	0.0403860i
$574$	1.64848	+	1.64848i	0.0688060	+	0.0688060i
$575$	−15.8727	+	9.16411i	−0.661937	+	0.382170i
$576$	−14.1459	+	11.3441i	−0.589414	+	0.472670i
$577$	19.0194	+	19.0194i	0.791788	+	0.791788i	0.981785	−	0.189997i	$-0.0608478\pi$
$577$	19.0194	+	19.0194i	0.791788	+	0.791788i	−0.189997	+	0.981785i	$0.560848\pi$
$578$	−13.5449	−	3.62933i	−0.563392	−	0.150960i
$579$	−6.84301	+	36.4373i	−0.284386	+	1.51428i
$580$	0.588184	+	0.157603i	0.0244230	+	0.00654412i
$581$			6.06634i			0.251674i
$582$	−1.52836	−	20.0290i	−0.0633525	−	0.830229i
$583$	29.4715	−	29.4715i	1.22059	−	1.22059i
$584$	17.0917			0.707260
$585$	0.208224	+	1.11640i	0.00860902	+	0.0461576i
$586$	10.8233			0.447107
$587$	−7.56353	+	7.56353i	−0.312180	+	0.312180i	−0.845754	−	0.533573i	$-0.820849\pi$
$587$	−7.56353	+	7.56353i	−0.312180	+	0.312180i	0.533573	+	0.845754i	$0.320849\pi$
$588$	11.0102	−	7.52858i	0.454053	−	0.310473i
$589$		−	17.1494i		−	0.706630i
$590$	−0.328848	−	0.0881146i	−0.0135385	−	0.00362762i
$591$	5.09774	+	4.37490i	0.209693	+	0.179960i
$592$	−2.15957	−	0.578656i	−0.0887580	−	0.0237826i
$593$	11.0116	+	11.0116i	0.452191	+	0.452191i	0.896081	−	0.443890i	$-0.146402\pi$
$593$	11.0116	+	11.0116i	0.452191	+	0.452191i	−0.443890	+	0.896081i	$0.646402\pi$
$594$	3.51224	+	15.1038i	0.144109	+	0.619718i
$595$	0.0474604	−	0.0274013i	0.00194569	−	0.00112334i
$596$	9.54955	+	9.54955i	0.391165	+	0.391165i
$597$	10.0134	+	14.6442i	0.409822	+	0.599345i
$598$	0.398147	+	12.4086i	0.0162814	+	0.507427i
$599$	−18.9127	+	10.9193i	−0.772752	+	0.446149i	−0.833856	−	0.551983i	$-0.813871\pi$
$599$	−18.9127	+	10.9193i	−0.772752	+	0.446149i	0.0611031	+	0.998131i	$0.480538\pi$
$600$	−4.66636	+	24.8472i	−0.190503	+	1.01438i
$601$	12.2925			0.501420			0.250710	−	0.968062i	$-0.419336\pi$
$601$	12.2925			0.501420			0.250710	+	0.968062i	$0.419336\pi$
$602$	0.384817	−	0.666523i	0.0156840	−	0.0271655i
$603$	−37.0723	−	27.2051i	−1.50970	−	1.10788i
$604$	0.0457096	−	0.0122479i	0.00185990	−	0.000498358i
$605$	0.0234265	−	0.0874290i	0.000952424	−	0.00355449i
$606$	−5.82421	+	2.04687i	−0.236592	+	0.0831485i
$607$	25.1603			1.02123			0.510613	−	0.859811i	$-0.329418\pi$
$607$	25.1603			1.02123			0.510613	+	0.859811i	$0.329418\pi$
$608$	8.15681	−	14.1280i	0.330802	−	0.572966i
$609$	−2.13241	+	2.48473i	−0.0864096	+	0.100686i
$610$	−0.532430	−	0.307399i	−0.0215575	−	0.0124462i
$611$	−16.4905	+	0.529120i	−0.667136	+	0.0214059i
$612$	−0.728953	−	4.74862i	−0.0294662	−	0.191952i
$613$	−0.567750	+	2.11887i	−0.0229312	+	0.0855804i	−0.976443	−	0.215775i	$-0.930772\pi$
$613$	−0.567750	+	2.11887i	−0.0229312	+	0.0855804i	0.953512	+	0.301355i	$0.0974390\pi$
$614$		−	23.7517i		−	0.958542i
$615$	−0.535355	+	1.11555i	−0.0215876	+	0.0449835i
$616$	0.881355	−	3.28926i	0.0355108	−	0.132528i
$617$	7.90933	−	7.90933i	0.318417	−	0.318417i	−0.529742	−	0.848159i	$-0.677711\pi$
$617$	7.90933	−	7.90933i	0.318417	−	0.318417i	0.848159	+	0.529742i	$0.177711\pi$
$618$	7.09139	−	8.26305i	0.285258	−	0.332389i
$619$	−2.85556	−	10.6571i	−0.114775	−	0.428345i	0.884495	−	0.466549i	$-0.154503\pi$
$619$	−2.85556	−	10.6571i	−0.114775	−	0.428345i	−0.999270	+	0.0382041i	$0.987836\pi$
$620$	0.577112	+	0.333196i	0.0231774	+	0.0133815i
$621$	18.2640	+	5.55221i	0.732911	+	0.222803i
$622$	−20.1530	−	5.39998i	−0.808061	−	0.216519i
$623$	−0.445233	+	0.771166i	−0.0178379	+	0.0308961i
$624$	2.42952	+	1.95329i	0.0972588	+	0.0781942i
$625$	12.4174	+	21.5075i	0.496695	+	0.860302i
$626$	2.08651	+	7.78697i	0.0833938	+	0.311230i
$627$	−9.43267	−	13.7948i	−0.376704	−	0.550913i
$628$	13.5104	−	7.80023i	0.539123	−	0.311263i
$629$	4.52224	−	4.52224i	0.180314	−	0.180314i
$630$	0.0870039	+	0.0638470i	0.00346632	+	0.00254373i
$631$	−0.654527	−	2.44273i	−0.0260563	−	0.0972435i	0.951673	−	0.307113i	$-0.0993629\pi$
$631$	−0.654527	−	2.44273i	−0.0260563	−	0.0972435i	−0.977729	+	0.209869i	$0.932696\pi$
$632$	−46.0974	+	12.3518i	−1.83366	+	0.491327i
$633$	25.8372	−	17.6670i	1.02694	−	0.702201i
$634$	−25.5611	−	14.7577i	−1.01516	−	0.586104i
$635$	1.30934	−	0.350837i	0.0519596	−	0.0139225i
$636$	−22.9246	−	11.0015i	−0.909021	−	0.436240i
$637$	−18.0583	−	16.9355i	−0.715495	−	0.671008i
$638$		−	15.4330i		−	0.611000i
$639$	−10.7552	+	14.6560i	−0.425469	+	0.579784i
$640$	0.267834	+	0.463903i	0.0105871	+	0.0183374i
$641$	8.99758	+	15.5843i	0.355383	+	0.615541i	0.987183	−	0.159590i	$-0.0510172\pi$
$641$	8.99758	+	15.5843i	0.355383	+	0.615541i	−0.631801	+	0.775131i	$0.717684\pi$
$642$	12.8077	−	14.9239i	0.505481	−	0.588998i
$643$	−25.2949	−	25.2949i	−0.997532	−	0.997532i	0.00246501	−	0.999997i	$-0.499215\pi$
$643$	−25.2949	−	25.2949i	−0.997532	−	0.997532i	−0.999997	+	0.00246501i	$0.999215\pi$
$644$	−1.06499	−	1.06499i	−0.0419666	−	0.0419666i
$645$	0.401474	+	0.0753976i	0.0158080	+	0.00296878i
$646$	−2.02776	−	3.51218i	−0.0797811	−	0.138185i
$647$	10.1566	+	17.5918i	0.399298	+	0.691605i	0.993639	−	0.112608i	$-0.0359205\pi$
$647$	10.1566	+	17.5918i	0.399298	+	0.691605i	−0.594341	+	0.804213i	$0.702587\pi$
$648$	22.2190	−	14.1303i	0.872843	−	0.555089i
$649$		−	11.0155i		−	0.432396i
$650$	16.8511	−	0.540687i	0.660953	−	0.0212075i
$651$	−2.95788	+	2.02255i	−0.115929	+	0.0792699i
$652$	−0.871165	+	0.233428i	−0.0341175	+	0.00914175i
$653$	25.3293	+	14.6239i	0.991213	+	0.572277i	0.905637	−	0.424055i	$-0.139394\pi$
$653$	25.3293	+	14.6239i	0.991213	+	0.572277i	0.0855762	+	0.996332i	$0.472727\pi$
$654$	1.33145	+	0.638965i	0.0520639	+	0.0249855i
$655$	−1.57546	+	0.422144i	−0.0615585	+	0.0164945i
$656$	0.879090	+	3.28081i	0.0343227	+	0.128094i
$657$	−17.4207	−	1.91488i	−0.679648	−	0.0747065i
$658$	−1.10863	+	1.10863i	−0.0432189	+	0.0432189i
$659$	36.4402	−	21.0388i	1.41951	−	0.819554i	0.423254	−	0.906011i	$-0.360888\pi$
$659$	36.4402	−	21.0388i	1.41951	−	0.819554i	0.996256	+	0.0864566i	$0.0275544\pi$
$660$	0.647490	−	0.0494082i	0.0252035	−	0.00192321i
$661$	−4.83701	−	18.0520i	−0.188138	−	0.702141i	−0.993937	−	0.109951i	$-0.964930\pi$
$661$	−4.83701	−	18.0520i	−0.188138	−	0.702141i	0.805799	−	0.592189i	$-0.201736\pi$
$662$	−7.33278	−	12.7007i	−0.284997	−	0.493628i
$663$	−8.31369	+	3.22490i	−0.322877	+	0.125245i
$664$	−24.2762	+	42.0477i	−0.942101	+	1.63177i
$665$	−0.112338	−	0.0301008i	−0.00435627	−	0.00116726i
$666$	11.7358	+	4.56915i	0.454751	+	0.177051i
$667$	−16.4532	−	9.49924i	−0.637069	−	0.367812i
$668$	4.50375	+	16.8082i	0.174255	+	0.650330i
$669$	1.84256	+	5.24286i	0.0712375	+	0.202701i
$670$	1.06656	−	1.06656i	0.0412049	−	0.0412049i
$671$	5.14850	−	19.2145i	0.198756	−	0.741767i
$672$	−3.39874	+	0.259349i	−0.131109	+	0.0100046i
$673$		−	6.01382i		−	0.231816i	−0.993260	−	0.115908i	$-0.963022\pi$
$673$		−	6.01382i		−	0.231816i	0.993260	−	0.115908i	$-0.0369777\pi$
$674$	−1.51965	+	5.67142i	−0.0585349	+	0.218455i
$675$	7.53996	−	24.8027i	0.290213	−	0.954658i
$676$	−6.46542	+	13.0677i	−0.248670	+	0.502605i
$677$	23.1275	+	13.3527i	0.888863	+	0.513185i	0.873570	−	0.486698i	$-0.161799\pi$
$677$	23.1275	+	13.3527i	0.888863	+	0.513185i	0.0152925	+	0.999883i	$0.495132\pi$
$678$	−1.65562	−	4.71094i	−0.0635839	−	0.180923i
$679$	2.26157	−	3.91715i	0.0867911	−	0.150327i
$680$	0.438617			0.0168202
$681$	−4.99151	−	4.28374i	−0.191275	−	0.164153i
$682$	4.37127	−	16.3138i	0.167385	−	0.624688i
$683$	29.2534	−	7.83841i	1.11935	−	0.299929i	0.348729	−	0.937224i	$-0.386613\pi$
$683$	29.2534	−	7.83841i	1.11935	−	0.299929i	0.770620	+	0.637295i	$0.219947\pi$
$684$	−6.03192	+	8.21966i	−0.230636	+	0.314287i
$685$	−0.967766	+	1.67622i	−0.0369764	+	0.0640451i
$686$	−4.75092			−0.181391
$687$	23.0598	+	19.7900i	0.879785	+	0.755036i
$688$	0.971079	−	0.560653i	0.0370220	−	0.0213747i
$689$	−10.7472	+	45.9572i	−0.409436	+	1.75083i
$690$	−0.270917	+	0.564527i	−0.0103136	+	0.0214912i
$691$	30.2032	+	30.2032i	1.14898	+	1.14898i	0.986753	+	0.162231i	$0.0518689\pi$
$691$	30.2032	+	30.2032i	1.14898	+	1.14898i	0.162231	+	0.986753i	$0.448131\pi$
$692$	−14.8966	+	8.60054i	−0.566283	+	0.326944i
$693$	−1.26683	+	3.25384i	−0.0481231	+	0.123603i
$694$	−12.0886	−	12.0886i	−0.458879	−	0.458879i
$695$	0.921108	+	0.246810i	0.0349396	+	0.00936205i
$696$	−24.7238	+	8.68898i	−0.937152	+	0.329355i
$697$	−9.38480	−	2.51465i	−0.355475	−	0.0952492i
$698$			7.51395i			0.284407i
$699$	22.5999	+	10.8457i	0.854806	+	0.410222i
$700$	−1.44627	+	1.44627i	−0.0546638	+	0.0546638i
$701$	−23.1973			−0.876151			−0.438075	−	0.898938i	$-0.644340\pi$
$701$	−23.1973			−0.876151			−0.438075	+	0.898938i	$0.644340\pi$
$702$	−12.4012	−	12.4321i	−0.468054	−	0.469221i
$703$	−13.5722			−0.511884
$704$	13.6082	−	13.6082i	0.512879	−	0.512879i
$705$	−0.750232	−	0.360037i	−0.0282554	−	0.0135598i
$706$			16.1889i			0.609278i
$707$	−1.34273	−	0.359784i	−0.0504986	−	0.0135311i
$708$	−6.34025	+	2.22823i	−0.238281	+	0.0837421i
$709$	8.81969	+	2.36323i	0.331230	+	0.0887529i	0.420602	−	0.907245i	$-0.361819\pi$
$709$	8.81969	+	2.36323i	0.331230	+	0.0887529i	−0.0893711	+	0.995998i	$0.528486\pi$
$710$	−0.421651	−	0.421651i	−0.0158243	−	0.0158243i
$711$	48.3686	−	7.42500i	1.81397	−	0.278459i
$712$	−6.17209	+	3.56346i	−0.231309	+	0.133546i
$713$	−14.7016	−	14.7016i	−0.550578	−	0.550578i
$714$	−0.366623	+	0.763957i	−0.0137205	+	0.0285904i
$715$	−0.349134	−	1.15364i	−0.0130569	−	0.0431437i
$716$	18.1361	−	10.4709i	0.677776	−	0.391314i
$717$	−26.9174	−	23.1006i	−1.00525	−	0.862708i
$718$	−29.0092			−1.08261
$719$	−7.26683	+	12.5865i	−0.271007	+	0.469398i	−0.969120	−	0.246590i	$-0.920690\pi$
$719$	−7.26683	+	12.5865i	−0.271007	+	0.469398i	0.698113	+	0.715988i	$0.254023\pi$
$720$	0.0632659	+	0.143938i	0.00235778	+	0.00536424i
$721$	2.36834	−	0.634594i	0.0882015	−	0.0236335i
$722$	2.38158	−	8.88819i	0.0886334	−	0.330784i
$723$	−31.7449	−	27.2436i	−1.18060	−	1.01320i
$724$	15.9478			0.592695
$725$	−12.9001	+	22.3436i	−0.479096	+	0.829819i
$726$	0.464035	+	1.32037i	0.0172220	+	0.0490037i
$727$	−23.7883	−	13.7342i	−0.882259	−	0.509372i	−0.0108564	−	0.999941i	$-0.503456\pi$
$727$	−23.7883	−	13.7342i	−0.882259	−	0.509372i	−0.871403	+	0.490569i	$0.836789\pi$
$728$	1.11698	+	3.69082i	0.0413980	+	0.136791i
$729$	−24.2298	+	11.9130i	−0.897399	+	0.441220i
$730$	0.148789	−	0.555288i	0.00550693	−	0.0205521i
$731$			3.20751i			0.118634i
$732$	−12.1008	+	0.923382i	−0.447260	+	0.0341292i
$733$	9.56277	−	35.6888i	0.353209	−	1.31819i	−0.529514	−	0.848301i	$-0.677626\pi$
$733$	9.56277	−	35.6888i	0.353209	−	1.31819i	0.882723	−	0.469893i	$-0.155708\pi$
$734$	0.868713	−	0.868713i	0.0320648	−	0.0320648i
$735$	−0.414007	−	1.17802i	−0.0152709	−	0.0434520i
$736$	−5.11889	−	19.1039i	−0.188685	−	0.704181i
$737$	42.2653	+	24.4019i	1.55686	+	0.898856i
$738$	−2.90299	−	18.9109i	−0.106861	−	0.696122i
$739$	−6.91898	−	1.85394i	−0.254519	−	0.0681981i	0.129304	−	0.991605i	$-0.458726\pi$
$739$	−6.91898	−	1.85394i	−0.254519	−	0.0681981i	−0.383822	+	0.923407i	$0.625393\pi$
$740$	0.263693	−	0.456730i	0.00969355	−	0.0167897i
$741$	17.3148	+	7.63625i	0.636077	+	0.280525i
$742$	2.24248	+	3.88409i	0.0823241	+	0.142589i
$743$	−4.09506	−	15.2830i	−0.150233	−	0.560678i	−0.999467	−	0.0326604i	$-0.989602\pi$
$743$	−4.09506	−	15.2830i	−0.150233	−	0.560678i	0.849233	−	0.528018i	$-0.177065\pi$
$744$	−28.5958	+	2.18207i	−1.04837	+	0.0799986i
$745$	1.09491	−	0.632146i	0.0401144	−	0.0231600i
$746$	19.1015	−	19.1015i	0.699355	−	0.699355i
$747$	29.4544	−	40.1373i	1.07768	−	1.46855i
$748$	1.31970	+	4.92518i	0.0482529	+	0.180082i
$749$	4.27745	−	1.14614i	0.156294	−	0.0418790i
$750$	1.53496	+	0.736628i	0.0560488	+	0.0268978i
$751$	−32.7770	−	18.9238i	−1.19605	−	0.690539i	−0.236377	−	0.971661i	$-0.575960\pi$
$751$	−32.7770	−	18.9238i	−1.19605	−	0.690539i	−0.959672	+	0.281123i	$0.909293\pi$
$752$	−2.20641	+	0.591204i	−0.0804593	+	0.0215590i
$753$	11.2249	−	7.67537i	0.409057	−	0.279706i
$754$	9.21902	+	14.8469i	0.335737	+	0.540692i
$755$		−	0.00443010i		−	0.000161228i
$756$	2.12909	+	0.0709681i	0.0774342	+	0.00258108i
$757$	8.84072	+	15.3126i	0.321322	+	0.556545i	0.980761	−	0.195212i	$-0.0625396\pi$
$757$	8.84072	+	15.3126i	0.321322	+	0.556545i	−0.659439	+	0.751758i	$0.729206\pi$
$758$	−8.06476	−	13.9686i	−0.292925	−	0.507361i
$759$	−19.9121	−	3.73953i	−0.722763	−	0.135736i
$760$	−0.658190	−	0.658190i	−0.0238751	−	0.0238751i
$761$	−33.1394	−	33.1394i	−1.20130	−	1.20130i	−0.973771	−	0.227530i	$-0.926935\pi$
$761$	−33.1394	−	33.1394i	−1.20130	−	1.20130i	−0.227530	−	0.973771i	$-0.573065\pi$
$762$	−13.6501	+	15.9054i	−0.494490	+	0.576190i
$763$	0.166273	+	0.287993i	0.00601949	+	0.0104261i
$764$	4.11355	+	7.12488i	0.148823	+	0.257769i
$765$	−0.447061	−	0.0491407i	−0.0161635	−	0.00177669i
$766$			30.0516i			1.08581i
$767$	6.58017	+	10.5971i	0.237596	+	0.382640i
$768$	−26.3440	−	12.6425i	−0.950608	−	0.456197i
$769$	18.4717	−	4.94948i	0.666107	−	0.178483i	0.0901064	−	0.995932i	$-0.471279\pi$
$769$	18.4717	−	4.94948i	0.666107	−	0.178483i	0.576001	+	0.817449i	$0.304613\pi$
$770$	−0.0991914	−	0.0572682i	−0.00357461	−	0.00206380i
$771$	37.6794	−	25.7645i	1.35699	−	0.927885i
$772$	−23.1879	+	6.21318i	−0.834551	+	0.223617i
$773$	5.12420	+	19.1238i	0.184305	+	0.687834i	0.994778	+	0.102059i	$0.0325431\pi$
$773$	5.12420	+	19.1238i	0.184305	+	0.687834i	−0.810474	+	0.585775i	$0.800790\pi$
$774$	−5.78233	+	2.54155i	−0.207841	+	0.0913540i
$775$	−19.9649	+	19.9649i	−0.717160	+	0.717160i
$776$	31.3513	−	18.1007i	1.12545	−	0.649776i
$777$	1.60066	+	2.34089i	0.0574233	+	0.0839789i
$778$	−3.89016	−	14.5183i	−0.139469	−	0.520505i
$779$	10.3094	+	17.8563i	0.369371	+	0.639770i
$780$	−0.593384	+	0.434314i	−0.0212465	+	0.0155509i
$781$	9.64697	−	16.7090i	0.345196	−	0.597897i
$782$	−4.74918	−	1.27254i	−0.169830	−	0.0455059i
$783$	26.1732	−	6.08630i	0.935353	−	0.217507i
$784$	−2.96833	−	1.71377i	−0.106012	−	0.0612060i
$785$	−0.377992	−	1.41069i	−0.0134911	−	0.0503495i
$786$	16.4244	−	19.1381i	0.585840	−	0.682634i
$787$	4.56589	−	4.56589i	0.162757	−	0.162757i	−0.621030	−	0.783787i	$-0.713286\pi$
$787$	4.56589	−	4.56589i	0.162757	−	0.162757i	0.783787	+	0.621030i	$0.213286\pi$
$788$	−1.12579	+	4.20150i	−0.0401046	+	0.149672i
$789$	15.8267	−	32.9791i	0.563445	−	1.17409i
$790$			1.60517i			0.0571095i
$791$	0.291013	−	1.08608i	0.0103472	−	0.0386164i
$792$	−21.8020	+	17.4837i	−0.774701	+	0.621258i
$793$	6.52492	+	21.5602i	0.231707	+	0.765625i
$794$	24.5124	+	14.1522i	0.869913	+	0.502244i
$795$	−1.55028	+	1.80642i	−0.0549828	+	0.0640671i
$796$	−5.74349	+	9.94802i	−0.203573	+	0.352598i
$797$	−49.4625			−1.75205			−0.876026	−	0.482263i	$-0.839815\pi$
$797$	−49.4625			−1.75205			−0.876026	+	0.482263i	$0.839815\pi$
$798$	1.69655	−	0.596239i	0.0600572	−	0.0211066i
$799$	1.69115	−	6.31146i	0.0598286	−	0.223283i
$800$	−25.9433	+	6.95150i	−0.917235	+	0.245772i
$801$	6.69014	−	2.94056i	0.236384	−	0.103900i
$802$	−5.31907	+	9.21290i	−0.187823	+	0.325319i
$803$	18.6006			0.656401
$804$	5.49565	−	29.2630i	0.193816	−	1.03203i
$805$	−0.122107	+	0.0704986i	−0.00430371	+	0.00248475i
$806$	5.53990	+	18.3054i	0.195135	+	0.644781i
$807$	−4.27226	−	6.24798i	−0.150391	−	0.219939i
$808$	−7.86711	−	7.86711i	−0.276764	−	0.276764i
$809$	42.4000	−	24.4797i	1.49071	−	0.860659i	0.490762	−	0.871294i	$-0.336719\pi$
$809$	42.4000	−	24.4797i	1.49071	−	0.860659i	0.999943	+	0.0106348i	$0.00338524\pi$
$810$	−0.265651	−	0.844874i	−0.00933401	−	0.0296859i
$811$	2.24360	+	2.24360i	0.0787834	+	0.0787834i	0.745400	−	0.666617i	$-0.232258\pi$
$811$	2.24360	+	2.24360i	0.0787834	+	0.0787834i	−0.666617	+	0.745400i	$0.732258\pi$
$812$	−2.04789	−	0.548731i	−0.0718669	−	0.0192567i
$813$	18.5774	+	15.9432i	0.651537	+	0.559152i
$814$	−12.9109	−	3.45945i	−0.452525	−	0.121254i
$815$			0.0844318i			0.00295752i
$816$	−1.01910	+	0.696842i	−0.0356756	+	0.0243944i
$817$	4.81320	−	4.81320i	0.168393	−	0.168393i
$818$	−11.0443			−0.386156
$819$	−0.724979	−	3.88701i	−0.0253328	−	0.135823i
$820$	−0.801201			−0.0279791
$821$	8.81907	−	8.81907i	0.307788	−	0.307788i	−0.536263	−	0.844051i	$-0.680165\pi$
$821$	8.81907	−	8.81907i	0.307788	−	0.307788i	0.844051	+	0.536263i	$0.180165\pi$
$822$	−2.27709	−	29.8410i	−0.0794225	−	1.04082i
$823$			12.4797i			0.435016i	0.976059	+	0.217508i	$0.0697928\pi$
$823$			12.4797i			0.435016i	−0.976059	+	0.217508i	$0.930207\pi$
$824$	18.9552	+	5.07903i	0.660336	+	0.176936i
$825$	−5.07831	+	27.0408i	−0.176804	+	0.941439i
$826$	1.14496	+	0.306790i	0.0398381	+	0.0106746i
$827$	−9.01542	−	9.01542i	−0.313497	−	0.313497i	0.532766	−	0.846263i	$-0.321153\pi$
$827$	−9.01542	−	9.01542i	−0.313497	−	0.313497i	−0.846263	+	0.532766i	$0.821153\pi$
$828$	1.87547	+	12.2174i	0.0651770	+	0.424582i
$829$	−12.1868	+	7.03605i	−0.423265	+	0.244372i	−0.696473	−	0.717583i	$-0.745249\pi$
$829$	−12.1868	+	7.03605i	−0.423265	+	0.244372i	0.273208	+	0.961955i	$0.411915\pi$
$830$	1.15474	+	1.15474i	0.0400817	+	0.0400817i
$831$	−42.4756	+	3.24120i	−1.47346	+	0.112436i
$832$	−4.96242	+	21.2203i	−0.172041	+	0.735682i
$833$	8.49097	−	4.90226i	0.294195	−	0.169853i
$834$	−13.9108	+	4.88884i	−0.481691	+	0.169287i
$835$	1.62902			0.0563747
$836$	5.41039	−	9.37107i	0.187122	−	0.324105i
$837$	29.3908	+	0.979672i	1.01589	+	0.0338624i
$838$	2.61136	−	0.699711i	0.0902079	−	0.0241711i
$839$	−13.5515	+	50.5750i	−0.467851	+	1.74604i	0.179410	+	0.983774i	$0.442581\pi$
$839$	−13.5515	+	50.5750i	−0.467851	+	1.74604i	−0.647260	+	0.762269i	$0.724085\pi$
$840$	−0.0358979	+	0.191147i	−0.00123859	+	0.00659522i
$841$	2.25637			0.0778057
$842$	−1.17507	+	2.03529i	−0.0404957	+	0.0701407i
$843$	35.8867	+	6.73959i	1.23600	+	0.232124i
$844$	17.5516	+	10.1334i	0.604152	+	0.348808i
$845$	1.02501	+	0.901267i	0.0352614	+	0.0310045i
$846$	12.7180	−	1.95232i	0.437253	−	0.0671220i
$847$	−0.0815646	+	0.304403i	−0.00280259	+	0.0104594i
$848$			6.53429i			0.224388i
$849$	3.94011	+	5.76224i	0.135224	+	0.197759i
$850$	−1.72812	+	6.44944i	−0.0592741	+	0.221214i
$851$	−11.6349	+	11.6349i	−0.398840	+	0.398840i
$852$	−11.5687	−	2.17263i	−0.396338	−	0.0744331i
$853$	3.77435	+	14.0861i	0.129231	+	0.482297i	0.999955	−	0.00947475i	$-0.00301595\pi$
$853$	3.77435	+	14.0861i	0.129231	+	0.482297i	−0.870724	+	0.491772i	$0.836349\pi$
$854$	1.85377	+	1.07028i	0.0634348	+	0.0366241i
$855$	0.597120	+	0.744601i	0.0204211	+	0.0254648i
$856$	34.2349	+	9.17322i	1.17013	+	0.313534i
$857$	−6.89566	+	11.9436i	−0.235551	+	0.407986i	−0.959433	−	0.281938i	$-0.909023\pi$
$857$	−6.89566	+	11.9436i	−0.235551	+	0.407986i	0.723882	+	0.689924i	$0.242356\pi$
$858$	14.5247	+	11.6776i	0.495866	+	0.398667i
$859$	14.9164	+	25.8359i	0.508940	+	0.881510i	0.999946	+	0.0103542i	$0.00329591\pi$
$859$	14.9164	+	25.8359i	0.508940	+	0.881510i	−0.491006	+	0.871156i	$0.663371\pi$
$860$	0.0684581	+	0.255489i	0.00233440	+	0.00871210i
$861$	1.86396	−	3.88405i	0.0635235	−	0.132368i
$862$	12.5571	−	7.24983i	0.427696	−	0.246930i
$863$	33.0412	−	33.0412i	1.12473	−	1.12473i	0.133714	−	0.991020i	$-0.457310\pi$
$863$	33.0412	−	33.0412i	1.12473	−	1.12473i	0.991020	−	0.133714i	$-0.0426904\pi$
$864$	23.7467	+	14.7862i	0.807878	+	0.503038i
$865$	0.416775	+	1.55542i	0.0141708	+	0.0528860i
$866$	−4.74247	+	1.27074i	−0.161156	+	0.0431816i
$867$	1.97165	+	25.8383i	0.0669606	+	0.877513i
$868$	−2.00934	−	1.16009i	−0.0682015	−	0.0393761i
$869$	−50.1670	+	13.4422i	−1.70180	+	0.455996i
$870$	0.0670653	+	0.878884i	0.00227373	+	0.0297970i
$871$	−55.2367	+	1.77234i	−1.87163	+	0.0600534i
$872$			2.66156i			0.0901319i
$873$	−33.9827	+	14.9367i	−1.15014	+	0.505529i
$874$	5.21706	+	9.03621i	0.176470	+	0.305654i
$875$	0.191687	+	0.332012i	0.00648021	+	0.0112241i
$876$	−3.76256	−	10.7061i	−0.127125	−	0.361724i
$877$	−7.18363	−	7.18363i	−0.242574	−	0.242574i	0.575340	−	0.817914i	$-0.304870\pi$
$877$	−7.18363	−	7.18363i	−0.242574	−	0.242574i	−0.817914	+	0.575340i	$0.804870\pi$
$878$	−10.4555	−	10.4555i	−0.352856	−	0.352856i
$879$	−6.63160	−	18.8697i	−0.223678	−	0.636458i
$880$	−0.0834359	−	0.144515i	−0.00281262	−	0.00487160i
$881$	−2.67563	−	4.63432i	−0.0901441	−	0.156134i	0.817428	−	0.576031i	$-0.195399\pi$
$881$	−2.67563	−	4.63432i	−0.0901441	−	0.156134i	−0.907572	+	0.419897i	$0.862066\pi$
$882$	15.5655	+	11.4226i	0.524119	+	0.384620i
$883$			11.6579i			0.392321i	0.980572	+	0.196161i	$0.0628474\pi$
$883$			11.6579i			0.392321i	−0.980572	+	0.196161i	$0.937153\pi$
$884$	−4.21166	−	3.94979i	−0.141653	−	0.132846i
$885$	0.0478685	+	0.627313i	0.00160908	+	0.0210869i
$886$	23.7868	−	6.37364i	0.799132	−	0.214127i
$887$	8.35407	+	4.82322i	0.280502	+	0.161948i	0.633651	−	0.773619i	$-0.281556\pi$
$887$	8.35407	+	4.82322i	0.280502	+	0.161948i	−0.353149	+	0.935567i	$0.614889\pi$
$888$	1.72690	+	22.6309i	0.0579511	+	0.759444i
$889$	−4.55876	+	1.22152i	−0.152896	+	0.0409683i
$890$	0.0620422	+	0.231545i	0.00207966	+	0.00776139i
$891$	24.1805	−	15.3777i	0.810077	−	0.515172i
$892$	−2.54440	+	2.54440i	−0.0851929	+	0.0851929i
$893$	−12.0087	+	6.93325i	−0.401857	+	0.232012i
$894$	−8.45797	+	17.6244i	−0.282877	+	0.589449i
$895$	−0.507409	−	1.89367i	−0.0169608	−	0.0632986i
$896$	−0.932524	−	1.61518i	−0.0311534	−	0.0539593i
$897$	21.3896	−	8.29710i	0.714180	−	0.277032i
$898$	−5.93349	+	10.2771i	−0.198003	+	0.342951i
$899$	−28.2699	−	7.57490i	−0.942854	−	0.252637i
$900$	16.5913	−	2.54690i	0.553043	−	0.0848967i
$901$	−16.1873	−	9.34572i	−0.539276	−	0.311351i
$902$	5.25557	+	19.6141i	0.174991	+	0.653077i
$903$	−1.39782	−	0.262513i	−0.0465165	−	0.00873590i
$904$	6.36336	−	6.36336i	0.211642	−	0.211642i
$905$	0.386408	−	1.44209i	0.0128446	−	0.0479368i
$906$	0.0386640	+	0.0565444i	0.00128453	+	0.00187856i
$907$		−	43.6107i		−	1.44807i	−0.689764	−	0.724035i	$-0.742286\pi$
$907$		−	43.6107i		−	1.44807i	0.689764	−	0.724035i	$-0.257714\pi$
$908$	1.10233	−	4.11396i	0.0365821	−	0.136526i
$909$	7.13716	+	8.89995i	0.236725	+	0.295193i
$910$	0.129634	−	0.00415946i	0.00429731	−	0.000137885i
$911$	15.2019	+	8.77681i	0.503661	+	0.290789i	0.730224	−	0.683208i	$-0.239416\pi$
$911$	15.2019	+	8.77681i	0.503661	+	0.290789i	−0.226563	+	0.973996i	$0.572749\pi$
$912$	2.57495	+	0.483580i	0.0852650	+	0.0160129i
$913$	−26.4194	+	45.7597i	−0.874354	+	1.51443i
$914$	12.2879			0.406448
$915$	−0.209700	+	1.11660i	−0.00693248	+	0.0369138i
$916$	−5.09255	+	19.0056i	−0.168262	+	0.627964i
$917$	5.48532	−	1.46979i	0.181141	−	0.0485367i
$918$	6.13502	−	3.27454i	0.202486	−	0.108076i
$919$	−2.44511	+	4.23505i	−0.0806566	+	0.139701i	−0.903532	−	0.428520i	$-0.859035\pi$
$919$	−2.44511	+	4.23505i	−0.0806566	+	0.139701i	0.822876	+	0.568222i	$0.192368\pi$
$920$	−1.12848			−0.0372050
$921$	−41.4095	+	14.5530i	−1.36449	+	0.479539i
$922$	27.1954	−	15.7013i	0.895632	−	0.517094i
$923$	0.700671	+	21.8371i	0.0230629	+	0.718777i
$924$	−2.25438	+	0.172025i	−0.0741636	+	0.00565922i
$925$	15.8003	+	15.8003i	0.519512	+	0.519512i
$926$	−12.5308	+	7.23465i	−0.411787	+	0.237745i
$927$	−18.7510	−	7.30045i	−0.615865	−	0.239778i
$928$	−19.6864	−	19.6864i	−0.646237	−	0.646237i
$929$	−31.5303	−	8.44852i	−1.03448	−	0.277187i	−0.298653	−	0.954362i	$-0.596537\pi$
$929$	−31.5303	−	8.44852i	−1.03448	−	0.277187i	−0.735822	+	0.677175i	$0.763204\pi$
$930$	−0.178043	+	0.948038i	−0.00583827	+	0.0310874i
$931$	−20.0979	−	5.38522i	−0.658682	−	0.176493i
$932$			16.2314i			0.531678i
$933$	2.93356	+	38.4440i	0.0960403	+	1.25860i
$934$	13.8682	−	13.8682i	0.453783	−	0.453783i
$935$	0.477339			0.0156107
$936$	10.5299	−	29.8433i	0.344182	−	0.975458i
$937$	35.2389			1.15121			0.575603	−	0.817729i	$-0.304767\pi$
$937$	35.2389			1.15121			0.575603	+	0.817729i	$0.304767\pi$
$938$	−3.71347	+	3.71347i	−0.121249	+	0.121249i
$939$	12.2976	−	8.40888i	0.401317	−	0.274413i
$940$		−	0.538823i		−	0.0175745i
$941$	−23.6245	−	6.33017i	−0.770137	−	0.206358i	−0.147705	−	0.989031i	$-0.547189\pi$
$941$	−23.6245	−	6.33017i	−0.770137	−	0.206358i	−0.622432	+	0.782674i	$0.713855\pi$
$942$	17.1364	+	14.7066i	0.558336	+	0.479167i
$943$	24.1454	+	6.46975i	0.786283	+	0.210684i
$944$	1.22115	+	1.22115i	0.0397451	+	0.0397451i
$945$	0.0580042	−	0.190805i	0.00188688	−	0.00620689i
$946$	5.80552	−	3.35182i	0.188754	−	0.108977i
$947$	2.70978	+	2.70978i	0.0880561	+	0.0880561i	0.749763	−	0.661707i	$-0.230168\pi$
$947$	2.70978	+	2.70978i	0.0880561	+	0.0880561i	−0.661707	+	0.749763i	$0.730168\pi$
$948$	17.8849	+	26.1558i	0.580874	+	0.849501i
$949$	−17.8942	+	11.1112i	−0.580869	+	0.360684i
$950$	12.2713	−	7.08482i	0.398132	−	0.229862i
$951$	−10.0674	+	53.6063i	−0.326457	+	1.73830i
$952$	−1.52714			−0.0494950
$953$	12.0041	−	20.7918i	0.388852	−	0.673512i	−0.603443	−	0.797406i	$-0.706205\pi$
$953$	12.0041	−	20.7918i	0.388852	−	0.673512i	0.992295	+	0.123894i	$0.0395384\pi$
$954$	4.02160	−	36.5868i	0.130204	−	1.18454i
$955$	0.743943	−	0.199339i	0.0240734	−	0.00645046i
$956$	5.94446	−	22.1850i	0.192257	−	0.717515i
$957$	−26.9064	+	9.45606i	−0.869761	+	0.305671i
$958$	21.2619			0.686942
$959$	3.36949	−	5.83613i	0.108806	−	0.188458i
$960$	−0.715828	+	0.834099i	−0.0231032	+	0.0269204i
$961$	−0.890953	−	0.514392i	−0.0287404	−	0.0165933i
$962$	14.4870	−	4.38431i	0.467080	−	0.141356i
$963$	−33.8662	−	13.1853i	−1.09132	−	0.424891i
$964$	7.01057	−	26.1638i	0.225795	−	0.842679i
$965$			2.24733i			0.0723441i
$966$	0.943256	−	1.96552i	0.0303488	−	0.0632397i
$967$	−2.77473	+	10.3554i	−0.0892294	+	0.333009i	−0.996081	−	0.0884405i	$-0.971812\pi$
$967$	−2.77473	+	10.3554i	−0.0892294	+	0.333009i	0.906852	+	0.421449i	$0.138478\pi$
$968$	−1.78351	+	1.78351i	−0.0573241	+	0.0573241i
$969$	−4.88080	+	5.68722i	−0.156794	+	0.182700i
$970$	−0.315145	−	1.17614i	−0.0101187	−	0.0377634i
$971$	−46.2535	−	26.7045i	−1.48435	−	0.856988i	−0.484505	−	0.874788i	$-0.661000\pi$
$971$	−46.2535	−	26.7045i	−1.48435	−	0.856988i	−0.999842	+	0.0178003i	$0.994334\pi$
$972$	−13.7423	−	10.8071i	−0.440785	−	0.346637i
$973$	−3.20704	−	0.859324i	−0.102813	−	0.0275487i
$974$	−2.99405	+	5.18584i	−0.0959355	+	0.166165i
$975$	−11.2675	−	29.0473i	−0.360850	−	0.930260i
$976$	1.55932	+	2.70082i	0.0499126	+	0.0864512i
$977$	−9.64944	−	36.0122i	−0.308713	−	1.15213i	−0.929702	−	0.368313i	$-0.879936\pi$
$977$	−9.64944	−	36.0122i	−0.308713	−	1.15213i	0.620989	−	0.783819i	$-0.286731\pi$
$978$	−0.736886	−	1.07766i	−0.0235630	−	0.0344598i
$979$	−6.71698	+	3.87805i	−0.214676	+	0.123943i
$980$	0.571704	−	0.571704i	0.0182624	−	0.0182624i
$981$	0.298189	−	2.71280i	0.00952045	−	0.0866130i
$982$	−3.34964	−	12.5010i	−0.106891	−	0.398924i
$983$	15.8187	−	4.23860i	0.504537	−	0.135190i	0.00243220	−	0.999997i	$-0.499226\pi$
$983$	15.8187	−	4.23860i	0.504537	−	0.135190i	0.502105	+	0.864807i	$0.332559\pi$
$984$	28.4628	−	19.4624i	0.907362	−	0.620438i
$985$	0.352648	+	0.203601i	0.0112363	+	0.00648727i
$986$	−6.68529	+	1.79132i	−0.212903	+	0.0570472i
$987$	2.61210	+	1.25355i	0.0831439	+	0.0399008i
$988$	0.392963	+	12.2471i	0.0125018	+	0.389632i
$989$		−	8.25236i		−	0.262410i
$990$	0.378231	+	0.860521i	0.0120210	+	0.0273492i
$991$	−25.9576	−	44.9599i	−0.824571	−	1.42820i	−0.902247	−	0.431220i	$-0.858083\pi$
$991$	−25.9576	−	44.9599i	−0.824571	−	1.42820i	0.0776754	−	0.996979i	$-0.475250\pi$
$992$	−15.2339	−	26.3859i	−0.483676	−	0.837752i
$993$	−17.6500	+	20.5661i	−0.560104	+	0.652646i
$994$	1.46807	+	1.46807i	0.0465644	+	0.0465644i
$995$	0.760397	+	0.760397i	0.0241062	+	0.0241062i
$996$	31.6824	+	5.95001i	1.00389	+	0.188533i
$997$	−0.731834	−	1.26757i	−0.0231774	−	0.0401445i	0.854204	−	0.519938i	$-0.174045\pi$
$997$	−0.731834	−	1.26757i	−0.0231774	−	0.0401445i	−0.877381	+	0.479793i	$0.840712\pi$
$998$	−1.84259	−	3.19146i	−0.0583262	−	0.101024i
$999$	0.775318	−	23.2600i	0.0245300	−	0.735915i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.x.a.11.5	✓	48
3.2	odd	2		351.2.ba.a.89.8		48
9.4	even	3		351.2.bf.a.206.5		48
9.5	odd	6		117.2.bc.a.50.8	yes	48
13.6	odd	12		117.2.bc.a.110.8	yes	48
39.32	even	12		351.2.bf.a.305.5		48
117.32	even	12	inner	117.2.x.a.32.5	yes	48
117.58	odd	12		351.2.ba.a.71.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.11.5	✓	48	1.1	even	1	trivial
117.2.x.a.32.5	yes	48	117.32	even	12	inner
117.2.bc.a.50.8	yes	48	9.5	odd	6
117.2.bc.a.110.8	yes	48	13.6	odd	12
351.2.ba.a.71.8		48	117.58	odd	12
351.2.ba.a.89.8		48	3.2	odd	2
351.2.bf.a.206.5		48	9.4	even	3
351.2.bf.a.305.5		48	39.32	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.662754 + 0.662754i) q^{2} +(1.56154 + 0.749386i) q^{3} +1.12151i q^{4} +(0.101414 + 0.0271738i) q^{5} +(-1.53158 + 0.538261i) q^{6} +(-0.353095 - 0.0946115i) q^{7} +(-2.06880 - 2.06880i) q^{8} +(1.87684 + 2.34040i) q^{9} +(-0.0852221 + 0.0492030i) q^{10} +(-2.25143 - 2.25143i) q^{11} +(-0.840447 + 1.75129i) q^{12} +(3.51083 + 0.821016i) q^{13} +(0.296719 - 0.171311i) q^{14} +(0.137999 + 0.118431i) q^{15} +0.499177 q^{16} +(-0.713952 + 1.23660i) q^{17} +(-2.79499 - 0.307224i) q^{18} +(2.92701 - 0.784289i) q^{19} +(-0.0304758 + 0.113737i) q^{20} +(-0.480473 - 0.412345i) q^{21} +2.98429 q^{22} +(1.83687 - 3.18155i) q^{23} +(-1.68019 - 4.78084i) q^{24} +(-4.32058 - 2.49449i) q^{25} +(-2.87095 + 1.78269i) q^{26} +(1.17691 + 5.06111i) q^{27} +(0.106108 - 0.396001i) q^{28} -5.17142i q^{29} +(-0.169950 + 0.0129684i) q^{30} +(1.46476 - 5.46656i) q^{31} +(3.80676 - 3.80676i) q^{32} +(-1.82852 - 5.20290i) q^{33} +(-0.346388 - 1.29274i) q^{34} +(-0.0332378 - 0.0191899i) q^{35} +(-2.62479 + 2.10490i) q^{36} +(-4.32627 - 1.15922i) q^{37} +(-1.42009 + 2.45967i) q^{38} +(4.86706 + 3.91302i) q^{39} +(-0.153588 - 0.266022i) q^{40} +(1.76108 + 6.57243i) q^{41} +(0.591718 - 0.0451524i) q^{42} +(1.94536 - 1.12315i) q^{43} +(2.52501 - 2.52501i) q^{44} +(0.126741 + 0.288350i) q^{45} +(0.891194 + 3.32598i) q^{46} +(-4.42009 + 1.18436i) q^{47} +(0.779487 + 0.374076i) q^{48} +(-5.94645 - 3.43319i) q^{49} +(4.51671 - 1.21025i) q^{50} +(-2.04156 + 1.39598i) q^{51} +(-0.920781 + 3.93745i) q^{52} +13.0901i q^{53} +(-4.13428 - 2.57427i) q^{54} +(-0.167147 - 0.289507i) q^{55} +(0.534750 + 0.926214i) q^{56} +(5.15838 + 0.968755i) q^{57} +(3.42738 + 3.42738i) q^{58} +(2.44633 + 2.44633i) q^{59} +(-0.132822 + 0.154768i) q^{60} +(3.12378 + 5.41055i) q^{61} +(2.65221 + 4.59376i) q^{62} +(-0.441275 - 1.00395i) q^{63} +6.04425i q^{64} +(0.333737 + 0.178665i) q^{65} +(4.66010 + 2.23639i) q^{66} +(-14.8055 + 3.96713i) q^{67} +(-1.38687 - 0.800708i) q^{68} +(5.25257 - 3.59161i) q^{69} +(0.0347467 - 0.00931034i) q^{70} +(1.56835 + 5.85317i) q^{71} +(0.959005 - 8.72461i) q^{72} +(-4.13084 + 4.13084i) q^{73} +(3.63553 - 2.09897i) q^{74} +(-4.87744 - 7.13304i) q^{75} +(0.879591 + 3.28268i) q^{76} +(0.581958 + 1.00798i) q^{77} +(-5.81903 + 0.632294i) q^{78} +(8.15587 - 14.1264i) q^{79} +(0.0506235 + 0.0135645i) q^{80} +(-1.95493 + 8.78511i) q^{81} +(-5.52307 - 3.18874i) q^{82} +(-4.29512 - 16.0296i) q^{83} +(0.462450 - 0.538857i) q^{84} +(-0.106008 + 0.106008i) q^{85} +(-0.544920 + 2.03367i) q^{86} +(3.87539 - 8.07541i) q^{87} +9.31551i q^{88} +(0.630472 - 2.35295i) q^{89} +(-0.275103 - 0.107107i) q^{90} +(-1.16198 - 0.622062i) q^{91} +(3.56816 + 2.06008i) q^{92} +(6.38385 - 7.43860i) q^{93} +(2.14449 - 3.71437i) q^{94} +0.318151 q^{95} +(8.79716 - 3.09169i) q^{96} +(-3.20249 + 11.9519i) q^{97} +(6.21639 - 1.66568i) q^{98} +(1.04367 - 9.49483i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9} - 12 q^{10} - 6 q^{11} + 18 q^{12} - 2 q^{13} - 12 q^{14} - 26 q^{15} - 28 q^{16} - 14 q^{18} - 4 q^{19} - 18 q^{20} - 8 q^{21}+ \cdots - 8 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^5 - 8 * q^6 - 4 * q^7 + 30 * q^8 - 2 * q^9 - 12 * q^10 - 6 * q^11 + 18 * q^12 - 2 * q^13 - 12 * q^14 - 26 * q^15 - 28 * q^16 - 14 * q^18 - 4 * q^19 - 18 * q^20 - 8 * q^21 - 4 * q^22 - 6 * q^23 + 6 * q^24 - 48 * q^26 - 32 * q^27 + 42 * q^30 - 18 * q^31 + 54 * q^32 + 28 * q^33 + 6 * q^34 + 6 * q^35 + 24 * q^36 - 6 * q^37 + 36 * q^38 + 10 * q^39 - 12 * q^40 + 18 * q^41 - 70 * q^42 - 30 * q^43 + 12 * q^44 + 40 * q^45 - 12 * q^46 - 36 * q^47 - 14 * q^48 - 6 * q^49 - 60 * q^50 + 56 * q^52 + 34 * q^54 - 4 * q^55 - 6 * q^56 - 56 * q^57 + 50 * q^58 - 6 * q^59 + 44 * q^60 + 2 * q^61 + 18 * q^62 + 22 * q^63 + 72 * q^65 + 32 * q^66 + 26 * q^67 + 42 * q^68 + 30 * q^69 - 16 * q^70 - 48 * q^71 + 30 * q^72 - 22 * q^73 + 30 * q^74 - 24 * q^75 + 6 * q^76 + 72 * q^77 - 20 * q^78 + 8 * q^79 - 54 * q^80 + 82 * q^81 - 12 * q^82 + 54 * q^83 - 38 * q^84 - 24 * q^85 - 54 * q^86 + 2 * q^87 - 114 * q^90 - 16 * q^91 + 120 * q^92 + 52 * q^93 + 26 * q^94 - 12 * q^95 + 94 * q^96 - 24 * q^97 + 36 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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