LMFDB - Embedded newform 552.2.t.b.523.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(19,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 0, 15]))

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

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

chi := DirichletCharacter("552.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.t (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			523.11
Character	$\chi$	$=$	552.523
Dual form			552.2.t.b.19.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.218084 - 1.39730i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-1.90488 + 0.609457i) q^{4} +(-0.659581 + 0.423887i) q^{5} +(-0.184414 + 1.40214i) q^{6} +(-0.167612 + 1.16577i) q^{7} +(1.26702 + 2.52877i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.218084 - 1.39730i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-1.90488 + 0.609457i) q^{4} +(-0.659581 + 0.423887i) q^{5} +(-0.184414 + 1.40214i) q^{6} +(-0.167612 + 1.16577i) q^{7} +(1.26702 + 2.52877i) q^{8} +(0.841254 + 0.540641i) q^{9} +(0.736140 + 0.829187i) q^{10} +(1.56705 - 0.715646i) q^{11} +(1.99942 - 0.0481031i) q^{12} +(3.17756 - 0.456864i) q^{13} +(1.66548 - 0.0200316i) q^{14} +(0.752286 - 0.220891i) q^{15} +(3.25713 - 2.32188i) q^{16} +(-3.13544 - 2.71687i) q^{17} +(0.571972 - 1.29339i) q^{18} +(6.17872 - 5.35389i) q^{19} +(0.998081 - 1.20944i) q^{20} +(0.489258 - 1.07133i) q^{21} +(-1.34172 - 2.03356i) q^{22} +(-3.84566 - 2.86546i) q^{23} +(-0.503256 - 2.78330i) q^{24} +(-1.82171 + 3.98898i) q^{25} +(-1.33135 - 4.34036i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(-0.391205 - 2.32280i) q^{28} +(4.90056 + 4.24636i) q^{29} +(-0.472712 - 1.00299i) q^{30} +(-1.95081 - 6.64385i) q^{31} +(-3.95469 - 4.04481i) q^{32} +(-1.70519 + 0.245169i) q^{33} +(-3.11249 + 4.97364i) q^{34} +(-0.383601 - 0.839968i) q^{35} +(-1.93198 - 0.517148i) q^{36} +(6.79820 + 4.36894i) q^{37} +(-8.82846 - 7.46591i) q^{38} +(-3.17756 - 0.456864i) q^{39} +(-1.90761 - 1.13086i) q^{40} +(7.75417 - 4.98330i) q^{41} +(-1.60366 - 0.450000i) q^{42} +(-0.0435530 + 0.148328i) q^{43} +(-2.54888 + 2.31827i) q^{44} -0.784045 q^{45} +(-3.16522 + 5.99845i) q^{46} +0.275978i q^{47} +(-3.77934 + 1.31019i) q^{48} +(5.38552 + 1.58133i) q^{49} +(5.97108 + 1.67553i) q^{50} +(2.24300 + 3.49017i) q^{51} +(-5.77442 + 2.80685i) q^{52} +(1.95474 - 13.5955i) q^{53} +(-0.913192 + 1.07985i) q^{54} +(-0.730241 + 1.13628i) q^{55} +(-3.16033 + 1.05320i) q^{56} +(-7.43680 + 3.39627i) q^{57} +(4.86469 - 7.77360i) q^{58} +(-1.26639 - 8.80793i) q^{59} +(-1.29839 + 0.879256i) q^{60} +(-8.34065 + 2.44903i) q^{61} +(-8.85799 + 4.17478i) q^{62} +(-0.771267 + 0.890090i) q^{63} +(-4.78934 + 6.40798i) q^{64} +(-1.90220 + 1.64826i) q^{65} +(0.714450 + 2.32919i) q^{66} +(13.8670 + 6.33284i) q^{67} +(7.62844 + 3.26440i) q^{68} +(2.88259 + 3.83284i) q^{69} +(-1.09003 + 0.719188i) q^{70} +(-1.06252 - 0.485239i) q^{71} +(-0.301274 + 2.81234i) q^{72} +(7.09826 + 8.19183i) q^{73} +(4.62213 - 10.4519i) q^{74} +(2.87174 - 3.31417i) q^{75} +(-8.50674 + 13.9642i) q^{76} +(0.571622 + 1.94677i) q^{77} +(0.0546004 + 4.53963i) q^{78} +(-2.25077 - 15.6544i) q^{79} +(-1.16412 + 2.91212i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-8.65421 - 9.74810i) q^{82} +(-3.61212 + 5.62056i) q^{83} +(-0.279051 + 2.33893i) q^{84} +(3.21972 + 0.462926i) q^{85} +(0.216757 + 0.0285085i) q^{86} +(-3.50571 - 5.45499i) q^{87} +(3.79518 + 3.05596i) q^{88} +(0.156826 - 0.534100i) q^{89} +(0.170988 + 1.09554i) q^{90} +3.78088i q^{91} +(9.07190 + 3.11459i) q^{92} +6.92433i q^{93} +(0.385623 - 0.0601863i) q^{94} +(-1.80592 + 6.15040i) q^{95} +(2.65494 + 4.99513i) q^{96} +(5.76257 + 8.96673i) q^{97} +(1.03509 - 7.87004i) q^{98} +(1.70519 + 0.245169i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{2} - 24 q^{3} - 4 q^{4} - 7 q^{6} + 4 q^{8} - 24 q^{9}+O(q^{10}) $ 240 * q + 4 * q^2 - 24 * q^3 - 4 * q^4 - 7 * q^6 + 4 * q^8 - 24 * q^9	$ 240 q + 4 q^{2} - 24 q^{3} - 4 q^{4} - 7 q^{6} + 4 q^{8} - 24 q^{9} - 4 q^{12} - 4 q^{16} - 44 q^{17} + 4 q^{18} + 55 q^{20} + 4 q^{24} - 24 q^{25} - 24 q^{27} + 4 q^{32} - 55 q^{34} + 7 q^{36} + 22 q^{38} + 11 q^{40} - 44 q^{42} + 77 q^{44} - 48 q^{46} + 51 q^{48} + 8 q^{49} - 33 q^{50} + 165 q^{52} - 7 q^{54} - 22 q^{56} - 59 q^{58} + 11 q^{60} + 29 q^{62} - 4 q^{64} + 55 q^{66} + 132 q^{70} + 4 q^{72} - 144 q^{73} - 66 q^{74} - 24 q^{75} - 55 q^{76} - 24 q^{81} - 26 q^{82} - 44 q^{84} - 110 q^{86} - 198 q^{88} - 47 q^{92} - 73 q^{94} + 4 q^{96} + 53 q^{98}+O(q^{100}) $ 240 * q + 4 * q^2 - 24 * q^3 - 4 * q^4 - 7 * q^6 + 4 * q^8 - 24 * q^9 - 4 * q^12 - 4 * q^16 - 44 * q^17 + 4 * q^18 + 55 * q^20 + 4 * q^24 - 24 * q^25 - 24 * q^27 + 4 * q^32 - 55 * q^34 + 7 * q^36 + 22 * q^38 + 11 * q^40 - 44 * q^42 + 77 * q^44 - 48 * q^46 + 51 * q^48 + 8 * q^49 - 33 * q^50 + 165 * q^52 - 7 * q^54 - 22 * q^56 - 59 * q^58 + 11 * q^60 + 29 * q^62 - 4 * q^64 + 55 * q^66 + 132 * q^70 + 4 * q^72 - 144 * q^73 - 66 * q^74 - 24 * q^75 - 55 * q^76 - 24 * q^81 - 26 * q^82 - 44 * q^84 - 110 * q^86 - 198 * q^88 - 47 * q^92 - 73 * q^94 + 4 * q^96 + 53 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{7}{22}\right)$	$1$	$-1$	$-1$

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 $

$2$	−0.218084	−	1.39730i	−0.154209	−	0.988038i
$2$	−0.218084	−	1.39730i	−0.154209	−	0.988038i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$4$	−1.90488	+	0.609457i	−0.952439	+	0.304728i
$5$	−0.659581	+	0.423887i	−0.294973	+	0.189568i	−0.679754	−	0.733440i	$-0.737913\pi$
$5$	−0.659581	+	0.423887i	−0.294973	+	0.189568i	0.384781	+	0.923008i	$0.374277\pi$
$6$	−0.184414	+	1.40214i	−0.0752867	+	0.572421i
$7$	−0.167612	+	1.16577i	−0.0633515	+	0.440620i	0.933316	+	0.359055i	$0.116901\pi$
$7$	−0.167612	+	1.16577i	−0.0633515	+	0.440620i	−0.996668	+	0.0815649i	$0.974008\pi$
$8$	1.26702	+	2.52877i	0.447958	+	0.894055i
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$	0.736140	+	0.829187i	0.232788	+	0.262212i
$11$	1.56705	−	0.715646i	0.472482	−	0.215775i	−0.164920	−	0.986307i	$-0.552736\pi$
$11$	1.56705	−	0.715646i	0.472482	−	0.215775i	0.637402	+	0.770532i	$0.280009\pi$
$12$	1.99942	−	0.0481031i	0.577183	−	0.0138862i
$13$	3.17756	−	0.456864i	0.881296	−	0.126711i	0.313213	−	0.949683i	$-0.398595\pi$
$13$	3.17756	−	0.456864i	0.881296	−	0.126711i	0.568082	+	0.822972i	$0.307685\pi$
$14$	1.66548	−	0.0200316i	0.445118	−	0.00535367i
$15$	0.752286	−	0.220891i	0.194239	−	0.0570338i
$16$	3.25713	−	2.32188i	0.814281	−	0.580471i
$17$	−3.13544	−	2.71687i	−0.760455	−	0.658938i	0.185717	−	0.982603i	$-0.440539\pi$
$17$	−3.13544	−	2.71687i	−0.760455	−	0.658938i	−0.946172	+	0.323665i	$0.895085\pi$
$18$	0.571972	−	1.29339i	0.134815	−	0.304854i
$19$	6.17872	−	5.35389i	1.41750	−	1.22827i	0.481409	−	0.876496i	$-0.340125\pi$
$19$	6.17872	−	5.35389i	1.41750	−	1.22827i	0.936086	−	0.351770i	$-0.114420\pi$
$20$	0.998081	−	1.20944i	0.223178	−	0.270439i
$21$	0.489258	−	1.07133i	0.106765	−	0.233783i
$22$	−1.34172	−	2.03356i	−0.286055	−	0.433556i
$23$	−3.84566	−	2.86546i	−0.801877	−	0.597490i
$23$	−3.84566	−	2.86546i	−0.801877	−	0.597490i
$24$	−0.503256	−	2.78330i	−0.102727	−	0.568138i
$25$	−1.82171	+	3.98898i	−0.364342	+	0.797797i
$26$	−1.33135	−	4.34036i	−0.261099	−	0.851214i
$27$	−0.654861	−	0.755750i	−0.126028	−	0.145444i
$28$	−0.391205	−	2.32280i	−0.0739308	−	0.438969i
$29$	4.90056	+	4.24636i	0.910010	+	0.788528i	0.977880	−	0.209166i	$-0.0670748\pi$
$29$	4.90056	+	4.24636i	0.910010	+	0.788528i	−0.0678699	+	0.997694i	$0.521620\pi$
$30$	−0.472712	−	1.00299i	−0.0863050	−	0.183121i
$31$	−1.95081	−	6.64385i	−0.350376	−	1.19327i	−0.926622	−	0.375994i	$-0.877301\pi$
$31$	−1.95081	−	6.64385i	−0.350376	−	1.19327i	0.576246	−	0.817276i	$-0.304517\pi$
$32$	−3.95469	−	4.04481i	−0.699096	−	0.715027i
$33$	−1.70519	+	0.245169i	−0.296836	+	0.0426785i
$34$	−3.11249	+	4.97364i	−0.533787	+	0.852973i
$35$	−0.383601	−	0.839968i	−0.0648403	−	0.141981i
$36$	−1.93198	−	0.517148i	−0.321997	−	0.0861913i
$37$	6.79820	+	4.36894i	1.11762	+	0.718249i	0.962940	−	0.269716i	$-0.0869297\pi$
$37$	6.79820	+	4.36894i	1.11762	+	0.718249i	0.154678	+	0.987965i	$0.450566\pi$
$38$	−8.82846	−	7.46591i	−1.43216	−	1.21113i
$39$	−3.17756	−	0.456864i	−0.508816	−	0.0731567i
$40$	−1.90761	−	1.13086i	−0.301620	−	0.178804i
$41$	7.75417	−	4.98330i	1.21100	−	0.778261i	0.230172	−	0.973150i	$-0.426071\pi$
$41$	7.75417	−	4.98330i	1.21100	−	0.778261i	0.980825	+	0.194889i	$0.0624346\pi$
$42$	−1.60366	−	0.450000i	−0.247450	−	0.0694365i
$43$	−0.0435530	+	0.148328i	−0.00664178	+	0.0226198i	−0.962747	−	0.270403i	$-0.912843\pi$
$43$	−0.0435530	+	0.148328i	−0.00664178	+	0.0226198i	0.956105	+	0.293023i	$0.0946612\pi$
$44$	−2.54888	+	2.31827i	−0.384258	+	0.349492i
$45$	−0.784045			−0.116879
$46$	−3.16522	+	5.99845i	−0.466686	+	0.884423i
$47$			0.275978i			0.0402555i	0.999797	+	0.0201277i	$0.00640729\pi$
$47$			0.275978i			0.0402555i	−0.999797	+	0.0201277i	$0.993593\pi$
$48$	−3.77934	+	1.31019i	−0.545501	+	0.189110i
$49$	5.38552	+	1.58133i	0.769361	+	0.225905i
$50$	5.97108	+	1.67553i	0.844439	+	0.236956i
$51$	2.24300	+	3.49017i	0.314083	+	0.488722i
$52$	−5.77442	+	2.80685i	−0.800768	+	0.389240i
$53$	1.95474	−	13.5955i	0.268504	−	1.86749i	−0.194183	−	0.980965i	$-0.562206\pi$
$53$	1.95474	−	13.5955i	0.268504	−	1.86749i	0.462687	−	0.886521i	$-0.346885\pi$
$54$	−0.913192	+	1.07985i	−0.124270	+	0.146949i
$55$	−0.730241	+	1.13628i	−0.0984656	+	0.153216i
$56$	−3.16033	+	1.05320i	−0.422317	+	0.140739i
$57$	−7.43680	+	3.39627i	−0.985028	+	0.449847i
$58$	4.86469	−	7.77360i	0.638765	−	1.02072i
$59$	−1.26639	−	8.80793i	−0.164870	−	1.14670i	−0.889292	−	0.457339i	$-0.848803\pi$
$59$	−1.26639	−	8.80793i	−0.164870	−	1.14670i	0.724422	−	0.689356i	$-0.242107\pi$
$60$	−1.29839	+	0.879256i	−0.167621	+	0.113511i
$61$	−8.34065	+	2.44903i	−1.06791	+	0.313567i	−0.768033	−	0.640411i	$-0.778764\pi$
$61$	−8.34065	+	2.44903i	−1.06791	+	0.313567i	−0.299878	+	0.953978i	$0.596946\pi$
$62$	−8.85799	+	4.17478i	−1.12497	+	0.530197i
$63$	−0.771267	+	0.890090i	−0.0971706	+	0.112141i
$64$	−4.78934	+	6.40798i	−0.598668	+	0.800998i
$65$	−1.90220	+	1.64826i	−0.235938	+	0.204442i
$66$	0.714450	+	2.32919i	0.0879427	+	0.286704i
$67$	13.8670	+	6.33284i	1.69412	+	0.773680i	0.998470	+	0.0553007i	$0.0176117\pi$
$67$	13.8670	+	6.33284i	1.69412	+	0.773680i	0.695652	+	0.718379i	$0.255116\pi$
$68$	7.62844	+	3.26440i	0.925084	+	0.395866i
$69$	2.88259	+	3.83284i	0.347024	+	0.461419i
$70$	−1.09003	+	0.719188i	−0.130283	+	0.0859594i
$71$	−1.06252	−	0.485239i	−0.126098	−	0.0575872i	0.351367	−	0.936238i	$-0.385717\pi$
$71$	−1.06252	−	0.485239i	−0.126098	−	0.0575872i	−0.477465	+	0.878651i	$0.658444\pi$
$72$	−0.301274	+	2.81234i	−0.0355055	+	0.331437i
$73$	7.09826	+	8.19183i	0.830789	+	0.958781i	0.999639	−	0.0268605i	$-0.00855099\pi$
$73$	7.09826	+	8.19183i	0.830789	+	0.958781i	−0.168851	+	0.985642i	$0.554006\pi$
$74$	4.62213	−	10.4519i	0.537311	−	1.21501i
$75$	2.87174	−	3.31417i	0.331600	−	0.382687i
$76$	−8.50674	+	13.9642i	−0.975790	+	1.60180i
$77$	0.571622	+	1.94677i	0.0651424	+	0.221855i
$78$	0.0546004	+	4.53963i	0.00618228	+	0.514011i
$79$	−2.25077	−	15.6544i	−0.253231	−	1.76126i	−0.578540	−	0.815654i	$-0.696377\pi$
$79$	−2.25077	−	15.6544i	−0.253231	−	1.76126i	0.325309	−	0.945608i	$-0.394532\pi$
$80$	−1.16412	+	2.91212i	−0.130153	+	0.325585i
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$	−8.65421	−	9.74810i	−0.955698	−	1.07650i
$83$	−3.61212	+	5.62056i	−0.396481	+	0.616937i	−0.980899	−	0.194516i	$-0.937686\pi$
$83$	−3.61212	+	5.62056i	−0.396481	+	0.616937i	0.584418	+	0.811453i	$0.301323\pi$
$84$	−0.279051	+	2.33893i	−0.0304469	+	0.255198i
$85$	3.21972	+	0.462926i	0.349228	+	0.0502113i
$86$	0.216757	+	0.0285085i	0.0233735	+	0.00307416i
$87$	−3.50571	−	5.45499i	−0.375852	−	0.584837i
$88$	3.79518	+	3.05596i	0.404567	+	0.325767i
$89$	0.156826	−	0.534100i	0.0166235	−	0.0566145i	−0.950764	−	0.309917i	$-0.899699\pi$
$89$	0.156826	−	0.534100i	0.0166235	−	0.0566145i	0.967387	+	0.253303i	$0.0815169\pi$
$90$	0.170988	+	1.09554i	0.0180237	+	0.115480i
$91$			3.78088i			0.396344i
$92$	9.07190	+	3.11459i	0.945811	+	0.324718i
$93$			6.92433i			0.718020i
$94$	0.385623	−	0.0601863i	0.0397739	−	0.00620775i
$95$	−1.80592	+	6.15040i	−0.185284	+	0.631018i
$96$	2.65494	+	4.99513i	0.270969	+	0.509813i
$97$	5.76257	+	8.96673i	0.585100	+	0.910434i	1.00000		0.000566677i	$0.000180379\pi$
$97$	5.76257	+	8.96673i	0.585100	+	0.910434i	−0.414899	+	0.909867i	$0.636183\pi$
$98$	1.03509	−	7.87004i	0.104560	−	0.794994i
$99$	1.70519	+	0.245169i	0.171378	+	0.0246405i
$100$	1.03902	−	8.70878i	0.103902	−	0.870878i
$101$	−3.66331	+	5.70023i	−0.364513	+	0.567194i	−0.974267	−	0.225397i	$-0.927632\pi$
$101$	−3.66331	+	5.70023i	−0.364513	+	0.567194i	0.609754	+	0.792591i	$0.291268\pi$
$102$	4.38765	−	3.89529i	0.434442	−	0.385691i
$103$	1.50940	+	3.30513i	0.148726	+	0.325664i	0.969302	−	0.245873i	$-0.0790747\pi$
$103$	1.50940	+	3.30513i	0.148726	+	0.325664i	−0.820576	+	0.571537i	$0.806347\pi$
$104$	5.18132	+	7.45645i	0.508070	+	0.731165i
$105$	0.131416	+	0.914016i	0.0128249	+	0.0891989i
$106$	−19.4233	+	0.233614i	−1.88655	+	0.0226906i
$107$	−0.776887	−	2.64583i	−0.0751045	−	0.255782i	0.913379	−	0.407110i	$-0.133463\pi$
$107$	−0.776887	−	2.64583i	−0.0751045	−	0.255782i	−0.988484	+	0.151327i	$0.951645\pi$
$108$	1.70803	+	1.04050i	0.164355	+	0.100122i
$109$	6.56111	−	7.57193i	0.628440	−	0.725259i	−0.348846	−	0.937180i	$-0.613426\pi$
$109$	6.56111	−	7.57193i	0.628440	−	0.725259i	0.977287	+	0.211921i	$0.0679719\pi$
$110$	1.74697	+	0.772559i	0.166567	+	0.0736606i
$111$	−5.29196	−	6.10724i	−0.502290	−	0.579674i
$112$	2.16085	+	4.18624i	0.204181	+	0.395562i
$113$	−0.810225	−	0.370017i	−0.0762196	−	0.0348083i	0.376940	−	0.926237i	$-0.376976\pi$
$113$	−0.810225	−	0.370017i	−0.0762196	−	0.0348083i	−0.453160	+	0.891429i	$0.649703\pi$
$114$	6.36745	+	9.65075i	0.596366	+	0.903875i
$115$	3.75116	+	0.259876i	0.349797	+	0.0242335i
$116$	−11.9229	−	5.10212i	−1.10702	−	0.473720i
$117$	2.92013	+	1.33358i	0.269966	+	0.123289i
$118$	−12.0311	+	3.69039i	−1.10755	+	0.339728i
$119$	3.69278	−	3.19982i	0.338517	−	0.293327i
$120$	1.51174	+	1.62248i	0.138002	+	0.148112i
$121$	−5.25998	+	6.07034i	−0.478180	+	0.551849i
$122$	5.24099	+	11.1203i	0.474497	+	1.00678i
$123$	−8.84403	+	2.59684i	−0.797439	+	0.234149i
$124$	7.76519	+	11.4668i	0.697335	+	1.02975i
$125$	−1.04722	−	7.28358i	−0.0936663	−	0.651463i
$126$	1.41192	+	0.883575i	0.125784	+	0.0787151i
$127$	−7.47481	+	3.41363i	−0.663282	+	0.302911i	−0.718463	−	0.695566i	$-0.755154\pi$
$127$	−7.47481	+	3.41363i	−0.663282	+	0.302911i	0.0551804	+	0.998476i	$0.482427\pi$
$128$	9.99833	+	5.29465i	0.883736	+	0.467986i
$129$	0.0835777	−	0.130049i	0.00735860	−	0.0114502i
$130$	2.71795	+	2.29847i	0.238380	+	0.201590i
$131$	1.98090	−	13.7775i	0.173072	−	1.20374i	−0.699273	−	0.714855i	$-0.746493\pi$
$131$	1.98090	−	13.7775i	0.173072	−	1.20374i	0.872345	−	0.488890i	$-0.162598\pi$
$132$	3.09876	−	1.50626i	0.269713	−	0.131103i
$133$	5.20577	+	8.10034i	0.451398	+	0.702389i
$134$	5.82469	−	20.7574i	0.503177	−	1.79317i
$135$	0.752286	+	0.220891i	0.0647465	+	0.0190113i
$136$	2.89769	−	11.3711i	0.248475	−	0.975065i
$137$			5.74024i			0.490422i	0.969470	+	0.245211i	$0.0788572\pi$
$137$			5.74024i			0.490422i	−0.969470	+	0.245211i	$0.921143\pi$
$138$	4.72697	−	4.86372i	0.402386	−	0.414028i
$139$	10.6830			0.906120			0.453060	−	0.891480i	$-0.350332\pi$
$139$	10.6830			0.906120			0.453060	+	0.891480i	$0.350332\pi$
$140$	1.24264	+	1.36625i	0.105022	+	0.115469i
$141$	0.0777519	−	0.264799i	0.00654789	−	0.0223001i
$142$	−0.446303	+	1.59049i	−0.0374529	+	0.133471i
$143$	4.65243	−	2.98993i	0.389055	−	0.250031i
$144$	3.99537	−	0.192357i	0.332948	−	0.0160297i
$145$	−5.03229	−	0.723534i	−0.417909	−	0.0600862i
$146$	9.89840	−	11.7049i	0.819198	−	0.968703i
$147$	−4.72186	−	3.03456i	−0.389452	−	0.250286i
$148$	−15.6124	−	4.17909i	−1.28333	−	0.343519i
$149$	5.95975	+	13.0500i	0.488242	+	1.06910i	0.980114	+	0.198433i	$0.0635853\pi$
$149$	5.95975	+	13.0500i	0.488242	+	1.06910i	−0.491872	+	0.870667i	$0.663687\pi$
$150$	−5.25716	−	3.28991i	−0.429245	−	0.268620i
$151$	−1.18824	+	0.170843i	−0.0966976	+	0.0139030i	−0.190494	−	0.981688i	$-0.561009\pi$
$151$	−1.18824	+	0.170843i	−0.0966976	+	0.0139030i	0.0937962	+	0.995591i	$0.470100\pi$
$152$	21.3673	+	8.84108i	1.73312	+	0.717107i
$153$	−1.16885	−	3.98072i	−0.0944955	−	0.321822i
$154$	2.59555	−	1.22329i	0.209155	−	0.0985751i
$155$	4.10296	+	3.55523i	0.329557	+	0.285563i
$156$	6.33130	−	1.06631i	0.506910	−	0.0853734i
$157$	−6.26439	−	7.22949i	−0.499953	−	0.576976i	0.448545	−	0.893760i	$-0.351942\pi$
$157$	−6.26439	−	7.22949i	−0.499953	−	0.576976i	−0.948498	+	0.316784i	$0.897397\pi$
$158$	−21.3830	+	6.55898i	−1.70114	+	0.521804i
$159$	−5.70586	+	12.4941i	−0.452504	+	0.990845i
$160$	4.32297	+	0.991537i	0.341761	+	0.0783879i
$161$	3.98505	−	4.00287i	0.314066	−	0.315471i
$162$	1.18043	−	0.778835i	0.0927434	−	0.0611910i
$163$	−3.37059	+	7.38057i	−0.264005	+	0.578091i	−0.994489	−	0.104839i	$-0.966567\pi$
$163$	−3.37059	+	7.38057i	−0.264005	+	0.578091i	0.730484	+	0.682930i	$0.239295\pi$
$164$	−11.7336	+	14.2184i	−0.916244	+	1.11027i
$165$	1.02079	−	0.884517i	0.0794682	−	0.0688595i
$166$	8.64134	+	3.82144i	0.670698	+	0.296602i
$167$	12.6603	+	10.9703i	0.979687	+	0.848903i	0.988525	−	0.151057i	$-0.0482679\pi$
$167$	12.6603	+	10.9703i	0.979687	+	0.848903i	−0.00883815	+	0.999961i	$0.502813\pi$
$168$	3.32903	−	0.120166i	0.256841	−	0.00927104i
$169$	−2.58527	+	0.759103i	−0.198867	+	0.0583925i
$170$	−0.0553249	−	4.59986i	−0.00424322	−	0.352793i
$171$	8.09240	−	1.16351i	0.618841	−	0.0889759i
$172$	−0.00743626	−	0.309091i	−0.000567009	−	0.0235679i
$173$	−5.26667	+	2.40521i	−0.400418	+	0.182865i	−0.605437	−	0.795893i	$-0.707002\pi$
$173$	−5.26667	+	2.40521i	−0.400418	+	0.182865i	0.205019	+	0.978758i	$0.434274\pi$
$174$	−6.85771	+	6.08817i	−0.519881	+	0.461543i
$175$	−4.34490	−	2.79230i	−0.328443	−	0.211078i
$176$	3.44242	−	5.96945i	0.259482	−	0.449964i
$177$	−1.26639	+	8.80793i	−0.0951877	+	0.662045i
$178$	−0.780497	−	0.102654i	−0.0585008	−	0.00769421i
$179$	−11.8959	+	7.64504i	−0.889142	+	0.571417i	−0.903552	−	0.428479i	$-0.859050\pi$
$179$	−11.8959	+	7.64504i	−0.889142	+	0.571417i	0.0144093	+	0.999896i	$0.495413\pi$
$180$	1.49351	−	0.477842i	0.111320	−	0.0356162i
$181$	6.16136	+	1.80914i	0.457970	+	0.134472i	0.502577	−	0.864532i	$-0.332385\pi$
$181$	6.16136	+	1.80914i	0.457970	+	0.134472i	−0.0446068	+	0.999005i	$0.514204\pi$
$182$	5.28301	−	0.824549i	0.391603	−	0.0611197i
$183$	8.69276			0.642588
$184$	2.37357	−	13.3554i	0.174982	−	0.984572i
$185$	−6.33590			−0.465825
$186$	9.67535	−	1.51009i	0.709431	−	0.110725i
$187$	−6.85769	−	2.01360i	−0.501484	−	0.147249i
$188$	−0.168196	−	0.525704i	−0.0122670	−	0.0383409i
$189$	0.990793	−	0.636744i	0.0720696	−	0.0463163i
$190$	8.98778	+	1.18210i	0.652042	+	0.0857587i
$191$	−1.21924	+	8.47997i	−0.0882208	+	0.613589i	0.896965	+	0.442101i	$0.145767\pi$
$191$	−1.21924	+	8.47997i	−0.0882208	+	0.613589i	−0.985186	+	0.171488i	$0.945142\pi$
$192$	6.40068	−	4.79910i	0.461929	−	0.346345i
$193$	−14.4734	−	9.30151i	−1.04182	−	0.669537i	−0.0963841	−	0.995344i	$-0.530728\pi$
$193$	−14.4734	−	9.30151i	−1.04182	−	0.669537i	−0.945436	+	0.325807i	$0.894364\pi$
$194$	11.2725	−	10.0075i	0.809316	−	0.718498i
$195$	2.28951	−	1.04559i	0.163955	−	0.0748760i
$196$	−11.2225	+	0.269997i	−0.801609	+	0.0192855i
$197$	−14.9493	+	2.14939i	−1.06510	+	0.153138i	−0.652509	−	0.757781i	$-0.726284\pi$
$197$	−14.9493	+	2.14939i	−1.06510	+	0.153138i	−0.412586	+	0.910919i	$0.635374\pi$
$198$	−0.0293005	−	2.43613i	−0.00208230	−	0.173128i
$199$	−0.244647	+	0.0718348i	−0.0173426	+	0.00509223i	−0.290392	−	0.956908i	$-0.593786\pi$
$199$	−0.244647	+	0.0718348i	−0.0173426	+	0.00509223i	0.273050	+	0.962000i	$0.411968\pi$
$200$	−12.3954	+	0.447428i	−0.876484	+	0.0316380i
$201$	−11.5211	−	9.98310i	−0.812636	−	0.704153i
$202$	8.76382	+	3.87561i	0.616620	+	0.272687i
$203$	−5.77167	+	5.00118i	−0.405092	+	0.351014i
$204$	−6.39975	−	5.28135i	−0.448072	−	0.369768i
$205$	−3.00214	+	6.57378i	−0.209679	+	0.459133i
$206$	4.28907	−	2.82988i	0.298833	−	0.197167i
$207$	−1.68599	−	4.48970i	−0.117185	−	0.312056i
$208$	9.28892	−	8.86597i	0.644070	−	0.614745i
$209$	5.85085	−	12.8116i	0.404712	−	0.886195i
$210$	1.24849	−	0.382959i	0.0861542	−	0.0264267i
$211$	−12.1198	−	13.9870i	−0.834362	−	0.962905i	0.165366	−	0.986232i	$-0.447120\pi$
$211$	−12.1198	−	13.9870i	−0.834362	−	0.962905i	−0.999728	+	0.0233270i	$0.992574\pi$
$212$	4.56233	+	27.0891i	0.313342	+	1.86049i
$213$	0.882777	+	0.764931i	0.0604869	+	0.0524122i
$214$	−3.52759	+	1.66256i	−0.241141	+	0.113650i
$215$	−0.0341475	−	0.116296i	−0.00232884	−	0.00793131i
$216$	1.08140	−	2.61354i	0.0735797	−	0.177829i
$217$	8.07218	−	1.16060i	0.547975	−	0.0787869i
$218$	−12.0111	−	7.51651i	−0.813495	−	0.509082i
$219$	−4.50283	−	9.85981i	−0.304273	−	0.666265i
$220$	0.698508	−	2.60952i	0.0470934	−	0.175934i
$221$	−11.2043	−	7.20054i	−0.753680	−	0.484361i
$222$	−7.37954	+	8.72633i	−0.495282	+	0.585673i
$223$	−8.10412	−	1.16520i	−0.542692	−	0.0780273i	−0.134483	−	0.990916i	$-0.542937\pi$
$223$	−8.10412	−	1.16520i	−0.542692	−	0.0780273i	−0.408209	+	0.912889i	$0.633846\pi$
$224$	5.37817	−	3.93230i	0.359344	−	0.262738i
$225$	−3.68913	+	2.37086i	−0.245942	+	0.158057i
$226$	−0.340327	+	1.21282i	−0.0226382	+	0.0806756i
$227$	−1.66452	+	5.66884i	−0.110478	+	0.376254i	−0.996108	−	0.0881372i	$-0.971909\pi$
$227$	−1.66452	+	5.66884i	−0.110478	+	0.376254i	0.885630	+	0.464391i	$0.153727\pi$
$228$	12.0963	−	11.0019i	0.801099	−	0.728618i
$229$	21.9459			1.45023			0.725114	−	0.688629i	$-0.241787\pi$
$229$	21.9459			1.45023			0.725114	+	0.688629i	$0.241787\pi$
$230$	−0.454944	−	5.29816i	−0.0299981	−	0.349350i
$231$		−	2.02895i		−	0.133495i
$232$	−4.52897	+	17.7726i	−0.297341	+	1.16683i
$233$	−26.7498	−	7.85446i	−1.75244	−	0.514563i	−0.761419	−	0.648260i	$-0.775497\pi$
$233$	−26.7498	−	7.85446i	−1.75244	−	0.514563i	−0.991022	+	0.133697i	$0.957315\pi$
$234$	1.22657	−	4.37112i	0.0801835	−	0.285749i
$235$	−0.116983	−	0.182029i	−0.00763114	−	0.0118743i
$236$	7.78037	+	16.0062i	0.506459	+	1.04192i
$237$	−2.25077	+	15.6544i	−0.146203	+	1.01687i
$238$	−5.27643	−	4.46209i	−0.342020	−	0.289234i
$239$	−10.5865	+	16.4729i	−0.684785	+	1.06555i	0.308653	+	0.951175i	$0.400122\pi$
$239$	−10.5865	+	16.4729i	−0.684785	+	1.06555i	−0.993438	+	0.114371i	$0.963515\pi$
$240$	1.93741	−	2.46619i	0.125059	−	0.159192i
$241$	−5.68824	+	2.59773i	−0.366412	+	0.167335i	−0.590108	−	0.807324i	$-0.700915\pi$
$241$	−5.68824	+	2.59773i	−0.366412	+	0.167335i	0.223696	+	0.974659i	$0.428188\pi$
$242$	9.62919	+	6.02591i	0.618988	+	0.387360i
$243$	−0.142315	−	0.989821i	−0.00912950	−	0.0634971i
$244$	14.3953	−	9.74838i	0.921567	−	0.624076i
$245$	−4.22249	+	1.23984i	−0.269765	+	0.0792102i
$246$	5.55730	+	11.7914i	0.354321	+	0.751793i
$247$	17.1872	−	19.8351i	1.09360	−	1.26208i
$248$	14.3290	−	13.3510i	0.909895	−	0.847790i
$249$	5.04929	−	4.37524i	0.319986	−	0.277269i
$250$	−9.94894	+	3.05171i	−0.629226	+	0.193007i
$251$	−4.00127	−	1.82732i	−0.252558	−	0.115339i	0.285114	−	0.958494i	$-0.407969\pi$
$251$	−4.00127	−	1.82732i	−0.252558	−	0.115339i	−0.537672	+	0.843154i	$0.680696\pi$
$252$	0.926700	−	2.16557i	0.0583766	−	0.136418i
$253$	−8.07699	−	1.73817i	−0.507796	−	0.109278i
$254$	6.40000	+	9.70007i	0.401571	+	0.608637i
$255$	−2.95888	−	1.35127i	−0.185292	−	0.0846200i
$256$	5.21773	−	15.1253i	0.326108	−	0.945333i
$257$	−1.23812	−	1.42886i	−0.0772317	−	0.0891301i	0.715819	−	0.698286i	$-0.246054\pi$
$257$	−1.23812	−	1.42886i	−0.0772317	−	0.0891301i	−0.793050	+	0.609156i	$0.791508\pi$
$258$	−0.199945	−	0.0884211i	−0.0124480	−	0.00550486i
$259$	−6.23264	+	7.19285i	−0.387278	+	0.446942i
$260$	2.61891	−	4.29905i	0.162418	−	0.266616i
$261$	1.82686	+	6.22170i	0.113080	+	0.385114i
$262$	−19.6832	+	0.236741i	−1.21604	+	0.0146259i
$263$	1.78158	+	12.3911i	0.109857	+	0.764070i	0.968052	+	0.250748i	$0.0806765\pi$
$263$	1.78158	+	12.3911i	0.109857	+	0.764070i	−0.858196	+	0.513323i	$0.828414\pi$
$264$	−2.78048	−	4.00140i	−0.171127	−	0.246269i
$265$	4.47365	+	9.79592i	0.274814	+	0.601759i
$266$	10.1833	−	9.04057i	0.624378	−	0.554313i
$267$	−0.300947	+	0.468282i	−0.0184176	+	0.0286584i
$268$	−30.2745	−	3.61196i	−1.84931	−	0.220636i
$269$	6.41078	+	0.921731i	0.390872	+	0.0561989i	0.334949	−	0.942236i	$-0.391281\pi$
$269$	6.41078	+	0.921731i	0.390872	+	0.0561989i	0.0559229	+	0.998435i	$0.482190\pi$
$270$	0.144589	−	1.09934i	0.00879940	−	0.0669037i
$271$	−13.4163	−	20.8762i	−0.814982	−	1.26814i	−0.960360	−	0.278761i	$-0.910076\pi$
$271$	−13.4163	−	20.8762i	−0.814982	−	1.26814i	0.145378	−	0.989376i	$-0.453560\pi$
$272$	−16.5208	−	1.56908i	−1.00172	−	0.0951392i
$273$	1.06520	−	3.62772i	0.0644686	−	0.219560i
$274$	8.02082	−	1.25186i	0.484556	−	0.0756274i
$275$			7.55462i			0.455561i
$276$	−7.82694	−	5.54427i	−0.471127	−	0.333726i
$277$		−	7.15987i		−	0.430195i	−0.976593	−	0.215098i	$-0.930993\pi$
$277$		−	7.15987i		−	0.430195i	0.976593	−	0.215098i	$-0.0690069\pi$
$278$	−2.32979	−	14.9273i	−0.139732	−	0.895281i
$279$	1.95081	−	6.64385i	0.116792	−	0.397757i
$280$	1.63806	−	2.03429i	0.0978926	−	0.121572i
$281$	5.02717	+	7.82244i	0.299896	+	0.466647i	0.958198	−	0.286107i	$-0.0923612\pi$
$281$	5.02717	+	7.82244i	0.299896	+	0.466647i	−0.658302	+	0.752754i	$0.728725\pi$
$282$	−0.386959	−	0.0508941i	−0.0230431	−	0.00303070i
$283$	−10.2594	−	1.47509i	−0.609861	−	0.0876847i	−0.169537	−	0.985524i	$-0.554227\pi$
$283$	−10.2594	−	1.47509i	−0.609861	−	0.0876847i	−0.440324	+	0.897839i	$0.645136\pi$
$284$	2.31971	+	0.276758i	0.137650	+	0.0164226i
$285$	3.46554	−	5.39248i	0.205281	−	0.319423i
$286$	−5.19244	−	5.84876i	−0.307036	−	0.345845i
$287$	4.50969	+	9.87484i	0.266199	+	0.582894i
$288$	−1.14011	−	5.54077i	−0.0671814	−	0.326493i
$289$	0.0302198	+	0.210183i	0.00177763	+	0.0123637i
$290$	0.0864705	+	7.18939i	0.00507772	+	0.422176i
$291$	−3.00292	−	10.2270i	−0.176035	−	0.599519i
$292$	−18.5139	−	11.2784i	−1.08344	−	0.660016i
$293$	14.8496	−	17.1373i	0.867521	−	1.00117i	−0.132429	−	0.991193i	$-0.542278\pi$
$293$	14.8496	−	17.1373i	0.867521	−	1.00117i	0.999950	−	0.00998064i	$-0.00317699\pi$
$294$	−3.21041	+	7.25963i	−0.187235	+	0.423390i
$295$	4.56885	+	5.27274i	0.266009	+	0.306991i
$296$	−2.43461	+	22.7266i	−0.141509	+	1.32096i
$297$	−1.56705	−	0.715646i	−0.0909293	−	0.0415260i
$298$	16.9351	−	11.1736i	0.981021	−	0.647266i
$299$	−13.5289	−	7.34822i	−0.782399	−	0.424958i
$300$	−3.45048	+	8.06329i	−0.199214	+	0.465534i
$301$	−0.165616	−	0.0756344i	−0.00954597	−	0.00435950i
$302$	0.497855	+	1.62307i	0.0286483	+	0.0933969i
$303$	5.12086	−	4.43725i	0.294186	−	0.254913i
$304$	7.69376	−	31.7845i	0.441267	−	1.82297i
$305$	4.46322	−	5.15083i	0.255563	−	0.294935i
$306$	−5.30734	+	2.50136i	−0.303401	+	0.142993i
$307$	19.6980	−	5.78384i	1.12422	−	0.330101i	0.333788	−	0.942648i	$-0.391673\pi$
$307$	19.6980	−	5.78384i	1.12422	−	0.330101i	0.790434	+	0.612547i	$0.209855\pi$
$308$	−2.27534	−	3.35998i	−0.129650	−	0.191452i
$309$	−0.517097	−	3.59649i	−0.0294166	−	0.204597i
$310$	4.07293	−	6.50839i	0.231327	−	0.369652i
$311$	7.21030	−	3.29283i	0.408859	−	0.186719i	−0.200359	−	0.979723i	$-0.564211\pi$
$311$	7.21030	−	3.29283i	0.408859	−	0.186719i	0.609218	+	0.793003i	$0.291484\pi$
$312$	−2.87071	−	8.61416i	−0.162522	−	0.487681i
$313$	−1.96332	+	3.05499i	−0.110973	+	0.172678i	−0.892298	−	0.451447i	$-0.850908\pi$
$313$	−1.96332	+	3.05499i	−0.110973	+	0.172678i	0.781325	+	0.624125i	$0.214544\pi$
$314$	−8.73559	+	10.3299i	−0.492978	+	0.582947i
$315$	0.131416	−	0.914016i	0.00740444	−	0.0514990i
$316$	13.8281	+	28.4481i	0.777894	+	1.60033i
$317$	−17.7478	−	27.6161i	−0.996814	−	1.55107i	−0.824368	−	0.566055i	$-0.808469\pi$
$317$	−17.7478	−	27.6161i	−0.996814	−	1.55107i	−0.172447	−	0.985019i	$-0.555167\pi$
$318$	18.7023	+	5.24801i	1.04877	+	0.294294i
$319$	10.7183	+	3.14717i	0.600109	+	0.176208i
$320$	0.442699	−	6.25672i	0.0247476	−	0.349761i
$321$			2.75753i			0.153911i
$322$	−6.46228	−	4.69533i	−0.360129	−	0.261661i
$323$	−33.9188			−1.88729
$324$	−1.34570	−	1.47956i	−0.0747609	−	0.0821978i
$325$	−3.96616	+	13.5075i	−0.220003	+	0.749261i
$326$	11.0479	+	3.10014i	0.611888	+	0.171701i
$327$	−8.42860	+	5.41673i	−0.466103	+	0.299546i
$328$	22.4263	+	13.2946i	1.23828	+	0.734070i
$329$	−0.321726	−	0.0462573i	−0.0177373	−	0.00255025i
$330$	−1.45855	−	1.23344i	−0.0802906	−	0.0678988i
$331$	9.51990	+	6.11807i	0.523261	+	0.336280i	0.775461	−	0.631396i	$-0.217518\pi$
$331$	9.51990	+	6.11807i	0.523261	+	0.336280i	−0.252200	+	0.967675i	$0.581154\pi$
$332$	3.45515	−	12.9079i	0.189626	−	0.708414i
$333$	3.35699	+	7.35077i	0.183962	+	0.402820i
$334$	12.5677	−	20.0827i	0.687673	−	1.09888i
$335$	−11.8308	+	1.70101i	−0.646386	+	0.0929363i
$336$	−0.893918	−	4.62544i	−0.0487672	−	0.252339i
$337$	−5.09042	−	17.3364i	−0.277293	−	0.944372i	−0.973911	−	0.226930i	$-0.927131\pi$
$337$	−5.09042	−	17.3364i	−0.277293	−	0.944372i	0.696618	−	0.717442i	$-0.254687\pi$
$338$	1.62450	+	3.44684i	0.0883610	+	0.187483i
$339$	0.673159	+	0.583296i	0.0365610	+	0.0316803i
$340$	−6.41531	+	1.08046i	−0.347919	+	0.0585963i
$341$	−7.81165	−	9.01513i	−0.423025	−	0.488197i
$342$	−3.39060	−	11.0537i	−0.183342	−	0.597718i
$343$	−6.17096	+	13.5125i	−0.333201	+	0.729607i
$344$	−0.430270	+	0.0777984i	−0.0231986	+	0.00419461i
$345$	−3.52599	−	1.30617i	−0.189833	−	0.0703219i
$346$	4.50937	+	6.83457i	0.242425	+	0.367429i
$347$	−5.53338	+	12.1164i	−0.297048	+	0.650443i	−0.998030	−	0.0627349i	$-0.980018\pi$
$347$	−5.53338	+	12.1164i	−0.297048	+	0.650443i	0.700983	+	0.713178i	$0.252745\pi$
$348$	10.0025	+	8.25452i	0.536192	+	0.442489i
$349$	−11.4621	+	9.93199i	−0.613554	+	0.531647i	−0.905259	−	0.424861i	$-0.860323\pi$
$349$	−11.4621	+	9.93199i	−0.613554	+	0.531647i	0.291705	+	0.956508i	$0.405777\pi$
$350$	−2.95411	+	6.68007i	−0.157904	+	0.357065i
$351$	−2.42613	−	2.10225i	−0.129497	−	0.112210i
$352$	−9.09183	−	3.50824i	−0.484596	−	0.186990i
$353$	6.67672	−	1.96046i	0.355366	−	0.104345i	−0.0991768	−	0.995070i	$-0.531621\pi$
$353$	6.67672	−	1.96046i	0.355366	−	0.104345i	0.454543	+	0.890725i	$0.349803\pi$
$354$	12.5835	−	0.151348i	0.668805	−	0.00804406i
$355$	0.906507	−	0.130336i	0.0481124	−	0.00691752i
$356$	0.0267765	+	1.11297i	0.00141915	+	0.0589875i
$357$	−4.44469	+	2.02982i	−0.235238	+	0.107430i
$358$	13.2767	+	14.9549i	0.701696	+	0.790389i
$359$	19.9507	+	12.8215i	1.05296	+	0.676694i	0.948158	−	0.317799i	$-0.102944\pi$
$359$	19.9507	+	12.8215i	1.05296	+	0.676694i	0.104799	+	0.994493i	$0.466580\pi$
$360$	−0.993398	−	1.98267i	−0.0523567	−	0.104496i
$361$	6.80844	−	47.3537i	0.358339	−	2.49230i
$362$	1.18421	−	9.00379i	0.0622406	−	0.473229i
$363$	6.75713	−	4.34254i	0.354657	−	0.227924i
$364$	−2.30428	−	7.20211i	−0.120777	−	0.377493i
$365$	−8.15428	−	2.39431i	−0.426815	−	0.125324i
$366$	−1.89575	−	12.1464i	−0.0990926	−	0.634901i
$367$	−14.5219			−0.758039			−0.379020	−	0.925389i	$-0.623739\pi$
$367$	−14.5219			−0.758039			−0.379020	+	0.925389i	$0.623739\pi$
$368$	−19.1791	−	0.403982i	−0.999778	−	0.0210590i
$369$	9.21740			0.479839
$370$	1.38176	+	8.85314i	0.0718343	+	0.460253i
$371$	15.5216	+	4.55755i	0.805841	+	0.236616i
$372$	−4.22008	−	13.1900i	−0.218801	−	0.683870i
$373$	−6.70174	+	4.30695i	−0.347003	+	0.223005i	−0.702519	−	0.711665i	$-0.747941\pi$
$373$	−6.70174	+	4.30695i	−0.347003	+	0.223005i	0.355516	+	0.934670i	$0.384305\pi$
$374$	−1.31804	+	10.0214i	−0.0681544	+	0.518193i
$375$	−1.04722	+	7.28358i	−0.0540782	+	0.376122i
$376$	−0.697883	+	0.349668i	−0.0359906	+	0.0180327i
$377$	17.5118	+	11.2541i	0.901903	+	0.579618i
$378$	−1.10580	−	1.24557i	−0.0568761	−	0.0640651i
$379$	17.4948	−	7.98959i	0.898646	−	0.410398i	0.0881261	−	0.996109i	$-0.471912\pi$
$379$	17.4948	−	7.98959i	0.898646	−	0.410398i	0.810520	+	0.585712i	$0.199185\pi$
$380$	−0.308343	−	12.8164i	−0.0158177	−	0.657467i
$381$	8.13376	−	1.16946i	0.416705	−	0.0599132i
$382$	12.1149	−	0.145713i	0.619854	−	0.00745530i
$383$	−1.29090	+	0.379043i	−0.0659621	+	0.0193682i	−0.314547	−	0.949242i	$-0.601853\pi$
$383$	−1.29090	+	0.379043i	−0.0659621	+	0.0193682i	0.248585	+	0.968610i	$0.420034\pi$
$384$	−8.10165	−	7.89704i	−0.413436	−	0.402994i
$385$	−1.20224	−	1.04175i	−0.0612718	−	0.0530923i
$386$	−9.84055	+	22.2522i	−0.500871	+	1.13261i
$387$	−0.116831	+	0.101235i	−0.00593887	+	0.00514606i
$388$	−16.4418	−	13.5685i	−0.834708	−	0.688836i
$389$	5.93165	−	12.9885i	0.300747	−	0.658543i	−0.697572	−	0.716515i	$-0.745736\pi$
$389$	5.93165	−	12.9885i	0.300747	−	0.658543i	0.998318	+	0.0579718i	$0.0184634\pi$
$390$	−1.96030	−	2.97111i	−0.0992637	−	0.150448i
$391$	4.27275	+	19.4326i	0.216082	+	0.982751i
$392$	2.82472	+	15.6223i	0.142670	+	0.789046i
$393$	−5.78223	+	12.6613i	−0.291675	+	0.638679i
$394$	6.26354	+	20.4199i	0.315553	+	1.02874i
$395$	8.12027	+	9.37130i	0.408575	+	0.471521i
$396$	−3.39760	+	0.572222i	−0.170736	+	0.0287552i
$397$	28.0715	+	24.3241i	1.40887	+	1.22079i	0.941626	+	0.336662i	$0.109298\pi$
$397$	28.0715	+	24.3241i	1.40887	+	1.22079i	0.467242	+	0.884129i	$0.345248\pi$
$398$	0.153728	+	0.326178i	0.00770570	+	0.0163498i
$399$	−2.71277	−	9.23886i	−0.135809	−	0.462521i
$400$	3.32842	+	17.2224i	0.166421	+	0.861121i
$401$	1.73642	−	0.249659i	0.0867125	−	0.0124674i	−0.0988220	−	0.995105i	$-0.531507\pi$
$401$	1.73642	−	0.249659i	0.0867125	−	0.0124674i	0.185534	+	0.982638i	$0.440598\pi$
$402$	−11.4368	+	18.2756i	−0.570415	+	0.911502i
$403$	−9.23414	−	20.2199i	−0.459985	−	1.00723i
$404$	3.50412	−	13.0909i	0.174337	−	0.651295i
$405$	−0.659581	−	0.423887i	−0.0327748	−	0.0210631i
$406$	8.24684	+	6.97406i	0.409284	+	0.346117i
$407$	13.7797	+	1.98122i	0.683035	+	0.0982056i
$408$	−5.98393	+	10.0941i	−0.296248	+	0.499734i
$409$	7.59700	−	4.88229i	0.375647	−	0.241414i	−0.339170	−	0.940725i	$-0.610146\pi$
$409$	7.59700	−	4.88229i	0.375647	−	0.241414i	0.714817	+	0.699311i	$0.246510\pi$
$410$	9.84024	+	2.76125i	0.485975	+	0.136368i
$411$	1.61721	−	5.50772i	0.0797712	−	0.271676i
$412$	−4.88955	−	5.37595i	−0.240891	−	0.264854i
$413$	10.4803			0.515701
$414$	−5.90576	+	3.33497i	−0.290252	+	0.163905i
$415$		−	5.23834i		−	0.257140i
$416$	−14.4142	−	11.0458i	−0.706713	−	0.541567i
$417$	−10.2503	−	3.00975i	−0.501957	−	0.147388i
$418$	−19.1775	−	5.38137i	−0.938004	−	0.263212i
$419$	5.48731	+	8.53843i	0.268073	+	0.417129i	0.949026	−	0.315197i	$-0.102071\pi$
$419$	5.48731	+	8.53843i	0.268073	+	0.417129i	−0.680953	+	0.732327i	$0.738434\pi$
$420$	−0.807384	−	1.66100i	−0.0393963	−	0.0810484i
$421$	3.89265	−	27.0740i	0.189716	−	1.31950i	−0.643027	−	0.765844i	$-0.722322\pi$
$421$	3.89265	−	27.0740i	0.189716	−	1.31950i	0.832743	−	0.553660i	$-0.186769\pi$
$422$	−16.9009	+	19.9853i	−0.822721	+	0.972870i
$423$	−0.149205	+	0.232167i	−0.00725458	+	0.0112883i
$424$	36.8566	−	12.2826i	1.78991	−	0.596498i
$425$	16.5494	−	7.55786i	0.802764	−	0.366610i
$426$	0.876316	−	1.40032i	0.0424576	−	0.0678458i
$427$	−1.45702	−	10.1338i	−0.0705099	−	0.490407i
$428$	3.09240	+	4.56651i	0.149477	+	0.220731i
$429$	−5.30633	+	1.55808i	−0.256192	+	0.0752248i
$430$	−0.155053	+	0.0730765i	−0.00747731	+	0.00352406i
$431$	20.8001	−	24.0046i	1.00191	−	1.15626i	0.0142059	−	0.999899i	$-0.495478\pi$
$431$	20.8001	−	24.0046i	1.00191	−	1.15626i	0.987700	−	0.156362i	$-0.0499766\pi$
$432$	−3.88772	−	0.941062i	−0.187048	−	0.0452768i
$433$	−12.0250	+	10.4197i	−0.577884	+	0.500740i	−0.894052	−	0.447964i	$-0.852149\pi$
$433$	−12.0250	+	10.4197i	−0.577884	+	0.500740i	0.316167	+	0.948703i	$0.397604\pi$
$434$	−3.38212	−	11.0261i	−0.162347	−	0.529271i
$435$	4.62460	+	2.11198i	0.221733	+	0.101262i
$436$	−7.88336	+	18.4223i	−0.377544	+	0.882269i
$437$	−39.1026	+	2.88439i	−1.87053	+	0.137979i
$438$	−12.7951	+	8.44206i	−0.611373	+	0.403377i
$439$	35.0798	+	16.0204i	1.67427	+	0.764613i	0.999650	+	0.0264472i	$0.00841938\pi$
$439$	35.0798	+	16.0204i	1.67427	+	0.764613i	0.674619	+	0.738166i	$0.264308\pi$
$440$	−3.79861	−	0.406929i	−0.181091	−	0.0193996i
$441$	3.67566	+	4.24194i	0.175031	+	0.201997i
$442$	−7.61783	+	17.2260i	−0.362343	+	0.819358i
$443$	−10.6817	+	12.3274i	−0.507503	+	0.585690i	−0.950458	−	0.310854i	$-0.899385\pi$
$443$	−10.6817	+	12.3274i	−0.507503	+	0.585690i	0.442954	+	0.896544i	$0.353930\pi$
$444$	13.8026	+	8.40834i	0.655044	+	0.399042i
$445$	0.122959	+	0.418758i	0.00582879	+	0.0198510i
$446$	0.139254	+	11.5780i	0.00659388	+	0.548233i
$447$	−2.04172	−	14.2005i	−0.0965700	−	0.671659i
$448$	−6.66748	−	6.65733i	−0.315009	−	0.314529i
$449$	14.9583	+	32.7541i	0.705926	+	1.54576i	0.832634	+	0.553823i	$0.186832\pi$
$449$	14.9583	+	32.7541i	0.705926	+	1.54576i	−0.126708	+	0.991940i	$0.540441\pi$
$450$	4.11733	+	4.63776i	0.194093	+	0.218626i
$451$	8.58486	−	13.3583i	0.404245	−	0.629018i
$452$	1.76889	+	0.211041i	0.0832016	+	0.00992654i
$453$	1.18824	+	0.170843i	0.0558284	+	0.00802691i
$454$	8.28406	+	1.08955i	0.388790	+	0.0511350i
$455$	−1.60266	−	2.49379i	−0.0751340	−	0.116911i
$456$	−18.0109	−	14.5028i	−0.843439	−	0.679157i
$457$	−6.25238	+	21.2937i	−0.292474	+	0.996075i	0.673876	+	0.738844i	$0.264628\pi$
$457$	−6.25238	+	21.2937i	−0.292474	+	0.996075i	−0.966350	+	0.257231i	$0.917190\pi$
$458$	−4.78606	−	30.6650i	−0.223638	−	1.43288i
$459$			4.14878i			0.193648i
$460$	−7.30388	+	1.79114i	−0.340545	+	0.0835121i
$461$			22.3275i			1.03990i	0.854198	+	0.519948i	$0.174049\pi$
$461$			22.3275i			1.03990i	−0.854198	+	0.519948i	$0.825951\pi$
$462$	−2.83505	+	0.442483i	−0.131899	+	0.0205862i
$463$	−7.50087	+	25.5456i	−0.348595	+	1.18721i	0.579534	+	0.814948i	$0.303235\pi$
$463$	−7.50087	+	25.5456i	−0.348595	+	1.18721i	−0.928129	+	0.372258i	$0.878584\pi$
$464$	25.8213	+	2.45240i	1.19872	+	0.113850i
$465$	−2.93513	−	4.56716i	−0.136114	−	0.211797i
$466$	−5.14130	+	39.0904i	−0.238166	+	1.81083i
$467$	22.2555	+	3.19985i	1.02986	+	0.148072i	0.636471	−	0.771300i	$-0.280393\pi$
$467$	22.2555	+	3.19985i	1.02986	+	0.148072i	0.393389	+	0.919372i	$0.371302\pi$
$468$	−6.37525	−	0.760613i	−0.294696	−	0.0351593i
$469$	−9.70691	+	15.1043i	−0.448224	+	0.697450i
$470$	−0.228837	+	0.203158i	−0.0105555	+	0.00937098i
$471$	3.97386	+	8.70153i	0.183106	+	0.400945i
$472$	20.6687	−	14.3622i	0.951354	−	0.661074i
$473$	0.0379007	+	0.263605i	0.00174268	+	0.0121206i
$474$	22.3648	−	0.268992i	1.02725	−	0.0123552i
$475$	10.1008	+	34.4000i	0.463455	+	1.57838i
$476$	−5.08416	+	8.34585i	−0.233032	+	0.382532i
$477$	8.99472	−	10.3805i	0.411840	−	0.475289i
$478$	25.3263	+	11.2000i	1.15840	+	0.512277i
$479$	−23.4880	−	27.1066i	−1.07320	−	1.23853i	−0.969802	−	0.243893i	$-0.921575\pi$
$479$	−23.4880	−	27.1066i	−1.07320	−	1.23853i	−0.103393	−	0.994641i	$-0.532970\pi$
$480$	−3.86852	−	2.16930i	−0.176573	−	0.0990143i
$481$	23.5977	+	10.7767i	1.07596	+	0.491375i
$482$	4.87032	+	7.38164i	0.221837	+	0.336224i
$483$	−4.95137	+	2.71801i	−0.225295	+	0.123674i
$484$	6.32002	−	14.7690i	0.287274	−	0.671318i
$485$	−7.60176	−	3.47161i	−0.345178	−	0.157638i
$486$	−1.35204	+	0.414720i	−0.0613297	+	0.0188121i
$487$	12.6585	−	10.9686i	0.573609	−	0.497035i	−0.319068	−	0.947732i	$-0.603370\pi$
$487$	12.6585	−	10.9686i	0.573609	−	0.497035i	0.892677	+	0.450697i	$0.148824\pi$
$488$	−16.7608	−	17.9886i	−0.758725	−	0.814306i
$489$	5.31341	−	6.13200i	0.240281	−	0.277299i
$490$	2.65328	+	5.62969i	0.119863	+	0.254324i
$491$	−25.1265	+	7.37782i	−1.13395	+	0.332956i	−0.794257	−	0.607582i	$-0.792140\pi$
$491$	−25.1265	+	7.37782i	−1.13395	+	0.332956i	−0.339688	+	0.940538i	$0.610322\pi$
$492$	15.2641	−	10.3367i	0.688161	−	0.466015i
$493$	−3.82858	−	26.6284i	−0.172431	−	1.19928i
$494$	−31.4638	−	19.6899i	−1.41562	−	0.885892i
$495$	−1.22864	+	0.561099i	−0.0552230	+	0.0252195i
$496$	−21.7803	−	17.1103i	−0.977963	−	0.768275i
$497$	0.743769	−	1.15733i	0.0333626	−	0.0519132i
$498$	−7.21468	−	6.10119i	−0.323298	−	0.273401i
$499$	−1.78771	+	12.4338i	−0.0800289	+	0.556613i	0.909876	+	0.414880i	$0.136177\pi$
$499$	−1.78771	+	12.4338i	−0.0800289	+	0.556613i	−0.989905	+	0.141733i	$0.954733\pi$
$500$	6.43385	+	13.2361i	0.287731	+	0.591936i
$501$	−9.05683	−	14.0927i	−0.404630	−	0.629616i
$502$	−1.68069	+	5.98948i	−0.0750131	+	0.267323i
$503$	0.490946	+	0.144155i	0.0218902	+	0.00642755i	0.292659	−	0.956217i	$-0.405460\pi$
$503$	0.490946	+	0.144155i	0.0218902	+	0.00642755i	−0.270769	+	0.962644i	$0.587278\pi$
$504$	−3.22804	−	0.822599i	−0.143788	−	0.0366415i
$505$		−	5.31259i		−	0.236407i
$506$	−0.667282	+	11.6650i	−0.0296643	+	0.518574i
$507$	2.69441			0.119663
$508$	12.1581	−	11.0581i	0.539431	−	0.490625i
$509$	2.15578	−	7.34191i	0.0955533	−	0.325425i	−0.897819	−	0.440364i	$-0.854849\pi$
$509$	2.15578	−	7.34191i	0.0955533	−	0.325425i	0.993372	+	0.114940i	$0.0366675\pi$
$510$	−1.24285	+	4.42912i	−0.0550342	+	0.196125i
$511$	−10.7395	+	6.90189i	−0.475090	+	0.305322i
$512$	−22.2725	−	3.99212i	−0.984313	−	0.176429i
$513$	−8.09240	−	1.16351i	−0.357288	−	0.0513703i
$514$	−1.72653	+	2.04163i	−0.0761541	+	0.0900525i
$515$	−2.39657	−	1.54018i	−0.105606	−	0.0678685i
$516$	−0.0799458	+	0.298665i	−0.00351942	+	0.0131480i
$517$	0.197502	+	0.432470i	0.00868614	+	0.0190200i
$518$	11.4098	+	7.14021i	0.501318	+	0.313723i
$519$	5.73096	−	0.823988i	0.251561	−	0.0361691i
$520$	−6.57819	−	2.72184i	−0.288473	−	0.119361i
$521$	−7.39505	−	25.1852i	−0.323983	−	1.10338i	−0.947015	−	0.321188i	$-0.895918\pi$
$521$	−7.39505	−	25.1852i	−0.323983	−	1.10338i	0.623032	−	0.782196i	$-0.285900\pi$
$522$	8.29516	−	3.90952i	0.363069	−	0.171115i
$523$	−7.06253	−	6.11971i	−0.308823	−	0.267596i	0.486635	−	0.873605i	$-0.338224\pi$
$523$	−7.06253	−	6.11971i	−0.308823	−	0.267596i	−0.795458	+	0.606009i	$0.792770\pi$
$524$	4.62340	+	27.4517i	0.201974	+	1.19923i
$525$	3.38222	+	3.90329i	0.147612	+	0.170353i
$526$	16.9256	−	5.19170i	0.737990	−	0.226369i
$527$	−11.9338	+	26.1315i	−0.519846	+	1.13830i
$528$	−4.98477	+	4.75780i	−0.216934	+	0.207057i
$529$	6.57828	+	22.0392i	0.286012	+	0.958226i
$530$	12.7122	−	8.38735i	0.552182	−	0.364323i
$531$	3.69657	−	8.09437i	0.160418	−	0.351266i
$532$	−14.8532	−	12.2575i	−0.643967	−	0.531429i
$533$	22.3626	−	19.3773i	0.968633	−	0.839325i
$534$	0.719961	+	0.318387i	0.0311558	+	0.0137780i
$535$	1.63395	+	1.41583i	0.0706420	+	0.0612116i
$536$	1.55540	+	43.0902i	0.0671832	+	1.86121i
$537$	13.5679	−	3.98390i	0.585498	−	0.171918i
$538$	−0.110157	−	9.15878i	−0.00474922	−	0.394863i
$539$	9.57104	−	1.37611i	0.412254	−	0.0592732i
$540$	−1.56764	+	0.0377150i	−0.0674603	+	0.00162300i
$541$	−26.7221	+	12.2036i	−1.14887	+	0.524673i	−0.896538	−	0.442967i	$-0.853926\pi$
$541$	−26.7221	+	12.2036i	−1.14887	+	0.524673i	−0.252335	+	0.967640i	$0.581199\pi$
$542$	−26.2443	+	23.2993i	−1.12729	+	1.00079i
$543$	−5.40209	−	3.47171i	−0.231826	−	0.148985i
$544$	1.41045	+	23.4266i	0.0604726	+	1.00441i
$545$	−1.11794	+	7.77547i	−0.0478874	+	0.333064i
$546$	−5.30131	−	0.697246i	−0.226875	−	0.0298394i
$547$	−28.1984	+	18.1220i	−1.20568	+	0.774841i	−0.979929	−	0.199345i	$-0.936118\pi$
$547$	−28.1984	+	18.1220i	−1.20568	+	0.774841i	−0.225746	+	0.974186i	$0.572482\pi$
$548$	−3.49843	−	10.9345i	−0.149445	−	0.467097i
$549$	−8.34065	−	2.44903i	−0.355970	−	0.104522i
$550$	10.5561	−	1.64754i	0.450112	−	0.0702515i
$551$	53.0137			2.25846
$552$	−6.04007	+	12.1457i	−0.257082	+	0.516955i
$553$	18.6267			0.792089
$554$	−10.0045	+	1.56145i	−0.425049	+	0.0663399i
$555$	6.07925	+	1.78503i	0.258050	+	0.0757703i
$556$	−20.3498	+	6.51082i	−0.863024	+	0.276120i
$557$	−12.4500	+	8.00113i	−0.527523	+	0.339019i	−0.777142	−	0.629326i	$-0.783331\pi$
$557$	−12.4500	+	8.00113i	−0.527523	+	0.339019i	0.249618	+	0.968344i	$0.419695\pi$
$558$	−9.70887	−	1.27694i	−0.411009	−	0.0540573i
$559$	−0.0706266	+	0.491218i	−0.00298718	+	0.0207763i
$560$	−3.19974	−	1.84521i	−0.135214	−	0.0779742i
$561$	6.01261	+	3.86407i	0.253853	+	0.163141i
$562$	9.83392	−	8.73041i	0.414819	−	0.368270i
$563$	3.74617	−	1.71082i	0.157882	−	0.0721024i	−0.334907	−	0.942251i	$-0.608705\pi$
$563$	3.74617	−	1.71082i	0.157882	−	0.0721024i	0.492789	+	0.870149i	$0.335978\pi$
$564$	0.0132754	+	0.551795i	0.000558994	+	0.0232348i
$565$	0.691254	−	0.0993874i	0.0290813	−	0.00418126i
$566$	0.176289	+	14.6572i	0.00741000	+	0.616087i
$567$	−1.13005	+	0.331813i	−0.0474577	+	0.0139348i
$568$	−0.119179	−	3.30168i	−0.00500064	−	0.138536i
$569$	27.2993	+	23.6550i	1.14445	+	0.991669i	0.999998	+	0.00215682i	$0.000686539\pi$
$569$	27.2993	+	23.6550i	1.14445	+	0.991669i	0.144449	+	0.989512i	$0.453859\pi$
$570$	−8.29067	−	3.66637i	−0.347258	−	0.153567i
$571$	−1.88768	+	1.63568i	−0.0789970	+	0.0684513i	−0.693464	−	0.720491i	$-0.743916\pi$
$571$	−1.88768	+	1.63568i	−0.0789970	+	0.0684513i	0.614467	+	0.788942i	$0.289371\pi$
$572$	−7.04007	+	8.53091i	−0.294360	+	0.356695i
$573$	3.55893	−	7.79298i	0.148677	−	0.325556i
$574$	12.8146	−	8.45492i	0.534871	−	0.352902i
$575$	18.4360	−	10.1203i	0.768833	−	0.422044i
$576$	−7.49347	+	2.80142i	−0.312228	+	0.116726i
$577$	3.73332	−	8.17483i	0.155420	−	0.340323i	−0.815865	−	0.578243i	$-0.803739\pi$
$577$	3.73332	−	8.17483i	0.155420	−	0.340323i	0.971285	+	0.237921i	$0.0764658\pi$
$578$	0.287098	−	0.0880636i	0.0119417	−	0.00366296i
$579$	11.2666	+	13.0024i	0.468225	+	0.540360i
$580$	10.0269	−	1.68872i	0.416343	−	0.0701202i
$581$	−5.94685	−	5.15297i	−0.246717	−	0.213781i
$582$	−13.6353	+	6.42633i	−0.565201	+	0.266380i
$583$	−6.66641	−	22.7037i	−0.276094	−	0.940291i
$584$	−11.7216	+	28.3290i	−0.485045	+	1.17226i
$585$	−2.49135	+	0.358202i	−0.103005	+	0.0148098i
$586$	−27.1844	−	17.0119i	−1.12298	−	0.702755i
$587$	19.0906	+	41.8026i	0.787954	+	1.72538i	0.682417	+	0.730963i	$0.260929\pi$
$587$	19.0906	+	41.8026i	0.787954	+	1.72538i	0.105537	+	0.994415i	$0.466344\pi$
$588$	10.8440	+	2.90269i	0.447199	+	0.119705i
$589$	−47.6239	−	30.6060i	−1.96231	−	1.26110i
$590$	6.37119	−	7.53395i	0.262298	−	0.310168i
$591$	14.9493	+	2.14939i	0.614933	+	0.0884140i
$592$	32.2868	−	1.55444i	1.32698	−	0.0638872i
$593$	−14.0934	+	9.05725i	−0.578745	+	0.371937i	−0.797022	−	0.603950i	$-0.793593\pi$
$593$	−14.0934	+	9.05725i	−0.578745	+	0.371937i	0.218277	+	0.975887i	$0.429956\pi$
$594$	−0.658222	+	2.34570i	−0.0270072	+	0.0962453i
$595$	−1.07933	+	3.67586i	−0.0442482	+	0.150696i
$596$	−19.3060	−	21.2265i	−0.790806	−	0.869472i
$597$	0.254975			0.0104354
$598$	−7.31720	+	20.5065i	−0.299222	+	0.838572i
$599$			23.9903i			0.980217i	0.871661	+	0.490108i	$0.163043\pi$
$599$			23.9903i			0.980217i	−0.871661	+	0.490108i	$0.836957\pi$
$600$	12.0193	+	3.06287i	0.490686	+	0.125041i
$601$	−12.5682	−	3.69037i	−0.512669	−	0.150533i	0.0151580	−	0.999885i	$-0.495175\pi$
$601$	−12.5682	−	3.69037i	−0.512669	−	0.150533i	−0.527827	+	0.849352i	$0.676993\pi$
$602$	−0.0695655	+	0.247910i	−0.00283528	+	0.0101041i
$603$	8.24186	+	12.8246i	0.335634	+	0.522257i
$604$	2.15933	−	1.04962i	0.0878619	−	0.0427083i
$605$	0.896245	−	6.23352i	0.0364375	−	0.253429i
$606$	−7.31694	−	6.18767i	−0.297230	−	0.251357i
$607$	−11.6636	+	18.1489i	−0.473411	+	0.736642i	−0.993044	−	0.117748i	$-0.962433\pi$
$607$	−11.6636	+	18.1489i	−0.473411	+	0.736642i	0.519632	+	0.854390i	$0.326069\pi$
$608$	−46.0903	−	3.81876i	−1.86921	−	0.154871i
$609$	6.94687	−	3.17253i	0.281501	−	0.128557i
$610$	−8.17059	−	5.11313i	−0.330818	−	0.207024i
$611$	0.126084	+	0.876934i	0.00510082	+	0.0354770i
$612$	4.65259	+	6.87043i	0.188070	+	0.277721i
$613$	8.75062	−	2.56941i	0.353434	−	0.103778i	−0.100196	−	0.994968i	$-0.531947\pi$
$613$	8.75062	−	2.56941i	0.353434	−	0.103778i	0.453630	+	0.891190i	$0.350129\pi$
$614$	−12.3776	−	26.2625i	−0.499518	−	1.05987i
$615$	4.73258	−	5.46169i	0.190836	−	0.220237i
$616$	−4.19867	+	3.91209i	−0.169169	+	0.157622i
$617$	25.0738	−	21.7266i	1.00943	−	0.874678i	0.0172976	−	0.999850i	$-0.494494\pi$
$617$	25.0738	−	21.7266i	1.00943	−	0.874678i	0.992135	+	0.125172i	$0.0399483\pi$
$618$	−4.91260	+	1.50688i	−0.197614	+	0.0606155i
$619$	−11.5723	−	5.28488i	−0.465129	−	0.212417i	0.169044	−	0.985609i	$-0.445932\pi$
$619$	−11.5723	−	5.28488i	−0.465129	−	0.212417i	−0.634173	+	0.773191i	$0.718659\pi$
$620$	−9.98239	−	4.27171i	−0.400903	−	0.171556i
$621$	0.352804	+	4.78284i	0.0141576	+	0.191929i
$622$	−6.17352	−	9.35682i	−0.247536	−	0.375174i
$623$	0.596352	+	0.272345i	0.0238923	+	0.0109113i
$624$	−11.4105	+	5.88985i	−0.456785	+	0.235783i
$625$	−10.5806	−	12.2106i	−0.423223	−	0.488425i
$626$	4.69689	+	2.07710i	0.187726	+	0.0830175i
$627$	−9.22328	+	10.6442i	−0.368342	+	0.425090i
$628$	16.3390	+	9.95343i	0.651996	+	0.397185i
$629$	−9.44549	−	32.1684i	−0.376616	−	1.28264i
$630$	−1.30581	+	0.0157057i	−0.0520248	+	0.000625729i
$631$	−4.66575	−	32.4510i	−0.185741	−	1.29185i	−0.842887	−	0.538091i	$-0.819146\pi$
$631$	−4.66575	−	32.4510i	−0.185741	−	1.29185i	0.657146	−	0.753763i	$-0.271763\pi$
$632$	36.7347	−	25.5261i	1.46123	−	1.01537i
$633$	7.68828	+	16.8350i	0.305582	+	0.669130i
$634$	−34.7174	+	30.8215i	−1.37880	+	1.22408i
$635$	3.48325	−	5.42004i	0.138228	−	0.215088i
$636$	3.25436	−	27.2772i	0.129044	−	1.08161i
$637$	17.8353	+	2.56432i	0.706659	+	0.101602i
$638$	2.06005	−	15.6630i	0.0815581	−	0.620103i
$639$	−0.631513	−	0.982653i	−0.0249823	−	0.0388731i
$640$	−8.83904	+	0.745909i	−0.349394	+	0.0294846i
$641$	5.63009	−	19.1743i	0.222375	−	0.757341i	−0.770422	−	0.637534i	$-0.779954\pi$
$641$	5.63009	−	19.1743i	0.222375	−	0.757341i	0.992797	−	0.119806i	$-0.0382274\pi$
$642$	3.85309	−	0.601374i	0.152069	−	0.0237344i
$643$			10.6795i			0.421157i	0.977577	+	0.210578i	$0.0675347\pi$
$643$			10.6795i			0.421157i	−0.977577	+	0.210578i	$0.932465\pi$
$644$	−5.15146	+	10.0537i	−0.202996	+	0.396171i
$645$			0.121206i			0.00477246i
$646$	7.39715	+	47.3946i	0.291037	+	1.86472i
$647$	−12.0782	+	41.1345i	−0.474842	+	1.61716i	0.279127	+	0.960254i	$0.409955\pi$
$647$	−12.0782	+	41.1345i	−0.474842	+	1.61716i	−0.753969	+	0.656910i	$0.771863\pi$
$648$	−1.77391	+	2.20301i	−0.0696858	+	0.0865423i
$649$	−8.28786	−	12.8962i	−0.325327	−	0.506218i
$650$	19.7389	+	2.59613i	0.774225	+	0.101829i
$651$	−8.07218	−	1.16060i	−0.316374	−	0.0454877i
$652$	1.92243	−	16.1133i	0.0752883	−	0.631047i
$653$	−12.0203	+	18.7039i	−0.470390	+	0.731941i	−0.992673	−	0.120831i	$-0.961444\pi$
$653$	−12.0203	+	18.7039i	−0.470390	+	0.731941i	0.522283	+	0.852772i	$0.325080\pi$
$654$	9.40693	+	10.5960i	0.367840	+	0.414335i
$655$	4.53353	+	9.92705i	0.177140	+	0.387882i
$656$	13.6857	−	34.2355i	0.534335	−	1.33667i
$657$	1.54260	+	10.7290i	0.0601825	+	0.418579i
$658$	0.00552827	+	0.459635i	0.000215514	+	0.0179185i
$659$	10.5630	+	35.9744i	0.411478	+	1.40137i	0.861232	+	0.508213i	$0.169694\pi$
$659$	10.5630	+	35.9744i	0.411478	+	1.40137i	−0.449754	+	0.893153i	$0.648488\pi$
$660$	−1.40540	+	2.30702i	−0.0547051	+	0.0898007i
$661$	16.5744	−	19.1278i	0.644668	−	0.743986i	−0.335525	−	0.942031i	$-0.608914\pi$
$661$	16.5744	−	19.1278i	0.644668	−	0.743986i	0.980193	+	0.198045i	$0.0634592\pi$
$662$	6.47262	−	14.6364i	0.251566	−	0.568859i
$663$	8.72179	+	10.0655i	0.338726	+	0.390911i
$664$	−18.7897	−	2.01286i	−0.729182	−	0.0781143i
$665$	−6.86726	−	3.13617i	−0.266301	−	0.121616i
$666$	9.53911	−	6.29379i	0.369633	−	0.243880i
$667$	−6.67813	−	30.3724i	−0.258578	−	1.17602i
$668$	−30.8023	−	13.1811i	−1.19178	−	0.509991i
$669$	7.44757	+	3.40119i	0.287940	+	0.131498i
$670$	4.95693	+	16.1602i	0.191503	+	0.624322i
$671$	−11.3175	+	9.80670i	−0.436909	+	0.378584i
$672$	−6.26817	+	2.25780i	−0.241800	+	0.0870967i
$673$	4.31900	−	4.98440i	0.166485	−	0.192134i	−0.666376	−	0.745616i	$-0.732156\pi$
$673$	4.31900	−	4.98440i	0.166485	−	0.192134i	0.832862	+	0.553481i	$0.186701\pi$
$674$	−23.1139	+	10.8936i	−0.890315	+	0.419606i
$675$	4.20764	−	1.23547i	0.161952	−	0.0475534i
$676$	4.46198	−	3.02161i	0.171615	−	0.116216i
$677$	0.393849	+	2.73928i	0.0151369	+	0.105279i	0.995989	−	0.0894738i	$-0.0285185\pi$
$677$	0.393849	+	2.73928i	0.0151369	+	0.105279i	−0.980852	+	0.194753i	$0.937609\pi$
$678$	0.668232	−	1.06781i	0.0256633	−	0.0410090i
$679$	−11.4190	+	5.21490i	−0.438222	+	0.200129i
$680$	2.90880	+	8.72846i	0.111548	+	0.334721i
$681$	3.19419	−	4.97026i	0.122402	−	0.190461i
$682$	−10.8932	+	12.8813i	−0.417123	+	0.493249i
$683$	2.45113	−	17.0480i	0.0937899	−	0.652323i	−0.887645	−	0.460528i	$-0.847660\pi$
$683$	2.45113	−	17.0480i	0.0937899	−	0.652323i	0.981435	−	0.191795i	$-0.0614309\pi$
$684$	−14.7059	+	7.14832i	−0.562295	+	0.273323i
$685$	−2.43321	−	3.78615i	−0.0929683	−	0.144661i
$686$	20.2268	+	5.67580i	0.772262	+	0.216703i
$687$	−21.0570	−	6.18288i	−0.803373	−	0.235892i
$688$	0.202542	+	0.584248i	0.00772186	+	0.0222742i
$689$		−	44.0935i		−	1.67983i
$690$	−1.05615	+	5.21172i	−0.0402068	+	0.198407i
$691$	−15.1224			−0.575282			−0.287641	−	0.957738i	$-0.592871\pi$
$691$	−15.1224			−0.575282			−0.287641	+	0.957738i	$0.592871\pi$
$692$	8.56650	−	7.79144i	0.325650	−	0.296186i
$693$	−0.571622	+	1.94677i	−0.0217141	+	0.0739516i
$694$	18.1370	+	5.08938i	0.688470	+	0.193190i
$695$	−7.04630	+	4.52838i	−0.267281	+	0.171771i
$696$	9.35263	−	15.7767i	0.354510	−	0.598014i
$697$	−37.8517	−	5.44225i	−1.43373	−	0.206140i
$698$	16.3777	+	13.8500i	0.619903	+	0.524230i
$699$	23.4534	+	15.0726i	0.887090	+	0.570098i
$700$	9.97829	+	2.67096i	0.377144	+	0.100953i
$701$	−3.03536	−	6.64651i	−0.114644	−	0.251035i	0.843608	−	0.536959i	$-0.180427\pi$
$701$	−3.03536	−	6.64651i	−0.114644	−	0.251035i	−0.958252	+	0.285923i	$0.907700\pi$
$702$	−2.40837	+	3.84850i	−0.0908982	+	0.145252i
$703$	65.3950	−	9.40238i	2.46642	−	0.354618i
$704$	−2.91927	+	13.4691i	−0.110024	+	0.507635i
$705$	0.0609610	+	0.207614i	0.00229592	+	0.00781920i
$706$	−4.19543	−	8.90181i	−0.157897	−	0.335024i
$707$	−6.03114	−	5.22601i	−0.226824	−	0.196544i
$708$	−2.95574	−	17.5499i	−0.111083	−	0.659564i
$709$	17.3394	+	20.0107i	0.651195	+	0.751519i	0.981313	−	0.192421i	$-0.0616338\pi$
$709$	17.3394	+	20.0107i	0.651195	+	0.751519i	−0.330117	+	0.943940i	$0.607088\pi$
$710$	−0.379813	−	1.23824i	−0.0142541	−	0.0464701i
$711$	6.56996	−	14.3862i	0.246393	−	0.539525i
$712$	1.54932	−	0.280137i	0.0580631	−	0.0104986i
$713$	−11.5355	+	31.1400i	−0.432009	+	1.16620i
$714$	3.80558	+	5.76789i	0.142420	+	0.215858i
$715$	−1.80126	+	3.94420i	−0.0673632	+	0.147505i
$716$	18.0010	−	21.8129i	0.672727	−	0.815187i
$717$	14.7987	−	12.8231i	0.552666	−	0.478888i
$718$	13.5646	−	30.6732i	0.506225	−	1.14471i
$719$	−15.0085	−	13.0049i	−0.559722	−	0.485002i	0.328445	−	0.944523i	$-0.393476\pi$
$719$	−15.0085	−	13.0049i	−0.559722	−	0.485002i	−0.888167	+	0.459521i	$0.848021\pi$
$720$	−2.55373	+	1.82046i	−0.0951720	+	0.0678445i
$721$	−4.10601	+	1.20563i	−0.152916	+	0.0449001i
$722$	−67.6521	+	0.813686i	−2.51775	+	0.0302823i
$723$	6.18969	−	0.889944i	0.230197	−	0.0330974i
$724$	−12.8392	+	0.308893i	−0.477166	+	0.0114799i
$725$	−25.8660	+	11.8126i	−0.960640	+	0.438710i
$726$	−7.54145	−	8.49468i	−0.279889	−	0.315267i
$727$	−26.0484	−	16.7403i	−0.966083	−	0.620864i	−0.0404077	−	0.999183i	$-0.512866\pi$
$727$	−26.0484	−	16.7403i	−0.966083	−	0.620864i	−0.925675	+	0.378320i	$0.876502\pi$
$728$	−9.56096	+	4.79043i	−0.354353	+	0.177545i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	−1.56725	+	11.9161i	−0.0580064	+	0.441035i
$731$	0.539546	−	0.346745i	0.0199558	−	0.0128248i
$732$	−16.5587	+	5.29786i	−0.612026	+	0.195815i
$733$	−23.1264	−	6.79053i	−0.854193	−	0.250814i	−0.174814	−	0.984601i	$-0.555933\pi$
$733$	−23.1264	−	6.79053i	−0.854193	−	0.250814i	−0.679379	+	0.733788i	$0.737751\pi$
$734$	3.16701	+	20.2915i	0.116896	+	0.748972i
$735$	4.40076			0.162324
$736$	3.61817	+	26.8870i	0.133367	+	0.991067i
$737$	26.2623			0.967384
$738$	−2.01017	−	12.8794i	−0.0739953	−	0.474099i
$739$	22.4973	+	6.60580i	0.827577	+	0.242998i	0.667976	−	0.744183i	$-0.267161\pi$
$739$	22.4973	+	6.60580i	0.827577	+	0.242998i	0.159601	+	0.987182i	$0.448979\pi$
$740$	12.0691	−	3.86146i	0.443670	−	0.141950i
$741$	−22.0792	+	14.1895i	−0.811101	+	0.521263i
$742$	2.98324	−	22.6822i	0.109518	−	0.832690i
$743$	5.25777	−	36.5686i	0.192889	−	1.34157i	−0.631425	−	0.775437i	$-0.717529\pi$
$743$	5.25777	−	36.5686i	0.192889	−	1.34157i	0.824313	−	0.566134i	$-0.191561\pi$
$744$	−17.5100	+	8.77324i	−0.641949	+	0.321643i
$745$	−9.46268	−	6.08129i	−0.346686	−	0.222801i
$746$	7.47963	+	8.42504i	0.273849	+	0.308463i
$747$	−6.07741	+	2.77546i	−0.222361	+	0.101549i
$748$	14.2903	−	0.343803i	0.522504	−	0.0125707i
$749$	3.21465	−	0.462197i	0.117461	−	0.0168883i
$750$	10.4057	−	0.125155i	0.379963	−	0.00457001i
$751$	−40.1403	+	11.7863i	−1.46474	+	0.430087i	−0.914386	−	0.404844i	$-0.867326\pi$
$751$	−40.1403	+	11.7863i	−1.46474	+	0.430087i	−0.550355	+	0.834931i	$0.685508\pi$
$752$	0.640787	+	0.898893i	0.0233671	+	0.0327793i
$753$	3.32438	+	2.88059i	0.121147	+	0.104975i
$754$	11.9063	−	26.9235i	0.433604	−	0.980497i
$755$	0.711322	−	0.616364i	0.0258876	−	0.0224318i
$756$	−1.49927	+	1.81677i	−0.0545280	+	0.0660751i
$757$	−11.4903	+	25.1603i	−0.417623	+	0.914467i	0.577552	+	0.816354i	$0.304008\pi$
$757$	−11.4903	+	25.1603i	−0.417623	+	0.914467i	−0.995175	+	0.0981133i	$0.968719\pi$
$758$	−14.9792	−	22.7030i	−0.544068	−	0.824609i
$759$	7.26012	+	3.94332i	0.263525	+	0.143133i
$760$	−17.8411	+	3.22590i	−0.647164	+	0.117016i
$761$	19.3538	−	42.3789i	0.701575	−	1.53623i	−0.136476	−	0.990643i	$-0.543578\pi$
$761$	19.3538	−	42.3789i	0.701575	−	1.53623i	0.838051	−	0.545591i	$-0.183695\pi$
$762$	−3.40792	−	11.1102i	−0.123456	−	0.402482i
$763$	7.72740	+	8.91790i	0.279751	+	0.322850i
$764$	−2.84568	−	16.8964i	−0.102953	−	0.611290i
$765$	2.45832	+	2.13015i	0.0888809	+	0.0770157i
$766$	0.811162	+	1.72111i	0.0293085	+	0.0621863i
$767$	−8.04805	−	27.4091i	−0.290598	−	0.989687i
$768$	−9.26767	+	13.0426i	−0.334418	+	0.470636i
$769$	17.1525	−	2.46615i	0.618533	−	0.0889317i	0.174077	−	0.984732i	$-0.444306\pi$
$769$	17.1525	−	2.46615i	0.618533	−	0.0889317i	0.444457	+	0.895800i	$0.353397\pi$
$770$	−1.19344	+	1.90707i	−0.0430086	+	0.0687262i
$771$	0.785408	+	1.71980i	0.0282858	+	0.0619372i
$772$	33.2390	+	8.89732i	1.19630	+	0.320221i
$773$	42.8170	+	27.5168i	1.54002	+	0.989711i	0.987750	+	0.156046i	$0.0498749\pi$
$773$	42.8170	+	27.5168i	1.54002	+	0.989711i	0.552271	+	0.833665i	$0.313761\pi$
$774$	0.166934	+	0.141170i	0.00600033	+	0.00507426i
$775$	30.0560	+	4.32140i	1.07964	+	0.155229i
$776$	−15.3735	+	25.9332i	−0.551877	+	0.930948i
$777$	8.00664	−	5.14555i	0.287237	−	0.184596i
$778$	−19.4424	−	5.45569i	−0.697044	−	0.195596i
$779$	21.2308	−	72.3054i	0.760671	−	2.59061i
$780$	−3.72401	+	3.38707i	−0.133341	+	0.121277i
$781$	−2.01228			−0.0720052
$782$	26.2214	−	10.2083i	0.937674	−	0.365046i
$783$		−	6.48436i		−	0.231732i
$784$	21.2130	−	7.35395i	0.757607	−	0.262641i
$785$	7.19636	+	2.11304i	0.256849	+	0.0754177i
$786$	18.9526	+	5.31826i	0.676018	+	0.189696i
$787$	−26.2054	−	40.7764i	−0.934122	−	1.45352i	−0.890766	−	0.454462i	$-0.849832\pi$
$787$	−26.2054	−	40.7764i	−0.934122	−	1.45352i	−0.0433553	−	0.999060i	$-0.513805\pi$
$788$	27.1667	−	13.2053i	0.967773	−	0.470419i
$789$	1.78158	−	12.3911i	0.0634258	−	0.441136i
$790$	11.3236	−	13.3902i	0.402875	−	0.476401i
$791$	0.567159	−	0.882517i	0.0201659	−	0.0313787i
$792$	1.54053	+	4.62267i	0.0547402	+	0.164259i
$793$	−25.3840	+	11.5925i	−0.901412	+	0.411661i
$794$	27.8660	−	44.5289i	0.988928	−	1.58027i
$795$	−1.53260	−	10.6595i	−0.0543558	−	0.378053i
$796$	0.422242	−	0.285938i	0.0149660	−	0.0101348i
$797$	47.4251	−	13.9253i	1.67988	−	0.493258i	0.703754	−	0.710444i	$-0.251506\pi$
$797$	47.4251	−	13.9253i	1.67988	−	0.493258i	0.976130	+	0.217186i	$0.0696877\pi$
$798$	−12.3178	+	5.80540i	−0.436046	+	0.205509i
$799$	0.749795	−	0.865310i	0.0265259	−	0.0306125i
$800$	23.3390	−	8.40673i	0.825157	−	0.297223i
$801$	0.420686	−	0.364527i	0.0148642	−	0.0128799i
$802$	−0.727532	−	2.37184i	−0.0256901	−	0.0837527i
$803$	16.9858	+	7.75713i	0.599414	+	0.273743i
$804$	28.0306	+	11.9950i	0.988562	+	0.423030i
$805$	−0.931696	+	4.32943i	−0.0328380	+	0.152592i
$806$	−26.2395	+	17.3125i	−0.924245	+	0.609806i
$807$	−5.89142	−	2.69052i	−0.207388	−	0.0947108i
$808$	−19.0560	−	2.04139i	−0.670389	−	0.0718160i
$809$	13.2613	+	15.3043i	0.466242	+	0.538072i	0.939362	−	0.342926i	$-0.111418\pi$
$809$	13.2613	+	15.3043i	0.466242	+	0.538072i	−0.473121	+	0.880998i	$0.656873\pi$
$810$	−0.448452	+	1.01407i	−0.0157570	+	0.0356309i
$811$	1.17043	−	1.35075i	0.0410994	−	0.0474312i	−0.734828	−	0.678254i	$-0.762737\pi$
$811$	1.17043	−	1.35075i	0.0410994	−	0.0474312i	0.775927	+	0.630823i	$0.217282\pi$
$812$	7.94633	−	13.0442i	0.278861	−	0.457762i
$813$	6.99135	+	23.8104i	0.245197	+	0.835066i
$814$	−0.236779	−	19.6864i	−0.00829909	−	0.690009i
$815$	−0.905348	−	6.29683i	−0.0317130	−	0.220568i
$816$	15.4095	+	6.15995i	0.539440	+	0.215641i
$817$	0.525030	+	1.14966i	0.0183685	+	0.0402213i
$818$	−8.47880	−	9.55051i	−0.296454	−	0.333926i
$819$	−2.04410	+	3.18068i	−0.0714265	+	0.111142i
$820$	1.71229	−	14.3519i	0.0597957	−	0.501191i
$821$	16.6255	+	2.39039i	0.580234	+	0.0834250i	0.426182	−	0.904638i	$-0.359858\pi$
$821$	16.6255	+	2.39039i	0.580234	+	0.0834250i	0.154052	+	0.988063i	$0.450768\pi$
$822$	−8.04861	−	1.05858i	−0.280728	−	0.0369222i
$823$	13.4043	+	20.8575i	0.467245	+	0.727048i	0.992278	−	0.124034i	$-0.0395833\pi$
$823$	13.4043	+	20.8575i	0.467245	+	0.727048i	−0.525033	+	0.851082i	$0.675947\pi$
$824$	−6.44546	+	8.00457i	−0.224538	+	0.278852i
$825$	2.12838	−	7.24861i	0.0741008	−	0.252364i
$826$	−2.28559	−	14.6441i	−0.0795257	−	0.509533i
$827$			4.43719i			0.154296i	0.997020	+	0.0771482i	$0.0245814\pi$
$827$			4.43719i			0.154296i	−0.997020	+	0.0771482i	$0.975419\pi$
$828$	5.94789	+	7.52480i	0.206704	+	0.261505i
$829$		−	21.0931i		−	0.732593i	−0.930498	−	0.366297i	$-0.880626\pi$
$829$		−	21.0931i		−	0.732593i	0.930498	−	0.366297i	$-0.119374\pi$
$830$	−7.31952	+	1.14240i	−0.254064	+	0.0396533i
$831$	−2.01717	+	6.86985i	−0.0699748	+	0.238312i
$832$	−12.2908	+	22.5498i	−0.426108	+	0.781774i
$833$	−12.5897	−	19.5899i	−0.436207	−	0.678751i
$834$	−1.97009	+	14.9790i	−0.0682187	+	0.518682i
$835$	−13.0007	−	1.86921i	−0.449907	−	0.0646868i
$836$	−3.33706	+	27.9703i	−0.115415	+	0.967374i
$837$	−3.74358	+	5.82512i	−0.129397	+	0.201346i
$838$	10.7340	−	9.52950i	0.370801	−	0.329191i
$839$	10.9973	+	24.0808i	0.379670	+	0.831361i	0.998933	+	0.0461775i	$0.0147040\pi$
$839$	10.9973	+	24.0808i	0.379670	+	0.831361i	−0.619264	+	0.785183i	$0.712569\pi$
$840$	−2.14483	+	1.49039i	−0.0740037	+	0.0514235i
$841$	1.85678	+	12.9142i	0.0640269	+	0.445317i
$842$	−38.6793	+	0.465216i	−1.33298	+	0.0160324i
$843$	−2.61970	−	8.92189i	−0.0902274	−	0.307286i
$844$	31.6112	+	19.2571i	1.08810	+	0.662855i
$845$	1.38342	−	1.59655i	0.0475910	−	0.0549230i
$846$	0.356946	+	0.157851i	0.0122720	+	0.00542704i
$847$	−6.19499	−	7.14940i	−0.212862	−	0.245656i
$848$	−25.2003	−	48.8209i	−0.865383	−	1.67652i
$849$	9.42828	+	4.30575i	0.323578	+	0.147773i
$850$	−14.1697	−	21.4762i	−0.486018	−	0.736627i
$851$	−13.6246	−	36.2815i	−0.467045	−	1.24371i
$852$	−2.14778	−	0.919086i	−0.0735816	−	0.0314874i
$853$	26.6244	+	12.1590i	0.911602	+	0.416315i	0.815301	−	0.579038i	$-0.196572\pi$
$853$	26.6244	+	12.1590i	0.911602	+	0.416315i	0.0963011	+	0.995352i	$0.469299\pi$
$854$	−13.8421	+	4.24590i	−0.473668	+	0.145292i
$855$	−4.84439	+	4.19769i	−0.165675	+	0.143558i
$856$	5.70637	−	5.31688i	0.195040	−	0.181727i
$857$	−6.90522	+	7.96905i	−0.235878	+	0.272218i	−0.861331	−	0.508044i	$-0.830369\pi$
$857$	−6.90522	+	7.96905i	−0.235878	+	0.272218i	0.625453	+	0.780262i	$0.284914\pi$
$858$	3.33433	+	7.07473i	0.113832	+	0.241527i
$859$	−34.6679	+	10.1794i	−1.18285	+	0.347317i	−0.813273	−	0.581882i	$-0.802316\pi$
$859$	−34.6679	+	10.1794i	−1.18285	+	0.347317i	−0.369580	+	0.929199i	$0.620498\pi$
$860$	0.135924	+	0.200718i	0.00463498	+	0.00684443i
$861$	−1.54495	−	10.7454i	−0.0526518	−	0.366201i
$862$	−38.0777	−	23.8289i	−1.29693	−	0.811616i
$863$	−25.1572	+	11.4889i	−0.856362	+	0.391087i	−0.794695	−	0.607009i	$-0.792369\pi$
$863$	−25.1572	+	11.4889i	−0.856362	+	0.391087i	−0.0616673	+	0.998097i	$0.519642\pi$
$864$	−0.467091	+	5.63754i	−0.0158908	+	0.191793i
$865$	2.45426	−	3.81890i	0.0834474	−	0.129847i
$866$	17.1819	+	14.5301i	0.583865	+	0.493753i
$867$	0.0302198	−	0.210183i	0.00102632	−	0.00713819i
$868$	−14.6692	+	7.13045i	−0.497905	+	0.242023i
$869$	−14.7301	−	22.9205i	−0.499684	−	0.777524i
$870$	1.94252	−	6.92253i	0.0658575	−	0.234696i
$871$	46.9564	+	13.7876i	1.59106	+	0.467176i
$872$	27.4607	+	6.99778i	0.929936	+	0.236975i
$873$			10.6588i			0.360745i
$874$	12.5580	+	54.0090i	0.424781	+	1.82688i
$875$	8.66651			0.292981
$876$	14.5865	+	16.0375i	0.492831	+	0.541856i
$877$	12.3307	−	41.9945i	0.416378	−	1.41805i	−0.438270	−	0.898844i	$-0.644408\pi$
$877$	12.3307	−	41.9945i	0.416378	−	1.41805i	0.854647	−	0.519209i	$-0.173773\pi$
$878$	14.7349	−	52.5108i	0.497280	−	1.77215i
$879$	−19.0762	+	12.2595i	−0.643424	+	0.413504i
$880$	0.259815	+	5.39653i	0.00875837	+	0.181917i
$881$	−6.19971	−	0.891384i	−0.208874	−	0.0300315i	0.0370836	−	0.999312i	$-0.488193\pi$
$881$	−6.19971	−	0.891384i	−0.208874	−	0.0300315i	−0.245957	+	0.969281i	$0.579102\pi$
$882$	5.12564	−	6.06109i	0.172589	−	0.204087i
$883$	12.9523	+	8.32395i	0.435880	+	0.280123i	0.740123	−	0.672471i	$-0.234767\pi$
$883$	12.9523	+	8.32395i	0.435880	+	0.280123i	−0.304243	+	0.952594i	$0.598404\pi$
$884$	25.7312	+	6.88765i	0.865433	+	0.231657i
$885$	−2.89828	−	6.34635i	−0.0974246	−	0.213330i
$886$	19.5545	+	12.2371i	0.656946	+	0.411114i
$887$	39.7833	−	5.71997i	1.33579	−	0.192058i	0.562862	−	0.826551i	$-0.309700\pi$
$887$	39.7833	−	5.71997i	1.33579	−	0.192058i	0.772929	+	0.634493i	$0.218791\pi$
$888$	8.73881	−	21.1201i	0.293255	−	0.708744i
$889$	−2.72664	−	9.28608i	−0.0914485	−	0.311445i
$890$	0.558315	−	0.263134i	0.0187147	−	0.00882028i
$891$	1.30195	+	1.12815i	0.0436169	+	0.0377943i
$892$	16.1475	−	2.71955i	0.540658	−	0.0910573i
$893$	1.47755	+	1.70519i	0.0494444	+	0.0570619i
$894$	−19.3970	+	5.94979i	−0.648733	+	0.198991i
$895$	4.60568	−	10.0850i	0.153951	−	0.337106i
$896$	−7.84819	+	10.7683i	−0.262190	+	0.359744i
$897$	10.9107	+	10.8621i	0.364297	+	0.362675i
$898$	42.5051	−	28.0444i	1.41841	−	0.935853i
$899$	18.6521	−	40.8424i	0.622082	−	1.36217i
$900$	5.58240	−	6.76456i	0.186080	−	0.225485i
$901$	−43.0662	+	37.3171i	−1.43474	+	1.24321i
$902$	−20.5377	−	9.08237i	−0.683832	−	0.302410i
$903$	0.137599	+	0.119230i	0.00457901	+	0.00396773i
$904$	−0.0908797	−	2.51769i	−0.00302261	−	0.0837371i
$905$	−4.83078	+	1.41845i	−0.160581	+	0.0471507i
$906$	−0.0204177	−	1.69758i	−0.000678332	−	0.0563984i
$907$	−40.9480	+	5.88744i	−1.35966	+	0.195489i	−0.783267	−	0.621685i	$-0.786448\pi$
$907$	−40.9480	+	5.88744i	−1.35966	+	0.195489i	−0.576390	+	0.817175i	$0.695539\pi$
$908$	−0.284201	−	11.8129i	−0.00943153	−	0.392025i
$909$	−6.16355	+	2.81480i	−0.204432	+	0.0933610i
$910$	−3.13505	+	2.78325i	−0.103926	+	0.0922640i
$911$	20.6563	+	13.2750i	0.684374	+	0.439820i	0.836082	−	0.548605i	$-0.184841\pi$
$911$	20.6563	+	13.2750i	0.684374	+	0.439820i	−0.151708	+	0.988425i	$0.548477\pi$
$912$	−16.3368	+	28.3295i	−0.540967	+	0.938082i
$913$	−1.63802	+	11.3927i	−0.0542105	+	0.377043i
$914$	31.1171	+	4.09263i	1.02926	+	0.135372i
$915$	−5.73358	+	3.68475i	−0.189546	+	0.121814i
$916$	−41.8043	+	13.3751i	−1.38125	+	0.441925i
$917$	15.7294	+	4.61856i	0.519429	+	0.152518i
$918$	5.79707	−	0.904782i	0.191332	−	0.0298623i
$919$	−23.1112			−0.762367			−0.381183	−	0.924499i	$-0.624483\pi$
$919$	−23.1112			−0.762367			−0.381183	+	0.924499i	$0.624483\pi$
$920$	4.09561	+	9.81508i	0.135028	+	0.323593i
$921$	−20.5295			−0.676472
$922$	31.1982	−	4.86928i	1.02746	−	0.160361i
$923$	−3.59792	−	1.05644i	−0.118427	−	0.0347733i
$924$	1.23656	+	3.86491i	0.0406798	+	0.127146i
$925$	−29.8120	+	19.1590i	−0.980212	+	0.629944i
$926$	37.3307	+	4.90985i	1.22676	+	0.161348i
$927$	−0.517097	+	3.59649i	−0.0169837	+	0.118124i
$928$	−2.20448	−	36.6148i	−0.0723655	−	1.20194i
$929$	−46.5531	−	29.9179i	−1.52736	−	0.981573i	−0.990441	−	0.137937i	$-0.955953\pi$
$929$	−46.5531	−	29.9179i	−1.52736	−	0.981573i	−0.536916	−	0.843636i	$-0.680411\pi$
$930$	−5.74157	+	5.09728i	−0.188273	+	0.167146i
$931$	41.7419	−	19.0629i	1.36804	−	0.624761i
$932$	55.7422	−	1.34107i	1.82590	−	0.0439283i
$933$	−7.84593	+	1.12807i	−0.256864	+	0.0369315i
$934$	−0.382419	−	31.7954i	−0.0125131	−	1.04038i
$935$	5.37674	−	1.57875i	0.175838	−	0.0516307i
$936$	0.327539	+	9.07400i	0.0107060	+	0.296593i
$937$	−11.2999	−	9.79143i	−0.369152	−	0.319872i	0.450454	−	0.892800i	$-0.351262\pi$
$937$	−11.2999	−	9.79143i	−0.369152	−	0.319872i	−0.819606	+	0.572928i	$0.805808\pi$
$938$	23.2221	+	10.2694i	0.758227	+	0.335309i
$939$	2.74448	−	2.37811i	0.0895627	−	0.0776065i
$940$	0.333778	+	0.275448i	0.0108866	+	0.00898412i
$941$	−7.48736	+	16.3950i	−0.244081	+	0.534463i	−0.991533	−	0.129853i	$-0.958550\pi$
$941$	−7.48736	+	16.3950i	−0.244081	+	0.534463i	0.747452	+	0.664315i	$0.231277\pi$
$942$	11.2920	−	7.45032i	0.367913	−	0.242745i
$943$	−44.0994	−	3.05515i	−1.43607	−	0.0994895i
$944$	−24.5758	−	25.7481i	−0.799873	−	0.838030i
$945$	−0.383601	+	0.839968i	−0.0124785	+	0.0273242i
$946$	0.360070	−	0.110447i	0.0117069	−	0.00359093i
$947$	−6.78762	−	7.83333i	−0.220568	−	0.254549i	0.634671	−	0.772782i	$-0.281135\pi$
$947$	−6.78762	−	7.83333i	−0.220568	−	0.254549i	−0.855239	+	0.518233i	$0.826590\pi$
$948$	−5.25326	−	31.1916i	−0.170618	−	1.01305i
$949$	26.2977	+	22.7871i	0.853659	+	0.739699i
$950$	45.8643	−	21.6159i	1.48803	−	0.701311i
$951$	9.24852	+	31.4976i	0.299904	+	1.02138i
$952$	12.7704	+	5.28398i	0.413891	+	0.171255i
$953$	−21.4411	+	3.08276i	−0.694545	+	0.0998605i	−0.480541	−	0.876972i	$-0.659560\pi$
$953$	−21.4411	+	3.08276i	−0.694545	+	0.0998605i	−0.214004	+	0.976833i	$0.568651\pi$
$954$	−16.4662	−	10.3045i	−0.533113	−	0.333620i
$955$	−2.79036	−	6.11004i	−0.0902941	−	0.197716i
$956$	10.1265	−	37.8310i	0.327514	−	1.22354i
$957$	−9.39746	−	6.03938i	−0.303777	−	0.195225i
$958$	−32.7536	+	38.7313i	−1.05822	+	1.25135i
$959$	−6.69180	−	0.962136i	−0.216090	−	0.0310690i
$960$	−2.18749	+	5.87855i	−0.0706009	+	0.189730i
$961$	−14.2562	+	9.16190i	−0.459877	+	0.295545i
$962$	9.91198	−	35.3232i	0.319575	−	1.13887i
$963$	0.776887	−	2.64583i	0.0250348	−	0.0852608i
$964$	9.25220	−	8.41510i	0.297993	−	0.271032i
$965$	13.4892			0.434232
$966$	4.87768	+	6.32578i	0.156937	+	0.203528i
$967$			13.4700i			0.433166i	0.976264	+	0.216583i	$0.0694912\pi$
$967$			13.4700i			0.433166i	−0.976264	+	0.216583i	$0.930509\pi$
$968$	−22.0150	−	5.61006i	−0.707588	−	0.180314i
$969$	32.5449	+	9.55603i	1.04549	+	0.306984i
$970$	−3.19304	+	11.3790i	−0.102522	+	0.365358i
$971$	4.27536	+	6.65260i	0.137203	+	0.213492i	0.903055	−	0.429525i	$-0.141319\pi$
$971$	4.27536	+	6.65260i	0.137203	+	0.213492i	−0.765852	+	0.643017i	$0.777683\pi$
$972$	0.874346	+	1.79875i	0.0280447	+	0.0576951i
$973$	−1.79060	+	12.4539i	−0.0574041	+	0.399254i
$974$	−18.0870	−	15.2955i	−0.579546	−	0.490101i
$975$	7.61100	−	11.8430i	0.243747	−	0.379278i
$976$	−21.4802	+	27.3428i	−0.687563	+	0.875222i
$977$	−20.9311	+	9.55889i	−0.669644	+	0.305816i	−0.721072	−	0.692861i	$-0.756350\pi$
$977$	−20.9311	+	9.55889i	−0.669644	+	0.305816i	0.0514276	+	0.998677i	$0.483623\pi$
$978$	−9.72700	−	6.08712i	−0.311035	−	0.194645i
$979$	−0.136473	−	0.949191i	−0.00436170	−	0.0303363i
$980$	7.28771	−	4.93516i	0.232797	−	0.157648i
$981$	9.61325	−	2.82271i	0.306927	−	0.0901220i
$982$	15.7887	+	33.5003i	0.503838	+	1.06904i
$983$	5.55837	−	6.41470i	0.177285	−	0.204597i	−0.660152	−	0.751132i	$-0.729508\pi$
$983$	5.55837	−	6.41470i	0.177285	−	0.204597i	0.837436	+	0.546535i	$0.184053\pi$
$984$	−17.7723	−	19.0743i	−0.566561	−	0.608065i
$985$	8.94919	−	7.75452i	0.285145	−	0.247079i
$986$	−36.3728	+	11.1569i	−1.15834	+	0.355308i
$987$	0.295662	+	0.135024i	0.00941103	+	0.00429787i
$988$	−20.6509	+	48.2584i	−0.656994	+	1.53530i
$989$	0.592518	−	0.445620i	0.0188410	−	0.0141699i
$990$	1.05197	+	1.59440i	0.0334337	+	0.0506734i
$991$	−51.6788	−	23.6009i	−1.64163	−	0.749709i	−0.641780	−	0.766889i	$-0.721804\pi$
$991$	−51.6788	−	23.6009i	−1.64163	−	0.749709i	−0.999852	+	0.0171799i	$0.994531\pi$
$992$	−19.1582	+	34.1650i	−0.608275	+	1.08474i
$993$	−7.41062	−	8.55231i	−0.235169	−	0.271399i
$994$	−1.77933	−	0.786872i	−0.0564371	−	0.0249581i
$995$	0.130915	−	0.151083i	0.00415027	−	0.00478967i
$996$	−6.95177	+	11.4116i	−0.220275	+	0.361591i
$997$	0.818187	+	2.78649i	0.0259122	+	0.0882490i	0.971434	−	0.237310i	$-0.0762657\pi$
$997$	0.818187	+	2.78649i	0.0259122	+	0.0882490i	−0.945522	+	0.325559i	$0.894448\pi$
$998$	17.7636	−	0.213652i	0.562296	−	0.00676303i
$999$	−1.15005	−	7.99879i	−0.0363860	−	0.253070i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.t.b.523.11	yes	240
8.3	odd	2	inner	552.2.t.b.523.20	yes	240
23.19	odd	22	inner	552.2.t.b.19.20	yes	240
184.19	even	22	inner	552.2.t.b.19.11	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.t.b.19.11	✓	240	184.19	even	22	inner
552.2.t.b.19.20	yes	240	23.19	odd	22	inner
552.2.t.b.523.11	yes	240	1.1	even	1	trivial
552.2.t.b.523.20	yes	240	8.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.t (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.218084 - 1.39730i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-1.90488 + 0.609457i) q^{4} +(-0.659581 + 0.423887i) q^{5} +(-0.184414 + 1.40214i) q^{6} +(-0.167612 + 1.16577i) q^{7} +(1.26702 + 2.52877i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.218084 - 1.39730i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-1.90488 + 0.609457i) q^{4} +(-0.659581 + 0.423887i) q^{5} +(-0.184414 + 1.40214i) q^{6} +(-0.167612 + 1.16577i) q^{7} +(1.26702 + 2.52877i) q^{8} +(0.841254 + 0.540641i) q^{9} +(0.736140 + 0.829187i) q^{10} +(1.56705 - 0.715646i) q^{11} +(1.99942 - 0.0481031i) q^{12} +(3.17756 - 0.456864i) q^{13} +(1.66548 - 0.0200316i) q^{14} +(0.752286 - 0.220891i) q^{15} +(3.25713 - 2.32188i) q^{16} +(-3.13544 - 2.71687i) q^{17} +(0.571972 - 1.29339i) q^{18} +(6.17872 - 5.35389i) q^{19} +(0.998081 - 1.20944i) q^{20} +(0.489258 - 1.07133i) q^{21} +(-1.34172 - 2.03356i) q^{22} +(-3.84566 - 2.86546i) q^{23} +(-0.503256 - 2.78330i) q^{24} +(-1.82171 + 3.98898i) q^{25} +(-1.33135 - 4.34036i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(-0.391205 - 2.32280i) q^{28} +(4.90056 + 4.24636i) q^{29} +(-0.472712 - 1.00299i) q^{30} +(-1.95081 - 6.64385i) q^{31} +(-3.95469 - 4.04481i) q^{32} +(-1.70519 + 0.245169i) q^{33} +(-3.11249 + 4.97364i) q^{34} +(-0.383601 - 0.839968i) q^{35} +(-1.93198 - 0.517148i) q^{36} +(6.79820 + 4.36894i) q^{37} +(-8.82846 - 7.46591i) q^{38} +(-3.17756 - 0.456864i) q^{39} +(-1.90761 - 1.13086i) q^{40} +(7.75417 - 4.98330i) q^{41} +(-1.60366 - 0.450000i) q^{42} +(-0.0435530 + 0.148328i) q^{43} +(-2.54888 + 2.31827i) q^{44} -0.784045 q^{45} +(-3.16522 + 5.99845i) q^{46} +0.275978i q^{47} +(-3.77934 + 1.31019i) q^{48} +(5.38552 + 1.58133i) q^{49} +(5.97108 + 1.67553i) q^{50} +(2.24300 + 3.49017i) q^{51} +(-5.77442 + 2.80685i) q^{52} +(1.95474 - 13.5955i) q^{53} +(-0.913192 + 1.07985i) q^{54} +(-0.730241 + 1.13628i) q^{55} +(-3.16033 + 1.05320i) q^{56} +(-7.43680 + 3.39627i) q^{57} +(4.86469 - 7.77360i) q^{58} +(-1.26639 - 8.80793i) q^{59} +(-1.29839 + 0.879256i) q^{60} +(-8.34065 + 2.44903i) q^{61} +(-8.85799 + 4.17478i) q^{62} +(-0.771267 + 0.890090i) q^{63} +(-4.78934 + 6.40798i) q^{64} +(-1.90220 + 1.64826i) q^{65} +(0.714450 + 2.32919i) q^{66} +(13.8670 + 6.33284i) q^{67} +(7.62844 + 3.26440i) q^{68} +(2.88259 + 3.83284i) q^{69} +(-1.09003 + 0.719188i) q^{70} +(-1.06252 - 0.485239i) q^{71} +(-0.301274 + 2.81234i) q^{72} +(7.09826 + 8.19183i) q^{73} +(4.62213 - 10.4519i) q^{74} +(2.87174 - 3.31417i) q^{75} +(-8.50674 + 13.9642i) q^{76} +(0.571622 + 1.94677i) q^{77} +(0.0546004 + 4.53963i) q^{78} +(-2.25077 - 15.6544i) q^{79} +(-1.16412 + 2.91212i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-8.65421 - 9.74810i) q^{82} +(-3.61212 + 5.62056i) q^{83} +(-0.279051 + 2.33893i) q^{84} +(3.21972 + 0.462926i) q^{85} +(0.216757 + 0.0285085i) q^{86} +(-3.50571 - 5.45499i) q^{87} +(3.79518 + 3.05596i) q^{88} +(0.156826 - 0.534100i) q^{89} +(0.170988 + 1.09554i) q^{90} +3.78088i q^{91} +(9.07190 + 3.11459i) q^{92} +6.92433i q^{93} +(0.385623 - 0.0601863i) q^{94} +(-1.80592 + 6.15040i) q^{95} +(2.65494 + 4.99513i) q^{96} +(5.76257 + 8.96673i) q^{97} +(1.03509 - 7.87004i) q^{98} +(1.70519 + 0.245169i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{2} - 24 q^{3} - 4 q^{4} - 7 q^{6} + 4 q^{8} - 24 q^{9}+O(q^{10}) \) 240 * q + 4 * q^2 - 24 * q^3 - 4 * q^4 - 7 * q^6 + 4 * q^8 - 24 * q^9	\( 240 q + 4 q^{2} - 24 q^{3} - 4 q^{4} - 7 q^{6} + 4 q^{8} - 24 q^{9} - 4 q^{12} - 4 q^{16} - 44 q^{17} + 4 q^{18} + 55 q^{20} + 4 q^{24} - 24 q^{25} - 24 q^{27} + 4 q^{32} - 55 q^{34} + 7 q^{36} + 22 q^{38} + 11 q^{40} - 44 q^{42} + 77 q^{44} - 48 q^{46} + 51 q^{48} + 8 q^{49} - 33 q^{50} + 165 q^{52} - 7 q^{54} - 22 q^{56} - 59 q^{58} + 11 q^{60} + 29 q^{62} - 4 q^{64} + 55 q^{66} + 132 q^{70} + 4 q^{72} - 144 q^{73} - 66 q^{74} - 24 q^{75} - 55 q^{76} - 24 q^{81} - 26 q^{82} - 44 q^{84} - 110 q^{86} - 198 q^{88} - 47 q^{92} - 73 q^{94} + 4 q^{96} + 53 q^{98}+O(q^{100}) \) 240 * q + 4 * q^2 - 24 * q^3 - 4 * q^4 - 7 * q^6 + 4 * q^8 - 24 * q^9 - 4 * q^12 - 4 * q^16 - 44 * q^17 + 4 * q^18 + 55 * q^20 + 4 * q^24 - 24 * q^25 - 24 * q^27 + 4 * q^32 - 55 * q^34 + 7 * q^36 + 22 * q^38 + 11 * q^40 - 44 * q^42 + 77 * q^44 - 48 * q^46 + 51 * q^48 + 8 * q^49 - 33 * q^50 + 165 * q^52 - 7 * q^54 - 22 * q^56 - 59 * q^58 + 11 * q^60 + 29 * q^62 - 4 * q^64 + 55 * q^66 + 132 * q^70 + 4 * q^72 - 144 * q^73 - 66 * q^74 - 24 * q^75 - 55 * q^76 - 24 * q^81 - 26 * q^82 - 44 * q^84 - 110 * q^86 - 198 * q^88 - 47 * q^92 - 73 * q^94 + 4 * q^96 + 53 * q^98

Introduction

L-functions

Modular forms

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