LMFDB - Embedded newform 990.2.bg.a.301.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(31,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([10, 0, 18])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.bg (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [88,11,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$11$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			301.7
Character	$\chi$	$=$	990.301
Dual form			990.2.bg.a.421.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.104528 + 0.994522i) q^{2} +(-0.00703919 + 1.73204i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-0.104528 - 0.994522i) q^{5} +(-1.72181 - 0.188048i) q^{6} +(1.23119 - 1.36737i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-2.99990 - 0.0243843i) q^{9} +1.00000 q^{10} +(-1.47381 - 2.97117i) q^{11} +(0.366996 - 1.69272i) q^{12} +(3.10807 - 1.38380i) q^{13} +(1.23119 + 1.36737i) q^{14} +(1.72328 - 0.174046i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-0.0478740 + 0.0347825i) q^{17} +(0.337826 - 2.98092i) q^{18} +(-1.28042 + 3.94074i) q^{19} +(-0.104528 + 0.994522i) q^{20} +(2.35967 + 2.14209i) q^{21} +(3.10895 - 1.15517i) q^{22} +(3.45785 - 5.98917i) q^{23} +(1.64509 + 0.541923i) q^{24} +(-0.978148 + 0.207912i) q^{25} +(1.05134 + 3.23569i) q^{26} +(0.0633513 - 5.19577i) q^{27} +(-1.48857 + 1.08151i) q^{28} +(5.25082 - 5.83163i) q^{29} +(-0.00703919 + 1.73204i) q^{30} +(6.81548 - 3.03445i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(5.15656 - 2.53179i) q^{33} +(-0.0295877 - 0.0512475i) q^{34} +(-1.48857 - 1.08151i) q^{35} +(2.92928 + 0.647566i) q^{36} +(-0.363903 - 1.11998i) q^{37} +(-3.78531 - 1.68533i) q^{38} +(2.37491 + 5.39302i) q^{39} +(-0.978148 - 0.207912i) q^{40} +(1.42844 + 1.58645i) q^{41} +(-2.37700 + 2.12284i) q^{42} +(2.62307 + 4.54329i) q^{43} +(0.823866 + 3.21267i) q^{44} +(0.289324 + 2.98602i) q^{45} +(5.59492 + 4.06494i) q^{46} +(-0.874288 + 0.185836i) q^{47} +(-0.710913 + 1.57943i) q^{48} +(0.377816 + 3.59467i) q^{49} +(-0.104528 - 0.994522i) q^{50} +(-0.0599075 - 0.0831643i) q^{51} +(-3.32786 + 0.707358i) q^{52} +(0.197016 + 0.143141i) q^{53} +(5.16068 + 0.606110i) q^{54} +(-2.80084 + 1.77631i) q^{55} +(-0.919990 - 1.59347i) q^{56} +(-6.81649 - 2.24548i) q^{57} +(5.25082 + 5.83163i) q^{58} +(5.69767 + 1.21108i) q^{59} +(-1.72181 - 0.188048i) q^{60} +(-10.4424 - 4.64924i) q^{61} +(2.30541 + 7.09533i) q^{62} +(-3.72678 + 4.07196i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-1.70110 - 2.94639i) q^{65} +(1.97891 + 5.39295i) q^{66} +(-1.08921 + 1.88657i) q^{67} +(0.0540595 - 0.0240688i) q^{68} +(10.3491 + 6.03128i) q^{69} +(1.23119 - 1.36737i) q^{70} +(7.04819 - 5.12081i) q^{71} +(-0.950211 + 2.84554i) q^{72} +(-3.27871 - 10.0908i) q^{73} +(1.15188 - 0.244840i) q^{74} +(-0.353225 - 1.69565i) q^{75} +(2.07177 - 3.58841i) q^{76} +(-5.87724 - 1.64282i) q^{77} +(-5.61173 + 1.79818i) q^{78} +(-0.883390 + 8.40490i) q^{79} +(0.309017 - 0.951057i) q^{80} +(8.99881 + 0.146301i) q^{81} +(-1.72707 + 1.25479i) q^{82} +(-9.27762 - 4.13066i) q^{83} +(-1.86274 - 2.58588i) q^{84} +(0.0395961 + 0.0439760i) q^{85} +(-4.79259 + 2.13380i) q^{86} +(10.0636 + 9.13566i) q^{87} +(-3.28119 + 0.483538i) q^{88} -8.19011 q^{89} +(-2.99990 - 0.0243843i) q^{90} +(1.93444 - 5.95360i) q^{91} +(-4.62750 + 5.13936i) q^{92} +(5.20780 + 11.8260i) q^{93} +(-0.0934297 - 0.888924i) q^{94} +(4.05299 + 0.861490i) q^{95} +(-1.49647 - 0.872114i) q^{96} +(-1.85641 + 17.6626i) q^{97} -3.61447 q^{98} +(4.34885 + 8.94916i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 11 q^{2} - 8 q^{3} + 11 q^{4} + 11 q^{5} + q^{6} - 2 q^{7} - 22 q^{8} + 6 q^{9} + 88 q^{10} + 3 q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{14} + 7 q^{15} + 11 q^{16} + 18 q^{17} - 6 q^{18} + 12 q^{19}+ \cdots - 128 q^{99}+O(q^{100}) $ 88 * q + 11 * q^2 - 8 * q^3 + 11 * q^4 + 11 * q^5 + q^6 - 2 * q^7 - 22 * q^8 + 6 * q^9 + 88 * q^10 + 3 * q^11 + 2 * q^12 + 2 * q^13 - 2 * q^14 + 7 * q^15 + 11 * q^16 + 18 * q^17 - 6 * q^18 + 12 * q^19 + 11 * q^20 + 36 * q^21 + 3 * q^22 + 46 * q^23 + 7 * q^24 + 11 * q^25 + 26 * q^26 + 16 * q^27 + 4 * q^28 - 9 * q^29 - 8 * q^30 - 20 * q^31 - 44 * q^32 + 35 * q^33 + 26 * q^34 + 4 * q^35 + 15 * q^36 + 4 * q^37 + 4 * q^38 - 33 * q^39 + 11 * q^40 + 22 * q^41 - 29 * q^42 - 2 * q^43 + 14 * q^44 + 8 * q^46 - 16 * q^47 + q^48 - 5 * q^49 + 11 * q^50 - 13 * q^51 - 13 * q^52 + 64 * q^53 - 4 * q^54 + 4 * q^55 + 8 * q^56 - 25 * q^57 - 9 * q^58 - 27 * q^59 + q^60 + 4 * q^61 + q^63 - 22 * q^64 + 22 * q^65 + 40 * q^66 - 6 * q^67 - 9 * q^68 - 54 * q^69 - 2 * q^70 + 52 * q^71 + 6 * q^72 - 22 * q^73 - 2 * q^74 + q^75 + 4 * q^76 + 12 * q^77 - 32 * q^78 + 2 * q^79 - 22 * q^80 - 30 * q^81 + 36 * q^82 + 33 * q^83 + 8 * q^84 - 4 * q^85 - 17 * q^86 - 192 * q^87 + 3 * q^88 - 76 * q^89 + 6 * q^90 - 24 * q^91 - 19 * q^92 - 28 * q^93 - q^94 - 6 * q^95 + 7 * q^96 - 38 * q^97 - 128 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.104528	+	0.994522i	−0.0739128	+	0.703233i
$2$	−0.104528	+	0.994522i	−0.0739128	+	0.703233i
$3$	−0.00703919	+	1.73204i	−0.00406408	+	0.999992i
$3$	−0.00703919	+	1.73204i	−0.00406408	+	0.999992i
$4$	−0.978148	−	0.207912i	−0.489074	−	0.103956i
$5$	−0.104528	−	0.994522i	−0.0467465	−	0.444764i
$5$	−0.104528	−	0.994522i	−0.0467465	−	0.444764i
$6$	−1.72181	−	0.188048i	−0.702927	−	0.0767702i
$7$	1.23119	−	1.36737i	0.465345	−	0.516818i	−0.464098	−	0.885784i	$-0.653621\pi$
$7$	1.23119	−	1.36737i	0.465345	−	0.516818i	0.929443	+	0.368966i	$0.120288\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−2.99990	−	0.0243843i	−0.999967	−	0.00812809i
$10$	1.00000			0.316228
$11$	−1.47381	−	2.97117i	−0.444372	−	0.895842i
$11$	−1.47381	−	2.97117i	−0.444372	−	0.895842i
$12$	0.366996	−	1.69272i	0.105943	−	0.488647i
$13$	3.10807	−	1.38380i	0.862022	−	0.383797i	0.0723893	−	0.997376i	$-0.476938\pi$
$13$	3.10807	−	1.38380i	0.862022	−	0.383797i	0.789633	+	0.613579i	$0.210271\pi$
$14$	1.23119	+	1.36737i	0.329048	+	0.365445i
$15$	1.72328	−	0.174046i	0.444950	−	0.0449386i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	−0.0478740	+	0.0347825i	−0.0116111	+	0.00843599i	−0.593576	−	0.804778i	$-0.702284\pi$
$17$	−0.0478740	+	0.0347825i	−0.0116111	+	0.00843599i	0.581965	+	0.813214i	$0.302284\pi$
$18$	0.337826	−	2.98092i	0.0796263	−	0.702609i
$19$	−1.28042	+	3.94074i	−0.293749	+	0.904067i	0.689889	+	0.723915i	$0.257659\pi$
$19$	−1.28042	+	3.94074i	−0.293749	+	0.904067i	−0.983639	+	0.180153i	$0.942341\pi$
$20$	−0.104528	+	0.994522i	−0.0233733	+	0.222382i
$21$	2.35967	+	2.14209i	0.514922	+	0.467441i
$22$	3.10895	−	1.15517i	0.662831	−	0.246283i
$23$	3.45785	−	5.98917i	0.721011	−	1.24883i	−0.239584	−	0.970876i	$-0.577011\pi$
$23$	3.45785	−	5.98917i	0.721011	−	1.24883i	0.960595	−	0.277952i	$-0.0896557\pi$
$24$	1.64509	+	0.541923i	0.335802	+	0.110620i
$25$	−0.978148	+	0.207912i	−0.195630	+	0.0415823i
$26$	1.05134	+	3.23569i	0.206184	+	0.634570i
$27$	0.0633513	−	5.19577i	0.0121920	−	0.999926i
$28$	−1.48857	+	1.08151i	−0.281314	+	0.204387i
$29$	5.25082	−	5.83163i	0.975053	−	1.08291i	−0.0214851	−	0.999769i	$-0.506839\pi$
$29$	5.25082	−	5.83163i	0.975053	−	1.08291i	0.996538	−	0.0831370i	$-0.0264939\pi$
$30$	−0.00703919	+	1.73204i	−0.00128517	+	0.316225i
$31$	6.81548	−	3.03445i	1.22410	−	0.545003i	0.310092	−	0.950707i	$-0.399640\pi$
$31$	6.81548	−	3.03445i	1.22410	−	0.545003i	0.914005	+	0.405704i	$0.132974\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	5.15656	−	2.53179i	0.897641	−	0.440727i
$34$	−0.0295877	−	0.0512475i	−0.00507426	−	0.00878887i
$35$	−1.48857	−	1.08151i	−0.251615	−	0.182809i
$36$	2.92928	+	0.647566i	0.488213	+	0.107928i
$37$	−0.363903	−	1.11998i	−0.0598252	−	0.184123i	0.916678	−	0.399627i	$-0.130860\pi$
$37$	−0.363903	−	1.11998i	−0.0598252	−	0.184123i	−0.976503	+	0.215504i	$0.930860\pi$
$38$	−3.78531	−	1.68533i	−0.614058	−	0.273396i
$39$	2.37491	+	5.39302i	0.380291	+	0.863575i
$40$	−0.978148	−	0.207912i	−0.154659	−	0.0328737i
$41$	1.42844	+	1.58645i	0.223086	+	0.247762i	0.844290	−	0.535887i	$-0.180023\pi$
$41$	1.42844	+	1.58645i	0.223086	+	0.247762i	−0.621204	+	0.783649i	$0.713356\pi$
$42$	−2.37700	+	2.12284i	−0.366780	+	0.327561i
$43$	2.62307	+	4.54329i	0.400014	+	0.692845i	0.993727	−	0.111832i	$-0.0356718\pi$
$43$	2.62307	+	4.54329i	0.400014	+	0.692845i	−0.593713	+	0.804677i	$0.702338\pi$
$44$	0.823866	+	3.21267i	0.124203	+	0.484328i
$45$	0.289324	+	2.98602i	0.0431299	+	0.445129i
$46$	5.59492	+	4.06494i	0.824925	+	0.599343i
$47$	−0.874288	+	0.185836i	−0.127528	+	0.0271069i	−0.271233	−	0.962514i	$-0.587432\pi$
$47$	−0.874288	+	0.185836i	−0.127528	+	0.0271069i	0.143705	+	0.989621i	$0.454098\pi$
$48$	−0.710913	+	1.57943i	−0.102612	+	0.227971i
$49$	0.377816	+	3.59467i	0.0539736	+	0.513525i
$50$	−0.104528	−	0.994522i	−0.0147826	−	0.140647i
$51$	−0.0599075	−	0.0831643i	−0.00838873	−	0.0116453i
$52$	−3.32786	+	0.707358i	−0.461491	+	0.0980928i
$53$	0.197016	+	0.143141i	0.0270623	+	0.0196619i	0.601234	−	0.799073i	$-0.294676\pi$
$53$	0.197016	+	0.143141i	0.0270623	+	0.0196619i	−0.574172	+	0.818735i	$0.694676\pi$
$54$	5.16068	+	0.606110i	0.702280	+	0.0824811i
$55$	−2.80084	+	1.77631i	−0.377665	+	0.239518i
$56$	−0.919990	−	1.59347i	−0.122939	−	0.212936i
$57$	−6.81649	−	2.24548i	−0.902866	−	0.297421i
$58$	5.25082	+	5.83163i	0.689467	+	0.765730i
$59$	5.69767	+	1.21108i	0.741774	+	0.157669i	0.563273	−	0.826271i	$-0.309542\pi$
$59$	5.69767	+	1.21108i	0.741774	+	0.157669i	0.178501	+	0.983940i	$0.442875\pi$
$60$	−1.72181	−	0.188048i	−0.222285	−	0.0242769i
$61$	−10.4424	−	4.64924i	−1.33701	−	0.595274i	−0.391290	−	0.920267i	$-0.627971\pi$
$61$	−10.4424	−	4.64924i	−1.33701	−	0.595274i	−0.945716	+	0.324994i	$0.894638\pi$
$62$	2.30541	+	7.09533i	0.292788	+	0.901108i
$63$	−3.72678	+	4.07196i	−0.469530	+	0.513018i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−1.70110	−	2.94639i	−0.210996	−	0.365455i
$66$	1.97891	+	5.39295i	0.243587	+	0.663826i
$67$	−1.08921	+	1.88657i	−0.133068	+	0.230481i	−0.924858	−	0.380313i	$-0.875816\pi$
$67$	−1.08921	+	1.88657i	−0.133068	+	0.230481i	0.791790	+	0.610794i	$0.209150\pi$
$68$	0.0540595	−	0.0240688i	0.00655568	−	0.00291878i
$69$	10.3491	+	6.03128i	1.24589	+	0.726081i
$70$	1.23119	−	1.36737i	0.147155	−	0.163432i
$71$	7.04819	−	5.12081i	0.836467	−	0.607728i	−0.0849149	−	0.996388i	$-0.527062\pi$
$71$	7.04819	−	5.12081i	0.836467	−	0.607728i	0.921381	+	0.388660i	$0.127062\pi$
$72$	−0.950211	+	2.84554i	−0.111983	+	0.335350i
$73$	−3.27871	−	10.0908i	−0.383744	−	1.18104i	−0.937387	−	0.348289i	$-0.886763\pi$
$73$	−3.27871	−	10.0908i	−0.383744	−	1.18104i	0.553643	−	0.832754i	$-0.313237\pi$
$74$	1.15188	−	0.244840i	0.133903	−	0.0284620i
$75$	−0.353225	−	1.69565i	−0.0407869	−	0.195797i
$76$	2.07177	−	3.58841i	0.237648	−	0.411619i
$77$	−5.87724	−	1.64282i	−0.669773	−	0.187216i
$78$	−5.61173	+	1.79818i	−0.635403	+	0.203604i
$79$	−0.883390	+	8.40490i	−0.0993892	+	0.945625i	0.825247	+	0.564772i	$0.191036\pi$
$79$	−0.883390	+	8.40490i	−0.0993892	+	0.945625i	−0.924636	+	0.380852i	$0.875631\pi$
$80$	0.309017	−	0.951057i	0.0345492	−	0.106331i
$81$	8.99881	+	0.146301i	0.999868	+	0.0162556i
$82$	−1.72707	+	1.25479i	−0.190723	+	0.138568i
$83$	−9.27762	−	4.13066i	−1.01835	−	0.453399i	−0.171474	−	0.985189i	$-0.554853\pi$
$83$	−9.27762	−	4.13066i	−1.01835	−	0.453399i	−0.846876	+	0.531790i	$0.821520\pi$
$84$	−1.86274	−	2.58588i	−0.203242	−	0.282143i
$85$	0.0395961	+	0.0439760i	0.00429480	+	0.00476986i
$86$	−4.79259	+	2.13380i	−0.516798	+	0.230093i
$87$	10.0636	+	9.13566i	1.07893	+	0.979446i
$88$	−3.28119	+	0.483538i	−0.349776	+	0.0515453i
$89$	−8.19011			−0.868150			−0.434075	−	0.900877i	$-0.642925\pi$
$89$	−8.19011			−0.868150			−0.434075	+	0.900877i	$0.642925\pi$
$90$	−2.99990	−	0.0243843i	−0.316217	−	0.00257033i
$91$	1.93444	−	5.95360i	0.202784	−	0.624106i
$92$	−4.62750	+	5.13936i	−0.482451	+	0.535816i
$93$	5.20780	+	11.8260i	0.540023	+	1.22630i
$94$	−0.0934297	−	0.888924i	−0.00963653	−	0.0916855i
$95$	4.05299	+	0.861490i	0.415828	+	0.0883870i
$96$	−1.49647	−	0.872114i	−0.152733	−	0.0890098i
$97$	−1.85641	+	17.6626i	−0.188490	+	1.79337i	0.335911	+	0.941894i	$0.390956\pi$
$97$	−1.85641	+	17.6626i	−0.188490	+	1.79337i	−0.524401	+	0.851471i	$0.675711\pi$
$98$	−3.61447			−0.365117
$99$	4.34885	+	8.94916i	0.437076	+	0.899425i
$100$	1.00000			0.100000
$101$	1.33529	−	12.7045i	0.132867	−	1.26414i	−0.701395	−	0.712773i	$-0.747439\pi$
$101$	1.33529	−	12.7045i	0.132867	−	1.26414i	0.834261	−	0.551369i	$-0.185894\pi$
$102$	0.0889708	−	0.0508863i	0.00880942	−	0.00503850i
$103$	11.1505	+	2.37012i	1.09870	+	0.233535i	0.721373	−	0.692547i	$-0.243511\pi$
$103$	11.1505	+	2.37012i	1.09870	+	0.233535i	0.377323	+	0.926082i	$0.376845\pi$
$104$	−0.355627	−	3.38356i	−0.0348721	−	0.331786i
$105$	1.88370	−	2.57065i	0.183830	−	0.250870i
$106$	−0.162950	+	0.180975i	−0.0158271	+	0.0175778i
$107$	−2.53552	+	7.80352i	−0.245118	+	0.754395i	0.750499	+	0.660871i	$0.229813\pi$
$107$	−2.53552	+	7.80352i	−0.245118	+	0.754395i	−0.995617	+	0.0935236i	$0.970187\pi$
$108$	−1.14223	+	5.06905i	−0.109911	+	0.487770i
$109$	13.9729			1.33836			0.669181	−	0.743100i	$-0.266645\pi$
$109$	13.9729			1.33836			0.669181	+	0.743100i	$0.266645\pi$
$110$	−1.47381	−	2.97117i	−0.140523	−	0.283290i
$111$	1.94240	−	0.622409i	0.184365	−	0.0590764i
$112$	1.68091	−	0.748387i	0.158831	−	0.0707159i
$113$	−10.4117	−	11.5633i	−0.979448	−	1.08779i	−0.996127	−	0.0879258i	$-0.971976\pi$
$113$	−10.4117	−	11.5633i	−0.979448	−	1.08779i	0.0166795	−	0.999861i	$-0.494691\pi$
$114$	2.94570	−	6.54443i	0.275890	−	0.612942i
$115$	−6.31780	−	2.81287i	−0.589138	−	0.262301i
$116$	−6.34854	+	4.61249i	−0.589447	+	0.428259i
$117$	−9.35763	+	4.07548i	−0.865113	+	0.376778i
$118$	−1.80001	+	5.53987i	−0.165705	+	0.509986i
$119$	−0.0113812	+	0.108285i	−0.00104332	+	0.00992649i
$120$	0.366996	−	1.69272i	0.0335020	−	0.154524i
$121$	−6.65574	+	8.75792i	−0.605067	+	0.796174i
$122$	5.71529	−	9.89917i	0.517438	−	0.896229i
$123$	−2.75784	+	2.46295i	−0.248666	+	0.222077i
$124$	−7.29744	+	1.55112i	−0.655330	+	0.139295i
$125$	0.309017	+	0.951057i	0.0276393	+	0.0850651i
$126$	−3.66010	−	4.13200i	−0.326067	−	0.368108i
$127$	14.5326	−	10.5586i	1.28956	−	0.936922i	0.289766	−	0.957098i	$-0.406423\pi$
$127$	14.5326	−	10.5586i	1.28956	−	0.936922i	0.999796	+	0.0201756i	$0.00642254\pi$
$128$	0.669131	−	0.743145i	0.0591433	−	0.0656853i
$129$	−7.88761	+	4.51127i	−0.694465	+	0.397195i
$130$	3.10807	−	1.38380i	0.272595	−	0.121367i
$131$	1.35199	−	2.34171i	0.118124	−	0.204596i	−0.800900	−	0.598798i	$-0.795645\pi$
$131$	1.35199	−	2.34171i	0.118124	−	0.204596i	0.919024	+	0.394201i	$0.128979\pi$
$132$	−5.57026	+	1.40435i	−0.484829	+	0.122233i
$133$	3.81201	+	6.60260i	0.330543	+	0.572518i
$134$	−1.76238	−	1.28044i	−0.152246	−	0.110613i
$135$	−5.17393	+	0.480101i	−0.445301	+	0.0413205i
$136$	0.0182862	+	0.0562792i	0.00156803	+	0.00482590i
$137$	−1.98323	−	0.882989i	−0.169438	−	0.0754388i	0.320265	−	0.947328i	$-0.396228\pi$
$137$	−1.98323	−	0.882989i	−0.169438	−	0.0754388i	−0.489703	+	0.871889i	$0.662895\pi$
$138$	−7.08002	+	9.66198i	−0.602691	+	0.822483i
$139$	−3.84365	−	0.816993i	−0.326014	−	0.0692964i	0.0419973	−	0.999118i	$-0.486628\pi$
$139$	−3.84365	−	0.816993i	−0.326014	−	0.0692964i	−0.368011	+	0.929821i	$0.619961\pi$
$140$	1.23119	+	1.36737i	0.104054	+	0.115564i
$141$	−0.315720	−	1.51561i	−0.0265884	−	0.127637i
$142$	4.35602	+	7.54485i	0.365549	+	0.633150i
$143$	−8.69222	−	7.19514i	−0.726880	−	0.601688i
$144$	−2.73063	−	1.24245i	−0.227552	−	0.103537i
$145$	−6.34854	−	4.61249i	−0.527218	−	0.383046i
$146$	10.3783	−	2.20597i	0.858913	−	0.182568i
$147$	−6.22877	+	0.629087i	−0.513740	+	0.0518862i
$148$	0.123094	+	1.17116i	0.0101183	+	0.0962689i
$149$	−0.158800	−	1.51088i	−0.0130094	−	0.123777i	0.986090	−	0.166214i	$-0.0531543\pi$
$149$	−0.158800	−	1.51088i	−0.0130094	−	0.123777i	−0.999099	+	0.0424376i	$0.986488\pi$
$150$	1.72328	−	0.174046i	0.140706	−	0.0142108i
$151$	22.2181	−	4.72261i	1.80809	−	0.384321i	0.824660	−	0.565629i	$-0.191366\pi$
$151$	22.2181	−	4.72261i	1.80809	−	0.384321i	0.983426	+	0.181308i	$0.0580331\pi$
$152$	3.35219	+	2.43551i	0.271899	+	0.197546i
$153$	0.144465	−	0.103177i	0.0116793	−	0.00834133i
$154$	2.24816	−	5.67332i	0.181162	−	0.457169i
$155$	−3.73024	−	6.46096i	−0.299620	−	0.518957i
$156$	−1.20174	−	5.76895i	−0.0962165	−	0.461885i
$157$	−11.8983	−	13.2144i	−0.949589	−	1.05463i	−0.998441	−	0.0558196i	$-0.982223\pi$
$157$	−11.8983	−	13.2144i	−0.949589	−	1.05463i	0.0488517	−	0.998806i	$-0.484444\pi$
$158$	−8.26651	−	1.75710i	−0.657649	−	0.139788i
$159$	−0.249312	+	0.340232i	−0.0197717	+	0.0269821i
$160$	0.913545	+	0.406737i	0.0722221	+	0.0321554i
$161$	−3.93216	−	12.1019i	−0.309898	−	0.953767i
$162$	−1.08613	+	8.93422i	−0.0853345	+	0.701939i
$163$	−0.527811	−	0.383477i	−0.0413413	−	0.0300362i	0.566923	−	0.823771i	$-0.308134\pi$
$163$	−0.527811	−	0.383477i	−0.0413413	−	0.0300362i	−0.608264	+	0.793735i	$0.708134\pi$
$164$	−1.06739	−	1.84877i	−0.0833490	−	0.144365i
$165$	−3.05692	−	4.86366i	−0.237981	−	0.378636i
$166$	5.07781	−	8.79502i	0.394114	−	0.682626i
$167$	−3.50977	+	1.56265i	−0.271594	+	0.120921i	−0.538015	−	0.842935i	$-0.680826\pi$
$167$	−3.50977	+	1.56265i	−0.271594	+	0.120921i	0.266421	+	0.963857i	$0.414159\pi$
$168$	2.76642	−	1.58224i	0.213434	−	0.122072i
$169$	−0.953527	+	1.05900i	−0.0733482	+	0.0814614i
$170$	−0.0478740	+	0.0347825i	−0.00367177	+	0.00266769i
$171$	3.93724	−	11.7906i	0.301088	−	0.901650i
$172$	−1.62115	−	4.98938i	−0.123611	−	0.380436i
$173$	−0.489603	+	0.104068i	−0.0372238	+	0.00791216i	−0.226486	−	0.974014i	$-0.572724\pi$
$173$	−0.489603	+	0.104068i	−0.0372238	+	0.00791216i	0.189262	+	0.981927i	$0.439390\pi$
$174$	−10.1376	+	9.05356i	−0.768526	+	0.686349i
$175$	−0.919990	+	1.59347i	−0.0695447	+	0.120455i
$176$	−0.137911	−	3.31376i	−0.0103955	−	0.249784i
$177$	−2.13774	+	9.86005i	−0.160682	+	0.741127i
$178$	0.856100	−	8.14524i	0.0641674	−	0.610512i
$179$	−1.20978	+	3.72333i	−0.0904235	+	0.278295i	−0.986034	−	0.166544i	$-0.946739\pi$
$179$	−1.20978	+	3.72333i	−0.0904235	+	0.278295i	0.895610	+	0.444839i	$0.146739\pi$
$180$	0.337826	−	2.98092i	0.0251800	−	0.222185i
$181$	10.3795	−	7.54114i	0.771501	−	0.560528i	−0.130915	−	0.991394i	$-0.541792\pi$
$181$	10.3795	−	7.54114i	0.771501	−	0.560528i	0.902416	+	0.430865i	$0.141792\pi$
$182$	5.71878	+	2.54616i	0.423904	+	0.188734i
$183$	8.12615	−	18.0538i	0.600702	−	1.33458i
$184$	−4.62750	−	5.13936i	−0.341144	−	0.378879i
$185$	−1.07580	+	0.478978i	−0.0790946	+	0.0352152i
$186$	−12.3056	+	3.94311i	−0.902290	+	0.289123i
$187$	0.173902	+	0.0909790i	0.0127170	+	0.00665304i
$188$	0.893820			0.0651886
$189$	−7.02654	−	6.48358i	−0.511106	−	0.471611i
$190$	−1.28042	+	3.94074i	−0.0928917	+	0.285891i
$191$	4.22175	−	4.68873i	0.305475	−	0.339265i	−0.570788	−	0.821098i	$-0.693362\pi$
$191$	4.22175	−	4.68873i	0.305475	−	0.339265i	0.876263	+	0.481833i	$0.160029\pi$
$192$	1.02376	−	1.39711i	0.0738835	−	0.100828i
$193$	1.10637	+	10.5264i	0.0796384	+	0.757708i	0.959353	+	0.282207i	$0.0910666\pi$
$193$	1.10637	+	10.5264i	0.0796384	+	0.757708i	−0.879715	+	0.475501i	$0.842267\pi$
$194$	−17.3718	−	3.69249i	−1.24722	−	0.265105i
$195$	5.11523	−	2.92563i	0.366310	−	0.209509i
$196$	0.377816	−	3.59467i	0.0269868	−	0.256762i
$197$	−0.496020			−0.0353400			−0.0176700	−	0.999844i	$-0.505625\pi$
$197$	−0.496020			−0.0353400			−0.0176700	+	0.999844i	$0.505625\pi$
$198$	−9.35472	+	3.38958i	−0.664811	+	0.240887i
$199$	8.05807			0.571221			0.285611	−	0.958346i	$-0.407804\pi$
$199$	8.05807			0.571221			0.285611	+	0.958346i	$0.407804\pi$
$200$	−0.104528	+	0.994522i	−0.00739128	+	0.0703233i
$201$	−3.25993	−	1.89983i	−0.229938	−	0.134004i
$202$	12.4953	+	2.65596i	0.879166	+	0.186873i
$203$	−1.50926	−	14.3596i	−0.105929	−	1.00785i
$204$	0.0413076	+	0.0938024i	0.00289211	+	0.00656748i
$205$	1.42844	−	1.58645i	0.0997669	−	0.110802i
$206$	−3.52269	+	10.8417i	−0.245437	+	0.755378i
$207$	−10.5192	+	17.8826i	−0.731138	+	1.24293i
$208$	3.40220			0.235900
$209$	13.5957	−	2.00356i	0.940436	−	0.138589i
$210$	2.35967	+	2.14209i	0.162833	+	0.147818i
$211$	18.8447	−	8.39022i	1.29733	−	0.577606i	0.362258	−	0.932078i	$-0.382006\pi$
$211$	18.8447	−	8.39022i	1.29733	−	0.577606i	0.935067	+	0.354471i	$0.115339\pi$
$212$	−0.162950	−	0.180975i	−0.0111915	−	0.0124294i
$213$	8.81982	+	12.2438i	0.604324	+	0.838929i
$214$	−7.49574	−	3.33732i	−0.512398	−	0.228134i
$215$	4.24422	−	3.08360i	0.289453	−	0.210300i
$216$	−4.92189	−	1.66583i	−0.334892	−	0.113345i
$217$	4.24191	−	13.0553i	0.287960	−	0.886249i
$218$	−1.46057	+	13.8964i	−0.0989220	+	0.941180i
$219$	17.5008	−	5.60782i	1.18259	−	0.378941i
$220$	3.10895	−	1.15517i	0.209606	−	0.0778814i
$221$	−0.100663	+	0.174354i	−0.00677136	+	0.0117283i
$222$	0.415963	+	1.99682i	0.0279176	+	0.134018i
$223$	−24.7148	+	5.25329i	−1.65502	+	0.351786i	−0.938367	−	0.345640i	$-0.887662\pi$
$223$	−24.7148	+	5.25329i	−1.65502	+	0.351786i	−0.716657	+	0.697426i	$0.754329\pi$
$224$	0.568585	+	1.74992i	0.0379902	+	0.116922i
$225$	2.93942	−	0.599863i	0.195961	−	0.0399909i
$226$	12.5883	−	9.14594i	0.837361	−	0.608379i
$227$	2.22344	−	2.46938i	0.147575	−	0.163899i	−0.664825	−	0.746999i	$-0.731494\pi$
$227$	2.22344	−	2.46938i	0.147575	−	0.163899i	0.812400	+	0.583100i	$0.198161\pi$
$228$	6.20067	+	3.61364i	0.410649	+	0.239319i
$229$	−16.5502	+	7.36863i	−1.09367	+	0.486933i	−0.872655	−	0.488338i	$-0.837603\pi$
$229$	−16.5502	+	7.36863i	−1.09367	+	0.486933i	−0.221015	+	0.975271i	$0.570937\pi$
$230$	3.45785	−	5.98917i	0.228004	−	0.394914i
$231$	2.88679	−	10.1680i	0.189937	−	0.669007i
$232$	−3.92361	−	6.79590i	−0.257598	−	0.446173i
$233$	−3.39105	−	2.46374i	−0.222155	−	0.161405i	0.471141	−	0.882058i	$-0.343842\pi$
$233$	−3.39105	−	2.46374i	−0.222155	−	0.161405i	−0.693296	+	0.720653i	$0.743842\pi$
$234$	−3.07501	−	9.73237i	−0.201020	−	0.636225i
$235$	0.276206	+	0.850074i	0.0180177	+	0.0554527i
$236$	−5.32137	−	2.36923i	−0.346392	−	0.154223i
$237$	−14.5514	−	1.58923i	−0.945213	−	0.103231i
$238$	−0.106502	−	0.0226378i	−0.00690352	−	0.00146739i
$239$	5.10663	+	5.67149i	0.330320	+	0.366858i	0.885312	−	0.464998i	$-0.153945\pi$
$239$	5.10663	+	5.67149i	0.330320	+	0.366858i	−0.554991	+	0.831856i	$0.687278\pi$
$240$	1.64509	+	0.541923i	0.106190	+	0.0349810i
$241$	9.18066	+	15.9014i	0.591378	+	1.02430i	0.994047	+	0.108952i	$0.0347494\pi$
$241$	9.18066	+	15.9014i	0.591378	+	1.02430i	−0.402669	+	0.915346i	$0.631917\pi$
$242$	−8.01423	−	7.53473i	−0.515174	−	0.484351i
$243$	−0.316743	+	15.5852i	−0.0203191	+	0.999794i
$244$	9.24753	+	6.71873i	0.592013	+	0.430122i
$245$	3.53549	−	0.751492i	0.225874	−	0.0480110i
$246$	−2.16119	−	3.00018i	−0.137792	−	0.191285i
$247$	1.47355	+	14.0199i	0.0937600	+	0.892066i
$248$	−0.779832	−	7.41960i	−0.0495194	−	0.471145i
$249$	7.21976	−	16.0401i	0.457534	−	1.01650i
$250$	−0.978148	+	0.207912i	−0.0618635	+	0.0131495i
$251$	16.5695	+	12.0384i	1.04585	+	0.759858i	0.971420	−	0.237368i	$-0.0762848\pi$
$251$	16.5695	+	12.0384i	1.04585	+	0.759858i	0.0744347	+	0.997226i	$0.476285\pi$
$252$	4.49195	−	3.20813i	0.282966	−	0.202093i
$253$	−22.8911	−	1.44694i	−1.43915	−	0.0909685i
$254$	8.98166	+	15.5567i	0.563559	+	0.976114i
$255$	−0.0764467	+	0.0682724i	−0.00478728	+	0.00427538i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	−21.6131	−	4.59401i	−1.34819	−	0.286566i	−0.523439	−	0.852063i	$-0.675351\pi$
$257$	−21.6131	−	4.59401i	−1.34819	−	0.286566i	−0.824750	+	0.565497i	$0.808684\pi$
$258$	−3.66208	−	8.31596i	−0.227991	−	0.517729i
$259$	−1.97946	−	0.881311i	−0.122997	−	0.0547620i
$260$	1.05134	+	3.23569i	0.0652012	+	0.200669i
$261$	−15.8941	+	17.3663i	−0.983823	+	1.07495i
$262$	2.18756	+	1.58936i	0.135148	+	0.0981908i
$263$	−9.09464	−	15.7524i	−0.560799	−	0.971333i	−0.997427	−	0.0716905i	$-0.977161\pi$
$263$	−9.09464	−	15.7524i	−0.560799	−	0.971333i	0.436628	−	0.899642i	$-0.356173\pi$
$264$	−0.814408	−	5.68654i	−0.0501234	−	0.349982i
$265$	0.121763	−	0.210899i	0.00747982	−	0.0129554i
$266$	−6.96489	+	3.10097i	−0.427045	+	0.190133i
$267$	0.0576517	−	14.1856i	0.00352823	−	0.868143i
$268$	1.45765	−	1.61888i	0.0890399	−	0.0988888i
$269$	−14.2368	+	10.3437i	−0.868034	+	0.630664i	−0.930059	−	0.367411i	$-0.880244\pi$
$269$	−14.2368	+	10.3437i	−0.868034	+	0.630664i	0.0620244	+	0.998075i	$0.480244\pi$
$270$	0.0633513	−	5.19577i	0.00385544	−	0.316204i
$271$	−8.91756	−	27.4454i	−0.541703	−	1.66719i	−0.728702	−	0.684831i	$-0.759876\pi$
$271$	−8.91756	−	27.4454i	−0.541703	−	1.66719i	0.186999	−	0.982360i	$-0.440124\pi$
$272$	−0.0578824	+	0.0123033i	−0.00350963	+	0.000745996i
$273$	10.2982	+	3.39243i	0.623277	+	0.205319i
$274$	1.08546	−	1.88006i	0.0655747	−	0.113579i
$275$	2.05935	+	2.59982i	0.124183	+	0.156775i
$276$	−8.86899	−	8.05118i	−0.533851	−	0.484624i
$277$	−0.116377	+	1.10725i	−0.00699239	+	0.0665281i	−0.997462	−	0.0712059i	$-0.977315\pi$
$277$	−0.116377	+	1.10725i	−0.00699239	+	0.0665281i	0.990469	+	0.137734i	$0.0439819\pi$
$278$	1.21429	−	3.73719i	0.0728282	−	0.224142i
$279$	−20.5198	+	8.93685i	−1.22849	+	0.535035i
$280$	−1.48857	+	1.08151i	−0.0889594	+	0.0646328i
$281$	−25.4632	−	11.3369i	−1.51901	−	0.676305i	−0.533477	−	0.845815i	$-0.679115\pi$
$281$	−25.4632	−	11.3369i	−1.51901	−	0.676305i	−0.985529	+	0.169510i	$0.945782\pi$
$282$	1.54031	−	0.155566i	0.0917239	−	0.00926384i
$283$	−9.66479	−	10.7338i	−0.574512	−	0.638060i	0.383925	−	0.923364i	$-0.374572\pi$
$283$	−9.66479	−	10.7338i	−0.574512	−	0.638060i	−0.958437	+	0.285304i	$0.907905\pi$
$284$	−7.95885	+	3.54351i	−0.472271	+	0.210268i
$285$	−1.52066	+	7.01386i	−0.0900762	+	0.415465i
$286$	8.06431	−	7.89251i	0.476852	−	0.466694i
$287$	3.92795			0.231859
$288$	1.52107	−	2.58580i	0.0896298	−	0.152370i
$289$	−5.25221	+	16.1646i	−0.308953	+	0.950861i
$290$	5.25082	−	5.83163i	0.308339	−	0.342445i
$291$	−30.5792	−	3.33971i	−1.79258	−	0.195777i
$292$	1.10906	+	10.5520i	0.0649029	+	0.617510i
$293$	8.27276	+	1.75843i	0.483300	+	0.102729i	0.443117	−	0.896464i	$-0.353873\pi$
$293$	8.27276	+	1.75843i	0.483300	+	0.102729i	0.0401829	+	0.999192i	$0.487206\pi$
$294$	0.0254430	−	6.26040i	0.00148386	−	0.365114i
$295$	0.608874	−	5.79305i	0.0354500	−	0.337285i
$296$	−1.17761			−0.0684474
$297$	−15.5309	+	7.46937i	−0.901194	+	0.433417i
$298$	1.51921			0.0880053
$299$	2.45941	−	23.3997i	0.142231	−	1.35324i
$300$	−0.00703919	+	1.73204i	−0.000406408	+	0.0999992i
$301$	9.44185	+	2.00693i	0.544219	+	0.115677i
$302$	2.37431	+	22.5901i	0.136626	+	1.29991i
$303$	21.9952	+	2.40221i	1.26359	+	0.138003i
$304$	−2.77257	+	3.07925i	−0.159018	+	0.176607i
$305$	−3.53224	+	10.8711i	−0.202256	+	0.622479i
$306$	0.0875107	+	0.154459i	0.00500265	+	0.00882982i
$307$	1.46285			0.0834890			0.0417445	−	0.999128i	$-0.486708\pi$
$307$	1.46285			0.0834890			0.0417445	+	0.999128i	$0.486708\pi$
$308$	5.40725	+	2.82886i	0.308106	+	0.161190i
$309$	−4.18363	+	19.2965i	−0.237998	+	1.09774i
$310$	6.81548	−	3.03445i	0.387093	−	0.172345i
$311$	16.9395	+	18.8132i	0.960548	+	1.06680i	0.997720	+	0.0674880i	$0.0214984\pi$
$311$	16.9395	+	18.8132i	0.960548	+	1.06680i	−0.0371718	+	0.999309i	$0.511835\pi$
$312$	5.86296	−	0.592141i	0.331925	−	0.0335234i
$313$	−4.65714	−	2.07349i	−0.263237	−	0.117201i	0.270874	−	0.962615i	$-0.412687\pi$
$313$	−4.65714	−	2.07349i	−0.263237	−	0.117201i	−0.534112	+	0.845414i	$0.679354\pi$
$314$	14.3857	−	10.4519i	0.811835	−	0.589832i
$315$	4.43920	+	3.28073i	0.250121	+	0.184848i
$316$	2.61156	−	8.03756i	0.146912	−	0.452148i
$317$	1.23469	−	11.7473i	0.0693469	−	0.659792i	−0.903539	−	0.428506i	$-0.859040\pi$
$317$	1.23469	−	11.7473i	0.0693469	−	0.659792i	0.972886	−	0.231286i	$-0.0742933\pi$
$318$	−0.312308	−	0.283510i	−0.0175133	−	0.0158984i
$319$	−25.0655	−	7.00636i	−1.40340	−	0.392281i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−13.4981	−	4.44654i	−0.753392	−	0.248182i
$322$	12.4467	−	2.64562i	0.693626	−	0.147435i
$323$	−0.0757697	−	0.233195i	−0.00421594	−	0.0129753i
$324$	−8.77175	−	2.01406i	−0.487319	−	0.111892i
$325$	−2.75244	+	1.99976i	−0.152678	+	0.110927i
$326$	0.436548	−	0.484835i	0.0241781	−	0.0268525i
$327$	−0.0983579	+	24.2016i	−0.00543921	+	1.33835i
$328$	1.95022	−	0.868292i	0.107683	−	0.0479434i
$329$	−0.822306	+	1.42428i	−0.0453352	+	0.0785228i
$330$	5.15656	−	2.53179i	0.283859	−	0.139370i
$331$	−1.99365	−	3.45310i	−0.109581	−	0.189799i	0.806020	−	0.591889i	$-0.201617\pi$
$331$	−1.99365	−	3.45310i	−0.109581	−	0.189799i	−0.915600	+	0.402089i	$0.868284\pi$
$332$	8.21607	+	5.96932i	0.450915	+	0.327609i
$333$	1.06436	+	3.36869i	0.0583267	+	0.184603i
$334$	−1.18722	−	3.65388i	−0.0649617	−	0.199932i
$335$	1.99008	+	0.886042i	0.108730	+	0.0484097i
$336$	1.28440	+	2.91666i	0.0700699	+	0.159117i
$337$	18.3977	+	3.91054i	1.00218	+	0.213021i	0.679650	−	0.733537i	$-0.262132\pi$
$337$	18.3977	+	3.91054i	1.00218	+	0.213021i	0.322535	+	0.946558i	$0.395465\pi$
$338$	−0.953527	−	1.05900i	−0.0518650	−	0.0576019i
$339$	20.1014	−	17.9520i	1.09176	−	0.975019i
$340$	−0.0295877	−	0.0512475i	−0.00160462	−	0.00277928i
$341$	−19.0606	−	15.7778i	−1.03219	−	0.854414i
$342$	11.3145	+	5.14812i	0.611816	+	0.278378i
$343$	15.8004	+	11.4797i	0.853144	+	0.619845i
$344$	5.13150	−	1.09073i	0.276672	−	0.0588084i
$345$	4.91646	−	10.9229i	0.264693	−	0.588067i
$346$	−0.0523207	−	0.497799i	−0.00281278	−	0.0267618i
$347$	3.17444	+	30.2028i	0.170413	+	1.62137i	0.661281	+	0.750138i	$0.270013\pi$
$347$	3.17444	+	30.2028i	0.170413	+	1.62137i	−0.490868	+	0.871234i	$0.663320\pi$
$348$	−7.94431	−	11.0284i	−0.425859	−	0.591183i
$349$	−26.6504	+	5.66471i	−1.42656	+	0.303225i	−0.855551	−	0.517719i	$-0.826781\pi$
$349$	−26.6504	+	5.66471i	−1.42656	+	0.303225i	−0.571010	+	0.820943i	$0.693448\pi$
$350$	−1.48857	−	1.08151i	−0.0795677	−	0.0578093i
$351$	−6.99300	−	16.2364i	−0.373259	−	0.866638i
$352$	3.31002	+	0.209226i	0.176425	+	0.0111518i
$353$	8.22771	+	14.2508i	0.437917	+	0.758495i	0.997529	−	0.0702604i	$-0.0223830\pi$
$353$	8.22771	+	14.2508i	0.437917	+	0.758495i	−0.559612	+	0.828755i	$0.689050\pi$
$354$	−9.58258	−	3.15668i	−0.509309	−	0.167776i
$355$	−5.82950	−	6.47431i	−0.309398	−	0.343621i
$356$	8.01114	+	1.70282i	0.424589	+	0.0902493i
$357$	−0.187474	−	0.0204750i	−0.00992217	−	0.00108365i
$358$	−3.57648	−	1.59235i	−0.189023	−	0.0841583i
$359$	4.48206	+	13.7943i	0.236554	+	0.728038i	0.996911	+	0.0785333i	$0.0250237\pi$
$359$	4.48206	+	13.7943i	0.236554	+	0.728038i	−0.760358	+	0.649505i	$0.774976\pi$
$360$	2.92928	+	0.647566i	0.154386	+	0.0341297i
$361$	1.48139	+	1.07629i	0.0779680	+	0.0566470i
$362$	6.41487	+	11.1109i	0.337158	+	0.583975i
$363$	−15.1222	−	11.5896i	−0.793709	−	0.608298i
$364$	−3.12999	+	5.42130i	−0.164056	+	0.284154i
$365$	−9.69284	+	4.31553i	−0.507347	+	0.225885i
$366$	17.1055	+	9.96877i	0.894119	+	0.521076i
$367$	−8.04201	+	8.93156i	−0.419790	+	0.466224i	−0.915532	−	0.402246i	$-0.868230\pi$
$367$	−8.04201	+	8.93156i	−0.419790	+	0.466224i	0.495742	+	0.868470i	$0.334896\pi$
$368$	5.59492	−	4.06494i	0.291655	−	0.211900i
$369$	−4.24651	−	4.79402i	−0.221064	−	0.249567i
$370$	−0.363903	−	1.11998i	−0.0189184	−	0.0582248i
$371$	0.438290	−	0.0931614i	0.0227549	−	0.00483670i
$372$	−2.63523	−	12.6504i	−0.136630	−	0.655890i
$373$	−6.90703	+	11.9633i	−0.357633	+	0.619438i	−0.987565	−	0.157212i	$-0.949749\pi$
$373$	−6.90703	+	11.9633i	−0.357633	+	0.619438i	0.629932	+	0.776650i	$0.283083\pi$
$374$	−0.108658	+	0.163440i	−0.00561859	+	0.00845126i
$375$	−1.64944	+	0.528534i	−0.0851767	+	0.0272934i
$376$	−0.0934297	+	0.888924i	−0.00481827	+	0.0458428i
$377$	8.25009	−	25.3912i	0.424901	−	1.30771i
$378$	7.18254	−	6.31033i	0.369430	−	0.324569i
$379$	0.661011	−	0.480253i	0.0339539	−	0.0246689i	−0.570679	−	0.821173i	$-0.693320\pi$
$379$	0.661011	−	0.480253i	0.0339539	−	0.0246689i	0.604633	+	0.796504i	$0.293320\pi$
$380$	−3.78531	−	1.68533i	−0.194182	−	0.0864555i
$381$	18.1855	+	25.2454i	0.931673	+	1.29336i
$382$	4.22175	+	4.68873i	0.216004	+	0.239896i
$383$	7.97488	−	3.55064i	0.407497	−	0.181429i	−0.192743	−	0.981249i	$-0.561738\pi$
$383$	7.97488	−	3.55064i	0.407497	−	0.181429i	0.600240	+	0.799820i	$0.295072\pi$
$384$	1.28244	+	1.16419i	0.0654444	+	0.0594098i
$385$	−1.01948	+	6.01676i	−0.0519575	+	0.306643i
$386$	−10.5844			−0.538732
$387$	−7.75816	−	13.6934i	−0.394370	−	0.696074i
$388$	5.48811	−	16.8907i	0.278616	−	0.857493i
$389$	−18.5818	+	20.6372i	−0.942134	+	1.04635i	0.0567157	+	0.998390i	$0.481937\pi$
$389$	−18.5818	+	20.6372i	−0.942134	+	1.04635i	−0.998849	+	0.0479552i	$0.984730\pi$
$390$	2.37491	+	5.39302i	0.120258	+	0.273086i
$391$	0.0427772	+	0.406998i	0.00216334	+	0.0205828i
$392$	3.53549	+	0.751492i	0.178569	+	0.0379561i
$393$	4.04641	+	2.35818i	0.204114	+	0.118954i
$394$	0.0518482	−	0.493303i	0.00261208	−	0.0248523i
$395$	8.45119			0.425226
$396$	−2.39318	−	9.65778i	−0.120262	−	0.485322i
$397$	15.3874			0.772271			0.386136	−	0.922442i	$-0.373810\pi$
$397$	15.3874			0.772271			0.386136	+	0.922442i	$0.373810\pi$
$398$	−0.842297	+	8.01392i	−0.0422205	+	0.401702i
$399$	−11.4628	+	6.55607i	−0.573857	+	0.328214i
$400$	−0.978148	−	0.207912i	−0.0489074	−	0.0103956i
$401$	3.71208	+	35.3181i	0.185372	+	1.76370i	0.552485	+	0.833523i	$0.313680\pi$
$401$	3.71208	+	35.3181i	0.185372	+	1.76370i	−0.367113	+	0.930177i	$0.619654\pi$
$402$	2.23018	−	3.04349i	0.111231	−	0.151795i
$403$	16.9839	−	18.8625i	0.846028	−	0.939609i
$404$	−3.94752	+	12.1492i	−0.196397	+	0.604447i
$405$	−0.795133	−	8.96481i	−0.0395105	−	0.445465i
$406$	14.4387			0.716583
$407$	−2.79132	+	2.73186i	−0.138361	+	0.135413i
$408$	−0.0976064	+	0.0312763i	−0.00483224	+	0.00154841i
$409$	30.8845	−	13.7507i	1.52714	−	0.679926i	0.540276	−	0.841488i	$-0.318320\pi$
$409$	30.8845	−	13.7507i	1.52714	−	0.679926i	0.986863	+	0.161561i	$0.0516530\pi$
$410$	1.42844	+	1.58645i	0.0705458	+	0.0783491i
$411$	1.54333	−	3.42880i	0.0761268	−	0.169130i
$412$	−10.4141	−	4.63666i	−0.513066	−	0.228432i
$413$	8.67089	−	6.29977i	0.426667	−	0.309991i
$414$	−16.6851	−	12.3309i	−0.820027	−	0.606029i
$415$	−3.13826	+	9.65856i	−0.154051	+	0.474120i
$416$	−0.355627	+	3.38356i	−0.0174360	+	0.165893i
$417$	1.44212	−	6.65159i	0.0706208	−	0.325730i
$418$	0.571441	+	13.7307i	0.0279501	+	0.671589i
$419$	−4.56087	+	7.89966i	−0.222813	+	0.385924i	−0.955661	−	0.294469i	$-0.904857\pi$
$419$	−4.56087	+	7.89966i	−0.222813	+	0.385924i	0.732848	+	0.680392i	$0.238191\pi$
$420$	−2.37700	+	2.12284i	−0.115986	+	0.103584i
$421$	−23.6349	+	5.02376i	−1.15190	+	0.244843i	−0.743996	−	0.668184i	$-0.767072\pi$
$421$	−23.6349	+	5.02376i	−1.15190	+	0.244843i	−0.407899	+	0.913027i	$0.633739\pi$
$422$	6.37444	+	19.6185i	0.310303	+	0.955015i
$423$	2.62731	−	0.536170i	0.127744	−	0.0260695i
$424$	0.197016	−	0.143141i	0.00956795	−	0.00695152i
$425$	0.0395961	−	0.0439760i	0.00192069	−	0.00213315i
$426$	−13.0986	+	7.49168i	−0.634630	+	0.362973i
$427$	−19.2137	+	8.55450i	−0.929817	+	0.413981i
$428$	4.10255	−	7.10583i	0.198304	−	0.343473i
$429$	12.5234	−	15.0046i	0.604637	−	0.724429i
$430$	2.62307	+	4.54329i	0.126496	+	0.219097i
$431$	−2.37533	−	1.72578i	−0.114416	−	0.0831280i	0.529106	−	0.848556i	$-0.322527\pi$
$431$	−2.37533	−	1.72578i	−0.114416	−	0.0831280i	−0.643522	+	0.765428i	$0.722527\pi$
$432$	2.17118	−	4.72080i	0.104461	−	0.227130i
$433$	3.53014	+	10.8647i	0.169648	+	0.522122i	0.999349	−	0.0360862i	$-0.0114891\pi$
$433$	3.53014	+	10.8647i	0.169648	+	0.522122i	−0.829701	+	0.558208i	$0.811489\pi$
$434$	12.5403	+	5.58332i	0.601956	+	0.268008i
$435$	8.03368	−	10.9634i	0.385186	−	0.525657i
$436$	−13.6676	−	2.90513i	−0.654558	−	0.139130i
$437$	19.1742	+	21.2951i	0.917228	+	1.01868i
$438$	3.74777	+	17.9911i	0.179075	+	0.859647i
$439$	−3.66993	−	6.35651i	−0.175156	−	0.303380i	0.765059	−	0.643960i	$-0.222710\pi$
$439$	−3.66993	−	6.35651i	−0.175156	−	0.303380i	−0.940215	+	0.340580i	$0.889376\pi$
$440$	0.823866	+	3.21267i	0.0392763	+	0.153158i
$441$	−1.04576	−	10.7929i	−0.0497979	−	0.513947i
$442$	−0.162877	−	0.118337i	−0.00774726	−	0.00562872i
$443$	−29.8634	+	6.34766i	−1.41885	+	0.301586i	−0.852565	−	0.522622i	$-0.824954\pi$
$443$	−29.8634	+	6.34766i	−1.41885	+	0.301586i	−0.566287	+	0.824208i	$0.691621\pi$
$444$	−2.02936	+	0.204959i	−0.0963093	+	0.00972695i
$445$	0.856100	+	8.14524i	0.0405830	+	0.386122i
$446$	−2.64111	−	25.1285i	−0.125060	−	1.18987i
$447$	2.61803	−	0.264413i	0.123828	−	0.0125063i
$448$	−1.79977	+	0.382553i	−0.0850312	+	0.0180739i
$449$	18.5288	+	13.4620i	0.874429	+	0.635310i	0.931772	−	0.363045i	$-0.118263\pi$
$449$	18.5288	+	13.4620i	0.874429	+	0.635310i	−0.0573425	+	0.998355i	$0.518263\pi$
$450$	0.289324	+	2.98602i	0.0136389	+	0.140762i
$451$	2.60835	−	6.58229i	0.122822	−	0.309948i
$452$	7.78000	+	13.4754i	0.365940	+	0.633827i
$453$	8.02334	+	38.5159i	0.376969	+	1.80963i
$454$	2.22344	+	2.46938i	0.104351	+	0.115894i
$455$	−6.12319	−	1.30152i	−0.287059	−	0.0610164i
$456$	−4.24199	+	5.78897i	−0.198649	+	0.271094i
$457$	11.8514	+	5.27657i	0.554384	+	0.246828i	0.664753	−	0.747063i	$-0.268537\pi$
$457$	11.8514	+	5.27657i	0.554384	+	0.246828i	−0.110369	+	0.993891i	$0.535203\pi$
$458$	−5.59830	−	17.2298i	−0.261591	−	0.805095i
$459$	0.177689	+	0.250945i	0.00829380	+	0.0117131i
$460$	5.59492	+	4.06494i	0.260864	+	0.189529i
$461$	17.4901	+	30.2937i	0.814593	+	1.41092i	0.909620	+	0.415442i	$0.136373\pi$
$461$	17.4901	+	30.2937i	0.814593	+	1.41092i	−0.0950261	+	0.995475i	$0.530293\pi$
$462$	9.81057	+	3.93382i	0.456429	+	0.183018i
$463$	−10.5004	+	18.1873i	−0.487996	+	0.845234i	−0.999905	−	0.0138059i	$-0.995605\pi$
$463$	−10.5004	+	18.1873i	−0.487996	+	0.845234i	0.511909	+	0.859040i	$0.328939\pi$
$464$	7.16880	−	3.19176i	0.332803	−	0.148174i
$465$	11.2169	−	6.41542i	0.520170	−	0.297508i
$466$	2.80470	−	3.11494i	0.129925	−	0.144297i
$467$	−13.5456	+	9.84147i	−0.626817	+	0.455409i	−0.855296	−	0.518140i	$-0.826625\pi$
$467$	−13.5456	+	9.84147i	−0.626817	+	0.455409i	0.228479	+	0.973549i	$0.426625\pi$
$468$	10.0005	−	2.04086i	0.462273	−	0.0943386i
$469$	1.23862	+	3.81207i	0.0571940	+	0.176025i
$470$	−0.874288	+	0.185836i	−0.0403279	+	0.00857196i
$471$	22.9716	−	20.5153i	1.05848	−	0.945295i
$472$	2.91248	−	5.04456i	0.134058	−	0.232195i
$473$	9.63298	−	14.4896i	0.442925	−	0.666231i
$474$	3.10155	−	14.3055i	0.142459	−	0.657075i
$475$	0.433118	−	4.12084i	0.0198728	−	0.189077i
$476$	0.0336463	−	0.103553i	0.00154218	−	0.00474633i
$477$	−0.587539	−	0.434212i	−0.0269015	−	0.0198812i
$478$	−6.17421	+	4.48582i	−0.282402	+	0.205177i
$479$	−9.46166	−	4.21260i	−0.432314	−	0.192479i	0.179030	−	0.983844i	$-0.442704\pi$
$479$	−9.46166	−	4.21260i	−0.432314	−	0.192479i	−0.611344	+	0.791365i	$0.709371\pi$
$480$	−0.710913	+	1.57943i	−0.0324486	+	0.0720908i
$481$	−2.68086	−	2.97739i	−0.122237	−	0.135757i
$482$	−16.7739	+	7.46822i	−0.764030	+	0.340168i
$483$	20.9887	−	6.72546i	0.955019	−	0.306019i
$484$	8.33117	−	7.18273i	0.378690	−	0.326488i
$485$	17.7599			0.806435
$486$	−15.4668	−	1.94411i	−0.701586	−	0.0881866i
$487$	11.3536	−	34.9427i	0.514480	−	1.58341i	−0.269747	−	0.962931i	$-0.586940\pi$
$487$	11.3536	−	34.9427i	0.514480	−	1.58341i	0.784227	−	0.620474i	$-0.213060\pi$
$488$	−7.64855	+	8.49458i	−0.346234	+	0.384531i
$489$	0.667911	−	0.911488i	0.0302040	−	0.0412189i
$490$	0.377816	+	3.59467i	0.0170680	+	0.162391i
$491$	10.5033	+	2.23253i	0.474005	+	0.100753i	0.438719	−	0.898624i	$-0.355432\pi$
$491$	10.5033	+	2.23253i	0.474005	+	0.100753i	0.0352862	+	0.999377i	$0.488766\pi$
$492$	3.20965	−	1.83574i	0.144702	−	0.0827616i
$493$	−0.0485392	+	0.461820i	−0.00218610	+	0.0207993i
$494$	−14.0971			−0.634261
$495$	8.44556	−	5.26047i	0.379600	−	0.236440i
$496$	7.46047			0.334985
$497$	1.67559	−	15.9422i	0.0751605	−	0.715104i
$498$	15.1976	+	8.85686i	0.681019	+	0.396885i
$499$	5.75825	+	1.22395i	0.257775	+	0.0547917i	0.334986	−	0.942223i	$-0.391268\pi$
$499$	5.75825	+	1.22395i	0.257775	+	0.0547917i	−0.0772116	+	0.997015i	$0.524602\pi$
$500$	−0.104528	−	0.994522i	−0.00467465	−	0.0444764i
$501$	−2.68186	−	6.09004i	−0.119817	−	0.272083i
$502$	−13.7044	+	15.2203i	−0.611659	+	0.679316i
$503$	5.20108	−	16.0073i	0.231905	−	0.713730i	−0.765612	−	0.643303i	$-0.777564\pi$
$503$	5.20108	−	16.0073i	0.231905	−	0.713730i	0.997517	−	0.0704272i	$-0.0224362\pi$
$504$	2.72102	+	4.80268i	0.121204	+	0.213928i
$505$	−12.7745			−0.568456
$506$	3.83179	−	22.6144i	0.170344	−	1.00533i
$507$	−1.82751	−	1.65900i	−0.0811627	−	0.0736787i
$508$	−16.4103	+	7.30634i	−0.728090	+	0.324166i
$509$	4.14517	+	4.60368i	0.183732	+	0.204055i	0.827974	−	0.560767i	$-0.189494\pi$
$509$	4.14517	+	4.60368i	0.183732	+	0.204055i	−0.644242	+	0.764822i	$0.722827\pi$
$510$	−0.0599075	−	0.0831643i	−0.00265275	−	0.00368258i
$511$	−17.8346	−	7.94049i	−0.788958	−	0.351267i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	20.3940	+	6.90243i	0.900419	+	0.304750i
$514$	6.82803	−	21.0145i	0.301171	−	0.926910i
$515$	1.19159	−	11.3372i	0.0525077	−	0.499577i
$516$	8.65319	−	2.77276i	0.380936	−	0.122064i
$517$	1.84069	+	2.32377i	0.0809534	+	0.102199i
$518$	1.08339	−	1.87649i	0.0476015	−	0.0824483i
$519$	−0.176804	−	0.848742i	−0.00776082	−	0.0372556i
$520$	−3.32786	+	0.707358i	−0.145936	+	0.0310197i
$521$	7.83916	+	24.1265i	0.343440	+	1.05700i	0.962414	+	0.271588i	$0.0875487\pi$
$521$	7.83916	+	24.1265i	0.343440	+	1.05700i	−0.618974	+	0.785412i	$0.712451\pi$
$522$	−15.6097	−	17.6223i	−0.683220	−	0.771309i
$523$	−19.4029	+	14.0970i	−0.848430	+	0.616421i	−0.924713	−	0.380666i	$-0.875695\pi$
$523$	−19.4029	+	14.0970i	−0.848430	+	0.616421i	0.0762827	+	0.997086i	$0.475695\pi$
$524$	−1.80931	+	2.00945i	−0.0790402	+	0.0877830i
$525$	−2.75347	−	1.60467i	−0.120171	−	0.0700337i
$526$	16.6167	−	7.39824i	0.724524	−	0.322579i
$527$	−0.220739	+	0.382330i	−0.00961552	+	0.0166546i
$528$	5.74052	−	0.215541i	0.249824	−	0.00938024i
$529$	−12.4134	−	21.5007i	−0.539714	−	0.934812i
$530$	0.197016	+	0.143141i	0.00855784	+	0.00621763i
$531$	−17.0629	−	3.77205i	−0.740468	−	0.163693i
$532$	−2.35595	−	7.25088i	−0.102144	−	0.314365i
$533$	6.63503	+	2.95410i	0.287395	+	0.127956i
$534$	14.1018	+	1.54013i	0.610246	+	0.0666480i
$535$	8.02581	+	1.70594i	0.346986	+	0.0737541i
$536$	1.45765	+	1.61888i	0.0629607	+	0.0699250i
$537$	−6.44043	−	2.12160i	−0.277925	−	0.0915538i
$538$	−8.79884	−	15.2400i	−0.379345	−	0.657045i
$539$	10.1236	−	6.42044i	0.436053	−	0.276548i
$540$	5.16068	+	0.606110i	0.222080	+	0.0260828i
$541$	−32.1227	−	23.3385i	−1.38106	−	1.00340i	−0.996780	−	0.0801830i	$-0.974450\pi$
$541$	−32.1227	−	23.3385i	−1.38106	−	1.00340i	−0.384281	−	0.923216i	$-0.625550\pi$
$542$	28.2272	−	5.99988i	1.21246	−	0.257717i
$543$	12.9885	+	18.0307i	0.557388	+	0.773773i
$544$	−0.00618552	−	0.0588513i	−0.000265202	−	0.00252323i
$545$	−1.46057	−	13.8964i	−0.0625638	−	0.595255i
$546$	−4.45030	+	9.88721i	−0.190455	+	0.423133i
$547$	−12.0796	+	2.56760i	−0.516486	+	0.109783i	−0.458778	−	0.888551i	$-0.651713\pi$
$547$	−12.0796	+	2.56760i	−0.516486	+	0.109783i	−0.0577084	+	0.998333i	$0.518379\pi$
$548$	1.75630	+	1.27603i	0.0750256	+	0.0545093i
$549$	31.2127	+	14.2019i	1.33212	+	0.606121i
$550$	−2.80084	+	1.77631i	−0.119428	+	0.0757422i
$551$	16.2576	+	28.1591i	0.692599	+	1.19962i
$552$	8.93414	−	7.97883i	0.380262	−	0.339602i
$553$	10.4050	+	11.5559i	0.442465	+	0.491408i
$554$	−1.08902	−	0.231478i	−0.0462680	−	0.00983456i
$555$	−0.822035	−	1.86670i	−0.0348935	−	0.0792371i
$556$	3.58979	+	1.59828i	0.152241	+	0.0677821i
$557$	−3.82569	−	11.7743i	−0.162100	−	0.498891i	0.836711	−	0.547644i	$-0.184475\pi$
$557$	−3.82569	−	11.7743i	−0.162100	−	0.498891i	−0.998811	+	0.0487530i	$0.984475\pi$
$558$	−6.74299	−	21.3415i	−0.285454	−	0.903458i
$559$	14.4397	+	10.4910i	0.610733	+	0.443724i
$560$	−0.919990	−	1.59347i	−0.0388767	−	0.0673364i
$561$	−0.158803	+	0.300564i	−0.00670467	+	0.0126898i
$562$	13.9365	−	24.1387i	0.587874	−	1.01823i
$563$	18.8205	−	8.37942i	0.793189	−	0.353151i	0.0301851	−	0.999544i	$-0.490390\pi$
$563$	18.8205	−	8.37942i	0.793189	−	0.353151i	0.763004	+	0.646394i	$0.223724\pi$
$564$	−0.00629177	+	1.54813i	−0.000264931	+	0.0651880i
$565$	−10.4117	+	11.5633i	−0.438022	+	0.486473i
$566$	11.6853	−	8.48985i	0.491169	−	0.356855i
$567$	11.2793	−	12.1246i	0.473685	−	0.509185i
$568$	−2.69217	−	8.28565i	−0.112961	−	0.347658i
$569$	34.2240	−	7.27454i	1.43475	−	0.304964i	0.576035	−	0.817425i	$-0.304599\pi$
$569$	34.2240	−	7.27454i	1.43475	−	0.304964i	0.858711	+	0.512461i	$0.171266\pi$
$570$	−6.81649	−	2.24548i	−0.285511	−	0.0940528i
$571$	−18.2089	+	31.5387i	−0.762018	+	1.31985i	0.179790	+	0.983705i	$0.442458\pi$
$571$	−18.2089	+	31.5387i	−0.762018	+	1.31985i	−0.941809	+	0.336149i	$0.890875\pi$
$572$	7.00632	+	8.84512i	0.292949	+	0.369833i
$573$	8.09134	+	7.34524i	0.338020	+	0.306852i
$574$	−0.410582	+	3.90643i	−0.0171374	+	0.163051i
$575$	−2.13707	+	6.57722i	−0.0891219	+	0.274289i
$576$	2.41264	+	1.78302i	0.100527	+	0.0742927i
$577$	−34.5968	+	25.1361i	−1.44028	+	1.04643i	−0.452302	+	0.891865i	$0.649397\pi$
$577$	−34.5968	+	25.1361i	−1.44028	+	1.04643i	−0.987983	+	0.154563i	$0.950603\pi$
$578$	−15.5271	−	6.91310i	−0.645841	−	0.287547i
$579$	−18.2399	+	1.84218i	−0.758026	+	0.0765583i
$580$	5.25082	+	5.83163i	0.218028	+	0.242145i
$581$	−17.0706	+	7.60033i	−0.708209	+	0.315315i
$582$	6.51781	−	30.0626i	0.270172	−	1.24613i
$583$	0.134930	−	0.796332i	0.00558824	−	0.0329807i
$584$	−10.6101			−0.439051
$585$	5.03129	+	8.88037i	0.208018	+	0.367158i
$586$	−2.61354	+	8.04364i	−0.107964	+	0.332280i
$587$	−30.9329	+	34.3544i	−1.27674	+	1.41796i	−0.415631	+	0.909533i	$0.636439\pi$
$587$	−30.9329	+	34.3544i	−1.27674	+	1.41796i	−0.861106	+	0.508426i	$0.830228\pi$
$588$	6.22345	+	0.679694i	0.256651	+	0.0280301i
$589$	3.23126	+	30.7434i	0.133142	+	1.26676i
$590$	5.69767	+	1.21108i	0.234569	+	0.0498593i
$591$	0.00349158	−	0.859125i	0.000143625	−	0.0353397i
$592$	0.123094	−	1.17116i	0.00505914	−	0.0481345i
$593$	19.4576			0.799027			0.399513	−	0.916727i	$-0.369179\pi$
$593$	19.4576			0.799027			0.399513	+	0.916727i	$0.369179\pi$
$594$	−5.80503	−	16.2266i	−0.238183	−	0.665784i
$595$	0.108882			0.00446371
$596$	−0.158800	+	1.51088i	−0.00650472	+	0.0618883i
$597$	−0.0567223	+	13.9569i	−0.00232149	+	0.571216i
$598$	23.0144	+	4.89187i	0.941130	+	0.200043i
$599$	1.05049	+	9.99472i	0.0429218	+	0.408373i	0.994796	+	0.101885i	$0.0324874\pi$
$599$	1.05049	+	9.99472i	0.0429218	+	0.408373i	−0.951874	+	0.306488i	$0.900846\pi$
$600$	−1.72181	−	0.188048i	−0.0702927	−	0.00767702i
$601$	−12.6462	+	14.0451i	−0.515851	+	0.572910i	−0.943642	−	0.330967i	$-0.892625\pi$
$601$	−12.6462	+	14.0451i	−0.515851	+	0.572910i	0.427791	+	0.903877i	$0.359292\pi$
$602$	−2.98288	+	9.18035i	−0.121573	+	0.374163i
$603$	3.31352	−	5.63295i	0.134937	−	0.229391i
$604$	−22.7145			−0.924240
$605$	9.40565	+	5.70383i	0.382394	+	0.231894i
$606$	−4.68817	+	21.6236i	−0.190444	+	0.878400i
$607$	24.6580	−	10.9785i	1.00084	−	0.445602i	0.160133	−	0.987095i	$-0.448808\pi$
$607$	24.6580	−	10.9785i	1.00084	−	0.445602i	0.840705	+	0.541494i	$0.182141\pi$
$608$	−2.77257	−	3.07925i	−0.112442	−	0.124880i
$609$	24.8821	−	2.51301i	1.00827	−	0.101832i
$610$	−10.4424	−	4.64924i	−0.422799	−	0.188242i
$611$	−2.46019	+	1.78743i	−0.0995285	+	0.0723117i
$612$	−0.162760	+	0.0708859i	−0.00657918	+	0.00286539i
$613$	−8.82241	+	27.1526i	−0.356334	+	1.09668i	0.598898	+	0.800825i	$0.295605\pi$
$613$	−8.82241	+	27.1526i	−0.356334	+	1.09668i	−0.955232	+	0.295858i	$0.904395\pi$
$614$	−0.152909	+	1.45483i	−0.00617091	+	0.0587122i
$615$	2.73773	+	2.48529i	0.110396	+	0.100216i
$616$	−3.37858	+	5.08193i	−0.136127	+	0.204757i
$617$	22.9901	−	39.8201i	0.925548	−	1.60310i	0.134872	−	0.990863i	$-0.456938\pi$
$617$	22.9901	−	39.8201i	0.925548	−	1.60310i	0.790677	−	0.612234i	$-0.209729\pi$
$618$	−18.7535	−	6.17774i	−0.754374	−	0.248505i
$619$	27.7094	−	5.88982i	1.11374	−	0.236732i	0.385939	−	0.922524i	$-0.373878\pi$
$619$	27.7094	−	5.88982i	1.11374	−	0.236732i	0.727797	+	0.685793i	$0.240544\pi$
$620$	2.30541	+	7.09533i	0.0925876	+	0.284955i
$621$	−30.8993	−	18.3456i	−1.23994	−	0.736183i
$622$	−20.4808	+	14.8801i	−0.821204	+	0.596639i
$623$	−10.0836	+	11.1989i	−0.403989	+	0.448675i
$624$	−0.0239488	+	5.89274i	−0.000958717	+	0.235898i
$625$	0.913545	−	0.406737i	0.0365418	−	0.0162695i
$626$	2.54894	−	4.41489i	0.101876	−	0.176455i
$627$	3.37453	+	23.5624i	0.134766	+	0.940991i
$628$	8.89088	+	15.3995i	0.354785	+	0.614505i
$629$	0.0563770	+	0.0409603i	0.00224790	+	0.00163319i
$630$	−3.72678	+	4.07196i	−0.148478	+	0.162231i
$631$	5.39955	+	16.6181i	0.214953	+	0.661556i	0.999157	+	0.0410536i	$0.0130714\pi$
$631$	5.39955	+	16.6181i	0.214953	+	0.661556i	−0.784204	+	0.620503i	$0.786929\pi$
$632$	7.72055	+	3.43741i	0.307107	+	0.136733i
$633$	14.3995	+	32.6988i	0.572329	+	1.29966i
$634$	11.5538	+	2.45585i	0.458862	+	0.0975341i
$635$	−12.0198	−	13.3493i	−0.476991	−	0.529753i
$636$	0.314602	−	0.280962i	0.0124748	−	0.0111409i
$637$	6.14859	+	10.6497i	0.243616	+	0.421955i
$638$	9.58804	−	24.1958i	0.379594	−	0.957922i
$639$	−21.2687	+	15.1901i	−0.841379	+	0.600910i
$640$	−0.809017	−	0.587785i	−0.0319792	−	0.0232343i
$641$	43.6909	−	9.28678i	1.72569	−	0.366806i	0.764911	−	0.644136i	$-0.222783\pi$
$641$	43.6909	−	9.28678i	1.72569	−	0.366806i	0.960775	+	0.277330i	$0.0894495\pi$
$642$	5.83312	−	12.9594i	0.230215	−	0.511467i
$643$	0.977774	+	9.30290i	0.0385597	+	0.366871i	0.996738	+	0.0807003i	$0.0257157\pi$
$643$	0.977774	+	9.30290i	0.0385597	+	0.366871i	−0.958179	+	0.286170i	$0.907618\pi$
$644$	1.33010	+	12.6550i	0.0524132	+	0.498678i
$645$	5.31104	+	7.37284i	0.209122	+	0.290305i
$646$	0.239838	−	0.0509791i	0.00943629	−	0.00200574i
$647$	−14.6295	−	10.6289i	−0.575144	−	0.417866i	0.261826	−	0.965115i	$-0.415675\pi$
$647$	−14.6295	−	10.6289i	−0.575144	−	0.417866i	−0.836970	+	0.547249i	$0.815675\pi$
$648$	2.91993	−	8.51317i	0.114706	−	0.334429i
$649$	−4.79899	−	18.7137i	−0.188377	−	0.734576i
$650$	−1.70110	−	2.94639i	−0.0667227	−	0.115567i
$651$	22.5823	+	7.43905i	0.885071	+	0.291559i
$652$	0.436548	+	0.484835i	0.0170965	+	0.0189876i
$653$	−39.9406	−	8.48963i	−1.56299	−	0.332225i	−0.656462	−	0.754359i	$-0.727948\pi$
$653$	−39.9406	−	8.48963i	−1.56299	−	0.332225i	−0.906533	+	0.422135i	$0.861281\pi$
$654$	−24.0587	−	2.62757i	−0.940770	−	0.102746i
$655$	−2.47020	−	1.09981i	−0.0965189	−	0.0429730i
$656$	0.659682	+	2.03029i	0.0257563	+	0.0792696i
$657$	9.58976	+	30.3515i	0.374132	+	1.18412i
$658$	−1.33052	−	0.966678i	−0.0518690	−	0.0376850i
$659$	−7.78311	−	13.4807i	−0.303187	−	0.525135i	0.673669	−	0.739033i	$-0.264717\pi$
$659$	−7.78311	−	13.4807i	−0.303187	−	0.525135i	−0.976856	+	0.213898i	$0.931384\pi$
$660$	1.97891	+	5.39295i	0.0770290	+	0.209920i
$661$	1.30737	−	2.26444i	0.0508510	−	0.0880765i	−0.839479	−	0.543391i	$-0.817140\pi$
$661$	1.30737	−	2.26444i	0.0508510	−	0.0880765i	0.890330	+	0.455315i	$0.150473\pi$
$662$	3.64257	−	1.62178i	0.141573	−	0.0630322i
$663$	−0.301279	−	0.175580i	−0.0117007	−	0.00681897i
$664$	−6.79543	+	7.54709i	−0.263714	+	0.292884i
$665$	6.16796	−	4.48129i	0.239183	−	0.173777i
$666$	−3.46150	+	0.706407i	−0.134130	+	0.0273727i
$667$	−16.7701	−	51.6129i	−0.649339	−	1.99846i
$668$	3.75796	−	0.798780i	0.145400	−	0.0309057i
$669$	−8.92492	−	42.8439i	−0.345057	−	1.65644i
$670$	−1.08921	+	1.88657i	−0.0420798	+	0.0728844i
$671$	1.57641	+	37.8782i	0.0608565	+	1.46227i
$672$	−3.03494	+	0.972492i	−0.117075	+	0.0375147i
$673$	0.479256	−	4.55982i	0.0184740	−	0.175768i	−0.981394	−	0.192004i	$-0.938501\pi$
$673$	0.479256	−	4.55982i	0.0184740	−	0.175768i	0.999868	+	0.0162355i	$0.00516815\pi$
$674$	−5.81220	+	17.8881i	−0.223878	+	0.689025i
$675$	1.01829	+	5.09540i	0.0391941	+	0.196122i
$676$	1.15287	−	0.837608i	0.0443411	−	0.0322157i
$677$	−29.5279	−	13.1467i	−1.13485	−	0.505268i	−0.248660	−	0.968591i	$-0.579990\pi$
$677$	−29.5279	−	13.1467i	−1.13485	−	0.505268i	−0.886189	+	0.463323i	$0.846657\pi$
$678$	15.7525	+	21.8678i	0.604971	+	0.839827i
$679$	21.8657	+	24.2844i	0.839130	+	0.931948i
$680$	0.0540595	−	0.0240688i	0.00207309	−	0.000922998i
$681$	4.26141	+	3.86847i	0.163298	+	0.148240i
$682$	17.6837	−	17.3070i	0.677144	−	0.662719i
$683$	42.6656			1.63255			0.816276	−	0.577662i	$-0.196035\pi$
$683$	42.6656			1.63255			0.816276	+	0.577662i	$0.196035\pi$
$684$	−6.30260	+	10.7144i	−0.240986	+	0.409673i
$685$	−0.670848	+	2.06466i	−0.0256318	+	0.0788865i
$686$	−13.0684	+	14.5139i	−0.498954	+	0.554144i
$687$	−12.6462	−	28.7175i	−0.482484	−	1.09564i
$688$	0.548371	+	5.21740i	0.0209064	+	0.198912i
$689$	0.810417	+	0.172260i	0.0308744	+	0.00656257i
$690$	10.3491	+	6.03128i	0.393984	+	0.229607i
$691$	2.32675	−	22.1375i	0.0885136	−	0.842151i	−0.856726	−	0.515772i	$-0.827505\pi$
$691$	2.32675	−	22.1375i	0.0885136	−	0.842151i	0.945239	−	0.326378i	$-0.105828\pi$
$692$	0.500541			0.0190277
$693$	17.5911	+	5.07160i	0.668230	+	0.192654i
$694$	−30.3692			−1.15280
$695$	−0.410747	+	3.90799i	−0.0155805	+	0.148239i
$696$	11.7984	−	6.74801i	0.447216	−	0.255783i
$697$	−0.123566	−	0.0262647i	−0.00468039	−	0.000994848i
$698$	−2.84795	−	27.0965i	−0.107797	−	1.02562i
$699$	4.29116	−	5.85607i	0.162306	−	0.221497i
$700$	1.23119	−	1.36737i	0.0465345	−	0.0516818i
$701$	8.49329	−	26.1396i	0.320787	−	0.987281i	−0.652520	−	0.757772i	$-0.726288\pi$
$701$	8.49329	−	26.1396i	0.320787	−	0.987281i	0.973307	−	0.229509i	$-0.0737120\pi$
$702$	16.8785	−	5.25752i	0.637037	−	0.198432i
$703$	4.87948			0.184033
$704$	−0.554071	+	3.27002i	−0.0208823	+	0.123243i
$705$	−1.47430	+	0.472415i	−0.0555255	+	0.0177922i
$706$	−15.0328	+	6.69303i	−0.565766	+	0.251895i
$707$	−15.7277	−	17.4674i	−0.591502	−	0.656930i
$708$	4.14104	−	9.20013i	0.155630	−	0.345762i
$709$	−18.2187	−	8.11150i	−0.684219	−	0.304634i	0.0350300	−	0.999386i	$-0.488847\pi$
$709$	−18.2187	−	8.11150i	−0.684219	−	0.304634i	−0.719249	+	0.694752i	$0.755514\pi$
$710$	7.04819	−	5.12081i	0.264514	−	0.192181i
$711$	2.85503	−	25.1923i	0.107072	−	0.944786i
$712$	−2.53088	+	7.78926i	−0.0948488	+	0.291915i
$713$	5.39308	−	51.3117i	0.201972	−	1.92164i
$714$	0.0399591	−	0.184307i	0.00149543	−	0.00689750i
$715$	−6.24714	+	9.39670i	−0.233630	+	0.351417i
$716$	1.95747	−	3.39044i	0.0731541	−	0.126707i
$717$	−9.85917	+	8.80495i	−0.368197	+	0.328827i
$718$	−14.1873	+	3.01560i	−0.529465	+	0.112541i
$719$	15.6310	+	48.1073i	0.582939	+	1.79410i	0.607395	+	0.794400i	$0.292214\pi$
$719$	15.6310	+	48.1073i	0.582939	+	1.79410i	−0.0244567	+	0.999701i	$0.507786\pi$
$720$	−0.950211	+	2.84554i	−0.0354123	+	0.106047i
$721$	16.9692	−	12.3289i	0.631967	−	0.459151i
$722$	−1.22525	+	1.36077i	−0.0455989	+	0.0506427i
$723$	−27.6064	+	15.7893i	−1.02669	+	0.587211i
$724$	−11.7206	+	5.21833i	−0.435591	+	0.193938i
$725$	−3.92361	+	6.79590i	−0.145719	+	0.252393i
$726$	13.1068	−	13.8279i	0.486441	−	0.513201i
$727$	10.0253	+	17.3643i	0.371817	+	0.644006i	0.989845	−	0.142150i	$-0.0454016\pi$
$727$	10.0253	+	17.3643i	0.371817	+	0.644006i	−0.618028	+	0.786156i	$0.712068\pi$
$728$	−5.06443	−	3.67953i	−0.187700	−	0.136372i
$729$	−26.9920	−	0.658317i	−0.999703	−	0.0243821i
$730$	−3.27871	−	10.0908i	−0.121351	−	0.373479i
$731$	−0.283604	−	0.126268i	−0.0104895	−	0.00467021i
$732$	−11.7022	+	15.9698i	−0.432525	+	0.590260i
$733$	2.79509	+	0.594115i	0.103239	+	0.0219441i	0.259241	−	0.965813i	$-0.416527\pi$
$733$	2.79509	+	0.594115i	0.103239	+	0.0219441i	−0.156002	+	0.987757i	$0.549861\pi$
$734$	−8.04201	−	8.93156i	−0.296836	−	0.329670i
$735$	1.27672	+	6.12889i	0.0470927	+	0.226067i
$736$	3.45785	+	5.98917i	0.127458	+	0.220764i
$737$	7.21060	+	0.455782i	0.265606	+	0.0167889i
$738$	5.21164	−	3.72213i	0.191843	−	0.137014i
$739$	13.9563	+	10.1398i	0.513389	+	0.372999i	0.814108	−	0.580714i	$-0.197226\pi$
$739$	13.9563	+	10.1398i	0.513389	+	0.372999i	−0.300718	+	0.953713i	$0.597226\pi$
$740$	1.15188	−	0.244840i	0.0423439	−	0.00900048i
$741$	−24.2934	+	2.45356i	−0.892440	+	0.0901338i
$742$	0.0468373	+	0.445627i	0.00171945	+	0.0163595i
$743$	−0.837936	−	7.97242i	−0.0307409	−	0.292480i	−0.999082	−	0.0428477i	$-0.986357\pi$
$743$	−0.837936	−	7.97242i	−0.0307409	−	0.292480i	0.968341	−	0.249632i	$-0.0803097\pi$
$744$	12.8565	−	1.29847i	0.471343	−	0.0476042i
$745$	−1.48601	+	0.315861i	−0.0544432	+	0.0115722i
$746$	−11.1758	−	8.11970i	−0.409176	−	0.297283i
$747$	27.7312	+	12.6178i	1.01463	+	0.461661i
$748$	−0.151186	−	0.125147i	−0.00552792	−	0.00457583i
$749$	7.54862	+	13.0746i	0.275820	+	0.477735i
$750$	−0.353225	−	1.69565i	−0.0128980	−	0.0619164i
$751$	25.9795	+	28.8531i	0.948004	+	1.05287i	0.998533	+	0.0541427i	$0.0172426\pi$
$751$	25.9795	+	28.8531i	0.948004	+	1.05287i	−0.0505290	+	0.998723i	$0.516091\pi$
$752$	−0.874288	−	0.185836i	−0.0318820	−	0.00677673i
$753$	−20.9676	+	28.6142i	−0.764102	+	1.04276i
$754$	24.3897	+	10.8590i	0.888221	+	0.395461i
$755$	−7.01917	−	21.6028i	−0.255454	−	0.786206i
$756$	5.52498	+	7.80280i	0.200942	+	0.283785i
$757$	−25.5859	−	18.5892i	−0.929935	−	0.675637i	0.0160418	−	0.999871i	$-0.494894\pi$
$757$	−25.5859	−	18.5892i	−0.929935	−	0.675637i	−0.945977	+	0.324234i	$0.894894\pi$
$758$	0.408527	+	0.707590i	0.0148384	+	0.0257008i
$759$	2.66729	−	39.6380i	0.0968166	−	1.43877i
$760$	2.07177	−	3.58841i	0.0751509	−	0.130165i
$761$	−21.7564	+	9.68659i	−0.788671	+	0.351139i	−0.761228	−	0.648485i	$-0.775403\pi$
$761$	−21.7564	+	9.68659i	−0.788671	+	0.351139i	−0.0274428	+	0.999623i	$0.508736\pi$
$762$	−27.0080	+	15.4471i	−0.978396	+	0.559588i
$763$	17.2033	−	19.1061i	0.622800	−	0.691689i
$764$	−5.10434	+	3.70852i	−0.184669	+	0.134170i
$765$	−0.117712	−	0.132889i	−0.00425589	−	0.00480461i
$766$	2.69759	+	8.30233i	0.0974679	+	0.299975i
$767$	19.3846	−	4.12033i	0.699938	−	0.148777i
$768$	−1.29186	+	1.15373i	−0.0466161	+	0.0416316i
$769$	−4.88460	+	8.46037i	−0.176143	+	0.305089i	−0.940556	−	0.339638i	$-0.889695\pi$
$769$	−4.88460	+	8.46037i	−0.176143	+	0.305089i	0.764413	+	0.644727i	$0.223029\pi$
$770$	−5.87724	−	1.64282i	−0.211801	−	0.0592030i
$771$	8.10913	−	37.4024i	0.292043	−	1.34701i
$772$	1.10637	−	10.5264i	0.0398192	−	0.378854i
$773$	7.32474	−	22.5432i	0.263452	−	0.810823i	−0.728593	−	0.684946i	$-0.759826\pi$
$773$	7.32474	−	22.5432i	0.263452	−	0.810823i	0.992046	−	0.125877i	$-0.0401744\pi$
$774$	14.4293	−	6.28432i	0.518651	−	0.225885i
$775$	−6.03565	+	4.38516i	−0.216807	+	0.157519i
$776$	16.2245	+	7.22360i	0.582424	+	0.259312i
$777$	1.54040	−	3.42229i	0.0552614	−	0.122774i
$778$	−18.5818	−	20.6372i	−0.666189	−	0.739878i
$779$	−8.08079	+	3.59780i	−0.289524	+	0.128905i
$780$	−5.61173	+	1.79818i	−0.200932	+	0.0643852i
$781$	−25.6025	−	13.3943i	−0.916131	−	0.479285i
$782$	−0.409240			−0.0146344
$783$	−29.9671	−	27.6515i	−1.07094	−	0.988183i
$784$	−1.11693	+	3.43757i	−0.0398905	+	0.122770i
$785$	−11.8983	+	13.2144i	−0.424669	+	0.471643i
$786$	−2.76822	+	3.77775i	−0.0987392	+	0.134748i
$787$	−1.09591	−	10.4269i	−0.0390650	−	0.371679i	−0.996537	−	0.0831523i	$-0.973501\pi$
$787$	−1.09591	−	10.4269i	−0.0390650	−	0.371679i	0.957472	−	0.288527i	$-0.0931655\pi$
$788$	0.485181	+	0.103128i	0.0172839	+	0.00367380i
$789$	27.3477	−	15.6414i	0.973604	−	0.556847i
$790$	−0.883390	+	8.40490i	−0.0314296	+	0.299033i
$791$	−28.6301			−1.01797
$792$	9.85503	−	1.37056i	0.350183	−	0.0487006i
$793$	−38.8891			−1.38099
$794$	−1.60842	+	15.3031i	−0.0570807	+	0.543087i
$795$	0.364428	+	0.212382i	0.0129249	+	0.00753241i
$796$	−7.88198	−	1.67537i	−0.279369	−	0.0593818i
$797$	4.17252	+	39.6989i	0.147798	+	1.40621i	0.777263	+	0.629176i	$0.216608\pi$
$797$	4.17252	+	39.6989i	0.147798	+	1.40621i	−0.629464	+	0.777029i	$0.716726\pi$
$798$	−5.32197	−	12.0853i	−0.188396	−	0.427814i
$799$	0.0353918	−	0.0393066i	0.00125207	−	0.00139057i
$800$	0.309017	−	0.951057i	0.0109254	−	0.0336249i
$801$	24.5695	+	0.199710i	0.868121	+	0.00705640i
$802$	−35.5126			−1.25399
$803$	−25.1494	+	24.6137i	−0.887504	+	0.868597i
$804$	2.79370	+	2.53609i	0.0985262	+	0.0894411i
$805$	−11.6246	+	5.17562i	−0.409714	+	0.182417i
$806$	16.9839	+	18.8625i	0.598232	+	0.664404i
$807$	−17.8154	−	24.7315i	−0.627131	−	0.870590i
$808$	−11.6700	−	5.19584i	−0.410551	−	0.182789i
$809$	−19.2713	+	14.0014i	−0.677543	+	0.492264i	−0.872542	−	0.488539i	$-0.837530\pi$
$809$	−19.2713	+	14.0014i	−0.677543	+	0.492264i	0.194998	+	0.980804i	$0.437530\pi$
$810$	8.99881	+	0.146301i	0.316186	+	0.00514049i
$811$	12.1317	−	37.3377i	0.426003	−	1.31110i	−0.476027	−	0.879431i	$-0.657924\pi$
$811$	12.1317	−	37.3377i	0.426003	−	1.31110i	0.902030	−	0.431673i	$-0.142076\pi$
$812$	−1.50926	+	14.3596i	−0.0529646	+	0.503925i
$813$	47.5993	−	15.2523i	1.66938	−	0.534923i
$814$	−2.42512	−	3.06159i	−0.0850003	−	0.107309i
$815$	−0.326205	+	0.565004i	−0.0114265	+	0.0197912i
$816$	−0.0209023	−	0.100341i	−0.000731726	−	0.00351264i
$817$	−21.2626	+	4.51950i	−0.743883	+	0.158117i
$818$	10.4470	+	32.1526i	0.365272	+	1.12419i
$819$	−5.94830	+	17.8130i	−0.207851	+	0.622438i
$820$	−1.72707	+	1.25479i	−0.0603119	+	0.0438192i
$821$	−24.2315	+	26.9118i	−0.845684	+	0.939227i	−0.998800	−	0.0489810i	$-0.984403\pi$
$821$	−24.2315	+	26.9118i	−0.845684	+	0.939227i	0.153116	+	0.988208i	$0.451069\pi$
$822$	3.24870	+	1.89328i	0.113311	+	0.0660358i
$823$	13.4943	−	6.00807i	0.470383	−	0.209428i	−0.157835	−	0.987466i	$-0.550451\pi$
$823$	13.4943	−	6.00807i	0.470383	−	0.209428i	0.628218	+	0.778038i	$0.283785\pi$
$824$	5.69983	−	9.87239i	0.198563	−	0.343921i
$825$	−4.51748	+	3.54857i	−0.157279	+	0.123545i
$826$	5.35891	+	9.28190i	0.186460	+	0.322958i
$827$	−27.7418	−	20.1556i	−0.964677	−	0.700879i	−0.0104446	−	0.999945i	$-0.503325\pi$
$827$	−27.7418	−	20.1556i	−0.964677	−	0.700879i	−0.954232	+	0.299067i	$0.903325\pi$
$828$	14.0074	−	15.3047i	0.486790	−	0.531877i
$829$	3.33907	+	10.2766i	0.115971	+	0.356921i	0.992148	−	0.125068i	$-0.0399148\pi$
$829$	3.33907	+	10.2766i	0.115971	+	0.356921i	−0.876178	+	0.481988i	$0.839915\pi$
$830$	−9.27762	−	4.13066i	−0.322031	−	0.143377i
$831$	−1.91698	−	0.209363i	−0.0664992	−	0.00726271i
$832$	−3.32786	−	0.707358i	−0.115373	−	0.0245232i
$833$	−0.143119	−	0.158950i	−0.00495879	−	0.00550729i
$834$	6.46441	+	2.12950i	0.223844	+	0.0737385i
$835$	1.92096	+	3.32720i	0.0664775	+	0.115142i
$836$	−13.7152	−	0.866935i	−0.474350	−	0.0299836i
$837$	−15.3345	−	35.6039i	−0.530038	−	1.23065i
$838$	−7.37965	−	5.36163i	−0.254926	−	0.185214i
$839$	31.3284	−	6.65906i	1.08158	−	0.229896i	0.367542	−	0.930007i	$-0.380199\pi$
$839$	31.3284	−	6.65906i	1.08158	−	0.229896i	0.714035	+	0.700110i	$0.246866\pi$
$840$	−1.86274	−	2.58588i	−0.0642707	−	0.0892213i
$841$	−3.40543	−	32.4005i	−0.117429	−	1.11726i
$842$	−2.52571	−	24.0306i	−0.0870419	−	0.828148i
$843$	19.8152	−	44.0233i	0.682473	−	1.51624i
$844$	−20.1774	+	4.28883i	−0.694533	+	0.147628i
$845$	1.15287	+	0.837608i	0.0396599	+	0.0288146i
$846$	0.258604	+	2.66896i	0.00889099	+	0.0917608i
$847$	3.78086	+	19.8835i	0.129912	+	0.683205i
$848$	0.121763	+	0.210899i	0.00418135	+	0.00724231i
$849$	18.6594	−	16.6642i	0.640390	−	0.571914i
$850$	0.0395961	+	0.0439760i	0.00135814	+	0.00150836i
$851$	−7.96605	−	1.69324i	−0.273073	−	0.0580434i
$852$	−6.08146	−	13.8100i	−0.208347	−	0.473121i
$853$	−14.2977	−	6.36575i	−0.489545	−	0.217959i	0.147093	−	0.989123i	$-0.453008\pi$
$853$	−14.2977	−	6.36575i	−0.489545	−	0.217959i	−0.636637	+	0.771163i	$0.719675\pi$
$854$	−6.49926	−	20.0027i	−0.222400	−	0.684477i
$855$	−12.1376	−	2.68321i	−0.415096	−	0.0917640i
$856$	6.63807	+	4.82284i	0.226885	+	0.164841i
$857$	−8.16092	−	14.1351i	−0.278772	−	0.482847i	0.692308	−	0.721602i	$-0.256594\pi$
$857$	−8.16092	−	14.1351i	−0.278772	−	0.482847i	−0.971080	+	0.238755i	$0.923261\pi$
$858$	13.6133	+	14.0232i	0.464752	+	0.478745i
$859$	15.8280	−	27.4149i	0.540045	−	0.935385i	−0.458856	−	0.888511i	$-0.651741\pi$
$859$	15.8280	−	27.4149i	0.540045	−	0.935385i	0.998901	−	0.0468742i	$-0.0149260\pi$
$860$	−4.79259	+	2.13380i	−0.163426	+	0.0727619i
$861$	−0.0276496	+	6.80335i	−0.000942295	+	0.231857i
$862$	1.96462	−	2.18193i	0.0669151	−	0.0743168i
$863$	−6.88978	+	5.00572i	−0.234531	+	0.170397i	−0.698843	−	0.715275i	$-0.746302\pi$
$863$	−6.88978	+	5.00572i	−0.234531	+	0.170397i	0.464312	+	0.885672i	$0.346302\pi$
$864$	4.46799	+	2.65275i	0.152004	+	0.0902483i
$865$	0.154676	+	0.476042i	0.00525913	+	0.0161859i
$866$	−11.1741	+	2.37514i	−0.379713	+	0.0807104i
$867$	−27.9608	−	9.21080i	−0.949597	−	0.312815i
$868$	−6.86356	+	11.8880i	−0.232964	+	0.403506i
$869$	26.2744	−	9.76255i	0.891297	−	0.331172i
$870$	10.0636	+	9.13566i	0.341189	+	0.309728i
$871$	−0.774704	+	7.37082i	−0.0262498	+	0.249751i
$872$	4.31786	−	13.2890i	0.146221	−	0.450023i
$873$	5.99975	−	52.9408i	0.203061	−	1.79177i
$874$	−23.1827	+	16.8432i	−0.784168	+	0.569731i
$875$	1.68091	+	0.748387i	0.0568250	+	0.0253001i
$876$	−18.2843	+	1.84666i	−0.617769	+	0.0623928i
$877$	−15.8613	−	17.6158i	−0.535599	−	0.594843i	0.413232	−	0.910626i	$-0.364400\pi$
$877$	−15.8613	−	17.6158i	−0.535599	−	0.594843i	−0.948832	+	0.315782i	$0.897733\pi$
$878$	6.70530	−	2.98539i	0.226293	−	0.100752i
$879$	−3.10390	+	14.3163i	−0.104692	+	0.482878i
$880$	−3.28119	+	0.483538i	−0.110609	+	0.0163001i
$881$	25.2116			0.849400			0.424700	−	0.905334i	$-0.360380\pi$
$881$	25.2116			0.849400			0.424700	+	0.905334i	$0.360380\pi$
$882$	10.8431	+	0.0881363i	0.365105	+	0.00296771i
$883$	−9.85752	+	30.3383i	−0.331732	+	1.02097i	0.636578	+	0.771213i	$0.280350\pi$
$883$	−9.85752	+	30.3383i	−0.331732	+	1.02097i	−0.968309	+	0.249753i	$0.919650\pi$
$884$	0.134714	−	0.149615i	0.00453092	−	0.00503210i
$885$	10.0295	+	1.09537i	0.337138	+	0.0368205i
$886$	−3.19131	−	30.3633i	−0.107214	−	1.02007i
$887$	−32.7179	−	6.95441i	−1.09856	−	0.233506i	−0.377245	−	0.926113i	$-0.623129\pi$
$887$	−32.7179	−	6.95441i	−1.09856	−	0.233506i	−0.721315	+	0.692607i	$0.756462\pi$
$888$	0.00828945	−	2.03967i	0.000278176	−	0.0684468i
$889$	3.45489	−	32.8711i	0.115873	−	1.10246i
$890$	−8.19011			−0.274533
$891$	−12.8279	−	26.9526i	−0.429751	−	0.902948i
$892$	25.2669			0.845999
$893$	0.387129	−	3.68329i	0.0129548	−	0.123257i
$894$	−0.0106940	+	2.63132i	−0.000357661	+	0.0880046i
$895$	3.82939	+	0.813962i	0.128002	+	0.0272078i
$896$	−0.192330	−	1.82990i	−0.00642530	−	0.0611327i
$897$	40.5118	+	4.42450i	1.35265	+	0.147730i
$898$	−15.3250	+	17.0202i	−0.511403	+	0.567970i
$899$	18.0911	−	55.6787i	0.603372	−	1.85699i
$900$	−2.99990	−	0.0243843i	−0.0999967	−	0.000812809i
$901$	−0.0144107			−0.000480091
$902$	6.27358	+	3.28210i	0.208887	+	0.109282i
$903$	−3.54254	+	16.3395i	−0.117888	+	0.543745i
$904$	−14.2148	+	6.32882i	−0.472776	+	0.210493i
$905$	−8.58478	−	9.53436i	−0.285368	−	0.316933i
$906$	−39.1435	+	3.95338i	−1.30046	+	0.131342i
$907$	−9.71445	−	4.32515i	−0.322563	−	0.143614i	0.239066	−	0.971003i	$-0.423159\pi$
$907$	−9.71445	−	4.32515i	−0.322563	−	0.143614i	−0.561629	+	0.827389i	$0.689825\pi$
$908$	−2.68827	+	1.95314i	−0.0892133	+	0.0648173i
$909$	−4.31554	+	38.0796i	−0.143137	+	1.26302i
$910$	1.93444	−	5.95360i	0.0641261	−	0.197360i
$911$	−4.48764	+	42.6970i	−0.148682	+	1.41462i	0.624794	+	0.780790i	$0.285183\pi$
$911$	−4.48764	+	42.6970i	−0.148682	+	1.41462i	−0.773476	+	0.633826i	$0.781484\pi$
$912$	−5.31385	−	4.82386i	−0.175959	−	0.159734i
$913$	1.40058	+	33.6532i	0.0463523	+	1.11376i
$914$	−6.48648	+	11.2349i	−0.214554	+	0.371618i
$915$	−18.8043	−	6.19450i	−0.621652	−	0.204784i
$916$	17.7206	−	3.76663i	0.585505	−	0.124453i
$917$	−1.53744	−	4.73175i	−0.0507707	−	0.156256i
$918$	−0.268144	+	0.150484i	−0.00885008	+	0.00496673i
$919$	22.8991	−	16.6372i	0.755372	−	0.548810i	−0.142115	−	0.989850i	$-0.545390\pi$
$919$	22.8991	−	16.6372i	0.755372	−	0.548810i	0.897487	+	0.441040i	$0.145390\pi$
$920$	−4.62750	+	5.13936i	−0.152564	+	0.169440i
$921$	−0.0102973	+	2.53370i	−0.000339306	+	0.0834883i
$922$	−31.9559	+	14.2277i	−1.05241	+	0.468564i
$923$	14.8201	−	25.6691i	0.487808	−	0.844909i
$924$	−4.93776	+	9.34563i	−0.162440	+	0.307449i
$925$	0.588807	+	1.01984i	0.0193598	+	0.0335322i
$926$	−16.9900	−	12.3440i	−0.558327	−	0.405649i
$927$	−33.3927	−	7.38203i	−1.09676	−	0.242458i
$928$	2.42493	+	7.46316i	0.0796021	+	0.244990i
$929$	−19.5634	−	8.71017i	−0.641853	−	0.285771i	0.0598863	−	0.998205i	$-0.480926\pi$
$929$	−19.5634	−	8.71017i	−0.641853	−	0.285771i	−0.701739	+	0.712434i	$0.747593\pi$
$930$	5.20780	+	11.8260i	0.170770	+	0.387790i
$931$	−14.6494	−	3.11383i	−0.480116	−	0.102052i
$932$	2.80470	+	3.11494i	0.0918711	+	0.102033i
$933$	−32.7043	+	29.2073i	−1.07069	+	0.956205i
$934$	−8.37165	−	14.5001i	−0.273929	−	0.474459i
$935$	0.0723028	−	0.182459i	0.00236456	−	0.00596706i
$936$	0.984340	+	10.1590i	0.0321742	+	0.332058i
$937$	18.3866	+	13.3587i	0.600665	+	0.436409i	0.846115	−	0.533000i	$-0.178936\pi$
$937$	18.3866	+	13.3587i	0.600665	+	0.436409i	−0.245450	+	0.969409i	$0.578936\pi$
$938$	−3.92066	+	0.833361i	−0.128014	+	0.0272102i
$939$	3.62415	−	8.05175i	0.118270	−	0.262759i
$940$	−0.0934297	−	0.888924i	−0.00304734	−	0.0289935i
$941$	1.43372	+	13.6409i	0.0467379	+	0.444682i	0.992718	+	0.120458i	$0.0384364\pi$
$941$	1.43372	+	13.6409i	0.0467379	+	0.444682i	−0.945980	+	0.324224i	$0.894897\pi$
$942$	18.0017	+	24.9902i	0.586528	+	0.814225i
$943$	14.4408	−	3.06950i	0.470259	−	0.0999566i
$944$	4.71249	+	3.42383i	0.153379	+	0.111436i
$945$	−5.71359	+	7.66577i	−0.185863	+	0.249368i
$946$	13.4033	+	11.0948i	0.435778	+	0.360723i
$947$	15.0566	+	26.0787i	0.489272	+	0.847444i	0.999924	−	0.0123434i	$-0.00392913\pi$
$947$	15.0566	+	26.0787i	0.489272	+	0.847444i	−0.510652	+	0.859788i	$0.670596\pi$
$948$	13.9030	+	4.57990i	0.451547	+	0.148748i
$949$	−24.1542	−	26.8259i	−0.784077	−	0.870806i
$950$	4.05299	+	0.861490i	0.131496	+	0.0279504i
$951$	20.3380	+	2.22121i	0.659505	+	0.0720278i
$952$	0.0994684	+	0.0442862i	0.00322379	+	0.00143532i
$953$	−3.91644	−	12.0536i	−0.126866	−	0.390453i	0.867370	−	0.497663i	$-0.165808\pi$
$953$	−3.91644	−	12.0536i	−0.126866	−	0.390453i	−0.994236	+	0.107210i	$0.965808\pi$
$954$	0.493248	−	0.538933i	0.0159695	−	0.0174486i
$955$	−5.10434	−	3.70852i	−0.165173	−	0.120005i
$956$	−3.81587	−	6.60928i	−0.123414	−	0.213759i
$957$	12.3117	−	43.3651i	0.397981	−	1.40179i
$958$	5.17854	−	8.96949i	0.167311	−	0.289791i
$959$	−3.64909	+	1.62468i	−0.117835	+	0.0524637i
$960$	−1.49647	−	0.872114i	−0.0482983	−	0.0281474i
$961$	16.4998	−	18.3249i	0.532253	−	0.591127i
$962$	3.24131	−	2.35495i	0.104504	−	0.0759266i
$963$	7.79658	−	23.3480i	0.251241	−	0.752378i
$964$	−5.67396	−	17.4627i	−0.182746	−	0.562434i
$965$	10.3531	−	2.20062i	0.333278	−	0.0708405i
$966$	4.49470	+	21.5767i	0.144615	+	0.694219i
$967$	15.8046	−	27.3744i	0.508242	−	0.880300i	−0.491713	−	0.870757i	$-0.663629\pi$
$967$	15.8046	−	27.3744i	0.508242	−	0.880300i	0.999954	−	0.00954284i	$-0.00303763\pi$
$968$	6.27254	+	9.03633i	0.201607	+	0.290439i
$969$	0.404436	−	0.129594i	0.0129923	−	0.00416317i
$970$	−1.85641	+	17.6626i	−0.0596059	+	0.567112i
$971$	−14.9331	+	45.9593i	−0.479225	+	1.47490i	0.360949	+	0.932586i	$0.382453\pi$
$971$	−14.9331	+	45.9593i	−0.479225	+	1.47490i	−0.840174	+	0.542317i	$0.817547\pi$
$972$	3.55017	−	15.1788i	0.113872	−	0.486861i
$973$	−5.84938	+	4.24983i	−0.187523	+	0.136243i
$974$	33.5645	+	14.9439i	1.07548	+	0.478833i
$975$	−3.44429	−	4.78140i	−0.110306	−	0.153127i
$976$	−7.64855	−	8.49458i	−0.244824	−	0.271905i
$977$	28.6548	−	12.7579i	0.916748	−	0.408162i	0.106542	−	0.994308i	$-0.466022\pi$
$977$	28.6548	−	12.7579i	0.916748	−	0.408162i	0.810206	+	0.586146i	$0.199355\pi$
$978$	0.836679	+	0.759529i	0.0267541	+	0.0242871i
$979$	12.0707	+	24.3342i	0.385781	+	0.777725i
$980$	−3.61447			−0.115460
$981$	−41.9173	−	0.340719i	−1.33832	−	0.0108783i
$982$	−3.31819	+	10.2123i	−0.105888	+	0.325889i
$983$	−37.0573	+	41.1563i	−1.18194	+	1.31268i	−0.242432	+	0.970168i	$0.577945\pi$
$983$	−37.0573	+	41.1563i	−1.18194	+	1.31268i	−0.939513	+	0.342514i	$0.888721\pi$
$984$	1.49019	+	3.38396i	0.0475054	+	0.107877i
$985$	0.0518482	+	0.493303i	0.00165202	+	0.0157179i
$986$	−0.454216	−	0.0965466i	−0.0144652	−	0.00307467i
$987$	−2.46111	−	1.43429i	−0.0783379	−	0.0456539i
$988$	1.47355	−	14.0199i	0.0468800	−	0.446033i
$989$	36.2807			1.15366
$990$	4.34885	+	8.94916i	0.138215	+	0.284423i
$991$	22.1307			0.703006			0.351503	−	0.936187i	$-0.385671\pi$
$991$	22.1307			0.703006			0.351503	+	0.936187i	$0.385671\pi$
$992$	−0.779832	+	7.41960i	−0.0247597	+	0.235573i
$993$	5.99492	−	3.42876i	0.190243	−	0.108808i
$994$	15.6797	+	3.33282i	0.497330	+	0.105711i
$995$	−0.842297	−	8.01392i	−0.0267026	−	0.254058i
$996$	−10.3969	+	14.1885i	−0.329439	+	0.449580i
$997$	−26.3436	+	29.2575i	−0.834310	+	0.926595i	−0.998205	−	0.0598826i	$-0.980927\pi$
$997$	−26.3436	+	29.2575i	−0.834310	+	0.926595i	0.163895	+	0.986478i	$0.447594\pi$
$998$	−1.81915	+	5.59876i	−0.0575841	+	0.177226i
$999$	−5.84219	+	1.81980i	−0.184839	+	0.0575759i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.bg.a.301.7	✓	88
9.7	even	3	inner	990.2.bg.a.961.3	yes	88
11.3	even	5	inner	990.2.bg.a.751.3	yes	88
99.25	even	15	inner	990.2.bg.a.421.7	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.bg.a.301.7	✓	88	1.1	even	1	trivial
990.2.bg.a.421.7	yes	88	99.25	even	15	inner
990.2.bg.a.751.3	yes	88	11.3	even	5	inner
990.2.bg.a.961.3	yes	88	9.7	even	3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.104528 + 0.994522i) q^{2} +(-0.00703919 + 1.73204i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-0.104528 - 0.994522i) q^{5} +(-1.72181 - 0.188048i) q^{6} +(1.23119 - 1.36737i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-2.99990 - 0.0243843i) q^{9} +1.00000 q^{10} +(-1.47381 - 2.97117i) q^{11} +(0.366996 - 1.69272i) q^{12} +(3.10807 - 1.38380i) q^{13} +(1.23119 + 1.36737i) q^{14} +(1.72328 - 0.174046i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-0.0478740 + 0.0347825i) q^{17} +(0.337826 - 2.98092i) q^{18} +(-1.28042 + 3.94074i) q^{19} +(-0.104528 + 0.994522i) q^{20} +(2.35967 + 2.14209i) q^{21} +(3.10895 - 1.15517i) q^{22} +(3.45785 - 5.98917i) q^{23} +(1.64509 + 0.541923i) q^{24} +(-0.978148 + 0.207912i) q^{25} +(1.05134 + 3.23569i) q^{26} +(0.0633513 - 5.19577i) q^{27} +(-1.48857 + 1.08151i) q^{28} +(5.25082 - 5.83163i) q^{29} +(-0.00703919 + 1.73204i) q^{30} +(6.81548 - 3.03445i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(5.15656 - 2.53179i) q^{33} +(-0.0295877 - 0.0512475i) q^{34} +(-1.48857 - 1.08151i) q^{35} +(2.92928 + 0.647566i) q^{36} +(-0.363903 - 1.11998i) q^{37} +(-3.78531 - 1.68533i) q^{38} +(2.37491 + 5.39302i) q^{39} +(-0.978148 - 0.207912i) q^{40} +(1.42844 + 1.58645i) q^{41} +(-2.37700 + 2.12284i) q^{42} +(2.62307 + 4.54329i) q^{43} +(0.823866 + 3.21267i) q^{44} +(0.289324 + 2.98602i) q^{45} +(5.59492 + 4.06494i) q^{46} +(-0.874288 + 0.185836i) q^{47} +(-0.710913 + 1.57943i) q^{48} +(0.377816 + 3.59467i) q^{49} +(-0.104528 - 0.994522i) q^{50} +(-0.0599075 - 0.0831643i) q^{51} +(-3.32786 + 0.707358i) q^{52} +(0.197016 + 0.143141i) q^{53} +(5.16068 + 0.606110i) q^{54} +(-2.80084 + 1.77631i) q^{55} +(-0.919990 - 1.59347i) q^{56} +(-6.81649 - 2.24548i) q^{57} +(5.25082 + 5.83163i) q^{58} +(5.69767 + 1.21108i) q^{59} +(-1.72181 - 0.188048i) q^{60} +(-10.4424 - 4.64924i) q^{61} +(2.30541 + 7.09533i) q^{62} +(-3.72678 + 4.07196i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-1.70110 - 2.94639i) q^{65} +(1.97891 + 5.39295i) q^{66} +(-1.08921 + 1.88657i) q^{67} +(0.0540595 - 0.0240688i) q^{68} +(10.3491 + 6.03128i) q^{69} +(1.23119 - 1.36737i) q^{70} +(7.04819 - 5.12081i) q^{71} +(-0.950211 + 2.84554i) q^{72} +(-3.27871 - 10.0908i) q^{73} +(1.15188 - 0.244840i) q^{74} +(-0.353225 - 1.69565i) q^{75} +(2.07177 - 3.58841i) q^{76} +(-5.87724 - 1.64282i) q^{77} +(-5.61173 + 1.79818i) q^{78} +(-0.883390 + 8.40490i) q^{79} +(0.309017 - 0.951057i) q^{80} +(8.99881 + 0.146301i) q^{81} +(-1.72707 + 1.25479i) q^{82} +(-9.27762 - 4.13066i) q^{83} +(-1.86274 - 2.58588i) q^{84} +(0.0395961 + 0.0439760i) q^{85} +(-4.79259 + 2.13380i) q^{86} +(10.0636 + 9.13566i) q^{87} +(-3.28119 + 0.483538i) q^{88} -8.19011 q^{89} +(-2.99990 - 0.0243843i) q^{90} +(1.93444 - 5.95360i) q^{91} +(-4.62750 + 5.13936i) q^{92} +(5.20780 + 11.8260i) q^{93} +(-0.0934297 - 0.888924i) q^{94} +(4.05299 + 0.861490i) q^{95} +(-1.49647 - 0.872114i) q^{96} +(-1.85641 + 17.6626i) q^{97} -3.61447 q^{98} +(4.34885 + 8.94916i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 11 q^{2} - 8 q^{3} + 11 q^{4} + 11 q^{5} + q^{6} - 2 q^{7} - 22 q^{8} + 6 q^{9} + 88 q^{10} + 3 q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{14} + 7 q^{15} + 11 q^{16} + 18 q^{17} - 6 q^{18} + 12 q^{19}+ \cdots - 128 q^{99}+O(q^{100}) \) 88 * q + 11 * q^2 - 8 * q^3 + 11 * q^4 + 11 * q^5 + q^6 - 2 * q^7 - 22 * q^8 + 6 * q^9 + 88 * q^10 + 3 * q^11 + 2 * q^12 + 2 * q^13 - 2 * q^14 + 7 * q^15 + 11 * q^16 + 18 * q^17 - 6 * q^18 + 12 * q^19 + 11 * q^20 + 36 * q^21 + 3 * q^22 + 46 * q^23 + 7 * q^24 + 11 * q^25 + 26 * q^26 + 16 * q^27 + 4 * q^28 - 9 * q^29 - 8 * q^30 - 20 * q^31 - 44 * q^32 + 35 * q^33 + 26 * q^34 + 4 * q^35 + 15 * q^36 + 4 * q^37 + 4 * q^38 - 33 * q^39 + 11 * q^40 + 22 * q^41 - 29 * q^42 - 2 * q^43 + 14 * q^44 + 8 * q^46 - 16 * q^47 + q^48 - 5 * q^49 + 11 * q^50 - 13 * q^51 - 13 * q^52 + 64 * q^53 - 4 * q^54 + 4 * q^55 + 8 * q^56 - 25 * q^57 - 9 * q^58 - 27 * q^59 + q^60 + 4 * q^61 + q^63 - 22 * q^64 + 22 * q^65 + 40 * q^66 - 6 * q^67 - 9 * q^68 - 54 * q^69 - 2 * q^70 + 52 * q^71 + 6 * q^72 - 22 * q^73 - 2 * q^74 + q^75 + 4 * q^76 + 12 * q^77 - 32 * q^78 + 2 * q^79 - 22 * q^80 - 30 * q^81 + 36 * q^82 + 33 * q^83 + 8 * q^84 - 4 * q^85 - 17 * q^86 - 192 * q^87 + 3 * q^88 - 76 * q^89 + 6 * q^90 - 24 * q^91 - 19 * q^92 - 28 * q^93 - q^94 - 6 * q^95 + 7 * q^96 - 38 * q^97 - 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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