LMFDB - Embedded newform 552.2.bb.a.133.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [552,2,Mod(13,552)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(552, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 11, 0, 14])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("552.13"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			133.22
Character	$\chi$	$=$	552.133
Dual form			552.2.bb.a.469.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0169381 + 1.41411i) q^{2} +(-0.755750 - 0.654861i) q^{3} +(-1.99943 - 0.0479047i) q^{4} +(-4.14042 - 0.595303i) q^{5} +(0.938847 - 1.05762i) q^{6} +(-0.0911276 - 0.199542i) q^{7} +(0.101609 - 2.82660i) q^{8} +(0.142315 + 0.989821i) q^{9} +(0.911956 - 5.84494i) q^{10} +(1.00493 + 3.42246i) q^{11} +(1.47969 + 1.34555i) q^{12} +(0.385957 + 0.176261i) q^{13} +(0.283718 - 0.125485i) q^{14} +(2.73928 + 3.16130i) q^{15} +(3.99541 + 0.191564i) q^{16} +(1.76125 - 1.13188i) q^{17} +(-1.40213 + 0.184483i) q^{18} +(3.17850 - 4.94584i) q^{19} +(8.24995 + 1.38861i) q^{20} +(-0.0618023 + 0.210479i) q^{21} +(-4.85677 + 1.36311i) q^{22} +(4.45930 + 1.76485i) q^{23} +(-1.92782 + 2.06966i) q^{24} +(11.9912 + 3.52095i) q^{25} +(-0.255790 + 0.542801i) q^{26} +(0.540641 - 0.841254i) q^{27} +(0.172644 + 0.403334i) q^{28} +(0.283534 + 0.441187i) q^{29} +(-4.51683 + 3.82011i) q^{30} +(-3.25640 - 3.75808i) q^{31} +(-0.338568 + 5.64671i) q^{32} +(1.48176 - 3.24461i) q^{33} +(1.57078 + 2.50977i) q^{34} +(0.258519 + 0.880435i) q^{35} +(-0.237131 - 1.98589i) q^{36} +(3.88113 - 0.558022i) q^{37} +(6.94014 + 4.57853i) q^{38} +(-0.176261 - 0.385957i) q^{39} +(-2.10339 + 11.6428i) q^{40} +(-0.393302 + 2.73548i) q^{41} +(-0.296595 - 0.0909605i) q^{42} +(3.77564 + 3.27161i) q^{43} +(-1.84532 - 6.89111i) q^{44} -4.18300i q^{45} +(-2.57122 + 6.27605i) q^{46} -12.1022 q^{47} +(-2.89408 - 2.76121i) q^{48} +(4.55251 - 5.25388i) q^{49} +(-5.18212 + 16.8973i) q^{50} +(-2.07229 - 0.297950i) q^{51} +(-0.763249 - 0.370910i) q^{52} +(5.83907 - 2.66661i) q^{53} +(1.18047 + 0.778776i) q^{54} +(-2.12342 - 14.7687i) q^{55} +(-0.573284 + 0.237306i) q^{56} +(-5.64099 + 1.65634i) q^{57} +(-0.628691 + 0.393476i) q^{58} +(-4.28842 - 1.95846i) q^{59} +(-5.32555 - 6.45201i) q^{60} +(1.70276 - 1.47545i) q^{61} +(5.36951 - 4.54125i) q^{62} +(0.184542 - 0.118598i) q^{63} +(-7.97935 - 0.574417i) q^{64} +(-1.49310 - 0.959555i) q^{65} +(4.56315 + 2.15034i) q^{66} +(1.22351 - 4.16688i) q^{67} +(-3.57570 + 2.17875i) q^{68} +(-2.21438 - 4.25400i) q^{69} +(-1.24941 + 0.350662i) q^{70} +(1.36258 + 0.400090i) q^{71} +(2.81229 - 0.301692i) q^{72} +(9.58497 + 6.15989i) q^{73} +(0.723367 + 5.49780i) q^{74} +(-6.75665 - 10.5136i) q^{75} +(-6.59210 + 9.73658i) q^{76} +(0.591348 - 0.512406i) q^{77} +(0.548772 - 0.242715i) q^{78} +(3.32782 - 7.28692i) q^{79} +(-16.4286 - 3.17164i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-3.86161 - 0.602507i) q^{82} +(-1.57312 + 0.226180i) q^{83} +(0.133652 - 0.417877i) q^{84} +(-7.96612 + 3.63800i) q^{85} +(-4.69037 + 5.28376i) q^{86} +(0.0746357 - 0.519102i) q^{87} +(9.77605 - 2.49277i) q^{88} +(-7.92669 + 9.14789i) q^{89} +(5.91523 + 0.0708521i) q^{90} -0.0930768i q^{91} +(-8.83149 - 3.74230i) q^{92} +4.97265i q^{93} +(0.204988 - 17.1139i) q^{94} +(-16.1046 + 18.5857i) q^{95} +(3.95368 - 4.04579i) q^{96} +(-0.773454 + 5.37949i) q^{97} +(7.35246 + 6.52675i) q^{98} +(-3.24461 + 1.48176i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32}+ \cdots - 132 q^{98}+O(q^{100}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Character values

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

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{6}{11}\right)$	$1$	$-1$	$1$

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 $

$2$	−0.0169381	+	1.41411i	−0.0119770	+	0.999928i
$2$	−0.0169381	+	1.41411i	−0.0119770	+	0.999928i
$3$	−0.755750	−	0.654861i	−0.436332	−	0.378084i
$3$	−0.755750	−	0.654861i	−0.436332	−	0.378084i
$4$	−1.99943	−	0.0479047i	−0.999713	−	0.0239524i
$5$	−4.14042	−	0.595303i	−1.85165	−	0.266228i	−0.875485	−	0.483245i	$-0.839458\pi$
$5$	−4.14042	−	0.595303i	−1.85165	−	0.266228i	−0.976168	+	0.217017i	$0.930367\pi$
$6$	0.938847	−	1.05762i	0.383283	−	0.431773i
$7$	−0.0911276	−	0.199542i	−0.0344430	−	0.0754197i	0.891629	−	0.452768i	$-0.149563\pi$
$7$	−0.0911276	−	0.199542i	−0.0344430	−	0.0754197i	−0.926072	+	0.377348i	$0.876836\pi$
$8$	0.101609	−	2.82660i	0.0359243	−	0.999355i
$9$	0.142315	+	0.989821i	0.0474383	+	0.329940i
$10$	0.911956	−	5.84494i	0.288386	−	1.84833i
$11$	1.00493	+	3.42246i	0.302997	+	1.03191i	0.960458	+	0.278424i	$0.0898120\pi$
$11$	1.00493	+	3.42246i	0.302997	+	1.03191i	−0.657462	+	0.753488i	$0.728370\pi$
$12$	1.47969	+	1.34555i	0.427151	+	0.388427i
$13$	0.385957	+	0.176261i	0.107045	+	0.0488859i	0.468218	−	0.883613i	$-0.344896\pi$
$13$	0.385957	+	0.176261i	0.107045	+	0.0488859i	−0.361173	+	0.932499i	$0.617623\pi$
$14$	0.283718	−	0.125485i	0.0758268	−	0.0335372i
$15$	2.73928	+	3.16130i	0.707280	+	0.816244i
$16$	3.99541	+	0.191564i	0.998853	+	0.0478910i
$17$	1.76125	−	1.13188i	0.427165	−	0.274522i	−0.309344	−	0.950950i	$-0.600109\pi$
$17$	1.76125	−	1.13188i	0.427165	−	0.274522i	0.736509	+	0.676428i	$0.236473\pi$
$18$	−1.40213	+	0.184483i	−0.330485	+	0.0434832i
$19$	3.17850	−	4.94584i	0.729198	−	1.13465i	−0.256568	−	0.966526i	$-0.582592\pi$
$19$	3.17850	−	4.94584i	0.729198	−	1.13465i	0.985765	−	0.168127i	$-0.0537720\pi$
$20$	8.24995	+	1.38861i	1.84475	+	0.310503i
$21$	−0.0618023	+	0.210479i	−0.0134864	+	0.0459304i
$22$	−4.85677	+	1.36311i	−1.03547	+	0.290616i
$23$	4.45930	+	1.76485i	0.929827	+	0.367996i
$23$	4.45930	+	1.76485i	0.929827	+	0.367996i
$24$	−1.92782	+	2.06966i	−0.393515	+	0.422468i
$25$	11.9912	+	3.52095i	2.39825	+	0.704190i
$26$	−0.255790	+	0.542801i	−0.0501645	+	0.106452i
$27$	0.540641	−	0.841254i	0.104046	−	0.161899i
$28$	0.172644	+	0.403334i	0.0326266	+	0.0762230i
$29$	0.283534	+	0.441187i	0.0526509	+	0.0819265i	0.866581	−	0.499036i	$-0.166313\pi$
$29$	0.283534	+	0.441187i	0.0526509	+	0.0819265i	−0.813930	+	0.580963i	$0.802676\pi$
$30$	−4.51683	+	3.82011i	−0.824657	+	0.697453i
$31$	−3.25640	−	3.75808i	−0.584866	−	0.674971i	0.383778	−	0.923426i	$-0.374623\pi$
$31$	−3.25640	−	3.75808i	−0.584866	−	0.674971i	−0.968644	+	0.248454i	$0.920077\pi$
$32$	−0.338568	+	5.64671i	−0.0598509	+	0.998207i
$33$	1.48176	−	3.24461i	0.257942	−	0.564815i
$34$	1.57078	+	2.50977i	0.269386	+	0.430422i
$35$	0.258519	+	0.880435i	0.0436977	+	0.148821i
$36$	−0.237131	−	1.98589i	−0.0395218	−	0.330982i
$37$	3.88113	−	0.558022i	0.638054	−	0.0917382i	0.184307	−	0.982869i	$-0.440996\pi$
$37$	3.88113	−	0.558022i	0.638054	−	0.0917382i	0.453747	+	0.891131i	$0.350087\pi$
$38$	6.94014	+	4.57853i	1.12584	+	0.742735i
$39$	−0.176261	−	0.385957i	−0.0282243	−	0.0618026i
$40$	−2.10339	+	11.6428i	−0.332575	+	1.84089i
$41$	−0.393302	+	2.73548i	−0.0614235	+	0.427210i	0.935787	+	0.352566i	$0.114691\pi$
$41$	−0.393302	+	2.73548i	−0.0614235	+	0.427210i	−0.997210	+	0.0746434i	$0.976218\pi$
$42$	−0.296595	−	0.0909605i	−0.0457656	−	0.0140355i
$43$	3.77564	+	3.27161i	0.575779	+	0.498916i	0.893376	−	0.449310i	$-0.148330\pi$
$43$	3.77564	+	3.27161i	0.575779	+	0.498916i	−0.317596	+	0.948226i	$0.602876\pi$
$44$	−1.84532	−	6.89111i	−0.278193	−	1.03887i
$45$		−	4.18300i		−	0.623565i
$46$	−2.57122	+	6.27605i	−0.379106	+	0.925353i
$47$	−12.1022			−1.76529			−0.882643	−	0.470044i	$-0.844238\pi$
$47$	−12.1022			−1.76529			−0.882643	+	0.470044i	$0.844238\pi$
$48$	−2.89408	−	2.76121i	−0.417725	−	0.398547i
$49$	4.55251	−	5.25388i	0.650359	−	0.750554i
$50$	−5.18212	+	16.8973i	−0.732863	+	2.38964i
$51$	−2.07229	−	0.297950i	−0.290178	−	0.0417213i
$52$	−0.763249	−	0.370910i	−0.105844	−	0.0514359i
$53$	5.83907	−	2.66661i	0.802058	−	0.366288i	0.0281644	−	0.999603i	$-0.491034\pi$
$53$	5.83907	−	2.66661i	0.802058	−	0.366288i	0.773894	+	0.633316i	$0.218307\pi$
$54$	1.18047	+	0.778776i	0.160642	+	0.105978i
$55$	−2.12342	−	14.7687i	−0.286321	−	1.99141i
$56$	−0.573284	+	0.237306i	−0.0766083	+	0.0317114i
$57$	−5.64099	+	1.65634i	−0.747167	+	0.219388i
$58$	−0.628691	+	0.393476i	−0.0825512	+	0.0516659i
$59$	−4.28842	−	1.95846i	−0.558305	−	0.254969i	0.116217	−	0.993224i	$-0.462923\pi$
$59$	−4.28842	−	1.95846i	−0.558305	−	0.254969i	−0.674522	+	0.738254i	$0.735650\pi$
$60$	−5.32555	−	6.45201i	−0.687526	−	0.832951i
$61$	1.70276	−	1.47545i	0.218016	−	0.188912i	−0.539005	−	0.842303i	$-0.681199\pi$
$61$	1.70276	−	1.47545i	0.218016	−	0.188912i	0.757021	+	0.653390i	$0.226654\pi$
$62$	5.36951	−	4.54125i	0.681928	−	0.576740i
$63$	0.184542	−	0.118598i	0.0232501	−	0.0149419i
$64$	−7.97935	−	0.574417i	−0.997419	−	0.0718021i
$65$	−1.49310	−	0.959555i	−0.185196	−	0.119018i
$66$	4.56315	+	2.15034i	0.561685	+	0.264688i
$67$	1.22351	−	4.16688i	0.149475	−	0.509066i	−0.850378	−	0.526171i	$-0.823627\pi$
$67$	1.22351	−	4.16688i	0.149475	−	0.509066i	0.999854	+	0.0171057i	$0.00544518\pi$
$68$	−3.57570	+	2.17875i	−0.433618	+	0.264212i
$69$	−2.21438	−	4.25400i	−0.266580	−	0.512121i
$70$	−1.24941	+	0.350662i	−0.149333	+	0.0419121i
$71$	1.36258	+	0.400090i	0.161709	+	0.0474819i	0.361585	−	0.932339i	$-0.382236\pi$
$71$	1.36258	+	0.400090i	0.161709	+	0.0474819i	−0.199876	+	0.979821i	$0.564054\pi$
$72$	2.81229	−	0.301692i	0.331432	−	0.0355548i
$73$	9.58497	+	6.15989i	1.12184	+	0.720960i	0.963841	−	0.266480i	$-0.0858605\pi$
$73$	9.58497	+	6.15989i	1.12184	+	0.720960i	0.157995	+	0.987440i	$0.449497\pi$
$74$	0.723367	+	5.49780i	0.0840897	+	0.639107i
$75$	−6.75665	−	10.5136i	−0.780191	−	1.21400i
$76$	−6.59210	+	9.73658i	−0.756166	+	1.11686i
$77$	0.591348	−	0.512406i	0.0673903	−	0.0583940i
$78$	0.548772	−	0.242715i	0.0621362	−	0.0274821i
$79$	3.32782	−	7.28692i	0.374409	−	0.819842i	−0.624827	−	0.780763i	$-0.714830\pi$
$79$	3.32782	−	7.28692i	0.374409	−	0.819842i	0.999236	−	0.0390788i	$-0.0124423\pi$
$80$	−16.4286	−	3.17164i	−1.83678	−	0.354600i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	−3.86161	−	0.602507i	−0.426444	−	0.0665358i
$83$	−1.57312	+	0.226180i	−0.172672	+	0.0248265i	−0.228108	−	0.973636i	$-0.573254\pi$
$83$	−1.57312	+	0.226180i	−0.172672	+	0.0248265i	0.0554365	+	0.998462i	$0.482345\pi$
$84$	0.133652	−	0.417877i	0.0145826	−	0.0455942i
$85$	−7.96612	+	3.63800i	−0.864047	+	0.394597i
$86$	−4.69037	+	5.28376i	−0.505776	+	0.569762i
$87$	0.0746357	−	0.519102i	0.00800178	−	0.0556536i
$88$	9.77605	−	2.49277i	1.04213	−	0.265730i
$89$	−7.92669	+	9.14789i	−0.840228	+	0.969674i	−0.999847	−	0.0175044i	$-0.994428\pi$
$89$	−7.92669	+	9.14789i	−0.840228	+	0.969674i	0.159619	+	0.987179i	$0.448973\pi$
$90$	5.91523	+	0.0708521i	0.623520	+	0.00746846i
$91$		−	0.0930768i		−	0.00975710i
$92$	−8.83149	−	3.74230i	−0.920746	−	0.390162i
$93$			4.97265i			0.515640i
$94$	0.204988	−	17.1139i	0.0211429	−	1.76516i
$95$	−16.1046	+	18.5857i	−1.65230	+	1.90685i
$96$	3.95368	−	4.04579i	0.403521	−	0.412921i
$97$	−0.773454	+	5.37949i	−0.0785324	+	0.546205i	0.912134	+	0.409893i	$0.134434\pi$
$97$	−0.773454	+	5.37949i	−0.0785324	+	0.546205i	−0.990666	+	0.136312i	$0.956475\pi$
$98$	7.35246	+	6.52675i	0.742711	+	0.659302i
$99$	−3.24461	+	1.48176i	−0.326096	+	0.148923i
$100$	−23.8069	−	7.61431i	−2.38069	−	0.761431i
$101$	18.7060	−	2.68952i	1.86132	−	0.267618i	0.882197	−	0.470880i	$-0.156064\pi$
$101$	18.7060	−	2.68952i	1.86132	−	0.267618i	0.979124	+	0.203262i	$0.0651545\pi$
$102$	0.456435	−	2.92540i	0.0451938	−	0.289658i
$103$	8.50963	−	2.49865i	0.838479	−	0.246200i	0.165823	−	0.986155i	$-0.446972\pi$
$103$	8.50963	−	2.49865i	0.838479	−	0.246200i	0.672655	+	0.739956i	$0.265154\pi$
$104$	0.537436	−	1.07304i	0.0526999	−	0.105220i
$105$	0.381187	−	0.834683i	0.0372000	−	0.0814567i
$106$	3.67199	+	8.30227i	0.356655	+	0.806388i
$107$	10.7233	−	9.29181i	1.03666	−	0.898273i	0.0417612	−	0.999128i	$-0.486703\pi$
$107$	10.7233	−	9.29181i	1.03666	−	0.898273i	0.994901	+	0.100855i	$0.0321577\pi$
$108$	−1.12127	+	1.65613i	−0.107894	+	0.159361i
$109$	10.3561	+	16.1144i	0.991933	+	1.54348i	0.830820	+	0.556541i	$0.187872\pi$
$109$	10.3561	+	16.1144i	0.991933	+	1.54348i	0.161113	+	0.986936i	$0.448492\pi$
$110$	20.9205	−	2.75260i	1.99470	−	0.262450i
$111$	−3.29859	−	2.11987i	−0.313088	−	0.201209i
$112$	−0.325867	−	0.814708i	−0.0307916	−	0.0769826i
$113$	11.8372	+	3.47573i	1.11355	+	0.326969i	0.786224	−	0.617941i	$-0.212033\pi$
$113$	11.8372	+	3.47573i	1.11355	+	0.326969i	0.327329	+	0.944910i	$0.393851\pi$
$114$	−2.24671	−	8.00504i	−0.210423	−	0.749741i
$115$	−17.4127	−	9.96185i	−1.62375	−	0.928947i
$116$	−0.545770	−	0.895704i	−0.0506735	−	0.0831641i
$117$	−0.119539	+	0.407113i	−0.0110514	+	0.0376376i
$118$	2.84212	−	6.03114i	0.261638	−	0.555211i
$119$	−0.386356	−	0.248296i	−0.0354172	−	0.0227613i
$120$	9.21407	−	7.42164i	0.841126	−	0.677500i
$121$	−1.44960	+	0.931599i	−0.131781	+	0.0846908i
$122$	2.05761	+	2.43289i	0.186288	+	0.220263i
$123$	2.08860	−	1.80978i	0.188322	−	0.163182i
$124$	6.33089	+	7.67000i	0.568531	+	0.688787i
$125$	−28.5278	−	13.0282i	−2.55161	−	1.16528i
$126$	0.164585	+	0.262972i	0.0146624	+	0.0234274i
$127$	−19.3735	+	5.68859i	−1.71912	+	0.504780i	−0.984752	−	0.173966i	$-0.944342\pi$
$127$	−19.3735	+	5.68859i	−1.71912	+	0.504780i	−0.734373	+	0.678746i	$0.762524\pi$
$128$	0.947445	−	11.2740i	0.0837431	−	0.996487i
$129$	−0.710988	−	4.94503i	−0.0625990	−	0.435386i
$130$	1.38221	−	2.09515i	0.121228	−	0.183757i
$131$	2.55262	−	1.16574i	0.223023	−	0.101851i	−0.300770	−	0.953697i	$-0.597244\pi$
$131$	2.55262	−	1.16574i	0.223023	−	0.101851i	0.523793	+	0.851845i	$0.324516\pi$
$132$	−3.11811	+	6.41638i	−0.271397	+	0.558474i
$133$	−1.27655	−	0.183540i	−0.110691	−	0.0159150i
$134$	5.87172	+	1.80076i	0.507239	+	0.155562i
$135$	−2.73928	+	3.16130i	−0.235760	+	0.272081i
$136$	−3.02043	−	5.09335i	−0.258999	−	0.436751i
$137$	21.0275			1.79650			0.898252	−	0.439482i	$-0.144838\pi$
$137$	21.0275			1.79650			0.898252	+	0.439482i	$0.144838\pi$
$138$	6.05314	−	3.05933i	0.515278	−	0.260427i
$139$		−	18.2457i		−	1.54758i	−0.633444	−	0.773789i	$-0.718359\pi$
$139$		−	18.2457i		−	1.54758i	0.633444	−	0.773789i	$-0.281641\pi$
$140$	−0.474713	−	1.77275i	−0.0401206	−	0.149825i
$141$	9.14623	+	7.92525i	0.770251	+	0.667426i
$142$	−0.588852	+	1.92007i	−0.0494153	+	0.161128i
$143$	−0.215388	+	1.49805i	−0.0180116	+	0.125274i
$144$	0.378992	+	3.98201i	0.0315827	+	0.331834i
$145$	−0.911310	−	1.99549i	−0.0756802	−	0.165717i
$146$	−8.87312	+	13.4499i	−0.734345	+	1.11312i
$147$	−6.88112	+	0.989356i	−0.567545	+	0.0816007i
$148$	−7.78676	+	0.929799i	−0.640068	+	0.0764290i
$149$	−3.33962	−	11.3737i	−0.273592	−	0.931770i	−0.975592	−	0.219593i	$-0.929527\pi$
$149$	−3.33962	−	11.3737i	−0.273592	−	0.931770i	0.701999	−	0.712178i	$-0.252291\pi$
$150$	14.9818	−	9.37658i	1.22326	−	0.765595i
$151$	4.59862	−	10.0696i	0.374230	−	0.819450i	−0.625015	−	0.780612i	$-0.714907\pi$
$151$	4.59862	−	10.0696i	0.374230	−	0.819450i	0.999246	−	0.0388372i	$-0.0123654\pi$
$152$	−13.6570	−	9.48689i	−1.10773	−	0.769489i
$153$	1.37101	+	1.58224i	0.110840	+	0.127916i
$154$	0.714583	+	0.844911i	0.0575827	+	0.0680849i
$155$	11.2457	+	17.4986i	0.903273	+	1.40552i
$156$	0.333931	+	0.780137i	0.0267359	+	0.0624609i
$157$	−4.96388	+	7.72394i	−0.396160	+	0.616438i	−0.980837	−	0.194829i	$-0.937585\pi$
$157$	−4.96388	+	7.72394i	−0.396160	+	0.616438i	0.584677	+	0.811266i	$0.301221\pi$
$158$	10.2482	+	4.82934i	0.815299	+	0.384202i
$159$	−6.15914	−	1.80849i	−0.488451	−	0.143422i
$160$	4.76332	−	23.1782i	0.376573	−	1.83240i
$161$	−0.0542043	−	1.05064i	−0.00427190	−	0.0828021i
$162$	−0.382149	−	1.36160i	−0.0300245	−	0.106978i
$163$	−5.90544	+	20.1121i	−0.462550	+	1.57530i	0.316662	+	0.948538i	$0.397438\pi$
$163$	−5.90544	+	20.1121i	−0.462550	+	1.57530i	−0.779212	+	0.626761i	$0.784380\pi$
$164$	0.917421	−	5.45055i	0.0716386	−	0.425616i
$165$	−8.06666	+	12.5520i	−0.627989	+	0.977169i
$166$	−0.293198	−	2.22839i	−0.0227566	−	0.172957i
$167$	4.75697	−	3.05712i	0.368105	−	0.236567i	−0.343490	−	0.939156i	$-0.611609\pi$
$167$	4.75697	−	3.05712i	0.368105	−	0.236567i	0.711596	+	0.702589i	$0.247973\pi$
$168$	0.588662	+	0.196077i	0.0454162	+	0.0151277i
$169$	−8.39529	−	9.68869i	−0.645792	−	0.745284i
$170$	−5.00961	−	11.3266i	−0.384220	−	0.868711i
$171$	5.34785	+	2.44228i	0.408960	+	0.186766i
$172$	−7.39238	−	6.72221i	−0.563664	−	0.512564i
$173$	−0.754096	−	2.56821i	−0.0573329	−	0.195258i	0.925847	−	0.377899i	$-0.123353\pi$
$173$	−0.754096	−	2.56821i	−0.0573329	−	0.195258i	−0.983180	+	0.182641i	$0.941535\pi$
$174$	0.732805	+	0.114336i	0.0555538	+	0.00866778i
$175$	−0.390158	−	2.71361i	−0.0294932	−	0.205130i
$176$	3.35947	+	13.8667i	0.253230	+	1.04524i
$177$	1.95846	+	4.28842i	0.147207	+	0.322338i
$178$	−12.8019	−	11.3642i	−0.959541	−	0.851781i
$179$	10.8041	+	1.55340i	0.807537	+	0.116106i	0.533704	−	0.845671i	$-0.320799\pi$
$179$	10.8041	+	1.55340i	0.807537	+	0.116106i	0.273833	+	0.961777i	$0.411709\pi$
$180$	−0.200385	+	8.36360i	−0.0149359	+	0.623386i
$181$	−4.85288	−	4.20505i	−0.360712	−	0.312559i	0.455584	−	0.890193i	$-0.349431\pi$
$181$	−4.85288	−	4.20505i	−0.360712	−	0.312559i	−0.816296	+	0.577634i	$0.803976\pi$
$182$	0.131621	+	0.00157654i	0.00975640	+	0.000116861i
$183$	−2.25308			−0.166552
$184$	5.44163	−	12.4253i	0.401162	−	0.916007i
$185$	−16.4017			−1.20588
$186$	−7.03189	−	0.0842273i	−0.515603	−	0.00617585i
$187$	5.64375	+	4.89034i	0.412712	+	0.357617i
$188$	24.1974	+	0.579752i	1.76478	+	0.0422828i
$189$	−0.217132	−	0.0312189i	−0.0157941	−	0.00227084i
$190$	−26.0095	−	23.0885i	−1.88693	−	1.67502i
$191$	−2.18215	−	4.77824i	−0.157895	−	0.345741i	0.814107	−	0.580715i	$-0.197227\pi$
$191$	−2.18215	−	4.77824i	−0.157895	−	0.345741i	−0.972002	+	0.234974i	$0.924500\pi$
$192$	5.65423	+	5.65948i	0.408059	+	0.408438i
$193$	−2.51780	−	17.5117i	−0.181236	−	1.26052i	−0.853847	−	0.520525i	$-0.825736\pi$
$193$	−2.51780	−	17.5117i	−0.181236	−	1.26052i	0.672611	−	0.739996i	$-0.265173\pi$
$194$	−7.59410	−	1.18487i	−0.545225	−	0.0850686i
$195$	0.500033	+	1.70295i	0.0358081	+	0.121951i
$196$	−9.35410	+	10.2867i	−0.668150	+	0.734761i
$197$	−3.66287	−	1.67278i	−0.260969	−	0.119180i	0.280634	−	0.959815i	$-0.409455\pi$
$197$	−3.66287	−	1.67278i	−0.260969	−	0.119180i	−0.541603	+	0.840634i	$0.682182\pi$
$198$	−2.04042	−	4.61334i	−0.145007	−	0.327856i
$199$	10.0474	+	11.5953i	0.712242	+	0.821971i	0.990351	−	0.138578i	$-0.0442533\pi$
$199$	10.0474	+	11.5953i	0.712242	+	0.821971i	−0.278110	+	0.960549i	$0.589708\pi$
$200$	11.1707	−	33.5367i	0.789890	−	2.37140i
$201$	−3.65339	+	2.34789i	−0.257690	+	0.165608i
$202$	3.48644	+	26.4980i	0.245305	+	1.86439i
$203$	0.0621975	−	0.0967812i	0.00436541	−	0.00679271i
$204$	4.12911	+	0.695001i	0.289096	+	0.0486598i
$205$	3.25688	−	11.0919i	0.227470	−	0.774692i
$206$	3.38924	+	12.0759i	0.236139	+	0.841367i
$207$	−1.11226	+	4.66507i	−0.0773074	+	0.324245i
$208$	1.50829	+	0.778170i	0.104581	+	0.0539564i
$209$	20.1211	+	5.90809i	1.39181	+	0.408671i
$210$	1.17388	+	0.553179i	0.0810053	+	0.0381730i
$211$	−4.94464	+	7.69401i	−0.340403	+	0.529677i	−0.968680	−	0.248312i	$-0.920124\pi$
$211$	−4.94464	+	7.69401i	−0.340403	+	0.529677i	0.628277	+	0.777990i	$0.283760\pi$
$212$	−11.8025	+	5.05198i	−0.810601	+	0.346971i
$213$	−0.767767	−	1.19467i	−0.0526065	−	0.0818574i
$214$	12.9580	+	15.3214i	0.885793	+	1.04735i
$215$	−13.6851	−	15.7935i	−0.933318	−	1.07711i
$216$	−2.32295	−	1.61366i	−0.158057	−	0.109795i
$217$	−0.453146	+	0.992252i	−0.0307616	+	0.0673584i
$218$	−22.9629	+	14.3717i	−1.55525	+	0.973375i
$219$	−3.20997	−	10.9322i	−0.216910	−	0.738726i
$220$	3.53812	+	29.6306i	0.238540	+	1.99770i
$221$	0.879272	−	0.126420i	0.0591463	−	0.00850395i
$222$	3.05361	−	4.62867i	0.204945	−	0.310656i
$223$	3.12298	+	6.83836i	0.209130	+	0.457931i	0.984909	−	0.173074i	$-0.0553701\pi$
$223$	3.12298	+	6.83836i	0.209130	+	0.457931i	−0.775779	+	0.631005i	$0.782643\pi$
$224$	1.15761	−	0.447013i	0.0773459	−	0.0298673i
$225$	−1.77858	+	12.3703i	−0.118572	+	0.824685i
$226$	−5.11557	+	16.6803i	−0.340282	+	1.10956i
$227$	−3.16819	−	2.74525i	−0.210280	−	0.182209i	0.543352	−	0.839505i	$-0.317155\pi$
$227$	−3.16819	−	2.74525i	−0.210280	−	0.182209i	−0.753633	+	0.657296i	$0.771700\pi$
$228$	11.3581	−	3.04151i	0.752207	−	0.201429i
$229$			4.56557i			0.301701i	0.988557	+	0.150851i	$0.0482013\pi$
$229$			4.56557i			0.301701i	−0.988557	+	0.150851i	$0.951799\pi$
$230$	14.3821	−	24.4548i	0.948328	−	1.61250i
$231$	−0.782465			−0.0514824
$232$	1.27587	−	0.756609i	0.0837650	−	0.0496738i
$233$	−8.04701	+	9.28674i	−0.527177	+	0.608395i	−0.955413	−	0.295272i	$-0.904590\pi$
$233$	−8.04701	+	9.28674i	−0.527177	+	0.608395i	0.428236	+	0.903667i	$0.359135\pi$
$234$	−0.573679	−	0.175938i	−0.0375026	−	0.0115014i
$235$	50.1082	+	7.20447i	3.26870	+	0.469968i
$236$	8.48057	+	4.12123i	0.552038	+	0.268269i
$237$	−7.28692	+	3.32782i	−0.473336	+	0.216165i
$238$	0.357663	−	0.542145i	0.0231838	−	0.0351421i
$239$	−1.92636	−	13.3981i	−0.124606	−	0.866651i	−0.952233	−	0.305373i	$-0.901219\pi$
$239$	−1.92636	−	13.3981i	−0.124606	−	0.866651i	0.827627	−	0.561278i	$-0.189690\pi$
$240$	10.3390	+	13.1554i	0.667377	+	0.849180i
$241$	23.0331	−	6.76314i	1.48369	−	0.435652i	0.563171	−	0.826340i	$-0.309581\pi$
$241$	23.0331	−	6.76314i	1.48369	−	0.435652i	0.920523	+	0.390688i	$0.127763\pi$
$242$	−1.29283	−	2.06567i	−0.0831064	−	0.132786i
$243$	0.909632	+	0.415415i	0.0583529	+	0.0266489i
$244$	−3.47523	+	2.86849i	−0.222479	+	0.183636i
$245$	−21.9770	+	19.0432i	−1.40406	+	1.21662i
$246$	2.52385	+	2.98416i	0.160915	+	0.190263i
$247$	2.09852	−	1.34864i	0.133526	−	0.0858118i
$248$	−10.9535	+	8.82268i	−0.695547	+	0.560241i
$249$	1.33700	+	0.859236i	0.0847288	+	0.0544519i
$250$	18.9066	−	40.1209i	1.19576	−	2.53747i
$251$	−2.49452	+	8.49557i	−0.157453	+	0.536236i	−0.999997	−	0.00239171i	$-0.999239\pi$
$251$	−2.49452	+	8.49557i	−0.157453	+	0.536236i	0.842544	+	0.538627i	$0.181057\pi$
$252$	−0.374659	+	0.228287i	−0.0236013	+	0.0143807i
$253$	−1.55887	+	17.0353i	−0.0980051	+	1.07100i
$254$	−7.71615	−	27.4927i	−0.484154	−	1.72505i
$255$	8.40277	+	2.46728i	0.526202	+	0.154507i
$256$	15.9266	+	1.53075i	0.995413	+	0.0956721i
$257$	−19.9982	−	12.8521i	−1.24746	−	0.801691i	−0.260939	−	0.965355i	$-0.584032\pi$
$257$	−19.9982	−	12.8521i	−1.24746	−	0.801691i	−0.986516	+	0.163664i	$0.947669\pi$
$258$	7.00487	−	0.921658i	0.436104	−	0.0573799i
$259$	−0.465027	−	0.723596i	−0.0288953	−	0.0449620i
$260$	2.93937	+	1.99009i	0.182292	+	0.123420i
$261$	−0.396346	+	0.343436i	−0.0245332	+	0.0212581i
$262$	1.60525	+	3.62943i	0.0991728	+	0.224227i
$263$	−6.38503	+	13.9813i	−0.393718	+	0.862121i	0.604151	+	0.796870i	$0.293512\pi$
$263$	−6.38503	+	13.9813i	−0.393718	+	0.862121i	−0.997869	+	0.0652516i	$0.979215\pi$
$264$	−9.02067	−	4.51804i	−0.555184	−	0.278066i
$265$	−25.7637	+	7.56489i	−1.58265	+	0.464708i
$266$	0.281169	−	1.80208i	0.0172396	−	0.110492i
$267$	11.9812	−	1.72263i	0.733237	−	0.105424i
$268$	−2.64593	+	8.27276i	−0.161626	+	0.505339i
$269$	6.84613	−	3.12652i	0.417416	−	0.190627i	−0.195625	−	0.980679i	$-0.562673\pi$
$269$	6.84613	−	3.12652i	0.417416	−	0.190627i	0.613041	+	0.790051i	$0.289946\pi$
$270$	−4.42403	−	3.92720i	−0.269238	−	0.239002i
$271$	−3.08485	+	21.4556i	−0.187391	+	1.30333i	0.651340	+	0.758786i	$0.274207\pi$
$271$	−3.08485	+	21.4556i	−0.187391	+	1.30333i	−0.838731	+	0.544547i	$0.816702\pi$
$272$	7.25373	−	4.18495i	0.439822	−	0.253750i
$273$	−0.0609523	+	0.0703427i	−0.00368900	+	0.00425734i
$274$	−0.356166	+	29.7353i	−0.0215168	+	1.79637i
$275$			44.5779i			2.68815i
$276$	4.22370	+	8.61164i	0.254237	+	0.518360i
$277$			27.3752i			1.64482i	0.568896	+	0.822409i	$0.307371\pi$
$277$			27.3752i			1.64482i	−0.568896	+	0.822409i	$0.692629\pi$
$278$	25.8014	+	0.309047i	1.54747	+	0.0185354i
$279$	3.25640	−	3.75808i	0.194955	−	0.224990i
$280$	2.51491	−	0.641270i	0.150294	−	0.0383232i
$281$	4.01441	−	27.9208i	0.239479	−	1.66562i	−0.415216	−	0.909723i	$-0.636294\pi$
$281$	4.01441	−	27.9208i	0.239479	−	1.66562i	0.654695	−	0.755893i	$-0.272797\pi$
$282$	−11.3621	+	12.7995i	−0.676604	+	0.762202i
$283$	−26.5348	+	12.1180i	−1.57733	+	0.720342i	−0.995658	−	0.0930829i	$-0.970328\pi$
$283$	−26.5348	+	12.1180i	−1.57733	+	0.720342i	−0.581670	+	0.813425i	$0.697601\pi$
$284$	−2.70521	−	0.865225i	−0.160525	−	0.0513416i
$285$	24.3421	−	3.49986i	1.44190	−	0.207314i
$286$	−2.11477	−	0.329956i	−0.125049	−	0.0195107i
$287$	0.581682	−	0.170797i	0.0343356	−	0.0100819i
$288$	−5.63742	+	0.468490i	−0.332188	+	0.0276060i
$289$	−5.24123	+	11.4767i	−0.308308	+	0.675100i
$290$	2.83728	−	1.25490i	0.166611	−	0.0736900i
$291$	4.10736	−	3.55904i	0.240777	−	0.208635i
$292$	−18.8694	−	12.7754i	−1.10425	−	0.747624i
$293$	14.1643	+	22.0401i	0.827486	+	1.28759i	0.955253	+	0.295789i	$0.0955827\pi$
$293$	14.1643	+	22.0401i	0.827486	+	1.28759i	−0.127767	+	0.991804i	$0.540781\pi$
$294$	−1.28251	−	9.74743i	−0.0747973	−	0.568482i
$295$	16.5900	+	10.6618i	0.965908	+	0.620751i
$296$	−1.18295	−	11.0271i	−0.0687574	−	0.640937i
$297$	3.42246	+	1.00493i	0.198592	+	0.0583117i
$298$	16.1403	−	4.52995i	0.934980	−	0.262413i
$299$	1.41002	+	1.46715i	0.0815438	+	0.0848477i
$300$	13.0058	+	21.3447i	0.750889	+	1.23234i
$301$	0.308757	−	1.05153i	0.0177965	−	0.0606092i
$302$	14.1616	+	6.67352i	0.814909	+	0.384018i
$303$	−15.8984	−	10.2173i	−0.913336	−	0.586966i
$304$	13.6469	−	19.1518i	0.782701	−	1.09843i
$305$	−7.92850	+	5.09534i	−0.453985	+	0.291758i
$306$	−2.26068	+	1.91197i	−0.129234	+	0.109300i
$307$	1.52762	−	1.32369i	0.0871859	−	0.0755470i	−0.610177	−	0.792265i	$-0.708902\pi$
$307$	1.52762	−	1.32369i	0.0871859	−	0.0755470i	0.697363	+	0.716718i	$0.254356\pi$
$308$	−1.20690	+	0.996189i	−0.0687697	+	0.0567631i
$309$	−8.06742	−	3.68427i	−0.458939	−	0.209591i
$310$	−24.9354	+	15.6062i	−1.41624	+	0.886374i
$311$	11.4572	−	3.36413i	0.649676	−	0.190762i	0.0597423	−	0.998214i	$-0.480972\pi$
$311$	11.4572	−	3.36413i	0.649676	−	0.190762i	0.589934	+	0.807452i	$0.299154\pi$
$312$	−1.10886	+	0.459002i	−0.0627767	+	0.0259859i
$313$	−2.68627	−	18.6834i	−0.151837	−	1.05605i	−0.913138	−	0.407652i	$-0.866348\pi$
$313$	−2.68627	−	18.6834i	−0.151837	−	1.05605i	0.761300	−	0.648399i	$-0.224561\pi$
$314$	−10.8384	−	7.15031i	−0.611649	−	0.403515i
$315$	−0.834683	+	0.381187i	−0.0470290	+	0.0214774i
$316$	−7.00282	+	14.4102i	−0.393939	+	0.810639i
$317$	−28.6864	−	4.12448i	−1.61119	−	0.231654i	−0.722905	−	0.690948i	$-0.757193\pi$
$317$	−28.6864	−	4.12448i	−1.61119	−	0.231654i	−0.888284	+	0.459294i	$0.848102\pi$
$318$	2.66173	−	8.67908i	0.149262	−	0.486698i
$319$	−1.22502	+	1.41375i	−0.0685878	+	0.0791546i
$320$	32.6959	+	7.12846i	1.82776	+	0.398493i
$321$	−14.1890			−0.791952
$322$	1.48664	−	0.0588551i	0.0828474	−	0.00327986i
$323$		−	12.3085i		−	0.684865i
$324$	1.93193	−	0.517339i	0.107330	−	0.0287411i
$325$	4.00750	+	3.47252i	0.222296	+	0.192621i
$326$	−28.3407	−	8.69161i	−1.56965	−	0.481384i
$327$	2.72607	−	18.9602i	0.150752	−	1.04850i
$328$	7.69214	+	1.38966i	0.424728	+	0.0767311i
$329$	1.10284	+	2.41489i	0.0608017	+	0.133137i
$330$	−17.6133	−	11.6198i	−0.969578	−	0.639647i
$331$	−24.1538	+	3.47279i	−1.32761	+	0.190882i	−0.769374	−	0.638798i	$-0.779432\pi$
$331$	−24.1538	+	3.47279i	−1.32761	+	0.190882i	−0.558239	+	0.829680i	$0.688523\pi$
$332$	3.15616	−	0.376870i	0.173217	−	0.0206834i
$333$	1.10468	+	3.76221i	0.0605363	+	0.206168i
$334$	4.24253	+	6.77867i	0.232141	+	0.370912i
$335$	−7.54639	+	16.5243i	−0.412304	+	0.902819i
$336$	−0.287246	+	0.829113i	−0.0156706	+	0.0452318i
$337$	1.23243	+	1.42230i	0.0671350	+	0.0774779i	0.788324	−	0.615261i	$-0.210949\pi$
$337$	1.23243	+	1.42230i	0.0671350	+	0.0774779i	−0.721189	+	0.692739i	$0.756404\pi$
$338$	13.8431	−	11.7078i	0.752965	−	0.636819i
$339$	−6.66987	−	10.3785i	−0.362258	−	0.563684i
$340$	16.1019	−	6.89230i	0.873250	−	0.373788i
$341$	9.58946	−	14.9215i	0.519299	−	0.808044i
$342$	−3.54424	+	7.52109i	−0.191651	+	0.406694i
$343$	−2.93658	−	0.862259i	−0.158561	−	0.0465576i
$344$	9.63117	−	10.3398i	0.519278	−	0.557484i
$345$	6.63605	+	18.9316i	0.357273	+	1.01924i
$346$	3.64452	−	1.02288i	0.195930	−	0.0549901i
$347$	−3.07269	+	10.4646i	−0.164951	+	0.561770i	0.834983	+	0.550275i	$0.185477\pi$
$347$	−3.07269	+	10.4646i	−0.164951	+	0.561770i	−0.999934	+	0.0114949i	$0.996341\pi$
$348$	−0.174096	+	1.03433i	−0.00933252	+	0.0554460i
$349$	16.6696	−	25.9385i	0.892305	−	1.38845i	−0.0289857	−	0.999580i	$-0.509228\pi$
$349$	16.6696	−	25.9385i	0.892305	−	1.38845i	0.921291	−	0.388874i	$-0.127136\pi$
$350$	3.84396	−	0.505764i	0.205468	−	0.0270342i
$351$	0.356944	−	0.229394i	0.0190523	−	0.0122442i
$352$	−19.6659	+	4.51579i	−1.04820	+	0.240693i
$353$	8.96925	+	10.3511i	0.477385	+	0.550932i	0.942451	−	0.334344i	$-0.108515\pi$
$353$	8.96925	+	10.3511i	0.477385	+	0.550932i	−0.465066	+	0.885276i	$0.653969\pi$
$354$	−6.09749	+	2.69684i	−0.324078	+	0.143335i
$355$	−5.40349	−	2.46769i	−0.286787	−	0.130971i
$356$	16.2871	−	17.9108i	0.863212	−	0.949271i
$357$	0.129389	+	0.440659i	0.00684800	+	0.0233222i
$358$	−2.37968	+	15.2519i	−0.125770	+	0.806088i
$359$	−1.88427	−	13.1054i	−0.0994478	−	0.691674i	−0.977163	−	0.212492i	$-0.931842\pi$
$359$	−1.88427	−	13.1054i	−0.0994478	−	0.691674i	0.877715	−	0.479183i	$-0.159067\pi$
$360$	−11.8237	−	0.425031i	−0.623162	−	0.0224011i
$361$	−6.46560	−	14.1577i	−0.340295	−	0.745141i
$362$	6.02861	−	6.79130i	0.316857	−	0.356943i
$363$	1.70560	+	0.245228i	0.0895208	+	0.0128711i
$364$	−0.00445882	+	0.186100i	−0.000233706	+	0.00975430i
$365$	−36.0188	−	31.2105i	−1.88531	−	1.63363i
$366$	0.0381629	−	3.18611i	0.00199481	−	0.166540i
$367$	27.6525			1.44345			0.721725	−	0.692180i	$-0.243349\pi$
$367$	27.6525			1.44345			0.721725	+	0.692180i	$0.243349\pi$
$368$	17.4786	+	7.90553i	0.911137	+	0.412104i
$369$	−2.76361			−0.143868
$370$	0.277814	−	23.1938i	0.0144428	−	1.20579i
$371$	−1.06420	−	0.922136i	−0.0552506	−	0.0478749i
$372$	0.238214	−	9.94246i	0.0123508	−	0.515492i
$373$	15.3936	+	2.21327i	0.797051	+	0.114599i	0.528796	−	0.848749i	$-0.322644\pi$
$373$	15.3936	+	2.21327i	0.797051	+	0.114599i	0.268256	+	0.963348i	$0.413553\pi$
$374$	−7.01109	+	7.89807i	−0.362535	+	0.408399i
$375$	13.0282	+	28.5278i	0.672775	+	1.47317i
$376$	−1.22969	+	34.2081i	−0.0634166	+	1.76415i
$377$	0.0316679	+	0.220255i	0.00163098	+	0.0113437i
$378$	0.0478249	−	0.306521i	0.00245985	−	0.0157657i
$379$	−6.59480	−	22.4598i	−0.338752	−	1.15368i	−0.936109	−	0.351709i	$-0.885601\pi$
$379$	−6.59480	−	22.4598i	−0.338752	−	1.15368i	0.597357	−	0.801975i	$-0.296217\pi$
$380$	33.0903	−	36.3892i	1.69750	−	1.86673i
$381$	18.3668	+	8.38783i	0.940959	+	0.429721i
$382$	6.79393	−	3.00487i	0.347607	−	0.153742i
$383$	−4.32831	−	4.99514i	−0.221167	−	0.255240i	0.634313	−	0.773076i	$-0.281283\pi$
$383$	−4.32831	−	4.99514i	−0.221167	−	0.255240i	−0.855480	+	0.517836i	$0.826738\pi$
$384$	−8.09891	+	7.89985i	−0.413296	+	0.403138i
$385$	−2.75347	+	1.76954i	−0.140330	+	0.0901844i
$386$	24.8062	−	3.26384i	1.26260	−	0.166125i
$387$	−2.70098	+	4.20280i	−0.137298	+	0.213641i
$388$	1.80417	−	10.7188i	0.0915927	−	0.544167i
$389$	3.49589	−	11.9059i	0.177249	−	0.603654i	−0.822159	−	0.569257i	$-0.807231\pi$
$389$	3.49589	−	11.9059i	0.177249	−	0.603654i	0.999408	−	0.0343968i	$-0.0109510\pi$
$390$	−2.41664	+	0.678257i	−0.122371	+	0.0343449i
$391$	9.85152	−	1.93907i	0.498213	−	0.0980632i
$392$	−14.3880	−	13.4020i	−0.726706	−	0.676902i
$393$	−2.69254	−	0.790600i	−0.135821	−	0.0398805i
$394$	2.42754	−	5.15138i	0.122298	−	0.259523i
$395$	−18.1165	+	28.1899i	−0.911541	+	1.41839i
$396$	6.55835	−	2.80725i	0.329569	−	0.141069i
$397$	20.1829	+	31.4053i	1.01295	+	1.57619i	0.800785	+	0.598952i	$0.204416\pi$
$397$	20.1829	+	31.4053i	1.01295	+	1.57619i	0.212168	+	0.977233i	$0.431948\pi$
$398$	−16.5673	+	14.0118i	−0.830443	+	0.702346i
$399$	0.844559	+	0.974673i	0.0422808	+	0.0487947i
$400$	47.2355	+	16.3647i	2.36177	+	0.818236i
$401$	9.37783	−	20.5346i	0.468307	−	1.02545i	−0.517208	−	0.855860i	$-0.673029\pi$
$401$	9.37783	−	20.5346i	0.468307	−	1.02545i	0.985515	−	0.169589i	$-0.0542440\pi$
$402$	−3.25830	−	5.20608i	−0.162509	−	0.259655i
$403$	−0.594427	−	2.02443i	−0.0296105	−	0.100844i
$404$	−37.5302	+	4.48140i	−1.86720	+	0.222958i
$405$	4.14042	−	0.595303i	0.205739	−	0.0295808i
$406$	0.135806	+	0.0895935i	0.00673994	+	0.00444645i
$407$	5.81006	+	12.7223i	0.287994	+	0.630619i
$408$	−1.05275	+	5.82726i	−0.0521188	+	0.288492i
$409$	−0.122094	+	0.849182i	−0.00603716	+	0.0419893i	−0.992617	−	0.121288i	$-0.961297\pi$
$409$	−0.122094	+	0.849182i	−0.00603716	+	0.0419893i	0.986580	+	0.163277i	$0.0522066\pi$
$410$	15.6300	+	4.79346i	0.771912	+	0.236732i
$411$	−15.8915	−	13.7701i	−0.783872	−	0.679229i
$412$	−17.1341	+	4.58822i	−0.844135	+	0.226045i
$413$			1.03419i			0.0508891i
$414$	−6.57809	−	1.65188i	−0.323296	−	0.0811854i
$415$	6.64801			0.326338
$416$	−1.12597	+	2.11971i	−0.0552051	+	0.103928i
$417$	−11.9484	+	13.7892i	−0.585114	+	0.675258i
$418$	−8.69552	+	28.3534i	−0.425312	+	1.38681i
$419$	−27.6349	−	3.97330i	−1.35005	−	0.194108i	−0.570940	−	0.820992i	$-0.693421\pi$
$419$	−27.6349	−	3.97330i	−1.35005	−	0.194108i	−0.779113	+	0.626883i	$0.784330\pi$
$420$	−0.802140	+	1.65063i	−0.0391404	+	0.0805423i
$421$	10.8951	−	4.97564i	0.530996	−	0.242498i	−0.131828	−	0.991273i	$-0.542085\pi$
$421$	10.8951	−	4.97564i	0.530996	−	0.242498i	0.662825	+	0.748775i	$0.269358\pi$
$422$	−10.7964	−	7.12259i	−0.525562	−	0.346722i
$423$	−1.72232	−	11.9790i	−0.0837421	−	0.582439i
$424$	−6.94415	−	16.7757i	−0.337238	−	0.814699i
$425$	25.1048	−	7.37145i	1.21776	−	0.357568i
$426$	1.70240	−	1.06547i	0.0824816	−	0.0516224i
$427$	−0.449583	−	0.205318i	−0.0217568	−	0.00993602i
$428$	−21.8856	+	18.0646i	−1.05788	+	0.873185i
$429$	1.14380	−	0.991105i	0.0552230	−	0.0478510i
$430$	22.5656	−	19.0848i	1.08821	−	0.920351i
$431$	31.9957	−	20.5624i	1.54118	−	0.990454i	0.553695	−	0.832720i	$-0.313217\pi$
$431$	31.9957	−	20.5624i	1.54118	−	0.990454i	0.987482	−	0.157734i	$-0.0504190\pi$
$432$	2.32124	−	3.25759i	0.111681	−	0.156731i
$433$	−3.62917	−	2.33232i	−0.174407	−	0.112084i	0.450525	−	0.892764i	$-0.351237\pi$
$433$	−3.62917	−	2.33232i	−0.174407	−	0.112084i	−0.624932	+	0.780679i	$0.714873\pi$
$434$	−1.39548	−	0.657606i	−0.0669852	−	0.0315661i
$435$	−0.618046	+	2.10487i	−0.0296331	+	0.100921i
$436$	−19.9343	−	32.7156i	−0.954678	−	1.56679i
$437$	22.9025	−	16.4454i	1.09558	−	0.786690i
$438$	15.5137	−	4.35409i	0.741271	−	0.208046i
$439$	−18.0713	−	5.30621i	−0.862496	−	0.253252i	−0.179575	−	0.983744i	$-0.557472\pi$
$439$	−18.0713	−	5.30621i	−0.862496	−	0.253252i	−0.682921	+	0.730493i	$0.739291\pi$
$440$	−41.9609	+	4.50142i	−2.00041	+	0.214597i
$441$	5.84829	+	3.75847i	0.278490	+	0.178975i
$442$	0.163879	+	1.24553i	0.00779494	+	0.0592439i
$443$	−4.36640	−	6.79426i	−0.207454	−	0.322805i	0.721898	−	0.691999i	$-0.243270\pi$
$443$	−4.36640	−	6.79426i	−0.207454	−	0.322805i	−0.929352	+	0.369195i	$0.879634\pi$
$444$	6.49373	+	4.39655i	0.308179	+	0.208651i
$445$	38.2656	−	33.1573i	1.81396	−	1.57181i
$446$	−9.72311	+	4.30041i	−0.460403	+	0.203630i
$447$	−4.92428	+	10.7827i	−0.232910	+	0.510002i
$448$	0.612519	+	1.64456i	0.0289388	+	0.0776981i
$449$	−35.4833	+	10.4188i	−1.67456	+	0.491696i	−0.974875	−	0.222754i	$-0.928495\pi$
$449$	−35.4833	+	10.4188i	−1.67456	+	0.491696i	−0.699687	+	0.714450i	$0.746677\pi$
$450$	−17.4628	−	2.72464i	−0.823206	−	0.128441i
$451$	−9.75732	+	1.40289i	−0.459454	+	0.0660595i
$452$	−23.5012	−	7.51652i	−1.10540	−	0.353547i
$453$	−10.0696	+	4.59862i	−0.473109	+	0.216062i
$454$	3.93576	−	4.43368i	0.184714	−	0.208083i
$455$	−0.0554089	+	0.385377i	−0.00259761	+	0.0180668i
$456$	4.10865	+	16.1131i	0.192405	+	0.754566i
$457$	−6.07736	+	7.01364i	−0.284287	+	0.328084i	−0.879875	−	0.475206i	$-0.842374\pi$
$457$	−6.07736	+	7.01364i	−0.284287	+	0.328084i	0.595588	+	0.803290i	$0.296919\pi$
$458$	−6.45623	−	0.0773321i	−0.301680	−	0.00361349i
$459$		−	2.09360i		−	0.0977207i
$460$	34.3383	+	20.7521i	1.60103	+	0.967573i
$461$		−	7.94036i		−	0.369819i	−0.982756	−	0.184910i	$-0.940801\pi$
$461$		−	7.94036i		−	0.369819i	0.982756	−	0.184910i	$-0.0591993\pi$
$462$	0.0132535	−	1.10649i	0.000616607	−	0.0514787i
$463$	18.2666	−	21.0808i	0.848923	−	0.979709i	−0.151038	−	0.988528i	$-0.548262\pi$
$463$	18.2666	−	21.0808i	0.848923	−	0.979709i	0.999961	+	0.00881848i	$0.00280705\pi$
$464$	1.04832	+	1.81704i	0.0486670	+	0.0843540i
$465$	2.96024	−	20.5889i	0.137278	−	0.954787i
$466$	−12.9962	−	11.5367i	−0.602037	−	0.534426i
$467$	7.72357	−	3.52723i	0.357404	−	0.163221i	−0.228618	−	0.973516i	$-0.573421\pi$
$467$	7.72357	−	3.52723i	0.357404	−	0.163221i	0.586022	+	0.810295i	$0.300693\pi$
$468$	0.258513	−	0.808266i	0.0119497	−	0.0373621i
$469$	−0.942962	+	0.135577i	−0.0435419	+	0.00626039i
$470$	−11.0367	+	70.7366i	−0.509083	+	3.26283i
$471$	8.80955	−	2.58672i	0.405923	−	0.119190i
$472$	−5.97152	+	11.9227i	−0.274862	+	0.548785i
$473$	−7.40273	+	16.2097i	−0.340378	+	0.745323i
$474$	−4.58249	−	10.3609i	−0.210481	−	0.475891i
$475$	55.5282	−	48.1155i	2.54781	−	2.20769i
$476$	0.760596	+	0.514958i	0.0348619	+	0.0236031i
$477$	3.47046	+	5.40014i	0.158901	+	0.247255i
$478$	18.9790	−	2.49714i	0.868081	−	0.114217i
$479$	5.77870	+	3.71374i	0.264035	+	0.169685i	0.665960	−	0.745988i	$-0.268022\pi$
$479$	5.77870	+	3.71374i	0.264035	+	0.169685i	−0.401924	+	0.915673i	$0.631659\pi$
$480$	−18.7784	+	14.3976i	−0.857112	+	0.657159i
$481$	1.59631	+	0.468718i	0.0727853	+	0.0213717i
$482$	9.17370	+	32.6860i	0.417850	+	1.48881i
$483$	−0.647059	+	0.829518i	−0.0294422	+	0.0377444i
$484$	2.94299	−	1.79322i	0.133772	−	0.0815100i
$485$	6.40485	−	21.8129i	0.290829	−	0.990474i
$486$	−0.602851	+	1.27929i	−0.0273459	+	0.0580296i
$487$	7.42887	+	4.77424i	0.336634	+	0.216342i	0.698026	−	0.716072i	$-0.254062\pi$
$487$	7.42887	+	4.77424i	0.336634	+	0.216342i	−0.361392	+	0.932414i	$0.617698\pi$
$488$	−3.99750	−	4.96295i	−0.180958	−	0.224662i
$489$	17.6336	−	11.3325i	0.797421	−	0.512471i
$490$	−26.5569	−	31.4005i	−1.19972	−	1.41853i
$491$	26.8461	−	23.2623i	1.21155	−	1.04981i	0.214217	−	0.976786i	$-0.431280\pi$
$491$	26.8461	−	23.2623i	1.21155	−	1.04981i	0.997330	−	0.0730250i	$-0.0232653\pi$
$492$	−4.26269	+	3.51846i	−0.192177	+	0.158625i
$493$	0.998746	+	0.456112i	0.0449813	+	0.0205423i
$494$	1.87158	+	2.99039i	0.0842064	+	0.134544i
$495$	14.3162	−	4.20361i	0.643464	−	0.188938i
$496$	−12.2907	−	15.6389i	−0.551870	−	0.702207i
$497$	−0.0443342	−	0.308351i	−0.00198866	−	0.0138314i
$498$	−1.23770	+	1.87611i	−0.0554628	+	0.0840705i
$499$	−37.8851	+	17.3016i	−1.69597	+	0.774524i	−0.697660	+	0.716429i	$0.745775\pi$
$499$	−37.8851	+	17.3016i	−1.69597	+	0.774524i	−0.998311	+	0.0580953i	$0.981497\pi$
$500$	56.4152	+	27.4156i	2.52297	+	1.22606i
$501$	−5.59706	−	0.804736i	−0.250058	−	0.0359530i
$502$	−11.9714	−	3.67144i	−0.534311	−	0.163864i
$503$	10.8259	−	12.4937i	0.482702	−	0.557068i	−0.461199	−	0.887297i	$-0.652580\pi$
$503$	10.8259	−	12.4937i	0.482702	−	0.557068i	0.943901	+	0.330229i	$0.107126\pi$
$504$	−0.316478	−	0.533677i	−0.0140970	−	0.0237719i
$505$	−79.0520			−3.51777
$506$	−24.0634	−	2.49296i	−1.06975	−	0.110825i
$507$			12.8200i			0.569355i
$508$	39.0085	−	10.4458i	1.73072	−	0.463459i
$509$	16.9672	+	14.7022i	0.752059	+	0.651663i	0.944076	−	0.329729i	$-0.106957\pi$
$509$	16.9672	+	14.7022i	0.752059	+	0.651663i	−0.192017	+	0.981392i	$0.561503\pi$
$510$	−3.63133	+	11.8407i	−0.160798	+	0.524314i
$511$	0.355698	−	2.47394i	0.0157352	−	0.109441i
$512$	−2.43442	+	22.4961i	−0.107587	+	0.994196i
$513$	−2.44228	−	5.34785i	−0.107829	−	0.236113i
$514$	18.5130	−	28.0620i	0.816574	−	1.23776i
$515$	−36.7209	+	5.27967i	−1.61812	+	0.232650i
$516$	1.18468	+	9.92129i	0.0521526	+	0.436760i
$517$	−12.1618	−	41.4193i	−0.534876	−	1.82162i
$518$	1.03112	−	0.645343i	0.0453049	−	0.0283548i
$519$	−1.11192	+	2.43476i	−0.0488077	+	0.106874i
$520$	−2.86399	+	4.12289i	−0.125594	+	0.180801i
$521$	12.2814	+	14.1735i	0.538058	+	0.620952i	0.958059	−	0.286572i	$-0.0925158\pi$
$521$	12.2814	+	14.1735i	0.538058	+	0.620952i	−0.420001	+	0.907524i	$0.637970\pi$
$522$	−0.478943	−	0.566294i	−0.0209628	−	0.0247860i
$523$	−3.46903	−	5.39792i	−0.151690	−	0.236034i	0.757089	−	0.653312i	$-0.226621\pi$
$523$	−3.46903	−	5.39792i	−0.151690	−	0.236034i	−0.908779	+	0.417277i	$0.862984\pi$
$524$	−5.15962	+	2.20853i	−0.225399	+	0.0964801i
$525$	−1.48217	+	2.30631i	−0.0646874	+	0.100656i
$526$	−19.6629	−	9.26596i	−0.857344	−	0.404015i
$527$	−9.98903	−	2.93304i	−0.435129	−	0.127765i
$528$	6.54181	−	12.6797i	0.284696	−	0.551813i
$529$	16.7706	+	15.7400i	0.729158	+	0.684346i
$530$	−10.2612	−	36.5608i	−0.445719	−	1.58810i
$531$	1.32822	−	4.52349i	0.0576397	−	0.196303i
$532$	2.54358	+	0.428128i	0.110278	+	0.0185617i
$533$	−0.633955	+	0.986454i	−0.0274597	+	0.0427281i
$534$	2.23306	+	16.9719i	0.0966339	+	0.734447i
$535$	−49.9305	+	32.0884i	−2.15868	+	1.38730i
$536$	−11.6538	−	3.88176i	−0.503367	−	0.167667i
$537$	−7.14794	−	8.24916i	−0.308456	−	0.355978i
$538$	4.30529	+	9.73415i	0.185614	+	0.419669i
$539$	22.5562	+	10.3011i	0.971562	+	0.443698i
$540$	5.62843	−	6.18956i	0.242209	−	0.266356i
$541$	5.12532	+	17.4552i	0.220355	+	0.750459i	0.993257	+	0.115934i	$0.0369860\pi$
$541$	5.12532	+	17.4552i	0.220355	+	0.750459i	−0.772902	+	0.634525i	$0.781196\pi$
$542$	−30.2883	−	4.72573i	−1.30100	−	0.202988i
$543$	0.913844	+	6.35593i	0.0392168	+	0.272759i
$544$	5.79512	+	10.3285i	0.248464	+	0.442829i
$545$	−33.2856	−	72.8853i	−1.42580	−	3.12206i
$546$	−0.0984401	−	0.0873849i	−0.00421285	−	0.00373973i
$547$	7.68198	+	1.10450i	0.328458	+	0.0472251i	0.304571	−	0.952490i	$-0.401487\pi$
$547$	7.68198	+	1.10450i	0.328458	+	0.0472251i	0.0238867	+	0.999715i	$0.492396\pi$
$548$	−42.0430	−	1.00732i	−1.79599	−	0.0430305i
$549$	1.70276	+	1.47545i	0.0726722	+	0.0629708i
$550$	−63.0382	−	0.755065i	−2.68796	−	0.0321961i
$551$	3.08326			0.131351
$552$	−12.2494	+	5.82693i	−0.521368	+	0.248010i
$553$	−1.75730			−0.0747280
$554$	−38.7117	−	0.463685i	−1.64470	−	0.0197001i
$555$	12.3956	+	10.7408i	0.526163	+	0.455923i
$556$	−0.874054	+	36.4809i	−0.0370681	+	1.54713i
$557$	−38.3557	−	5.51472i	−1.62518	−	0.233666i	−0.731329	−	0.682025i	$-0.761100\pi$
$557$	−38.3557	−	5.51472i	−1.62518	−	0.233666i	−0.893854	+	0.448359i	$0.852009\pi$
$558$	5.25919	+	4.66856i	0.222639	+	0.197636i
$559$	0.880578	+	1.92820i	0.0372445	+	0.0815541i
$560$	0.864230	+	3.56722i	0.0365204	+	0.150743i
$561$	−1.06277	−	7.39175i	−0.0448703	−	0.312080i
$562$	39.4152	+	6.14975i	1.66263	+	0.259411i
$563$	0.807531	+	2.75020i	0.0340334	+	0.115907i	0.974758	−	0.223265i	$-0.0716714\pi$
$563$	0.807531	+	2.75020i	0.0340334	+	0.115907i	−0.940724	+	0.339172i	$0.889853\pi$
$564$	−17.9075	−	16.2841i	−0.754044	−	0.685684i
$565$	−46.9421	−	21.4377i	−1.97487	−	0.901892i
$566$	−16.6868	−	37.7284i	−0.701398	−	1.58584i
$567$	0.143654	+	0.165785i	0.00603289	+	0.00696232i
$568$	1.26935	−	3.81082i	0.0532606	−	0.159899i
$569$	10.1861	−	6.54621i	0.427023	−	0.274431i	−0.309426	−	0.950923i	$-0.600137\pi$
$569$	10.1861	−	6.54621i	0.427023	−	0.274431i	0.736450	+	0.676492i	$0.236501\pi$
$570$	4.53689	+	34.4817i	0.190029	+	1.44428i
$571$	1.38147	−	2.14961i	0.0578127	−	0.0899583i	−0.811144	−	0.584847i	$-0.801155\pi$
$571$	1.38147	−	2.14961i	0.0578127	−	0.0899583i	0.868957	+	0.494888i	$0.164791\pi$
$572$	0.502416	−	2.98493i	0.0210071	−	0.124806i
$573$	−1.47992	+	5.04015i	−0.0618247	+	0.210555i
$574$	0.231674	+	0.825457i	0.00966989	+	0.0344539i
$575$	47.2586	+	36.8637i	1.97082	+	1.53732i
$576$	−0.567010	−	7.97988i	−0.0236254	−	0.332495i
$577$	−5.86008	−	1.72067i	−0.243958	−	0.0716326i	0.157468	−	0.987524i	$-0.449667\pi$
$577$	−5.86008	−	1.72067i	−0.243958	−	0.0716326i	−0.401426	+	0.915892i	$0.631485\pi$
$578$	−16.1406	−	7.60608i	−0.671358	−	0.316371i
$579$	−9.56490	+	14.8833i	−0.397504	+	0.618528i
$580$	1.72650	+	4.03349i	0.0716892	+	0.167482i
$581$	0.188487	+	0.293291i	0.00781974	+	0.0121678i
$582$	4.96332	+	5.86854i	0.205736	+	0.243259i
$583$	14.9942	+	17.3043i	0.620997	+	0.716669i
$584$	18.3855	−	26.4670i	0.760796	−	1.09521i
$585$	0.737299	−	1.61446i	0.0304835	−	0.0667497i
$586$	−31.4070	+	19.6566i	−1.29741	+	0.812005i
$587$	−7.72367	−	26.3044i	−0.318790	−	1.08570i	−0.950559	−	0.310543i	$-0.899489\pi$
$587$	−7.72367	−	26.3044i	−0.318790	−	1.08570i	0.631769	−	0.775156i	$-0.282329\pi$
$588$	13.8057	−	1.64851i	0.569337	−	0.0679832i
$589$	−28.9373	+	4.16056i	−1.19234	+	0.171433i
$590$	−15.3579	+	23.2795i	−0.632276	+	0.958404i
$591$	1.67278	+	3.66287i	0.0688089	+	0.150670i
$592$	15.6136	−	1.48604i	0.641715	−	0.0610760i
$593$	−0.628062	+	4.36826i	−0.0257914	+	0.179383i	−0.998645	−	0.0520378i	$-0.983428\pi$
$593$	−0.628062	+	4.36826i	−0.0257914	+	0.179383i	0.972854	+	0.231421i	$0.0743375\pi$
$594$	−1.47905	+	4.82273i	−0.0606861	+	0.197879i
$595$	1.45187	+	1.25805i	0.0595207	+	0.0515750i
$596$	6.13247	+	22.9009i	0.251196	+	0.938056i
$597$		−	15.3428i		−	0.627940i
$598$	−2.09860	+	1.96908i	−0.0858183	+	0.0805217i
$599$	1.93249			0.0789592			0.0394796	−	0.999220i	$-0.487430\pi$
$599$	1.93249			0.0789592			0.0394796	+	0.999220i	$0.487430\pi$
$600$	−30.4042	+	18.0301i	−1.24124	+	0.736075i
$601$	−14.0388	+	16.2017i	−0.572656	+	0.660881i	−0.966009	−	0.258507i	$-0.916770\pi$
$601$	−14.0388	+	16.2017i	−0.572656	+	0.660881i	0.393353	+	0.919387i	$0.371315\pi$
$602$	1.48175	+	0.454428i	0.0603917	+	0.0185211i
$603$	4.29859	+	0.618044i	0.175052	+	0.0251687i
$604$	−9.67697	+	19.9131i	−0.393750	+	0.810251i
$605$	6.55652	−	2.99426i	0.266561	−	0.121734i
$606$	14.7176	−	22.3090i	0.597863	−	0.906241i
$607$	−4.49715	−	31.2784i	−0.182534	−	1.26955i	−0.850745	−	0.525579i	$-0.823849\pi$
$607$	−4.49715	−	31.2784i	−0.182534	−	1.26955i	0.668211	−	0.743972i	$-0.267060\pi$
$608$	26.8516	+	19.6226i	1.08898	+	0.795800i
$609$	−0.110384	+	0.0324116i	−0.00447298	+	0.00131339i
$610$	−7.07109	−	11.2981i	−0.286300	−	0.457446i
$611$	−4.67093	−	2.13314i	−0.188966	−	0.0862977i
$612$	−2.66545	−	3.22924i	−0.107744	−	0.130534i
$613$	−18.7906	+	16.2822i	−0.758946	+	0.657631i	−0.945797	−	0.324758i	$-0.894717\pi$
$613$	−18.7906	+	16.2822i	−0.758946	+	0.657631i	0.186851	+	0.982388i	$0.440172\pi$
$614$	1.84597	+	2.18265i	0.0744974	+	0.0880845i
$615$	−9.72503	+	6.24990i	−0.392151	+	0.252020i
$616$	−1.38828	−	1.72357i	−0.0559354	−	0.0694446i
$617$	33.0977	+	21.2706i	1.33246	+	0.856322i	0.996339	−	0.0854950i	$-0.0272472\pi$
$617$	33.0977	+	21.2706i	1.33246	+	0.856322i	0.336125	+	0.941817i	$0.390884\pi$
$618$	5.34661	−	11.3458i	0.215072	−	0.456396i
$619$	1.40277	−	4.77738i	0.0563819	−	0.192019i	−0.926486	−	0.376328i	$-0.877187\pi$
$619$	1.40277	−	4.77738i	0.0563819	−	0.192019i	0.982868	+	0.184309i	$0.0590047\pi$
$620$	−21.6466	−	35.5259i	−0.869348	−	1.42675i
$621$	3.89556	−	2.79725i	0.156323	−	0.112250i
$622$	4.56319	+	16.2587i	0.182967	+	0.651914i
$623$	2.54773	+	0.748080i	0.102072	+	0.0299712i
$624$	−0.630299	−	1.57582i	−0.0252321	−	0.0630834i
$625$	57.7938	+	37.1418i	2.31175	+	1.48567i
$626$	26.4660	−	3.48223i	1.05779	−	0.139178i
$627$	−11.3375	−	17.6416i	−0.452778	−	0.704536i
$628$	10.2949	−	15.2057i	0.410812	−	0.606772i
$629$	6.20400	−	5.37580i	0.247370	−	0.214347i
$630$	−0.524903	−	1.18679i	−0.0209126	−	0.0472829i
$631$	−7.58590	+	16.6108i	−0.301990	+	0.661266i	−0.998410	−	0.0563685i	$-0.982048\pi$
$631$	−7.58590	+	16.6108i	−0.301990	+	0.661266i	0.696420	+	0.717634i	$0.254775\pi$
$632$	−20.2591	−	10.1468i	−0.805863	−	0.403620i
$633$	8.77541	−	2.57669i	0.348791	−	0.102414i
$634$	6.31837	−	40.4959i	0.250935	−	1.60830i
$635$	83.6011	−	12.0200i	3.31761	−	0.477000i
$636$	12.2281	+	3.91098i	0.484876	+	0.155081i
$637$	2.68313	−	1.22534i	0.106309	−	0.0485499i
$638$	−1.97845	−	1.75626i	−0.0783274	−	0.0695309i
$639$	−0.202102	+	1.40565i	−0.00799504	+	0.0556067i
$640$	−10.6342	+	46.1150i	−0.420356	+	1.82285i
$641$	−19.8396	+	22.8962i	−0.783618	+	0.904344i	−0.997365	−	0.0725452i	$-0.976888\pi$
$641$	−19.8396	+	22.8962i	−0.783618	+	0.904344i	0.213747	+	0.976889i	$0.431433\pi$
$642$	0.240334	−	20.0648i	0.00948524	−	0.791895i
$643$			31.1709i			1.22926i	0.788815	+	0.614631i	$0.210695\pi$
$643$			31.1709i			1.22926i	−0.788815	+	0.614631i	$0.789305\pi$
$644$	0.0580468	+	2.10328i	0.00228736	+	0.0828807i
$645$			20.8978i			0.822849i
$646$	17.4056	+	0.208483i	0.684816	+	0.00820266i
$647$	−3.76390	+	4.34378i	−0.147974	+	0.170771i	−0.824898	−	0.565282i	$-0.808767\pi$
$647$	−3.76390	+	4.34378i	−0.147974	+	0.170771i	0.676923	+	0.736053i	$0.263313\pi$
$648$	0.698852	+	2.74073i	0.0274535	+	0.107666i
$649$	2.39320	−	16.6451i	0.0939414	−	0.653377i
$650$	−4.97841	+	5.60824i	−0.195269	+	0.219973i
$651$	0.992252	−	0.453146i	0.0388894	−	0.0177602i
$652$	12.7710	−	39.9297i	0.500149	−	1.56377i
$653$	−4.63630	+	0.666599i	−0.181432	+	0.0260860i	−0.232432	−	0.972613i	$-0.574668\pi$
$653$	−4.63630	+	0.666599i	−0.181432	+	0.0260860i	0.0509997	+	0.998699i	$0.483759\pi$
$654$	26.7657	+	4.17612i	1.04662	+	0.163299i
$655$	−11.2629	+	3.30708i	−0.440077	+	0.129218i
$656$	−2.09542	+	10.8540i	−0.0818125	+	0.423778i
$657$	−4.73310	+	10.3641i	−0.184656	+	0.404340i
$658$	−3.43361	+	1.51864i	−0.133856	+	0.0592028i
$659$	15.8866	−	13.7658i	0.618852	−	0.536239i	−0.288031	−	0.957621i	$-0.593000\pi$
$659$	15.8866	−	13.7658i	0.618852	−	0.536239i	0.906883	+	0.421382i	$0.138455\pi$
$660$	16.7300	−	24.7103i	0.651214	−	0.961847i
$661$	−6.86170	−	10.6770i	−0.266889	−	0.415288i	0.681780	−	0.731557i	$-0.261206\pi$
$661$	−6.86170	−	10.6770i	−0.266889	−	0.415288i	−0.948669	+	0.316269i	$0.897570\pi$
$662$	−4.50180	−	34.2150i	−0.174967	−	1.32980i
$663$	−0.747297	−	0.480259i	−0.0290226	−	0.0186517i
$664$	0.479477	+	4.46955i	0.0186073	+	0.173452i
$665$	5.17620	+	1.51987i	0.200724	+	0.0589380i
$666$	−5.33890	+	1.49842i	−0.206878	+	0.0580627i
$667$	0.485733	+	2.46778i	0.0188077	+	0.0955528i
$668$	−9.65766	+	5.88460i	−0.373666	+	0.227682i
$669$	2.11799	−	7.21320i	0.0818861	−	0.278879i
$670$	−23.2394	−	10.9513i	−0.897816	−	0.423087i
$671$	6.76084	+	4.34493i	0.260999	+	0.167734i
$672$	−1.16759	−	0.420242i	−0.0450409	−	0.0162112i
$673$	−15.8247	+	10.1699i	−0.609997	+	0.392021i	−0.808856	−	0.588007i	$-0.799913\pi$
$673$	−15.8247	+	10.1699i	−0.609997	+	0.392021i	0.198859	+	0.980028i	$0.436276\pi$
$674$	−2.03217	+	1.71871i	−0.0782764	+	0.0662022i
$675$	9.44497	−	8.18411i	0.363537	−	0.315007i
$676$	16.3216	+	19.7740i	0.627755	+	0.760538i
$677$	25.0723	+	11.4502i	0.963608	+	0.440065i	0.834161	−	0.551521i	$-0.185952\pi$
$677$	25.0723	+	11.4502i	0.963608	+	0.440065i	0.129447	+	0.991586i	$0.458680\pi$
$678$	14.7894	−	9.25615i	0.567982	−	0.355480i
$679$	1.14392	−	0.335884i	0.0438995	−	0.0128900i
$680$	9.47375	+	22.8867i	0.363302	+	0.877664i
$681$	0.596600	+	4.14945i	0.0228618	+	0.159007i
$682$	20.9382	+	13.8133i	0.801767	+	0.528939i
$683$	9.27224	−	4.23449i	0.354792	−	0.162028i	−0.230043	−	0.973181i	$-0.573887\pi$
$683$	9.27224	−	4.23449i	0.354792	−	0.162028i	0.584835	+	0.811152i	$0.301159\pi$
$684$	−10.5756	−	5.13935i	−0.404369	−	0.196508i
$685$	−87.0629	−	12.5177i	−3.32650	−	0.478279i
$686$	1.26907	−	4.13805i	0.0484533	−	0.157992i
$687$	2.98981	−	3.45043i	0.114068	−	0.131642i
$688$	14.4585	+	13.7947i	0.551225	+	0.525918i
$689$	2.72365			0.103763
$690$	−26.8838	+	9.06346i	−1.02345	+	0.345040i
$691$		−	26.9353i		−	1.02467i	−0.858786	−	0.512334i	$-0.828781\pi$
$691$		−	26.9353i		−	1.02467i	0.858786	−	0.512334i	$-0.171219\pi$
$692$	1.38473	+	5.17108i	0.0526395	+	0.196575i
$693$	0.591348	+	0.512406i	0.0224634	+	0.0194647i
$694$	−14.7461	−	4.52238i	−0.559754	−	0.171667i
$695$	−10.8617	+	75.5448i	−0.412008	+	2.86558i
$696$	−1.45971	−	0.263711i	−0.0553302	−	0.00999593i
$697$	2.40354	+	5.26302i	0.0910406	+	0.199351i
$698$	36.3975	+	24.0121i	1.37767	+	0.908871i
$699$	12.1630	−	1.74878i	0.460048	−	0.0661450i
$700$	0.650098	+	5.44435i	0.0245714	+	0.205777i
$701$	−8.50475	−	28.9645i	−0.321220	−	1.09397i	−0.948919	−	0.315519i	$-0.897821\pi$
$701$	−8.50475	−	28.9645i	−0.321220	−	1.09397i	0.627699	−	0.778456i	$-0.283997\pi$
$702$	0.318343	+	0.508645i	0.0120151	+	0.0191976i
$703$	9.57627	−	20.9691i	0.361176	−	0.790865i
$704$	−6.05274	−	27.8863i	−0.228121	−	1.05100i
$705$	−33.1513	−	38.2587i	−1.24855	−	1.44090i
$706$	−14.7895	+	12.5082i	−0.556610	+	0.470752i
$707$	−2.24131	−	3.48755i	−0.0842931	−	0.131163i
$708$	−3.71036	−	8.66821i	−0.139444	−	0.325771i
$709$	11.0443	−	17.1852i	0.414777	−	0.645405i	−0.569510	−	0.821985i	$-0.692867\pi$
$709$	11.0443	−	17.1852i	0.414777	−	0.645405i	0.984286	+	0.176579i	$0.0565032\pi$
$710$	3.58112	−	7.59934i	0.134397	−	0.285198i
$711$	7.68635	+	2.25691i	0.288260	+	0.0846409i
$712$	25.0520	+	23.3351i	0.938864	+	0.874520i
$713$	−7.88879	−	22.5054i	−0.295437	−	0.842835i
$714$	−0.625333	+	0.175507i	−0.0234025	+	0.00656818i
$715$	1.78359	−	6.07436i	0.0667025	−	0.227168i
$716$	−21.5276	−	3.62347i	−0.804524	−	0.135415i
$717$	−7.31805	+	11.3871i	−0.273297	+	0.425259i
$718$	18.5644	−	2.44258i	0.692816	−	0.0911564i
$719$	11.6629	−	7.49530i	0.434953	−	0.279528i	−0.304786	−	0.952421i	$-0.598585\pi$
$719$	11.6629	−	7.49530i	0.434953	−	0.279528i	0.739740	+	0.672893i	$0.234949\pi$
$720$	0.801312	−	16.7128i	0.0298631	−	0.622849i
$721$	−1.27405	−	1.47033i	−0.0474480	−	0.0547579i
$722$	20.1301	−	8.90328i	0.749164	−	0.331346i
$723$	−21.8362	−	9.97226i	−0.812097	−	0.370872i
$724$	9.50154	+	8.64016i	0.353122	+	0.321109i
$725$	1.84653	+	6.28870i	0.0685783	+	0.233556i
$726$	−0.375670	+	2.40776i	−0.0139424	+	0.0893602i
$727$	2.58715	+	17.9941i	0.0959523	+	0.667363i	0.979858	+	0.199697i	$0.0639958\pi$
$727$	2.58715	+	17.9941i	0.0959523	+	0.667363i	−0.883905	+	0.467666i	$0.845095\pi$
$728$	−0.263091	−	0.00945745i	−0.00975080	−	0.000350516i
$729$	−0.415415	−	0.909632i	−0.0153857	−	0.0336901i
$730$	44.7452	−	50.4060i	1.65610	−	1.86561i
$731$	10.3529	+	1.48852i	0.382916	+	0.0550550i
$732$	4.50486	+	0.107933i	0.166505	+	0.00398932i
$733$	16.6952	+	14.4665i	0.616652	+	0.534332i	0.906210	−	0.422829i	$-0.138963\pi$
$733$	16.6952	+	14.4665i	0.616652	+	0.534332i	−0.289558	+	0.957161i	$0.593508\pi$
$734$	−0.468381	+	39.1038i	−0.0172883	+	1.44335i
$735$	29.0797			1.07262
$736$	−11.4754	+	24.5828i	−0.422987	+	0.906136i
$737$	15.4905			0.570601
$738$	0.0468103	−	3.90805i	0.00172311	−	0.143857i
$739$	1.14943	+	0.995984i	0.0422823	+	0.0366379i	0.675746	−	0.737135i	$-0.263822\pi$
$739$	1.14943	+	0.995984i	0.0422823	+	0.0366379i	−0.633463	+	0.773773i	$0.718367\pi$
$740$	32.7940	+	0.785719i	1.20553	+	0.0288836i
$741$	−2.46913	−	0.355007i	−0.0907057	−	0.0130415i
$742$	1.32203	−	1.48928i	0.0485332	−	0.0546732i
$743$	−5.89959	−	12.9183i	−0.216435	−	0.473926i	0.770007	−	0.638035i	$-0.220252\pi$
$743$	−5.89959	−	12.9183i	−0.216435	−	0.473926i	−0.986442	+	0.164109i	$0.947525\pi$
$744$	14.0557	+	0.505267i	0.515307	+	0.0185240i
$745$	7.05664	+	49.0800i	0.258535	+	1.79815i
$746$	−3.39055	+	21.7308i	−0.124137	+	0.795622i
$747$	−0.447755	−	1.52491i	−0.0163825	−	0.0557937i
$748$	−11.0500	−	10.0482i	−0.404028	−	0.367400i
$749$	−2.83129	−	1.29301i	−0.103453	−	0.0472455i
$750$	−40.5623	+	17.9402i	−1.48112	+	0.655083i
$751$	30.9257	+	35.6902i	1.12850	+	1.30235i	0.947818	+	0.318812i	$0.103284\pi$
$751$	30.9257	+	35.6902i	1.12850	+	1.30235i	0.180678	+	0.983542i	$0.442171\pi$
$752$	−48.3532	−	2.31834i	−1.76326	−	0.0845413i
$753$	7.44865	−	4.78696i	0.271444	−	0.174446i
$754$	−0.312002	+	0.0410513i	−0.0113625	+	0.00149500i
$755$	−25.0347	+	38.9547i	−0.911104	+	1.41771i
$756$	0.432645	+	0.0728216i	0.0157351	+	0.00264850i
$757$	−5.47853	+	18.6582i	−0.199120	+	0.678142i	0.798024	+	0.602626i	$0.205879\pi$
$757$	−5.47853	+	18.6582i	−0.199120	+	0.678142i	−0.997145	+	0.0755165i	$0.975939\pi$
$758$	31.8724	−	8.94536i	1.15766	−	0.324910i
$759$	12.3339	−	11.8536i	0.447691	−	0.430258i
$760$	50.8980	+	47.4098i	1.84626	+	1.71973i
$761$	−25.9982	−	7.63376i	−0.942434	−	0.276724i	−0.225800	−	0.974174i	$-0.572500\pi$
$761$	−25.9982	−	7.63376i	−0.942434	−	0.276724i	−0.716633	+	0.697450i	$0.754318\pi$
$762$	−12.1724	+	25.8306i	−0.440961	+	0.935744i
$763$	2.27176	−	3.53493i	0.0822434	−	0.127973i
$764$	4.13414	+	9.65827i	0.149568	+	0.349424i
$765$	−4.73467	−	7.36729i	−0.171182	−	0.266365i
$766$	7.13700	−	6.03611i	0.257870	−	0.218094i
$767$	−1.30995	−	1.51176i	−0.0472995	−	0.0545866i
$768$	−11.0341	−	11.5866i	−0.398159	−	0.418095i
$769$	−0.762684	+	1.67004i	−0.0275031	+	0.0602233i	−0.922885	−	0.385076i	$-0.874175\pi$
$769$	−0.762684	+	1.67004i	−0.0275031	+	0.0602233i	0.895382	+	0.445299i	$0.146903\pi$
$770$	−2.45570	−	3.92368i	−0.0884972	−	0.141400i
$771$	6.69733	+	22.8090i	0.241198	+	0.821446i
$772$	4.19527	+	35.1340i	0.150991	+	1.26450i
$773$	17.3726	−	2.49780i	0.624848	−	0.0898396i	0.177384	−	0.984142i	$-0.443236\pi$
$773$	17.3726	−	2.49780i	0.624848	−	0.0898396i	0.447464	+	0.894302i	$0.352327\pi$
$774$	−5.89749	−	3.89067i	−0.211981	−	0.139847i
$775$	−25.8162	−	56.5297i	−0.927347	−	2.03061i
$776$	15.1271	+	2.73285i	0.543031	+	0.0981037i
$777$	−0.122411	+	0.851385i	−0.00439146	+	0.0305433i
$778$	16.7771	+	5.14525i	0.601488	+	0.184466i
$779$	12.2791	+	10.6399i	0.439945	+	0.381215i
$780$	−0.918199	−	3.42889i	−0.0328768	−	0.122774i
$781$			5.06545i			0.181256i
$782$	2.57520	+	13.9640i	0.0920890	+	0.499351i
$783$	0.524441			0.0187420
$784$	19.1956	−	20.1193i	0.685557	−	0.718547i
$785$	25.1506	−	29.0254i	0.897665	−	1.03596i
$786$	1.16360	−	3.79416i	0.0415044	−	0.135333i
$787$	−6.58190	−	0.946334i	−0.234619	−	0.0337332i	0.0240022	−	0.999712i	$-0.492359\pi$
$787$	−6.58190	−	0.946334i	−0.234619	−	0.0337332i	−0.258621	+	0.965979i	$0.583268\pi$
$788$	7.24351	+	3.52006i	0.258039	+	0.125397i
$789$	13.9813	−	6.38503i	0.497746	−	0.227313i
$790$	−39.5568	−	26.0963i	−1.40737	−	0.928464i
$791$	−0.385147	−	2.67876i	−0.0136943	−	0.0952456i
$792$	3.85868	+	9.32179i	0.137112	+	0.331235i
$793$	0.917258	−	0.269331i	0.0325728	−	0.00956424i
$794$	−44.7524	+	28.0090i	−1.58820	+	0.994002i
$795$	24.4248	+	11.1544i	0.866259	+	0.395607i
$796$	−19.5336	−	23.6653i	−0.692349	−	0.838795i
$797$	8.03093	−	6.95884i	0.284470	−	0.246495i	−0.500923	−	0.865492i	$-0.667006\pi$
$797$	8.03093	−	6.95884i	0.284470	−	0.246495i	0.785393	+	0.618997i	$0.212461\pi$
$798$	−1.39260	+	1.17779i	−0.0492976	+	0.0416934i
$799$	−21.3149	+	13.6983i	−0.754068	+	0.484610i
$800$	−23.9416	+	66.5191i	−0.846465	+	2.35180i
$801$	−10.1829	−	6.54413i	−0.359794	−	0.231225i
$802$	28.8794	+	13.6091i	1.01977	+	0.480555i
$803$	−11.4498	+	38.9945i	−0.404055	+	1.37608i
$804$	7.41717	−	4.51942i	0.261583	−	0.159388i
$805$	−0.401021	+	4.38237i	−0.0141341	+	0.154458i
$806$	2.87284	−	0.806297i	0.101192	−	0.0284006i
$807$	−7.22139	−	2.12039i	−0.254205	−	0.0746414i
$808$	−5.70151	−	53.1478i	−0.200578	−	1.86973i
$809$	−36.0191	−	23.1481i	−1.26636	−	0.813843i	−0.277223	−	0.960806i	$-0.589414\pi$
$809$	−36.0191	−	23.1481i	−1.26636	−	0.813843i	−0.989142	+	0.146963i	$0.953050\pi$
$810$	0.771694	+	5.86510i	0.0271146	+	0.206079i
$811$	−12.0579	−	18.7624i	−0.423409	−	0.658837i	0.562370	−	0.826886i	$-0.309890\pi$
$811$	−12.0579	−	18.7624i	−0.423409	−	0.658837i	−0.985779	+	0.168049i	$0.946253\pi$
$812$	−0.128996	+	0.190527i	−0.00452686	+	0.00668620i
$813$	16.3818	−	14.1949i	0.574534	−	0.497837i
$814$	−18.0891	+	8.00058i	−0.634023	+	0.280420i
$815$	36.4238	−	79.7570i	1.27587	−	2.79376i
$816$	−8.22256	−	1.58741i	−0.287847	−	0.0555704i
$817$	28.1817	−	8.27490i	0.985953	−	0.289502i
$818$	−1.19877	−	0.187038i	−0.0419140	−	0.00653963i
$819$	0.0921294	−	0.0132462i	0.00321926	−	0.000462860i
$820$	−7.04324	+	22.0214i	−0.245961	+	0.769021i
$821$	5.27194	−	2.40762i	0.183992	−	0.0840264i	−0.321289	−	0.946981i	$-0.604116\pi$
$821$	5.27194	−	2.40762i	0.183992	−	0.0840264i	0.505281	+	0.862955i	$0.331389\pi$
$822$	19.7416	−	22.2392i	0.688569	−	0.775681i
$823$	5.52209	−	38.4070i	0.192488	−	1.33878i	−0.632907	−	0.774228i	$-0.718138\pi$
$823$	5.52209	−	38.4070i	0.192488	−	1.33878i	0.825395	−	0.564556i	$-0.190952\pi$
$824$	−6.19804	−	24.3072i	−0.215919	−	0.846782i
$825$	29.1923	−	33.6897i	1.01635	−	1.17293i
$826$	−1.46246	−	0.0175172i	−0.0508855	−	0.000609501i
$827$		−	19.4206i		−	0.675322i	−0.941268	−	0.337661i	$-0.890364\pi$
$827$		−	19.4206i		−	0.675322i	0.941268	−	0.337661i	$-0.109636\pi$
$828$	2.44736	−	9.27418i	0.0850517	−	0.322300i
$829$		−	17.5507i		−	0.609563i	−0.952422	−	0.304781i	$-0.901417\pi$
$829$		−	17.5507i		−	0.609563i	0.952422	−	0.304781i	$-0.0985834\pi$
$830$	−0.112605	+	9.40103i	−0.00390856	+	0.326315i
$831$	17.9270	−	20.6888i	0.621880	−	0.717687i
$832$	−2.97844	−	1.62815i	−0.103259	−	0.0564458i
$833$	2.07131	−	14.4063i	0.0717667	−	0.499148i
$834$	−19.2970	−	17.1299i	−0.668202	−	0.593160i
$835$	−21.5158	+	9.82593i	−0.744584	+	0.340040i
$836$	−39.9477	−	12.7767i	−1.38162	−	0.441891i
$837$	−4.92204	+	0.707683i	−0.170131	+	0.0244611i
$838$	6.08677	−	39.0115i	0.210264	−	1.34763i
$839$	−30.3624	+	8.91520i	−1.04823	+	0.307787i	−0.760100	−	0.649806i	$-0.774850\pi$
$839$	−30.3624	+	8.91520i	−1.04823	+	0.307787i	−0.288126	+	0.957593i	$0.593032\pi$
$840$	−2.32058	−	1.16227i	−0.0800677	−	0.0401023i
$841$	11.9328	−	26.1291i	0.411475	−	0.901005i
$842$	6.85157	+	15.4912i	0.236121	+	0.533863i
$843$	−21.3181	+	18.4723i	−0.734236	+	0.636219i
$844$	10.2550	−	15.1467i	0.352992	−	0.521372i
$845$	28.9924	+	45.1130i	0.997368	+	1.55193i
$846$	16.9688	−	2.23265i	0.583400	−	0.0767602i
$847$	0.317991	+	0.204360i	0.0109263	+	0.00702191i
$848$	23.8403	−	9.53566i	0.818680	−	0.327456i
$849$	27.9893	+	8.21839i	0.960589	+	0.282054i
$850$	9.99882	+	35.6259i	0.342957	+	1.22196i
$851$	18.2919	+	4.36122i	0.627039	+	0.149501i
$852$	1.47786	+	2.42543i	0.0506308	+	0.0830939i
$853$	−5.62093	+	19.1431i	−0.192457	+	0.655449i	0.805561	+	0.592514i	$0.201864\pi$
$853$	−5.62093	+	19.1431i	−0.192457	+	0.655449i	−0.998018	+	0.0629352i	$0.979954\pi$
$854$	0.297957	−	0.632283i	0.0101959	−	0.0216363i
$855$	−20.6884	−	13.2957i	−0.707530	−	0.454702i
$856$	−25.1747	−	31.2547i	−0.860452	−	1.06826i
$857$	27.2665	−	17.5231i	0.931404	−	0.598577i	0.0154591	−	0.999881i	$-0.495079\pi$
$857$	27.2665	−	17.5231i	0.931404	−	0.598577i	0.915945	+	0.401303i	$0.131443\pi$
$858$	1.38216	+	1.63424i	0.0471861	+	0.0557921i
$859$	0.733713	−	0.635766i	0.0250340	−	0.0216921i	−0.642254	−	0.766492i	$-0.722001\pi$
$859$	0.733713	−	0.635766i	0.0250340	−	0.0216921i	0.667288	+	0.744800i	$0.267455\pi$
$860$	26.6058	+	32.2335i	0.907251	+	1.09915i
$861$	−0.551455	−	0.251841i	−0.0187935	−	0.00858272i
$862$	28.5355	+	45.5937i	0.971924	+	1.55293i
$863$	−22.0918	+	6.48674i	−0.752014	+	0.220811i	−0.635205	−	0.772343i	$-0.719085\pi$
$863$	−22.0918	+	6.48674i	−0.752014	+	0.220811i	−0.116809	+	0.993154i	$0.537266\pi$
$864$	4.56727	+	3.33766i	0.155382	+	0.113550i
$865$	1.59341	+	11.0824i	0.0541776	+	0.376813i
$866$	3.35964	−	5.09254i	0.114165	−	0.173052i
$867$	11.4767	−	5.24123i	0.389769	−	0.178001i
$868$	0.953566	−	1.96223i	0.0323661	−	0.0666023i
$869$	28.2834	+	4.06654i	0.959450	+	0.137948i
$870$	−2.96606	−	0.909639i	−0.100559	−	0.0308397i
$871$	1.20668	−	1.39258i	0.0408868	−	0.0471859i
$872$	46.6012	−	27.6351i	1.57812	−	0.935844i
$873$	−5.43481			−0.183940
$874$	22.8677	+	32.6653i	0.773512	+	1.10492i
$875$			6.87973i			0.232577i
$876$	5.89440	+	22.0118i	0.199153	+	0.743710i
$877$	26.0713	+	22.5909i	0.880367	+	0.762842i	0.972500	−	0.232905i	$-0.0748230\pi$
$877$	26.0713	+	22.5909i	0.880367	+	0.762842i	−0.0921328	+	0.995747i	$0.529368\pi$
$878$	7.80967	−	25.4650i	0.263564	−	0.859401i
$879$	3.72852	−	25.9324i	0.125760	−	0.874678i
$880$	−5.65477	−	59.4137i	−0.190622	−	2.00284i
$881$	4.53411	+	9.92832i	0.152758	+	0.334494i	0.970504	−	0.241086i	$-0.0775037\pi$
$881$	4.53411	+	9.92832i	0.152758	+	0.334494i	−0.817746	+	0.575580i	$0.804776\pi$
$882$	−5.41396	+	8.20648i	−0.182297	+	0.276327i
$883$	−6.15362	+	0.884758i	−0.207086	+	0.0297745i	−0.245077	−	0.969504i	$-0.578813\pi$
$883$	−6.15362	+	0.884758i	−0.207086	+	0.0297745i	0.0379911	+	0.999278i	$0.487904\pi$
$884$	−1.76410	+	0.210647i	−0.0593330	+	0.00708481i
$885$	−5.55593	−	18.9218i	−0.186761	−	0.636048i
$886$	9.68180	−	6.05950i	0.325266	−	0.203573i
$887$	−3.51755	+	7.70237i	−0.118108	+	0.258620i	−0.959448	−	0.281886i	$-0.909040\pi$
$887$	−3.51755	+	7.70237i	−0.118108	+	0.258620i	0.841340	+	0.540506i	$0.181767\pi$
$888$	−6.32720	+	9.10839i	−0.212327	+	0.305658i
$889$	2.90058	+	3.34744i	0.0972822	+	0.112270i
$890$	46.2401	+	54.6735i	1.54997	+	1.83266i
$891$	−1.92844	−	3.00071i	−0.0646051	−	0.100528i
$892$	−5.91657	−	13.8224i	−0.198101	−	0.462808i
$893$	−38.4668	+	59.8555i	−1.28724	+	2.00299i
$894$	−15.1645	−	7.14612i	−0.507176	−	0.239002i
$895$	−43.8088	−	12.8634i	−1.46437	−	0.429977i
$896$	−2.33596	+	0.838315i	−0.0780391	+	0.0280061i
$897$	−0.104843	−	2.03217i	−0.00350060	−	0.0678522i
$898$	−14.1324	−	50.3539i	−0.471604	−	1.68033i
$899$	0.734720	−	2.50223i	0.0245043	−	0.0834539i
$900$	4.14873	−	24.6483i	0.138291	−	0.821608i
$901$	7.26574	−	11.3057i	0.242057	−	0.376648i
$902$	−1.81857	−	13.8217i	−0.0605519	−	0.460212i
$903$	−0.921949	+	0.592501i	−0.0306806	+	0.0197172i
$904$	11.0273	−	33.1060i	0.366761	−	1.10109i
$905$	17.5897	+	20.2996i	0.584702	+	0.674782i
$906$	−6.33240	−	14.3174i	−0.210380	−	0.475663i
$907$	20.8657	+	9.52906i	0.692836	+	0.316407i	0.730529	−	0.682882i	$-0.239274\pi$
$907$	20.8657	+	9.52906i	0.692836	+	0.316407i	−0.0376932	+	0.999289i	$0.512001\pi$
$908$	6.20305	+	5.64070i	0.205856	+	0.187193i
$909$	5.32430	+	18.1329i	0.176596	+	0.601430i
$910$	−0.544028	−	0.0848819i	−0.0180344	−	0.00281381i
$911$	6.11432	+	42.5260i	0.202576	+	1.40895i	0.796602	+	0.604504i	$0.206629\pi$
$911$	6.11432	+	42.5260i	0.202576	+	1.40895i	−0.594026	+	0.804446i	$0.702462\pi$
$912$	−22.8553	+	5.53716i	−0.756816	+	0.183354i
$913$	−2.35496	−	5.15664i	−0.0779377	−	0.170660i
$914$	−9.81514	−	8.71286i	−0.324656	−	0.288196i
$915$	9.32870	+	1.34126i	0.308397	+	0.0443408i
$916$	0.218712	−	9.12852i	0.00722646	−	0.301615i
$917$	−0.465228	−	0.403122i	−0.0153632	−	0.0133123i
$918$	2.96058	+	0.0354616i	0.0977137	+	0.00117041i
$919$	−33.3342			−1.09959			−0.549797	−	0.835298i	$-0.685295\pi$
$919$	−33.3342			−1.09959			−0.549797	+	0.835298i	$0.685295\pi$
$920$	−29.9275	+	48.2067i	−0.986679	+	1.58933i
$921$	−2.02133			−0.0666051
$922$	11.2286	+	0.134495i	0.369793	+	0.00442934i
$923$	0.455378	+	0.394587i	0.0149889	+	0.0129880i
$924$	1.56448	+	0.0374838i	0.0514677	+	0.00123313i
$925$	48.5043	+	6.97387i	1.59481	+	0.229299i
$926$	29.5013	+	26.1882i	0.969472	+	0.860596i
$927$	3.68427	+	8.06742i	0.121007	+	0.264969i
$928$	−2.58725	+	1.45166i	−0.0849308	+	0.0476532i
$929$	6.93626	+	48.2427i	0.227571	+	1.58279i	0.708293	+	0.705919i	$0.249466\pi$
$929$	6.93626	+	48.2427i	0.227571	+	1.58279i	−0.480721	+	0.876873i	$0.659625\pi$
$930$	29.0649	+	4.53484i	0.953074	+	0.148703i
$931$	−11.5147	−	39.2154i	−0.377379	−	1.28523i
$932$	16.5343	−	18.1827i	0.541598	−	0.595593i
$933$	−10.8618	−	4.96041i	−0.355599	−	0.162396i
$934$	4.85708	+	10.9817i	0.158929	+	0.359333i
$935$	−20.4563	−	23.6078i	−0.668992	−	0.772058i
$936$	1.13860	+	0.379256i	0.0372163	+	0.0123964i
$937$	20.4359	−	13.1334i	0.667612	−	0.429048i	−0.162452	−	0.986716i	$-0.551940\pi$
$937$	20.4359	−	13.1334i	0.667612	−	0.429048i	0.830064	+	0.557669i	$0.188304\pi$
$938$	−0.175750	−	1.33575i	−0.00573843	−	0.0436138i
$939$	−10.2049	+	15.8791i	−0.333025	+	0.518196i
$940$	−99.8425	−	16.8052i	−3.25650	−	0.548126i
$941$	8.55367	−	29.1311i	0.278842	−	0.949648i	−0.694347	−	0.719640i	$-0.744307\pi$
$941$	8.55367	−	29.1311i	0.278842	−	0.949648i	0.973189	−	0.230008i	$-0.0738751\pi$
$942$	3.50869	+	12.5015i	0.114319	+	0.407321i
$943$	−6.58155	+	11.5042i	−0.214325	+	0.374628i
$944$	−16.7588	−	8.64635i	−0.545454	−	0.281415i
$945$	0.880435	+	0.258519i	0.0286406	+	0.00840963i
$946$	−22.7970	−	10.7428i	−0.741193	−	0.349280i
$947$	−18.9337	+	29.4614i	−0.615262	+	0.957367i	0.384156	+	0.923268i	$0.374492\pi$
$947$	−18.9337	+	29.4614i	−0.615262	+	0.957367i	−0.999418	+	0.0340988i	$0.989144\pi$
$948$	14.7291	−	6.30466i	0.478378	−	0.204766i
$949$	2.61364	+	4.06691i	0.0848424	+	0.132017i
$950$	67.1001	+	79.3381i	2.17702	+	2.57407i
$951$	18.9788	+	21.9027i	0.615429	+	0.710243i
$952$	−0.741091	+	1.06685i	−0.0240189	+	0.0345767i
$953$	−10.7854	+	23.6167i	−0.349373	+	0.765021i	0.650611	+	0.759411i	$0.274513\pi$
$953$	−10.7854	+	23.6167i	−0.349373	+	0.765021i	−0.999984	+	0.00560944i	$0.998214\pi$
$954$	−7.69518	+	4.81615i	−0.249141	+	0.155929i
$955$	6.19052	+	21.0830i	0.200320	+	0.682229i
$956$	3.20977	+	26.8808i	0.103812	+	0.869387i
$957$	1.85161	−	0.266222i	0.0598542	−	0.00860573i
$958$	−5.34953	+	8.10882i	−0.172835	+	0.261984i
$959$	−1.91619	−	4.19587i	−0.0618770	−	0.135492i
$960$	−20.0418	−	26.7986i	−0.646846	−	0.864922i
$961$	0.892699	−	6.20886i	0.0287967	−	0.200286i
$962$	−0.689858	+	2.24942i	−0.0222419	+	0.0725241i
$963$	10.7233	+	9.29181i	0.345554	+	0.299424i
$964$	−46.3770	+	12.4190i	−1.49370	+	0.399989i
$965$			74.0047i			2.38230i
$966$	−1.16207	−	0.929064i	−0.0373890	−	0.0298922i
$967$	−45.9396			−1.47732			−0.738659	−	0.674079i	$-0.764541\pi$
$967$	−45.9396			−1.47732			−0.738659	+	0.674079i	$0.764541\pi$
$968$	2.48597	+	4.19209i	0.0799020	+	0.134739i
$969$	−8.06037	+	9.30217i	−0.258937	+	0.298829i
$970$	30.7374	+	9.42665i	0.986920	+	0.302672i
$971$	−23.9688	−	3.44620i	−0.769197	−	0.110594i	−0.253466	−	0.967344i	$-0.581571\pi$
$971$	−23.9688	−	3.44620i	−0.769197	−	0.110594i	−0.515731	+	0.856751i	$0.672480\pi$
$972$	−1.79884	−	0.874167i	−0.0576979	−	0.0280389i
$973$	−3.64077	+	1.66268i	−0.116718	+	0.0533032i
$974$	−6.87715	+	10.4244i	−0.220358	+	0.334019i
$975$	−0.754651	−	5.24871i	−0.0241682	−	0.168093i
$976$	7.08588	−	5.56885i	0.226814	−	0.178255i
$977$	−30.2206	+	8.87357i	−0.966843	+	0.283891i	−0.726783	−	0.686867i	$-0.758985\pi$
$977$	−30.2206	+	8.87357i	−0.966843	+	0.283891i	−0.240060	+	0.970758i	$0.577167\pi$
$978$	15.7267	+	25.1279i	0.502884	+	0.803502i
$979$	−39.2741	−	17.9359i	−1.25520	−	0.573233i
$980$	44.8536	−	37.0226i	1.43280	−	1.18264i
$981$	−14.4765	+	12.5440i	−0.462200	+	0.400499i
$982$	32.4407	+	38.3574i	1.03523	+	1.22403i
$983$	−1.02169	+	0.656603i	−0.0325870	+	0.0209424i	−0.556833	−	0.830625i	$-0.687984\pi$
$983$	−1.02169	+	0.656603i	−0.0325870	+	0.0209424i	0.524246	+	0.851567i	$0.324347\pi$
$984$	−4.90330	−	6.08752i	−0.156312	−	0.194063i
$985$	14.1700	+	9.10652i	0.451494	+	0.290158i
$986$	−0.661910	+	1.40461i	−0.0210795	+	0.0447320i
$987$	0.747944	−	2.54726i	0.0238073	−	0.0810802i
$988$	−4.26045	+	2.59597i	−0.135543	+	0.0825889i
$989$	11.0628	+	21.2525i	0.351776	+	0.675790i
$990$	5.70188	+	20.3159i	0.181218	+	0.645681i
$991$	22.2694	+	6.53888i	0.707410	+	0.207714i	0.615596	−	0.788062i	$-0.288915\pi$
$991$	22.2694	+	6.53888i	0.707410	+	0.207714i	0.0918139	+	0.995776i	$0.470734\pi$
$992$	22.3233	−	17.1156i	0.708766	−	0.543420i
$993$	20.5284	+	13.1928i	0.651450	+	0.418661i
$994$	0.436794	−	0.0574706i	0.0138543	−	0.00182286i
$995$	−34.6978	−	53.9908i	−1.09999	−	1.71162i
$996$	−2.63207	−	1.78203i	−0.0834002	−	0.0564657i
$997$	9.22150	−	7.99047i	0.292048	−	0.253061i	−0.496497	−	0.868039i	$-0.665381\pi$
$997$	9.22150	−	7.99047i	0.292048	−	0.253061i	0.788544	+	0.614978i	$0.210835\pi$
$998$	−23.8246	−	53.8669i	−0.754156	−	1.70513i
$999$	1.62886	−	3.56670i	0.0515348	−	0.112845i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.133.22	✓	480
8.5	even	2	inner	552.2.bb.a.133.32	yes	480
23.9	even	11	inner	552.2.bb.a.469.32	yes	480
184.101	even	22	inner	552.2.bb.a.469.22	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.133.22	✓	480	1.1	even	1	trivial
552.2.bb.a.133.32	yes	480	8.5	even	2	inner
552.2.bb.a.469.22	yes	480	184.101	even	22	inner
552.2.bb.a.469.32	yes	480	23.9	even	11	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0169381 + 1.41411i) q^{2} +(-0.755750 - 0.654861i) q^{3} +(-1.99943 - 0.0479047i) q^{4} +(-4.14042 - 0.595303i) q^{5} +(0.938847 - 1.05762i) q^{6} +(-0.0911276 - 0.199542i) q^{7} +(0.101609 - 2.82660i) q^{8} +(0.142315 + 0.989821i) q^{9} +(0.911956 - 5.84494i) q^{10} +(1.00493 + 3.42246i) q^{11} +(1.47969 + 1.34555i) q^{12} +(0.385957 + 0.176261i) q^{13} +(0.283718 - 0.125485i) q^{14} +(2.73928 + 3.16130i) q^{15} +(3.99541 + 0.191564i) q^{16} +(1.76125 - 1.13188i) q^{17} +(-1.40213 + 0.184483i) q^{18} +(3.17850 - 4.94584i) q^{19} +(8.24995 + 1.38861i) q^{20} +(-0.0618023 + 0.210479i) q^{21} +(-4.85677 + 1.36311i) q^{22} +(4.45930 + 1.76485i) q^{23} +(-1.92782 + 2.06966i) q^{24} +(11.9912 + 3.52095i) q^{25} +(-0.255790 + 0.542801i) q^{26} +(0.540641 - 0.841254i) q^{27} +(0.172644 + 0.403334i) q^{28} +(0.283534 + 0.441187i) q^{29} +(-4.51683 + 3.82011i) q^{30} +(-3.25640 - 3.75808i) q^{31} +(-0.338568 + 5.64671i) q^{32} +(1.48176 - 3.24461i) q^{33} +(1.57078 + 2.50977i) q^{34} +(0.258519 + 0.880435i) q^{35} +(-0.237131 - 1.98589i) q^{36} +(3.88113 - 0.558022i) q^{37} +(6.94014 + 4.57853i) q^{38} +(-0.176261 - 0.385957i) q^{39} +(-2.10339 + 11.6428i) q^{40} +(-0.393302 + 2.73548i) q^{41} +(-0.296595 - 0.0909605i) q^{42} +(3.77564 + 3.27161i) q^{43} +(-1.84532 - 6.89111i) q^{44} -4.18300i q^{45} +(-2.57122 + 6.27605i) q^{46} -12.1022 q^{47} +(-2.89408 - 2.76121i) q^{48} +(4.55251 - 5.25388i) q^{49} +(-5.18212 + 16.8973i) q^{50} +(-2.07229 - 0.297950i) q^{51} +(-0.763249 - 0.370910i) q^{52} +(5.83907 - 2.66661i) q^{53} +(1.18047 + 0.778776i) q^{54} +(-2.12342 - 14.7687i) q^{55} +(-0.573284 + 0.237306i) q^{56} +(-5.64099 + 1.65634i) q^{57} +(-0.628691 + 0.393476i) q^{58} +(-4.28842 - 1.95846i) q^{59} +(-5.32555 - 6.45201i) q^{60} +(1.70276 - 1.47545i) q^{61} +(5.36951 - 4.54125i) q^{62} +(0.184542 - 0.118598i) q^{63} +(-7.97935 - 0.574417i) q^{64} +(-1.49310 - 0.959555i) q^{65} +(4.56315 + 2.15034i) q^{66} +(1.22351 - 4.16688i) q^{67} +(-3.57570 + 2.17875i) q^{68} +(-2.21438 - 4.25400i) q^{69} +(-1.24941 + 0.350662i) q^{70} +(1.36258 + 0.400090i) q^{71} +(2.81229 - 0.301692i) q^{72} +(9.58497 + 6.15989i) q^{73} +(0.723367 + 5.49780i) q^{74} +(-6.75665 - 10.5136i) q^{75} +(-6.59210 + 9.73658i) q^{76} +(0.591348 - 0.512406i) q^{77} +(0.548772 - 0.242715i) q^{78} +(3.32782 - 7.28692i) q^{79} +(-16.4286 - 3.17164i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-3.86161 - 0.602507i) q^{82} +(-1.57312 + 0.226180i) q^{83} +(0.133652 - 0.417877i) q^{84} +(-7.96612 + 3.63800i) q^{85} +(-4.69037 + 5.28376i) q^{86} +(0.0746357 - 0.519102i) q^{87} +(9.77605 - 2.49277i) q^{88} +(-7.92669 + 9.14789i) q^{89} +(5.91523 + 0.0708521i) q^{90} -0.0930768i q^{91} +(-8.83149 - 3.74230i) q^{92} +4.97265i q^{93} +(0.204988 - 17.1139i) q^{94} +(-16.1046 + 18.5857i) q^{95} +(3.95368 - 4.04579i) q^{96} +(-0.773454 + 5.37949i) q^{97} +(7.35246 + 6.52675i) q^{98} +(-3.24461 + 1.48176i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32}+ \cdots - 132 q^{98}+O(q^{100}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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