LMFDB - Embedded newform 552.2.bb.a.469.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(13,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 11, 0, 14]))

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

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

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

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

Embedding invariants

Embedding label			469.22
Character	$\chi$	$=$	552.469
Dual form			552.2.bb.a.133.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0169381 - 1.41411i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(-1.99943 + 0.0479047i) q^{4} +(-4.14042 + 0.595303i) q^{5} +(0.938847 + 1.05762i) q^{6} +(-0.0911276 + 0.199542i) q^{7} +(0.101609 + 2.82660i) q^{8} +(0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$	$-1$	$1$

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	−0.976168	−	0.217017i	$-0.930367\pi$
$5$	−4.14042	+	0.595303i	−1.85165	+	0.266228i	−0.875485	+	0.483245i	$0.839458\pi$
$6$	0.938847	+	1.05762i	0.383283	+	0.431773i
$7$	−0.0911276	+	0.199542i	−0.0344430	+	0.0754197i	−0.926072	−	0.377348i	$-0.876836\pi$
$7$	−0.0911276	+	0.199542i	−0.0344430	+	0.0754197i	0.891629	+	0.452768i	$0.149563\pi$
$8$	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	−0.657462	−	0.753488i	$-0.728370\pi$
$11$	1.00493	−	3.42246i	0.302997	−	1.03191i	0.960458	−	0.278424i	$-0.0898120\pi$
$12$	1.47969	−	1.34555i	0.427151	−	0.388427i
$13$	0.385957	−	0.176261i	0.107045	−	0.0488859i	−0.361173	−	0.932499i	$-0.617623\pi$
$13$	0.385957	−	0.176261i	0.107045	−	0.0488859i	0.468218	+	0.883613i	$0.344896\pi$
$14$	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	0.736509	−	0.676428i	$-0.236473\pi$
$17$	1.76125	+	1.13188i	0.427165	+	0.274522i	−0.309344	+	0.950950i	$0.600109\pi$
$18$	−1.40213	−	0.184483i	−0.330485	−	0.0434832i
$19$	3.17850	+	4.94584i	0.729198	+	1.13465i	0.985765	+	0.168127i	$0.0537720\pi$
$19$	3.17850	+	4.94584i	0.729198	+	1.13465i	−0.256568	+	0.966526i	$0.582592\pi$
$20$	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	−0.813930	−	0.580963i	$-0.802676\pi$
$29$	0.283534	−	0.441187i	0.0526509	−	0.0819265i	0.866581	+	0.499036i	$0.166313\pi$
$30$	−4.51683	−	3.82011i	−0.824657	−	0.697453i
$31$	−3.25640	+	3.75808i	−0.584866	+	0.674971i	−0.968644	−	0.248454i	$-0.920077\pi$
$31$	−3.25640	+	3.75808i	−0.584866	+	0.674971i	0.383778	+	0.923426i	$0.374623\pi$
$32$	−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	0.453747	−	0.891131i	$-0.350087\pi$
$37$	3.88113	+	0.558022i	0.638054	+	0.0917382i	0.184307	+	0.982869i	$0.440996\pi$
$38$	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	−0.997210	−	0.0746434i	$-0.976218\pi$
$41$	−0.393302	−	2.73548i	−0.0614235	−	0.427210i	0.935787	−	0.352566i	$-0.114691\pi$
$42$	−0.296595	+	0.0909605i	−0.0457656	+	0.0140355i
$43$	3.77564	−	3.27161i	0.575779	−	0.498916i	−0.317596	−	0.948226i	$-0.602876\pi$
$43$	3.77564	−	3.27161i	0.575779	−	0.498916i	0.893376	+	0.449310i	$0.148330\pi$
$44$	−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	0.773894	−	0.633316i	$-0.218307\pi$
$53$	5.83907	+	2.66661i	0.802058	+	0.366288i	0.0281644	+	0.999603i	$0.491034\pi$
$54$	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	−0.674522	−	0.738254i	$-0.735650\pi$
$59$	−4.28842	+	1.95846i	−0.558305	+	0.254969i	0.116217	+	0.993224i	$0.462923\pi$
$60$	−5.32555	+	6.45201i	−0.687526	+	0.832951i
$61$	1.70276	+	1.47545i	0.218016	+	0.188912i	0.757021	−	0.653390i	$-0.226654\pi$
$61$	1.70276	+	1.47545i	0.218016	+	0.188912i	−0.539005	+	0.842303i	$0.681199\pi$
$62$	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	0.999854	−	0.0171057i	$-0.00544518\pi$
$67$	1.22351	+	4.16688i	0.149475	+	0.509066i	−0.850378	+	0.526171i	$0.823627\pi$
$68$	−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	−0.199876	−	0.979821i	$-0.564054\pi$
$71$	1.36258	−	0.400090i	0.161709	−	0.0474819i	0.361585	+	0.932339i	$0.382236\pi$
$72$	2.81229	+	0.301692i	0.331432	+	0.0355548i
$73$	9.58497	−	6.15989i	1.12184	−	0.720960i	0.157995	−	0.987440i	$-0.449497\pi$
$73$	9.58497	−	6.15989i	1.12184	−	0.720960i	0.963841	+	0.266480i	$0.0858605\pi$
$74$	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	0.999236	+	0.0390788i	$0.0124423\pi$
$79$	3.32782	+	7.28692i	0.374409	+	0.819842i	−0.624827	+	0.780763i	$0.714830\pi$
$80$	−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	0.0554365	−	0.998462i	$-0.482345\pi$
$83$	−1.57312	−	0.226180i	−0.172672	−	0.0248265i	−0.228108	+	0.973636i	$0.573254\pi$
$84$	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	0.159619	−	0.987179i	$-0.448973\pi$
$89$	−7.92669	−	9.14789i	−0.840228	−	0.969674i	−0.999847	+	0.0175044i	$0.994428\pi$
$90$	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	−0.990666	−	0.136312i	$-0.956475\pi$
$97$	−0.773454	−	5.37949i	−0.0785324	−	0.546205i	0.912134	−	0.409893i	$-0.134434\pi$
$98$	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	0.979124	−	0.203262i	$-0.0651545\pi$
$101$	18.7060	+	2.68952i	1.86132	+	0.267618i	0.882197	+	0.470880i	$0.156064\pi$
$102$	0.456435	+	2.92540i	0.0451938	+	0.289658i
$103$	8.50963	+	2.49865i	0.838479	+	0.246200i	0.672655	−	0.739956i	$-0.265154\pi$
$103$	8.50963	+	2.49865i	0.838479	+	0.246200i	0.165823	+	0.986155i	$0.446972\pi$
$104$	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	0.994901	−	0.100855i	$-0.0321577\pi$
$107$	10.7233	+	9.29181i	1.03666	+	0.898273i	0.0417612	+	0.999128i	$0.486703\pi$
$108$	−1.12127	−	1.65613i	−0.107894	−	0.159361i
$109$	10.3561	−	16.1144i	0.991933	−	1.54348i	0.161113	−	0.986936i	$-0.448492\pi$
$109$	10.3561	−	16.1144i	0.991933	−	1.54348i	0.830820	−	0.556541i	$-0.187872\pi$
$110$	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	0.327329	−	0.944910i	$-0.393851\pi$
$113$	11.8372	−	3.47573i	1.11355	−	0.326969i	0.786224	+	0.617941i	$0.212033\pi$
$114$	−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	−0.734373	−	0.678746i	$-0.762524\pi$
$127$	−19.3735	−	5.68859i	−1.71912	−	0.504780i	−0.984752	+	0.173966i	$0.944342\pi$
$128$	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	0.523793	−	0.851845i	$-0.324516\pi$
$131$	2.55262	+	1.16574i	0.223023	+	0.101851i	−0.300770	+	0.953697i	$0.597244\pi$
$132$	−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	$0.281641\pi$
$139$			18.2457i			1.54758i	−0.633444	+	0.773789i	$0.718359\pi$
$140$	−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	0.701999	+	0.712178i	$0.252291\pi$
$149$	−3.33962	+	11.3737i	−0.273592	+	0.931770i	−0.975592	+	0.219593i	$0.929527\pi$
$150$	14.9818	+	9.37658i	1.22326	+	0.765595i
$151$	4.59862	+	10.0696i	0.374230	+	0.819450i	0.999246	+	0.0388372i	$0.0123654\pi$
$151$	4.59862	+	10.0696i	0.374230	+	0.819450i	−0.625015	+	0.780612i	$0.714907\pi$
$152$	−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	0.584677	−	0.811266i	$-0.301221\pi$
$157$	−4.96388	−	7.72394i	−0.396160	−	0.616438i	−0.980837	+	0.194829i	$0.937585\pi$
$158$	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	−0.779212	−	0.626761i	$-0.784380\pi$
$163$	−5.90544	−	20.1121i	−0.462550	−	1.57530i	0.316662	−	0.948538i	$-0.397438\pi$
$164$	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	0.711596	−	0.702589i	$-0.247973\pi$
$167$	4.75697	+	3.05712i	0.368105	+	0.236567i	−0.343490	+	0.939156i	$0.611609\pi$
$168$	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	−0.983180	−	0.182641i	$-0.941535\pi$
$173$	−0.754096	+	2.56821i	−0.0573329	+	0.195258i	0.925847	+	0.377899i	$0.123353\pi$
$174$	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	0.273833	−	0.961777i	$-0.411709\pi$
$179$	10.8041	−	1.55340i	0.807537	−	0.116106i	0.533704	+	0.845671i	$0.320799\pi$
$180$	−0.200385	−	8.36360i	−0.0149359	−	0.623386i
$181$	−4.85288	+	4.20505i	−0.360712	+	0.312559i	−0.816296	−	0.577634i	$-0.803976\pi$
$181$	−4.85288	+	4.20505i	−0.360712	+	0.312559i	0.455584	+	0.890193i	$0.349431\pi$
$182$	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	−0.972002	−	0.234974i	$-0.924500\pi$
$191$	−2.18215	+	4.77824i	−0.157895	+	0.345741i	0.814107	+	0.580715i	$0.197227\pi$
$192$	5.65423	−	5.65948i	0.408059	−	0.408438i
$193$	−2.51780	+	17.5117i	−0.181236	+	1.26052i	0.672611	+	0.739996i	$0.265173\pi$
$193$	−2.51780	+	17.5117i	−0.181236	+	1.26052i	−0.853847	+	0.520525i	$0.825736\pi$
$194$	−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	−0.541603	−	0.840634i	$-0.682182\pi$
$197$	−3.66287	+	1.67278i	−0.260969	+	0.119180i	0.280634	+	0.959815i	$0.409455\pi$
$198$	−2.04042	+	4.61334i	−0.145007	+	0.327856i
$199$	10.0474	−	11.5953i	0.712242	−	0.821971i	−0.278110	−	0.960549i	$-0.589708\pi$
$199$	10.0474	−	11.5953i	0.712242	−	0.821971i	0.990351	+	0.138578i	$0.0442533\pi$
$200$	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	0.628277	−	0.777990i	$-0.283760\pi$
$211$	−4.94464	−	7.69401i	−0.340403	−	0.529677i	−0.968680	+	0.248312i	$0.920124\pi$
$212$	−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	−0.775779	−	0.631005i	$-0.782643\pi$
$223$	3.12298	−	6.83836i	0.209130	−	0.457931i	0.984909	+	0.173074i	$0.0553701\pi$
$224$	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	−0.753633	−	0.657296i	$-0.771700\pi$
$227$	−3.16819	+	2.74525i	−0.210280	+	0.182209i	0.543352	+	0.839505i	$0.317155\pi$
$228$	11.3581	+	3.04151i	0.752207	+	0.201429i
$229$		−	4.56557i		−	0.301701i	−0.988557	−	0.150851i	$-0.951799\pi$
$229$		−	4.56557i		−	0.301701i	0.988557	−	0.150851i	$-0.0482013\pi$
$230$	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	0.428236	−	0.903667i	$-0.359135\pi$
$233$	−8.04701	−	9.28674i	−0.527177	−	0.608395i	−0.955413	+	0.295272i	$0.904590\pi$
$234$	−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	0.827627	+	0.561278i	$0.189690\pi$
$239$	−1.92636	+	13.3981i	−0.124606	+	0.866651i	−0.952233	+	0.305373i	$0.901219\pi$
$240$	10.3390	−	13.1554i	0.667377	−	0.849180i
$241$	23.0331	+	6.76314i	1.48369	+	0.435652i	0.920523	−	0.390688i	$-0.127763\pi$
$241$	23.0331	+	6.76314i	1.48369	+	0.435652i	0.563171	+	0.826340i	$0.309581\pi$
$242$	−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	0.842544	−	0.538627i	$-0.181057\pi$
$251$	−2.49452	−	8.49557i	−0.157453	−	0.536236i	−0.999997	+	0.00239171i	$0.999239\pi$
$252$	−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	−0.986516	−	0.163664i	$-0.947669\pi$
$257$	−19.9982	+	12.8521i	−1.24746	+	0.801691i	−0.260939	+	0.965355i	$0.584032\pi$
$258$	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	−0.997869	−	0.0652516i	$-0.979215\pi$
$263$	−6.38503	−	13.9813i	−0.393718	−	0.862121i	0.604151	−	0.796870i	$-0.293512\pi$
$264$	−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	0.613041	−	0.790051i	$-0.289946\pi$
$269$	6.84613	+	3.12652i	0.417416	+	0.190627i	−0.195625	+	0.980679i	$0.562673\pi$
$270$	−4.42403	+	3.92720i	−0.269238	+	0.239002i
$271$	−3.08485	−	21.4556i	−0.187391	−	1.30333i	−0.838731	−	0.544547i	$-0.816702\pi$
$271$	−3.08485	−	21.4556i	−0.187391	−	1.30333i	0.651340	−	0.758786i	$-0.274207\pi$
$272$	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	$-0.692629\pi$
$277$		−	27.3752i		−	1.64482i	0.568896	−	0.822409i	$-0.307371\pi$
$278$	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	0.654695	+	0.755893i	$0.272797\pi$
$281$	4.01441	+	27.9208i	0.239479	+	1.66562i	−0.415216	+	0.909723i	$0.636294\pi$
$282$	−11.3621	−	12.7995i	−0.676604	−	0.762202i
$283$	−26.5348	−	12.1180i	−1.57733	−	0.720342i	−0.581670	−	0.813425i	$-0.697601\pi$
$283$	−26.5348	−	12.1180i	−1.57733	−	0.720342i	−0.995658	+	0.0930829i	$0.970328\pi$
$284$	−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	−0.127767	−	0.991804i	$-0.540781\pi$
$293$	14.1643	−	22.0401i	0.827486	−	1.28759i	0.955253	−	0.295789i	$-0.0955827\pi$
$294$	−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	0.697363	−	0.716718i	$-0.254356\pi$
$307$	1.52762	+	1.32369i	0.0871859	+	0.0755470i	−0.610177	+	0.792265i	$0.708902\pi$
$308$	−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	0.589934	−	0.807452i	$-0.299154\pi$
$311$	11.4572	+	3.36413i	0.649676	+	0.190762i	0.0597423	+	0.998214i	$0.480972\pi$
$312$	−1.10886	−	0.459002i	−0.0627767	−	0.0259859i
$313$	−2.68627	+	18.6834i	−0.151837	+	1.05605i	0.761300	+	0.648399i	$0.224561\pi$
$313$	−2.68627	+	18.6834i	−0.151837	+	1.05605i	−0.913138	+	0.407652i	$0.866348\pi$
$314$	−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	−0.888284	−	0.459294i	$-0.848102\pi$
$317$	−28.6864	+	4.12448i	−1.61119	+	0.231654i	−0.722905	+	0.690948i	$0.757193\pi$
$318$	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	−0.558239	−	0.829680i	$-0.688523\pi$
$331$	−24.1538	−	3.47279i	−1.32761	−	0.190882i	−0.769374	+	0.638798i	$0.779432\pi$
$332$	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	−0.721189	−	0.692739i	$-0.756404\pi$
$337$	1.23243	−	1.42230i	0.0671350	−	0.0774779i	0.788324	+	0.615261i	$0.210949\pi$
$338$	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	−0.999934	−	0.0114949i	$-0.996341\pi$
$347$	−3.07269	−	10.4646i	−0.164951	−	0.561770i	0.834983	−	0.550275i	$-0.185477\pi$
$348$	−0.174096	−	1.03433i	−0.00933252	−	0.0554460i
$349$	16.6696	+	25.9385i	0.892305	+	1.38845i	0.921291	+	0.388874i	$0.127136\pi$
$349$	16.6696	+	25.9385i	0.892305	+	1.38845i	−0.0289857	+	0.999580i	$0.509228\pi$
$350$	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	−0.465066	−	0.885276i	$-0.653969\pi$
$353$	8.96925	−	10.3511i	0.477385	−	0.550932i	0.942451	+	0.334344i	$0.108515\pi$
$354$	−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	0.877715	+	0.479183i	$0.159067\pi$
$359$	−1.88427	+	13.1054i	−0.0994478	+	0.691674i	−0.977163	+	0.212492i	$0.931842\pi$
$360$	−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	0.268256	−	0.963348i	$-0.413553\pi$
$373$	15.3936	−	2.21327i	0.797051	−	0.114599i	0.528796	+	0.848749i	$0.322644\pi$
$374$	−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	0.597357	+	0.801975i	$0.296217\pi$
$379$	−6.59480	+	22.4598i	−0.338752	+	1.15368i	−0.936109	+	0.351709i	$0.885601\pi$
$380$	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	−0.855480	−	0.517836i	$-0.826738\pi$
$383$	−4.32831	+	4.99514i	−0.221167	+	0.255240i	0.634313	+	0.773076i	$0.281283\pi$
$384$	−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	0.999408	+	0.0343968i	$0.0109510\pi$
$389$	3.49589	+	11.9059i	0.177249	+	0.603654i	−0.822159	+	0.569257i	$0.807231\pi$
$390$	−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	0.212168	−	0.977233i	$-0.431948\pi$
$397$	20.1829	−	31.4053i	1.01295	−	1.57619i	0.800785	−	0.598952i	$-0.204416\pi$
$398$	−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	0.985515	+	0.169589i	$0.0542440\pi$
$401$	9.37783	+	20.5346i	0.468307	+	1.02545i	−0.517208	+	0.855860i	$0.673029\pi$
$402$	−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	0.986580	−	0.163277i	$-0.0522066\pi$
$409$	−0.122094	−	0.849182i	−0.00603716	−	0.0419893i	−0.992617	+	0.121288i	$0.961297\pi$
$410$	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	−0.779113	−	0.626883i	$-0.784330\pi$
$419$	−27.6349	+	3.97330i	−1.35005	+	0.194108i	−0.570940	+	0.820992i	$0.693421\pi$
$420$	−0.802140	−	1.65063i	−0.0391404	−	0.0805423i
$421$	10.8951	+	4.97564i	0.530996	+	0.242498i	0.662825	−	0.748775i	$-0.269358\pi$
$421$	10.8951	+	4.97564i	0.530996	+	0.242498i	−0.131828	+	0.991273i	$0.542085\pi$
$422$	−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	0.987482	+	0.157734i	$0.0504190\pi$
$431$	31.9957	+	20.5624i	1.54118	+	0.990454i	0.553695	+	0.832720i	$0.313217\pi$
$432$	2.32124	+	3.25759i	0.111681	+	0.156731i
$433$	−3.62917	+	2.33232i	−0.174407	+	0.112084i	−0.624932	−	0.780679i	$-0.714873\pi$
$433$	−3.62917	+	2.33232i	−0.174407	+	0.112084i	0.450525	+	0.892764i	$0.351237\pi$
$434$	−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	−0.682921	−	0.730493i	$-0.739291\pi$
$439$	−18.0713	+	5.30621i	−0.862496	+	0.253252i	−0.179575	+	0.983744i	$0.557472\pi$
$440$	−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	−0.929352	−	0.369195i	$-0.879634\pi$
$443$	−4.36640	+	6.79426i	−0.207454	+	0.322805i	0.721898	+	0.691999i	$0.243270\pi$
$444$	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	−0.699687	−	0.714450i	$-0.746677\pi$
$449$	−35.4833	−	10.4188i	−1.67456	−	0.491696i	−0.974875	+	0.222754i	$0.928495\pi$
$450$	−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	0.595588	−	0.803290i	$-0.296919\pi$
$457$	−6.07736	−	7.01364i	−0.284287	−	0.328084i	−0.879875	+	0.475206i	$0.842374\pi$
$458$	−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	$0.0591993\pi$
$461$			7.94036i			0.369819i	−0.982756	+	0.184910i	$0.940801\pi$
$462$	0.0132535	+	1.10649i	0.000616607	+	0.0514787i
$463$	18.2666	+	21.0808i	0.848923	+	0.979709i	0.999961	−	0.00881848i	$-0.00280705\pi$
$463$	18.2666	+	21.0808i	0.848923	+	0.979709i	−0.151038	+	0.988528i	$0.548262\pi$
$464$	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	0.586022	−	0.810295i	$-0.300693\pi$
$467$	7.72357	+	3.52723i	0.357404	+	0.163221i	−0.228618	+	0.973516i	$0.573421\pi$
$468$	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	−0.401924	−	0.915673i	$-0.631659\pi$
$479$	5.77870	−	3.71374i	0.264035	−	0.169685i	0.665960	+	0.745988i	$0.268022\pi$
$480$	−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	−0.361392	−	0.932414i	$-0.617698\pi$
$487$	7.42887	−	4.77424i	0.336634	−	0.216342i	0.698026	+	0.716072i	$0.254062\pi$
$488$	−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	0.997330	+	0.0730250i	$0.0232653\pi$
$491$	26.8461	+	23.2623i	1.21155	+	1.04981i	0.214217	+	0.976786i	$0.431280\pi$
$492$	−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	−0.998311	−	0.0580953i	$-0.981497\pi$
$499$	−37.8851	−	17.3016i	−1.69597	−	0.774524i	−0.697660	−	0.716429i	$-0.745775\pi$
$500$	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	0.943901	−	0.330229i	$-0.107126\pi$
$503$	10.8259	+	12.4937i	0.482702	+	0.557068i	−0.461199	+	0.887297i	$0.652580\pi$
$504$	−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	−0.192017	−	0.981392i	$-0.561503\pi$
$509$	16.9672	−	14.7022i	0.752059	−	0.651663i	0.944076	+	0.329729i	$0.106957\pi$
$510$	−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	−0.420001	−	0.907524i	$-0.637970\pi$
$521$	12.2814	−	14.1735i	0.538058	−	0.620952i	0.958059	+	0.286572i	$0.0925158\pi$
$522$	−0.478943	+	0.566294i	−0.0209628	+	0.0247860i
$523$	−3.46903	+	5.39792i	−0.151690	+	0.236034i	−0.908779	−	0.417277i	$-0.862984\pi$
$523$	−3.46903	+	5.39792i	−0.151690	+	0.236034i	0.757089	+	0.653312i	$0.226621\pi$
$524$	−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	−0.772902	−	0.634525i	$-0.781196\pi$
$541$	5.12532	−	17.4552i	0.220355	−	0.750459i	0.993257	−	0.115934i	$-0.0369860\pi$
$542$	−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	0.0238867	−	0.999715i	$-0.492396\pi$
$547$	7.68198	−	1.10450i	0.328458	−	0.0472251i	0.304571	+	0.952490i	$0.401487\pi$
$548$	−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	−0.893854	−	0.448359i	$-0.852009\pi$
$557$	−38.3557	+	5.51472i	−1.62518	+	0.233666i	−0.731329	+	0.682025i	$0.761100\pi$
$558$	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	−0.940724	−	0.339172i	$-0.889853\pi$
$563$	0.807531	−	2.75020i	0.0340334	−	0.115907i	0.974758	+	0.223265i	$0.0716714\pi$
$564$	−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	0.736450	−	0.676492i	$-0.236501\pi$
$569$	10.1861	+	6.54621i	0.427023	+	0.274431i	−0.309426	+	0.950923i	$0.600137\pi$
$570$	4.53689	−	34.4817i	0.190029	−	1.44428i
$571$	1.38147	+	2.14961i	0.0578127	+	0.0899583i	0.868957	−	0.494888i	$-0.164791\pi$
$571$	1.38147	+	2.14961i	0.0578127	+	0.0899583i	−0.811144	+	0.584847i	$0.801155\pi$
$572$	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	−0.401426	−	0.915892i	$-0.631485\pi$
$577$	−5.86008	+	1.72067i	−0.243958	+	0.0716326i	0.157468	+	0.987524i	$0.449667\pi$
$578$	−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	0.631769	+	0.775156i	$0.282329\pi$
$587$	−7.72367	+	26.3044i	−0.318790	+	1.08570i	−0.950559	+	0.310543i	$0.899489\pi$
$588$	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	0.972854	−	0.231421i	$-0.0743375\pi$
$593$	−0.628062	−	4.36826i	−0.0257914	−	0.179383i	−0.998645	+	0.0520378i	$0.983428\pi$
$594$	−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	0.393353	−	0.919387i	$-0.371315\pi$
$601$	−14.0388	−	16.2017i	−0.572656	−	0.660881i	−0.966009	+	0.258507i	$0.916770\pi$
$602$	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	0.668211	+	0.743972i	$0.267060\pi$
$607$	−4.49715	+	31.2784i	−0.182534	+	1.26955i	−0.850745	+	0.525579i	$0.823849\pi$
$608$	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	0.186851	−	0.982388i	$-0.440172\pi$
$613$	−18.7906	−	16.2822i	−0.758946	−	0.657631i	−0.945797	+	0.324758i	$0.894717\pi$
$614$	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	0.336125	−	0.941817i	$-0.390884\pi$
$617$	33.0977	−	21.2706i	1.33246	−	0.856322i	0.996339	+	0.0854950i	$0.0272472\pi$
$618$	5.34661	+	11.3458i	0.215072	+	0.456396i
$619$	1.40277	+	4.77738i	0.0563819	+	0.192019i	0.982868	−	0.184309i	$-0.0590047\pi$
$619$	1.40277	+	4.77738i	0.0563819	+	0.192019i	−0.926486	+	0.376328i	$0.877187\pi$
$620$	−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	0.696420	−	0.717634i	$-0.254775\pi$
$631$	−7.58590	−	16.6108i	−0.301990	−	0.661266i	−0.998410	+	0.0563685i	$0.982048\pi$
$632$	−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	0.213747	−	0.976889i	$-0.431433\pi$
$641$	−19.8396	−	22.8962i	−0.783618	−	0.904344i	−0.997365	+	0.0725452i	$0.976888\pi$
$642$	0.240334	+	20.0648i	0.00948524	+	0.791895i
$643$		−	31.1709i		−	1.22926i	−0.788815	−	0.614631i	$-0.789305\pi$
$643$		−	31.1709i		−	1.22926i	0.788815	−	0.614631i	$-0.210695\pi$
$644$	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	0.676923	−	0.736053i	$-0.263313\pi$
$647$	−3.76390	−	4.34378i	−0.147974	−	0.170771i	−0.824898	+	0.565282i	$0.808767\pi$
$648$	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	0.0509997	−	0.998699i	$-0.483759\pi$
$653$	−4.63630	−	0.666599i	−0.181432	−	0.0260860i	−0.232432	+	0.972613i	$0.574668\pi$
$654$	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	0.906883	−	0.421382i	$-0.138455\pi$
$659$	15.8866	+	13.7658i	0.618852	+	0.536239i	−0.288031	+	0.957621i	$0.593000\pi$
$660$	16.7300	+	24.7103i	0.651214	+	0.961847i
$661$	−6.86170	+	10.6770i	−0.266889	+	0.415288i	−0.948669	−	0.316269i	$-0.897570\pi$
$661$	−6.86170	+	10.6770i	−0.266889	+	0.415288i	0.681780	+	0.731557i	$0.261206\pi$
$662$	−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	0.198859	−	0.980028i	$-0.436276\pi$
$673$	−15.8247	−	10.1699i	−0.609997	−	0.392021i	−0.808856	+	0.588007i	$0.799913\pi$
$674$	−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	0.129447	−	0.991586i	$-0.458680\pi$
$677$	25.0723	−	11.4502i	0.963608	−	0.440065i	0.834161	+	0.551521i	$0.185952\pi$
$678$	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	0.584835	−	0.811152i	$-0.301159\pi$
$683$	9.27224	+	4.23449i	0.354792	+	0.162028i	−0.230043	+	0.973181i	$0.573887\pi$
$684$	−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	$0.171219\pi$
$691$			26.9353i			1.02467i	−0.858786	+	0.512334i	$0.828781\pi$
$692$	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	0.627699	+	0.778456i	$0.283997\pi$
$701$	−8.50475	+	28.9645i	−0.321220	+	1.09397i	−0.948919	+	0.315519i	$0.897821\pi$
$702$	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	0.984286	−	0.176579i	$-0.0565032\pi$
$709$	11.0443	+	17.1852i	0.414777	+	0.645405i	−0.569510	+	0.821985i	$0.692867\pi$
$710$	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	0.739740	−	0.672893i	$-0.234949\pi$
$719$	11.6629	+	7.49530i	0.434953	+	0.279528i	−0.304786	+	0.952421i	$0.598585\pi$
$720$	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	−0.883905	−	0.467666i	$-0.845095\pi$
$727$	2.58715	−	17.9941i	0.0959523	−	0.667363i	0.979858	−	0.199697i	$-0.0639958\pi$
$728$	−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	−0.289558	−	0.957161i	$-0.593508\pi$
$733$	16.6952	−	14.4665i	0.616652	−	0.534332i	0.906210	+	0.422829i	$0.138963\pi$
$734$	−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	−0.633463	−	0.773773i	$-0.718367\pi$
$739$	1.14943	−	0.995984i	0.0422823	−	0.0366379i	0.675746	+	0.737135i	$0.263822\pi$
$740$	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	−0.986442	−	0.164109i	$-0.947525\pi$
$743$	−5.89959	+	12.9183i	−0.216435	+	0.473926i	0.770007	+	0.638035i	$0.220252\pi$
$744$	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	0.180678	−	0.983542i	$-0.442171\pi$
$751$	30.9257	−	35.6902i	1.12850	−	1.30235i	0.947818	−	0.318812i	$-0.103284\pi$
$752$	−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	−0.997145	−	0.0755165i	$-0.975939\pi$
$757$	−5.47853	−	18.6582i	−0.199120	−	0.678142i	0.798024	−	0.602626i	$-0.205879\pi$
$758$	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	−0.716633	−	0.697450i	$-0.754318\pi$
$761$	−25.9982	+	7.63376i	−0.942434	+	0.276724i	−0.225800	+	0.974174i	$0.572500\pi$
$762$	−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	0.895382	−	0.445299i	$-0.146903\pi$
$769$	−0.762684	−	1.67004i	−0.0275031	−	0.0602233i	−0.922885	+	0.385076i	$0.874175\pi$
$770$	−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	0.447464	−	0.894302i	$-0.352327\pi$
$773$	17.3726	+	2.49780i	0.624848	+	0.0898396i	0.177384	+	0.984142i	$0.443236\pi$
$774$	−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	−0.258621	−	0.965979i	$-0.583268\pi$
$787$	−6.58190	+	0.946334i	−0.234619	+	0.0337332i	0.0240022	+	0.999712i	$0.492359\pi$
$788$	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	0.785393	−	0.618997i	$-0.212461\pi$
$797$	8.03093	+	6.95884i	0.284470	+	0.246495i	−0.500923	+	0.865492i	$0.667006\pi$
$798$	−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	−0.989142	−	0.146963i	$-0.953050\pi$
$809$	−36.0191	+	23.1481i	−1.26636	+	0.813843i	−0.277223	+	0.960806i	$0.589414\pi$
$810$	0.771694	−	5.86510i	0.0271146	−	0.206079i
$811$	−12.0579	+	18.7624i	−0.423409	+	0.658837i	−0.985779	−	0.168049i	$-0.946253\pi$
$811$	−12.0579	+	18.7624i	−0.423409	+	0.658837i	0.562370	+	0.826886i	$0.309890\pi$
$812$	−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	0.505281	−	0.862955i	$-0.331389\pi$
$821$	5.27194	+	2.40762i	0.183992	+	0.0840264i	−0.321289	+	0.946981i	$0.604116\pi$
$822$	19.7416	+	22.2392i	0.688569	+	0.775681i
$823$	5.52209	+	38.4070i	0.192488	+	1.33878i	0.825395	+	0.564556i	$0.190952\pi$
$823$	5.52209	+	38.4070i	0.192488	+	1.33878i	−0.632907	+	0.774228i	$0.718138\pi$
$824$	−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	$0.109636\pi$
$827$			19.4206i			0.675322i	−0.941268	+	0.337661i	$0.890364\pi$
$828$	2.44736	+	9.27418i	0.0850517	+	0.322300i
$829$			17.5507i			0.609563i	0.952422	+	0.304781i	$0.0985834\pi$
$829$			17.5507i			0.609563i	−0.952422	+	0.304781i	$0.901417\pi$
$830$	−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	−0.288126	−	0.957593i	$-0.593032\pi$
$839$	−30.3624	−	8.91520i	−1.04823	−	0.307787i	−0.760100	+	0.649806i	$0.774850\pi$
$840$	−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	−0.998018	−	0.0629352i	$-0.979954\pi$
$853$	−5.62093	−	19.1431i	−0.192457	−	0.655449i	0.805561	−	0.592514i	$-0.201864\pi$
$854$	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	0.915945	−	0.401303i	$-0.131443\pi$
$857$	27.2665	+	17.5231i	0.931404	+	0.598577i	0.0154591	+	0.999881i	$0.495079\pi$
$858$	1.38216	−	1.63424i	0.0471861	−	0.0557921i
$859$	0.733713	+	0.635766i	0.0250340	+	0.0216921i	0.667288	−	0.744800i	$-0.267455\pi$
$859$	0.733713	+	0.635766i	0.0250340	+	0.0216921i	−0.642254	+	0.766492i	$0.722001\pi$
$860$	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	−0.116809	−	0.993154i	$-0.537266\pi$
$863$	−22.0918	−	6.48674i	−0.752014	−	0.220811i	−0.635205	+	0.772343i	$0.719085\pi$
$864$	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	−0.0921328	−	0.995747i	$-0.529368\pi$
$877$	26.0713	−	22.5909i	0.880367	−	0.762842i	0.972500	+	0.232905i	$0.0748230\pi$
$878$	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	−0.817746	−	0.575580i	$-0.804776\pi$
$881$	4.53411	−	9.92832i	0.152758	−	0.334494i	0.970504	+	0.241086i	$0.0775037\pi$
$882$	−5.41396	−	8.20648i	−0.182297	−	0.276327i
$883$	−6.15362	−	0.884758i	−0.207086	−	0.0297745i	0.0379911	−	0.999278i	$-0.487904\pi$
$883$	−6.15362	−	0.884758i	−0.207086	−	0.0297745i	−0.245077	+	0.969504i	$0.578813\pi$
$884$	−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	0.841340	−	0.540506i	$-0.181767\pi$
$887$	−3.51755	−	7.70237i	−0.118108	−	0.258620i	−0.959448	+	0.281886i	$0.909040\pi$
$888$	−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	−0.0376932	−	0.999289i	$-0.512001\pi$
$907$	20.8657	−	9.52906i	0.692836	−	0.316407i	0.730529	+	0.682882i	$0.239274\pi$
$908$	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	−0.594026	−	0.804446i	$-0.702462\pi$
$911$	6.11432	−	42.5260i	0.202576	−	1.40895i	0.796602	−	0.604504i	$-0.206629\pi$
$912$	−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	−0.480721	−	0.876873i	$-0.659625\pi$
$929$	6.93626	−	48.2427i	0.227571	−	1.58279i	0.708293	−	0.705919i	$-0.249466\pi$
$930$	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	0.830064	−	0.557669i	$-0.188304\pi$
$937$	20.4359	+	13.1334i	0.667612	+	0.429048i	−0.162452	+	0.986716i	$0.551940\pi$
$938$	−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	0.973189	+	0.230008i	$0.0738751\pi$
$941$	8.55367	+	29.1311i	0.278842	+	0.949648i	−0.694347	+	0.719640i	$0.744307\pi$
$942$	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	−0.999418	−	0.0340988i	$-0.989144\pi$
$947$	−18.9337	−	29.4614i	−0.615262	−	0.957367i	0.384156	−	0.923268i	$-0.374492\pi$
$948$	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	−0.999984	−	0.00560944i	$-0.998214\pi$
$953$	−10.7854	−	23.6167i	−0.349373	−	0.765021i	0.650611	−	0.759411i	$-0.274513\pi$
$954$	−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	−0.515731	−	0.856751i	$-0.672480\pi$
$971$	−23.9688	+	3.44620i	−0.769197	+	0.110594i	−0.253466	+	0.967344i	$0.581571\pi$
$972$	−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	−0.240060	−	0.970758i	$-0.577167\pi$
$977$	−30.2206	−	8.87357i	−0.966843	−	0.283891i	−0.726783	+	0.686867i	$0.758985\pi$
$978$	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	0.524246	−	0.851567i	$-0.324347\pi$
$983$	−1.02169	−	0.656603i	−0.0325870	−	0.0209424i	−0.556833	+	0.830625i	$0.687984\pi$
$984$	−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	0.0918139	−	0.995776i	$-0.470734\pi$
$991$	22.2694	−	6.53888i	0.707410	−	0.207714i	0.615596	+	0.788062i	$0.288915\pi$
$992$	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	0.788544	−	0.614978i	$-0.210835\pi$
$997$	9.22150	+	7.99047i	0.292048	+	0.253061i	−0.496497	+	0.868039i	$0.665381\pi$
$998$	−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.469.22	yes	480
8.5	even	2	inner	552.2.bb.a.469.32	yes	480
23.18	even	11	inner	552.2.bb.a.133.32	yes	480
184.133	even	22	inner	552.2.bb.a.133.22	✓	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.133.22	✓	480	184.133	even	22	inner
552.2.bb.a.133.32	yes	480	23.18	even	11	inner
552.2.bb.a.469.22	yes	480	1.1	even	1	trivial
552.2.bb.a.469.32	yes	480	8.5	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.0169381 - 1.41411i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(-1.99943 + 0.0479047i) q^{4} +(-4.14042 + 0.595303i) q^{5} +(0.938847 + 1.05762i) q^{6} +(-0.0911276 + 0.199542i) q^{7} +(0.101609 + 2.82660i) q^{8} +(0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) \) 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

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