LMFDB - Embedded newform 63.2.f.a.43.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [63,2,Mod(22,63)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(63, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("63.22"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	63.f (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$0.503057532734$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			43.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	63.43
Dual form			63.2.f.a.22.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.26604 + 2.19285i) q^{2} +(-1.11334 + 1.32683i) q^{3} +(-2.20574 - 3.82045i) q^{4} +(0.439693 + 0.761570i) q^{5} +(-1.50000 - 4.12122i) q^{6} +(-0.500000 + 0.866025i) q^{7} +6.10607 q^{8} +(-0.520945 - 2.95442i) q^{9} -2.22668 q^{10} +(-1.93969 + 3.35965i) q^{11} +(7.52481 + 1.32683i) q^{12} +(2.72668 + 4.72275i) q^{13} +(-1.26604 - 2.19285i) q^{14} +(-1.50000 - 0.264490i) q^{15} +(-3.31908 + 5.74881i) q^{16} +1.65270 q^{17} +(7.13816 + 2.59808i) q^{18} +2.41147 q^{19} +(1.93969 - 3.35965i) q^{20} +(-0.592396 - 1.62760i) q^{21} +(-4.91147 - 8.50692i) q^{22} +(-1.58125 - 2.73881i) q^{23} +(-6.79813 + 8.10170i) q^{24} +(2.11334 - 3.66041i) q^{25} -13.8084 q^{26} +(4.50000 + 2.59808i) q^{27} +4.41147 q^{28} +(3.02481 - 5.23913i) q^{29} +(2.47906 - 2.95442i) q^{30} +(2.27719 + 3.94421i) q^{31} +(-2.29813 - 3.98048i) q^{32} +(-2.29813 - 6.31407i) q^{33} +(-2.09240 + 3.62414i) q^{34} -0.879385 q^{35} +(-10.1382 + 8.50692i) q^{36} -4.55438 q^{37} +(-3.05303 + 5.28801i) q^{38} +(-9.30200 - 1.64019i) q^{39} +(2.68479 + 4.65020i) q^{40} +(0.592396 + 1.02606i) q^{41} +(4.31908 + 0.761570i) q^{42} +(-0.0923963 + 0.160035i) q^{43} +17.1138 q^{44} +(2.02094 - 1.69577i) q^{45} +8.00774 q^{46} +(0.511144 - 0.885328i) q^{47} +(-3.93242 - 10.8042i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(5.35117 + 9.26849i) q^{50} +(-1.84002 + 2.19285i) q^{51} +(12.0287 - 20.8343i) q^{52} +7.29086 q^{53} +(-11.3944 + 6.57856i) q^{54} -3.41147 q^{55} +(-3.05303 + 5.28801i) q^{56} +(-2.68479 + 3.19961i) q^{57} +(7.65910 + 13.2660i) q^{58} +(-3.33022 - 5.76811i) q^{59} +(2.29813 + 6.31407i) q^{60} +(1.29813 - 2.24843i) q^{61} -11.5321 q^{62} +(2.81908 + 1.02606i) q^{63} -1.63816 q^{64} +(-2.39780 + 4.15312i) q^{65} +(16.7554 + 2.95442i) q^{66} +(1.47906 + 2.56180i) q^{67} +(-3.64543 - 6.31407i) q^{68} +(5.39440 + 0.951178i) q^{69} +(1.11334 - 1.92836i) q^{70} -3.68004 q^{71} +(-3.18092 - 18.0399i) q^{72} -12.7811 q^{73} +(5.76604 - 9.98708i) q^{74} +(2.50387 + 6.87933i) q^{75} +(-5.31908 - 9.21291i) q^{76} +(-1.93969 - 3.35965i) q^{77} +(15.3735 - 18.3214i) q^{78} +(2.97906 - 5.15988i) q^{79} -5.83750 q^{80} +(-8.45723 + 3.07818i) q^{81} -3.00000 q^{82} +(0.109470 - 0.189608i) q^{83} +(-4.91147 + 5.85327i) q^{84} +(0.726682 + 1.25865i) q^{85} +(-0.233956 - 0.405223i) q^{86} +(3.58378 + 9.84635i) q^{87} +(-11.8439 + 20.5142i) q^{88} +11.0273 q^{89} +(1.15998 + 6.57856i) q^{90} -5.45336 q^{91} +(-6.97565 + 12.0822i) q^{92} +(-7.76857 - 1.36981i) q^{93} +(1.29426 + 2.24173i) q^{94} +(1.06031 + 1.83651i) q^{95} +(7.84002 + 1.38241i) q^{96} +(-6.25150 + 10.8279i) q^{97} +2.53209 q^{98} +(10.9363 + 3.98048i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{4} - 3 q^{5} - 9 q^{6} - 3 q^{7} + 12 q^{8} - 6 q^{11} + 18 q^{12} + 3 q^{13} - 3 q^{14} - 9 q^{15} - 3 q^{16} + 12 q^{17} + 9 q^{18} - 6 q^{19} + 6 q^{20} - 9 q^{22} - 12 q^{23} - 27 q^{24}+ \cdots + 18 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^4 - 3 * q^5 - 9 * q^6 - 3 * q^7 + 12 * q^8 - 6 * q^11 + 18 * q^12 + 3 * q^13 - 3 * q^14 - 9 * q^15 - 3 * q^16 + 12 * q^17 + 9 * q^18 - 6 * q^19 + 6 * q^20 - 9 * q^22 - 12 * q^23 - 27 * q^24 + 6 * q^25 - 6 * q^26 + 27 * q^27 + 6 * q^28 - 9 * q^29 + 18 * q^30 + 3 * q^31 - 9 * q^34 + 6 * q^35 - 27 * q^36 - 6 * q^37 - 6 * q^38 - 18 * q^39 + 9 * q^40 + 9 * q^42 + 3 * q^43 + 30 * q^44 + 9 * q^45 - 3 * q^47 - 3 * q^49 + 6 * q^50 + 9 * q^51 + 21 * q^52 + 12 * q^53 - 27 * q^54 - 6 * q^56 - 9 * q^57 + 9 * q^58 + 3 * q^59 - 6 * q^61 - 60 * q^62 + 24 * q^64 - 15 * q^65 + 36 * q^66 + 12 * q^67 - 6 * q^68 - 9 * q^69 + 18 * q^71 - 36 * q^72 - 42 * q^73 + 30 * q^74 - 9 * q^75 - 15 * q^76 - 6 * q^77 + 54 * q^78 + 21 * q^79 - 30 * q^80 - 18 * q^82 + 18 * q^83 - 9 * q^84 - 9 * q^85 - 6 * q^86 + 9 * q^87 - 27 * q^88 + 24 * q^89 + 27 * q^90 - 6 * q^91 - 3 * q^92 - 27 * q^93 + 18 * q^94 + 12 * q^95 + 27 * q^96 + 3 * q^97 + 6 * q^98 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.26604	+	2.19285i	−0.895229	+	1.55058i	−0.0617072	+	0.998094i	$0.519654\pi$
$2$	−1.26604	+	2.19285i	−0.895229	+	1.55058i	−0.833521	+	0.552487i	$0.813679\pi$
$3$	−1.11334	+	1.32683i	−0.642788	+	0.766044i
$3$	−1.11334	+	1.32683i	−0.642788	+	0.766044i
$4$	−2.20574	−	3.82045i	−1.10287	−	1.91022i
$5$	0.439693	+	0.761570i	0.196637	+	0.340584i	0.947436	−	0.319946i	$-0.103665\pi$
$5$	0.439693	+	0.761570i	0.196637	+	0.340584i	−0.750799	+	0.660530i	$0.770331\pi$
$6$	−1.50000	−	4.12122i	−0.612372	−	1.68248i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	6.10607			2.15882
$9$	−0.520945	−	2.95442i	−0.173648	−	0.984808i
$10$	−2.22668			−0.704139
$11$	−1.93969	+	3.35965i	−0.584839	+	1.01297i	0.410056	+	0.912060i	$0.365509\pi$
$11$	−1.93969	+	3.35965i	−0.584839	+	1.01297i	−0.994895	+	0.100911i	$0.967824\pi$
$12$	7.52481	+	1.32683i	2.17223	+	0.383022i
$13$	2.72668	+	4.72275i	0.756245	+	1.30986i	0.944753	+	0.327784i	$0.106302\pi$
$13$	2.72668	+	4.72275i	0.756245	+	1.30986i	−0.188507	+	0.982072i	$0.560365\pi$
$14$	−1.26604	−	2.19285i	−0.338365	−	0.586065i
$15$	−1.50000	−	0.264490i	−0.387298	−	0.0682911i
$16$	−3.31908	+	5.74881i	−0.829769	+	1.43720i
$17$	1.65270			0.400840			0.200420	−	0.979710i	$-0.435769\pi$
$17$	1.65270			0.400840			0.200420	+	0.979710i	$0.435769\pi$
$18$	7.13816	+	2.59808i	1.68248	+	0.612372i
$19$	2.41147			0.553230			0.276615	−	0.960981i	$-0.410787\pi$
$19$	2.41147			0.553230			0.276615	+	0.960981i	$0.410787\pi$
$20$	1.93969	−	3.35965i	0.433728	−	0.751240i
$21$	−0.592396	−	1.62760i	−0.129271	−	0.355170i
$22$	−4.91147	−	8.50692i	−1.04713	−	1.81368i
$23$	−1.58125	−	2.73881i	−0.329714	−	0.571081i	0.652741	−	0.757581i	$-0.273619\pi$
$23$	−1.58125	−	2.73881i	−0.329714	−	0.571081i	−0.982455	+	0.186500i	$0.940286\pi$
$24$	−6.79813	+	8.10170i	−1.38766	+	1.65375i
$25$	2.11334	−	3.66041i	0.422668	−	0.732083i
$26$	−13.8084			−2.70805
$27$	4.50000	+	2.59808i	0.866025	+	0.500000i
$28$	4.41147			0.833690
$29$	3.02481	−	5.23913i	0.561694	−	0.972883i	−0.435655	−	0.900114i	$-0.643483\pi$
$29$	3.02481	−	5.23913i	0.561694	−	0.972883i	0.997349	−	0.0727688i	$-0.0231835\pi$
$30$	2.47906	−	2.95442i	0.452612	−	0.539401i
$31$	2.27719	+	3.94421i	0.408995	+	0.708400i	0.994777	−	0.102068i	$-0.0325459\pi$
$31$	2.27719	+	3.94421i	0.408995	+	0.708400i	−0.585782	+	0.810468i	$0.699213\pi$
$32$	−2.29813	−	3.98048i	−0.406256	−	0.703657i
$33$	−2.29813	−	6.31407i	−0.400054	−	1.09914i
$34$	−2.09240	+	3.62414i	−0.358843	+	0.621534i
$35$	−0.879385			−0.148643
$36$	−10.1382	+	8.50692i	−1.68969	+	1.41782i
$37$	−4.55438			−0.748735			−0.374368	−	0.927280i	$-0.622140\pi$
$37$	−4.55438			−0.748735			−0.374368	+	0.927280i	$0.622140\pi$
$38$	−3.05303	+	5.28801i	−0.495267	+	0.857828i
$39$	−9.30200	−	1.64019i	−1.48951	−	0.262641i
$40$	2.68479	+	4.65020i	0.424503	+	0.735261i
$41$	0.592396	+	1.02606i	0.0925168	+	0.160244i	0.908570	−	0.417734i	$-0.137175\pi$
$41$	0.592396	+	1.02606i	0.0925168	+	0.160244i	−0.816053	+	0.577977i	$0.803842\pi$
$42$	4.31908	+	0.761570i	0.666448	+	0.117513i
$43$	−0.0923963	+	0.160035i	−0.0140903	+	0.0244051i	−0.872985	−	0.487748i	$-0.837819\pi$
$43$	−0.0923963	+	0.160035i	−0.0140903	+	0.0244051i	0.858894	+	0.512153i	$0.171152\pi$
$44$	17.1138			2.58000
$45$	2.02094	−	1.69577i	0.301265	−	0.252791i
$46$	8.00774			1.18068
$47$	0.511144	−	0.885328i	0.0745581	−	0.129138i	−0.826336	−	0.563178i	$-0.809579\pi$
$47$	0.511144	−	0.885328i	0.0745581	−	0.129138i	0.900894	+	0.434039i	$0.142912\pi$
$48$	−3.93242	−	10.8042i	−0.567596	−	1.55946i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	5.35117	+	9.26849i	0.756769	+	1.31076i
$51$	−1.84002	+	2.19285i	−0.257655	+	0.307061i
$52$	12.0287	−	20.8343i	1.66808	−	2.88920i
$53$	7.29086			1.00148			0.500738	−	0.865599i	$-0.333062\pi$
$53$	7.29086			1.00148			0.500738	+	0.865599i	$0.333062\pi$
$54$	−11.3944	+	6.57856i	−1.55058	+	0.895229i
$55$	−3.41147			−0.460003
$56$	−3.05303	+	5.28801i	−0.407979	+	0.706640i
$57$	−2.68479	+	3.19961i	−0.355609	+	0.423799i
$58$	7.65910	+	13.2660i	1.00569	+	1.74190i
$59$	−3.33022	−	5.76811i	−0.433558	−	0.750944i	0.563619	−	0.826035i	$-0.309409\pi$
$59$	−3.33022	−	5.76811i	−0.433558	−	0.750944i	−0.997177	+	0.0750906i	$0.976075\pi$
$60$	2.29813	+	6.31407i	0.296688	+	0.815143i
$61$	1.29813	−	2.24843i	0.166209	−	0.287882i	−0.770875	−	0.636986i	$-0.780181\pi$
$61$	1.29813	−	2.24843i	0.166209	−	0.287882i	0.937084	+	0.349104i	$0.113514\pi$
$62$	−11.5321			−1.46458
$63$	2.81908	+	1.02606i	0.355170	+	0.129271i
$64$	−1.63816			−0.204769
$65$	−2.39780	+	4.15312i	−0.297411	+	0.515131i
$66$	16.7554	+	2.95442i	2.06244	+	0.363664i
$67$	1.47906	+	2.56180i	0.180695	+	0.312974i	0.942118	−	0.335283i	$-0.108832\pi$
$67$	1.47906	+	2.56180i	0.180695	+	0.312974i	−0.761422	+	0.648256i	$0.775499\pi$
$68$	−3.64543	−	6.31407i	−0.442073	−	0.765693i
$69$	5.39440	+	0.951178i	0.649409	+	0.114508i
$70$	1.11334	−	1.92836i	0.133070	−	0.230483i
$71$	−3.68004			−0.436741			−0.218370	−	0.975866i	$-0.570074\pi$
$71$	−3.68004			−0.436741			−0.218370	+	0.975866i	$0.570074\pi$
$72$	−3.18092	−	18.0399i	−0.374875	−	2.12602i
$73$	−12.7811			−1.49591			−0.747955	−	0.663750i	$-0.768964\pi$
$73$	−12.7811			−1.49591			−0.747955	+	0.663750i	$0.768964\pi$
$74$	5.76604	−	9.98708i	0.670289	−	1.16097i
$75$	2.50387	+	6.87933i	0.289122	+	0.794356i
$76$	−5.31908	−	9.21291i	−0.610140	−	1.05679i
$77$	−1.93969	−	3.35965i	−0.221048	−	0.382867i
$78$	15.3735	−	18.3214i	1.74070	−	2.07449i
$79$	2.97906	−	5.15988i	0.335170	−	0.580531i	−0.648348	−	0.761345i	$-0.724540\pi$
$79$	2.97906	−	5.15988i	0.335170	−	0.580531i	0.983517	+	0.180813i	$0.0578729\pi$
$80$	−5.83750			−0.652652
$81$	−8.45723	+	3.07818i	−0.939693	+	0.342020i
$82$	−3.00000			−0.331295
$83$	0.109470	−	0.189608i	0.0120159	−	0.0208122i	−0.859955	−	0.510370i	$-0.829508\pi$
$83$	0.109470	−	0.189608i	0.0120159	−	0.0208122i	0.871971	+	0.489558i	$0.162842\pi$
$84$	−4.91147	+	5.85327i	−0.535886	+	0.638644i
$85$	0.726682	+	1.25865i	0.0788197	+	0.136520i
$86$	−0.233956	−	0.405223i	−0.0252281	−	0.0436963i
$87$	3.58378	+	9.84635i	0.384221	+	1.05564i
$88$	−11.8439	+	20.5142i	−1.26256	+	2.18682i
$89$	11.0273			1.16890			0.584448	−	0.811431i	$-0.301311\pi$
$89$	11.0273			1.16890			0.584448	+	0.811431i	$0.301311\pi$
$90$	1.15998	+	6.57856i	0.122272	+	0.693441i
$91$	−5.45336			−0.571668
$92$	−6.97565	+	12.0822i	−0.727262	+	1.25965i
$93$	−7.76857	−	1.36981i	−0.805563	−	0.142043i
$94$	1.29426	+	2.24173i	0.133493	+	0.231217i
$95$	1.06031	+	1.83651i	0.108785	+	0.188422i
$96$	7.84002	+	1.38241i	0.800169	+	0.141091i
$97$	−6.25150	+	10.8279i	−0.634743	+	1.09941i	0.351826	+	0.936065i	$0.385561\pi$
$97$	−6.25150	+	10.8279i	−0.634743	+	1.09941i	−0.986569	+	0.163342i	$0.947773\pi$
$98$	2.53209			0.255780
$99$	10.9363	+	3.98048i	1.09914	+	0.400054i
$100$	−18.6459			−1.86459
$101$	4.85844	−	8.41507i	0.483433	−	0.837330i	−0.516386	−	0.856356i	$-0.672723\pi$
$101$	4.85844	−	8.41507i	0.483433	−	0.837330i	0.999819	+	0.0190255i	$0.00605638\pi$
$102$	−2.47906	−	6.81115i	−0.245463	−	0.674404i
$103$	−3.29813	−	5.71253i	−0.324975	−	0.562873i	0.656533	−	0.754298i	$-0.272022\pi$
$103$	−3.29813	−	5.71253i	−0.324975	−	0.562873i	−0.981507	+	0.191425i	$0.938689\pi$
$104$	16.6493	+	28.8374i	1.63260	+	2.82774i
$105$	0.979055	−	1.16679i	0.0955460	−	0.113867i
$106$	−9.23055	+	15.9878i	−0.896550	+	1.55287i
$107$	2.38919			0.230971			0.115486	−	0.993309i	$-0.463158\pi$
$107$	2.38919			0.230971			0.115486	+	0.993309i	$0.463158\pi$
$108$		−	22.9227i		−	2.20574i
$109$	3.95811			0.379118			0.189559	−	0.981869i	$-0.439294\pi$
$109$	3.95811			0.379118			0.189559	+	0.981869i	$0.439294\pi$
$110$	4.31908	−	7.48086i	0.411808	−	0.713272i
$111$	5.07057	−	6.04288i	0.481278	−	0.573564i
$112$	−3.31908	−	5.74881i	−0.313623	−	0.543212i
$113$	−8.22668	−	14.2490i	−0.773901	−	1.34044i	−0.935410	−	0.353565i	$-0.884969\pi$
$113$	−8.22668	−	14.2490i	−0.773901	−	1.34044i	0.161509	−	0.986871i	$-0.448364\pi$
$114$	−3.61721	−	9.93821i	−0.338783	−	0.930798i
$115$	1.39053	−	2.40847i	0.129668	−	0.224591i
$116$	−26.6878			−2.47790
$117$	12.5326	−	10.5161i	1.15864	−	0.972210i
$118$	16.8648			1.55253
$119$	−0.826352	+	1.43128i	−0.0757515	+	0.131206i
$120$	−9.15910	−	1.61500i	−0.836108	−	0.147428i
$121$	−2.02481	−	3.50708i	−0.184074	−	0.318826i
$122$	3.28699	+	5.69323i	0.297590	+	0.515441i
$123$	−2.02094	−	0.356347i	−0.182222	−	0.0321307i
$124$	10.0458	−	17.3998i	0.902136	−	1.56255i
$125$	8.11381			0.725721
$126$	−5.81908	+	4.88279i	−0.518405	+	0.434993i
$127$	17.6536			1.56651			0.783253	−	0.621702i	$-0.213559\pi$
$127$	17.6536			1.56651			0.783253	+	0.621702i	$0.213559\pi$
$128$	6.67024	−	11.5532i	0.589572	−	1.02117i
$129$	−0.109470	−	0.300767i	−0.00963833	−	0.0264811i
$130$	−6.07145	−	10.5161i	−0.532502	−	0.922320i
$131$	9.59879	+	16.6256i	0.838650	+	1.45259i	0.891023	+	0.453958i	$0.149988\pi$
$131$	9.59879	+	16.6256i	0.838650	+	1.45259i	−0.0523729	+	0.998628i	$0.516678\pi$
$132$	−19.0535	+	22.7071i	−1.65839	+	1.97640i
$133$	−1.20574	+	2.08840i	−0.104551	+	0.181087i
$134$	−7.49020			−0.647055
$135$			4.56942i			0.393273i
$136$	10.0915			0.865341
$137$	−9.07785	+	15.7233i	−0.775573	+	1.34333i	0.158899	+	0.987295i	$0.449206\pi$
$137$	−9.07785	+	15.7233i	−0.775573	+	1.34333i	−0.934472	+	0.356037i	$0.884128\pi$
$138$	−8.91534	+	10.6249i	−0.758925	+	0.904451i
$139$	−11.0287	−	19.1022i	−0.935441	−	1.62023i	−0.773846	−	0.633374i	$-0.781670\pi$
$139$	−11.0287	−	19.1022i	−0.935441	−	1.62023i	−0.161595	−	0.986857i	$-0.551664\pi$
$140$	1.93969	+	3.35965i	0.163934	+	0.283942i
$141$	0.605600	+	1.66387i	0.0510007	+	0.140123i
$142$	4.65910	−	8.06980i	0.390983	−	0.677202i
$143$	−21.1557			−1.76913
$144$	18.7135	+	6.81115i	1.55946	+	0.567596i
$145$	5.31996			0.441798
$146$	16.1814	−	28.0270i	1.33918	−	2.31953i
$147$	1.70574	+	0.300767i	0.140687	+	0.0248069i
$148$	10.0458	+	17.3998i	0.825756	+	1.43025i
$149$	7.57785	+	13.1252i	0.620802	+	1.07526i	0.989337	+	0.145646i	$0.0465261\pi$
$149$	7.57785	+	13.1252i	0.620802	+	1.07526i	−0.368535	+	0.929614i	$0.620141\pi$
$150$	−18.2554	−	3.21891i	−1.49054	−	0.262823i
$151$	9.47818	−	16.4167i	0.771323	−	1.33597i	−0.165515	−	0.986207i	$-0.552929\pi$
$151$	9.47818	−	16.4167i	0.771323	−	1.33597i	0.936838	−	0.349764i	$-0.113738\pi$
$152$	14.7246			1.19432
$153$	−0.860967	−	4.88279i	−0.0696051	−	0.394750i
$154$	9.82295			0.791556
$155$	−2.00253	+	3.46848i	−0.160847	+	0.278595i
$156$	14.2515	+	39.1557i	1.14103	+	3.13496i
$157$	9.02869	+	15.6381i	0.720568	+	1.24806i	0.960773	+	0.277337i	$0.0894520\pi$
$157$	9.02869	+	15.6381i	0.720568	+	1.24806i	−0.240205	+	0.970722i	$0.577215\pi$
$158$	7.54323	+	13.0653i	0.600107	+	1.03942i
$159$	−8.11721	+	9.67372i	−0.643737	+	0.767176i
$160$	2.02094	−	3.50038i	0.159770	−	0.276729i
$161$	3.16250			0.249240
$162$	3.95723	−	22.4426i	0.310910	−	1.76326i
$163$	0.958111			0.0750450			0.0375225	−	0.999296i	$-0.488053\pi$
$163$	0.958111			0.0750450			0.0375225	+	0.999296i	$0.488053\pi$
$164$	2.61334	−	4.52644i	0.204068	−	0.353456i
$165$	3.79813	−	4.52644i	0.295684	−	0.352383i
$166$	0.277189	+	0.480105i	0.0215140	+	0.0372634i
$167$	−9.91921	−	17.1806i	−0.767572	−	1.32947i	−0.938876	−	0.344255i	$-0.888131\pi$
$167$	−9.91921	−	17.1806i	−0.767572	−	1.32947i	0.171304	−	0.985218i	$-0.445202\pi$
$168$	−3.61721	−	9.93821i	−0.279074	−	0.766749i
$169$	−8.36959	+	14.4965i	−0.643814	+	1.11512i
$170$	−3.68004			−0.282247
$171$	−1.25624	−	7.12452i	−0.0960674	−	0.544825i
$172$	0.815207			0.0621590
$173$	−11.3414	+	19.6438i	−0.862268	+	1.49349i	0.00746626	+	0.999972i	$0.497623\pi$
$173$	−11.3414	+	19.6438i	−0.862268	+	1.49349i	−0.869734	+	0.493520i	$0.835710\pi$
$174$	−26.1288	−	4.60722i	−1.98082	−	0.349272i
$175$	2.11334	+	3.66041i	0.159754	+	0.276701i
$176$	−12.8760	−	22.3019i	−0.970564	−	1.68107i
$177$	11.3610	+	2.00324i	0.853943	+	0.150573i
$178$	−13.9611	+	24.1813i	−1.04643	+	1.81247i
$179$	−7.34730			−0.549163			−0.274581	−	0.961564i	$-0.588539\pi$
$179$	−7.34730			−0.549163			−0.274581	+	0.961564i	$0.588539\pi$
$180$	−10.9363	−	3.98048i	−0.815143	−	0.296688i
$181$	−3.44562			−0.256111			−0.128056	−	0.991767i	$-0.540874\pi$
$181$	−3.44562			−0.256111			−0.128056	+	0.991767i	$0.540874\pi$
$182$	6.90420	−	11.9584i	0.511773	−	0.886417i
$183$	1.53802	+	4.22567i	0.113694	+	0.312371i
$184$	−9.65523	−	16.7233i	−0.711793	−	1.23286i
$185$	−2.00253	−	3.46848i	−0.147229	−	0.255008i
$186$	12.8391	−	15.3011i	0.941412	−	1.12193i
$187$	−3.20574	+	5.55250i	−0.234427	+	0.406039i
$188$	−4.50980			−0.328911
$189$	−4.50000	+	2.59808i	−0.327327	+	0.188982i
$190$	−5.36959			−0.389551
$191$	−2.82888	+	4.89976i	−0.204690	+	0.354534i	−0.950034	−	0.312146i	$-0.898952\pi$
$191$	−2.82888	+	4.89976i	−0.204690	+	0.354534i	0.745344	+	0.666680i	$0.232285\pi$
$192$	1.82383	−	2.17355i	0.131623	−	0.156863i
$193$	−4.79813	−	8.31061i	−0.345377	−	0.598211i	0.640045	−	0.768337i	$-0.278916\pi$
$193$	−4.79813	−	8.31061i	−0.345377	−	0.598211i	−0.985422	+	0.170127i	$0.945582\pi$
$194$	−15.8293	−	27.4172i	−1.13648	−	1.96844i
$195$	−2.84090	−	7.80531i	−0.203441	−	0.558950i
$196$	−2.20574	+	3.82045i	−0.157553	+	0.272889i
$197$	8.31996			0.592772			0.296386	−	0.955068i	$-0.404218\pi$
$197$	8.31996			0.592772			0.296386	+	0.955068i	$0.404218\pi$
$198$	−22.5744	+	18.9422i	−1.60430	+	1.34616i
$199$	6.59627			0.467597			0.233798	−	0.972285i	$-0.424884\pi$
$199$	6.59627			0.467597			0.233798	+	0.972285i	$0.424884\pi$
$200$	12.9042	−	22.3507i	0.912465	−	1.58044i
$201$	−5.04576	−	0.889704i	−0.355900	−	0.0627548i
$202$	12.3020	+	21.3077i	0.865566	+	1.49920i
$203$	3.02481	+	5.23913i	0.212300	+	0.367715i
$204$	12.4363	+	2.19285i	0.870714	+	0.153530i
$205$	−0.520945	+	0.902302i	−0.0363843	+	0.0630195i
$206$	16.7023			1.16371
$207$	−7.26786	+	6.09845i	−0.505151	+	0.423872i
$208$	−36.2003			−2.51004
$209$	−4.67752	+	8.10170i	−0.323551	+	0.560406i
$210$	1.31908	+	3.62414i	0.0910250	+	0.250089i
$211$	1.68479	+	2.91815i	0.115986	+	0.200893i	0.918173	−	0.396179i	$-0.129664\pi$
$211$	1.68479	+	2.91815i	0.115986	+	0.200893i	−0.802188	+	0.597072i	$0.796331\pi$
$212$	−16.0817	−	27.8544i	−1.10450	−	1.91304i
$213$	4.09714	−	4.88279i	0.280732	−	0.334563i
$214$	−3.02481	+	5.23913i	−0.206772	+	0.358140i
$215$	−0.162504			−0.0110827
$216$	27.4773	+	15.8640i	1.86959	+	1.07941i
$217$	−4.55438			−0.309171
$218$	−5.01114	+	8.67956i	−0.339398	+	0.587854i
$219$	14.2297	−	16.9583i	0.961552	−	1.14593i
$220$	7.52481	+	13.0334i	0.507323	+	0.878709i
$221$	4.50640	+	7.80531i	0.303133	+	0.525042i
$222$	6.83157	+	18.7696i	0.458505	+	1.25973i
$223$	3.13816	−	5.43545i	0.210146	−	0.363984i	−0.741614	−	0.670827i	$-0.765939\pi$
$223$	3.13816	−	5.43545i	0.210146	−	0.363984i	0.951760	+	0.306843i	$0.0992726\pi$
$224$	4.59627			0.307101
$225$	−11.9153	−	4.33683i	−0.794356	−	0.289122i
$226$	41.6614			2.77127
$227$	3.08125	−	5.33688i	0.204510	−	0.354221i	−0.745467	−	0.666543i	$-0.767773\pi$
$227$	3.08125	−	5.33688i	0.204510	−	0.354221i	0.949976	+	0.312322i	$0.101107\pi$
$228$	18.1459	+	3.19961i	1.20174	+	0.211899i
$229$	−11.6925	−	20.2521i	−0.772664	−	1.33829i	−0.936098	−	0.351740i	$-0.885590\pi$
$229$	−11.6925	−	20.2521i	−0.772664	−	1.33829i	0.163434	−	0.986554i	$-0.447743\pi$
$230$	3.52094	+	6.09845i	0.232164	+	0.402120i
$231$	6.61721	+	1.16679i	0.435381	+	0.0767693i
$232$	18.4697	−	31.9905i	1.21260	−	2.10028i
$233$	−8.52528			−0.558510			−0.279255	−	0.960217i	$-0.590087\pi$
$233$	−8.52528			−0.558510			−0.279255	+	0.960217i	$0.590087\pi$
$234$	7.19341	+	40.7959i	0.470248	+	2.66691i
$235$	0.898986			0.0586434
$236$	−14.6912	+	25.4459i	−0.956315	+	1.65639i
$237$	3.52956	+	9.69739i	0.229270	+	0.629913i
$238$	−2.09240	−	3.62414i	−0.135630	−	0.234918i
$239$	−7.28106	−	12.6112i	−0.470973	−	0.815748i	0.528476	−	0.848948i	$-0.322764\pi$
$239$	−7.28106	−	12.6112i	−0.470973	−	0.815748i	−0.999449	+	0.0331997i	$0.989430\pi$
$240$	6.49912	−	7.74535i	0.419517	−	0.499960i
$241$	2.70187	−	4.67977i	0.174043	−	0.301451i	−0.765787	−	0.643094i	$-0.777650\pi$
$241$	2.70187	−	4.67977i	0.174043	−	0.301451i	0.939830	+	0.341644i	$0.110984\pi$
$242$	10.2540			0.659154
$243$	5.33157	−	14.6484i	0.342020	−	0.939693i
$244$	−11.4534			−0.733226
$245$	0.439693	−	0.761570i	0.0280909	−	0.0486549i
$246$	3.34002	−	3.98048i	0.212952	−	0.253786i
$247$	6.57532	+	11.3888i	0.418378	+	0.724651i
$248$	13.9047	+	24.0836i	0.882947	+	1.52931i
$249$	0.129700	+	0.356347i	0.00821939	+	0.0225826i
$250$	−10.2724	+	17.7924i	−0.649686	+	1.12529i
$251$	−12.0669			−0.761654			−0.380827	−	0.924646i	$-0.624361\pi$
$251$	−12.0669			−0.761654			−0.380827	+	0.924646i	$0.624361\pi$
$252$	−2.29813	−	13.0334i	−0.144769	−	0.821025i
$253$	12.2686			0.771318
$254$	−22.3503	+	38.7118i	−1.40238	+	2.42900i
$255$	−2.47906	−	0.437124i	−0.155244	−	0.0273738i
$256$	15.2515	+	26.4164i	0.953219	+	1.65102i
$257$	−5.28312	−	9.15063i	−0.329552	−	0.570801i	0.652871	−	0.757469i	$-0.273564\pi$
$257$	−5.28312	−	9.15063i	−0.329552	−	0.570801i	−0.982423	+	0.186668i	$0.940231\pi$
$258$	0.798133	+	0.140732i	0.0496896	+	0.00876162i
$259$	2.27719	−	3.94421i	0.141498	−	0.245081i
$260$	21.1557			1.31202
$261$	−17.0544	−	6.20729i	−1.05564	−	0.384221i
$262$	−48.6100			−3.00314
$263$	14.1766	−	24.5547i	0.874169	−	1.51411i	0.0165240	−	0.999863i	$-0.494740\pi$
$263$	14.1766	−	24.5547i	0.874169	−	1.51411i	0.857645	−	0.514242i	$-0.171927\pi$
$264$	−14.0326	−	38.5541i	−0.863644	−	2.37284i
$265$	3.20574	+	5.55250i	0.196927	+	0.341087i
$266$	−3.05303	−	5.28801i	−0.187193	−	0.324229i
$267$	−12.2772	+	14.6314i	−0.751352	+	0.895426i
$268$	6.52481	−	11.3013i	0.398567	−	0.690337i
$269$	7.48339			0.456271			0.228135	−	0.973629i	$-0.426737\pi$
$269$	7.48339			0.456271			0.228135	+	0.973629i	$0.426737\pi$
$270$	−10.0201	−	5.78509i	−0.609802	−	0.352069i
$271$	13.6382			0.828459			0.414229	−	0.910172i	$-0.364051\pi$
$271$	13.6382			0.828459			0.414229	+	0.910172i	$0.364051\pi$
$272$	−5.48545	+	9.50108i	−0.332604	+	0.576088i
$273$	6.07145	−	7.23567i	0.367461	−	0.437923i
$274$	−22.9859	−	39.8128i	−1.38863	−	2.40518i
$275$	8.19846	+	14.2002i	0.494386	+	0.856302i
$276$	−8.26470	−	22.7071i	−0.497476	−	1.36681i
$277$	3.07532	−	5.32661i	0.184778	−	0.320045i	−0.758724	−	0.651413i	$-0.774177\pi$
$277$	3.07532	−	5.32661i	0.184778	−	0.320045i	0.943502	+	0.331368i	$0.107510\pi$
$278$	55.8512			3.34973
$279$	10.4666	−	8.78249i	0.626617	−	0.525794i
$280$	−5.36959			−0.320894
$281$	−1.65611	+	2.86846i	−0.0987951	+	0.171118i	−0.911186	−	0.411995i	$-0.864832\pi$
$281$	−1.65611	+	2.86846i	−0.0987951	+	0.171118i	0.812391	+	0.583113i	$0.198165\pi$
$282$	−4.41534	−	0.778544i	−0.262930	−	0.0463616i
$283$	−14.5116	−	25.1348i	−0.862626	−	1.49411i	−0.869385	−	0.494134i	$-0.835485\pi$
$283$	−14.5116	−	25.1348i	−0.862626	−	1.49411i	0.00675974	−	0.999977i	$-0.497848\pi$
$284$	8.11721	+	14.0594i	0.481668	+	0.834273i
$285$	−3.61721	−	0.637812i	−0.214265	−	0.0377807i
$286$	26.7841	−	46.3913i	1.58377	−	2.74318i
$287$	−1.18479			−0.0699361
$288$	−10.5628	+	8.86327i	−0.622421	+	0.522273i
$289$	−14.2686			−0.839328
$290$	−6.73530	+	11.6659i	−0.395510	+	0.685044i
$291$	−7.40673	−	20.3498i	−0.434190	−	1.19293i
$292$	28.1917	+	48.8294i	1.64979	+	2.85752i
$293$	4.20961	+	7.29125i	0.245928	+	0.425960i	0.962392	−	0.271664i	$-0.0875740\pi$
$293$	4.20961	+	7.29125i	0.245928	+	0.425960i	−0.716464	+	0.697624i	$0.754241\pi$
$294$	−2.81908	+	3.35965i	−0.164412	+	0.195939i
$295$	2.92855	−	5.07239i	0.170507	−	0.295326i
$296$	−27.8093			−1.61638
$297$	−17.4572	+	10.0789i	−1.01297	+	0.584839i
$298$	−38.3756			−2.22304
$299$	8.62314	−	14.9357i	0.498689	−	0.863755i
$300$	20.7592	−	24.7399i	1.19854	−	1.42836i
$301$	−0.0923963	−	0.160035i	−0.00532563	−	0.00922427i
$302$	23.9996	+	41.5685i	1.38102	+	2.39200i
$303$	5.75624	+	15.8152i	0.330688	+	0.908557i
$304$	−8.00387	+	13.8631i	−0.459053	+	0.795104i
$305$	2.28312			0.130731
$306$	11.7973	+	4.29385i	0.674404	+	0.245463i
$307$	−12.6878			−0.724130			−0.362065	−	0.932153i	$-0.617928\pi$
$307$	−12.6878			−0.724130			−0.362065	+	0.932153i	$0.617928\pi$
$308$	−8.55690	+	14.8210i	−0.487575	+	0.844504i
$309$	11.2515	+	1.98394i	0.640075	+	0.112863i
$310$	−5.07057	−	8.78249i	−0.287989	−	0.498812i
$311$	8.24510	+	14.2809i	0.467537	+	0.809797i	0.999312	−	0.0370881i	$-0.0118082\pi$
$311$	8.24510	+	14.2809i	0.467537	+	0.809797i	−0.531775	+	0.846886i	$0.678475\pi$
$312$	−56.7987	−	10.0151i	−3.21559	−	0.566995i
$313$	−14.2592	+	24.6977i	−0.805980	+	1.39600i	0.109648	+	0.993970i	$0.465028\pi$
$313$	−14.2592	+	24.6977i	−0.805980	+	1.39600i	−0.915628	+	0.402027i	$0.868306\pi$
$314$	−45.7229			−2.58029
$315$	0.458111	+	2.59808i	0.0258116	+	0.146385i
$316$	−26.2841			−1.47859
$317$	12.9474	−	22.4256i	0.727200	−	1.25955i	−0.230862	−	0.972987i	$-0.574154\pi$
$317$	12.9474	−	22.4256i	0.727200	−	1.25955i	0.958062	−	0.286561i	$-0.0925122\pi$
$318$	−10.9363	−	30.0472i	−0.613277	−	1.68496i
$319$	11.7344	+	20.3246i	0.657002	+	1.13796i
$320$	−0.720285	−	1.24757i	−0.0402652	−	0.0697413i
$321$	−2.65998	+	3.17004i	−0.148465	+	0.176934i
$322$	−4.00387	+	6.93491i	−0.223127	+	0.386467i
$323$	3.98545			0.221756
$324$	30.4145	+	25.5208i	1.68969	+	1.41782i
$325$	23.0496			1.27856
$326$	−1.21301	+	2.10100i	−0.0671825	+	0.116363i
$327$	−4.40673	+	5.25173i	−0.243693	+	0.290421i
$328$	3.61721	+	6.26519i	0.199727	+	0.345937i
$329$	0.511144	+	0.885328i	0.0281803	+	0.0488097i
$330$	5.11721	+	14.0594i	0.281693	+	0.773946i
$331$	−4.10947	+	7.11781i	−0.225877	+	0.391230i	−0.956582	−	0.291463i	$-0.905858\pi$
$331$	−4.10947	+	7.11781i	−0.225877	+	0.391230i	0.730705	+	0.682693i	$0.239191\pi$
$332$	−0.965852			−0.0530080
$333$	2.37258	+	13.4556i	0.130016	+	0.737360i
$334$	50.2327			2.74861
$335$	−1.30066	+	2.25281i	−0.0710626	+	0.123084i
$336$	11.3229	+	1.99654i	0.617717	+	0.108920i
$337$	−2.28564	−	3.95885i	−0.124507	−	0.215652i	0.797033	−	0.603936i	$-0.206402\pi$
$337$	−2.28564	−	3.95885i	−0.124507	−	0.215652i	−0.921540	+	0.388283i	$0.873068\pi$
$338$	−21.1925	−	36.7065i	−1.15272	−	1.99657i
$339$	28.0651	+	4.94864i	1.52429	+	0.268773i
$340$	3.20574	−	5.55250i	0.173856	−	0.301127i
$341$	−17.6682			−0.956786
$342$	17.2135	+	6.26519i	0.930798	+	0.338783i
$343$	1.00000			0.0539949
$344$	−0.564178	+	0.977185i	−0.0304184	+	0.0526863i
$345$	1.64749	+	4.52644i	0.0886978	+	0.243695i
$346$	−28.7173	−	49.7399i	−1.54385	−	2.67403i
$347$	−11.2331	−	19.4563i	−0.603023	−	1.04447i	−0.992361	−	0.123372i	$-0.960629\pi$
$347$	−11.2331	−	19.4563i	−0.603023	−	1.04447i	0.389337	−	0.921095i	$-0.372704\pi$
$348$	29.7126	−	35.4101i	1.59276	−	1.89818i
$349$	−13.0496	+	22.6026i	−0.698531	+	1.20989i	0.270445	+	0.962735i	$0.412829\pi$
$349$	−13.0496	+	22.6026i	−0.698531	+	1.20989i	−0.968976	+	0.247155i	$0.920504\pi$
$350$	−10.7023			−0.572064
$351$			28.3365i			1.51249i
$352$	17.8307			0.950379
$353$	0.177519	−	0.307471i	0.00944836	−	0.0163650i	−0.861263	−	0.508160i	$-0.830326\pi$
$353$	0.177519	−	0.307471i	0.00944836	−	0.0163650i	0.870711	+	0.491795i	$0.163659\pi$
$354$	−18.7763	+	22.3767i	−0.997950	+	1.18931i
$355$	−1.61809	−	2.80261i	−0.0858792	−	0.148747i
$356$	−24.3234	−	42.1294i	−1.28914	−	2.23285i
$357$	−0.979055	−	2.68993i	−0.0518171	−	0.142366i
$358$	9.30200	−	16.1115i	0.491626	−	0.851522i
$359$	5.45605			0.287959			0.143980	−	0.989581i	$-0.454010\pi$
$359$	5.45605			0.287959			0.143980	+	0.989581i	$0.454010\pi$
$360$	12.3400	−	10.3545i	0.650376	−	0.545731i
$361$	−13.1848			−0.693936
$362$	4.36231	−	7.55574i	0.229278	−	0.397121i
$363$	6.90760	+	1.21800i	0.362555	+	0.0639283i
$364$	12.0287	+	20.8343i	0.630474	+	1.09201i
$365$	−5.61974	−	9.73367i	−0.294150	−	0.509484i
$366$	−11.2135	−	1.97724i	−0.586138	−	0.103352i
$367$	−5.46198	+	9.46043i	−0.285113	+	0.493830i	−0.972637	−	0.232332i	$-0.925364\pi$
$367$	−5.46198	+	9.46043i	−0.285113	+	0.493830i	0.687523	+	0.726162i	$0.258698\pi$
$368$	20.9932			1.09435
$369$	2.72281	−	2.28471i	0.141744	−	0.118937i
$370$	10.1411			0.527213
$371$	−3.64543	+	6.31407i	−0.189261	+	0.327810i
$372$	11.9021	+	32.7009i	0.617097	+	1.69546i
$373$	−0.865715	−	1.49946i	−0.0448250	−	0.0776392i	0.842742	−	0.538317i	$-0.180940\pi$
$373$	−0.865715	−	1.49946i	−0.0448250	−	0.0776392i	−0.887567	+	0.460678i	$0.847606\pi$
$374$	−8.11721	−	14.0594i	−0.419731	−	0.726995i
$375$	−9.03343	+	10.7656i	−0.466484	+	0.555935i
$376$	3.12108	−	5.40587i	0.160957	−	0.278787i
$377$	32.9908			1.69911
$378$		−	13.1571i		−	0.676729i
$379$	−12.1334			−0.623251			−0.311626	−	0.950205i	$-0.600873\pi$
$379$	−12.1334			−0.623251			−0.311626	+	0.950205i	$0.600873\pi$
$380$	4.67752	−	8.10170i	0.239952	−	0.415608i
$381$	−19.6545	+	23.4233i	−1.00693	+	1.20001i
$382$	−7.16297	−	12.4066i	−0.366489	−	0.634778i
$383$	4.35591	+	7.54467i	0.222577	+	0.385514i	0.955590	−	0.294700i	$-0.0952198\pi$
$383$	4.35591	+	7.54467i	0.222577	+	0.385514i	−0.733013	+	0.680215i	$0.761887\pi$
$384$	7.90286	+	21.7129i	0.403291	+	1.10803i
$385$	1.70574	−	2.95442i	0.0869324	−	0.150571i
$386$	24.2986			1.23677
$387$	0.520945	+	0.189608i	0.0264811	+	0.00963833i
$388$	55.1566			2.80015
$389$	−1.82160	+	3.15511i	−0.0923590	+	0.159970i	−0.908503	−	0.417878i	$-0.862774\pi$
$389$	−1.82160	+	3.15511i	−0.0923590	+	0.159970i	0.816144	+	0.577848i	$0.196107\pi$
$390$	20.7126	+	3.65219i	1.04882	+	0.184936i
$391$	−2.61334	−	4.52644i	−0.132162	−	0.228912i
$392$	−3.05303	−	5.28801i	−0.154201	−	0.267085i
$393$	−32.7460	−	5.77401i	−1.65182	−	0.291260i
$394$	−10.5334	+	18.2444i	−0.530667	+	0.919142i
$395$	5.23947			0.263627
$396$	−8.91534	−	50.5614i	−0.448013	−	2.54081i
$397$	−15.4456			−0.775194			−0.387597	−	0.921829i	$-0.626695\pi$
$397$	−15.4456			−0.775194			−0.387597	+	0.921829i	$0.626695\pi$
$398$	−8.35117	+	14.4646i	−0.418606	+	0.725047i
$399$	−1.42855	−	3.92490i	−0.0715169	−	0.196491i
$400$	14.0287	+	24.2984i	0.701434	+	1.21492i
$401$	−9.21095	−	15.9538i	−0.459973	−	0.796697i	0.538986	−	0.842315i	$-0.318808\pi$
$401$	−9.21095	−	15.9538i	−0.459973	−	0.796697i	−0.998959	+	0.0456182i	$0.985474\pi$
$402$	8.33915	−	9.93821i	0.415919	−	0.495673i
$403$	−12.4183	+	21.5092i	−0.618601	+	1.07145i
$404$	−42.8658			−2.13265
$405$	−6.06283	−	5.08732i	−0.301265	−	0.252791i
$406$	−15.3182			−0.760230
$407$	8.83409	−	15.3011i	0.437890	−	0.758447i
$408$	−11.2353	+	13.3897i	−0.556230	+	0.662889i
$409$	14.3182	+	24.7999i	0.707989	+	1.22627i	0.965602	+	0.260025i	$0.0837309\pi$
$409$	14.3182	+	24.7999i	0.707989	+	1.22627i	−0.257612	+	0.966248i	$0.582936\pi$
$410$	−1.31908	−	2.28471i	−0.0651446	−	0.112834i
$411$	−10.7554	−	29.5501i	−0.530523	−	1.45760i
$412$	−14.5496	+	25.2007i	−0.716809	+	1.24155i
$413$	6.66044			0.327739
$414$	−4.17159	−	23.6583i	−0.205022	−	1.16274i
$415$	0.192533			0.00945109
$416$	12.5326	−	21.7070i	0.614459	−	1.06427i
$417$	37.6241	+	6.63414i	1.84246	+	0.324875i
$418$	−11.8439	−	20.5142i	−0.579304	−	1.00338i
$419$	17.3478	+	30.0472i	0.847494	+	1.46790i	0.883438	+	0.468548i	$0.155223\pi$
$419$	17.3478	+	30.0472i	0.847494	+	1.46790i	−0.0359442	+	0.999354i	$0.511444\pi$
$420$	−6.61721	−	1.16679i	−0.322887	−	0.0569337i
$421$	13.7010	−	23.7308i	0.667745	−	1.15657i	−0.310788	−	0.950479i	$-0.600593\pi$
$421$	13.7010	−	23.7308i	0.667745	−	1.15657i	0.978533	−	0.206090i	$-0.0660738\pi$
$422$	−8.53209			−0.415336
$423$	−2.88191	−	1.04893i	−0.140123	−	0.0510007i
$424$	44.5185			2.16201
$425$	3.49273	−	6.04958i	0.169422	−	0.293448i
$426$	5.52007	+	15.1663i	0.267448	+	0.734808i
$427$	1.29813	+	2.24843i	0.0628211	+	0.108809i
$428$	−5.26991	−	9.12776i	−0.254731	−	0.441207i
$429$	23.5535	−	28.0700i	1.13717	−	1.35523i
$430$	0.205737	−	0.356347i	0.00992152	−	0.0171846i
$431$	26.5921			1.28090			0.640449	−	0.768000i	$-0.278748\pi$
$431$	26.5921			1.28090			0.640449	+	0.768000i	$0.278748\pi$
$432$	−29.8717	+	17.2464i	−1.43720	+	0.829769i
$433$	37.1830			1.78690			0.893451	−	0.449160i	$-0.148277\pi$
$433$	37.1830			1.78690			0.893451	+	0.449160i	$0.148277\pi$
$434$	5.76604	−	9.98708i	0.276779	−	0.479395i
$435$	−5.92292	+	7.05866i	−0.283982	+	0.338437i
$436$	−8.73055	−	15.1218i	−0.418118	−	0.724201i
$437$	−3.81315	−	6.60457i	−0.182408	−	0.315939i
$438$	19.1716	+	52.6735i	0.916054	+	2.51684i
$439$	−12.5373	+	21.7152i	−0.598373	+	1.03641i	0.394689	+	0.918815i	$0.370853\pi$
$439$	−12.5373	+	21.7152i	−0.598373	+	1.03641i	−0.993061	+	0.117597i	$0.962481\pi$
$440$	−20.8307			−0.993064
$441$	−2.29813	+	1.92836i	−0.109435	+	0.0918268i
$442$	−22.8212			−1.08549
$443$	−1.02229	+	1.77066i	−0.0485704	+	0.0841264i	−0.889288	−	0.457347i	$-0.848800\pi$
$443$	−1.02229	+	1.77066i	−0.0485704	+	0.0841264i	0.840718	+	0.541473i	$0.182133\pi$
$444$	−34.2708	−	6.04288i	−1.62642	−	0.286782i
$445$	4.84864	+	8.39809i	0.229848	+	0.398108i
$446$	7.94609	+	13.7630i	0.376258	+	0.651698i
$447$	−25.8516	−	4.55834i	−1.22274	−	0.215602i
$448$	0.819078	−	1.41868i	0.0386978	−	0.0670265i
$449$	−10.2344			−0.482992			−0.241496	−	0.970402i	$-0.577638\pi$
$449$	−10.2344			−0.482992			−0.241496	+	0.970402i	$0.577638\pi$
$450$	24.5954	−	20.6380i	1.15944	−	0.972884i
$451$	−4.59627			−0.216430
$452$	−36.2918	+	62.8592i	−1.70702	+	2.95665i
$453$	11.2297	+	30.8533i	0.527616	+	1.44961i
$454$	7.80200	+	13.5135i	0.366166	+	0.634218i
$455$	−2.39780	−	4.15312i	−0.112411	−	0.194701i
$456$	−16.3935	+	19.5370i	−0.767697	+	0.914906i
$457$	21.2973	−	36.8879i	0.996244	−	1.72554i	0.423129	−	0.906070i	$-0.360932\pi$
$457$	21.2973	−	36.8879i	0.996244	−	1.72554i	0.573115	−	0.819475i	$-0.305735\pi$
$458$	59.2131			2.76684
$459$	7.43717	+	4.29385i	0.347137	+	0.200420i
$460$	−12.2686			−0.572025
$461$	−0.252374	+	0.437124i	−0.0117542	+	0.0203589i	−0.871843	−	0.489786i	$-0.837075\pi$
$461$	−0.252374	+	0.437124i	−0.0117542	+	0.0203589i	0.860088	+	0.510145i	$0.170408\pi$
$462$	−10.9363	+	13.0334i	−0.508802	+	0.606367i
$463$	−1.34002	−	2.32099i	−0.0622761	−	0.107865i	0.833206	−	0.552962i	$-0.186503\pi$
$463$	−1.34002	−	2.32099i	−0.0622761	−	0.107865i	−0.895482	+	0.445097i	$0.853169\pi$
$464$	20.0792	+	34.7782i	0.932153	+	1.61454i
$465$	−2.37258	−	6.51860i	−0.110026	−	0.302293i
$466$	10.7934	−	18.6947i	0.499994	−	0.866015i
$467$	−31.4165			−1.45378			−0.726892	−	0.686752i	$-0.759036\pi$
$467$	−31.4165			−1.45378			−0.726892	+	0.686752i	$0.759036\pi$
$468$	−67.8196	−	24.6843i	−3.13496	−	1.14103i
$469$	−2.95811			−0.136593
$470$	−1.13816	+	1.97134i	−0.0524992	+	0.0909313i
$471$	−30.8011	−	5.43107i	−1.41924	−	0.250250i
$472$	−20.3346	−	35.2205i	−0.935974	−	1.62115i
$473$	−0.358441	−	0.620838i	−0.0164811	−	0.0285461i
$474$	−25.7335	−	4.53752i	−1.18198	−	0.208415i
$475$	5.09627	−	8.82699i	0.233833	−	0.405010i
$476$	7.29086			0.334176
$477$	−3.79813	−	21.5403i	−0.173905	−	0.986262i
$478$	36.8726			1.68651
$479$	8.22028	−	14.2380i	0.375594	−	0.650549i	−0.614821	−	0.788666i	$-0.710772\pi$
$479$	8.22028	−	14.2380i	0.375594	−	0.650549i	0.990416	+	0.138118i	$0.0441052\pi$
$480$	2.39440	+	6.57856i	0.109289	+	0.300269i
$481$	−12.4183	−	21.5092i	−0.566227	−	0.980735i
$482$	6.84137	+	11.8496i	0.311616	+	0.539734i
$483$	−3.52094	+	4.19610i	−0.160209	+	0.190929i
$484$	−8.93242	+	15.4714i	−0.406019	+	0.703246i
$485$	−10.9949			−0.499255
$486$	25.3717	+	30.2368i	1.15088	+	1.37157i
$487$	−2.97535			−0.134826			−0.0674129	−	0.997725i	$-0.521474\pi$
$487$	−2.97535			−0.134826			−0.0674129	+	0.997725i	$0.521474\pi$
$488$	7.92649	−	13.7291i	0.358815	−	0.621486i
$489$	−1.06670	+	1.27125i	−0.0482380	+	0.0574878i
$490$	1.11334	+	1.92836i	0.0502956	+	0.0871146i
$491$	13.2430	+	22.9376i	0.597650	+	1.03516i	0.993167	+	0.116702i	$0.0372321\pi$
$491$	13.2430	+	22.9376i	0.597650	+	1.03516i	−0.395517	+	0.918459i	$0.629435\pi$
$492$	3.09627	+	8.50692i	0.139590	+	0.383522i
$493$	4.99912	−	8.65873i	0.225149	−	0.389970i
$494$	−33.2986			−1.49817
$495$	1.77719	+	10.0789i	0.0798787	+	0.453015i
$496$	−30.2327			−1.35749
$497$	1.84002	−	3.18701i	0.0825363	−	0.142957i
$498$	−0.945622	−	0.166739i	−0.0423744	−	0.00747174i
$499$	6.72193	+	11.6427i	0.300915	+	0.521200i	0.976343	−	0.216225i	$-0.0693746\pi$
$499$	6.72193	+	11.6427i	0.300915	+	0.521200i	−0.675428	+	0.737426i	$0.736041\pi$
$500$	−17.8969	−	30.9984i	−0.800375	−	1.38629i
$501$	33.8391	+	5.96675i	1.51182	+	0.266575i
$502$	15.2772	−	26.4609i	0.681854	−	1.18101i
$503$	−22.6631			−1.01050			−0.505250	−	0.862973i	$-0.668600\pi$
$503$	−22.6631			−1.01050			−0.505250	+	0.862973i	$0.668600\pi$
$504$	17.2135	+	6.26519i	0.766749	+	0.279074i
$505$	8.54488			0.380242
$506$	−15.5326	+	26.9032i	−0.690506	+	1.19599i
$507$	−9.91622	−	27.2446i	−0.440395	−	1.20997i
$508$	−38.9393	−	67.4448i	−1.72765	−	2.99238i
$509$	−4.77379	−	8.26844i	−0.211594	−	0.366492i	0.740619	−	0.671925i	$-0.234532\pi$
$509$	−4.77379	−	8.26844i	−0.211594	−	0.366492i	−0.952214	+	0.305433i	$0.901199\pi$
$510$	4.09714	−	4.88279i	0.181425	−	0.216213i
$511$	6.39053	−	11.0687i	0.282700	−	0.489651i
$512$	−50.5553			−2.23425
$513$	10.8516	+	6.26519i	0.479111	+	0.276615i
$514$	26.7547			1.18010
$515$	2.90033	−	5.02352i	0.127804	−	0.221363i
$516$	−0.907604	+	1.08164i	−0.0399550	+	0.0476165i
$517$	1.98293	+	3.43453i	0.0872090	+	0.151050i
$518$	5.76604	+	9.98708i	0.253345	+	0.438807i
$519$	−13.4372	−	36.9183i	−0.589826	−	1.62053i
$520$	−14.6411	+	25.3592i	−0.642057	+	1.11208i
$521$	−3.11287			−0.136377			−0.0681887	−	0.997672i	$-0.521722\pi$
$521$	−3.11287			−0.136377			−0.0681887	+	0.997672i	$0.521722\pi$
$522$	35.2033	−	29.5390i	1.54081	−	1.29289i
$523$	−16.1489			−0.706142			−0.353071	−	0.935597i	$-0.614863\pi$
$523$	−16.1489			−0.706142			−0.353071	+	0.935597i	$0.614863\pi$
$524$	42.3448	−	73.3434i	1.84984	−	3.20402i
$525$	−7.20961	−	1.27125i	−0.314653	−	0.0554818i
$526$	35.8965	+	62.1746i	1.56516	+	2.71094i
$527$	3.76352	+	6.51860i	0.163941	+	0.283955i
$528$	43.9261	+	7.74535i	1.91164	+	0.337073i
$529$	6.49928	−	11.2571i	0.282578	−	0.489439i
$530$	−16.2344			−0.705178
$531$	−15.3066	+	12.8438i	−0.664249	+	0.557371i
$532$	10.6382			0.461223
$533$	−3.23055	+	5.59548i	−0.139931	+	0.242367i
$534$	−16.5410	−	45.4461i	−0.715800	−	1.96664i
$535$	1.05051	+	1.81953i	0.0454174	+	0.0786652i
$536$	9.03121	+	15.6425i	0.390089	+	0.675654i
$537$	8.18004	−	9.74860i	0.352995	−	0.420683i
$538$	−9.47431	+	16.4100i	−0.408466	+	0.707485i
$539$	3.87939			0.167097
$540$	17.4572	−	10.0789i	0.751240	−	0.433728i
$541$	−5.01548			−0.215632			−0.107816	−	0.994171i	$-0.534386\pi$
$541$	−5.01548			−0.215632			−0.107816	+	0.994171i	$0.534386\pi$
$542$	−17.2665	+	29.9065i	−0.741660	+	1.28459i
$543$	3.83615	−	4.57175i	0.164625	−	0.196192i
$544$	−3.79813	−	6.57856i	−0.162844	−	0.282053i
$545$	1.74035	+	3.01438i	0.0745485	+	0.129122i
$546$	8.18004	+	22.4745i	0.350074	+	0.961819i
$547$	−8.23901	+	14.2704i	−0.352275	+	0.610157i	−0.986648	−	0.162870i	$-0.947925\pi$
$547$	−8.23901	+	14.2704i	−0.352275	+	0.610157i	0.634373	+	0.773027i	$0.281258\pi$
$548$	80.0934			3.42142
$549$	−7.31908	−	2.66393i	−0.312371	−	0.113694i
$550$	−41.5185			−1.77035
$551$	7.29426	−	12.6340i	0.310746	−	0.538228i
$552$	32.9386	+	5.80796i	1.40196	+	0.247203i
$553$	2.97906	+	5.15988i	0.126682	+	0.219420i
$554$	7.78699	+	13.4875i	0.330837	+	0.573027i
$555$	6.83157	+	1.20459i	0.289984	+	0.0511320i
$556$	−48.6528	+	84.2691i	−2.06334	+	3.57380i
$557$	−34.5631			−1.46448			−0.732242	−	0.681045i	$-0.761526\pi$
$557$	−34.5631			−1.46448			−0.732242	+	0.681045i	$0.761526\pi$
$558$	6.00758	+	34.0707i	0.254321	+	1.44233i
$559$	−1.00774			−0.0426229
$560$	2.91875	−	5.05542i	0.123340	−	0.213630i
$561$	−3.79813	−	10.4353i	−0.160357	−	0.440578i
$562$	−4.19341	−	7.26320i	−0.176888	−	0.306380i
$563$	18.6052	+	32.2251i	0.784115	+	1.35813i	0.929526	+	0.368756i	$0.120216\pi$
$563$	18.6052	+	32.2251i	0.784115	+	1.35813i	−0.145411	+	0.989371i	$0.546450\pi$
$564$	5.02094	−	5.98373i	0.211420	−	0.251960i
$565$	7.23442	−	12.5304i	0.304354	−	0.527157i
$566$	73.4894			3.08899
$567$	1.56283	−	8.86327i	0.0656328	−	0.372222i
$568$	−22.4706			−0.942845
$569$	−0.202333	+	0.350452i	−0.00848226	+	0.0146917i	−0.870235	−	0.492636i	$-0.836033\pi$
$569$	−0.202333	+	0.350452i	−0.00848226	+	0.0146917i	0.861753	+	0.507328i	$0.169367\pi$
$570$	5.97818	−	7.12452i	0.250398	−	0.298413i
$571$	18.8897	+	32.7178i	0.790507	+	1.36920i	0.925653	+	0.378373i	$0.123516\pi$
$571$	18.8897	+	32.7178i	0.790507	+	1.36920i	−0.135146	+	0.990826i	$0.543150\pi$
$572$	46.6639	+	80.8243i	1.95112	+	3.37943i
$573$	−3.35163	−	9.20854i	−0.140017	−	0.384692i
$574$	1.50000	−	2.59808i	0.0626088	−	0.108442i
$575$	−13.3669			−0.557438
$576$	0.853388	+	4.83981i	0.0355578	+	0.201659i
$577$	−2.21120			−0.0920535			−0.0460267	−	0.998940i	$-0.514656\pi$
$577$	−2.21120			−0.0920535			−0.0460267	+	0.998940i	$0.514656\pi$
$578$	18.0646	−	31.2889i	0.751390	−	1.30145i
$579$	16.3687	+	2.88624i	0.680260	+	0.119948i
$580$	−11.7344	−	20.3246i	−0.487245	−	0.843934i
$581$	0.109470	+	0.189608i	0.00454160	+	0.00786628i
$582$	54.0014	+	9.52190i	2.23843	+	0.394696i
$583$	−14.1420	+	24.4947i	−0.585703	+	1.01447i
$584$	−78.0420			−3.22940
$585$	13.5192	+	4.92058i	0.558950	+	0.203441i
$586$	−21.3182			−0.880647
$587$	−12.1049	+	20.9663i	−0.499622	+	0.865371i	−1.00000		0.000436347i	$-0.999861\pi$
$587$	−12.1049	+	20.9663i	−0.499622	+	0.865371i	0.500378	+	0.865807i	$0.333194\pi$
$588$	−2.61334	−	7.18009i	−0.107772	−	0.296102i
$589$	5.49138	+	9.51135i	0.226268	+	0.391908i
$590$	7.41534	+	12.8438i	0.305285	+	0.528769i
$591$	−9.26295	+	11.0391i	−0.381027	+	0.454090i
$592$	15.1163	−	26.1823i	0.621277	−	1.07608i
$593$	12.2385			0.502577			0.251288	−	0.967912i	$-0.419146\pi$
$593$	12.2385			0.502577			0.251288	+	0.967912i	$0.419146\pi$
$594$		−	51.0415i		−	2.09426i
$595$	−1.45336			−0.0595821
$596$	33.4295	−	57.9016i	1.36932	−	2.37174i
$597$	−7.34389	+	8.75211i	−0.300566	+	0.358200i
$598$	21.8346	+	37.8186i	0.892882	+	1.54652i
$599$	−19.8084	−	34.3092i	−0.809349	−	1.40183i	−0.913315	−	0.407253i	$-0.866487\pi$
$599$	−19.8084	−	34.3092i	−0.809349	−	1.40183i	0.103966	−	0.994581i	$-0.466847\pi$
$600$	15.2888	+	42.0056i	0.624163	+	1.71487i
$601$	15.0039	−	25.9875i	0.612021	−	1.06005i	−0.378879	−	0.925446i	$-0.623690\pi$
$601$	15.0039	−	25.9875i	0.612021	−	1.06005i	0.990899	−	0.134605i	$-0.0429764\pi$
$602$	0.467911			0.0190706
$603$	6.79813	−	5.70431i	0.276841	−	0.232298i
$604$	−83.6255			−3.40267
$605$	1.78059	−	3.08408i	0.0723914	−	0.125386i
$606$	−41.9680	−	7.40008i	−1.70483	−	0.300608i
$607$	9.74216	+	16.8739i	0.395422	+	0.684891i	0.993155	−	0.116804i	$-0.0372650\pi$
$607$	9.74216	+	16.8739i	0.395422	+	0.684891i	−0.597733	+	0.801695i	$0.703932\pi$
$608$	−5.54189	−	9.59883i	−0.224753	−	0.389284i
$609$	−10.3191	−	1.81953i	−0.418150	−	0.0737312i
$610$	−2.89053	+	5.00654i	−0.117034	+	0.202709i
$611$	5.57491			0.225537
$612$	−16.7554	+	14.0594i	−0.677296	+	0.568318i
$613$	−18.5276			−0.748325			−0.374162	−	0.927363i	$-0.622070\pi$
$613$	−18.5276			−0.748325			−0.374162	+	0.927363i	$0.622070\pi$
$614$	16.0633	−	27.8225i	0.648262	−	1.12282i
$615$	−0.617211	−	1.69577i	−0.0248884	−	0.0683802i
$616$	−11.8439	−	20.5142i	−0.477204	−	0.826542i
$617$	−13.9201	−	24.1103i	−0.560402	−	0.970644i	−0.997461	−	0.0712118i	$-0.977313\pi$
$617$	−13.9201	−	24.1103i	−0.560402	−	0.970644i	0.437059	−	0.899433i	$-0.356020\pi$
$618$	−18.5954	+	22.1611i	−0.748016	+	0.891451i
$619$	22.4907	−	38.9550i	0.903976	−	1.56573i	0.0816906	−	0.996658i	$-0.473968\pi$
$619$	22.4907	−	38.9550i	0.903976	−	1.56573i	0.822286	−	0.569075i	$-0.192699\pi$
$620$	17.6682			0.709571
$621$		−	16.4329i		−	0.659428i
$622$	−41.7547			−1.67421
$623$	−5.51367	+	9.54996i	−0.220901	+	0.382611i
$624$	40.3032	−	48.0315i	1.61342	−	1.92280i
$625$	−6.99912	−	12.1228i	−0.279965	−	0.484913i
$626$	−36.1057	−	62.5368i	−1.44307	−	2.49947i
$627$	−5.54189	−	15.2262i	−0.221322	−	0.608076i
$628$	39.8298	−	68.9873i	1.58938	−	2.75289i
$629$	−7.52704			−0.300123
$630$	−6.27719	−	2.28471i	−0.250089	−	0.0910250i
$631$	9.43613			0.375646			0.187823	−	0.982203i	$-0.439857\pi$
$631$	9.43613			0.375646			0.187823	+	0.982203i	$0.439857\pi$
$632$	18.1903	−	31.5065i	0.723572	−	1.25326i
$633$	−5.74763	−	1.01346i	−0.228448	−	0.0402815i
$634$	32.7841	+	56.7836i	1.30202	+	2.25517i
$635$	7.76217	+	13.4445i	0.308032	+	0.533528i
$636$	54.8624	+	9.67372i	2.17543	+	0.383588i
$637$	2.72668	−	4.72275i	0.108035	−	0.187122i
$638$	−59.4252			−2.35267
$639$	1.91710	+	10.8724i	0.0758393	+	0.430106i
$640$	11.7314			0.463725
$641$	−18.6951	+	32.3808i	−0.738410	+	1.27896i	0.214800	+	0.976658i	$0.431090\pi$
$641$	−18.6951	+	32.3808i	−0.738410	+	1.27896i	−0.953211	+	0.302306i	$0.902243\pi$
$642$	−3.58378	−	9.84635i	−0.141440	−	0.388604i
$643$	−0.805874	−	1.39581i	−0.0317806	−	0.0550456i	0.849698	−	0.527270i	$-0.176784\pi$
$643$	−0.805874	−	1.39581i	−0.0317806	−	0.0550456i	−0.881478	+	0.472225i	$0.843451\pi$
$644$	−6.97565	−	12.0822i	−0.274879	−	0.476105i
$645$	0.180922	−	0.215615i	0.00712380	−	0.00848982i
$646$	−5.04576	+	8.73951i	−0.198523	+	0.343851i
$647$	−41.1762			−1.61880			−0.809402	−	0.587255i	$-0.800209\pi$
$647$	−41.1762			−1.61880			−0.809402	+	0.587255i	$0.800209\pi$
$648$	−51.6404	+	18.7956i	−2.02863	+	0.738360i
$649$	25.8384			1.01425
$650$	−29.1819	+	50.5445i	−1.14461	+	1.98252i
$651$	5.07057	−	6.04288i	0.198731	−	0.236839i
$652$	−2.11334	−	3.66041i	−0.0827648	−	0.143353i
$653$	−1.52600	−	2.64310i	−0.0597169	−	0.103433i	0.834621	−	0.550824i	$-0.185686\pi$
$653$	−1.52600	−	2.64310i	−0.0597169	−	0.103433i	−0.894338	+	0.447391i	$0.852353\pi$
$654$	−5.93717	−	16.3122i	−0.232162	−	0.637859i
$655$	−8.44104	+	14.6203i	−0.329819	+	0.571263i
$656$	−7.86484			−0.307070
$657$	6.65822	+	37.7607i	0.259762	+	1.47318i
$658$	−2.58853			−0.100911
$659$	−20.8175	+	36.0569i	−0.810934	+	1.40458i	0.101277	+	0.994858i	$0.467707\pi$
$659$	−20.8175	+	36.0569i	−0.810934	+	1.40458i	−0.912211	+	0.409721i	$0.865626\pi$
$660$	−25.6707	−	4.52644i	−0.999231	−	0.176191i
$661$	−10.1505	−	17.5812i	−0.394808	−	0.683828i	0.598269	−	0.801296i	$-0.295856\pi$
$661$	−10.1505	−	17.5812i	−0.394808	−	0.683828i	−0.993077	+	0.117468i	$0.962522\pi$
$662$	−10.4055	−	18.0229i	−0.404423	−	0.700481i
$663$	−15.3735	−	2.71075i	−0.597056	−	0.105277i
$664$	0.668434	−	1.15776i	0.0259403	−	0.0449298i
$665$	−2.12061			−0.0822339
$666$	−32.5099	−	11.8326i	−1.25973	−	0.458505i
$667$	−19.1320			−0.740793
$668$	−43.7584	+	75.7917i	−1.69306	+	2.93247i
$669$	3.71806	+	10.2153i	0.143749	+	0.394946i
$670$	−3.29339	−	5.70431i	−0.127235	−	0.220377i
$671$	5.03596	+	8.72254i	0.194411	+	0.336730i
$672$	−5.11721	+	6.09845i	−0.197401	+	0.235253i
$673$	0.415345	−	0.719398i	0.0160104	−	0.0277307i	−0.857909	−	0.513801i	$-0.828237\pi$
$673$	0.415345	−	0.719398i	0.0160104	−	0.0277307i	0.873920	+	0.486071i	$0.161570\pi$
$674$	11.5749			0.445849
$675$	19.0201	−	10.9812i	0.732083	−	0.422668i
$676$	73.8444			2.84017
$677$	−5.43360	+	9.41127i	−0.208830	+	0.361705i	−0.951346	−	0.308124i	$-0.900299\pi$
$677$	−5.43360	+	9.41127i	−0.208830	+	0.361705i	0.742516	+	0.669828i	$0.233632\pi$
$678$	−46.3833	+	55.2775i	−1.78134	+	2.12292i
$679$	−6.25150	−	10.8279i	−0.239910	−	0.415537i
$680$	4.43717	+	7.68540i	0.170158	+	0.294722i
$681$	3.65064	+	10.0301i	0.139893	+	0.384353i
$682$	22.3687	−	38.7437i	0.856542	−	1.48357i
$683$	32.6946			1.25102			0.625512	−	0.780215i	$-0.284890\pi$
$683$	32.6946			1.25102			0.625512	+	0.780215i	$0.284890\pi$
$684$	−24.4479	+	20.5142i	−0.934789	+	0.784381i
$685$	−15.9659			−0.610024
$686$	−1.26604	+	2.19285i	−0.0483378	+	0.0837235i
$687$	39.8888	+	7.03347i	1.52185	+	0.268344i
$688$	−0.613341	−	1.06234i	−0.0233834	−	0.0405012i
$689$	19.8799	+	34.4329i	0.757362	+	1.31179i
$690$	−12.0116	−	2.11797i	−0.457274	−	0.0806298i
$691$	−7.49912	+	12.9889i	−0.285280	+	0.494120i	−0.972677	−	0.232162i	$-0.925420\pi$
$691$	−7.49912	+	12.9889i	−0.285280	+	0.494120i	0.687397	+	0.726282i	$0.258753\pi$
$692$	100.064			3.80387
$693$	−8.91534	+	7.48086i	−0.338666	+	0.284174i
$694$	56.8863			2.15937
$695$	9.69846	−	16.7982i	0.367884	−	0.637193i
$696$	21.8828	+	60.1225i	0.829465	+	2.27894i
$697$	0.979055	+	1.69577i	0.0370844	+	0.0642320i
$698$	−33.0428	−	57.2318i	−1.25069	−	2.16626i
$699$	9.49154	−	11.3116i	0.359003	−	0.427843i
$700$	9.32295	−	16.1478i	0.352374	−	0.610330i
$701$	26.4688			0.999714			0.499857	−	0.866108i	$-0.333386\pi$
$701$	26.4688			0.999714			0.499857	+	0.866108i	$0.333386\pi$
$702$	−62.1378	−	35.8753i	−2.34524	−	1.35403i
$703$	−10.9828			−0.414223
$704$	3.17752	−	5.50362i	0.119757	−	0.207426i
$705$	−1.00088	+	1.19280i	−0.0376952	+	0.0449234i
$706$	0.449493	+	0.778544i	0.0169169	+	0.0293009i
$707$	4.85844	+	8.41507i	0.182720	+	0.316481i
$708$	−17.4060	−	47.8226i	−0.654158	−	1.79728i
$709$	−7.68004	+	13.3022i	−0.288430	+	0.499576i	−0.973435	−	0.228963i	$-0.926467\pi$
$709$	−7.68004	+	13.3022i	−0.288430	+	0.499576i	0.685005	+	0.728538i	$0.259800\pi$
$710$	8.19429			0.307526
$711$	−16.7964	−	6.11338i	−0.629913	−	0.229270i
$712$	67.3337			2.52344
$713$	7.20162	−	12.4736i	0.269703	−	0.467139i
$714$	7.13816	+	1.25865i	0.267139	+	0.0471038i
$715$	−9.30200	−	16.1115i	−0.347875	−	0.602538i
$716$	16.2062	+	28.0700i	0.605654	+	1.04902i
$717$	24.8391	+	4.37981i	0.927635	+	0.163567i
$718$	−6.90760	+	11.9643i	−0.257789	+	0.446504i
$719$	26.7306			0.996883			0.498442	−	0.866923i	$-0.333906\pi$
$719$	26.7306			0.996883			0.498442	+	0.866923i	$0.333906\pi$
$720$	3.04101	+	17.2464i	0.113332	+	0.642737i
$721$	6.59627			0.245658
$722$	16.6925	−	28.9123i	0.621232	−	1.07600i
$723$	3.20115	+	8.79509i	0.119052	+	0.327093i
$724$	7.60014	+	13.1638i	0.282457	+	0.489230i
$725$	−12.7849	−	22.1441i	−0.474820	−	0.822413i
$726$	−11.4162	+	13.6053i	−0.423696	+	0.504941i
$727$	22.8221	−	39.5290i	0.846424	−	1.46605i	−0.0379552	−	0.999279i	$-0.512084\pi$
$727$	22.8221	−	39.5290i	0.846424	−	1.46605i	0.884379	−	0.466770i	$-0.154582\pi$
$728$	−33.2986			−1.23413
$729$	13.5000	+	23.3827i	0.500000	+	0.866025i
$730$	28.4593			1.05333
$731$	−0.152704	+	0.264490i	−0.00564795	+	0.00978253i
$732$	12.7515	−	15.1966i	0.471309	−	0.561684i
$733$	−2.98751	−	5.17452i	−0.110346	−	0.191125i	0.805564	−	0.592509i	$-0.201863\pi$
$733$	−2.98751	−	5.17452i	−0.110346	−	0.191125i	−0.915910	+	0.401384i	$0.868529\pi$
$734$	−13.8302	−	23.9546i	−0.510483	−	0.884182i
$735$	0.520945	+	1.43128i	0.0192153	+	0.0527937i
$736$	−7.26786	+	12.5883i	−0.267897	+	0.464011i
$737$	−11.4757			−0.422711
$738$	1.56283	+	8.86327i	0.0575287	+	0.326261i
$739$	−35.5963			−1.30943			−0.654715	−	0.755876i	$-0.727211\pi$
$739$	−35.5963			−1.30943			−0.654715	+	0.755876i	$0.727211\pi$
$740$	−8.83409	+	15.3011i	−0.324748	+	0.562480i
$741$	−22.4315	−	3.95529i	−0.824043	−	0.145301i
$742$	−9.23055	−	15.9878i	−0.338864	−	0.586930i
$743$	14.6544	+	25.3821i	0.537616	+	0.931178i	0.999032	+	0.0439943i	$0.0140083\pi$
$743$	14.6544	+	25.3821i	0.537616	+	0.931178i	−0.461416	+	0.887184i	$0.652658\pi$
$744$	−47.4354	−	8.36414i	−1.73907	−	0.306644i
$745$	−6.66385	+	11.5421i	−0.244145	+	0.422871i
$746$	4.38413			0.160515
$747$	−0.617211	−	0.224647i	−0.0225826	−	0.00821939i
$748$	28.2841			1.03417
$749$	−1.19459	+	2.06910i	−0.0436495	+	0.0756031i
$750$	−12.1707	−	33.4388i	−0.444412	−	1.22101i
$751$	8.66684	+	15.0114i	0.316258	+	0.547774i	0.979704	−	0.200450i	$-0.0642403\pi$
$751$	8.66684	+	15.0114i	0.316258	+	0.547774i	−0.663446	+	0.748224i	$0.730907\pi$
$752$	3.39306	+	5.87695i	0.123732	+	0.214310i
$753$	13.4345	−	16.0107i	0.489582	−	0.583461i
$754$	−41.7679	+	72.3440i	−1.52110	+	2.63461i
$755$	16.6699			0.606681
$756$	19.8516	+	11.4613i	0.721997	+	0.416845i
$757$	−2.77156			−0.100734			−0.0503671	−	0.998731i	$-0.516039\pi$
$757$	−2.77156			−0.100734			−0.0503671	+	0.998731i	$0.516039\pi$
$758$	15.3614	−	26.6068i	0.557952	−	0.966402i
$759$	−13.6591	+	16.2783i	−0.495794	+	0.590864i
$760$	6.47431	+	11.2138i	0.234848	+	0.406768i
$761$	−3.75372	−	6.50163i	−0.136072	−	0.235684i	0.789934	−	0.613191i	$-0.210115\pi$
$761$	−3.75372	−	6.50163i	−0.136072	−	0.235684i	−0.926007	+	0.377508i	$0.876781\pi$
$762$	−26.4805	−	72.7545i	−0.959286	−	2.63562i
$763$	−1.97906	+	3.42782i	−0.0716466	+	0.124096i
$764$	24.9590			0.902987
$765$	3.34002	−	2.80261i	0.120759	−	0.101329i
$766$	−22.0591			−0.797029
$767$	18.1609	−	31.4556i	0.655752	−	1.13580i
$768$	−52.0301	−	9.17431i	−1.87747	−	0.331049i
$769$	−1.02182	−	1.76985i	−0.0368478	−	0.0638223i	0.847013	−	0.531572i	$-0.178398\pi$
$769$	−1.02182	−	1.76985i	−0.0368478	−	0.0638223i	−0.883861	+	0.467749i	$0.845065\pi$
$770$	4.31908	+	7.48086i	0.155649	+	0.269592i
$771$	18.0232	+	3.17798i	0.649090	+	0.114452i
$772$	−21.1668	+	36.6620i	−0.761811	+	1.31950i
$773$	−24.9418			−0.897094			−0.448547	−	0.893759i	$-0.648058\pi$
$773$	−24.9418			−0.897094			−0.448547	+	0.893759i	$0.648058\pi$
$774$	−1.07532	+	0.902302i	−0.0386517	+	0.0324326i
$775$	19.2499			0.691477
$776$	−38.1721	+	66.1159i	−1.37030	+	2.37342i
$777$	2.69800	+	7.41268i	0.0967901	+	0.265929i
$778$	−4.61246	−	7.98902i	−0.165365	−	0.286420i
$779$	1.42855	+	2.47432i	0.0511831	+	0.0886516i
$780$	−23.5535	+	28.0700i	−0.843351	+	1.00507i
$781$	7.13816	−	12.3636i	0.255423	−	0.442406i
$782$	13.2344			0.473262
$783$	27.2233	−	15.7174i	0.972883	−	0.561694i
$784$	6.63816			0.237077
$785$	−7.93969	+	13.7520i	−0.283380	+	0.490828i
$786$	54.1195	−	64.4971i	1.93038	−	2.30054i
$787$	−3.55350	−	6.15484i	−0.126669	−	0.219396i	0.795715	−	0.605671i	$-0.207095\pi$
$787$	−3.55350	−	6.15484i	−0.126669	−	0.219396i	−0.922384	+	0.386274i	$0.873762\pi$
$788$	−18.3516	−	31.7860i	−0.653750	−	1.13233i
$789$	16.7964	+	46.1477i	0.597967	+	1.64290i
$790$	−6.63341	+	11.4894i	−0.236006	+	0.408774i
$791$	16.4534			0.585014
$792$	66.7777	+	24.3051i	2.37284	+	0.863644i
$793$	14.1584			0.502779
$794$	19.5548	−	33.8700i	0.693975	−	1.20200i
$795$	−10.9363	−	1.92836i	−0.387870	−	0.0683920i
$796$	−14.5496	−	25.2007i	−0.515698	−	0.893215i
$797$	−16.8314	−	29.1528i	−0.596199	−	1.03265i	−0.993376	−	0.114905i	$-0.963344\pi$
$797$	−16.8314	−	29.1528i	−0.596199	−	1.03265i	0.397178	−	0.917742i	$-0.369990\pi$
$798$	10.4153	+	1.83651i	0.368699	+	0.0650116i
$799$	0.844770	−	1.46318i	0.0298858	−	0.0517638i
$800$	−19.4270			−0.686847
$801$	−5.74463	−	32.5794i	−0.202977	−	1.15114i
$802$	46.6459			1.64712
$803$	24.7913	−	42.9398i	0.874867	−	1.51531i
$804$	7.73055	+	21.2395i	0.272636	+	0.749060i
$805$	1.39053	+	2.40847i	0.0490097	+	0.0848873i
$806$	−31.4443	−	54.4632i	−1.10758	−	1.91838i
$807$	−8.33157	+	9.92917i	−0.293285	+	0.349523i
$808$	29.6660	−	51.3830i	1.04364	−	1.80765i
$809$	−12.8161			−0.450592			−0.225296	−	0.974290i	$-0.572335\pi$
$809$	−12.8161			−0.450592			−0.225296	+	0.974290i	$0.572335\pi$
$810$	18.8316	−	6.85413i	0.661674	−	0.240830i
$811$	−26.1239			−0.917335			−0.458667	−	0.888608i	$-0.651673\pi$
$811$	−26.1239			−0.917335			−0.458667	+	0.888608i	$0.651673\pi$
$812$	13.3439	−	23.1123i	0.468279	−	0.811083i
$813$	−15.1839	+	18.0955i	−0.532523	+	0.634636i
$814$	22.3687	+	38.7437i	0.784023	+	1.35797i
$815$	0.421274	+	0.729669i	0.0147566	+	0.0255592i
$816$	−6.49912	−	17.8562i	−0.227515	−	0.625092i
$817$	−0.222811	+	0.385920i	−0.00779518	+	0.0135016i
$818$	−72.5099			−2.53525
$819$	2.84090	+	16.1115i	0.0992691	+	0.562983i
$820$	4.59627			0.160509
$821$	−13.8320	+	23.9578i	−0.482741	+	0.836132i	−0.999804	−	0.0198153i	$-0.993692\pi$
$821$	−13.8320	+	23.9578i	−0.482741	+	0.836132i	0.517062	+	0.855948i	$0.327026\pi$
$822$	78.4159	+	13.8268i	2.73507	+	0.482266i
$823$	−13.9162	−	24.1036i	−0.485089	−	0.840199i	0.514764	−	0.857332i	$-0.327879\pi$
$823$	−13.9162	−	24.1036i	−0.485089	−	0.840199i	−0.999853	+	0.0171330i	$0.994546\pi$
$824$	−20.1386	−	34.8811i	−0.701562	−	1.21514i
$825$	−27.9688	−	4.93166i	−0.973750	−	0.171698i
$826$	−8.43242	+	14.6054i	−0.293401	+	0.508186i
$827$	4.65507			0.161873			0.0809363	−	0.996719i	$-0.474209\pi$
$827$	4.65507			0.161873			0.0809363	+	0.996719i	$0.474209\pi$
$828$	39.3298	+	14.3149i	1.36681	+	0.497476i
$829$	−9.97359			−0.346397			−0.173199	−	0.984887i	$-0.555410\pi$
$829$	−9.97359			−0.346397			−0.173199	+	0.984887i	$0.555410\pi$
$830$	−0.243756	+	0.422197i	−0.00846089	+	0.0146547i
$831$	3.64362	+	10.0108i	0.126396	+	0.347269i
$832$	−4.46673	−	7.73660i	−0.154856	−	0.268218i
$833$	−0.826352	−	1.43128i	−0.0286314	−	0.0495910i
$834$	−62.1814	+	74.1050i	−2.15317	+	2.56604i
$835$	8.72281	−	15.1084i	0.301865	−	0.522846i
$836$	41.2695			1.42734
$837$			23.6652i			0.817990i
$838$	−87.8522			−3.03480
$839$	3.36484	−	5.82807i	0.116167	−	0.201207i	−0.802079	−	0.597218i	$-0.796273\pi$
$839$	3.36484	−	5.82807i	0.116167	−	0.201207i	0.918246	+	0.396011i	$0.129606\pi$
$840$	5.97818	−	7.12452i	0.206267	−	0.245819i
$841$	−3.79901	−	6.58008i	−0.131000	−	0.226899i
$842$	34.6921	+	60.0885i	1.19557	+	2.07079i
$843$	−1.96214	−	5.39094i	−0.0675798	−	0.185674i
$844$	7.43242	−	12.8733i	0.255834	−	0.443118i
$845$	−14.7202			−0.506390
$846$	5.94878	−	4.99162i	0.204523	−	0.171615i
$847$	4.04963			0.139147
$848$	−24.1989	+	41.9138i	−0.830995	+	1.43932i
$849$	49.5060	+	8.72924i	1.69904	+	0.299587i
$850$	8.84389	+	15.3181i	0.303343	+	0.525406i
$851$	7.20162	+	12.4736i	0.246868	+	0.427588i
$852$	−27.6917	−	4.88279i	−0.948701	−	0.167281i
$853$	−2.89528	+	5.01477i	−0.0991324	+	0.171702i	−0.911326	−	0.411686i	$-0.864940\pi$
$853$	−2.89528	+	5.01477i	−0.0991324	+	0.171702i	0.812193	+	0.583388i	$0.198273\pi$
$854$	−6.57398			−0.224957
$855$	4.87346	−	4.08931i	0.166669	−	0.139852i
$856$	14.5885			0.498626
$857$	17.4538	−	30.2309i	0.596211	−	1.03267i	−0.397163	−	0.917748i	$-0.630005\pi$
$857$	17.4538	−	30.2309i	0.596211	−	1.03267i	0.993375	−	0.114921i	$-0.0366614\pi$
$858$	31.7335	+	87.1872i	1.08337	+	2.97652i
$859$	6.30747	+	10.9249i	0.215208	+	0.372751i	0.953337	−	0.301909i	$-0.0976237\pi$
$859$	6.30747	+	10.9249i	0.215208	+	0.372751i	−0.738129	+	0.674660i	$0.764290\pi$
$860$	0.358441	+	0.620838i	0.0122227	+	0.0211704i
$861$	1.31908	−	1.57202i	0.0449541	−	0.0535742i
$862$	−33.6668	+	58.3127i	−1.14670	+	1.98614i
$863$	−24.2053			−0.823959			−0.411979	−	0.911193i	$-0.635162\pi$
$863$	−24.2053			−0.823959			−0.411979	+	0.911193i	$0.635162\pi$
$864$		−	23.8829i		−	0.812513i
$865$	−19.9469			−0.678214
$866$	−47.0754	+	81.5369i	−1.59969	+	2.77074i
$867$	15.8858	−	18.9319i	0.539509	−	0.642962i
$868$	10.0458	+	17.3998i	0.340975	+	0.590587i
$869$	11.5569	+	20.0171i	0.392041	+	0.679035i
$870$	−7.97993	−	21.9247i	−0.270545	−	0.743316i
$871$	−8.06583	+	13.9704i	−0.273300	+	0.473370i
$872$	24.1685			0.818448
$873$	35.2469	+	12.8288i	1.19293	+	0.434190i
$874$	19.3105			0.653186
$875$	−4.05690	+	7.02676i	−0.137148	+	0.237548i
$876$	−96.1751	−	16.9583i	−3.24946	−	0.572967i
$877$	0.562834	+	0.974856i	0.0190055	+	0.0329186i	0.875372	−	0.483450i	$-0.160617\pi$
$877$	0.562834	+	0.974856i	0.0190055	+	0.0329186i	−0.856366	+	0.516369i	$0.827283\pi$
$878$	−31.7456	−	54.9849i	−1.07136	−	1.85565i
$879$	−14.3610	−	2.53223i	−0.484383	−	0.0854099i
$880$	11.3229	−	19.6119i	0.381697	−	0.661118i
$881$	−4.38331			−0.147678			−0.0738388	−	0.997270i	$-0.523525\pi$
$881$	−4.38331			−0.147678			−0.0738388	+	0.997270i	$0.523525\pi$
$882$	−1.31908	−	7.48086i	−0.0444157	−	0.251894i
$883$	−6.88949			−0.231850			−0.115925	−	0.993258i	$-0.536983\pi$
$883$	−6.88949			−0.231850			−0.115925	+	0.993258i	$0.536983\pi$
$884$	19.8799	−	34.4329i	0.668632	−	1.15810i
$885$	3.46972	+	9.53298i	0.116633	+	0.320448i
$886$	−2.58853	−	4.48346i	−0.0869632	−	0.150625i
$887$	−19.5376	−	33.8401i	−0.656009	−	1.13624i	−0.981640	−	0.190744i	$-0.938910\pi$
$887$	−19.5376	−	33.8401i	−0.656009	−	1.13624i	0.325631	−	0.945497i	$-0.394423\pi$
$888$	30.9613	−	36.8982i	1.03899	−	1.23822i
$889$	−8.82682	+	15.2885i	−0.296042	+	0.512760i
$890$	−24.5544			−0.823065
$891$	6.06283	−	34.3840i	0.203113	−	1.15191i
$892$	−27.6878			−0.927056
$893$	1.23261	−	2.13495i	0.0412478	−	0.0714432i
$894$	42.7251	−	50.9178i	1.42894	−	1.70295i
$895$	−3.23055	−	5.59548i	−0.107985	−	0.187036i
$896$	6.67024	+	11.5532i	0.222837	+	0.385965i
$897$	10.2166	+	28.0700i	0.341123	+	0.937229i
$898$	12.9572	−	22.4426i	0.432388	−	0.748919i
$899$	27.5523			0.918921
$900$	9.71348	+	55.0879i	0.323783	+	1.83626i
$901$	12.0496			0.401431
$902$	5.81908	−	10.0789i	0.193754	−	0.335592i
$903$	0.315207	+	0.0555796i	0.0104894	+	0.00184957i
$904$	−50.2327	−	87.0055i	−1.67071	−	2.89376i
$905$	−1.51501	−	2.62408i	−0.0503608	−	0.0872275i
$906$	−81.8740	−	14.4366i	−2.72008	−	0.479624i
$907$	−21.2469	+	36.8007i	−0.705492	+	1.22195i	0.261022	+	0.965333i	$0.415941\pi$
$907$	−21.2469	+	36.8007i	−0.705492	+	1.22195i	−0.966514	+	0.256615i	$0.917393\pi$
$908$	−27.1857			−0.902190
$909$	−27.3926	−	9.97011i	−0.908557	−	0.330688i
$910$	12.1429			0.402533
$911$	7.74675	−	13.4178i	0.256661	−	0.444550i	−0.708684	−	0.705526i	$-0.750711\pi$
$911$	7.74675	−	13.4178i	0.256661	−	0.444550i	0.965345	+	0.260976i	$0.0840442\pi$
$912$	−9.48293	−	26.0541i	−0.314011	−	0.862738i
$913$	0.424678	+	0.735564i	0.0140548	+	0.0243436i
$914$	53.9265	+	93.4035i	1.78373	+	3.08951i
$915$	−2.54189	+	3.02931i	−0.0840323	+	0.100146i
$916$	−51.5813	+	89.3414i	−1.70429	+	2.95192i
$917$	−19.1976			−0.633960
$918$	−18.8316	+	10.8724i	−0.621534	+	0.358843i
$919$	6.52940			0.215385			0.107693	−	0.994184i	$-0.465654\pi$
$919$	6.52940			0.215385			0.107693	+	0.994184i	$0.465654\pi$
$920$	8.49067	−	14.7063i	0.279929	−	0.484851i
$921$	14.1258	−	16.8345i	0.465462	−	0.554716i
$922$	−0.639033	−	1.10684i	−0.0210454	−	0.0364518i
$923$	−10.0343	−	17.3799i	−0.330283	−	0.572068i
$924$	−10.1382	−	27.8544i	−0.333521	−	0.916341i
$925$	−9.62495	+	16.6709i	−0.316466	+	0.548136i
$926$	6.78611			0.223005
$927$	−15.1591	+	12.7200i	−0.497890	+	0.417779i
$928$	−27.8057			−0.912767
$929$	−29.1386	+	50.4696i	−0.956007	+	1.65585i	−0.223961	+	0.974598i	$0.571899\pi$
$929$	−29.1386	+	50.4696i	−0.956007	+	1.65585i	−0.732046	+	0.681255i	$0.761435\pi$
$930$	17.2981	+	3.05013i	0.567228	+	0.100018i
$931$	−1.20574	−	2.08840i	−0.0395164	−	0.0684445i
$932$	18.8045	+	32.5704i	0.615963	+	1.06688i
$933$	−28.1279	−	4.95972i	−0.920868	−	0.162374i
$934$	39.7747	−	68.8918i	1.30147	−	2.25421i
$935$	−5.63816			−0.184387
$936$	76.5246	−	64.2118i	2.50129	−	2.09883i
$937$	32.4175			1.05903			0.529516	−	0.848300i	$-0.322374\pi$
$937$	32.4175			1.05903			0.529516	+	0.848300i	$0.322374\pi$
$938$	3.74510	−	6.48670i	0.122282	−	0.211798i
$939$	−16.8942	−	46.4165i	−0.551323	−	1.51475i
$940$	−1.98293	−	3.43453i	−0.0646759	−	0.112022i
$941$	13.6613	+	23.6621i	0.445346	+	0.771363i	0.998076	−	0.0619979i	$-0.0197472\pi$
$941$	13.6613	+	23.6621i	0.445346	+	0.771363i	−0.552730	+	0.833360i	$0.686414\pi$
$942$	50.9051	−	60.6664i	1.65858	−	1.97662i
$943$	1.87346	−	3.24492i	0.0610081	−	0.105669i
$944$	44.2131			1.43901
$945$	−3.95723	−	2.28471i	−0.128729	−	0.0743216i
$946$	1.81521			0.0590175
$947$	19.1065	−	33.0935i	0.620879	−	1.07539i	−0.368443	−	0.929650i	$-0.620109\pi$
$947$	19.1065	−	33.0935i	0.620879	−	1.07539i	0.989322	−	0.145744i	$-0.0465575\pi$
$948$	29.2631	−	34.8744i	0.950422	−	1.13267i
$949$	−34.8499	−	60.3618i	−1.13127	−	1.95943i
$950$	12.9042	+	22.3507i	0.418668	+	0.725153i
$951$	15.3400	+	42.1464i	0.497434	+	1.36669i
$952$	−5.04576	+	8.73951i	−0.163534	+	0.283249i
$953$	58.9377			1.90918			0.954590	−	0.297924i	$-0.0962943\pi$
$953$	58.9377			1.90918			0.954590	+	0.297924i	$0.0962943\pi$
$954$	52.0433	+	18.9422i	1.68496	+	0.613277i
$955$	−4.97535			−0.160998
$956$	−32.1202	+	55.6338i	−1.03884	+	1.79933i
$957$	−40.0317	−	7.05866i	−1.29404	−	0.228174i
$958$	20.8145	+	36.0518i	0.672486	+	1.16478i
$959$	−9.07785	−	15.7233i	−0.293139	−	0.507732i
$960$	2.45723	+	0.433277i	0.0793069	+	0.0139839i
$961$	5.12882	−	8.88338i	0.165446	−	0.286561i
$962$	62.8887			2.02761
$963$	−1.24463	−	7.05866i	−0.0401077	−	0.227462i
$964$	−23.8384			−0.767784
$965$	4.21941	−	7.30823i	0.135828	−	0.235260i
$966$	−4.74376	−	13.0334i	−0.152628	−	0.419342i
$967$	−12.3594	−	21.4071i	−0.397451	−	0.688405i	0.595960	−	0.803014i	$-0.296772\pi$
$967$	−12.3594	−	21.4071i	−0.397451	−	0.688405i	−0.993411	+	0.114609i	$0.963438\pi$
$968$	−12.3637	−	21.4145i	−0.397383	−	0.688287i
$969$	−4.43717	+	5.28801i	−0.142542	+	0.169875i
$970$	13.9201	−	24.1103i	0.446947	−	0.774135i
$971$	8.17623			0.262388			0.131194	−	0.991357i	$-0.458119\pi$
$971$	8.17623			0.262388			0.131194	+	0.991357i	$0.458119\pi$
$972$	−67.7233	+	11.9415i	−2.17223	+	0.383022i
$973$	22.0574			0.707127
$974$	3.76692	−	6.52450i	0.120700	−	0.209058i
$975$	−25.6621	+	30.5829i	−0.821845	+	0.979436i
$976$	8.61721	+	14.9254i	0.275830	+	0.477752i
$977$	7.92427	+	13.7252i	0.253520	+	0.439109i	0.964492	−	0.264111i	$-0.0850784\pi$
$977$	7.92427	+	13.7252i	0.253520	+	0.439109i	−0.710973	+	0.703220i	$0.751745\pi$
$978$	−1.43717	−	3.94858i	−0.0459555	−	0.126262i
$979$	−21.3897	+	37.0480i	−0.683616	+	1.18406i
$980$	−3.87939			−0.123922
$981$	−2.06196	−	11.6939i	−0.0658332	−	0.373359i
$982$	−67.0651			−2.14013
$983$	−26.6532	+	46.1646i	−0.850104	+	1.47242i	0.0310096	+	0.999519i	$0.490128\pi$
$983$	−26.6532	+	46.1646i	−0.850104	+	1.47242i	−0.881114	+	0.472904i	$0.843206\pi$
$984$	−12.3400	−	2.17588i	−0.393386	−	0.0693645i
$985$	3.65822	+	6.33623i	0.116561	+	0.201889i
$986$	12.6582	+	21.9247i	0.403120	+	0.698224i
$987$	−1.74376	−	0.307471i	−0.0555044	−	0.00978692i
$988$	29.0069	−	50.2414i	0.922831	−	1.59839i
$989$	0.584407			0.0185831
$990$	−24.3516	−	8.86327i	−0.773946	−	0.281693i
$991$	40.2094			1.27730			0.638648	−	0.769499i	$-0.279494\pi$
$991$	40.2094			1.27730			0.638648	+	0.769499i	$0.279494\pi$
$992$	10.4666	−	18.1286i	0.332314	−	0.575584i
$993$	−4.86887	−	13.3771i	−0.154509	−	0.424510i
$994$	4.65910	+	8.06980i	0.147778	+	0.255958i
$995$	2.90033	+	5.02352i	0.0919466	+	0.159256i
$996$	1.07532	−	1.28152i	0.0340729	−	0.0406065i
$997$	−14.3601	+	24.8724i	−0.454789	+	0.787717i	−0.998676	−	0.0514412i	$-0.983619\pi$
$997$	−14.3601	+	24.8724i	−0.454789	+	0.787717i	0.543887	+	0.839158i	$0.316952\pi$
$998$	−34.0411			−1.07755
$999$	−20.4947	−	11.8326i	−0.648424	−	0.374368i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.2.f.a.43.1	yes	6
3.2	odd	2		189.2.f.b.127.3		6
4.3	odd	2		1008.2.r.h.673.3		6
7.2	even	3		441.2.h.d.214.3		6
7.3	odd	6		441.2.g.b.79.1		6
7.4	even	3		441.2.g.c.79.1		6
7.5	odd	6		441.2.h.e.214.3		6
7.6	odd	2		441.2.f.c.295.1		6
9.2	odd	6		567.2.a.c.1.1		3
9.4	even	3	inner	63.2.f.a.22.1	✓	6
9.5	odd	6		189.2.f.b.64.3		6
9.7	even	3		567.2.a.h.1.3		3
12.11	even	2		3024.2.r.k.2017.1		6
21.2	odd	6		1323.2.h.c.802.1		6
21.5	even	6		1323.2.h.b.802.1		6
21.11	odd	6		1323.2.g.d.667.3		6
21.17	even	6		1323.2.g.e.667.3		6
21.20	even	2		1323.2.f.d.883.3		6
36.7	odd	6		9072.2.a.ca.1.1		3
36.11	even	6		9072.2.a.bs.1.3		3
36.23	even	6		3024.2.r.k.1009.1		6
36.31	odd	6		1008.2.r.h.337.3		6
63.4	even	3		441.2.h.d.373.3		6
63.5	even	6		1323.2.g.e.361.3		6
63.13	odd	6		441.2.f.c.148.1		6
63.20	even	6		3969.2.a.l.1.1		3
63.23	odd	6		1323.2.g.d.361.3		6
63.31	odd	6		441.2.h.e.373.3		6
63.32	odd	6		1323.2.h.c.226.1		6
63.34	odd	6		3969.2.a.q.1.3		3
63.40	odd	6		441.2.g.b.67.1		6
63.41	even	6		1323.2.f.d.442.3		6
63.58	even	3		441.2.g.c.67.1		6
63.59	even	6		1323.2.h.b.226.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.a.22.1	✓	6	9.4	even	3	inner
63.2.f.a.43.1	yes	6	1.1	even	1	trivial
189.2.f.b.64.3		6	9.5	odd	6
189.2.f.b.127.3		6	3.2	odd	2
441.2.f.c.148.1		6	63.13	odd	6
441.2.f.c.295.1		6	7.6	odd	2
441.2.g.b.67.1		6	63.40	odd	6
441.2.g.b.79.1		6	7.3	odd	6
441.2.g.c.67.1		6	63.58	even	3
441.2.g.c.79.1		6	7.4	even	3
441.2.h.d.214.3		6	7.2	even	3
441.2.h.d.373.3		6	63.4	even	3
441.2.h.e.214.3		6	7.5	odd	6
441.2.h.e.373.3		6	63.31	odd	6
567.2.a.c.1.1		3	9.2	odd	6
567.2.a.h.1.3		3	9.7	even	3
1008.2.r.h.337.3		6	36.31	odd	6
1008.2.r.h.673.3		6	4.3	odd	2
1323.2.f.d.442.3		6	63.41	even	6
1323.2.f.d.883.3		6	21.20	even	2
1323.2.g.d.361.3		6	63.23	odd	6
1323.2.g.d.667.3		6	21.11	odd	6
1323.2.g.e.361.3		6	63.5	even	6
1323.2.g.e.667.3		6	21.17	even	6
1323.2.h.b.226.1		6	63.59	even	6
1323.2.h.b.802.1		6	21.5	even	6
1323.2.h.c.226.1		6	63.32	odd	6
1323.2.h.c.802.1		6	21.2	odd	6
3024.2.r.k.1009.1		6	36.23	even	6
3024.2.r.k.2017.1		6	12.11	even	2
3969.2.a.l.1.1		3	63.20	even	6
3969.2.a.q.1.3		3	63.34	odd	6
9072.2.a.bs.1.3		3	36.11	even	6
9072.2.a.ca.1.1		3	36.7	odd	6

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	63.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26604 + 2.19285i) q^{2} +(-1.11334 + 1.32683i) q^{3} +(-2.20574 - 3.82045i) q^{4} +(0.439693 + 0.761570i) q^{5} +(-1.50000 - 4.12122i) q^{6} +(-0.500000 + 0.866025i) q^{7} +6.10607 q^{8} +(-0.520945 - 2.95442i) q^{9} -2.22668 q^{10} +(-1.93969 + 3.35965i) q^{11} +(7.52481 + 1.32683i) q^{12} +(2.72668 + 4.72275i) q^{13} +(-1.26604 - 2.19285i) q^{14} +(-1.50000 - 0.264490i) q^{15} +(-3.31908 + 5.74881i) q^{16} +1.65270 q^{17} +(7.13816 + 2.59808i) q^{18} +2.41147 q^{19} +(1.93969 - 3.35965i) q^{20} +(-0.592396 - 1.62760i) q^{21} +(-4.91147 - 8.50692i) q^{22} +(-1.58125 - 2.73881i) q^{23} +(-6.79813 + 8.10170i) q^{24} +(2.11334 - 3.66041i) q^{25} -13.8084 q^{26} +(4.50000 + 2.59808i) q^{27} +4.41147 q^{28} +(3.02481 - 5.23913i) q^{29} +(2.47906 - 2.95442i) q^{30} +(2.27719 + 3.94421i) q^{31} +(-2.29813 - 3.98048i) q^{32} +(-2.29813 - 6.31407i) q^{33} +(-2.09240 + 3.62414i) q^{34} -0.879385 q^{35} +(-10.1382 + 8.50692i) q^{36} -4.55438 q^{37} +(-3.05303 + 5.28801i) q^{38} +(-9.30200 - 1.64019i) q^{39} +(2.68479 + 4.65020i) q^{40} +(0.592396 + 1.02606i) q^{41} +(4.31908 + 0.761570i) q^{42} +(-0.0923963 + 0.160035i) q^{43} +17.1138 q^{44} +(2.02094 - 1.69577i) q^{45} +8.00774 q^{46} +(0.511144 - 0.885328i) q^{47} +(-3.93242 - 10.8042i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(5.35117 + 9.26849i) q^{50} +(-1.84002 + 2.19285i) q^{51} +(12.0287 - 20.8343i) q^{52} +7.29086 q^{53} +(-11.3944 + 6.57856i) q^{54} -3.41147 q^{55} +(-3.05303 + 5.28801i) q^{56} +(-2.68479 + 3.19961i) q^{57} +(7.65910 + 13.2660i) q^{58} +(-3.33022 - 5.76811i) q^{59} +(2.29813 + 6.31407i) q^{60} +(1.29813 - 2.24843i) q^{61} -11.5321 q^{62} +(2.81908 + 1.02606i) q^{63} -1.63816 q^{64} +(-2.39780 + 4.15312i) q^{65} +(16.7554 + 2.95442i) q^{66} +(1.47906 + 2.56180i) q^{67} +(-3.64543 - 6.31407i) q^{68} +(5.39440 + 0.951178i) q^{69} +(1.11334 - 1.92836i) q^{70} -3.68004 q^{71} +(-3.18092 - 18.0399i) q^{72} -12.7811 q^{73} +(5.76604 - 9.98708i) q^{74} +(2.50387 + 6.87933i) q^{75} +(-5.31908 - 9.21291i) q^{76} +(-1.93969 - 3.35965i) q^{77} +(15.3735 - 18.3214i) q^{78} +(2.97906 - 5.15988i) q^{79} -5.83750 q^{80} +(-8.45723 + 3.07818i) q^{81} -3.00000 q^{82} +(0.109470 - 0.189608i) q^{83} +(-4.91147 + 5.85327i) q^{84} +(0.726682 + 1.25865i) q^{85} +(-0.233956 - 0.405223i) q^{86} +(3.58378 + 9.84635i) q^{87} +(-11.8439 + 20.5142i) q^{88} +11.0273 q^{89} +(1.15998 + 6.57856i) q^{90} -5.45336 q^{91} +(-6.97565 + 12.0822i) q^{92} +(-7.76857 - 1.36981i) q^{93} +(1.29426 + 2.24173i) q^{94} +(1.06031 + 1.83651i) q^{95} +(7.84002 + 1.38241i) q^{96} +(-6.25150 + 10.8279i) q^{97} +2.53209 q^{98} +(10.9363 + 3.98048i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} - 3 q^{5} - 9 q^{6} - 3 q^{7} + 12 q^{8} - 6 q^{11} + 18 q^{12} + 3 q^{13} - 3 q^{14} - 9 q^{15} - 3 q^{16} + 12 q^{17} + 9 q^{18} - 6 q^{19} + 6 q^{20} - 9 q^{22} - 12 q^{23} - 27 q^{24}+ \cdots + 18 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 - 3 * q^5 - 9 * q^6 - 3 * q^7 + 12 * q^8 - 6 * q^11 + 18 * q^12 + 3 * q^13 - 3 * q^14 - 9 * q^15 - 3 * q^16 + 12 * q^17 + 9 * q^18 - 6 * q^19 + 6 * q^20 - 9 * q^22 - 12 * q^23 - 27 * q^24 + 6 * q^25 - 6 * q^26 + 27 * q^27 + 6 * q^28 - 9 * q^29 + 18 * q^30 + 3 * q^31 - 9 * q^34 + 6 * q^35 - 27 * q^36 - 6 * q^37 - 6 * q^38 - 18 * q^39 + 9 * q^40 + 9 * q^42 + 3 * q^43 + 30 * q^44 + 9 * q^45 - 3 * q^47 - 3 * q^49 + 6 * q^50 + 9 * q^51 + 21 * q^52 + 12 * q^53 - 27 * q^54 - 6 * q^56 - 9 * q^57 + 9 * q^58 + 3 * q^59 - 6 * q^61 - 60 * q^62 + 24 * q^64 - 15 * q^65 + 36 * q^66 + 12 * q^67 - 6 * q^68 - 9 * q^69 + 18 * q^71 - 36 * q^72 - 42 * q^73 + 30 * q^74 - 9 * q^75 - 15 * q^76 - 6 * q^77 + 54 * q^78 + 21 * q^79 - 30 * q^80 - 18 * q^82 + 18 * q^83 - 9 * q^84 - 9 * q^85 - 6 * q^86 + 9 * q^87 - 27 * q^88 + 24 * q^89 + 27 * q^90 - 6 * q^91 - 3 * q^92 - 27 * q^93 + 18 * q^94 + 12 * q^95 + 27 * q^96 + 3 * q^97 + 6 * q^98 + 18 * q^99

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