LMFDB - Embedded newform 63.2.f.a.22.1

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			22.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	63.22
Dual form			63.2.f.a.43.1

$q$-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 $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−1.26604	−	2.19285i	−0.895229	−	1.55058i	−0.833521	−	0.552487i	$-0.813679\pi$
$2$	−1.26604	−	2.19285i	−0.895229	−	1.55058i	−0.0617072	−	0.998094i	$-0.519654\pi$
$3$	−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	−0.750799	−	0.660530i	$-0.770331\pi$
$5$	0.439693	−	0.761570i	0.196637	−	0.340584i	0.947436	+	0.319946i	$0.103665\pi$
$6$	−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	−0.994895	−	0.100911i	$-0.967824\pi$
$11$	−1.93969	−	3.35965i	−0.584839	−	1.01297i	0.410056	−	0.912060i	$-0.365509\pi$
$12$	7.52481	−	1.32683i	2.17223	−	0.383022i
$13$	2.72668	−	4.72275i	0.756245	−	1.30986i	−0.188507	−	0.982072i	$-0.560365\pi$
$13$	2.72668	−	4.72275i	0.756245	−	1.30986i	0.944753	−	0.327784i	$-0.106302\pi$
$14$	−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	−0.982455	−	0.186500i	$-0.940286\pi$
$23$	−1.58125	+	2.73881i	−0.329714	+	0.571081i	0.652741	+	0.757581i	$0.273619\pi$
$24$	−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	0.997349	+	0.0727688i	$0.0231835\pi$
$29$	3.02481	+	5.23913i	0.561694	+	0.972883i	−0.435655	+	0.900114i	$0.643483\pi$
$30$	2.47906	+	2.95442i	0.452612	+	0.539401i
$31$	2.27719	−	3.94421i	0.408995	−	0.708400i	−0.585782	−	0.810468i	$-0.699213\pi$
$31$	2.27719	−	3.94421i	0.408995	−	0.708400i	0.994777	+	0.102068i	$0.0325459\pi$
$32$	−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	−0.816053	−	0.577977i	$-0.803842\pi$
$41$	0.592396	−	1.02606i	0.0925168	−	0.160244i	0.908570	+	0.417734i	$0.137175\pi$
$42$	4.31908	−	0.761570i	0.666448	−	0.117513i
$43$	−0.0923963	−	0.160035i	−0.0140903	−	0.0244051i	0.858894	−	0.512153i	$-0.171152\pi$
$43$	−0.0923963	−	0.160035i	−0.0140903	−	0.0244051i	−0.872985	+	0.487748i	$0.837819\pi$
$44$	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	0.900894	−	0.434039i	$-0.142912\pi$
$47$	0.511144	+	0.885328i	0.0745581	+	0.129138i	−0.826336	+	0.563178i	$0.809579\pi$
$48$	−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	−0.997177	−	0.0750906i	$-0.976075\pi$
$59$	−3.33022	+	5.76811i	−0.433558	+	0.750944i	0.563619	+	0.826035i	$0.309409\pi$
$60$	2.29813	−	6.31407i	0.296688	−	0.815143i
$61$	1.29813	+	2.24843i	0.166209	+	0.287882i	0.937084	−	0.349104i	$-0.113514\pi$
$61$	1.29813	+	2.24843i	0.166209	+	0.287882i	−0.770875	+	0.636986i	$0.780181\pi$
$62$	−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	−0.761422	−	0.648256i	$-0.775499\pi$
$67$	1.47906	−	2.56180i	0.180695	−	0.312974i	0.942118	+	0.335283i	$0.108832\pi$
$68$	−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	0.983517	−	0.180813i	$-0.0578729\pi$
$79$	2.97906	+	5.15988i	0.335170	+	0.580531i	−0.648348	+	0.761345i	$0.724540\pi$
$80$	−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	0.871971	−	0.489558i	$-0.162842\pi$
$83$	0.109470	+	0.189608i	0.0120159	+	0.0208122i	−0.859955	+	0.510370i	$0.829508\pi$
$84$	−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	−0.986569	−	0.163342i	$-0.947773\pi$
$97$	−6.25150	−	10.8279i	−0.634743	−	1.09941i	0.351826	−	0.936065i	$-0.385561\pi$
$98$	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	0.999819	−	0.0190255i	$-0.00605638\pi$
$101$	4.85844	+	8.41507i	0.483433	+	0.837330i	−0.516386	+	0.856356i	$0.672723\pi$
$102$	−2.47906	+	6.81115i	−0.245463	+	0.674404i
$103$	−3.29813	+	5.71253i	−0.324975	+	0.562873i	−0.981507	−	0.191425i	$-0.938689\pi$
$103$	−3.29813	+	5.71253i	−0.324975	+	0.562873i	0.656533	+	0.754298i	$0.272022\pi$
$104$	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	0.161509	+	0.986871i	$0.448364\pi$
$113$	−8.22668	+	14.2490i	−0.773901	+	1.34044i	−0.935410	+	0.353565i	$0.884969\pi$
$114$	−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	−0.0523729	−	0.998628i	$-0.516678\pi$
$131$	9.59879	−	16.6256i	0.838650	−	1.45259i	0.891023	−	0.453958i	$-0.149988\pi$
$132$	−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	−0.934472	−	0.356037i	$-0.884128\pi$
$137$	−9.07785	−	15.7233i	−0.775573	−	1.34333i	0.158899	−	0.987295i	$-0.449206\pi$
$138$	−8.91534	−	10.6249i	−0.758925	−	0.904451i
$139$	−11.0287	+	19.1022i	−0.935441	+	1.62023i	−0.161595	+	0.986857i	$0.551664\pi$
$139$	−11.0287	+	19.1022i	−0.935441	+	1.62023i	−0.773846	+	0.633374i	$0.781670\pi$
$140$	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	−0.368535	−	0.929614i	$-0.620141\pi$
$149$	7.57785	−	13.1252i	0.620802	−	1.07526i	0.989337	−	0.145646i	$-0.0465261\pi$
$150$	−18.2554	+	3.21891i	−1.49054	+	0.262823i
$151$	9.47818	+	16.4167i	0.771323	+	1.33597i	0.936838	+	0.349764i	$0.113738\pi$
$151$	9.47818	+	16.4167i	0.771323	+	1.33597i	−0.165515	+	0.986207i	$0.552929\pi$
$152$	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	−0.240205	−	0.970722i	$-0.577215\pi$
$157$	9.02869	−	15.6381i	0.720568	−	1.24806i	0.960773	−	0.277337i	$-0.0894520\pi$
$158$	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	0.171304	+	0.985218i	$0.445202\pi$
$167$	−9.91921	+	17.1806i	−0.767572	+	1.32947i	−0.938876	+	0.344255i	$0.888131\pi$
$168$	−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	−0.869734	−	0.493520i	$-0.835710\pi$
$173$	−11.3414	−	19.6438i	−0.862268	−	1.49349i	0.00746626	−	0.999972i	$-0.497623\pi$
$174$	−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	0.745344	−	0.666680i	$-0.232285\pi$
$191$	−2.82888	−	4.89976i	−0.204690	−	0.354534i	−0.950034	+	0.312146i	$0.898952\pi$
$192$	1.82383	+	2.17355i	0.131623	+	0.156863i
$193$	−4.79813	+	8.31061i	−0.345377	+	0.598211i	−0.985422	−	0.170127i	$-0.945582\pi$
$193$	−4.79813	+	8.31061i	−0.345377	+	0.598211i	0.640045	+	0.768337i	$0.278916\pi$
$194$	−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	−0.802188	−	0.597072i	$-0.796331\pi$
$211$	1.68479	−	2.91815i	0.115986	−	0.200893i	0.918173	+	0.396179i	$0.129664\pi$
$212$	−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	0.951760	−	0.306843i	$-0.0992726\pi$
$223$	3.13816	+	5.43545i	0.210146	+	0.363984i	−0.741614	+	0.670827i	$0.765939\pi$
$224$	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	0.949976	−	0.312322i	$-0.101107\pi$
$227$	3.08125	+	5.33688i	0.204510	+	0.354221i	−0.745467	+	0.666543i	$0.767773\pi$
$228$	18.1459	−	3.19961i	1.20174	−	0.211899i
$229$	−11.6925	+	20.2521i	−0.772664	+	1.33829i	0.163434	+	0.986554i	$0.447743\pi$
$229$	−11.6925	+	20.2521i	−0.772664	+	1.33829i	−0.936098	+	0.351740i	$0.885590\pi$
$230$	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	−0.999449	−	0.0331997i	$-0.989430\pi$
$239$	−7.28106	+	12.6112i	−0.470973	+	0.815748i	0.528476	+	0.848948i	$0.322764\pi$
$240$	6.49912	+	7.74535i	0.419517	+	0.499960i
$241$	2.70187	+	4.67977i	0.174043	+	0.301451i	0.939830	−	0.341644i	$-0.110984\pi$
$241$	2.70187	+	4.67977i	0.174043	+	0.301451i	−0.765787	+	0.643094i	$0.777650\pi$
$242$	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	−0.982423	−	0.186668i	$-0.940231\pi$
$257$	−5.28312	+	9.15063i	−0.329552	+	0.570801i	0.652871	+	0.757469i	$0.273564\pi$
$258$	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	0.857645	+	0.514242i	$0.171927\pi$
$263$	14.1766	+	24.5547i	0.874169	+	1.51411i	0.0165240	+	0.999863i	$0.494740\pi$
$264$	−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	0.943502	−	0.331368i	$-0.107510\pi$
$277$	3.07532	+	5.32661i	0.184778	+	0.320045i	−0.758724	+	0.651413i	$0.774177\pi$
$278$	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	0.812391	−	0.583113i	$-0.198165\pi$
$281$	−1.65611	−	2.86846i	−0.0987951	−	0.171118i	−0.911186	+	0.411995i	$0.864832\pi$
$282$	−4.41534	+	0.778544i	−0.262930	+	0.0463616i
$283$	−14.5116	+	25.1348i	−0.862626	+	1.49411i	0.00675974	+	0.999977i	$0.497848\pi$
$283$	−14.5116	+	25.1348i	−0.862626	+	1.49411i	−0.869385	+	0.494134i	$0.835485\pi$
$284$	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	−0.716464	−	0.697624i	$-0.754241\pi$
$293$	4.20961	−	7.29125i	0.245928	−	0.425960i	0.962392	+	0.271664i	$0.0875740\pi$
$294$	−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	−0.531775	−	0.846886i	$-0.678475\pi$
$311$	8.24510	−	14.2809i	0.467537	−	0.809797i	0.999312	+	0.0370881i	$0.0118082\pi$
$312$	−56.7987	+	10.0151i	−3.21559	+	0.566995i
$313$	−14.2592	−	24.6977i	−0.805980	−	1.39600i	−0.915628	−	0.402027i	$-0.868306\pi$
$313$	−14.2592	−	24.6977i	−0.805980	−	1.39600i	0.109648	−	0.993970i	$-0.465028\pi$
$314$	−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	0.958062	+	0.286561i	$0.0925122\pi$
$317$	12.9474	+	22.4256i	0.727200	+	1.25955i	−0.230862	+	0.972987i	$0.574154\pi$
$318$	−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	0.730705	−	0.682693i	$-0.239191\pi$
$331$	−4.10947	−	7.11781i	−0.225877	−	0.391230i	−0.956582	+	0.291463i	$0.905858\pi$
$332$	−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	−0.921540	−	0.388283i	$-0.873068\pi$
$337$	−2.28564	+	3.95885i	−0.124507	+	0.215652i	0.797033	+	0.603936i	$0.206402\pi$
$338$	−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	0.389337	+	0.921095i	$0.372704\pi$
$347$	−11.2331	+	19.4563i	−0.603023	+	1.04447i	−0.992361	+	0.123372i	$0.960629\pi$
$348$	29.7126	+	35.4101i	1.59276	+	1.89818i
$349$	−13.0496	−	22.6026i	−0.698531	−	1.20989i	−0.968976	−	0.247155i	$-0.920504\pi$
$349$	−13.0496	−	22.6026i	−0.698531	−	1.20989i	0.270445	−	0.962735i	$-0.412829\pi$
$350$	−10.7023			−0.572064
$351$		−	28.3365i		−	1.51249i
$352$	17.8307			0.950379
$353$	0.177519	+	0.307471i	0.00944836	+	0.0163650i	0.870711	−	0.491795i	$-0.163659\pi$
$353$	0.177519	+	0.307471i	0.00944836	+	0.0163650i	−0.861263	+	0.508160i	$0.830326\pi$
$354$	−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	0.687523	−	0.726162i	$-0.258698\pi$
$367$	−5.46198	−	9.46043i	−0.285113	−	0.493830i	−0.972637	+	0.232332i	$0.925364\pi$
$368$	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	−0.887567	−	0.460678i	$-0.847606\pi$
$373$	−0.865715	+	1.49946i	−0.0448250	+	0.0776392i	0.842742	+	0.538317i	$0.180940\pi$
$374$	−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	−0.733013	−	0.680215i	$-0.761887\pi$
$383$	4.35591	−	7.54467i	0.222577	−	0.385514i	0.955590	+	0.294700i	$0.0952198\pi$
$384$	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	0.816144	−	0.577848i	$-0.196107\pi$
$389$	−1.82160	−	3.15511i	−0.0923590	−	0.159970i	−0.908503	+	0.417878i	$0.862774\pi$
$390$	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	−0.998959	−	0.0456182i	$-0.985474\pi$
$401$	−9.21095	+	15.9538i	−0.459973	+	0.796697i	0.538986	+	0.842315i	$0.318808\pi$
$402$	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	−0.257612	−	0.966248i	$-0.582936\pi$
$409$	14.3182	−	24.7999i	0.707989	−	1.22627i	0.965602	−	0.260025i	$-0.0837309\pi$
$410$	−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	−0.0359442	−	0.999354i	$-0.511444\pi$
$419$	17.3478	−	30.0472i	0.847494	−	1.46790i	0.883438	−	0.468548i	$-0.155223\pi$
$420$	−6.61721	+	1.16679i	−0.322887	+	0.0569337i
$421$	13.7010	+	23.7308i	0.667745	+	1.15657i	0.978533	+	0.206090i	$0.0660738\pi$
$421$	13.7010	+	23.7308i	0.667745	+	1.15657i	−0.310788	+	0.950479i	$0.600593\pi$
$422$	−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	−0.993061	−	0.117597i	$-0.962481\pi$
$439$	−12.5373	−	21.7152i	−0.598373	−	1.03641i	0.394689	−	0.918815i	$-0.370853\pi$
$440$	−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	0.840718	−	0.541473i	$-0.182133\pi$
$443$	−1.02229	−	1.77066i	−0.0485704	−	0.0841264i	−0.889288	+	0.457347i	$0.848800\pi$
$444$	−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	0.573115	+	0.819475i	$0.305735\pi$
$457$	21.2973	+	36.8879i	0.996244	+	1.72554i	0.423129	+	0.906070i	$0.360932\pi$
$458$	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	0.860088	−	0.510145i	$-0.170408\pi$
$461$	−0.252374	−	0.437124i	−0.0117542	−	0.0203589i	−0.871843	+	0.489786i	$0.837075\pi$
$462$	−10.9363	−	13.0334i	−0.508802	−	0.606367i
$463$	−1.34002	+	2.32099i	−0.0622761	+	0.107865i	−0.895482	−	0.445097i	$-0.853169\pi$
$463$	−1.34002	+	2.32099i	−0.0622761	+	0.107865i	0.833206	+	0.552962i	$0.186503\pi$
$464$	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	0.990416	−	0.138118i	$-0.0441052\pi$
$479$	8.22028	+	14.2380i	0.375594	+	0.650549i	−0.614821	+	0.788666i	$0.710772\pi$
$480$	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	−0.395517	−	0.918459i	$-0.629435\pi$
$491$	13.2430	−	22.9376i	0.597650	−	1.03516i	0.993167	−	0.116702i	$-0.0372321\pi$
$492$	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	−0.675428	−	0.737426i	$-0.736041\pi$
$499$	6.72193	−	11.6427i	0.300915	−	0.521200i	0.976343	+	0.216225i	$0.0693746\pi$
$500$	−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	−0.952214	−	0.305433i	$-0.901199\pi$
$509$	−4.77379	+	8.26844i	−0.211594	+	0.366492i	0.740619	+	0.671925i	$0.234532\pi$
$510$	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	0.634373	−	0.773027i	$-0.281258\pi$
$547$	−8.23901	−	14.2704i	−0.352275	−	0.610157i	−0.986648	+	0.162870i	$0.947925\pi$
$548$	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	−0.145411	−	0.989371i	$-0.546450\pi$
$563$	18.6052	−	32.2251i	0.784115	−	1.35813i	0.929526	−	0.368756i	$-0.120216\pi$
$564$	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	0.861753	−	0.507328i	$-0.169367\pi$
$569$	−0.202333	−	0.350452i	−0.00848226	−	0.0146917i	−0.870235	+	0.492636i	$0.836033\pi$
$570$	5.97818	+	7.12452i	0.250398	+	0.298413i
$571$	18.8897	−	32.7178i	0.790507	−	1.36920i	−0.135146	−	0.990826i	$-0.543150\pi$
$571$	18.8897	−	32.7178i	0.790507	−	1.36920i	0.925653	−	0.378373i	$-0.123516\pi$
$572$	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	0.500378	−	0.865807i	$-0.333194\pi$
$587$	−12.1049	−	20.9663i	−0.499622	−	0.865371i	−1.00000		0.000436347i	$0.999861\pi$
$588$	−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	0.103966	+	0.994581i	$0.466847\pi$
$599$	−19.8084	+	34.3092i	−0.809349	+	1.40183i	−0.913315	+	0.407253i	$0.866487\pi$
$600$	15.2888	−	42.0056i	0.624163	−	1.71487i
$601$	15.0039	+	25.9875i	0.612021	+	1.06005i	0.990899	+	0.134605i	$0.0429764\pi$
$601$	15.0039	+	25.9875i	0.612021	+	1.06005i	−0.378879	+	0.925446i	$0.623690\pi$
$602$	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	−0.597733	−	0.801695i	$-0.703932\pi$
$607$	9.74216	−	16.8739i	0.395422	−	0.684891i	0.993155	+	0.116804i	$0.0372650\pi$
$608$	−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	0.437059	+	0.899433i	$0.356020\pi$
$617$	−13.9201	+	24.1103i	−0.560402	+	0.970644i	−0.997461	+	0.0712118i	$0.977313\pi$
$618$	−18.5954	−	22.1611i	−0.748016	−	0.891451i
$619$	22.4907	+	38.9550i	0.903976	+	1.56573i	0.822286	+	0.569075i	$0.192699\pi$
$619$	22.4907	+	38.9550i	0.903976	+	1.56573i	0.0816906	+	0.996658i	$0.473968\pi$
$620$	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	−0.953211	−	0.302306i	$-0.902243\pi$
$641$	−18.6951	−	32.3808i	−0.738410	−	1.27896i	0.214800	−	0.976658i	$-0.431090\pi$
$642$	−3.58378	+	9.84635i	−0.141440	+	0.388604i
$643$	−0.805874	+	1.39581i	−0.0317806	+	0.0550456i	−0.881478	−	0.472225i	$-0.843451\pi$
$643$	−0.805874	+	1.39581i	−0.0317806	+	0.0550456i	0.849698	+	0.527270i	$0.176784\pi$
$644$	−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	−0.894338	−	0.447391i	$-0.852353\pi$
$653$	−1.52600	+	2.64310i	−0.0597169	+	0.103433i	0.834621	+	0.550824i	$0.185686\pi$
$654$	−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	−0.912211	−	0.409721i	$-0.865626\pi$
$659$	−20.8175	−	36.0569i	−0.810934	−	1.40458i	0.101277	−	0.994858i	$-0.467707\pi$
$660$	−25.6707	+	4.52644i	−0.999231	+	0.176191i
$661$	−10.1505	+	17.5812i	−0.394808	+	0.683828i	−0.993077	−	0.117468i	$-0.962522\pi$
$661$	−10.1505	+	17.5812i	−0.394808	+	0.683828i	0.598269	+	0.801296i	$0.295856\pi$
$662$	−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	0.873920	−	0.486071i	$-0.161570\pi$
$673$	0.415345	+	0.719398i	0.0160104	+	0.0277307i	−0.857909	+	0.513801i	$0.828237\pi$
$674$	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	0.742516	−	0.669828i	$-0.233632\pi$
$677$	−5.43360	−	9.41127i	−0.208830	−	0.361705i	−0.951346	+	0.308124i	$0.900299\pi$
$678$	−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	0.687397	−	0.726282i	$-0.258753\pi$
$691$	−7.49912	−	12.9889i	−0.285280	−	0.494120i	−0.972677	+	0.232162i	$0.925420\pi$
$692$	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	0.685005	−	0.728538i	$-0.259800\pi$
$709$	−7.68004	−	13.3022i	−0.288430	−	0.499576i	−0.973435	+	0.228963i	$0.926467\pi$
$710$	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	0.884379	+	0.466770i	$0.154582\pi$
$727$	22.8221	+	39.5290i	0.846424	+	1.46605i	−0.0379552	+	0.999279i	$0.512084\pi$
$728$	−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	−0.915910	−	0.401384i	$-0.868529\pi$
$733$	−2.98751	+	5.17452i	−0.110346	+	0.191125i	0.805564	+	0.592509i	$0.201863\pi$
$734$	−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	−0.461416	−	0.887184i	$-0.652658\pi$
$743$	14.6544	−	25.3821i	0.537616	−	0.931178i	0.999032	−	0.0439943i	$-0.0140083\pi$
$744$	−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	−0.663446	−	0.748224i	$-0.730907\pi$
$751$	8.66684	−	15.0114i	0.316258	−	0.547774i	0.979704	+	0.200450i	$0.0642403\pi$
$752$	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	−0.926007	−	0.377508i	$-0.876781\pi$
$761$	−3.75372	+	6.50163i	−0.136072	+	0.235684i	0.789934	+	0.613191i	$0.210115\pi$
$762$	−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	−0.883861	−	0.467749i	$-0.845065\pi$
$769$	−1.02182	+	1.76985i	−0.0368478	+	0.0638223i	0.847013	+	0.531572i	$0.178398\pi$
$770$	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	−0.922384	−	0.386274i	$-0.873762\pi$
$787$	−3.55350	+	6.15484i	−0.126669	+	0.219396i	0.795715	+	0.605671i	$0.207095\pi$
$788$	−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	0.397178	+	0.917742i	$0.369990\pi$
$797$	−16.8314	+	29.1528i	−0.596199	+	1.03265i	−0.993376	+	0.114905i	$0.963344\pi$
$798$	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	0.517062	−	0.855948i	$-0.327026\pi$
$821$	−13.8320	−	23.9578i	−0.482741	−	0.836132i	−0.999804	+	0.0198153i	$0.993692\pi$
$822$	78.4159	−	13.8268i	2.73507	−	0.482266i
$823$	−13.9162	+	24.1036i	−0.485089	+	0.840199i	−0.999853	−	0.0171330i	$-0.994546\pi$
$823$	−13.9162	+	24.1036i	−0.485089	+	0.840199i	0.514764	+	0.857332i	$0.327879\pi$
$824$	−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	0.918246	−	0.396011i	$-0.129606\pi$
$839$	3.36484	+	5.82807i	0.116167	+	0.201207i	−0.802079	+	0.597218i	$0.796273\pi$
$840$	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	0.812193	−	0.583388i	$-0.198273\pi$
$853$	−2.89528	−	5.01477i	−0.0991324	−	0.171702i	−0.911326	+	0.411686i	$0.864940\pi$
$854$	−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	0.993375	+	0.114921i	$0.0366614\pi$
$857$	17.4538	+	30.2309i	0.596211	+	1.03267i	−0.397163	+	0.917748i	$0.630005\pi$
$858$	31.7335	−	87.1872i	1.08337	−	2.97652i
$859$	6.30747	−	10.9249i	0.215208	−	0.372751i	−0.738129	−	0.674660i	$-0.764290\pi$
$859$	6.30747	−	10.9249i	0.215208	−	0.372751i	0.953337	+	0.301909i	$0.0976237\pi$
$860$	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	−0.856366	−	0.516369i	$-0.827283\pi$
$877$	0.562834	−	0.974856i	0.0190055	−	0.0329186i	0.875372	+	0.483450i	$0.160617\pi$
$878$	−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	0.325631	+	0.945497i	$0.394423\pi$
$887$	−19.5376	+	33.8401i	−0.656009	+	1.13624i	−0.981640	+	0.190744i	$0.938910\pi$
$888$	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	−0.966514	−	0.256615i	$-0.917393\pi$
$907$	−21.2469	−	36.8007i	−0.705492	−	1.22195i	0.261022	−	0.965333i	$-0.415941\pi$
$908$	−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	0.965345	−	0.260976i	$-0.0840442\pi$
$911$	7.74675	+	13.4178i	0.256661	+	0.444550i	−0.708684	+	0.705526i	$0.750711\pi$
$912$	−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	−0.732046	−	0.681255i	$-0.761435\pi$
$929$	−29.1386	−	50.4696i	−0.956007	−	1.65585i	−0.223961	−	0.974598i	$-0.571899\pi$
$930$	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	−0.552730	−	0.833360i	$-0.686414\pi$
$941$	13.6613	−	23.6621i	0.445346	−	0.771363i	0.998076	+	0.0619979i	$0.0197472\pi$
$942$	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	0.989322	+	0.145744i	$0.0465575\pi$
$947$	19.1065	+	33.0935i	0.620879	+	1.07539i	−0.368443	+	0.929650i	$0.620109\pi$
$948$	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	−0.993411	−	0.114609i	$-0.963438\pi$
$967$	−12.3594	+	21.4071i	−0.397451	+	0.688405i	0.595960	+	0.803014i	$0.296772\pi$
$968$	−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	−0.710973	−	0.703220i	$-0.751745\pi$
$977$	7.92427	−	13.7252i	0.253520	−	0.439109i	0.964492	+	0.264111i	$0.0850784\pi$
$978$	−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	−0.881114	−	0.472904i	$-0.843206\pi$
$983$	−26.6532	−	46.1646i	−0.850104	−	1.47242i	0.0310096	−	0.999519i	$-0.490128\pi$
$984$	−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	0.543887	−	0.839158i	$-0.316952\pi$
$997$	−14.3601	−	24.8724i	−0.454789	−	0.787717i	−0.998676	+	0.0514412i	$0.983619\pi$
$998$	−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.22.1	✓	6
3.2	odd	2		189.2.f.b.64.3		6
4.3	odd	2		1008.2.r.h.337.3		6
7.2	even	3		441.2.g.c.67.1		6
7.3	odd	6		441.2.h.e.373.3		6
7.4	even	3		441.2.h.d.373.3		6
7.5	odd	6		441.2.g.b.67.1		6
7.6	odd	2		441.2.f.c.148.1		6
9.2	odd	6		189.2.f.b.127.3		6
9.4	even	3		567.2.a.h.1.3		3
9.5	odd	6		567.2.a.c.1.1		3
9.7	even	3	inner	63.2.f.a.43.1	yes	6
12.11	even	2		3024.2.r.k.1009.1		6
21.2	odd	6		1323.2.g.d.361.3		6
21.5	even	6		1323.2.g.e.361.3		6
21.11	odd	6		1323.2.h.c.226.1		6
21.17	even	6		1323.2.h.b.226.1		6
21.20	even	2		1323.2.f.d.442.3		6
36.7	odd	6		1008.2.r.h.673.3		6
36.11	even	6		3024.2.r.k.2017.1		6
36.23	even	6		9072.2.a.bs.1.3		3
36.31	odd	6		9072.2.a.ca.1.1		3
63.2	odd	6		1323.2.h.c.802.1		6
63.11	odd	6		1323.2.g.d.667.3		6
63.13	odd	6		3969.2.a.q.1.3		3
63.16	even	3		441.2.h.d.214.3		6
63.20	even	6		1323.2.f.d.883.3		6
63.25	even	3		441.2.g.c.79.1		6
63.34	odd	6		441.2.f.c.295.1		6
63.38	even	6		1323.2.g.e.667.3		6
63.41	even	6		3969.2.a.l.1.1		3
63.47	even	6		1323.2.h.b.802.1		6
63.52	odd	6		441.2.g.b.79.1		6
63.61	odd	6		441.2.h.e.214.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.a.22.1	✓	6	1.1	even	1	trivial
63.2.f.a.43.1	yes	6	9.7	even	3	inner
189.2.f.b.64.3		6	3.2	odd	2
189.2.f.b.127.3		6	9.2	odd	6
441.2.f.c.148.1		6	7.6	odd	2
441.2.f.c.295.1		6	63.34	odd	6
441.2.g.b.67.1		6	7.5	odd	6
441.2.g.b.79.1		6	63.52	odd	6
441.2.g.c.67.1		6	7.2	even	3
441.2.g.c.79.1		6	63.25	even	3
441.2.h.d.214.3		6	63.16	even	3
441.2.h.d.373.3		6	7.4	even	3
441.2.h.e.214.3		6	63.61	odd	6
441.2.h.e.373.3		6	7.3	odd	6
567.2.a.c.1.1		3	9.5	odd	6
567.2.a.h.1.3		3	9.4	even	3
1008.2.r.h.337.3		6	4.3	odd	2
1008.2.r.h.673.3		6	36.7	odd	6
1323.2.f.d.442.3		6	21.20	even	2
1323.2.f.d.883.3		6	63.20	even	6
1323.2.g.d.361.3		6	21.2	odd	6
1323.2.g.d.667.3		6	63.11	odd	6
1323.2.g.e.361.3		6	21.5	even	6
1323.2.g.e.667.3		6	63.38	even	6
1323.2.h.b.226.1		6	21.17	even	6
1323.2.h.b.802.1		6	63.47	even	6
1323.2.h.c.226.1		6	21.11	odd	6
1323.2.h.c.802.1		6	63.2	odd	6
3024.2.r.k.1009.1		6	12.11	even	2
3024.2.r.k.2017.1		6	36.11	even	6
3969.2.a.l.1.1		3	63.41	even	6
3969.2.a.q.1.3		3	63.13	odd	6
9072.2.a.bs.1.3		3	36.23	even	6
9072.2.a.ca.1.1		3	36.31	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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