LMFDB - Embedded newform 209.2.f.c.191.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [209,2,Mod(20,209)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(209, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([6, 0]))

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

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("209.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	209.f (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.66887340224$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			191.4
Character	$\chi$	$=$	209.191
Dual form			209.2.f.c.58.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.419632 - 0.304881i) q^{2} +(-1.04377 + 3.21239i) q^{3} +(-0.534895 - 1.64624i) q^{4} +(0.137996 - 0.100260i) q^{5} +(1.41740 - 1.02980i) q^{6} +(1.19515 + 3.67829i) q^{7} +(-0.598018 + 1.84051i) q^{8} +(-6.80296 - 4.94264i) q^{9} -0.0884751 q^{10} +(-3.27289 + 0.536842i) q^{11} +5.84667 q^{12} +(-1.50385 - 1.09261i) q^{13} +(0.619916 - 1.90791i) q^{14} +(0.178039 + 0.547947i) q^{15} +(-1.98866 + 1.44485i) q^{16} +(-1.40558 + 1.02121i) q^{17} +(1.34783 + 4.14819i) q^{18} +(0.309017 - 0.951057i) q^{19} +(-0.238865 - 0.173546i) q^{20} -13.0636 q^{21} +(1.53708 + 0.772565i) q^{22} -2.88746 q^{23} +(-5.28825 - 3.84214i) q^{24} +(-1.53609 + 4.72761i) q^{25} +(0.297948 + 0.916989i) q^{26} +(14.7806 - 10.7387i) q^{27} +(5.41606 - 3.93499i) q^{28} +(0.995192 + 3.06288i) q^{29} +(0.0923476 - 0.284217i) q^{30} +(6.55581 + 4.76307i) q^{31} +5.14547 q^{32} +(1.69160 - 11.0741i) q^{33} +0.901176 q^{34} +(0.533711 + 0.387764i) q^{35} +(-4.49789 + 13.8431i) q^{36} +(1.02844 + 3.16521i) q^{37} +(-0.419632 + 0.304881i) q^{38} +(5.07956 - 3.69052i) q^{39} +(0.102005 + 0.313941i) q^{40} +(1.84076 - 5.66528i) q^{41} +(5.48190 + 3.98283i) q^{42} +9.94286 q^{43} +(2.63442 + 5.10080i) q^{44} -1.43433 q^{45} +(1.21167 + 0.880331i) q^{46} +(-2.99615 + 9.22119i) q^{47} +(-2.56571 - 7.89645i) q^{48} +(-6.43830 + 4.67770i) q^{49} +(2.08595 - 1.51553i) q^{50} +(-1.81344 - 5.58119i) q^{51} +(-0.994294 + 3.06012i) q^{52} +(-0.0793422 - 0.0576455i) q^{53} -9.47643 q^{54} +(-0.397822 + 0.402222i) q^{55} -7.48464 q^{56} +(2.73263 + 1.98537i) q^{57} +(0.516200 - 1.58870i) q^{58} +(-0.256040 - 0.788012i) q^{59} +(0.806818 - 0.586188i) q^{60} +(2.98109 - 2.16589i) q^{61} +(-1.29886 - 3.99748i) q^{62} +(10.0499 - 30.9304i) q^{63} +(1.81812 + 1.32094i) q^{64} -0.317070 q^{65} +(-4.08614 + 4.13134i) q^{66} -1.78116 q^{67} +(2.43300 + 1.76768i) q^{68} +(3.01384 - 9.27566i) q^{69} +(-0.105741 - 0.325437i) q^{70} +(-2.85043 + 2.07096i) q^{71} +(13.1653 - 9.56513i) q^{72} +(-0.545031 - 1.67743i) q^{73} +(0.533445 - 1.64178i) q^{74} +(-13.5836 - 9.86908i) q^{75} -1.73096 q^{76} +(-5.88624 - 11.3970i) q^{77} -3.25672 q^{78} +(-2.30171 - 1.67229i) q^{79} +(-0.129567 + 0.398767i) q^{80} +(11.2739 + 34.6976i) q^{81} +(-2.49968 + 1.81612i) q^{82} +(-13.3475 + 9.69750i) q^{83} +(6.98763 + 21.5057i) q^{84} +(-0.0915778 + 0.281847i) q^{85} +(-4.17235 - 3.03139i) q^{86} -10.8779 q^{87} +(0.969183 - 6.34482i) q^{88} +2.70601 q^{89} +(0.601893 + 0.437301i) q^{90} +(2.22161 - 6.83742i) q^{91} +(1.54449 + 4.75344i) q^{92} +(-22.1436 + 16.0883i) q^{93} +(4.06864 - 2.95604i) q^{94} +(-0.0527099 - 0.162224i) q^{95} +(-5.37068 + 16.5293i) q^{96} +(11.3066 + 8.21474i) q^{97} +4.12786 q^{98} +(24.9188 + 12.5246i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 3 q^{2} + 3 q^{3} - 13 q^{4} - 9 q^{5} + 10 q^{6} + 4 q^{7} - q^{8} - 21 q^{9} - 22 q^{10} + 8 q^{11} + 20 q^{12} + 13 q^{13} - 20 q^{14} - 9 q^{15} - 41 q^{16} + 21 q^{17} + 27 q^{18} - 10 q^{19}+ \cdots + 110 q^{99}+O(q^{100}) $ 40 * q + 3 * q^2 + 3 * q^3 - 13 * q^4 - 9 * q^5 + 10 * q^6 + 4 * q^7 - q^8 - 21 * q^9 - 22 * q^10 + 8 * q^11 + 20 * q^12 + 13 * q^13 - 20 * q^14 - 9 * q^15 - 41 * q^16 + 21 * q^17 + 27 * q^18 - 10 * q^19 - 26 * q^20 - 22 * q^21 + q^22 + 16 * q^23 + 12 * q^24 - 53 * q^25 - 14 * q^26 - 24 * q^27 + 29 * q^28 + 11 * q^29 + 10 * q^30 - 13 * q^31 - 4 * q^32 + 34 * q^33 - 38 * q^34 + 25 * q^35 - 61 * q^36 - 7 * q^37 + 3 * q^38 - 16 * q^39 + 77 * q^40 + 17 * q^41 - 12 * q^42 - 24 * q^43 + 29 * q^44 + 130 * q^45 + 32 * q^46 - 5 * q^47 - 6 * q^48 - 42 * q^49 - 5 * q^50 + 40 * q^51 - 19 * q^52 - 30 * q^53 + 52 * q^54 + 72 * q^55 + 74 * q^56 - 7 * q^57 - 67 * q^58 - 23 * q^59 - 94 * q^60 + 36 * q^61 + 35 * q^62 - 7 * q^63 - 111 * q^64 - 26 * q^65 - 9 * q^66 + 52 * q^67 + 70 * q^68 - 95 * q^69 - 38 * q^70 - 34 * q^71 + 112 * q^72 + 31 * q^73 + 80 * q^74 - 84 * q^75 + 42 * q^76 - 25 * q^77 - 90 * q^78 + 32 * q^79 - 58 * q^80 - 28 * q^81 - 50 * q^82 - 83 * q^83 + 135 * q^84 - 23 * q^85 - 45 * q^86 - 42 * q^87 + 101 * q^88 + 96 * q^89 - 4 * q^90 + 33 * q^91 - 48 * q^92 - 91 * q^93 + 67 * q^94 - 9 * q^95 - 18 * q^96 - 10 * q^97 - 90 * q^98 + 110 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/209\mathbb{Z}\right)^\times$.

$n$	$78$	$134$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−0.419632	−	0.304881i	−0.296725	−	0.215583i	0.429454	−	0.903089i	$-0.358706\pi$
$2$	−0.419632	−	0.304881i	−0.296725	−	0.215583i	−0.726179	+	0.687505i	$0.758706\pi$
$3$	−1.04377	+	3.21239i	−0.602621	+	1.85468i	−0.0902356	+	0.995920i	$0.528762\pi$
$3$	−1.04377	+	3.21239i	−0.602621	+	1.85468i	−0.512385	+	0.858756i	$0.671238\pi$
$4$	−0.534895	−	1.64624i	−0.267447	−	0.823119i
$5$	0.137996	−	0.100260i	0.0617138	−	0.0448377i	−0.556501	−	0.830847i	$-0.687856\pi$
$5$	0.137996	−	0.100260i	0.0617138	−	0.0448377i	0.618214	+	0.786009i	$0.287856\pi$
$6$	1.41740	−	1.02980i	0.578650	−	0.420414i
$7$	1.19515	+	3.67829i	0.451724	+	1.39026i	0.874939	+	0.484233i	$0.160901\pi$
$7$	1.19515	+	3.67829i	0.451724	+	1.39026i	−0.423216	+	0.906029i	$0.639099\pi$
$8$	−0.598018	+	1.84051i	−0.211431	+	0.650718i
$9$	−6.80296	−	4.94264i	−2.26765	−	1.64755i
$10$	−0.0884751			−0.0279783
$11$	−3.27289	+	0.536842i	−0.986813	+	0.161864i
$11$	−3.27289	+	0.536842i	−0.986813	+	0.161864i
$12$	5.84667			1.68779
$13$	−1.50385	−	1.09261i	−0.417092	−	0.303035i	0.359374	−	0.933193i	$-0.382990\pi$
$13$	−1.50385	−	1.09261i	−0.417092	−	0.303035i	−0.776467	+	0.630158i	$0.782990\pi$
$14$	0.619916	−	1.90791i	0.165680	−	0.509910i
$15$	0.178039	+	0.547947i	0.0459694	+	0.141479i
$16$	−1.98866	+	1.44485i	−0.497166	+	0.361212i
$17$	−1.40558	+	1.02121i	−0.340904	+	0.247681i	−0.745043	−	0.667016i	$-0.767571\pi$
$17$	−1.40558	+	1.02121i	−0.340904	+	0.247681i	0.404139	+	0.914697i	$0.367571\pi$
$18$	1.34783	+	4.14819i	0.317686	+	0.977737i
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$20$	−0.238865	−	0.173546i	−0.0534119	−	0.0388060i
$21$	−13.0636			−2.85070
$22$	1.53708	+	0.772565i	0.327707	+	0.164711i
$23$	−2.88746			−0.602077			−0.301039	−	0.953612i	$-0.597333\pi$
$23$	−2.88746			−0.602077			−0.301039	+	0.953612i	$0.597333\pi$
$24$	−5.28825	−	3.84214i	−1.07946	−	0.784273i
$25$	−1.53609	+	4.72761i	−0.307219	+	0.945522i
$26$	0.297948	+	0.916989i	0.0584324	+	0.179836i
$27$	14.7806	−	10.7387i	2.84452	−	2.06667i
$28$	5.41606	−	3.93499i	1.02354	−	0.743644i
$29$	0.995192	+	3.06288i	0.184802	+	0.568763i	0.999945	−	0.0104971i	$-0.00334139\pi$
$29$	0.995192	+	3.06288i	0.184802	+	0.568763i	−0.815142	+	0.579261i	$0.803341\pi$
$30$	0.0923476	−	0.284217i	0.0168603	−	0.0518906i
$31$	6.55581	+	4.76307i	1.17746	+	0.855474i	0.991883	−	0.127156i	$-0.0405850\pi$
$31$	6.55581	+	4.76307i	1.17746	+	0.855474i	0.185576	+	0.982630i	$0.440585\pi$
$32$	5.14547			0.909598
$33$	1.69160	−	11.0741i	0.294469	−	1.92776i
$34$	0.901176			0.154550
$35$	0.533711	+	0.387764i	0.0902137	+	0.0655441i
$36$	−4.49789	+	13.8431i	−0.749649	+	2.30718i
$37$	1.02844	+	3.16521i	0.169074	+	0.520357i	0.999313	−	0.0370503i	$-0.0117962\pi$
$37$	1.02844	+	3.16521i	0.169074	+	0.520357i	−0.830239	+	0.557407i	$0.811796\pi$
$38$	−0.419632	+	0.304881i	−0.0680734	+	0.0494582i
$39$	5.07956	−	3.69052i	0.813381	−	0.590956i
$40$	0.102005	+	0.313941i	0.0161285	+	0.0496384i
$41$	1.84076	−	5.66528i	0.287479	−	0.884768i	−0.698166	−	0.715936i	$-0.746000\pi$
$41$	1.84076	−	5.66528i	0.287479	−	0.884768i	0.985645	−	0.168832i	$-0.0539996\pi$
$42$	5.48190	+	3.98283i	0.845875	+	0.614564i
$43$	9.94286			1.51627			0.758136	−	0.652096i	$-0.226110\pi$
$43$	9.94286			1.51627			0.758136	+	0.652096i	$0.226110\pi$
$44$	2.63442	+	5.10080i	0.397154	+	0.768974i
$45$	−1.43433			−0.213818
$46$	1.21167	+	0.880331i	0.178651	+	0.129798i
$47$	−2.99615	+	9.22119i	−0.437033	+	1.34505i	0.453956	+	0.891024i	$0.350012\pi$
$47$	−2.99615	+	9.22119i	−0.437033	+	1.34505i	−0.890989	+	0.454025i	$0.849988\pi$
$48$	−2.56571	−	7.89645i	−0.370329	−	1.13976i
$49$	−6.43830	+	4.67770i	−0.919757	+	0.668243i
$50$	2.08595	−	1.51553i	0.294998	−	0.214329i
$51$	−1.81344	−	5.58119i	−0.253932	−	0.781523i
$52$	−0.994294	+	3.06012i	−0.137884	+	0.424363i
$53$	−0.0793422	−	0.0576455i	−0.0108985	−	0.00791822i	0.582323	−	0.812958i	$-0.302144\pi$
$53$	−0.0793422	−	0.0576455i	−0.0108985	−	0.00791822i	−0.593221	+	0.805040i	$0.702144\pi$
$54$	−9.47643			−1.28958
$55$	−0.397822	+	0.402222i	−0.0536424	+	0.0542356i
$56$	−7.48464			−1.00018
$57$	2.73263	+	1.98537i	0.361945	+	0.262968i
$58$	0.516200	−	1.58870i	0.0677804	−	0.208607i
$59$	−0.256040	−	0.788012i	−0.0333336	−	0.102590i	0.933005	−	0.359862i	$-0.117176\pi$
$59$	−0.256040	−	0.788012i	−0.0333336	−	0.102590i	−0.966339	+	0.257272i	$0.917176\pi$
$60$	0.806818	−	0.586188i	0.104160	−	0.0756765i
$61$	2.98109	−	2.16589i	0.381689	−	0.277314i	−0.380352	−	0.924842i	$-0.624197\pi$
$61$	2.98109	−	2.16589i	0.381689	−	0.277314i	0.762042	+	0.647528i	$0.224197\pi$
$62$	−1.29886	−	3.99748i	−0.164955	−	0.507681i
$63$	10.0499	−	30.9304i	1.26617	−	3.89687i
$64$	1.81812	+	1.32094i	0.227265	+	0.165118i
$65$	−0.317070			−0.0393277
$66$	−4.08614	+	4.13134i	−0.502970	+	0.508532i
$67$	−1.78116			−0.217604			−0.108802	−	0.994063i	$-0.534701\pi$
$67$	−1.78116			−0.217604			−0.108802	+	0.994063i	$0.534701\pi$
$68$	2.43300	+	1.76768i	0.295045	+	0.214362i
$69$	3.01384	−	9.27566i	0.362824	−	1.11666i
$70$	−0.105741	−	0.325437i	−0.0126384	−	0.0388971i
$71$	−2.85043	+	2.07096i	−0.338284	+	0.245778i	−0.743937	−	0.668249i	$-0.767044\pi$
$71$	−2.85043	+	2.07096i	−0.338284	+	0.245778i	0.405653	+	0.914027i	$0.367044\pi$
$72$	13.1653	−	9.56513i	1.55154	−	1.12726i
$73$	−0.545031	−	1.67743i	−0.0637911	−	0.196329i	0.914081	−	0.405531i	$-0.132913\pi$
$73$	−0.545031	−	1.67743i	−0.0637911	−	0.196329i	−0.977872	+	0.209202i	$0.932913\pi$
$74$	0.533445	−	1.64178i	0.0620117	−	0.190853i
$75$	−13.5836	−	9.86908i	−1.56850	−	1.13958i
$76$	−1.73096			−0.198554
$77$	−5.88624	−	11.3970i	−0.670800	−	1.29881i
$78$	−3.25672			−0.368751
$79$	−2.30171	−	1.67229i	−0.258962	−	0.188147i	0.450727	−	0.892662i	$-0.351165\pi$
$79$	−2.30171	−	1.67229i	−0.258962	−	0.188147i	−0.709689	+	0.704515i	$0.751165\pi$
$80$	−0.129567	+	0.398767i	−0.0144861	+	0.0445835i
$81$	11.2739	+	34.6976i	1.25266	+	3.85529i
$82$	−2.49968	+	1.81612i	−0.276043	+	0.200557i
$83$	−13.3475	+	9.69750i	−1.46507	+	1.06444i	−0.483070	+	0.875582i	$0.660478\pi$
$83$	−13.3475	+	9.69750i	−1.46507	+	1.06444i	−0.982005	+	0.188857i	$0.939522\pi$
$84$	6.98763	+	21.5057i	0.762413	+	2.34647i
$85$	−0.0915778	+	0.281847i	−0.00993300	+	0.0305706i
$86$	−4.17235	−	3.03139i	−0.449916	−	0.326883i
$87$	−10.8779			−1.16624
$88$	0.969183	−	6.34482i	0.103315	−	0.676360i
$89$	2.70601			0.286836			0.143418	−	0.989662i	$-0.454191\pi$
$89$	2.70601			0.286836			0.143418	+	0.989662i	$0.454191\pi$
$90$	0.601893	+	0.437301i	0.0634451	+	0.0460955i
$91$	2.22161	−	6.83742i	0.232888	−	0.716756i
$92$	1.54449	+	4.75344i	0.161024	+	0.495581i
$93$	−22.1436	+	16.0883i	−2.29619	+	1.66828i
$94$	4.06864	−	2.95604i	0.419649	−	0.304893i
$95$	−0.0527099	−	0.162224i	−0.00540792	−	0.0166439i
$96$	−5.37068	+	16.5293i	−0.548143	+	1.68701i
$97$	11.3066	+	8.21474i	1.14801	+	0.834081i	0.988216	−	0.153069i	$-0.0489156\pi$
$97$	11.3066	+	8.21474i	1.14801	+	0.834081i	0.159798	+	0.987150i	$0.448916\pi$
$98$	4.12786			0.416977
$99$	24.9188	+	12.5246i	2.50443	+	1.25877i
$100$	8.60442			0.860442
$101$	−12.1370	−	8.81803i	−1.20767	−	0.877427i	−0.212657	−	0.977127i	$-0.568212\pi$
$101$	−12.1370	−	8.81803i	−1.20767	−	0.877427i	−0.995018	+	0.0997001i	$0.968212\pi$
$102$	−0.940621	+	2.89493i	−0.0931353	+	0.286641i
$103$	1.06119	+	3.26602i	0.104562	+	0.321810i	0.989628	−	0.143657i	$-0.0458863\pi$
$103$	1.06119	+	3.26602i	0.104562	+	0.321810i	−0.885065	+	0.465467i	$0.845886\pi$
$104$	2.91029	−	2.11445i	0.285377	−	0.207339i
$105$	−1.80272	+	1.30975i	−0.175928	+	0.127819i
$106$	0.0157196	+	0.0483798i	0.00152682	+	0.00469906i
$107$	2.07487	−	6.38581i	0.200586	−	0.617339i	−0.799280	−	0.600959i	$-0.794786\pi$
$107$	2.07487	−	6.38581i	0.200586	−	0.617339i	0.999866	−	0.0163806i	$-0.00521434\pi$
$108$	−25.5845	−	18.5882i	−2.46187	−	1.78865i
$109$	6.36541			0.609696			0.304848	−	0.952401i	$-0.401394\pi$
$109$	6.36541			0.609696			0.304848	+	0.952401i	$0.401394\pi$
$110$	0.289569	−	0.0474971i	0.0276093	−	0.00452867i
$111$	−11.2413			−1.06698
$112$	−7.69131	−	5.58807i	−0.726761	−	0.528023i
$113$	−1.43197	+	4.40716i	−0.134709	+	0.414591i	−0.995545	−	0.0942917i	$-0.969941\pi$
$113$	−1.43197	+	4.40716i	−0.134709	+	0.414591i	0.860836	+	0.508883i	$0.169941\pi$
$114$	−0.541397	−	1.66625i	−0.0507065	−	0.156059i
$115$	−0.398458	+	0.289497i	−0.0371564	+	0.0269957i
$116$	4.50991	−	3.27664i	0.418735	−	0.304229i
$117$	4.83025	+	14.8660i	0.446556	+	1.37436i
$118$	−0.132807	+	0.408737i	−0.0122259	+	0.0376273i
$119$	−5.43620	−	3.94963i	−0.498335	−	0.362062i
$120$	−1.11497			−0.101782
$121$	10.4236	−	3.51405i	0.947600	−	0.319459i
$122$	−1.91130			−0.173041
$123$	16.2778	+	11.8265i	1.46772	+	1.06636i
$124$	4.33448	−	13.3402i	0.389248	−	1.19798i
$125$	0.525565	+	1.61752i	0.0470080	+	0.144676i
$126$	−13.6474	+	9.91540i	−1.21580	+	0.883334i
$127$	9.31550	−	6.76811i	0.826617	−	0.600572i	−0.0919832	−	0.995761i	$-0.529321\pi$
$127$	9.31550	−	6.76811i	0.826617	−	0.600572i	0.918600	+	0.395188i	$0.129321\pi$
$128$	−3.54028	−	10.8959i	−0.312920	−	0.963069i
$129$	−10.3781	+	31.9404i	−0.913737	+	2.81219i
$130$	0.133053	+	0.0966687i	0.0116695	+	0.00847841i
$131$	12.9911			1.13504			0.567521	−	0.823359i	$-0.307903\pi$
$131$	12.9911			1.13504			0.567521	+	0.823359i	$0.307903\pi$
$132$	−19.1355	+	3.13874i	−1.66553	+	0.273192i
$133$	3.86758			0.335362
$134$	0.747435	+	0.543043i	0.0645685	+	0.0469118i
$135$	0.962998	−	2.96380i	0.0828817	−	0.255083i
$136$	−1.03899	−	3.19769i	−0.0890928	−	0.274200i
$137$	−7.34208	+	5.33433i	−0.627276	+	0.455743i	−0.855455	−	0.517876i	$-0.826723\pi$
$137$	−7.34208	+	5.33433i	−0.627276	+	0.455743i	0.228179	+	0.973619i	$0.426723\pi$
$138$	−4.09268	+	2.97350i	−0.348392	+	0.253121i
$139$	−2.27445	−	7.00003i	−0.192916	−	0.593734i	−0.999995	−	0.00329042i	$-0.998953\pi$
$139$	−2.27445	−	7.00003i	−0.192916	−	0.593734i	0.807079	−	0.590444i	$-0.201047\pi$
$140$	0.352872	−	1.08603i	0.0298231	−	0.0917862i
$141$	−26.4948	−	19.2496i	−2.23126	−	1.62111i
$142$	1.82753			0.153363
$143$	5.50849	+	2.76866i	0.460643	+	0.231527i
$144$	20.6702			1.72251
$145$	0.444418	+	0.322888i	0.0369069	+	0.0268144i
$146$	−0.282705	+	0.870076i	−0.0233968	+	0.0720080i
$147$	−8.30651	−	25.5648i	−0.685109	−	2.10855i
$148$	4.66058	−	3.38611i	0.383097	−	0.278336i
$149$	−4.41239	+	3.20579i	−0.361477	+	0.262629i	−0.753668	−	0.657255i	$-0.771717\pi$
$149$	−4.41239	+	3.20579i	−0.361477	+	0.262629i	0.392191	+	0.919884i	$0.371717\pi$
$150$	2.69124	+	8.28277i	0.219738	+	0.676285i
$151$	−4.71996	+	14.5265i	−0.384105	+	1.18215i	0.553023	+	0.833166i	$0.313474\pi$
$151$	−4.71996	+	14.5265i	−0.384105	+	1.18215i	−0.937128	+	0.348987i	$0.886526\pi$
$152$	1.56563	+	1.13750i	0.126989	+	0.0922632i
$153$	14.6096			1.18112
$154$	−1.00467	+	6.57716i	−0.0809589	+	0.530003i
$155$	1.38222			0.111023
$156$	−8.79250	−	6.38813i	−0.703964	−	0.511459i
$157$	1.94841	−	5.99658i	0.155500	−	0.478579i	−0.842711	−	0.538366i	$-0.819042\pi$
$157$	1.94841	−	5.99658i	0.155500	−	0.478579i	0.998211	+	0.0597865i	$0.0190420\pi$
$158$	0.456023	+	1.40349i	0.0362792	+	0.111656i
$159$	0.267995	−	0.194710i	0.0212534	−	0.0154415i
$160$	0.710055	−	0.515885i	0.0561347	−	0.0407843i
$161$	−3.45094	−	10.6209i	−0.271972	−	0.837045i
$162$	5.84773	−	17.9975i	0.459441	−	1.41401i
$163$	−8.52848	−	6.19630i	−0.668002	−	0.485332i	0.201354	−	0.979519i	$-0.435466\pi$
$163$	−8.52848	−	6.19630i	−0.668002	−	0.485332i	−0.869356	+	0.494187i	$0.835466\pi$
$164$	−10.3110			−0.805154
$165$	−0.876861	−	1.69779i	−0.0682635	−	0.132173i
$166$	8.55761			0.664200
$167$	4.51945	+	3.28357i	0.349726	+	0.254090i	0.748754	−	0.662848i	$-0.230653\pi$
$167$	4.51945	+	3.28357i	0.349726	+	0.254090i	−0.399028	+	0.916939i	$0.630653\pi$
$168$	7.81224	−	24.0436i	0.602728	−	1.85500i
$169$	−2.94946	−	9.07750i	−0.226881	−	0.698269i
$170$	0.124359	−	0.0903520i	0.00953789	−	0.00692968i
$171$	−6.80296	+	4.94264i	−0.520236	+	0.377973i
$172$	−5.31839	−	16.3683i	−0.405523	−	1.24807i
$173$	4.71124	−	14.4997i	0.358189	−	1.10239i	−0.595948	−	0.803023i	$-0.703224\pi$
$173$	4.71124	−	14.4997i	0.358189	−	1.10239i	0.954137	−	0.299369i	$-0.0967763\pi$
$174$	4.56474	+	3.31648i	0.346052	+	0.251421i
$175$	−19.2254			−1.45330
$176$	5.73302	−	5.79642i	0.432142	−	0.436922i
$177$	2.79865			0.210359
$178$	−1.13553	−	0.825009i	−0.0851114	−	0.0618371i
$179$	0.242992	−	0.747854i	0.0181621	−	0.0558972i	−0.941565	−	0.336832i	$-0.890645\pi$
$179$	0.242992	−	0.747854i	0.0181621	−	0.0558972i	0.959727	+	0.280935i	$0.0906445\pi$
$180$	0.767217	+	2.36125i	0.0571850	+	0.175997i
$181$	1.99833	−	1.45187i	0.148535	−	0.107917i	−0.511036	−	0.859559i	$-0.670738\pi$
$181$	1.99833	−	1.45187i	0.148535	−	0.107917i	0.659571	+	0.751643i	$0.270738\pi$
$182$	−3.01686	+	2.19188i	−0.223624	+	0.162473i
$183$	3.84611	+	11.8371i	0.284313	+	0.875025i
$184$	1.72675	−	5.31440i	0.127298	−	0.391782i
$185$	0.459265	+	0.333675i	0.0337658	+	0.0245323i
$186$	14.1972			1.04099
$187$	4.05208	−	4.09690i	0.296317	−	0.299595i
$188$	16.7829			1.22402
$189$	57.1650	+	41.5328i	4.15814	+	3.02107i
$190$	−0.0273403	+	0.0841448i	−0.00198347	+	0.00610450i
$191$	4.21998	+	12.9878i	0.305347	+	0.939761i	0.979548	+	0.201213i	$0.0644883\pi$
$191$	4.21998	+	12.9878i	0.305347	+	0.939761i	−0.674201	+	0.738548i	$0.735512\pi$
$192$	−6.14108	+	4.46176i	−0.443195	+	0.322000i
$193$	−20.4929	+	14.8890i	−1.47511	+	1.07173i	−0.496018	+	0.868312i	$0.665205\pi$
$193$	−20.4929	+	14.8890i	−1.47511	+	1.07173i	−0.979092	+	0.203418i	$0.934795\pi$
$194$	−2.24011	−	6.89435i	−0.160830	−	0.494985i
$195$	0.330949	−	1.01856i	0.0236997	−	0.0729402i
$196$	11.1444	+	8.09689i	0.796030	+	0.578350i
$197$	12.4717			0.888570			0.444285	−	0.895886i	$-0.353458\pi$
$197$	12.4717			0.888570			0.444285	+	0.895886i	$0.353458\pi$
$198$	−6.63821	−	12.8530i	−0.471757	−	0.913422i
$199$	−9.06674			−0.642724			−0.321362	−	0.946956i	$-0.604141\pi$
$199$	−9.06674			−0.642724			−0.321362	+	0.946956i	$0.604141\pi$
$200$	−7.78260	−	5.65439i	−0.550313	−	0.399826i
$201$	1.85913	−	5.72180i	0.131133	−	0.403585i
$202$	2.40462	+	7.40066i	0.169189	+	0.520709i
$203$	−10.0768	+	7.32120i	−0.707251	+	0.513848i
$204$	−8.21797	+	5.97070i	−0.575373	+	0.418033i
$205$	−0.313984	−	0.966342i	−0.0219296	−	0.0674922i
$206$	0.550435	−	1.69406i	0.0383506	−	0.118031i
$207$	19.6433	+	14.2717i	1.36530	+	0.991951i
$208$	4.56930			0.316824
$209$	−0.500812	+	3.27860i	−0.0346419	+	0.226785i
$210$	1.15580			0.0797578
$211$	5.74188	+	4.17172i	0.395287	+	0.287193i	0.767619	−	0.640907i	$-0.221442\pi$
$211$	5.74188	+	4.17172i	0.395287	+	0.287193i	−0.372332	+	0.928100i	$0.621442\pi$
$212$	−0.0524584	+	0.161450i	−0.00360286	+	0.0110885i
$213$	−3.67754	−	11.3183i	−0.251981	−	0.775518i
$214$	−2.81759	+	2.04710i	−0.192607	+	0.139937i
$215$	1.37208	−	0.996872i	0.0935749	−	0.0679861i
$216$	10.9257	+	33.6257i	0.743397	+	2.28794i
$217$	−9.68480	+	29.8067i	−0.657447	+	2.02341i
$218$	−2.67113	−	1.94069i	−0.180912	−	0.131440i
$219$	5.95747			0.402568
$220$	0.874946	+	0.439763i	0.0589889	+	0.0296488i
$221$	3.22957			0.217244
$222$	4.71723	+	3.42727i	0.316600	+	0.230023i
$223$	−3.74034	+	11.5116i	−0.250472	+	0.770873i	0.744216	+	0.667939i	$0.232823\pi$
$223$	−3.74034	+	11.5116i	−0.250472	+	0.770873i	−0.994688	+	0.102934i	$0.967177\pi$
$224$	6.14959	+	18.9265i	0.410887	+	1.26458i
$225$	33.8169	−	24.5694i	2.25446	−	1.63796i
$226$	1.94456	−	1.41281i	0.129350	−	0.0939786i
$227$	−3.06216	−	9.42437i	−0.203243	−	0.625518i	−0.999781	−	0.0209291i	$-0.993338\pi$
$227$	−3.06216	−	9.42437i	−0.203243	−	0.625518i	0.796538	−	0.604588i	$-0.206662\pi$
$228$	1.80672	−	5.56051i	0.119653	−	0.368254i
$229$	−17.9164	−	13.0170i	−1.18395	−	0.860187i	−0.191335	−	0.981525i	$-0.561282\pi$
$229$	−17.9164	−	13.0170i	−1.18395	−	0.860187i	−0.992611	+	0.121338i	$0.961282\pi$
$230$	0.255468			0.0168451
$231$	42.7556	−	7.01307i	2.81311	−	0.461426i
$232$	−6.23241			−0.409178
$233$	0.441443	+	0.320727i	0.0289199	+	0.0210115i	0.602151	−	0.798382i	$-0.294310\pi$
$233$	0.441443	+	0.320727i	0.0289199	+	0.0210115i	−0.573231	+	0.819394i	$0.694310\pi$
$234$	2.50542	−	7.71089i	0.163784	−	0.504077i
$235$	0.511061	+	1.57288i	0.0333379	+	0.102604i
$236$	−1.16030	+	0.843007i	−0.0755290	+	0.0548751i
$237$	7.77450	−	5.64851i	0.505008	−	0.366910i
$238$	1.07704	+	3.31479i	0.0698141	+	0.214866i
$239$	5.57643	−	17.1625i	0.360709	−	1.11015i	−0.591916	−	0.806000i	$-0.701628\pi$
$239$	5.57643	−	17.1625i	0.360709	−	1.11015i	0.952625	−	0.304148i	$-0.0983719\pi$
$240$	−1.14576	−	0.832442i	−0.0739584	−	0.0537339i
$241$	3.04329			0.196035			0.0980177	−	0.995185i	$-0.468750\pi$
$241$	3.04329			0.196035			0.0980177	+	0.995185i	$0.468750\pi$
$242$	−5.44545	−	1.70335i	−0.350047	−	0.109495i
$243$	−68.4205			−4.38918
$244$	−5.16014	−	3.74906i	−0.330344	−	0.240009i
$245$	−0.419474	+	1.29101i	−0.0267992	+	0.0824796i
$246$	−3.22501	−	9.92556i	−0.205619	−	0.632831i
$247$	−1.50385	+	1.09261i	−0.0956876	+	0.0695211i
$248$	−12.6870	+	9.21762i	−0.805624	+	0.585320i
$249$	−17.2205	−	52.9993i	−1.09131	−	3.35869i
$250$	0.272608	−	0.839000i	0.0172412	−	0.0530630i
$251$	2.08363	+	1.51384i	0.131517	+	0.0955529i	0.651599	−	0.758564i	$-0.274099\pi$
$251$	2.08363	+	1.51384i	0.131517	+	0.0955529i	−0.520082	+	0.854117i	$0.674099\pi$
$252$	−56.2945			−3.54622
$253$	9.45034	−	1.55011i	0.594137	−	0.0974545i
$254$	−5.97255			−0.374751
$255$	−0.809819	−	0.588368i	−0.0507128	−	0.0368450i
$256$	−0.447405	+	1.37697i	−0.0279628	+	0.0860607i
$257$	6.09111	+	18.7465i	0.379953	+	1.16937i	0.940076	+	0.340965i	$0.110754\pi$
$257$	6.09111	+	18.7465i	0.379953	+	1.16937i	−0.560123	+	0.828409i	$0.689246\pi$
$258$	14.0930	−	10.2392i	0.877391	−	0.637462i
$259$	−10.4134	+	7.56578i	−0.647058	+	0.470115i
$260$	0.169599	+	0.521973i	0.0105181	+	0.0323714i
$261$	8.36849	−	25.7556i	0.517997	−	1.59423i
$262$	−5.45150	−	3.96075i	−0.336795	−	0.244696i
$263$	19.2011			1.18399			0.591997	−	0.805940i	$-0.298340\pi$
$263$	19.2011			1.18399			0.591997	+	0.805940i	$0.298340\pi$
$264$	19.3705	+	9.73593i	1.19217	+	0.599205i
$265$	−0.0167285			−0.00102762
$266$	−1.62296	−	1.17915i	−0.0995102	−	0.0722984i
$267$	−2.82445	+	8.69275i	−0.172853	+	0.531988i
$268$	0.952736	+	2.93222i	0.0581976	+	0.179114i
$269$	−9.90171	+	7.19401i	−0.603718	+	0.438627i	−0.847197	−	0.531280i	$-0.821711\pi$
$269$	−9.90171	+	7.19401i	−0.603718	+	0.438627i	0.243479	+	0.969906i	$0.421711\pi$
$270$	−1.30771	+	0.950108i	−0.0795848	+	0.0578217i
$271$	6.85336	+	21.0925i	0.416312	+	1.28128i	0.911072	+	0.412246i	$0.135256\pi$
$271$	6.85336	+	21.0925i	0.416312	+	1.28128i	−0.494761	+	0.869029i	$0.664744\pi$
$272$	1.31973	−	4.06170i	0.0800202	−	0.246277i
$273$	19.6456	+	14.2734i	1.18901	+	0.863864i
$274$	4.70731			0.284379
$275$	2.48949	−	16.2976i	0.150122	−	0.982781i
$276$	−16.8820			−1.01618
$277$	−14.3527	−	10.4278i	−0.862370	−	0.626549i	0.0661585	−	0.997809i	$-0.478926\pi$
$277$	−14.3527	−	10.4278i	−0.862370	−	0.626549i	−0.928529	+	0.371260i	$0.878926\pi$
$278$	−1.17974	+	3.63087i	−0.0707562	+	0.217765i
$279$	−21.0568	−	64.8061i	−1.26064	−	3.87984i
$280$	−1.03285	+	0.750411i	−0.0617247	+	0.0448456i
$281$	17.5929	−	12.7820i	1.04950	−	0.762508i	0.0773850	−	0.997001i	$-0.475343\pi$
$281$	17.5929	−	12.7820i	1.04950	−	0.762508i	0.972118	+	0.234493i	$0.0753429\pi$
$282$	5.24924	+	16.1555i	0.312588	+	0.962047i
$283$	1.11140	−	3.42054i	0.0660660	−	0.203330i	−0.912574	−	0.408911i	$-0.865908\pi$
$283$	1.11140	−	3.42054i	0.0660660	−	0.203330i	0.978640	+	0.205581i	$0.0659085\pi$
$284$	4.93397	+	3.58474i	0.292777	+	0.212715i
$285$	0.576145			0.0341279
$286$	−1.46743	−	2.84125i	−0.0867708	−	0.168007i
$287$	23.0385			1.35992
$288$	−35.0044	−	25.4322i	−2.06266	−	1.49861i
$289$	−4.32051	+	13.2972i	−0.254148	+	0.782186i
$290$	−0.0880496	−	0.270989i	−0.00517045	−	0.0159130i
$291$	−38.1905	+	27.7470i	−2.23877	+	1.62656i
$292$	−2.46992	+	1.79450i	−0.144541	+	0.105015i
$293$	−6.87552	−	21.1607i	−0.401672	−	1.23622i	−0.923642	−	0.383256i	$-0.874803\pi$
$293$	−6.87552	−	21.1607i	−0.401672	−	1.23622i	0.521970	−	0.852964i	$-0.325197\pi$
$294$	−4.30854	+	13.2603i	−0.251279	+	0.773357i
$295$	−0.114339	−	0.0830720i	−0.00665706	−	0.00483664i
$296$	−6.44062			−0.374353
$297$	−42.6102	+	43.0814i	−2.47249	+	2.49984i
$298$	2.82897			0.163878
$299$	4.34230	+	3.15487i	0.251122	+	0.182451i
$300$	−8.98103	+	27.6408i	−0.518520	+	1.59584i
$301$	11.8832	+	36.5727i	0.684936	+	2.10802i
$302$	6.40951	−	4.65678i	0.368826	−	0.267968i
$303$	40.9952	−	29.7848i	2.35511	−	1.71109i
$304$	0.759601	+	2.33781i	0.0435661	+	0.134083i
$305$	0.194227	−	0.597769i	0.0111214	−	0.0342281i
$306$	−6.13067	−	4.45419i	−0.350467	−	0.254629i
$307$	−14.6203			−0.834425			−0.417212	−	0.908809i	$-0.636993\pi$
$307$	−14.6203			−0.834425			−0.417212	+	0.908809i	$0.636993\pi$
$308$	−15.6137	+	15.7864i	−0.889672	+	0.899512i
$309$	−11.5994			−0.659865
$310$	−0.580026	−	0.421413i	−0.0329432	−	0.0239347i
$311$	3.71161	−	11.4231i	0.210466	−	0.647747i	−0.788979	−	0.614421i	$-0.789390\pi$
$311$	3.71161	−	11.4231i	0.210466	−	0.647747i	0.999445	−	0.0333267i	$-0.0106102\pi$
$312$	3.75476	+	11.5560i	0.212572	+	0.654228i
$313$	−9.45053	+	6.86621i	−0.534176	+	0.388101i	−0.821917	−	0.569607i	$-0.807096\pi$
$313$	−9.45053	+	6.86621i	−0.534176	+	0.388101i	0.287742	+	0.957708i	$0.407096\pi$
$314$	−2.64586	+	1.92233i	−0.149314	+	0.108483i
$315$	−1.71424	−	5.27589i	−0.0965865	−	0.297263i
$316$	−1.52181	+	4.68366i	−0.0856086	+	0.263476i
$317$	21.6892	+	15.7581i	1.21819	+	0.885063i	0.995948	−	0.0899295i	$-0.0286642\pi$
$317$	21.6892	+	15.7581i	1.21819	+	0.885063i	0.222237	+	0.974993i	$0.428664\pi$
$318$	−0.171823			−0.00963534
$319$	−4.90144	−	9.49022i	−0.274428	−	0.531350i
$320$	0.383331			0.0214289
$321$	18.3480	+	13.3306i	1.02409	+	0.744043i
$322$	−1.78998	+	5.50900i	−0.0997519	+	0.307005i
$323$	0.536884	+	1.65236i	0.0298730	+	0.0919398i
$324$	51.0902	−	37.1192i	2.83834	−	2.06218i
$325$	7.47549	−	5.43126i	0.414665	−	0.301272i
$326$	1.68969	+	5.20034i	0.0935834	+	0.288020i
$327$	−6.64402	+	20.4482i	−0.367415	+	1.13079i
$328$	9.32619	+	6.77587i	0.514953	+	0.374135i
$329$	−37.4990			−2.06739
$330$	−0.149664	+	0.979786i	−0.00823874	+	0.0539354i
$331$	20.2401			1.11250			0.556248	−	0.831016i	$-0.312240\pi$
$331$	20.2401			1.11250			0.556248	+	0.831016i	$0.312240\pi$
$332$	23.1039	+	16.7860i	1.26799	+	0.921249i
$333$	8.64806	−	26.6160i	0.473911	−	1.45855i
$334$	−0.895410	−	2.75579i	−0.0489946	−	0.150790i
$335$	−0.245794	+	0.178580i	−0.0134292	+	0.00975686i
$336$	25.9790	−	18.8749i	1.41727	−	1.02971i
$337$	2.22585	+	6.85047i	0.121250	+	0.373169i	0.993199	−	0.116427i	$-0.0371442\pi$
$337$	2.22585	+	6.85047i	0.121250	+	0.373169i	−0.871949	+	0.489596i	$0.837144\pi$
$338$	−1.52987	+	4.70845i	−0.0832138	+	0.256106i
$339$	−12.6629	−	9.20013i	−0.687754	−	0.499682i
$340$	0.512972			0.0278198
$341$	−24.0135	−	12.0696i	−1.30040	−	0.653605i
$342$	4.36166			0.235852
$343$	−2.99808	−	2.17823i	−0.161881	−	0.117613i
$344$	−5.94601	+	18.2999i	−0.320587	+	0.986666i
$345$	−0.514079	−	1.58217i	−0.0276771	−	0.0851814i
$346$	−6.39767	+	4.64818i	−0.343941	+	0.249888i
$347$	−3.93134	+	2.85629i	−0.211045	+	0.153333i	−0.688287	−	0.725439i	$-0.741637\pi$
$347$	−3.93134	+	2.85629i	−0.211045	+	0.153333i	0.477241	+	0.878772i	$0.341637\pi$
$348$	5.81856	+	17.9077i	0.311907	+	0.959952i
$349$	4.12619	−	12.6991i	0.220870	−	0.679768i	−0.777815	−	0.628494i	$-0.783672\pi$
$349$	4.12619	−	12.6991i	0.220870	−	0.679768i	0.998685	−	0.0512743i	$-0.0163283\pi$
$350$	8.06759	+	5.86145i	0.431231	+	0.313308i
$351$	−33.9609			−1.81270
$352$	−16.8405	+	2.76230i	−0.897604	+	0.147231i
$353$	24.8315			1.32165			0.660825	−	0.750540i	$-0.270207\pi$
$353$	24.8315			1.32165			0.660825	+	0.750540i	$0.270207\pi$
$354$	−1.17440	−	0.853255i	−0.0624189	−	0.0453500i
$355$	−0.185714	+	0.571569i	−0.00985668	+	0.0303357i
$356$	−1.44743	−	4.45473i	−0.0767136	−	0.236100i
$357$	18.3619	−	13.3407i	0.971815	−	0.706065i
$358$	−0.329974	+	0.239740i	−0.0174397	+	0.0126707i
$359$	8.05895	+	24.8029i	0.425335	+	1.30905i	0.902673	+	0.430327i	$0.141602\pi$
$359$	8.05895	+	24.8029i	0.425335	+	1.30905i	−0.477338	+	0.878720i	$0.658398\pi$
$360$	0.857756	−	2.63990i	0.0452077	−	0.139135i
$361$	−0.809017	−	0.587785i	−0.0425798	−	0.0309361i
$362$	−1.28121			−0.0673390
$363$	0.408656	+	37.1526i	0.0214489	+	1.95000i
$364$	−12.4443			−0.652260
$365$	−0.243392	−	0.176835i	−0.0127397	−	0.00925595i
$366$	1.99496	−	6.13985i	0.104278	−	0.320935i
$367$	−6.63876	−	20.4320i	−0.346541	−	1.06654i	−0.960754	−	0.277402i	$-0.910527\pi$
$367$	−6.63876	−	20.4320i	−0.346541	−	1.06654i	0.614213	−	0.789140i	$-0.289473\pi$
$368$	5.74218	−	4.17194i	0.299332	−	0.217477i
$369$	−40.5241	+	29.4425i	−2.10960	+	1.53271i
$370$	−0.0909912	−	0.280042i	−0.00473041	−	0.0145587i
$371$	0.117211	−	0.360738i	0.00608529	−	0.0187286i
$372$	38.3297	+	27.8481i	1.98730	+	1.44386i
$373$	6.34856			0.328716			0.164358	−	0.986401i	$-0.447445\pi$
$373$	6.34856			0.328716			0.164358	+	0.986401i	$0.447445\pi$
$374$	−2.94945	+	0.483789i	−0.152512	+	0.0250161i
$375$	−5.74469			−0.296654
$376$	−15.1799	−	11.0289i	−0.782845	−	0.568770i
$377$	1.84992	−	5.69347i	0.0952757	−	0.293229i
$378$	−11.3257	−	34.8570i	−0.582533	−	1.79285i
$379$	−19.9449	+	14.4908i	−1.02450	+	0.744342i	−0.967200	−	0.254015i	$-0.918249\pi$
$379$	−19.9449	+	14.4908i	−1.02450	+	0.744342i	−0.0572986	+	0.998357i	$0.518249\pi$
$380$	−0.238865	+	0.173546i	−0.0122535	+	0.00890271i
$381$	12.0186	+	36.9894i	0.615731	+	1.89502i
$382$	2.18888	−	6.73668i	0.111993	−	0.344678i
$383$	15.6089	+	11.3405i	0.797576	+	0.579473i	0.910202	−	0.414165i	$-0.135926\pi$
$383$	15.6089	+	11.3405i	0.797576	+	0.579473i	−0.112626	+	0.993637i	$0.535926\pi$
$384$	38.6971			1.97475
$385$	−1.95495	−	0.982590i	−0.0996333	−	0.0500774i
$386$	13.1388			0.668749
$387$	−67.6409	−	49.1440i	−3.43838	−	2.49813i
$388$	7.47556	−	23.0074i	0.379514	−	1.16802i
$389$	7.38074	+	22.7156i	0.374218	+	1.15173i	0.944005	+	0.329932i	$0.107026\pi$
$389$	7.38074	+	22.7156i	0.374218	+	1.15173i	−0.569786	+	0.821793i	$0.692974\pi$
$390$	−0.449415	+	0.326519i	−0.0227570	+	0.0165339i
$391$	4.05856	−	2.94872i	0.205250	−	0.149123i
$392$	−4.75913	−	14.6471i	−0.240372	−	0.739790i
$393$	−13.5598	+	41.7326i	−0.683999	+	2.10513i
$394$	−5.23352	−	3.80237i	−0.263661	−	0.191561i
$395$	−0.485291			−0.0244176
$396$	7.28955	−	47.7215i	0.366314	−	2.39810i
$397$	8.87044			0.445195			0.222597	−	0.974910i	$-0.428546\pi$
$397$	8.87044			0.445195			0.222597	+	0.974910i	$0.428546\pi$
$398$	3.80470	+	2.76428i	0.190712	+	0.138561i
$399$	−4.03686	+	12.4242i	−0.202096	+	0.621987i
$400$	−3.77591	−	11.6210i	−0.188795	−	0.581052i
$401$	5.72558	−	4.15988i	0.285922	−	0.207734i	−0.435574	−	0.900153i	$-0.643455\pi$
$401$	5.72558	−	4.15988i	0.285922	−	0.207734i	0.721496	+	0.692418i	$0.243455\pi$
$402$	−2.52462	+	1.83424i	−0.125916	+	0.0914837i
$403$	−4.65476	−	14.3259i	−0.231870	−	0.713623i
$404$	−8.02456	+	24.6971i	−0.399237	+	1.22872i
$405$	5.03455	+	3.65782i	0.250169	+	0.181758i
$406$	6.46063			0.320636
$407$	−5.06518	−	9.80727i	−0.251072	−	0.486128i
$408$	11.3567			0.562241
$409$	−21.3138	−	15.4854i	−1.05390	−	0.765703i	−0.0809491	−	0.996718i	$-0.525795\pi$
$409$	−21.3138	−	15.4854i	−1.05390	−	0.765703i	−0.972950	+	0.231016i	$0.925795\pi$
$410$	−0.162861	+	0.501236i	−0.00804315	+	0.0247543i
$411$	−9.47253	−	29.1535i	−0.467246	−	1.43803i
$412$	4.80901	−	3.49395i	0.236923	−	0.172135i
$413$	2.59253	−	1.88358i	0.127570	−	0.0926850i
$414$	−3.89180	−	11.9777i	−0.191271	−	0.588673i
$415$	−0.869627	+	2.67644i	−0.0426883	+	0.131381i
$416$	−7.73800	−	5.62198i	−0.379387	−	0.275640i
$417$	24.8608			1.21744
$418$	1.20974	−	1.22312i	0.0591702	−	0.0598246i
$419$	−37.8555			−1.84936			−0.924681	−	0.380743i	$-0.875668\pi$
$419$	−37.8555			−1.84936			−0.924681	+	0.380743i	$0.875668\pi$
$420$	3.12043	+	2.26713i	0.152262	+	0.110624i
$421$	7.17557	−	22.0841i	0.349716	−	1.07631i	−0.609295	−	0.792944i	$-0.708547\pi$
$421$	7.17557	−	22.0841i	0.349716	−	1.07631i	0.959010	−	0.283371i	$-0.0914527\pi$
$422$	−1.13760	−	3.50118i	−0.0553775	−	0.170435i
$423$	65.9597	−	47.9225i	3.20707	−	2.33007i
$424$	0.153545	−	0.111557i	0.00745681	−	0.00541769i
$425$	−2.66880	−	8.21372i	−0.129456	−	0.398424i
$426$	−1.90752	+	5.87074i	−0.0924197	+	0.284439i
$427$	11.5296	+	8.37675i	0.557957	+	0.405379i
$428$	−11.6224			−0.561789
$429$	−14.6436	+	14.8056i	−0.707001	+	0.714820i
$430$	−0.879695			−0.0424227
$431$	30.2899	+	22.0069i	1.45901	+	1.06004i	0.983619	+	0.180262i	$0.0576947\pi$
$431$	30.2899	+	22.0069i	1.45901	+	1.06004i	0.475395	+	0.879773i	$0.342305\pi$
$432$	−13.8778	+	42.7113i	−0.667694	+	2.05495i
$433$	−5.82091	−	17.9149i	−0.279735	−	0.860936i	−0.987928	−	0.154917i	$-0.950489\pi$
$433$	−5.82091	−	17.9149i	−0.279735	−	0.860936i	0.708193	−	0.706019i	$-0.249511\pi$
$434$	13.1516	−	9.55517i	0.631295	−	0.458663i
$435$	−1.50111	+	1.09062i	−0.0719729	+	0.0522914i
$436$	−3.40482	−	10.4790i	−0.163062	−	0.501852i
$437$	−0.892274	+	2.74614i	−0.0426833	+	0.131366i
$438$	−2.49995	−	1.81632i	−0.119452	−	0.0867870i
$439$	40.9831			1.95601			0.978007	−	0.208570i	$-0.0668808\pi$
$439$	40.9831			1.95601			0.978007	+	0.208570i	$0.0668808\pi$
$440$	−0.502389	−	0.972732i	−0.0239504	−	0.0463732i
$441$	66.9197			3.18665
$442$	−1.35523	−	0.984634i	−0.0644618	−	0.0468343i
$443$	5.18271	−	15.9507i	0.246238	−	0.757842i	−0.749193	−	0.662352i	$-0.769558\pi$
$443$	5.18271	−	15.9507i	0.246238	−	0.757842i	0.995430	−	0.0954899i	$-0.0304418\pi$
$444$	6.01294	+	18.5059i	0.285361	+	0.878252i
$445$	0.373418	−	0.271304i	0.0177017	−	0.0128611i
$446$	5.07923	−	3.69028i	0.240509	−	0.174740i
$447$	−5.69274	−	17.5204i	−0.269257	−	0.828689i
$448$	−2.68588	+	8.26629i	−0.126896	+	0.390546i
$449$	1.48194	+	1.07669i	0.0699371	+	0.0508123i	0.622204	−	0.782855i	$-0.286237\pi$
$449$	1.48194	+	1.07669i	0.0699371	+	0.0508123i	−0.552267	+	0.833667i	$0.686237\pi$
$450$	−21.6814			−1.02207
$451$	−2.98325	+	19.5300i	−0.140476	+	0.919633i
$452$	8.02119			0.377285
$453$	−41.7384	−	30.3247i	−1.96104	−	1.42478i
$454$	−1.58833	+	4.88837i	−0.0745439	+	0.229422i
$455$	−0.378946	−	1.16628i	−0.0177653	−	0.0546759i
$456$	−5.28825	+	3.84214i	−0.247645	+	0.179924i
$457$	−10.6094	+	7.70819i	−0.496288	+	0.360574i	−0.807597	−	0.589734i	$-0.799232\pi$
$457$	−10.6094	+	7.70819i	−0.496288	+	0.360574i	0.311310	+	0.950309i	$0.399232\pi$
$458$	3.54965	+	10.9247i	0.165864	+	0.510478i
$459$	−9.80876	+	30.1883i	−0.457834	+	1.40907i
$460$	0.689714	+	0.501107i	0.0321581	+	0.0233642i
$461$	−14.8982			−0.693877			−0.346938	−	0.937888i	$-0.612779\pi$
$461$	−14.8982			−0.693877			−0.346938	+	0.937888i	$0.612779\pi$
$462$	−20.0798	−	10.0925i	−0.934196	−	0.469543i
$463$	−8.76927			−0.407543			−0.203771	−	0.979019i	$-0.565320\pi$
$463$	−8.76927			−0.407543			−0.203771	+	0.979019i	$0.565320\pi$
$464$	−6.40450	−	4.65314i	−0.297322	−	0.216017i
$465$	−1.44272	+	4.44024i	−0.0669047	+	0.205911i
$466$	−0.0874602	−	0.269175i	−0.00405152	−	0.0124693i
$467$	−7.90889	+	5.74615i	−0.365980	+	0.265900i	−0.755542	−	0.655100i	$-0.772626\pi$
$467$	−7.90889	+	5.74615i	−0.365980	+	0.265900i	0.389562	+	0.921000i	$0.372626\pi$
$468$	21.8892	−	15.9035i	1.01183	−	0.735138i
$469$	−2.12876	−	6.55164i	−0.0982968	−	0.302526i
$470$	0.265084	−	0.815845i	0.0122274	−	0.0376321i
$471$	17.2297	+	12.5181i	0.793902	+	0.576803i
$472$	1.60346			0.0738052
$473$	−32.5419	+	5.33774i	−1.49628	+	0.245430i
$474$	−4.98456			−0.228948
$475$	4.02155	+	2.92182i	0.184521	+	0.134063i
$476$	−3.59423	+	11.0619i	−0.164741	+	0.507022i
$477$	0.254841	+	0.784320i	0.0116684	+	0.0359116i
$478$	−7.57256	+	5.50179i	−0.346361	+	0.251646i
$479$	−9.12673	+	6.63096i	−0.417011	+	0.302976i	−0.776434	−	0.630199i	$-0.782973\pi$
$479$	−9.12673	+	6.63096i	−0.417011	+	0.302976i	0.359423	+	0.933175i	$0.382973\pi$
$480$	0.916091	+	2.81944i	0.0418137	+	0.128689i
$481$	1.91172	−	5.88367i	0.0871670	−	0.268272i
$482$	−1.27706	−	0.927840i	−0.0581686	−	0.0422620i
$483$	37.7205			1.71634
$484$	−11.3605	−	15.2801i	−0.516386	−	0.694549i
$485$	2.38388			0.108247
$486$	28.7115	+	20.8601i	1.30238	+	0.946234i
$487$	−5.74234	+	17.6731i	−0.260210	+	0.800845i	0.732548	+	0.680715i	$0.238331\pi$
$487$	−5.74234	+	17.6731i	−0.260210	+	0.800845i	−0.992758	+	0.120129i	$0.961669\pi$
$488$	2.20359	+	6.78196i	0.0997520	+	0.307005i
$489$	28.8067	−	20.9293i	1.30269	−	0.946456i
$490$	0.569629	−	0.413860i	0.0257332	−	0.0186963i
$491$	0.280920	+	0.864582i	0.0126777	+	0.0390180i	0.957195	−	0.289443i	$-0.0934701\pi$
$491$	0.280920	+	0.864582i	0.0126777	+	0.0390180i	−0.944518	+	0.328461i	$0.893470\pi$
$492$	10.7623	−	33.1230i	0.485203	−	1.49330i
$493$	−4.52669	−	3.28883i	−0.203872	−	0.148121i
$494$	0.964179			0.0433805
$495$	4.69441	−	0.770010i	0.210998	−	0.0346094i
$496$	−19.9192			−0.894399
$497$	−11.0243	−	8.00960i	−0.494506	−	0.359280i
$498$	−8.93218	+	27.4904i	−0.400260	+	1.23188i
$499$	7.08063	+	21.7919i	0.316972	+	0.975541i	0.974935	+	0.222490i	$0.0714185\pi$
$499$	7.08063	+	21.7919i	0.316972	+	0.975541i	−0.657962	+	0.753051i	$0.728581\pi$
$500$	2.38170	−	1.73041i	0.106513	−	0.0773862i
$501$	−15.2654	+	11.0910i	−0.682007	+	0.495507i
$502$	−0.412815	−	1.27052i	−0.0184249	−	0.0567059i
$503$	9.47499	−	29.1610i	0.422469	−	1.30023i	−0.482929	−	0.875660i	$-0.660427\pi$
$503$	9.47499	−	29.1610i	0.422469	−	1.30023i	0.905397	−	0.424565i	$-0.139573\pi$
$504$	50.9177	+	36.9939i	2.26806	+	1.64784i
$505$	−2.55895			−0.113872
$506$	−4.43827	−	2.23075i	−0.197305	−	0.0991689i
$507$	32.2390			1.43179
$508$	−16.1247	−	11.7153i	−0.715419	−	0.519782i
$509$	6.27231	−	19.3042i	0.278015	−	0.855642i	−0.710391	−	0.703807i	$-0.751482\pi$
$509$	6.27231	−	19.3042i	0.278015	−	0.855642i	0.988406	−	0.151835i	$-0.0485182\pi$
$510$	0.160444	+	0.493796i	0.00710459	+	0.0218657i
$511$	5.51869	−	4.00956i	0.244133	−	0.177373i
$512$	−17.9296	+	13.0266i	−0.792385	+	0.575701i
$513$	−5.64567	−	17.3756i	−0.249263	−	0.767151i
$514$	3.15942	−	9.72370i	0.139356	−	0.428894i
$515$	0.473892	+	0.344302i	0.0208822	+	0.0151718i
$516$	58.1326			2.55915
$517$	4.85573	−	31.7884i	0.213555	−	1.39805i
$518$	6.67647			0.293347
$519$	41.6613	+	30.2687i	1.82873	+	1.32865i
$520$	0.189614	−	0.583571i	0.00831511	−	0.0255913i
$521$	6.65335	+	20.4769i	0.291488	+	0.897109i	0.984378	+	0.176066i	$0.0563371\pi$
$521$	6.65335	+	20.4769i	0.291488	+	0.897109i	−0.692890	+	0.721043i	$0.743663\pi$
$522$	−11.3641	+	8.25648i	−0.497392	+	0.361376i
$523$	19.6579	−	14.2823i	0.859580	−	0.624521i	−0.0681909	−	0.997672i	$-0.521723\pi$
$523$	19.6579	−	14.2823i	0.859580	−	0.624521i	0.927771	+	0.373151i	$0.121723\pi$
$524$	−6.94889	−	21.3865i	−0.303564	−	0.934273i
$525$	20.0669	−	61.7595i	0.875790	−	2.69540i
$526$	−8.05742	−	5.85406i	−0.351320	−	0.255249i
$527$	−14.0788			−0.613284
$528$	12.6364	+	24.4668i	0.549931	+	1.06478i
$529$	−14.6626			−0.637503
$530$	0.00701981	+	0.00510019i	0.000304921	+	0.000221538i
$531$	−2.15303	+	6.62633i	−0.0934334	+	0.287558i
$532$	−2.06875	−	6.36695i	−0.0896916	−	0.276042i
$533$	−8.95816	+	6.50849i	−0.388021	+	0.281914i
$534$	3.83548	−	2.78664i	0.165978	−	0.120590i
$535$	−0.353917	−	1.08924i	−0.0153012	−	0.0470921i
$536$	1.06517	−	3.27825i	0.0460083	−	0.141599i
$537$	2.14877	+	1.56117i	0.0927264	+	0.0673697i
$538$	6.34839			0.273699
$539$	18.5607	−	18.7659i	0.799464	−	0.808306i
$540$	−5.39422			−0.232130
$541$	18.9942	+	13.8001i	0.816623	+	0.593311i	0.915743	−	0.401764i	$-0.131603\pi$
$541$	18.9942	+	13.8001i	0.816623	+	0.593311i	−0.0991205	+	0.995075i	$0.531603\pi$
$542$	3.55480	−	10.9405i	0.152692	−	0.469936i
$543$	2.57819	+	7.93484i	0.110641	+	0.340517i
$544$	−7.23237	+	5.25462i	−0.310085	+	0.225290i
$545$	0.878402	−	0.638197i	0.0376266	−	0.0273373i
$546$	−3.89226	−	11.9791i	−0.166573	−	0.512660i
$547$	−10.1654	+	31.2860i	−0.434643	+	1.33769i	0.458809	+	0.888535i	$0.348276\pi$
$547$	−10.1654	+	31.2860i	−0.434643	+	1.33769i	−0.893452	+	0.449159i	$0.851724\pi$
$548$	12.7088	+	9.23349i	0.542894	+	0.394435i
$549$	−30.9855			−1.32243
$550$	−6.01349	+	6.08000i	−0.256416	+	0.259252i
$551$	3.22051			0.137198
$552$	15.2696	+	11.0940i	0.649917	+	0.472193i
$553$	3.40028	−	10.4650i	0.144594	−	0.445016i
$554$	2.84361	+	8.75173i	0.120813	+	0.371825i
$555$	−1.55126	+	1.12706i	−0.0658474	+	0.0478410i
$556$	−10.3071	+	7.48856i	−0.437119	+	0.317586i
$557$	0.367785	+	1.13193i	0.0155836	+	0.0479613i	0.958546	−	0.284938i	$-0.0919731\pi$
$557$	0.367785	+	1.13193i	0.0155836	+	0.0479613i	−0.942962	+	0.332899i	$0.891973\pi$
$558$	−10.9220	+	33.6145i	−0.462366	+	1.42302i
$559$	−14.9526	−	10.8637i	−0.632426	−	0.459484i
$560$	−1.62163			−0.0685264
$561$	8.93140	+	17.2931i	0.377084	+	0.730115i
$562$	−11.2795			−0.475798
$563$	34.9225	+	25.3727i	1.47181	+	1.06933i	0.980085	+	0.198577i	$0.0636321\pi$
$563$	34.9225	+	25.3727i	1.47181	+	1.06933i	0.491721	+	0.870753i	$0.336368\pi$
$564$	−17.5175	+	53.9132i	−0.737619	+	2.27016i
$565$	0.244256	+	0.751742i	0.0102759	+	0.0316260i
$566$	−1.50924	+	1.09653i	−0.0634380	+	0.0460904i
$567$	−114.154	+	82.9377i	−4.79401	+	3.48305i
$568$	−2.10701	−	6.48472i	−0.0884083	−	0.272093i
$569$	5.41048	−	16.6517i	0.226819	−	0.698077i	−0.771283	−	0.636492i	$-0.780385\pi$
$569$	5.41048	−	16.6517i	0.226819	−	0.698077i	0.998102	−	0.0615844i	$-0.0196153\pi$
$570$	−0.241769	−	0.175656i	−0.0101266	−	0.00735740i
$571$	−9.81872			−0.410901			−0.205450	−	0.978668i	$-0.565866\pi$
$571$	−9.81872			−0.410901			−0.205450	+	0.978668i	$0.565866\pi$
$572$	1.61141	−	10.5492i	0.0673765	−	0.441085i
$573$	−46.1265			−1.92696
$574$	−9.66771	−	7.02400i	−0.403522	−	0.293176i
$575$	4.43541	−	13.6508i	0.184969	−	0.569277i
$576$	−5.83967	−	17.9726i	−0.243319	−	0.748860i
$577$	20.6325	−	14.9904i	0.858943	−	0.624059i	−0.0686540	−	0.997641i	$-0.521870\pi$
$577$	20.6325	−	14.9904i	0.858943	−	0.624059i	0.927597	+	0.373582i	$0.121870\pi$
$578$	5.86708	−	4.26268i	0.244038	−	0.177304i
$579$	−26.4393	−	81.3719i	−1.09878	−	3.38170i
$580$	0.293834	−	0.904328i	0.0122008	−	0.0375502i
$581$	−51.6224	−	37.5059i	−2.14166	−	1.55601i
$582$	24.4855			1.01496
$583$	0.290625	+	0.146073i	0.0120364	+	0.00604973i
$584$	3.41327			0.141242
$585$	2.15702	+	1.56717i	0.0891818	+	0.0647943i
$586$	−3.56629	+	10.9759i	−0.147322	+	0.453411i
$587$	−2.68199	−	8.25433i	−0.110698	−	0.340693i	0.880328	−	0.474366i	$-0.157323\pi$
$587$	−2.68199	−	8.25433i	−0.110698	−	0.340693i	−0.991025	+	0.133673i	$0.957323\pi$
$588$	−37.6426	+	27.3490i	−1.55236	+	1.12785i
$589$	6.55581	−	4.76307i	0.270127	−	0.196259i
$590$	0.0226532	+	0.0697194i	0.000932617	+	0.00287030i
$591$	−13.0176	+	40.0639i	−0.535471	+	1.64801i
$592$	−6.61846	−	4.80859i	−0.272017	−	0.197632i
$593$	−8.19433			−0.336501			−0.168250	−	0.985744i	$-0.553812\pi$
$593$	−8.19433			−0.336501			−0.168250	+	0.985744i	$0.553812\pi$
$594$	31.0153	−	5.08734i	1.27257	−	0.208736i
$595$	−1.14616			−0.0469882
$596$	7.63766	+	5.54908i	0.312851	+	0.227299i
$597$	9.46359	−	29.1259i	0.387319	−	1.19205i
$598$	−0.860312	−	2.64777i	−0.0351808	−	0.108275i
$599$	−34.7197	+	25.2253i	−1.41861	+	1.03068i	−0.426607	+	0.904437i	$0.640291\pi$
$599$	−34.7197	+	25.2253i	−1.41861	+	1.03068i	−0.992000	+	0.126241i	$0.959709\pi$
$600$	26.2874	−	19.0989i	1.07318	−	0.779709i
$601$	8.20064	+	25.2390i	0.334511	+	1.02952i	0.966962	+	0.254919i	$0.0820489\pi$
$601$	8.20064	+	25.2390i	0.334511	+	1.02952i	−0.632451	+	0.774600i	$0.717951\pi$
$602$	6.16374	−	18.9701i	0.251215	−	0.773162i
$603$	12.1172	+	8.80366i	0.493451	+	0.358513i
$604$	26.4388			1.07578
$605$	1.08610	−	1.53000i	0.0441562	−	0.0622032i
$606$	−26.2837			−1.06770
$607$	−11.9880	−	8.70980i	−0.486578	−	0.353520i	0.317289	−	0.948329i	$-0.397228\pi$
$607$	−11.9880	−	8.70980i	−0.486578	−	0.353520i	−0.803867	+	0.594809i	$0.797228\pi$
$608$	1.59004	−	4.89363i	0.0644845	−	0.198463i
$609$	−13.0008	−	40.0122i	−0.526817	−	1.62138i
$610$	−0.263752	+	0.191627i	−0.0106790	+	0.00775875i
$611$	14.5809	−	10.5936i	0.589880	−	0.428573i
$612$	−7.81461	−	24.0509i	−0.315887	−	0.972200i
$613$	6.58935	−	20.2799i	0.266141	−	0.819099i	−0.725287	−	0.688447i	$-0.758293\pi$
$613$	6.58935	−	20.2799i	0.266141	−	0.819099i	0.991428	−	0.130652i	$-0.0417072\pi$
$614$	6.13515	+	4.45745i	0.247595	+	0.179888i
$615$	3.43200			0.138391
$616$	24.4964	−	4.01807i	0.986988	−	0.161893i
$617$	−1.21006			−0.0487150			−0.0243575	−	0.999703i	$-0.507754\pi$
$617$	−1.21006			−0.0487150			−0.0243575	+	0.999703i	$0.507754\pi$
$618$	4.86747	+	3.53642i	0.195798	+	0.142256i
$619$	−12.8073	+	39.4167i	−0.514768	+	1.58429i	0.268936	+	0.963158i	$0.413328\pi$
$619$	−12.8073	+	39.4167i	−0.514768	+	1.58429i	−0.783704	+	0.621134i	$0.786672\pi$
$620$	−0.739344	−	2.27547i	−0.0296928	−	0.0913850i
$621$	−42.6783	+	31.0076i	−1.71262	+	1.24429i
$622$	−5.04021	+	3.66193i	−0.202094	+	0.146830i
$623$	3.23408	+	9.95347i	0.129571	+	0.398777i
$624$	−4.76930	+	14.6784i	−0.190925	+	0.587606i
$625$	−19.8730	−	14.4386i	−0.794921	−	0.577544i
$626$	6.05913			0.242171
$627$	−10.0094	−	5.03090i	−0.399737	−	0.200915i
$628$	−10.9140			−0.435515
$629$	−4.67791	−	3.39870i	−0.186520	−	0.135515i
$630$	−0.889167	+	2.73657i	−0.0354252	+	0.109028i
$631$	−3.49284	−	10.7499i	−0.139048	−	0.427945i	0.857150	−	0.515067i	$-0.172233\pi$
$631$	−3.49284	−	10.7499i	−0.139048	−	0.427945i	−0.996198	+	0.0871222i	$0.972233\pi$
$632$	4.45432	−	3.23626i	0.177184	−	0.128731i
$633$	−19.3944	+	14.0908i	−0.770858	+	0.560061i
$634$	−4.29714	−	13.2252i	−0.170661	−	0.525241i
$635$	0.606932	−	1.86795i	0.0240854	−	0.0741272i
$636$	−0.463887	−	0.337034i	−0.0183943	−	0.0133643i
$637$	14.7931			0.586125
$638$	−0.836585	+	5.47676i	−0.0331207	+	0.216827i
$639$	29.6274			1.17204
$640$	−1.58097	−	1.14864i	−0.0624932	−	0.0454040i
$641$	13.7097	−	42.1942i	0.541502	−	1.66657i	−0.187663	−	0.982233i	$-0.560091\pi$
$641$	13.7097	−	42.1942i	0.541502	−	1.66657i	0.729165	−	0.684338i	$-0.239909\pi$
$642$	−3.63518	−	11.1879i	−0.143469	−	0.441552i
$643$	8.36435	−	6.07706i	0.329858	−	0.239656i	−0.410512	−	0.911855i	$-0.634650\pi$
$643$	8.36435	−	6.07706i	0.329858	−	0.239656i	0.740370	+	0.672199i	$0.234650\pi$
$644$	−15.6386	+	11.3621i	−0.616249	+	0.447731i
$645$	1.77021	+	5.44816i	0.0697021	+	0.214521i
$646$	0.278479	−	0.857070i	0.0109566	−	0.0337210i
$647$	35.6183	+	25.8782i	1.40030	+	1.01738i	0.994645	+	0.103353i	$0.0329570\pi$
$647$	35.6183	+	25.8782i	1.40030	+	1.01738i	0.405656	+	0.914026i	$0.367043\pi$
$648$	−70.6034			−2.77356
$649$	1.26103	+	2.44162i	0.0494997	+	0.0958420i
$650$	−4.79284			−0.187991
$651$	−85.6423	−	62.2227i	−3.35658	−	2.43870i
$652$	−5.63874	+	17.3543i	−0.220830	+	0.679645i
$653$	12.7832	+	39.3425i	0.500244	+	1.53959i	0.808623	+	0.588328i	$0.200214\pi$
$653$	12.7832	+	39.3425i	0.500244	+	1.53959i	−0.308379	+	0.951264i	$0.599786\pi$
$654$	9.02231	−	6.55509i	0.352800	−	0.256324i
$655$	1.79273	−	1.30249i	0.0700477	−	0.0508926i
$656$	4.52481	+	13.9259i	0.176664	+	0.543717i
$657$	−4.58313	+	14.1054i	−0.178805	+	0.550305i
$658$	15.7358	+	11.4327i	0.613446	+	0.445694i
$659$	18.3451			0.714625			0.357312	−	0.933985i	$-0.383693\pi$
$659$	18.3451			0.714625			0.357312	+	0.933985i	$0.383693\pi$
$660$	−2.32594	+	2.35166i	−0.0905369	+	0.0915383i
$661$	35.6295			1.38583			0.692914	−	0.721020i	$-0.256326\pi$
$661$	35.6295			1.38583			0.692914	+	0.721020i	$0.256326\pi$
$662$	−8.49340	−	6.17082i	−0.330105	−	0.239836i
$663$	−3.37093	+	10.3746i	−0.130916	+	0.402918i
$664$	−9.86632	−	30.3654i	−0.382887	−	1.17841i
$665$	0.533711	−	0.387764i	0.0206964	−	0.0150368i
$666$	−11.7437	+	8.53231i	−0.455060	+	0.330620i
$667$	−2.87358	−	8.84396i	−0.111265	−	0.342439i
$668$	2.98811	−	9.19645i	0.115613	−	0.355821i
$669$	−33.0757	−	24.0309i	−1.27878	−	0.929088i
$670$	0.157589			0.00608818
$671$	−8.59403	+	8.68908i	−0.331769	+	0.335438i
$672$	−67.2181			−2.59300
$673$	−10.9578	−	7.96130i	−0.422392	−	0.306886i	0.356208	−	0.934407i	$-0.384070\pi$
$673$	−10.9578	−	7.96130i	−0.422392	−	0.306886i	−0.778599	+	0.627521i	$0.784070\pi$
$674$	1.15454	−	3.55330i	0.0444711	−	0.136868i
$675$	28.0641	+	86.3725i	1.08019	+	3.32448i
$676$	−13.3661	+	9.71101i	−0.514079	+	0.373501i
$677$	36.3345	−	26.3985i	1.39645	−	1.01458i	0.401324	−	0.915936i	$-0.368550\pi$
$677$	36.3345	−	26.3985i	1.39645	−	1.01458i	0.995123	−	0.0986419i	$-0.0314498\pi$
$678$	2.50882	+	7.72135i	0.0963506	+	0.296537i
$679$	−16.7031	+	51.4068i	−0.641006	+	1.97281i
$680$	−0.463978	−	0.337099i	−0.0177927	−	0.0129272i
$681$	33.4710			1.28261
$682$	6.39704	+	12.3860i	0.244955	+	0.474286i
$683$	26.3888			1.00974			0.504869	−	0.863196i	$-0.331541\pi$
$683$	26.3888			1.00974			0.504869	+	0.863196i	$0.331541\pi$
$684$	11.7756	+	8.55550i	0.450253	+	0.327128i
$685$	−0.478358	+	1.47223i	−0.0182771	+	0.0562512i
$686$	0.593990	+	1.82811i	0.0226787	+	0.0697977i
$687$	60.5163	−	43.9676i	2.30884	−	1.67747i
$688$	−19.7730	+	14.3659i	−0.753838	+	0.547696i
$689$	0.0563346	+	0.173380i	0.00214618	+	0.00660525i
$690$	−0.266650	+	0.820664i	−0.0101512	+	0.0312422i
$691$	27.4385	+	19.9352i	1.04381	+	0.758371i	0.971025	−	0.238977i	$-0.0768120\pi$
$691$	27.4385	+	19.9352i	1.04381	+	0.758371i	0.0727827	+	0.997348i	$0.476812\pi$
$692$	−26.3900			−1.00320
$693$	−16.2875	+	106.627i	−0.618711	+	4.05043i
$694$	2.52054			0.0956786
$695$	−1.01569	−	0.737941i	−0.0385273	−	0.0279917i
$696$	6.50520	−	20.0209i	0.246579	−	0.758892i
$697$	3.19813	+	9.84282i	0.121138	+	0.372823i
$698$	−5.60320	+	4.07097i	−0.212084	+	0.154088i
$699$	−1.49107	+	1.08332i	−0.0563973	+	0.0409750i
$700$	10.2836	+	31.6495i	0.388682	+	1.19624i
$701$	−10.3684	+	31.9106i	−0.391608	+	1.20525i	0.539964	+	0.841688i	$0.318438\pi$
$701$	−10.3684	+	31.9106i	−0.391608	+	1.20525i	−0.931572	+	0.363557i	$0.881562\pi$
$702$	14.2511	+	10.3540i	0.537874	+	0.390788i
$703$	3.32810			0.125522
$704$	−6.65964	−	3.34725i	−0.250995	−	0.126154i
$705$	−5.58615			−0.210387
$706$	−10.4201	−	7.57066i	−0.392166	−	0.284926i
$707$	17.9298	−	55.1821i	0.674318	−	2.07534i
$708$	−1.49698	−	4.60724i	−0.0562601	−	0.173151i
$709$	20.1123	−	14.6124i	0.755332	−	0.548781i	−0.142143	−	0.989846i	$-0.545399\pi$
$709$	20.1123	−	14.6124i	0.755332	−	0.548781i	0.897475	+	0.441065i	$0.145399\pi$
$710$	0.252192	−	0.183228i	0.00946460	−	0.00687644i
$711$	7.39291	+	22.7530i	0.277256	+	0.853306i
$712$	−1.61824	+	4.98043i	−0.0606461	+	0.186649i
$713$	−18.9296	−	13.7532i	−0.708921	−	0.515061i
$714$	−11.7726			−0.440578
$715$	1.03774	−	0.170217i	0.0388091	−	0.00636574i
$716$	−1.36112			−0.0508675
$717$	49.3121	+	35.8274i	1.84160	+	1.33800i
$718$	4.18013	−	12.8651i	0.156001	−	0.480122i
$719$	−5.07985	−	15.6342i	−0.189447	−	0.583056i	0.810550	−	0.585669i	$-0.199168\pi$
$719$	−5.07985	−	15.6342i	−0.189447	−	0.583056i	−0.999997	+	0.00261289i	$0.999168\pi$
$720$	2.85240	−	2.07239i	0.106303	−	0.0772335i
$721$	−10.7451	+	7.80674i	−0.400167	+	0.290738i
$722$	0.160285	+	0.493308i	0.00596520	+	0.0183590i
$723$	−3.17649	+	9.77624i	−0.118135	+	0.363582i
$724$	−3.45902	−	2.51313i	−0.128554	−	0.0933996i
$725$	−16.0088			−0.594553
$726$	11.1556	−	15.7150i	0.414024	−	0.583239i
$727$	−1.58400			−0.0587473			−0.0293736	−	0.999569i	$-0.509351\pi$
$727$	−1.58400			−0.0587473			−0.0293736	+	0.999569i	$0.509351\pi$
$728$	11.2558	+	8.17779i	0.417166	+	0.303089i
$729$	37.5935	−	115.701i	1.39235	−	4.28521i
$730$	0.0482217	+	0.148411i	0.00178476	+	0.00549294i
$731$	−13.9755	+	10.1538i	−0.516903	+	0.375552i
$732$	17.4294	−	12.6632i	0.644211	−	0.468046i
$733$	2.73067	+	8.40415i	0.100860	+	0.310414i	0.988736	−	0.149667i	$-0.0478202\pi$
$733$	2.73067	+	8.40415i	0.100860	+	0.310414i	−0.887877	+	0.460081i	$0.847820\pi$
$734$	−3.44349	+	10.5980i	−0.127101	+	0.391178i
$735$	−3.70940	−	2.69503i	−0.136823	−	0.0994078i
$736$	−14.8573			−0.547648
$737$	5.82955	−	0.956203i	0.214734	−	0.0352222i
$738$	25.9817			0.956398
$739$	8.16858	+	5.93482i	0.300486	+	0.218316i	0.727803	−	0.685786i	$-0.240541\pi$
$739$	8.16858	+	5.93482i	0.300486	+	0.218316i	−0.427317	+	0.904102i	$0.640541\pi$
$740$	0.303650	−	0.934540i	0.0111624	−	0.0343544i
$741$	−1.94022	−	5.97138i	−0.0712758	−	0.219364i
$742$	−0.159168	+	0.115642i	−0.00584323	+	0.00424536i
$743$	−4.95608	+	3.60081i	−0.181821	+	0.132101i	−0.674973	−	0.737843i	$-0.735845\pi$
$743$	−4.95608	+	3.60081i	−0.181821	+	0.132101i	0.493152	+	0.869943i	$0.335845\pi$
$744$	−16.3684	−	50.3766i	−0.600093	−	1.84690i
$745$	−0.287480	+	0.884774i	−0.0105325	+	0.0324156i
$746$	−2.66406	−	1.93555i	−0.0975383	−	0.0708657i
$747$	138.734			5.07600
$748$	−8.91190	−	4.47928i	−0.325851	−	0.163779i
$749$	25.9686			0.948872
$750$	2.41066	+	1.75145i	0.0880248	+	0.0639537i
$751$	5.74787	−	17.6901i	0.209743	−	0.645521i	−0.789743	−	0.613438i	$-0.789786\pi$
$751$	5.74787	−	17.6901i	0.209743	−	0.645521i	0.999485	−	0.0320830i	$-0.0102141\pi$
$752$	−7.36489	−	22.6668i	−0.268570	−	0.826573i
$753$	−7.03788	+	5.11332i	−0.256475	+	0.186340i
$754$	−2.51212	+	1.82516i	−0.0914859	+	0.0664684i
$755$	0.805096	+	2.47783i	0.0293005	+	0.0901775i
$756$	37.7956	−	116.323i	1.37461	−	4.23062i
$757$	−3.78053	−	2.74671i	−0.137406	−	0.0998310i	0.516959	−	0.856010i	$-0.327064\pi$
$757$	−3.78053	−	2.74671i	−0.137406	−	0.0998310i	−0.654365	+	0.756179i	$0.727064\pi$
$758$	12.7875			0.464462
$759$	−4.88442	+	31.9762i	−0.177293	+	1.16066i
$760$	0.330097			0.0119739
$761$	−26.6059	−	19.3303i	−0.964464	−	0.700724i	−0.0102809	−	0.999947i	$-0.503273\pi$
$761$	−26.6059	−	19.3303i	−0.964464	−	0.700724i	−0.954183	+	0.299223i	$0.903273\pi$
$762$	6.23397	−	19.1862i	0.225833	−	0.695042i
$763$	7.60761	+	23.4138i	0.275414	+	0.847637i
$764$	19.1237	−	13.8942i	0.691871	−	0.502674i
$765$	2.01607	−	1.46476i	0.0728912	−	0.0529586i
$766$	−3.09248	−	9.51769i	−0.111736	−	0.343888i
$767$	−0.475943	+	1.46480i	−0.0171853	+	0.0528909i
$768$	−3.95639	−	2.87448i	−0.142764	−	0.103724i
$769$	15.5803			0.561840			0.280920	−	0.959731i	$-0.409360\pi$
$769$	15.5803			0.561840			0.280920	+	0.959731i	$0.409360\pi$
$770$	0.520786	+	1.00835i	0.0187678	+	0.0363385i
$771$	−66.5788			−2.39778
$772$	35.4723	+	25.7721i	1.27668	+	0.927559i
$773$	1.42657	−	4.39053i	0.0513101	−	0.157916i	−0.922118	−	0.386908i	$-0.873543\pi$
$773$	1.42657	−	4.39053i	0.0513101	−	0.157916i	0.973428	+	0.228992i	$0.0735430\pi$
$774$	13.4013	+	41.2449i	0.481699	+	1.48252i
$775$	−32.5883	+	23.6768i	−1.17061	+	0.850496i
$776$	−21.8809	+	15.8974i	−0.785477	+	0.570683i
$777$	−13.4351	−	41.3489i	−0.481981	−	1.48338i
$778$	3.82835	−	11.7824i	0.137253	−	0.422421i
$779$	−4.81917	−	3.50134i	−0.172665	−	0.125448i
$780$	−1.85381			−0.0663769
$781$	8.21737	−	8.30825i	0.294041	−	0.297293i
$782$	−2.60211			−0.0930513
$783$	47.6009	+	34.5841i	1.70112	+	1.23593i
$784$	6.04504	−	18.6047i	0.215894	−	0.664455i
$785$	−0.332345	−	1.02285i	−0.0118619	−	0.0365072i
$786$	18.4136	−	13.3783i	0.656791	−	0.477187i
$787$	2.97468	−	2.16123i	0.106036	−	0.0770395i	−0.533504	−	0.845798i	$-0.679125\pi$
$787$	2.97468	−	2.16123i	0.106036	−	0.0770395i	0.639540	+	0.768758i	$0.279125\pi$
$788$	−6.67103	−	20.5313i	−0.237646	−	0.731398i
$789$	−20.0416	+	61.6816i	−0.713499	+	2.19592i
$790$	0.203644	+	0.147956i	0.00724532	+	0.00526403i
$791$	−17.9222			−0.637241
$792$	−37.9535	+	38.3733i	−1.34862	+	1.36353i
$793$	−6.84958			−0.243236
$794$	−3.72233	−	2.70443i	−0.132100	−	0.0959766i
$795$	0.0174607	−	0.0537384i	0.000619266	−	0.00190590i
$796$	4.84975	+	14.9260i	0.171895	+	0.529038i
$797$	−23.4806	+	17.0597i	−0.831726	+	0.604284i	−0.920047	−	0.391808i	$-0.871850\pi$
$797$	−23.4806	+	17.0597i	−0.831726	+	0.604284i	0.0883211	+	0.996092i	$0.471850\pi$
$798$	5.48190	−	3.98283i	0.194057	−	0.140991i
$799$	−5.20549	−	16.0208i	−0.184157	−	0.566777i
$800$	−7.90392	+	24.3258i	−0.279446	+	0.860046i
$801$	−18.4089	−	13.3748i	−0.650445	−	0.472576i
$802$	−3.67091			−0.129624
$803$	2.68434	+	5.19746i	0.0947284	+	0.183414i
$804$	−10.4139			−0.367269
$805$	−1.54107	−	1.11965i	−0.0543156	−	0.0394626i
$806$	−2.41440	+	7.43075i	−0.0850435	+	0.261737i
$807$	−12.7749	−	39.3171i	−0.449697	−	1.38403i
$808$	23.4878	−	17.0649i	0.826298	−	0.600340i
$809$	−19.8571	+	14.4270i	−0.698139	+	0.507228i	−0.879326	−	0.476221i	$-0.842006\pi$
$809$	−19.8571	+	14.4270i	−0.698139	+	0.507228i	0.181187	+	0.983449i	$0.442006\pi$
$810$	−0.997463	−	3.06988i	−0.0350473	−	0.107864i
$811$	7.06368	−	21.7398i	0.248039	−	0.763386i	−0.747082	−	0.664731i	$-0.768546\pi$
$811$	7.06368	−	21.7398i	0.248039	−	0.763386i	0.995122	−	0.0986549i	$-0.0314540\pi$
$812$	17.4424	+	12.6727i	0.612110	+	0.444724i
$813$	−74.9106			−2.62723
$814$	−0.864533	+	5.65972i	−0.0303019	+	0.198373i
$815$	−1.79814			−0.0629861
$816$	11.6703	+	8.47896i	0.408542	+	0.296823i
$817$	3.07251	−	9.45622i	0.107494	−	0.330831i
$818$	4.22276	+	12.9963i	0.147646	+	0.454406i
$819$	−48.9084	+	35.5341i	−1.70900	+	1.24166i
$820$	−1.42288	+	1.03378i	−0.0496891	+	0.0361013i
$821$	9.59788	+	29.5392i	0.334968	+	1.03093i	0.966738	+	0.255770i	$0.0823290\pi$
$821$	9.59788	+	29.5392i	0.334968	+	1.03093i	−0.631769	+	0.775157i	$0.717671\pi$
$822$	−4.91335	+	15.1217i	−0.171373	+	0.527431i
$823$	−40.7202	−	29.5849i	−1.41942	−	1.03127i	−0.991868	−	0.127274i	$-0.959377\pi$
$823$	−40.7202	−	29.5849i	−1.41942	−	1.03127i	−0.427548	−	0.903992i	$-0.640623\pi$
$824$	−6.64574			−0.231515
$825$	49.7558	+	25.0081i	1.73227	+	0.870672i
$826$	−1.66218			−0.0578345
$827$	−2.63114	−	1.91163i	−0.0914936	−	0.0664740i	0.541098	−	0.840960i	$-0.318009\pi$
$827$	−2.63114	−	1.91163i	−0.0914936	−	0.0664740i	−0.632592	+	0.774486i	$0.718009\pi$
$828$	12.9875	−	39.9714i	0.451346	−	1.38910i
$829$	−12.2435	−	37.6817i	−0.425235	−	1.30874i	−0.902769	−	0.430126i	$-0.858469\pi$
$829$	−12.2435	−	37.6817i	−0.425235	−	1.30874i	0.477534	−	0.878613i	$-0.341531\pi$
$830$	1.18092	−	0.857987i	0.0409903	−	0.0297812i
$831$	48.4793	−	35.2222i	1.68173	−	1.22185i
$832$	−1.29090	−	3.97299i	−0.0447540	−	0.137739i
$833$	4.27262	−	13.1498i	0.148038	−	0.455613i
$834$	−10.4324	−	7.57959i	−0.361245	−	0.262460i
$835$	0.952878			0.0329757
$836$	5.66523	−	0.929249i	0.195936	−	0.0321388i
$837$	148.048			5.11728
$838$	15.8854	+	11.5414i	0.548752	+	0.398692i
$839$	2.88935	−	8.89251i	0.0997515	−	0.307004i	−0.888711	−	0.458467i	$-0.848399\pi$
$839$	2.88935	−	8.89251i	0.0997515	−	0.307004i	0.988463	+	0.151464i	$0.0483986\pi$
$840$	−1.33256	−	4.10118i	−0.0459775	−	0.141504i
$841$	15.0706	−	10.9495i	0.519677	−	0.377568i
$842$	−9.74413	+	7.07953i	−0.335805	+	0.243977i
$843$	22.6978	+	69.8567i	0.781754	+	2.40599i
$844$	3.79634	−	11.6839i	0.130675	−	0.402177i
$845$	−1.31712	−	0.956947i	−0.0453105	−	0.0329200i
$846$	−42.2895			−1.45394
$847$	25.3834	+	34.1412i	0.872185	+	1.17311i
$848$	0.241074			0.00827851
$849$	9.82808	+	7.14052i	0.337299	+	0.245062i
$850$	−1.38429	+	4.26041i	−0.0474808	+	0.146131i
$851$	−2.96957	−	9.13941i	−0.101796	−	0.313295i
$852$	−16.6655	+	12.1082i	−0.570952	+	0.414821i
$853$	27.0538	−	19.6557i	0.926304	−	0.672999i	−0.0187808	−	0.999824i	$-0.505978\pi$
$853$	27.0538	−	19.6557i	0.926304	−	0.672999i	0.945085	+	0.326824i	$0.105978\pi$
$854$	−2.28429	−	7.03031i	−0.0781667	−	0.240572i
$855$	−0.443233	+	1.36413i	−0.0151583	+	0.0466523i
$856$	10.5123	+	7.63765i	0.359304	+	0.261049i
$857$	−39.6462			−1.35429			−0.677145	−	0.735850i	$-0.736783\pi$
$857$	−39.6462			−1.35429			−0.677145	+	0.735850i	$0.736783\pi$
$858$	10.6589	−	1.74834i	0.363888	−	0.0596874i
$859$	−19.0129			−0.648712			−0.324356	−	0.945935i	$-0.605148\pi$
$859$	−19.0129			−0.648712			−0.324356	+	0.945935i	$0.605148\pi$
$860$	−2.37501	−	1.72554i	−0.0809870	−	0.0588405i
$861$	−24.0469	+	74.0088i	−0.819516	+	2.52221i
$862$	−6.00114	−	18.4696i	−0.204400	−	0.629078i
$863$	9.81174	−	7.12865i	0.333995	−	0.242662i	−0.408129	−	0.912924i	$-0.633818\pi$
$863$	9.81174	−	7.12865i	0.333995	−	0.242662i	0.742124	+	0.670263i	$0.233818\pi$
$864$	76.0529	−	55.2557i	2.58737	−	1.87984i
$865$	−0.803609	−	2.47325i	−0.0273235	−	0.0840931i
$866$	−3.01927	+	9.29236i	−0.102599	+	0.315767i
$867$	−38.2061	−	27.7584i	−1.29755	−	0.942723i
$868$	54.2493			1.84134
$869$	8.43099	+	4.23756i	0.286002	+	0.143749i
$870$	0.962427			0.0326293
$871$	2.67860	+	1.94612i	0.0907610	+	0.0659417i
$872$	−3.80663	+	11.7156i	−0.128909	+	0.396740i
$873$	−36.3160	−	111.769i	−1.22911	−	3.78281i
$874$	1.21167	−	0.880331i	0.0409854	−	0.0297776i
$875$	−5.32159	+	3.86636i	−0.179902	+	0.130707i
$876$	−3.18662	−	9.80740i	−0.107666	−	0.331361i
$877$	−7.11521	+	21.8984i	−0.240264	+	0.739455i	0.756116	+	0.654438i	$0.227095\pi$
$877$	−7.11521	+	21.8984i	−0.240264	+	0.739455i	−0.996379	+	0.0850174i	$0.972905\pi$
$878$	−17.1978	−	12.4950i	−0.580399	−	0.421684i
$879$	75.1529			2.53484
$880$	0.209984	−	1.37468i	0.00707858	−	0.0463404i
$881$	−21.8516			−0.736200			−0.368100	−	0.929786i	$-0.619992\pi$
$881$	−21.8516			−0.736200			−0.368100	+	0.929786i	$0.619992\pi$
$882$	−28.0817	−	20.4025i	−0.945560	−	0.686989i
$883$	−12.7845	+	39.3465i	−0.430231	+	1.32412i	0.467663	+	0.883907i	$0.345096\pi$
$883$	−12.7845	+	39.3465i	−0.430231	+	1.32412i	−0.897895	+	0.440210i	$0.854904\pi$
$884$	−1.72748	−	5.31664i	−0.0581014	−	0.178818i
$885$	0.386203	−	0.280593i	0.0129821	−	0.00943203i
$886$	−7.03790	+	5.11334i	−0.236443	+	0.171786i
$887$	−1.77338	−	5.45789i	−0.0595441	−	0.183258i	0.916860	−	0.399208i	$-0.130715\pi$
$887$	−1.77338	−	5.45789i	−0.0595441	−	0.183258i	−0.976404	+	0.215951i	$0.930715\pi$
$888$	6.72252	−	20.6898i	0.225593	−	0.694304i
$889$	36.0284	+	26.1762i	1.20836	+	0.877922i
$890$	−0.239414			−0.00802518
$891$	−55.5255	−	107.509i	−1.86018	−	3.60169i
$892$	20.9515			0.701508
$893$	7.84401	+	5.69901i	0.262490	+	0.190710i
$894$	−2.95279	+	9.08776i	−0.0987561	+	0.303940i
$895$	−0.0414479	−	0.127563i	−0.00138545	−	0.00426398i
$896$	35.8470	−	26.0444i	1.19756	−	0.870081i
$897$	−14.6670	+	10.6562i	−0.489718	+	0.355801i
$898$	−0.293607	−	0.903631i	−0.00979781	−	0.0301545i
$899$	−8.06446	+	24.8199i	−0.268965	+	0.827789i
$900$	−58.5356	−	42.5286i	−1.95119	−	1.41762i
$901$	0.170390			0.00567652
$902$	7.20620	−	7.28590i	0.239940	−	0.242594i
$903$	−129.889			−4.32244
$904$	−7.25508	−	5.27112i	−0.241300	−	0.175315i
$905$	0.130197	−	0.400706i	0.00432790	−	0.0133199i
$906$	8.26937	+	25.4505i	0.274731	+	0.845536i
$907$	−6.96792	+	5.06249i	−0.231366	+	0.168097i	−0.697428	−	0.716655i	$-0.745672\pi$
$907$	−6.96792	+	5.06249i	−0.231366	+	0.168097i	0.466062	+	0.884752i	$0.345672\pi$
$908$	−13.8768	+	10.0821i	−0.460518	+	0.334586i
$909$	38.9831	+	119.977i	1.29299	+	3.97940i
$910$	−0.196557	+	0.604941i	−0.00651581	+	0.0200536i
$911$	−26.0411	−	18.9199i	−0.862779	−	0.626846i	0.0658606	−	0.997829i	$-0.479021\pi$
$911$	−26.0411	−	18.9199i	−0.862779	−	0.626846i	−0.928640	+	0.370983i	$0.879021\pi$
$912$	−8.30282			−0.274934
$913$	38.4787	−	38.9043i	1.27346	−	1.28755i
$914$	6.80214			0.224995
$915$	1.71754	+	1.24787i	0.0567801	+	0.0412532i
$916$	−11.8457	+	36.4573i	−0.391393	+	1.20458i
$917$	15.5263	+	47.7851i	0.512725	+	1.57800i
$918$	13.3199	−	9.67747i	0.439622	−	0.319404i
$919$	−3.08842	+	2.24387i	−0.101877	+	0.0740183i	−0.637558	−	0.770403i	$-0.720055\pi$
$919$	−3.08842	+	2.24387i	−0.101877	+	0.0740183i	0.535680	+	0.844421i	$0.320055\pi$
$920$	−0.294537	−	0.906491i	−0.00971059	−	0.0298861i
$921$	15.2602	−	46.9662i	0.502842	−	1.54759i
$922$	6.25175	+	4.54216i	0.205891	+	0.149588i
$923$	6.54937			0.215575
$924$	−34.4149	−	66.6346i	−1.13217	−	2.19212i
$925$	−16.5437			−0.543952
$926$	3.67987	+	2.67358i	0.120928	+	0.0878594i
$927$	8.92349	−	27.4637i	0.293086	−	0.902026i
$928$	5.12072	+	15.7600i	0.168096	+	0.517346i
$929$	25.2417	−	18.3392i	0.828153	−	0.601688i	−0.0908835	−	0.995862i	$-0.528969\pi$
$929$	25.2417	−	18.3392i	0.828153	−	0.601688i	0.919036	+	0.394174i	$0.128969\pi$
$930$	1.95916	−	1.42341i	0.0642434	−	0.0466755i
$931$	2.45921	+	7.56868i	0.0805974	+	0.248053i
$932$	0.291867	−	0.898275i	0.00956043	−	0.0294240i
$933$	32.8216	+	23.8463i	1.07453	+	0.780692i
$934$	5.07072			0.165919
$935$	0.148416	−	0.971618i	0.00485374	−	0.0317753i
$936$	−30.2495			−0.988737
$937$	35.2278	+	25.5945i	1.15084	+	0.836135i	0.988593	−	0.150614i	$-0.0481252\pi$
$937$	35.2278	+	25.5945i	1.15084	+	0.836135i	0.162249	+	0.986750i	$0.448125\pi$
$938$	−1.10417	+	3.39830i	−0.0360525	+	0.110958i
$939$	−12.1928	−	37.5256i	−0.397897	−	1.22460i
$940$	2.31597	−	1.68265i	0.0755388	−	0.0548821i
$941$	13.7506	−	9.99043i	0.448258	−	0.325679i	−0.340650	−	0.940190i	$-0.610647\pi$
$941$	13.7506	−	9.99043i	0.448258	−	0.325679i	0.788908	+	0.614512i	$0.210647\pi$
$942$	−3.41361	−	10.5060i	−0.111221	−	0.342304i
$943$	−5.31512	+	16.3583i	−0.173084	+	0.532699i
$944$	1.64773	+	1.19715i	0.0536292	+	0.0389639i
$945$	12.0526			0.392072
$946$	15.2830	+	7.68151i	0.496893	+	0.249747i
$947$	32.7956			1.06571			0.532857	−	0.846205i	$-0.321118\pi$
$947$	32.7956			1.06571			0.532857	+	0.846205i	$0.321118\pi$
$948$	−13.4573	−	9.77732i	−0.437074	−	0.317553i
$949$	−1.01314	+	3.11811i	−0.0328878	+	0.101218i
$950$	−0.796763	−	2.45219i	−0.0258504	−	0.0795594i
$951$	−73.2597	+	53.2263i	−2.37561	+	1.72598i
$952$	10.5203	−	7.64342i	0.340964	−	0.247725i
$953$	13.7505	+	42.3196i	0.445422	+	1.37087i	0.882021	+	0.471211i	$0.156183\pi$
$953$	13.7505	+	42.3196i	0.445422	+	1.37087i	−0.436599	+	0.899656i	$0.643817\pi$
$954$	0.132185	−	0.406822i	0.00427964	−	0.0131714i
$955$	1.88450	+	1.36917i	0.0609808	+	0.0443052i
$956$	−31.2363			−1.01025
$957$	35.6023	−	5.83973i	1.15086	−	0.188772i
$958$	5.85152			0.189054
$959$	−28.3961	−	20.6310i	−0.916957	−	0.666208i
$960$	−0.400110	+	1.23141i	−0.0129135	+	0.0397436i
$961$	10.7122	+	32.9689i	0.345556	+	1.06351i
$962$	−2.59604	+	1.88613i	−0.0836997	+	0.0608114i
$963$	−45.6781	+	33.1870i	−1.47195	+	1.06944i
$964$	−1.62784	−	5.00997i	−0.0524292	−	0.161360i
$965$	−1.33517	+	4.10924i	−0.0429807	+	0.132281i
$966$	−15.8288	−	11.5003i	−0.509282	−	0.370015i
$967$	18.0067			0.579057			0.289529	−	0.957169i	$-0.406501\pi$
$967$	18.0067			0.579057			0.289529	+	0.957169i	$0.406501\pi$
$968$	0.234135	+	21.2862i	0.00752539	+	0.684164i
$969$	−5.86841			−0.188521
$970$	−1.00035	−	0.726800i	−0.0321194	−	0.0233361i
$971$	−12.2813	+	37.7981i	−0.394127	+	1.21300i	0.535513	+	0.844527i	$0.320118\pi$
$971$	−12.2813	+	37.7981i	−0.394127	+	1.21300i	−0.929640	+	0.368470i	$0.879882\pi$
$972$	36.5978	+	112.636i	1.17387	+	3.61282i
$973$	23.0298	−	16.7321i	0.738302	−	0.536408i
$974$	7.79786	−	5.66548i	0.249860	−	0.181534i
$975$	9.64465	+	29.6832i	0.308876	+	0.950623i
$976$	−2.79900	+	8.61444i	−0.0895939	+	0.275742i
$977$	36.7645	+	26.7110i	1.17620	+	0.854561i	0.991738	−	0.128279i	$-0.0409452\pi$
$977$	36.7645	+	26.7110i	1.17620	+	0.854561i	0.184464	+	0.982839i	$0.440945\pi$
$978$	−18.4692			−0.590579
$979$	−8.85645	+	1.45270i	−0.283054	+	0.0464284i
$980$	2.34968			0.0750579
$981$	−43.3037	−	31.4619i	−1.38258	−	1.00450i
$982$	0.145711	−	0.448454i	0.00464984	−	0.0143107i
$983$	3.38810	+	10.4275i	0.108064	+	0.332586i	0.990437	−	0.137964i	$-0.0440557\pi$
$983$	3.38810	+	10.4275i	0.108064	+	0.332586i	−0.882374	+	0.470550i	$0.844056\pi$
$984$	−31.5012	+	22.8869i	−1.00422	+	0.729609i
$985$	1.72104	−	1.25041i	0.0548370	−	0.0398414i
$986$	0.896843	+	2.76020i	0.0285613	+	0.0879027i
$987$	39.1404	−	120.462i	1.24585	−	3.83434i
$988$	2.60310	+	1.89126i	0.0828155	+	0.0601690i
$989$	−28.7096			−0.912913
$990$	−2.20469	−	1.10812i	−0.0700696	−	0.0352182i
$991$	−23.4414			−0.744640			−0.372320	−	0.928104i	$-0.621438\pi$
$991$	−23.4414			−0.744640			−0.372320	+	0.928104i	$0.621438\pi$
$992$	33.7327	+	24.5082i	1.07101	+	0.778137i
$993$	−21.1260	+	65.0192i	−0.670413	+	2.06332i
$994$	2.18417	+	6.72218i	0.0692776	+	0.213215i
$995$	−1.25118	+	0.909032i	−0.0396649	+	0.0288183i
$996$	−78.0382	+	56.6981i	−2.47274	+	1.79655i
$997$	6.87603	+	21.1622i	0.217766	+	0.670215i	0.998946	+	0.0459087i	$0.0146183\pi$
$997$	6.87603	+	21.1622i	0.217766	+	0.670215i	−0.781180	+	0.624306i	$0.785382\pi$
$998$	3.67268	−	11.3034i	0.116257	−	0.357801i
$999$	49.1912	+	35.7395i	1.55634	+	1.13075i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	209.2.f.c.191.4	yes	40
11.3	even	5	inner	209.2.f.c.58.4	✓	40
11.5	even	5		2299.2.a.x.1.13		20
11.6	odd	10		2299.2.a.y.1.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.f.c.58.4	✓	40	11.3	even	5	inner
209.2.f.c.191.4	yes	40	1.1	even	1	trivial
2299.2.a.x.1.13		20	11.5	even	5
2299.2.a.y.1.8		20	11.6	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.419632 - 0.304881i) q^{2} +(-1.04377 + 3.21239i) q^{3} +(-0.534895 - 1.64624i) q^{4} +(0.137996 - 0.100260i) q^{5} +(1.41740 - 1.02980i) q^{6} +(1.19515 + 3.67829i) q^{7} +(-0.598018 + 1.84051i) q^{8} +(-6.80296 - 4.94264i) q^{9} -0.0884751 q^{10} +(-3.27289 + 0.536842i) q^{11} +5.84667 q^{12} +(-1.50385 - 1.09261i) q^{13} +(0.619916 - 1.90791i) q^{14} +(0.178039 + 0.547947i) q^{15} +(-1.98866 + 1.44485i) q^{16} +(-1.40558 + 1.02121i) q^{17} +(1.34783 + 4.14819i) q^{18} +(0.309017 - 0.951057i) q^{19} +(-0.238865 - 0.173546i) q^{20} -13.0636 q^{21} +(1.53708 + 0.772565i) q^{22} -2.88746 q^{23} +(-5.28825 - 3.84214i) q^{24} +(-1.53609 + 4.72761i) q^{25} +(0.297948 + 0.916989i) q^{26} +(14.7806 - 10.7387i) q^{27} +(5.41606 - 3.93499i) q^{28} +(0.995192 + 3.06288i) q^{29} +(0.0923476 - 0.284217i) q^{30} +(6.55581 + 4.76307i) q^{31} +5.14547 q^{32} +(1.69160 - 11.0741i) q^{33} +0.901176 q^{34} +(0.533711 + 0.387764i) q^{35} +(-4.49789 + 13.8431i) q^{36} +(1.02844 + 3.16521i) q^{37} +(-0.419632 + 0.304881i) q^{38} +(5.07956 - 3.69052i) q^{39} +(0.102005 + 0.313941i) q^{40} +(1.84076 - 5.66528i) q^{41} +(5.48190 + 3.98283i) q^{42} +9.94286 q^{43} +(2.63442 + 5.10080i) q^{44} -1.43433 q^{45} +(1.21167 + 0.880331i) q^{46} +(-2.99615 + 9.22119i) q^{47} +(-2.56571 - 7.89645i) q^{48} +(-6.43830 + 4.67770i) q^{49} +(2.08595 - 1.51553i) q^{50} +(-1.81344 - 5.58119i) q^{51} +(-0.994294 + 3.06012i) q^{52} +(-0.0793422 - 0.0576455i) q^{53} -9.47643 q^{54} +(-0.397822 + 0.402222i) q^{55} -7.48464 q^{56} +(2.73263 + 1.98537i) q^{57} +(0.516200 - 1.58870i) q^{58} +(-0.256040 - 0.788012i) q^{59} +(0.806818 - 0.586188i) q^{60} +(2.98109 - 2.16589i) q^{61} +(-1.29886 - 3.99748i) q^{62} +(10.0499 - 30.9304i) q^{63} +(1.81812 + 1.32094i) q^{64} -0.317070 q^{65} +(-4.08614 + 4.13134i) q^{66} -1.78116 q^{67} +(2.43300 + 1.76768i) q^{68} +(3.01384 - 9.27566i) q^{69} +(-0.105741 - 0.325437i) q^{70} +(-2.85043 + 2.07096i) q^{71} +(13.1653 - 9.56513i) q^{72} +(-0.545031 - 1.67743i) q^{73} +(0.533445 - 1.64178i) q^{74} +(-13.5836 - 9.86908i) q^{75} -1.73096 q^{76} +(-5.88624 - 11.3970i) q^{77} -3.25672 q^{78} +(-2.30171 - 1.67229i) q^{79} +(-0.129567 + 0.398767i) q^{80} +(11.2739 + 34.6976i) q^{81} +(-2.49968 + 1.81612i) q^{82} +(-13.3475 + 9.69750i) q^{83} +(6.98763 + 21.5057i) q^{84} +(-0.0915778 + 0.281847i) q^{85} +(-4.17235 - 3.03139i) q^{86} -10.8779 q^{87} +(0.969183 - 6.34482i) q^{88} +2.70601 q^{89} +(0.601893 + 0.437301i) q^{90} +(2.22161 - 6.83742i) q^{91} +(1.54449 + 4.75344i) q^{92} +(-22.1436 + 16.0883i) q^{93} +(4.06864 - 2.95604i) q^{94} +(-0.0527099 - 0.162224i) q^{95} +(-5.37068 + 16.5293i) q^{96} +(11.3066 + 8.21474i) q^{97} +4.12786 q^{98} +(24.9188 + 12.5246i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 3 q^{2} + 3 q^{3} - 13 q^{4} - 9 q^{5} + 10 q^{6} + 4 q^{7} - q^{8} - 21 q^{9} - 22 q^{10} + 8 q^{11} + 20 q^{12} + 13 q^{13} - 20 q^{14} - 9 q^{15} - 41 q^{16} + 21 q^{17} + 27 q^{18} - 10 q^{19}+ \cdots + 110 q^{99}+O(q^{100}) \) 40 * q + 3 * q^2 + 3 * q^3 - 13 * q^4 - 9 * q^5 + 10 * q^6 + 4 * q^7 - q^8 - 21 * q^9 - 22 * q^10 + 8 * q^11 + 20 * q^12 + 13 * q^13 - 20 * q^14 - 9 * q^15 - 41 * q^16 + 21 * q^17 + 27 * q^18 - 10 * q^19 - 26 * q^20 - 22 * q^21 + q^22 + 16 * q^23 + 12 * q^24 - 53 * q^25 - 14 * q^26 - 24 * q^27 + 29 * q^28 + 11 * q^29 + 10 * q^30 - 13 * q^31 - 4 * q^32 + 34 * q^33 - 38 * q^34 + 25 * q^35 - 61 * q^36 - 7 * q^37 + 3 * q^38 - 16 * q^39 + 77 * q^40 + 17 * q^41 - 12 * q^42 - 24 * q^43 + 29 * q^44 + 130 * q^45 + 32 * q^46 - 5 * q^47 - 6 * q^48 - 42 * q^49 - 5 * q^50 + 40 * q^51 - 19 * q^52 - 30 * q^53 + 52 * q^54 + 72 * q^55 + 74 * q^56 - 7 * q^57 - 67 * q^58 - 23 * q^59 - 94 * q^60 + 36 * q^61 + 35 * q^62 - 7 * q^63 - 111 * q^64 - 26 * q^65 - 9 * q^66 + 52 * q^67 + 70 * q^68 - 95 * q^69 - 38 * q^70 - 34 * q^71 + 112 * q^72 + 31 * q^73 + 80 * q^74 - 84 * q^75 + 42 * q^76 - 25 * q^77 - 90 * q^78 + 32 * q^79 - 58 * q^80 - 28 * q^81 - 50 * q^82 - 83 * q^83 + 135 * q^84 - 23 * q^85 - 45 * q^86 - 42 * q^87 + 101 * q^88 + 96 * q^89 - 4 * q^90 + 33 * q^91 - 48 * q^92 - 91 * q^93 + 67 * q^94 - 9 * q^95 - 18 * q^96 - 10 * q^97 - 90 * q^98 + 110 * q^99

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