LMFDB - Embedded newform 87.2.k.a.2.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [87,2,Mod(2,87)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(87, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([14, 1]))

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

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

chi := DirichletCharacter("87.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	87.k (of order $28$, degree $12$, 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:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			2.7
Character	$\chi$	$=$	87.2
Dual form			87.2.k.a.44.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.255714 - 2.26953i) q^{2} +(0.238726 - 1.71552i) q^{3} +(-3.13550 - 0.715657i) q^{4} +(1.22248 + 1.53294i) q^{5} +(-3.83237 - 0.980478i) q^{6} +(0.968527 + 4.24339i) q^{7} +(-0.917355 + 2.62165i) q^{8} +(-2.88602 - 0.819080i) q^{9} +(3.79166 - 2.38246i) q^{10} +(-0.304506 - 0.870228i) q^{11} +(-1.97625 + 5.20817i) q^{12} +(-0.526689 + 1.09368i) q^{13} +(9.87816 - 1.11300i) q^{14} +(2.92163 - 1.73124i) q^{15} +(-0.0799573 - 0.0385054i) q^{16} +(-4.38493 - 4.38493i) q^{17} +(-2.59692 + 6.34044i) q^{18} +(0.885852 + 1.40983i) q^{19} +(-2.73603 - 5.68142i) q^{20} +(7.51084 - 0.648517i) q^{21} +(-2.05287 + 0.468555i) q^{22} +(2.41688 + 1.92740i) q^{23} +(4.27849 + 2.19960i) q^{24} +(0.257151 - 1.12665i) q^{25} +(2.34745 + 1.47500i) q^{26} +(-2.09412 + 4.75549i) q^{27} -13.9983i q^{28} +(-4.21298 + 3.35422i) q^{29} +(-3.18198 - 7.07342i) q^{30} +(10.4895 + 1.18188i) q^{31} +(-3.06329 + 4.87519i) q^{32} +(-1.56559 + 0.314640i) q^{33} +(-11.0730 + 8.83042i) q^{34} +(-5.32087 + 6.67217i) q^{35} +(8.46293 + 4.63363i) q^{36} +(-5.88562 - 2.05947i) q^{37} +(3.42616 - 1.64995i) q^{38} +(1.75050 + 1.16464i) q^{39} +(-5.14029 + 1.79866i) q^{40} +(2.44440 - 2.44440i) q^{41} +(0.448801 - 17.2119i) q^{42} +(-0.647855 - 5.74987i) q^{43} +(0.331993 + 2.94652i) q^{44} +(-2.27250 - 5.42541i) q^{45} +(4.99231 - 4.99231i) q^{46} +(-2.99334 + 1.04741i) q^{47} +(-0.0851447 + 0.127976i) q^{48} +(-10.7616 + 5.18250i) q^{49} +(-2.49121 - 0.871712i) q^{50} +(-8.56923 + 6.47564i) q^{51} +(2.43413 - 3.05231i) q^{52} +(1.71289 - 1.36599i) q^{53} +(10.2572 + 5.96870i) q^{54} +(0.961757 - 1.53063i) q^{55} +(-12.0132 - 1.35356i) q^{56} +(2.63006 - 1.18313i) q^{57} +(6.53516 + 10.4192i) q^{58} -4.23167i q^{59} +(-10.3998 + 3.33741i) q^{60} +(-3.53348 - 2.22023i) q^{61} +(5.36462 - 23.5040i) q^{62} +(0.680491 - 13.0398i) q^{63} +(10.1423 + 8.08820i) q^{64} +(-2.32042 + 0.529620i) q^{65} +(0.313740 + 3.63360i) q^{66} +(0.236814 + 0.491748i) q^{67} +(10.6108 + 16.8871i) q^{68} +(3.88346 - 3.68609i) q^{69} +(13.7820 + 13.7820i) q^{70} +(6.12060 + 2.94753i) q^{71} +(4.79484 - 6.81474i) q^{72} +(8.47945 - 0.955405i) q^{73} +(-6.17905 + 12.8309i) q^{74} +(-1.87141 - 0.710109i) q^{75} +(-1.76864 - 5.05447i) q^{76} +(3.39780 - 2.13498i) q^{77} +(3.09080 - 3.67498i) q^{78} +(-3.08062 + 8.80389i) q^{79} +(-0.0387197 - 0.169642i) q^{80} +(7.65822 + 4.72776i) q^{81} +(-4.92257 - 6.17270i) q^{82} +(-4.18332 - 0.954815i) q^{83} +(-24.0144 - 3.34176i) q^{84} +(1.36135 - 12.0823i) q^{85} -13.2151 q^{86} +(4.74847 + 8.02820i) q^{87} +2.56077 q^{88} +(-0.344100 + 3.05397i) q^{89} +(-12.8942 + 3.77014i) q^{90} +(-5.15103 - 1.17569i) q^{91} +(-6.19877 - 7.77301i) q^{92} +(4.53166 - 17.7128i) q^{93} +(1.61169 + 7.06129i) q^{94} +(-1.07824 + 3.08145i) q^{95} +(7.63221 + 6.41897i) q^{96} +(4.21195 - 2.64655i) q^{97} +(9.00992 + 25.7489i) q^{98} +(0.166024 + 2.76091i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{3} - 28 q^{4} - 14 q^{6} - 20 q^{7} - 14 q^{9} - 4 q^{10} - 8 q^{12} - 28 q^{13} - 16 q^{15} - 48 q^{16} - 28 q^{18} - 20 q^{19} + 26 q^{21} - 28 q^{22} + 58 q^{24} - 20 q^{25} + 36 q^{27}+ \cdots + 82 q^{99}+O(q^{100}) $ 96 * q - 12 * q^3 - 28 * q^4 - 14 * q^6 - 20 * q^7 - 14 * q^9 - 4 * q^10 - 8 * q^12 - 28 * q^13 - 16 * q^15 - 48 * q^16 - 28 * q^18 - 20 * q^19 + 26 * q^21 - 28 * q^22 + 58 * q^24 - 20 * q^25 + 36 * q^27 + 96 * q^30 - 32 * q^31 + 28 * q^33 - 28 * q^34 + 22 * q^36 - 4 * q^37 - 40 * q^39 - 48 * q^40 - 14 * q^42 - 32 * q^43 + 42 * q^45 + 120 * q^46 - 20 * q^48 + 4 * q^49 - 14 * q^51 + 72 * q^52 - 30 * q^54 + 148 * q^55 + 112 * q^58 + 20 * q^60 + 12 * q^61 - 14 * q^63 + 224 * q^64 - 32 * q^66 + 28 * q^67 + 10 * q^69 + 52 * q^70 - 44 * q^72 + 16 * q^73 - 144 * q^75 - 100 * q^76 - 102 * q^78 - 60 * q^79 - 146 * q^81 - 108 * q^82 - 64 * q^84 - 104 * q^85 - 70 * q^87 - 312 * q^88 - 96 * q^90 - 112 * q^91 - 70 * q^93 + 56 * q^94 - 168 * q^96 + 32 * q^97 + 82 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{1}{28}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.255714	−	2.26953i	0.180817	−	1.60480i	−0.495783	−	0.868446i	$-0.665119\pi$
$2$	0.255714	−	2.26953i	0.180817	−	1.60480i	0.676600	−	0.736350i	$-0.263452\pi$
$3$	0.238726	−	1.71552i	0.137829	−	0.990456i
$3$	0.238726	−	1.71552i	0.137829	−	0.990456i
$4$	−3.13550	−	0.715657i	−1.56775	−	0.357829i
$5$	1.22248	+	1.53294i	0.546710	+	0.685553i	0.976039	−	0.217595i	$-0.0698213\pi$
$5$	1.22248	+	1.53294i	0.546710	+	0.685553i	−0.429329	+	0.903148i	$0.641250\pi$
$6$	−3.83237	−	0.980478i	−1.56456	−	0.400279i
$7$	0.968527	+	4.24339i	0.366069	+	1.60385i	0.737470	+	0.675380i	$0.236020\pi$
$7$	0.968527	+	4.24339i	0.366069	+	1.60385i	−0.371401	+	0.928472i	$0.621123\pi$
$8$	−0.917355	+	2.62165i	−0.324334	+	0.926893i
$9$	−2.88602	−	0.819080i	−0.962006	−	0.273027i
$10$	3.79166	−	2.38246i	1.19903	−	0.753399i
$11$	−0.304506	−	0.870228i	−0.0918120	−	0.262384i	0.888816	−	0.458265i	$-0.151529\pi$
$11$	−0.304506	−	0.870228i	−0.0918120	−	0.262384i	−0.980628	+	0.195881i	$0.937243\pi$
$12$	−1.97625	+	5.20817i	−0.570495	+	1.50347i
$13$	−0.526689	+	1.09368i	−0.146077	+	0.303332i	−0.961150	−	0.276026i	$-0.910982\pi$
$13$	−0.526689	+	1.09368i	−0.146077	+	0.303332i	0.815073	+	0.579358i	$0.196697\pi$
$14$	9.87816	−	1.11300i	2.64005	−	0.297462i
$15$	2.92163	−	1.73124i	0.754362	−	0.447004i
$16$	−0.0799573	−	0.0385054i	−0.0199893	−	0.00962635i
$17$	−4.38493	−	4.38493i	−1.06350	−	1.06350i	−0.997842	−	0.0656596i	$-0.979085\pi$
$17$	−4.38493	−	4.38493i	−1.06350	−	1.06350i	−0.0656596	−	0.997842i	$-0.520915\pi$
$18$	−2.59692	+	6.34044i	−0.612100	+	1.49446i
$19$	0.885852	+	1.40983i	0.203228	+	0.323436i	0.932751	−	0.360520i	$-0.117401\pi$
$19$	0.885852	+	1.40983i	0.203228	+	0.323436i	−0.729523	+	0.683956i	$0.760258\pi$
$20$	−2.73603	−	5.68142i	−0.611794	−	1.27040i
$21$	7.51084	−	0.648517i	1.63900	−	0.141518i
$22$	−2.05287	+	0.468555i	−0.437674	+	0.0998962i
$23$	2.41688	+	1.92740i	0.503954	+	0.401890i	0.842198	−	0.539168i	$-0.181261\pi$
$23$	2.41688	+	1.92740i	0.503954	+	0.401890i	−0.338244	+	0.941059i	$0.609833\pi$
$24$	4.27849	+	2.19960i	0.873344	+	0.448991i
$25$	0.257151	−	1.12665i	0.0514302	−	0.225330i
$26$	2.34745	+	1.47500i	0.460374	+	0.289272i
$27$	−2.09412	+	4.75549i	−0.403013	+	0.915194i
$28$		−	13.9983i		−	2.64543i
$29$	−4.21298	+	3.35422i	−0.782332	+	0.622862i
$29$	−4.21298	+	3.35422i	−0.782332	+	0.622862i
$30$	−3.18198	−	7.07342i	−0.580948	−	1.29142i
$31$	10.4895	+	1.18188i	1.88397	+	0.212272i	0.977638	−	0.210295i	$-0.0674425\pi$
$31$	10.4895	+	1.18188i	1.88397	+	0.212272i	0.906331	+	0.422567i	$0.138871\pi$
$32$	−3.06329	+	4.87519i	−0.541518	+	0.861821i
$33$	−1.56559	+	0.314640i	−0.272534	+	0.0547718i
$34$	−11.0730	+	8.83042i	−1.89900	+	1.51440i
$35$	−5.32087	+	6.67217i	−0.899392	+	1.12780i
$36$	8.46293	+	4.63363i	1.41049	+	0.772271i
$37$	−5.88562	−	2.05947i	−0.967590	−	0.338574i	−0.200200	−	0.979755i	$-0.564159\pi$
$37$	−5.88562	−	2.05947i	−0.967590	−	0.338574i	−0.767390	+	0.641181i	$0.778445\pi$
$38$	3.42616	−	1.64995i	0.555796	−	0.267657i
$39$	1.75050	+	1.16464i	0.280304	+	0.186491i
$40$	−5.14029	+	1.79866i	−0.812751	+	0.284394i
$41$	2.44440	−	2.44440i	0.381752	−	0.381752i	−0.489981	−	0.871733i	$-0.662996\pi$
$41$	2.44440	−	2.44440i	0.381752	−	0.381752i	0.871733	+	0.489981i	$0.162996\pi$
$42$	0.448801	−	17.2119i	0.0692515	−	2.65585i
$43$	−0.647855	−	5.74987i	−0.0987970	−	0.876847i	−0.941166	−	0.337946i	$-0.890268\pi$
$43$	−0.647855	−	5.74987i	−0.0987970	−	0.876847i	0.842369	−	0.538902i	$-0.181161\pi$
$44$	0.331993	+	2.94652i	0.0500499	+	0.444205i
$45$	−2.27250	−	5.42541i	−0.338765	−	0.808773i
$46$	4.99231	−	4.99231i	0.736076	−	0.736076i
$47$	−2.99334	+	1.04741i	−0.436623	+	0.152781i	−0.539635	−	0.841899i	$-0.681438\pi$
$47$	−2.99334	+	1.04741i	−0.436623	+	0.152781i	0.103012	+	0.994680i	$0.467152\pi$
$48$	−0.0851447	+	0.127976i	−0.0122896	+	0.0184718i
$49$	−10.7616	+	5.18250i	−1.53737	+	0.740357i
$50$	−2.49121	−	0.871712i	−0.352310	−	0.123279i
$51$	−8.56923	+	6.47564i	−1.19993	+	0.906771i
$52$	2.43413	−	3.05231i	0.337554	−	0.423279i
$53$	1.71289	−	1.36599i	0.235284	−	0.187633i	−0.498749	−	0.866746i	$-0.666207\pi$
$53$	1.71289	−	1.36599i	0.235284	−	0.187633i	0.734033	+	0.679114i	$0.237636\pi$
$54$	10.2572	+	5.96870i	1.39583	+	0.812237i
$55$	0.961757	−	1.53063i	0.129683	−	0.206390i
$56$	−12.0132	−	1.35356i	−1.60533	−	0.180877i
$57$	2.63006	−	1.18313i	0.348360	−	0.156710i
$58$	6.53516	+	10.4192i	0.858108	+	1.36811i
$59$		−	4.23167i		−	0.550917i	−0.961313	−	0.275458i	$-0.911170\pi$
$59$		−	4.23167i		−	0.550917i	0.961313	−	0.275458i	$-0.0888297\pi$
$60$	−10.3998	+	3.33741i	−1.34260	+	0.430857i
$61$	−3.53348	−	2.22023i	−0.452416	−	0.284272i	0.286487	−	0.958084i	$-0.407513\pi$
$61$	−3.53348	−	2.22023i	−0.452416	−	0.284272i	−0.738902	+	0.673813i	$0.764655\pi$
$62$	5.36462	−	23.5040i	0.681308	−	2.98501i
$63$	0.680491	−	13.0398i	0.0857339	−	1.64286i
$64$	10.1423	+	8.08820i	1.26779	+	1.01103i
$65$	−2.32042	+	0.529620i	−0.287812	+	0.0656913i
$66$	0.313740	+	3.63360i	0.0386187	+	0.447265i
$67$	0.236814	+	0.491748i	0.0289314	+	0.0600766i	0.914934	−	0.403604i	$-0.132243\pi$
$67$	0.236814	+	0.491748i	0.0289314	+	0.0600766i	−0.886002	+	0.463681i	$0.846528\pi$
$68$	10.6108	+	16.8871i	1.28675	+	2.04786i
$69$	3.88346	−	3.68609i	0.467514	−	0.443753i
$70$	13.7820	+	13.7820i	1.64727	+	1.64727i
$71$	6.12060	+	2.94753i	0.726382	+	0.349807i	0.760260	−	0.649619i	$-0.225072\pi$
$71$	6.12060	+	2.94753i	0.726382	+	0.349807i	−0.0338783	+	0.999426i	$0.510786\pi$
$72$	4.79484	−	6.81474i	0.565078	−	0.803125i
$73$	8.47945	−	0.955405i	0.992445	−	0.111822i	0.399217	−	0.916856i	$-0.369282\pi$
$73$	8.47945	−	0.955405i	0.992445	−	0.111822i	0.593228	+	0.805035i	$0.297853\pi$
$74$	−6.17905	+	12.8309i	−0.718300	+	1.49157i
$75$	−1.87141	−	0.710109i	−0.216091	−	0.0819964i
$76$	−1.76864	−	5.05447i	−0.202877	−	0.579788i
$77$	3.39780	−	2.13498i	0.387215	−	0.243303i
$78$	3.09080	−	3.67498i	0.349964	−	0.416110i
$79$	−3.08062	+	8.80389i	−0.346596	+	0.990515i	0.630216	+	0.776420i	$0.282966\pi$
$79$	−3.08062	+	8.80389i	−0.346596	+	0.990515i	−0.976813	+	0.214096i	$0.931320\pi$
$80$	−0.0387197	−	0.169642i	−0.00432899	−	0.0189666i
$81$	7.65822	+	4.72776i	0.850913	+	0.525307i
$82$	−4.92257	−	6.17270i	−0.543606	−	0.681661i
$83$	−4.18332	−	0.954815i	−0.459179	−	0.104805i	−0.0133267	−	0.999911i	$-0.504242\pi$
$83$	−4.18332	−	0.954815i	−0.459179	−	0.104805i	−0.445852	+	0.895107i	$0.647099\pi$
$84$	−24.0144	−	3.34176i	−2.62018	−	0.364616i
$85$	1.36135	−	12.0823i	0.147659	−	1.31051i
$86$	−13.2151			−1.42503
$87$	4.74847	+	8.02820i	0.509090	+	0.860713i
$88$	2.56077			0.272979
$89$	−0.344100	+	3.05397i	−0.0364745	+	0.323720i	0.962204	+	0.272329i	$0.0877940\pi$
$89$	−0.344100	+	3.05397i	−0.0364745	+	0.323720i	−0.998679	+	0.0513908i	$0.983635\pi$
$90$	−12.8942	+	3.77014i	−1.35917	+	0.397408i
$91$	−5.15103	−	1.17569i	−0.539975	−	0.123246i
$92$	−6.19877	−	7.77301i	−0.646266	−	0.810392i
$93$	4.53166	−	17.7128i	0.469912	−	1.83673i
$94$	1.61169	+	7.06129i	0.166234	+	0.728317i
$95$	−1.07824	+	3.08145i	−0.110626	+	0.316150i
$96$	7.63221	+	6.41897i	0.778959	+	0.655133i
$97$	4.21195	−	2.64655i	0.427659	−	0.268716i	−0.300958	−	0.953637i	$-0.597306\pi$
$97$	4.21195	−	2.64655i	0.427659	−	0.268716i	0.728617	+	0.684921i	$0.240164\pi$
$98$	9.00992	+	25.7489i	0.910140	+	2.60103i
$99$	0.166024	+	2.76091i	0.0166860	+	0.277482i
$100$	−1.61259	+	3.34859i	−0.161259	+	0.334859i
$101$	−3.60138	+	0.405778i	−0.358351	+	0.0403764i	−0.289305	−	0.957237i	$-0.593424\pi$
$101$	−3.60138	+	0.405778i	−0.358351	+	0.0403764i	−0.0690460	+	0.997613i	$0.521996\pi$
$102$	12.5053	+	21.1040i	1.23821	+	2.08961i
$103$	−8.82327	−	4.24906i	−0.869382	−	0.418672i	−0.0546471	−	0.998506i	$-0.517403\pi$
$103$	−8.82327	−	4.24906i	−0.869382	−	0.418672i	−0.814735	+	0.579833i	$0.803118\pi$
$104$	−2.38409	−	2.38409i	−0.233779	−	0.233779i
$105$	10.1760	+	10.7209i	0.993076	+	1.04625i
$106$	−2.66213	−	4.23675i	−0.258569	−	0.411510i
$107$	1.05757	+	2.19606i	0.102239	+	0.212301i	0.945813	−	0.324711i	$-0.105267\pi$
$107$	1.05757	+	2.19606i	0.102239	+	0.212301i	−0.843574	+	0.537012i	$0.819553\pi$
$108$	9.96941	−	13.4122i	0.959306	−	1.29059i
$109$	5.21028	−	1.18921i	0.499055	−	0.113906i	0.0344182	−	0.999408i	$-0.489042\pi$
$109$	5.21028	−	1.18921i	0.499055	−	0.113906i	0.464636	+	0.885502i	$0.346185\pi$
$110$	−3.22786	−	2.57414i	−0.307765	−	0.245434i
$111$	−4.93811	+	9.60525i	−0.468705	+	0.911690i
$112$	0.0859528	−	0.376584i	0.00812177	−	0.0355838i
$113$	−7.53601	−	4.73519i	−0.708928	−	0.445449i	0.128705	−	0.991683i	$-0.458918\pi$
$113$	−7.53601	−	4.73519i	−0.708928	−	0.445449i	−0.837633	+	0.546234i	$0.816061\pi$
$114$	−2.01261	−	6.27153i	−0.188498	−	0.587383i
$115$			6.06115i			0.565205i
$116$	15.6103	−	7.50209i	1.44938	−	0.696552i
$117$	2.41585	−	2.72498i	0.223345	−	0.251925i
$118$	−9.60389	−	1.08210i	−0.884110	−	0.0996152i
$119$	14.3601	−	22.8539i	1.31638	−	2.09501i
$120$	1.85852	+	9.24765i	0.169659	+	0.844191i
$121$	7.93557	−	6.32841i	0.721416	−	0.575310i
$122$	−5.94243	+	7.45158i	−0.538003	+	0.674634i
$123$	−3.60988	−	4.77697i	−0.325492	−	0.430724i
$124$	−32.0440	−	11.2127i	−2.87764	−	1.00693i
$125$	10.8741	−	5.23671i	0.972612	−	0.468385i
$126$	−29.4202	−	4.87886i	−2.62096	−	0.434643i
$127$	−14.2831	+	4.99786i	−1.26742	+	0.443488i	−0.878481	−	0.477776i	$-0.841443\pi$
$127$	−14.2831	+	4.99786i	−1.26742	+	0.443488i	−0.388936	+	0.921265i	$0.627157\pi$
$128$	12.8073	−	12.8073i	1.13201	−	1.13201i
$129$	−10.0187	−	0.261238i	−0.882096	−	0.0230007i
$130$	0.608623	+	5.40168i	0.0533798	+	0.473758i
$131$	−0.560570	−	4.97520i	−0.0489772	−	0.434685i	−0.994141	−	0.108089i	$-0.965527\pi$
$131$	−0.560570	−	4.97520i	−0.0489772	−	0.434685i	0.945164	−	0.326596i	$-0.105902\pi$
$132$	5.13408	+	0.133871i	0.446864	+	0.0116520i
$133$	−5.12447	+	5.12447i	−0.444348	+	0.444348i
$134$	1.17659	−	0.411707i	0.101642	−	0.0355661i
$135$	−9.84991	+	2.60333i	−0.847745	+	0.224059i
$136$	15.5183	−	7.47321i	1.33068	−	0.640822i
$137$	−7.12142	−	2.49189i	−0.608424	−	0.212897i	0.00844278	−	0.999964i	$-0.497313\pi$
$137$	−7.12142	−	2.49189i	−0.608424	−	0.212897i	−0.616867	+	0.787068i	$0.711598\pi$
$138$	−7.37261	−	9.75620i	−0.627598	−	0.830503i
$139$	11.9796	−	15.0219i	1.01609	−	1.27414i	0.0548353	−	0.998495i	$-0.482537\pi$
$139$	11.9796	−	15.0219i	1.01609	−	1.27414i	0.961259	−	0.275647i	$-0.0888920\pi$
$140$	21.4586	−	17.1126i	1.81358	−	1.44628i
$141$	1.08227	+	5.38518i	0.0911437	+	0.453514i
$142$	8.25461	−	13.1371i	0.692711	−	1.10244i
$143$	1.11213	+	0.125307i	0.0930011	+	0.0104787i
$144$	0.199219	+	0.176619i	0.0166016	+	0.0147182i
$145$	−10.2921	−	2.35780i	−0.854714	−	0.195805i
$146$		−	19.4886i		−	1.61289i
$147$	6.32161	+	19.6989i	0.521397	+	1.62474i
$148$	16.9805	+	10.6695i	1.39579	+	0.877032i
$149$	−3.80232	+	16.6591i	−0.311498	+	1.36476i	0.540555	+	0.841308i	$0.318214\pi$
$149$	−3.80232	+	16.6591i	−0.311498	+	1.36476i	−0.852054	+	0.523455i	$0.824643\pi$
$150$	−2.09016	+	4.06562i	−0.170661	+	0.331956i
$151$	3.51415	+	2.80244i	0.285977	+	0.228059i	0.755962	−	0.654615i	$-0.227169\pi$
$151$	3.51415	+	2.80244i	0.285977	+	0.228059i	−0.469985	+	0.882674i	$0.655741\pi$
$152$	−4.50871	+	1.02908i	−0.365704	+	0.0834697i
$153$	9.06338	+	16.2466i	0.732731	+	1.31346i
$154$	−3.97652	−	8.25734i	−0.320437	−	0.665395i
$155$	11.0115	+	17.5246i	0.884461	+	1.40761i
$156$	−4.65520	−	4.90447i	−0.372714	−	0.392672i
$157$	−9.97951	−	9.97951i	−0.796451	−	0.796451i	0.186083	−	0.982534i	$-0.440421\pi$
$157$	−9.97951	−	9.97951i	−0.796451	−	0.796451i	−0.982534	+	0.186083i	$0.940421\pi$
$158$	19.1929	+	9.24282i	1.52691	+	0.735319i
$159$	−1.93446	−	3.26460i	−0.153413	−	0.258899i
$160$	−11.2182	+	1.26399i	−0.886877	+	0.0999270i
$161$	−5.83789	+	12.1225i	−0.460090	+	0.955388i
$162$	12.6881	−	16.1716i	0.996870	−	1.27056i
$163$	2.13312	+	6.09610i	0.167079	+	0.477483i	0.996731	−	0.0807978i	$-0.0257468\pi$
$163$	2.13312	+	6.09610i	0.167079	+	0.477483i	−0.829652	+	0.558281i	$0.811461\pi$
$164$	−9.41378	+	5.91507i	−0.735093	+	0.461889i
$165$	−2.39623	−	2.01532i	−0.186546	−	0.156892i
$166$	−3.23671	+	9.24999i	−0.251217	+	0.717938i
$167$	0.00133704	+	0.00585796i	0.000103463	+	0.000453303i	0.974980	−	0.222294i	$-0.0713546\pi$
$167$	0.00133704	+	0.00585796i	0.000103463	+	0.000453303i	−0.974876	+	0.222748i	$0.928497\pi$
$168$	−5.18992	+	20.2857i	−0.400411	+	1.56508i
$169$	7.18663	+	9.01175i	0.552818	+	0.693212i
$170$	−27.0731	−	6.17925i	−2.07641	−	0.473927i
$171$	−1.40183	−	4.79437i	−0.107200	−	0.366634i
$172$	−2.08359	+	18.4924i	−0.158872	+	1.41003i
$173$	−20.1966			−1.53552			−0.767758	−	0.640740i	$-0.778628\pi$
$173$	−20.1966			−1.53552			−0.767758	+	0.640740i	$0.778628\pi$
$174$	19.4345	−	8.72386i	1.47332	−	0.661354i
$175$	5.02989			0.380224
$176$	−0.00916101	+	0.0813062i	−0.000690537	+	0.00612869i
$177$	−7.25952	−	1.01021i	−0.545659	−	0.0759322i
$178$	6.84307	+	1.56189i	0.512910	+	0.117068i
$179$	7.25204	+	9.09377i	0.542043	+	0.679700i	0.975125	−	0.221654i	$-0.0711456\pi$
$179$	7.25204	+	9.09377i	0.542043	+	0.679700i	−0.433083	+	0.901354i	$0.642574\pi$
$180$	3.24269	+	18.6377i	0.241696	+	1.38917i
$181$	−1.34322	−	5.88504i	−0.0998409	−	0.437432i	−0.999998	−	0.00186673i	$-0.999406\pi$
$181$	−1.34322	−	5.88504i	−0.0998409	−	0.437432i	0.900157	−	0.435565i	$-0.143451\pi$
$182$	−3.98545	+	11.3898i	−0.295421	+	0.844265i
$183$	−4.65239	+	5.53173i	−0.343914	+	0.408917i
$184$	−7.27009	+	4.56810i	−0.535958	+	0.336765i
$185$	−4.03801	−	11.5400i	−0.296881	−	0.848436i
$186$	−39.0408	−	14.8141i	−2.86261	−	1.08623i
$187$	−2.48065	+	5.15113i	−0.181403	+	0.376688i
$188$	10.1352	−	1.14196i	0.739185	−	0.0832862i
$189$	−22.2076	−	4.28035i	−1.61537	−	0.311349i
$190$	6.71770	+	3.23507i	0.487353	+	0.234697i
$191$	9.46401	+	9.46401i	0.684792	+	0.684792i	0.961076	−	0.276284i	$-0.0891030\pi$
$191$	9.46401	+	9.46401i	0.684792	+	0.684792i	−0.276284	+	0.961076i	$0.589103\pi$
$192$	16.2967	−	15.4684i	1.17611	−	1.11634i
$193$	2.46006	+	3.91517i	0.177079	+	0.281820i	0.923457	−	0.383703i	$-0.125351\pi$
$193$	2.46006	+	3.91517i	0.177079	+	0.281820i	−0.746377	+	0.665523i	$0.768209\pi$
$194$	−4.92935	−	10.2359i	−0.353906	−	0.734894i
$195$	0.354629	+	4.10716i	0.0253955	+	0.294120i
$196$	37.4518	−	8.54812i	2.67513	−	0.610580i
$197$	11.0474	+	8.81001i	0.787094	+	0.627687i	0.932288	−	0.361716i	$-0.117809\pi$
$197$	11.0474	+	8.81001i	0.787094	+	0.627687i	−0.145194	+	0.989403i	$0.546381\pi$
$198$	6.30841	+	0.329209i	0.448319	+	0.0233958i
$199$	0.625226	−	2.73929i	0.0443211	−	0.194183i	−0.947921	−	0.318506i	$-0.896819\pi$
$199$	0.625226	−	2.73929i	0.0443211	−	0.194183i	0.992242	+	0.124323i	$0.0396759\pi$
$200$	2.71779	+	1.70770i	0.192177	+	0.120753i
$201$	0.900138	−	0.288865i	0.0634908	−	0.0203750i
$202$			8.27719i			0.582381i
$203$	−18.3136	−	14.6287i	−1.28537	−	1.02673i
$204$	31.5032	−	14.1717i	2.20566	−	0.992219i
$205$	6.73536	+	0.758893i	0.470418	+	0.0530034i
$206$	−11.8996	+	18.9381i	−0.829083	+	1.31948i
$207$	−5.39647	−	7.54212i	−0.375081	−	0.524214i
$208$	0.0842252	−	0.0671674i	0.00583997	−	0.00465722i
$209$	0.957123	−	1.20019i	0.0662056	−	0.0830192i
$210$	26.9335	−	20.3532i	1.85859	−	1.40450i
$211$	13.9685	+	4.88779i	0.961631	+	0.336489i	0.765030	−	0.643994i	$-0.222724\pi$
$211$	13.9685	+	4.88779i	0.961631	+	0.336489i	0.196601	+	0.980484i	$0.437010\pi$
$212$	−6.34835	+	3.05720i	−0.436006	+	0.209970i
$213$	6.51769	−	9.79636i	0.446585	−	0.671236i
$214$	5.25445	−	1.83861i	0.359187	−	0.125685i
$215$	8.02224	−	8.02224i	0.547112	−	0.547112i
$216$	−10.5462	−	9.85251i	−0.717576	−	0.670378i
$217$	5.14417	+	45.6558i	0.349209	+	3.09931i
$218$	−1.36661	−	12.1290i	−0.0925583	−	0.821477i
$219$	0.385253	−	14.7748i	0.0260330	−	0.998385i
$220$	−4.11100	+	4.11100i	−0.277163	+	0.277163i
$221$	7.10521	−	2.48622i	0.477948	−	0.167241i
$222$	20.5366	+	13.6634i	1.37833	+	0.917025i
$223$	7.63961	−	3.67904i	0.511586	−	0.246367i	−0.160237	−	0.987079i	$-0.551226\pi$
$223$	7.63961	−	3.67904i	0.511586	−	0.246367i	0.671823	+	0.740712i	$0.265512\pi$
$224$	−23.6542	−	8.27698i	−1.58047	−	0.553029i
$225$	−1.66496	+	3.04091i	−0.110997	+	0.202728i
$226$	−12.6737	+	15.8923i	−0.843041	+	1.05714i
$227$	18.0225	−	14.3725i	1.19620	−	0.953935i	0.196550	−	0.980494i	$-0.437026\pi$
$227$	18.0225	−	14.3725i	1.19620	−	0.953935i	0.999647	+	0.0265586i	$0.00845485\pi$
$228$	−9.09327	+	1.82750i	−0.602217	+	0.121029i
$229$	6.64157	−	10.5700i	0.438887	−	0.698485i	−0.551900	−	0.833910i	$-0.686097\pi$
$229$	6.64157	−	10.5700i	0.438887	−	0.698485i	0.990788	+	0.135425i	$0.0432399\pi$
$230$	13.7559	+	1.54992i	0.907039	+	0.102199i
$231$	−2.85145	−	6.33867i	−0.187612	−	0.417054i
$232$	−4.92877	−	14.1220i	−0.323590	−	0.927153i
$233$			17.4712i			1.14457i	0.820053	+	0.572287i	$0.193944\pi$
$233$			17.4712i			1.14457i	−0.820053	+	0.572287i	$0.806056\pi$
$234$	−5.56665	−	6.17964i	−0.363903	−	0.403976i
$235$	−5.26492	−	3.30817i	−0.343446	−	0.215801i
$236$	−3.02843	+	13.2684i	−0.197134	+	0.863700i
$237$	14.3678	+	7.38658i	0.933291	+	0.479810i
$238$	−48.1954	−	38.4346i	−3.12405	−	2.49134i
$239$	−7.31189	+	1.66889i	−0.472967	+	0.107952i	−0.452359	−	0.891836i	$-0.649417\pi$
$239$	−7.31189	+	1.66889i	−0.472967	+	0.107952i	−0.0206079	+	0.999788i	$0.506560\pi$
$240$	−0.300268	+	0.0259264i	−0.0193822	+	0.00167354i
$241$	0.500275	+	1.03883i	0.0322256	+	0.0669171i	0.916460	−	0.400126i	$-0.131034\pi$
$241$	0.500275	+	1.03883i	0.0322256	+	0.0669171i	−0.884235	+	0.467043i	$0.845319\pi$
$242$	−12.3332	−	19.6282i	−0.792811	−	1.26175i
$243$	9.93879	−	12.0092i	0.637574	−	0.770389i
$244$	9.49030	+	9.49030i	0.607554	+	0.607554i
$245$	−21.1003	−	10.1614i	−1.34805	−	0.649185i
$246$	−11.7645	+	6.97117i	−0.750080	+	0.444466i
$247$	−2.00847	+	0.226300i	−0.127796	+	0.0143991i
$248$	−12.7211	+	26.4156i	−0.807789	+	1.67739i
$249$	−2.63667	+	6.94863i	−0.167092	+	0.440351i
$250$	−9.10417	−	26.0182i	−0.575798	−	1.64554i
$251$	3.03879	−	1.90940i	0.191807	−	0.120520i	−0.432705	−	0.901536i	$-0.642441\pi$
$251$	3.03879	−	1.90940i	0.191807	−	0.120520i	0.624512	+	0.781015i	$0.285298\pi$
$252$	−11.4657	+	40.3993i	−0.722273	+	2.54492i
$253$	0.941321	−	2.69014i	0.0591804	−	0.169128i
$254$	7.69039	+	33.6938i	0.482538	+	2.11414i
$255$	−20.4025	−	5.21980i	−1.27765	−	0.326877i
$256$	−9.61502	−	12.0568i	−0.600938	−	0.753553i
$257$	28.3839	+	6.47844i	1.77054	+	0.404114i	0.978482	−	0.206334i	$-0.0661535\pi$
$257$	28.3839	+	6.47844i	1.77054	+	0.404114i	0.792056	+	0.610448i	$0.209011\pi$
$258$	−3.15480	+	22.6709i	−0.196410	+	1.41143i
$259$	3.03875	−	26.9697i	0.188819	−	1.67581i
$260$	7.65469			0.474724
$261$	14.9061	−	6.22956i	0.922666	−	0.385600i
$262$	−11.4347			−0.706437
$263$	2.13091	−	18.9124i	0.131398	−	1.16619i	−0.738954	−	0.673756i	$-0.764680\pi$
$263$	2.13091	−	18.9124i	0.131398	−	1.16619i	0.870352	−	0.492431i	$-0.163892\pi$
$264$	0.611324	−	4.39306i	0.0376244	−	0.270374i
$265$	4.18796	+	0.955873i	0.257264	+	0.0587188i
$266$	10.3197	+	12.9405i	0.632743	+	0.793434i
$267$	5.15700	+	1.31937i	0.315603	+	0.0807443i
$268$	−0.390605	−	1.71135i	−0.0238600	−	0.104538i
$269$	4.65375	−	13.2997i	0.283744	−	0.810895i	−0.710494	−	0.703703i	$-0.751529\pi$
$269$	4.65375	−	13.2997i	0.283744	−	0.810895i	0.994238	−	0.107191i	$-0.0341858\pi$
$270$	3.38957	+	23.0203i	0.206283	+	1.40097i
$271$	−17.1301	+	10.7636i	−1.04058	+	0.653841i	−0.940030	−	0.341091i	$-0.889203\pi$
$271$	−17.1301	+	10.7636i	−1.04058	+	0.653841i	−0.100551	+	0.994932i	$0.532061\pi$
$272$	0.181764	+	0.519450i	0.0110210	+	0.0314963i
$273$	−3.24661	+	8.55603i	−0.196493	+	0.517834i
$274$	−7.47646	+	15.5250i	−0.451670	+	0.937901i
$275$	−1.05875	+	0.119292i	−0.0638450	+	0.00719360i
$276$	−14.8146	+	8.77849i	−0.891732	+	0.528403i
$277$	−10.5176	−	5.06501i	−0.631942	−	0.304327i	0.0903559	−	0.995910i	$-0.471200\pi$
$277$	−10.5176	−	5.06501i	−0.631942	−	0.304327i	−0.722297	+	0.691583i	$0.756914\pi$
$278$	−31.0293	−	31.0293i	−1.86101	−	1.86101i
$279$	−29.3048	−	12.0027i	−1.75443	−	0.718581i
$280$	−12.6109	−	20.0702i	−0.753648	−	1.19942i
$281$	−2.12781	−	4.41844i	−0.126935	−	0.263582i	0.827810	−	0.561008i	$-0.189586\pi$
$281$	−2.12781	−	4.41844i	−0.126935	−	0.263582i	−0.954745	+	0.297426i	$0.903872\pi$
$282$	12.4985	−	1.07918i	0.744278	−	0.0642640i
$283$	−7.85956	+	1.79389i	−0.467202	+	0.106636i	−0.449640	−	0.893210i	$-0.648448\pi$
$283$	−7.85956	+	1.79389i	−0.467202	+	0.106636i	−0.0175624	+	0.999846i	$0.505591\pi$
$284$	−17.0817	−	13.6222i	−1.01361	−	0.808330i
$285$	5.02888	+	2.58537i	0.297885	+	0.153144i
$286$	0.568776	−	2.49197i	0.0336324	−	0.147353i
$287$	12.7400	+	8.00509i	0.752020	+	0.472526i
$288$	12.8339	−	11.5608i	0.756244	−	0.681228i
$289$			21.4552i			1.26207i
$290$	−7.98292	+	22.7553i	−0.468773	+	1.33624i
$291$	−3.53470	−	7.85749i	−0.207208	−	0.460614i
$292$	−27.2711	−	3.07271i	−1.59592	−	0.179817i
$293$	−5.38901	+	8.57656i	−0.314829	+	0.501048i	−0.966228	−	0.257687i	$-0.917040\pi$
$293$	−5.38901	+	8.57656i	−0.314829	+	0.501048i	0.651399	+	0.758735i	$0.274182\pi$
$294$	46.3236	−	9.30977i	2.70165	−	0.542957i
$295$	6.48691	−	5.17314i	0.377683	−	0.301192i
$296$	10.7984	−	13.5408i	0.627644	−	0.787041i
$297$	4.77603	+	0.374285i	0.277134	+	0.0217182i
$298$	36.8358	+	12.8894i	2.13384	+	0.746664i
$299$	−3.38090	+	1.62816i	−0.195523	+	0.0941587i
$300$	5.35960	+	3.56583i	0.309437	+	0.205873i
$301$	23.7715	−	8.31801i	1.37017	−	0.479442i
$302$	7.25883	−	7.25883i	0.417699	−	0.417699i
$303$	−0.163624	+	6.27511i	−0.00939996	+	0.360496i
$304$	−0.0165444	−	0.146836i	−0.000948888	−	0.00842161i
$305$	−0.916123	−	8.13081i	−0.0524570	−	0.465569i
$306$	39.1897	−	16.4151i	2.24033	−	0.938388i
$307$	−19.9438	+	19.9438i	−1.13825	+	1.13825i	−0.149489	+	0.988763i	$0.547763\pi$
$307$	−19.9438	+	19.9438i	−1.13825	+	1.13825i	−0.988763	+	0.149489i	$0.952237\pi$
$308$	−12.1817	+	4.26257i	−0.694117	+	0.242882i
$309$	−9.39570	+	14.1221i	−0.534503	+	0.803380i
$310$	42.5884	−	20.5095i	2.41886	−	1.16486i
$311$	28.2925	+	9.89997i	1.60432	+	0.561376i	0.976225	−	0.216760i	$-0.0695490\pi$
$311$	28.2925	+	9.89997i	1.60432	+	0.561376i	0.628096	+	0.778136i	$0.283835\pi$
$312$	−4.65909	+	3.52080i	−0.263769	+	0.199326i
$313$	−2.90318	+	3.64047i	−0.164097	+	0.205772i	−0.857081	−	0.515182i	$-0.827724\pi$
$313$	−2.90318	+	3.64047i	−0.164097	+	0.205772i	0.692984	+	0.720953i	$0.256296\pi$
$314$	−25.2006	+	20.0968i	−1.42215	+	1.13413i
$315$	20.8212	−	14.8978i	1.17314	−	0.839395i
$316$	15.9598	−	25.3999i	0.897811	−	1.42886i
$317$	−23.2288	−	2.61725i	−1.30466	−	0.147000i	−0.567867	−	0.823120i	$-0.692231\pi$
$317$	−23.2288	−	2.61725i	−1.30466	−	0.147000i	−0.736791	+	0.676121i	$0.763660\pi$
$318$	−7.90376	+	3.55551i	−0.443221	+	0.199383i
$319$	4.20181	+	2.64488i	0.235256	+	0.148085i
$320$			25.4352i			1.42187i
$321$	4.01985	−	1.29002i	0.224366	−	0.0720019i
$322$	26.0195	+	16.3491i	1.45001	+	0.911102i
$323$	2.29759	−	10.0664i	0.127841	−	0.560109i
$324$	−20.6289	−	20.3046i	−1.14605	−	1.12803i
$325$	1.09676	+	0.874636i	0.0608373	+	0.0485161i
$326$	14.3807	−	3.28230i	0.796474	−	0.181790i
$327$	−0.796287	−	9.22224i	−0.0440348	−	0.509991i
$328$	4.16598	+	8.65075i	0.230028	+	0.477658i
$329$	−7.34372	−	11.6875i	−0.404872	−	0.644351i
$330$	−5.18656	+	4.92295i	−0.285511	+	0.271000i
$331$	−11.5323	−	11.5323i	−0.633875	−	0.633875i	0.315163	−	0.949038i	$-0.397941\pi$
$331$	−11.5323	−	11.5323i	−0.633875	−	0.633875i	−0.949038	+	0.315163i	$0.897941\pi$
$332$	12.4335	+	5.98764i	0.682375	+	0.328615i
$333$	15.2991	+	10.7645i	0.838388	+	0.589889i
$334$	0.0136367	−	0.00153649i	0.000746167	−	8.40728e-5i
$335$	−0.464322	+	0.964175i	−0.0253686	+	0.0526785i
$336$	−0.625518	−	0.237354i	−0.0341248	−	0.0129487i
$337$	−2.05189	−	5.86397i	−0.111774	−	0.319431i	0.874386	−	0.485232i	$-0.161265\pi$
$337$	−2.05189	−	5.86397i	−0.111774	−	0.319431i	−0.986159	+	0.165801i	$0.946979\pi$
$338$	22.2901	−	14.0058i	1.21242	−	0.761816i
$339$	−9.92235	+	11.7978i	−0.538908	+	0.640766i
$340$	−12.9153	+	36.9099i	−0.700432	+	2.00172i
$341$	−2.16561	−	9.48815i	−0.117274	−	0.513812i
$342$	−11.2394	+	1.95549i	−0.607757	+	0.105741i
$343$	−13.4180	−	16.8256i	−0.724502	−	0.908497i
$344$	15.6685	+	3.57622i	0.844787	+	0.192817i
$345$	10.3980	+	1.44696i	0.559810	+	0.0779015i
$346$	−5.16454	+	45.8366i	−0.277648	+	2.46419i
$347$	−21.7588			−1.16807			−0.584037	−	0.811727i	$-0.698528\pi$
$347$	−21.7588			−1.16807			−0.584037	+	0.811727i	$0.698528\pi$
$348$	−9.14340	−	28.5707i	−0.490138	−	1.53155i
$349$	−27.3902			−1.46616			−0.733081	−	0.680142i	$-0.761918\pi$
$349$	−27.3902			−1.46616			−0.733081	+	0.680142i	$0.761918\pi$
$350$	1.28621	−	11.4155i	0.0687510	−	0.610182i
$351$	−4.09804	−	4.79496i	−0.218737	−	0.255936i
$352$	5.17532	+	1.18123i	0.275846	+	0.0629600i
$353$	1.83355	+	2.29920i	0.0975900	+	0.122374i	0.828229	−	0.560390i	$-0.189349\pi$
$353$	1.83355	+	2.29920i	0.0975900	+	0.122374i	−0.730639	+	0.682764i	$0.760778\pi$
$354$	−4.14906	+	16.2173i	−0.220520	+	0.861942i
$355$	2.96393	+	12.9858i	0.157309	+	0.689216i
$356$	3.26452	−	9.32946i	0.173019	−	0.494460i
$357$	−35.7782	−	30.0908i	−1.89358	−	1.59257i
$358$	22.4930	−	14.1333i	1.18879	−	0.746967i
$359$	11.1483	+	31.8601i	0.588387	+	1.68151i	0.723197	+	0.690641i	$0.242672\pi$
$359$	11.1483	+	31.8601i	0.588387	+	1.68151i	−0.134811	+	0.990871i	$0.543043\pi$
$360$	16.3082	−	0.980673i	0.859518	−	0.0516860i
$361$	7.04092	−	14.6206i	0.370575	−	0.769506i
$362$	−13.6997	+	1.54359i	−0.720042	+	0.0811292i
$363$	−8.96208	−	15.1244i	−0.470387	−	0.793825i
$364$	15.3097	+	7.37275i	0.802444	+	0.386437i
$365$	11.8306	+	11.8306i	0.619239	+	0.619239i
$366$	11.3647	+	11.9733i	0.594043	+	0.625852i
$367$	−2.28042	−	3.62926i	−0.119037	−	0.189446i	0.781891	−	0.623415i	$-0.214255\pi$
$367$	−2.28042	−	3.62926i	−0.119037	−	0.189446i	−0.900928	+	0.433969i	$0.857113\pi$
$368$	−0.119032	−	0.247172i	−0.00620497	−	0.0128847i
$369$	−9.05675	+	5.05243i	−0.471476	+	0.263019i
$370$	−27.2229	+	6.21344i	−1.41525	+	0.323021i
$371$	7.45540	+	5.94548i	0.387065	+	0.308674i
$372$	−26.8853	+	52.2954i	−1.39394	+	2.71139i
$373$	−4.09626	+	17.9469i	−0.212096	+	0.929255i	0.751043	+	0.660253i	$0.229551\pi$
$373$	−4.09626	+	17.9469i	−0.212096	+	0.929255i	−0.963140	+	0.269002i	$0.913306\pi$
$374$	11.0563	+	6.94712i	0.571706	+	0.359227i
$375$	−6.38774	−	19.9049i	−0.329861	−	1.02789i
$376$		−	8.80833i		−	0.454255i
$377$	−1.44951	−	6.37429i	−0.0746535	−	0.328293i
$378$	−15.3932	+	49.3062i	−0.791738	+	2.53604i
$379$	21.1100	+	2.37852i	1.08435	+	0.122176i	0.636004	−	0.771686i	$-0.280586\pi$
$379$	21.1100	+	2.37852i	1.08435	+	0.122176i	0.448342	+	0.893862i	$0.352015\pi$
$380$	5.58609	−	8.89022i	0.286561	−	0.456059i
$381$	5.16419	+	25.6960i	0.264569	+	1.31645i
$382$	23.8989	−	19.0587i	1.22277	−	0.975130i
$383$	−1.11105	+	1.39321i	−0.0567718	+	0.0711896i	−0.809407	−	0.587248i	$-0.800211\pi$
$383$	−1.11105	+	1.39321i	−0.0567718	+	0.0711896i	0.752635	+	0.658438i	$0.228783\pi$
$384$	−18.9137	−	25.0286i	−0.965185	−	1.27723i
$385$	7.42655	+	2.59866i	0.378492	+	0.132440i
$386$	9.51464	−	4.58201i	0.484283	−	0.233218i
$387$	−2.83988	+	17.1249i	−0.144359	+	0.870507i
$388$	−15.1006	+	5.28393i	−0.766617	+	0.268251i
$389$	18.1731	−	18.1731i	0.921411	−	0.921411i	−0.0757178	−	0.997129i	$-0.524125\pi$
$389$	18.1731	−	18.1731i	0.921411	−	0.921411i	0.997129	+	0.0757178i	$0.0241248\pi$
$390$	9.41198	+	0.245418i	0.476594	+	0.0124272i
$391$	−2.14635	−	19.0493i	−0.108545	−	0.963367i
$392$	−3.71451	−	32.9672i	−0.187611	−	1.66510i
$393$	−8.66887	−	0.226042i	−0.437287	−	0.0114023i
$394$	22.8195	−	22.8195i	1.14963	−	1.14963i
$395$	−17.2619	+	6.04019i	−0.868538	+	0.303915i
$396$	1.45530	−	8.77565i	0.0731315	−	0.440993i
$397$	18.9892	−	9.14473i	0.953042	−	0.458961i	0.108290	−	0.994119i	$-0.465462\pi$
$397$	18.9892	−	9.14473i	0.953042	−	0.458961i	0.844752	+	0.535159i	$0.179748\pi$
$398$	−6.05702	−	2.11944i	−0.303611	−	0.106238i
$399$	7.56779	+	10.0145i	0.378863	+	0.501351i
$400$	−0.0639433	+	0.0801823i	−0.00319716	+	0.00400912i
$401$	−28.3608	+	22.6170i	−1.41627	+	1.12944i	−0.443878	+	0.896087i	$0.646397\pi$
$401$	−28.3608	+	22.6170i	−1.41627	+	1.12944i	−0.972393	+	0.233350i	$0.925031\pi$
$402$	−0.425409	−	2.11675i	−0.0212175	−	0.105574i
$403$	−6.81730	+	10.8497i	−0.339594	+	0.540461i
$404$	11.5825	+	1.30504i	0.576252	+	0.0649280i
$405$	2.11464	+	17.5192i	0.105077	+	0.870536i
$406$	−37.8833	+	37.8225i	−1.88012	+	1.87710i
$407$			5.74895i			0.284965i
$408$	−9.11582	−	28.4060i	−0.451300	−	1.40631i
$409$	23.8836	+	15.0071i	1.18097	+	0.742052i	0.971795	−	0.235826i	$-0.0757796\pi$
$409$	23.8836	+	15.0071i	1.18097	+	0.742052i	0.209174	+	0.977878i	$0.432922\pi$
$410$	3.44466	−	15.0920i	0.170119	−	0.745342i
$411$	−5.97496	+	11.6221i	−0.294723	+	0.573274i
$412$	24.6245	+	19.6374i	1.21316	+	0.967464i
$413$	17.9567	−	4.09849i	0.883589	−	0.201673i
$414$	−18.4970	+	10.3188i	−0.909078	+	0.507141i
$415$	−3.65035	−	7.58003i	−0.179189	−	0.372089i
$416$	−3.71851	−	5.91797i	−0.182315	−	0.290152i
$417$	−22.9106	−	24.1373i	−1.12193	−	1.18201i
$418$	−2.47912	−	2.47912i	−0.121258	−	0.121258i
$419$	−14.1065	−	6.79335i	−0.689149	−	0.331877i	0.0563240	−	0.998413i	$-0.482062\pi$
$419$	−14.1065	−	6.79335i	−0.689149	−	0.331877i	−0.745473	+	0.666536i	$0.767776\pi$
$420$	−24.2344	−	40.8979i	−1.18252	−	1.99561i
$421$	−30.8054	+	3.47094i	−1.50137	+	0.169163i	−0.824045	−	0.566525i	$-0.808288\pi$
$421$	−30.8054	+	3.47094i	−1.50137	+	0.169163i	−0.677321	+	0.735688i	$0.736859\pi$
$422$	14.6649	−	30.4520i	0.713876	−	1.48238i
$423$	9.49675	−	0.571074i	0.461748	−	0.0277666i
$424$	2.00981	+	5.74369i	0.0976048	+	0.278938i
$425$	−6.06788	+	3.81270i	−0.294335	+	0.184943i
$426$	−20.5664	−	17.2971i	−0.996447	−	0.838049i
$427$	5.99905	−	17.1443i	0.290314	−	0.829671i
$428$	−1.74437	−	7.64260i	−0.0843175	−	0.369419i
$429$	0.480462	−	1.87797i	0.0231969	−	0.0906693i
$430$	−16.1553	−	20.2581i	−0.779076	−	0.976931i
$431$	−12.2814	−	2.80314i	−0.591573	−	0.135023i	−0.0837541	−	0.996486i	$-0.526691\pi$
$431$	−12.2814	−	2.80314i	−0.591573	−	0.135023i	−0.507819	+	0.861464i	$0.669548\pi$
$432$	0.350552	−	0.299601i	0.0168659	−	0.0144146i
$433$	0.0498950	−	0.442830i	0.00239780	−	0.0212811i	−0.992456	−	0.122599i	$-0.960877\pi$
$433$	0.0498950	−	0.442830i	0.00239780	−	0.0212811i	0.994854	+	0.101318i	$0.0323058\pi$
$434$	104.932			5.03691
$435$	−6.50185	+	17.0935i	−0.311740	+	0.819569i
$436$	−17.1879			−0.823152
$437$	−0.576296	+	5.11477i	−0.0275680	+	0.244673i
$438$	−33.4332	−	4.65245i	−1.59750	−	0.222303i
$439$	−4.58884	−	1.04737i	−0.219013	−	0.0499883i	0.111606	−	0.993753i	$-0.464400\pi$
$439$	−4.58884	−	1.04737i	−0.219013	−	0.0499883i	−0.330619	+	0.943764i	$0.607258\pi$
$440$	3.13050	+	3.92552i	0.149241	+	0.187142i
$441$	35.3030	−	6.14220i	1.68109	−	0.292486i
$442$	−3.82564	−	16.7612i	−0.181967	−	0.797249i
$443$	4.46740	−	12.7671i	0.212253	−	0.606583i	−0.787703	−	0.616056i	$-0.788730\pi$
$443$	4.46740	−	12.7671i	0.212253	−	0.606583i	0.999955	+	0.00947284i	$0.00301534\pi$
$444$	22.3575	−	26.5833i	1.06104	−	1.26159i
$445$	−5.10221	+	3.20593i	−0.241868	+	0.151976i
$446$	−6.39613	−	18.2791i	−0.302865	−	0.865539i
$447$	27.6712	+	10.4999i	1.30880	+	0.496629i
$448$	−24.4983	+	50.8713i	−1.15744	+	2.40344i
$449$	−26.9196	+	3.03311i	−1.27042	+	0.143142i	−0.721311	−	0.692612i	$-0.756460\pi$
$449$	−26.9196	+	3.03311i	−1.27042	+	0.143142i	−0.549105	+	0.835753i	$0.685031\pi$
$450$	6.47568	+	4.55628i	0.305266	+	0.214785i
$451$	−2.87152	−	1.38285i	−0.135215	−	0.0651160i
$452$	20.2404	+	20.2404i	0.952027	+	0.952027i
$453$	5.64656	−	5.35958i	0.265299	−	0.251815i
$454$	−28.0101	−	44.5778i	−1.31458	−	2.09214i
$455$	−4.49477	−	9.33349i	−0.210718	−	0.437561i
$456$	0.689065	+	7.98045i	0.0322684	+	0.373719i
$457$	−10.7710	+	2.45840i	−0.503845	+	0.114999i	−0.466886	−	0.884318i	$-0.654624\pi$
$457$	−10.7710	+	2.45840i	−0.503845	+	0.114999i	−0.0369587	+	0.999317i	$0.511767\pi$
$458$	−22.2905	−	17.7761i	−1.04157	−	0.830623i
$459$	30.0350	−	11.6699i	1.40192	−	0.544705i
$460$	4.33770	−	19.0047i	0.202246	−	0.886100i
$461$	0.0837455	+	0.0526208i	0.00390042	+	0.00245079i	0.533981	−	0.845497i	$-0.320695\pi$
$461$	0.0837455	+	0.0526208i	0.00390042	+	0.00245079i	−0.530080	+	0.847947i	$0.677838\pi$
$462$	−15.1149	+	4.85056i	−0.703210	+	0.225669i
$463$		−	23.8232i		−	1.10716i	−0.832796	−	0.553580i	$-0.813261\pi$
$463$		−	23.8232i		−	1.10716i	0.832796	−	0.553580i	$-0.186739\pi$
$464$	0.466014	−	0.105971i	0.0216342	−	0.00491959i
$465$	32.6926	−	14.7068i	1.51608	−	0.682011i
$466$	39.6513	+	4.46763i	1.83681	+	0.206959i
$467$	12.6736	−	20.1700i	0.586466	−	0.933355i	−0.413275	−	0.910606i	$-0.635615\pi$
$467$	12.6736	−	20.1700i	0.586466	−	0.933355i	0.999741	−	0.0227488i	$-0.00724180\pi$
$468$	−9.52504	+	6.81527i	−0.440295	+	0.315036i
$469$	−1.85732	+	1.48116i	−0.0857632	+	0.0683938i
$470$	−8.85429	+	11.1029i	−0.408418	+	0.512140i
$471$	−19.5024	+	14.7377i	−0.898624	+	0.679076i
$472$	11.0940	+	3.88194i	0.510641	+	0.178681i
$473$	−4.80643	+	2.31465i	−0.221000	+	0.106428i
$474$	20.4381	−	30.7193i	0.938753	−	1.41098i
$475$	1.81618	−	0.635509i	0.0833321	−	0.0291592i
$476$	−61.3815	+	61.3815i	−2.81342	+	2.81342i
$477$	−6.06229	+	2.53927i	−0.277573	+	0.116265i
$478$	1.91784	+	17.0213i	0.0877198	+	0.778535i
$479$	3.60700	+	32.0131i	0.164808	+	1.46271i	0.755146	+	0.655557i	$0.227566\pi$
$479$	3.60700	+	32.0131i	0.164808	+	1.46271i	−0.590337	+	0.807157i	$0.701005\pi$
$480$	−0.509685	+	19.5468i	−0.0232638	+	0.892186i
$481$	5.35229	−	5.35229i	0.244043	−	0.244043i
$482$	2.48558	−	0.869743i	0.113215	−	0.0396157i
$483$	19.4027	+	12.9090i	0.882856	+	0.587379i
$484$	−29.4110	+	14.1636i	−1.33686	+	0.643799i
$485$	9.20603	+	3.22133i	0.418025	+	0.146273i
$486$	−24.7137	−	25.6273i	−1.12103	−	1.16248i
$487$	13.2800	−	16.6526i	0.601775	−	0.754602i	−0.383878	−	0.923384i	$-0.625412\pi$
$487$	13.2800	−	16.6526i	0.601775	−	0.754602i	0.985654	+	0.168781i	$0.0539832\pi$
$488$	9.06212	−	7.22680i	0.410223	−	0.327142i
$489$	10.9672	−	2.20411i	0.495954	−	0.0996731i
$490$	−28.4571	+	45.2892i	−1.28556	+	2.04596i
$491$	22.6585	+	2.55300i	1.02256	+	0.115215i	0.607289	−	0.794481i	$-0.292257\pi$
$491$	22.6585	+	2.55300i	1.02256	+	0.115215i	0.415274	+	0.909696i	$0.363686\pi$
$492$	7.90010	+	17.5616i	0.356164	+	0.791738i
$493$	33.1816	+	3.76564i	1.49443	+	0.169596i
$494$			4.61614i			0.207690i
$495$	−4.02936	+	3.62967i	−0.181106	+	0.163141i
$496$	−0.793203	−	0.498402i	−0.0356159	−	0.0223789i
$497$	−6.57955	+	28.8269i	−0.295133	+	1.29306i
$498$	15.0959	+	7.76086i	0.676461	+	0.347772i
$499$	−14.9065	−	11.8876i	−0.667308	−	0.532160i	0.230209	−	0.973141i	$-0.426059\pi$
$499$	−14.9065	−	11.8876i	−0.667308	−	0.532160i	−0.897516	+	0.440981i	$0.854631\pi$
$500$	−37.8435	+	8.63754i	−1.69241	+	0.386283i
$501$	0.0103686		0.000895272i	0.000463237		3.99978e-5i
$502$	−3.55637	−	7.38487i	−0.158728	−	0.329603i
$503$	15.6116	+	24.8457i	0.696085	+	1.10781i	0.988456	+	0.151508i	$0.0484129\pi$
$503$	15.6116	+	24.8457i	0.696085	+	1.10781i	−0.292371	+	0.956305i	$0.594444\pi$
$504$	33.5616	+	13.7461i	1.49495	+	0.612302i
$505$	−5.02465	−	5.02465i	−0.223594	−	0.223594i
$506$	−5.86463	−	2.82426i	−0.260715	−	0.125554i
$507$	17.1755	−	10.1775i	0.762790	−	0.451997i
$508$	48.3613	−	5.44901i	2.14569	−	0.241761i
$509$	13.5768	−	28.1924i	0.601779	−	1.24961i	−0.348237	−	0.937406i	$-0.613220\pi$
$509$	13.5768	−	28.1924i	0.601779	−	1.24961i	0.950016	−	0.312200i	$-0.101066\pi$
$510$	−17.0637	+	44.9692i	−0.755593	+	1.99127i
$511$	12.2667	+	35.0563i	0.542649	+	1.55080i
$512$	0.850076	−	0.534138i	0.0375684	−	0.0236058i
$513$	−8.55949	+	1.26032i	−0.377911	+	0.0556445i
$514$	21.9611	−	62.7613i	0.968664	−	2.76828i
$515$	−4.27271	−	18.7200i	−0.188278	−	0.824900i
$516$	31.2266	+	7.98906i	1.37468	+	0.351699i
$517$	1.82298	+	2.28594i	0.0801745	+	0.100536i
$518$	−60.4313	−	13.7930i	−2.65520	−	0.606032i
$519$	−4.82145	+	34.6476i	−0.211638	+	1.52086i
$520$	0.740167	−	6.56917i	0.0324585	−	0.288077i
$521$	−15.7366			−0.689434			−0.344717	−	0.938707i	$-0.612025\pi$
$521$	−15.7366			−0.689434			−0.344717	+	0.938707i	$0.612025\pi$
$522$	−10.3264	−	35.4228i	−0.451976	−	1.55041i
$523$	8.79883			0.384746			0.192373	−	0.981322i	$-0.438382\pi$
$523$	8.79883			0.384746			0.192373	+	0.981322i	$0.438382\pi$
$524$	−1.80287	+	16.0009i	−0.0787587	+	0.699003i
$525$	1.20077	−	8.62887i	0.0524058	−	0.376595i
$526$	−42.3772	−	9.67232i	−1.84773	−	0.421733i
$527$	−40.8132	−	51.1782i	−1.77785	−	2.22936i
$528$	0.137295	+	0.0351258i	0.00597502	+	0.00152866i
$529$	−2.99153	−	13.1068i	−0.130067	−	0.569859i
$530$	3.24030	−	9.26024i	0.140750	−	0.402239i
$531$	−3.46608	+	12.2127i	−0.150415	+	0.529986i
$532$	19.7352	−	12.4004i	0.855627	−	0.537626i
$533$	1.38596	+	3.96084i	0.0600324	+	0.171563i
$534$	4.31307	−	11.3666i	0.186645	−	0.491879i
$535$	−2.07358	+	4.30583i	−0.0896486	+	0.186157i
$536$	−1.50643	+	0.169734i	−0.0650680	+	0.00733141i
$537$	17.3318	−	10.2701i	0.747922	−	0.443187i
$538$	−28.9939	−	13.9627i	−1.25002	−	0.601976i
$539$	7.78692	+	7.78692i	0.335406	+	0.335406i
$540$	32.7475	−	1.11359i	1.40923	−	0.0479212i
$541$	7.17314	+	11.4160i	0.308398	+	0.490812i	0.964580	−	0.263790i	$-0.0849727\pi$
$541$	7.17314	+	11.4160i	0.308398	+	0.490812i	−0.656182	+	0.754602i	$0.727830\pi$
$542$	20.0478	+	41.6297i	0.861126	+	1.78815i
$543$	−10.4166	+	0.899410i	−0.447018	+	0.0385974i
$544$	34.8097	−	7.94508i	1.49245	−	0.340643i
$545$	8.19247	+	6.53328i	0.350927	+	0.279855i
$546$	18.5879	+	9.55615i	0.795490	+	0.408965i
$547$	−3.44838	+	15.1083i	−0.147442	+	0.645985i	0.846149	+	0.532947i	$0.178915\pi$
$547$	−3.44838	+	15.1083i	−0.147442	+	0.645985i	−0.993591	+	0.113039i	$0.963942\pi$
$548$	20.5459	+	12.9098i	0.877676	+	0.551480i
$549$	8.37914	+	9.30184i	0.357613	+	0.396993i
$550$			2.43336i			0.103759i
$551$	−8.46094	−	2.96823i	−0.360448	−	0.126451i
$552$	6.10111	+	13.5625i	0.259680	+	0.577259i
$553$	−40.3420	−	4.54546i	−1.71552	−	0.193293i
$554$	−14.1847	+	22.5748i	−0.602649	+	0.959110i
$555$	−20.7611	+	4.17240i	−0.881258	+	0.177108i
$556$	−48.3125	+	38.5279i	−2.04891	+	1.63395i
$557$	4.04179	−	5.06825i	0.171256	−	0.214748i	−0.688795	−	0.724956i	$-0.741860\pi$
$557$	4.04179	−	5.06825i	0.171256	−	0.214748i	0.860051	+	0.510208i	$0.170431\pi$
$558$	−34.7340	+	63.4388i	−1.47041	+	2.68558i
$559$	6.62974	+	2.31985i	0.280408	+	0.0981191i
$560$	0.682357	−	0.328606i	0.0288348	−	0.0138861i
$561$	8.24467	+	5.48532i	0.348090	+	0.231590i
$562$	−10.5719	+	3.69926i	−0.445948	+	0.156044i
$563$	−25.9488	+	25.9488i	−1.09361	+	1.09361i	−0.0984717	+	0.995140i	$0.531395\pi$
$563$	−25.9488	+	25.9488i	−1.09361	+	1.09361i	−0.995140	+	0.0984717i	$0.968605\pi$
$564$	0.460480	−	17.6598i	0.0193897	−	0.743610i
$565$	−1.95386	−	17.3409i	−0.0821993	−	0.729539i
$566$	2.06149	+	18.2962i	0.0866507	+	0.769047i
$567$	−12.6446	+	37.0758i	−0.531022	+	1.55704i
$568$	−13.3421	+	13.3421i	−0.559824	+	0.559824i
$569$	11.3456	−	3.97000i	0.475632	−	0.166431i	−0.0818078	−	0.996648i	$-0.526069\pi$
$569$	11.3456	−	3.97000i	0.475632	−	0.166431i	0.557440	+	0.830217i	$0.311784\pi$
$570$	7.15352	−	10.7520i	0.299628	−	0.450354i
$571$	−7.18785	+	3.46149i	−0.300802	+	0.144859i	−0.578197	−	0.815897i	$-0.696243\pi$
$571$	−7.18785	+	3.46149i	−0.300802	+	0.144859i	0.277395	+	0.960756i	$0.410529\pi$
$572$	−3.39741	−	1.18881i	−0.142053	−	0.0497065i
$573$	18.4950	−	13.9764i	0.772640	−	0.583872i
$574$	21.4256	−	26.8668i	0.894286	−	1.12140i
$575$	2.79301	−	2.22735i	0.116477	−	0.0928870i
$576$	−22.6459	−	31.6500i	−0.943581	−	1.31875i
$577$	18.2757	−	29.0856i	0.760828	−	1.21085i	−0.211534	−	0.977371i	$-0.567846\pi$
$577$	18.2757	−	29.0856i	0.760828	−	1.21085i	0.972362	−	0.233480i	$-0.0750112\pi$
$578$	48.6932	+	5.48640i	2.02537	+	0.228204i
$579$	7.30383	−	3.28563i	0.303537	−	0.136546i
$580$	30.5835	+	14.7585i	1.26991	+	0.612814i
$581$		−	18.6762i		−	0.774821i
$582$	−18.7366	+	6.01281i	−0.776659	+	0.249239i
$583$	−1.71031	−	1.07466i	−0.0708336	−	0.0445077i
$584$	−5.27393	+	23.1066i	−0.218237	+	0.956158i
$585$	7.13057	+	0.372113i	0.294813	+	0.0153850i
$586$	18.0867	+	14.4236i	0.747153	+	0.595835i
$587$	−26.4964	+	6.04763i	−1.09362	+	0.249613i	−0.731037	−	0.682338i	$-0.760963\pi$
$587$	−26.4964	+	6.04763i	−1.09362	+	0.249613i	−0.362587	+	0.931950i	$0.618106\pi$
$588$	−5.72375	−	66.2899i	−0.236043	−	2.73375i
$589$	7.62590	+	15.8353i	0.314220	+	0.652484i
$590$	−10.0818	−	16.0451i	−0.415060	−	0.660565i
$591$	17.7510	−	16.8489i	0.730181	−	0.693069i
$592$	0.391298	+	0.391298i	0.0160822	+	0.0160822i
$593$	13.5958	+	6.54740i	0.558313	+	0.268869i	0.691688	−	0.722196i	$-0.256867\pi$
$593$	13.5958	+	6.54740i	0.558313	+	0.268869i	−0.133375	+	0.991066i	$0.542582\pi$
$594$	2.07075	−	10.7436i	0.0849638	−	0.440816i
$595$	52.5886	−	5.92532i	2.15592	−	0.242914i
$596$	23.8444	−	49.5133i	0.976703	−	2.02814i
$597$	−4.55006	−	1.72653i	−0.186221	−	0.0706622i
$598$	2.83060	+	8.08938i	0.115752	+	0.330799i
$599$	8.47719	−	5.32657i	0.346369	−	0.217638i	−0.347600	−	0.937643i	$-0.613003\pi$
$599$	8.47719	−	5.32657i	0.346369	−	0.217638i	0.693969	+	0.720005i	$0.255861\pi$
$600$	3.57840	−	4.25475i	0.146088	−	0.173699i
$601$	−9.04221	+	25.8412i	−0.368840	+	1.05408i	0.598615	+	0.801037i	$0.295718\pi$
$601$	−9.04221	+	25.8412i	−0.368840	+	1.05408i	−0.967454	+	0.253046i	$0.918568\pi$
$602$	−12.7992	−	56.0771i	−0.521658	−	2.28553i
$603$	−0.280667	−	1.61316i	−0.0114297	−	0.0656931i
$604$	−9.01303	−	11.3020i	−0.366735	−	0.459871i
$605$	19.4022	+	4.42842i	0.788811	+	0.180041i
$606$	14.1997	+	1.97598i	0.576823	+	0.0802688i
$607$	−2.92661	+	25.9744i	−0.118788	+	1.05427i	0.782980	+	0.622047i	$0.213699\pi$
$607$	−2.92661	+	25.9744i	−0.118788	+	1.05427i	−0.901767	+	0.432222i	$0.857730\pi$
$608$	−9.58679			−0.388796
$609$	−29.4678	+	27.9252i	−1.19410	+	1.13159i
$610$	−18.6874			−0.756629
$611$	0.431021	−	3.82542i	0.0174372	−	0.154760i
$612$	−16.7912	−	57.4275i	−0.678746	−	2.32137i
$613$	−39.7512	−	9.07296i	−1.60554	−	0.366453i	−0.676501	−	0.736442i	$-0.736504\pi$
$613$	−39.7512	−	9.07296i	−1.60554	−	0.366453i	−0.929036	+	0.369989i	$0.879362\pi$
$614$	40.1630	+	50.3628i	1.62085	+	2.03248i
$615$	2.90981	−	11.3735i	0.117335	−	0.458623i
$616$	2.48018	+	10.8664i	0.0999292	+	0.437818i
$617$	−5.38521	+	15.3901i	−0.216801	+	0.619580i	−0.999998	−	0.00219326i	$-0.999302\pi$
$617$	−5.38521	+	15.3901i	−0.216801	+	0.619580i	0.783197	+	0.621774i	$0.213588\pi$
$618$	29.6479	+	24.9350i	1.19261	+	1.00303i
$619$	11.7667	−	7.39350i	0.472943	−	0.297170i	−0.274391	−	0.961618i	$-0.588476\pi$
$619$	11.7667	−	7.39350i	0.472943	−	0.297170i	0.747334	+	0.664448i	$0.231333\pi$
$620$	−21.9848	−	62.8289i	−0.882930	−	2.52327i
$621$	−14.2269	+	7.45725i	−0.570908	+	0.299249i
$622$	29.7030	−	61.6790i	1.19098	−	2.47310i
$623$	−13.2925	+	1.49770i	−0.532551	+	0.0600041i
$624$	−0.0951202	−	0.160525i	−0.00380785	−	0.00642613i
$625$	16.1151	+	7.76062i	0.644603	+	0.310425i
$626$	7.51976	+	7.51976i	0.300550	+	0.300550i
$627$	−1.83047	−	1.92848i	−0.0731018	−	0.0770161i
$628$	24.1488	+	38.4327i	0.963644	+	1.53363i
$629$	16.7774	+	34.8387i	0.668959	+	1.38911i
$630$	−28.4866	−	51.0638i	−1.13493	−	2.03443i
$631$	−26.7244	+	6.09968i	−1.06388	+	0.242824i	−0.718421	−	0.695608i	$-0.755135\pi$
$631$	−26.7244	+	6.09968i	−1.06388	+	0.242824i	−0.345462	+	0.938433i	$0.612278\pi$
$632$	−20.2547	−	16.1526i	−0.805689	−	0.642515i
$633$	11.7197	−	22.7964i	0.465818	−	0.906075i
$634$	−11.8798	+	52.0490i	−0.471809	+	2.06713i
$635$	−25.1222	−	15.7853i	−0.996945	−	0.626422i
$636$	3.72918	+	11.6206i	0.147871	+	0.460785i
$637$		−	14.4993i		−	0.574482i
$638$	7.07708	−	8.85979i	0.280184	−	0.350762i
$639$	−15.2499	−	13.5199i	−0.603277	−	0.534838i
$640$	35.2894	+	3.97617i	1.39494	+	0.157172i
$641$	3.31074	−	5.26902i	0.130767	−	0.208114i	−0.774923	−	0.632056i	$-0.782211\pi$
$641$	3.31074	−	5.26902i	0.130767	−	0.208114i	0.905689	+	0.423942i	$0.139354\pi$
$642$	−1.89980	−	9.45304i	−0.0749791	−	0.373082i
$643$	−24.5458	+	19.5746i	−0.967990	+	0.771947i	−0.973652	−	0.228037i	$-0.926769\pi$
$643$	−24.5458	+	19.5746i	−0.967990	+	0.771947i	0.00566202	+	0.999984i	$0.498198\pi$
$644$	26.9803	−	33.8322i	1.06317	−	1.33318i
$645$	−11.8472	−	15.6774i	−0.466483	−	0.617298i
$646$	−22.2584	−	7.78855i	−0.875745	−	0.306436i
$647$	−11.9368	+	5.74846i	−0.469284	+	0.225995i	−0.653553	−	0.756881i	$-0.726722\pi$
$647$	−11.9368	+	5.74846i	−0.469284	+	0.225995i	0.184269	+	0.982876i	$0.441008\pi$
$648$	−19.4198	+	15.7401i	−0.762883	+	0.618330i
$649$	−3.68252	+	1.28857i	−0.144552	+	0.0505808i
$650$	2.26547	−	2.26547i	0.0888589	−	0.0888589i
$651$	79.5514	+	2.07431i	3.11787	+	0.0812986i
$652$	−2.32567	−	20.6409i	−0.0910803	−	0.808360i
$653$	2.23808	+	19.8635i	0.0875829	+	0.777320i	0.958345	+	0.285614i	$0.0921977\pi$
$653$	2.23808	+	19.8635i	0.0875829	+	0.777320i	−0.870762	+	0.491705i	$0.836374\pi$
$654$	−21.1337	−	0.551064i	−0.826395	−	0.0215483i
$655$	6.94141	−	6.94141i	0.271223	−	0.271223i
$656$	−0.289570	+	0.101325i	−0.0113058	+	0.00395608i
$657$	−25.2544	−	4.18803i	−0.985269	−	0.163391i
$658$	−28.4029	+	13.6781i	−1.10726	+	0.533228i
$659$	−42.3962	−	14.8351i	−1.65152	−	0.577893i	−0.665779	−	0.746149i	$-0.731901\pi$
$659$	−42.3962	−	14.8351i	−1.65152	−	0.577893i	−0.985743	+	0.168257i	$0.946186\pi$
$660$	6.07109	+	8.03390i	0.236317	+	0.312719i
$661$	2.32376	−	2.91390i	0.0903837	−	0.113338i	−0.734583	−	0.678519i	$-0.762622\pi$
$661$	2.32376	−	2.91390i	0.0903837	−	0.113338i	0.824967	+	0.565181i	$0.191194\pi$
$662$	−29.1219	+	23.2240i	−1.13186	+	0.902625i
$663$	−2.56896	−	12.7827i	−0.0997701	−	0.496437i
$664$	6.34078	−	10.0913i	0.246070	−	0.391618i
$665$	−14.1201	−	1.59095i	−0.547554	−	0.0616945i
$666$	28.3424	−	31.9692i	1.09825	−	1.23878i
$667$	−16.6472	−	0.0133585i	−0.644581	−	0.000517242i
$668$		−	0.0193245i		−	0.000747688i
$669$	−4.48770	−	13.9842i	−0.173504	−	0.540660i
$670$	2.06949	+	1.30034i	0.0799512	+	0.0502367i
$671$	−0.856143	+	3.75101i	−0.0330510	+	0.144806i
$672$	−19.8462	+	38.6034i	−0.765584	+	1.48916i
$673$	4.00224	+	3.19168i	0.154275	+	0.123030i	0.697585	−	0.716502i	$-0.254258\pi$
$673$	4.00224	+	3.19168i	0.154275	+	0.123030i	−0.543310	+	0.839532i	$0.682829\pi$
$674$	−13.8331	+	3.15732i	−0.532832	+	0.121616i
$675$	4.81928	+	3.58222i	0.185494	+	0.137880i
$676$	−16.0844	−	33.3995i	−0.618629	−	1.28460i
$677$	−17.3756	−	27.6531i	−0.667799	−	1.06280i	−0.993110	−	0.117188i	$-0.962612\pi$
$677$	−17.3756	−	27.6531i	−0.667799	−	1.06280i	0.325311	−	0.945607i	$-0.394531\pi$
$678$	24.2380	+	25.5359i	0.930856	+	0.980700i
$679$	15.3097	+	15.3097i	0.587533	+	0.587533i
$680$	30.4268	+	14.6528i	1.16681	+	0.561908i
$681$	−20.3538	−	34.3491i	−0.779961	−	1.31626i
$682$	−22.0874	+	2.48865i	−0.845769	+	0.0952953i
$683$	−13.3272	+	27.6741i	−0.509950	+	1.05892i	0.474008	+	0.880520i	$0.342807\pi$
$683$	−13.3272	+	27.6741i	−0.509950	+	1.05892i	−0.983958	+	0.178401i	$0.942908\pi$
$684$	0.964302	+	16.0360i	0.0368710	+	0.613150i
$685$	−4.88587	−	13.9630i	−0.186680	−	0.533500i
$686$	−41.6173	+	26.1499i	−1.58896	+	0.998407i
$687$	−16.5475	−	13.9171i	−0.631328	−	0.530970i
$688$	−0.169600	+	0.484690i	−0.00646595	+	0.0184786i
$689$	0.591791	+	2.59281i	0.0225454	+	0.0987780i
$690$	5.94282	−	23.2286i	0.226239	−	0.884296i
$691$	21.6766	+	27.1816i	0.824617	+	1.03404i	0.998783	+	0.0493209i	$0.0157057\pi$
$691$	21.6766	+	27.1816i	0.824617	+	1.03404i	−0.174166	+	0.984716i	$0.555723\pi$
$692$	63.3263	+	14.4538i	2.40730	+	0.549451i
$693$	−11.5548	+	3.37852i	−0.438932	+	0.128339i
$694$	−5.56403	+	49.3822i	−0.211208	+	1.87452i
$695$	37.6725			1.42900
$696$	−25.4032	+	5.08413i	−0.962904	+	0.192713i
$697$	−21.4371			−0.811987
$698$	−7.00405	+	62.1627i	−0.265107	+	2.35289i
$699$	29.9722	+	4.17083i	1.13365	+	0.157755i
$700$	−15.7712	−	3.59968i	−0.596096	−	0.136055i
$701$	−19.0197	−	23.8500i	−0.718366	−	0.900802i	0.279878	−	0.960035i	$-0.409706\pi$
$701$	−19.0197	−	23.8500i	−0.718366	−	0.900802i	−0.998244	+	0.0592332i	$0.981134\pi$
$702$	−11.9302	+	8.07446i	−0.450277	+	0.304751i
$703$	−2.31030	−	10.1221i	−0.0871346	−	0.381762i
$704$	3.95019	−	11.2890i	0.148879	−	0.425471i
$705$	−6.93211	+	8.24234i	−0.261078	+	0.310424i
$706$	5.68695	−	3.57335i	0.214031	−	0.134485i
$707$	−5.20991	−	14.8891i	−0.195939	−	0.559961i
$708$	22.0393	+	8.36285i	0.828286	+	0.314295i
$709$	9.99034	−	20.7451i	0.375195	−	0.779100i	−0.624804	−	0.780782i	$-0.714821\pi$
$709$	9.99034	−	20.7451i	0.375195	−	0.779100i	0.999999	+	0.00168159i	$0.000535266\pi$
$710$	30.2296	−	3.40606i	1.13450	−	0.127827i
$711$	16.1018	−	22.8849i	0.603865	−	0.858252i
$712$	−7.69077	−	3.70368i	−0.288224	−	0.138801i
$713$	23.0739	+	23.0739i	0.864124	+	0.864124i
$714$	−77.4408	+	73.5049i	−2.89815	+	2.75085i
$715$	1.16747	+	1.85802i	0.0436610	+	0.0694860i
$716$	−16.2307	−	33.7035i	−0.606571	−	1.25956i
$717$	1.11747	+	12.9421i	0.0417329	+	0.483331i
$718$	75.1581	−	17.1544i	2.80488	−	0.640195i
$719$	23.5343	+	18.7679i	0.877679	+	0.699926i	0.954849	−	0.297092i	$-0.0960168\pi$
$719$	23.5343	+	18.7679i	0.877679	+	0.699926i	−0.0771694	+	0.997018i	$0.524588\pi$
$720$	−0.0272046	+	0.521305i	−0.00101386	+	0.0194279i
$721$	9.48487	−	41.5559i	0.353235	−	1.54762i
$722$	−31.3814	−	19.7182i	−1.16789	−	0.733837i
$723$	1.90157	−	0.610236i	0.0707200	−	0.0226949i
$724$			19.4138i			0.721509i
$725$	2.69566	+	5.60911i	0.100114	+	0.208317i
$726$	−36.6169	+	16.4722i	−1.35898	+	0.611339i
$727$	1.74604	+	0.196731i	0.0647569	+	0.00729635i	0.144283	−	0.989536i	$-0.453912\pi$
$727$	1.74604	+	0.196731i	0.0647569	+	0.00729635i	−0.0795266	+	0.996833i	$0.525341\pi$
$728$	7.80756	−	12.4257i	0.289368	−	0.460526i
$729$	−18.2293	−	19.9171i	−0.675161	−	0.737670i
$730$	29.8750	−	23.8245i	1.10572	−	0.881784i
$731$	−22.3720	+	28.0536i	−0.827458	+	1.03760i
$732$	18.5464	−	14.0152i	0.685494	−	0.518017i
$733$	−33.5056	−	11.7241i	−1.23756	−	0.433040i	−0.369373	−	0.929281i	$-0.620428\pi$
$733$	−33.5056	−	11.7241i	−1.23756	−	0.433040i	−0.868185	+	0.496241i	$0.834713\pi$
$734$	−8.81984	+	4.24741i	−0.325546	+	0.156775i
$735$	−22.4692	+	33.7722i	−0.828789	+	1.24571i
$736$	−16.8000	+	5.87859i	−0.619257	+	0.216688i
$737$	0.355822	−	0.355822i	0.0131069	−	0.0131069i
$738$	9.15068	+	21.8465i	0.336841	+	0.804181i
$739$	2.01850	+	17.9146i	0.0742516	+	0.659001i	0.974619	+	0.223870i	$0.0718692\pi$
$739$	2.01850	+	17.9146i	0.0742516	+	0.659001i	−0.900367	+	0.435131i	$0.856702\pi$
$740$	4.40252	+	39.0734i	0.161840	+	1.43637i
$741$	−0.0912521	+	3.49959i	−0.00335223	+	0.128561i
$742$	15.3999	−	15.3999i	0.565347	−	0.565347i
$743$	46.8311	−	16.3869i	1.71807	−	0.601178i	0.722173	−	0.691712i	$-0.243143\pi$
$743$	46.8311	−	16.3869i	1.71807	−	0.601178i	0.995893	+	0.0905344i	$0.0288575\pi$
$744$	42.2796	+	28.1293i	1.55005	+	1.03127i
$745$	−30.1856	+	14.5366i	−1.10592	+	0.532581i
$746$	39.6835	+	13.8858i	1.45291	+	0.508397i
$747$	11.2911	+	6.18209i	0.413119	+	0.226191i
$748$	11.4645	−	14.3761i	0.419185	−	0.525641i
$749$	−8.29447	+	6.61462i	−0.303073	+	0.241693i
$750$	−46.8082	+	9.40715i	−1.70919	+	0.343501i
$751$	−5.16453	+	8.21930i	−0.188456	+	0.299926i	−0.927567	−	0.373658i	$-0.878103\pi$
$751$	−5.16453	+	8.21930i	−0.188456	+	0.299926i	0.739110	+	0.673584i	$0.235246\pi$
$752$	0.279670	+	0.0315113i	0.0101985	+	0.00114910i
$753$	−2.55017	−	5.66893i	−0.0929334	−	0.206587i
$754$	−14.8373	+	1.65970i	−0.540341	+	0.0604428i
$755$			8.81292i			0.320735i
$756$	66.5687	+	29.3141i	2.42108	+	1.06614i
$757$	25.8506	+	16.2430i	0.939556	+	0.590362i	0.912414	−	0.409269i	$-0.134216\pi$
$757$	25.8506	+	16.2430i	0.939556	+	0.590362i	0.0271425	+	0.999632i	$0.491359\pi$
$758$	10.7962	−	47.3014i	0.392137	−	1.71806i
$759$	−4.39027	−	2.25706i	−0.159357	−	0.0819262i
$760$	−7.08934	−	5.65356i	−0.257157	−	0.205076i
$761$	44.6863	−	10.1994i	1.61988	−	0.369726i	0.686079	−	0.727527i	$-0.259331\pi$
$761$	44.6863	−	10.1994i	1.61988	−	0.369726i	0.933798	+	0.357801i	$0.116473\pi$
$762$	59.6383	−	5.14942i	2.16047	−	0.186544i
$763$	10.0926	+	20.9575i	0.365377	+	0.758712i
$764$	−22.9014	−	36.4474i	−0.828544	−	1.31862i
$765$	−13.8253	+	33.7548i	−0.499855	+	1.22041i
$766$	2.87781	+	2.87781i	0.103980	+	0.103980i
$767$	4.62810	+	2.22878i	0.167111	+	0.0804764i
$768$	−22.9791	+	13.6165i	−0.829188	+	0.491342i
$769$	11.9833	−	1.35019i	0.432127	−	0.0486890i	0.106778	−	0.994283i	$-0.465947\pi$
$769$	11.9833	−	1.35019i	0.432127	−	0.0486890i	0.325349	+	0.945594i	$0.394518\pi$
$770$	7.79680	−	16.1902i	0.280977	−	0.583455i
$771$	17.8899	−	47.1465i	0.644288	−	1.69794i
$772$	−4.91161	−	14.0366i	−0.176773	−	0.505187i
$773$	19.6078	−	12.3204i	0.705242	−	0.443133i	−0.131080	−	0.991372i	$-0.541844\pi$
$773$	19.6078	−	12.3204i	0.705242	−	0.443133i	0.836322	+	0.548239i	$0.184702\pi$
$774$	38.1392	+	10.8243i	1.37088	+	0.389070i
$775$	4.02896	−	11.5141i	0.144724	−	0.413598i
$776$	3.07446	+	13.4701i	0.110367	+	0.483548i
$777$	−45.5416	−	11.6514i	−1.63379	−	0.417992i
$778$	−36.5971	−	45.8914i	−1.31207	−	1.64529i
$779$	5.61156	+	1.28080i	0.201055	+	0.0458895i
$780$	1.82738	−	13.1318i	0.0654306	−	0.470193i
$781$	0.701261	−	6.22386i	0.0250931	−	0.222707i
$782$	−43.7818			−1.56564
$783$	−7.12845	−	27.0589i	−0.254750	−	0.967007i
$784$	1.06002			0.0378578
$785$	3.09826	−	27.4978i	0.110581	−	0.981438i
$786$	−2.72976	+	19.6164i	−0.0973673	+	0.699695i
$787$	6.47817	+	1.47860i	0.230922	+	0.0527064i	0.336416	−	0.941714i	$-0.390785\pi$
$787$	6.47817	+	1.47860i	0.230922	+	0.0527064i	−0.105494	+	0.994420i	$0.533642\pi$
$788$	−28.3342	−	35.5299i	−1.00936	−	1.26570i
$789$	−31.9359	−	8.17051i	−1.13695	−	0.290878i
$790$	9.29426	+	40.7208i	0.330675	+	1.44878i
$791$	12.7944	−	36.5644i	0.454918	−	1.30008i
$792$	−7.39044	−	2.09748i	−0.262608	−	0.0745306i
$793$	4.28927	−	2.69513i	0.152316	−	0.0957067i
$794$	−15.8984	−	45.4350i	−0.564212	−	1.61243i
$795$	2.63960	−	6.95633i	0.0936168	−	0.246716i
$796$	−3.92079	+	8.14161i	−0.138969	+	0.288572i
$797$	−0.273912	+	0.0308625i	−0.00970248	+	0.00109321i	−0.116814	−	0.993154i	$-0.537268\pi$
$797$	−0.273912	+	0.0308625i	−0.00970248	+	0.00109321i	0.107112	+	0.994247i	$0.465840\pi$
$798$	24.6633	−	14.6144i	0.873072	−	0.517346i
$799$	17.7184	+	8.53274i	0.626832	+	0.301867i
$800$	4.70492	+	4.70492i	0.166344	+	0.166344i
$801$	3.49452	−	8.53197i	0.123473	−	0.301462i
$802$	44.0775	+	70.1490i	1.55643	+	2.47705i
$803$	−3.41347	−	7.08813i	−0.120459	−	0.250135i
$804$	−3.02911	+	0.261546i	−0.106829	+	0.00922402i
$805$	−25.7198	+	5.87038i	−0.906505	+	0.206904i
$806$	22.8803	+	18.2465i	0.805925	+	0.642704i
$807$	−21.7049	−	11.1586i	−0.764047	−	0.392801i
$808$	2.23993	−	9.81380i	0.0788006	−	0.345248i
$809$	−36.3670	−	22.8509i	−1.27860	−	0.803395i	−0.290447	−	0.956891i	$-0.593804\pi$
$809$	−36.3670	−	22.8509i	−1.27860	−	0.803395i	−0.988149	+	0.153496i	$0.950947\pi$
$810$	40.3010	−	0.319312i	1.41603	−	0.0112195i
$811$		−	50.3099i		−	1.76662i	−0.468790	−	0.883310i	$-0.655310\pi$
$811$		−	50.3099i		−	1.76662i	0.468790	−	0.883310i	$-0.344690\pi$
$812$	46.9533	+	58.9746i	1.64774	+	2.06960i
$813$	14.3757	+	31.9566i	0.504178	+	1.12077i
$814$	13.0474	+	1.47009i	0.457311	+	0.0515266i
$815$	−6.73727	+	10.7223i	−0.235996	+	0.375586i
$816$	0.934519	−	0.187813i	0.0327147	−	0.00657475i
$817$	7.53241	−	6.00690i	0.263526	−	0.210155i
$818$	40.1663	−	50.3670i	1.40438	−	1.76104i
$819$	13.9030	+	7.61217i	0.485810	+	0.265991i
$820$	−20.5756	−	7.19972i	−0.718532	−	0.251425i
$821$	−5.26094	+	2.53354i	−0.183608	+	0.0884210i	−0.523430	−	0.852069i	$-0.675348\pi$
$821$	−5.26094	+	2.53354i	−0.183608	+	0.0884210i	0.339821	+	0.940490i	$0.389633\pi$
$822$	24.8487	+	16.5323i	0.866697	+	0.576629i
$823$	−9.37832	+	3.28162i	−0.326908	+	0.114390i	−0.488743	−	0.872428i	$-0.662544\pi$
$823$	−9.37832	+	3.28162i	−0.326908	+	0.114390i	0.161835	+	0.986818i	$0.448259\pi$
$824$	19.2336	−	19.2336i	0.670034	−	0.670034i
$825$	−0.0481029	+	1.84478i	−0.00167473	+	0.0642271i
$826$	−4.70986	−	41.8011i	−0.163877	−	1.45445i
$827$	−1.83444	−	16.2811i	−0.0637897	−	0.566150i	−0.984435	−	0.175749i	$-0.943765\pi$
$827$	−1.83444	−	16.2811i	−0.0637897	−	0.566150i	0.920645	−	0.390400i	$-0.127663\pi$
$828$	11.5231	+	27.5103i	0.400454	+	0.956051i
$829$	−8.35437	+	8.35437i	−0.290159	+	0.290159i	−0.837143	−	0.546984i	$-0.815776\pi$
$829$	−8.35437	+	8.35437i	−0.290159	+	0.290159i	0.546984	+	0.837143i	$0.315776\pi$
$830$	−18.1365	+	6.34624i	−0.629528	+	0.220281i
$831$	−11.2000	+	16.8340i	−0.388522	+	0.583965i
$832$	−14.1877	+	6.83245i	−0.491871	+	0.236873i
$833$	69.9136	+	24.4638i	2.42236	+	0.847621i
$834$	−60.6388	+	45.8238i	−2.09975	+	1.58675i
$835$	−0.00734542	+	0.00921086i	−0.000254199	+	0.000318755i
$836$	−3.85999	+	3.07824i	−0.133500	+	0.106463i
$837$	−27.5867	+	47.4077i	−0.953535	+	1.63865i
$838$	−19.0249	+	30.2780i	−0.657205	+	1.04594i
$839$	−47.2967	−	5.32906i	−1.63286	−	0.183979i	−0.752604	−	0.658473i	$-0.771203\pi$
$839$	−47.2967	−	5.32906i	−1.63286	−	0.183979i	−0.880259	+	0.474494i	$0.842631\pi$
$840$	−37.4414	+	16.8430i	−1.29185	+	0.581140i
$841$	6.49847	−	28.2625i	0.224085	−	0.974570i
$842$			70.8013i			2.43997i
$843$	−8.08790	+	2.59550i	−0.278562	+	0.0893939i
$844$	−40.3002	−	25.3223i	−1.38719	−	0.871630i
$845$	−5.02898	+	22.0334i	−0.173002	+	0.757972i
$846$	1.13238	−	21.6991i	0.0389322	−	0.746032i
$847$	34.5397	+	27.5445i	1.18680	+	0.946441i
$848$	−0.189556	+	0.0432649i	−0.00650938	+	0.00148572i
$849$	1.20118	+	13.9115i	0.0412243	+	0.477441i
$850$	7.10138	+	14.7462i	0.243575	+	0.505789i
$851$	−10.2554	−	16.3214i	−0.351551	−	0.559491i
$852$	−27.4471	+	26.0521i	−0.940320	+	0.892529i
$853$	26.7792	+	26.7792i	0.916904	+	0.916904i	0.996803	−	0.0798992i	$-0.0254599\pi$
$853$	26.7792	+	26.7792i	0.916904	+	0.916904i	−0.0798992	+	0.996803i	$0.525460\pi$
$854$	−37.3754	−	17.9990i	−1.27896	−	0.615914i
$855$	5.63579	−	8.00994i	0.192740	−	0.273934i
$856$	−6.72746	+	0.758003i	−0.229940	+	0.0259080i
$857$	21.2466	−	44.1191i	0.725771	−	1.50708i	−0.131000	−	0.991382i	$-0.541819\pi$
$857$	21.2466	−	44.1191i	0.725771	−	1.50708i	0.856771	−	0.515697i	$-0.172467\pi$
$858$	−4.13924	−	1.57064i	−0.141311	−	0.0536209i
$859$	4.15623	+	11.8778i	0.141809	+	0.405266i	0.992780	−	0.119945i	$-0.0382720\pi$
$859$	4.15623	+	11.8778i	0.141809	+	0.405266i	−0.850972	+	0.525211i	$0.823986\pi$
$860$	−30.8949	+	19.4125i	−1.05351	+	0.661962i
$861$	16.7743	−	19.9448i	0.571666	−	0.679715i
$862$	−9.50233	+	27.1561i	−0.323651	+	0.924940i
$863$	11.1910	+	49.0310i	0.380946	+	1.66903i	0.694522	+	0.719471i	$0.255616\pi$
$863$	11.1910	+	49.0310i	0.380946	+	1.66903i	−0.313576	+	0.949563i	$0.601527\pi$
$864$	−16.7690	−	24.7767i	−0.570495	−	0.842919i
$865$	−24.6899	−	30.9602i	−0.839482	−	1.05268i
$866$	−0.992256	−	0.226476i	−0.0337182	−	0.00769596i
$867$	36.8069	+	5.12193i	1.25003	+	0.173950i
$868$	16.5443	−	146.835i	0.561551	−	4.98391i
$869$	8.59946			0.291717
$870$	37.1314	+	19.1272i	1.25887	+	0.648471i
$871$	−0.662543			−0.0224494
$872$	−1.66198	+	14.7505i	−0.0562817	+	0.499514i
$873$	−14.3235	+	4.18805i	−0.484777	+	0.141744i
$874$	11.4607	+	2.61584i	0.387665	+	0.0884820i
$875$	32.7533	+	41.0714i	1.10726	+	1.38847i
$876$	−11.7816	+	46.0505i	−0.398064	+	1.55590i
$877$	4.63487	+	20.3067i	0.156509	+	0.685709i	0.990907	+	0.134547i	$0.0429581\pi$
$877$	4.63487	+	20.3067i	0.156509	+	0.685709i	−0.834399	+	0.551162i	$0.814185\pi$
$878$	−3.55047	+	10.1467i	−0.119822	+	0.342433i
$879$	13.4268	+	11.2924i	0.452873	+	0.380883i
$880$	−0.135837	+	0.0853520i	−0.00457906	+	0.00287722i
$881$	−7.03466	−	20.1039i	−0.237004	−	0.677317i	−0.999539	−	0.0303706i	$-0.990331\pi$
$881$	−7.03466	−	20.1039i	−0.237004	−	0.677317i	0.762535	−	0.646947i	$-0.223954\pi$
$882$	−4.91242	−	81.6916i	−0.165410	−	2.75070i
$883$	−19.3867	+	40.2568i	−0.652413	+	1.35475i	0.267854	+	0.963460i	$0.413686\pi$
$883$	−19.3867	+	40.2568i	−0.652413	+	1.35475i	−0.920267	+	0.391291i	$0.872029\pi$
$884$	−24.0577	+	2.71065i	−0.809146	+	0.0911689i
$885$	−7.32603	−	12.3634i	−0.246262	−	0.415591i
$886$	−27.8329	−	13.4036i	−0.935063	−	0.450303i
$887$	−7.23403	−	7.23403i	−0.242895	−	0.242895i	0.575152	−	0.818047i	$-0.304943\pi$
$887$	−7.23403	−	7.23403i	−0.242895	−	0.242895i	−0.818047	+	0.575152i	$0.804943\pi$
$888$	−20.6516	−	21.7574i	−0.693022	−	0.730131i
$889$	−35.0414	−	55.7681i	−1.17525	−	1.87040i
$890$	5.97124	+	12.3994i	0.200156	+	0.415629i
$891$	1.78226	−	8.10403i	0.0597079	−	0.271495i
$892$	−26.5869	+	6.06829i	−0.890196	+	0.203182i
$893$	−4.12833	−	3.29223i	−0.138149	−	0.110170i
$894$	30.9057	−	60.1156i	1.03364	−	2.01057i
$895$	−5.07475	+	22.2339i	−0.169630	+	0.743198i
$896$	66.7505	+	41.9421i	2.22998	+	1.40119i
$897$	1.98602	+	6.18869i	0.0663114	+	0.206634i
$898$			61.8704i			2.06464i
$899$	−48.1564	+	30.2048i	−1.60611	+	1.00739i
$900$	7.39674	−	8.34324i	0.246558	−	0.278108i
$901$	−13.5007	−	1.52116i	−0.449772	−	0.0506772i
$902$	−3.87271	+	6.16338i	−0.128947	+	0.205218i
$903$	−8.59483	−	42.7662i	−0.286018	−	1.42317i
$904$	19.3272	−	15.4129i	0.642813	−	0.512626i
$905$	7.37937	−	9.25343i	0.245298	−	0.307595i
$906$	−10.7198	−	14.1855i	−0.356141	−	0.471283i
$907$	−48.7098	−	17.0443i	−1.61738	−	0.565946i	−0.638366	−	0.769733i	$-0.720390\pi$
$907$	−48.7098	−	17.0443i	−1.61738	−	0.565946i	−0.979015	+	0.203786i	$0.934675\pi$
$908$	−66.7954	+	32.1670i	−2.21668	+	1.06750i
$909$	10.7260	+	1.77874i	0.355760	+	0.0589969i
$910$	−22.3320	+	7.81430i	−0.740298	+	0.259041i
$911$	20.6095	−	20.6095i	0.682822	−	0.682822i	−0.277813	−	0.960635i	$-0.589610\pi$
$911$	20.6095	−	20.6095i	0.682822	−	0.682822i	0.960635	+	0.277813i	$0.0896095\pi$
$912$	−0.255849	−	0.00667130i	−0.00847202	−	0.000220909i
$913$	0.442939	+	3.93119i	0.0146591	+	0.130103i
$914$	2.82512	+	25.0736i	0.0934467	+	0.829362i
$915$	−14.1673	−	0.369413i	−0.468356	−	0.0122124i
$916$	−28.3891	+	28.3891i	−0.938004	+	0.938004i
$917$	20.5688	−	7.19733i	0.679241	−	0.237677i
$918$	−18.8048	−	71.1494i	−0.620651	−	2.34828i
$919$	22.1518	−	10.6677i	0.730720	−	0.351896i	−0.0312473	−	0.999512i	$-0.509948\pi$
$919$	22.1518	−	10.6677i	0.730720	−	0.351896i	0.761967	+	0.647615i	$0.224234\pi$
$920$	−15.8902	−	5.56022i	−0.523884	−	0.183315i
$921$	29.4529	+	38.9751i	0.970505	+	1.28427i
$922$	0.140839	−	0.176607i	0.00463829	−	0.00581623i
$923$	−6.44730	+	5.14155i	−0.212216	+	0.169236i
$924$	4.40442	+	21.9156i	0.144895	+	0.720969i
$925$	−3.83380	+	6.10145i	−0.126054	+	0.200615i
$926$	−54.0675	−	6.09194i	−1.77677	−	0.200194i
$927$	21.9838	+	19.4898i	0.722043	+	0.640130i
$928$	−3.44687	−	30.8140i	−0.113149	−	1.01152i
$929$		−	57.3986i		−	1.88319i	−0.336754	−	0.941593i	$-0.609329\pi$
$929$		−	57.3986i		−	1.88319i	0.336754	−	0.941593i	$-0.390671\pi$
$930$	−25.0175	−	77.9574i	−0.820355	−	2.55632i
$931$	−16.8396	−	10.5810i	−0.551895	−	0.346778i
$932$	12.5034	−	54.7809i	0.409562	−	1.79441i
$933$	23.7378	−	46.1730i	0.777140	−	1.51164i
$934$	−42.5354	−	33.9209i	−1.39180	−	1.10992i
$935$	−10.9289	+	2.49446i	−0.357414	+	0.0815775i
$936$	4.92776	+	8.83328i	0.161069	+	0.288725i
$937$	−3.97769	−	8.25977i	−0.129946	−	0.269835i	0.825837	−	0.563909i	$-0.190703\pi$
$937$	−3.97769	−	8.25977i	−0.129946	−	0.269835i	−0.955783	+	0.294074i	$0.904989\pi$
$938$	2.88660	+	4.59399i	0.0942508	+	0.149999i
$939$	5.55224	+	5.84954i	0.181190	+	0.190892i
$940$	14.1407	+	14.1407i	0.461217	+	0.461217i
$941$	−47.6168	−	22.9310i	−1.55226	−	0.747530i	−0.555779	−	0.831330i	$-0.687580\pi$
$941$	−47.6168	−	22.9310i	−1.55226	−	0.747530i	−0.996483	+	0.0838000i	$0.973294\pi$
$942$	28.4605	+	48.0299i	0.927293	+	1.56490i
$943$	10.6192	−	1.19649i	0.345807	−	0.0389631i
$944$	−0.162942	+	0.338353i	−0.00530332	+	0.0110125i
$945$	−20.5869	−	39.2757i	−0.669691	−	1.27764i
$946$	4.02409	+	11.5002i	0.130835	+	0.373904i
$947$	−11.8423	+	7.44101i	−0.384823	+	0.241800i	−0.710525	−	0.703672i	$-0.751542\pi$
$947$	−11.8423	+	7.44101i	−0.384823	+	0.241800i	0.325702	+	0.945473i	$0.394399\pi$
$948$	−39.7641	−	33.4431i	−1.29148	−	1.08618i
$949$	−3.42113	+	9.77701i	−0.111054	+	0.317375i
$950$	−0.977881	−	4.28438i	−0.0317267	−	0.139004i
$951$	−10.0353	+	39.2246i	−0.325416	+	1.27195i
$952$	46.7416	+	58.6122i	1.51491	+	1.89963i
$953$	18.1576	+	4.14436i	0.588183	+	0.134249i	0.506247	−	0.862389i	$-0.331032\pi$
$953$	18.1576	+	4.14436i	0.588183	+	0.134249i	0.0819364	+	0.996638i	$0.473890\pi$
$954$	4.21271	+	14.4078i	0.136392	+	0.466471i
$955$	−2.93821	+	26.0774i	−0.0950784	+	0.843844i
$956$	24.1208			0.780121
$957$	5.54043	−	6.57689i	0.179097	−	0.212601i
$958$	73.5768			2.37716
$959$	3.67679	−	32.6325i	0.118730	−	1.05376i
$960$	43.6346	+	6.07206i	1.40830	+	0.195975i
$961$	78.4100	+	17.8966i	2.52935	+	0.577308i
$962$	−10.7785	−	13.5158i	−0.347513	−	0.435767i
$963$	−1.25341	−	7.20410i	−0.0403906	−	0.232149i
$964$	−0.825165	−	3.61528i	−0.0265768	−	0.116440i
$965$	−2.99435	+	8.55735i	−0.0963914	+	0.275471i
$966$	34.2588	−	40.7340i	1.10226	−	1.31060i
$967$	38.1798	−	23.9900i	1.22778	−	0.771465i	0.247463	−	0.968897i	$-0.420403\pi$
$967$	38.1798	−	23.9900i	1.22778	−	0.771465i	0.980316	+	0.197433i	$0.0632603\pi$
$968$	9.31113	+	26.6097i	0.299271	+	0.855267i
$969$	−16.7206	−	6.34467i	−0.537143	−	0.203820i
$970$	9.66500	−	20.0696i	0.310325	−	0.644396i
$971$	49.5958	−	5.58810i	1.59160	−	0.179331i	0.728748	−	0.684782i	$-0.240102\pi$
$971$	49.5958	−	5.58810i	1.59160	−	0.179331i	0.862855	+	0.505451i	$0.168674\pi$
$972$	−39.7575	+	30.5420i	−1.27522	+	0.979636i
$973$	75.3464	+	36.2849i	2.41550	+	1.16324i
$974$	−34.3977	−	34.3977i	−1.10217	−	1.10217i
$975$	1.76228	−	1.67271i	0.0564382	−	0.0535697i
$976$	0.197036	+	0.313582i	0.00630698	+	0.0100375i
$977$	19.9205	+	41.3653i	0.637313	+	1.32339i	0.930132	+	0.367226i	$0.119692\pi$
$977$	19.9205	+	41.3653i	0.637313	+	1.32339i	−0.292819	+	0.956168i	$0.594593\pi$
$978$	−2.19780	−	25.4540i	−0.0702780	−	0.813929i
$979$	2.76243	−	0.630507i	0.0882877	−	0.0201511i
$980$	58.8879	+	46.9615i	1.88110	+	1.50013i
$981$	−16.0110	−	0.835547i	−0.511193	−	0.0266770i
$982$	11.5882	−	50.7712i	0.369794	−	1.62017i
$983$	−12.8754	−	8.09013i	−0.410661	−	0.258035i	0.310821	−	0.950468i	$-0.399396\pi$
$983$	−12.8754	−	8.09013i	−0.410661	−	0.258035i	−0.721482	+	0.692433i	$0.756539\pi$
$984$	15.8351	−	5.08166i	0.504803	−	0.161997i
$985$			27.7051i			0.882758i
$986$	17.0312	−	74.3436i	0.542385	−	2.36758i
$987$	−21.8032	+	9.80819i	−0.694004	+	0.312198i
$988$	6.45950	+	0.727811i	0.205504	+	0.0231548i
$989$	9.51650	−	15.1454i	0.302607	−	0.481596i
$990$	7.20726	+	10.0729i	0.229062	+	0.320137i
$991$	−43.3214	+	34.5476i	−1.37615	+	1.09744i	−0.392025	+	0.919955i	$0.628225\pi$
$991$	−43.3214	+	34.5476i	−1.37615	+	1.09744i	−0.984123	+	0.177487i	$0.943203\pi$
$992$	−37.8943	+	47.5179i	−1.20314	+	1.50869i
$993$	−22.5370	+	17.0309i	−0.715191	+	0.540459i
$994$	63.7408	+	22.3039i	2.02174	+	0.707436i
$995$	4.96351	−	2.39030i	0.157354	−	0.0757776i
$996$	13.2401	−	19.9005i	0.419529	−	0.630570i
$997$	29.9398	−	10.4764i	0.948204	−	0.331791i	0.188510	−	0.982071i	$-0.439634\pi$
$997$	29.9398	−	10.4764i	0.948204	−	0.331791i	0.759694	+	0.650280i	$0.225349\pi$
$998$	−30.7909	+	30.7909i	−0.974670	+	0.974670i
$999$	22.1190	−	23.6762i	0.699813	−	0.749083i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.2.k.a.2.7	yes	96
3.2	odd	2	inner	87.2.k.a.2.2	✓	96
29.15	odd	28	inner	87.2.k.a.44.2	yes	96
87.44	even	28	inner	87.2.k.a.44.7	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.k.a.2.2	✓	96	3.2	odd	2	inner
87.2.k.a.2.7	yes	96	1.1	even	1	trivial
87.2.k.a.44.2	yes	96	29.15	odd	28	inner
87.2.k.a.44.7	yes	96	87.44	even	28	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.k (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.255714 - 2.26953i) q^{2} +(0.238726 - 1.71552i) q^{3} +(-3.13550 - 0.715657i) q^{4} +(1.22248 + 1.53294i) q^{5} +(-3.83237 - 0.980478i) q^{6} +(0.968527 + 4.24339i) q^{7} +(-0.917355 + 2.62165i) q^{8} +(-2.88602 - 0.819080i) q^{9} +(3.79166 - 2.38246i) q^{10} +(-0.304506 - 0.870228i) q^{11} +(-1.97625 + 5.20817i) q^{12} +(-0.526689 + 1.09368i) q^{13} +(9.87816 - 1.11300i) q^{14} +(2.92163 - 1.73124i) q^{15} +(-0.0799573 - 0.0385054i) q^{16} +(-4.38493 - 4.38493i) q^{17} +(-2.59692 + 6.34044i) q^{18} +(0.885852 + 1.40983i) q^{19} +(-2.73603 - 5.68142i) q^{20} +(7.51084 - 0.648517i) q^{21} +(-2.05287 + 0.468555i) q^{22} +(2.41688 + 1.92740i) q^{23} +(4.27849 + 2.19960i) q^{24} +(0.257151 - 1.12665i) q^{25} +(2.34745 + 1.47500i) q^{26} +(-2.09412 + 4.75549i) q^{27} -13.9983i q^{28} +(-4.21298 + 3.35422i) q^{29} +(-3.18198 - 7.07342i) q^{30} +(10.4895 + 1.18188i) q^{31} +(-3.06329 + 4.87519i) q^{32} +(-1.56559 + 0.314640i) q^{33} +(-11.0730 + 8.83042i) q^{34} +(-5.32087 + 6.67217i) q^{35} +(8.46293 + 4.63363i) q^{36} +(-5.88562 - 2.05947i) q^{37} +(3.42616 - 1.64995i) q^{38} +(1.75050 + 1.16464i) q^{39} +(-5.14029 + 1.79866i) q^{40} +(2.44440 - 2.44440i) q^{41} +(0.448801 - 17.2119i) q^{42} +(-0.647855 - 5.74987i) q^{43} +(0.331993 + 2.94652i) q^{44} +(-2.27250 - 5.42541i) q^{45} +(4.99231 - 4.99231i) q^{46} +(-2.99334 + 1.04741i) q^{47} +(-0.0851447 + 0.127976i) q^{48} +(-10.7616 + 5.18250i) q^{49} +(-2.49121 - 0.871712i) q^{50} +(-8.56923 + 6.47564i) q^{51} +(2.43413 - 3.05231i) q^{52} +(1.71289 - 1.36599i) q^{53} +(10.2572 + 5.96870i) q^{54} +(0.961757 - 1.53063i) q^{55} +(-12.0132 - 1.35356i) q^{56} +(2.63006 - 1.18313i) q^{57} +(6.53516 + 10.4192i) q^{58} -4.23167i q^{59} +(-10.3998 + 3.33741i) q^{60} +(-3.53348 - 2.22023i) q^{61} +(5.36462 - 23.5040i) q^{62} +(0.680491 - 13.0398i) q^{63} +(10.1423 + 8.08820i) q^{64} +(-2.32042 + 0.529620i) q^{65} +(0.313740 + 3.63360i) q^{66} +(0.236814 + 0.491748i) q^{67} +(10.6108 + 16.8871i) q^{68} +(3.88346 - 3.68609i) q^{69} +(13.7820 + 13.7820i) q^{70} +(6.12060 + 2.94753i) q^{71} +(4.79484 - 6.81474i) q^{72} +(8.47945 - 0.955405i) q^{73} +(-6.17905 + 12.8309i) q^{74} +(-1.87141 - 0.710109i) q^{75} +(-1.76864 - 5.05447i) q^{76} +(3.39780 - 2.13498i) q^{77} +(3.09080 - 3.67498i) q^{78} +(-3.08062 + 8.80389i) q^{79} +(-0.0387197 - 0.169642i) q^{80} +(7.65822 + 4.72776i) q^{81} +(-4.92257 - 6.17270i) q^{82} +(-4.18332 - 0.954815i) q^{83} +(-24.0144 - 3.34176i) q^{84} +(1.36135 - 12.0823i) q^{85} -13.2151 q^{86} +(4.74847 + 8.02820i) q^{87} +2.56077 q^{88} +(-0.344100 + 3.05397i) q^{89} +(-12.8942 + 3.77014i) q^{90} +(-5.15103 - 1.17569i) q^{91} +(-6.19877 - 7.77301i) q^{92} +(4.53166 - 17.7128i) q^{93} +(1.61169 + 7.06129i) q^{94} +(-1.07824 + 3.08145i) q^{95} +(7.63221 + 6.41897i) q^{96} +(4.21195 - 2.64655i) q^{97} +(9.00992 + 25.7489i) q^{98} +(0.166024 + 2.76091i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{3} - 28 q^{4} - 14 q^{6} - 20 q^{7} - 14 q^{9} - 4 q^{10} - 8 q^{12} - 28 q^{13} - 16 q^{15} - 48 q^{16} - 28 q^{18} - 20 q^{19} + 26 q^{21} - 28 q^{22} + 58 q^{24} - 20 q^{25} + 36 q^{27}+ \cdots + 82 q^{99}+O(q^{100}) \) 96 * q - 12 * q^3 - 28 * q^4 - 14 * q^6 - 20 * q^7 - 14 * q^9 - 4 * q^10 - 8 * q^12 - 28 * q^13 - 16 * q^15 - 48 * q^16 - 28 * q^18 - 20 * q^19 + 26 * q^21 - 28 * q^22 + 58 * q^24 - 20 * q^25 + 36 * q^27 + 96 * q^30 - 32 * q^31 + 28 * q^33 - 28 * q^34 + 22 * q^36 - 4 * q^37 - 40 * q^39 - 48 * q^40 - 14 * q^42 - 32 * q^43 + 42 * q^45 + 120 * q^46 - 20 * q^48 + 4 * q^49 - 14 * q^51 + 72 * q^52 - 30 * q^54 + 148 * q^55 + 112 * q^58 + 20 * q^60 + 12 * q^61 - 14 * q^63 + 224 * q^64 - 32 * q^66 + 28 * q^67 + 10 * q^69 + 52 * q^70 - 44 * q^72 + 16 * q^73 - 144 * q^75 - 100 * q^76 - 102 * q^78 - 60 * q^79 - 146 * q^81 - 108 * q^82 - 64 * q^84 - 104 * q^85 - 70 * q^87 - 312 * q^88 - 96 * q^90 - 112 * q^91 - 70 * q^93 + 56 * q^94 - 168 * q^96 + 32 * q^97 + 82 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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