LMFDB - Embedded newform 512.2.o.a.157.40

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(5,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(128))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("512.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.o (of order $128$, degree $64$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$4032$
Relative dimension:	$63$ over $\Q(\zeta_{128})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{128}]$

Embedding invariants

Embedding label			157.40
Character	$\chi$	$=$	512.157
Dual form			512.2.o.a.437.40

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.629097 - 1.26658i) q^{2} +(2.11447 - 0.815642i) q^{3} +(-1.20847 - 1.59361i) q^{4} +(0.924429 - 1.18455i) q^{5} +(0.297128 - 3.19127i) q^{6} +(-0.371192 + 1.03741i) q^{7} +(-2.77869 + 0.528101i) q^{8} +(1.58286 - 1.43462i) q^{9} +O(q^{10})$	\(q+(0.629097 - 1.26658i) q^{2} +(2.11447 - 0.815642i) q^{3} +(-1.20847 - 1.59361i) q^{4} +(0.924429 - 1.18455i) q^{5} +(0.297128 - 3.19127i) q^{6} +(-0.371192 + 1.03741i) q^{7} +(-2.77869 + 0.528101i) q^{8} +(1.58286 - 1.43462i) q^{9} +(-0.918773 - 1.91606i) q^{10} +(-0.264531 - 1.17801i) q^{11} +(-3.85510 - 2.38396i) q^{12} +(3.20030 - 0.885643i) q^{13} +(1.08046 + 1.12278i) q^{14} +(0.988513 - 3.25869i) q^{15} +(-1.07918 + 3.85167i) q^{16} +(-2.73412 + 0.829387i) q^{17} +(-0.821299 - 2.90735i) q^{18} +(-2.24159 - 4.45327i) q^{19} +(-3.00485 - 0.0416848i) q^{20} +(0.0612817 + 2.49634i) q^{21} +(-1.65846 - 0.406031i) q^{22} +(6.94801 - 1.03064i) q^{23} +(-5.44472 + 3.38307i) q^{24} +(0.666320 + 2.66010i) q^{25} +(0.891558 - 4.61061i) q^{26} +(-0.880124 + 1.74851i) q^{27} +(2.10181 - 0.662151i) q^{28} +(-0.267733 - 1.54299i) q^{29} +(-3.50554 - 3.30207i) q^{30} +(-4.39164 + 6.57256i) q^{31} +(4.19956 + 3.78995i) q^{32} +(-1.52018 - 2.27510i) q^{33} +(-0.669539 + 3.98476i) q^{34} +(0.885723 + 1.39871i) q^{35} +(-4.19908 - 0.788760i) q^{36} +(4.16943 - 3.59658i) q^{37} +(-7.05063 + 0.0376228i) q^{38} +(6.04458 - 4.48297i) q^{39} +(-1.94314 + 3.77968i) q^{40} +(-2.70005 + 10.7792i) q^{41} +(3.20038 + 1.49282i) q^{42} +(1.37247 + 3.09625i) q^{43} +(-1.55761 + 1.84515i) q^{44} +(-0.236133 - 3.20118i) q^{45} +(3.06558 - 9.44862i) q^{46} +(0.453104 + 0.552109i) q^{47} +(0.859688 + 9.02447i) q^{48} +(4.47263 + 3.67059i) q^{49} +(3.78842 + 0.829509i) q^{50} +(-5.10474 + 3.98378i) q^{51} +(-5.27885 - 4.02975i) q^{52} +(1.52399 - 8.78298i) q^{53} +(1.66095 + 2.21473i) q^{54} +(-1.63995 - 0.775637i) q^{55} +(0.483569 - 3.07867i) q^{56} +(-8.37205 - 7.58799i) q^{57} +(-2.12275 - 0.631581i) q^{58} +(0.570779 - 2.06253i) q^{59} +(-6.38767 + 2.36274i) q^{60} +(3.94048 + 0.0967333i) q^{61} +(5.56193 + 9.69716i) q^{62} +(0.900751 + 2.17461i) q^{63} +(7.44222 - 2.93485i) q^{64} +(1.90937 - 4.60962i) q^{65} +(-3.83795 + 0.494171i) q^{66} +(-5.91353 + 5.63014i) q^{67} +(4.62584 + 3.35483i) q^{68} +(13.8507 - 7.84635i) q^{69} +(2.32879 - 0.241919i) q^{70} +(0.589298 - 0.0289503i) q^{71} +(-3.64066 + 4.82229i) q^{72} +(-0.135257 - 0.378018i) q^{73} +(-1.93239 - 7.54353i) q^{74} +(3.57860 + 5.08122i) q^{75} +(-4.38787 + 8.95389i) q^{76} +(1.32027 + 0.162840i) q^{77} +(-1.87543 - 10.4762i) q^{78} +(-0.670104 + 0.0659995i) q^{79} +(3.56486 + 4.83894i) q^{80} +(-1.06301 + 10.7930i) q^{81} +(11.9542 + 10.2010i) q^{82} +(-11.0846 - 9.56164i) q^{83} +(3.90413 - 3.11442i) q^{84} +(-1.54506 + 4.00541i) q^{85} +(4.78508 + 0.209487i) q^{86} +(-1.82464 - 3.04423i) q^{87} +(1.35716 + 3.13362i) q^{88} +(1.01680 + 0.150828i) q^{89} +(-4.20312 - 1.71477i) q^{90} +(-0.269150 + 3.64878i) q^{91} +(-10.0389 - 9.82691i) q^{92} +(-3.92515 + 17.4795i) q^{93} +(0.984339 - 0.226565i) q^{94} +(-7.34730 - 1.46147i) q^{95} +(11.9711 + 4.58840i) q^{96} +(-2.42863 + 0.483085i) q^{97} +(7.46284 - 3.35581i) q^{98} +(-2.10872 - 1.48513i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) $ 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{91}{128}\right)$	$1$

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 $

$2$	0.629097	−	1.26658i	0.444839	−	0.895611i
$2$	0.629097	−	1.26658i	0.444839	−	0.895611i
$3$	2.11447	−	0.815642i	1.22079	−	0.470911i	0.338209	−	0.941071i	$-0.390179\pi$
$3$	2.11447	−	0.815642i	1.22079	−	0.470911i	0.882581	+	0.470160i	$0.155804\pi$
$4$	−1.20847	−	1.59361i	−0.604237	−	0.796805i
$5$	0.924429	−	1.18455i	0.413417	−	0.529745i	−0.535809	−	0.844339i	$-0.679993\pi$
$5$	0.924429	−	1.18455i	0.413417	−	0.529745i	0.949226	+	0.314594i	$0.101868\pi$
$6$	0.297128	−	3.19127i	0.121302	−	1.30283i
$7$	−0.371192	+	1.03741i	−0.140298	+	0.392105i	−0.991055	−	0.133453i	$-0.957394\pi$
$7$	−0.371192	+	1.03741i	−0.140298	+	0.392105i	0.850758	+	0.525558i	$0.176144\pi$
$8$	−2.77869	+	0.528101i	−0.982415	+	0.186712i
$9$	1.58286	−	1.43462i	0.527621	−	0.478208i
$10$	−0.918773	−	1.91606i	−0.290542	−	0.605912i
$11$	−0.264531	−	1.17801i	−0.0797590	−	0.355183i	0.919524	−	0.393033i	$-0.128574\pi$
$11$	−0.264531	−	1.17801i	−0.0797590	−	0.355183i	−0.999283	+	0.0378498i	$0.987949\pi$
$12$	−3.85510	−	2.38396i	−1.11287	−	0.688190i
$13$	3.20030	−	0.885643i	0.887604	−	0.245633i	0.207050	−	0.978330i	$-0.433614\pi$
$13$	3.20030	−	0.885643i	0.887604	−	0.245633i	0.680555	+	0.732697i	$0.261739\pi$
$14$	1.08046	+	1.12278i	0.288764	+	0.300076i
$15$	0.988513	−	3.25869i	0.255233	−	0.841391i
$16$	−1.07918	+	3.85167i	−0.269795	+	0.962918i
$17$	−2.73412	+	0.829387i	−0.663122	+	0.201156i	−0.603865	−	0.797087i	$-0.706373\pi$
$17$	−2.73412	+	0.829387i	−0.663122	+	0.201156i	−0.0592576	+	0.998243i	$0.518873\pi$
$18$	−0.821299	−	2.90735i	−0.193582	−	0.685269i
$19$	−2.24159	−	4.45327i	−0.514256	−	1.02165i	−0.989867	−	0.141996i	$-0.954648\pi$
$19$	−2.24159	−	4.45327i	−0.514256	−	1.02165i	0.475611	−	0.879656i	$-0.342227\pi$
$20$	−3.00485	−	0.0416848i	−0.671905	−	0.00932102i
$21$	0.0612817	+	2.49634i	0.0133728	+	0.544746i
$22$	−1.65846	−	0.406031i	−0.353586	−	0.0865661i
$23$	6.94801	−	1.03064i	1.44876	−	0.214903i	0.624461	−	0.781056i	$-0.285319\pi$
$23$	6.94801	−	1.03064i	1.44876	−	0.214903i	0.824300	+	0.566153i	$0.191569\pi$
$24$	−5.44472	+	3.38307i	−1.11140	+	0.690566i
$25$	0.666320	+	2.66010i	0.133264	+	0.532020i
$26$	0.891558	−	4.61061i	0.174849	−	0.904215i
$27$	−0.880124	+	1.74851i	−0.169380	+	0.336500i
$28$	2.10181	−	0.662151i	0.397204	−	0.125135i
$29$	−0.267733	−	1.54299i	−0.0497169	−	0.286525i	0.949948	−	0.312408i	$-0.101135\pi$
$29$	−0.267733	−	1.54299i	−0.0497169	−	0.286525i	−0.999665	+	0.0258823i	$0.991760\pi$
$30$	−3.50554	−	3.30207i	−0.640021	−	0.602872i
$31$	−4.39164	+	6.57256i	−0.788762	+	1.18047i	0.191252	+	0.981541i	$0.438745\pi$
$31$	−4.39164	+	6.57256i	−0.788762	+	1.18047i	−0.980015	+	0.198925i	$0.936255\pi$
$32$	4.19956	+	3.78995i	0.742384	+	0.669974i
$33$	−1.52018	−	2.27510i	−0.264629	−	0.396045i
$34$	−0.669539	+	3.98476i	−0.114825	+	0.683381i
$35$	0.885723	+	1.39871i	0.149714	+	0.236425i
$36$	−4.19908	−	0.788760i	−0.699847	−	0.131460i
$37$	4.16943	−	3.59658i	0.685450	−	0.591273i	−0.239713	−	0.970844i	$-0.577053\pi$
$37$	4.16943	−	3.59658i	0.685450	−	0.591273i	0.925163	+	0.379570i	$0.123928\pi$
$38$	−7.05063	+	0.0376228i	−1.14376	+	0.00610322i
$39$	6.04458	−	4.48297i	0.967908	−	0.717849i
$40$	−1.94314	+	3.77968i	−0.307238	+	0.597619i
$41$	−2.70005	+	10.7792i	−0.421677	+	1.68343i	0.271319	+	0.962490i	$0.412540\pi$
$41$	−2.70005	+	10.7792i	−0.421677	+	1.68343i	−0.692996	+	0.720941i	$0.743710\pi$
$42$	3.20038	+	1.49282i	0.493829	+	0.230347i
$43$	1.37247	+	3.09625i	0.209300	+	0.472173i	0.987850	−	0.155409i	$-0.0496696\pi$
$43$	1.37247	+	3.09625i	0.209300	+	0.472173i	−0.778550	+	0.627582i	$0.784045\pi$
$44$	−1.55761	+	1.84515i	−0.234818	+	0.278167i
$45$	−0.236133	−	3.20118i	−0.0352007	−	0.477204i
$46$	3.06558	−	9.44862i	0.451995	−	1.39312i
$47$	0.453104	+	0.552109i	0.0660920	+	0.0805333i	0.805007	−	0.593265i	$-0.202161\pi$
$47$	0.453104	+	0.552109i	0.0660920	+	0.0805333i	−0.738915	+	0.673799i	$0.764661\pi$
$48$	0.859688	+	9.02447i	0.124085	+	1.30257i
$49$	4.47263	+	3.67059i	0.638947	+	0.524370i
$50$	3.78842	+	0.829509i	0.535764	+	0.117310i
$51$	−5.10474	+	3.98378i	−0.714807	+	0.557841i
$52$	−5.27885	−	4.02975i	−0.732045	−	0.558826i
$53$	1.52399	−	8.78298i	0.209336	−	1.20644i	−0.674370	−	0.738394i	$-0.735585\pi$
$53$	1.52399	−	8.78298i	0.209336	−	1.20644i	0.883706	−	0.468042i	$-0.155040\pi$
$54$	1.66095	+	2.21473i	0.226026	+	0.301387i
$55$	−1.63995	−	0.775637i	−0.221130	−	0.104587i
$56$	0.483569	−	3.07867i	0.0646197	−	0.411405i
$57$	−8.37205	−	7.58799i	−1.10891	−	1.00505i
$58$	−2.12275	−	0.631581i	−0.278731	−	0.0829306i
$59$	0.570779	−	2.06253i	0.0743091	−	0.268519i	−0.917224	−	0.398371i	$-0.869576\pi$
$59$	0.570779	−	2.06253i	0.0743091	−	0.268519i	0.991533	+	0.129853i	$0.0414505\pi$
$60$	−6.38767	+	2.36274i	−0.824645	+	0.305029i
$61$	3.94048	+	0.0967333i	0.504526	+	0.0123854i	0.276010	−	0.961155i	$-0.410988\pi$
$61$	3.94048	+	0.0967333i	0.504526	+	0.0123854i	0.228516	+	0.973540i	$0.426613\pi$
$62$	5.56193	+	9.69716i	0.706366	+	1.23154i
$63$	0.900751	+	2.17461i	0.113484	+	0.273975i
$64$	7.44222	−	2.93485i	0.930277	−	0.366857i
$65$	1.90937	−	4.60962i	0.236828	−	0.571753i
$66$	−3.83795	+	0.494171i	−0.472419	+	0.0608282i
$67$	−5.91353	+	5.63014i	−0.722452	+	0.687832i	−0.958878	−	0.283818i	$-0.908399\pi$
$67$	−5.91353	+	5.63014i	−0.722452	+	0.687832i	0.236426	+	0.971649i	$0.424024\pi$
$68$	4.62584	+	3.35483i	0.560965	+	0.406833i
$69$	13.8507	−	7.84635i	1.66743	−	0.944589i
$70$	2.32879	−	0.241919i	0.278344	−	0.0289149i
$71$	0.589298	−	0.0289503i	0.0699368	−	0.00343577i	−0.0140692	−	0.999901i	$-0.504479\pi$
$71$	0.589298	−	0.0289503i	0.0699368	−	0.00343577i	0.0840060	+	0.996465i	$0.473229\pi$
$72$	−3.64066	+	4.82229i	−0.429056	+	0.568312i
$73$	−0.135257	−	0.378018i	−0.0158306	−	0.0442436i	0.933369	−	0.358919i	$-0.116854\pi$
$73$	−0.135257	−	0.378018i	−0.0158306	−	0.0442436i	−0.949199	+	0.314675i	$0.898104\pi$
$74$	−1.93239	−	7.54353i	−0.224636	−	0.876918i
$75$	3.57860	+	5.08122i	0.413221	+	0.586729i
$76$	−4.38787	+	8.95389i	−0.503324	+	1.02708i
$77$	1.32027	+	0.162840i	0.150459	+	0.0185574i
$78$	−1.87543	−	10.4762i	−0.212351	−	1.18620i
$79$	−0.670104	+	0.0659995i	−0.0753926	+	0.00742553i	−0.135643	−	0.990758i	$-0.543310\pi$
$79$	−0.670104	+	0.0659995i	−0.0753926	+	0.00742553i	0.0602505	+	0.998183i	$0.480810\pi$
$80$	3.56486	+	4.83894i	0.398563	+	0.541009i
$81$	−1.06301	+	10.7930i	−0.118113	+	1.19922i
$82$	11.9542	+	10.2010i	1.32012	+	1.12651i
$83$	−11.0846	−	9.56164i	−1.21669	−	1.04953i	−0.997266	−	0.0738979i	$-0.976456\pi$
$83$	−11.0846	−	9.56164i	−1.21669	−	1.04953i	−0.219427	−	0.975629i	$-0.570419\pi$
$84$	3.90413	−	3.11442i	0.425976	−	0.339811i
$85$	−1.54506	+	4.00541i	−0.167585	+	0.434447i
$86$	4.78508	+	0.209487i	0.515988	+	0.0225896i
$87$	−1.82464	−	3.04423i	−0.195622	−	0.326375i
$88$	1.35716	+	3.13362i	0.144673	+	0.334045i
$89$	1.01680	+	0.150828i	0.107780	+	0.0159877i	0.200403	−	0.979714i	$-0.435775\pi$
$89$	1.01680	+	0.150828i	0.107780	+	0.0159877i	−0.0926224	+	0.995701i	$0.529525\pi$
$90$	−4.20312	−	1.71477i	−0.443048	−	0.180753i
$91$	−0.269150	+	3.64878i	−0.0282146	+	0.382496i
$92$	−10.0389	−	9.82691i	−1.04663	−	1.02453i
$93$	−3.92515	+	17.4795i	−0.407019	+	1.81254i
$94$	0.984339	−	0.226565i	0.101527	−	0.0233684i
$95$	−7.34730	−	1.46147i	−0.753817	−	0.149944i
$96$	11.9711	+	4.58840i	1.22179	+	0.468302i
$97$	−2.42863	+	0.483085i	−0.246590	+	0.0490498i	−0.316838	−	0.948480i	$-0.602621\pi$
$97$	−2.42863	+	0.483085i	−0.246590	+	0.0490498i	0.0702476	+	0.997530i	$0.477621\pi$
$98$	7.46284	−	3.35581i	0.753860	−	0.338988i
$99$	−2.10872	−	1.48513i	−0.211934	−	0.149261i
$100$	3.43393	−	4.27651i	0.343393	−	0.427651i
$101$	11.5475	−	3.81478i	1.14902	−	0.379585i	0.324760	−	0.945796i	$-0.394716\pi$
$101$	11.5475	−	3.81478i	1.14902	−	0.379585i	0.824260	+	0.566212i	$0.191591\pi$
$102$	1.83442	+	8.97177i	0.181634	+	0.888338i
$103$	−7.81646	−	4.68501i	−0.770179	−	0.461627i	0.0742871	−	0.997237i	$-0.476332\pi$
$103$	−7.81646	−	4.68501i	−0.770179	−	0.461627i	−0.844466	+	0.535610i	$0.820082\pi$
$104$	−8.42494	+	4.15101i	−0.826133	+	0.407040i
$105$	3.01368	+	2.23510i	0.294105	+	0.218123i
$106$	−10.1657	−	7.45561i	−0.987375	−	0.724153i
$107$	−8.70181	−	8.28481i	−0.841236	−	0.800923i	0.140717	−	0.990050i	$-0.455059\pi$
$107$	−8.70181	−	8.28481i	−0.841236	−	0.800923i	−0.981953	+	0.189127i	$0.939434\pi$
$108$	3.85004	−	0.710451i	0.370471	−	0.0683632i
$109$	−4.13863	+	12.5278i	−0.396409	+	1.19995i	0.537755	+	0.843101i	$0.319273\pi$
$109$	−4.13863	+	12.5278i	−0.396409	+	1.19995i	−0.934164	+	0.356845i	$0.883852\pi$
$110$	−2.01409	+	1.58918i	−0.192036	+	0.151522i
$111$	5.88263	−	11.0056i	0.558354	−	1.04461i
$112$	−3.59519	−	2.54927i	−0.339714	−	0.240883i
$113$	−3.85484	+	2.06046i	−0.362633	+	0.193831i	−0.642643	−	0.766166i	$-0.722162\pi$
$113$	−3.85484	+	2.06046i	−0.362633	+	0.193831i	0.280010	+	0.959997i	$0.409662\pi$
$114$	−14.8777	+	5.83034i	−1.39342	+	0.546061i
$115$	5.20210	−	9.18300i	0.485099	−	0.856319i
$116$	−2.13537	+	2.29132i	−0.198264	+	0.212744i
$117$	3.79508	−	5.99308i	0.350855	−	0.554061i
$118$	−2.25329	−	2.02047i	−0.207433	−	0.185999i
$119$	0.154468	−	3.14428i	0.0141601	−	0.288235i
$120$	−1.02585	+	9.57692i	−0.0936472	+	0.874249i
$121$	8.62615	−	4.07987i	0.784196	−	0.370897i
$122$	2.60146	−	4.93009i	0.235525	−	0.446350i
$123$	3.08279	+	24.9946i	0.277966	+	2.25369i
$124$	15.7813	−	0.944205i	1.41720	−	0.0847921i
$125$	10.6353	+	4.71430i	0.951250	+	0.421660i
$126$	3.32098	+	0.227160i	0.295857	+	0.0202370i
$127$	2.19600	−	2.19600i	0.194863	−	0.194863i	−0.602931	−	0.797794i	$-0.706000\pi$
$127$	2.19600	−	2.19600i	0.194863	−	0.194863i	0.797794	+	0.602931i	$0.206000\pi$
$128$	0.964636	−	11.2725i	0.0852626	−	0.996359i
$129$	5.42748	+	5.42748i	0.477863	+	0.477863i
$130$	−4.63730	−	5.31827i	−0.406718	−	0.466443i
$131$	1.74661	−	3.94029i	0.152602	−	0.344265i	−0.821557	−	0.570126i	$-0.806894\pi$
$131$	1.74661	−	3.94029i	0.152602	−	0.344265i	0.974160	+	0.225861i	$0.0725194\pi$
$132$	−1.78853	+	5.17197i	−0.155672	+	0.450162i
$133$	5.45195	−	0.672433i	0.472744	−	0.0583074i
$134$	3.41088	+	11.0319i	0.294655	+	0.953010i
$135$	1.25757	+	2.65892i	0.108235	+	0.228843i
$136$	7.15928	−	3.74850i	0.613903	−	0.321431i
$137$	9.40096	+	0.461839i	0.803178	+	0.0394576i	0.446516	−	0.894776i	$-0.352665\pi$
$137$	9.40096	+	0.461839i	0.803178	+	0.0394576i	0.356662	+	0.934233i	$0.383915\pi$
$138$	−1.22461	−	22.4792i	−0.104245	−	1.91356i
$139$	−0.603464	−	0.382140i	−0.0511852	−	0.0324127i	0.509160	−	0.860672i	$-0.329956\pi$
$139$	−0.603464	−	0.382140i	−0.0511852	−	0.0324127i	−0.560345	+	0.828260i	$0.689331\pi$
$140$	1.15862	−	3.10180i	0.0979215	−	0.262150i
$141$	1.40840	+	0.797848i	0.118609	+	0.0671909i
$142$	0.334057	−	0.764608i	0.0280335	−	0.0641645i
$143$	−1.88987	−	3.53571i	−0.158039	−	0.295671i
$144$	3.81751	+	7.64489i	0.318125	+	0.637074i
$145$	−2.07524	−	1.10924i	−0.172339	−	0.0921172i
$146$	−0.563881	−	0.0664954i	−0.0466671	−	0.00550320i
$147$	12.4511	+	4.11330i	1.02695	+	0.339259i
$148$	−10.7702	−	2.29807i	−0.885304	−	0.188901i
$149$	4.73261	−	4.97082i	0.387711	−	0.407225i	−0.501181	−	0.865342i	$-0.667101\pi$
$149$	4.73261	−	4.97082i	0.387711	−	0.407225i	0.888892	+	0.458117i	$0.151476\pi$
$150$	8.68709	−	1.33602i	0.709298	−	0.109086i
$151$	−6.18845	+	8.34416i	−0.503609	+	0.679038i	−0.979726	−	0.200344i	$-0.935794\pi$
$151$	−6.18845	+	8.34416i	−0.503609	+	0.679038i	0.476117	+	0.879382i	$0.342044\pi$
$152$	8.58046	+	11.1905i	0.695967	+	0.907668i
$153$	−3.13789	+	5.23525i	−0.253683	+	0.423245i
$154$	1.03683	−	1.56980i	0.0835502	−	0.126498i
$155$	3.72574	+	11.2780i	0.299258	+	0.905868i
$156$	−14.4488	−	4.21515i	−1.15683	−	0.337482i
$157$	1.76530	−	2.50654i	0.140887	−	0.200044i	−0.741000	−	0.671505i	$-0.765648\pi$
$157$	1.76530	−	2.50654i	0.140887	−	0.200044i	0.881887	+	0.471461i	$0.156273\pi$
$158$	−0.337967	+	0.890264i	−0.0268872	+	0.0708256i
$159$	−3.94133	−	19.8144i	−0.312568	−	1.57138i
$160$	8.37156	−	1.47103i	0.661830	−	0.116296i
$161$	−1.50985	+	7.59052i	−0.118993	+	0.598217i
$162$	13.0015	+	8.13621i	1.02149	+	0.639241i
$163$	−20.1983	−	4.53568i	−1.58205	−	0.355262i	−0.662758	−	0.748833i	$-0.730614\pi$
$163$	−20.1983	−	4.53568i	−1.58205	−	0.355262i	−0.919294	+	0.393572i	$0.871239\pi$
$164$	20.4408	−	8.72358i	1.59616	−	0.681197i
$165$	−4.10026	−	0.302453i	−0.319205	−	0.0235460i
$166$	−19.0839	+	8.02439i	−1.48120	+	0.622813i
$167$	−0.826135	+	5.56935i	−0.0639282	+	0.430969i	0.933456	+	0.358691i	$0.116777\pi$
$167$	−0.826135	+	5.56935i	−0.0639282	+	0.430969i	−0.997385	+	0.0722780i	$0.976973\pi$
$168$	−1.48860	−	6.90419i	−0.114848	−	0.532670i
$169$	−1.69290	+	1.01468i	−0.130223	+	0.0780526i
$170$	4.10120	+	4.47673i	0.314547	+	0.343350i
$171$	−9.93691	−	3.83309i	−0.759894	−	0.293124i
$172$	3.27561	−	5.92892i	0.249763	−	0.452076i
$173$	−11.0501	+	12.8102i	−0.840126	+	0.973940i	−0.999913	−	0.0132119i	$-0.995794\pi$
$173$	−11.0501	+	12.8102i	−0.840126	+	0.973940i	0.159787	+	0.987152i	$0.448919\pi$
$174$	−5.00364	+	0.395947i	−0.379325	+	0.0300166i
$175$	−3.00695	−	0.296159i	−0.227304	−	0.0223875i
$176$	4.82278	+	0.252398i	0.363531	+	0.0190252i
$177$	−0.475390	−	4.82671i	−0.0357325	−	0.362798i
$178$	0.830701	−	1.19298i	0.0622637	−	0.0894173i
$179$	−0.948966	+	7.69401i	−0.0709290	+	0.575077i	0.914450	+	0.404699i	$0.132624\pi$
$179$	−0.948966	+	7.69401i	−0.0709290	+	0.575077i	−0.985379	+	0.170378i	$0.945501\pi$
$180$	−4.81607	+	4.24485i	−0.358969	+	0.316393i
$181$	−6.98404	+	4.91872i	−0.519120	+	0.365606i	−0.805580	−	0.592487i	$-0.798146\pi$
$181$	−6.98404	+	4.91872i	−0.519120	+	0.365606i	0.286460	+	0.958092i	$0.407521\pi$
$182$	4.45217	+	2.63634i	0.330017	+	0.195418i
$183$	8.41092	−	3.00948i	0.621753	−	0.222467i
$184$	−18.7621	+	6.53308i	−1.38316	+	0.481625i
$185$	−0.405968	−	8.26366i	−0.0298473	−	0.607557i
$186$	19.6700	+	15.9678i	1.44227	+	1.17082i
$187$	1.70029	+	3.00142i	0.124337	+	0.219486i
$188$	0.332281	−	1.38928i	0.0242341	−	0.101324i
$189$	−1.48723	−	1.56208i	−0.108180	−	0.113625i
$190$	−6.47324	+	8.38657i	−0.469618	+	0.608426i
$191$	−6.94939	−	2.87853i	−0.502840	−	0.208283i	0.116821	−	0.993153i	$-0.462730\pi$
$191$	−6.94939	−	2.87853i	−0.502840	−	0.208283i	−0.619661	+	0.784870i	$0.712730\pi$
$192$	13.3426	−	12.2758i	0.962917	−	0.885933i
$193$	1.77693	−	0.736028i	0.127906	−	0.0529805i	−0.317812	−	0.948154i	$-0.602948\pi$
$193$	1.77693	−	0.736028i	0.127906	−	0.0529805i	0.445719	+	0.895173i	$0.352948\pi$
$194$	−0.915977	+	3.37998i	−0.0657633	+	0.242668i
$195$	0.277504	−	11.3043i	0.0198725	−	0.809516i
$196$	0.444432	−	11.5634i	0.0317451	−	0.825960i
$197$	26.3422	+	7.28987i	1.87680	+	0.519382i	0.999200	+	0.0399955i	$0.0127344\pi$
$197$	26.3422	+	7.28987i	1.87680	+	0.519382i	0.877604	+	0.479386i	$0.159141\pi$
$198$	−3.20762	+	1.73658i	−0.227956	+	0.123413i
$199$	1.34865	−	1.48800i	0.0956030	−	0.105482i	−0.691270	−	0.722596i	$-0.742949\pi$
$199$	1.34865	−	1.48800i	0.0956030	−	0.105482i	0.786873	+	0.617115i	$0.211699\pi$
$200$	−3.25630	−	7.03970i	−0.230255	−	0.497782i
$201$	−7.91180	+	16.7281i	−0.558055	+	1.17991i
$202$	2.43276	−	17.0258i	0.171168	−	1.19793i
$203$	1.70009	+	0.294994i	0.119323	+	0.0207045i
$204$	12.5175	+	3.32067i	0.876403	+	0.232493i
$205$	10.2725	+	13.1630i	0.717461	+	0.919341i
$206$	−10.8513	+	6.95289i	−0.756044	+	0.484431i
$207$	9.51918	−	11.5992i	0.661629	−	0.806197i
$208$	−0.0424975	+	13.2823i	−0.00294667	+	0.920961i
$209$	−4.65303	+	3.81864i	−0.321857	+	0.264141i
$210$	4.72684	−	2.41099i	0.326183	−	0.166374i
$211$	−14.6467	+	1.08041i	−1.00832	+	0.0743783i	−0.567633	−	0.823282i	$-0.692141\pi$
$211$	−14.6467	+	1.08041i	−1.00832	+	0.0743783i	−0.440689	+	0.897660i	$0.645266\pi$
$212$	−15.8383	+	8.18536i	−1.08778	+	0.562173i
$213$	1.22244	−	0.541871i	0.0837602	−	0.0371284i
$214$	−15.9677	+	5.80963i	−1.09153	+	0.397138i
$215$	4.93640	+	1.23650i	0.336660	+	0.0843288i
$216$	1.52220	−	5.32335i	0.103573	−	0.362208i
$217$	−5.18831	−	6.99563i	−0.352206	−	0.474894i
$218$	13.2639	+	13.1231i	0.898347	+	0.888811i
$219$	−0.594324	−	0.688986i	−0.0401607	−	0.0465574i
$220$	0.745771	+	3.55077i	0.0502799	+	0.239393i
$221$	−8.01548	+	5.07575i	−0.539180	+	0.341432i
$222$	−10.2388	−	14.3744i	−0.687184	−	0.964749i
$223$	−5.65427	+	3.77806i	−0.378638	+	0.252998i	−0.730296	−	0.683131i	$-0.760618\pi$
$223$	−5.65427	+	3.77806i	−0.378638	+	0.252998i	0.351658	+	0.936129i	$0.385618\pi$
$224$	−5.49059	+	2.94988i	−0.366855	+	0.197097i
$225$	4.87094	+	3.25466i	0.324729	+	0.216977i
$226$	0.184673	+	6.17871i	0.0122843	+	0.411002i
$227$	−17.2789	+	2.99817i	−1.14684	+	0.198996i	−0.712446	−	0.701727i	$-0.752413\pi$
$227$	−17.2789	+	2.99817i	−1.14684	+	0.198996i	−0.434394	+	0.900723i	$0.643038\pi$
$228$	−1.97487	+	22.5117i	−0.130789	+	1.49087i
$229$	2.59300	+	1.30521i	0.171350	+	0.0862505i	0.533213	−	0.845981i	$-0.320984\pi$
$229$	2.59300	+	1.30521i	0.171350	+	0.0862505i	−0.361863	+	0.932231i	$0.617859\pi$
$230$	−8.35842	−	12.3659i	−0.551138	−	0.815383i
$231$	2.92450	−	0.732549i	0.192418	−	0.0481982i
$232$	1.55880	+	4.14609i	0.102340	+	0.272204i
$233$	−3.11852	−	21.0233i	−0.204301	−	1.37729i	−0.812250	−	0.583309i	$-0.801758\pi$
$233$	−3.11852	−	21.0233i	−0.204301	−	1.37729i	0.607949	−	0.793976i	$-0.291992\pi$
$234$	−5.20328	−	8.57702i	−0.340149	−	0.560697i
$235$	1.07286	−	0.0263373i	0.0699857	−	0.00171805i
$236$	−3.97664	+	1.58292i	−0.258857	+	0.103039i
$237$	−1.36308	+	0.686119i	−0.0885418	+	0.0445682i
$238$	−3.88532	−	2.17370i	−0.251848	−	0.140900i
$239$	−8.26023	−	27.2303i	−0.534310	−	1.76138i	−0.641477	−	0.767142i	$-0.721678\pi$
$239$	−8.26023	−	27.2303i	−0.534310	−	1.76138i	0.107167	−	0.994241i	$-0.465822\pi$
$240$	11.4846	+	7.32414i	0.741329	+	0.472771i
$241$	−24.3782	−	7.39505i	−1.57034	−	0.476357i	−0.619229	−	0.785211i	$-0.712555\pi$
$241$	−24.3782	−	7.39505i	−1.57034	−	0.476357i	−0.951110	+	0.308854i	$0.900055\pi$
$242$	0.259189	−	13.4924i	0.0166613	−	0.867323i
$243$	4.98918	+	18.0286i	0.320056	+	1.15653i
$244$	−4.60781	−	6.39648i	−0.294985	−	0.409493i
$245$	8.48262	−	1.90484i	0.541935	−	0.121695i
$246$	33.5972	+	11.8194i	2.14208	+	0.753579i
$247$	−11.1178	−	12.2666i	−0.707407	−	0.780504i
$248$	8.73204	−	20.5823i	0.554485	−	1.30698i
$249$	−31.2369	−	11.1768i	−1.97956	−	0.708298i
$250$	12.6617	−	10.5048i	0.800796	−	0.664379i
$251$	23.7908	+	18.5665i	1.50166	+	1.17191i	0.938360	+	0.345660i	$0.112345\pi$
$251$	23.7908	+	18.5665i	1.50166	+	1.17191i	0.563304	+	0.826250i	$0.309530\pi$
$252$	2.37694	−	4.06340i	0.149733	−	0.255970i
$253$	−3.05207	−	7.91218i	−0.191882	−	0.497435i
$254$	−1.39992	−	4.16291i	−0.0878388	−	0.261204i
$255$			9.72953i			0.609287i
$256$	−13.6707	−	8.31329i	−0.854421	−	0.519581i
$257$		−	26.8045i		−	1.67202i	−0.548715	−	0.836009i	$-0.684883\pi$
$257$		−	26.8045i		−	1.67202i	0.548715	−	0.836009i	$-0.315117\pi$
$258$	10.2888	−	3.45995i	0.640551	−	0.215407i
$259$	2.18347	+	5.66044i	0.135674	+	0.351723i
$260$	−9.65335	+	2.52782i	−0.598676	+	0.156769i
$261$	−2.63739	−	2.05824i	−0.163250	−	0.127402i
$262$	−3.89193	−	4.69106i	−0.240444	−	0.289815i
$263$	−12.9226	−	4.62378i	−0.796842	−	0.285115i	−0.0931798	−	0.995649i	$-0.529703\pi$
$263$	−12.9226	−	4.62378i	−0.796842	−	0.285115i	−0.703662	+	0.710535i	$0.748453\pi$
$264$	5.42558	+	5.51900i	0.333921	+	0.339671i
$265$	−8.99502	−	9.92448i	−0.552560	−	0.609656i
$266$	2.57811	−	7.32838i	0.158074	−	0.449332i
$267$	2.27301	−	0.510422i	0.139106	−	0.0312373i
$268$	16.1186	+	2.61996i	0.984600	+	0.160040i
$269$	−6.38363	−	23.0675i	−0.389216	−	1.40645i	−0.853653	−	0.520841i	$-0.825618\pi$
$269$	−6.38363	−	23.0675i	−0.389216	−	1.40645i	0.464437	−	0.885606i	$-0.346257\pi$
$270$	4.15888	+	0.0798922i	0.253101	+	0.00486208i
$271$	−23.5218	−	7.13527i	−1.42885	−	0.433437i	−0.521297	−	0.853375i	$-0.674552\pi$
$271$	−23.5218	−	7.13527i	−1.42885	−	0.433437i	−0.907552	+	0.419939i	$0.862052\pi$
$272$	−0.243915	−	11.4260i	−0.0147895	−	0.692803i
$273$	2.40699	+	7.93477i	0.145677	+	0.480234i
$274$	6.49907	−	11.6166i	0.392623	−	0.701783i
$275$	2.95736	−	1.48861i	0.178335	−	0.0897665i
$276$	−29.2423	−	12.5906i	−1.76018	−	0.757862i
$277$	−13.5121	+	0.331704i	−0.811864	+	0.0199301i	−0.428359	−	0.903609i	$-0.640908\pi$
$277$	−13.5121	+	0.331704i	−0.811864	+	0.0199301i	−0.383505	+	0.923539i	$0.625283\pi$
$278$	−0.863650	+	0.523936i	−0.0517983	+	0.0314236i
$279$	2.47778	+	16.7038i	0.148341	+	1.00003i
$280$	−3.19981	−	3.41883i	−0.191225	−	0.204314i
$281$	1.03955	−	0.260393i	0.0620143	−	0.0155338i	−0.211849	−	0.977302i	$-0.567948\pi$
$281$	1.03955	−	0.260393i	0.0620143	−	0.0155338i	0.273863	+	0.961769i	$0.411698\pi$
$282$	1.89656	−	1.28193i	0.112939	−	0.0763380i
$283$	−7.70195	−	3.87684i	−0.457833	−	0.230454i	0.205679	−	0.978620i	$-0.434060\pi$
$283$	−7.70195	−	3.87684i	−0.457833	−	0.230454i	−0.663512	+	0.748166i	$0.730935\pi$
$284$	−0.758287	−	0.904125i	−0.0449960	−	0.0536499i
$285$	−16.7277	+	2.90253i	−0.990863	+	0.171931i
$286$	−5.66718	+	0.169384i	−0.335108	+	0.0100159i
$287$	−10.1803	−	6.80223i	−0.600922	−	0.401523i
$288$	12.0845	−	0.0258184i	0.712085	−	0.00152136i
$289$	−7.34744	+	4.90940i	−0.432202	+	0.288788i
$290$	−2.71047	+	1.93065i	−0.159164	+	0.113372i
$291$	−4.74125	+	3.00236i	−0.277937	+	0.176002i
$292$	−0.438958	+	0.672371i	−0.0256881	+	0.0393475i
$293$	15.8617	+	18.3881i	0.926649	+	1.07424i	0.997052	+	0.0767249i	$0.0244463\pi$
$293$	15.8617	+	18.3881i	0.926649	+	1.07424i	−0.0704035	+	0.997519i	$0.522429\pi$
$294$	13.0428	−	13.1828i	0.760672	−	0.768834i
$295$	−1.91552	−	2.58278i	−0.111526	−	0.150375i
$296$	−9.68620	+	12.1956i	−0.562999	+	0.708857i
$297$	2.29258	+	0.574260i	0.133029	+	0.0333220i
$298$	−3.31869	−	9.12138i	−0.192247	−	0.528388i
$299$	21.3230	−	9.45182i	1.23314	−	0.546613i
$300$	3.77284	−	11.8434i	0.217825	−	0.683780i
$301$	−3.72154	+	0.274517i	−0.214506	+	0.0158229i
$302$	6.67545	+	13.0875i	0.384129	+	0.753100i
$303$	21.3054	−	17.4849i	1.22396	−	1.00448i
$304$	19.5716	−	3.82798i	1.12251	−	0.219550i
$305$	3.75728	−	4.57825i	0.215141	−	0.262150i
$306$	4.65685	+	7.26788i	0.266214	+	0.415477i
$307$	−5.51325	−	7.06458i	−0.314658	−	0.403197i	0.604805	−	0.796374i	$-0.293251\pi$
$307$	−5.51325	−	7.06458i	−0.314658	−	0.403197i	−0.919463	+	0.393177i	$0.871376\pi$
$308$	−1.33601	−	2.30079i	−0.0761264	−	0.131100i
$309$	−20.3490	−	3.53088i	−1.15761	−	0.200865i
$310$	16.6284	+	2.37597i	0.944427	+	0.134946i
$311$	0.720440	−	1.52324i	0.0408524	−	0.0863752i	−0.882531	−	0.470254i	$-0.844162\pi$
$311$	0.720440	−	1.52324i	0.0408524	−	0.0863752i	0.923383	+	0.383879i	$0.125412\pi$
$312$	−14.4285	+	15.6489i	−0.816856	+	0.885945i
$313$	2.00780	−	2.21526i	0.113488	−	0.125214i	−0.681558	−	0.731764i	$-0.738697\pi$
$313$	2.00780	−	2.21526i	0.113488	−	0.125214i	0.795045	+	0.606550i	$0.207447\pi$
$314$	−2.06420	−	3.81276i	−0.116489	−	0.215167i
$315$	3.40860	+	0.943287i	0.192053	+	0.0531482i
$316$	0.914981	+	0.988126i	0.0514717	+	0.0555864i
$317$	−0.559855	+	22.8060i	−0.0314446	+	1.28091i	0.751881	+	0.659299i	$0.229147\pi$
$317$	−0.559855	+	22.8060i	−0.0314446	+	1.28091i	−0.783326	+	0.621611i	$0.786478\pi$
$318$	−27.5761	−	7.47315i	−1.54639	−	0.419073i
$319$	−1.74683	+	0.723560i	−0.0978036	+	0.0405116i
$320$	3.40333	−	11.5287i	0.190252	−	0.644475i
$321$	−25.1572	−	10.4204i	−1.40414	−	0.581612i
$322$	8.66420	+	6.68753i	0.482837	+	0.372681i
$323$	9.82227	+	10.3167i	0.546526	+	0.574034i
$324$	18.4844	−	11.3490i	1.02691	−	0.630499i
$325$	4.48832	+	7.92300i	0.248967	+	0.439489i
$326$	−18.4515	+	22.7295i	−1.02193	+	1.25887i
$327$	1.46719	+	29.8653i	0.0811358	+	1.65156i
$328$	1.81010	−	31.3780i	0.0999459	−	1.73256i
$329$	−0.740954	+	0.265117i	−0.0408501	+	0.0146164i
$330$	−2.96254	+	5.00305i	−0.163083	+	0.275409i
$331$	−21.6359	+	15.2377i	−1.18921	+	0.837539i	−0.989812	−	0.142378i	$-0.954525\pi$
$331$	−21.6359	+	15.2377i	−1.18921	+	0.837539i	−0.199402	+	0.979918i	$0.563900\pi$
$332$	−1.84207	+	29.2195i	−0.101097	+	1.60363i
$333$	1.43991	−	11.6745i	0.0789064	−	0.639756i
$334$	6.53434	+	4.55003i	0.357543	+	0.248967i
$335$	1.20253	+	12.2095i	0.0657013	+	0.667077i
$336$	−9.68121	−	2.45796i	−0.528154	−	0.134093i
$337$	7.40490	+	0.729319i	0.403371	+	0.0397285i	0.297668	−	0.954669i	$-0.403791\pi$
$337$	7.40490	+	0.729319i	0.403371	+	0.0397285i	0.105702	+	0.994398i	$0.466291\pi$
$338$	0.220187	+	2.78253i	0.0119766	+	0.151350i
$339$	−6.47036	+	7.50094i	−0.351422	+	0.407395i
$340$	8.25021	−	2.37821i	0.447430	−	0.128977i
$341$	8.90426	+	3.43475i	0.482193	+	0.186002i
$342$	−11.1062	+	10.1746i	−0.600555	+	0.550177i
$343$	−12.0836	+	7.24261i	−0.652452	+	0.391064i
$344$	−5.44880	−	7.87870i	−0.293780	−	0.424791i
$345$	3.50966	−	23.6602i	0.188954	−	1.27382i
$346$	9.27357	+	22.0548i	0.498550	+	1.18567i
$347$	25.6022	+	1.88853i	1.37440	+	0.101382i	0.740510	−	0.672045i	$-0.234584\pi$
$347$	25.6022	+	1.88853i	1.37440	+	0.101382i	0.633886	+	0.773427i	$0.281459\pi$
$348$	−2.64628	+	6.58663i	−0.141855	+	0.353080i
$349$	−15.0227	−	3.37345i	−0.804145	−	0.180577i	−0.202440	−	0.979295i	$-0.564887\pi$
$349$	−15.0227	−	3.37345i	−0.804145	−	0.180577i	−0.601706	+	0.798718i	$0.705512\pi$
$350$	−2.26678	+	3.62225i	−0.121164	+	0.193617i
$351$	−1.26811	+	6.37523i	−0.0676868	+	0.340284i
$352$	3.35368	−	5.94968i	0.178752	−	0.317119i
$353$	−0.569440	−	2.86277i	−0.0303082	−	0.152370i	0.962668	−	0.270686i	$-0.0872504\pi$
$353$	−0.569440	−	2.86277i	−0.0303082	−	0.152370i	−0.992976	+	0.118316i	$0.962250\pi$
$354$	−6.41250	−	2.43435i	−0.340821	−	0.129384i
$355$	0.510471	−	0.724813i	0.0270930	−	0.0384691i
$356$	−0.988414	−	1.80265i	−0.0523858	−	0.0955403i
$357$	−2.23798	−	6.77448i	−0.118447	−	0.358543i
$358$	9.14813	+	6.04222i	0.483494	+	0.319342i
$359$	9.85226	−	16.4375i	0.519982	−	0.867538i	−0.479970	−	0.877285i	$-0.659353\pi$
$359$	9.85226	−	16.4375i	0.519982	−	0.867538i	0.999952	+	0.00974690i	$0.00310258\pi$
$360$	2.34669	+	8.77039i	0.123681	+	0.462240i
$361$	−3.48864	+	4.70389i	−0.183613	+	0.247573i
$362$	1.83633	+	11.9402i	0.0965156	+	0.627565i
$363$	14.9120	−	15.6626i	0.782679	−	0.822074i
$364$	6.13999	−	3.98054i	0.321823	−	0.208637i
$365$	−0.572815	−	0.189232i	−0.0299825	−	0.00990488i
$366$	1.47953	−	12.5464i	0.0773362	−	0.655811i
$367$	19.3398	+	10.3373i	1.00953	+	0.539604i	0.891315	−	0.453384i	$-0.149783\pi$
$367$	19.3398	+	10.3373i	1.00953	+	0.539604i	0.118213	+	0.992988i	$0.462283\pi$
$368$	−3.52847	+	27.8737i	−0.183934	+	1.45302i
$369$	11.1903	+	20.9356i	0.582544	+	1.08986i
$370$	−10.7220	−	4.68445i	−0.557411	−	0.243533i
$371$	8.54588	+	4.84118i	0.443680	+	0.251342i
$372$	32.5989	−	14.8684i	1.69018	−	0.770888i
$373$	−27.5136	−	17.4228i	−1.42460	−	0.902119i	−0.424607	−	0.905378i	$-0.639588\pi$
$373$	−27.5136	−	17.4228i	−1.42460	−	0.902119i	−0.999995	+	0.00325870i	$0.998963\pi$
$374$	4.87120	−	0.265370i	0.251884	−	0.0137219i
$375$	26.3332	+	1.29367i	1.35984	+	0.0668047i
$376$	−1.55060	−	1.29485i	−0.0799663	−	0.0667770i
$377$	−2.22336	−	4.70091i	−0.114509	−	0.242109i
$378$	−2.91412	+	0.900998i	−0.149886	+	0.0463423i
$379$	21.0225	−	2.59288i	1.07985	−	0.133187i	0.437216	−	0.899357i	$-0.355965\pi$
$379$	21.0225	−	2.59288i	1.07985	−	0.133187i	0.642639	+	0.766169i	$0.277840\pi$
$380$	6.55001	+	13.4749i	0.336009	+	0.691246i
$381$	2.85222	−	6.43451i	0.146124	−	0.329650i
$382$	−8.01774	+	6.99111i	−0.410223	+	0.357697i
$383$	24.5486	+	24.5486i	1.25437	+	1.25437i	0.953739	+	0.300635i	$0.0971986\pi$
$383$	24.5486	+	24.5486i	1.25437	+	1.25437i	0.300635	+	0.953739i	$0.402801\pi$
$384$	−7.15463	−	24.6222i	−0.365108	−	1.25650i
$385$	1.41339	−	1.41339i	0.0720331	−	0.0720331i
$386$	0.185619	−	2.71366i	0.00944773	−	0.138122i
$387$	6.61439	+	2.93196i	0.336228	+	0.149040i
$388$	3.70479	+	3.28649i	0.188082	+	0.166846i
$389$	−2.25685	−	18.2981i	−0.114427	−	0.927750i	−0.934616	−	0.355658i	$-0.884257\pi$
$389$	−2.25685	−	18.2981i	−0.114427	−	0.927750i	0.820189	−	0.572092i	$-0.193868\pi$
$390$	−14.1432	−	7.46296i	−0.716171	−	0.377902i
$391$	−18.1419	+	8.58049i	−0.917477	+	0.433934i
$392$	−14.3665	−	7.83744i	−0.725617	−	0.395850i
$393$	0.479294	−	9.75625i	0.0241772	−	0.492138i
$394$	25.8050	−	28.7786i	1.30004	−	1.44984i
$395$	−0.541284	+	0.854781i	−0.0272350	+	0.0430087i
$396$	0.181620	+	5.15521i	0.00912673	+	0.259059i
$397$	2.92643	−	5.16588i	0.146873	−	0.259268i	−0.786939	−	0.617031i	$-0.788335\pi$
$397$	2.92643	−	5.16588i	0.146873	−	0.259268i	0.933812	+	0.357763i	$0.116460\pi$
$398$	−1.03625	−	2.64427i	−0.0519426	−	0.132545i
$399$	10.9795	−	5.86867i	0.549663	−	0.293801i
$400$	−10.9649	−	0.304280i	−0.548245	−	0.0152140i
$401$	−11.8576	+	22.1840i	−0.592139	+	1.10781i	0.390205	+	0.920728i	$0.372404\pi$
$401$	−11.8576	+	22.1840i	−0.592139	+	1.10781i	−0.982344	+	0.187086i	$0.940096\pi$
$402$	16.2103	+	20.5446i	0.808494	+	1.02467i
$403$	−8.23365	+	24.9236i	−0.410147	+	1.24153i
$404$	−20.0341	−	13.7921i	−0.996736	−	0.686185i
$405$	11.8021	+	11.2365i	0.586450	+	0.558346i
$406$	1.44316	−	1.96773i	0.0716228	−	0.0976570i
$407$	−5.33974	−	3.96022i	−0.264681	−	0.196301i
$408$	12.0807	−	13.7655i	0.598081	−	0.681494i
$409$	−11.6929	−	7.00848i	−0.578179	−	0.346547i	0.194933	−	0.980817i	$-0.437551\pi$
$409$	−11.6929	−	7.00848i	−0.578179	−	0.346547i	−0.773112	+	0.634269i	$0.781301\pi$
$410$	23.1344	−	4.73018i	1.14253	−	0.233607i
$411$	20.2548	−	6.69127i	0.999093	−	0.330056i
$412$	1.97992	+	18.1181i	0.0975438	+	0.892614i
$413$	1.92783	+	1.35773i	0.0948622	+	0.0668095i
$414$	−8.70282	−	19.3538i	−0.427720	−	0.951189i
$415$	−21.5731	+	4.29116i	−1.05898	+	0.210645i
$416$	16.7964	+	8.40967i	0.823511	+	0.412318i
$417$	−1.58770	−	0.315813i	−0.0777498	−	0.0154654i
$418$	1.90943	+	8.29575i	0.0933932	+	0.405758i
$419$	2.73099	−	12.1617i	0.133418	−	0.594136i	−0.862670	−	0.505767i	$-0.831210\pi$
$419$	2.73099	−	12.1617i	0.133418	−	0.594136i	0.996088	−	0.0883691i	$-0.0281655\pi$
$420$	−0.0800829	−	7.50369i	−0.00390765	−	0.366142i
$421$	1.11051	−	15.0548i	0.0541228	−	0.733725i	−0.900301	−	0.435269i	$-0.856653\pi$
$421$	1.11051	−	15.0548i	0.0541228	−	0.733725i	0.954423	−	0.298456i	$-0.0964717\pi$
$422$	−7.84578	+	19.2310i	−0.381927	+	0.936151i
$423$	1.50927	+	0.223879i	0.0733833	+	0.0108854i
$424$	0.403599	+	25.2100i	0.0196005	+	1.22431i
$425$	−4.02805	−	6.72040i	−0.195389	−	0.325987i
$426$	0.0827084	−	1.88921i	0.00400724	−	0.0915327i
$427$	−1.56303	+	4.05200i	−0.0756402	+	0.196090i
$428$	−2.68684	+	23.8793i	−0.129873	+	1.15425i
$429$	−6.87995	−	5.93469i	−0.332167	−	0.286529i
$430$	4.67161	−	5.47449i	0.225285	−	0.264003i
$431$	2.75187	−	27.9402i	0.132553	−	1.34583i	−0.666921	−	0.745129i	$-0.732388\pi$
$431$	2.75187	−	27.9402i	0.132553	−	1.34583i	0.799474	−	0.600701i	$-0.205112\pi$
$432$	−5.78486	−	5.27690i	−0.278324	−	0.253885i
$433$	18.6892	−	1.84073i	0.898146	−	0.0884597i	0.361603	−	0.932332i	$-0.382230\pi$
$433$	18.6892	−	1.84073i	0.898146	−	0.0884597i	0.536543	+	0.843873i	$0.319730\pi$
$434$	−12.1245	+	2.17051i	−0.581995	+	0.104188i
$435$	−5.29277	−	0.652801i	−0.253769	−	0.0312994i
$436$	24.9659	−	8.54418i	1.19565	−	0.409192i
$437$	−20.1643	−	28.6311i	−0.964590	−	1.36961i
$438$	−1.24655	+	0.319322i	−0.0595623	+	0.0152578i
$439$	4.73475	+	13.2328i	0.225977	+	0.631565i	0.999999	−	0.00159487i	$-0.000507665\pi$
$439$	4.73475	+	13.2328i	0.225977	+	0.631565i	−0.774021	+	0.633160i	$0.781758\pi$
$440$	4.96651	+	1.28920i	0.236769	+	0.0614600i
$441$	12.3455	−	0.606495i	0.587880	−	0.0288807i
$442$	1.38635	+	13.3454i	0.0659420	+	0.634777i
$443$	19.5406	−	11.0696i	0.928400	−	0.525932i	0.0473095	−	0.998880i	$-0.484935\pi$
$443$	19.5406	−	11.0696i	0.928400	−	0.525932i	0.881090	+	0.472948i	$0.156810\pi$
$444$	−24.6477	+	3.92540i	−1.16973	+	0.186291i
$445$	1.11862	−	1.06502i	0.0530277	−	0.0504866i
$446$	1.22815	+	9.53839i	0.0581548	+	0.451656i
$447$	5.95257	−	14.3708i	0.281547	−	0.679714i
$448$	0.282161	+	8.81005i	0.0133308	+	0.416236i
$449$	3.05189	+	7.36791i	0.144027	+	0.347713i	0.979388	−	0.201990i	$-0.0647409\pi$
$449$	3.05189	+	7.36791i	0.144027	+	0.347713i	−0.835360	+	0.549703i	$0.814741\pi$
$450$	7.18659	−	4.12196i	0.338779	−	0.194311i
$451$	13.4123	+	0.329252i	0.631559	+	0.0155039i
$452$	7.94204	+	3.65310i	0.373562	+	0.171827i
$453$	−6.27946	+	22.6910i	−0.295035	+	1.06612i
$454$	−7.07266	+	23.7713i	−0.331936	+	1.11564i
$455$	4.07334	+	3.69186i	0.190961	+	0.173077i
$456$	27.2705	+	16.6634i	1.27706	+	0.780334i
$457$	34.5256	+	16.3294i	1.61504	+	0.763858i	0.999702	−	0.0244050i	$-0.00776914\pi$
$457$	34.5256	+	16.3294i	1.61504	+	0.763858i	0.615339	+	0.788263i	$0.289019\pi$
$458$	3.28440	−	2.46315i	0.153470	−	0.115096i
$459$	0.956179	−	5.51060i	0.0446306	−	0.257213i
$460$	−20.9207	+	2.80729i	−0.975433	+	0.130891i
$461$	−11.6408	+	9.08459i	−0.542168	+	0.423112i	−0.848798	−	0.528717i	$-0.822673\pi$
$461$	−11.6408	+	9.08459i	−0.542168	+	0.423112i	0.306631	+	0.951829i	$0.400798\pi$
$462$	0.911958	−	4.16497i	0.0424281	−	0.193772i
$463$	14.4298	+	11.8422i	0.670609	+	0.550355i	0.906910	−	0.421325i	$-0.138435\pi$
$463$	14.4298	+	11.8422i	0.670609	+	0.550355i	−0.236301	+	0.971680i	$0.575935\pi$
$464$	6.23201	+	0.633939i	0.289314	+	0.0294299i
$465$	17.0767	+	20.8081i	0.791915	+	0.964951i
$466$	−28.5897	−	9.27585i	−1.32439	−	0.429696i
$467$	2.33655	+	31.6759i	0.108123	+	1.46578i	0.730417	+	0.683001i	$0.239326\pi$
$467$	2.33655	+	31.6759i	0.108123	+	1.46578i	−0.622295	+	0.782783i	$0.713799\pi$
$468$	−14.1369	+	1.19462i	−0.653478	+	0.0552211i
$469$	−3.64573	−	8.22464i	−0.168344	−	0.379778i
$470$	0.641575	−	1.37544i	0.0295937	−	0.0634442i
$471$	1.68825	−	6.73986i	0.0777903	−	0.310556i
$472$	−0.496794	+	6.03256i	−0.0228668	+	0.277671i
$473$	3.28434	−	2.43584i	0.151014	−	0.112000i
$474$	0.0115158	+	2.15810i	0.000528938	+	0.0991247i
$475$	10.3525	−	8.93016i	0.475007	−	0.409744i
$476$	−5.19742	+	3.55362i	−0.238223	+	0.162880i
$477$	−10.1880	−	16.0886i	−0.466477	−	0.736647i
$478$	−39.6860	−	6.66823i	−1.81520	−	0.304998i
$479$	−14.6821	−	21.9733i	−0.670842	−	1.00399i	−0.998252	−	0.0591031i	$-0.981176\pi$
$479$	−14.6821	−	21.9733i	−0.670842	−	1.00399i	0.327410	−	0.944882i	$-0.393824\pi$
$480$	16.5016	−	9.93865i	0.753191	−	0.453635i
$481$	10.1582	−	15.2028i	0.463172	−	0.693186i
$482$	−24.7027	+	26.2249i	−1.12518	+	1.19451i
$483$	2.99861	+	17.2814i	0.136442	+	0.786333i
$484$	−16.9262	−	8.81630i	−0.769373	−	0.400741i
$485$	−1.67286	+	3.32340i	−0.0759607	+	0.150908i
$486$	25.9734	+	5.02250i	1.17818	+	0.227825i
$487$	9.61562	+	38.3877i	0.435725	+	1.73951i	0.647379	+	0.762169i	$0.275865\pi$
$487$	9.61562	+	38.3877i	0.435725	+	1.73951i	−0.211653	+	0.977345i	$0.567885\pi$
$488$	−11.0004	+	1.81218i	−0.497967	+	0.0820334i
$489$	−46.4082	+	6.88400i	−2.09865	+	0.311305i
$490$	2.92375	−	11.9423i	0.132082	−	0.539497i
$491$	−0.420342	−	17.1229i	−0.0189698	−	0.772744i	−0.931501	−	0.363738i	$-0.881501\pi$
$491$	−0.420342	−	17.1229i	−0.0189698	−	0.772744i	0.912532	−	0.409006i	$-0.134124\pi$
$492$	36.1062	−	35.1181i	1.62779	−	1.58325i
$493$	2.01175	+	3.99666i	0.0906046	+	0.180001i
$494$	−22.5308	+	6.36474i	−1.01371	+	0.286363i
$495$	−3.70856	+	1.12498i	−0.166687	+	0.0505640i
$496$	−20.5760	−	24.0081i	−0.923888	−	1.07800i
$497$	−0.188709	+	0.622091i	−0.00846477	+	0.0279046i
$498$	−33.8074	+	32.5330i	−1.51494	+	1.45784i
$499$	35.8068	−	9.90908i	1.60293	−	0.443591i	0.653337	−	0.757067i	$-0.273369\pi$
$499$	35.8068	−	9.90908i	1.60293	−	0.443591i	0.949596	+	0.313476i	$0.101494\pi$
$500$	−5.33973	−	22.6456i	−0.238800	−	1.01274i
$501$	2.79575	+	12.4501i	0.124905	+	0.556228i
$502$	38.4828	−	18.4529i	1.71757	−	0.823595i
$503$	16.4072	−	14.8706i	0.731560	−	0.663048i	−0.218243	−	0.975894i	$-0.570033\pi$
$503$	16.4072	−	14.8706i	0.731560	−	0.663048i	0.949804	+	0.312847i	$0.101283\pi$
$504$	−3.65132	−	5.56686i	−0.162643	−	0.247968i
$505$	6.15607	−	17.2051i	0.273941	−	0.765615i
$506$	−11.9415	−	1.11183i	−0.530864	−	0.0494269i
$507$	−2.75197	+	3.52632i	−0.122219	+	0.156609i
$508$	−6.15336	−	0.845755i	−0.273011	−	0.0375243i
$509$	25.8362	−	9.96612i	1.14517	−	0.441741i	0.288436	−	0.957499i	$-0.406865\pi$
$509$	25.8362	−	9.96612i	1.14517	−	0.441741i	0.856734	+	0.515759i	$0.172490\pi$
$510$	12.3233	+	6.12081i	0.545684	+	0.271034i
$511$	0.442367			0.0195691
$512$	−19.1297	+	12.0853i	−0.845422	+	0.534099i
$513$	9.75946			0.430891
$514$	−33.9502	−	16.8626i	−1.49748	−	0.743779i
$515$	−12.7754	+	4.92800i	−0.562950	+	0.217154i
$516$	2.09031	−	15.2082i	0.0920208	−	0.669506i
$517$	0.530529	−	0.679810i	0.0233326	−	0.0298980i
$518$	8.54305	+	0.795412i	0.375360	+	0.0349484i
$519$	−12.9167	+	36.0997i	−0.566979	+	1.58460i
$520$	−2.87119	+	13.8170i	−0.125910	+	0.605917i
$521$	−5.57173	+	5.04992i	−0.244102	+	0.221241i	−0.784436	−	0.620209i	$-0.787048\pi$
$521$	−5.57173	+	5.04992i	−0.244102	+	0.221241i	0.540335	+	0.841450i	$0.318298\pi$
$522$	−4.26611	+	2.04565i	−0.186723	+	0.0895355i
$523$	3.96043	+	17.6366i	0.173177	+	0.771194i	0.982864	+	0.184332i	$0.0590120\pi$
$523$	3.96043	+	17.6366i	0.173177	+	0.771194i	−0.809687	+	0.586862i	$0.800363\pi$
$524$	−8.39003	+	1.97833i	−0.366520	+	0.0864236i
$525$	−6.59968	+	1.82638i	−0.288034	+	0.0797096i
$526$	−13.9860	+	13.4588i	−0.609818	+	0.586830i
$527$	6.55610	−	21.6126i	0.285588	−	0.941458i
$528$	10.4035	−	3.39997i	0.452754	−	0.147965i
$529$	25.2030	−	7.64525i	1.09578	−	0.332402i
$530$	−18.2289	+	5.14950i	−0.791814	+	0.223680i
$531$	−2.05549	−	4.08356i	−0.0892007	−	0.177211i
$532$	−7.66013	−	7.87565i	−0.332109	−	0.341453i
$533$	0.905550	+	36.8880i	0.0392237	+	1.59780i
$534$	0.783452	−	3.20007i	0.0339033	−	0.138480i
$535$	−17.8579	+	2.64898i	−0.772066	+	0.114525i
$536$	13.4586	−	18.7674i	0.581321	−	0.810626i
$537$	4.26899	+	17.0428i	0.184221	+	0.735450i
$538$	−33.2328	−	6.42626i	−1.43277	−	0.277056i
$539$	3.14084	−	6.23978i	0.135286	−	0.268767i
$540$	2.71753	−	5.21732i	0.116944	−	0.224518i
$541$	3.13795	+	18.0845i	0.134911	+	0.777512i	0.972796	+	0.231664i	$0.0744171\pi$
$541$	3.13795	+	18.0845i	0.134911	+	0.777512i	−0.837885	+	0.545847i	$0.816208\pi$
$542$	−23.8349	+	25.3036i	−1.02380	+	1.08688i
$543$	−10.7556	+	16.0970i	−0.461569	+	0.690787i
$544$	−14.6254	−	6.87912i	−0.627061	−	0.294940i
$545$	11.0139	+	16.4835i	0.471784	+	0.706074i
$546$	11.5643	+	1.94309i	0.494906	+	0.0831564i
$547$	−21.8605	−	34.5215i	−0.934688	−	1.47603i	−0.878573	−	0.477609i	$-0.841504\pi$
$547$	−21.8605	−	34.5215i	−0.934688	−	1.47603i	−0.0561148	−	0.998424i	$-0.517871\pi$
$548$	−10.6248	−	15.5396i	−0.453870	−	0.663818i
$549$	6.37601	−	5.49999i	0.272122	−	0.234734i
$550$	−0.0249847	−	4.68222i	−0.00106535	−	0.199651i
$551$	−6.27119	+	4.65103i	−0.267162	+	0.198141i
$552$	−34.3432	+	29.1171i	−1.46174	+	1.23931i
$553$	0.180269	−	0.719673i	0.00766581	−	0.0306036i
$554$	−8.08029	+	17.3229i	−0.343299	+	0.735980i
$555$	−7.59859	−	17.1422i	−0.322542	−	0.727644i
$556$	0.120290	+	1.42349i	0.00510143	+	0.0603695i
$557$	−1.08530	−	14.7130i	−0.0459856	−	0.623411i	−0.970319	−	0.241827i	$-0.922253\pi$
$557$	−1.08530	−	14.7130i	−0.0459856	−	0.623411i	0.924334	−	0.381585i	$-0.124622\pi$
$558$	22.7156	+	7.37001i	0.961627	+	0.311997i
$559$	7.13449	+	8.69340i	0.301757	+	0.367692i
$560$	−6.34322	+	1.90205i	−0.268050	+	0.0803764i
$561$	6.04329	+	4.95960i	0.255148	+	0.209394i
$562$	0.324167	−	1.48049i	0.0136741	−	0.0624507i
$563$	13.6145	−	10.6249i	0.573783	−	0.447784i	−0.286155	−	0.958183i	$-0.592377\pi$
$563$	13.6145	−	10.6249i	0.573783	−	0.447784i	0.859938	+	0.510399i	$0.170502\pi$
$564$	−0.430555	−	3.20861i	−0.0181297	−	0.135107i
$565$	−1.12282	+	6.47098i	−0.0472375	+	0.272236i
$566$	−9.75561	+	7.31627i	−0.410059	+	0.307526i
$567$	−10.8022	−	5.10904i	−0.453648	−	0.214560i
$568$	−1.62219	+	0.391653i	−0.0680654	+	0.0164334i
$569$	7.66626	+	6.94829i	0.321386	+	0.291288i	0.816269	−	0.577672i	$-0.196039\pi$
$569$	7.66626	+	6.94829i	0.321386	+	0.291288i	−0.494882	+	0.868960i	$0.664789\pi$
$570$	−6.84704	+	23.0130i	−0.286791	+	0.963909i
$571$	−6.86155	+	24.7945i	−0.287147	+	1.03762i	0.668647	+	0.743580i	$0.266874\pi$
$571$	−6.86155	+	24.7945i	−0.287147	+	1.03762i	−0.955794	+	0.294036i	$0.905001\pi$
$572$	−3.35067	+	7.28453i	−0.140098	+	0.304581i
$573$	−17.0421	−	0.418361i	−0.711945	−	0.0174773i
$574$	−15.0200	+	8.61490i	−0.626922	+	0.359579i
$575$	7.37120	+	17.7957i	0.307400	+	0.742130i
$576$	7.56961	−	15.3223i	0.315400	−	0.638428i
$577$	5.23256	−	12.6325i	0.217834	−	0.525899i	−0.776753	−	0.629806i	$-0.783134\pi$
$577$	5.23256	−	12.6325i	0.217834	−	0.525899i	0.994587	+	0.103907i	$0.0331344\pi$
$578$	1.59592	+	12.3946i	0.0663816	+	0.515549i
$579$	3.15693	−	3.00565i	0.131198	−	0.124910i
$580$	0.740180	+	4.64761i	0.0307343	+	0.192981i
$581$	14.0339	−	7.95010i	0.582224	−	0.329826i
$582$	0.820042	+	7.89397i	0.0339918	+	0.327216i
$583$	−10.7496	+	0.528093i	−0.445202	+	0.0218714i
$584$	0.575468	+	0.978964i	0.0238130	+	0.0405098i
$585$	−3.59080	−	10.0356i	−0.148461	−	0.414922i
$586$	33.2686	−	8.52227i	1.37431	−	0.352052i
$587$	9.33346	+	13.2525i	0.385233	+	0.546989i	0.963101	−	0.269141i	$-0.0867399\pi$
$587$	9.33346	+	13.2525i	0.385233	+	0.546989i	−0.577867	+	0.816131i	$0.696115\pi$
$588$	−8.49189	−	24.8131i	−0.350199	−	1.02327i
$589$	39.1137	+	4.82421i	1.61165	+	0.198778i
$590$	−4.47635	+	0.801349i	−0.184288	+	0.0329910i
$591$	61.6457	−	6.07158i	2.53577	−	0.249751i
$592$	9.35326	+	19.9406i	0.384417	+	0.819555i
$593$	−3.60979	+	36.6508i	−0.148236	+	1.50507i	0.577101	+	0.816673i	$0.304184\pi$
$593$	−3.60979	+	36.6508i	−0.148236	+	1.50507i	−0.725337	+	0.688394i	$0.758316\pi$
$594$	2.16960	−	2.54248i	0.0890199	−	0.104319i
$595$	−3.58175	−	3.08964i	−0.146837	−	0.126663i
$596$	−13.6408	−	1.53483i	−0.558748	−	0.0628690i
$597$	1.63800	−	4.24635i	0.0670388	−	0.173792i
$598$	1.44268	−	32.9535i	0.0589955	−	1.34757i
$599$	0.697894	+	1.16437i	0.0285152	+	0.0475747i	0.871656	−	0.490118i	$-0.163046\pi$
$599$	0.697894	+	1.16437i	0.0285152	+	0.0475747i	−0.843141	+	0.537692i	$0.819296\pi$
$600$	−12.6272	−	12.2293i	−0.515504	−	0.499258i
$601$	31.9951	+	4.74603i	1.30511	+	0.193595i	0.762827	−	0.646602i	$-0.223811\pi$
$601$	31.9951	+	4.74603i	1.30511	+	0.193595i	0.542281	+	0.840197i	$0.317561\pi$
$602$	−1.99351	+	4.88634i	−0.0812493	+	0.199152i
$603$	−1.28316	+	17.3954i	−0.0522545	+	0.708397i
$604$	20.7759	−	0.221730i	0.845360	−	0.00902209i
$605$	3.14148	−	13.9896i	0.127719	−	0.568759i
$606$	−8.74293	−	37.9847i	−0.355157	−	1.54302i
$607$	42.1810	+	8.39033i	1.71207	+	0.340553i	0.951254	−	0.308409i	$-0.0997966\pi$
$607$	42.1810	+	8.39033i	1.71207	+	0.340553i	0.760821	+	0.648962i	$0.224797\pi$
$608$	7.46399	−	27.1973i	0.302705	−	1.10300i
$609$	3.83541	−	0.762911i	0.155419	−	0.0309147i
$610$	−3.43506	−	7.63907i	−0.139081	−	0.309297i
$611$	1.93904	+	1.36563i	0.0784452	+	0.0552474i
$612$	12.1350	−	1.32610i	0.490528	−	0.0536043i
$613$	0.340976	−	0.112643i	0.0137719	−	0.00454962i	−0.306788	−	0.951778i	$-0.599254\pi$
$613$	0.340976	−	0.112643i	0.0137719	−	0.00454962i	0.320559	+	0.947228i	$0.396129\pi$
$614$	−12.4163	+	2.53870i	−0.501079	+	0.102453i
$615$	32.4571	+	19.4540i	1.30880	+	0.784463i
$616$	−3.75463	+	0.244755i	−0.151278	+	0.00986146i
$617$	−35.9918	−	26.6934i	−1.44898	−	1.07463i	−0.981681	−	0.190532i	$-0.938979\pi$
$617$	−35.9918	−	26.6934i	−1.44898	−	1.07463i	−0.467295	−	0.884101i	$-0.654771\pi$
$618$	−17.2736	+	23.5524i	−0.694847	+	0.947417i
$619$	−26.7731	−	25.4901i	−1.07610	−	1.02453i	−0.999623	−	0.0274615i	$-0.991258\pi$
$619$	−26.7731	−	25.4901i	−1.07610	−	1.02453i	−0.0764776	−	0.997071i	$-0.524367\pi$
$620$	13.4702	−	19.5665i	0.540977	−	0.785810i
$621$	−4.31303	+	13.0557i	−0.173076	+	0.523909i
$622$	−1.47609	−	1.87077i	−0.0591858	−	0.0750109i
$623$	−0.533898	+	0.998854i	−0.0213902	+	0.0400182i
$624$	10.7437	+	28.1197i	0.430093	+	1.12569i
$625$	3.32351	−	1.77645i	0.132940	−	0.0710581i
$626$	−1.54272	−	3.93666i	−0.0616595	−	0.157341i
$627$	−6.72405	+	11.8696i	−0.268533	+	0.474027i
$628$	−6.12777	+	0.215883i	−0.244525	+	0.00861468i
$629$	−8.41679	+	13.2916i	−0.335599	+	0.529969i
$630$	3.33909	−	3.72386i	0.133033	−	0.148362i
$631$	1.52276	−	30.9965i	0.0606201	−	1.23395i	−0.755142	−	0.655562i	$-0.772432\pi$
$631$	1.52276	−	30.9965i	0.0606201	−	1.23395i	0.815762	−	0.578388i	$-0.196318\pi$
$632$	1.82716	−	0.537275i	0.0726804	−	0.0213716i
$633$	−30.0889	+	14.2310i	−1.19592	+	0.565630i
$634$	28.5335	+	15.0563i	1.13321	+	0.597961i
$635$	−0.571216	−	4.63130i	−0.0226680	−	0.183788i
$636$	−26.8134	+	30.2261i	−1.06322	+	1.19854i
$637$	17.5646	+	7.78586i	0.695935	+	0.308487i
$638$	−0.182474	+	2.66769i	−0.00722422	+	0.105615i
$639$	0.891245	−	0.891245i	0.0352571	−	0.0352571i
$640$	−12.4611	−	11.5633i	−0.492567	−	0.457079i
$641$	−0.910762	−	0.910762i	−0.0359729	−	0.0359729i	0.688892	−	0.724864i	$-0.258098\pi$
$641$	−0.910762	−	0.910762i	−0.0359729	−	0.0359729i	−0.724864	+	0.688892i	$0.758098\pi$
$642$	−29.0247	+	25.3082i	−1.14551	+	0.998835i
$643$	17.6906	−	39.9094i	0.697649	−	1.57387i	−0.116484	−	0.993193i	$-0.537162\pi$
$643$	17.6906	−	39.9094i	0.697649	−	1.57387i	0.814133	−	0.580679i	$-0.197213\pi$
$644$	13.9209	−	6.76684i	0.548562	−	0.266651i
$645$	11.4464	−	1.41178i	0.450702	−	0.0555888i
$646$	19.2461	−	5.95057i	0.757227	−	0.234122i
$647$	8.95954	+	18.9434i	0.352236	+	0.744740i	0.999852	−	0.0172270i	$-0.00548380\pi$
$647$	8.95954	+	18.9434i	0.352236	+	0.744740i	−0.647616	+	0.761967i	$0.724234\pi$
$648$	−2.74598	−	30.5516i	−0.107872	−	1.20018i
$649$	−2.58067	−	0.126780i	−0.101300	−	0.00497655i
$650$	12.8587	−	0.700508i	0.504361	−	0.0274762i
$651$	−16.6765	−	10.5603i	−0.653602	−	0.413889i
$652$	17.1810	+	37.6694i	0.672860	+	1.47525i
$653$	20.4138	+	11.5643i	0.798852	+	0.452544i	0.837318	−	0.546716i	$-0.184122\pi$
$653$	20.4138	+	11.5643i	0.798852	+	0.452544i	−0.0384660	+	0.999260i	$0.512247\pi$
$654$	38.7500	+	16.9299i	1.51524	+	0.662010i
$655$	−3.05284	−	5.71147i	−0.119284	−	0.223165i
$656$	−38.6041	−	22.0324i	−1.50724	−	0.860222i
$657$	−0.756406	−	0.404308i	−0.0295102	−	0.0157735i
$658$	−0.130338	+	1.10527i	−0.00508110	+	0.0430877i
$659$	−13.6527	−	4.51025i	−0.531835	−	0.175694i	0.0352123	−	0.999380i	$-0.488789\pi$
$659$	−13.6527	−	4.51025i	−0.531835	−	0.175694i	−0.567047	+	0.823685i	$0.691914\pi$
$660$	4.47307	+	6.89972i	0.174114	+	0.268571i
$661$	1.62191	−	1.70354i	0.0630850	−	0.0662602i	−0.691946	−	0.721949i	$-0.743247\pi$
$661$	1.62191	−	1.70354i	0.0630850	−	0.0662602i	0.755031	+	0.655689i	$0.227622\pi$
$662$	5.68878	+	36.9896i	0.221101	+	1.43764i
$663$	−12.8085	+	17.2703i	−0.497441	+	0.670722i
$664$	35.8502	+	20.7150i	1.39126	+	0.803900i
$665$	4.24341	−	7.07970i	0.164552	−	0.274539i
$666$	−13.8808	−	9.16813i	−0.537872	−	0.355258i
$667$	−3.45048	−	10.4447i	−0.133603	−	0.404422i
$668$	9.87373	−	5.41388i	0.382026	−	0.209469i
$669$	−8.87425	+	12.6005i	−0.343098	+	0.487162i
$670$	16.2209	+	6.15786i	0.626668	+	0.237899i
$671$	−0.928425	−	4.66751i	−0.0358414	−	0.180187i
$672$	−9.20364	+	10.7158i	−0.355038	+	0.413370i
$673$	−7.27060	+	36.5518i	−0.280261	+	1.40897i	0.542249	+	0.840218i	$0.317573\pi$
$673$	−7.27060	+	36.5518i	−0.280261	+	1.40897i	−0.822510	+	0.568750i	$0.807427\pi$
$674$	5.58214	−	8.92012i	0.215016	−	0.343590i
$675$	−5.23764	−	1.17615i	−0.201597	−	0.0452701i
$676$	3.66283	+	1.47160i	0.140878	+	0.0566000i
$677$	8.56346	+	0.631679i	0.329120	+	0.0242774i	0.237116	−	0.971481i	$-0.423798\pi$
$677$	8.56346	+	0.631679i	0.329120	+	0.0242774i	0.0920041	+	0.995759i	$0.470673\pi$
$678$	5.43010	+	12.9141i	0.208542	+	0.495962i
$679$	0.400331	−	2.69881i	0.0153633	−	0.103571i
$680$	2.17797	−	11.9457i	0.0835214	−	0.458097i
$681$	−34.0903	+	20.4329i	−1.30634	+	0.782991i
$682$	9.95204	−	9.11721i	0.381083	−	0.349116i
$683$	−10.5691	−	4.07696i	−0.404416	−	0.156001i	0.149133	−	0.988817i	$-0.452352\pi$
$683$	−10.5691	−	4.07696i	−0.404416	−	0.156001i	−0.553549	+	0.832817i	$0.686727\pi$
$684$	5.90005	+	20.4677i	0.225594	+	0.782603i
$685$	9.23759	−	10.7089i	0.352950	−	0.409167i
$686$	1.57165	+	19.8612i	0.0600058	+	0.758303i
$687$	6.54740	+	0.644863i	0.249799	+	0.0246031i
$688$	−13.4069	+	1.94490i	−0.511132	+	0.0741487i
$689$	−2.90135	−	29.4579i	−0.110533	−	1.12226i
$690$	−27.7598	−	19.3299i	−1.05680	−	0.735875i
$691$	−0.587014	+	4.75938i	−0.0223311	+	0.181055i	−0.999508	−	0.0313727i	$-0.990012\pi$
$691$	−0.587014	+	4.75938i	−0.0223311	+	0.181055i	0.977177	+	0.212428i	$0.0681371\pi$
$692$	33.7682	+	2.12883i	1.28367	+	0.0809259i
$693$	2.32343	−	1.63634i	0.0882597	−	0.0621595i
$694$	18.4982	−	31.2392i	0.702183	−	1.18582i
$695$	−1.01052	+	0.361570i	−0.0383313	+	0.0137151i
$696$	6.67776	+	7.49536i	0.253120	+	0.284111i
$697$	−1.55787	−	31.7111i	−0.0590084	−	1.20114i
$698$	−13.7235	+	16.9053i	−0.519442	+	0.639874i
$699$	−23.7415	−	41.9097i	−0.897987	−	1.58517i
$700$	3.16186	+	5.14981i	0.119507	+	0.194645i
$701$	−21.0293	−	22.0878i	−0.794268	−	0.834245i	0.194933	−	0.980817i	$-0.437551\pi$
$701$	−21.0293	−	22.0878i	−0.794268	−	0.834245i	−0.989200	+	0.146571i	$0.953176\pi$
$702$	7.27700	+	5.61681i	0.274653	+	0.211993i
$703$	−25.3627	−	10.5056i	−0.956572	−	0.396225i
$704$	−5.42598	−	7.99064i	−0.204499	−	0.301159i
$705$	2.24705	−	0.930759i	0.0846289	−	0.0350544i
$706$	−3.98417	−	1.07971i	−0.149946	−	0.0406356i
$707$	−0.328842	+	13.3956i	−0.0123674	+	0.503792i
$708$	−7.11739	+	6.59054i	−0.267488	+	0.247688i
$709$	37.7158	+	10.4374i	1.41645	+	0.391984i	0.889119	−	0.457677i	$-0.151318\pi$
$709$	37.7158	+	10.4374i	1.41645	+	0.391984i	0.527330	+	0.849661i	$0.323193\pi$
$710$	−0.596902	−	1.10253i	−0.0224013	−	0.0413773i
$711$	−0.965999	+	1.06582i	−0.0362278	+	0.0399712i
$712$	−2.90502	+	0.117868i	−0.108870	+	0.00441730i
$713$	−23.7392	+	50.1924i	−0.889042	+	1.87972i
$714$	−9.98836	−	1.42720i	−0.373805	−	0.0534118i
$715$	−5.93526	−	1.02987i	−0.221966	−	0.0385148i
$716$	13.4080	−	7.78573i	0.501082	−	0.290967i
$717$	−39.6762	−	50.8404i	−1.48174	−	1.89867i
$718$	−14.6215	−	22.8195i	−0.545668	−	0.851616i
$719$	−26.0654	+	31.7608i	−0.972076	+	1.18448i	0.0107500	+	0.999942i	$0.496578\pi$
$719$	−26.0654	+	31.7608i	−0.972076	+	1.18448i	−0.982826	+	0.184536i	$0.940922\pi$
$720$	12.5847	+	2.54515i	0.469005	+	0.0948520i
$721$	7.76170	−	6.36986i	0.289061	−	0.237226i
$722$	3.76318	+	7.37786i	0.140051	+	0.274575i
$723$	−57.5787	+	4.24726i	−2.14138	+	0.157957i
$724$	16.2786	+	5.18569i	0.604988	+	0.192725i
$725$	3.92610	−	1.74032i	0.145812	−	0.0646339i
$726$	−10.4569	−	28.7407i	−0.388092	−	1.06667i
$727$	−19.2002	−	4.80939i	−0.712094	−	0.178370i	−0.130026	−	0.991511i	$-0.541506\pi$
$727$	−19.2002	−	4.80939i	−0.712094	−	0.178370i	−0.582068	+	0.813140i	$0.697756\pi$
$728$	−1.17904	−	10.2810i	−0.0436981	−	0.381038i
$729$	5.87295	+	7.91876i	0.217517	+	0.293287i
$730$	−0.600035	+	0.606473i	−0.0222083	+	0.0224466i
$731$	−6.32049	−	7.32721i	−0.233772	−	0.271007i
$732$	−14.9603	−	9.76685i	−0.552949	−	0.360993i
$733$	−29.2222	+	18.5048i	−1.07935	+	0.683489i	−0.951296	−	0.308278i	$-0.900247\pi$
$733$	−29.2222	+	18.5048i	−1.07935	+	0.683489i	−0.128051	+	0.991768i	$0.540872\pi$
$734$	25.2597	−	17.9923i	0.932353	−	0.664108i
$735$	16.3826	−	10.9465i	0.604281	−	0.403768i
$736$	33.0847	+	22.0044i	1.21952	+	0.811092i
$737$	8.19667	+	5.47684i	0.301928	+	0.201742i
$738$	33.5565	−	1.00296i	1.23523	−	0.0369194i
$739$	21.4435	−	3.72079i	0.788810	−	0.136872i	0.237738	−	0.971329i	$-0.423594\pi$
$739$	21.4435	−	3.72079i	0.788810	−	0.136872i	0.551072	+	0.834458i	$0.314219\pi$
$740$	−12.6784	+	10.6334i	−0.466069	+	0.390891i
$741$	−33.5133	−	16.8692i	−1.23114	−	0.619706i
$742$	11.5080	−	7.77851i	0.422470	−	0.285558i
$743$	33.5401	−	8.40136i	1.23047	−	0.308216i	0.427377	−	0.904074i	$-0.359438\pi$
$743$	33.5401	−	8.40136i	1.23047	−	0.308216i	0.803090	+	0.595858i	$0.203188\pi$
$744$	1.67584	−	50.6429i	0.0614394	−	1.85666i
$745$	−1.51320	−	10.2012i	−0.0554394	−	0.373742i
$746$	−39.3762	+	23.8877i	−1.44167	+	0.874591i
$747$	−31.2628	+	0.767458i	−1.14385	+	0.0280798i
$748$	2.72834	−	6.33673i	0.0997582	−	0.231694i
$749$	11.8248	−	5.95211i	0.432069	−	0.217485i
$750$	18.2047	−	32.5394i	0.664741	−	1.18817i
$751$	−5.71073	−	18.8258i	−0.208387	−	0.686961i	−0.997366	−	0.0725400i	$-0.976890\pi$
$751$	−5.71073	−	18.8258i	−0.208387	−	0.686961i	0.788978	−	0.614421i	$-0.210610\pi$
$752$	−2.61552	+	1.14938i	−0.0953783	+	0.0419137i
$753$	65.4487	+	19.8536i	2.38508	+	0.723507i
$754$	−7.35281	−	0.141248i	−0.267773	−	0.00514393i
$755$	4.16326	+	15.0441i	0.151517	+	0.547511i
$756$	−0.692075	+	4.25780i	−0.0251705	+	0.154855i
$757$	18.1967	−	4.08620i	0.661369	−	0.148515i	0.124551	−	0.992213i	$-0.460251\pi$
$757$	18.1967	−	4.08620i	0.661369	−	0.148515i	0.536819	+	0.843698i	$0.319626\pi$
$758$	9.94110	−	28.2580i	0.361077	−	1.02638i
$759$	−12.9070	−	14.2407i	−0.468495	−	0.516904i
$760$	21.1877	+	0.180853i	0.768557	+	0.00656025i
$761$	21.7530	+	7.78336i	0.788547	+	0.282147i	0.700204	−	0.713943i	$-0.253093\pi$
$761$	21.7530	+	7.78336i	0.788547	+	0.282147i	0.0883438	+	0.996090i	$0.471843\pi$
$762$	−6.35553	−	7.66052i	−0.230237	−	0.277511i
$763$	−11.4603	−	8.94370i	−0.414890	−	0.323784i
$764$	3.81090	+	14.5532i	0.137874	+	0.526518i
$765$	3.30064	+	8.55659i	0.119335	+	0.309364i
$766$	46.5363	−	15.6494i	1.68143	−	0.565437i
$767$		−	7.10623i		−	0.256591i
$768$	−35.6871	−	6.42780i	−1.28775	−	0.231943i
$769$		−	17.7601i		−	0.640447i	−0.947342	−	0.320223i	$-0.896242\pi$
$769$		−	17.7601i		−	0.640447i	0.947342	−	0.320223i	$-0.103758\pi$
$770$	−0.901020	−	2.67934i	−0.0324705	−	0.0965567i
$771$	−21.8629	−	56.6773i	−0.787372	−	2.04118i
$772$	−3.32031	−	1.94226i	−0.119501	−	0.0699035i
$773$	−39.2551	−	30.6350i	−1.41191	−	1.10186i	−0.979786	−	0.200049i	$-0.935890\pi$
$773$	−39.2551	−	30.6350i	−1.41191	−	1.10186i	−0.432122	−	0.901815i	$-0.642235\pi$
$774$	7.87466	−	6.53320i	0.283049	−	0.234831i
$775$	−20.4099	−	7.30278i	−0.733145	−	0.262323i
$776$	6.49329	−	2.62490i	0.233096	−	0.0942286i
$777$	9.23379	+	10.1879i	0.331260	+	0.365489i
$778$	−24.5959	−	8.65277i	−0.881804	−	0.310217i
$779$	54.0552	−	12.1385i	1.93673	−	0.434907i
$780$	−18.3499	+	13.2187i	−0.657033	+	0.473305i
$781$	−0.189991	−	0.686540i	−0.00679842	−	0.0245663i
$782$	−0.545108	+	28.3762i	−0.0194930	+	1.01473i
$783$	2.93356	+	0.889886i	0.104837	+	0.0318019i
$784$	−18.9647	+	13.2659i	−0.677310	+	0.473781i
$785$	−1.33721	−	4.40820i	−0.0477272	−	0.157335i
$786$	−12.0556	−	6.74469i	−0.430009	−	0.240575i
$787$	−44.4460	+	22.3722i	−1.58433	+	0.797484i	−0.999902	−	0.0139641i	$-0.995555\pi$
$787$	−44.4460	+	22.3722i	−1.58433	+	0.797484i	−0.584425	+	0.811448i	$0.698680\pi$
$788$	−20.2167	−	50.7888i	−0.720189	−	1.80928i
$789$	−31.0958	+	0.763360i	−1.10704	+	0.0271763i
$790$	0.742133	+	1.22332i	0.0264039	+	0.0435239i
$791$	−0.706656	−	4.76389i	−0.0251258	−	0.169384i
$792$	6.64376	+	3.01309i	0.236076	+	0.107065i
$793$	12.6964	−	3.18028i	0.450862	−	0.112935i
$794$	−4.70201	−	6.95641i	−0.166868	−	0.246874i
$795$	−27.1145	−	13.6483i	−0.961654	−	0.484056i
$796$	−4.00110	−	0.351003i	−0.141815	−	0.0124410i
$797$	50.5422	−	8.76990i	1.79030	−	0.310646i	0.823714	−	0.567005i	$-0.191898\pi$
$797$	50.5422	−	8.76990i	1.79030	−	0.310646i	0.966581	+	0.256360i	$0.0825232\pi$
$798$	−0.525994	−	17.5985i	−0.0186200	−	0.622979i
$799$	−1.69675	−	1.13374i	−0.0600269	−	0.0401087i
$800$	−7.28338	+	13.6966i	−0.257506	+	0.484247i
$801$	1.82583	−	1.21998i	0.0645127	−	0.0431060i
$802$	20.6383	+	28.9745i	0.728764	+	1.02312i
$803$	−0.409528	+	0.259331i	−0.0144519	+	0.00915159i
$804$	36.2193	−	7.60716i	1.27735	−	0.268284i
$805$	7.59558	+	8.80539i	0.267709	+	0.310349i
$806$	26.3881	+	26.1080i	0.929481	+	0.919614i
$807$	−32.3128	−	43.5687i	−1.13746	−	1.53369i
$808$	−30.0723	+	16.6983i	−1.05794	+	0.587445i
$809$	−36.8825	−	9.23857i	−1.29672	−	0.324811i	−0.467628	−	0.883926i	$-0.654891\pi$
$809$	−36.8825	−	9.23857i	−1.29672	−	0.324811i	−0.829090	+	0.559115i	$0.811141\pi$
$810$	21.6566	−	7.87947i	0.760936	−	0.276856i
$811$	7.26363	−	3.21974i	0.255060	−	0.113061i	−0.273749	−	0.961801i	$-0.588264\pi$
$811$	7.26363	−	3.21974i	0.255060	−	0.113061i	0.528809	+	0.848741i	$0.322639\pi$
$812$	−1.58441	−	3.06578i	−0.0556021	−	0.107588i
$813$	−55.5561	+	4.09806i	−1.94844	+	0.143725i
$814$	−8.37517	+	4.27187i	−0.293550	+	0.149729i
$815$	−24.0446	+	19.7329i	−0.842246	+	0.691213i
$816$	−9.83527	−	23.9610i	−0.344303	−	0.838803i
$817$	10.7119	−	13.0525i	0.374762	−	0.456649i
$818$	−16.2328	+	10.4011i	−0.567568	+	0.363666i
$819$	4.80860	+	6.16165i	0.168026	+	0.215306i
$820$	8.56259	−	32.2774i	0.299019	−	1.12718i
$821$	−11.4126	−	1.98027i	−0.398301	−	0.0691118i	−0.0317173	−	0.999497i	$-0.510098\pi$
$821$	−11.4126	−	1.98027i	−0.398301	−	0.0691118i	−0.366584	+	0.930385i	$0.619473\pi$
$822$	4.26714	−	29.8638i	0.148834	−	1.04162i
$823$	12.6395	−	26.7239i	0.440585	−	0.931538i	−0.554469	−	0.832204i	$-0.687079\pi$
$823$	12.6395	−	26.7239i	0.440585	−	0.931538i	0.995054	−	0.0993342i	$-0.0316713\pi$
$824$	24.1937	+	8.89029i	0.842826	+	0.309708i
$825$	5.03908	−	5.55976i	0.175438	−	0.193566i
$826$	2.93247	−	1.58761i	0.102034	−	0.0552401i
$827$	−2.42735	−	0.671737i	−0.0844071	−	0.0233586i	0.224253	−	0.974531i	$-0.428006\pi$
$827$	−2.42735	−	0.671737i	−0.0844071	−	0.0233586i	−0.308660	+	0.951172i	$0.599881\pi$
$828$	−29.9882	−	1.15257i	−1.04216	−	0.0400547i
$829$	−0.163198	+	6.64797i	−0.00566812	+	0.230894i	0.990176	+	0.139824i	$0.0446536\pi$
$829$	−0.163198	+	6.64797i	−0.00566812	+	0.230894i	−0.995845	+	0.0910697i	$0.970971\pi$
$830$	−8.13647	+	30.0238i	−0.282421	+	1.04214i
$831$	−28.3004	+	11.7224i	−0.981730	+	0.406646i
$832$	21.2181	−	15.9836i	0.735606	−	0.554131i
$833$	−15.2731	−	6.32631i	−0.529180	−	0.219194i
$834$	−1.39882	+	1.81228i	−0.0484371	+	0.0627540i
$835$	5.83345	+	6.12706i	0.201875	+	0.212036i
$836$	11.7085	+	2.80038i	0.404946	+	0.0968531i
$837$	−7.62697	−	13.4635i	−0.263627	−	0.465366i
$838$	−13.6857	−	11.1099i	−0.472765	−	0.383785i
$839$	0.340883	+	6.93883i	0.0117686	+	0.239555i	0.997472	+	0.0710640i	$0.0226394\pi$
$839$	0.340883	+	6.93883i	0.0117686	+	0.239555i	−0.985703	+	0.168491i	$0.946111\pi$
$840$	−9.55444	−	4.61911i	−0.329659	−	0.159375i
$841$	24.9957	−	8.94359i	0.861919	−	0.308400i
$842$	−18.3695	−	10.8775i	−0.633056	−	0.374862i
$843$	1.98571	−	1.39849i	0.0683914	−	0.0481667i
$844$	19.4219	+	22.0355i	0.668531	+	0.758494i
$845$	−0.363024	+	2.94332i	−0.0124884	+	0.101253i
$846$	1.23304	−	1.77078i	0.0423928	−	0.0608806i
$847$	1.03055	+	10.4633i	0.0354099	+	0.359523i
$848$	32.1845	+	15.3483i	1.10522	+	0.527064i
$849$	−19.4477	−	1.91543i	−0.667442	−	0.0657373i
$850$	−11.0460	+	0.874088i	−0.378874	+	0.0299810i
$851$	25.2625	−	29.2862i	0.865987	−	1.00392i
$852$	−2.34082	−	1.29326i	−0.0801951	−	0.0443062i
$853$	17.6490	+	6.80798i	0.604291	+	0.233101i	0.642646	−	0.766164i	$-0.277837\pi$
$853$	17.6490	+	6.80798i	0.604291	+	0.233101i	−0.0383549	+	0.999264i	$0.512212\pi$
$854$	4.14890	+	4.52880i	0.141972	+	0.154972i
$855$	−13.7264	+	8.22731i	−0.469434	+	0.281368i
$856$	28.5548	+	18.4255i	0.975984	+	0.629770i
$857$	7.72426	−	52.0727i	0.263856	−	1.77877i	−0.301043	−	0.953611i	$-0.597335\pi$
$857$	7.72426	−	52.0727i	0.263856	−	1.77877i	0.564899	−	0.825160i	$-0.308915\pi$
$858$	−11.8449	+	4.98055i	−0.404380	+	0.170033i
$859$	8.81830	+	0.650477i	0.300877	+	0.0221940i	0.223161	−	0.974782i	$-0.428362\pi$
$859$	8.81830	+	0.650477i	0.300877	+	0.0221940i	0.0777156	+	0.996976i	$0.475237\pi$
$860$	−3.99501	−	9.36097i	−0.136229	−	0.319207i
$861$	−27.0741	−	6.07968i	−0.922681	−	0.207195i
$862$	−33.6574	−	21.0625i	−1.14638	−	0.717393i
$863$	7.67839	−	38.6019i	0.261375	−	1.31402i	−0.597513	−	0.801859i	$-0.703844\pi$
$863$	7.67839	−	38.6019i	0.261375	−	1.31402i	0.858888	−	0.512163i	$-0.171156\pi$
$864$	−10.3229	+	4.00733i	−0.351192	+	0.136332i
$865$	4.95918	+	24.9315i	0.168617	+	0.847696i
$866$	9.42589	−	24.8295i	0.320305	−	0.843739i
$867$	−11.5316	+	16.3737i	−0.391635	+	0.556079i
$868$	−4.87836	+	16.7222i	−0.165582	+	0.567588i
$869$	0.255011	+	0.771930i	0.00865066	+	0.0261859i
$870$	−4.15650	+	6.29307i	−0.140918	+	0.213355i
$871$	−13.9388	+	23.2554i	−0.472297	+	0.787981i
$872$	4.88402	−	36.9965i	0.165394	−	1.25286i
$873$	−3.15115	+	4.24883i	−0.106650	+	0.143801i
$874$	−48.9491	+	7.52806i	−1.65573	+	0.254641i
$875$	−8.83842	+	9.28329i	−0.298793	+	0.313832i
$876$	−0.379750	+	1.77974i	−0.0128306	+	0.0601319i
$877$	−28.3162	−	9.35441i	−0.956171	−	0.315876i	−0.207065	−	0.978327i	$-0.566391\pi$
$877$	−28.3162	−	9.35441i	−0.956171	−	0.315876i	−0.749105	+	0.662451i	$0.769516\pi$
$878$	19.7390	+	2.32771i	0.666160	+	0.0785566i
$879$	48.5371	+	25.9436i	1.63712	+	0.875057i
$880$	4.75729	−	5.47948i	0.160368	−	0.184713i
$881$	12.8085	+	23.9630i	0.431529	+	0.807333i	0.999881	−	0.0154522i	$-0.00491879\pi$
$881$	12.8085	+	23.9630i	0.431529	+	0.807333i	−0.568352	+	0.822786i	$0.692419\pi$
$882$	6.99833	−	16.0182i	0.235646	−	0.539359i
$883$	−5.79220	−	3.28124i	−0.194923	−	0.110423i	0.392335	−	0.919823i	$-0.371667\pi$
$883$	−5.79220	−	3.28124i	−0.194923	−	0.110423i	−0.587258	+	0.809400i	$0.699792\pi$
$884$	17.7753	+	6.63963i	0.597847	+	0.223315i
$885$	−6.15693	−	3.89883i	−0.206963	−	0.131058i
$886$	−1.72767	−	31.7136i	−0.0580422	−	1.06544i
$887$	−18.4680	−	0.907277i	−0.620096	−	0.0304634i	−0.263404	−	0.964685i	$-0.584845\pi$
$887$	−18.4680	−	0.907277i	−0.620096	−	0.0304634i	−0.356692	+	0.934222i	$0.616095\pi$
$888$	−10.5339	+	33.6878i	−0.353495	+	1.13049i
$889$	1.46302	+	3.09329i	0.0490680	+	0.103746i
$890$	−0.645211	−	2.08683i	−0.0216275	−	0.0699505i
$891$	12.9954	−	1.60283i	0.435362	−	0.0536968i
$892$	12.8538	+	4.44501i	0.430377	+	0.148830i
$893$	1.44302	−	3.25540i	0.0482888	−	0.108938i
$894$	−14.4571	−	16.5800i	−0.483516	−	0.554519i
$895$	8.23666	+	8.23666i	0.275321	+	0.275321i
$896$	11.3362	+	5.18500i	0.378715	+	0.173219i
$897$	37.3775	−	37.3775i	1.24800	−	1.24800i
$898$	11.2520	+	0.769654i	0.375485	+	0.0256837i
$899$	11.3172	+	5.01655i	0.377448	+	0.167311i
$900$	−0.699752	−	11.6955i	−0.0233251	−	0.389851i
$901$	3.11771	+	25.2777i	0.103866	+	0.842123i
$902$	8.85464	−	16.7806i	0.294827	−	0.558734i
$903$	−7.64518	+	3.61590i	−0.254416	+	0.120330i
$904$	9.62328	−	7.76111i	0.320065	−	0.258131i
$905$	−0.629803	+	12.8199i	−0.0209354	+	0.426149i
$906$	24.7897	+	22.2283i	0.823584	+	0.738487i
$907$	−15.1270	+	23.8881i	−0.502282	+	0.793191i	−0.997124	−	0.0757929i	$-0.975851\pi$
$907$	−15.1270	+	23.8881i	−0.502282	+	0.793191i	0.494841	+	0.868983i	$0.335226\pi$
$908$	25.6590	+	23.9126i	0.851524	+	0.793567i
$909$	12.8054	−	22.6046i	0.424727	−	0.749748i
$910$	7.23858	−	2.83669i	0.239956	−	0.0940354i
$911$	24.3902	−	13.0368i	0.808083	−	0.431929i	−0.0149744	−	0.999888i	$-0.504767\pi$
$911$	24.3902	−	13.0368i	0.808083	−	0.431929i	0.823057	+	0.567959i	$0.192267\pi$
$912$	38.2614	−	24.0576i	1.26696	−	0.796626i
$913$	−8.33148	+	15.5871i	−0.275732	+	0.515858i
$914$	42.4026	−	33.4569i	1.40255	−	1.10665i
$915$	4.21044	−	12.7452i	0.139193	−	0.421343i
$916$	−1.05358	−	5.70954i	−0.0348114	−	0.188648i
$917$	3.43938	+	3.27457i	0.113578	+	0.108136i
$918$	−6.37811	−	4.67778i	−0.210509	−	0.154390i
$919$	36.6225	+	27.1611i	1.20806	+	0.895961i	0.996678	−	0.0814416i	$-0.0259524\pi$
$919$	36.6225	+	27.1611i	1.20806	+	0.895961i	0.211386	+	0.977403i	$0.432202\pi$
$920$	−9.60548	+	28.2639i	−0.316683	+	0.931834i
$921$	−17.4198	−	10.4410i	−0.574001	−	0.344043i
$922$	4.18320	+	20.4592i	0.137766	+	0.673788i
$923$	1.86029	−	0.614557i	0.0612323	−	0.0202284i
$924$	−4.70158	−	3.77524i	−0.154671	−	0.124196i
$925$	12.3454	+	8.69463i	0.405915	+	0.285878i
$926$	24.0769	−	10.8266i	0.791216	−	0.355786i
$927$	−19.0936	+	3.79796i	−0.627117	+	0.124741i
$928$	4.72347	−	7.49456i	0.155056	−	0.246021i
$929$	−45.3996	−	9.03055i	−1.48951	−	0.296283i	−0.617815	−	0.786324i	$-0.711982\pi$
$929$	−45.3996	−	9.03055i	−1.48951	−	0.296283i	−0.871699	+	0.490041i	$0.836982\pi$
$930$	37.0981	−	8.53885i	1.21650	−	0.280000i
$931$	6.32035	−	28.1458i	0.207141	−	0.922442i
$932$	−29.7343	+	30.3759i	−0.973981	+	0.994995i
$933$	0.280930	−	3.80847i	0.00919723	−	0.124684i
$934$	41.5901	+	16.9677i	1.36087	+	0.555202i
$935$	5.12712	+	0.760536i	0.167675	+	0.0248722i
$936$	−7.38039	+	18.6571i	−0.241236	+	0.609826i
$937$	7.34215	+	12.2496i	0.239857	+	0.400178i	0.953993	−	0.299830i	$-0.0969299\pi$
$937$	7.34215	+	12.2496i	0.239857	+	0.400178i	−0.714135	+	0.700008i	$0.753180\pi$
$938$	−12.7107	−	0.556466i	−0.415020	−	0.0181693i
$939$	2.43857	−	6.32176i	0.0795798	−	0.206303i
$940$	−1.33850	−	1.67789i	−0.0436569	−	0.0547268i
$941$	−20.5396	−	17.7176i	−0.669571	−	0.577576i	0.251078	−	0.967967i	$-0.419215\pi$
$941$	−20.5396	−	17.7176i	−0.669571	−	0.577576i	−0.920649	+	0.390391i	$0.872340\pi$
$942$	−7.47453	−	6.37833i	−0.243534	−	0.207817i
$943$	−7.65051	+	77.6769i	−0.249135	+	2.52951i
$944$	7.32821	+	4.42429i	0.238513	+	0.143999i
$945$	−3.22520	+	0.317654i	−0.104916	+	0.0103333i
$946$	−1.01902	−	5.69228i	−0.0331313	−	0.185072i
$947$	−6.79228	−	0.837748i	−0.220720	−	0.0272232i	0.0112917	−	0.999936i	$-0.496406\pi$
$947$	−6.79228	−	0.837748i	−0.220720	−	0.0272232i	−0.232011	+	0.972713i	$0.574531\pi$
$948$	2.74066	+	1.34307i	0.0890124	+	0.0436208i
$949$	−0.767651	−	1.08998i	−0.0249190	−	0.0353823i
$950$	−4.79805	−	18.7303i	−0.155669	−	0.607691i
$951$	17.4177	+	48.6792i	0.564807	+	1.57853i
$952$	1.23128	+	8.81854i	0.0399059	+	0.285811i
$953$	1.19839	−	0.0588730i	0.0388196	−	0.00190708i	−0.0296486	−	0.999560i	$-0.509439\pi$
$953$	1.19839	−	0.0588730i	0.0388196	−	0.00190708i	0.0684682	+	0.997653i	$0.478189\pi$
$954$	−26.7868	+	2.78267i	−0.867256	+	0.0900924i
$955$	−9.83397	+	5.57087i	−0.318220	+	0.180269i
$956$	−33.4122	+	46.0707i	−1.08063	+	1.49003i
$957$	−3.10345	+	2.95473i	−0.100320	+	0.0955129i
$958$	−37.0675	+	4.77278i	−1.19760	+	0.154201i
$959$	−3.96868	+	9.58125i	−0.128155	+	0.309395i
$960$	−2.20705	−	27.1530i	−0.0712323	−	0.876361i
$961$	−12.0488	−	29.0884i	−0.388671	−	0.938335i
$962$	−12.8651	−	22.4302i	−0.414788	−	0.723178i
$963$	−25.6594	−	0.629902i	−0.826862	−	0.0202983i
$964$	17.6756	+	47.7861i	0.569293	+	1.53909i
$965$	0.770785	−	2.78526i	0.0248125	−	0.0896607i
$966$	23.7748	+	7.07370i	0.764943	+	0.227593i
$967$	34.6952	+	31.4459i	1.11572	+	1.01123i	0.999839	+	0.0179678i	$0.00571964\pi$
$967$	34.6952	+	31.4459i	1.11572	+	1.01123i	0.115883	+	0.993263i	$0.463030\pi$
$968$	−21.8148	+	15.8922i	−0.701155	+	0.510793i
$969$	29.1836	+	13.8028i	0.937513	+	0.443410i
$970$	3.15698	+	4.20956i	0.101365	+	0.135161i
$971$	−7.38242	+	42.5459i	−0.236913	+	1.36536i	0.591978	+	0.805954i	$0.298347\pi$
$971$	−7.38242	+	42.5459i	−0.236913	+	1.36536i	−0.828891	+	0.559410i	$0.811028\pi$
$972$	22.7012	−	29.7379i	0.728142	−	0.953843i
$973$	0.620438	−	0.484194i	0.0198903	−	0.0155226i
$974$	54.6705	+	11.9706i	1.75175	+	0.383562i
$975$	15.9528	+	13.0921i	0.510897	+	0.419282i
$976$	−4.62507	+	15.0730i	−0.148045	+	0.482476i
$977$	14.1494	+	17.2411i	0.452679	+	0.551591i	0.948477	−	0.316847i	$-0.102624\pi$
$977$	14.1494	+	17.2411i	0.452679	+	0.551591i	−0.495797	+	0.868438i	$0.665124\pi$
$978$	−20.4761	+	63.1106i	−0.654753	+	2.01805i
$979$	−0.0912980	−	1.23770i	−0.00291790	−	0.0395569i
$980$	−13.2866	−	11.2160i	−0.424424	−	0.358283i
$981$	11.4218	+	25.7672i	0.364670	+	0.822683i
$982$	−21.9520	−	10.2395i	−0.700516	−	0.326757i
$983$	−3.01488	+	12.0361i	−0.0961597	+	0.383891i	−0.998931	−	0.0462302i	$-0.985279\pi$
$983$	−3.01488	+	12.0361i	−0.0961597	+	0.383891i	0.902771	+	0.430121i	$0.141529\pi$
$984$	−21.7658	−	67.8242i	−0.693868	−	2.16216i
$985$	32.9867	−	24.4646i	1.05104	−	0.779507i
$986$	6.32769	−	0.0337651i	0.201515	−	0.00107530i
$987$	−1.35048	+	1.16494i	−0.0429864	+	0.0370803i
$988$	−6.11258	+	32.5412i	−0.194467	+	1.03527i
$989$	12.7271	+	20.0982i	0.404697	+	0.639087i
$990$	−0.908161	+	5.40492i	−0.0288633	+	0.171780i
$991$	−10.4596	−	15.6539i	−0.332260	−	0.497263i	0.627295	−	0.778781i	$-0.284162\pi$
$991$	−10.4596	−	15.6539i	−0.332260	−	0.497263i	−0.959556	+	0.281519i	$0.909162\pi$
$992$	−43.3526	+	10.9578i	−1.37645	+	0.347909i
$993$	−33.3199	+	49.8668i	−1.05738	+	1.58247i
$994$	0.669215	+	0.630372i	0.0212262	+	0.0199942i
$995$	−0.515879	−	2.97309i	−0.0163545	−	0.0942532i
$996$	19.9377	+	63.2863i	0.631749	+	2.00530i
$997$	−5.59006	+	11.1055i	−0.177039	+	0.351716i	−0.964261	−	0.264953i	$-0.914643\pi$
$997$	−5.59006	+	11.1055i	−0.177039	+	0.351716i	0.787222	+	0.616669i	$0.211518\pi$
$998$	9.97526	−	51.5861i	0.315761	−	1.63293i
$999$	2.61902	+	10.4557i	0.0828621	+	0.330804i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.o.a.157.40	✓	4032
512.437	even	128	inner	512.2.o.a.437.40	yes	4032

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
512.2.o.a.157.40	✓	4032	1.1	even	1	trivial
512.2.o.a.437.40	yes	4032	512.437	even	128	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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.o (of order \(128\), degree \(64\), minimal)

\(f(q)\)	\(=\)	\(q+(0.629097 - 1.26658i) q^{2} +(2.11447 - 0.815642i) q^{3} +(-1.20847 - 1.59361i) q^{4} +(0.924429 - 1.18455i) q^{5} +(0.297128 - 3.19127i) q^{6} +(-0.371192 + 1.03741i) q^{7} +(-2.77869 + 0.528101i) q^{8} +(1.58286 - 1.43462i) q^{9} +O(q^{10})\)	\(q+(0.629097 - 1.26658i) q^{2} +(2.11447 - 0.815642i) q^{3} +(-1.20847 - 1.59361i) q^{4} +(0.924429 - 1.18455i) q^{5} +(0.297128 - 3.19127i) q^{6} +(-0.371192 + 1.03741i) q^{7} +(-2.77869 + 0.528101i) q^{8} +(1.58286 - 1.43462i) q^{9} +(-0.918773 - 1.91606i) q^{10} +(-0.264531 - 1.17801i) q^{11} +(-3.85510 - 2.38396i) q^{12} +(3.20030 - 0.885643i) q^{13} +(1.08046 + 1.12278i) q^{14} +(0.988513 - 3.25869i) q^{15} +(-1.07918 + 3.85167i) q^{16} +(-2.73412 + 0.829387i) q^{17} +(-0.821299 - 2.90735i) q^{18} +(-2.24159 - 4.45327i) q^{19} +(-3.00485 - 0.0416848i) q^{20} +(0.0612817 + 2.49634i) q^{21} +(-1.65846 - 0.406031i) q^{22} +(6.94801 - 1.03064i) q^{23} +(-5.44472 + 3.38307i) q^{24} +(0.666320 + 2.66010i) q^{25} +(0.891558 - 4.61061i) q^{26} +(-0.880124 + 1.74851i) q^{27} +(2.10181 - 0.662151i) q^{28} +(-0.267733 - 1.54299i) q^{29} +(-3.50554 - 3.30207i) q^{30} +(-4.39164 + 6.57256i) q^{31} +(4.19956 + 3.78995i) q^{32} +(-1.52018 - 2.27510i) q^{33} +(-0.669539 + 3.98476i) q^{34} +(0.885723 + 1.39871i) q^{35} +(-4.19908 - 0.788760i) q^{36} +(4.16943 - 3.59658i) q^{37} +(-7.05063 + 0.0376228i) q^{38} +(6.04458 - 4.48297i) q^{39} +(-1.94314 + 3.77968i) q^{40} +(-2.70005 + 10.7792i) q^{41} +(3.20038 + 1.49282i) q^{42} +(1.37247 + 3.09625i) q^{43} +(-1.55761 + 1.84515i) q^{44} +(-0.236133 - 3.20118i) q^{45} +(3.06558 - 9.44862i) q^{46} +(0.453104 + 0.552109i) q^{47} +(0.859688 + 9.02447i) q^{48} +(4.47263 + 3.67059i) q^{49} +(3.78842 + 0.829509i) q^{50} +(-5.10474 + 3.98378i) q^{51} +(-5.27885 - 4.02975i) q^{52} +(1.52399 - 8.78298i) q^{53} +(1.66095 + 2.21473i) q^{54} +(-1.63995 - 0.775637i) q^{55} +(0.483569 - 3.07867i) q^{56} +(-8.37205 - 7.58799i) q^{57} +(-2.12275 - 0.631581i) q^{58} +(0.570779 - 2.06253i) q^{59} +(-6.38767 + 2.36274i) q^{60} +(3.94048 + 0.0967333i) q^{61} +(5.56193 + 9.69716i) q^{62} +(0.900751 + 2.17461i) q^{63} +(7.44222 - 2.93485i) q^{64} +(1.90937 - 4.60962i) q^{65} +(-3.83795 + 0.494171i) q^{66} +(-5.91353 + 5.63014i) q^{67} +(4.62584 + 3.35483i) q^{68} +(13.8507 - 7.84635i) q^{69} +(2.32879 - 0.241919i) q^{70} +(0.589298 - 0.0289503i) q^{71} +(-3.64066 + 4.82229i) q^{72} +(-0.135257 - 0.378018i) q^{73} +(-1.93239 - 7.54353i) q^{74} +(3.57860 + 5.08122i) q^{75} +(-4.38787 + 8.95389i) q^{76} +(1.32027 + 0.162840i) q^{77} +(-1.87543 - 10.4762i) q^{78} +(-0.670104 + 0.0659995i) q^{79} +(3.56486 + 4.83894i) q^{80} +(-1.06301 + 10.7930i) q^{81} +(11.9542 + 10.2010i) q^{82} +(-11.0846 - 9.56164i) q^{83} +(3.90413 - 3.11442i) q^{84} +(-1.54506 + 4.00541i) q^{85} +(4.78508 + 0.209487i) q^{86} +(-1.82464 - 3.04423i) q^{87} +(1.35716 + 3.13362i) q^{88} +(1.01680 + 0.150828i) q^{89} +(-4.20312 - 1.71477i) q^{90} +(-0.269150 + 3.64878i) q^{91} +(-10.0389 - 9.82691i) q^{92} +(-3.92515 + 17.4795i) q^{93} +(0.984339 - 0.226565i) q^{94} +(-7.34730 - 1.46147i) q^{95} +(11.9711 + 4.58840i) q^{96} +(-2.42863 + 0.483085i) q^{97} +(7.46284 - 3.35581i) q^{98} +(-2.10872 - 1.48513i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Introduction

L-functions

Modular forms

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