LMFDB - Embedded newform 640.2.bm.a.101.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(21,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 13, 0]))

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

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

chi := DirichletCharacter("640.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (of order $32$, degree $16$, 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:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			101.19
Character	$\chi$	$=$	640.101
Dual form			640.2.bm.a.621.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.894324 - 1.09553i) q^{2} +(-1.28986 + 0.689446i) q^{3} +(-0.400370 + 1.95952i) q^{4} +(0.634393 + 0.773010i) q^{5} +(1.90886 + 0.796494i) q^{6} +(-1.26430 + 0.844781i) q^{7} +(2.50477 - 1.31382i) q^{8} +(-0.478302 + 0.715829i) q^{9} +(0.279503 - 1.38632i) q^{10} +(-4.83452 + 1.46654i) q^{11} +(-0.834558 - 2.80354i) q^{12} +(2.63983 + 2.16645i) q^{13} +(2.05618 + 0.629575i) q^{14} +(-1.35123 - 0.559697i) q^{15} +(-3.67941 - 1.56906i) q^{16} +(0.000747962 - 0.000309816i) q^{17} +(1.21197 - 0.116189i) q^{18} +(-0.778556 - 7.90481i) q^{19} +(-1.76872 + 0.933614i) q^{20} +(1.04835 - 1.96132i) q^{21} +(5.93026 + 3.98480i) q^{22} +(5.21131 - 1.03659i) q^{23} +(-2.32499 + 3.42155i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(0.0125501 - 4.82953i) q^{26} +(0.553486 - 5.61963i) q^{27} +(-1.14917 - 2.81565i) q^{28} +(-1.18799 + 3.91629i) q^{29} +(0.595271 + 1.98086i) q^{30} +(-5.85584 - 5.85584i) q^{31} +(1.57163 + 5.43415i) q^{32} +(5.22477 - 5.22477i) q^{33} +(-0.00100833 - 0.000542339i) q^{34} +(-1.45509 - 0.441397i) q^{35} +(-1.21118 - 1.22384i) q^{36} +(-5.84997 - 0.576172i) q^{37} +(-7.96367 + 7.92239i) q^{38} +(-4.89867 - 0.974406i) q^{39} +(2.60461 + 1.10273i) q^{40} +(-1.60239 - 8.05574i) q^{41} +(-3.08625 + 0.605559i) q^{42} +(-2.56086 - 1.36881i) q^{43} +(-0.938104 - 10.0605i) q^{44} +(-0.856775 + 0.0843850i) q^{45} +(-5.79621 - 4.78209i) q^{46} +(2.04957 + 4.94810i) q^{47} +(5.82771 - 0.512877i) q^{48} +(-1.79397 + 4.33104i) q^{49} +(1.24895 - 0.663412i) q^{50} +(-0.000751167 + 0.000915299i) q^{51} +(-5.30211 + 4.30541i) q^{52} +(-1.08796 - 3.58653i) q^{53} +(-6.65147 + 4.41941i) q^{54} +(-4.20064 - 2.80677i) q^{55} +(-2.05689 + 3.77705i) q^{56} +(6.45416 + 9.65934i) q^{57} +(5.35286 - 2.20095i) q^{58} +(-7.02430 + 5.76470i) q^{59} +(1.63773 - 2.42367i) q^{60} +(-6.20334 - 11.6056i) q^{61} +(-1.17823 + 11.6523i) q^{62} -1.30909i q^{63} +(4.54773 - 6.58165i) q^{64} +3.41500i q^{65} +(-10.3965 - 1.05125i) q^{66} +(0.708401 + 1.32532i) q^{67} +(0.000307628 + 0.00158969i) q^{68} +(-6.00719 + 4.92997i) q^{69} +(0.817759 + 1.98885i) q^{70} +(1.54955 + 2.31907i) q^{71} +(-0.257561 + 2.42139i) q^{72} +(-5.08158 - 3.39540i) q^{73} +(4.60056 + 6.92410i) q^{74} +(-0.424559 - 1.39958i) q^{75} +(15.8013 + 1.63926i) q^{76} +(4.87340 - 5.93826i) q^{77} +(3.31351 + 6.23808i) q^{78} +(-1.04785 + 2.52973i) q^{79} +(-1.12129 - 3.83962i) q^{80} +(2.17213 + 5.24399i) q^{81} +(-7.39225 + 8.95991i) q^{82} +(-9.55781 + 0.941362i) q^{83} +(3.42351 + 2.83951i) q^{84} +(0.000713993 + 0.000381637i) q^{85} +(0.790667 + 4.02965i) q^{86} +(-1.16772 - 5.87053i) q^{87} +(-10.1826 + 10.0250i) q^{88} +(13.2883 + 2.64320i) q^{89} +(0.858681 + 0.863155i) q^{90} +(-5.16773 - 0.508977i) q^{91} +(-0.0552295 + 10.6267i) q^{92} +(11.5905 + 3.51594i) q^{93} +(3.58781 - 6.67057i) q^{94} +(5.61659 - 5.61659i) q^{95} +(-5.77373 - 5.92575i) q^{96} +(3.96464 + 3.96464i) q^{97} +(6.34917 - 1.90800i) q^{98} +(1.26257 - 4.16214i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

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 $

$2$	−0.894324	−	1.09553i	−0.632382	−	0.774656i
$2$	−0.894324	−	1.09553i	−0.632382	−	0.774656i
$3$	−1.28986	+	0.689446i	−0.744702	+	0.398052i	−0.799673	−	0.600436i	$-0.794994\pi$
$3$	−1.28986	+	0.689446i	−0.744702	+	0.398052i	0.0549704	+	0.998488i	$0.482494\pi$
$4$	−0.400370	+	1.95952i	−0.200185	+	0.979758i
$5$	0.634393	+	0.773010i	0.283709	+	0.345701i
$5$	0.634393	+	0.773010i	0.283709	+	0.345701i
$6$	1.90886	+	0.796494i	0.779290	+	0.325167i
$7$	−1.26430	+	0.844781i	−0.477862	+	0.319297i	−0.771069	−	0.636752i	$-0.780278\pi$
$7$	−1.26430	+	0.844781i	−0.477862	+	0.319297i	0.293207	+	0.956049i	$0.405278\pi$
$8$	2.50477	−	1.31382i	0.885569	−	0.464507i
$9$	−0.478302	+	0.715829i	−0.159434	+	0.238610i
$10$	0.279503	−	1.38632i	0.0883866	−	0.438392i
$11$	−4.83452	+	1.46654i	−1.45766	+	0.442177i	−0.916941	−	0.399024i	$-0.869349\pi$
$11$	−4.83452	+	1.46654i	−1.45766	+	0.442177i	−0.540722	+	0.841201i	$0.681849\pi$
$12$	−0.834558	−	2.80354i	−0.240916	−	0.809312i
$13$	2.63983	+	2.16645i	0.732158	+	0.600866i	0.924823	−	0.380398i	$-0.124213\pi$
$13$	2.63983	+	2.16645i	0.732158	+	0.600866i	−0.192665	+	0.981265i	$0.561713\pi$
$14$	2.05618	+	0.629575i	0.549537	+	0.168261i
$15$	−1.35123	−	0.559697i	−0.348886	−	0.144513i
$16$	−3.67941	−	1.56906i	−0.919852	−	0.392266i
$17$	0.000747962	0	0.000309816i	0.000181408	0	7.51415e-5i	−0.382593	−	0.923917i	$-0.624969\pi$
$17$	0.000747962	0	0.000309816i	0.000181408	0	7.51415e-5i	0.382774	+	0.923842i	$0.374969\pi$
$18$	1.21197	−	0.116189i	0.285664	−	0.0273861i
$19$	−0.778556	−	7.90481i	−0.178613	−	1.81349i	−0.499439	−	0.866349i	$-0.666461\pi$
$19$	−0.778556	−	7.90481i	−0.178613	−	1.81349i	0.320826	−	0.947138i	$-0.396039\pi$
$20$	−1.76872	+	0.933614i	−0.395497	+	0.208762i
$21$	1.04835	−	1.96132i	0.228768	−	0.427995i
$22$	5.93026	+	3.98480i	1.26434	+	0.849563i
$23$	5.21131	−	1.03659i	1.08663	−	0.216145i	0.380895	−	0.924618i	$-0.375616\pi$
$23$	5.21131	−	1.03659i	1.08663	−	0.216145i	0.705737	+	0.708474i	$0.250616\pi$
$24$	−2.32499	+	3.42155i	−0.474588	+	0.698422i
$25$	−0.195090	+	0.980785i	−0.0390181	+	0.196157i
$26$	0.0125501	−	4.82953i	0.00246127	−	0.947148i
$27$	0.553486	−	5.61963i	0.106518	−	1.08150i
$28$	−1.14917	−	2.81565i	−0.217173	−	0.532108i
$29$	−1.18799	+	3.91629i	−0.220605	+	0.727236i	0.774862	+	0.632130i	$0.217819\pi$
$29$	−1.18799	+	3.91629i	−0.220605	+	0.727236i	−0.995467	+	0.0951064i	$0.969681\pi$
$30$	0.595271	+	1.98086i	0.108681	+	0.361654i
$31$	−5.85584	−	5.85584i	−1.05174	−	1.05174i	−0.998586	−	0.0531536i	$-0.983073\pi$
$31$	−5.85584	−	5.85584i	−1.05174	−	1.05174i	−0.0531536	−	0.998586i	$-0.516927\pi$
$32$	1.57163	+	5.43415i	0.277827	+	0.960631i
$33$	5.22477	−	5.22477i	0.909515	−	0.909515i
$34$	−0.00100833		0.000542339i	−0.000172928		9.30104e-5i
$35$	−1.45509	−	0.441397i	−0.245955	−	0.0746097i
$36$	−1.21118	−	1.22384i	−0.201864	−	0.203973i
$37$	−5.84997	−	0.576172i	−0.961730	−	0.0947221i	−0.395050	−	0.918660i	$-0.629273\pi$
$37$	−5.84997	−	0.576172i	−0.961730	−	0.0947221i	−0.566680	+	0.823938i	$0.691773\pi$
$38$	−7.96367	+	7.92239i	−1.29188	+	1.28518i
$39$	−4.89867	−	0.974406i	−0.784415	−	0.156030i
$40$	2.60461	+	1.10273i	0.411825	+	0.174357i
$41$	−1.60239	−	8.05574i	−0.250251	−	1.25810i	−0.877614	−	0.479369i	$-0.840866\pi$
$41$	−1.60239	−	8.05574i	−0.250251	−	1.25810i	0.627363	−	0.778727i	$-0.284134\pi$
$42$	−3.08625	+	0.605559i	−0.476218	+	0.0934398i
$43$	−2.56086	−	1.36881i	−0.390527	−	0.208741i	0.264434	−	0.964404i	$-0.414815\pi$
$43$	−2.56086	−	1.36881i	−0.390527	−	0.208741i	−0.654961	+	0.755663i	$0.727315\pi$
$44$	−0.938104	−	10.0605i	−0.141424	−	1.51667i
$45$	−0.856775	+	0.0843850i	−0.127721	+	0.0125794i
$46$	−5.79621	−	4.78209i	−0.854605	−	0.705081i
$47$	2.04957	+	4.94810i	0.298960	+	0.721754i	0.999963	+	0.00859568i	$0.00273612\pi$
$47$	2.04957	+	4.94810i	0.298960	+	0.721754i	−0.701003	+	0.713159i	$0.747264\pi$
$48$	5.82771	−	0.512877i	0.841158	−	0.0740274i
$49$	−1.79397	+	4.33104i	−0.256282	+	0.618720i
$50$	1.24895	−	0.663412i	0.176629	−	0.0938207i
$51$	−0.000751167	0	0.000915299i	−0.000105184	0	0.000128168i
$52$	−5.30211	+	4.30541i	−0.735271	+	0.597053i
$53$	−1.08796	−	3.58653i	−0.149443	−	0.492648i	0.849973	−	0.526827i	$-0.176618\pi$
$53$	−1.08796	−	3.58653i	−0.149443	−	0.492648i	−0.999416	+	0.0341791i	$0.989118\pi$
$54$	−6.65147	+	4.41941i	−0.905150	+	0.601406i
$55$	−4.20064	−	2.80677i	−0.566414	−	0.378465i
$56$	−2.05689	+	3.77705i	−0.274864	+	0.504730i
$57$	6.45416	+	9.65934i	0.854875	+	1.27941i
$58$	5.35286	−	2.20095i	0.702865	−	0.288999i
$59$	−7.02430	+	5.76470i	−0.914486	+	0.750500i	−0.968753	−	0.248027i	$-0.920218\pi$
$59$	−7.02430	+	5.76470i	−0.914486	+	0.750500i	0.0542668	+	0.998526i	$0.482718\pi$
$60$	1.63773	−	2.42367i	0.211430	−	0.312894i
$61$	−6.20334	−	11.6056i	−0.794256	−	1.48595i	−0.872285	−	0.488998i	$-0.837363\pi$
$61$	−6.20334	−	11.6056i	−0.794256	−	1.48595i	0.0780288	−	0.996951i	$-0.475137\pi$
$62$	−1.17823	+	11.6523i	−0.149635	+	1.47984i
$63$		−	1.30909i		−	0.164929i
$64$	4.54773	−	6.58165i	0.568466	−	0.822707i
$65$			3.41500i			0.423579i
$66$	−10.3965	−	1.05125i	−1.27972	−	0.129400i
$67$	0.708401	+	1.32532i	0.0865449	+	0.161914i	0.921470	−	0.388449i	$-0.126989\pi$
$67$	0.708401	+	1.32532i	0.0865449	+	0.161914i	−0.834925	+	0.550363i	$0.814489\pi$
$68$	0.000307628		0.00158969i	3.73054e−5		0.000192778i
$69$	−6.00719	+	4.92997i	−0.723181	+	0.593499i
$70$	0.817759	+	1.98885i	0.0977408	+	0.237713i
$71$	1.54955	+	2.31907i	0.183898	+	0.275223i	0.911952	−	0.410297i	$-0.134575\pi$
$71$	1.54955	+	2.31907i	0.183898	+	0.275223i	−0.728054	+	0.685520i	$0.759575\pi$
$72$	−0.257561	+	2.42139i	−0.0303539	+	0.285364i
$73$	−5.08158	−	3.39540i	−0.594754	−	0.397402i	0.221445	−	0.975173i	$-0.428923\pi$
$73$	−5.08158	−	3.39540i	−0.594754	−	0.397402i	−0.816199	+	0.577771i	$0.803923\pi$
$74$	4.60056	+	6.92410i	0.534804	+	0.804911i
$75$	−0.424559	−	1.39958i	−0.0490238	−	0.161610i
$76$	15.8013	+	1.63926i	1.81253	+	0.188036i
$77$	4.87340	−	5.93826i	0.555376	−	0.676727i
$78$	3.31351	+	6.23808i	0.375181	+	0.706323i
$79$	−1.04785	+	2.52973i	−0.117892	+	0.284617i	−0.971800	−	0.235808i	$-0.924226\pi$
$79$	−1.04785	+	2.52973i	−0.117892	+	0.284617i	0.853907	+	0.520425i	$0.174226\pi$
$80$	−1.12129	−	3.83962i	−0.125364	−	0.429283i
$81$	2.17213	+	5.24399i	0.241348	+	0.582665i
$82$	−7.39225	+	8.95991i	−0.816338	+	0.989456i
$83$	−9.55781	+	0.941362i	−1.04911	+	0.103328i	−0.607849	−	0.794053i	$-0.707967\pi$
$83$	−9.55781	+	0.941362i	−1.04911	+	0.103328i	−0.441257	+	0.897381i	$0.645467\pi$
$84$	3.42351	+	2.83951i	0.373536	+	0.309816i
$85$	0.000713993	0	0.000381637i	7.74435e−5	0	4.13944e-5i
$86$	0.790667	+	4.02965i	0.0852598	+	0.434528i
$87$	−1.16772	−	5.87053i	−0.125193	−	0.629387i
$88$	−10.1826	+	10.0250i	−1.08547	+	1.06867i
$89$	13.2883	+	2.64320i	1.40856	+	0.280179i	0.840054	−	0.542503i	$-0.182523\pi$
$89$	13.2883	+	2.64320i	1.40856	+	0.280179i	0.568502	+	0.822682i	$0.307523\pi$
$90$	0.858681	+	0.863155i	0.0905129	+	0.0909845i
$91$	−5.16773	−	0.508977i	−0.541725	−	0.0533553i
$92$	−0.0552295	+	10.6267i	−0.00575807	+	1.10791i
$93$	11.5905	+	3.51594i	1.20188	+	0.364586i
$94$	3.58781	−	6.67057i	0.370054	−	0.688016i
$95$	5.61659	−	5.61659i	0.576250	−	0.576250i
$96$	−5.77373	−	5.92575i	−0.589279	−	0.604795i
$97$	3.96464	+	3.96464i	0.402548	+	0.402548i	0.879130	−	0.476582i	$-0.158125\pi$
$97$	3.96464	+	3.96464i	0.402548	+	0.402548i	−0.476582	+	0.879130i	$0.658125\pi$
$98$	6.34917	−	1.90800i	0.641363	−	0.192737i
$99$	1.26257	−	4.16214i	0.126893	−	0.418311i
$100$	−1.84376	−	0.774960i	−0.184376	−	0.0774960i
$101$	−0.536694	+	5.44914i	−0.0534030	+	0.542210i	0.930845	+	0.365415i	$0.119073\pi$
$101$	−0.536694	+	5.44914i	−0.0534030	+	0.542210i	−0.984248	+	0.176795i	$0.943427\pi$
$102$	0.00167452		4.35144e-6i	0.000165803		4.30857e-7i
$103$	2.42588	−	12.1957i	0.239029	−	1.20168i	−0.655684	−	0.755036i	$-0.727620\pi$
$103$	2.42588	−	12.1957i	0.239029	−	1.20168i	0.894712	−	0.446643i	$-0.147380\pi$
$104$	9.45851	+	1.95819i	0.927483	+	0.192016i
$105$	2.18118	−	0.433865i	0.212862	−	0.0423409i
$106$	−2.95616	+	4.39941i	−0.287127	+	0.427309i
$107$	4.13500	−	7.73604i	0.399746	−	0.747872i	−0.598849	−	0.800862i	$-0.704375\pi$
$107$	4.13500	−	7.73604i	0.399746	−	0.747872i	0.998595	+	0.0529901i	$0.0168752\pi$
$108$	10.7902	+	3.33450i	1.03828	+	0.320862i
$109$	−0.703417	−	7.14191i	−0.0673751	−	0.684071i	−0.968249	−	0.249989i	$-0.919573\pi$
$109$	−0.703417	−	7.14191i	−0.0673751	−	0.684071i	0.900873	−	0.434082i	$-0.142927\pi$
$110$	0.681823	+	7.11209i	0.0650093	+	0.678111i
$111$	7.94290	−	3.29006i	0.753907	−	0.312278i
$112$	5.97740	−	1.12452i	0.564812	−	0.106257i
$113$	1.23397	+	0.511126i	0.116082	+	0.0480827i	0.439968	−	0.898013i	$-0.354990\pi$
$113$	1.23397	+	0.511126i	0.116082	+	0.0480827i	−0.323887	+	0.946096i	$0.604990\pi$
$114$	4.80998	−	15.7093i	0.450496	−	1.47131i
$115$	4.10732	+	3.37079i	0.383009	+	0.314327i
$116$	−7.19839	−	3.89586i	−0.668354	−	0.361721i
$117$	−2.81345	+	0.853450i	−0.260103	+	0.0789015i
$118$	12.5974	+	2.53983i	1.15968	+	0.233810i
$119$	−0.000683925		0.00102357i	−6.26953e−5		9.38301e-5i
$120$	−4.11986	+	0.373366i	−0.376090	+	0.0340835i
$121$	12.0757	−	8.06873i	1.09779	−	0.733520i
$122$	−7.16652	+	17.1751i	−0.648826	+	1.55496i
$123$	7.62086	+	9.28604i	0.687149	+	0.837294i
$124$	13.8191	−	9.13011i	1.24099	−	0.819908i
$125$	−0.881921	+	0.471397i	−0.0788814	+	0.0421630i
$126$	−1.43414	+	1.17075i	−0.127764	+	0.104298i
$127$	−16.5287			−1.46668			−0.733341	−	0.679861i	$-0.762040\pi$
$127$	−16.5287			−1.46668			−0.733341	+	0.679861i	$0.762040\pi$
$128$	−11.2775	+	0.903957i	−0.996803	+	0.0798993i
$129$	4.24687			0.373916
$130$	3.74124	−	3.05412i	0.328128	−	0.267864i
$131$	−14.8214	+	7.92221i	−1.29495	+	0.692167i	−0.967541	−	0.252714i	$-0.918677\pi$
$131$	−14.8214	+	7.92221i	−1.29495	+	0.692167i	−0.327413	+	0.944881i	$0.606177\pi$
$132$	8.14618	+	12.3299i	0.709034	+	1.07318i
$133$	7.66216	+	9.33637i	0.664394	+	0.809566i
$134$	0.818393	−	1.96134i	0.0706983	−	0.169434i
$135$	4.69516	−	3.13721i	0.404095	−	0.270008i
$136$	0.00146643	−	0.00175871i	0.000125745	−	0.000150808i
$137$	8.32182	−	12.4545i	0.710981	−	1.06406i	−0.283483	−	0.958977i	$-0.591490\pi$
$137$	8.32182	−	12.4545i	0.710981	−	1.06406i	0.994464	−	0.105081i	$-0.0335101\pi$
$138$	10.7733	+	2.17206i	0.917085	+	0.184898i
$139$	−13.8910	+	4.21380i	−1.17822	+	0.357410i	−0.817868	−	0.575405i	$-0.804844\pi$
$139$	−13.8910	+	4.21380i	−1.17822	+	0.357410i	−0.360355	+	0.932815i	$0.617344\pi$
$140$	1.44750	−	2.67455i	0.122336	−	0.226041i
$141$	−6.05511	−	4.96930i	−0.509932	−	0.418490i
$142$	1.15481	−	3.77157i	0.0969092	−	0.316504i
$143$	−15.9395	−	6.60236i	−1.33293	−	0.552117i
$144$	2.88305	−	1.88334i	0.240254	−	0.156945i
$145$	−3.78099	+	1.56614i	−0.313994	+	0.130061i
$146$	0.824813	+	8.60360i	0.0682620	+	0.712039i
$147$	−0.672035	−	6.82329i	−0.0554285	−	0.562775i
$148$	3.47117	−	11.2324i	0.285329	−	0.923301i
$149$	−9.90610	+	18.5330i	−0.811539	+	1.51828i	0.0431059	+	0.999071i	$0.486275\pi$
$149$	−9.90610	+	18.5330i	−0.811539	+	1.51828i	−0.854645	+	0.519213i	$0.826225\pi$
$150$	−1.15359	+	1.71680i	−0.0941903	+	0.140176i
$151$	10.1057	−	2.01014i	0.822386	−	0.163583i	0.234076	−	0.972218i	$-0.424793\pi$
$151$	10.1057	−	2.01014i	0.822386	−	0.163583i	0.588310	+	0.808635i	$0.299793\pi$
$152$	−12.3356	−	18.7768i	−1.00055	−	1.52300i
$153$	−0.000135976	0	0.000683599i	−1.09930e−5	0	5.52657e-5i
$154$	−10.8639	−	0.0282312i	−0.875441	−	0.00227493i
$155$	0.811720	−	8.24153i	0.0651989	−	0.661976i
$156$	3.87065	−	9.20890i	0.309900	−	0.737302i
$157$	3.04307	−	10.0317i	0.242863	−	0.800613i	−0.747757	−	0.663972i	$-0.768869\pi$
$157$	3.04307	−	10.0317i	0.242863	−	0.800613i	0.990621	−	0.136641i	$-0.0436307\pi$
$158$	3.70852	−	1.11445i	0.295034	−	0.0886609i
$159$	3.87604	+	3.87604i	0.307390	+	0.307390i
$160$	−3.20363	+	4.66227i	−0.253269	+	0.368585i
$161$	−5.71298	+	5.71298i	−0.450246	+	0.450246i
$162$	3.80236	−	7.06946i	0.298741	−	0.555429i
$163$	23.0151	+	6.98156i	1.80268	+	0.546838i	0.998847	−	0.0480137i	$-0.0152891\pi$
$163$	23.0151	+	6.98156i	1.80268	+	0.546838i	0.803836	+	0.594851i	$0.202789\pi$
$164$	16.4269	+	0.0853749i	1.28273	+	0.00666666i
$165$	7.35336	+	0.724243i	0.572458	+	0.0563822i
$166$	9.57906	+	9.62898i	0.743479	+	0.747353i
$167$	22.6943	+	4.51417i	1.75614	+	0.349317i	0.964985	−	0.262305i	$-0.0844826\pi$
$167$	22.6943	+	4.51417i	1.75614	+	0.349317i	0.791150	+	0.611622i	$0.209483\pi$
$168$	0.0490367	−	6.29000i	0.00378326	−	0.485284i
$169$	−0.260984	−	1.31205i	−0.0200757	−	0.100927i
$170$	−0.000220446	−	0.00112351i	−1.69075e−5	−	8.61692e-5i
$171$	6.03088	+	3.22357i	0.461193	+	0.246513i
$172$	3.70749	−	4.47001i	0.282693	−	0.340835i
$173$	−6.89012	+	0.678618i	−0.523846	+	0.0515944i	−0.356485	−	0.934301i	$-0.616025\pi$
$173$	−6.89012	+	0.678618i	−0.523846	+	0.0515944i	−0.167362	+	0.985896i	$0.553525\pi$
$174$	−5.38702	+	6.52942i	−0.408389	+	0.494994i
$175$	−0.581895	−	1.40482i	−0.0439871	−	0.106194i
$176$	20.0893	+	2.18969i	1.51429	+	0.165054i
$177$	5.08594	−	12.2785i	0.382282	−	0.922911i
$178$	−8.98832	−	16.9216i	−0.673703	−	1.26833i
$179$	−8.32001	+	10.1380i	−0.621867	+	0.757747i	−0.984729	−	0.174096i	$-0.944300\pi$
$179$	−8.32001	+	10.1380i	−0.621867	+	0.757747i	0.362862	+	0.931843i	$0.381800\pi$
$180$	0.177673	−	1.71265i	0.0132430	−	0.127653i
$181$	−5.10435	−	16.8268i	−0.379403	−	1.25072i	−0.914034	−	0.405638i	$-0.867049\pi$
$181$	−5.10435	−	16.8268i	−0.379403	−	1.25072i	0.534631	−	0.845086i	$-0.320451\pi$
$182$	4.06402	+	6.11659i	0.301246	+	0.453392i
$183$	16.0029	+	10.6928i	1.18297	+	0.790434i
$184$	11.6912	−	9.44317i	0.861888	−	0.696160i
$185$	−3.26580	−	4.88761i	−0.240106	−	0.359344i
$186$	−6.51385	−	15.8421i	−0.477619	−	1.16160i
$187$	−0.00316168	+	0.00259473i	−0.000231205	+	0.000189745i
$188$	−10.5165	+	2.03509i	−0.766992	+	0.148425i
$189$	4.04758	+	7.57250i	0.294418	+	0.550818i
$190$	−11.1762	−	1.13009i	−0.810806	−	0.0819854i
$191$		−	7.25596i		−	0.525023i	−0.964929	−	0.262512i	$-0.915449\pi$
$191$		−	7.25596i		−	0.525023i	0.964929	−	0.262512i	$-0.0845508\pi$
$192$	−1.32825	+	11.6248i	−0.0958583	+	0.838950i
$193$			19.6751i			1.41624i	0.706091	+	0.708121i	$0.250457\pi$
$193$			19.6751i			1.41624i	−0.706091	+	0.708121i	$0.749543\pi$
$194$	0.797708	−	7.88904i	0.0572721	−	0.566400i
$195$	−2.35446	−	4.40488i	−0.168606	−	0.315440i
$196$	−7.76848	−	5.24934i	−0.554892	−	0.374953i
$197$	−2.67402	+	2.19451i	−0.190516	+	0.156352i	−0.724816	−	0.688943i	$-0.758075\pi$
$197$	−2.67402	+	2.19451i	−0.190516	+	0.156352i	0.534300	+	0.845295i	$0.320575\pi$
$198$	−5.68889	+	2.33912i	−0.404292	+	0.166234i
$199$	3.26353	+	4.88422i	0.231345	+	0.346233i	0.928921	−	0.370278i	$-0.120738\pi$
$199$	3.26353	+	4.88422i	0.231345	+	0.346233i	−0.697575	+	0.716511i	$0.745738\pi$
$200$	0.799924	+	2.71295i	0.0565632	+	0.191835i
$201$	−1.82748	−	1.22108i	−0.128900	−	0.0861285i
$202$	6.44968	−	4.28534i	0.453798	−	0.301515i
$203$	−1.80642	−	5.95497i	−0.126786	−	0.417957i
$204$	−0.00149280	−	0.00183838i	−0.000104517	−	0.000128712i
$205$	5.21063	−	6.34917i	0.363926	−	0.443445i
$206$	−15.5303	+	8.24929i	−1.08205	+	0.574755i
$207$	−1.75055	+	4.22621i	−0.121672	+	0.293742i
$208$	−6.31372	−	12.1133i	−0.437777	−	0.839909i
$209$	15.3566	+	37.0742i	1.06224	+	2.56447i
$210$	−2.42600	−	2.00154i	−0.167410	−	0.138119i
$211$	−12.8596	+	1.26656i	−0.885292	+	0.0871937i	−0.530434	−	0.847726i	$-0.677971\pi$
$211$	−12.8596	+	1.26656i	−0.885292	+	0.0871937i	−0.354858	+	0.934920i	$0.615471\pi$
$212$	7.46345	−	0.695940i	0.512592	−	0.0477973i
$213$	−3.59758	−	1.92294i	−0.246502	−	0.131758i
$214$	−12.1731	+	2.38851i	−0.832136	+	0.163275i
$215$	−0.566488	−	2.84793i	−0.0386342	−	0.194227i
$216$	−5.99686	−	14.8031i	−0.408035	−	1.00722i
$217$	12.3505	+	2.45666i	0.838404	+	0.166769i
$218$	−7.19509	+	7.15779i	−0.487313	+	0.484787i
$219$	8.89548	+	0.876128i	0.601101	+	0.0592032i
$220$	7.18173	−	7.10746i	0.484192	−	0.479185i
$221$	0.00264570		0.000802564i	0.000177969		5.39863e-5i
$222$	−10.7079	−	5.75931i	−0.718666	−	0.386539i
$223$	−2.76259	+	2.76259i	−0.184997	+	0.184997i	−0.793529	−	0.608532i	$-0.791759\pi$
$223$	−2.76259	+	2.76259i	−0.184997	+	0.184997i	0.608532	+	0.793529i	$0.291759\pi$
$224$	−6.57768	−	5.54274i	−0.439490	−	0.370340i
$225$	−0.608763	−	0.608763i	−0.0405842	−	0.0405842i
$226$	−0.543613	−	1.80896i	−0.0361606	−	0.120330i
$227$	−7.04497	+	23.2242i	−0.467591	+	1.54144i	0.333412	+	0.942781i	$0.391800\pi$
$227$	−7.04497	+	23.2242i	−0.467591	+	1.54144i	−0.801003	+	0.598660i	$0.795700\pi$
$228$	−21.5117	+	8.77973i	−1.42465	+	0.581452i
$229$	1.13159	−	11.4892i	0.0747776	−	0.759230i	−0.882549	−	0.470221i	$-0.844174\pi$
$229$	1.13159	−	11.4892i	0.0747776	−	0.759230i	0.957326	−	0.289009i	$-0.0933257\pi$
$230$	0.0195266	−	7.51426i	0.00128755	−	0.495476i
$231$	−2.19191	+	11.0195i	−0.144217	+	0.725028i
$232$	2.16967	+	11.3702i	0.142446	+	0.746491i
$233$	−11.3449	+	2.25664i	−0.743229	+	0.147837i	−0.552159	−	0.833739i	$-0.686196\pi$
$233$	−11.3449	+	2.25664i	−0.743229	+	0.147837i	−0.191070	+	0.981576i	$0.561196\pi$
$234$	3.45111	+	2.31896i	0.225606	+	0.151595i
$235$	−2.52470	+	4.72338i	−0.164693	+	0.308119i
$236$	−8.48370	−	16.0722i	−0.552242	−	1.04621i
$237$	−0.392532	−	3.98544i	−0.0254977	−	0.258882i
$238$	0.00173300		0.000166139i	0.000112334		1.07692e-5i
$239$	−23.9121	+	9.90473i	−1.54675	+	0.640684i	−0.982724	−	0.185076i	$-0.940747\pi$
$239$	−23.9121	+	9.90473i	−1.54675	+	0.640684i	−0.564023	+	0.825759i	$0.690747\pi$
$240$	4.09352	+	4.17952i	0.264236	+	0.269787i
$241$	17.1861	+	7.11870i	1.10705	+	0.458556i	0.859921	−	0.510426i	$-0.170512\pi$
$241$	17.1861	+	7.11870i	1.10705	+	0.458556i	0.247130	+	0.968982i	$0.420512\pi$
$242$	−19.6391	−	6.01323i	−1.26245	−	0.386545i
$243$	6.67797	+	5.48047i	0.428392	+	0.351572i
$244$	25.2251	−	7.50900i	1.61487	−	0.480714i
$245$	−4.48602	+	1.36082i	−0.286601	+	0.0869396i
$246$	3.35762	−	16.6536i	0.214074	−	1.06179i
$247$	15.0701	−	22.5541i	0.958891	−	1.43508i
$248$	−22.3611	−	6.97398i	−1.41993	−	0.442848i
$249$	11.6792	−	7.80381i	0.740141	−	0.494547i
$250$	1.30515	+	0.544590i	0.0825451	+	0.0344429i
$251$	0.879036	+	1.07111i	0.0554842	+	0.0676077i	0.800013	−	0.599983i	$-0.204826\pi$
$251$	0.879036	+	1.07111i	0.0554842	+	0.0676077i	−0.744529	+	0.667590i	$0.767326\pi$
$252$	2.56518	+	0.524119i	0.161591	+	0.0330164i
$253$	−23.6740	+	12.6540i	−1.48837	+	0.795550i
$254$	14.7820	+	18.1076i	0.927504	+	1.13617i
$255$	−0.00118407			−7.41494e−5
$256$	11.0761	+	11.5464i	0.692255	+	0.721653i
$257$	0.664203			0.0414318			0.0207159	−	0.999785i	$-0.493405\pi$
$257$	0.664203			0.0414318			0.0207159	+	0.999785i	$0.493405\pi$
$258$	−3.79807	−	4.65257i	−0.236458	−	0.289656i
$259$	7.88288	−	4.21349i	0.489819	−	0.261814i
$260$	−6.69175	−	1.36726i	−0.415005	−	0.0847941i
$261$	−2.23518	−	2.72357i	−0.138354	−	0.168585i
$262$	21.9342	+	9.15228i	1.35510	+	0.565430i
$263$	−18.7456	+	12.5254i	−1.15591	+	0.772351i	−0.977361	−	0.211580i	$-0.932139\pi$
$263$	−18.7456	+	12.5254i	−1.15591	+	0.772351i	−0.178545	+	0.983932i	$0.557139\pi$
$264$	6.22240	−	19.9513i	0.382963	−	1.22792i
$265$	2.08223	−	3.11628i	0.127910	−	0.191431i
$266$	3.37582	−	16.7439i	0.206985	−	1.02663i
$267$	−18.9624	+	5.75218i	−1.16048	+	0.352028i
$268$	−2.88062	+	0.857502i	−0.175962	+	0.0523803i
$269$	−5.58739	−	4.58545i	−0.340669	−	0.279580i	0.448466	−	0.893800i	$-0.351971\pi$
$269$	−5.58739	−	4.58545i	−0.340669	−	0.279580i	−0.789135	+	0.614220i	$0.789471\pi$
$270$	−7.63590	−	2.33801i	−0.464706	−	0.142287i
$271$	7.23115	+	2.99524i	0.439261	+	0.181948i	0.591343	−	0.806420i	$-0.298598\pi$
$271$	7.23115	+	2.99524i	0.439261	+	0.181948i	−0.152082	+	0.988368i	$0.548598\pi$
$272$	−0.00323818		3.36602e-5i	−0.000196343		2.04095e-6i
$273$	7.01657	−	2.90636i	0.424662	−	0.175901i
$274$	−21.0866	+	2.02154i	−1.27389	+	0.122126i
$275$	−0.495189	−	5.02773i	−0.0298610	−	0.303184i
$276$	−7.25527	−	13.7450i	−0.436716	−	0.827352i
$277$	3.09199	−	5.78471i	0.185780	−	0.347570i	−0.771739	−	0.635939i	$-0.780613\pi$
$277$	3.09199	−	5.78471i	0.185780	−	0.347570i	0.957519	+	0.288369i	$0.0931131\pi$
$278$	17.0394	+	11.4495i	1.02196	+	0.686698i
$279$	6.99264	−	1.39092i	0.418639	−	0.0832724i
$280$	−4.22458	+	0.806137i	−0.252467	+	0.0481759i
$281$	2.12671	−	10.6917i	0.126869	−	0.637814i	−0.864056	−	0.503396i	$-0.832084\pi$
$281$	2.12671	−	10.6917i	0.126869	−	0.637814i	0.990925	−	0.134418i	$-0.0429163\pi$
$282$	−0.0287867	+	11.0777i	−0.00171422	+	0.659668i
$283$	−2.81061	+	28.5367i	−0.167074	+	1.69633i	0.437050	+	0.899437i	$0.356023\pi$
$283$	−2.81061	+	28.5367i	−0.167074	+	1.69633i	−0.604124	+	0.796891i	$0.706477\pi$
$284$	−5.16464	+	2.10788i	−0.306465	+	0.125080i
$285$	−3.37229	+	11.1170i	−0.199757	+	0.658512i
$286$	7.02200	+	23.3669i	0.415220	+	1.38171i
$287$	8.83124	+	8.83124i	0.521292	+	0.521292i
$288$	−4.64164	−	1.47415i	−0.273511	−	0.0868650i
$289$	−12.0208	+	12.0208i	−0.707107	+	0.707107i
$290$	5.09717	+	2.74155i	0.299316	+	0.160989i
$291$	−7.84723	−	2.38043i	−0.460013	−	0.139543i
$292$	8.68785	−	8.59801i	0.508418	−	0.503161i
$293$	−12.6742	−	1.24830i	−0.740437	−	0.0729267i	−0.279236	−	0.960222i	$-0.590081\pi$
$293$	−12.6742	−	1.24830i	−0.740437	−	0.0729267i	−0.461201	+	0.887296i	$0.652581\pi$
$294$	−6.87410	+	6.83846i	−0.400905	+	0.398827i
$295$	−8.91234	−	1.77277i	−0.518897	−	0.103215i
$296$	−15.4098	+	6.24266i	−0.895678	+	0.362847i
$297$	5.56556	+	27.9799i	0.322946	+	1.62356i
$298$	29.1627	−	5.72208i	1.68935	−	0.331471i
$299$	16.0027	+	8.55363i	0.925460	+	0.494669i
$300$	2.91248	−	0.271579i	0.168152	−	0.0156796i
$301$	4.39404	−	0.432775i	0.253268	−	0.0249447i
$302$	−11.2399	−	9.27333i	−0.646783	−	0.533620i
$303$	−3.06463	−	7.39867i	−0.176058	−	0.425042i
$304$	−9.53852	+	30.3066i	−0.547072	+	1.73820i
$305$	5.03592	−	12.1578i	0.288356	−	0.696152i
$306$	0.000870510	0	0.000462393i	4.97637e−5	0	2.64332e-5i
$307$	10.1083	−	12.3170i	0.576912	−	0.702969i	−0.400023	−	0.916505i	$-0.630998\pi$
$307$	10.1083	−	12.3170i	0.576912	−	0.702969i	0.976935	+	0.213536i	$0.0684980\pi$
$308$	9.68495	+	11.9270i	0.551851	+	0.679605i
$309$	5.27923	+	17.4033i	0.300325	+	0.990038i
$310$	−9.75478	+	6.48133i	−0.554034	+	0.368115i
$311$	−4.77532	−	3.19077i	−0.270784	−	0.180932i	0.412763	−	0.910838i	$-0.364564\pi$
$311$	−4.77532	−	3.19077i	−0.270784	−	0.180932i	−0.683547	+	0.729906i	$0.739564\pi$
$312$	−13.5502	+	3.99533i	−0.767131	+	0.226191i
$313$	−10.6449	−	15.9311i	−0.601683	−	0.900482i	0.398176	−	0.917309i	$-0.369643\pi$
$313$	−10.6449	−	15.9311i	−0.601683	−	0.900482i	−0.999858	+	0.0168274i	$0.994643\pi$
$314$	−13.7115	+	5.63778i	−0.773783	+	0.318158i
$315$	1.01194	−	0.830476i	0.0570162	−	0.0467920i
$316$	−4.53753	−	3.06611i	−0.255256	−	0.172482i
$317$	6.80747	+	12.7359i	0.382346	+	0.715319i	0.997315	−	0.0732325i	$-0.0233315\pi$
$317$	6.80747	+	12.7359i	0.382346	+	0.715319i	−0.614969	+	0.788551i	$0.710832\pi$
$318$	0.779881	−	7.71274i	0.0437336	−	0.432509i
$319$		−	20.6756i		−	1.15761i
$320$	7.97274	−	0.659914i	0.445689	−	0.0368903i
$321$			12.8293i			0.716061i
$322$	11.3680	+	1.14948i	0.633513	+	0.0640583i
$323$	−0.00303137	−	0.00567129i	−0.000168670	−	0.000315559i
$324$	−11.1453	+	2.15679i	−0.619185	+	0.119822i
$325$	−2.63983	+	2.16645i	−0.146432	+	0.120173i
$326$	−12.9345	−	31.4575i	−0.716373	−	1.74227i
$327$	5.83127	+	8.72711i	0.322470	+	0.482610i
$328$	−14.5974	−	18.0725i	−0.806009	−	0.997888i
$329$	−6.77134	−	4.52446i	−0.373316	−	0.249442i
$330$	−5.78285	−	8.70353i	−0.318336	−	0.479113i
$331$	5.23843	+	17.2688i	0.287930	+	0.949178i	0.974928	+	0.222519i	$0.0714279\pi$
$331$	5.23843	+	17.2688i	0.287930	+	0.949178i	−0.686998	+	0.726659i	$0.741072\pi$
$332$	1.98205	−	19.1056i	0.108779	−	1.04855i
$333$	3.21050	−	3.91200i	0.175934	−	0.214376i
$334$	−15.3506	−	28.8994i	−0.839948	−	1.58130i
$335$	−0.575085	+	1.38838i	−0.0314203	+	0.0758552i
$336$	−6.93473	+	5.57157i	−0.378321	+	0.303954i
$337$	−6.56114	−	15.8400i	−0.357408	−	0.862859i	−0.995663	−	0.0930341i	$-0.970343\pi$
$337$	−6.56114	−	15.8400i	−0.357408	−	0.862859i	0.638255	−	0.769825i	$-0.279657\pi$
$338$	−1.20399	+	1.45932i	−0.0654884	+	0.0793764i
$339$	−1.94404	+	0.191471i	−0.105586	+	0.0103993i
$340$	−0.00103369	+	0.00124629i	−5.60595e−5	+	6.75893e-5i
$341$	36.8980	+	19.7224i	1.99814	+	1.06803i
$342$	−1.86204	−	9.48992i	−0.100688	−	0.513156i
$343$	−3.46718	−	17.4307i	−0.187210	−	0.941169i
$344$	−8.21272	−	0.0640262i	−0.442800	−	0.00345206i
$345$	−7.62184	−	1.51608i	−0.410346	−	0.0816229i
$346$	6.90545	+	6.94143i	0.371239	+	0.373174i
$347$	−22.9813	−	2.26346i	−1.23370	−	0.121509i	−0.539932	−	0.841709i	$-0.681550\pi$
$347$	−22.9813	−	2.26346i	−1.23370	−	0.121509i	−0.693766	+	0.720200i	$0.744050\pi$
$348$	11.9709	+	0.0622160i	0.641708	+	0.00333513i
$349$	−20.1093	−	6.10008i	−1.07642	−	0.326530i	−0.298192	−	0.954506i	$-0.596384\pi$
$349$	−20.1093	−	6.10008i	−1.07642	−	0.326530i	−0.778233	+	0.627976i	$0.783884\pi$
$350$	−1.01862	+	1.89385i	−0.0544474	+	0.101230i
$351$	13.6358	−	13.6358i	0.727825	−	0.727825i
$352$	−15.5674	−	23.9667i	−0.829747	−	1.27743i
$353$	3.96088	+	3.96088i	0.210817	+	0.210817i	0.804614	−	0.593798i	$-0.202372\pi$
$353$	3.96088	+	3.96088i	0.210817	+	0.210817i	−0.593798	+	0.804614i	$0.702372\pi$
$354$	−18.0000	+	5.40919i	−0.956688	+	0.287495i
$355$	−0.809638	+	2.66902i	−0.0429711	+	0.141657i
$356$	−10.4996	+	24.9804i	−0.556480	+	1.32396i
$357$	0.000176476	−	0.00179179i	9.34009e−6	−	9.48315e-5i
$358$	18.5472	+	0.0481970i	0.980251	+	0.00254729i
$359$	2.23067	−	11.2144i	0.117730	−	0.591871i	−0.876208	−	0.481933i	$-0.839935\pi$
$359$	2.23067	−	11.2144i	0.117730	−	0.591871i	0.993938	−	0.109938i	$-0.0350652\pi$
$360$	−2.03516	+	1.33702i	−0.107262	+	0.0704670i
$361$	−43.2449	+	8.60195i	−2.27605	+	0.452734i
$362$	−13.8693	+	20.6405i	−0.728954	+	1.08484i
$363$	−10.0130	+	18.7331i	−0.525548	+	0.983232i
$364$	3.06635	−	9.92247i	0.160721	−	0.520079i
$365$	−0.599038	−	6.08213i	−0.0313551	−	0.318353i
$366$	−2.59750	−	27.0945i	−0.135774	−	1.41625i
$367$	−16.8549	+	6.98152i	−0.879818	+	0.364433i	−0.776426	−	0.630208i	$-0.782970\pi$
$367$	−16.8549	+	6.98152i	−0.879818	+	0.364433i	−0.103392	+	0.994641i	$0.532970\pi$
$368$	−20.8010	−	4.36282i	−1.08433	−	0.227428i
$369$	6.53296	+	2.70604i	0.340092	+	0.140871i
$370$	−2.43384	+	7.94888i	−0.126529	+	0.413243i
$371$	4.40534	+	3.61537i	0.228714	+	0.187701i
$372$	−11.5300	+	21.3041i	−0.597805	+	1.10457i
$373$	−11.4405	+	3.47045i	−0.592368	+	0.179693i	−0.572215	−	0.820104i	$-0.693916\pi$
$373$	−11.4405	+	3.47045i	−0.592368	+	0.179693i	−0.0201538	+	0.999797i	$0.506416\pi$
$374$	0.00567017	+	0.00114319i	0.000293197	+	5.91131e-5i
$375$	0.812554	−	1.21607i	0.0419601	−	0.0627978i
$376$	11.6346	+	9.70107i	0.600010	+	0.500294i
$377$	−11.6206	+	7.76461i	−0.598489	+	0.399898i
$378$	4.67604	−	11.2065i	0.240510	−	0.576401i
$379$	2.52368	+	3.07512i	0.129633	+	0.157958i	0.833782	−	0.552094i	$-0.186171\pi$
$379$	2.52368	+	3.07512i	0.129633	+	0.157958i	−0.704149	+	0.710052i	$0.748671\pi$
$380$	8.75708	+	13.2545i	0.449229	+	0.679942i
$381$	21.3197	−	11.3956i	1.09224	−	0.583815i
$382$	−7.94912	+	6.48918i	−0.406712	+	0.332015i
$383$	4.11449			0.210241			0.105120	−	0.994460i	$-0.466477\pi$
$383$	4.11449			0.210241			0.105120	+	0.994460i	$0.466477\pi$
$384$	13.9232	−	8.94123i	0.710517	−	0.456280i
$385$	7.68199			0.391510
$386$	21.5546	−	17.5959i	1.09710	−	0.895606i
$387$	2.20469	−	1.17843i	0.112071	−	0.0599031i
$388$	−9.35609	+	6.18145i	−0.474983	+	0.313815i
$389$	−5.64859	−	6.88282i	−0.286395	−	0.348973i	0.609863	−	0.792507i	$-0.291225\pi$
$389$	−5.64859	−	6.88282i	−0.286395	−	0.348973i	−0.896258	+	0.443534i	$0.853725\pi$
$390$	−2.72003	+	6.51877i	−0.137734	+	0.330091i
$391$	0.00357671	−	0.00238988i	0.000180882	−	0.000120861i
$392$	1.19673	+	13.2052i	0.0604442	+	0.666964i
$393$	13.6557	−	20.4371i	0.688836	−	1.03092i
$394$	4.79558	+	0.966862i	0.241598	+	0.0487098i
$395$	−2.62026	+	0.794847i	−0.131840	+	0.0399931i
$396$	7.65028	+	4.14042i	0.384441	+	0.208064i
$397$	−22.0638	−	18.1073i	−1.10735	−	0.908780i	−0.110974	−	0.993823i	$-0.535397\pi$
$397$	−22.0638	−	18.1073i	−1.10735	−	0.908780i	−0.996377	+	0.0850437i	$0.972897\pi$
$398$	2.43215	−	7.94336i	0.121913	−	0.398165i
$399$	−16.3200	−	6.75999i	−0.817024	−	0.338423i
$400$	2.25673	−	3.30260i	0.112837	−	0.165130i
$401$	−4.41797	+	1.82998i	−0.220623	+	0.0913850i	−0.490257	−	0.871578i	$-0.663097\pi$
$401$	−4.41797	+	1.82998i	−0.220623	+	0.0913850i	0.269634	+	0.962963i	$0.413097\pi$
$402$	0.296626	+	3.09410i	0.0147944	+	0.154320i
$403$	−2.77203	−	28.1448i	−0.138084	−	1.40199i
$404$	−10.4628	−	3.23333i	−0.520544	−	0.160864i
$405$	−2.67567	+	5.00583i	−0.132955	+	0.248742i
$406$	−4.90832	+	7.30466i	−0.243596	+	0.362524i
$407$	29.1268	−	5.79368i	1.44376	−	0.287182i
$408$	−0.000678956		0.00327951i	−3.36133e−5		0.000162360i
$409$	−5.22130	+	26.2492i	−0.258176	+	1.29794i	0.606287	+	0.795246i	$0.292658\pi$
$409$	−5.22130	+	26.2492i	−0.258176	+	1.29794i	−0.864464	+	0.502695i	$0.832342\pi$
$410$	−11.6157	−	0.0301847i	−0.573658	−	0.00149072i
$411$	−2.14731	+	21.8020i	−0.105919	+	1.07541i
$412$	22.9264	+	9.63634i	1.12950	+	0.474748i
$413$	4.01095	−	13.2223i	0.197366	−	0.650628i
$414$	6.19550	−	1.86182i	0.304492	−	0.0915033i
$415$	−6.79109	−	6.79109i	−0.333361	−	0.333361i
$416$	−7.62401	+	17.7501i	−0.373798	+	0.870270i
$417$	15.0123	−	15.0123i	0.735158	−	0.735158i
$418$	26.8821	−	49.9800i	1.31484	−	2.44460i
$419$	3.36789	+	1.02164i	0.164532	+	0.0499103i	0.371476	−	0.928443i	$-0.378852\pi$
$419$	3.36789	+	1.02164i	0.164532	+	0.0499103i	−0.206944	+	0.978353i	$0.566352\pi$
$420$	−0.0231162	+	4.44777i	−0.00112796	+	0.217029i
$421$	−13.0688	−	1.28716i	−0.636934	−	0.0627325i	−0.225604	−	0.974219i	$-0.572435\pi$
$421$	−13.0688	−	1.28716i	−0.636934	−	0.0627325i	−0.411330	+	0.911487i	$0.634935\pi$
$422$	12.8882	+	12.9554i	0.627388	+	0.630657i
$423$	−4.52231	−	0.899543i	−0.219882	−	0.0437373i
$424$	−7.43716	−	7.55403i	−0.361181	−	0.366856i
$425$	0.000157943	0	0.000794033i	7.66136e−6	0	3.85162e-5i
$426$	1.11076	+	5.66099i	0.0538163	+	0.274276i
$427$	17.6471	+	9.43258i	0.854004	+	0.456475i
$428$	13.5034	+	11.1999i	0.652710	+	0.541367i
$429$	25.1117	−	2.47329i	1.21241	−	0.119412i
$430$	−2.61337	+	3.16758i	−0.126028	+	0.152754i
$431$	−13.7125	−	33.1048i	−0.660506	−	1.59460i	−0.797012	−	0.603963i	$-0.793587\pi$
$431$	−13.7125	−	33.1048i	−0.660506	−	1.59460i	0.136506	−	0.990639i	$-0.456413\pi$
$432$	−10.8541	+	19.8085i	−0.522216	+	0.953035i
$433$	0.548041	−	1.32309i	0.0263372	−	0.0635835i	−0.910164	−	0.414249i	$-0.864044\pi$
$433$	0.548041	−	1.32309i	0.0263372	−	0.0635835i	0.936501	+	0.350665i	$0.114044\pi$
$434$	−8.35397	−	15.7273i	−0.401003	−	0.754937i
$435$	3.79719	−	4.62688i	0.182061	−	0.221842i
$436$	14.2763	+	1.48105i	0.683712	+	0.0709295i
$437$	−12.2514	−	40.3873i	−0.586062	−	1.93199i
$438$	−6.99561	−	10.5288i	−0.334263	−	0.503085i
$439$	5.70257	+	3.81033i	0.272169	+	0.181857i	0.684163	−	0.729329i	$-0.260168\pi$
$439$	5.70257	+	3.81033i	0.272169	+	0.181857i	−0.411994	+	0.911186i	$0.635168\pi$
$440$	−14.2092	−	1.51142i	−0.677398	−	0.0720542i
$441$	−2.24222	−	3.35572i	−0.106773	−	0.159796i
$442$	−0.00148688	−	0.00361619i	−7.07236e−5	−	0.000172005i
$443$	3.75805	−	3.08415i	0.178550	−	0.146533i	−0.540873	−	0.841104i	$-0.681906\pi$
$443$	3.75805	−	3.08415i	0.178550	−	0.146533i	0.719424	+	0.694572i	$0.244406\pi$
$444$	3.26682	+	16.8815i	0.155036	+	0.801160i
$445$	6.38678	+	11.9488i	0.302762	+	0.566428i
$446$	5.49715	+	0.555850i	0.260298	+	0.0263202i
$447$		−	30.7347i		−	1.45370i
$448$	−0.189657	+	12.1630i	−0.00896046	+	0.574650i
$449$			16.1972i			0.764392i	0.924081	+	0.382196i	$0.124832\pi$
$449$			16.1972i			0.764392i	−0.924081	+	0.382196i	$0.875168\pi$
$450$	−0.122487	+	1.21135i	−0.00577408	+	0.0571035i
$451$	19.5608	+	36.5957i	0.921083	+	1.72322i
$452$	−1.49560	+	2.21334i	−0.0703473	+	0.104107i
$453$	−11.6490	+	9.56010i	−0.547319	+	0.449173i
$454$	31.7432	−	13.0519i	1.48978	−	0.612558i
$455$	−2.88493	−	4.31760i	−0.135248	−	0.202412i
$456$	28.8569	+	15.7148i	1.35135	+	0.735911i
$457$	−2.81581	−	1.88146i	−0.131718	−	0.0880111i	0.487966	−	0.872863i	$-0.337739\pi$
$457$	−2.81581	−	1.88146i	−0.131718	−	0.0880111i	−0.619684	+	0.784852i	$0.712739\pi$
$458$	−13.5988	+	9.03540i	−0.635430	+	0.422196i
$459$	−0.00132707	−	0.00437475i	−6.19422e−5	−	0.000204196i
$460$	−8.24956	+	6.69879i	−0.384638	+	0.312333i
$461$	25.0612	−	30.5372i	1.16722	−	1.42226i	0.280556	−	0.959838i	$-0.409481\pi$
$461$	25.0612	−	30.5372i	1.16722	−	1.42226i	0.886661	−	0.462421i	$-0.153019\pi$
$462$	14.0324	−	7.45368i	0.652848	−	0.346777i
$463$	−7.00116	+	16.9023i	−0.325372	+	0.785517i	0.673552	+	0.739139i	$0.264768\pi$
$463$	−7.00116	+	16.9023i	−0.325372	+	0.785517i	−0.998924	+	0.0463771i	$0.985232\pi$
$464$	10.5160	−	12.5456i	0.488194	−	0.582414i
$465$	4.63508	+	11.1901i	0.214947	+	0.518927i
$466$	12.6182	+	10.4105i	0.584528	+	0.482257i
$467$	33.0238	−	3.25256i	1.52816	−	0.150511i	0.701278	−	0.712888i	$-0.252613\pi$
$467$	33.0238	−	3.25256i	1.52816	−	0.150511i	0.826881	+	0.562377i	$0.190113\pi$
$468$	−0.545929	−	5.85469i	−0.0252356	−	0.270633i
$469$	−2.01524	−	1.07717i	−0.0930552	−	0.0497391i
$470$	7.43250	−	1.45835i	0.342836	−	0.0672686i
$471$	2.99114	+	15.0375i	0.137825	+	0.692891i
$472$	−10.0205	+	23.6679i	−0.461229	+	1.08940i
$473$	14.3879	+	2.86193i	0.661557	+	0.131592i
$474$	−4.01512	+	3.99431i	−0.184421	+	0.183465i
$475$	7.90481	+	0.778556i	0.362697	+	0.0357226i
$476$	−0.00173187	−	0.00174997i	−7.93802e−5	−	8.02096e-5i
$477$	3.08772	+	0.936649i	0.141377	+	0.0428862i
$478$	32.2361	+	17.3384i	1.47445	+	0.793040i
$479$	21.0965	−	21.0965i	0.963922	−	0.963922i	−0.0354491	−	0.999371i	$-0.511286\pi$
$479$	21.0965	−	21.0965i	0.963922	−	0.963922i	0.999371	+	0.0354491i	$0.0112862\pi$
$480$	0.917852	−	8.22241i	0.0418940	−	0.375300i
$481$	−14.1947	−	14.1947i	−0.647223	−	0.647223i
$482$	−7.57116	−	25.1943i	−0.344857	−	1.14757i
$483$	3.43017	−	11.3077i	0.156078	−	0.514520i
$484$	10.9760	+	26.8930i	0.498911	+	1.22241i
$485$	−0.549567	+	5.57984i	−0.0249545	+	0.253368i
$486$	0.0317478	−	12.2172i	0.00144011	−	0.554185i
$487$	0.452570	−	2.27522i	0.0205079	−	0.103100i	−0.969176	−	0.246371i	$-0.920762\pi$
$487$	0.452570	−	2.27522i	0.0205079	−	0.103100i	0.989684	+	0.143271i	$0.0457619\pi$
$488$	−30.7857	−	20.9193i	−1.39360	−	0.946973i
$489$	−34.4997	+	6.86242i	−1.56013	+	0.310329i
$490$	5.50278	+	3.69756i	0.248590	+	0.167039i
$491$	−10.6514	+	19.9274i	−0.480691	+	0.899310i	0.518334	+	0.855178i	$0.326552\pi$
$491$	−10.6514	+	19.9274i	−0.480691	+	0.899310i	−0.999026	+	0.0441323i	$0.985948\pi$
$492$	−21.2473	+	11.2153i	−0.957903	+	0.505626i
$493$	0.000324755		0.00329730i	1.46262e−5		0.000148503i
$494$	−38.1862	+	3.66085i	−1.71808	+	0.164709i
$495$	4.01834	−	1.66445i	0.180611	−	0.0748116i
$496$	12.3578	+	30.7342i	0.554883	+	1.38001i
$497$	−3.91821	−	1.62297i	−0.175756	−	0.0728003i
$498$	−18.9943	−	5.81581i	−0.851156	−	0.260613i
$499$	−29.0000	−	23.7997i	−1.29822	−	1.06542i	−0.993601	−	0.112945i	$-0.963972\pi$
$499$	−29.0000	−	23.7997i	−1.29822	−	1.06542i	−0.304617	−	0.952475i	$-0.598528\pi$
$500$	−0.570615	−	1.91687i	−0.0255187	−	0.0857251i
$501$	−32.3848	+	9.82381i	−1.44684	+	0.438895i
$502$	0.387288	−	1.92093i	0.0172855	−	0.0857352i
$503$	−23.0695	+	34.5260i	−1.02862	+	1.53944i	−0.199867	+	0.979823i	$0.564051\pi$
$503$	−23.0695	+	34.5260i	−1.02862	+	1.53944i	−0.828753	+	0.559615i	$0.810949\pi$
$504$	−1.71991	−	3.27896i	−0.0766109	−	0.146056i
$505$	−4.55272	+	3.04203i	−0.202593	+	0.135369i
$506$	35.0350	+	14.6188i	1.55750	+	0.649883i
$507$	1.24122	+	1.51243i	0.0551247	+	0.0671696i
$508$	6.61758	−	32.3882i	0.293608	−	1.43699i
$509$	21.5404	−	11.5136i	0.954763	−	0.510331i	0.0810161	−	0.996713i	$-0.474183\pi$
$509$	21.5404	−	11.5136i	0.954763	−	0.510331i	0.873747	+	0.486382i	$0.161683\pi$
$510$	0.00105894	+	0.00129719i	4.68908e−5	+	5.74403e-5i
$511$	9.29303			0.411099
$512$	2.74387	−	22.4604i	0.121263	−	0.992620i
$513$	−44.8530			−1.98031
$514$	−0.594012	−	0.727654i	−0.0262008	−	0.0320954i
$515$	10.9664	−	5.86164i	0.483236	−	0.258295i
$516$	−1.70032	+	8.32180i	−0.0748523	+	0.366347i
$517$	−17.1653	−	20.9159i	−0.754927	−	0.919881i
$518$	−11.6659	−	4.86771i	−0.512568	−	0.213875i
$519$	8.41944	−	5.62569i	0.369572	−	0.246940i
$520$	4.48671	+	8.55379i	0.196755	+	0.375108i
$521$	−18.1854	+	27.2163i	−0.796716	+	1.19237i	0.181216	+	0.983443i	$0.441997\pi$
$521$	−18.1854	+	27.2163i	−0.796716	+	1.19237i	−0.977931	+	0.208926i	$0.933003\pi$
$522$	−0.984780	+	4.88445i	−0.0431026	+	0.213787i
$523$	14.0752	−	4.26967i	0.615467	−	0.186700i	0.0328680	−	0.999460i	$-0.489536\pi$
$523$	14.0752	−	4.26967i	0.615467	−	0.186700i	0.582599	+	0.812760i	$0.302036\pi$
$524$	−9.58965	−	32.2146i	−0.418926	−	1.40730i
$525$	1.71911	+	1.41084i	0.0750281	+	0.0615740i
$526$	30.4866	+	9.33461i	1.32928	+	0.407008i
$527$	−0.00619418	−	0.00256571i	−0.000269823	−	0.000111764i
$528$	−27.4220	+	11.0261i	−1.19339	+	0.479848i
$529$	4.83396	−	2.00229i	0.210172	−	0.0870561i
$530$	−5.27616	+	0.505816i	−0.229182	+	0.0219712i
$531$	−0.766802	−	7.78547i	−0.0332764	−	0.337861i
$532$	−21.3625	+	11.2761i	−0.926180	+	0.488882i
$533$	13.2224	−	24.7373i	0.572724	−	1.07149i
$534$	23.2602	+	15.6296i	1.00657	+	0.676357i
$535$	8.60326	−	1.71129i	0.371951	−	0.0739857i
$536$	3.51562	+	2.38892i	0.151852	+	0.103185i
$537$	3.74209	−	18.8128i	0.161483	−	0.811831i
$538$	−0.0265631	+	10.2220i	−0.00114522	+	0.440703i
$539$	2.32139	−	23.5694i	0.0999891	−	1.01521i
$540$	4.26761	+	10.4563i	0.183649	+	0.449967i
$541$	−3.33669	+	10.9996i	−0.143456	+	0.472910i	−0.998995	−	0.0448286i	$-0.985726\pi$
$541$	−3.33669	+	10.9996i	−0.143456	+	0.472910i	0.855539	+	0.517738i	$0.173226\pi$
$542$	−3.18561	−	10.6006i	−0.136834	−	0.455337i
$543$	18.1850	+	18.1850i	0.780395	+	0.780395i
$544$	0.00285911	+	0.00357762i	0.000122583	+	0.000153389i
$545$	5.07453	−	5.07453i	0.217369	−	0.217369i
$546$	−9.45909	−	5.08763i	−0.404812	−	0.217731i
$547$	11.8598	+	3.59764i	0.507090	+	0.153824i	0.533455	−	0.845828i	$-0.320893\pi$
$547$	11.8598	+	3.59764i	0.507090	+	0.153824i	−0.0263652	+	0.999652i	$0.508393\pi$
$548$	21.0729	+	21.2931i	0.900192	+	0.909598i
$549$	11.2747	+	1.11046i	0.481193	+	0.0473934i
$550$	−5.06517	+	5.03892i	−0.215980	+	0.214860i
$551$	31.8824	+	6.34181i	1.35824	+	0.270170i
$552$	−8.56950	+	20.2408i	−0.364742	+	0.861507i
$553$	−0.812270	−	4.08356i	−0.0345412	−	0.173650i
$554$	−9.10256	+	1.78604i	−0.386731	+	0.0758814i
$555$	7.58217	+	4.05275i	0.321845	+	0.172030i
$556$	−2.69546	−	28.9068i	−0.114313	−	1.22592i
$557$	34.7508	−	3.42266i	1.47244	−	0.145023i	0.670270	−	0.742118i	$-0.266178\pi$
$557$	34.7508	−	3.42266i	1.47244	−	0.145023i	0.802171	+	0.597095i	$0.203678\pi$
$558$	−7.77748	−	6.41671i	−0.329247	−	0.271641i
$559$	−3.79477	−	9.16139i	−0.160502	−	0.387486i
$560$	4.66129	+	3.90721i	0.196975	+	0.165110i
$561$	0.00228921	−	0.00552665i	9.66506e−5	−	0.000233335i
$562$	−13.6151	+	7.23197i	−0.574316	+	0.305062i
$563$	13.3909	−	16.3168i	0.564358	−	0.687673i	−0.410151	−	0.912017i	$-0.634524\pi$
$563$	13.3909	−	16.3168i	0.564358	−	0.687673i	0.974510	+	0.224345i	$0.0720242\pi$
$564$	12.1617	−	9.87552i	0.512100	−	0.415835i
$565$	0.387715	+	1.27812i	0.0163113	+	0.0537711i
$566$	33.7763	−	22.4419i	1.41973	−	0.943303i
$567$	−7.17626	−	4.79502i	−0.301374	−	0.201372i
$568$	6.92811	+	3.77289i	0.290697	+	0.158307i
$569$	19.0936	+	28.5757i	0.800447	+	1.19795i	0.976911	+	0.213647i	$0.0685342\pi$
$569$	19.0936	+	28.5757i	0.800447	+	1.19795i	−0.176464	+	0.984307i	$0.556466\pi$
$570$	15.1949	−	6.24771i	0.636443	−	0.261688i
$571$	1.59809	−	1.31152i	0.0668781	−	0.0548855i	−0.600360	−	0.799730i	$-0.704976\pi$
$571$	1.59809	−	1.31152i	0.0668781	−	0.0548855i	0.667239	+	0.744844i	$0.267476\pi$
$572$	19.3191	−	28.5903i	0.807774	−	1.19542i
$573$	5.00259	+	9.35919i	0.208986	+	0.390986i
$574$	1.77690	−	17.5729i	0.0741663	−	0.733478i
$575$			5.31340i			0.221584i
$576$	2.53615	+	6.40342i	0.105673	+	0.266809i
$577$			27.9801i			1.16483i	0.812893	+	0.582414i	$0.197892\pi$
$577$			27.9801i			1.16483i	−0.812893	+	0.582414i	$0.802108\pi$
$578$	23.9197	+	2.41866i	0.994927	+	0.100603i
$579$	−13.5649	−	25.3781i	−0.563737	−	1.05468i
$580$	−1.55507	−	8.03594i	−0.0645710	−	0.333674i
$581$	11.2887	−	9.26442i	0.468335	−	0.384353i
$582$	4.41013	+	10.7258i	0.182806	+	0.444597i
$583$	10.5195	+	15.7436i	0.435675	+	0.652034i
$584$	−17.1891	−	1.82839i	−0.711291	−	0.0756594i
$585$	−2.44456	−	1.63340i	−0.101070	−	0.0675329i
$586$	9.96732	+	15.0014i	0.411746	+	0.619702i
$587$	3.64759	+	12.0245i	0.150552	+	0.496305i	0.999481	−	0.0322023i	$-0.0102521\pi$
$587$	3.64759	+	12.0245i	0.150552	+	0.496305i	−0.848929	+	0.528507i	$0.822752\pi$
$588$	13.6394	+	1.41498i	0.562480	+	0.0583526i
$589$	−41.7302	+	50.8484i	−1.71946	+	2.09517i
$590$	6.02839	+	11.3492i	0.248185	+	0.467238i
$591$	1.93612	−	4.67420i	0.0796412	−	0.192271i
$592$	20.6204	+	11.2990i	0.847493	+	0.464384i
$593$	−10.3580	−	25.0064i	−0.425351	−	1.02689i	−0.980744	−	0.195300i	$-0.937432\pi$
$593$	−10.3580	−	25.0064i	−0.425351	−	1.02689i	0.555393	−	0.831588i	$-0.312568\pi$
$594$	25.6754	−	31.1204i	1.05348	−	1.27688i
$595$	−0.00122510		0.000120662i	−5.02244e−5		4.94667e-6i
$596$	−32.3496	−	26.8312i	−1.32509	−	1.09905i
$597$	−7.57690	−	4.04994i	−0.310102	−	0.165753i
$598$	−4.94085	−	25.1811i	−0.202046	−	1.02973i
$599$	6.03268	+	30.3283i	0.246489	+	1.23918i	0.883538	+	0.468359i	$0.155155\pi$
$599$	6.03268	+	30.3283i	0.246489	+	1.23918i	−0.637050	+	0.770823i	$0.719845\pi$
$600$	−2.90223	−	2.94783i	−0.118483	−	0.120345i
$601$	−9.50426	−	1.89051i	−0.387687	−	0.0771157i	−0.00260135	−	0.999997i	$-0.500828\pi$
$601$	−9.50426	−	1.89051i	−0.387687	−	0.0771157i	−0.385085	+	0.922881i	$0.625828\pi$
$602$	−4.40381	−	4.42676i	−0.179486	−	0.180421i
$603$	−1.28754	−	0.126811i	−0.0524325	−	0.00516415i
$604$	−0.107100	+	20.6070i	−0.00435783	+	0.838487i
$605$	13.8980	+	4.21590i	0.565032	+	0.171401i
$606$	−5.36469	+	9.97419i	−0.217926	+	0.405174i
$607$	−8.17601	+	8.17601i	−0.331854	+	0.331854i	−0.853290	−	0.521436i	$-0.825396\pi$
$607$	−8.17601	+	8.17601i	−0.331854	+	0.331854i	0.521436	+	0.853290i	$0.325396\pi$
$608$	41.7323	−	16.6542i	1.69247	−	0.675417i
$609$	6.43566	+	6.43566i	0.260786	+	0.260786i
$610$	−17.8229	+	5.35600i	−0.721630	+	0.216858i
$611$	−5.30931	+	17.5025i	−0.214792	+	0.708073i
$612$	−0.00128508		0.000540140i	−5.19464e−5		2.18339e-5i
$613$	−3.61664	+	36.7203i	−0.146075	+	1.48312i	0.590650	+	0.806928i	$0.298871\pi$
$613$	−3.61664	+	36.7203i	−0.146075	+	1.48312i	−0.736725	+	0.676193i	$0.763629\pi$
$614$	−22.5338	−	0.0585565i	−0.909388	−	0.00236315i
$615$	−2.34359	+	11.7820i	−0.0945025	+	0.475096i
$616$	4.40491	−	21.2768i	0.177479	−	0.857265i
$617$	21.1301	−	4.20303i	0.850664	−	0.169208i	0.249541	−	0.968364i	$-0.419720\pi$
$617$	21.1301	−	4.20303i	0.850664	−	0.169208i	0.601123	+	0.799156i	$0.294720\pi$
$618$	14.3445	−	21.3477i	0.577019	−	0.858731i
$619$	2.77275	−	5.18746i	0.111446	−	0.208501i	−0.820015	−	0.572342i	$-0.806035\pi$
$619$	2.77275	−	5.18746i	0.111446	−	0.208501i	0.931461	+	0.363841i	$0.118535\pi$
$620$	15.8244	+	4.89024i	0.635524	+	0.196397i
$621$	−2.94089	−	29.8594i	−0.118014	−	1.19822i
$622$	0.775103	+	8.08509i	0.0310788	+	0.324182i
$623$	−19.0334	+	7.88388i	−0.762556	+	0.315861i
$624$	16.4953	+	11.2716i	0.660341	+	0.451224i
$625$	−0.923880	−	0.382683i	−0.0369552	−	0.0153073i
$626$	−7.93310	+	25.9094i	−0.317070	+	1.03555i
$627$	−45.3686	−	37.2330i	−1.81185	−	1.48694i
$628$	18.4388	+	9.97932i	0.735790	+	0.398218i
$629$	−0.00455407	+	0.00138146i	−0.000181583	+	5.50825e-5i
$630$	−1.81481	−	0.365893i	−0.0723038	−	0.0145775i
$631$	8.31722	−	12.4476i	0.331103	−	0.495531i	−0.628145	−	0.778097i	$-0.716185\pi$
$631$	8.31722	−	12.4476i	0.331103	−	0.495531i	0.959248	+	0.282565i	$0.0911854\pi$
$632$	0.699005	+	7.71309i	0.0278049	+	0.306810i
$633$	15.7139	−	10.4997i	0.624571	−	0.417325i
$634$	7.86446	−	18.8478i	0.312337	−	0.748542i
$635$	−10.4857	−	12.7768i	−0.416111	−	0.507033i
$636$	−9.14701	+	6.04331i	−0.362702	+	0.239633i
$637$	−14.1188	+	7.54665i	−0.559407	+	0.299009i
$638$	−22.6507	+	18.4907i	−0.896752	+	0.732053i
$639$	−2.40121			−0.0949904
$640$	−7.85316	−	8.14419i	−0.310424	−	0.321927i
$641$	6.91644			0.273183			0.136592	−	0.990627i	$-0.456385\pi$
$641$	6.91644			0.273183			0.136592	+	0.990627i	$0.456385\pi$
$642$	14.0549	−	11.4735i	0.554701	−	0.452824i
$643$	11.5449	−	6.17090i	0.455288	−	0.243357i	−0.227778	−	0.973713i	$-0.573146\pi$
$643$	11.5449	−	6.17090i	0.455288	−	0.243357i	0.683066	+	0.730356i	$0.260646\pi$
$644$	−8.90737	−	13.4820i	−0.351000	−	0.531265i
$645$	2.69418	+	3.28287i	0.106083	+	0.129263i
$646$	−0.00350204	+	0.00839292i	−0.000137786	+	0.000330215i
$647$	−5.49855	+	3.67402i	−0.216170	+	0.144441i	−0.658941	−	0.752194i	$-0.728995\pi$
$647$	−5.49855	+	3.67402i	−0.216170	+	0.144441i	0.442771	+	0.896635i	$0.353995\pi$
$648$	12.3304	+	10.2812i	0.484383	+	0.403883i
$649$	25.5050	−	38.1709i	1.00116	−	1.49834i
$650$	4.73428	+	0.954503i	0.185694	+	0.0374387i
$651$	−17.6241	+	5.34622i	−0.690744	+	0.209535i
$652$	−22.8950	+	42.3033i	−0.896639	+	1.65672i
$653$	−12.3720	−	10.1534i	−0.484152	−	0.397333i	0.360408	−	0.932795i	$-0.382638\pi$
$653$	−12.3720	−	10.1534i	−0.484152	−	0.397333i	−0.844560	+	0.535462i	$0.820138\pi$
$654$	4.34577	−	14.1932i	0.169933	−	0.554998i
$655$	−15.5266	−	6.43131i	−0.606673	−	0.251292i
$656$	−6.74414	+	32.1546i	−0.263314	+	1.25543i
$657$	4.86106	−	2.01352i	0.189648	−	0.0785547i
$658$	1.09909	+	11.4645i	0.0428468	+	0.446934i
$659$	−0.145410	−	1.47637i	−0.00566436	−	0.0575112i	0.991937	−	0.126732i	$-0.0404488\pi$
$659$	−0.145410	−	1.47637i	−0.00566436	−	0.0575112i	−0.997601	+	0.0692206i	$0.977949\pi$
$660$	−4.36323	+	14.1191i	−0.169838	+	0.549584i
$661$	−7.60055	+	14.2196i	−0.295627	+	0.553079i	−0.985257	−	0.171083i	$-0.945273\pi$
$661$	−7.60055	+	14.2196i	−0.295627	+	0.553079i	0.689630	+	0.724162i	$0.257773\pi$
$662$	14.2336	−	21.1827i	0.553205	−	0.823290i
$663$	−0.00396591		0.000788868i	−0.000154023		3.06371e-5i
$664$	−22.7033	+	14.9152i	−0.881059	+	0.578821i
$665$	−2.35629	+	11.8459i	−0.0913729	+	0.459363i
$666$	−7.15693	−	0.0185981i	−0.277326	−	0.000720662i
$667$	−2.13140	+	21.6404i	−0.0825280	+	0.837921i
$668$	−17.9317	+	42.6624i	−0.693798	+	1.65066i
$669$	1.65871	−	5.46802i	0.0641293	−	0.211406i
$670$	2.03532	−	0.611637i	0.0786313	−	0.0236296i
$671$	47.0103	+	47.0103i	1.81481	+	1.81481i
$672$	12.3057	+	2.61441i	0.474703	+	0.100853i
$673$	32.3085	−	32.3085i	1.24540	−	1.24540i	0.287673	−	0.957729i	$-0.407118\pi$
$673$	32.3085	−	32.3085i	1.24540	−	1.24540i	0.957729	−	0.287673i	$-0.0928818\pi$
$674$	−11.4854	+	21.3540i	−0.442401	+	0.822525i
$675$	5.40367	+	1.63919i	0.207988	+	0.0630923i
$676$	2.67548	+	0.0139052i	0.102903	+	0.000534814i
$677$	−25.8112	−	2.54219i	−0.992007	−	0.0977041i	−0.411028	−	0.911623i	$-0.634830\pi$
$677$	−25.8112	−	2.54219i	−0.992007	−	0.0977041i	−0.580979	+	0.813919i	$0.697330\pi$
$678$	1.94837	+	1.95852i	0.0748265	+	0.0752164i
$679$	−8.36175	−	1.66326i	−0.320895	−	0.0638299i
$680$	0.00228979		1.78512e-5i	8.78095e−5		6.84561e-7i
$681$	−6.92475	−	34.8131i	−0.265357	−	1.33404i
$682$	−11.3923	−	58.0610i	−0.436233	−	2.22327i
$683$	32.1897	+	17.2057i	1.23170	+	0.658359i	0.953277	−	0.302098i	$-0.0976870\pi$
$683$	32.1897	+	17.2057i	1.23170	+	0.658359i	0.278427	+	0.960457i	$0.410187\pi$
$684$	−8.73122	+	10.5270i	−0.333847	+	0.402509i
$685$	14.9067	−	1.46819i	0.569558	−	0.0560965i
$686$	−15.9951	+	19.3871i	−0.610694	+	0.740202i
$687$	6.46160	+	15.5997i	0.246526	+	0.595165i
$688$	7.27469	+	9.05454i	0.277345	+	0.345201i
$689$	4.89801	−	11.8249i	0.186600	−	0.450491i
$690$	5.15549	+	9.70582i	0.196266	+	0.369494i
$691$	13.7997	−	16.8150i	0.524967	−	0.639674i	−0.441256	−	0.897381i	$-0.645467\pi$
$691$	13.7997	−	16.8150i	0.524967	−	0.639674i	0.966223	+	0.257707i	$0.0829670\pi$
$692$	1.42884	−	13.7730i	0.0543162	−	0.523571i
$693$	1.91982	+	6.32881i	0.0729280	+	0.240411i
$694$	18.0730	+	27.2009i	0.686042	+	1.03253i
$695$	−12.0697	−	8.06472i	−0.457830	−	0.305912i
$696$	−10.6377	−	13.1701i	−0.403222	−	0.499213i
$697$	−0.00369432	−	0.00552895i	−0.000139933	−	0.000209424i
$698$	11.3014	+	27.4858i	0.427764	+	1.04035i
$699$	13.0775	−	10.7324i	0.494637	−	0.405938i
$700$	2.98574	−	0.577785i	0.112850	−	0.0218382i
$701$	1.13296	+	2.11962i	0.0427912	+	0.0800568i	0.902408	−	0.430883i	$-0.141798\pi$
$701$	1.13296	+	2.11962i	0.0427912	+	0.0800568i	−0.859617	+	0.510939i	$0.829298\pi$
$702$	−27.1332	−	2.74360i	−1.02408	−	0.103551i
$703$			46.6915i			1.76100i
$704$	−12.3339	+	38.4885i	−0.464850	+	1.45059i
$705$		−	7.83315i		−	0.295014i
$706$	0.796953	−	7.88158i	0.0299937	−	0.296627i
$707$	−3.92479	−	7.34276i	−0.147607	−	0.276153i
$708$	22.0237	+	14.8819i	0.827703	+	0.559297i
$709$	−13.1737	+	10.8114i	−0.494749	+	0.406030i	−0.848407	−	0.529345i	$-0.822438\pi$
$709$	−13.1737	+	10.8114i	−0.494749	+	0.406030i	0.353658	+	0.935375i	$0.384938\pi$
$710$	3.64807	−	1.49998i	0.136910	−	0.0562934i
$711$	−1.30967	−	1.96006i	−0.0491164	−	0.0735079i
$712$	36.7568	−	10.8379i	1.37752	−	0.406166i
$713$	−36.5867	−	24.4465i	−1.37018	−	0.915527i
$714$	−0.00212078	+	0.00140910i	−7.93683e−5	+	5.27344e-5i
$715$	−5.00822	−	16.5099i	−0.187297	−	0.617435i
$716$	−16.5344	−	20.3621i	−0.617920	−	0.760969i
$717$	24.0146	−	29.2618i	0.896841	−	1.09280i
$718$	−14.2806	+	7.58549i	−0.532947	+	0.283088i
$719$	7.28709	−	17.5926i	0.271763	−	0.656093i	−0.727796	−	0.685793i	$-0.759455\pi$
$719$	7.28709	−	17.5926i	0.271763	−	0.656093i	0.999559	+	0.0297006i	$0.00945538\pi$
$720$	3.28483	+	1.03385i	0.122418	+	0.0385292i
$721$	7.23565	+	17.4684i	0.269470	+	0.650558i
$722$	48.0986	+	39.6831i	1.79005	+	1.47685i
$723$	−27.0756	+	2.66671i	−1.00695	+	0.0991762i
$724$	35.0160	−	3.26511i	1.30136	−	0.121347i
$725$	−3.60927	−	1.92920i	−0.134045	−	0.0716485i
$726$	29.4775	−	5.78386i	1.09401	−	0.214659i
$727$	−2.23609	−	11.2416i	−0.0829319	−	0.416927i	−0.999841	−	0.0178307i	$-0.994324\pi$
$727$	−2.23609	−	11.2416i	−0.0829319	−	0.416927i	0.916909	−	0.399096i	$-0.130676\pi$
$728$	−13.6127	+	5.51462i	−0.504519	+	0.204385i
$729$	−29.0931	−	5.78698i	−1.07752	−	0.214333i
$730$	−6.12742	+	6.09566i	−0.226786	+	0.225610i
$731$	−0.00233950		0.000230421i	−8.65296e−5		8.52242e-6i
$732$	−27.3598	+	27.0769i	−1.01125	+	1.00079i
$733$	−26.7375	−	8.11074i	−0.987573	−	0.299577i	−0.245133	−	0.969489i	$-0.578832\pi$
$733$	−26.7375	−	8.11074i	−0.987573	−	0.299577i	−0.742440	+	0.669912i	$0.766332\pi$
$734$	22.7222	+	12.2213i	0.838691	+	0.451096i
$735$	4.84814	−	4.84814i	0.178826	−	0.178826i
$736$	13.8232	+	26.6899i	0.509531	+	0.983802i
$737$	−5.36841	−	5.36841i	−0.197748	−	0.197748i
$738$	−2.87804	−	9.57713i	−0.105942	−	0.352539i
$739$	7.89778	−	26.0355i	0.290525	−	0.957731i	−0.683244	−	0.730190i	$-0.739431\pi$
$739$	7.89778	−	26.0355i	0.290525	−	0.957731i	0.973768	−	0.227541i	$-0.0730686\pi$
$740$	10.8849	−	4.44253i	0.400136	−	0.163311i
$741$	−3.88861	+	39.4817i	−0.142852	+	1.45040i
$742$	0.0209435	−	8.05950i	0.000768861	−	0.295874i
$743$	−6.94953	+	34.9376i	−0.254953	+	1.28174i	0.614970	+	0.788550i	$0.289168\pi$
$743$	−6.94953	+	34.9376i	−0.254953	+	1.28174i	−0.869923	+	0.493187i	$0.835832\pi$
$744$	33.6509	−	6.42128i	1.23370	−	0.235415i
$745$	−20.6106	+	4.09970i	−0.755113	+	0.150201i
$746$	14.0335	+	9.42974i	0.513804	+	0.345247i
$747$	3.89766	−	7.29201i	0.142608	−	0.266801i
$748$	−0.00381857	−	0.00723422i	−0.000139621	−	0.000264509i
$749$	1.30736	+	13.2739i	0.0477700	+	0.485017i
$750$	−2.05893	+	0.197386i	−0.0751815	+	0.00720752i
$751$	4.11757	−	1.70555i	0.150252	−	0.0622366i	−0.306290	−	0.951938i	$-0.599088\pi$
$751$	4.11757	−	1.70555i	0.150252	−	0.0622366i	0.456542	+	0.889702i	$0.349088\pi$
$752$	0.222677	−	21.4220i	0.00812020	−	0.781179i
$753$	−1.87231	−	0.775534i	−0.0682306	−	0.0282620i
$754$	18.8989	+	5.78659i	0.688258	+	0.210735i
$755$	7.96482	+	6.53656i	0.289869	+	0.237890i
$756$	−16.4590	+	4.89951i	−0.598607	+	0.178193i
$757$	−15.0577	+	4.56770i	−0.547281	+	0.166016i	−0.551804	−	0.833974i	$-0.686060\pi$
$757$	−15.0577	+	4.56770i	−0.547281	+	0.166016i	0.00452263	+	0.999990i	$0.498560\pi$
$758$	1.11189	−	5.51492i	0.0403857	−	0.200311i
$759$	21.8119	−	32.6438i	0.791722	−	1.18490i
$760$	6.68904	−	21.4475i	0.242637	−	0.777981i
$761$	−2.70233	+	1.80564i	−0.0979592	+	0.0654543i	−0.603585	−	0.797299i	$-0.706262\pi$
$761$	−2.70233	+	1.80564i	−0.0979592	+	0.0654543i	0.505626	+	0.862753i	$0.331262\pi$
$762$	−31.5510	−	13.1650i	−1.14297	−	0.476917i
$763$	6.92268	+	8.43531i	0.250618	+	0.305379i
$764$	14.2182	+	2.90507i	0.514396	+	0.105102i
$765$	−0.000614692	0	0.000328560i	−2.22242e−5	0	1.18791e-5i
$766$	−3.67969	−	4.50755i	−0.132953	−	0.162864i
$767$	−31.0319			−1.12050
$768$	−22.2473	−	7.25697i	−0.802779	−	0.261863i
$769$	−4.96644			−0.179095			−0.0895473	−	0.995983i	$-0.528542\pi$
$769$	−4.96644			−0.179095			−0.0895473	+	0.995983i	$0.528542\pi$
$770$	−6.87019	−	8.41585i	−0.247584	−	0.303286i
$771$	−0.856730	+	0.457932i	−0.0308544	+	0.0164920i
$772$	−38.5536	−	7.87730i	−1.38757	−	0.283510i
$773$	−28.3820	−	34.5836i	−1.02083	−	1.24389i	−0.969471	−	0.245205i	$-0.921145\pi$
$773$	−28.3820	−	34.5836i	−1.02083	−	1.24389i	−0.0513594	−	0.998680i	$-0.516355\pi$
$774$	−3.26272	−	1.36141i	−0.117276	−	0.0489347i
$775$	6.88574	−	4.60090i	0.247343	−	0.165269i
$776$	15.1393	+	4.72166i	0.543470	+	0.169498i
$777$	−7.26286	+	10.8696i	−0.260554	+	0.389946i
$778$	−2.48867	+	12.3437i	−0.0892232	+	0.442542i
$779$	−62.4316	+	18.9384i	−2.23684	+	0.678539i
$780$	9.57409	−	2.85002i	0.342807	−	0.102047i
$781$	−10.8923	−	8.93910i	−0.389758	−	0.319866i
$782$	−0.00581692	−	0.00178106i	−0.000208013	−	6.36907e-5i
$783$	21.3506	+	8.84370i	0.763007	+	0.316048i
$784$	13.3964	−	13.1208i	0.478444	−	0.468600i
$785$	9.68508	−	4.01169i	0.345675	−	0.143183i
$786$	−34.6020	+	3.31724i	−1.23421	+	0.118322i
$787$	−1.58649	−	16.1079i	−0.0565524	−	0.574186i	−0.981151	−	0.193243i	$-0.938099\pi$
$787$	−1.58649	−	16.1079i	−0.0565524	−	0.574186i	0.924599	−	0.380943i	$-0.124401\pi$
$788$	−3.22958	−	6.11839i	−0.115049	−	0.217959i
$789$	15.5437	−	29.0802i	0.553370	−	1.03528i
$790$	3.21414	+	2.15972i	0.114354	+	0.0768394i
$791$	−1.99190	+	0.396213i	−0.0708238	+	0.0140877i
$792$	−2.30587	−	12.0840i	−0.0819356	−	0.429386i
$793$	8.76730	−	44.0762i	0.311336	−	1.56519i
$794$	−0.104894	+	40.3654i	−0.00372255	+	1.43251i
$795$	−0.537285	+	5.45515i	−0.0190555	+	0.193474i
$796$	−10.8773	+	4.43944i	−0.385536	+	0.157352i
$797$	−10.6176	+	35.0015i	−0.376094	+	1.23982i	0.540959	+	0.841049i	$0.318061\pi$
$797$	−10.6176	+	35.0015i	−0.376094	+	1.23982i	−0.917053	+	0.398766i	$0.869439\pi$
$798$	7.18964	+	23.9247i	0.254511	+	0.846926i
$799$	0.00306600	+	0.00306600i	0.000108467	+	0.000108467i
$800$	−5.63634	+	0.481278i	−0.199275	+	0.0170158i
$801$	−8.24790	+	8.24790i	−0.291425	+	0.291425i
$802$	5.95590	+	3.20342i	0.210310	+	0.113117i
$803$	29.5465	+	8.96282i	1.04267	+	0.316291i
$804$	3.12440	−	3.09209i	0.110189	−	0.109050i
$805$	−8.04047	−	0.791917i	−0.283389	−	0.0279114i
$806$	−28.3544	+	28.2074i	−0.998742	+	0.993565i
$807$	10.3684	+	2.06240i	0.364984	+	0.0725999i
$808$	5.81493	+	14.3540i	0.204568	+	0.504971i
$809$	−4.02343	−	20.2271i	−0.141456	−	0.711148i	−0.984789	−	0.173756i	$-0.944410\pi$
$809$	−4.02343	−	20.2271i	−0.141456	−	0.711148i	0.843332	−	0.537392i	$-0.180590\pi$
$810$	7.87695	−	1.54556i	0.276768	−	0.0543053i
$811$	−41.5109	−	22.1880i	−1.45764	−	0.779127i	−0.463388	−	0.886155i	$-0.653367\pi$
$811$	−41.5109	−	22.1880i	−1.45764	−	0.779127i	−0.994256	+	0.107028i	$0.965867\pi$
$812$	12.3921	−	1.15552i	0.434877	−	0.0405508i
$813$	−11.3922	+	1.12204i	−0.399543	+	0.0393516i
$814$	−32.3959	−	26.7278i	−1.13548	−	0.936811i
$815$	9.20381	+	22.2200i	0.322396	+	0.778332i
$816$	0.00420001	−	0.00218913i	0.000147030	−	7.66349e-5i
$817$	−8.82638	+	21.3088i	−0.308796	+	0.745499i
$818$	33.4263	−	17.7552i	1.16872	−	0.620797i
$819$	2.83608	−	3.45577i	0.0991005	−	0.120754i
$820$	10.3551	+	12.7523i	0.361617	+	0.445331i
$821$	−9.39549	−	30.9728i	−0.327905	−	1.08096i	−0.953647	−	0.300927i	$-0.902704\pi$
$821$	−9.39549	−	30.9728i	−0.327905	−	1.08096i	0.625742	−	0.780030i	$-0.284796\pi$
$822$	25.8051	−	17.1456i	0.900057	−	0.598022i
$823$	−31.5976	−	21.1128i	−1.10142	−	0.735947i	−0.134473	−	0.990917i	$-0.542934\pi$
$823$	−31.5976	−	21.1128i	−1.10142	−	0.735947i	−0.966949	+	0.254970i	$0.917934\pi$
$824$	−9.94676	−	33.7346i	−0.346512	−	1.17520i
$825$	4.10507	+	6.14368i	0.142920	+	0.213895i
$826$	−18.0725	+	7.43093i	−0.628824	+	0.258555i
$827$	17.6116	−	14.4535i	0.612416	−	0.502597i	−0.276290	−	0.961074i	$-0.589105\pi$
$827$	17.6116	−	14.4535i	0.612416	−	0.502597i	0.888706	+	0.458478i	$0.151605\pi$
$828$	−7.58046	−	5.12229i	−0.263439	−	0.178012i
$829$	23.5755	+	44.1067i	0.818811	+	1.53189i	0.846573	+	0.532273i	$0.178662\pi$
$829$	23.5755	+	44.1067i	0.818811	+	1.53189i	−0.0277613	+	0.999615i	$0.508838\pi$
$830$	−1.36641	+	13.5133i	−0.0474287	+	0.469053i
$831$			9.59324i			0.332786i
$832$	26.2641	−	7.52201i	0.910544	−	0.260779i
$833$			0.00379526i			0.000131498i
$834$	−29.8724	−	3.02057i	−1.03440	−	0.104594i
$835$	10.9076	+	20.4067i	0.377473	+	0.706202i
$836$	−78.7958	+	15.2482i	−2.72521	+	0.527369i
$837$	−36.1488	+	29.6666i	−1.24949	+	1.02543i
$838$	−1.89275	−	4.60330i	−0.0653840	−	0.159018i
$839$	−15.9093	−	23.8099i	−0.549249	−	0.822010i	0.448159	−	0.893954i	$-0.352080\pi$
$839$	−15.9093	−	23.8099i	−0.549249	−	0.822010i	−0.997409	+	0.0719438i	$0.977080\pi$
$840$	4.89334	−	3.95242i	0.168836	−	0.136372i
$841$	10.1866	+	6.80649i	0.351263	+	0.234707i
$842$	10.2776	+	15.4684i	0.354189	+	0.533076i
$843$	4.62818	+	15.2571i	0.159403	+	0.525482i
$844$	2.66676	−	25.7057i	0.0917935	−	0.884827i
$845$	0.848665	−	1.03410i	0.0291950	−	0.0355742i
$846$	3.05893	+	5.75880i	0.105168	+	0.197992i
$847$	−8.45105	+	20.4026i	−0.290382	+	0.701043i
$848$	−1.62444	+	14.9034i	−0.0557834	+	0.511784i
$849$	−16.0492	−	38.7461i	−0.550806	−	1.32976i
$850$	0.000728634	0	0.000883153i	2.49919e−5	0	3.02919e-5i
$851$	−31.0833	+	3.06143i	−1.06552	+	0.104945i
$852$	5.20840	−	6.27962i	0.178437	−	0.215136i
$853$	35.5585	+	19.0064i	1.21750	+	0.650768i	0.949837	−	0.312744i	$-0.101248\pi$
$853$	35.5585	+	19.0064i	1.21750	+	0.650768i	0.267664	+	0.963512i	$0.413748\pi$
$854$	−5.44857	−	27.7687i	−0.186446	−	0.950226i
$855$	1.33409	+	6.70694i	0.0456251	+	0.229373i
$856$	0.193416	−	24.8097i	0.00661081	−	0.847977i
$857$	−36.5250	−	7.26527i	−1.24767	−	0.248177i	−0.473295	−	0.880904i	$-0.656936\pi$
$857$	−36.5250	−	7.26527i	−1.24767	−	0.248177i	−0.774375	+	0.632727i	$0.781936\pi$
$858$	−25.1676	−	25.2987i	−0.859207	−	0.863684i
$859$	26.9606	+	2.65539i	0.919885	+	0.0906007i	0.546863	−	0.837222i	$-0.315822\pi$
$859$	26.9606	+	2.65539i	0.919885	+	0.0906007i	0.373021	+	0.927823i	$0.378322\pi$
$860$	5.80737	+	0.0301824i	0.198030	+	0.00102921i
$861$	−17.4797	−	5.30242i	−0.595708	−	0.180706i
$862$	−24.0039	+	44.6288i	−0.817577	+	1.52006i
$863$	−2.30076	+	2.30076i	−0.0783187	+	0.0783187i	−0.745181	−	0.666862i	$-0.767637\pi$
$863$	−2.30076	+	2.30076i	−0.0783187	+	0.0783187i	0.666862	+	0.745181i	$0.267637\pi$
$864$	31.4078	−	5.82424i	1.06852	−	0.198145i
$865$	−4.89563	−	4.89563i	−0.166456	−	0.166456i
$866$	−1.93961	+	0.582874i	−0.0659105	+	0.0198068i
$867$	7.21749	−	23.7929i	0.245119	−	0.808049i
$868$	−9.75862	+	23.2174i	−0.331229	+	0.788048i
$869$	1.35591	−	13.7668i	0.0459960	−	0.467005i
$870$	−8.46480	−	0.0219967i	−0.286984	−	0.000745759i
$871$	−1.00120	+	5.03335i	−0.0339242	+	0.170549i
$872$	−11.1451	−	16.9647i	−0.377421	−	0.574496i
$873$	−4.73430	+	0.941710i	−0.160232	+	0.0318721i
$874$	−33.2888	+	49.5411i	−1.12601	+	1.67575i
$875$	0.716790	−	1.34102i	0.0242319	−	0.0453347i
$876$	−5.27827	+	17.0801i	−0.178336	+	0.577082i
$877$	−0.421957	−	4.28420i	−0.0142485	−	0.144667i	0.985428	−	0.170091i	$-0.0544063\pi$
$877$	−0.421957	−	4.28420i	−0.0142485	−	0.144667i	−0.999677	+	0.0254243i	$0.991906\pi$
$878$	−0.925608	−	9.65500i	−0.0312378	−	0.325840i
$879$	17.2087	−	7.12806i	0.580433	−	0.240423i
$880$	11.0518	+	16.9183i	0.372558	+	0.570317i
$881$	2.48736	+	1.03030i	0.0838013	+	0.0347116i	0.424190	−	0.905573i	$-0.360559\pi$
$881$	2.48736	+	1.03030i	0.0838013	+	0.0347116i	−0.340389	+	0.940285i	$0.610559\pi$
$882$	−1.67102	+	5.45752i	−0.0562662	+	0.183764i
$883$	33.5278	+	27.5156i	1.12830	+	0.925973i	0.997854	−	0.0654817i	$-0.0208584\pi$
$883$	33.5278	+	27.5156i	1.12830	+	0.925973i	0.130448	+	0.991455i	$0.458358\pi$
$884$	−0.00263189	+	0.00486297i	−8.85202e−5	+	0.000163559i
$885$	12.7179	−	3.85794i	0.427508	−	0.129683i
$886$	−6.73969	−	1.35882i	−0.226424	−	0.0456506i
$887$	−1.59906	+	2.39316i	−0.0536912	+	0.0803546i	−0.857344	−	0.514744i	$-0.827887\pi$
$887$	−1.59906	+	2.39316i	−0.0536912	+	0.0803546i	0.803653	+	0.595099i	$0.202887\pi$
$888$	15.5726	−	18.6764i	0.522581	−	0.626739i
$889$	20.8973	−	13.9631i	0.700872	−	0.468307i
$890$	7.37844	−	17.6830i	0.247326	−	0.592736i
$891$	−18.1917	−	22.1667i	−0.609445	−	0.742611i
$892$	−4.30729	−	6.51940i	−0.144219	−	0.218286i
$893$	37.5181	−	20.0538i	1.25549	−	0.671076i
$894$	−33.6708	+	27.4868i	−1.12612	+	0.919296i
$895$	−13.1149			−0.438383
$896$	13.4946	−	10.6699i	0.450823	−	0.356457i
$897$	−26.5385			−0.886096
$898$	17.7445	−	14.4855i	0.592141	−	0.483388i
$899$	29.8899	−	15.9765i	0.996882	−	0.532845i
$900$	1.43661	−	0.949150i	0.0478870	−	0.0316383i
$901$	−0.00192492	−	0.00234552i	−6.41283e−5	−	7.81406e-5i
$902$	22.5980	−	54.1579i	0.752430	−	1.80326i
$903$	−5.36933	+	3.58767i	−0.178680	+	0.119390i
$904$	3.76233	−	0.340965i	0.125133	−	0.0113403i
$905$	9.76911	−	14.6205i	0.324736	−	0.486002i
$906$	20.8914	+	4.21202i	0.694069	+	0.139935i
$907$	−19.6361	+	5.95655i	−0.652006	+	0.197784i	−0.598924	−	0.800806i	$-0.704405\pi$
$907$	−19.6361	+	5.95655i	−0.652006	+	0.197784i	−0.0530827	+	0.998590i	$0.516905\pi$
$908$	−42.6875	−	23.1030i	−1.41664	−	0.766700i
$909$	−3.64396	−	2.99052i	−0.120862	−	0.0991892i
$910$	−2.15000	+	7.02186i	−0.0712718	+	0.232772i
$911$	−2.87981	−	1.19286i	−0.0954124	−	0.0395211i	0.334467	−	0.942408i	$-0.391444\pi$
$911$	−2.87981	−	1.19286i	−0.0954124	−	0.0395211i	−0.429879	+	0.902886i	$0.641444\pi$
$912$	−8.59139	−	45.6676i	−0.284489	−	1.51221i
$913$	44.8269	−	18.5679i	1.48355	−	0.614508i
$914$	0.457046	+	4.76744i	0.0151177	+	0.157693i
$915$	1.88649	+	19.1539i	0.0623654	+	0.633207i
$916$	22.0603	+	6.81731i	0.728892	+	0.225250i
$917$	12.0462	−	22.5369i	0.397802	−	0.744235i
$918$	−0.00360584	+	0.00536629i	−0.000119011	+	0.000177114i
$919$	18.6243	−	3.70461i	0.614360	−	0.122204i	0.121905	−	0.992542i	$-0.461100\pi$
$919$	18.6243	−	3.70461i	0.614360	−	0.122204i	0.492455	+	0.870338i	$0.336100\pi$
$920$	14.7165	+	3.04675i	0.485188	+	0.100448i
$921$	−4.54642	+	22.8564i	−0.149810	+	0.753143i
$922$	−55.8672	−	0.145177i	−1.83989	−	0.00478116i
$923$	−0.933598	+	9.47898i	−0.0307297	+	0.312004i
$924$	−20.7153	−	8.70695i	−0.681482	−	0.286438i
$925$	1.70637	−	5.62516i	0.0561053	−	0.184954i
$926$	24.7783	−	7.44615i	0.814265	−	0.244696i
$927$	7.56974	+	7.56974i	0.248623	+	0.248623i
$928$	−23.1488	−	0.300790i	−0.759896	−	0.00987391i
$929$	−9.01479	+	9.01479i	−0.295766	+	0.295766i	−0.839353	−	0.543587i	$-0.817066\pi$
$929$	−9.01479	+	9.01479i	−0.295766	+	0.295766i	0.543587	+	0.839353i	$0.317066\pi$
$930$	8.11379	−	15.0854i	0.266062	−	0.494670i
$931$	35.6327	+	10.8091i	1.16782	+	0.354253i
$932$	0.120233	−	23.1340i	0.00393838	−	0.757780i
$933$	8.35937	+	0.823326i	0.273673	+	0.0269545i
$934$	−33.0972	−	33.2697i	−1.08297	−	1.08862i
$935$	−0.00401150		0.000797937i	−0.000131190		2.60953e-5i
$936$	−5.92575	+	5.83407i	−0.193689	+	0.190693i
$937$	−3.08191	−	15.4938i	−0.100682	−	0.506160i	−0.997911	−	0.0645966i	$-0.979424\pi$
$937$	−3.08191	−	15.4938i	−0.100682	−	0.506160i	0.897230	−	0.441564i	$-0.145576\pi$
$938$	0.622208	+	3.17110i	0.0203158	+	0.103540i
$939$	24.7141	+	13.2099i	0.806513	+	0.431090i
$940$	−8.24472	−	6.83829i	−0.268913	−	0.223040i
$941$	2.87715	−	0.283375i	0.0937925	−	0.00923776i	−0.0510120	−	0.998698i	$-0.516245\pi$
$941$	2.87715	−	0.283375i	0.0937925	−	0.00923776i	0.144805	+	0.989460i	$0.453745\pi$
$942$	13.7990	−	16.7253i	0.449594	−	0.544938i
$943$	−16.7011	−	40.3199i	−0.543861	−	1.31300i
$944$	34.8904	−	10.1891i	1.13559	−	0.331627i
$945$	−3.28586	+	7.93277i	−0.106889	+	0.258053i
$946$	−9.73212	−	18.3219i	−0.316418	−	0.595696i
$947$	19.4891	−	23.7476i	0.633312	−	0.771693i	−0.353171	−	0.935559i	$-0.614897\pi$
$947$	19.4891	−	23.7476i	0.633312	−	0.771693i	0.986483	+	0.163866i	$0.0523965\pi$
$948$	7.96670	+	0.826479i	0.258746	+	0.0268428i
$949$	−6.05853	−	19.9723i	−0.196668	−	0.648328i
$950$	−6.21653	−	9.35623i	−0.201691	−	0.303556i
$951$	−17.5614	−	11.7342i	−0.569468	−	0.380506i
$952$	−0.000368287		0.00346235i	−1.19363e−5		0.000112216i
$953$	−9.76060	−	14.6078i	−0.316177	−	0.473192i	0.639009	−	0.769199i	$-0.279345\pi$
$953$	−9.76060	−	14.6078i	−0.316177	−	0.473192i	−0.955186	+	0.296007i	$0.904345\pi$
$954$	−1.73529	−	4.22035i	−0.0561822	−	0.136639i
$955$	5.60893	−	4.60313i	0.181501	−	0.148954i
$956$	−9.83478	−	50.8218i	−0.318079	−	1.64369i
$957$	14.2547	+	26.6687i	0.460789	+	0.862076i
$958$	−41.9789	−	4.24473i	−1.35628	−	0.137141i
$959$			22.7764i			0.735487i
$960$	−9.82875	+	6.34797i	−0.317222	+	0.204880i
$961$			37.5817i			1.21231i
$962$	−2.85606	+	28.2454i	−0.0920830	+	0.910667i
$963$	3.55991	+	6.66012i	0.114716	+	0.214619i
$964$	−20.8300	+	30.8263i	−0.670889	+	0.992847i
$965$	−15.2090	+	12.4817i	−0.489596	+	0.401801i
$966$	−15.4556	+	6.35494i	−0.497277	+	0.204467i
$967$	7.30213	+	10.9284i	0.234821	+	0.351434i	0.930100	−	0.367305i	$-0.119720\pi$
$967$	7.30213	+	10.9284i	0.234821	+	0.351434i	−0.695280	+	0.718739i	$0.744720\pi$
$968$	19.6459	−	36.0756i	0.631445	−	1.15952i
$969$	0.00782009	+	0.00522522i	0.000251218	+	0.000167858i
$970$	6.60437	−	4.38812i	0.212054	−	0.140894i
$971$	−12.2832	−	40.4921i	−0.394185	−	1.29945i	−0.899652	−	0.436608i	$-0.856180\pi$
$971$	−12.2832	−	40.4921i	−0.394185	−	1.29945i	0.505466	−	0.862846i	$-0.331320\pi$
$972$	−13.4127	+	10.8914i	−0.430213	+	0.349341i
$973$	14.0028	−	17.0624i	0.448908	−	0.546996i
$974$	−2.89732	+	1.53898i	−0.0928360	+	0.0493121i
$975$	1.91137	−	4.61445i	0.0612127	−	0.147781i
$976$	4.61465	+	52.4353i	0.147711	+	1.67841i
$977$	−0.0544998	−	0.131574i	−0.00174360	−	0.00420943i	0.923005	−	0.384787i	$-0.125725\pi$
$977$	−0.0544998	−	0.131574i	−0.00174360	−	0.00420943i	−0.924749	+	0.380578i	$0.875725\pi$
$978$	38.3719	+	31.6582i	1.22700	+	1.01232i
$979$	−68.1189	+	6.70912i	−2.17709	+	0.214424i
$980$	−0.870480	−	9.33527i	−0.0278065	−	0.298204i
$981$	5.44884	+	2.91246i	0.173968	+	0.0929878i
$982$	31.3569	−	6.15260i	1.00064	−	0.196337i
$983$	1.59247	+	8.00587i	0.0507918	+	0.255348i	0.997836	−	0.0657565i	$-0.0209460\pi$
$983$	1.59247	+	8.00587i	0.0507918	+	0.255348i	−0.947044	+	0.321104i	$0.895946\pi$
$984$	31.2887	+	13.2469i	0.997447	+	0.422296i
$985$	−3.39275	−	0.674861i	−0.108102	−	0.0215029i
$986$	0.00332185	−	0.00330463i	0.000105789	−	0.000105241i
$987$	11.8535	+	1.16746i	0.377300	+	0.0371608i
$988$	38.1614	+	38.5602i	1.21408	+	1.22676i
$989$	−14.7643	−	4.47870i	−0.469477	−	0.142414i
$990$	−5.41716	−	2.91366i	−0.172169	−	0.0926020i
$991$	−1.87147	+	1.87147i	−0.0594491	+	0.0594491i	−0.736206	−	0.676757i	$-0.763385\pi$
$991$	−1.87147	+	1.87147i	−0.0594491	+	0.0594491i	0.676757	+	0.736206i	$0.263385\pi$
$992$	22.6183	−	41.0247i	0.718132	−	1.30254i
$993$	−18.6627	−	18.6627i	−0.592244	−	0.592244i
$994$	1.72613	+	5.74397i	0.0547495	+	0.182188i
$995$	−1.70519	+	5.62126i	−0.0540581	+	0.178206i
$996$	10.6157	+	26.0101i	0.336371	+	0.824160i
$997$	2.02636	−	20.5740i	0.0641755	−	0.651585i	−0.908259	−	0.418409i	$-0.862588\pi$
$997$	2.02636	−	20.5740i	0.0641755	−	0.651585i	0.972434	−	0.233176i	$-0.0749120\pi$
$998$	−0.137869	+	53.0550i	−0.00436418	+	1.67943i
$999$	−6.47575	+	32.5558i	−0.204884	+	1.03002i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.101.19	✓	1024
128.109	even	32	inner	640.2.bm.a.621.19	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.101.19	✓	1024	1.1	even	1	trivial
640.2.bm.a.621.19	yes	1024	128.109	even	32	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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.894324 - 1.09553i) q^{2} +(-1.28986 + 0.689446i) q^{3} +(-0.400370 + 1.95952i) q^{4} +(0.634393 + 0.773010i) q^{5} +(1.90886 + 0.796494i) q^{6} +(-1.26430 + 0.844781i) q^{7} +(2.50477 - 1.31382i) q^{8} +(-0.478302 + 0.715829i) q^{9} +(0.279503 - 1.38632i) q^{10} +(-4.83452 + 1.46654i) q^{11} +(-0.834558 - 2.80354i) q^{12} +(2.63983 + 2.16645i) q^{13} +(2.05618 + 0.629575i) q^{14} +(-1.35123 - 0.559697i) q^{15} +(-3.67941 - 1.56906i) q^{16} +(0.000747962 - 0.000309816i) q^{17} +(1.21197 - 0.116189i) q^{18} +(-0.778556 - 7.90481i) q^{19} +(-1.76872 + 0.933614i) q^{20} +(1.04835 - 1.96132i) q^{21} +(5.93026 + 3.98480i) q^{22} +(5.21131 - 1.03659i) q^{23} +(-2.32499 + 3.42155i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(0.0125501 - 4.82953i) q^{26} +(0.553486 - 5.61963i) q^{27} +(-1.14917 - 2.81565i) q^{28} +(-1.18799 + 3.91629i) q^{29} +(0.595271 + 1.98086i) q^{30} +(-5.85584 - 5.85584i) q^{31} +(1.57163 + 5.43415i) q^{32} +(5.22477 - 5.22477i) q^{33} +(-0.00100833 - 0.000542339i) q^{34} +(-1.45509 - 0.441397i) q^{35} +(-1.21118 - 1.22384i) q^{36} +(-5.84997 - 0.576172i) q^{37} +(-7.96367 + 7.92239i) q^{38} +(-4.89867 - 0.974406i) q^{39} +(2.60461 + 1.10273i) q^{40} +(-1.60239 - 8.05574i) q^{41} +(-3.08625 + 0.605559i) q^{42} +(-2.56086 - 1.36881i) q^{43} +(-0.938104 - 10.0605i) q^{44} +(-0.856775 + 0.0843850i) q^{45} +(-5.79621 - 4.78209i) q^{46} +(2.04957 + 4.94810i) q^{47} +(5.82771 - 0.512877i) q^{48} +(-1.79397 + 4.33104i) q^{49} +(1.24895 - 0.663412i) q^{50} +(-0.000751167 + 0.000915299i) q^{51} +(-5.30211 + 4.30541i) q^{52} +(-1.08796 - 3.58653i) q^{53} +(-6.65147 + 4.41941i) q^{54} +(-4.20064 - 2.80677i) q^{55} +(-2.05689 + 3.77705i) q^{56} +(6.45416 + 9.65934i) q^{57} +(5.35286 - 2.20095i) q^{58} +(-7.02430 + 5.76470i) q^{59} +(1.63773 - 2.42367i) q^{60} +(-6.20334 - 11.6056i) q^{61} +(-1.17823 + 11.6523i) q^{62} -1.30909i q^{63} +(4.54773 - 6.58165i) q^{64} +3.41500i q^{65} +(-10.3965 - 1.05125i) q^{66} +(0.708401 + 1.32532i) q^{67} +(0.000307628 + 0.00158969i) q^{68} +(-6.00719 + 4.92997i) q^{69} +(0.817759 + 1.98885i) q^{70} +(1.54955 + 2.31907i) q^{71} +(-0.257561 + 2.42139i) q^{72} +(-5.08158 - 3.39540i) q^{73} +(4.60056 + 6.92410i) q^{74} +(-0.424559 - 1.39958i) q^{75} +(15.8013 + 1.63926i) q^{76} +(4.87340 - 5.93826i) q^{77} +(3.31351 + 6.23808i) q^{78} +(-1.04785 + 2.52973i) q^{79} +(-1.12129 - 3.83962i) q^{80} +(2.17213 + 5.24399i) q^{81} +(-7.39225 + 8.95991i) q^{82} +(-9.55781 + 0.941362i) q^{83} +(3.42351 + 2.83951i) q^{84} +(0.000713993 + 0.000381637i) q^{85} +(0.790667 + 4.02965i) q^{86} +(-1.16772 - 5.87053i) q^{87} +(-10.1826 + 10.0250i) q^{88} +(13.2883 + 2.64320i) q^{89} +(0.858681 + 0.863155i) q^{90} +(-5.16773 - 0.508977i) q^{91} +(-0.0552295 + 10.6267i) q^{92} +(11.5905 + 3.51594i) q^{93} +(3.58781 - 6.67057i) q^{94} +(5.61659 - 5.61659i) q^{95} +(-5.77373 - 5.92575i) q^{96} +(3.96464 + 3.96464i) q^{97} +(6.34917 - 1.90800i) q^{98} +(1.26257 - 4.16214i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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