LMFDB - Embedded newform 768.2.z.a.637.49

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(13,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(64))

chi = DirichletCharacter(H, H._module([0, 47, 0]))

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

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

chi := DirichletCharacter("768.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.z (of order $64$, degree $32$, 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:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$2048$
Relative dimension:	$64$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			637.49
Character	$\chi$	$=$	768.637
Dual form			768.2.z.a.469.49

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.05231 - 0.944795i) q^{2} +(0.427555 - 0.903989i) q^{3} +(0.214725 - 1.98844i) q^{4} +(4.31229 + 0.639668i) q^{5} +(-0.404163 - 1.35523i) q^{6} +(0.272230 + 2.76400i) q^{7} +(-1.65271 - 2.29533i) q^{8} +(-0.634393 - 0.773010i) q^{9} +O(q^{10})$	\(q+(1.05231 - 0.944795i) q^{2} +(0.427555 - 0.903989i) q^{3} +(0.214725 - 1.98844i) q^{4} +(4.31229 + 0.639668i) q^{5} +(-0.404163 - 1.35523i) q^{6} +(0.272230 + 2.76400i) q^{7} +(-1.65271 - 2.29533i) q^{8} +(-0.634393 - 0.773010i) q^{9} +(5.14224 - 3.40110i) q^{10} +(-0.826139 + 0.0405856i) q^{11} +(-1.70572 - 1.04428i) q^{12} +(-3.15934 - 2.34312i) q^{13} +(2.89788 + 2.65139i) q^{14} +(2.42200 - 3.62477i) q^{15} +(-3.90779 - 0.853935i) q^{16} +(-1.96119 - 2.93513i) q^{17} +(-1.39792 - 0.214077i) q^{18} +(5.37838 + 1.34721i) q^{19} +(2.19790 - 8.43738i) q^{20} +(2.61502 + 0.935669i) q^{21} +(-0.831012 + 0.823241i) q^{22} +(-0.426292 + 0.797536i) q^{23} +(-2.78158 + 0.512651i) q^{24} +(13.4020 + 4.06545i) q^{25} +(-5.53838 + 0.519226i) q^{26} +(-0.970031 + 0.242980i) q^{27} +(5.55450 + 0.0521863i) q^{28} +(0.289293 - 0.262200i) q^{29} +(-0.875970 - 6.10268i) q^{30} +(3.38175 + 8.16426i) q^{31} +(-4.91901 + 2.79345i) q^{32} +(-0.316531 + 0.764174i) q^{33} +(-4.83688 - 1.23575i) q^{34} +(-0.594106 + 12.0933i) q^{35} +(-1.67330 + 1.09547i) q^{36} +(-10.4241 - 6.24795i) q^{37} +(6.93258 - 3.66378i) q^{38} +(-3.46895 + 1.85419i) q^{39} +(-5.65872 - 10.9553i) q^{40} +(4.68011 - 1.41970i) q^{41} +(3.63583 - 1.48604i) q^{42} +(-0.129067 + 0.0610441i) q^{43} +(-0.0966907 + 1.65144i) q^{44} +(-2.24122 - 3.73925i) q^{45} +(0.304916 + 1.24202i) q^{46} +(-8.64249 - 1.71910i) q^{47} +(-2.44274 + 3.16749i) q^{48} +(-0.700082 + 0.139255i) q^{49} +(17.9441 - 8.38401i) q^{50} +(-3.49184 + 0.517965i) q^{51} +(-5.33755 + 5.77902i) q^{52} +(0.652453 + 0.591349i) q^{53} +(-0.791210 + 1.17217i) q^{54} +(-3.58852 - 0.353438i) q^{55} +(5.89438 - 5.19295i) q^{56} +(3.51742 - 4.28599i) q^{57} +(0.0567015 - 0.549238i) q^{58} +(-4.72373 + 3.50335i) q^{59} +(-6.68758 - 5.59432i) q^{60} +(-10.6608 + 3.81451i) q^{61} +(11.2722 + 5.39630i) q^{62} +(1.96390 - 1.96390i) q^{63} +(-2.53710 + 7.58704i) q^{64} +(-12.1252 - 12.1252i) q^{65} +(0.388898 + 1.10321i) q^{66} +(1.73385 + 4.84578i) q^{67} +(-6.25744 + 3.26946i) q^{68} +(0.538701 + 0.726354i) q^{69} +(10.8005 + 13.2873i) q^{70} +(2.33820 + 1.91891i) q^{71} +(-0.725847 + 2.73371i) q^{72} +(0.612296 - 6.21674i) q^{73} +(-16.8724 + 3.27381i) q^{74} +(9.40521 - 10.3771i) q^{75} +(3.83373 - 10.4053i) q^{76} +(-0.337079 - 2.27240i) q^{77} +(-1.89859 + 5.22863i) q^{78} +(1.27633 + 6.41656i) q^{79} +(-16.3053 - 6.18211i) q^{80} +(-0.195090 + 0.980785i) q^{81} +(3.58362 - 5.91571i) q^{82} +(-6.30520 + 3.77919i) q^{83} +(2.42203 - 4.99890i) q^{84} +(-6.57971 - 13.9116i) q^{85} +(-0.0781446 + 0.186179i) q^{86} +(-0.113337 - 0.373622i) q^{87} +(1.45853 + 1.82919i) q^{88} +(8.47544 + 15.8564i) q^{89} +(-5.89129 - 1.81737i) q^{90} +(5.61632 - 9.37027i) q^{91} +(1.49432 + 1.01891i) q^{92} +(8.82629 + 0.433608i) q^{93} +(-10.7188 + 6.35635i) q^{94} +(22.3314 + 9.24996i) q^{95} +(0.422102 + 5.64108i) q^{96} +(-11.2629 + 4.66523i) q^{97} +(-0.605138 + 0.807974i) q^{98} +(0.555470 + 0.612867i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2048 q+O(q^{10}) $ 2048 * q	$ 2048 q+O(q^{100}) $ 2048 * q

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{64}\right)$

Coefficient data

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

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

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

$2$	1.05231	−	0.944795i	0.744098	−	0.668071i
$2$	1.05231	−	0.944795i	0.744098	−	0.668071i
$3$	0.427555	−	0.903989i	0.246849	−	0.521918i
$3$	0.427555	−	0.903989i	0.246849	−	0.521918i
$4$	0.214725	−	1.98844i	0.107362	−	0.994220i
$5$	4.31229	+	0.639668i	1.92852	+	0.286068i	0.996985	−	0.0775940i	$-0.0247238\pi$
$5$	4.31229	+	0.639668i	1.92852	+	0.286068i	0.931531	+	0.363662i	$0.118474\pi$
$6$	−0.404163	−	1.35523i	−0.164999	−	0.553271i
$7$	0.272230	+	2.76400i	0.102893	+	1.04469i	0.898528	+	0.438916i	$0.144638\pi$
$7$	0.272230	+	2.76400i	0.102893	+	1.04469i	−0.795635	+	0.605777i	$0.792862\pi$
$8$	−1.65271	−	2.29533i	−0.584321	−	0.811522i
$9$	−0.634393	−	0.773010i	−0.211464	−	0.257670i
$10$	5.14224	−	3.40110i	1.62612	−	1.07552i
$11$	−0.826139	+	0.0405856i	−0.249090	+	0.0122370i	−0.173230	−	0.984881i	$-0.555420\pi$
$11$	−0.826139	+	0.0405856i	−0.249090	+	0.0122370i	−0.0758605	+	0.997118i	$0.524170\pi$
$12$	−1.70572	−	1.04428i	−0.492399	−	0.301457i
$13$	−3.15934	−	2.34312i	−0.876242	−	0.649865i	0.0611548	−	0.998128i	$-0.480522\pi$
$13$	−3.15934	−	2.34312i	−0.876242	−	0.649865i	−0.937397	+	0.348263i	$0.886772\pi$
$14$	2.89788	+	2.65139i	0.774492	+	0.708614i
$15$	2.42200	−	3.62477i	0.625357	−	0.935912i
$16$	−3.90779	−	0.853935i	−0.976947	−	0.213484i
$17$	−1.96119	−	2.93513i	−0.475658	−	0.711873i	0.513604	−	0.858028i	$-0.328310\pi$
$17$	−1.96119	−	2.93513i	−0.475658	−	0.711873i	−0.989262	+	0.146155i	$0.953310\pi$
$18$	−1.39792	−	0.214077i	−0.329492	−	0.0504585i
$19$	5.37838	+	1.34721i	1.23388	+	0.309072i	0.804447	−	0.594024i	$-0.202462\pi$
$19$	5.37838	+	1.34721i	1.23388	+	0.309072i	0.429438	+	0.903096i	$0.358712\pi$
$20$	2.19790	−	8.43738i	0.491465	−	1.88666i
$21$	2.61502	+	0.935669i	0.570644	+	0.204180i
$22$	−0.831012	+	0.823241i	−0.177172	+	0.175516i
$23$	−0.426292	+	0.797536i	−0.0888880	+	0.166298i	−0.922437	−	0.386148i	$-0.873805\pi$
$23$	−0.426292	+	0.797536i	−0.0888880	+	0.166298i	0.833549	+	0.552446i	$0.186305\pi$
$24$	−2.78158	+	0.512651i	−0.567788	+	0.104645i
$25$	13.4020	+	4.06545i	2.68040	+	0.813090i
$26$	−5.53838	+	0.519226i	−1.08617	+	0.101829i
$27$	−0.970031	+	0.242980i	−0.186683	+	0.0467616i
$28$	5.55450	+	0.0521863i	1.04970	+	0.00986229i
$29$	0.289293	−	0.262200i	0.0537203	−	0.0486892i	−0.644257	−	0.764809i	$-0.722833\pi$
$29$	0.289293	−	0.262200i	0.0537203	−	0.0486892i	0.697978	+	0.716119i	$0.254083\pi$
$30$	−0.875970	−	6.10268i	−0.159929	−	1.11419i
$31$	3.38175	+	8.16426i	0.607380	+	1.46635i	0.865839	+	0.500323i	$0.166785\pi$
$31$	3.38175	+	8.16426i	0.607380	+	1.46635i	−0.258459	+	0.966022i	$0.583215\pi$
$32$	−4.91901	+	2.79345i	−0.869566	+	0.493817i
$33$	−0.316531	+	0.764174i	−0.0551010	+	0.133026i
$34$	−4.83688	−	1.23575i	−0.829517	−	0.211929i
$35$	−0.594106	+	12.0933i	−0.100422	+	2.04414i
$36$	−1.67330	+	1.09547i	−0.278884	+	0.182578i
$37$	−10.4241	−	6.24795i	−1.71371	−	1.02716i	−0.880076	−	0.474833i	$-0.842509\pi$
$37$	−10.4241	−	6.24795i	−1.71371	−	1.02716i	−0.833630	−	0.552323i	$-0.813741\pi$
$38$	6.93258	−	3.66378i	1.12461	−	0.594343i
$39$	−3.46895	+	1.85419i	−0.555476	+	0.296908i
$40$	−5.65872	−	10.9553i	−0.894722	−	1.73219i
$41$	4.68011	−	1.41970i	0.730910	−	0.221719i	0.0971730	−	0.995268i	$-0.469020\pi$
$41$	4.68011	−	1.41970i	0.730910	−	0.221719i	0.633737	+	0.773548i	$0.281520\pi$
$42$	3.63583	−	1.48604i	0.561021	−	0.229301i
$43$	−0.129067	+	0.0610441i	−0.0196825	+	0.00930914i	−0.437371	−	0.899281i	$-0.644090\pi$
$43$	−0.129067	+	0.0610441i	−0.0196825	+	0.00930914i	0.417688	+	0.908590i	$0.362840\pi$
$44$	−0.0966907	+	1.65144i	−0.0145767	+	0.248964i
$45$	−2.24122	−	3.73925i	−0.334101	−	0.557414i
$46$	0.304916	+	1.24202i	0.0449574	+	0.183125i
$47$	−8.64249	−	1.71910i	−1.26064	−	0.250756i	−0.480851	−	0.876803i	$-0.659672\pi$
$47$	−8.64249	−	1.71910i	−1.26064	−	0.250756i	−0.779786	+	0.626046i	$0.784672\pi$
$48$	−2.44274	+	3.16749i	−0.352580	+	0.457188i
$49$	−0.700082	+	0.139255i	−0.100012	+	0.0198936i
$50$	17.9441	−	8.38401i	2.53768	−	1.18568i
$51$	−3.49184	+	0.517965i	−0.488955	+	0.0725296i
$52$	−5.33755	+	5.77902i	−0.740185	+	0.801406i
$53$	0.652453	+	0.591349i	0.0896213	+	0.0812280i	0.715140	−	0.698981i	$-0.246363\pi$
$53$	0.652453	+	0.591349i	0.0896213	+	0.0812280i	−0.625519	+	0.780209i	$0.715113\pi$
$54$	−0.791210	+	1.17217i	−0.107670	+	0.159512i
$55$	−3.58852	−	0.353438i	−0.483875	−	0.0476576i
$56$	5.89438	−	5.19295i	0.787669	−	0.693937i
$57$	3.51742	−	4.28599i	0.465894	−	0.567693i
$58$	0.0567015	−	0.549238i	0.00744528	−	0.0721185i
$59$	−4.72373	+	3.50335i	−0.614977	+	0.456098i	−0.857808	−	0.513971i	$-0.828174\pi$
$59$	−4.72373	+	3.50335i	−0.614977	+	0.456098i	0.242831	+	0.970069i	$0.421924\pi$
$60$	−6.68758	−	5.59432i	−0.863363	−	0.722224i
$61$	−10.6608	+	3.81451i	−1.36498	+	0.488397i	−0.914571	−	0.404425i	$-0.867472\pi$
$61$	−10.6608	+	3.81451i	−1.36498	+	0.488397i	−0.450408	+	0.892823i	$0.648722\pi$
$62$	11.2722	+	5.39630i	1.43157	+	0.685331i
$63$	1.96390	−	1.96390i	0.247428	−	0.247428i
$64$	−2.53710	+	7.58704i	−0.317137	+	0.948380i
$65$	−12.1252	−	12.1252i	−1.50394	−	1.50394i
$66$	0.388898	+	1.10321i	0.0478700	+	0.135795i
$67$	1.73385	+	4.84578i	0.211823	+	0.592006i	0.999717	−	0.0238053i	$-0.00757819\pi$
$67$	1.73385	+	4.84578i	0.211823	+	0.592006i	−0.787893	+	0.615812i	$0.788828\pi$
$68$	−6.25744	+	3.26946i	−0.758826	+	0.396480i
$69$	0.538701	+	0.726354i	0.0648520	+	0.0874428i
$70$	10.8005	+	13.2873i	1.29091	+	1.58813i
$71$	2.33820	+	1.91891i	0.277493	+	0.227733i	0.762837	−	0.646591i	$-0.223806\pi$
$71$	2.33820	+	1.91891i	0.277493	+	0.227733i	−0.485344	+	0.874323i	$0.661306\pi$
$72$	−0.725847	+	2.73371i	−0.0855419	+	0.322170i
$73$	0.612296	−	6.21674i	0.0716638	−	0.727615i	−0.890471	−	0.455040i	$-0.849625\pi$
$73$	0.612296	−	6.21674i	0.0716638	−	0.727615i	0.962135	−	0.272575i	$-0.0878752\pi$
$74$	−16.8724	+	3.27381i	−1.96138	+	0.380573i
$75$	9.40521	−	10.3771i	1.08602	−	1.19824i
$76$	3.83373	−	10.4053i	0.439759	−	1.19357i
$77$	−0.337079	−	2.27240i	−0.0384137	−	0.258964i
$78$	−1.89859	+	5.22863i	−0.214973	+	0.592026i
$79$	1.27633	+	6.41656i	0.143599	+	0.721919i	0.983747	+	0.179562i	$0.0574681\pi$
$79$	1.27633	+	6.41656i	0.143599	+	0.721919i	−0.840148	+	0.542357i	$0.817532\pi$
$80$	−16.3053	−	6.18211i	−1.82299	−	0.691180i
$81$	−0.195090	+	0.980785i	−0.0216767	+	0.108976i
$82$	3.58362	−	5.91571i	0.395745	−	0.653281i
$83$	−6.30520	+	3.77919i	−0.692085	+	0.414820i	−0.816450	−	0.577417i	$-0.804061\pi$
$83$	−6.30520	+	3.77919i	−0.692085	+	0.414820i	0.124364	+	0.992237i	$0.460311\pi$
$84$	2.42203	−	4.99890i	0.264265	−	0.545424i
$85$	−6.57971	−	13.9116i	−0.713670	−	1.50893i
$86$	−0.0781446	+	0.186179i	−0.00842655	+	0.0200762i
$87$	−0.113337	−	0.373622i	−0.0121510	−	0.0400565i
$88$	1.45853	+	1.82919i	0.155479	+	0.194992i
$89$	8.47544	+	15.8564i	0.898395	+	1.68078i	0.716649	+	0.697434i	$0.245675\pi$
$89$	8.47544	+	15.8564i	0.898395	+	1.68078i	0.181746	+	0.983345i	$0.441825\pi$
$90$	−5.89129	−	1.81737i	−0.620996	−	0.191567i
$91$	5.61632	−	9.37027i	0.588751	−	0.982271i
$92$	1.49432	+	1.01891i	0.155793	+	0.106228i
$93$	8.82629	+	0.433608i	0.915244	+	0.0449630i
$94$	−10.7188	+	6.35635i	−1.10556	+	0.655607i
$95$	22.3314	+	9.24996i	2.29115	+	0.949026i
$96$	0.422102	+	5.64108i	0.0430806	+	0.575741i
$97$	−11.2629	+	4.66523i	−1.14357	+	0.473682i	−0.872372	−	0.488842i	$-0.837419\pi$
$97$	−11.2629	+	4.66523i	−1.14357	+	0.473682i	−0.271197	+	0.962524i	$0.587419\pi$
$98$	−0.605138	+	0.807974i	−0.0611282	+	0.0816177i
$99$	0.555470	+	0.612867i	0.0558269	+	0.0615955i
$100$	10.9616	−	25.7761i	1.09616	−	2.57761i
$101$	−1.29837	−	5.18340i	−0.129193	−	0.515767i	−0.999720	−	0.0236473i	$-0.992472\pi$
$101$	−1.29837	−	5.18340i	−0.129193	−	0.515767i	0.870527	−	0.492120i	$-0.163778\pi$
$102$	−3.18514	+	3.84413i	−0.315375	+	0.380626i
$103$	−2.04120	+	6.72893i	−0.201125	+	0.663021i	0.797121	+	0.603820i	$0.206355\pi$
$103$	−2.04120	+	6.72893i	−0.201125	+	0.663021i	−0.998246	+	0.0592012i	$0.981145\pi$
$104$	−0.156779	+	11.1242i	−0.0153735	+	1.09082i
$105$	10.6782	+	5.70762i	1.04209	+	0.557007i
$106$	1.24529	+	0.00584982i	0.120953	+	0.000568185i
$107$	6.58433	−	18.4020i	0.636531	−	1.77899i	0.00954517	−	0.999954i	$-0.496962\pi$
$107$	6.58433	−	18.4020i	0.636531	−	1.77899i	0.626986	−	0.779031i	$-0.284288\pi$
$108$	0.274862	+	1.98102i	0.0264486	+	0.190624i
$109$	−1.71111	+	6.83112i	−0.163894	+	0.654302i	0.831252	+	0.555896i	$0.187625\pi$
$109$	−1.71111	+	6.83112i	−0.163894	+	0.654302i	−0.995146	+	0.0984067i	$0.968625\pi$
$110$	−4.11017	+	3.01848i	−0.391889	+	0.287801i
$111$	−10.1049	+	6.75190i	−0.959118	+	0.640862i
$112$	1.29646	−	11.0336i	0.122504	−	1.04258i
$113$	3.90439	+	2.60883i	0.367294	+	0.245418i	0.725497	−	0.688226i	$-0.241610\pi$
$113$	3.90439	+	2.60883i	0.367294	+	0.245418i	−0.358202	+	0.933644i	$0.616610\pi$
$114$	−0.347954	−	7.83344i	−0.0325889	−	0.733669i
$115$	−2.34845	+	3.16652i	−0.218995	+	0.295280i
$116$	−0.459250	−	0.631542i	−0.0426403	−	0.0586372i
$117$	0.193003	+	3.92866i	0.0178431	+	0.363205i
$118$	−1.66089	+	8.14958i	−0.152897	+	0.750230i
$119$	7.57879	−	6.21975i	0.694746	−	0.570164i
$120$	−12.3229	+	0.431414i	−1.12492	+	0.0393825i
$121$	−10.2662	+	1.01113i	−0.933288	+	0.0919209i
$122$	−7.61460	+	14.0863i	−0.689394	+	1.27532i
$123$	0.717615	−	4.83777i	0.0647052	−	0.436207i
$124$	16.9603	−	4.97133i	1.52308	−	0.446439i
$125$	35.4882	+	16.7847i	3.17416	+	1.50126i
$126$	0.211154	−	3.92212i	0.0188111	−	0.349410i
$127$		−	5.61631i		−	0.498367i	−0.968456	−	0.249184i	$-0.919838\pi$
$127$		−	5.61631i		−	0.498367i	0.968456	−	0.249184i	$-0.0801623\pi$
$128$	4.49837	+	10.3810i	0.397604	+	0.917557i
$129$			0.142775i			0.0125706i
$130$	−24.2153	−	1.30367i	−2.12382	−	0.114340i
$131$	7.23260	+	3.42076i	0.631915	+	0.298873i	0.716547	−	0.697539i	$-0.245722\pi$
$131$	7.23260	+	3.42076i	0.631915	+	0.298873i	−0.0846322	+	0.996412i	$0.526972\pi$
$132$	1.45155	+	0.793490i	0.126341	+	0.0690645i
$133$	−2.25954	+	15.2326i	−0.195927	+	1.32083i
$134$	6.40282	+	3.46115i	0.553119	+	0.298998i
$135$	−4.33849	+	0.427304i	−0.373397	+	0.0367764i
$136$	−3.49581	+	9.35249i	−0.299763	+	0.801969i
$137$	12.2435	−	10.0479i	1.04603	−	0.858454i	0.0558750	−	0.998438i	$-0.482205\pi$
$137$	12.2435	−	10.0479i	1.04603	−	0.858454i	0.990154	+	0.139984i	$0.0447052\pi$
$138$	1.25314	+	0.255390i	0.106674	+	0.0217402i
$139$	−0.283138	−	5.76341i	−0.0240155	−	0.488846i	−0.980434	−	0.196847i	$-0.936930\pi$
$139$	−0.283138	−	5.76341i	−0.0240155	−	0.488846i	0.956419	−	0.291999i	$-0.0943204\pi$
$140$	23.9192	+	3.77808i	2.02155	+	0.319306i
$141$	−5.24919	+	7.07771i	−0.442061	+	0.596050i
$142$	4.27349	−	0.189824i	0.358623	−	0.0159297i
$143$	2.70515	+	1.80752i	0.226216	+	0.151153i
$144$	1.81897	+	3.56249i	0.151581	+	0.296874i
$145$	1.41524	−	0.945630i	0.117529	−	0.0785303i
$146$	−5.22922	−	7.12045i	−0.432774	−	0.589293i
$147$	−0.173439	+	0.692406i	−0.0143050	+	0.0571087i
$148$	−14.6620	+	19.3860i	−1.20521	+	1.59352i
$149$	−3.85684	+	10.7791i	−0.315964	+	0.883061i	0.673616	+	0.739081i	$0.264740\pi$
$149$	−3.85684	+	10.7791i	−0.315964	+	0.883061i	−0.989581	+	0.143980i	$0.954010\pi$
$150$	0.0930394	−	19.8059i	0.00759664	−	1.61715i
$151$	−20.3242	−	10.8635i	−1.65396	−	0.884059i	−0.990762	−	0.135614i	$-0.956699\pi$
$151$	−20.3242	−	10.8635i	−1.65396	−	0.884059i	−0.663197	−	0.748445i	$-0.730801\pi$
$152$	−5.79660	−	14.5717i	−0.470166	−	1.18192i
$153$	−1.02472	+	3.37804i	−0.0828436	+	0.273099i
$154$	−2.50166	−	2.07280i	−0.201590	−	0.167031i
$155$	9.36067	+	37.3699i	0.751867	+	3.00162i
$156$	2.94208	+	7.29594i	0.235555	+	0.584142i
$157$	−1.47050	−	1.62244i	−0.117358	−	0.129485i	0.679438	−	0.733733i	$-0.262224\pi$
$157$	−1.47050	−	1.62244i	−0.117358	−	0.129485i	−0.796796	+	0.604248i	$0.793474\pi$
$158$	7.40544	+	5.54636i	0.589145	+	0.441244i
$159$	0.813533	−	0.336976i	0.0645174	−	0.0267240i
$160$	−22.9991	+	8.89964i	−1.81824	+	0.703578i
$161$	−2.32044	−	0.961157i	−0.182876	−	0.0757498i
$162$	0.721345	+	1.21641i	0.0566742	+	0.0955705i
$163$	−17.9308	−	0.880881i	−1.40444	−	0.0689960i	−0.667329	−	0.744763i	$-0.732563\pi$
$163$	−17.9308	−	0.880881i	−1.40444	−	0.0689960i	−0.737116	+	0.675767i	$0.763813\pi$
$164$	−1.81804	−	9.61096i	−0.141965	−	0.750490i
$165$	−1.85379	+	3.09287i	−0.144318	+	0.240779i
$166$	−3.06448	+	9.93401i	−0.237850	+	0.771029i
$167$	8.16762	+	15.2805i	0.632029	+	1.18244i	0.970417	+	0.241437i	$0.0776187\pi$
$167$	8.16762	+	15.2805i	0.632029	+	1.18244i	−0.338387	+	0.941007i	$0.609881\pi$
$168$	−2.17420	−	7.54872i	−0.167743	−	0.582397i
$169$	0.717476	+	2.36520i	0.0551905	+	0.181939i
$170$	−20.0676	−	8.42291i	−1.53911	−	0.646008i
$171$	−2.37060	−	5.01221i	−0.181284	−	0.383293i
$172$	0.0936687	+	0.269750i	0.00714217	+	0.0205682i
$173$	1.68345	−	1.00902i	0.127991	−	0.0767146i	−0.448674	−	0.893695i	$-0.648104\pi$
$173$	1.68345	−	1.00902i	0.127991	−	0.0767146i	0.576665	+	0.816981i	$0.304354\pi$
$174$	−0.472262	−	0.286087i	−0.0358021	−	0.0216882i
$175$	−7.58847	+	38.1498i	−0.573635	+	2.88386i
$176$	3.26303	+	0.546870i	0.245960	+	0.0412219i
$177$	1.14734	+	5.76808i	0.0862395	+	0.433555i
$178$	23.8999	+	8.67838i	1.79137	+	0.650472i
$179$	−1.39254	−	9.38777i	−0.104084	−	0.701675i	−0.976911	−	0.213646i	$-0.931466\pi$
$179$	−1.39254	−	9.38777i	−0.104084	−	0.701675i	0.872827	−	0.488029i	$-0.162284\pi$
$180$	−7.91652	+	3.65362i	−0.590062	+	0.272325i
$181$	14.0856	−	15.5410i	1.04697	−	1.15516i	0.0593602	−	0.998237i	$-0.481094\pi$
$181$	14.0856	−	15.5410i	1.04697	−	1.15516i	0.987612	−	0.156919i	$-0.0501560\pi$
$182$	−2.94285	−	15.1667i	−0.218139	−	1.12423i
$183$	−1.10982	+	11.2682i	−0.0820402	+	0.832968i
$184$	2.53515	−	0.339615i	0.186894	−	0.0250367i
$185$	−40.9550	−	33.6109i	−3.01107	−	2.47112i
$186$	9.69769	−	7.88274i	0.711069	−	0.577991i
$187$	1.73934	+	2.34523i	0.127193	+	0.171500i
$188$	−5.27408	+	16.8159i	−0.384652	+	1.22643i
$189$	−0.935669	−	2.61502i	−0.0680599	−	0.190215i
$190$	32.2389	−	11.3647i	2.33886	−	0.824484i
$191$	2.23017	+	2.23017i	0.161370	+	0.161370i	0.783173	−	0.621804i	$-0.213600\pi$
$191$	2.23017	+	2.23017i	0.161370	+	0.161370i	−0.621804	+	0.783173i	$0.713600\pi$
$192$	5.77385	+	5.53739i	0.416692	+	0.399626i
$193$	9.15654	−	9.15654i	0.659102	−	0.659102i	−0.296065	−	0.955168i	$-0.595675\pi$
$193$	9.15654	−	9.15654i	0.659102	−	0.659102i	0.955168	+	0.296065i	$0.0956746\pi$
$194$	−7.44436	+	15.5504i	−0.534474	+	1.11645i
$195$	−16.1452	+	5.77684i	−1.15618	+	0.413688i
$196$	0.126575	+	1.42197i	0.00904107	+	0.101569i
$197$	16.5089	−	12.2438i	1.17621	−	0.872335i	0.182376	−	0.983229i	$-0.441621\pi$
$197$	16.5089	−	12.2438i	1.17621	−	0.872335i	0.993832	+	0.110893i	$0.0353712\pi$
$198$	1.16356	+	0.120122i	0.0826908	+	0.00853672i
$199$	8.09692	−	9.86612i	0.573975	−	0.699391i	−0.402402	−	0.915463i	$-0.631825\pi$
$199$	8.09692	−	9.86612i	0.573975	−	0.699391i	0.976377	+	0.216072i	$0.0693247\pi$
$200$	−12.8180	−	37.4810i	−0.906373	−	2.65031i
$201$	5.12185	+	0.504458i	0.361267	+	0.0355817i
$202$	−6.26354	−	4.22786i	−0.440701	−	0.297471i
$203$	0.803473	+	0.728226i	0.0563928	+	0.0511114i
$204$	0.280158	+	7.05453i	0.0196150	+	0.493916i
$205$	21.0901	−	3.12843i	1.47300	−	0.218499i
$206$	4.20948	+	9.00945i	0.293288	+	0.627718i
$207$	0.886941	−	0.176423i	0.0616466	−	0.0122623i
$208$	10.3451	+	11.8543i	0.717306	+	0.821947i
$209$	−4.49797	−	0.894702i	−0.311131	−	0.0618878i
$210$	16.6293	−	4.08251i	1.14753	−	0.281720i
$211$	1.07256	+	1.78947i	0.0738384	+	0.123192i	0.892433	−	0.451179i	$-0.148997\pi$
$211$	1.07256	+	1.78947i	0.0738384	+	0.123192i	−0.818595	+	0.574371i	$0.805247\pi$
$212$	1.31596	−	1.17039i	0.0903805	−	0.0803825i
$213$	2.73438	−	1.29327i	0.187357	−	0.0886131i
$214$	−10.4573	−	25.5855i	−0.714847	−	1.74899i
$215$	−0.595623	+	0.180680i	−0.0406211	+	0.0123223i
$216$	2.16090	+	1.82497i	0.147031	+	0.124173i
$217$	−21.6454	+	11.5697i	−1.46939	+	0.785403i
$218$	4.65339	+	8.80512i	0.315167	+	0.596358i
$219$	−5.35808	−	3.21151i	−0.362066	−	0.217014i
$220$	−1.47333	+	7.05966i	−0.0993322	+	0.475962i
$221$	−0.681309	+	13.8684i	−0.0458298	+	0.932886i
$222$	−4.25439	+	16.6522i	−0.285536	+	1.11762i
$223$	0.224788	−	0.542686i	0.0150529	−	0.0363410i	−0.916174	−	0.400780i	$-0.868739\pi$
$223$	0.224788	−	0.542686i	0.0150529	−	0.0363410i	0.931227	+	0.364439i	$0.118739\pi$
$224$	−9.06019	−	12.8357i	−0.605360	−	0.857619i
$225$	−5.35950	−	12.9390i	−0.357300	−	0.862598i
$226$	6.57345	−	0.943543i	0.437260	−	0.0627636i
$227$	15.5094	−	14.0569i	1.02940	−	0.932992i	0.0316120	−	0.999500i	$-0.489936\pi$
$227$	15.5094	−	14.0569i	1.02940	−	0.932992i	0.997786	+	0.0665084i	$0.0211859\pi$
$228$	−7.76715	−	7.91449i	−0.514392	−	0.524150i
$229$	19.4381	−	4.86900i	1.28451	−	0.321753i	0.460160	−	0.887836i	$-0.347792\pi$
$229$	19.4381	−	4.86900i	1.28451	−	0.321753i	0.824348	+	0.566083i	$0.191542\pi$
$230$	0.520407	+	5.55098i	0.0343146	+	0.366021i
$231$	−2.19834	−	0.666860i	−0.144640	−	0.0438762i
$232$	−1.07995	−	0.230683i	−0.0709023	−	0.0151451i
$233$	6.39611	−	11.9663i	0.419023	−	0.783937i	−0.580517	−	0.814248i	$-0.697150\pi$
$233$	6.39611	−	11.9663i	0.419023	−	0.783937i	0.999541	+	0.0303105i	$0.00964961\pi$
$234$	3.91488	+	3.95183i	0.255924	+	0.258339i
$235$	−36.1693	−	12.9416i	−2.35942	−	0.844215i
$236$	5.95191	+	10.1451i	0.387436	+	0.660390i
$237$	6.34620	+	1.58964i	0.412230	+	0.103258i
$238$	2.09887	−	13.7055i	0.136049	−	0.888397i
$239$	−6.30873	−	9.44167i	−0.408078	−	0.610731i	0.569326	−	0.822112i	$-0.307204\pi$
$239$	−6.30873	−	9.44167i	−0.408078	−	0.610731i	−0.977404	+	0.211380i	$0.932204\pi$
$240$	−12.5600	+	12.0966i	−0.810742	+	0.780833i
$241$	−1.05349	+	1.57666i	−0.0678613	+	0.101562i	−0.863848	−	0.503752i	$-0.831952\pi$
$241$	−1.05349	+	1.57666i	−0.0678613	+	0.101562i	0.795987	+	0.605314i	$0.206952\pi$
$242$	−9.84792	+	10.7635i	−0.633048	+	0.691901i
$243$	0.803208	+	0.595699i	0.0515258	+	0.0382141i
$244$	5.29577	+	22.0175i	0.339027	+	1.40953i
$245$	−3.10804	+	0.152688i	−0.198565	+	0.00975488i
$246$	−3.81554	−	5.76884i	−0.243270	−	0.367808i
$247$	−13.8354	−	16.8585i	−0.880327	−	1.07268i
$248$	13.1506	−	21.2554i	0.835067	−	1.34972i
$249$	0.720528	+	7.31564i	0.0456616	+	0.463610i
$250$	53.2027	−	15.8663i	3.36483	−	1.00347i
$251$	5.23281	+	0.776214i	0.330292	+	0.0489942i	0.309817	−	0.950796i	$-0.399732\pi$
$251$	5.23281	+	0.776214i	0.330292	+	0.0489942i	0.0204750	+	0.999790i	$0.493482\pi$
$252$	−3.48340	−	4.32679i	−0.219433	−	0.272562i
$253$	0.319808	−	0.676177i	0.0201062	−	0.0425109i
$254$	−5.30626	−	5.91012i	−0.332945	−	0.370834i
$255$	−15.3892			−0.963706
$256$	14.5416	+	6.67399i	0.908849	+	0.417125i
$257$	−12.6221			−0.787342			−0.393671	−	0.919251i	$-0.628795\pi$
$257$	−12.6221			−0.787342			−0.393671	+	0.919251i	$0.628795\pi$
$258$	0.134893	+	0.150244i	0.00839807	+	0.00935377i
$259$	14.4316	−	30.5130i	0.896734	−	1.89598i
$260$	−26.7137	+	21.5066i	−1.65671	+	1.33378i
$261$	−0.386208	−	0.0572886i	−0.0239057	−	0.00354607i
$262$	10.8429	−	3.23361i	0.669875	−	0.199773i
$263$	0.916062	+	9.30093i	0.0564868	+	0.573520i	0.981218	+	0.192900i	$0.0617894\pi$
$263$	0.916062	+	9.30093i	0.0564868	+	0.573520i	−0.924732	+	0.380620i	$0.875711\pi$
$264$	2.27717	−	0.536414i	0.140150	−	0.0330140i
$265$	2.43530	+	2.96742i	0.149599	+	0.182287i
$266$	12.0139	+	18.1642i	0.736621	+	1.11372i
$267$	17.9578	−	0.882209i	1.09900	−	0.0539903i
$268$	10.0078	−	2.40714i	0.611326	−	0.147040i
$269$	−3.02584	−	2.24412i	−0.184489	−	0.136826i	0.499513	−	0.866306i	$-0.333512\pi$
$269$	−3.02584	−	2.24412i	−0.184489	−	0.136826i	−0.684002	+	0.729480i	$0.739762\pi$
$270$	−4.16173	+	4.54864i	−0.253275	+	0.276821i
$271$	−11.1763	+	16.7266i	−0.678914	+	1.01607i	0.318756	+	0.947837i	$0.396735\pi$
$271$	−11.1763	+	16.7266i	−0.678914	+	1.01607i	−0.997670	+	0.0682295i	$0.978265\pi$
$272$	5.15750	+	13.1446i	0.312719	+	0.797007i
$273$	−6.06934	−	9.08340i	−0.367333	−	0.549752i
$274$	3.39070	−	22.1411i	0.204840	−	1.33759i
$275$	−11.2369	−	2.81470i	−0.677611	−	0.169733i
$276$	1.55998	−	0.915208i	0.0939000	−	0.0550890i
$277$	9.95662	+	3.56254i	0.598235	+	0.214052i	0.618555	−	0.785741i	$-0.287718\pi$
$277$	9.95662	+	3.56254i	0.598235	+	0.214052i	−0.0203196	+	0.999794i	$0.506468\pi$
$278$	−5.74319	−	5.79741i	−0.344454	−	0.347705i
$279$	4.16570	−	7.79348i	0.249394	−	0.466584i
$280$	28.7400	−	18.6231i	1.71755	−	1.11294i
$281$	−5.11324	−	1.55108i	−0.305030	−	0.0925299i	0.134059	−	0.990973i	$-0.457199\pi$
$281$	−5.11324	−	1.55108i	−0.305030	−	0.0925299i	−0.439089	+	0.898443i	$0.644699\pi$
$282$	1.16320	+	12.4074i	0.0692673	+	0.738848i
$283$	−14.4213	+	3.61235i	−0.857259	+	0.214732i	−0.646602	−	0.762828i	$-0.723810\pi$
$283$	−14.4213	+	3.61235i	−0.857259	+	0.214732i	−0.210657	+	0.977560i	$0.567560\pi$
$284$	4.31770	−	4.23733i	0.256209	−	0.251439i
$285$	17.9098	−	16.2325i	1.06088	−	0.961528i
$286$	4.55440	−	0.653731i	0.269307	−	0.0386560i
$287$	5.19810	+	12.5493i	0.306834	+	0.740764i
$288$	5.27995	+	2.03030i	0.311124	+	0.119637i
$289$	1.73692	−	4.19328i	0.102171	−	0.246664i
$290$	0.595844	−	2.33221i	0.0349892	−	0.136952i
$291$	−0.598175	+	12.1761i	−0.0350657	+	0.713778i
$292$	−12.2301	−	2.55240i	−0.715715	−	0.149368i
$293$	13.7291	+	8.22892i	0.802064	+	0.480739i	0.855481	−	0.517833i	$-0.173261\pi$
$293$	13.7291	+	8.22892i	0.802064	+	0.480739i	−0.0534171	+	0.998572i	$0.517011\pi$
$294$	0.471670	+	0.892491i	0.0275083	+	0.0520512i
$295$	−22.6111	+	12.0859i	−1.31647	+	0.703667i
$296$	2.88685	+	34.2527i	0.167795	+	1.99090i
$297$	0.791519	−	0.240105i	0.0459286	−	0.0139323i
$298$	6.12548	+	14.9869i	0.354839	+	0.868170i
$299$	3.21553	−	1.52083i	0.185959	−	0.0879519i
$300$	−18.6146	−	20.9299i	−1.07472	−	1.20839i
$301$	−0.203862	−	0.340123i	−0.0117504	−	0.0196044i
$302$	−31.6512	+	7.77038i	−1.82132	+	0.447135i
$303$	−5.24086	−	1.04247i	−0.301080	−	0.0598885i
$304$	−19.8671	−	9.85741i	−1.13946	−	0.565361i
$305$	−48.4126	+	9.62987i	−2.77210	+	0.551405i
$306$	2.11323	+	4.52291i	0.120806	+	0.258557i
$307$	12.3584	−	1.83319i	0.705330	−	0.104626i	0.215577	−	0.976487i	$-0.430837\pi$
$307$	12.3584	−	1.83319i	0.705330	−	0.104626i	0.489753	+	0.871861i	$0.337087\pi$
$308$	−4.59091	+	0.182320i	−0.261591	+	0.0103886i
$309$	5.21016	+	4.72221i	0.296395	+	0.268637i
$310$	45.1572	+	30.4809i	2.56476	+	1.73120i
$311$	−19.7463	−	1.94484i	−1.11971	−	0.110282i	−0.478818	−	0.877914i	$-0.658935\pi$
$311$	−19.7463	−	1.94484i	−1.11971	−	0.110282i	−0.640890	+	0.767632i	$0.721435\pi$
$312$	9.98915	+	4.89795i	0.565524	+	0.277292i
$313$	−15.2538	+	18.5868i	−0.862194	+	1.05059i	0.136011	+	0.990707i	$0.456572\pi$
$313$	−15.2538	+	18.5868i	−0.862194	+	1.05059i	−0.998206	+	0.0598794i	$0.980928\pi$
$314$	−3.08030	−	0.318000i	−0.173831	−	0.0179458i
$315$	9.72515	−	7.21266i	0.547950	−	0.406388i
$316$	13.0330	−	1.16012i	0.733164	−	0.0652616i
$317$	12.0774	−	4.32135i	0.678333	−	0.242711i	0.0248932	−	0.999690i	$-0.492075\pi$
$317$	12.0774	−	4.32135i	0.678333	−	0.242711i	0.653439	+	0.756979i	$0.273325\pi$
$318$	0.537718	−	1.12323i	0.0301537	−	0.0629874i
$319$	−0.228354	+	0.228354i	−0.0127854	+	0.0127854i
$320$	−15.7939	+	31.0946i	−0.882906	+	1.73824i
$321$	−13.8200	−	13.8200i	−0.771358	−	0.771358i
$322$	−3.34992	+	1.18090i	−0.186684	+	0.0658090i
$323$	−6.59377	−	18.4284i	−0.366887	−	1.02538i
$324$	1.90834	+	0.598524i	0.106019	+	0.0332514i
$325$	−32.8155	−	44.2466i	−1.82028	−	2.45436i
$326$	−19.7010	+	16.0139i	−1.09114	+	0.886929i
$327$	5.44367	+	4.46750i	0.301035	+	0.247053i
$328$	−10.9935	−	8.39606i	−0.607017	−	0.463595i
$329$	2.39884	−	24.3558i	0.132252	−	1.34278i
$330$	0.971354	+	5.00612i	0.0534713	+	0.275578i
$331$	0.678697	−	0.748826i	0.0373045	−	0.0411592i	−0.722013	−	0.691879i	$-0.756783\pi$
$331$	0.678697	−	0.748826i	0.0373045	−	0.0411592i	0.759318	+	0.650720i	$0.225533\pi$
$332$	6.16081	+	13.3490i	0.338118	+	0.732621i
$333$	1.78323	+	12.0216i	0.0977205	+	0.658778i
$334$	23.0319	+	8.36319i	1.26025	+	0.457613i
$335$	4.37717	+	22.0055i	0.239150	+	1.20229i
$336$	−9.41993	−	5.88945i	−0.513899	−	0.321296i
$337$	0.949254	−	4.77222i	0.0517092	−	0.259960i	−0.946280	−	0.323349i	$-0.895191\pi$
$337$	0.949254	−	4.77222i	0.0517092	−	0.259960i	0.997989	+	0.0633897i	$0.0201911\pi$
$338$	2.98964	+	1.81107i	0.162615	+	0.0985090i
$339$	4.02770	−	2.41411i	0.218755	−	0.131116i
$340$	−29.0753	+	10.0962i	−1.57683	+	0.547543i
$341$	−3.12515	−	6.60757i	−0.169236	−	0.357820i
$342$	−7.23012	−	3.03468i	−0.390960	−	0.164097i
$343$	5.06812	+	16.7073i	0.273653	+	0.902112i
$344$	0.353427	+	0.195363i	0.0190555	+	0.0105333i
$345$	1.85841	+	3.47684i	0.100053	+	0.187187i
$346$	0.818200	−	2.65233i	0.0439867	−	0.142590i
$347$	8.15686	−	13.6089i	0.437883	−	0.730564i	−0.557117	−	0.830434i	$-0.688093\pi$
$347$	8.15686	−	13.6089i	0.437883	−	0.730564i	0.995001	+	0.0998697i	$0.0318426\pi$
$348$	−0.767261	+	0.145138i	−0.0411295	+	0.00778021i
$349$	−2.59067	−	0.127271i	−0.138675	−	0.00681268i	−0.0203884	−	0.999792i	$-0.506490\pi$
$349$	−2.59067	−	0.127271i	−0.138675	−	0.00681268i	−0.118287	+	0.992979i	$0.537740\pi$
$350$	28.0583	+	47.3151i	1.49978	+	2.52910i
$351$	3.63399	+	1.50525i	0.193968	+	0.0803441i
$352$	3.95041	−	2.50742i	0.210558	−	0.133646i
$353$	8.53771	−	3.53643i	0.454416	−	0.188225i	−0.143722	−	0.989618i	$-0.545907\pi$
$353$	8.53771	−	3.53643i	0.454416	−	0.188225i	0.598139	+	0.801393i	$0.295907\pi$
$354$	6.65701	+	4.98582i	0.353816	+	0.264993i
$355$	8.85553	+	9.77057i	0.470002	+	0.518568i
$356$	33.3495	−	13.4481i	1.76752	−	0.712750i
$357$	−2.38224	−	9.51043i	−0.126081	−	0.503345i
$358$	−10.3349	−	8.56320i	−0.546217	−	0.452579i
$359$	−1.92047	+	6.33094i	−0.101359	+	0.334134i	−0.992923	−	0.118759i	$-0.962108\pi$
$359$	−1.92047	+	6.33094i	−0.101359	+	0.334134i	0.891565	+	0.452894i	$0.149608\pi$
$360$	−4.87873	+	11.3242i	−0.257132	+	0.596840i
$361$	10.3555	+	5.53512i	0.545025	+	0.291322i
$362$	0.139339	−	29.6620i	0.00732350	−	1.55900i
$363$	−3.47530	+	9.71282i	−0.182406	+	0.509791i
$364$	−17.4263	−	13.1798i	−0.913384	−	0.690807i
$365$	6.61705	−	26.4168i	0.346352	−	1.38272i
$366$	9.47825	+	12.9062i	0.495436	+	0.674618i
$367$	−17.7879	+	11.8855i	−0.928519	+	0.620417i	−0.925160	−	0.379578i	$-0.876069\pi$
$367$	−17.7879	+	11.8855i	−0.928519	+	0.620417i	−0.00335933	+	0.999994i	$0.501069\pi$
$368$	2.34690	−	2.75258i	0.122341	−	0.143488i
$369$	−4.06647	−	2.71713i	−0.211692	−	0.141448i
$370$	−74.8529	+	3.32489i	−3.89142	+	0.172853i
$371$	−1.45687	+	1.96436i	−0.0756369	+	0.101985i
$372$	2.75743	−	17.4574i	0.142966	−	0.905126i
$373$	−0.280373	−	5.70712i	−0.0145171	−	0.295503i	−0.995065	−	0.0992238i	$-0.968364\pi$
$373$	−0.280373	−	5.70712i	−0.0145171	−	0.295503i	0.980548	−	0.196279i	$-0.0628860\pi$
$374$	4.04609	+	0.824594i	0.209218	+	0.0426387i
$375$	30.3463	−	24.9046i	1.56708	−	1.28607i
$376$	10.3376	+	22.6785i	0.533122	+	1.16956i
$377$	−1.52834	+	0.150528i	−0.0787134	+	0.00775260i
$378$	−3.45527	−	1.86780i	−0.177720	−	0.0960694i
$379$	4.06431	−	27.3993i	0.208770	−	1.40741i	−0.590791	−	0.806825i	$-0.701184\pi$
$379$	4.06431	−	27.3993i	0.208770	−	1.40741i	0.799561	−	0.600585i	$-0.205066\pi$
$380$	23.1881	−	42.4184i	1.18952	−	2.17602i
$381$	−5.07709	−	2.40128i	−0.260107	−	0.123021i
$382$	4.45389	+	0.239784i	0.227881	+	0.0122684i
$383$			11.6220i			0.593857i	0.954900	+	0.296928i	$0.0959623\pi$
$383$			11.6220i			0.593857i	−0.954900	+	0.296928i	$0.904038\pi$
$384$	11.3076	+	0.371958i	0.577038	+	0.0189814i
$385$		−	10.0149i		−	0.510405i
$386$	0.984493	−	18.2866i	0.0501094	−	0.930764i
$387$	0.129067	+	0.0610441i	0.00656084	+	0.00310305i
$388$	6.85811	+	23.3972i	0.348168	+	1.18782i
$389$	−2.64936	+	17.8605i	−0.134328	+	0.905566i	0.812301	+	0.583239i	$0.198215\pi$
$389$	−2.64936	+	17.8605i	−0.134328	+	0.905566i	−0.946629	+	0.322327i	$0.895535\pi$
$390$	−11.5319	+	21.3329i	−0.583938	+	1.08024i
$391$	3.17691	−	0.312898i	0.160663	−	0.0158239i
$392$	1.47667	+	1.37677i	0.0745830	+	0.0695375i
$393$	6.18467	−	5.07562i	0.311975	−	0.256031i
$394$	5.80460	−	28.4818i	0.292432	−	1.43489i
$395$	1.39945	+	28.4865i	0.0704141	+	1.43331i
$396$	1.33792	−	0.972921i	0.0672331	−	0.0488911i
$397$	3.58484	−	4.83359i	0.179918	−	0.242591i	−0.704037	−	0.710163i	$-0.748621\pi$
$397$	3.58484	−	4.83359i	0.179918	−	0.242591i	0.883955	+	0.467572i	$0.154871\pi$
$398$	−0.800972	−	18.0322i	−0.0401491	−	0.903871i
$399$	12.8040	+	8.55537i	0.641003	+	0.428304i
$400$	−48.9005	−	27.3313i	−2.44502	−	1.36657i
$401$	3.21363	−	2.14728i	0.160481	−	0.107230i	−0.472737	−	0.881204i	$-0.656734\pi$
$401$	3.21363	−	2.14728i	0.160481	−	0.107230i	0.633218	+	0.773974i	$0.281734\pi$
$402$	5.86640	−	4.30825i	0.292589	−	0.214876i
$403$	8.44580	−	33.7175i	0.420715	−	1.67959i
$404$	−10.5857	+	1.46873i	−0.526657	+	0.0730722i
$405$	−1.46866	+	4.10464i	−0.0729785	+	0.203961i
$406$	1.53353	+	0.00720385i	0.0761078	+	0.000357521i
$407$	8.86531	+	4.73861i	0.439437	+	0.234884i
$408$	6.95990	+	7.15888i	0.344566	+	0.354417i
$409$	9.57941	−	31.5791i	0.473671	−	1.56149i	−0.316496	−	0.948594i	$-0.602506\pi$
$409$	9.57941	−	31.5791i	0.473671	−	1.56149i	0.790167	−	0.612891i	$-0.209994\pi$
$410$	19.2377	−	23.2179i	0.950083	−	1.14665i
$411$	−3.84848	−	15.3640i	−0.189832	−	0.757850i
$412$	12.9418	+	5.50367i	0.637595	+	0.271146i
$413$	−10.9692	−	12.1027i	−0.539759	−	0.595533i
$414$	0.766655	−	1.02363i	0.0376790	−	0.0503087i
$415$	−29.6073	+	12.2637i	−1.45336	+	0.602003i
$416$	22.0862	+	2.70040i	1.08286	+	0.132398i
$417$	−5.33112	−	2.20822i	−0.261066	−	0.108137i
$418$	−5.57858	+	3.30815i	−0.272857	+	0.161807i
$419$	−19.2602	−	0.946192i	−0.940921	−	0.0462245i	−0.427177	−	0.904168i	$-0.640492\pi$
$419$	−19.2602	−	0.946192i	−0.940921	−	0.0462245i	−0.513744	+	0.857943i	$0.671742\pi$
$420$	13.6421	−	20.0074i	0.665668	−	0.976261i
$421$	2.98595	−	4.98175i	0.145526	−	0.242796i	−0.776331	−	0.630325i	$-0.782922\pi$
$421$	2.98595	−	4.98175i	0.145526	−	0.242796i	0.921857	+	0.387530i	$0.126672\pi$
$422$	2.81935	+	0.869724i	0.137244	+	0.0423375i
$423$	4.15386	+	7.77132i	0.201967	+	0.377854i
$424$	0.279027	−	2.47493i	0.0135507	−	0.120193i
$425$	−14.3512	−	47.3096i	−0.696137	−	2.29485i
$426$	1.65555	−	3.94435i	0.0802118	−	0.191104i
$427$	−13.4455	−	28.4281i	−0.650673	−	1.37573i
$428$	−35.1774	−	17.0439i	−1.70036	−	0.823848i
$429$	2.79058	−	1.67261i	0.134731	−	0.0807544i
$430$	−0.456076	+	0.752873i	−0.0219939	+	0.0363068i
$431$	7.31255	−	36.7627i	0.352233	−	1.77080i	−0.245796	−	0.969322i	$-0.579049\pi$
$431$	7.31255	−	36.7627i	0.352233	−	1.77080i	0.598029	−	0.801474i	$-0.295951\pi$
$432$	3.99816	−	0.121171i	0.192362	−	0.00582982i
$433$	4.75533	+	23.9066i	0.228526	+	1.14888i	0.909221	+	0.416313i	$0.136678\pi$
$433$	4.75533	+	23.9066i	0.228526	+	1.14888i	−0.680695	+	0.732567i	$0.738322\pi$
$434$	−11.8467	+	32.6254i	−0.568661	+	1.56607i
$435$	−0.249748	−	1.68367i	−0.0119745	−	0.0807256i
$436$	13.2158	+	4.86924i	0.632924	+	0.233194i
$437$	−3.36721	+	3.71515i	−0.161076	+	0.177720i
$438$	−8.67260	+	1.68277i	−0.414393	+	0.0804061i
$439$	1.28204	−	13.0168i	0.0611885	−	0.621257i	−0.914870	−	0.403749i	$-0.867707\pi$
$439$	1.28204	−	13.0168i	0.0611885	−	0.621257i	0.976058	−	0.217508i	$-0.0697930\pi$
$440$	5.11952	+	8.82097i	0.244063	+	0.420523i
$441$	0.551773	+	0.452828i	0.0262749	+	0.0215633i
$442$	12.3858	+	15.2375i	0.589132	+	0.724776i
$443$	16.0355	+	21.6214i	0.761869	+	1.02726i	0.998450	+	0.0556503i	$0.0177232\pi$
$443$	16.0355	+	21.6214i	0.761869	+	1.02726i	−0.236581	+	0.971612i	$0.576027\pi$
$444$	11.2560	+	21.5429i	0.534185	+	1.02238i
$445$	26.4057	+	73.7991i	1.25175	+	3.49841i
$446$	−0.276180	−	0.783455i	−0.0130775	−	0.0370976i
$447$	8.09521	+	8.09521i	0.382891	+	0.382891i
$448$	−21.6612	−	4.94712i	−1.02340	−	0.233729i
$449$	−21.2405	+	21.2405i	−1.00240	+	1.00240i	−0.00240635	+	0.999997i	$0.500766\pi$
$449$	−21.2405	+	21.2405i	−1.00240	+	1.00240i	−0.999997	+	0.00240635i	$0.999234\pi$
$450$	−17.8645	−	8.55222i	−0.842143	−	0.403156i
$451$	−3.80880	+	1.36281i	−0.179350	+	0.0641723i
$452$	6.02588	−	7.20347i	0.283433	−	0.338823i
$453$	−18.5102	+	13.7281i	−0.869685	+	0.645002i
$454$	3.03986	−	29.4455i	0.142668	−	1.38195i
$455$	30.2131	−	36.8148i	1.41641	−	1.72590i
$456$	−15.6510	−	0.990150i	−0.732927	−	0.0463680i
$457$	10.8144	+	1.06512i	0.505874	+	0.0498242i	0.347735	−	0.937593i	$-0.386951\pi$
$457$	10.8144	+	1.06512i	0.505874	+	0.0498242i	0.158139	+	0.987417i	$0.449451\pi$
$458$	15.8548	−	23.4888i	0.740846	−	1.09756i
$459$	2.61559	+	2.37063i	0.122085	+	0.110652i
$460$	5.79217	+	5.34969i	0.270061	+	0.249431i
$461$	−9.84438	+	1.46028i	−0.458499	+	0.0680118i	−0.371985	−	0.928239i	$-0.621323\pi$
$461$	−9.84438	+	1.46028i	−0.458499	+	0.0680118i	−0.0865138	+	0.996251i	$0.527573\pi$
$462$	−2.94339	+	1.37524i	−0.136939	+	0.0639819i
$463$	−20.4632	+	4.07038i	−0.951004	+	0.189166i	−0.646131	−	0.763227i	$-0.723614\pi$
$463$	−20.4632	+	4.07038i	−0.951004	+	0.189166i	−0.304873	+	0.952393i	$0.598614\pi$
$464$	−1.35440	+	0.777583i	−0.0628762	+	0.0360984i
$465$	37.7842	+	7.51574i	1.75220	+	0.348534i
$466$	−4.57497	−	18.6353i	−0.211932	−	0.863263i
$467$	−14.6953	−	24.5176i	−0.680017	−	1.13454i	−0.983362	−	0.181659i	$-0.941853\pi$
$467$	−14.6953	−	24.5176i	−0.680017	−	1.13454i	0.303344	−	0.952881i	$-0.401897\pi$
$468$	7.85335	+	0.459807i	0.363021	+	0.0212546i
$469$	−12.9217	+	6.11152i	−0.596670	+	0.282204i
$470$	−50.2885	+	20.5540i	−2.31964	+	0.948084i
$471$	−2.09539	+	0.635630i	−0.0965505	+	0.0292883i
$472$	15.8483	+	5.05249i	0.729478	+	0.232560i
$473$	0.104150	−	0.0556692i	0.00478881	−	0.00255967i
$474$	8.18008	−	4.32306i	0.375723	−	0.198565i
$475$	66.6040	+	39.9209i	3.05600	+	1.83170i
$476$	−10.7402	−	16.4055i	−0.492278	−	0.751945i
$477$	0.0432071	−	0.879501i	0.00197832	−	0.0402696i
$478$	−15.5592	−	3.97514i	−0.711661	−	0.181819i
$479$	4.77484	−	11.5275i	0.218168	−	0.526704i	−0.776466	−	0.630159i	$-0.782990\pi$
$479$	4.77484	−	11.5275i	0.218168	−	0.526704i	0.994634	+	0.103455i	$0.0329897\pi$
$480$	−1.78820	+	24.5960i	−0.0816196	+	1.12265i
$481$	18.2934	+	44.1642i	0.834108	+	2.01372i
$482$	0.381019	+	2.65447i	0.0173549	+	0.120908i
$483$	−1.86099	+	1.68670i	−0.0846780	+	0.0767477i
$484$	−0.193833	+	20.6308i	−0.00881059	+	0.937763i
$485$	−51.5529	+	12.9133i	−2.34090	+	0.586364i
$486$	1.40804	−	0.132004i	0.0638700	−	0.00598784i
$487$	−36.1228	−	10.9577i	−1.63688	−	0.496542i	−0.668019	−	0.744145i	$-0.732857\pi$
$487$	−36.1228	−	10.9577i	−1.63688	−	0.496542i	−0.968862	+	0.247602i	$0.920357\pi$
$488$	26.3748	+	18.1659i	1.19393	+	0.822330i
$489$	−8.46269	+	15.8326i	−0.382696	+	0.715974i
$490$	−3.12637	+	3.09713i	−0.141235	+	0.139914i
$491$	2.10617	+	0.753601i	0.0950503	+	0.0340096i	0.383986	−	0.923339i	$-0.374551\pi$
$491$	2.10617	+	0.753601i	0.0950503	+	0.0340096i	−0.288935	+	0.957349i	$0.593301\pi$
$492$	−9.46552	−	2.46572i	−0.426739	−	0.111163i
$493$	−1.33695	−	0.334887i	−0.0602130	−	0.0150826i
$494$	−30.4870	−	4.66879i	−1.37168	−	0.210059i
$495$	2.00332	+	2.99818i	0.0900425	+	0.134758i
$496$	−6.24340	−	34.7920i	−0.280337	−	1.56221i
$497$	−4.66733	+	6.98516i	−0.209359	+	0.313327i
$498$	7.67000	+	7.01759i	0.343701	+	0.314466i
$499$	−29.4058	−	21.8089i	−1.31639	−	0.976299i	−0.999614	−	0.0277972i	$-0.991151\pi$
$499$	−29.4058	−	21.8089i	−1.31639	−	0.976299i	−0.316773	−	0.948501i	$-0.602599\pi$
$500$	40.9955	−	66.9620i	1.83337	−	2.99463i
$501$	17.3056	−	0.850167i	0.773155	−	0.0379827i
$502$	6.23992	−	4.12711i	0.278501	−	0.184202i
$503$	−6.60645	−	8.04999i	−0.294567	−	0.358931i	0.604606	−	0.796525i	$-0.293331\pi$
$503$	−6.60645	−	8.04999i	−0.294567	−	0.358931i	−0.899173	+	0.437594i	$0.855831\pi$
$504$	−7.75356	−	1.26204i	−0.345371	−	0.0562159i
$505$	−2.28331	−	23.1829i	−0.101606	−	1.03162i
$506$	−0.302311	−	1.01370i	−0.0134394	−	0.0450646i
$507$	2.44488	+	0.362663i	0.108581	+	0.0161065i
$508$	−11.1677	−	1.20596i	−0.495487	−	0.0535059i
$509$	12.1829	−	25.7586i	0.539998	−	1.14173i	−0.430936	−	0.902383i	$-0.641817\pi$
$509$	12.1829	−	25.7586i	0.539998	−	1.14173i	0.970934	−	0.239347i	$-0.0769335\pi$
$510$	−16.1942	+	14.5396i	−0.717091	+	0.643824i
$511$	17.3498			0.767508
$512$	21.6079	−	6.71569i	0.954941	−	0.296794i
$513$	−5.54454			−0.244798
$514$	−13.2824	+	11.9253i	−0.585859	+	0.526000i
$515$	−13.1065	+	27.7114i	−0.577543	+	1.22111i
$516$	0.283899	+	0.0306573i	0.0124980	+	0.00134961i
$517$	7.20967	+	1.06945i	0.317081	+	0.0470345i
$518$	−13.6420	−	45.7441i	−0.599395	−	2.00988i
$519$	−0.192377	−	1.95324i	−0.00844442	−	0.0857376i
$520$	−7.79189	+	47.8706i	−0.341697	+	2.09927i
$521$	0.453859	+	0.553029i	0.0198839	+	0.0242286i	0.782857	−	0.622201i	$-0.213761\pi$
$521$	0.453859	+	0.553029i	0.0198839	+	0.0242286i	−0.762974	+	0.646430i	$0.776261\pi$
$522$	−0.460538	+	0.304602i	−0.0201572	+	0.0133321i
$523$	34.4536	−	1.69259i	1.50655	−	0.0740120i	0.721053	−	0.692879i	$-0.243658\pi$
$523$	34.4536	−	1.69259i	1.50655	−	0.0740120i	0.785495	+	0.618867i	$0.212408\pi$
$524$	8.35500	−	13.6471i	0.364990	−	0.596175i
$525$	31.2425	+	23.1710i	1.36354	+	1.01127i
$526$	9.75146	+	8.92200i	0.425184	+	0.389018i
$527$	17.3309	−	25.9375i	0.754946	−	1.12986i
$528$	1.88949	−	2.71593i	0.0822295	−	0.118196i
$529$	12.3238	+	18.4438i	0.535816	+	0.801906i
$530$	5.36631	+	0.821798i	0.233097	+	0.0356966i
$531$	5.70483	+	1.42899i	0.247569	+	0.0620127i
$532$	29.8039	+	7.76378i	1.29216	+	0.336602i
$533$	−18.1126	−	6.48078i	−0.784542	−	0.280714i
$534$	18.0637	−	17.8948i	0.781692	−	0.774383i
$535$	40.1647	−	75.1429i	1.73647	−	3.24871i
$536$	8.25713	−	11.9884i	0.356654	−	0.517821i
$537$	−9.08183	−	2.75494i	−0.391910	−	0.118885i
$538$	−5.30436	+	0.497286i	−0.228687	+	0.0214395i
$539$	0.572713	−	0.143457i	0.0246685	−	0.00617914i
$540$	−0.0819138	+	8.71857i	−0.00352501	+	0.375188i
$541$	−22.7427	+	20.6128i	−0.977787	+	0.886214i	−0.993519	−	0.113662i	$-0.963742\pi$
$541$	−22.7427	+	20.6128i	−0.977787	+	0.886214i	0.0157329	+	0.999876i	$0.494992\pi$
$542$	4.04217	+	28.1609i	0.173626	+	1.20962i
$543$	−8.02657	−	19.3778i	−0.344453	−	0.831583i
$544$	17.8462	+	8.95943i	0.765151	+	0.384132i
$545$	−11.7484	+	28.3632i	−0.503248	+	1.21495i
$546$	−14.9688	−	3.82430i	−0.640605	−	0.163665i
$547$	0.336472	−	6.84904i	0.0143865	−	0.292844i	−0.980811	−	0.194959i	$-0.937542\pi$
$547$	0.336472	−	6.84904i	0.0143865	−	0.292844i	0.995198	−	0.0978843i	$-0.0312075\pi$
$548$	−17.3508	−	26.5029i	−0.741187	−	1.13215i
$549$	9.71181	+	5.82104i	0.414490	+	0.248436i
$550$	−14.4841	+	7.65463i	−0.617602	+	0.326395i
$551$	1.90916	−	1.02047i	0.0813331	−	0.0434735i
$552$	0.776907	−	2.43695i	0.0330674	−	0.103723i
$553$	−17.3879	+	5.27456i	−0.739409	+	0.224297i
$554$	13.8433	−	5.65806i	0.588147	−	0.240388i
$555$	−47.8944	+	22.6524i	−2.03301	+	0.961540i
$556$	−11.5210	−	0.674545i	−0.488599	−	0.0286071i
$557$	−21.9671	−	36.6499i	−0.930775	−	1.55290i	−0.829833	−	0.558012i	$-0.811564\pi$
$557$	−21.9671	−	36.6499i	−0.930775	−	1.55290i	−0.100942	−	0.994892i	$-0.532186\pi$
$558$	−2.97962	−	12.1369i	−0.126137	−	0.513797i
$559$	0.550800	+	0.109561i	0.0232963	+	0.00463393i
$560$	12.6485	−	46.7507i	0.534499	−	1.97558i
$561$	2.86372	−	0.569630i	0.120906	−	0.0240498i
$562$	−6.84618	+	3.19874i	−0.288789	+	0.134931i
$563$	1.50901	−	0.223841i	0.0635973	−	0.00943378i	−0.114856	−	0.993382i	$-0.536641\pi$
$563$	1.50901	−	0.223841i	0.0635973	−	0.00943378i	0.178453	+	0.983948i	$0.442891\pi$
$564$	12.9465	+	11.9575i	0.545144	+	0.503499i
$565$	15.1681	+	13.7476i	0.638127	+	0.578364i
$566$	−11.7628	+	17.4265i	−0.494428	+	0.732491i
$567$	−2.76400	−	0.272230i	−0.116077	−	0.0114326i
$568$	0.540171	−	8.53834i	0.0226651	−	0.358261i
$569$	13.1769	−	16.0562i	0.552406	−	0.673109i	−0.419697	−	0.907664i	$-0.637863\pi$
$569$	13.1769	−	16.0562i	0.552406	−	0.673109i	0.972103	+	0.234556i	$0.0753635\pi$
$570$	3.51033	−	34.0027i	0.147031	−	1.42422i
$571$	−7.49556	+	5.55909i	−0.313680	+	0.232641i	−0.741072	−	0.671426i	$-0.765682\pi$
$571$	−7.49556	+	5.55909i	−0.313680	+	0.232641i	0.427392	+	0.904066i	$0.359432\pi$
$572$	4.17501	−	4.99091i	0.174566	−	0.208680i
$573$	2.96957	−	1.06253i	0.124056	−	0.0443878i
$574$	17.3266	+	8.29468i	0.723197	+	0.346213i
$575$	−8.95550	+	8.95550i	−0.373470	+	0.373470i
$576$	7.47438	−	2.85196i	0.311432	−	0.118832i
$577$	−23.5667	−	23.5667i	−0.981096	−	0.981096i	0.0187287	−	0.999825i	$-0.494038\pi$
$577$	−23.5667	−	23.5667i	−0.981096	−	0.981096i	−0.999825	+	0.0187287i	$0.994038\pi$
$578$	−2.13402	−	6.05368i	−0.0887634	−	0.251800i
$579$	−4.36249	−	12.1923i	−0.181299	−	0.506696i
$580$	−1.57644	−	3.01716i	−0.0654582	−	0.125281i
$581$	−12.1621	−	16.3987i	−0.504571	−	0.680335i
$582$	10.8745	+	13.3783i	0.450762	+	0.554547i
$583$	−0.563017	−	0.462056i	−0.0233178	−	0.0191364i
$584$	−15.2814	+	8.86905i	−0.632351	+	0.367004i
$585$	−1.68076	+	17.0650i	−0.0694907	+	0.705551i
$586$	22.2220	−	4.31181i	0.917982	−	0.178119i
$587$	27.9770	−	30.8679i	1.15474	−	1.27405i	0.198944	−	0.980011i	$-0.436249\pi$
$587$	27.9770	−	30.8679i	1.15474	−	1.27405i	0.955792	−	0.294043i	$-0.0950010\pi$
$588$	1.33957	+	0.493549i	0.0552428	+	0.0203536i
$589$	7.18932	+	48.4664i	0.296231	+	1.99703i
$590$	−12.3753	+	34.0810i	−0.509481	+	1.40309i
$591$	−4.00982	−	20.1587i	−0.164942	−	0.829220i
$592$	35.3997	+	33.3171i	1.45492	+	1.36933i
$593$	1.79762	−	9.03727i	0.0738196	−	0.371116i	−0.926162	−	0.377125i	$-0.876913\pi$
$593$	1.79762	−	9.03727i	0.0738196	−	0.371116i	0.999982	+	0.00600884i	$0.00191269\pi$
$594$	0.606076	−	1.00049i	0.0248676	−	0.0410506i
$595$	36.6605	−	21.9735i	1.50294	−	0.900825i
$596$	20.6055	+	9.98364i	0.844035	+	0.408946i
$597$	−5.45699	−	11.5378i	−0.223340	−	0.472212i
$598$	1.94687	−	4.63840i	0.0796133	−	0.189678i
$599$	7.71548	+	25.4345i	0.315246	+	1.03923i	0.961200	+	0.275851i	$0.0889596\pi$
$599$	7.71548	+	25.4345i	0.315246	+	1.03923i	−0.645954	+	0.763376i	$0.723540\pi$
$600$	−39.3629	−	4.43783i	−1.60698	−	0.181173i
$601$	−5.29180	−	9.90027i	−0.215857	−	0.403840i	0.750566	−	0.660795i	$-0.229781\pi$
$601$	−5.29180	−	9.90027i	−0.215857	−	0.403840i	−0.966423	+	0.256955i	$0.917281\pi$
$602$	−0.535873	−	0.165308i	−0.0218405	−	0.00673745i
$603$	2.64590	−	4.41441i	0.107749	−	0.179769i
$604$	−25.9655	+	38.0808i	−1.05652	+	1.54948i
$605$	−44.9175	−	2.20666i	−1.82616	−	0.0897134i
$606$	−6.49995	+	3.85453i	−0.264042	+	0.156580i
$607$	17.5321	+	7.26201i	0.711604	+	0.294756i	0.708968	−	0.705241i	$-0.249161\pi$
$607$	17.5321	+	7.26201i	0.711604	+	0.294756i	0.00263584	+	0.999997i	$0.499161\pi$
$608$	−30.2197	+	8.39728i	−1.22557	+	0.340555i
$609$	1.00184	−	0.414975i	0.0405965	−	0.0168156i
$610$	−41.8470	+	55.8736i	−1.69433	+	2.26226i
$611$	23.2765	+	25.6816i	0.941665	+	1.03897i
$612$	6.49700	+	2.76294i	0.262626	+	0.111685i
$613$	−7.49075	−	29.9048i	−0.302549	−	1.20784i	−0.910379	−	0.413775i	$-0.864210\pi$
$613$	−7.49075	−	29.9048i	−0.302549	−	1.20784i	0.607830	−	0.794067i	$-0.292040\pi$
$614$	11.2729	−	13.6052i	0.454937	−	0.549062i
$615$	6.18913	−	20.4028i	0.249570	−	0.822722i
$616$	−4.65882	+	4.52932i	−0.187709	+	0.182492i
$617$	36.3075	+	19.4068i	1.46169	+	0.781288i	0.994685	−	0.102969i	$-0.0328342\pi$
$617$	36.3075	+	19.4068i	1.46169	+	0.781288i	0.467002	+	0.884256i	$0.345334\pi$
$618$	9.94423	+	0.0467136i	0.400016	+	0.00187910i
$619$	−7.02286	+	19.6276i	−0.282273	+	0.788899i	0.713799	+	0.700350i	$0.246973\pi$
$619$	−7.02286	+	19.6276i	−0.282273	+	0.788899i	−0.996072	+	0.0885486i	$0.971777\pi$
$620$	76.3178	−	10.5889i	3.06499	−	0.425260i
$621$	0.219731	−	0.877216i	0.00881750	−	0.0352014i
$622$	−22.6167	+	16.6096i	−0.906848	+	0.665984i
$623$	−41.5199	+	27.7427i	−1.66346	+	1.11149i
$624$	15.1393	−	4.28353i	0.606056	−	0.171478i
$625$	84.0749	+	56.1771i	3.36300	+	2.24708i
$626$	1.50895	+	33.9708i	0.0603098	+	1.35775i
$627$	−2.73193	+	3.68358i	−0.109103	+	0.147108i
$628$	−3.54189	+	2.57562i	−0.141337	+	0.102778i
$629$	2.10505	+	42.8493i	0.0839340	+	1.70852i
$630$	3.41941	−	16.7783i	0.136233	−	0.668462i
$631$	−0.208537	+	0.171142i	−0.00830174	+	0.00681306i	−0.638535	−	0.769593i	$-0.720459\pi$
$631$	−0.208537	+	0.171142i	−0.00830174	+	0.00681306i	0.630233	+	0.776406i	$0.282959\pi$
$632$	12.6187	−	13.5343i	0.501946	−	0.538366i
$633$	2.07624	−	0.204492i	0.0825230	−	0.00812781i
$634$	8.62638	−	15.9581i	0.342597	−	0.633775i
$635$	3.59258	−	24.2192i	0.142567	−	0.961109i
$636$	−0.495371	−	1.69002i	−0.0196428	−	0.0670136i
$637$	2.53809	+	1.20043i	0.100563	+	0.0475626i
$638$	−0.0245522	+	0.456048i	−0.000972031	+	0.0180551i
$639$		−	3.02479i		−	0.119659i
$640$	12.7579	+	47.6433i	0.504301	+	1.88327i
$641$			23.4477i			0.926129i	0.886325	+	0.463065i	$0.153250\pi$
$641$			23.4477i			0.926129i	−0.886325	+	0.463065i	$0.846750\pi$
$642$	−27.6001	−	1.48590i	−1.08929	−	0.0586438i
$643$	−9.97746	−	4.71899i	−0.393473	−	0.186099i	0.220571	−	0.975371i	$-0.429208\pi$
$643$	−9.97746	−	4.71899i	−0.393473	−	0.186099i	−0.614043	+	0.789272i	$0.710458\pi$
$644$	−2.40946	+	4.40767i	−0.0949460	+	0.173686i
$645$	−0.0913285	+	0.615687i	−0.00359606	+	0.0242427i
$646$	−24.3497	−	13.1626i	−0.958027	−	0.517877i
$647$	13.3799	−	1.31780i	0.526018	−	0.0518082i	0.168477	−	0.985706i	$-0.446115\pi$
$647$	13.3799	−	1.31780i	0.526018	−	0.0518082i	0.357541	+	0.933897i	$0.383615\pi$
$648$	2.57366	−	1.17316i	0.101103	−	0.0460859i
$649$	3.76027	−	3.08597i	0.147604	−	0.121135i
$650$	−76.3362	−	15.5573i	−2.99415	−	0.610209i
$651$	1.20429	+	24.5139i	0.0471999	+	0.960775i
$652$	−5.60176	+	35.4651i	−0.219382	+	1.38892i
$653$	−8.02111	+	10.8152i	−0.313890	+	0.423232i	−0.931775	−	0.363037i	$-0.881740\pi$
$653$	−8.02111	+	10.8152i	−0.313890	+	0.423232i	0.617885	+	0.786269i	$0.287990\pi$
$654$	9.94931	−	0.441939i	0.389049	−	0.0172812i
$655$	29.0009	+	19.3778i	1.13316	+	0.757153i
$656$	−19.5012	+	1.55136i	−0.761394	+	0.0605703i
$657$	−5.19405	+	3.47055i	−0.202639	+	0.135399i
$658$	−20.4869	−	27.8963i	−0.798663	−	1.08751i
$659$	−7.70840	+	30.7737i	−0.300277	+	1.19877i	0.612552	+	0.790430i	$0.290143\pi$
$659$	−7.70840	+	30.7737i	−0.300277	+	1.19877i	−0.912829	+	0.408342i	$0.866107\pi$
$660$	5.75192	+	4.35027i	0.223893	+	0.169334i
$661$	−12.1734	+	34.0223i	−0.473490	+	1.32332i	0.433116	+	0.901338i	$0.357414\pi$
$661$	−12.1734	+	34.0223i	−0.473490	+	1.32332i	−0.906606	+	0.421978i	$0.861336\pi$
$662$	0.00671389	−	1.42923i	0.000260943	−	0.0555486i
$663$	12.2455	+	6.54538i	0.475578	+	0.254202i
$664$	19.0952	+	8.22662i	0.741036	+	0.319255i
$665$	−19.4876	+	64.2420i	−0.755697	+	2.49120i
$666$	13.2344	+	10.9657i	0.512824	+	0.424911i
$667$	0.0857905	+	0.342495i	0.00332182	+	0.0132615i
$668$	32.1382	−	12.9597i	1.24347	−	0.501426i
$669$	−0.394473	−	0.435234i	−0.0152512	−	0.0168271i
$670$	25.3968	+	19.0212i	0.981166	+	0.734851i
$671$	8.65252	−	3.58399i	0.334027	−	0.138358i
$672$	−15.4770	+	2.70236i	−0.597040	+	0.104246i
$673$	7.43390	+	3.07922i	0.286556	+	0.118695i	0.521331	−	0.853354i	$-0.325436\pi$
$673$	7.43390	+	3.07922i	0.286556	+	0.118695i	−0.234776	+	0.972050i	$0.575436\pi$
$674$	−3.50986	−	5.91872i	−0.135195	−	0.227981i
$675$	−13.9882	−	0.687195i	−0.538405	−	0.0264501i
$676$	4.85712	−	0.918791i	0.186812	−	0.0353381i
$677$	16.1441	−	26.9349i	0.620469	−	1.03519i	−0.373720	−	0.927542i	$-0.621918\pi$
$677$	16.1441	−	26.9349i	0.620469	−	1.03519i	0.994189	−	0.107649i	$-0.0343322\pi$
$678$	1.95756	−	6.34575i	0.0751797	−	0.243707i
$679$	−15.9608	−	29.8605i	−0.612518	−	1.14594i
$680$	−21.0575	+	38.0945i	−0.807517	+	1.46086i
$681$	−6.07618	−	20.0305i	−0.232840	−	0.767570i
$682$	−9.53143	−	4.00061i	−0.364977	−	0.153191i
$683$	1.90933	+	4.03694i	0.0730586	+	0.154469i	0.937213	−	0.348757i	$-0.113396\pi$
$683$	1.90933	+	4.03694i	0.0730586	+	0.154469i	−0.864155	+	0.503226i	$0.832146\pi$
$684$	−10.4755	+	3.63754i	−0.400541	+	0.139085i
$685$	59.2247	−	35.4979i	2.26286	−	1.35631i
$686$	21.1183	+	12.7930i	0.806299	+	0.488440i
$687$	3.90935	−	19.6536i	0.149151	−	0.749833i
$688$	0.556494	−	0.128333i	0.0212161	−	0.00489263i
$689$	−0.675715	−	3.39705i	−0.0257427	−	0.129417i
$690$	5.24053	+	1.90291i	0.199504	+	0.0724425i
$691$	−0.379586	−	2.55896i	−0.0144401	−	0.0973474i	0.980758	−	0.195226i	$-0.0625442\pi$
$691$	−0.379586	−	2.55896i	−0.0144401	−	0.0973474i	−0.995198	+	0.0978790i	$0.968794\pi$
$692$	−1.64490	−	3.56411i	−0.0625298	−	0.135487i
$693$	−1.54275	+	1.70216i	−0.0586041	+	0.0646597i
$694$	−4.27405	−	22.0274i	−0.162241	−	0.836148i
$695$	2.46570	−	25.0346i	0.0935292	−	0.949618i
$696$	−0.670274	+	0.877635i	−0.0254067	+	0.0332667i
$697$	−13.3456	−	10.9524i	−0.505499	−	0.414853i
$698$	−2.84644	+	2.31372i	−0.107739	+	0.0875757i
$699$	−8.08270	−	10.8983i	−0.305716	−	0.412210i
$700$	74.2292	+	23.2809i	2.80560	+	0.879937i
$701$	11.2359	+	31.4023i	0.424375	+	1.18605i	0.943507	+	0.331354i	$0.107505\pi$
$701$	11.2359	+	31.4023i	0.424375	+	1.18605i	−0.519132	+	0.854694i	$0.673745\pi$
$702$	5.24624	−	1.84938i	0.198007	−	0.0698004i
$703$	−47.6473	−	47.6473i	−1.79705	−	1.79705i
$704$	1.78807	−	6.37092i	0.0673905	−	0.240113i
$705$	−27.1634	+	27.1634i	−1.02303	+	1.02303i
$706$	5.64314	−	11.7878i	0.212382	−	0.443640i
$707$	13.9734	−	4.99978i	0.525526	−	0.188036i
$708$	11.7158	−	1.04287i	0.440308	−	0.0391935i
$709$	−3.62683	+	2.68984i	−0.136208	+	0.101019i	−0.661658	−	0.749806i	$-0.730147\pi$
$709$	−3.62683	+	2.68984i	−0.136208	+	0.101019i	0.525450	+	0.850825i	$0.323897\pi$
$710$	18.5500	+	1.91504i	0.696168	+	0.0718701i
$711$	4.15037	−	5.05724i	0.155651	−	0.189661i
$712$	22.3883	−	45.6601i	0.839039	−	1.71118i
$713$	−7.95291	−	0.783293i	−0.297839	−	0.0293346i
$714$	−11.4923	−	7.75722i	−0.430087	−	0.290307i
$715$	10.5092	+	9.52496i	0.393021	+	0.356213i
$716$	−18.9660	+	0.753202i	−0.708794	+	0.0281485i
$717$	−11.2325	+	1.66618i	−0.419485	+	0.0622248i
$718$	3.96051	+	8.47658i	0.147805	+	0.316343i
$719$	8.63728	−	1.71806i	0.322116	−	0.0640729i	−0.0313839	−	0.999507i	$-0.509991\pi$
$719$	8.63728	−	1.71806i	0.322116	−	0.0640729i	0.353500	+	0.935435i	$0.384991\pi$
$720$	5.56513	+	16.5260i	0.207400	+	0.615889i
$721$	−19.1544	−	3.81005i	−0.713348	−	0.141894i
$722$	16.1268	−	3.95913i	0.600176	−	0.147343i
$723$	0.974859	+	1.62645i	0.0362554	+	0.0604885i
$724$	−27.8779	−	31.3453i	−1.03607	−	1.16494i
$725$	4.94306	−	2.33789i	0.183580	−	0.0868271i
$726$	5.51952	+	13.5044i	0.204849	+	0.501195i
$727$	12.0566	−	3.65732i	0.447154	−	0.135643i	−0.0586739	−	0.998277i	$-0.518687\pi$
$727$	12.0566	−	3.65732i	0.447154	−	0.135643i	0.505828	+	0.862635i	$0.331187\pi$
$728$	−30.7900	+	2.59501i	−1.14115	+	0.0961775i
$729$	0.881921	−	0.471397i	0.0326638	−	0.0174591i
$730$	−17.9952	−	34.0505i	−0.666033	−	1.26026i
$731$	0.432297	+	0.259109i	0.0159891	+	0.00958348i
$732$	22.1678	+	4.62637i	0.819346	+	0.170996i
$733$	0.678741	−	13.8161i	0.0250699	−	0.510309i	−0.953120	−	0.302594i	$-0.902147\pi$
$733$	0.678741	−	13.8161i	0.0250699	−	0.510309i	0.978189	−	0.207715i	$-0.0666026\pi$
$734$	−7.48907	+	29.3131i	−0.276427	+	1.08197i
$735$	−1.19083	+	2.87491i	−0.0439244	+	0.106043i
$736$	−0.130944	−	5.11391i	−0.00482664	−	0.188501i
$737$	−1.62907	−	3.93292i	−0.0600075	−	0.144871i
$738$	−6.84633	+	0.982711i	−0.252017	+	0.0361741i
$739$	9.76831	−	8.85348i	0.359333	−	0.325681i	−0.471850	−	0.881679i	$-0.656414\pi$
$739$	9.76831	−	8.85348i	0.359333	−	0.325681i	0.831184	+	0.555998i	$0.187664\pi$
$740$	−75.6273	+	74.2195i	−2.78012	+	2.72836i
$741$	−21.1553	+	5.29913i	−0.777160	+	0.194668i
$742$	0.322836	+	3.44357i	0.0118517	+	0.126417i
$743$	−51.2108	−	15.5346i	−1.87874	−	0.569911i	−0.994740	−	0.102430i	$-0.967338\pi$
$743$	−51.2108	−	15.5346i	−1.87874	−	0.569911i	−0.884003	−	0.467480i	$-0.845162\pi$
$744$	−13.5920	−	20.9759i	−0.498308	−	0.769014i
$745$	−23.5269	+	44.0157i	−0.861958	+	1.61261i
$746$	−5.68709	−	5.74078i	−0.208219	−	0.210185i
$747$	6.92133	+	2.47649i	0.253238	+	0.0906101i
$748$	5.03682	−	2.95499i	0.184164	−	0.108045i
$749$	52.6555	+	13.1895i	1.92399	+	0.481934i
$750$	8.40409	−	54.8784i	0.306874	−	2.00388i
$751$	25.5485	+	38.2360i	0.932278	+	1.39525i	0.918532	+	0.395347i	$0.129376\pi$
$751$	25.5485	+	38.2360i	0.932278	+	1.39525i	0.0137463	+	0.999906i	$0.495624\pi$
$752$	32.3050	+	14.0980i	1.17804	+	0.514101i
$753$	2.93901	−	4.39853i	0.107103	−	0.160291i
$754$	−1.46607	+	1.60237i	−0.0533912	+	0.0583548i
$755$	−80.6948	−	59.8473i	−2.93678	−	2.17807i
$756$	−5.40072	+	1.29901i	−0.196422	+	0.0472446i
$757$	−42.6963	+	2.09753i	−1.55182	+	0.0762362i	−0.806809	−	0.590813i	$-0.798807\pi$
$757$	−42.6963	+	2.09753i	−1.55182	+	0.0762362i	−0.745014	+	0.667049i	$0.767557\pi$
$758$	−21.6098	−	32.6726i	−0.784905	−	1.18672i
$759$	−0.474522	−	0.578206i	−0.0172240	−	0.0209876i
$760$	−15.6756	−	66.5454i	−0.568612	−	2.41386i
$761$	−1.50511	−	15.2817i	−0.0545602	−	0.553959i	−0.983144	−	0.182835i	$-0.941472\pi$
$761$	−1.50511	−	15.2817i	−0.0545602	−	0.553959i	0.928583	−	0.371124i	$-0.121028\pi$
$762$	−7.61141	+	2.26990i	−0.275732	+	0.0822300i
$763$	−19.3470	−	2.86986i	−0.700409	−	0.103896i
$764$	4.91344	−	3.95569i	0.177762	−	0.143112i
$765$	−6.57971	+	13.9116i	−0.237890	+	0.502976i
$766$	10.9804	+	12.2300i	0.396738	+	0.441887i
$767$	23.1326			0.835271
$768$	12.2505	−	10.2919i	0.442054	−	0.371378i
$769$	−30.1302			−1.08652			−0.543261	−	0.839564i	$-0.682810\pi$
$769$	−30.1302			−1.08652			−0.543261	+	0.839564i	$0.682810\pi$
$770$	−9.46200	−	10.5388i	−0.340987	−	0.379791i
$771$	−5.39662	+	11.4102i	−0.194355	+	0.410928i
$772$	−16.2411	−	20.1734i	−0.584530	−	0.726056i
$773$	19.1453	+	2.83994i	0.688609	+	0.102146i	0.481860	−	0.876248i	$-0.339961\pi$
$773$	19.1453	+	2.83994i	0.688609	+	0.102146i	0.206750	+	0.978394i	$0.433711\pi$
$774$	0.193493	−	0.0577043i	0.00695496	−	0.00207414i
$775$	12.1308	+	123.166i	0.435750	+	4.42424i
$776$	29.3225	+	18.1417i	1.05262	+	0.651250i
$777$	−21.4131	−	26.0920i	−0.768191	−	0.936044i
$778$	14.0866	+	21.2980i	0.505029	+	0.763570i
$779$	27.0840	−	1.33055i	0.970387	−	0.0476720i
$780$	8.02013	+	33.3442i	0.287167	+	1.19391i
$781$	−2.00956	−	1.49039i	−0.0719076	−	0.0533303i
$782$	3.04748	−	3.33079i	0.108978	−	0.119109i
$783$	−0.216914	+	0.324634i	−0.00775186	+	0.0116015i
$784$	2.85469	+	0.0536462i	0.101953	+	0.00191593i
$785$	−5.30339	−	7.93709i	−0.189286	−	0.283287i
$786$	1.71278	−	11.1844i	0.0610928	−	0.398934i
$787$	−24.8305	−	6.21972i	−0.885113	−	0.221709i	−0.226337	−	0.974049i	$-0.572675\pi$
$787$	−24.8305	−	6.21972i	−0.885113	−	0.221709i	−0.658775	+	0.752340i	$0.728925\pi$
$788$	−20.8012	−	35.4559i	−0.741013	−	1.26307i
$789$	8.79961	+	3.14855i	0.313274	+	0.112091i
$790$	28.3866	+	28.6545i	1.00995	+	1.01948i
$791$	−6.14791	+	11.5019i	−0.218595	+	0.408962i
$792$	0.488702	−	2.28788i	0.0173653	−	0.0812963i
$793$	42.6190	+	12.9283i	1.51344	+	0.459098i
$794$	−0.794384	−	8.47338i	−0.0281916	−	0.300709i
$795$	3.72374	−	0.932749i	0.132068	−	0.0330812i
$796$	−17.8796	−	18.2187i	−0.633725	−	0.645746i
$797$	−1.18411	+	1.07322i	−0.0419434	+	0.0380152i	−0.692262	−	0.721647i	$-0.743386\pi$
$797$	−1.18411	+	1.07322i	−0.0419434	+	0.0380152i	0.650318	+	0.759662i	$0.274636\pi$
$798$	21.5569	−	3.09424i	0.763106	−	0.109535i
$799$	11.9038	+	28.7383i	0.421125	+	1.01669i
$800$	−77.2811	+	17.4398i	−2.73230	+	0.616590i
$801$	6.88043	−	16.6108i	0.243108	−	0.586915i
$802$	1.35301	−	5.29583i	0.0477763	−	0.187002i
$803$	−0.253531	+	5.16075i	−0.00894692	+	0.182119i
$804$	2.10287	−	10.0762i	0.0741626	−	0.355359i
$805$	−9.39159	−	5.62910i	−0.331010	−	0.198400i
$806$	−22.9685	−	43.4609i	−0.809031	−	1.53085i
$807$	−3.32237	+	1.77584i	−0.116953	+	0.0625127i
$808$	−9.75178	+	11.5469i	−0.343067	+	0.406217i
$809$	−0.191140	+	0.0579818i	−0.00672014	+	0.00203853i	−0.293643	−	0.955915i	$-0.594868\pi$
$809$	−0.191140	+	0.0579818i	−0.00672014	+	0.00203853i	0.286923	+	0.957954i	$0.407368\pi$
$810$	2.33255	+	5.70695i	0.0819574	+	0.200522i
$811$	14.0362	−	6.63864i	0.492878	−	0.233114i	−0.164922	−	0.986307i	$-0.552737\pi$
$811$	14.0362	−	6.63864i	0.492878	−	0.233114i	0.657800	+	0.753193i	$0.271487\pi$
$812$	1.62056	−	1.44129i	0.0568705	−	0.0505794i
$813$	10.3421	+	17.2548i	0.362715	+	0.605153i
$814$	13.8061	−	3.38940i	0.483903	−	0.118798i
$815$	−76.7592	−	15.2684i	−2.68876	−	0.534827i
$816$	14.0877	+	0.957707i	0.493167	+	0.0335264i
$817$	−0.776411	+	0.154438i	−0.0271632	+	0.00540309i
$818$	−19.7552	−	42.2817i	−0.690725	−	1.47834i
$819$	−10.8063	+	1.60296i	−0.377602	+	0.0560119i
$820$	−1.69211	−	42.6082i	−0.0590910	−	1.48794i
$821$	5.77068	+	5.23024i	0.201398	+	0.182537i	0.766027	−	0.642808i	$-0.222231\pi$
$821$	5.77068	+	5.23024i	0.201398	+	0.182537i	−0.564629	+	0.825345i	$0.690981\pi$
$822$	−18.5656	−	12.5317i	−0.647551	−	0.437094i
$823$	30.8473	+	3.03819i	1.07527	+	0.105905i	0.620117	−	0.784509i	$-0.287085\pi$
$823$	30.8473	+	3.03819i	1.07527	+	0.105905i	0.455151	+	0.890414i	$0.349585\pi$
$824$	18.8186	−	6.43574i	0.655578	−	0.224200i
$825$	−7.34886	+	8.95461i	−0.255854	+	0.311759i
$826$	−22.9776	−	2.37213i	−0.799492	−	0.0825369i
$827$	3.58676	−	2.66012i	0.124724	−	0.0925016i	−0.531539	−	0.847034i	$-0.678386\pi$
$827$	3.58676	−	2.66012i	0.124724	−	0.0925016i	0.656263	+	0.754532i	$0.272136\pi$
$828$	−0.160359	−	1.80151i	−0.00557287	−	0.0626068i
$829$	25.5108	−	9.12791i	0.886027	−	0.317026i	0.145745	−	0.989322i	$-0.453442\pi$
$829$	25.5108	−	9.12791i	0.886027	−	0.317026i	0.740282	+	0.672297i	$0.234692\pi$
$830$	−19.5694	+	40.8781i	−0.679264	+	1.41890i
$831$	7.47750	−	7.47750i	0.259392	−	0.259392i
$832$	25.7929	−	18.0253i	0.894208	−	0.624914i
$833$	1.78172	+	1.78172i	0.0617331	+	0.0617331i
$834$	−7.69632	+	2.71307i	−0.266502	+	0.0939461i
$835$	25.4467	+	71.1187i	0.880619	+	2.46117i
$836$	−2.74489	+	8.75182i	−0.0949339	+	0.302688i
$837$	−5.26416	−	7.09789i	−0.181956	−	0.245339i
$838$	−21.1617	+	17.2012i	−0.731019	+	0.594207i
$839$	18.3645	+	15.0714i	0.634015	+	0.520322i	0.895601	−	0.444858i	$-0.146746\pi$
$839$	18.3645	+	15.0714i	0.634015	+	0.520322i	−0.261587	+	0.965180i	$0.584246\pi$
$840$	−4.54710	−	33.9431i	−0.156890	−	1.17115i
$841$	−2.82756	+	28.7087i	−0.0975019	+	0.989954i
$842$	−1.56458	−	8.06347i	−0.0539191	−	0.277886i
$843$	−3.58835	+	3.95914i	−0.123589	+	0.136360i
$844$	3.78855	−	1.74849i	0.130407	−	0.0601854i
$845$	1.58102	+	10.6584i	0.0543889	+	0.366660i
$846$	11.7135	+	4.25332i	0.402717	+	0.146232i
$847$	−5.58952	−	28.1004i	−0.192058	−	0.965542i
$848$	−2.04467	−	2.86802i	−0.0702144	−	0.0984882i
$849$	−2.90038	+	14.5812i	−0.0995408	+	0.500425i
$850$	−59.7999	−	36.2256i	−2.05112	−	1.24253i
$851$	9.42666	−	5.65012i	0.323142	−	0.193684i
$852$	−1.98444	−	5.71485i	−0.0679859	−	0.195788i
$853$	6.53434	+	13.8157i	0.223731	+	0.473040i	0.984365	−	0.176141i	$-0.0563615\pi$
$853$	6.53434	+	13.8157i	0.223731	+	0.473040i	−0.760633	+	0.649182i	$0.775112\pi$
$854$	−41.0076	−	17.2120i	−1.40325	−	0.588983i
$855$	−7.01656	−	23.1305i	−0.239961	−	0.791046i
$856$	−53.1206	+	15.2999i	−1.81562	+	0.522940i
$857$	16.5301	+	30.9256i	0.564657	+	1.05640i	0.988579	+	0.150700i	$0.0481529\pi$
$857$	16.5301	+	30.9256i	0.564657	+	1.05640i	−0.423922	+	0.905698i	$0.639347\pi$
$858$	1.35629	−	4.39664i	0.0463030	−	0.150099i
$859$	17.1166	−	28.5573i	0.584010	−	0.974363i	−0.413936	−	0.910306i	$-0.635846\pi$
$859$	17.1166	−	28.5573i	0.584010	−	0.974363i	0.997946	−	0.0640565i	$-0.0204038\pi$
$860$	0.231377	+	1.22316i	0.00788987	+	0.0417093i
$861$	13.5669	+	0.666501i	0.462360	+	0.0227143i
$862$	−27.0381	−	45.5947i	−0.920921	−	1.55296i
$863$	37.3061	+	15.4527i	1.26991	+	0.526016i	0.912938	−	0.408097i	$-0.133808\pi$
$863$	37.3061	+	15.4527i	1.26991	+	0.526016i	0.356977	+	0.934113i	$0.383808\pi$
$864$	4.09284	−	3.90495i	0.139241	−	0.132849i
$865$	7.90499	−	3.27435i	0.268778	−	0.111331i
$866$	27.5910	+	20.6645i	0.937579	+	0.702207i
$867$	−3.04806	−	3.36301i	−0.103517	−	0.114214i
$868$	18.3579	+	45.5249i	0.623106	+	1.54522i
$869$	−1.31485	−	5.24917i	−0.0446032	−	0.178066i
$870$	−1.85353	−	1.53578i	−0.0628406	−	0.0520679i
$871$	5.87645	−	19.3721i	0.199116	−	0.656398i
$872$	18.5076	−	7.36230i	0.626748	−	0.249319i
$873$	10.7513	+	5.74671i	0.363878	+	0.194497i
$874$	−0.0333096	+	7.09082i	−0.00112671	+	0.239851i
$875$	−36.7318	+	102.659i	−1.24176	+	3.47049i
$876$	−7.53641	+	9.96463i	−0.254632	+	0.336674i
$877$	−13.7666	+	54.9592i	−0.464863	+	1.85584i	0.0502806	+	0.998735i	$0.483988\pi$
$877$	−13.7666	+	54.9592i	−0.464863	+	1.85584i	−0.515144	+	0.857104i	$0.672262\pi$
$878$	−10.9491	−	14.9090i	−0.369514	−	0.503154i
$879$	13.3088	−	8.89267i	0.448895	−	0.299942i
$880$	13.7213	+	4.44552i	0.462546	+	0.149858i
$881$	30.1835	+	20.1680i	1.01691	+	0.679477i	0.948041	−	0.318149i	$-0.103061\pi$
$881$	30.1835	+	20.1680i	1.01691	+	0.679477i	0.0688679	+	0.997626i	$0.478061\pi$
$882$	1.00847	−	0.0447952i	0.0339569	−	0.00150833i
$883$	−34.0079	+	45.8543i	−1.14446	+	1.54312i	−0.348987	+	0.937128i	$0.613474\pi$
$883$	−34.0079	+	45.8543i	−1.14446	+	1.54312i	−0.795470	+	0.605993i	$0.792776\pi$
$884$	27.4301	+	4.33262i	0.922574	+	0.145722i
$885$	1.25802	+	25.6076i	0.0422878	+	0.860788i
$886$	37.3021	+	7.60219i	1.25319	+	0.255400i
$887$	−25.0703	+	20.5747i	−0.841778	+	0.690829i	−0.953001	−	0.302966i	$-0.902023\pi$
$887$	−25.0703	+	20.5747i	−0.841778	+	0.690829i	0.111223	+	0.993795i	$0.464523\pi$
$888$	32.1984	+	12.0352i	1.08051	+	0.403877i
$889$	15.5235	−	1.52893i	0.520641	−	0.0512787i
$890$	97.5121	+	52.7117i	3.26861	+	1.76690i
$891$	0.121366	−	0.818183i	0.00406591	−	0.0274102i
$892$	−1.03083	−	0.563506i	−0.0345148	−	0.0188676i
$893$	−44.1666	−	20.8892i	−1.47798	−	0.699032i
$894$	16.1670	+	0.870381i	0.540706	+	0.0291099i
$895$		−	41.3736i		−	1.38297i
$896$	−27.4684	+	15.2595i	−0.917655	+	0.509784i
$897$		−	3.55704i		−	0.118766i
$898$	−2.28374	+	42.4197i	−0.0762094	+	1.41556i
$899$	3.11898	+	1.47517i	0.104024	+	0.0491996i
$900$	−26.8792	+	7.87872i	−0.895973	+	0.262624i
$901$	0.456100	−	3.07478i	0.0151949	−	0.102436i
$902$	−2.72048	+	5.03264i	−0.0905819	+	0.167569i
$903$	−0.394630	+	0.0388676i	−0.0131324	+	0.00129343i
$904$	−0.464694	−	13.2735i	−0.0154555	−	0.441471i
$905$	70.6822	−	58.0074i	2.34955	−	1.92823i
$906$	−6.50828	+	31.9346i	−0.216223	+	1.06096i
$907$	1.25313	+	25.5081i	0.0416096	+	0.846983i	0.925375	+	0.379053i	$0.123750\pi$
$907$	1.25313	+	25.5081i	0.0416096	+	0.846983i	−0.883765	+	0.467930i	$0.845000\pi$
$908$	−24.6211	−	33.8580i	−0.817080	−	1.12362i
$909$	−3.18314	+	4.29197i	−0.105578	+	0.142356i
$910$	−2.98877	−	67.2858i	−0.0990768	−	2.23050i
$911$	42.2348	+	28.2204i	1.39930	+	0.934984i	0.999834	+	0.0182371i	$0.00580537\pi$
$911$	42.2348	+	28.2204i	1.39930	+	0.934984i	0.399469	+	0.916747i	$0.369195\pi$
$912$	−17.4053	+	13.7451i	−0.576347	+	0.455145i
$913$	5.05559	−	3.37804i	0.167316	−	0.111797i
$914$	12.3864	−	9.09650i	0.409706	−	0.300886i
$915$	−11.9938	+	47.8818i	−0.396502	+	1.58292i
$916$	−5.50786	−	39.6971i	−0.181985	−	1.31163i
$917$	−7.48605	+	20.9221i	−0.247211	+	0.690909i
$918$	4.99218	+	0.0234511i	0.164767	+	0.000774001i
$919$	0.0415858	+	0.0222281i	0.00137179	+	0.000733237i	0.472082	−	0.881554i	$-0.343502\pi$
$919$	0.0415858	+	0.0222281i	0.00137179	+	0.000733237i	−0.470711	+	0.882288i	$0.656002\pi$
$920$	11.1495	+	0.157136i	0.367589	+	0.00518063i
$921$	3.62670	−	11.9556i	0.119504	−	0.393951i
$922$	−8.97971	+	10.8376i	−0.295731	+	0.356917i
$923$	−2.89091	−	11.5412i	−0.0951555	−	0.379882i
$924$	−1.79805	+	4.22808i	−0.0591515	+	0.139094i
$925$	−114.303	−	126.113i	−3.75824	−	4.14658i
$926$	−17.6880	+	23.6168i	−0.581263	+	0.776096i
$927$	6.49646	−	2.69092i	0.213372	−	0.0883814i
$928$	−0.690591	+	2.09789i	−0.0226698	+	0.0688665i
$929$	−20.5164	−	8.49818i	−0.673122	−	0.278816i	0.0198266	−	0.999803i	$-0.493689\pi$
$929$	−20.5164	−	8.49818i	−0.673122	−	0.278816i	−0.692948	+	0.720987i	$0.743689\pi$
$930$	46.8616	−	27.7894i	1.53665	−	0.911250i
$931$	−3.95291	−	0.194194i	−0.129551	−	0.00636446i
$932$	−22.4208	−	15.2877i	−0.734419	−	0.500767i
$933$	−10.2007	+	17.0189i	−0.333957	+	0.557174i
$934$	−38.6282	−	11.9162i	−1.26395	−	0.389909i
$935$	6.00037	+	11.2259i	0.196233	+	0.367126i
$936$	8.69860	−	6.93594i	0.284323	−	0.226708i
$937$	−11.0222	−	36.3353i	−0.360079	−	1.18702i	−0.930692	−	0.365803i	$-0.880794\pi$
$937$	−11.0222	−	36.3353i	−0.360079	−	1.18702i	0.570613	−	0.821219i	$-0.306706\pi$
$938$	−7.82356	+	18.6396i	−0.255448	+	0.608605i
$939$	10.2804	+	21.7361i	0.335489	+	0.709331i
$940$	−33.5000	+	69.1416i	−1.09265	+	2.25515i
$941$	−23.4024	+	14.0268i	−0.762895	+	0.457262i	−0.841914	−	0.539611i	$-0.818571\pi$
$941$	−23.4024	+	14.0268i	−0.762895	+	0.457262i	0.0790190	+	0.996873i	$0.474821\pi$
$942$	−1.60447	+	2.64860i	−0.0522764	+	0.0862959i
$943$	−0.862835	+	4.33776i	−0.0280978	+	0.141257i
$944$	21.4510	−	9.65660i	0.698169	−	0.314296i
$945$	−2.36213	−	11.8752i	−0.0768402	−	0.386302i
$946$	0.0570022	−	0.156982i	0.00185330	−	0.00510391i
$947$	4.62707	+	31.1931i	0.150359	+	1.01364i	0.924652	+	0.380813i	$0.124356\pi$
$947$	4.62707	+	31.1931i	0.150359	+	1.01364i	−0.774293	+	0.632828i	$0.781894\pi$
$948$	4.52360	−	12.2777i	0.146920	−	0.398762i
$949$	−16.5010	+	18.2061i	−0.535647	+	0.590995i
$950$	107.805	−	20.9178i	3.49766	−	0.678664i
$951$	1.25728	−	12.7654i	0.0407703	−	0.413947i
$952$	−26.8019	−	7.11639i	−0.868656	−	0.230644i
$953$	17.0105	+	13.9602i	0.551026	+	0.452215i	0.868244	−	0.496137i	$-0.165249\pi$
$953$	17.0105	+	13.9602i	0.551026	+	0.452215i	−0.317218	+	0.948353i	$0.602749\pi$
$954$	−0.785481	−	0.966332i	−0.0254309	−	0.0312862i
$955$	8.19058	+	11.0437i	0.265041	+	0.357367i
$956$	−20.1288	+	10.5172i	−0.651013	+	0.340149i
$957$	0.108796	+	0.304064i	0.00351687	+	0.00982900i
$958$	−5.86648	−	16.6418i	−0.189537	−	0.537671i
$959$	31.1055	+	31.1055i	1.00445	+	1.00445i
$960$	21.3564	+	27.5722i	0.689276	+	0.889888i
$961$	−33.2987	+	33.2987i	−1.07415	+	1.07415i
$962$	60.9766	+	29.1911i	1.96596	+	0.941158i
$963$	−18.4020	+	6.58433i	−0.592995	+	0.212177i
$964$	2.90888	+	2.43335i	0.0936888	+	0.0783730i
$965$	45.3428	−	33.6285i	1.45964	−	1.08254i
$966$	−0.364756	+	3.53320i	−0.0117358	+	0.113679i
$967$	−6.20189	+	7.55703i	−0.199439	+	0.243018i	−0.863121	−	0.504998i	$-0.831493\pi$
$967$	−6.20189	+	7.55703i	−0.199439	+	0.243018i	0.663681	+	0.748016i	$0.268993\pi$
$968$	19.2879	+	21.8932i	0.619936	+	0.703673i
$969$	−19.4782	−	1.91844i	−0.625731	−	0.0616292i
$970$	−42.0493	+	62.2958i	−1.35012	+	2.00020i
$971$	1.91928	+	1.73953i	0.0615926	+	0.0558243i	0.701775	−	0.712399i	$-0.252391\pi$
$971$	1.91928	+	1.73953i	0.0615926	+	0.0558243i	−0.640182	+	0.768223i	$0.721141\pi$
$972$	1.35698	−	1.46922i	0.0435252	−	0.0471252i
$973$	15.8530	−	2.35157i	0.508223	−	0.0753878i
$974$	−48.3653	+	22.5977i	−1.54972	+	0.724076i
$975$	−54.0289	+	10.7470i	−1.73031	+	0.344180i
$976$	44.9176	−	5.80261i	1.43778	−	0.185737i
$977$	11.1490	+	2.21768i	0.356689	+	0.0709498i	0.370182	−	0.928959i	$-0.379295\pi$
$977$	11.1490	+	2.21768i	0.356689	+	0.0709498i	−0.0134936	+	0.999909i	$0.504295\pi$
$978$	6.05314	+	24.6563i	0.193558	+	0.788423i
$979$	−7.64544	−	12.7556i	−0.244349	−	0.407672i
$980$	−0.363762	+	6.21293i	−0.0116199	+	0.198465i
$981$	6.36604	−	3.01091i	0.203252	−	0.0961310i
$982$	2.92835	−	1.19688i	0.0934475	−	0.0381939i
$983$	11.4783	−	3.48191i	0.366102	−	0.111056i	−0.101873	−	0.994797i	$-0.532484\pi$
$983$	11.4783	−	3.48191i	0.366102	−	0.111056i	0.467975	+	0.883742i	$0.344984\pi$
$984$	−12.2903	+	6.34826i	−0.391800	+	0.202375i
$985$	79.0231	−	42.2387i	2.51788	−	1.34584i
$986$	−1.72329	+	0.910733i	−0.0548806	+	0.0290037i
$987$	−20.9918	−	12.5820i	−0.668175	−	0.400489i
$988$	−36.4929	+	23.8910i	−1.16100	+	0.760073i
$989$	0.00633531	−	0.128958i	0.000201451	−	0.00410063i
$990$	4.94078	+	1.26230i	0.157028	+	0.0401184i
$991$	−15.8969	+	38.3784i	−0.504980	+	1.21913i	0.441761	+	0.897133i	$0.354354\pi$
$991$	−15.8969	+	38.3784i	−0.504980	+	1.21913i	−0.946741	+	0.321997i	$0.895646\pi$
$992$	−39.4413	−	30.7133i	−1.25226	−	0.975149i
$993$	−0.386751	−	0.933699i	−0.0122732	−	0.0296300i
$994$	1.68805	+	11.7602i	0.0535416	+	0.373012i
$995$	41.2273	−	37.3663i	1.30699	−	1.18459i
$996$	14.7014	+	0.138125i	0.465833	+	0.00437665i
$997$	5.42915	−	1.35993i	0.171943	−	0.0430694i	−0.156053	−	0.987749i	$-0.549877\pi$
$997$	5.42915	−	1.35993i	0.171943	−	0.0430694i	0.327995	+	0.944679i	$0.393627\pi$
$998$	−51.5491	+	4.83275i	−1.63176	+	0.152978i
$999$	11.6298	+	3.52786i	0.367951	+	0.111617i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.z.a.637.49	yes	2048
256.213	even	64	inner	768.2.z.a.469.49	✓	2048

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
768.2.z.a.469.49	✓	2048	256.213	even	64	inner
768.2.z.a.637.49	yes	2048	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.z (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(1.05231 - 0.944795i) q^{2} +(0.427555 - 0.903989i) q^{3} +(0.214725 - 1.98844i) q^{4} +(4.31229 + 0.639668i) q^{5} +(-0.404163 - 1.35523i) q^{6} +(0.272230 + 2.76400i) q^{7} +(-1.65271 - 2.29533i) q^{8} +(-0.634393 - 0.773010i) q^{9} +O(q^{10})\)	\(q+(1.05231 - 0.944795i) q^{2} +(0.427555 - 0.903989i) q^{3} +(0.214725 - 1.98844i) q^{4} +(4.31229 + 0.639668i) q^{5} +(-0.404163 - 1.35523i) q^{6} +(0.272230 + 2.76400i) q^{7} +(-1.65271 - 2.29533i) q^{8} +(-0.634393 - 0.773010i) q^{9} +(5.14224 - 3.40110i) q^{10} +(-0.826139 + 0.0405856i) q^{11} +(-1.70572 - 1.04428i) q^{12} +(-3.15934 - 2.34312i) q^{13} +(2.89788 + 2.65139i) q^{14} +(2.42200 - 3.62477i) q^{15} +(-3.90779 - 0.853935i) q^{16} +(-1.96119 - 2.93513i) q^{17} +(-1.39792 - 0.214077i) q^{18} +(5.37838 + 1.34721i) q^{19} +(2.19790 - 8.43738i) q^{20} +(2.61502 + 0.935669i) q^{21} +(-0.831012 + 0.823241i) q^{22} +(-0.426292 + 0.797536i) q^{23} +(-2.78158 + 0.512651i) q^{24} +(13.4020 + 4.06545i) q^{25} +(-5.53838 + 0.519226i) q^{26} +(-0.970031 + 0.242980i) q^{27} +(5.55450 + 0.0521863i) q^{28} +(0.289293 - 0.262200i) q^{29} +(-0.875970 - 6.10268i) q^{30} +(3.38175 + 8.16426i) q^{31} +(-4.91901 + 2.79345i) q^{32} +(-0.316531 + 0.764174i) q^{33} +(-4.83688 - 1.23575i) q^{34} +(-0.594106 + 12.0933i) q^{35} +(-1.67330 + 1.09547i) q^{36} +(-10.4241 - 6.24795i) q^{37} +(6.93258 - 3.66378i) q^{38} +(-3.46895 + 1.85419i) q^{39} +(-5.65872 - 10.9553i) q^{40} +(4.68011 - 1.41970i) q^{41} +(3.63583 - 1.48604i) q^{42} +(-0.129067 + 0.0610441i) q^{43} +(-0.0966907 + 1.65144i) q^{44} +(-2.24122 - 3.73925i) q^{45} +(0.304916 + 1.24202i) q^{46} +(-8.64249 - 1.71910i) q^{47} +(-2.44274 + 3.16749i) q^{48} +(-0.700082 + 0.139255i) q^{49} +(17.9441 - 8.38401i) q^{50} +(-3.49184 + 0.517965i) q^{51} +(-5.33755 + 5.77902i) q^{52} +(0.652453 + 0.591349i) q^{53} +(-0.791210 + 1.17217i) q^{54} +(-3.58852 - 0.353438i) q^{55} +(5.89438 - 5.19295i) q^{56} +(3.51742 - 4.28599i) q^{57} +(0.0567015 - 0.549238i) q^{58} +(-4.72373 + 3.50335i) q^{59} +(-6.68758 - 5.59432i) q^{60} +(-10.6608 + 3.81451i) q^{61} +(11.2722 + 5.39630i) q^{62} +(1.96390 - 1.96390i) q^{63} +(-2.53710 + 7.58704i) q^{64} +(-12.1252 - 12.1252i) q^{65} +(0.388898 + 1.10321i) q^{66} +(1.73385 + 4.84578i) q^{67} +(-6.25744 + 3.26946i) q^{68} +(0.538701 + 0.726354i) q^{69} +(10.8005 + 13.2873i) q^{70} +(2.33820 + 1.91891i) q^{71} +(-0.725847 + 2.73371i) q^{72} +(0.612296 - 6.21674i) q^{73} +(-16.8724 + 3.27381i) q^{74} +(9.40521 - 10.3771i) q^{75} +(3.83373 - 10.4053i) q^{76} +(-0.337079 - 2.27240i) q^{77} +(-1.89859 + 5.22863i) q^{78} +(1.27633 + 6.41656i) q^{79} +(-16.3053 - 6.18211i) q^{80} +(-0.195090 + 0.980785i) q^{81} +(3.58362 - 5.91571i) q^{82} +(-6.30520 + 3.77919i) q^{83} +(2.42203 - 4.99890i) q^{84} +(-6.57971 - 13.9116i) q^{85} +(-0.0781446 + 0.186179i) q^{86} +(-0.113337 - 0.373622i) q^{87} +(1.45853 + 1.82919i) q^{88} +(8.47544 + 15.8564i) q^{89} +(-5.89129 - 1.81737i) q^{90} +(5.61632 - 9.37027i) q^{91} +(1.49432 + 1.01891i) q^{92} +(8.82629 + 0.433608i) q^{93} +(-10.7188 + 6.35635i) q^{94} +(22.3314 + 9.24996i) q^{95} +(0.422102 + 5.64108i) q^{96} +(-11.2629 + 4.66523i) q^{97} +(-0.605138 + 0.807974i) q^{98} +(0.555470 + 0.612867i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2048 q+O(q^{10}) \) 2048 * q	\( 2048 q+O(q^{100}) \) 2048 * q

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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