LMFDB - Embedded newform 207.2.o.a.149.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [207,2,Mod(5,207)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("207.5"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(207, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([55, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.o (of order $66$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			149.8
Character	$\chi$	$=$	207.149
Dual form			207.2.o.a.182.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.596316 + 1.15669i) q^{2} +(-1.67548 - 0.439038i) q^{3} +(0.177772 + 0.249645i) q^{4} +(0.518882 - 2.13886i) q^{5} +(1.50695 - 1.67621i) q^{6} +(-2.98233 - 1.03220i) q^{7} +(-2.97099 + 0.427164i) q^{8} +(2.61449 + 1.47120i) q^{9} +(2.16459 + 1.87562i) q^{10} +(0.308894 - 6.48448i) q^{11} +(-0.188250 - 0.496325i) q^{12} +(-0.195519 - 0.564915i) q^{13} +(2.97234 - 2.83412i) q^{14} +(-1.80842 + 3.35582i) q^{15} +(1.07708 - 3.11201i) q^{16} +(-0.498465 - 1.09149i) q^{17} +(-3.26079 + 2.14686i) q^{18} +(2.29054 + 1.04605i) q^{19} +(0.626199 - 0.250692i) q^{20} +(4.54368 + 3.03878i) q^{21} +(7.31634 + 4.22409i) q^{22} +(-0.627719 - 4.75457i) q^{23} +(5.16539 + 0.588671i) q^{24} +(0.138686 + 0.0714977i) q^{25} +(0.770024 + 0.110713i) q^{26} +(-3.73463 - 3.61283i) q^{27} +(-0.272491 - 0.928020i) q^{28} +(1.09780 + 0.781740i) q^{29} +(-2.80326 - 4.09291i) q^{30} +(-4.11834 - 1.64873i) q^{31} +(-1.18525 - 1.24305i) q^{32} +(-3.36448 + 10.7290i) q^{33} +(1.55976 + 0.0743003i) q^{34} +(-3.75520 + 5.84321i) q^{35} +(0.0975040 + 0.914233i) q^{36} +(-1.94758 + 6.63286i) q^{37} +(-2.57584 + 2.02567i) q^{38} +(0.0795699 + 1.03235i) q^{39} +(-0.627950 + 6.57619i) q^{40} +(-10.4645 - 2.53865i) q^{41} +(-6.22440 + 3.44356i) q^{42} +(-0.922216 - 2.30358i) q^{43} +(1.67373 - 1.07564i) q^{44} +(4.50331 - 4.82866i) q^{45} +(5.87389 + 2.10915i) q^{46} +(-3.46639 + 2.00132i) q^{47} +(-3.17091 + 4.74124i) q^{48} +(2.32651 + 1.82958i) q^{49} +(-0.165401 + 0.117782i) q^{50} +(0.355966 + 2.04761i) q^{51} +(0.106271 - 0.149236i) q^{52} +(6.44700 + 7.44024i) q^{53} +(6.40595 - 2.16542i) q^{54} +(-13.7091 - 4.02536i) q^{55} +(9.30140 + 1.79270i) q^{56} +(-3.37850 - 2.75828i) q^{57} +(-1.55887 + 0.803652i) q^{58} +(3.80878 - 1.31823i) q^{59} +(-1.15925 + 0.145106i) q^{60} +(-1.30693 - 1.66190i) q^{61} +(4.36290 - 3.78048i) q^{62} +(-6.27872 - 7.08628i) q^{63} +(8.46407 - 2.48528i) q^{64} +(-1.30973 + 0.125064i) q^{65} +(-10.4039 - 10.2895i) q^{66} +(6.95211 - 0.331170i) q^{67} +(0.183871 - 0.318475i) q^{68} +(-1.03570 + 8.24180i) q^{69} +(-4.51950 - 7.82801i) q^{70} +(5.22568 + 8.13132i) q^{71} +(-8.39607 - 3.25411i) q^{72} +(6.46681 - 14.1603i) q^{73} +(-6.51080 - 6.20803i) q^{74} +(-0.200976 - 0.180682i) q^{75} +(0.146050 + 0.757780i) q^{76} +(-7.61447 + 19.0200i) q^{77} +(-1.24156 - 0.523567i) q^{78} +(0.120169 - 0.623495i) q^{79} +(-6.09728 - 3.91849i) q^{80} +(4.67113 + 7.69289i) q^{81} +(9.17657 - 10.5903i) q^{82} +(1.59516 + 6.57534i) q^{83} +(0.0491189 + 1.67452i) q^{84} +(-2.59318 + 0.499795i) q^{85} +(3.21447 + 0.306944i) q^{86} +(-1.49613 - 1.79177i) q^{87} +(1.85221 + 19.3973i) q^{88} +(0.587972 - 4.08944i) q^{89} +(2.89987 + 8.08834i) q^{90} +1.88658i q^{91} +(1.07537 - 1.00194i) q^{92} +(6.17635 + 4.57053i) q^{93} +(-0.247848 - 5.20297i) q^{94} +(3.42588 - 4.35636i) q^{95} +(1.44011 + 2.60308i) q^{96} +(13.2198 - 13.8646i) q^{97} +(-3.50360 + 1.60004i) q^{98} +(10.3476 - 16.4992i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23}+ \cdots + 242 q^{99}+O(q^{100}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.596316	+	1.15669i	−0.421659	+	0.817904i	0.578339	+	0.815797i	$0.303701\pi$
$2$	−0.596316	+	1.15669i	−0.421659	+	0.817904i	−0.999998	+	0.00210760i	$0.999329\pi$
$3$	−1.67548	−	0.439038i	−0.967341	−	0.253479i
$3$	−1.67548	−	0.439038i	−0.967341	−	0.253479i
$4$	0.177772	+	0.249645i	0.0888858	+	0.124823i
$5$	0.518882	−	2.13886i	0.232051	−	0.956528i	−0.729954	−	0.683496i	$-0.760458\pi$
$5$	0.518882	−	2.13886i	0.232051	−	0.956528i	0.962005	−	0.273032i	$-0.0880264\pi$
$6$	1.50695	−	1.67621i	0.615209	−	0.684311i
$7$	−2.98233	−	1.03220i	−1.12722	−	0.390133i	−0.301077	−	0.953600i	$-0.597346\pi$
$7$	−2.98233	−	1.03220i	−1.12722	−	0.390133i	−0.826139	+	0.563467i	$0.809467\pi$
$8$	−2.97099	+	0.427164i	−1.05040	+	0.151025i
$9$	2.61449	+	1.47120i	0.871497	+	0.490400i
$10$	2.16459	+	1.87562i	0.684502	+	0.593124i
$11$	0.308894	−	6.48448i	0.0931349	−	1.95514i	−0.158590	−	0.987344i	$-0.550695\pi$
$11$	0.308894	−	6.48448i	0.0931349	−	1.95514i	0.251725	−	0.967799i	$-0.419002\pi$
$12$	−0.188250	−	0.496325i	−0.0543430	−	0.143277i
$13$	−0.195519	−	0.564915i	−0.0542272	−	0.156679i	0.914634	−	0.404282i	$-0.132479\pi$
$13$	−0.195519	−	0.564915i	−0.0542272	−	0.156679i	−0.968862	+	0.247603i	$0.920357\pi$
$14$	2.97234	−	2.83412i	0.794392	−	0.757451i
$15$	−1.80842	+	3.35582i	−0.466932	+	0.866469i
$16$	1.07708	−	3.11201i	0.269269	−	0.778002i
$17$	−0.498465	−	1.09149i	−0.120896	−	0.264724i	0.839503	−	0.543356i	$-0.182846\pi$
$17$	−0.498465	−	1.09149i	−0.120896	−	0.264724i	−0.960398	+	0.278631i	$0.910119\pi$
$18$	−3.26079	+	2.14686i	−0.768575	+	0.506020i
$19$	2.29054	+	1.04605i	0.525485	+	0.239981i	0.660451	−	0.750869i	$-0.270365\pi$
$19$	2.29054	+	1.04605i	0.525485	+	0.239981i	−0.134966	+	0.990850i	$0.543092\pi$
$20$	0.626199	−	0.250692i	0.140022	−	0.0560565i
$21$	4.54368	+	3.03878i	0.991512	+	0.663117i
$22$	7.31634	+	4.22409i	1.55985	+	0.900579i
$23$	−0.627719	−	4.75457i	−0.130888	−	0.991397i
$23$	−0.627719	−	4.75457i	−0.130888	−	0.991397i
$24$	5.16539	+	0.588671i	1.05438	+	0.120162i
$25$	0.138686	+	0.0714977i	0.0277372	+	0.0142995i
$26$	0.770024	+	0.110713i	0.151014	+	0.0217125i
$27$	−3.73463	−	3.61283i	−0.718729	−	0.695290i
$28$	−0.272491	−	0.928020i	−0.0514960	−	0.175379i
$29$	1.09780	+	0.781740i	0.203856	+	0.145165i	0.677426	−	0.735591i	$-0.263095\pi$
$29$	1.09780	+	0.781740i	0.203856	+	0.145165i	−0.473570	+	0.880756i	$0.657035\pi$
$30$	−2.80326	−	4.09291i	−0.511803	−	0.747260i
$31$	−4.11834	−	1.64873i	−0.739675	−	0.296121i	−0.0289400	−	0.999581i	$-0.509213\pi$
$31$	−4.11834	−	1.64873i	−0.739675	−	0.296121i	−0.710735	+	0.703460i	$0.751637\pi$
$32$	−1.18525	−	1.24305i	−0.209524	−	0.219742i
$33$	−3.36448	+	10.7290i	−0.585680	+	1.86768i
$34$	1.55976	+	0.0743003i	0.267496	+	0.0127424i
$35$	−3.75520	+	5.84321i	−0.634745	+	0.987683i
$36$	0.0975040	+	0.914233i	0.0162507	+	0.152372i
$37$	−1.94758	+	6.63286i	−0.320181	+	1.09044i	0.629444	+	0.777046i	$0.283283\pi$
$37$	−1.94758	+	6.63286i	−0.320181	+	1.09044i	−0.949625	+	0.313390i	$0.898535\pi$
$38$	−2.57584	+	2.02567i	−0.417857	+	0.328606i
$39$	0.0795699	+	1.03235i	0.0127414	+	0.165308i
$40$	−0.627950	+	6.57619i	−0.0992876	+	1.03979i
$41$	−10.4645	−	2.53865i	−1.63428	−	0.396471i	−0.689526	−	0.724261i	$-0.742181\pi$
$41$	−10.4645	−	2.53865i	−1.63428	−	0.396471i	−0.944751	+	0.327790i	$0.893696\pi$
$42$	−6.22440	+	3.44356i	−0.960446	+	0.531352i
$43$	−0.922216	−	2.30358i	−0.140637	−	0.351293i	0.841282	−	0.540596i	$-0.181801\pi$
$43$	−0.922216	−	2.30358i	−0.140637	−	0.351293i	−0.981919	+	0.189303i	$0.939377\pi$
$44$	1.67373	−	1.07564i	0.252324	−	0.162159i
$45$	4.50331	−	4.82866i	0.671314	−	0.719814i
$46$	5.87389	+	2.10915i	0.866058	+	0.310977i
$47$	−3.46639	+	2.00132i	−0.505625	+	0.291923i	−0.731034	−	0.682342i	$-0.760962\pi$
$47$	−3.46639	+	2.00132i	−0.505625	+	0.291923i	0.225408	+	0.974264i	$0.427628\pi$
$48$	−3.17091	+	4.74124i	−0.457682	+	0.684340i
$49$	2.32651	+	1.82958i	0.332358	+	0.261369i
$50$	−0.165401	+	0.117782i	−0.0233913	+	0.0166569i
$51$	0.355966	+	2.04761i	0.0498453	+	0.286723i
$52$	0.106271	−	0.149236i	0.0147371	−	0.0206954i
$53$	6.44700	+	7.44024i	0.885564	+	1.02199i	0.999593	+	0.0285176i	$0.00907867\pi$
$53$	6.44700	+	7.44024i	0.885564	+	1.02199i	−0.114030	+	0.993477i	$0.536376\pi$
$54$	6.40595	−	2.16542i	0.871739	−	0.294676i
$55$	−13.7091	−	4.02536i	−1.84854	−	0.542780i
$56$	9.30140	+	1.79270i	1.24295	+	0.239559i
$57$	−3.37850	−	2.75828i	−0.447493	−	0.365343i
$58$	−1.55887	+	0.803652i	−0.204689	+	0.105525i
$59$	3.80878	−	1.31823i	0.495860	−	0.171619i	−0.0676806	−	0.997707i	$-0.521560\pi$
$59$	3.80878	−	1.31823i	0.495860	−	0.171619i	0.563541	+	0.826088i	$0.309439\pi$
$60$	−1.15925	+	0.145106i	−0.149659	+	0.0187331i
$61$	−1.30693	−	1.66190i	−0.167336	−	0.212785i	0.695152	−	0.718863i	$-0.255337\pi$
$61$	−1.30693	−	1.66190i	−0.167336	−	0.212785i	−0.862488	+	0.506078i	$0.831095\pi$
$62$	4.36290	−	3.78048i	0.554089	−	0.480121i
$63$	−6.27872	−	7.08628i	−0.791044	−	0.892787i
$64$	8.46407	−	2.48528i	1.05801	−	0.310660i
$65$	−1.30973	+	0.125064i	−0.162452	+	0.0155123i
$66$	−10.4039	−	10.2895i	−1.28063	−	1.26656i
$67$	6.95211	−	0.331170i	0.849335	−	0.0404588i	0.381600	−	0.924328i	$-0.375373\pi$
$67$	6.95211	−	0.331170i	0.849335	−	0.0404588i	0.467735	+	0.883869i	$0.345070\pi$
$68$	0.183871	−	0.318475i	0.0222977	−	0.0386207i
$69$	−1.03570	+	8.24180i	−0.124684	+	0.992196i
$70$	−4.51950	−	7.82801i	−0.540184	−	0.935626i
$71$	5.22568	+	8.13132i	0.620174	+	0.965010i	0.999214	+	0.0396298i	$0.0126179\pi$
$71$	5.22568	+	8.13132i	0.620174	+	0.965010i	−0.379040	+	0.925380i	$0.623746\pi$
$72$	−8.39607	−	3.25411i	−0.989487	−	0.383500i
$73$	6.46681	−	14.1603i	0.756882	−	1.65734i	0.00329427	−	0.999995i	$-0.498951\pi$
$73$	6.46681	−	14.1603i	0.756882	−	1.65734i	0.753588	−	0.657347i	$-0.228321\pi$
$74$	−6.51080	−	6.20803i	−0.756865	−	0.721669i
$75$	−0.200976	−	0.180682i	−0.0232067	−	0.0208633i
$76$	0.146050	+	0.757780i	0.0167531	+	0.0869234i
$77$	−7.61447	+	19.0200i	−0.867749	+	2.16753i
$78$	−1.24156	−	0.523567i	−0.140578	−	0.0592823i
$79$	0.120169	−	0.623495i	0.0135200	−	0.0701486i	−0.974542	−	0.224205i	$-0.928022\pi$
$79$	0.120169	−	0.623495i	0.0135200	−	0.0701486i	0.988062	+	0.154056i	$0.0492337\pi$
$80$	−6.09728	−	3.91849i	−0.681697	−	0.438100i
$81$	4.67113	+	7.69289i	0.519015	+	0.854765i
$82$	9.17657	−	10.5903i	1.01338	−	1.16951i
$83$	1.59516	+	6.57534i	0.175092	+	0.721737i	0.989871	+	0.141967i	$0.0453427\pi$
$83$	1.59516	+	6.57534i	0.175092	+	0.721737i	−0.814780	+	0.579771i	$0.803142\pi$
$84$	0.0491189	+	1.67452i	0.00535931	+	0.182705i
$85$	−2.59318	+	0.499795i	−0.281270	+	0.0542104i
$86$	3.21447	+	0.306944i	0.346625	+	0.0330987i
$87$	−1.49613	−	1.79177i	−0.160402	−	0.192098i
$88$	1.85221	+	19.3973i	0.197447	+	2.06776i
$89$	0.587972	−	4.08944i	0.0623249	−	0.433479i	−0.934638	−	0.355601i	$-0.884276\pi$
$89$	0.587972	−	4.08944i	0.0623249	−	0.433479i	0.996963	−	0.0778785i	$-0.0248146\pi$
$90$	2.89987	+	8.08834i	0.305673	+	0.852586i
$91$			1.88658i			0.197767i
$92$	1.07537	−	1.00194i	0.112115	−	0.104459i
$93$	6.17635	+	4.57053i	0.640457	+	0.473942i
$94$	−0.247848	−	5.20297i	−0.0255635	−	0.536645i
$95$	3.42588	−	4.35636i	0.351488	−	0.446953i
$96$	1.44011	+	2.60308i	0.146981	+	0.265675i
$97$	13.2198	−	13.8646i	1.34227	−	1.40773i	0.502720	−	0.864449i	$-0.332333\pi$
$97$	13.2198	−	13.8646i	1.34227	−	1.40773i	0.839550	−	0.543283i	$-0.182819\pi$
$98$	−3.50360	+	1.60004i	−0.353917	+	0.161628i
$99$	10.3476	−	16.4992i	1.03997	−	1.65823i
$100$	0.00680540	+	0.0473326i	0.000680540	+	0.00473326i
$101$	2.27892	−	0.552859i	0.226761	−	0.0550115i	−0.120769	−	0.992681i	$-0.538536\pi$
$101$	2.27892	−	0.552859i	0.226761	−	0.0550115i	0.347529	+	0.937669i	$0.387021\pi$
$102$	−2.58072	−	0.809280i	−0.255530	−	0.0801307i
$103$	1.72115	+	3.33856i	0.169590	+	0.328958i	0.958279	−	0.285834i	$-0.0922704\pi$
$103$	1.72115	+	3.33856i	0.169590	+	0.328958i	−0.788690	+	0.614792i	$0.789240\pi$
$104$	0.822197	+	1.59484i	0.0806230	+	0.156387i
$105$	8.85717	−	8.14153i	0.864371	−	0.794532i
$106$	−12.4505	+	3.02046i	−1.20930	+	0.293373i
$107$	−2.28352	−	15.8822i	−0.220756	−	1.53539i	−0.735190	−	0.677861i	$-0.762907\pi$
$107$	−2.28352	−	15.8822i	−0.220756	−	1.53539i	0.514434	−	0.857530i	$-0.328002\pi$
$108$	0.238017	−	1.57459i	0.0229032	−	0.151515i
$109$	−2.88148	+	1.31593i	−0.275996	+	0.126043i	−0.548605	−	0.836082i	$-0.684841\pi$
$109$	−2.88148	+	1.31593i	−0.275996	+	0.126043i	0.272609	+	0.962125i	$0.412114\pi$
$110$	12.8311	−	13.4568i	1.22339	−	1.28306i
$111$	6.17522	−	10.2582i	0.586126	−	0.973664i
$112$	−6.42440	+	8.16929i	−0.607049	+	0.771926i
$113$	0.759182	+	15.9372i	0.0714179	+	1.49925i	0.695862	+	0.718176i	$0.255023\pi$
$113$	0.759182	+	15.9372i	0.0714179	+	1.49925i	−0.624444	+	0.781070i	$0.714674\pi$
$114$	5.20513	−	2.26308i	0.487505	−	0.211957i
$115$	−10.4951	−	1.12446i	−0.978672	−	0.104856i
$116$			0.413032i			0.0383490i
$117$	0.319921	−	1.76461i	0.0295767	−	0.163139i
$118$	−0.746448	+	5.19166i	−0.0687161	+	0.477931i
$119$	0.359961	+	3.76969i	0.0329976	+	0.345567i
$120$	3.93931	−	10.7426i	0.359608	−	0.980661i
$121$	−31.0028	−	2.96041i	−2.81844	−	0.269128i
$122$	2.70165	−	0.520701i	0.244596	−	0.0471420i
$123$	16.4185	+	8.84777i	1.48041	+	0.797777i
$124$	−0.320525	−	1.32122i	−0.0287840	−	0.118649i
$125$	7.43131	−	8.57618i	0.664676	−	0.767077i
$126$	11.9407	−	3.03688i	1.06376	−	0.270547i
$127$	13.6862	+	8.79556i	1.21445	+	0.780480i	0.981398	−	0.191984i	$-0.0614922\pi$
$127$	13.6862	+	8.79556i	1.21445	+	0.780480i	0.233053	+	0.972464i	$0.425129\pi$
$128$	−1.52247	+	7.89931i	−0.134568	+	0.698207i
$129$	0.533798	+	4.26451i	0.0469983	+	0.375469i
$130$	0.636351	−	1.58953i	0.0558117	−	0.139411i
$131$	−0.659018	−	3.41931i	−0.0575787	−	0.298747i	0.941711	−	0.336422i	$-0.109217\pi$
$131$	−0.659018	−	3.41931i	−0.0575787	−	0.298747i	−0.999290	+	0.0376753i	$0.988005\pi$
$132$	−3.27656	+	1.06739i	−0.285188	+	0.0929043i
$133$	−5.75141	−	5.48396i	−0.498711	−	0.475520i
$134$	−3.76259	+	8.23892i	−0.325038	+	0.711734i
$135$	−9.66518	+	6.11321i	−0.831847	+	0.526142i
$136$	1.94718	+	3.02987i	0.166969	+	0.259809i
$137$	−4.67568	−	8.09851i	−0.399470	−	0.691902i	0.594191	−	0.804324i	$-0.297473\pi$
$137$	−4.67568	−	8.09851i	−0.399470	−	0.691902i	−0.993661	+	0.112422i	$0.964139\pi$
$138$	−8.91561	−	6.11271i	−0.758948	−	0.520348i
$139$	−8.26326	+	14.3124i	−0.700880	+	1.21396i	0.267277	+	0.963620i	$0.413876\pi$
$139$	−8.26326	+	14.3124i	−0.700880	+	1.21396i	−0.968158	+	0.250341i	$0.919457\pi$
$140$	−2.12630	+	0.101288i	−0.179705	+	0.00856040i
$141$	6.68654	−	1.83131i	0.563108	−	0.154224i
$142$	−12.5216	+	1.19567i	−1.05079	+	0.100338i
$143$	−3.72357	+	1.09334i	−0.311381	+	0.0914297i
$144$	7.39440	−	6.55173i	0.616200	−	0.545977i
$145$	2.24166	−	1.94241i	0.186160	−	0.161308i
$146$	12.5229	+	15.9241i	1.03640	+	1.31789i
$147$	−3.09477	−	4.08686i	−0.255252	−	0.337079i
$148$	−2.00209	+	0.692929i	−0.164571	+	0.0569584i
$149$	11.2613	−	5.80558i	0.922558	−	0.475612i	0.0695904	−	0.997576i	$-0.477831\pi$
$149$	11.2613	−	5.80558i	0.922558	−	0.475612i	0.852968	+	0.521964i	$0.174800\pi$
$150$	0.328838	−	0.124724i	0.0268495	−	0.0101837i
$151$	−0.616713	−	0.118862i	−0.0501874	−	0.00967283i	0.164096	−	0.986444i	$-0.447529\pi$
$151$	−0.616713	−	0.118862i	−0.0501874	−	0.00967283i	−0.214283	+	0.976772i	$0.568742\pi$
$152$	−7.25200	−	2.12938i	−0.588215	−	0.172715i
$153$	0.302563	−	3.58702i	0.0244608	−	0.289994i
$154$	−17.4597	−	20.1495i	−1.40694	−	1.62370i
$155$	−5.66334	+	7.95305i	−0.454891	+	0.638804i
$156$	−0.243575	+	0.203386i	−0.0195016	+	0.0162839i
$157$	14.6197	−	10.4106i	1.16678	−	0.830859i	0.178563	−	0.983929i	$-0.442855\pi$
$157$	14.6197	−	10.4106i	1.16678	−	0.830859i	0.988215	+	0.153070i	$0.0489159\pi$
$158$	0.649532	+	0.510798i	0.0516740	+	0.0406369i
$159$	−7.53530	−	15.2965i	−0.597588	−	1.21309i
$160$	−3.27371	+	1.89008i	−0.258810	+	0.149424i
$161$	−3.03558	+	14.8276i	−0.239237	+	1.16858i
$162$	−11.6838	+	0.815671i	−0.917963	+	0.0640852i
$163$	−14.6959	+	9.44451i	−1.15108	+	0.739751i	−0.969853	−	0.243691i	$-0.921642\pi$
$163$	−14.6959	+	9.44451i	−1.15108	+	0.739751i	−0.181222	+	0.983442i	$0.558005\pi$
$164$	−1.22652	−	3.06371i	−0.0957754	−	0.239235i
$165$	21.2021	+	12.7632i	1.65058	+	0.993617i
$166$	−8.55686	−	2.07587i	−0.664141	−	0.161119i
$167$	0.945799	−	9.90486i	0.0731881	−	0.766461i	−0.882154	−	0.470960i	$-0.843908\pi$
$167$	0.945799	−	9.90486i	0.0731881	−	0.766461i	0.955343	−	0.295501i	$-0.0954864\pi$
$168$	−14.7973	−	7.08730i	−1.14163	−	0.546797i
$169$	9.93779	−	7.81516i	0.764445	−	0.601166i
$170$	0.968247	−	3.29755i	0.0742612	−	0.252910i
$171$	4.44964	+	6.10474i	0.340272	+	0.466841i
$172$	0.411135	−	0.639739i	0.0313488	−	0.0487796i
$173$	−5.40029	−	0.257247i	−0.410576	−	0.0195582i	−0.158722	−	0.987323i	$-0.550737\pi$
$173$	−5.40029	−	0.257247i	−0.410576	−	0.0195582i	−0.251854	+	0.967765i	$0.581040\pi$
$174$	2.96469	−	0.662104i	0.224753	−	0.0501940i
$175$	−0.339808	−	0.356381i	−0.0256871	−	0.0269399i
$176$	−19.8471	−	7.94556i	−1.49603	−	0.598919i
$177$	−6.96029	+	0.536477i	−0.523168	+	0.0403241i
$178$	4.37960	+	3.11870i	0.328265	+	0.233756i
$179$	0.302687	+	1.03086i	0.0226239	+	0.0770500i	0.970031	−	0.242980i	$-0.0781251\pi$
$179$	0.302687	+	1.03086i	0.0226239	+	0.0770500i	−0.947407	+	0.320030i	$0.896307\pi$
$180$	2.00601	+	0.265832i	0.149519	+	0.0198139i
$181$	16.7056	+	2.40190i	1.24172	+	0.178532i	0.731696	−	0.681631i	$-0.238729\pi$
$181$	16.7056	+	2.40190i	1.24172	+	0.178532i	0.510020	+	0.860163i	$0.329638\pi$
$182$	−2.18219	−	1.12500i	−0.161755	−	0.0833903i
$183$	1.46011	+	3.35828i	0.107934	+	0.248251i
$184$	3.89593	+	13.8577i	0.287212	+	1.02160i
$185$	13.1762	+	7.60728i	0.968734	+	0.559299i
$186$	−8.96975	+	4.41865i	−0.657694	+	0.323991i
$187$	−7.23169	+	2.89513i	−0.528833	+	0.211713i
$188$	−1.11585	−	0.509590i	−0.0813815	−	0.0371657i
$189$	7.40874	+	14.6295i	0.538907	+	1.06414i
$190$	2.99606	+	6.56046i	0.217357	+	0.475946i
$191$	−3.37669	+	9.75631i	−0.244329	+	0.705942i	0.754441	+	0.656367i	$0.227908\pi$
$191$	−3.37669	+	9.75631i	−0.244329	+	0.705942i	−0.998770	+	0.0495748i	$0.984213\pi$
$192$	−15.2725	+	0.447993i	−1.10220	+	0.0323311i
$193$	11.5612	−	11.0236i	0.832197	−	0.793498i	−0.148525	−	0.988909i	$-0.547453\pi$
$193$	11.5612	−	11.0236i	0.832197	−	0.793498i	0.980721	+	0.195411i	$0.0626040\pi$
$194$	8.15382	+	23.5589i	0.585410	+	1.69143i
$195$	2.24933	+	0.365477i	0.161078	+	0.0261724i
$196$	−0.0431605	+	0.906050i	−0.00308289	+	0.0647178i
$197$	1.12307	+	0.973149i	0.0800157	+	0.0693340i	0.693950	−	0.720023i	$-0.255869\pi$
$197$	1.12307	+	0.973149i	0.0800157	+	0.0693340i	−0.613935	+	0.789357i	$0.710414\pi$
$198$	12.9140	+	21.8077i	0.917760	+	1.54980i
$199$	−0.536313	+	0.0771102i	−0.0380182	+	0.00546620i	−0.161298	−	0.986906i	$-0.551568\pi$
$199$	−0.536313	+	0.0771102i	−0.0380182	+	0.00546620i	0.123279	+	0.992372i	$0.460659\pi$
$200$	−0.442576	−	0.153177i	−0.0312949	−	0.0108313i
$201$	−11.7935	−	2.49737i	−0.831852	−	0.176151i
$202$	−0.719466	+	2.96568i	−0.0506215	+	0.208664i
$203$	−2.46710	−	3.46455i	−0.173156	−	0.243164i
$204$	−0.447896	+	0.452873i	−0.0313590	+	0.0317074i
$205$	−10.8597	+	21.0648i	−0.758472	+	1.47123i
$206$	−4.88803			−0.340565
$207$	5.35377	−	13.3543i	0.372113	−	0.928188i
$208$	−1.96861			−0.136499
$209$	7.49064	−	14.5298i	0.518138	−	1.00505i
$210$	4.13556	+	15.0999i	0.285381	+	1.04199i
$211$	2.57338	+	3.61381i	0.177159	+	0.248785i	0.893601	−	0.448861i	$-0.148170\pi$
$211$	2.57338	+	3.61381i	0.177159	+	0.248785i	−0.716443	+	0.697646i	$0.754231\pi$
$212$	−0.711326	+	2.93213i	−0.0488541	+	0.201379i
$213$	−5.18559	−	15.9182i	−0.355311	−	1.09069i
$214$	19.7325	+	6.82949i	1.34889	+	0.466854i
$215$	−5.40557	+	0.777204i	−0.368657	+	0.0530049i
$216$	12.6388	+	9.13840i	0.859962	+	0.621789i
$217$	10.5804	+	9.16799i	0.718246	+	0.622364i
$218$	0.196150	−	4.11770i	0.0132850	−	0.278886i
$219$	−17.0519	+	20.8862i	−1.15226	+	1.41136i
$220$	−1.43218	−	4.13801i	−0.0965575	−	0.278985i
$221$	−0.519138	+	0.494997i	−0.0349210	+	0.0332971i
$222$	8.18317	+	13.2599i	0.549219	+	0.889949i
$223$	4.89928	−	14.1555i	0.328080	−	0.947925i	−0.653509	−	0.756919i	$-0.726704\pi$
$223$	4.89928	−	14.1555i	0.328080	−	0.947925i	0.981589	−	0.191006i	$-0.0611750\pi$
$224$	2.25173	+	4.93059i	0.150450	+	0.329439i
$225$	0.257406	+	0.390965i	0.0171604	+	0.0260643i
$226$	−18.8871	−	8.62546i	−1.25635	−	0.573757i
$227$	−25.6064	+	10.2513i	−1.69956	+	0.680400i	−0.999435	−	0.0336211i	$-0.989296\pi$
$227$	−25.6064	+	10.2513i	−1.69956	+	0.680400i	−0.700124	+	0.714022i	$0.746872\pi$
$228$	0.0879894	−	1.33377i	0.00582724	−	0.0883311i
$229$	−7.92689	−	4.57659i	−0.523824	−	0.302430i	0.214674	−	0.976686i	$-0.431131\pi$
$229$	−7.92689	−	4.57659i	−0.523824	−	0.302430i	−0.738498	+	0.674256i	$0.764464\pi$
$230$	7.55904	−	11.4690i	0.498428	−	0.756246i
$231$	21.1084	−	28.5247i	1.38883	−	1.87679i
$232$	−3.59548	−	1.85360i	−0.236055	−	0.121695i
$233$	−4.56708	−	0.656647i	−0.299199	−	0.0430183i	−0.00891957	−	0.999960i	$-0.502839\pi$
$233$	−4.56708	−	0.656647i	−0.299199	−	0.0430183i	−0.290280	+	0.956942i	$0.593748\pi$
$234$	1.85034	+	1.42232i	0.120961	+	0.0929798i
$235$	2.48190	+	8.45258i	0.161901	+	0.551386i
$236$	1.00618	+	0.716499i	0.0654969	+	0.0466401i
$237$	−0.475079	+	0.991897i	−0.0308597	+	0.0644306i
$238$	−4.57502	−	1.83156i	−0.296554	−	0.118722i
$239$	2.61416	+	2.74165i	0.169096	+	0.177343i	0.802829	−	0.596209i	$-0.203327\pi$
$239$	2.61416	+	2.74165i	0.169096	+	0.177343i	−0.633734	+	0.773551i	$0.718478\pi$
$240$	8.49554	+	9.24230i	0.548384	+	0.596588i
$241$	1.69760	+	0.0808665i	0.109352	+	0.00520907i	0.102186	−	0.994765i	$-0.467416\pi$
$241$	1.69760	+	0.0808665i	0.109352	+	0.00520907i	0.00716533	+	0.999974i	$0.497719\pi$
$242$	21.9118	−	34.0954i	1.40854	−	2.19173i
$243$	−4.44894	−	14.9401i	−0.285400	−	0.958409i
$244$	0.182550	−	0.621708i	0.0116866	−	0.0398008i
$245$	5.12041	−	4.02674i	0.327131	−	0.257259i
$246$	−20.0248	+	13.7151i	−1.27673	+	0.874441i
$247$	0.143088	−	1.49848i	0.00910446	−	0.0953462i
$248$	12.9398	+	3.13916i	0.821679	+	0.199337i
$249$	0.214157	−	11.7172i	0.0135717	−	0.742548i
$250$	5.48859	+	13.7098i	0.347129	+	0.867087i
$251$	17.5086	−	11.2521i	1.10514	−	0.710227i	0.144908	−	0.989445i	$-0.453711\pi$
$251$	17.5086	−	11.2521i	1.10514	−	0.710227i	0.960228	+	0.279218i	$0.0900751\pi$
$252$	0.652878	−	2.82719i	0.0411274	−	0.178096i
$253$	−31.0248	+	2.60177i	−1.95051	+	0.163572i
$254$	−18.3350	+	10.5857i	−1.15044	+	0.664208i
$255$	4.56426	+	0.301107i	0.285825	+	0.0188560i
$256$	5.63899	+	4.43455i	0.352437	+	0.277160i
$257$	−20.1424	+	14.3433i	−1.25645	+	0.894712i	−0.997464	−	0.0711700i	$-0.977327\pi$
$257$	−20.1424	+	14.3433i	−1.25645	+	0.894712i	−0.258983	+	0.965882i	$0.583387\pi$
$258$	−5.25103	−	1.92555i	−0.326915	−	0.119880i
$259$	12.6547	−	17.7711i	0.786328	−	1.10424i
$260$	−0.264054	−	0.304734i	−0.0163759	−	0.0188988i
$261$	1.72009	+	3.65894i	0.106471	+	0.226482i
$262$	4.34807	+	1.27671i	0.268625	+	0.0788754i
$263$	11.7423	+	2.26314i	0.724060	+	0.139551i	0.537949	−	0.842978i	$-0.319199\pi$
$263$	11.7423	+	2.26314i	0.724060	+	0.139551i	0.186111	+	0.982529i	$0.440412\pi$
$264$	5.41278	−	33.3130i	0.333133	−	2.05027i
$265$	19.2589	−	9.92864i	1.18306	−	0.609911i
$266$	9.77290	−	3.38244i	0.599215	−	0.207390i
$267$	−2.78055	+	6.59364i	−0.170167	+	0.403524i
$268$	1.31856	+	1.67669i	0.0805440	+	0.102420i
$269$	−6.61353	+	5.73066i	−0.403234	+	0.349404i	−0.832744	−	0.553658i	$-0.813232\pi$
$269$	−6.61353	+	5.73066i	−0.403234	+	0.349404i	0.429510	+	0.903062i	$0.358686\pi$
$270$	−1.30760	−	14.8250i	−0.0795779	−	0.902223i
$271$	−2.25292	+	0.661517i	−0.136855	+	0.0401843i	−0.349443	−	0.936958i	$-0.613629\pi$
$271$	−2.25292	+	0.661517i	−0.136855	+	0.0401843i	0.212588	+	0.977142i	$0.431811\pi$
$272$	−3.93360	+	0.375613i	−0.238510	+	0.0227749i
$273$	0.828279	−	3.16093i	0.0501297	−	0.191308i
$274$	12.1557	−	0.579045i	0.734350	−	0.0349814i
$275$	0.506464	−	0.877222i	0.0305409	−	0.0528984i
$276$	−2.24165	+	1.20660i	−0.134931	+	0.0726288i
$277$	6.88982	+	11.9335i	0.413969	+	0.717015i	0.995320	−	0.0966379i	$-0.0308089\pi$
$277$	6.88982	+	11.9335i	0.413969	+	0.717015i	−0.581351	+	0.813653i	$0.697476\pi$
$278$	−11.6275	−	18.0927i	−0.697371	−	1.08513i
$279$	−8.34174	−	10.3695i	−0.499407	−	0.620806i
$280$	8.66066	−	18.9642i	0.517574	−	1.13333i
$281$	−9.57905	−	9.13361i	−0.571438	−	0.544865i	0.348307	−	0.937380i	$-0.386757\pi$
$281$	−9.57905	−	9.13361i	−0.571438	−	0.544865i	−0.919746	+	0.392515i	$0.871605\pi$
$282$	−1.86903	+	8.82630i	−0.111299	+	0.525598i
$283$	−1.14175	−	5.92399i	−0.0678703	−	0.352144i	0.932079	−	0.362256i	$-0.117993\pi$
$283$	−1.14175	−	5.92399i	−0.0678703	−	0.352144i	−0.999949	+	0.0101117i	$0.996781\pi$
$284$	−1.10097	+	2.75008i	−0.0653304	+	0.163187i
$285$	−7.65262	+	5.79492i	−0.453302	+	0.343262i
$286$	0.955769	−	4.95900i	0.0565158	−	0.293232i
$287$	28.5882	+	18.3725i	1.68751	+	1.08449i
$288$	−1.27004	−	4.99368i	−0.0748377	−	0.294255i
$289$	10.1898	−	11.7596i	0.599398	−	0.691742i
$290$	0.910032	+	3.75120i	0.0534389	+	0.220278i
$291$	−28.2367	+	17.4258i	−1.65526	+	1.02152i
$292$	4.68467	−	0.902897i	0.274150	−	0.0528380i
$293$	−17.7377	−	1.69375i	−1.03625	−	0.0989497i	−0.436958	−	0.899482i	$-0.643944\pi$
$293$	−17.7377	−	1.69375i	−1.03625	−	0.0989497i	−0.599290	+	0.800532i	$0.704550\pi$
$294$	6.57270	−	1.14263i	0.383328	−	0.0666395i
$295$	−0.843206	−	8.83045i	−0.0490933	−	0.514129i
$296$	2.95293	−	20.5381i	0.171636	−	1.19375i
$297$	−24.5809	+	23.1011i	−1.42633	+	1.34046i
$298$			16.4878i			0.955110i
$299$	−2.56320	+	1.28422i	−0.148234	+	0.0742682i
$300$	0.00937845	−	0.0822928i	0.000541465	−	0.00475118i
$301$	0.372606	+	7.82196i	0.0214766	+	0.450850i
$302$	0.505242	−	0.642468i	0.0290734	−	0.0369699i
$303$	−4.06101	−	0.0742237i	−0.233299	−	0.00426404i
$304$	5.72241	−	6.00149i	0.328203	−	0.344209i
$305$	−4.23272	+	1.93302i	−0.242365	+	0.110684i
$306$	3.96866	+	2.48897i	0.226873	+	0.142285i
$307$	−2.61309	−	18.1744i	−0.149137	−	1.03727i	−0.917637	−	0.397419i	$-0.869906\pi$
$307$	−2.61309	−	18.1744i	−0.149137	−	1.03727i	0.768501	−	0.639849i	$-0.221003\pi$
$308$	−6.10190	+	1.48030i	−0.347688	+	0.0843481i
$309$	−1.41800	−	6.34935i	−0.0806672	−	0.361202i
$310$	−5.82209	−	11.2933i	−0.330672	−	0.641415i
$311$	−8.20400	−	15.9135i	−0.465206	−	0.902374i	−0.998409	−	0.0563863i	$-0.982042\pi$
$311$	−8.20400	−	15.9135i	−0.465206	−	0.902374i	0.533203	−	0.845987i	$-0.320988\pi$
$312$	−0.677383	−	3.03310i	−0.0383493	−	0.171716i
$313$	3.45078	−	0.837150i	0.195050	−	0.0473185i	−0.137044	−	0.990565i	$-0.543760\pi$
$313$	3.45078	−	0.837150i	0.195050	−	0.0473185i	0.332094	+	0.943246i	$0.392245\pi$
$314$	3.32394	+	23.1185i	0.187581	+	1.30465i
$315$	−18.4145	+	9.75236i	−1.03754	+	0.549483i
$316$	0.177015	−	0.0808401i	0.00995788	−	0.00454761i
$317$	11.2173	−	11.7644i	0.630028	−	0.660754i	−0.328913	−	0.944360i	$-0.606682\pi$
$317$	11.2173	−	11.7644i	0.630028	−	0.660754i	0.958941	+	0.283606i	$0.0915308\pi$
$318$	22.1867	+	0.405510i	1.24417	+	0.0227399i
$319$	5.40828	−	6.87718i	0.302805	−	0.385048i
$320$	−0.923805	−	19.3931i	−0.0516423	−	1.08410i
$321$	−3.14689	+	27.6129i	−0.175642	+	1.54120i
$322$	−15.3408	−	12.3532i	−0.854912	−	0.688416i
$323$		−	3.02151i		−	0.168121i
$324$	−1.09010	+	2.53370i	−0.0605610	+	0.140761i
$325$	0.0132743	−	0.0923251i	0.000736328	−	0.00512127i
$326$	−2.16096	−	22.6306i	−0.119684	−	1.25339i
$327$	5.40562	−	0.939739i	0.298932	−	0.0519677i
$328$	32.1743	+	3.07227i	1.77653	+	0.169638i
$329$	12.4037	−	2.39061i	0.683837	−	0.131799i
$330$	−27.4063	+	16.9134i	−1.50867	+	0.931051i
$331$	4.26991	+	17.6008i	0.234695	+	0.967427i	0.960223	+	0.279234i	$0.0900806\pi$
$331$	4.26991	+	17.6008i	0.234695	+	0.967427i	−0.725528	+	0.688193i	$0.758404\pi$
$332$	−1.35793	+	1.56713i	−0.0745260	+	0.0860076i
$333$	−14.8502	+	14.4763i	−0.813787	+	0.793295i
$334$	10.8929	+	7.00042i	0.596031	+	0.383046i
$335$	2.89900	−	15.0414i	0.158389	−	0.821801i
$336$	14.3506	−	10.8670i	0.782890	−	0.592841i
$337$	−0.00731909	+	0.0182822i	−0.000398696	+	0.000995896i	−0.928567	−	0.371164i	$-0.878959\pi$
$337$	−0.00731909	+	0.0182822i	−0.000398696	+	0.000995896i	0.928168	+	0.372160i	$0.121383\pi$
$338$	3.11367	+	16.1553i	0.169361	+	0.878730i
$339$	5.72503	−	27.0358i	0.310941	−	1.46838i
$340$	−0.585766	−	0.558526i	−0.0317676	−	0.0302903i
$341$	−11.9633	+	26.1960i	−0.647849	+	1.41859i
$342$	−9.71468	+	1.50650i	−0.525310	+	0.0814623i
$343$	6.89355	+	10.7266i	0.372217	+	0.579180i
$344$	3.72390	+	6.44999i	0.200779	+	0.347760i
$345$	17.0907	+	6.49175i	0.920131	+	0.349504i
$346$	3.51783	−	6.09306i	0.189120	−	0.327565i
$347$	27.0673	−	1.28938i	1.45305	−	0.0692173i	0.693871	−	0.720099i	$-0.255904\pi$
$347$	27.0673	−	1.28938i	1.45305	−	0.0692173i	0.759179	+	0.650882i	$0.225601\pi$
$348$	0.181336	−	0.692028i	0.00972066	−	0.0370966i
$349$	9.56755	−	0.913590i	0.512139	−	0.0489034i	0.164212	−	0.986425i	$-0.447492\pi$
$349$	9.56755	−	0.913590i	0.512139	−	0.0489034i	0.347927	+	0.937522i	$0.386886\pi$
$350$	0.614856	−	0.180538i	0.0328654	−	0.00965016i
$351$	−1.31075	+	2.81613i	−0.0699629	+	0.150314i
$352$	−8.42664	+	7.30173i	−0.449142	+	0.389183i
$353$	1.04708	+	1.33147i	0.0557303	+	0.0708669i	0.813119	−	0.582097i	$-0.197768\pi$
$353$	1.04708	+	1.33147i	0.0557303	+	0.0708669i	−0.757389	+	0.652964i	$0.773525\pi$
$354$	3.53000	−	8.37082i	0.187617	−	0.444904i
$355$	20.1033	−	6.95781i	1.06697	−	0.369282i
$356$	1.12543	−	0.580201i	0.0596478	−	0.0307506i
$357$	1.05193	−	6.47409i	0.0556738	−	0.342645i
$358$	−1.37288	−	0.264601i	−0.0725591	−	0.0139846i
$359$	−16.4266	−	4.82329i	−0.866963	−	0.254563i	−0.182140	−	0.983273i	$-0.558302\pi$
$359$	−16.4266	−	4.82329i	−0.866963	−	0.254563i	−0.684823	+	0.728709i	$0.740121\pi$
$360$	−11.3167	+	16.2695i	−0.596440	+	0.857480i
$361$	−8.29002	−	9.56720i	−0.436317	−	0.503537i
$362$	−12.7401	+	17.8909i	−0.669603	+	0.940325i
$363$	50.6450	+	18.5715i	2.65817	+	0.974753i
$364$	−0.470976	+	0.335380i	−0.0246858	+	0.0175787i
$365$	−26.9315	−	21.1792i	−1.40966	−	1.10857i
$366$	−4.75518	−	0.313701i	−0.248557	−	0.0163974i
$367$	−1.00048	+	0.577625i	−0.0522244	+	0.0301518i	−0.525885	−	0.850556i	$-0.676266\pi$
$367$	−1.00048	+	0.577625i	−0.0522244	+	0.0301518i	0.473660	+	0.880708i	$0.342932\pi$
$368$	−15.4724	−	3.16758i	−0.806554	−	0.165121i
$369$	−23.6244	−	22.0326i	−1.22984	−	1.14697i
$370$	−16.6565	+	10.7045i	−0.865928	+	0.556498i
$371$	−11.5473	−	28.8438i	−0.599507	−	1.49750i
$372$	−0.0430318	+	2.35441i	−0.00223110	+	0.122070i
$373$	−26.6429	−	6.46349i	−1.37952	−	0.334667i	−0.523680	−	0.851915i	$-0.675441\pi$
$373$	−26.6429	−	6.46349i	−1.37952	−	0.334667i	−0.855835	+	0.517248i	$0.826956\pi$
$374$	0.963597	−	10.0912i	0.0498264	−	0.521806i
$375$	−16.2163	+	11.1066i	−0.837406	+	0.573544i
$376$	9.44372	−	7.42663i	0.487023	−	0.382999i
$377$	0.226976	−	0.773009i	0.0116899	−	0.0398120i
$378$	−21.3398	−	0.154192i	−1.09760	−	0.00793078i
$379$	−2.59313	+	4.03499i	−0.133200	+	0.207264i	−0.901446	−	0.432891i	$-0.857493\pi$
$379$	−2.59313	+	4.03499i	−0.133200	+	0.207264i	0.768246	+	0.640155i	$0.221130\pi$
$380$	1.69657	+	0.0808176i	0.0870322	+	0.00414585i
$381$	−19.0694	−	20.7456i	−0.976953	−	1.06283i
$382$	−9.27147	−	9.72364i	−0.474370	−	0.497504i
$383$	6.42346	+	2.57156i	0.328223	+	0.131401i	0.529921	−	0.848047i	$-0.322222\pi$
$383$	6.42346	+	2.57156i	0.328223	+	0.131401i	−0.201698	+	0.979448i	$0.564646\pi$
$384$	6.01896	−	12.5667i	0.307154	−	0.641294i
$385$	36.7302	+	26.1555i	1.87194	+	1.33301i
$386$	5.85678	+	19.9464i	0.298102	+	1.01524i
$387$	0.977910	−	7.37947i	0.0497099	−	0.375119i
$388$	5.81133	+	0.835543i	0.295026	+	0.0424183i
$389$	26.9220	+	13.8793i	1.36500	+	0.703707i	0.976049	−	0.217551i	$-0.0698070\pi$
$389$	26.9220	+	13.8793i	1.36500	+	0.703707i	0.388952	+	0.921258i	$0.372837\pi$
$390$	−1.76406	+	2.38385i	−0.0893266	+	0.120711i
$391$	−4.87666	+	3.05513i	−0.246623	+	0.154505i
$392$	−7.69356	−	4.44188i	−0.388584	−	0.224349i
$393$	−0.397032	+	6.01834i	−0.0200276	+	0.303585i
$394$	−1.79534	+	0.718746i	−0.0904479	+	0.0362099i
$395$	−1.27122	−	0.580545i	−0.0639618	−	0.0292104i
$396$	5.95844	−	0.349861i	0.299423	−	0.0175812i
$397$	14.3943	+	31.5190i	0.722427	+	1.58189i	0.810471	+	0.585778i	$0.199211\pi$
$397$	14.3943	+	31.5190i	0.722427	+	1.58189i	−0.0880442	+	0.996117i	$0.528062\pi$
$398$	0.230619	−	0.666331i	0.0115599	−	0.0334001i
$399$	7.22873	+	11.7134i	0.361889	+	0.586402i
$400$	0.371877	−	0.354584i	0.0185938	−	0.0177292i
$401$	−5.94486	−	17.1765i	−0.296872	−	0.857755i	−0.990511	−	0.137432i	$-0.956115\pi$
$401$	−5.94486	−	17.1765i	−0.296872	−	0.857755i	0.693639	−	0.720323i	$-0.256006\pi$
$402$	9.92136	−	12.1523i	0.494832	−	0.606100i
$403$	−0.126181	+	2.64887i	−0.00628553	+	0.131950i
$404$	0.543145	+	0.470638i	0.0270225	+	0.0234151i
$405$	18.8778	−	5.99921i	0.938045	−	0.298103i
$406$	5.47858	−	0.787702i	0.271898	−	0.0390930i
$407$	42.4090	+	14.6779i	2.10214	+	0.727557i
$408$	−1.93224	−	5.93138i	−0.0956601	−	0.293647i
$409$	0.710120	−	2.92716i	0.0351132	−	0.144739i	−0.951557	−	0.307474i	$-0.900516\pi$
$409$	0.710120	−	2.92716i	0.0351132	−	0.144739i	0.986670	+	0.162735i	$0.0520316\pi$
$410$	−17.8897	−	25.1226i	−0.883509	−	1.24071i
$411$	4.27847	+	15.6217i	0.211041	+	0.770563i
$412$	−0.527484	+	1.02318i	−0.0259873	+	0.0504083i
$413$	−12.7197			−0.625896
$414$	12.2543	+	14.1560i	0.602264	+	0.695731i
$415$	14.8914			0.730992
$416$	−0.470480	+	0.912603i	−0.0230672	+	0.0447441i
$417$	20.1286	−	20.3523i	0.985703	−	0.996656i
$418$	12.3397	+	17.3287i	0.603556	+	0.847575i
$419$	−7.68040	+	31.6590i	−0.375212	+	1.54664i	0.400943	+	0.916103i	$0.368682\pi$
$419$	−7.68040	+	31.6590i	−0.375212	+	1.54664i	−0.776155	+	0.630542i	$0.782833\pi$
$420$	3.60705	+	0.763818i	0.176006	+	0.0372705i
$421$	14.2216	+	4.92215i	0.693119	+	0.239891i	0.650840	−	0.759215i	$-0.274417\pi$
$421$	14.2216	+	4.92215i	0.693119	+	0.239891i	0.0422793	+	0.999106i	$0.486538\pi$
$422$	−5.71461	+	0.821637i	−0.278183	+	0.0399966i
$423$	−12.0072	+	0.132681i	−0.583810	+	0.00645117i
$424$	−22.3322	−	19.3509i	−1.08455	−	0.939765i
$425$	0.00890853	−	0.187013i	0.000432127	−	0.00907146i
$426$	21.5047	+	3.49413i	1.04190	+	0.169291i
$427$	2.18230	+	6.30535i	0.105609	+	0.305137i
$428$	3.55897	−	3.39348i	0.172030	−	0.164030i
$429$	6.71881	−	0.197084i	0.324387	−	0.00951531i
$430$	2.32444	−	6.71604i	0.112095	−	0.323876i
$431$	5.42763	+	11.8849i	0.261440	+	0.572473i	0.994143	−	0.108075i	$-0.0344688\pi$
$431$	5.42763	+	11.8849i	0.261440	+	0.572473i	−0.732703	+	0.680549i	$0.761741\pi$
$432$	−15.2657	+	7.73089i	−0.734469	+	0.371953i
$433$	−12.7214	−	5.80966i	−0.611350	−	0.279194i	0.0855821	−	0.996331i	$-0.472725\pi$
$433$	−12.7214	−	5.80966i	−0.611350	−	0.279194i	−0.696932	+	0.717137i	$0.745452\pi$
$434$	−16.9138	+	6.77127i	−0.811889	+	0.325031i
$435$	−4.60866	+	2.27030i	−0.220968	+	0.108853i
$436$	−0.840762	−	0.485414i	−0.0402652	−	0.0232471i
$437$	3.53572	−	11.5472i	0.169137	−	0.552375i
$438$	−13.9906	−	32.1786i	−0.668496	−	1.53755i
$439$	−19.7661	−	10.1901i	−0.943385	−	0.486349i	−0.0833143	−	0.996523i	$-0.526551\pi$
$439$	−19.7661	−	10.1901i	−0.943385	−	0.486349i	−0.860071	+	0.510174i	$0.829581\pi$
$440$	42.4492	+	6.10327i	2.02368	+	0.290962i
$441$	3.39094	+	8.20619i	0.161474	+	0.390771i
$442$	−0.262989	−	0.895657i	−0.0125091	−	0.0426020i
$443$	−13.2641	−	9.44531i	−0.630195	−	0.448760i	0.219804	−	0.975544i	$-0.429458\pi$
$443$	−13.2641	−	9.44531i	−0.630195	−	0.448760i	−0.849999	+	0.526784i	$0.823398\pi$
$444$	3.65869	−	0.282000i	0.173634	−	0.0133831i
$445$	−8.44165	−	3.37953i	−0.400173	−	0.160205i
$446$	13.4521	+	14.1081i	0.636974	+	0.668039i
$447$	−21.4169	+	4.78304i	−1.01299	+	0.226230i
$448$	−27.8080	−	1.32466i	−1.31380	−	0.0625842i
$449$	−1.63618	+	2.54595i	−0.0772162	+	0.120151i	−0.877714	−	0.479185i	$-0.840932\pi$
$449$	−1.63618	+	2.54595i	−0.0772162	+	0.120151i	0.800498	+	0.599336i	$0.204569\pi$
$450$	−0.605721	+	0.0646008i	−0.0285540	+	0.00304531i
$451$	−19.6943	+	67.0725i	−0.927366	+	3.15832i
$452$	−3.84368	+	3.02271i	−0.180792	+	0.142176i
$453$	0.981108	+	0.469911i	0.0460965	+	0.0220784i
$454$	3.41197	−	35.7317i	0.160131	−	1.67697i
$455$	4.03513	+	0.978912i	0.189170	+	0.0458921i
$456$	11.2157	+	6.75164i	0.525225	+	0.316175i
$457$	3.03695	+	7.58593i	0.142062	+	0.354855i	0.982287	−	0.187384i	$-0.0600010\pi$
$457$	3.03695	+	7.58593i	0.142062	+	0.354855i	−0.840224	+	0.542239i	$0.817577\pi$
$458$	10.0206	−	6.43987i	0.468234	−	0.300916i
$459$	−2.08178	+	5.87716i	−0.0971691	+	0.274323i
$460$	−1.58501	−	2.81995i	−0.0739016	−	0.131481i
$461$	−22.4245	+	12.9468i	−1.04441	+	0.602993i	−0.921080	−	0.389373i	$-0.872692\pi$
$461$	−22.4245	+	12.9468i	−1.04441	+	0.602993i	−0.123334	+	0.992365i	$0.539359\pi$
$462$	20.4070	+	41.4257i	0.949419	+	1.92730i
$463$	−17.4970	−	13.7598i	−0.813157	−	0.639474i	0.122467	−	0.992473i	$-0.460919\pi$
$463$	−17.4970	−	13.7598i	−0.813157	−	0.639474i	−0.935624	+	0.352999i	$0.885162\pi$
$464$	3.61520	−	2.57437i	0.167831	−	0.119512i
$465$	12.9805	−	10.8388i	0.601958	−	0.502637i
$466$	3.48296	−	4.89113i	0.161345	−	0.226577i
$467$	3.71329	+	4.28536i	0.171831	+	0.198303i	0.835132	−	0.550049i	$-0.185391\pi$
$467$	3.71329	+	4.28536i	0.171831	+	0.198303i	−0.663302	+	0.748352i	$0.730845\pi$
$468$	0.497401	−	0.233832i	0.0229923	−	0.0108089i
$469$	−21.0753	−	6.18827i	−0.973168	−	0.285748i
$470$	−11.2570	−	2.16961i	−0.519248	−	0.100077i
$471$	−29.0657	+	11.0243i	−1.33928	+	0.507971i
$472$	−10.7527	+	5.54342i	−0.494935	+	0.255157i
$473$	−15.2224	+	5.26853i	−0.699927	+	0.242247i
$474$	−0.864022	−	1.14100i	−0.0396858	−	0.0524080i
$475$	0.242875	+	0.308841i	0.0111439	+	0.0141706i
$476$	−0.877094	+	0.760006i	−0.0402015	+	0.0348348i
$477$	5.90955	+	28.9373i	0.270580	+	1.32495i
$478$	−4.73010	+	1.38888i	−0.216350	+	0.0635261i
$479$	9.34653	−	0.892486i	0.427054	−	0.0407787i	0.120683	−	0.992691i	$-0.461491\pi$
$479$	9.34653	−	0.892486i	0.427054	−	0.0407787i	0.306371	+	0.951912i	$0.400885\pi$
$480$	6.31487	−	1.72951i	0.288233	−	0.0789412i
$481$	4.12779	−	0.196631i	0.188211	−	0.00896560i
$482$	−1.10584	+	1.91537i	−0.0503697	+	0.0872429i
$483$	11.5960	−	23.5107i	0.527635	−	1.06978i
$484$	−4.77237	−	8.26599i	−0.216926	−	0.375727i
$485$	−22.7948	−	35.4694i	−1.03506	−	1.61058i
$486$	19.9341	+	3.76297i	0.904228	+	0.170692i
$487$	1.49396	−	3.27131i	0.0676976	−	0.148237i	−0.872759	−	0.488152i	$-0.837671\pi$
$487$	1.49396	−	3.27131i	0.0676976	−	0.148237i	0.940456	+	0.339915i	$0.110398\pi$
$488$	4.59279	+	4.37922i	0.207906	+	0.198238i
$489$	28.7693	−	9.37205i	1.30099	−	0.423819i
$490$	1.60431	+	8.32394i	0.0724753	+	0.376037i
$491$	0.325395	−	0.812797i	0.0146849	−	0.0366810i	−0.920844	−	0.389930i	$-0.872499\pi$
$491$	0.325395	−	0.812797i	0.0146849	−	0.0366810i	0.935529	+	0.353249i	$0.114923\pi$
$492$	0.709937	+	5.67168i	0.0320064	+	0.255699i
$493$	0.306043	−	1.58790i	0.0137835	−	0.0715156i
$494$	1.64796	+	1.05908i	0.0741451	+	0.0476501i
$495$	−29.9203	−	30.6931i	−1.34482	−	1.37955i
$496$	−9.56664	+	11.0405i	−0.429555	+	0.495733i
$497$	−7.19161	−	29.6442i	−0.322588	−	1.32972i
$498$	13.4255	+	7.23487i	0.601611	+	0.324202i
$499$	6.95497	−	1.34046i	0.311347	−	0.0600073i	−0.0311841	−	0.999514i	$-0.509928\pi$
$499$	6.95497	−	1.34046i	0.311347	−	0.0600073i	0.342531	+	0.939506i	$0.388716\pi$
$500$	3.46208	+	0.330588i	0.154829	+	0.0147844i
$501$	−5.93328	+	16.1802i	−0.265079	+	0.722877i
$502$	2.57455	+	26.9619i	0.114908	+	1.20337i
$503$	−1.39662	+	9.71367i	−0.0622720	+	0.433111i	0.934706	+	0.355423i	$0.115663\pi$
$503$	−1.39662	+	9.71367i	−0.0622720	+	0.433111i	−0.996978	+	0.0776885i	$0.975246\pi$
$504$	21.6810	+	18.3712i	0.965749	+	0.818319i
$505$		−	5.16115i		−	0.229668i
$506$	15.4911	−	37.4376i	0.688665	−	1.66430i
$507$	−20.0818	+	8.73112i	−0.891862	+	0.387762i
$508$	0.237240	+	4.98029i	0.0105258	+	0.220965i
$509$	−11.9065	+	15.1404i	−0.527748	+	0.671087i	−0.974712	−	0.223465i	$-0.928263\pi$
$509$	−11.9065	+	15.1404i	−0.527748	+	0.671087i	0.446963	+	0.894552i	$0.352505\pi$
$510$	−3.07003	+	5.09989i	−0.135943	+	0.225827i
$511$	−33.9024	+	35.5558i	−1.49975	+	1.57290i
$512$	−23.1274	+	10.5619i	−1.02210	+	0.466776i
$513$	−4.77508	−	12.1819i	−0.210825	−	0.537846i
$514$	−4.57958	−	31.8517i	−0.201997	−	1.40492i
$515$	8.03379	−	1.94898i	0.354011	−	0.0858821i
$516$	−0.969720	+	0.891368i	−0.0426895	+	0.0392403i
$517$	11.9068	+	23.0959i	0.523660	+	1.01576i
$518$	13.0095	+	25.2348i	0.571603	+	1.10875i
$519$	8.93515	+	2.80194i	0.392210	+	0.122992i
$520$	3.83776	−	0.931032i	0.168297	−	0.0408284i
$521$	−3.65335	−	25.4096i	−0.160056	−	1.11322i	−0.898523	−	0.438926i	$-0.855359\pi$
$521$	−3.65335	−	25.4096i	−0.160056	−	1.11322i	0.738467	−	0.674290i	$-0.235550\pi$
$522$	−5.25798	−	0.192266i	−0.230135	−	0.00841525i
$523$	−3.19646	+	1.45978i	−0.139772	+	0.0638315i	−0.484073	−	0.875028i	$-0.660843\pi$
$523$	−3.19646	+	1.45978i	−0.139772	+	0.0638315i	0.344301	+	0.938859i	$0.388116\pi$
$524$	0.736460	−	0.772377i	0.0321724	−	0.0337415i
$525$	0.412879	+	0.746299i	0.0180195	+	0.0325712i
$526$	−9.61986	+	12.2326i	−0.419446	+	0.533369i
$527$	0.253277	+	5.31694i	0.0110329	+	0.231610i
$528$	29.7650	+	22.0263i	1.29536	+	0.958570i
$529$	−22.2119	+	5.96907i	−0.965736	+	0.259525i
$530$			28.1972i			1.22481i
$531$	11.8974	+	2.15697i	0.516303	+	0.0936047i
$532$	0.346607	−	2.41070i	0.0150273	−	0.104517i
$533$	0.611880	+	6.40790i	0.0265035	+	0.277557i
$534$	−5.96872	−	7.14813i	−0.258292	−	0.309330i
$535$	−35.1547	−	3.35687i	−1.51987	−	0.145130i
$536$	−20.5132	+	3.95359i	−0.886034	+	0.170769i
$537$	−0.0545620	−	1.86008i	−0.00235453	−	0.0802683i
$538$	−2.68485	−	11.0671i	−0.115752	−	0.477136i
$539$	12.5825	−	14.5210i	0.541969	−	0.625465i
$540$	−3.24433	−	1.32611i	−0.139614	−	0.0570668i
$541$	−25.1449	−	16.1596i	−1.08106	−	0.694757i	−0.126261	−	0.991997i	$-0.540298\pi$
$541$	−25.1449	−	16.1596i	−1.08106	−	0.694757i	−0.954803	+	0.297240i	$0.903934\pi$
$542$	0.578281	−	3.00041i	0.0248393	−	0.128879i
$543$	−26.9354	−	11.3587i	−1.15591	−	0.487450i
$544$	−0.765968	+	1.91330i	−0.0328406	+	0.0820319i
$545$	1.31944	+	6.84591i	0.0565186	+	0.293247i
$546$	3.16231	+	2.84298i	0.135334	+	0.121668i
$547$	20.2929	+	19.3492i	0.867662	+	0.827314i	0.986187	−	0.165637i	$-0.0529681\pi$
$547$	20.2929	+	19.3492i	0.867662	+	0.827314i	−0.118525	+	0.992951i	$0.537817\pi$
$548$	1.19055	−	2.60695i	0.0508579	−	0.111363i
$549$	−0.971976	−	6.26779i	−0.0414829	−	0.267503i
$550$	0.712662	+	1.10892i	0.0303880	+	0.0472847i
$551$	1.69681	+	2.93896i	0.0722865	+	0.125204i
$552$	−0.443532	−	24.9287i	−0.0188780	−	1.06104i
$553$	−1.00195	+	1.73543i	−0.0426073	+	0.0737980i
$554$	−17.9119	+	0.853249i	−0.761004	+	0.0362511i
$555$	−18.7366	−	18.5307i	−0.795326	−	0.786586i
$556$	−5.04199	+	0.481452i	−0.213828	+	0.0204181i
$557$	−3.28157	+	0.963557i	−0.139045	+	0.0408272i	−0.350514	−	0.936557i	$-0.613993\pi$
$557$	−3.28157	+	0.963557i	−0.139045	+	0.0408272i	0.211470	+	0.977385i	$0.432175\pi$
$558$	16.9686	−	3.46532i	0.718339	−	0.146699i
$559$	−1.12102	+	0.971369i	−0.0474141	+	0.0410845i
$560$	14.1395	+	17.9798i	0.597502	+	0.759786i
$561$	13.3876	−	1.67576i	0.565227	−	0.0707507i
$562$	16.2769	−	5.63349i	0.686600	−	0.237635i
$563$	3.35413	−	1.72917i	0.141360	−	0.0728760i	−0.386096	−	0.922459i	$-0.626177\pi$
$563$	3.35413	−	1.72917i	0.141360	−	0.0728760i	0.527455	+	0.849583i	$0.323146\pi$
$564$	1.64585	+	1.34371i	0.0693029	+	0.0565803i
$565$	34.4814	+	6.64574i	1.45064	+	0.279588i
$566$	7.53307	+	2.21191i	0.316639	+	0.0929735i
$567$	−5.99031	−	27.7643i	−0.251570	−	1.16599i
$568$	−18.9989	−	21.9258i	−0.797174	−	0.919988i
$569$	5.90908	−	8.29815i	0.247722	−	0.347876i	−0.671928	−	0.740617i	$-0.734533\pi$
$569$	5.90908	−	8.29815i	0.247722	−	0.347876i	0.919649	+	0.392740i	$0.128473\pi$
$570$	−2.13956	−	12.3073i	−0.0896164	−	0.515497i
$571$	3.07529	−	2.18990i	0.128697	−	0.0916445i	−0.513896	−	0.857853i	$-0.671798\pi$
$571$	3.07529	−	2.18990i	0.128697	−	0.0916445i	0.642593	+	0.766208i	$0.277859\pi$
$572$	−0.934893	−	0.735208i	−0.0390898	−	0.0307406i
$573$	9.94098	−	14.8641i	0.415291	−	0.620955i
$574$	−38.2989	+	22.1119i	−1.59856	+	0.922931i
$575$	0.252885	−	0.704274i	0.0105460	−	0.0293702i
$576$	25.7856	+	5.95462i	1.07440	+	0.248109i
$577$	20.7665	−	13.3458i	0.864520	−	0.555593i	−0.0315518	−	0.999502i	$-0.510045\pi$
$577$	20.7665	−	13.3458i	0.864520	−	0.555593i	0.896072	+	0.443909i	$0.146409\pi$
$578$	7.52592	+	18.7988i	0.313037	+	0.781929i
$579$	−24.2105	+	13.3941i	−1.00615	+	0.556639i
$580$	0.883418	+	0.214315i	0.0366819	+	0.00889894i
$581$	2.02974	−	21.2564i	0.0842077	−	0.881863i
$582$	−3.31834	−	43.0524i	−0.137550	−	1.78458i
$583$	50.2375	−	39.5072i	2.08062	−	1.63622i
$584$	−13.1640	+	44.8326i	−0.544732	+	1.85519i
$585$	−3.60827	−	1.59989i	−0.149183	−	0.0661475i
$586$	12.5364	−	19.5070i	0.517874	−	0.805828i
$587$	34.2090	+	1.62958i	1.41196	+	0.0672598i	0.739639	−	0.673004i	$-0.234996\pi$
$587$	34.2090	+	1.62958i	1.41196	+	0.0672598i	0.672317	+	0.740263i	$0.265299\pi$
$588$	0.470105	−	1.49912i	0.0193868	−	0.0618228i
$589$	−7.70854	−	8.08448i	−0.317625	−	0.333115i
$590$	10.7169	+	4.29041i	0.441209	+	0.176633i
$591$	−1.45444	−	2.12357i	−0.0598278	−	0.0873519i
$592$	18.5438	+	13.2050i	0.762147	+	0.542722i
$593$	−10.2250	−	34.8230i	−0.419889	−	1.43001i	−0.849784	−	0.527131i	$-0.823268\pi$
$593$	−10.2250	−	34.8230i	−0.419889	−	1.43001i	0.429895	−	0.902879i	$-0.358550\pi$
$594$	−12.0629	−	42.2081i	−0.494945	−	1.73182i
$595$	8.24962	+	1.18612i	0.338201	+	0.0486260i
$596$	3.45127	+	1.77925i	0.141369	+	0.0728810i
$597$	0.932438	+	0.106265i	0.0381622	+	0.00434913i
$598$	0.0430334	−	3.73063i	0.00175977	−	0.152557i
$599$	23.0208	+	13.2911i	0.940603	+	0.543058i	0.890149	−	0.455669i	$-0.150600\pi$
$599$	23.0208	+	13.2911i	0.940603	+	0.543058i	0.0504540	+	0.998726i	$0.483933\pi$
$600$	0.674279	+	0.450954i	0.0275273	+	0.0184101i
$601$	−19.4754	+	7.79678i	−0.794418	+	0.318037i	−0.733135	−	0.680083i	$-0.761944\pi$
$601$	−19.4754	+	7.79678i	−0.794418	+	0.318037i	−0.0612834	+	0.998120i	$0.519519\pi$
$602$	−9.26978	−	4.23337i	−0.377808	−	0.172539i
$603$	18.6634	+	9.36211i	0.760034	+	0.381254i
$604$	−0.0799608	−	0.175090i	−0.00325356	−	0.00712430i
$605$	−22.4187	+	64.7747i	−0.911451	+	2.63346i
$606$	2.50750	−	4.65308i	0.101860	−	0.189018i
$607$	3.39523	−	3.23735i	0.137808	−	0.131400i	−0.618040	−	0.786146i	$-0.712073\pi$
$607$	3.39523	−	3.23735i	0.137808	−	0.131400i	0.755849	+	0.654747i	$0.227225\pi$
$608$	−1.41455	−	4.08708i	−0.0573677	−	0.165753i
$609$	2.61251	+	6.88795i	0.105864	+	0.279114i
$610$	0.288132	−	6.04864i	0.0116661	−	0.244902i
$611$	1.80832	+	1.56692i	0.0731569	+	0.0633908i
$612$	0.949271	−	0.562138i	0.0383720	−	0.0227231i
$613$	42.4989	−	6.11041i	1.71651	−	0.246797i	0.787360	−	0.616493i	$-0.211447\pi$
$613$	42.4989	−	6.11041i	1.71651	−	0.246797i	0.929153	+	0.369696i	$0.120538\pi$
$614$	22.5804	+	7.81515i	0.911271	+	0.315394i
$615$	27.4434	−	30.5259i	1.10663	−	1.23092i
$616$	14.4978	−	59.7609i	0.584135	−	2.40784i
$617$	−7.95443	−	11.1704i	−0.320233	−	0.449705i	0.622811	−	0.782373i	$-0.285991\pi$
$617$	−7.95443	−	11.1704i	−0.320233	−	0.449705i	−0.943044	+	0.332668i	$0.892051\pi$
$618$	8.18981	+	2.14603i	0.329443	+	0.0863259i
$619$	8.79314	−	17.0563i	0.353426	−	0.685551i	−0.643368	−	0.765557i	$-0.722464\pi$
$619$	8.79314	−	17.0563i	0.353426	−	0.685551i	0.996794	+	0.0800056i	$0.0254938\pi$
$620$	−2.99222			−0.120171
$621$	−14.8332	+	20.0244i	−0.595235	+	0.803551i
$622$	23.2992			0.934213
$623$	−5.97462	+	11.5892i	−0.239368	+	0.464310i
$624$	3.29838	+	0.864295i	0.132041	+	0.0345995i
$625$	−14.0348	−	19.7091i	−0.561391	−	0.788363i
$626$	−1.08943	+	4.49069i	−0.0435424	+	0.179484i
$627$	−18.9296	+	21.0558i	−0.755975	+	0.840887i
$628$	5.19793	+	1.79902i	0.207420	+	0.0717888i
$629$	8.21048	−	1.18049i	0.327373	−	0.0470691i
$630$	−0.299628	−	27.1154i	−0.0119375	−	1.08030i
$631$	−14.0704	−	12.1921i	−0.560135	−	0.485360i	0.328167	−	0.944620i	$-0.393569\pi$
$631$	−14.0704	−	12.1921i	−0.560135	−	0.485360i	−0.888302	+	0.459260i	$0.848115\pi$
$632$	−0.0906858	+	1.90373i	−0.00360729	+	0.0757263i
$633$	−2.72506	−	7.18469i	−0.108311	−	0.285566i
$634$	6.91870	+	19.9903i	0.274777	+	0.793915i
$635$	25.9140	−	24.7090i	1.02837	−	0.980545i
$636$	2.47913	−	4.60043i	0.0983039	−	0.182419i
$637$	0.578684	−	1.67200i	0.0229283	−	0.0662470i
$638$	4.72974	+	10.3567i	0.187252	+	0.410025i
$639$	1.69970	+	28.9473i	0.0672389	+	1.14514i
$640$	16.1055	+	7.35516i	0.636628	+	0.290738i
$641$	23.6988	−	9.48755i	0.936045	−	0.374736i	0.147045	−	0.989130i	$-0.453024\pi$
$641$	23.6988	−	9.48755i	0.936045	−	0.374736i	0.788999	+	0.614394i	$0.210599\pi$
$642$	−30.0631	−	20.1060i	−1.18650	−	0.793521i
$643$	−29.1207	−	16.8128i	−1.14841	−	0.663033i	−0.199908	−	0.979815i	$-0.564064\pi$
$643$	−29.1207	−	16.8128i	−1.14841	−	0.663033i	−0.948498	+	0.316782i	$0.897398\pi$
$644$	−4.24129	+	1.87812i	−0.167130	+	0.0740081i
$645$	9.39817	+	1.07106i	0.370052	+	0.0421728i
$646$	3.49495	+	1.80177i	0.137507	+	0.0708899i
$647$	13.5924	+	1.95430i	0.534374	+	0.0768314i	0.404219	−	0.914662i	$-0.367543\pi$
$647$	13.5924	+	1.95430i	0.534374	+	0.0768314i	0.130155	+	0.991494i	$0.458452\pi$
$648$	−17.1640	−	20.8602i	−0.674266	−	0.819464i
$649$	−7.37153	−	25.1051i	−0.289358	−	0.985462i
$650$	0.0988759	+	0.0704092i	0.00387823	+	0.00276168i
$651$	−13.7022	−	20.0060i	−0.537033	−	0.784098i
$652$	−4.97030	−	1.98981i	−0.194652	−	0.0779269i
$653$	21.7092	+	22.7680i	0.849547	+	0.890979i	0.995151	−	0.0983639i	$-0.0313609\pi$
$653$	21.7092	+	22.7680i	0.849547	+	0.890979i	−0.145604	+	0.989343i	$0.546512\pi$
$654$	−2.13647	+	6.81302i	−0.0835426	+	0.266410i
$655$	−7.65539	−	0.364671i	−0.299121	−	0.0142489i
$656$	−19.1714	+	29.8312i	−0.748516	+	1.16471i
$657$	37.7401	−	27.5081i	1.47238	−	1.07319i
$658$	−4.63131	+	15.7728i	−0.180547	+	0.614888i
$659$	25.6795	−	20.1946i	1.00033	−	0.786671i	0.0232936	−	0.999729i	$-0.492585\pi$
$659$	25.6795	−	20.1946i	1.00033	−	0.786671i	0.977040	+	0.213058i	$0.0683423\pi$
$660$	0.582851	+	7.56195i	0.0226874	+	0.294349i
$661$	2.04138	−	21.3783i	0.0794003	−	0.831518i	−0.864794	−	0.502128i	$-0.832551\pi$
$661$	2.04138	−	21.3783i	0.0794003	−	0.831518i	0.944194	−	0.329390i	$-0.106843\pi$
$662$	−22.9049	−	5.55667i	−0.890224	−	0.215966i
$663$	1.08713	−	0.601438i	0.0422206	−	0.0233579i
$664$	−7.54796	−	18.8539i	−0.292917	−	0.731673i
$665$	−14.7137	+	9.45594i	−0.570574	+	0.366686i
$666$	−7.88916	−	25.8095i	−0.305699	−	1.00010i
$667$	3.02773	−	5.71028i	0.117234	−	0.221103i
$668$	2.64084	−	1.52469i	0.102177	−	0.0589919i
$669$	−14.4235	+	21.5664i	−0.557644	+	0.833805i
$670$	15.6696	+	12.3227i	0.605369	+	0.476067i
$671$	−11.1803	+	7.96143i	−0.431609	+	0.307347i
$672$	−1.60801	−	9.24972i	−0.0620305	−	0.356816i
$673$	−21.9048	+	30.7609i	−0.844366	+	1.18575i	0.136418	+	0.990651i	$0.456441\pi$
$673$	−21.9048	+	30.7609i	−0.844366	+	1.18575i	−0.980784	+	0.195095i	$0.937498\pi$
$674$	−0.0167824	−	0.0193679i	−0.000646433	−	0.000746024i
$675$	−0.259632	−	0.768067i	−0.00999322	−	0.0295629i
$676$	3.71767	+	1.09161i	0.142987	+	0.0419849i
$677$	25.0694	+	4.83174i	0.963497	+	0.185699i	0.646658	−	0.762780i	$-0.276166\pi$
$677$	25.0694	+	4.83174i	0.963497	+	0.185699i	0.316839	+	0.948479i	$0.397378\pi$
$678$	27.8582	+	22.7440i	1.06989	+	0.873477i
$679$	−53.7368	+	27.7033i	−2.06223	+	1.06315i
$680$	7.49083	−	2.59260i	0.287260	−	0.0994217i
$681$	47.4038	−	5.93364i	1.81652	−	0.227378i
$682$	−23.1667	−	29.4589i	−0.887100	−	1.12804i
$683$	20.1963	−	17.5002i	0.772788	−	0.669625i	−0.176405	−	0.984318i	$-0.556447\pi$
$683$	20.1963	−	17.5002i	0.772788	−	0.669625i	0.949194	+	0.314693i	$0.101901\pi$
$684$	−0.733000	+	2.19608i	−0.0280270	+	0.0839692i
$685$	−19.7477	+	5.79845i	−0.754522	+	0.221548i
$686$	−16.5181	+	1.57728i	−0.630663	+	0.0602210i
$687$	11.2721	+	11.1482i	0.430057	+	0.425331i
$688$	−8.16207	+	0.388808i	−0.311176	+	0.0148231i
$689$	2.94259	−	5.09672i	0.112104	−	0.194169i
$690$	−17.7004	+	15.8975i	−0.673842	+	0.605207i
$691$	4.46011	+	7.72513i	0.169671	+	0.293878i	0.938304	−	0.345811i	$-0.112396\pi$
$691$	4.46011	+	7.72513i	0.169671	+	0.293878i	−0.768634	+	0.639689i	$0.779063\pi$
$692$	−0.895797	−	1.39389i	−0.0340531	−	0.0529876i
$693$	−47.8902	+	38.5253i	−1.81920	+	1.46345i
$694$	−14.6493	+	32.0774i	−0.556079	+	1.21764i
$695$	26.3246	+	25.1004i	0.998547	+	0.952113i
$696$	5.21037	+	4.68423i	0.197499	+	0.177555i
$697$	2.44527	+	12.6873i	0.0926212	+	0.480564i
$698$	−4.64854	+	11.6115i	−0.175950	+	0.439501i
$699$	7.36377	+	3.10532i	0.278523	+	0.117454i
$700$	0.0285605	−	0.148186i	0.00107949	−	0.00560090i
$701$	−2.48052	−	1.59413i	−0.0936880	−	0.0602096i	0.492958	−	0.870053i	$-0.335916\pi$
$701$	−2.48052	−	1.59413i	−0.0936880	−	0.0602096i	−0.586646	+	0.809844i	$0.699552\pi$
$702$	−2.47576	−	3.19544i	−0.0934417	−	0.120604i
$703$	−11.3993	+	13.1555i	−0.429934	+	0.496170i
$704$	−13.5012	−	55.6528i	−0.508846	−	2.09749i
$705$	−0.447384	−	15.2518i	−0.0168495	−	0.574417i
$706$	−2.16449	+	0.417170i	−0.0814615	+	0.0157004i
$707$	−7.36714	−	0.703477i	−0.277070	−	0.0264570i
$708$	−1.37127	−	1.64223i	−0.0515355	−	0.0617189i
$709$	1.54080	+	16.1359i	0.0578658	+	0.605998i	0.977171	+	0.212453i	$0.0681453\pi$
$709$	1.54080	+	16.1359i	0.0578658	+	0.605998i	−0.919305	+	0.393545i	$0.871249\pi$
$710$	−3.93986	+	27.4023i	−0.147860	+	1.02839i
$711$	1.23147	−	1.45333i	0.0461836	−	0.0545041i
$712$			12.4008i			0.464741i
$713$	−5.25387	+	20.6159i	−0.196759	+	0.772070i
$714$	6.86124	+	5.07735i	0.256775	+	0.190015i
$715$	0.406407	+	8.53153i	0.0151987	+	0.319061i
$716$	−0.203540	+	0.258822i	−0.00760664	+	0.00967263i
$717$	−3.17629	−	5.74130i	−0.118621	−	0.214413i
$718$	15.3745	−	16.1243i	0.573771	−	0.601754i
$719$	−34.2040	+	15.6204i	−1.27559	+	0.582544i	−0.933990	−	0.357300i	$-0.883697\pi$
$719$	−34.2040	+	15.6204i	−1.27559	+	0.582544i	−0.341604	+	0.939844i	$0.610970\pi$
$720$	−10.1764	−	19.2152i	−0.379253	−	0.716107i
$721$	−1.68699	−	11.7333i	−0.0628267	−	0.436969i
$722$	16.0098	−	3.88393i	0.595822	−	0.144545i
$723$	−2.80879	−	0.880800i	−0.104460	−	0.0327573i
$724$	2.37016	+	4.59746i	0.0880861	+	0.170863i
$725$	0.0963570	+	0.186907i	0.00357861	+	0.00694153i
$726$	−51.6819	+	47.5061i	−1.91810	+	1.76312i
$727$	5.78385	−	1.40315i	0.214511	−	0.0520399i	−0.127063	−	0.991895i	$-0.540555\pi$
$727$	5.78385	−	1.40315i	0.214511	−	0.0520399i	0.341574	+	0.939855i	$0.389040\pi$
$728$	−0.805879	−	5.60501i	−0.0298678	−	0.207735i
$729$	0.894860	+	26.9852i	0.0331430	+	0.999451i
$730$	40.5574	−	18.5219i	1.50110	−	0.685528i
$731$	−2.05464	+	2.15484i	−0.0759935	+	0.0796997i
$732$	−0.578813	+	0.961516i	−0.0213935	+	0.0355387i
$733$	15.6827	−	19.9422i	0.579254	−	0.736581i	−0.404809	−	0.914401i	$-0.632662\pi$
$733$	15.6827	−	19.9422i	0.579254	−	0.736581i	0.984063	+	0.177820i	$0.0569046\pi$
$734$	−0.0715343	−	1.50169i	−0.00264038	−	0.0554284i
$735$	−10.3471	+	4.49868i	−0.381657	+	0.165936i
$736$	−5.16617	+	6.41562i	−0.190428	+	0.236483i
$737$		−	45.1831i		−	1.66434i
$738$	39.5726	−	14.1877i	1.45669	−	0.522258i
$739$	−0.879372	+	6.11617i	−0.0323482	+	0.224987i	−0.999582	−	0.0288993i	$-0.990800\pi$
$739$	−0.879372	+	6.11617i	−0.0323482	+	0.224987i	0.967234	+	0.253886i	$0.0817089\pi$
$740$	0.443232	+	4.64174i	0.0162935	+	0.170634i
$741$	−0.897632	+	2.44786i	−0.0329753	+	0.0899245i
$742$	40.2492	+	3.84334i	1.47760	+	0.141093i
$743$	7.40833	−	1.42784i	0.271785	−	0.0523823i	−0.0515374	−	0.998671i	$-0.516412\pi$
$743$	7.40833	−	1.42784i	0.271785	−	0.0523823i	0.323323	+	0.946289i	$0.395200\pi$
$744$	−20.3022	−	10.9407i	−0.744316	−	0.401105i
$745$	−6.57407	−	27.0987i	−0.240855	−	0.992819i
$746$	23.3638	−	26.9633i	0.855410	−	0.987196i
$747$	−5.50312	+	19.5380i	−0.201348	+	0.714857i
$748$	−2.00834	−	1.29068i	−0.0734324	−	0.0471921i
$749$	−9.58334	+	49.7231i	−0.350167	+	1.81684i
$750$	−3.17691	−	25.3803i	−0.116004	−	0.926758i
$751$	−16.1319	+	40.2956i	−0.588662	+	1.47041i	0.272541	+	0.962144i	$0.412136\pi$
$751$	−16.1319	+	40.2956i	−0.588662	+	1.47041i	−0.861203	+	0.508262i	$0.830288\pi$
$752$	2.49456	+	12.9430i	0.0909674	+	0.471983i
$753$	−34.2755	+	11.1658i	−1.24907	+	0.406904i
$754$	0.758784	+	0.723499i	0.0276333	+	0.0263483i
$755$	−0.574230	+	1.25739i	−0.0208984	+	0.0457611i
$756$	−2.33513	+	4.45027i	−0.0849278	+	0.161855i
$757$	−22.6060	−	35.1756i	−0.821629	−	1.27848i	−0.957696	−	0.287780i	$-0.907083\pi$
$757$	−22.6060	−	35.1756i	−0.821629	−	1.27848i	0.136067	−	0.990700i	$-0.456554\pi$
$758$	−3.12092	−	5.40558i	−0.113357	−	0.196340i
$759$	53.1239	+	9.26184i	1.92827	+	0.336184i
$760$	−8.31738	+	14.4061i	−0.301703	+	0.522565i
$761$	18.7139	−	0.891451i	0.678377	−	0.0323151i	0.294434	−	0.955672i	$-0.404869\pi$
$761$	18.7139	−	0.891451i	0.678377	−	0.0323151i	0.383943	+	0.923357i	$0.374566\pi$
$762$	35.3676	−	9.68646i	1.28123	−	0.350903i
$763$	9.95184	−	0.950285i	0.360281	−	0.0344026i
$764$	−3.03590	+	0.891420i	−0.109835	+	0.0322504i
$765$	−7.51515	−	2.50838i	−0.271711	−	0.0906908i
$766$	−6.80492	+	5.89649i	−0.245872	+	0.213049i
$767$	−1.48938	−	1.89390i	−0.0537783	−	0.0683847i
$768$	−7.50111	−	9.90575i	−0.270673	−	0.357443i
$769$	2.46841	−	0.854326i	0.0890133	−	0.0308078i	−0.282198	−	0.959356i	$-0.591064\pi$
$769$	2.46841	−	0.854326i	0.0890133	−	0.0308078i	0.371212	+	0.928548i	$0.378942\pi$
$770$	−52.1566	+	26.8886i	−1.87959	+	0.968997i
$771$	40.0455	−	15.1887i	1.44220	−	0.547009i
$772$	4.80726	+	0.926523i	0.173017	+	0.0333463i
$773$	45.6343	+	13.3994i	1.64135	+	0.481944i	0.966640	−	0.256137i	$-0.0824499\pi$
$773$	45.6343	+	13.3994i	1.64135	+	0.481944i	0.674711	+	0.738082i	$0.264268\pi$
$774$	7.95262	+	5.53163i	0.285851	+	0.198830i
$775$	−0.453275	−	0.523108i	−0.0162821	−	0.0187906i
$776$	−33.3535	+	46.8385i	−1.19732	+	1.68140i
$777$	−29.0050	+	24.2193i	−1.04055	+	0.868862i
$778$	−32.1081	+	22.8640i	−1.15113	+	0.819716i
$779$	−21.3137	−	16.7613i	−0.763643	−	0.600535i
$780$	0.308628	+	0.626507i	0.0110507	+	0.0224326i
$781$	54.3415	−	31.3741i	1.94449	−	1.12265i
$782$	−0.625821	−	7.46261i	−0.0223793	−	0.266862i
$783$	−1.27558	−	6.88567i	−0.0455854	−	0.246074i
$784$	8.19951	−	5.26951i	0.292840	−	0.188197i
$785$	−14.6810	−	36.6714i	−0.523988	−	1.30886i
$786$	−6.72460	−	4.04807i	−0.239859	−	0.144390i
$787$	25.7351	+	6.24327i	0.917358	+	0.222549i	0.666526	−	0.745482i	$-0.267781\pi$
$787$	25.7351	+	6.24327i	0.917358	+	0.222549i	0.250832	+	0.968031i	$0.419296\pi$
$788$	−0.0432914	+	0.453368i	−0.00154219	+	0.0161506i
$789$	−18.6804	−	8.94716i	−0.665040	−	0.318527i
$790$	1.42956	−	1.12422i	0.0508614	−	0.0399978i
$791$	14.1862	−	48.3136i	0.504402	−	1.71784i
$792$	−23.6947	+	53.4390i	−0.841954	+	1.89887i
$793$	−0.683303	+	1.06324i	−0.0242648	+	0.0377568i
$794$	−45.0413	−	2.14558i	−1.59846	−	0.0761439i
$795$	−36.6270	+	8.17990i	−1.29902	+	0.290111i
$796$	−0.114591	−	0.120180i	−0.00406159	−	0.00425967i
$797$	2.42015	+	0.968883i	0.0857262	+	0.0343196i	0.414129	−	0.910218i	$-0.364086\pi$
$797$	2.42015	+	0.968883i	0.0857262	+	0.0343196i	−0.328403	+	0.944538i	$0.606510\pi$
$798$	−17.8594	+	1.37654i	−0.632215	+	0.0487290i
$799$	3.91229	+	2.78593i	0.138407	+	0.0985591i
$800$	−0.0755019	−	0.257136i	−0.00266940	−	0.00909113i
$801$	7.55363	−	9.82677i	0.266894	−	0.347212i
$802$	23.4130	+	3.36627i	0.826740	+	0.118867i
$803$	−89.8248	−	46.3079i	−3.16985	−	1.63417i
$804$	−1.47310	−	3.38816i	−0.0519522	−	0.119491i
$805$	30.1392	+	14.1865i	1.06227	+	0.500008i
$806$	−2.98868	−	1.72552i	−0.105272	−	0.0607787i
$807$	13.5968	−	6.69803i	0.478631	−	0.235782i
$808$	−6.53447	+	2.61601i	−0.229882	+	0.0920309i
$809$	10.1888	+	4.65306i	0.358218	+	0.163593i	0.586392	−	0.810028i	$-0.300548\pi$
$809$	10.1888	+	4.65306i	0.358218	+	0.163593i	−0.228173	+	0.973621i	$0.573275\pi$
$810$	−4.31789	+	25.4132i	−0.151715	+	0.892929i
$811$	3.27900	+	7.18000i	0.115141	+	0.252124i	0.958425	−	0.285344i	$-0.0921080\pi$
$811$	3.27900	+	7.18000i	0.115141	+	0.252124i	−0.843284	+	0.537468i	$0.819381\pi$
$812$	0.426329	−	1.23180i	0.0149612	−	0.0432276i
$813$	4.06516	−	0.119244i	0.142572	−	0.00418208i
$814$	−42.2670	+	40.3015i	−1.48146	+	1.41257i
$815$	12.5750	+	36.3332i	0.440484	+	1.27270i
$816$	6.75559	+	1.09766i	0.236493	+	0.0384260i
$817$	0.297302	−	6.24113i	0.0104013	−	0.218350i
$818$	2.96236	+	2.56690i	0.103576	+	0.0897495i
$819$	−2.77554	+	4.93245i	−0.0969851	+	0.172354i
$820$	−7.18927	+	1.03366i	−0.251060	+	0.0360970i
$821$	−13.9403	−	4.82479i	−0.486520	−	0.168386i	0.0727857	−	0.997348i	$-0.476811\pi$
$821$	−13.9403	−	4.82479i	−0.486520	−	0.168386i	−0.559306	+	0.828961i	$0.688932\pi$
$822$	−20.6208	−	4.36661i	−0.719234	−	0.152303i
$823$	−9.69075	+	39.9458i	−0.337798	+	1.39242i	0.509118	+	0.860697i	$0.329972\pi$
$823$	−9.69075	+	39.9458i	−0.337798	+	1.39242i	−0.846916	+	0.531727i	$0.821543\pi$
$824$	−6.53962	−	9.18361i	−0.227819	−	0.319926i
$825$	−1.23371	+	1.24741i	−0.0429521	+	0.0434294i
$826$	7.58496	−	14.7128i	0.263915	−	0.511923i
$827$	25.8835			0.900057			0.450029	−	0.893014i	$-0.351414\pi$
$827$	25.8835			0.900057			0.450029	+	0.893014i	$0.351414\pi$
$828$	4.28558	−	1.03747i	0.148934	−	0.0360546i
$829$	−29.0716			−1.00970			−0.504848	−	0.863208i	$-0.668452\pi$
$829$	−29.0716			−1.00970			−0.504848	+	0.863208i	$0.668452\pi$
$830$	−8.88001	+	17.2248i	−0.308229	+	0.597882i
$831$	−6.30451	−	23.0193i	−0.218701	−	0.798531i
$832$	−3.05886	−	4.29557i	−0.106047	−	0.148922i
$833$	0.837284	−	3.45133i	0.0290102	−	0.119582i
$834$	11.5383	+	35.4190i	0.399538	+	1.22646i
$835$	−20.6944	−	7.16239i	−0.716158	−	0.247865i
$836$	4.95892	−	0.712985i	0.171508	−	0.0246591i
$837$	9.42384	+	21.0363i	0.325736	+	0.727120i
$838$	−32.0398	−	27.7626i	−1.10680	−	0.959044i
$839$	1.33936	−	28.1166i	0.0462398	−	0.970693i	−0.849906	−	0.526934i	$-0.823342\pi$
$839$	1.33936	−	28.1166i	0.0462398	−	0.970693i	0.896146	−	0.443759i	$-0.146355\pi$
$840$	−22.8368	+	27.9719i	−0.787944	+	0.965121i
$841$	−8.89092	−	25.6886i	−0.306584	−	0.885815i
$842$	−14.1740	+	13.5149i	−0.488468	+	0.465753i
$843$	12.0396	+	19.5088i	0.414664	+	0.671918i
$844$	−0.444696	+	1.28486i	−0.0153071	+	0.0442269i
$845$	−11.5590	−	25.3107i	−0.397642	−	0.870715i
$846$	7.00661	−	13.9677i	0.240892	−	0.480221i
$847$	89.4050	+	40.8299i	3.07199	+	1.40293i
$848$	30.0980	−	12.0494i	1.03357	−	0.413779i
$849$	−0.687862	+	10.4268i	−0.0236074	+	0.357847i
$850$	0.211004	+	0.121823i	0.00723738	+	0.00417850i
$851$	32.7590	+	5.09636i	1.12296	+	0.174701i
$852$	3.05204	−	4.12436i	0.104561	−	0.141298i
$853$	−48.5024	−	25.0047i	−1.66069	−	0.856146i	−0.993824	−	0.110970i	$-0.964604\pi$
$853$	−48.5024	−	25.0047i	−1.66069	−	0.856146i	−0.666868	−	0.745176i	$-0.732366\pi$
$854$	−8.59468	−	1.23573i	−0.294104	−	0.0422858i
$855$	15.3660	−	6.34951i	0.525507	−	0.217149i
$856$	13.5686	+	46.2105i	0.463766	+	1.57944i
$857$	−3.69399	−	2.63048i	−0.126184	−	0.0898555i	0.515222	−	0.857057i	$-0.327709\pi$
$857$	−3.69399	−	2.63048i	−0.126184	−	0.0898555i	−0.641407	+	0.767201i	$0.721649\pi$
$858$	−3.77857	+	7.88911i	−0.128998	+	0.269330i
$859$	30.5288	+	12.2219i	1.04163	+	0.417006i	0.828483	−	0.560014i	$-0.189204\pi$
$859$	30.5288	+	12.2219i	1.04163	+	0.417006i	0.213147	+	0.977020i	$0.431629\pi$
$860$	−1.15498	−	1.21131i	−0.0393846	−	0.0413053i
$861$	−39.8328	−	43.3341i	−1.35750	−	1.47682i
$862$	−16.9837	−	0.809033i	−0.578467	−	0.0275558i
$863$	−8.73417	+	13.5906i	−0.297315	+	0.462631i	−0.957484	−	0.288486i	$-0.906848\pi$
$863$	−8.73417	+	13.5906i	−0.297315	+	0.462631i	0.660169	+	0.751117i	$0.270484\pi$
$864$	−0.0644839	+	8.92442i	−0.00219379	+	0.303615i
$865$	−3.35233	+	11.4170i	−0.113983	+	0.388189i
$866$	14.3059	−	11.2503i	0.486136	−	0.382301i
$867$	−22.2357	+	15.2293i	−0.755163	+	0.517216i
$868$	−0.407847	+	4.27116i	−0.0138432	+	0.144973i
$869$	−4.00592	−	0.971825i	−0.135891	−	0.0329669i
$870$	0.122176	−	6.68462i	0.00414214	−	0.226630i
$871$	−1.54635	−	3.86260i	−0.0523962	−	0.130879i
$872$	7.99874	−	5.14048i	0.270872	−	0.174079i
$873$	54.9607	−	16.7997i	1.86014	−	0.568585i
$874$	11.2481	+	10.9755i	0.380472	+	0.371252i
$875$	−31.0149	+	17.9065i	−1.04850	+	0.605349i
$876$	−8.24550	−	0.543959i	−0.278590	−	0.0183787i
$877$	37.4764	+	29.4718i	1.26549	+	0.995192i	0.999513	+	0.0312123i	$0.00993678\pi$
$877$	37.4764	+	29.4718i	1.26549	+	0.995192i	0.265977	+	0.963980i	$0.414306\pi$
$878$	23.5737	−	16.7868i	0.795574	−	0.566526i
$879$	28.9756	+	10.6254i	0.977323	+	0.358385i
$880$	−27.2927	+	38.3273i	−0.920038	+	1.29201i
$881$	7.49931	+	8.65466i	0.252658	+	0.291583i	0.867883	−	0.496769i	$-0.165480\pi$
$881$	7.49931	+	8.65466i	0.252658	+	0.291583i	−0.615225	+	0.788352i	$0.710935\pi$
$882$	−11.5141	−	0.971207i	−0.387700	−	0.0327022i
$883$	29.5127	+	8.66570i	0.993180	+	0.291624i	0.737654	−	0.675178i	$-0.235933\pi$
$883$	29.5127	+	8.66570i	0.993180	+	0.291624i	0.255525	+	0.966802i	$0.417752\pi$
$884$	−0.215862	−	0.0416039i	−0.00726021	−	0.00139929i
$885$	−2.46412	+	15.1655i	−0.0828306	+	0.509782i
$886$	18.8349	−	9.71006i	0.632770	−	0.326216i
$887$	11.7570	−	4.06912i	0.394760	−	0.136628i	−0.122474	−	0.992472i	$-0.539083\pi$
$887$	11.7570	−	4.06912i	0.394760	−	0.136628i	0.517234	+	0.855844i	$0.326962\pi$
$888$	−13.9646	+	33.1148i	−0.468621	+	1.11126i
$889$	−31.7379	−	40.3581i	−1.06446	−	1.35357i
$890$	8.94296	−	7.74912i	0.299769	−	0.259751i
$891$	51.3272	−	27.9136i	1.71953	−	0.935140i
$892$	4.40482	−	1.29337i	0.147484	−	0.0433052i
$893$	−10.0334	+	0.958072i	−0.335754	+	0.0320607i
$894$	7.23875	−	27.6250i	0.242100	−	0.923917i
$895$	2.36192	−	0.112512i	0.0789504	−	0.00376087i
$896$	12.6941	−	21.9869i	0.424081	−	0.734530i
$897$	4.85842	−	1.02634i	0.162218	−	0.0342686i
$898$	−1.96920	−	3.41075i	−0.0657129	−	0.113818i
$899$	−3.23223	−	5.02944i	−0.107801	−	0.167741i
$900$	−0.0518431	+	0.133763i	−0.00172810	+	0.00445876i
$901$	4.90731	−	10.7455i	0.163486	−	0.357985i
$902$	−65.8382	−	62.7766i	−2.19217	−	2.09023i
$903$	2.80984	−	13.2692i	0.0935056	−	0.441570i
$904$	−9.06332	−	47.0250i	−0.301441	−	1.56403i
$905$	13.8056	−	34.4846i	0.458912	−	1.14631i
$906$	−1.12859	+	0.854624i	−0.0374950	+	0.0283930i
$907$	2.23964	−	11.6204i	0.0743660	−	0.385848i	−0.925607	−	0.378486i	$-0.876445\pi$
$907$	2.23964	−	11.6204i	0.0743660	−	0.385848i	0.999973	−	0.00736121i	$-0.00234317\pi$
$908$	−7.11128	−	4.57014i	−0.235996	−	0.151665i
$909$	6.77157	+	1.90730i	0.224599	+	0.0632611i
$910$	−3.53851	+	4.08366i	−0.117301	+	0.135372i
$911$	−8.70747	−	35.8927i	−0.288491	−	1.18918i	−0.912934	−	0.408107i	$-0.866189\pi$
$911$	−8.70747	−	35.8927i	−0.288491	−	1.18918i	0.624443	−	0.781070i	$-0.285326\pi$
$912$	−12.2227	+	7.54305i	−0.404734	+	0.249775i
$913$	43.1304	−	8.31270i	1.42741	−	0.275110i
$914$	−10.5856	−	1.01080i	−0.350139	−	0.0334342i
$915$	7.94052	−	1.38042i	0.262506	−	0.0456352i
$916$	−0.266651	−	2.79250i	−0.00881041	−	0.0922668i
$917$	−1.56399	+	10.8778i	−0.0516474	+	0.359215i
$918$	−5.55667	−	5.91262i	−0.183397	−	0.195146i
$919$			32.1865i			1.06173i	0.847455	+	0.530867i	$0.178134\pi$
$919$			32.1865i			1.06173i	−0.847455	+	0.530867i	$0.821866\pi$
$920$	31.6611	−	1.14236i	1.04384	−	0.0376626i
$921$	−3.60107	+	31.5982i	−0.118659	+	1.04119i
$922$	−1.60336	−	33.6586i	−0.0528038	−	1.10849i
$923$	3.57179	−	4.54190i	0.117567	−	0.149498i
$924$	10.8735	+	0.198737i	0.357713	+	0.00653797i
$925$	−0.744337	+	0.780638i	−0.0244736	+	0.0256672i
$926$	26.3496	−	12.0335i	0.865903	−	0.395445i
$927$	−0.411768	+	11.2608i	−0.0135242	+	0.369853i
$928$	−0.329421	−	2.29117i	−0.0108138	−	0.0752115i
$929$	8.31920	−	2.01822i	0.272944	−	0.0662155i	−0.0969506	−	0.995289i	$-0.530909\pi$
$929$	8.31920	−	2.01822i	0.272944	−	0.0662155i	0.369895	+	0.929074i	$0.379394\pi$
$930$	4.79664	+	21.4778i	0.157288	+	0.704285i
$931$	3.41511	+	6.62438i	0.111926	+	0.217105i
$932$	−0.647968	−	1.25688i	−0.0212249	−	0.0411705i
$933$	6.75902	+	30.2647i	0.221280	+	0.990823i
$934$	−7.17114	+	1.73970i	−0.234647	+	0.0569247i
$935$	2.43989	+	16.9698i	0.0797930	+	0.554972i
$936$	−0.196703	+	5.37931i	−0.00642943	+	0.175828i
$937$	−17.1751	+	7.84362i	−0.561087	+	0.256240i	−0.675708	−	0.737169i	$-0.736162\pi$
$937$	−17.1751	+	7.84362i	−0.561087	+	0.256240i	0.114621	+	0.993409i	$0.463435\pi$
$938$	19.7255	−	20.6875i	0.644059	−	0.675470i
$939$	−6.14927	−	0.112391i	−0.200674	−	0.00366774i
$940$	−1.66894	+	2.12222i	−0.0544347	+	0.0692193i
$941$	1.08190	+	22.7118i	0.0352689	+	0.740385i	0.945370	+	0.325999i	$0.105701\pi$
$941$	1.08190	+	22.7118i	0.0352689	+	0.740385i	−0.910101	+	0.414386i	$0.863996\pi$
$942$	4.58069	−	40.1940i	0.149247	−	1.30959i
$943$	−5.50147	+	51.3477i	−0.179153	+	1.67211i
$944$		−	13.2728i		−	0.431992i
$945$	35.1348	−	8.25528i	1.14294	−	0.268544i
$946$	2.98330	−	20.7493i	0.0969956	−	0.674619i
$947$	5.03814	+	52.7618i	0.163717	+	1.71453i	0.587886	+	0.808944i	$0.299960\pi$
$947$	5.03814	+	52.7618i	0.163717	+	1.71453i	−0.424169	+	0.905583i	$0.639434\pi$
$948$	−0.332078	+	0.0577300i	−0.0107854	+	0.00187498i
$949$	−9.26377	−	0.884583i	−0.300715	−	0.0287148i
$950$	−0.502064	+	0.0967649i	−0.0162891	+	0.00313947i
$951$	−23.9595	+	14.7862i	−0.776939	+	0.479476i
$952$	−2.67972	−	11.0459i	−0.0868501	−	0.358001i
$953$	−26.3011	+	30.3531i	−0.851976	+	0.983233i	−0.999983	−	0.00575369i	$-0.998169\pi$
$953$	−26.3011	+	30.3531i	−0.851976	+	0.983233i	0.148008	+	0.988986i	$0.452714\pi$
$954$	−36.9954	−	10.4202i	−1.19777	−	0.337367i
$955$	19.1153	+	12.2847i	0.618557	+	0.397522i
$956$	−0.219717	+	1.14000i	−0.00710615	+	0.0368702i
$957$	−12.0808	+	9.14817i	−0.390518	+	0.295718i
$958$	−4.54115	+	11.3433i	−0.146718	+	0.366484i
$959$	5.58518	+	28.9787i	0.180355	+	0.935770i
$960$	−6.96646	+	32.8983i	−0.224842	+	1.06179i
$961$	−8.19339	−	7.81238i	−0.264303	−	0.252012i
$962$	−2.23403	+	4.89184i	−0.0720279	+	0.157719i
$963$	17.3957	−	44.8834i	0.560568	−	1.44635i
$964$	0.281597	+	0.438173i	0.00906961	+	0.0141126i
$965$	−17.5791	−	30.4479i	−0.565891	−	0.980152i
$966$	20.2798	+	27.4328i	0.652492	+	0.882635i
$967$	−1.19555	+	2.07075i	−0.0384463	+	0.0665909i	−0.884608	−	0.466335i	$-0.845574\pi$
$967$	−1.19555	+	2.07075i	−0.0384463	+	0.0665909i	0.846162	+	0.532926i	$0.178908\pi$
$968$	93.3737	−	4.44794i	3.00114	−	0.142962i
$969$	−1.32656	+	5.06249i	−0.0426151	+	0.162631i
$970$	54.6201	−	5.21559i	1.75375	−	0.167462i
$971$	42.9061	−	12.5984i	1.37692	−	0.404301i	0.492226	−	0.870468i	$-0.336184\pi$
$971$	42.9061	−	12.5984i	1.37692	−	0.404301i	0.884697	+	0.466167i	$0.154365\pi$
$972$	2.93883	−	3.76658i	0.0942631	−	0.120813i
$973$	39.4170	−	34.1550i	1.26365	−	1.09496i
$974$	2.89302	+	3.67878i	0.0926984	+	0.117876i
$975$	−0.0627751	+	0.148861i	−0.00201041	+	0.00476737i
$976$	−6.57952	+	2.27719i	−0.210605	+	0.0728912i
$977$	−18.4684	+	9.52111i	−0.590855	+	0.304607i	−0.727603	−	0.685999i	$-0.759366\pi$
$977$	−18.4684	+	9.52111i	−0.590855	+	0.304607i	0.136747	+	0.990606i	$0.456335\pi$
$978$	−6.31503	+	38.8659i	−0.201932	+	1.24280i
$979$	−26.3362	−	5.07589i	−0.841709	−	0.162226i
$980$	1.91552	+	0.562447i	0.0611890	+	0.0179667i
$981$	−9.46961	−	0.798755i	−0.302341	−	0.0255023i
$982$	0.746117	+	0.861065i	0.0238095	+	0.0274777i
$983$	−18.8527	+	26.4749i	−0.601307	+	0.844418i	−0.997269	−	0.0738491i	$-0.976472\pi$
$983$	−18.8527	+	26.4749i	−0.601307	+	0.844418i	0.395962	+	0.918267i	$0.370411\pi$
$984$	−52.5586	−	19.2733i	−1.67551	−	0.614409i
$985$	2.66417	−	1.89715i	0.0848877	−	0.0604482i
$986$	1.65422	+	1.30089i	0.0526810	+	0.0414288i
$987$	−21.8317	−	1.44025i	−0.694912	−	0.0458437i
$988$	0.399526	−	0.230666i	0.0127106	−	0.00733848i
$989$	−10.3737	+	5.83075i	−0.329863	+	0.185407i
$990$	53.3444	−	16.3057i	1.69540	−	0.518229i
$991$	32.4415	−	20.8489i	1.03054	−	0.662286i	0.0879081	−	0.996129i	$-0.471982\pi$
$991$	32.4415	−	20.8489i	1.03054	−	0.662286i	0.942629	+	0.333843i	$0.108345\pi$
$992$	2.83178	+	7.07345i	0.0899092	+	0.224582i
$993$	0.573253	−	31.3645i	0.0181916	−	0.995322i
$994$	38.5777	+	9.35884i	1.22361	+	0.296844i
$995$	−0.113355	+	1.18711i	−0.00359361	+	0.0376339i
$996$	2.96322	−	2.02952i	0.0938932	−	0.0643079i
$997$	−39.2863	+	30.8951i	−1.24421	+	0.978458i	−0.244249	+	0.969713i	$0.578541\pi$
$997$	−39.2863	+	30.8951i	−1.24421	+	0.978458i	−0.999962	+	0.00874525i	$0.997216\pi$
$998$	−2.59686	+	8.84409i	−0.0822021	+	0.279955i
$999$	31.2369	−	17.7350i	0.988292	−	0.561109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.o.a.149.8	yes	440
3.2	odd	2		621.2.s.a.287.15		440
9.2	odd	6	inner	207.2.o.a.11.8	✓	440
9.7	even	3		621.2.s.a.494.15		440
23.21	odd	22	inner	207.2.o.a.113.8	yes	440
69.44	even	22		621.2.s.a.44.15		440
207.182	even	66	inner	207.2.o.a.182.8	yes	440
207.205	odd	66		621.2.s.a.251.15		440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.8	✓	440	9.2	odd	6	inner
207.2.o.a.113.8	yes	440	23.21	odd	22	inner
207.2.o.a.149.8	yes	440	1.1	even	1	trivial
207.2.o.a.182.8	yes	440	207.182	even	66	inner
621.2.s.a.44.15		440	69.44	even	22
621.2.s.a.251.15		440	207.205	odd	66
621.2.s.a.287.15		440	3.2	odd	2
621.2.s.a.494.15		440	9.7	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.o (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.596316 + 1.15669i) q^{2} +(-1.67548 - 0.439038i) q^{3} +(0.177772 + 0.249645i) q^{4} +(0.518882 - 2.13886i) q^{5} +(1.50695 - 1.67621i) q^{6} +(-2.98233 - 1.03220i) q^{7} +(-2.97099 + 0.427164i) q^{8} +(2.61449 + 1.47120i) q^{9} +(2.16459 + 1.87562i) q^{10} +(0.308894 - 6.48448i) q^{11} +(-0.188250 - 0.496325i) q^{12} +(-0.195519 - 0.564915i) q^{13} +(2.97234 - 2.83412i) q^{14} +(-1.80842 + 3.35582i) q^{15} +(1.07708 - 3.11201i) q^{16} +(-0.498465 - 1.09149i) q^{17} +(-3.26079 + 2.14686i) q^{18} +(2.29054 + 1.04605i) q^{19} +(0.626199 - 0.250692i) q^{20} +(4.54368 + 3.03878i) q^{21} +(7.31634 + 4.22409i) q^{22} +(-0.627719 - 4.75457i) q^{23} +(5.16539 + 0.588671i) q^{24} +(0.138686 + 0.0714977i) q^{25} +(0.770024 + 0.110713i) q^{26} +(-3.73463 - 3.61283i) q^{27} +(-0.272491 - 0.928020i) q^{28} +(1.09780 + 0.781740i) q^{29} +(-2.80326 - 4.09291i) q^{30} +(-4.11834 - 1.64873i) q^{31} +(-1.18525 - 1.24305i) q^{32} +(-3.36448 + 10.7290i) q^{33} +(1.55976 + 0.0743003i) q^{34} +(-3.75520 + 5.84321i) q^{35} +(0.0975040 + 0.914233i) q^{36} +(-1.94758 + 6.63286i) q^{37} +(-2.57584 + 2.02567i) q^{38} +(0.0795699 + 1.03235i) q^{39} +(-0.627950 + 6.57619i) q^{40} +(-10.4645 - 2.53865i) q^{41} +(-6.22440 + 3.44356i) q^{42} +(-0.922216 - 2.30358i) q^{43} +(1.67373 - 1.07564i) q^{44} +(4.50331 - 4.82866i) q^{45} +(5.87389 + 2.10915i) q^{46} +(-3.46639 + 2.00132i) q^{47} +(-3.17091 + 4.74124i) q^{48} +(2.32651 + 1.82958i) q^{49} +(-0.165401 + 0.117782i) q^{50} +(0.355966 + 2.04761i) q^{51} +(0.106271 - 0.149236i) q^{52} +(6.44700 + 7.44024i) q^{53} +(6.40595 - 2.16542i) q^{54} +(-13.7091 - 4.02536i) q^{55} +(9.30140 + 1.79270i) q^{56} +(-3.37850 - 2.75828i) q^{57} +(-1.55887 + 0.803652i) q^{58} +(3.80878 - 1.31823i) q^{59} +(-1.15925 + 0.145106i) q^{60} +(-1.30693 - 1.66190i) q^{61} +(4.36290 - 3.78048i) q^{62} +(-6.27872 - 7.08628i) q^{63} +(8.46407 - 2.48528i) q^{64} +(-1.30973 + 0.125064i) q^{65} +(-10.4039 - 10.2895i) q^{66} +(6.95211 - 0.331170i) q^{67} +(0.183871 - 0.318475i) q^{68} +(-1.03570 + 8.24180i) q^{69} +(-4.51950 - 7.82801i) q^{70} +(5.22568 + 8.13132i) q^{71} +(-8.39607 - 3.25411i) q^{72} +(6.46681 - 14.1603i) q^{73} +(-6.51080 - 6.20803i) q^{74} +(-0.200976 - 0.180682i) q^{75} +(0.146050 + 0.757780i) q^{76} +(-7.61447 + 19.0200i) q^{77} +(-1.24156 - 0.523567i) q^{78} +(0.120169 - 0.623495i) q^{79} +(-6.09728 - 3.91849i) q^{80} +(4.67113 + 7.69289i) q^{81} +(9.17657 - 10.5903i) q^{82} +(1.59516 + 6.57534i) q^{83} +(0.0491189 + 1.67452i) q^{84} +(-2.59318 + 0.499795i) q^{85} +(3.21447 + 0.306944i) q^{86} +(-1.49613 - 1.79177i) q^{87} +(1.85221 + 19.3973i) q^{88} +(0.587972 - 4.08944i) q^{89} +(2.89987 + 8.08834i) q^{90} +1.88658i q^{91} +(1.07537 - 1.00194i) q^{92} +(6.17635 + 4.57053i) q^{93} +(-0.247848 - 5.20297i) q^{94} +(3.42588 - 4.35636i) q^{95} +(1.44011 + 2.60308i) q^{96} +(13.2198 - 13.8646i) q^{97} +(-3.50360 + 1.60004i) q^{98} +(10.3476 - 16.4992i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23}+ \cdots + 242 q^{99}+O(q^{100}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more