LMFDB - Embedded newform 230.2.l.a.113.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(7,230)] 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("230.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			113.1
Character	$\chi$	$=$	230.113
Dual form			230.2.l.a.57.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.977147 + 0.212565i) q^{2} +(-1.72503 + 2.30436i) q^{3} +(0.909632 - 0.415415i) q^{4} +(0.267486 - 2.22001i) q^{5} +(1.19578 - 2.61838i) q^{6} +(-3.05628 + 0.218590i) q^{7} +(-0.800541 + 0.599278i) q^{8} +(-1.48918 - 5.07170i) q^{9} +(0.210524 + 2.22614i) q^{10} +(-0.582269 - 0.906028i) q^{11} +(-0.611871 + 2.81273i) q^{12} +(0.0976911 - 1.36590i) q^{13} +(2.93997 - 0.863254i) q^{14} +(4.65429 + 4.44596i) q^{15} +(0.654861 - 0.755750i) q^{16} +(5.82495 - 2.17259i) q^{17} +(2.53322 + 4.63924i) q^{18} +(-2.12916 - 4.66221i) q^{19} +(-0.678912 - 2.13051i) q^{20} +(4.76846 - 7.41986i) q^{21} +(0.761553 + 0.761553i) q^{22} +(-2.80382 - 3.89084i) q^{23} -2.87851i q^{24} +(-4.85690 - 1.18765i) q^{25} +(0.194884 + 1.35545i) q^{26} +(6.16487 + 2.29938i) q^{27} +(-2.68929 + 1.46846i) q^{28} +(6.11633 + 2.79324i) q^{29} +(-5.49299 - 3.35502i) q^{30} +(-0.518143 + 3.60377i) q^{31} +(-0.479249 + 0.877679i) q^{32} +(3.09225 + 0.221162i) q^{33} +(-5.23001 + 3.36112i) q^{34} +(-0.332243 + 6.84345i) q^{35} +(-3.46147 - 3.99475i) q^{36} +(-7.48501 - 4.08713i) q^{37} +(3.07153 + 4.10308i) q^{38} +(2.97901 + 2.58133i) q^{39} +(1.11627 + 1.93751i) q^{40} +(-10.3436 - 3.03716i) q^{41} +(-3.08228 + 8.26390i) q^{42} +(-2.52405 - 1.88948i) q^{43} +(-0.906028 - 0.582269i) q^{44} +(-11.6576 + 1.94940i) q^{45} +(3.56680 + 3.20593i) q^{46} +(1.06238 - 1.06238i) q^{47} +(0.611871 + 2.81273i) q^{48} +(2.36433 - 0.339940i) q^{49} +(4.99836 + 0.128096i) q^{50} +(-5.04174 + 17.1706i) q^{51} +(-0.478552 - 1.28305i) q^{52} +(0.318337 + 4.45094i) q^{53} +(-6.51275 - 0.936392i) q^{54} +(-2.16714 + 1.05029i) q^{55} +(2.31568 - 2.00655i) q^{56} +(14.4163 + 3.13607i) q^{57} +(-6.57030 - 1.42928i) q^{58} +(4.89085 - 4.23795i) q^{59} +(6.08062 + 2.11073i) q^{60} +(-7.99883 - 1.15006i) q^{61} +(-0.259734 - 3.63155i) q^{62} +(5.65999 + 15.1750i) q^{63} +(0.281733 - 0.959493i) q^{64} +(-3.00618 - 0.582235i) q^{65} +(-3.06859 + 0.441197i) q^{66} +(-2.89371 - 13.3022i) q^{67} +(4.39603 - 4.39603i) q^{68} +(13.8026 + 0.250782i) q^{69} +(-1.13003 - 6.75768i) q^{70} +(2.34878 + 1.50947i) q^{71} +(4.23151 + 3.16767i) q^{72} +(-4.79092 + 12.8449i) q^{73} +(8.18274 + 2.40267i) q^{74} +(11.1150 - 9.14335i) q^{75} +(-3.87351 - 3.35641i) q^{76} +(1.97763 + 2.64180i) q^{77} +(-3.45963 - 1.88910i) q^{78} +(0.149343 + 0.172351i) q^{79} +(-1.50261 - 1.65595i) q^{80} +(-2.59304 + 1.66645i) q^{81} +(10.7528 + 0.769059i) q^{82} +(3.51122 - 6.43033i) q^{83} +(1.25522 - 8.73023i) q^{84} +(-3.26509 - 13.5126i) q^{85} +(2.86801 + 1.30978i) q^{86} +(-16.9875 + 9.27586i) q^{87} +(1.00909 + 0.376372i) q^{88} +(1.55864 + 10.8406i) q^{89} +(10.9768 - 4.38284i) q^{90} +4.19593i q^{91} +(-4.16675 - 2.37448i) q^{92} +(-7.41058 - 7.41058i) q^{93} +(-0.812278 + 1.26393i) q^{94} +(-10.9197 + 3.47968i) q^{95} +(-1.19578 - 2.61838i) q^{96} +(3.00843 + 5.50953i) q^{97} +(-2.23804 + 0.834746i) q^{98} +(-3.72800 + 4.30234i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{13}{22}\right)$

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 $

$2$	−0.977147	+	0.212565i	−0.690947	+	0.150306i
$2$	−0.977147	+	0.212565i	−0.690947	+	0.150306i
$3$	−1.72503	+	2.30436i	−0.995944	+	1.33043i	−0.0525977	+	0.998616i	$0.516750\pi$
$3$	−1.72503	+	2.30436i	−0.995944	+	1.33043i	−0.943346	+	0.331810i	$0.892341\pi$
$4$	0.909632	−	0.415415i	0.454816	−	0.207708i
$5$	0.267486	−	2.22001i	0.119624	−	0.992819i
$5$	0.267486	−	2.22001i	0.119624	−	0.992819i
$6$	1.19578	−	2.61838i	0.488173	−	1.06895i
$7$	−3.05628	+	0.218590i	−1.15517	+	0.0826191i	−0.635745	−	0.771899i	$-0.719307\pi$
$7$	−3.05628	+	0.218590i	−1.15517	+	0.0826191i	−0.519421	+	0.854518i	$0.673852\pi$
$8$	−0.800541	+	0.599278i	−0.283034	+	0.211877i
$9$	−1.48918	−	5.07170i	−0.496395	−	1.69057i
$10$	0.210524	+	2.22614i	0.0665735	+	0.703966i
$11$	−0.582269	−	0.906028i	−0.175561	−	0.273178i	0.742311	−	0.670056i	$-0.233730\pi$
$11$	−0.582269	−	0.906028i	−0.175561	−	0.273178i	−0.917871	+	0.396878i	$0.870094\pi$
$12$	−0.611871	+	2.81273i	−0.176632	+	0.811964i
$13$	0.0976911	−	1.36590i	0.0270946	−	0.378833i	−0.965755	−	0.259457i	$-0.916456\pi$
$13$	0.0976911	−	1.36590i	0.0270946	−	0.378833i	0.992849	−	0.119375i	$-0.0380891\pi$
$14$	2.93997	−	0.863254i	0.785741	−	0.230714i
$15$	4.65429	+	4.44596i	1.20173	+	1.14794i
$16$	0.654861	−	0.755750i	0.163715	−	0.188937i
$17$	5.82495	−	2.17259i	1.41276	−	0.526931i	0.476790	−	0.879017i	$-0.341800\pi$
$17$	5.82495	−	2.17259i	1.41276	−	0.526931i	0.935968	+	0.352086i	$0.114528\pi$
$18$	2.53322	+	4.63924i	0.597085	+	1.09348i
$19$	−2.12916	−	4.66221i	−0.488463	−	1.06958i	−0.980049	−	0.198756i	$-0.936310\pi$
$19$	−2.12916	−	4.66221i	−0.488463	−	1.06958i	0.491586	−	0.870829i	$-0.336417\pi$
$20$	−0.678912	−	2.13051i	−0.151809	−	0.476397i
$21$	4.76846	−	7.41986i	1.04056	−	1.61915i
$22$	0.761553	+	0.761553i	0.162364	+	0.162364i
$23$	−2.80382	−	3.89084i	−0.584636	−	0.811296i
$23$	−2.80382	−	3.89084i	−0.584636	−	0.811296i
$24$		−	2.87851i		−	0.587573i
$25$	−4.85690	−	1.18765i	−0.971380	−	0.237529i
$26$	0.194884	+	1.35545i	0.0382200	+	0.265826i
$27$	6.16487	+	2.29938i	1.18643	+	0.442515i
$28$	−2.68929	+	1.46846i	−0.508227	+	0.277513i
$29$	6.11633	+	2.79324i	1.13577	+	0.518691i	0.892402	−	0.451242i	$-0.149019\pi$
$29$	6.11633	+	2.79324i	1.13577	+	0.518691i	0.243373	+	0.969933i	$0.421746\pi$
$30$	−5.49299	−	3.35502i	−1.00288	−	0.612540i
$31$	−0.518143	+	3.60377i	−0.0930613	+	0.647256i	0.888890	+	0.458121i	$0.151477\pi$
$31$	−0.518143	+	3.60377i	−0.0930613	+	0.647256i	−0.981951	+	0.189135i	$0.939432\pi$
$32$	−0.479249	+	0.877679i	−0.0847201	+	0.155153i
$33$	3.09225	+	0.221162i	0.538291	+	0.0384994i
$34$	−5.23001	+	3.36112i	−0.896939	+	0.576428i
$35$	−0.332243	+	6.84345i	−0.0561592	+	1.15675i
$36$	−3.46147	−	3.99475i	−0.576911	−	0.665791i
$37$	−7.48501	−	4.08713i	−1.23053	−	0.671919i	−0.273488	−	0.961875i	$-0.588177\pi$
$37$	−7.48501	−	4.08713i	−1.23053	−	0.671919i	−0.957040	+	0.289956i	$0.906359\pi$
$38$	3.07153	+	4.10308i	0.498267	+	0.665607i
$39$	2.97901	+	2.58133i	0.477024	+	0.413343i
$40$	1.11627	+	1.93751i	0.176498	+	0.306347i
$41$	−10.3436	−	3.03716i	−1.61540	−	0.474325i	−0.655626	−	0.755086i	$-0.727595\pi$
$41$	−10.3436	−	3.03716i	−1.61540	−	0.474325i	−0.959778	+	0.280760i	$0.909413\pi$
$42$	−3.08228	+	8.26390i	−0.475606	+	1.27515i
$43$	−2.52405	−	1.88948i	−0.384915	−	0.288144i	0.389245	−	0.921134i	$-0.372736\pi$
$43$	−2.52405	−	1.88948i	−0.384915	−	0.288144i	−0.774159	+	0.632991i	$0.781827\pi$
$44$	−0.906028	−	0.582269i	−0.136589	−	0.0877804i
$45$	−11.6576	+	1.94940i	−1.73781	+	0.290599i
$46$	3.56680	+	3.20593i	0.525895	+	0.472688i
$47$	1.06238	−	1.06238i	0.154964	−	0.154964i	−0.625367	−	0.780331i	$-0.715051\pi$
$47$	1.06238	−	1.06238i	0.154964	−	0.154964i	0.780331	+	0.625367i	$0.215051\pi$
$48$	0.611871	+	2.81273i	0.0883160	+	0.405982i
$49$	2.36433	−	0.339940i	0.337762	−	0.0485628i
$50$	4.99836	+	0.128096i	0.706875	+	0.0181155i
$51$	−5.04174	+	17.1706i	−0.705984	+	2.40436i
$52$	−0.478552	−	1.28305i	−0.0663633	−	0.177927i
$53$	0.318337	+	4.45094i	0.0437270	+	0.611383i	0.971318	+	0.237785i	$0.0764215\pi$
$53$	0.318337	+	4.45094i	0.0437270	+	0.611383i	−0.927591	+	0.373598i	$0.878124\pi$
$54$	−6.51275	−	0.936392i	−0.886273	−	0.127427i
$55$	−2.16714	+	1.05029i	−0.292217	+	0.141622i
$56$	2.31568	−	2.00655i	0.309446	−	0.268137i
$57$	14.4163	+	3.13607i	1.90948	+	0.415383i
$58$	−6.57030	−	1.42928i	−0.862723	−	0.187674i
$59$	4.89085	−	4.23795i	0.636735	−	0.551734i	−0.275552	−	0.961286i	$-0.588861\pi$
$59$	4.89085	−	4.23795i	0.636735	−	0.551734i	0.912287	+	0.409552i	$0.134315\pi$
$60$	6.08062	+	2.11073i	0.785004	+	0.272494i
$61$	−7.99883	−	1.15006i	−1.02414	−	0.147250i	−0.390282	−	0.920695i	$-0.627623\pi$
$61$	−7.99883	−	1.15006i	−1.02414	−	0.147250i	−0.633863	+	0.773446i	$0.718532\pi$
$62$	−0.259734	−	3.63155i	−0.0329862	−	0.461207i
$63$	5.65999	+	15.1750i	0.713092	+	1.91187i
$64$	0.281733	−	0.959493i	0.0352166	−	0.119937i
$65$	−3.00618	−	0.582235i	−0.372871	−	0.0722174i
$66$	−3.06859	+	0.441197i	−0.377718	+	0.0543076i
$67$	−2.89371	−	13.3022i	−0.353523	−	1.62512i	−0.719500	−	0.694493i	$-0.755629\pi$
$67$	−2.89371	−	13.3022i	−0.353523	−	1.62512i	0.365977	−	0.930624i	$-0.380735\pi$
$68$	4.39603	−	4.39603i	0.533097	−	0.533097i
$69$	13.8026	+	0.250782i	1.66163	+	0.0301906i
$70$	−1.13003	−	6.75768i	−0.135064	−	0.807697i
$71$	2.34878	+	1.50947i	0.278749	+	0.179141i	0.672544	−	0.740057i	$-0.265202\pi$
$71$	2.34878	+	1.50947i	0.278749	+	0.179141i	−0.393795	+	0.919198i	$0.628838\pi$
$72$	4.23151	+	3.16767i	0.498688	+	0.373313i
$73$	−4.79092	+	12.8449i	−0.560735	+	1.50339i	0.278946	+	0.960307i	$0.410015\pi$
$73$	−4.79092	+	12.8449i	−0.560735	+	1.50339i	−0.839681	+	0.543081i	$0.817258\pi$
$74$	8.18274	+	2.40267i	0.951224	+	0.279304i
$75$	11.1150	−	9.14335i	1.28346	−	1.05578i
$76$	−3.87351	−	3.35641i	−0.444322	−	0.385007i
$77$	1.97763	+	2.64180i	0.225372	+	0.301061i
$78$	−3.45963	−	1.88910i	−0.391726	−	0.213899i
$79$	0.149343	+	0.172351i	0.0168024	+	0.0193910i	0.764089	−	0.645111i	$-0.223189\pi$
$79$	0.149343	+	0.172351i	0.0168024	+	0.0193910i	−0.747286	+	0.664502i	$0.768644\pi$
$80$	−1.50261	−	1.65595i	−0.167997	−	0.185141i
$81$	−2.59304	+	1.66645i	−0.288116	+	0.185161i
$82$	10.7528	+	0.769059i	1.18745	+	0.0849283i
$83$	3.51122	−	6.43033i	0.385407	−	0.705820i	−0.610898	−	0.791710i	$-0.709191\pi$
$83$	3.51122	−	6.43033i	0.385407	−	0.705820i	0.996305	+	0.0858893i	$0.0273732\pi$
$84$	1.25522	−	8.73023i	0.136955	−	0.952546i
$85$	−3.26509	−	13.5126i	−0.354148	−	1.46565i
$86$	2.86801	+	1.30978i	0.309265	+	0.141237i
$87$	−16.9875	+	9.27586i	−1.82125	+	0.994476i
$88$	1.00909	+	0.376372i	0.107570	+	0.0401214i
$89$	1.55864	+	10.8406i	0.165216	+	1.14910i	0.888609	+	0.458666i	$0.151672\pi$
$89$	1.55864	+	10.8406i	0.165216	+	1.14910i	−0.723393	+	0.690437i	$0.757418\pi$
$90$	10.9768	−	4.38284i	1.15705	−	0.461992i
$91$			4.19593i			0.439853i
$92$	−4.16675	−	2.37448i	−0.434414	−	0.247557i
$93$	−7.41058	−	7.41058i	−0.768442	−	0.768442i
$94$	−0.812278	+	1.26393i	−0.0837801	+	0.130364i
$95$	−10.9197	+	3.47968i	−1.12034	+	0.357008i
$96$	−1.19578	−	2.61838i	−0.122043	−	0.267238i
$97$	3.00843	+	5.50953i	0.305460	+	0.559408i	0.984647	−	0.174557i	$-0.0558494\pi$
$97$	3.00843	+	5.50953i	0.305460	+	0.559408i	−0.679187	+	0.733965i	$0.737668\pi$
$98$	−2.23804	+	0.834746i	−0.226076	+	0.0843221i
$99$	−3.72800	+	4.30234i	−0.374678	+	0.432401i
$100$	−4.91136	+	0.937309i	−0.491136	+	0.0937309i
$101$	−15.2871	+	4.48870i	−1.52112	+	0.446643i	−0.932321	−	0.361633i	$-0.882219\pi$
$101$	−15.2871	+	4.48870i	−1.52112	+	0.446643i	−0.588804	+	0.808276i	$0.700401\pi$
$102$	1.27665	−	17.8499i	0.126407	−	1.76740i
$103$	−0.754353	+	3.46771i	−0.0743286	+	0.341683i	−0.999261	−	0.0384496i	$-0.987758\pi$
$103$	−0.754353	+	3.46771i	−0.0743286	+	0.341683i	0.924932	+	0.380133i	$0.124122\pi$
$104$	0.740348	+	1.15200i	0.0725971	+	0.112963i
$105$	−15.1967	−	12.5707i	−1.48304	−	1.22678i
$106$	−1.25718	−	4.28155i	−0.122108	−	0.415861i
$107$	14.9847	−	11.2174i	1.44863	−	1.08443i	0.469098	−	0.883146i	$-0.344579\pi$
$107$	14.9847	−	11.2174i	1.44863	−	1.08443i	0.979533	−	0.201285i	$-0.0645117\pi$
$108$	6.56296	−	0.469392i	0.631521	−	0.0451673i
$109$	0.832474	−	1.82286i	0.0797366	−	0.174599i	−0.865565	−	0.500797i	$-0.833040\pi$
$109$	0.832474	−	1.82286i	0.0797366	−	0.174599i	0.945301	+	0.326198i	$0.105768\pi$
$110$	1.89436	−	1.48695i	0.180620	−	0.141775i
$111$	22.3301	−	10.1978i	2.11948	−	0.967932i
$112$	−1.83624	+	2.45293i	−0.173508	+	0.231780i
$113$	14.0537	−	3.05719i	1.32206	−	0.287596i	0.504484	−	0.863421i	$-0.331683\pi$
$113$	14.0537	−	3.05719i	1.32206	−	0.287596i	0.817573	+	0.575825i	$0.195319\pi$
$114$	−14.7535			−1.38179
$115$	−9.38769	+	5.18376i	−0.875406	+	0.483388i
$116$	6.72396			0.624304
$117$	−7.07291	+	1.53862i	−0.653891	+	0.142245i
$118$	−3.87824	+	5.18072i	−0.357021	+	0.476924i
$119$	−17.3278	+	7.91333i	−1.58843	+	0.725414i
$120$	−6.39032	−	0.769962i	−0.583354	−	0.0702876i
$121$	4.08771	−	8.95085i	0.371610	−	0.813713i
$122$	8.06049	−	0.576498i	0.729763	−	0.0521936i
$123$	24.8418	−	18.5963i	2.23991	−	1.67677i
$124$	1.02574	+	3.49335i	0.0921141	+	0.313712i
$125$	−3.93574	+	10.4647i	−0.352024	+	0.935991i
$126$	−8.75632	−	13.6251i	−0.780075	−	1.21382i
$127$	−1.59400	+	7.32749i	−0.141444	+	0.650210i	0.850756	+	0.525560i	$0.176144\pi$
$127$	−1.59400	+	7.32749i	−0.141444	+	0.650210i	−0.992201	+	0.124649i	$0.960219\pi$
$128$	−0.0713392	+	0.997452i	−0.00630555	+	0.0881631i
$129$	8.70812	−	2.55693i	0.766707	−	0.225125i
$130$	3.06125	−	0.0700809i	0.268489	−	0.00614651i
$131$	7.13870	−	8.23850i	0.623711	−	0.719801i	−0.352696	−	0.935738i	$-0.614735\pi$
$131$	7.13870	−	8.23850i	0.623711	−	0.719801i	0.976407	+	0.215937i	$0.0692806\pi$
$132$	2.90468	−	1.08339i	0.252820	−	0.0942970i
$133$	7.52643	+	13.7836i	0.652624	+	1.19519i
$134$	5.65515	+	12.3831i	0.488531	+	1.06973i
$135$	6.75366	−	13.0710i	0.581263	−	1.12497i
$136$	−3.36112	+	5.23001i	−0.288214	+	0.448470i
$137$	−6.04503	−	6.04503i	−0.516462	−	0.516462i	0.400037	−	0.916499i	$-0.368997\pi$
$137$	−6.04503	−	6.04503i	−0.516462	−	0.516462i	−0.916499	+	0.400037i	$0.868997\pi$
$138$	−13.5404	+	2.68889i	−1.15264	+	0.228894i
$139$			5.24409i			0.444798i	0.974956	+	0.222399i	$0.0713887\pi$
$139$			5.24409i			0.444798i	−0.974956	+	0.222399i	$0.928611\pi$
$140$	2.54065	+	6.36304i	0.214724	+	0.537775i
$141$	0.615479	+	4.28075i	0.0518327	+	0.360504i
$142$	−2.61597	−	0.975705i	−0.219527	−	0.0818794i
$143$	−1.29443	+	0.706811i	−0.108245	+	0.0591065i
$144$	−4.80814	−	2.19580i	−0.400678	−	0.182984i
$145$	7.83705	−	12.8312i	0.650832	−	1.06557i
$146$	1.95104	−	13.5698i	0.161469	−	1.12304i
$147$	−3.29519	+	6.03469i	−0.271783	+	0.497733i
$148$	−8.50646	−	0.608394i	−0.699227	−	0.0500097i
$149$	3.20237	−	2.05804i	0.262348	−	0.168601i	−0.402854	−	0.915264i	$-0.631982\pi$
$149$	3.20237	−	2.05804i	0.262348	−	0.168601i	0.665202	+	0.746663i	$0.268345\pi$
$150$	−8.91748	+	11.2971i	−0.728109	+	0.922402i
$151$	10.1970	+	11.7680i	0.829824	+	0.957668i	0.999613	−	0.0278127i	$-0.00885420\pi$
$151$	10.1970	+	11.7680i	0.829824	+	0.957668i	−0.169789	+	0.985480i	$0.554309\pi$
$152$	4.49844	+	2.45633i	0.364872	+	0.199235i
$153$	−19.6932	−	26.3070i	−1.59210	−	2.12679i
$154$	−2.49399	−	2.16105i	−0.200971	−	0.174143i
$155$	7.86181	+	2.11424i	0.631476	+	0.169820i
$156$	3.78213	+	1.11053i	0.302813	+	0.0889138i
$157$	3.95050	−	10.5917i	0.315284	−	0.845310i	−0.678562	−	0.734543i	$-0.737397\pi$
$157$	3.95050	−	10.5917i	0.315284	−	0.845310i	0.993846	−	0.110767i	$-0.0353307\pi$
$158$	−0.182566	−	0.136667i	−0.0145242	−	0.0108726i
$159$	−10.8057	−	6.94442i	−0.856949	−	0.550728i
$160$	1.82026	+	1.29871i	0.143905	+	0.102672i
$161$	9.41975	+	11.2786i	0.742380	+	0.888879i
$162$	2.17955	−	2.17955i	0.171242	−	0.171242i
$163$	1.60851	+	7.39420i	0.125988	+	0.579158i	0.996246	+	0.0865624i	$0.0275882\pi$
$163$	1.60851	+	7.39420i	0.125988	+	0.579158i	−0.870258	+	0.492596i	$0.836048\pi$
$164$	−10.6706	+	1.53420i	−0.833232	+	0.119801i
$165$	1.31812	−	6.80567i	0.102615	−	0.529821i
$166$	−2.06412	+	7.02974i	−0.160207	+	0.545614i
$167$	0.353216	+	0.947008i	0.0273327	+	0.0732817i	0.949899	−	0.312556i	$-0.101185\pi$
$167$	0.353216	+	0.947008i	0.0273327	+	0.0732817i	−0.922567	+	0.385838i	$0.873912\pi$
$168$	0.629212	+	8.79753i	0.0485448	+	0.678745i
$169$	11.0115	+	1.58322i	0.847041	+	0.121786i
$170$	6.06278	+	12.5097i	0.464994	+	0.959453i
$171$	−20.4746	+	17.7414i	−1.56573	+	1.35671i
$172$	−3.08088	−	0.670204i	−0.234915	−	0.0511026i
$173$	−11.7311	−	2.55195i	−0.891900	−	0.194021i	−0.256812	−	0.966461i	$-0.582672\pi$
$173$	−11.7311	−	2.55195i	−0.891900	−	0.194021i	−0.635087	+	0.772440i	$0.719036\pi$
$174$	14.6275	−	12.6748i	1.10891	−	0.960876i
$175$	15.1037	+	2.56811i	1.14173	+	0.194131i
$176$	−1.06604	−	0.153273i	−0.0803555	−	0.0115534i
$177$	1.32893	+	18.5809i	0.0998886	+	1.39662i
$178$	−3.82736	−	10.2616i	−0.286873	−	0.769136i
$179$	3.36380	−	11.4560i	0.251422	−	0.856265i	−0.732968	−	0.680263i	$-0.761865\pi$
$179$	3.36380	−	11.4560i	0.251422	−	0.856265i	0.984390	−	0.176001i	$-0.0563163\pi$
$180$	−9.79428	+	6.61596i	−0.730023	+	0.493125i
$181$	18.7808	−	2.70027i	1.39596	−	0.200709i	0.597074	−	0.802186i	$-0.296330\pi$
$181$	18.7808	−	2.70027i	1.39596	−	0.200709i	0.798890	+	0.601477i	$0.205421\pi$
$182$	−0.891909	−	4.10004i	−0.0661127	−	0.303915i
$183$	16.4483	−	16.4483i	1.21590	−	1.21590i
$184$	4.57626	+	1.43451i	0.337367	+	0.105754i
$185$	−11.0756	+	15.5236i	−0.814295	+	1.14131i
$186$	8.81646	+	5.66599i	0.646454	+	0.415451i
$187$	−5.36012	−	4.01253i	−0.391971	−	0.293426i
$188$	0.525047	−	1.40771i	0.0382930	−	0.102668i
$189$	−19.3442	−	5.67997i	−1.40708	−	0.413157i
$190$	9.93048	−	5.72131i	0.720432	−	0.415067i
$191$	5.44055	+	4.71426i	0.393664	+	0.341112i	0.829093	−	0.559111i	$-0.188858\pi$
$191$	5.44055	+	4.71426i	0.393664	+	0.341112i	−0.435428	+	0.900223i	$0.643403\pi$
$192$	1.72503	+	2.30436i	0.124493	+	0.166303i
$193$	3.03545	+	1.65748i	0.218497	+	0.119308i	0.584770	−	0.811199i	$-0.301185\pi$
$193$	3.03545	+	1.65748i	0.218497	+	0.119308i	−0.366273	+	0.930507i	$0.619367\pi$
$194$	−4.11081	−	4.74413i	−0.295139	−	0.340609i
$195$	6.52743	−	5.92297i	0.467439	−	0.424153i
$196$	2.00946	−	1.29140i	0.143533	−	0.0922428i
$197$	−24.9850	−	1.78697i	−1.78011	−	0.127316i	−0.857854	−	0.513894i	$-0.828202\pi$
$197$	−24.9850	−	1.78697i	−1.78011	−	0.127316i	−0.922257	+	0.386578i	$0.873657\pi$
$198$	2.72827	−	4.99646i	0.193890	−	0.355083i
$199$	−2.66992	+	18.5697i	−0.189266	+	1.31637i	0.644650	+	0.764478i	$0.277003\pi$
$199$	−2.66992	+	18.5697i	−0.189266	+	1.31637i	−0.833915	+	0.551892i	$0.813906\pi$
$200$	4.59988	−	1.95987i	0.325261	−	0.138584i
$201$	35.6447	+	16.2784i	2.51419	+	1.14819i
$202$	13.9836	−	7.63563i	0.983884	−	0.537241i
$203$	−19.3038	−	7.19995i	−1.35486	−	0.505337i
$204$	2.54679	+	17.7133i	0.178311	+	1.24018i
$205$	−9.50932	+	22.1506i	−0.664160	+	1.54706i
$206$		−	3.54881i		−	0.247257i
$207$	−15.5578	+	20.0143i	−1.08134	+	1.39109i
$208$	−0.968304	−	0.968304i	−0.0671398	−	0.0671398i
$209$	−2.98435	+	4.64374i	−0.206432	+	0.321214i
$210$	17.5215	+	9.05317i	1.20910	+	0.624728i
$211$	−6.07886	−	13.3108i	−0.418486	−	0.916356i	−0.995057	−	0.0993091i	$-0.968337\pi$
$211$	−6.07886	−	13.3108i	−0.418486	−	0.916356i	0.576571	−	0.817047i	$-0.304391\pi$
$212$	2.13856	+	3.91647i	0.146877	+	0.268984i
$213$	−7.53008	+	2.80858i	−0.515953	+	0.192440i
$214$	−12.2579	+	14.1463i	−0.837930	+	0.967023i
$215$	−4.86982	+	5.09802i	−0.332119	+	0.347682i
$216$	−6.31320	+	1.85372i	−0.429559	+	0.126130i
$217$	0.795847	−	11.1274i	0.0540256	−	0.755377i
$218$	−0.425972	+	1.95816i	−0.0288505	+	0.132623i
$219$	−21.3350	−	33.1979i	−1.44168	−	2.24331i
$220$	−1.53499	+	1.85564i	−0.103489	+	0.125108i
$221$	−2.39850	−	8.16854i	−0.161341	−	0.549475i
$222$	−19.6521	+	14.7113i	−1.31896	+	0.987361i
$223$	−7.78686	+	0.556927i	−0.521447	+	0.0372946i	−0.329582	−	0.944127i	$-0.606908\pi$
$223$	−7.78686	+	0.556927i	−0.521447	+	0.0372946i	−0.191864	+	0.981421i	$0.561453\pi$
$224$	1.27287	−	2.78719i	0.0850471	−	0.186227i
$225$	1.20944	+	26.4014i	0.0806296	+	1.76009i
$226$	−13.0826	+	5.97464i	−0.870244	+	0.397427i
$227$	−1.78641	+	2.38636i	−0.118568	+	0.158388i	−0.855898	−	0.517144i	$-0.826995\pi$
$227$	−1.78641	+	2.38636i	−0.118568	+	0.158388i	0.737330	+	0.675532i	$0.236086\pi$
$228$	14.4163	−	3.13607i	0.954742	−	0.207691i
$229$	−8.72074			−0.576283			−0.288141	−	0.957588i	$-0.593037\pi$
$229$	−8.72074			−0.576283			−0.288141	+	0.957588i	$0.593037\pi$
$230$	8.07126	−	7.06079i	0.532203	−	0.465575i
$231$	−9.49913			−0.624997
$232$	−6.57030	+	1.42928i	−0.431361	+	0.0938369i
$233$	−1.61281	+	2.15447i	−0.105659	+	0.141144i	−0.850254	−	0.526373i	$-0.823552\pi$
$233$	−1.61281	+	2.15447i	−0.105659	+	0.141144i	0.744595	+	0.667516i	$0.232643\pi$
$234$	6.58422	−	3.00691i	0.430424	−	0.196568i
$235$	−2.07433	−	2.64267i	−0.135314	−	0.172389i
$236$	2.68837	−	5.88671i	0.174998	−	0.383192i
$237$	−0.654780	+	0.0468308i	−0.0425325	+	0.00304199i
$238$	15.2497	−	11.4158i	0.988490	−	0.739975i
$239$	−5.27623	−	17.9692i	−0.341291	−	1.16233i	−0.934107	−	0.356992i	$-0.883802\pi$
$239$	−5.27623	−	17.9692i	−0.341291	−	1.16233i	0.592817	−	0.805337i	$-0.298016\pi$
$240$	6.40795	−	0.605995i	0.413631	−	0.0391168i
$241$	−2.91764	−	4.53993i	−0.187941	−	0.292443i	0.734478	−	0.678633i	$-0.237427\pi$
$241$	−2.91764	−	4.53993i	−0.187941	−	0.292443i	−0.922419	+	0.386190i	$0.873791\pi$
$242$	−2.09166	+	9.61520i	−0.134457	+	0.618088i
$243$	−0.775213	+	10.8389i	−0.0497300	+	0.695316i
$244$	−7.75374	+	2.27670i	−0.496382	+	0.145751i
$245$	−0.122243	−	5.33977i	−0.00780983	−	0.341146i
$246$	−20.3211	+	23.4518i	−1.29563	+	1.49523i
$247$	−6.57612	+	2.45276i	−0.418428	+	0.156066i
$248$	−1.74486	−	3.19548i	−0.110799	−	0.202913i
$249$	8.76087	+	19.1836i	0.555197	+	1.21571i
$250$	1.62137	−	11.0622i	0.102544	−	0.699632i
$251$	−6.45704	+	10.0473i	−0.407564	+	0.634183i	−0.982987	−	0.183673i	$-0.941201\pi$
$251$	−6.45704	+	10.0473i	−0.407564	+	0.634183i	0.575423	+	0.817856i	$0.304838\pi$
$252$	11.4524	+	11.4524i	0.721436	+	0.721436i
$253$	−1.89263	+	4.80585i	−0.118989	+	0.302141i
$254$		−	7.49886i		−	0.470521i
$255$	36.7703	+	15.7856i	2.30264	+	0.988533i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	14.5750	+	5.43620i	0.909164	+	0.339101i	0.760160	−	0.649736i	$-0.225121\pi$
$257$	14.5750	+	5.43620i	0.909164	+	0.339101i	0.149004	+	0.988837i	$0.452393\pi$
$258$	−7.96559	+	4.34954i	−0.495916	+	0.270791i
$259$	23.7697	+	10.8553i	1.47698	+	0.674513i
$260$	−2.97639	+	0.719194i	−0.184588	+	0.0446025i
$261$	5.05810	−	35.1798i	0.313088	−	2.17758i
$262$	−5.22434	+	9.56766i	−0.322761	+	0.591092i
$263$	11.8576	+	0.848075i	0.731173	+	0.0522945i	0.431961	−	0.901892i	$-0.357822\pi$
$263$	11.8576	+	0.848075i	0.731173	+	0.0522945i	0.299212	+	0.954187i	$0.403276\pi$
$264$	−2.60801	+	1.67607i	−0.160512	+	0.103155i
$265$	9.96628	+	0.483853i	0.612224	+	0.0297228i
$266$	−10.2843	−	11.8688i	−0.630574	−	0.727721i
$267$	−27.6694	−	15.1086i	−1.69334	−	0.924634i
$268$	−8.15812	−	10.8980i	−0.498337	−	0.665700i
$269$	−1.04648	−	0.906781i	−0.0638051	−	0.0552874i	0.622374	−	0.782720i	$-0.286168\pi$
$269$	−1.04648	−	0.906781i	−0.0638051	−	0.0552874i	−0.686180	+	0.727432i	$0.740714\pi$
$270$	−3.82087	+	14.2079i	−0.232531	+	0.864666i
$271$	−14.0821	−	4.13489i	−0.855429	−	0.251177i	−0.175522	−	0.984475i	$-0.556161\pi$
$271$	−14.0821	−	4.13489i	−0.855429	−	0.251177i	−0.679906	+	0.733299i	$0.737980\pi$
$272$	2.17259	−	5.82495i	0.131733	−	0.353189i
$273$	−9.66896	−	7.23809i	−0.585192	−	0.438069i
$274$	7.19185	+	4.62192i	0.434476	+	0.279221i
$275$	1.75198	+	5.09202i	0.105649	+	0.307060i
$276$	12.6594	−	5.50567i	0.762008	−	0.331403i
$277$	7.05036	−	7.05036i	0.423615	−	0.423615i	−0.462831	−	0.886446i	$-0.653166\pi$
$277$	7.05036	−	7.05036i	0.423615	−	0.423615i	0.886446	+	0.462831i	$0.153166\pi$
$278$	−1.11471	−	5.12424i	−0.0668559	−	0.307332i
$279$	19.0488	−	2.73881i	1.14042	−	0.163968i
$280$	−3.83515	−	5.67757i	−0.229194	−	0.339300i
$281$	6.84721	−	23.3195i	0.408471	−	1.39112i	−0.456689	−	0.889626i	$-0.650965\pi$
$281$	6.84721	−	23.3195i	0.408471	−	1.39112i	0.865160	−	0.501497i	$-0.167217\pi$
$282$	−1.51135	−	4.05209i	−0.0899998	−	0.241299i
$283$	1.03401	+	14.4573i	0.0614654	+	0.859399i	0.930882	+	0.365320i	$0.119040\pi$
$283$	1.03401	+	14.4573i	0.0614654	+	0.859399i	−0.869417	+	0.494080i	$0.835505\pi$
$284$	2.76359	+	0.397344i	0.163989	+	0.0235780i
$285$	10.8183	−	31.1655i	0.640820	−	1.84608i
$286$	1.11460	−	0.965808i	0.0659078	−	0.0571094i
$287$	32.2770	+	7.02142i	1.90525	+	0.414461i
$288$	5.16501	+	1.12358i	0.304351	+	0.0662076i
$289$	16.3621	−	14.1778i	0.962477	−	0.833991i
$290$	−4.93049	+	14.2038i	−0.289528	+	0.834078i
$291$	−17.8856	−	2.57156i	−1.04847	−	0.150747i
$292$	0.978012	+	13.6744i	0.0572338	+	0.800233i
$293$	−2.86297	−	7.67591i	−0.167256	−	0.448431i	0.826098	−	0.563526i	$-0.190556\pi$
$293$	−2.86297	−	7.67591i	−0.167256	−	0.448431i	−0.993355	+	0.115095i	$0.963283\pi$
$294$	1.93712	−	6.59722i	0.112975	−	0.384758i
$295$	−8.10006	−	11.9913i	−0.471604	−	0.698163i
$296$	8.44138	−	1.21369i	0.490645	−	0.0705442i
$297$	−1.50631	−	6.92440i	−0.0874050	−	0.401795i
$298$	−2.69172	+	2.69172i	−0.155927	+	0.155927i
$299$	−5.58840	+	3.44963i	−0.323186	+	0.199497i
$300$	6.31232	−	12.9344i	0.364442	−	0.746771i
$301$	8.12724	+	5.22306i	0.468447	+	0.301052i
$302$	−12.4655	−	9.33154i	−0.717308	−	0.536970i
$303$	16.0271	−	42.9702i	0.920731	−	2.46857i
$304$	−4.91777	−	1.44399i	−0.282053	−	0.0828183i
$305$	−4.69272	+	17.4499i	−0.268704	+	0.999176i
$306$	24.8351	+	21.5197i	1.41973	+	1.23020i
$307$	−8.29152	−	11.0762i	−0.473222	−	0.632151i	0.498890	−	0.866665i	$-0.333741\pi$
$307$	−8.29152	−	11.0762i	−0.473222	−	0.632151i	−0.972113	+	0.234514i	$0.924650\pi$
$308$	2.89636	+	1.58153i	0.165035	+	0.0901161i
$309$	−6.68958	−	7.72019i	−0.380557	−	0.439186i
$310$	−8.13156	−	0.394779i	−0.461841	−	0.0224219i
$311$	−15.3220	+	9.84685i	−0.868830	+	0.558363i	−0.897395	−	0.441229i	$-0.854543\pi$
$311$	−15.3220	+	9.84685i	−0.868830	+	0.558363i	0.0285643	+	0.999592i	$0.490906\pi$
$312$	−3.93175	−	0.281205i	−0.222592	−	0.0159201i
$313$	8.29943	−	15.1993i	0.469112	−	0.859114i	−0.530821	−	0.847484i	$-0.678116\pi$
$313$	8.29943	−	15.1993i	0.469112	−	0.859114i	0.999932	−	0.0116296i	$-0.00370191\pi$
$314$	−1.60879	+	11.1894i	−0.0907893	+	0.631454i
$315$	35.2027	−	8.50613i	1.98345	−	0.479266i
$316$	0.207444	+	0.0947366i	0.0116697	+	0.00532935i
$317$	28.1801	−	15.3875i	1.58275	−	0.864247i	0.584134	−	0.811657i	$-0.301434\pi$
$317$	28.1801	−	15.3875i	1.58275	−	0.864247i	0.998616	−	0.0525900i	$-0.0167476\pi$
$318$	12.0349	+	4.48879i	0.674885	+	0.251719i
$319$	−1.03060	−	7.16799i	−0.0577026	−	0.401330i
$320$	−2.05473	−	0.882101i	−0.114863	−	0.0493109i
$321$			53.8807i			3.00733i
$322$	−11.6019	−	9.01855i	−0.646550	−	0.502584i
$323$	−22.5313	−	22.5313i	−1.25368	−	1.25368i
$324$	−1.66645	+	2.59304i	−0.0925803	+	0.144058i
$325$	−2.09668	+	6.51802i	−0.116303	+	0.361555i
$326$	−3.14350	−	6.88330i	−0.174102	−	0.381231i
$327$	2.76450	+	5.06281i	0.152877	+	0.279974i
$328$	10.1006	−	3.76733i	0.557713	−	0.208016i
$329$	−3.01471	+	3.47917i	−0.166207	+	0.191813i
$330$	0.158656	+	6.93033i	0.00873370	+	0.381502i
$331$	−8.18471	+	2.40325i	−0.449872	+	0.132094i	−0.498818	−	0.866707i	$-0.666232\pi$
$331$	−8.18471	+	2.40325i	−0.449872	+	0.132094i	0.0489451	+	0.998801i	$0.484414\pi$
$332$	0.522668	−	7.30785i	0.0286851	−	0.401070i
$333$	−9.58210	+	44.0482i	−0.525096	+	2.41383i
$334$	−0.546445	−	0.850285i	−0.0299001	−	0.0465255i
$335$	−30.3050	+	2.86592i	−1.65574	+	0.156582i
$336$	−2.48488	−	8.46273i	−0.135561	−	0.461680i
$337$	−23.7140	+	17.7521i	−1.29178	+	0.967017i	−0.291840	+	0.956467i	$0.594267\pi$
$337$	−23.7140	+	17.7521i	−1.29178	+	0.967017i	−0.999944	+	0.0105500i	$0.996642\pi$
$338$	−11.0964	+	0.793632i	−0.603566	+	0.0431679i
$339$	−17.1980	+	37.6585i	−0.934070	+	2.04533i
$340$	−8.58336	−	10.9351i	−0.465498	−	0.593040i
$341$	3.56681	−	1.62891i	0.193154	−	0.0882104i
$342$	16.2355	−	21.6881i	0.877916	−	1.17276i
$343$	13.8067	−	3.00346i	0.745492	−	0.162172i
$344$	3.15293			0.169995
$345$	4.24874	−	30.5748i	0.228744	−	1.64609i
$346$	12.0055			0.645418
$347$	−8.11418	+	1.76513i	−0.435592	+	0.0947572i	−0.425014	−	0.905187i	$-0.639731\pi$
$347$	−8.11418	+	1.76513i	−0.435592	+	0.0947572i	−0.0105780	+	0.999944i	$0.503367\pi$
$348$	−11.5990	+	15.4945i	−0.621772	+	0.830590i
$349$	−8.32569	+	3.80221i	−0.445664	+	0.203528i	−0.625590	−	0.780152i	$-0.715142\pi$
$349$	−8.32569	+	3.80221i	−0.445664	+	0.203528i	0.179926	+	0.983680i	$0.442414\pi$
$350$	−15.3044	+	0.701093i	−0.818054	+	0.0374750i
$351$	3.74297	−	8.19597i	0.199785	−	0.437468i
$352$	1.07425	−	0.0768322i	0.0572579	−	0.00409517i
$353$	6.97633	−	5.22242i	0.371313	−	0.277961i	−0.397283	−	0.917696i	$-0.630047\pi$
$353$	6.97633	−	5.22242i	0.371313	−	0.277961i	0.768596	+	0.639735i	$0.220956\pi$
$354$	−5.24821	−	17.8738i	−0.278939	−	0.949980i
$355$	3.97931	−	4.81056i	0.211200	−	0.255318i
$356$	5.92115	+	9.21348i	0.313820	+	0.488314i
$357$	11.6557	−	53.5802i	0.616883	−	2.83577i
$358$	−0.851767	+	11.9093i	−0.0450173	+	0.629424i
$359$	−5.27713	+	1.54951i	−0.278516	+	0.0817798i	−0.418008	−	0.908444i	$-0.637271\pi$
$359$	−5.27713	+	1.54951i	−0.278516	+	0.0817798i	0.139491	+	0.990223i	$0.455453\pi$
$360$	8.16413	−	8.54669i	0.430287	−	0.450450i
$361$	−4.76054	+	5.49395i	−0.250555	+	0.289155i
$362$	−17.7776	+	6.63070i	−0.934370	+	0.348502i
$363$	13.5746	+	24.8600i	0.712482	+	1.30481i
$364$	1.74305	+	3.81675i	0.0913608	+	0.200052i
$365$	27.2344	+	14.0717i	1.42552	+	0.736549i
$366$	−12.5761	+	19.5688i	−0.657363	+	1.02288i
$367$	9.54962	+	9.54962i	0.498486	+	0.498486i	0.910966	−	0.412480i	$-0.135337\pi$
$367$	9.54962	+	9.54962i	0.498486	+	0.498486i	−0.412480	+	0.910966i	$0.635337\pi$
$368$	−4.77661	−	0.428975i	−0.248998	−	0.0223618i
$369$			56.9827i			2.96640i
$370$	7.52272	−	17.5231i	0.391088	−	0.910982i
$371$	−1.94586	−	13.5337i	−0.101024	−	0.702637i
$372$	−9.81937	−	3.66244i	−0.509111	−	0.189888i
$373$	25.1169	−	13.7148i	1.30050	−	0.710128i	0.328367	−	0.944550i	$-0.393502\pi$
$373$	25.1169	−	13.7148i	1.30050	−	0.710128i	0.972135	+	0.234422i	$0.0753198\pi$
$374$	6.09055	+	2.78146i	0.314935	+	0.143826i
$375$	−17.3252	−	27.1213i	−0.894671	−	1.40054i
$376$	−0.213819	+	1.48714i	−0.0110269	+	0.0766935i
$377$	4.41279	−	8.08143i	0.227270	−	0.416215i
$378$	20.1095	+	1.43826i	1.03432	+	0.0739761i
$379$	12.1453	−	7.80529i	0.623860	−	0.400931i	−0.190172	−	0.981751i	$-0.560904\pi$
$379$	12.1453	−	7.80529i	0.623860	−	0.400931i	0.814032	+	0.580820i	$0.197268\pi$
$380$	−8.48738	+	7.70143i	−0.435394	+	0.395075i
$381$	−14.1355	−	16.3133i	−0.724185	−	0.835754i
$382$	−6.31830	−	3.45005i	−0.323273	−	0.176520i
$383$	5.65868	+	7.55911i	0.289145	+	0.386253i	0.921469	−	0.388451i	$-0.126990\pi$
$383$	5.65868	+	7.55911i	0.289145	+	0.386253i	−0.632324	+	0.774704i	$0.717899\pi$
$384$	−2.17543	−	1.88502i	−0.111015	−	0.0961946i
$385$	6.39382	−	3.68371i	0.325859	−	0.187739i
$386$	−3.31841	−	0.974372i	−0.168902	−	0.0495942i
$387$	−5.82410	+	15.6150i	−0.296056	+	0.793756i
$388$	5.02531	+	3.76190i	0.255121	+	0.190981i
$389$	−8.36594	−	5.37646i	−0.424170	−	0.272597i	0.311093	−	0.950379i	$-0.399305\pi$
$389$	−8.36594	−	5.37646i	−0.424170	−	0.272597i	−0.735263	+	0.677782i	$0.762941\pi$
$390$	−5.11923	+	7.17512i	−0.259223	+	0.363326i
$391$	−24.7853	−	16.5724i	−1.25345	−	0.838101i
$392$	−1.68903	+	1.68903i	−0.0853088	+	0.0853088i
$393$	6.67006	+	30.6618i	0.336460	+	1.54668i
$394$	24.7939	−	3.56482i	1.24910	−	0.179593i
$395$	0.422568	−	0.285442i	0.0212617	−	0.0143621i
$396$	−1.60385	+	5.46221i	−0.0805964	+	0.274486i
$397$	0.722087	+	1.93599i	0.0362405	+	0.0971645i	0.953810	−	0.300412i	$-0.0971241\pi$
$397$	0.722087	+	1.93599i	0.0362405	+	0.0971645i	−0.917569	+	0.397576i	$0.869851\pi$
$398$	−1.33837	−	18.7128i	−0.0670864	−	0.937990i
$399$	−44.7458	−	6.43347i	−2.24009	−	0.322076i
$400$	−4.07816	+	2.89286i	−0.203908	+	0.144643i
$401$	−12.3005	+	10.6584i	−0.614258	+	0.532257i	−0.905475	−	0.424400i	$-0.860485\pi$
$401$	−12.3005	+	10.6584i	−0.614258	+	0.532257i	0.291217	+	0.956657i	$0.405940\pi$
$402$	−38.2904	−	8.32956i	−1.90975	−	0.415441i
$403$	4.87177	+	1.05979i	0.242680	+	0.0527918i
$404$	−12.0410	+	10.4336i	−0.599061	+	0.519089i
$405$	3.00593	+	6.20233i	0.149366	+	0.308196i
$406$	20.3931	+	2.93209i	1.01209	+	0.145517i
$407$	0.655239	+	9.16144i	0.0324790	+	0.454116i
$408$	−6.25383	−	16.7672i	−0.309611	−	0.830098i
$409$	10.1345	−	34.5149i	0.501118	−	1.70665i	−0.188144	−	0.982141i	$-0.560247\pi$
$409$	10.1345	−	34.5149i	0.501118	−	1.70665i	0.689263	−	0.724511i	$-0.257935\pi$
$410$	4.58356	−	23.6657i	0.226366	−	1.16877i
$411$	24.3578	−	3.50212i	1.20148	−	0.172747i
$412$	0.754353	+	3.46771i	0.0371643	+	0.170842i
$413$	−14.0215	+	14.0215i	−0.689951	+	0.689951i
$414$	10.9479	−	22.8639i	0.538058	−	1.12370i
$415$	−13.3362	−	9.51498i	−0.654648	−	0.467072i
$416$	1.15200	+	0.740348i	0.0564816	+	0.0362985i
$417$	−12.0843	−	9.04619i	−0.591770	−	0.442994i
$418$	1.92905	−	5.17199i	0.0943530	−	0.252970i
$419$	−10.9198	−	3.20635i	−0.533468	−	0.156640i	0.00389331	−	0.999992i	$-0.498761\pi$
$419$	−10.9198	−	3.20635i	−0.533468	−	0.156640i	−0.537361	+	0.843352i	$0.680579\pi$
$420$	−19.0455	−	5.12182i	−0.929323	−	0.249919i
$421$	−8.49226	−	7.35859i	−0.413888	−	0.358636i	0.422888	−	0.906182i	$-0.361016\pi$
$421$	−8.49226	−	7.35859i	−0.413888	−	0.358636i	−0.836775	+	0.547546i	$0.815562\pi$
$422$	8.76936	+	11.7145i	0.426886	+	0.570253i
$423$	−6.97016	−	3.80600i	−0.338901	−	0.185054i
$424$	−2.92219	−	3.37239i	−0.141914	−	0.163778i
$425$	−30.8715	+	3.63410i	−1.49749	+	0.176280i
$426$	6.76099	−	4.34503i	0.327571	−	0.210517i
$427$	24.6981	+	1.76644i	1.19522	+	0.0854840i
$428$	8.97071	−	16.4286i	0.433616	−	0.794108i
$429$	0.604170	−	4.20210i	0.0291696	−	0.202879i
$430$	3.67487	−	6.01667i	0.177218	−	0.290150i
$431$	−11.9527	−	5.45860i	−0.575740	−	0.262932i	0.106194	−	0.994345i	$-0.466134\pi$
$431$	−11.9527	−	5.45860i	−0.575740	−	0.262932i	−0.681934	+	0.731414i	$0.738861\pi$
$432$	5.77488	−	3.15332i	0.277844	−	0.151714i
$433$	−9.91616	−	3.69854i	−0.476540	−	0.177740i	0.0997051	−	0.995017i	$-0.468210\pi$
$433$	−9.91616	−	3.69854i	−0.476540	−	0.177740i	−0.576245	+	0.817277i	$0.695483\pi$
$434$	1.58764	+	11.0423i	0.0762091	+	0.530046i
$435$	16.0486	+	40.1935i	0.769471	+	1.92713i
$436$		−	2.00396i		−	0.0959722i
$437$	−12.1701	+	21.3562i	−0.582177	+	1.02161i
$438$	27.9041	+	27.9041i	1.33331	+	1.33331i
$439$	9.78974	−	15.2331i	0.467239	−	0.727038i	−0.525038	−	0.851079i	$-0.675949\pi$
$439$	9.78974	−	15.2331i	0.467239	−	0.727038i	0.992277	+	0.124041i	$0.0395854\pi$
$440$	1.10547	−	2.13952i	0.0527012	−	0.101998i
$441$	−5.24500	−	11.4849i	−0.249762	−	0.546902i
$442$	4.08003	+	7.47203i	0.194067	+	0.355408i
$443$	29.7524	−	11.0971i	1.41358	−	0.527237i	0.477376	−	0.878699i	$-0.341588\pi$
$443$	29.7524	−	11.0971i	1.41358	−	0.527237i	0.936202	+	0.351462i	$0.114315\pi$
$444$	16.0758	−	18.5525i	0.762925	−	0.880462i
$445$	24.4832	−	0.560493i	1.16061	−	0.0265699i
$446$	7.49052	−	2.19942i	0.354687	−	0.104145i
$447$	−0.781700	+	10.9296i	−0.0369731	+	0.516952i
$448$	−0.651319	+	2.99407i	−0.0307719	+	0.141456i
$449$	18.4580	+	28.7212i	0.871086	+	1.35544i	0.933946	+	0.357415i	$0.116342\pi$
$449$	18.4580	+	28.7212i	0.871086	+	1.35544i	−0.0628595	+	0.998022i	$0.520022\pi$
$450$	−6.79382	−	25.5409i	−0.320264	−	1.20401i
$451$	3.27102	+	11.1401i	0.154026	+	0.524565i
$452$	11.5137	−	8.61901i	0.541557	−	0.405404i
$453$	−44.7080	+	3.19758i	−2.10056	+	0.150235i
$454$	1.23833	−	2.71155i	0.0581175	−	0.127260i
$455$	9.31502	+	1.12235i	0.436695	+	0.0526168i
$456$	−13.4202	+	6.12881i	−0.628459	+	0.287008i
$457$	−2.01451	+	2.69107i	−0.0942347	+	0.125883i	−0.845180	−	0.534481i	$-0.820507\pi$
$457$	−2.01451	+	2.69107i	−0.0942347	+	0.125883i	0.750946	+	0.660364i	$0.229598\pi$
$458$	8.52145	−	1.85373i	0.398181	−	0.0866190i
$459$	40.9056			1.90931
$460$	−6.38593	+	8.61510i	−0.297746	+	0.401681i
$461$	6.32724			0.294689			0.147344	−	0.989085i	$-0.452927\pi$
$461$	6.32724			0.294689			0.147344	+	0.989085i	$0.452927\pi$
$462$	9.28205	−	2.01919i	0.431840	−	0.0939410i
$463$	5.52685	−	7.38300i	0.256854	−	0.343117i	−0.653515	−	0.756913i	$-0.726706\pi$
$463$	5.52685	−	7.38300i	0.256854	−	0.343117i	0.910370	+	0.413796i	$0.135797\pi$
$464$	6.11633	−	2.79324i	0.283944	−	0.129673i
$465$	−18.4338	+	14.4693i	−0.854847	+	0.671000i
$466$	1.11799	−	2.44806i	0.0517899	−	0.113404i
$467$	28.8442	−	2.06297i	1.33475	−	0.0954631i	0.614355	−	0.789029i	$-0.289416\pi$
$467$	28.8442	−	2.06297i	1.33475	−	0.0954631i	0.720393	+	0.693566i	$0.243962\pi$
$468$	−5.79458	+	4.33777i	−0.267855	+	0.200513i
$469$	11.7517	+	40.0226i	0.542643	+	1.84807i
$470$	2.58866	+	2.14135i	0.119406	+	0.0987731i
$471$	17.5924	+	27.3744i	0.810616	+	1.26134i
$472$	−1.37562	+	6.32363i	−0.0633181	+	0.291069i
$473$	−0.242247	+	3.38705i	−0.0111385	+	0.155737i
$474$	0.629862	−	0.184944i	0.0289305	−	0.00849476i
$475$	4.80407	+	25.1726i	0.220426	+	1.15500i
$476$	−12.4746	+	14.3964i	−0.571772	+	0.659860i
$477$	22.0997	−	8.24278i	1.01188	−	0.377411i
$478$	8.97527	+	16.4370i	0.410519	+	0.751810i
$479$	−4.10490	−	8.98848i	−0.187558	−	0.410694i	0.792372	−	0.610039i	$-0.208846\pi$
$479$	−4.10490	−	8.98848i	−0.187558	−	0.410694i	−0.979930	+	0.199344i	$0.936119\pi$
$480$	−6.13269	+	1.95425i	−0.279918	+	0.0891991i
$481$	−6.31382	+	9.82450i	−0.287886	+	0.447959i
$482$	3.81599	+	3.81599i	0.173814	+	0.173814i
$483$	−42.2394	+	2.25064i	−1.92196	+	0.102407i
$484$		−	9.84008i		−	0.447276i
$485$	13.0359	−	5.20503i	0.591931	−	0.236348i
$486$	−1.54648	−	10.7560i	−0.0701496	−	0.487901i
$487$	−0.782495	−	0.291855i	−0.0354582	−	0.0132252i	0.331673	−	0.943395i	$-0.392387\pi$
$487$	−0.782495	−	0.291855i	−0.0354582	−	0.0132252i	−0.367131	+	0.930169i	$0.619660\pi$
$488$	7.09259	−	3.87285i	0.321067	−	0.175316i
$489$	−19.8136	−	9.04859i	−0.896004	−	0.409191i
$490$	1.25450	+	5.19176i	0.0566725	+	0.234540i
$491$	−1.54744	+	10.7627i	−0.0698351	+	0.485714i	0.924649	+	0.380822i	$0.124359\pi$
$491$	−1.54744	+	10.7627i	−0.0698351	+	0.485714i	−0.994484	+	0.104892i	$0.966550\pi$
$492$	14.8717	−	27.2354i	0.670467	−	1.22787i
$493$	41.6959	+	2.98215i	1.87789	+	0.134309i
$494$	5.90446	−	3.79456i	0.265654	−	0.170726i
$495$	8.55405	+	9.42701i	0.384476	+	0.423713i
$496$	2.38423	+	2.75155i	0.107055	+	0.123548i
$497$	−7.50850	−	4.09995i	−0.336802	−	0.183908i
$498$	−12.6384	−	16.8830i	−0.566341	−	0.756544i
$499$	−25.4510	−	22.0535i	−1.13935	−	0.987248i	−0.139350	−	0.990243i	$-0.544501\pi$
$499$	−25.4510	−	22.0535i	−1.13935	−	0.987248i	−0.999996	+	0.00299502i	$0.999047\pi$
$500$	0.767116	+	11.1540i	0.0343065	+	0.498822i
$501$	−2.79156	−	0.819675i	−0.124718	−	0.0366204i
$502$	4.17376	−	11.1903i	0.186284	−	0.499446i
$503$	−33.2920	−	24.9221i	−1.48442	−	1.11122i	−0.966777	−	0.255623i	$-0.917720\pi$
$503$	−33.2920	−	24.9221i	−1.48442	−	1.11122i	−0.517640	−	0.855598i	$-0.673190\pi$
$504$	−13.6251	−	8.75632i	−0.606910	−	0.390038i
$505$	5.87588	+	35.1382i	0.261473	+	1.56363i
$506$	0.827825	−	5.09833i	0.0368013	−	0.226648i
$507$	−22.6435	+	22.6435i	−1.00563	+	1.00563i
$508$	1.59400	+	7.32749i	0.0707222	+	0.325105i
$509$	−16.6800	+	2.39822i	−0.739327	+	0.106299i	−0.501681	−	0.865053i	$-0.667285\pi$
$509$	−16.6800	+	2.39822i	−0.739327	+	0.106299i	−0.237646	+	0.971352i	$0.576376\pi$
$510$	−39.2854	−	7.60877i	−1.73959	−	0.336922i
$511$	11.8346	−	40.3050i	0.523533	−	1.78299i
$512$	0.349464	+	0.936950i	0.0154443	+	0.0414077i
$513$	−2.40581	−	33.6377i	−0.106219	−	1.48514i
$514$	−15.3975	−	2.21382i	−0.679153	−	0.0976475i
$515$	7.49657	+	2.60224i	0.330338	+	0.114668i
$516$	6.85899	−	5.94335i	0.301950	−	0.261641i
$517$	−1.58114	−	0.343956i	−0.0695385	−	0.0151272i
$518$	−25.5340	−	5.55457i	−1.12190	−	0.244054i
$519$	26.1171	−	22.6306i	1.14641	−	0.993372i
$520$	2.75549	−	1.33544i	0.120836	−	0.0585627i
$521$	13.0213	+	1.87217i	0.570472	+	0.0820214i	0.421514	−	0.906822i	$-0.361499\pi$
$521$	13.0213	+	1.87217i	0.570472	+	0.0820214i	0.148958	+	0.988844i	$0.452408\pi$
$522$	2.53551	+	35.4510i	0.110976	+	1.55165i
$523$	11.8051	+	31.6508i	0.516202	+	1.38399i	0.889779	+	0.456393i	$0.150859\pi$
$523$	11.8051	+	31.6508i	0.516202	+	1.38399i	−0.373576	+	0.927599i	$0.621869\pi$
$524$	3.07119	−	10.4595i	0.134166	−	0.456926i
$525$	−31.9721	+	30.3743i	−1.39538	+	1.32564i
$526$	−11.7669	+	1.69183i	−0.513062	+	0.0737672i
$527$	4.81136	+	22.1175i	0.209586	+	0.963452i
$528$	2.19214	−	2.19214i	0.0954005	−	0.0954005i
$529$	−7.27724	+	21.8184i	−0.316402	+	0.948625i
$530$	−9.84137	+	1.64569i	−0.427482	+	0.0714842i
$531$	−28.7770	−	18.4938i	−1.24881	−	0.802564i
$532$	12.5722	+	9.41143i	0.545074	+	0.408037i
$533$	−5.15894	+	13.8317i	−0.223459	+	0.599116i
$534$	30.2487	+	8.88181i	1.30899	+	0.384353i
$535$	−20.8946	−	36.2668i	−0.903354	−	1.56795i
$536$	10.2882	+	8.91479i	0.444383	+	0.385060i
$537$	20.5963	+	27.5134i	0.888794	+	1.18729i
$538$	1.21532	+	0.663613i	0.0523960	+	0.0286104i
$539$	−1.68467	−	1.94422i	−0.0725640	−	0.0837433i
$540$	0.713446	−	14.6954i	0.0307018	−	0.632389i
$541$	3.52453	−	2.26507i	0.151531	−	0.0973832i	−0.462678	−	0.886526i	$-0.653111\pi$
$541$	3.52453	−	2.26507i	0.151531	−	0.0973832i	0.614209	+	0.789143i	$0.289475\pi$
$542$	14.6392	+	1.04702i	0.628809	+	0.0449733i
$543$	−26.1749	+	47.9358i	−1.12327	+	2.05712i
$544$	−0.884761	+	6.15365i	−0.0379338	+	0.263835i
$545$	−3.82410	−	2.33569i	−0.163807	−	0.100050i
$546$	10.9866	+	5.01739i	0.470181	+	0.214725i
$547$	12.5588	−	6.85763i	0.536976	−	0.293211i	−0.187787	−	0.982210i	$-0.560131\pi$
$547$	12.5588	−	6.85763i	0.536976	−	0.293211i	0.724762	+	0.688999i	$0.241950\pi$
$548$	−8.00995	−	2.98756i	−0.342168	−	0.127622i
$549$	6.07899	+	42.2803i	0.259445	+	1.80448i
$550$	−2.79433	−	4.60324i	−0.119151	−	0.196283i
$551$		−	34.4629i		−	1.46817i
$552$	−11.1998	+	8.07081i	−0.476696	+	0.343516i
$553$	−0.494108	−	0.494108i	−0.0210116	−	0.0210116i
$554$	−5.39057	+	8.38789i	−0.229023	+	0.356368i
$555$	−16.6662	−	52.3008i	−0.707442	−	2.22004i
$556$	2.17847	+	4.77019i	0.0923878	+	0.202301i
$557$	15.2893	+	28.0002i	0.647827	+	1.18641i	0.970775	+	0.239990i	$0.0771442\pi$
$557$	15.2893	+	28.0002i	0.647827	+	1.18641i	−0.322948	+	0.946417i	$0.604674\pi$
$558$	−18.0313	+	6.72534i	−0.763327	+	0.284706i
$559$	−2.82742	+	3.26302i	−0.119587	+	0.138011i
$560$	4.95436	+	4.73260i	0.209360	+	0.199989i
$561$	18.4927	−	5.42994i	0.780762	−	0.229252i
$562$	−1.73382	+	24.2420i	−0.0731370	+	1.02259i
$563$	−4.69498	+	21.5825i	−0.197870	+	0.909593i	0.765921	+	0.642934i	$0.222283\pi$
$563$	−4.69498	+	21.5825i	−0.197870	+	0.909593i	−0.963791	+	0.266659i	$0.914080\pi$
$564$	2.33815	+	3.63823i	0.0984538	+	0.153197i
$565$	−3.02783	−	32.0170i	−0.127382	−	1.34697i
$566$	−4.08351	−	13.9071i	−0.171643	−	0.584561i
$567$	7.56079	−	5.65994i	0.317524	−	0.237695i
$568$	−2.78489	+	0.199179i	−0.116851	+	0.00835738i
$569$	−5.79131	+	12.6812i	−0.242785	+	0.531624i	−0.991320	−	0.131471i	$-0.958030\pi$
$569$	−5.79131	+	12.6812i	−0.242785	+	0.531624i	0.748536	+	0.663095i	$0.230757\pi$
$570$	−3.94635	+	32.7528i	−0.165294	+	1.37187i
$571$	−12.6559	+	5.77973i	−0.529631	+	0.241874i	−0.662237	−	0.749294i	$-0.730393\pi$
$571$	−12.6559	+	5.77973i	−0.529631	+	0.241874i	0.132606	+	0.991169i	$0.457666\pi$
$572$	−0.883832	+	1.18066i	−0.0369549	+	0.0493660i
$573$	−20.2485	+	4.40478i	−0.845892	+	0.184012i
$574$	−33.0318			−1.37872
$575$	8.99692	+	22.2274i	0.375197	+	0.926945i
$576$	−5.28581			−0.220242
$577$	7.77856	−	1.69212i	0.323826	−	0.0704440i	−0.0477140	−	0.998861i	$-0.515194\pi$
$577$	7.77856	−	1.69212i	0.323826	−	0.0704440i	0.371540	+	0.928417i	$0.378830\pi$
$578$	−12.9745	+	17.3319i	−0.539667	+	0.720910i
$579$	−9.05568	+	4.13559i	−0.376341	+	0.171869i
$580$	1.79857	−	14.9273i	0.0746815	−	0.619821i
$581$	−9.32569	+	20.4204i	−0.386895	+	0.847182i
$582$	18.0235	−	1.28906i	0.747097	−	0.0534334i
$583$	3.84732	−	2.88007i	0.159340	−	0.119280i
$584$	−3.86236	−	13.1540i	−0.159826	−	0.544316i
$585$	1.52384	+	16.1135i	0.0630031	+	0.666211i
$586$	4.42917	+	6.89192i	0.182967	+	0.284703i
$587$	3.76757	−	17.3193i	0.155504	−	0.714842i	−0.831680	−	0.555256i	$-0.812620\pi$
$587$	3.76757	−	17.3193i	0.155504	−	0.714842i	0.987184	−	0.159586i	$-0.0510161\pi$
$588$	−0.490509	+	6.85822i	−0.0202283	+	0.282828i
$589$	17.9047	−	5.25730i	0.737752	−	0.216623i
$590$	10.4639	+	9.99552i	0.430792	+	0.411509i
$591$	47.2176	−	54.4921i	1.94227	−	2.24150i
$592$	−7.99048	+	2.98030i	−0.328407	+	0.122489i
$593$	−10.1138	−	18.5221i	−0.415324	−	0.760610i	0.583343	−	0.812226i	$-0.301744\pi$
$593$	−10.1138	−	18.5221i	−0.415324	−	0.760610i	−0.998667	+	0.0516165i	$0.983563\pi$
$594$	2.94377	+	6.44597i	0.120785	+	0.264481i
$595$	12.9327	+	40.5846i	0.530191	+	1.66381i
$596$	2.05804	−	3.20237i	0.0843005	−	0.131174i
$597$	−38.1857	−	38.1857i	−1.56284	−	1.56284i
$598$	4.72742	−	4.55870i	0.193319	−	0.186419i
$599$		−	29.6876i		−	1.21300i	−0.795083	−	0.606501i	$-0.792573\pi$
$599$		−	29.6876i		−	1.21300i	0.795083	−	0.606501i	$-0.207427\pi$
$600$	−3.41865	+	13.9806i	−0.139566	+	0.570757i
$601$	2.79593	+	19.4461i	0.114049	+	0.793225i	0.963912	+	0.266222i	$0.0857753\pi$
$601$	2.79593	+	19.4461i	0.114049	+	0.793225i	−0.849863	+	0.527003i	$0.823316\pi$
$602$	−9.05175	−	3.37613i	−0.368922	−	0.137601i
$603$	−63.1552	+	34.4854i	−2.57188	+	1.40435i
$604$	14.1642	+	6.46856i	0.576332	+	0.263202i
$605$	−18.7776	−	11.4690i	−0.763417	−	0.466281i
$606$	−6.52682	+	45.3950i	−0.265134	+	1.84405i
$607$	−21.4156	+	39.2197i	−0.869232	+	1.59188i	−0.0647498	+	0.997902i	$0.520625\pi$
$607$	−21.4156	+	39.2197i	−0.869232	+	1.59188i	−0.804482	+	0.593977i	$0.797557\pi$
$608$	5.11232	+	0.365641i	0.207332	+	0.0148287i
$609$	49.8909	−	32.0629i	2.02168	−	1.29926i
$610$	0.876240	−	18.0486i	0.0354779	−	0.730766i
$611$	−1.34732	−	1.55489i	−0.0545068	−	0.0629043i
$612$	−28.8418	−	15.7488i	−1.16586	−	0.636609i
$613$	−6.13485	−	8.19520i	−0.247784	−	0.331001i	0.659355	−	0.751832i	$-0.270830\pi$
$613$	−6.13485	−	8.19520i	−0.247784	−	0.331001i	−0.907139	+	0.420831i	$0.861739\pi$
$614$	10.4564	+	9.06056i	0.421988	+	0.365655i
$615$	−34.6392	−	60.1233i	−1.39679	−	2.42440i
$616$	−3.16634	−	0.929723i	−0.127576	−	0.0374596i
$617$	7.14837	−	19.1655i	0.287783	−	0.771575i	−0.709949	−	0.704253i	$-0.751282\pi$
$617$	7.14837	−	19.1655i	0.287783	−	0.771575i	0.997731	−	0.0673217i	$-0.0214454\pi$
$618$	8.17775	+	6.12178i	0.328957	+	0.246254i
$619$	18.5156	+	11.8993i	0.744205	+	0.478272i	0.856981	−	0.515349i	$-0.172338\pi$
$619$	18.5156	+	11.8993i	0.744205	+	0.478272i	−0.112775	+	0.993621i	$0.535974\pi$
$620$	8.02964	−	1.34273i	0.322478	−	0.0539253i
$621$	−8.33865	−	30.4335i	−0.334618	−	1.22126i
$622$	12.8787	−	12.8787i	0.516390	−	0.516390i
$623$	−7.13330	−	32.7913i	−0.285790	−	1.31375i
$624$	3.90168	−	0.560976i	0.156192	−	0.0224570i
$625$	22.1790	+	11.5366i	0.887160	+	0.461462i
$626$	−4.87893	+	16.6161i	−0.195001	+	0.664113i
$627$	−5.55279	−	14.8876i	−0.221757	−	0.594554i
$628$	−0.806450	−	11.2756i	−0.0321809	−	0.449947i
$629$	−52.4795	−	7.54541i	−2.09249	−	0.300855i
$630$	−32.5901	+	15.7946i	−1.29842	+	0.629272i
$631$	6.69141	−	5.79814i	0.266381	−	0.230820i	−0.511420	−	0.859331i	$-0.670880\pi$
$631$	6.69141	−	5.79814i	0.266381	−	0.230820i	0.777801	+	0.628510i	$0.216335\pi$
$632$	−0.222841	−	0.0484762i	−0.00886415	−	0.00192828i
$633$	41.1592	+	8.95364i	1.63593	+	0.355875i
$634$	−24.2652	+	21.0259i	−0.963695	+	0.835047i
$635$	15.8407	+	5.49870i	0.628621	+	0.218209i
$636$	−12.7140	−	1.82800i	−0.504145	−	0.0724851i
$637$	−0.233349	−	3.26265i	−0.00924564	−	0.129271i
$638$	2.53071	+	6.78511i	0.100192	+	0.268625i
$639$	4.15781	−	14.1602i	0.164480	−	0.560169i
$640$	2.19527	+	0.425179i	0.0867758	+	0.0168067i
$641$	29.6107	−	4.25737i	1.16955	−	0.168156i	0.469952	−	0.882692i	$-0.344271\pi$
$641$	29.6107	−	4.25737i	1.16955	−	0.168156i	0.699599	+	0.714536i	$0.253362\pi$
$642$	−11.4532	−	52.6494i	−0.452020	−	2.07790i
$643$	−8.28887	+	8.28887i	−0.326881	+	0.326881i	−0.851399	−	0.524518i	$-0.824245\pi$
$643$	−8.28887	+	8.28887i	−0.326881	+	0.326881i	0.524518	+	0.851399i	$0.324245\pi$
$644$	13.2538	+	6.34628i	0.522273	+	0.250079i
$645$	−3.34712	−	20.0161i	−0.131793	−	0.788132i
$646$	26.8058	+	17.2270i	1.05466	+	0.677789i
$647$	13.1561	+	9.84857i	0.517222	+	0.387187i	0.825757	−	0.564026i	$-0.190748\pi$
$647$	13.1561	+	9.84857i	0.517222	+	0.387187i	−0.308536	+	0.951213i	$0.599839\pi$
$648$	1.07717	−	2.88801i	0.0423153	−	0.113452i
$649$	−6.68750	−	1.96363i	−0.262507	−	0.0770791i
$650$	0.663261	−	6.81475i	0.0260152	−	0.267296i
$651$	24.2687	+	21.0290i	0.951166	+	0.824190i
$652$	4.53481	+	6.05780i	0.177597	+	0.237242i
$653$	39.0717	+	21.3348i	1.52899	+	0.834894i	0.999907	−	0.0136734i	$-0.00435252\pi$
$653$	39.0717	+	21.3348i	1.52899	+	0.834894i	0.529087	+	0.848567i	$0.322534\pi$
$654$	−3.77750	−	4.35947i	−0.147712	−	0.170469i
$655$	−16.3801	−	18.0517i	−0.640022	−	0.705337i
$656$	−9.06897	+	5.82828i	−0.354084	+	0.227556i
$657$	72.2802	+	5.16958i	2.81992	+	0.201685i
$658$	2.20627	−	4.04048i	0.0860093	−	0.157514i
$659$	5.81469	−	40.4420i	0.226508	−	1.57540i	−0.486143	−	0.873879i	$-0.661596\pi$
$659$	5.81469	−	40.4420i	0.226508	−	1.57540i	0.712651	−	0.701519i	$-0.247494\pi$
$660$	−1.62818	−	6.73822i	−0.0633767	−	0.262285i
$661$	8.42094	+	3.84572i	0.327537	+	0.149581i	0.572395	−	0.819978i	$-0.306014\pi$
$661$	8.42094	+	3.84572i	0.327537	+	0.149581i	−0.244859	+	0.969559i	$0.578742\pi$
$662$	7.48682	−	4.08811i	0.290983	−	0.158889i
$663$	22.9608	+	8.56392i	0.891722	+	0.332595i
$664$	1.04267	+	7.25194i	0.0404635	+	0.281430i
$665$	32.6130	−	13.0218i	1.26468	−	0.504965i
$666$		−	45.0784i		−	1.74675i
$667$	−6.28104	−	31.6294i	−0.243203	−	1.22469i
$668$	0.714698	+	0.714698i	0.0276525	+	0.0276525i
$669$	12.1492	−	18.9045i	0.469714	−	0.730889i
$670$	29.0032	−	9.24220i	1.12049	−	0.357057i
$671$	3.61548	+	7.91681i	0.139574	+	0.305625i
$672$	4.22698	+	7.74113i	0.163059	+	0.298621i
$673$	−33.2549	+	12.4034i	−1.28188	+	0.478117i	−0.895845	−	0.444366i	$-0.853429\pi$
$673$	−33.2549	+	12.4034i	−1.28188	+	0.478117i	−0.386037	+	0.922483i	$0.626156\pi$
$674$	19.3986	−	22.3872i	0.747206	−	0.862321i
$675$	−27.2113	−	18.4895i	−1.04736	−	0.711662i
$676$	10.6741	−	3.13421i	0.410544	−	0.120547i
$677$	0.926220	−	12.9502i	0.0355975	−	0.497718i	−0.948110	−	0.317942i	$-0.897008\pi$
$677$	0.926220	−	12.9502i	0.0355975	−	0.497718i	0.983708	−	0.179776i	$-0.0575373\pi$
$678$	8.80013	−	40.4536i	0.337967	−	1.55361i
$679$	−10.3989	−	16.1811i	−0.399075	−	0.620972i
$680$	10.7116	+	8.86069i	0.410772	+	0.339792i
$681$	−2.41745	−	8.23307i	−0.0926368	−	0.315492i
$682$	−3.13905	+	2.34986i	−0.120201	+	0.0899810i
$683$	23.6463	−	1.69121i	0.904799	−	0.0647125i	0.388820	−	0.921314i	$-0.372883\pi$
$683$	23.6463	−	1.69121i	0.904799	−	0.0647125i	0.515979	+	0.856601i	$0.327428\pi$
$684$	−11.2543	+	24.6436i	−0.430320	+	0.942270i
$685$	−15.0370	+	11.8031i	−0.574535	+	0.450973i
$686$	−12.8527	+	5.86965i	−0.490720	+	0.224104i
$687$	15.0435	−	20.0958i	0.573945	−	0.766701i
$688$	−3.08088	+	0.670204i	−0.117457	+	0.0255513i
$689$	6.11063			0.232797
$690$	2.34749	+	30.7792i	0.0893676	+	1.17174i
$691$	24.1248			0.917750			0.458875	−	0.888501i	$-0.348253\pi$
$691$	24.1248			0.917750			0.458875	+	0.888501i	$0.348253\pi$
$692$	−11.7311	+	2.55195i	−0.445950	+	0.0970105i
$693$	10.4534	−	13.9641i	0.397090	−	0.530451i
$694$	7.55354	−	3.44959i	0.286728	−	0.130944i
$695$	11.6419	+	1.40272i	0.441604	+	0.0532083i
$696$	8.04035	−	17.6059i	0.304769	−	0.667350i
$697$	−66.8496	+	4.78118i	−2.53211	+	0.181100i
$698$	7.32720	−	5.48507i	0.277339	−	0.207613i
$699$	−2.18253	−	7.43302i	−0.0825510	−	0.281143i
$700$	14.8056	−	3.93825i	0.559600	−	0.148852i
$701$	−5.85348	−	9.10819i	−0.221083	−	0.344011i	0.712940	−	0.701225i	$-0.247363\pi$
$701$	−5.85348	−	9.10819i	−0.221083	−	0.344011i	−0.934023	+	0.357214i	$0.883727\pi$
$702$	−1.91526	+	8.80429i	−0.0722867	+	0.332296i
$703$	−3.11825	+	43.5989i	−0.117607	+	1.64436i
$704$	−1.03337	+	0.303425i	−0.0389467	+	0.0114358i
$705$	9.66795	−	0.221328i	0.364116	−	0.00833569i
$706$	−5.70680	+	6.58599i	−0.214778	+	0.247867i
$707$	45.7406	−	17.0603i	1.72025	−	0.641620i
$708$	8.92762	+	16.3497i	0.335520	+	0.614460i
$709$	−3.31934	−	7.26835i	−0.124661	−	0.272968i	0.837004	−	0.547197i	$-0.184305\pi$
$709$	−3.31934	−	7.26835i	−0.124661	−	0.272968i	−0.961665	+	0.274228i	$0.911578\pi$
$710$	−2.86581	+	5.54649i	−0.107552	+	0.208156i
$711$	0.651713	−	1.01408i	0.0244411	−	0.0380311i
$712$	−7.74430	−	7.74430i	−0.290230	−	0.290230i
$713$	15.4745	−	8.08829i	0.579523	−	0.302909i
$714$			54.8333i			2.05209i
$715$	1.22289	+	3.06270i	0.0457333	+	0.114539i
$716$	−1.69919	−	11.8182i	−0.0635019	−	0.441665i
$717$	50.5092	+	18.8389i	1.88630	+	0.703553i
$718$	4.82716	−	2.63583i	0.180148	−	0.0983683i
$719$	36.2841	+	16.5704i	1.35317	+	0.617972i	0.954249	−	0.299014i	$-0.0966576\pi$
$719$	36.2841	+	16.5704i	1.35317	+	0.617972i	0.398921	+	0.916985i	$0.369385\pi$
$720$	−6.16082	+	10.0868i	−0.229600	+	0.375912i
$721$	1.54751	−	10.7632i	0.0576324	−	0.400842i
$722$	3.48392	−	6.38032i	0.129658	−	0.237451i
$723$	15.4946	+	1.10820i	0.576252	+	0.0412144i
$724$	15.9619	−	10.2581i	0.593218	−	0.381238i
$725$	−26.3891	−	20.8305i	−0.980065	−	0.773626i
$726$	−18.5488	−	21.4064i	−0.688409	−	0.794466i
$727$	8.13743	+	4.44338i	0.301801	+	0.164796i	0.623013	−	0.782212i	$-0.285908\pi$
$727$	8.13743	+	4.44338i	0.301801	+	0.164796i	−0.321212	+	0.947007i	$0.604090\pi$
$728$	−2.51453	−	3.35902i	−0.0931946	−	0.124493i
$729$	−30.6280	−	26.5393i	−1.13437	−	0.982937i
$730$	−29.6032	−	7.96106i	−1.09566	−	0.294652i
$731$	−18.8076	−	5.52240i	−0.695623	−	0.204253i
$732$	8.12905	−	21.7948i	0.300458	−	0.805560i
$733$	−15.9794	−	11.9620i	−0.590213	−	0.441828i	0.261967	−	0.965077i	$-0.415629\pi$
$733$	−15.9794	−	11.9620i	−0.590213	−	0.441828i	−0.852180	+	0.523249i	$0.824720\pi$
$734$	−11.3613	−	7.30146i	−0.419353	−	0.269502i
$735$	12.5157	+	8.92955i	0.461647	+	0.329372i
$736$	4.75863	−	0.596170i	0.175406	−	0.0219751i
$737$	−10.3672	+	10.3672i	−0.381881	+	0.381881i
$738$	−12.1125	−	55.6804i	−0.445869	−	2.04963i
$739$	4.42741	−	0.636565i	0.162865	−	0.0234164i	−0.0604000	−	0.998174i	$-0.519238\pi$
$739$	4.42741	−	0.636565i	0.162865	−	0.0234164i	0.223265	+	0.974758i	$0.428329\pi$
$740$	−3.62600	+	18.7217i	−0.133295	+	0.688223i
$741$	5.69191	−	19.3848i	0.209097	−	0.712120i
$742$	4.77819	+	12.8108i	0.175413	+	0.470300i
$743$	2.35032	+	32.8618i	0.0862249	+	1.20558i	0.837816	+	0.545952i	$0.183832\pi$
$743$	2.35032	+	32.8618i	0.0862249	+	1.20558i	−0.751591	+	0.659629i	$0.770713\pi$
$744$	10.3735	+	1.49148i	0.380310	+	0.0546803i
$745$	−3.71228	−	7.65979i	−0.136007	−	0.280633i
$746$	−21.6276	+	18.7404i	−0.791842	+	0.686135i
$747$	−37.8415	−	8.23192i	−1.38455	−	0.301190i
$748$	−6.54260	−	1.42326i	−0.239221	−	0.0520394i
$749$	−43.3456	+	37.5592i	−1.58381	+	1.37238i
$750$	22.6943	+	22.8187i	0.828680	+	0.833222i
$751$	−8.85109	−	1.27259i	−0.322981	−	0.0464377i	−0.0210825	−	0.999778i	$-0.506711\pi$
$751$	−8.85109	−	1.27259i	−0.322981	−	0.0464377i	−0.301898	+	0.953340i	$0.597620\pi$
$752$	−0.107183	−	1.49861i	−0.00390854	−	0.0546486i
$753$	−12.0142	−	32.2113i	−0.437821	−	1.17384i
$754$	−2.59412	+	8.83475i	−0.0944721	+	0.321743i
$755$	28.8527	−	19.4898i	1.05006	−	0.709305i
$756$	−19.9556	+	2.86919i	−0.725780	+	0.104351i
$757$	−3.08141	−	14.1650i	−0.111996	−	0.514837i	−0.998628	−	0.0523617i	$-0.983325\pi$
$757$	−3.08141	−	14.1650i	−0.111996	−	0.514837i	0.886632	−	0.462475i	$-0.153039\pi$
$758$	−10.2086	+	10.2086i	−0.370792	+	0.370792i
$759$	−7.80959	−	12.6515i	−0.283470	−	0.459222i
$760$	6.65636	−	9.32955i	0.241452	−	0.338418i
$761$	−37.0139	−	23.7874i	−1.34175	−	0.862291i	−0.344676	−	0.938722i	$-0.612011\pi$
$761$	−37.0139	−	23.7874i	−1.34175	−	0.862291i	−0.997075	+	0.0764305i	$0.975648\pi$
$762$	17.2801	+	12.9357i	0.625993	+	0.468612i
$763$	−2.14582	+	5.75316i	−0.0776838	+	0.208278i
$764$	6.90727	+	2.02816i	0.249896	+	0.0733762i
$765$	−63.6694	+	36.6823i	−2.30197	+	1.32625i
$766$	−7.13617	−	6.18352i	−0.257840	−	0.223420i
$767$	−5.31082	−	7.09443i	−0.191763	−	0.256165i
$768$	2.52641	+	1.37952i	0.0911638	+	0.0497792i
$769$	−19.0076	−	21.9359i	−0.685431	−	0.791029i	0.301277	−	0.953537i	$-0.402587\pi$
$769$	−19.0076	−	21.9359i	−0.685431	−	0.791029i	−0.986707	+	0.162508i	$0.948042\pi$
$770$	−5.46467	+	4.95863i	−0.196933	+	0.178697i
$771$	−37.6692	+	24.2085i	−1.35662	+	0.871850i
$772$	3.44969	+	0.246726i	0.124157	+	0.00887988i
$773$	−4.78509	+	8.76323i	−0.172108	+	0.315192i	−0.949468	−	0.313864i	$-0.898376\pi$
$773$	−4.78509	+	8.76323i	−0.172108	+	0.315192i	0.777360	+	0.629056i	$0.216558\pi$
$774$	2.37179	−	16.4962i	0.0852523	−	0.592943i
$775$	6.79657	−	16.8878i	0.244140	−	0.606627i
$776$	−5.71011	−	2.60772i	−0.204981	−	0.0936117i
$777$	−66.0179	+	36.0485i	−2.36838	+	1.29323i
$778$	9.31760	+	3.47528i	0.334052	+	0.124595i
$779$	7.86335	+	54.6908i	0.281734	+	1.95950i
$780$	3.47706	−	8.09931i	0.124499	−	0.290002i
$781$		−	3.00698i		−	0.107598i
$782$	27.7416	+	10.9252i	0.992037	+	0.390683i
$783$	31.2837	+	31.2837i	1.11799	+	1.11799i
$784$	1.29140	−	2.00946i	0.0461214	−	0.0717663i
$785$	−22.4570	−	11.6033i	−0.801525	−	0.414139i
$786$	−13.0353	−	28.5432i	−0.464952	−	1.01810i
$787$	−7.06278	−	12.9345i	−0.251761	−	0.461066i	0.720981	−	0.692955i	$-0.243691\pi$
$787$	−7.06278	−	12.9345i	−0.251761	−	0.461066i	−0.972742	+	0.231889i	$0.925510\pi$
$788$	−23.4695	+	8.75368i	−0.836067	+	0.311837i
$789$	−22.4090	+	25.8614i	−0.797782	+	0.920689i
$790$	−0.352236	+	0.368742i	−0.0125320	+	0.0131192i
$791$	−42.2837	+	12.4156i	−1.50343	+	0.441448i
$792$	0.406120	−	5.67830i	0.0144309	−	0.201770i
$793$	−2.35228	+	10.8132i	−0.0835318	+	0.383990i
$794$	−1.11711	−	1.73826i	−0.0396447	−	0.0616884i
$795$	−18.3071	+	22.1313i	−0.649285	+	0.784916i
$796$	5.28549	+	18.0007i	0.187339	+	0.638018i
$797$	−1.85169	+	1.38615i	−0.0655901	+	0.0491001i	−0.631570	−	0.775319i	$-0.717589\pi$
$797$	−1.85169	+	1.38615i	−0.0655901	+	0.0491001i	0.565980	+	0.824419i	$0.308498\pi$
$798$	45.0907	−	3.22495i	1.59619	−	0.114162i
$799$	3.88020	−	8.49644i	0.137271	−	0.300583i
$800$	3.37004	−	3.69362i	0.119149	−	0.130589i
$801$	52.6592	−	24.0486i	1.86062	−	0.849717i
$802$	9.75378	−	13.0295i	0.344418	−	0.460089i
$803$	14.4275	−	3.13851i	0.509135	−	0.110756i
$804$	39.1859			1.38198
$805$	27.5583	−	17.8951i	0.971303	−	0.630719i
$806$	−4.98571			−0.175614
$807$	3.89476	−	0.847254i	0.137102	−	0.0298247i
$808$	9.54799	−	12.7546i	0.335897	−	0.448706i
$809$	37.5258	−	17.1375i	1.31934	−	0.602521i	0.373640	−	0.927574i	$-0.378109\pi$
$809$	37.5258	−	17.1375i	1.31934	−	0.602521i	0.945696	+	0.325053i	$0.105382\pi$
$810$	−4.25563	−	5.42163i	−0.149528	−	0.190497i
$811$	−12.5834	+	27.5539i	−0.441864	+	0.967547i	0.549389	+	0.835567i	$0.314861\pi$
$811$	−12.5834	+	27.5539i	−0.441864	+	0.967547i	−0.991252	+	0.131980i	$0.957867\pi$
$812$	−20.5503	+	1.46979i	−0.721175	+	0.0515795i
$813$	33.8203	−	25.3176i	1.18613	−	0.887926i
$814$	−2.58767	−	8.81279i	−0.0906977	−	0.308888i
$815$	16.8455	−	1.59306i	0.590070	−	0.0558025i
$816$	9.67502	+	15.0546i	0.338694	+	0.527017i
$817$	−3.43505	+	15.7907i	−0.120177	+	0.552446i
$818$	−2.56622	+	35.8804i	−0.0897256	+	1.25453i
$819$	21.2805	−	6.24852i	0.743601	−	0.218341i
$820$	0.551702	+	24.0992i	0.0192663	+	0.841580i
$821$	−9.85547	+	11.3738i	−0.343958	+	0.396949i	−0.901202	−	0.433400i	$-0.857314\pi$
$821$	−9.85547	+	11.3738i	−0.343958	+	0.396949i	0.557243	+	0.830349i	$0.311859\pi$
$822$	−23.0567	+	8.59971i	−0.804195	+	0.299949i
$823$	−19.1821	−	35.1295i	−0.668647	−	1.22454i	−0.963170	−	0.268892i	$-0.913343\pi$
$823$	−19.1821	−	35.1295i	−0.668647	−	1.22454i	0.294523	−	0.955644i	$-0.404839\pi$
$824$	−1.47423	−	3.22811i	−0.0513572	−	0.112457i
$825$	−14.7561	−	4.74666i	−0.513741	−	0.165257i
$826$	10.7206	−	16.6815i	0.373016	−	0.580424i
$827$	−9.01789	−	9.01789i	−0.313583	−	0.313583i	0.532713	−	0.846296i	$-0.321172\pi$
$827$	−9.01789	−	9.01789i	−0.313583	−	0.313583i	−0.846296	+	0.532713i	$0.821172\pi$
$828$	−5.83760	+	24.6686i	−0.202871	+	0.857291i
$829$		−	51.0735i		−	1.77386i	−0.461909	−	0.886928i	$-0.652835\pi$
$829$		−	51.0735i		−	1.77386i	0.461909	−	0.886928i	$-0.347165\pi$
$830$	15.0540	+	6.46272i	0.522531	+	0.224324i
$831$	4.08455	+	28.4086i	0.141691	+	0.985485i
$832$	−1.28305	−	0.478552i	−0.0444817	−	0.0165908i
$833$	13.0336	−	7.11686i	0.451586	−	0.246585i
$834$	13.7310	+	6.27075i	0.475467	+	0.217138i
$835$	2.19685	−	0.530831i	0.0760251	−	0.0183702i
$836$	−0.785582	+	5.46384i	−0.0271699	+	0.188971i
$837$	−11.4807	+	21.0253i	−0.396831	+	0.726742i
$838$	11.3518	+	0.811899i	0.392142	+	0.0280466i
$839$	−13.4874	+	8.66782i	−0.465637	+	0.299246i	−0.752342	−	0.658772i	$-0.771076\pi$
$839$	−13.4874	+	8.66782i	−0.465637	+	0.299246i	0.286706	+	0.958019i	$0.407440\pi$
$840$	19.6989	+	0.956363i	0.679678	+	0.0329977i
$841$	10.6164	+	12.2520i	0.366083	+	0.422482i
$842$	9.86237	+	5.38526i	0.339880	+	0.185588i
$843$	41.9249	+	56.0052i	1.44397	+	1.92892i
$844$	−11.0590	−	9.58272i	−0.380668	−	0.329851i
$845$	6.46020	−	24.0223i	0.222238	−	0.826391i
$846$	7.61990	+	2.23740i	0.261977	+	0.0769235i
$847$	−10.5366	+	28.2499i	−0.362044	+	0.970676i
$848$	3.57226	+	2.67416i	0.122672	+	0.0918311i
$849$	−35.0987	−	22.5565i	−1.20458	−	0.774138i
$850$	29.3935	−	10.1132i	1.00819	−	0.346882i
$851$	5.08425	+	40.5825i	0.174286	+	1.39115i
$852$	−5.68288	+	5.68288i	−0.194692	+	0.194692i
$853$	1.57777	+	7.25289i	0.0540218	+	0.248334i	0.996237	−	0.0866750i	$-0.0276242\pi$
$853$	1.57777	+	7.25289i	0.0540218	+	0.248334i	−0.942215	+	0.335009i	$0.891261\pi$
$854$	−24.5091	+	3.52388i	−0.838685	+	0.120585i
$855$	33.9093	+	50.1994i	1.15967	+	1.71678i
$856$	−5.27355	+	17.9601i	−0.180246	+	0.613862i
$857$	−10.0272	−	26.8841i	−0.342524	−	0.918342i	−0.987985	−	0.154549i	$-0.950608\pi$
$857$	−10.0272	−	26.8841i	−0.342524	−	0.918342i	0.645461	−	0.763793i	$-0.276665\pi$
$858$	0.302857	+	4.23449i	0.0103394	+	0.144563i
$859$	−5.50786	−	0.791911i	−0.187926	−	0.0270197i	0.0477092	−	0.998861i	$-0.484808\pi$
$859$	−5.50786	−	0.791911i	−0.187926	−	0.0270197i	−0.235635	+	0.971842i	$0.575717\pi$
$860$	−2.31196	+	6.66032i	−0.0788370	+	0.227115i
$861$	−71.8585	+	62.2657i	−2.44893	+	2.12201i
$862$	12.8398	+	2.79313i	0.437326	+	0.0951345i
$863$	52.6012	+	11.4427i	1.79056	+	0.389513i	0.980452	−	0.196761i	$-0.0630423\pi$
$863$	52.6012	+	11.4427i	1.79056	+	0.389513i	0.810113	+	0.586274i	$0.199406\pi$
$864$	−4.97262	+	4.30880i	−0.169172	+	0.146588i
$865$	−8.80326	+	25.3606i	−0.299320	+	0.862286i
$866$	10.4757	+	1.50618i	0.355980	+	0.0511822i
$867$	4.44587	+	62.1614i	0.150990	+	2.11111i
$868$	−3.89856	−	10.4524i	−0.132326	−	0.354779i
$869$	0.0691971	−	0.235664i	0.00234735	−	0.00799434i
$870$	−24.2256	−	35.8636i	−0.821324	−	1.21589i
$871$	−18.4521	+	2.65301i	−0.625226	+	0.0898939i
$872$	0.425972	+	1.95816i	0.0144252	+	0.0663117i
$873$	23.4626	−	23.4626i	0.794087	−	0.794087i
$874$	7.35242	−	23.4551i	0.248699	−	0.793380i
$875$	9.74127	−	32.8434i	0.329315	−	1.11031i
$876$	−33.1979	−	21.3350i	−1.12165	−	0.720842i
$877$	−5.25143	−	3.93117i	−0.177328	−	0.132746i	0.506927	−	0.861989i	$-0.330781\pi$
$877$	−5.25143	−	3.93117i	−0.177328	−	0.132746i	−0.684255	+	0.729243i	$0.739872\pi$
$878$	−6.32798	+	16.9660i	−0.213559	+	0.572574i
$879$	22.6268	+	6.64382i	0.763182	+	0.224091i
$880$	−0.625417	+	2.32561i	−0.0210828	+	0.0783964i
$881$	−8.69678	−	7.53580i	−0.293002	−	0.253888i	0.495938	−	0.868358i	$-0.334824\pi$
$881$	−8.69678	−	7.53580i	−0.293002	−	0.253888i	−0.788940	+	0.614470i	$0.789370\pi$
$882$	7.56643	+	10.1076i	0.254775	+	0.340340i
$883$	−44.6617	−	24.3871i	−1.50298	−	0.820691i	−0.503912	−	0.863755i	$-0.668106\pi$
$883$	−44.6617	−	24.3871i	−1.50298	−	0.820691i	−0.999072	+	0.0430636i	$0.986288\pi$
$884$	−5.57509	−	6.43399i	−0.187510	−	0.216399i
$885$	41.6052	+	2.01989i	1.39854	+	0.0678979i
$886$	−26.7136	+	17.1678i	−0.897461	+	0.576763i
$887$	−13.9565	−	0.998188i	−0.468613	−	0.0335159i	−0.164964	−	0.986300i	$-0.552751\pi$
$887$	−13.9565	−	0.998188i	−0.468613	−	0.0335159i	−0.303650	+	0.952784i	$0.598205\pi$
$888$	−11.7648	+	21.5457i	−0.394802	+	0.723025i
$889$	3.27000	−	22.7433i	0.109672	−	0.762786i
$890$	−23.8045	+	5.75196i	−0.797930	+	0.192806i
$891$	3.01969	+	1.37905i	0.101164	+	0.0461998i
$892$	−6.85182	+	3.74138i	−0.229416	+	0.125271i
$893$	−7.21503	−	2.69107i	−0.241442	−	0.0900532i
$894$	−1.55942	−	10.8460i	−0.0521547	−	0.362744i
$895$	−24.5328	−	10.5320i	−0.820040	−	0.352046i
$896$		−	3.06409i		−	0.102364i
$897$	1.69093	−	18.8284i	0.0564585	−	0.628663i
$898$	−24.1413	−	24.1413i	−0.805605	−	0.805605i
$899$	−13.2353	+	20.5945i	−0.441422	+	0.686866i
$900$	12.0677	+	23.5131i	0.402256	+	0.783770i
$901$	11.5244	+	25.2349i	0.383933	+	0.840695i
$902$	−5.56426	−	10.1902i	−0.185270	−	0.339296i
$903$	−26.0555	+	9.71822i	−0.867074	+	0.323402i
$904$	−9.41843	+	10.8694i	−0.313252	+	0.361512i
$905$	−0.971024	−	42.4158i	−0.0322779	−	1.40995i
$906$	43.0066	−	12.6279i	1.42880	−	0.419533i
$907$	−0.541411	+	7.56992i	−0.0179773	+	0.251355i	0.980514	+	0.196448i	$0.0629407\pi$
$907$	−0.541411	+	7.56992i	−0.0179773	+	0.251355i	−0.998491	+	0.0549069i	$0.982514\pi$
$908$	−0.633643	+	2.91281i	−0.0210282	+	0.0966650i
$909$	45.5307	+	70.8471i	1.51016	+	2.34985i
$910$	−9.34071	+	0.883344i	−0.309642	+	0.0292826i
$911$	−1.32102	−	4.49899i	−0.0437675	−	0.149058i	0.934710	−	0.355411i	$-0.115659\pi$
$911$	−1.32102	−	4.49899i	−0.0437675	−	0.149058i	−0.978478	+	0.206352i	$0.933841\pi$
$912$	11.8107	−	8.84142i	0.391093	−	0.292769i
$913$	−7.87054	+	0.562912i	−0.260477	+	0.0186297i
$914$	1.39644	−	3.05778i	0.0461902	−	0.101143i
$915$	−32.1158	−	40.9152i	−1.06172	−	1.35261i
$916$	−7.93267	+	3.62273i	−0.262103	+	0.119698i
$917$	−20.0170	+	26.7396i	−0.661021	+	0.883020i
$918$	−39.9708	+	8.69512i	−1.31923	+	0.286982i
$919$	20.3238			0.670419			0.335209	−	0.942144i	$-0.391193\pi$
$919$	20.3238			0.670419			0.335209	+	0.942144i	$0.391193\pi$
$920$	4.40872	−	9.77564i	0.145351	−	0.322293i
$921$	39.8267			1.31233
$922$	−6.18264	+	1.34495i	−0.203614	+	0.0442936i
$923$	2.29124	−	3.06074i	0.0754172	−	0.100746i
$924$	−8.64071	+	3.94608i	−0.284259	+	0.129817i
$925$	31.4999	+	28.7403i	1.03571	+	0.944976i
$926$	−3.83117	+	8.38910i	−0.125900	+	0.275683i
$927$	18.7105	−	1.33820i	0.614534	−	0.0439524i
$928$	−5.38281	+	4.02952i	−0.176699	+	0.132276i
$929$	1.13089	+	3.85146i	0.0371033	+	0.126362i	0.975962	−	0.217940i	$-0.0699337\pi$
$929$	1.13089	+	3.85146i	0.0371033	+	0.126362i	−0.938859	+	0.344302i	$0.888116\pi$
$930$	14.9369	−	18.0571i	0.489799	−	0.592114i
$931$	−6.61891	−	10.2992i	−0.216926	−	0.337544i
$932$	−0.572069	+	2.62976i	−0.0187388	+	0.0861407i
$933$	3.74011	−	52.2935i	0.122446	−	1.71201i
$934$	−27.7465	+	8.14710i	−0.907892	+	0.266581i
$935$	−10.3416	+	10.8262i	−0.338207	+	0.354055i
$936$	4.74010	−	5.47037i	0.154935	−	0.178804i
$937$	36.0532	−	13.4471i	1.17781	−	0.439299i	0.317095	−	0.948394i	$-0.397293\pi$
$937$	36.0532	−	13.4471i	1.17781	−	0.439299i	0.860710	+	0.509095i	$0.170020\pi$
$938$	−19.9906	−	36.6100i	−0.652715	−	1.19536i
$939$	20.7079	+	45.3441i	0.675778	+	1.47975i
$940$	−2.98468	−	1.54215i	−0.0973496	−	0.0502995i
$941$	15.8183	−	24.6137i	0.515661	−	0.802384i	−0.481597	−	0.876393i	$-0.659943\pi$
$941$	15.8183	−	24.6137i	0.515661	−	0.802384i	0.997258	+	0.0740090i	$0.0235793\pi$
$942$	−23.0092	−	23.0092i	−0.749681	−	0.749681i
$943$	17.1845	+	48.7610i	0.559605	+	1.58788i
$944$		−	6.47153i		−	0.210630i
$945$	−17.7839	+	41.4250i	−0.578511	+	1.34756i
$946$	−0.483259	−	3.36114i	−0.0157121	−	0.109280i
$947$	31.0788	+	11.5918i	1.00993	+	0.376683i	0.799331	−	0.600891i	$-0.205187\pi$
$947$	31.0788	+	11.5918i	1.00993	+	0.376683i	0.210594	+	0.977574i	$0.432460\pi$
$948$	−0.576155	+	0.314604i	−0.0187126	+	0.0102179i
$949$	17.0769	+	7.79875i	0.554339	+	0.253158i
$950$	−10.0451	−	23.5761i	−0.325906	−	0.764911i
$951$	−13.1530	+	91.4810i	−0.426514	+	2.96647i
$952$	9.12932	−	16.7191i	0.295883	−	0.541869i
$953$	3.43309	+	0.245539i	0.111209	+	0.00795379i	0.126833	−	0.991924i	$-0.459519\pi$
$953$	3.43309	+	0.245539i	0.111209	+	0.00795379i	−0.0156240	+	0.999878i	$0.504973\pi$
$954$	−19.8426	+	12.7520i	−0.642427	+	0.412863i
$955$	11.9210	−	10.8171i	0.385754	−	0.350032i
$956$	−12.2641	−	14.1535i	−0.396649	−	0.457757i
$957$	18.2955	+	9.99008i	0.591408	+	0.322933i
$958$	5.92173	+	7.91051i	0.191323	+	0.255577i
$959$	19.7967	+	17.1540i	0.639269	+	0.553930i
$960$	5.57714	−	3.21319i	0.180001	−	0.103705i
$961$	17.0256	+	4.99917i	0.549213	+	0.161264i
$962$	4.08119	−	10.9421i	0.131583	−	0.352787i
$963$	−79.2065	−	59.2933i	−2.55239	−	1.91070i
$964$	−4.53993	−	2.91764i	−0.146221	−	0.0939707i
$965$	4.49157	−	6.29538i	0.144589	−	0.202656i
$966$	40.7956	−	11.1778i	1.31258	−	0.359641i
$967$	−36.6857	+	36.6857i	−1.17973	+	1.17973i	−0.199920	+	0.979812i	$0.564068\pi$
$967$	−36.6857	+	36.6857i	−1.17973	+	1.17973i	−0.979812	+	0.199920i	$0.935932\pi$
$968$	2.09166	+	9.61520i	0.0672284	+	0.309044i
$969$	90.7875	−	13.0533i	2.91652	−	0.419332i
$970$	−11.6316	+	7.85706i	−0.373469	+	0.252275i
$971$	5.44131	−	18.5314i	0.174620	−	0.594701i	−0.824945	−	0.565213i	$-0.808794\pi$
$971$	5.44131	−	18.5314i	0.174620	−	0.594701i	0.999565	−	0.0294882i	$-0.00938775\pi$
$972$	3.79748	+	10.1814i	0.121804	+	0.326570i
$973$	−1.14630	−	16.0274i	−0.0367488	−	0.513815i
$974$	0.826650	+	0.118854i	0.0264876	+	0.00380834i
$975$	−11.4031	−	16.0753i	−0.365190	−	0.514821i
$976$	−6.10727	+	5.29198i	−0.195489	+	0.169392i
$977$	−27.2179	−	5.92089i	−0.870777	−	0.189426i	−0.245090	−	0.969500i	$-0.578818\pi$
$977$	−27.2179	−	5.92089i	−0.870777	−	0.189426i	−0.625687	+	0.780074i	$0.715181\pi$
$978$	21.2843	+	4.63011i	0.680595	+	0.148054i
$979$	8.91435	−	7.72433i	0.284904	−	0.246871i
$980$	−2.32942	−	4.80645i	−0.0744105	−	0.153536i
$981$	−10.4847	−	1.50748i	−0.334751	−	0.0481300i
$982$	−0.775698	−	10.8457i	−0.0247535	−	0.346099i
$983$	−1.79399	−	4.80987i	−0.0572193	−	0.153411i	0.905195	−	0.424997i	$-0.139725\pi$
$983$	−1.79399	−	4.80987i	−0.0572193	−	0.153411i	−0.962414	+	0.271586i	$0.912452\pi$
$984$	−8.74250	+	29.7742i	−0.278701	+	0.949168i
$985$	−10.6502	+	54.9891i	−0.339345	+	1.75210i
$986$	−41.3769	+	5.94910i	−1.31771	+	0.189458i
$987$	−2.81681	−	12.9487i	−0.0896600	−	0.412160i
$988$	−4.96293	+	4.96293i	−0.157892	+	0.157892i
$989$	−0.274691	+	15.1184i	−0.00873466	+	0.480739i
$990$	−10.3624	−	7.39328i	−0.329339	−	0.234974i
$991$	−46.5181	−	29.8953i	−1.47769	−	0.949657i	−0.997363	−	0.0725695i	$-0.976880\pi$
$991$	−46.5181	−	29.8953i	−1.47769	−	0.949657i	−0.480331	−	0.877087i	$-0.659484\pi$
$992$	−2.91463	−	2.18187i	−0.0925396	−	0.0692743i
$993$	8.58088	−	23.0062i	0.272306	−	0.730081i
$994$	8.20841	+	2.41021i	0.260355	+	0.0764472i
$995$	40.5108	+	10.8944i	1.28428	+	0.345375i
$996$	15.9383	+	13.8106i	0.505025	+	0.437607i
$997$	7.08621	+	9.46607i	0.224423	+	0.299793i	0.898594	−	0.438782i	$-0.144590\pi$
$997$	7.08621	+	9.46607i	0.224423	+	0.299793i	−0.674171	+	0.738575i	$0.735499\pi$
$998$	29.5572	+	16.1395i	0.935617	+	0.510886i
$999$	−36.7463	−	42.4074i	−1.16260	−	1.34171i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.113.1	yes	240
5.2	odd	4	inner	230.2.l.a.67.6	yes	240
23.11	odd	22	inner	230.2.l.a.103.6	yes	240
115.57	even	44	inner	230.2.l.a.57.1	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.57.1	✓	240	115.57	even	44	inner
230.2.l.a.67.6	yes	240	5.2	odd	4	inner
230.2.l.a.103.6	yes	240	23.11	odd	22	inner
230.2.l.a.113.1	yes	240	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.977147 + 0.212565i) q^{2} +(-1.72503 + 2.30436i) q^{3} +(0.909632 - 0.415415i) q^{4} +(0.267486 - 2.22001i) q^{5} +(1.19578 - 2.61838i) q^{6} +(-3.05628 + 0.218590i) q^{7} +(-0.800541 + 0.599278i) q^{8} +(-1.48918 - 5.07170i) q^{9} +(0.210524 + 2.22614i) q^{10} +(-0.582269 - 0.906028i) q^{11} +(-0.611871 + 2.81273i) q^{12} +(0.0976911 - 1.36590i) q^{13} +(2.93997 - 0.863254i) q^{14} +(4.65429 + 4.44596i) q^{15} +(0.654861 - 0.755750i) q^{16} +(5.82495 - 2.17259i) q^{17} +(2.53322 + 4.63924i) q^{18} +(-2.12916 - 4.66221i) q^{19} +(-0.678912 - 2.13051i) q^{20} +(4.76846 - 7.41986i) q^{21} +(0.761553 + 0.761553i) q^{22} +(-2.80382 - 3.89084i) q^{23} -2.87851i q^{24} +(-4.85690 - 1.18765i) q^{25} +(0.194884 + 1.35545i) q^{26} +(6.16487 + 2.29938i) q^{27} +(-2.68929 + 1.46846i) q^{28} +(6.11633 + 2.79324i) q^{29} +(-5.49299 - 3.35502i) q^{30} +(-0.518143 + 3.60377i) q^{31} +(-0.479249 + 0.877679i) q^{32} +(3.09225 + 0.221162i) q^{33} +(-5.23001 + 3.36112i) q^{34} +(-0.332243 + 6.84345i) q^{35} +(-3.46147 - 3.99475i) q^{36} +(-7.48501 - 4.08713i) q^{37} +(3.07153 + 4.10308i) q^{38} +(2.97901 + 2.58133i) q^{39} +(1.11627 + 1.93751i) q^{40} +(-10.3436 - 3.03716i) q^{41} +(-3.08228 + 8.26390i) q^{42} +(-2.52405 - 1.88948i) q^{43} +(-0.906028 - 0.582269i) q^{44} +(-11.6576 + 1.94940i) q^{45} +(3.56680 + 3.20593i) q^{46} +(1.06238 - 1.06238i) q^{47} +(0.611871 + 2.81273i) q^{48} +(2.36433 - 0.339940i) q^{49} +(4.99836 + 0.128096i) q^{50} +(-5.04174 + 17.1706i) q^{51} +(-0.478552 - 1.28305i) q^{52} +(0.318337 + 4.45094i) q^{53} +(-6.51275 - 0.936392i) q^{54} +(-2.16714 + 1.05029i) q^{55} +(2.31568 - 2.00655i) q^{56} +(14.4163 + 3.13607i) q^{57} +(-6.57030 - 1.42928i) q^{58} +(4.89085 - 4.23795i) q^{59} +(6.08062 + 2.11073i) q^{60} +(-7.99883 - 1.15006i) q^{61} +(-0.259734 - 3.63155i) q^{62} +(5.65999 + 15.1750i) q^{63} +(0.281733 - 0.959493i) q^{64} +(-3.00618 - 0.582235i) q^{65} +(-3.06859 + 0.441197i) q^{66} +(-2.89371 - 13.3022i) q^{67} +(4.39603 - 4.39603i) q^{68} +(13.8026 + 0.250782i) q^{69} +(-1.13003 - 6.75768i) q^{70} +(2.34878 + 1.50947i) q^{71} +(4.23151 + 3.16767i) q^{72} +(-4.79092 + 12.8449i) q^{73} +(8.18274 + 2.40267i) q^{74} +(11.1150 - 9.14335i) q^{75} +(-3.87351 - 3.35641i) q^{76} +(1.97763 + 2.64180i) q^{77} +(-3.45963 - 1.88910i) q^{78} +(0.149343 + 0.172351i) q^{79} +(-1.50261 - 1.65595i) q^{80} +(-2.59304 + 1.66645i) q^{81} +(10.7528 + 0.769059i) q^{82} +(3.51122 - 6.43033i) q^{83} +(1.25522 - 8.73023i) q^{84} +(-3.26509 - 13.5126i) q^{85} +(2.86801 + 1.30978i) q^{86} +(-16.9875 + 9.27586i) q^{87} +(1.00909 + 0.376372i) q^{88} +(1.55864 + 10.8406i) q^{89} +(10.9768 - 4.38284i) q^{90} +4.19593i q^{91} +(-4.16675 - 2.37448i) q^{92} +(-7.41058 - 7.41058i) q^{93} +(-0.812278 + 1.26393i) q^{94} +(-10.9197 + 3.47968i) q^{95} +(-1.19578 - 2.61838i) q^{96} +(3.00843 + 5.50953i) q^{97} +(-2.23804 + 0.834746i) q^{98} +(-3.72800 + 4.30234i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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