LMFDB - Embedded newform 253.2.i.b.12.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [253,2,Mod(12,253)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(253, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 20])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("253.12"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 253 = 11 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	253.i (of order $11$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [120] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.02021517114$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			12.3
Character	$\chi$	$=$	253.12
Dual form			253.2.i.b.232.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.49658 + 0.961792i) q^{2} +(0.268936 - 1.87049i) q^{3} +(0.483871 - 1.05953i) q^{4} +(-1.13030 + 0.331887i) q^{5} +(1.39654 + 3.05800i) q^{6} +(0.964130 + 1.11267i) q^{7} +(-0.211455 - 1.47070i) q^{8} +(-0.547943 - 0.160891i) q^{9} +(1.37238 - 1.58381i) q^{10} +(0.841254 + 0.540641i) q^{11} +(-1.85171 - 1.19002i) q^{12} +(1.90572 - 2.19931i) q^{13} +(-2.51305 - 0.737898i) q^{14} +(0.316813 + 2.20348i) q^{15} +(3.25652 + 3.75823i) q^{16} +(-3.17449 - 6.95115i) q^{17} +(0.974783 - 0.286222i) q^{18} +(3.44496 - 7.54341i) q^{19} +(-0.195277 + 1.35818i) q^{20} +(2.34052 - 1.50416i) q^{21} -1.77899 q^{22} +(4.60887 - 1.32600i) q^{23} -2.80781 q^{24} +(-3.03883 + 1.95294i) q^{25} +(-0.736769 + 5.12434i) q^{26} +(1.90676 - 4.17522i) q^{27} +(1.64542 - 0.483138i) q^{28} +(0.775835 + 1.69884i) q^{29} +(-2.59343 - 2.99298i) q^{30} +(0.482647 + 3.35689i) q^{31} +(-5.63698 - 1.65517i) q^{32} +(1.23751 - 1.42816i) q^{33} +(11.4364 + 7.34975i) q^{34} +(-1.45904 - 0.937668i) q^{35} +(-0.435602 + 0.502711i) q^{36} +(9.31424 + 2.73491i) q^{37} +(2.09954 + 14.6026i) q^{38} +(-3.60129 - 4.15610i) q^{39} +(0.727117 + 1.59217i) q^{40} +(2.39473 - 0.703156i) q^{41} +(-2.05608 + 4.50220i) q^{42} +(-0.670798 + 4.66551i) q^{43} +(0.979883 - 0.629732i) q^{44} +0.672740 q^{45} +(-5.62220 + 6.41725i) q^{46} -11.1406 q^{47} +(7.90554 - 5.08058i) q^{48} +(0.687726 - 4.78324i) q^{49} +(2.66952 - 5.84544i) q^{50} +(-13.8558 + 4.06844i) q^{51} +(-1.40812 - 3.08334i) q^{52} +(-0.970593 - 1.12012i) q^{53} +(1.16208 + 8.08244i) q^{54} +(-1.13030 - 0.331887i) q^{55} +(1.43253 - 1.65323i) q^{56} +(-13.1834 - 8.47248i) q^{57} +(-2.79503 - 1.79626i) q^{58} +(-3.19344 + 3.68543i) q^{59} +(2.48795 + 0.730529i) q^{60} +(0.712803 + 4.95765i) q^{61} +(-3.95094 - 4.55963i) q^{62} +(-0.349271 - 0.764797i) q^{63} +(0.485292 - 0.142495i) q^{64} +(-1.42411 + 3.11838i) q^{65} +(-0.478434 + 3.32758i) q^{66} +(-4.44384 + 2.85588i) q^{67} -8.90099 q^{68} +(-1.24079 - 8.97748i) q^{69} +3.08541 q^{70} +(1.04826 - 0.673678i) q^{71} +(-0.120757 + 0.839884i) q^{72} +(6.19732 - 13.5702i) q^{73} +(-16.5699 + 4.86536i) q^{74} +(2.83570 + 6.20933i) q^{75} +(-6.32555 - 7.30007i) q^{76} +(0.209526 + 1.45728i) q^{77} +(9.38691 + 2.75625i) q^{78} +(-6.87244 + 7.93122i) q^{79} +(-4.92817 - 3.16714i) q^{80} +(-8.73818 - 5.61569i) q^{81} +(-2.90761 + 3.35556i) q^{82} +(2.23059 + 0.654959i) q^{83} +(-0.461194 - 3.20767i) q^{84} +(5.89514 + 6.80335i) q^{85} +(-3.48334 - 7.62746i) q^{86} +(3.38632 - 0.994314i) q^{87} +(0.617235 - 1.35156i) q^{88} +(-2.35018 + 16.3459i) q^{89} +(-1.00681 + 0.647036i) q^{90} +4.28446 q^{91} +(0.825160 - 5.52485i) q^{92} +6.40884 q^{93} +(16.6728 - 10.7150i) q^{94} +(-1.39029 + 9.66969i) q^{95} +(-4.61197 + 10.0988i) q^{96} +(8.58446 - 2.52063i) q^{97} +(3.57125 + 7.81994i) q^{98} +(-0.373975 - 0.431590i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - q^{2} - 4 q^{3} - 19 q^{4} - 6 q^{5} - 25 q^{6} - 6 q^{8} - 26 q^{9} + 41 q^{10} - 12 q^{11} - 17 q^{12} - 18 q^{13} - 12 q^{14} + 19 q^{15} - 33 q^{16} - 10 q^{17} + 28 q^{18} + 28 q^{19} - 34 q^{20}+ \cdots - 26 q^{99}+O(q^{100}) $ 120 * q - q^2 - 4 * q^3 - 19 * q^4 - 6 * q^5 - 25 * q^6 - 6 * q^8 - 26 * q^9 + 41 * q^10 - 12 * q^11 - 17 * q^12 - 18 * q^13 - 12 * q^14 + 19 * q^15 - 33 * q^16 - 10 * q^17 + 28 * q^18 + 28 * q^19 - 34 * q^20 - 26 * q^21 + 10 * q^22 + 3 * q^23 + 108 * q^24 - 6 * q^25 - 26 * q^26 - 46 * q^27 - 3 * q^28 + 18 * q^29 + 16 * q^30 - 34 * q^31 - 63 * q^32 + 7 * q^33 - 24 * q^34 - 48 * q^35 - 122 * q^36 - 32 * q^37 + 143 * q^38 - 42 * q^39 + 8 * q^40 - 8 * q^41 + 174 * q^42 + 51 * q^43 - 19 * q^44 - 2 * q^45 - 67 * q^46 - 2 * q^47 - 111 * q^48 + 12 * q^49 - 113 * q^50 + 34 * q^51 + 127 * q^52 - 22 * q^53 - 27 * q^54 - 6 * q^55 + 191 * q^56 + 32 * q^57 - 71 * q^58 - 40 * q^59 + 12 * q^60 - 19 * q^61 + q^62 - 82 * q^63 - 6 * q^64 + 171 * q^65 - 3 * q^66 - 30 * q^67 - 152 * q^68 - 48 * q^69 + 86 * q^70 - 22 * q^71 - 130 * q^72 - 70 * q^73 - 27 * q^74 + 200 * q^75 + 4 * q^76 - 94 * q^78 - 6 * q^79 + 197 * q^80 + 4 * q^81 - 47 * q^82 + 50 * q^83 + 411 * q^84 - 98 * q^85 - 9 * q^86 - 72 * q^87 - 6 * q^88 - 41 * q^89 - 260 * q^90 + 30 * q^92 + 130 * q^93 + 33 * q^94 - 28 * q^95 - 265 * q^96 + 84 * q^97 - 117 * q^98 - 26 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/253\mathbb{Z}\right)^\times$.

$n$	$24$	$166$
$\chi(n)$	$1$	$e\left(\frac{10}{11}\right)$

Coefficient data

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

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

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

$2$	−1.49658	+	0.961792i	−1.05824	+	0.680090i	−0.949432	−	0.313973i	$-0.898340\pi$
$2$	−1.49658	+	0.961792i	−1.05824	+	0.680090i	−0.108808	+	0.994063i	$0.534703\pi$
$3$	0.268936	−	1.87049i	0.155271	−	1.07993i	−0.751933	−	0.659239i	$-0.770878\pi$
$3$	0.268936	−	1.87049i	0.155271	−	1.07993i	0.907204	−	0.420691i	$-0.138212\pi$
$4$	0.483871	−	1.05953i	0.241935	−	0.529765i
$5$	−1.13030	+	0.331887i	−0.505488	+	0.148425i	−0.524526	−	0.851394i	$-0.675758\pi$
$5$	−1.13030	+	0.331887i	−0.505488	+	0.148425i	0.0190388	+	0.999819i	$0.493939\pi$
$6$	1.39654	+	3.05800i	0.570136	+	1.24842i
$7$	0.964130	+	1.11267i	0.364407	+	0.420548i	0.908111	−	0.418729i	$-0.137524\pi$
$7$	0.964130	+	1.11267i	0.364407	+	0.420548i	−0.543704	+	0.839277i	$0.682979\pi$
$8$	−0.211455	−	1.47070i	−0.0747608	−	0.519973i
$9$	−0.547943	−	0.160891i	−0.182648	−	0.0536302i
$10$	1.37238	−	1.58381i	0.433985	−	0.500846i
$11$	0.841254	+	0.540641i	0.253647	+	0.163009i
$11$	0.841254	+	0.540641i	0.253647	+	0.163009i
$12$	−1.85171	−	1.19002i	−0.534543	−	0.343530i
$13$	1.90572	−	2.19931i	0.528550	−	0.609980i	−0.427201	−	0.904157i	$-0.640500\pi$
$13$	1.90572	−	2.19931i	0.528550	−	0.609980i	0.955751	+	0.294177i	$0.0950456\pi$
$14$	−2.51305	−	0.737898i	−0.671641	−	0.197211i
$15$	0.316813	+	2.20348i	0.0818008	+	0.568937i
$16$	3.25652	+	3.75823i	0.814130	+	0.939556i
$17$	−3.17449	−	6.95115i	−0.769926	−	1.68590i	−0.726816	−	0.686832i	$-0.759001\pi$
$17$	−3.17449	−	6.95115i	−0.769926	−	1.68590i	−0.0431100	−	0.999070i	$-0.513727\pi$
$18$	0.974783	−	0.286222i	0.229758	−	0.0674632i
$19$	3.44496	−	7.54341i	0.790328	−	1.73058i	0.114618	−	0.993410i	$-0.463435\pi$
$19$	3.44496	−	7.54341i	0.790328	−	1.73058i	0.675710	−	0.737168i	$-0.263837\pi$
$20$	−0.195277	+	1.35818i	−0.0436653	+	0.303699i
$21$	2.34052	−	1.50416i	0.510744	−	0.328235i
$22$	−1.77899			−0.379281
$23$	4.60887	−	1.32600i	0.961017	−	0.276491i
$23$	4.60887	−	1.32600i	0.961017	−	0.276491i
$24$	−2.80781			−0.573142
$25$	−3.03883	+	1.95294i	−0.607766	+	0.390587i
$26$	−0.736769	+	5.12434i	−0.144492	+	1.00497i
$27$	1.90676	−	4.17522i	0.366956	−	0.803521i
$28$	1.64542	−	0.483138i	0.310954	−	0.0913045i
$29$	0.775835	+	1.69884i	0.144069	+	0.315467i	0.967886	−	0.251388i	$-0.0808871\pi$
$29$	0.775835	+	1.69884i	0.144069	+	0.315467i	−0.823817	+	0.566855i	$0.808160\pi$
$30$	−2.59343	−	2.99298i	−0.473493	−	0.546440i
$31$	0.482647	+	3.35689i	0.0866860	+	0.602914i	0.986142	+	0.165903i	$0.0530539\pi$
$31$	0.482647	+	3.35689i	0.0866860	+	0.602914i	−0.899456	+	0.437011i	$0.856037\pi$
$32$	−5.63698	−	1.65517i	−0.996487	−	0.292595i
$33$	1.23751	−	1.42816i	0.215423	−	0.248611i
$34$	11.4364	+	7.34975i	1.96133	+	1.26047i
$35$	−1.45904	−	0.937668i	−0.246623	−	0.158495i
$36$	−0.435602	+	0.502711i	−0.0726003	+	0.0837852i
$37$	9.31424	+	2.73491i	1.53125	+	0.449616i	0.935433	−	0.353504i	$-0.115010\pi$
$37$	9.31424	+	2.73491i	1.53125	+	0.449616i	0.595818	+	0.803119i	$0.296828\pi$
$38$	2.09954	+	14.6026i	0.340591	+	2.36886i
$39$	−3.60129	−	4.15610i	−0.576667	−	0.665509i
$40$	0.727117	+	1.59217i	0.114967	+	0.251743i
$41$	2.39473	−	0.703156i	0.373994	−	0.109815i	−0.0893333	−	0.996002i	$-0.528474\pi$
$41$	2.39473	−	0.703156i	0.373994	−	0.109815i	0.463327	+	0.886187i	$0.346655\pi$
$42$	−2.05608	+	4.50220i	−0.317261	+	0.694704i
$43$	−0.670798	+	4.66551i	−0.102296	+	0.711483i	0.872537	+	0.488547i	$0.162473\pi$
$43$	−0.670798	+	4.66551i	−0.102296	+	0.711483i	−0.974833	+	0.222936i	$0.928436\pi$
$44$	0.979883	−	0.629732i	0.147723	−	0.0949357i
$45$	0.672740			0.100286
$46$	−5.62220	+	6.41725i	−0.828948	+	0.946171i
$47$	−11.1406			−1.62503			−0.812515	−	0.582941i	$-0.801902\pi$
$47$	−11.1406			−1.62503			−0.812515	+	0.582941i	$0.801902\pi$
$48$	7.90554	−	5.08058i	1.14107	−	0.733318i
$49$	0.687726	−	4.78324i	0.0982466	−	0.683320i
$50$	2.66952	−	5.84544i	0.377528	−	0.826670i
$51$	−13.8558	+	4.06844i	−1.94020	+	0.569695i
$52$	−1.40812	−	3.08334i	−0.195271	−	0.427583i
$53$	−0.970593	−	1.12012i	−0.133321	−	0.153861i	0.685163	−	0.728390i	$-0.259731\pi$
$53$	−0.970593	−	1.12012i	−0.133321	−	0.153861i	−0.818484	+	0.574529i	$0.805185\pi$
$54$	1.16208	+	8.08244i	0.158139	+	1.09988i
$55$	−1.13030	−	0.331887i	−0.152410	−	0.0447517i
$56$	1.43253	−	1.65323i	0.191430	−	0.220922i
$57$	−13.1834	−	8.47248i	−1.74619	−	1.12221i
$58$	−2.79503	−	1.79626i	−0.367005	−	0.235860i
$59$	−3.19344	+	3.68543i	−0.415750	+	0.479802i	−0.924538	−	0.381091i	$-0.875549\pi$
$59$	−3.19344	+	3.68543i	−0.415750	+	0.479802i	0.508787	+	0.860892i	$0.330094\pi$
$60$	2.48795	+	0.730529i	0.321193	+	0.0943109i
$61$	0.712803	+	4.95765i	0.0912650	+	0.634762i	0.983191	+	0.182581i	$0.0584450\pi$
$61$	0.712803	+	4.95765i	0.0912650	+	0.634762i	−0.891926	+	0.452182i	$0.850646\pi$
$62$	−3.95094	−	4.55963i	−0.501770	−	0.579074i
$63$	−0.349271	−	0.764797i	−0.0440040	−	0.0963554i
$64$	0.485292	−	0.142495i	0.0606615	−	0.0178118i
$65$	−1.42411	+	3.11838i	−0.176640	+	0.386787i
$66$	−0.478434	+	3.32758i	−0.0588912	+	0.409597i
$67$	−4.44384	+	2.85588i	−0.542902	+	0.348902i	−0.783173	−	0.621804i	$-0.786400\pi$
$67$	−4.44384	+	2.85588i	−0.542902	+	0.348902i	0.240271	+	0.970706i	$0.422764\pi$
$68$	−8.90099			−1.07940
$69$	−1.24079	−	8.97748i	−0.149373	−	1.08076i
$70$	3.08541			0.368777
$71$	1.04826	−	0.673678i	0.124406	−	0.0799509i	−0.476958	−	0.878926i	$-0.658261\pi$
$71$	1.04826	−	0.673678i	0.124406	−	0.0799509i	0.601364	+	0.798975i	$0.294624\pi$
$72$	−0.120757	+	0.839884i	−0.0142314	+	0.0989812i
$73$	6.19732	−	13.5702i	0.725342	−	1.58828i	−0.0809218	−	0.996720i	$-0.525786\pi$
$73$	6.19732	−	13.5702i	0.725342	−	1.58828i	0.806264	−	0.591556i	$-0.201486\pi$
$74$	−16.5699	+	4.86536i	−1.92621	+	0.565587i
$75$	2.83570	+	6.20933i	0.327439	+	0.716991i
$76$	−6.32555	−	7.30007i	−0.725590	−	0.837376i
$77$	0.209526	+	1.45728i	0.0238777	+	0.166073i
$78$	9.38691	+	2.75625i	1.06286	+	0.312083i
$79$	−6.87244	+	7.93122i	−0.773210	+	0.892332i	−0.996600	−	0.0823970i	$-0.973742\pi$
$79$	−6.87244	+	7.93122i	−0.773210	+	0.892332i	0.223389	+	0.974729i	$0.428288\pi$
$80$	−4.92817	−	3.16714i	−0.550986	−	0.354097i
$81$	−8.73818	−	5.61569i	−0.970909	−	0.623966i
$82$	−2.90761	+	3.35556i	−0.321092	+	0.370560i
$83$	2.23059	+	0.654959i	0.244839	+	0.0718911i	0.401849	−	0.915706i	$-0.368368\pi$
$83$	2.23059	+	0.654959i	0.244839	+	0.0718911i	−0.157011	+	0.987597i	$0.550186\pi$
$84$	−0.461194	−	3.20767i	−0.0503204	−	0.349986i
$85$	5.89514	+	6.80335i	0.639417	+	0.737927i
$86$	−3.48334	−	7.62746i	−0.375619	−	0.822490i
$87$	3.38632	−	0.994314i	0.363052	−	0.106602i
$88$	0.617235	−	1.35156i	0.0657975	−	0.144076i
$89$	−2.35018	+	16.3459i	−0.249118	+	1.73266i	0.354211	+	0.935165i	$0.384749\pi$
$89$	−2.35018	+	16.3459i	−0.249118	+	1.73266i	−0.603330	+	0.797492i	$0.706160\pi$
$90$	−1.00681	+	0.647036i	−0.106127	+	0.0682036i
$91$	4.28446			0.449133
$92$	0.825160	−	5.52485i	0.0860289	−	0.576005i
$93$	6.40884			0.664565
$94$	16.6728	−	10.7150i	1.71967	−	1.10517i
$95$	−1.39029	+	9.66969i	−0.142641	+	0.992089i
$96$	−4.61197	+	10.0988i	−0.470707	+	1.03071i
$97$	8.58446	−	2.52063i	0.871620	−	0.255931i	0.184816	−	0.982773i	$-0.440831\pi$
$97$	8.58446	−	2.52063i	0.871620	−	0.255931i	0.686804	+	0.726842i	$0.259013\pi$
$98$	3.57125	+	7.81994i	0.360750	+	0.789933i
$99$	−0.373975	−	0.431590i	−0.0375859	−	0.0433764i
$100$	0.598793	+	4.16470i	0.0598793	+	0.416470i
$101$	−1.81785	−	0.533770i	−0.180883	−	0.0531121i	0.190037	−	0.981777i	$-0.439139\pi$
$101$	−1.81785	−	0.533770i	−0.180883	−	0.0531121i	−0.370920	+	0.928665i	$0.620958\pi$
$102$	16.8233	−	19.4152i	1.66576	−	1.92239i
$103$	5.81020	+	3.73399i	0.572496	+	0.367921i	0.794629	−	0.607095i	$-0.207665\pi$
$103$	5.81020	+	3.73399i	0.572496	+	0.367921i	−0.222133	+	0.975016i	$0.571302\pi$
$104$	−3.63751	−	2.33769i	−0.356688	−	0.229229i
$105$	−2.14629	+	2.47695i	−0.209457	+	0.241726i
$106$	2.52989	+	0.742844i	0.245725	+	0.0721514i
$107$	1.57798	+	10.9751i	0.152549	+	1.06100i	0.911927	+	0.410351i	$0.134594\pi$
$107$	1.57798	+	10.9751i	0.152549	+	1.06100i	−0.759379	+	0.650649i	$0.774497\pi$
$108$	−3.50114	−	4.04053i	−0.336897	−	0.388800i
$109$	−0.944356	−	2.06785i	−0.0904529	−	0.198064i	0.858999	−	0.511978i	$-0.171087\pi$
$109$	−0.944356	−	2.06785i	−0.0904529	−	0.198064i	−0.949452	+	0.313914i	$0.898360\pi$
$110$	2.01080	−	0.590423i	0.191722	−	0.0562946i
$111$	7.62057	−	16.6867i	0.723312	−	1.58383i
$112$	−1.04194	+	7.24684i	−0.0984539	+	0.684762i
$113$	−1.11409	+	0.715982i	−0.104805	+	0.0673539i	−0.591993	−	0.805943i	$-0.701659\pi$
$113$	−1.11409	+	0.715982i	−0.104805	+	0.0673539i	0.487189	+	0.873297i	$0.338022\pi$
$114$	27.8788			2.61109
$115$	−4.76935	+	3.02841i	−0.444744	+	0.282401i
$116$	2.17538			0.201979
$117$	−1.39807	+	0.898486i	−0.129252	+	0.0830651i
$118$	1.23462	−	8.58695i	0.113656	−	0.790493i
$119$	4.67369	−	10.2340i	0.428437	−	0.938146i
$120$	3.17368	−	0.931878i	0.289716	−	0.0850684i
$121$	0.415415	+	0.909632i	0.0377650	+	0.0826938i
$122$	−5.83499	−	6.73394i	−0.528276	−	0.609663i
$123$	−0.671219	−	4.66843i	−0.0605218	−	0.420938i
$124$	3.79026	+	1.11292i	0.340375	+	0.0999431i
$125$	6.64385	−	7.66741i	0.594244	−	0.685794i
$126$	1.25829	+	0.808652i	0.112097	+	0.0720404i
$127$	−8.76779	−	5.63472i	−0.778016	−	0.500000i	0.0903587	−	0.995909i	$-0.471199\pi$
$127$	−8.76779	−	5.63472i	−0.778016	−	0.500000i	−0.868375	+	0.495909i	$0.834835\pi$
$128$	7.10534	−	8.19999i	0.628029	−	0.724784i
$129$	8.54640	+	2.50945i	0.752468	+	0.220945i
$130$	−0.867931	−	6.03659i	−0.0761226	−	0.529444i
$131$	1.10469	+	1.27488i	0.0965176	+	0.111387i	0.801953	−	0.597387i	$-0.203794\pi$
$131$	1.10469	+	1.27488i	0.0965176	+	0.111387i	−0.705436	+	0.708774i	$0.749249\pi$
$132$	−0.914385	−	2.00222i	−0.0795870	−	0.174271i
$133$	11.7147	−	3.43974i	1.01579	−	0.298263i
$134$	3.90379	−	8.54811i	0.337236	−	0.738444i
$135$	−0.769516	+	5.35210i	−0.0662294	+	0.460635i
$136$	−9.55183	+	6.13859i	−0.819063	+	0.526380i
$137$	18.2425			1.55856			0.779280	−	0.626676i	$-0.215585\pi$
$137$	18.2425			1.55856			0.779280	+	0.626676i	$0.215585\pi$
$138$	10.4914	+	12.2421i	0.893088	+	1.04212i
$139$	−21.6814			−1.83899			−0.919496	−	0.393099i	$-0.871403\pi$
$139$	−21.6814			−1.83899			−0.919496	+	0.393099i	$0.871403\pi$
$140$	−1.69947	+	1.09219i	−0.143632	+	0.0923065i
$141$	−2.99612	+	20.8385i	−0.252319	+	1.75492i
$142$	−0.920869	+	2.01642i	−0.0772776	+	0.169214i
$143$	2.79223	−	0.819872i	0.233498	−	0.0685611i
$144$	−1.17972	−	2.58324i	−0.0983104	−	0.215270i
$145$	−1.44075	−	1.66272i	−0.119648	−	0.138081i
$146$	3.77698	+	26.2695i	0.312585	+	2.17408i
$147$	−8.76207	−	2.57278i	−0.722683	−	0.212199i
$148$	7.40460	−	8.54536i	0.608654	−	0.702425i
$149$	12.1465	+	7.80611i	0.995083	+	0.639501i	0.933491	−	0.358600i	$-0.116746\pi$
$149$	12.1465	+	7.80611i	0.995083	+	0.639501i	0.0615922	+	0.998101i	$0.480382\pi$
$150$	−10.2159	−	6.56538i	−0.834128	−	0.536061i
$151$	2.78382	−	3.21270i	0.226544	−	0.261446i	−0.631086	−	0.775713i	$-0.717390\pi$
$151$	2.78382	−	3.21270i	0.226544	−	0.261446i	0.857630	+	0.514267i	$0.171936\pi$
$152$	−11.8226	−	3.47143i	−0.958939	−	0.281570i
$153$	0.621062	+	4.31958i	0.0502099	+	0.349218i
$154$	−1.71517	−	1.97942i	−0.138213	−	0.159506i
$155$	−1.65965	−	3.63412i	−0.133306	−	0.291899i
$156$	−6.14607	+	1.80465i	−0.492079	+	0.144488i
$157$	−6.21115	+	13.6005i	−0.495704	+	1.08544i	0.482138	+	0.876095i	$0.339860\pi$
$157$	−6.21115	+	13.6005i	−0.495704	+	1.08544i	−0.977842	+	0.209345i	$0.932867\pi$
$158$	2.65696	−	18.4796i	0.211376	−	1.47015i
$159$	−2.35621	+	1.51425i	−0.186860	+	0.120088i
$160$	6.92084			0.547140
$161$	5.91895	+	3.84970i	0.466479	+	0.303398i
$162$	18.4785			1.45181
$163$	−2.86372	+	1.84040i	−0.224304	+	0.144151i	−0.647967	−	0.761669i	$-0.724380\pi$
$163$	−2.86372	+	1.84040i	−0.224304	+	0.144151i	0.423663	+	0.905820i	$0.360744\pi$
$164$	0.413725	−	2.87752i	0.0323065	−	0.224697i
$165$	−0.924774	+	2.02497i	−0.0719935	+	0.157644i
$166$	−3.96818	+	1.16516i	−0.307991	+	0.0904342i
$167$	−7.33445	−	16.0602i	−0.567557	−	1.24278i	−0.948088	−	0.318008i	$-0.896986\pi$
$167$	−7.33445	−	16.0602i	−0.567557	−	1.24278i	0.380532	−	0.924768i	$-0.375741\pi$
$168$	−2.70710	−	3.12416i	−0.208857	−	0.241034i
$169$	0.644867	+	4.48515i	0.0496052	+	0.345012i
$170$	−15.3659	−	4.51185i	−1.17851	−	0.346043i
$171$	−3.10131	+	3.57910i	−0.237163	+	0.273700i
$172$	4.61866	+	2.96823i	0.352169	+	0.226326i
$173$	−9.54682	−	6.13537i	−0.725832	−	0.466464i	0.124829	−	0.992178i	$-0.460162\pi$
$173$	−9.54682	−	6.13537i	−0.725832	−	0.466464i	−0.850661	+	0.525715i	$0.823798\pi$
$174$	−4.11157	+	4.74501i	−0.311698	+	0.359718i
$175$	−5.10279	−	1.49831i	−0.385735	−	0.113262i
$176$	0.707710	+	4.92223i	0.0533456	+	0.371027i
$177$	6.03474	+	6.96446i	0.453599	+	0.523481i
$178$	−12.2041	−	26.7232i	−0.914735	−	2.00299i
$179$	−4.97495	+	1.46078i	−0.371845	+	0.109184i	−0.462315	−	0.886716i	$-0.652981\pi$
$179$	−4.97495	+	1.46078i	−0.371845	+	0.109184i	0.0904703	+	0.995899i	$0.471163\pi$
$180$	0.325519	−	0.712788i	0.0242628	−	0.0531281i
$181$	1.29035	−	8.97459i	0.0959111	−	0.667076i	−0.883977	−	0.467530i	$-0.845144\pi$
$181$	1.29035	−	8.97459i	0.0959111	−	0.667076i	0.979888	−	0.199546i	$-0.0639469\pi$
$182$	−6.41202	+	4.12076i	−0.475291	+	0.305451i
$183$	9.46496			0.699670
$184$	−2.92473	−	6.49790i	−0.215614	−	0.479032i
$185$	−11.4356			−0.840763
$186$	−9.59132	+	6.16397i	−0.703270	+	0.451964i
$187$	1.08753	−	7.56394i	0.0795281	−	0.553130i
$188$	−5.39063	+	11.8038i	−0.393152	+	0.860883i
$189$	6.48399	−	1.90387i	0.471641	−	0.138486i
$190$	−7.21955	−	15.8086i	−0.523761	−	1.14688i
$191$	9.92152	+	11.4500i	0.717896	+	0.828496i	0.991052	−	0.133474i	$-0.0426132\pi$
$191$	9.92152	+	11.4500i	0.717896	+	0.828496i	−0.273157	+	0.961970i	$0.588068\pi$
$192$	−0.136023	−	0.946058i	−0.00981658	−	0.0682758i
$193$	8.87795	+	2.60680i	0.639049	+	0.187642i	0.585176	−	0.810906i	$-0.301025\pi$
$193$	8.87795	+	2.60680i	0.639049	+	0.187642i	0.0538727	+	0.998548i	$0.482843\pi$
$194$	−10.4230	+	12.0288i	−0.748328	+	0.863616i
$195$	5.44991	+	3.50244i	0.390276	+	0.250815i
$196$	−4.73521	−	3.04314i	−0.338229	−	0.217367i
$197$	1.69754	−	1.95907i	0.120945	−	0.139578i	−0.692048	−	0.721851i	$-0.743291\pi$
$197$	1.69754	−	1.95907i	0.120945	−	0.139578i	0.812993	+	0.582274i	$0.197837\pi$
$198$	0.974783	+	0.286222i	0.0692748	+	0.0203409i
$199$	−2.12495	−	14.7794i	−0.150634	−	1.04768i	−0.915161	−	0.403089i	$-0.867936\pi$
$199$	−2.12495	−	14.7794i	−0.150634	−	1.04768i	0.764527	−	0.644592i	$-0.222973\pi$
$200$	3.51477	+	4.05626i	0.248532	+	0.286821i
$201$	4.14680	+	9.08023i	0.292493	+	0.640470i
$202$	3.23393	−	0.949568i	0.227539	−	0.0668114i
$203$	−1.14224	+	2.50115i	−0.0801693	+	0.175546i
$204$	−2.39380	+	16.6493i	−0.167600	+	1.16568i
$205$	−2.47341	+	1.58956i	−0.172750	+	0.111020i
$206$	−12.2867			−0.856058
$207$	−2.73874	−	0.0149501i	−0.190356	−	0.00103910i
$208$	14.4715			1.00342
$209$	6.97636	−	4.48344i	0.482565	−	0.310126i
$210$	0.829779	−	5.77124i	0.0572602	−	0.398253i
$211$	−6.51572	+	14.2674i	−0.448561	+	0.982211i	0.541387	+	0.840774i	$0.317899\pi$
$211$	−6.51572	+	14.2674i	−0.448561	+	0.982211i	−0.989947	+	0.141437i	$0.954828\pi$
$212$	−1.65645	+	0.486376i	−0.113765	+	0.0334045i
$213$	−0.978194	−	2.14195i	−0.0670248	−	0.146764i
$214$	−12.9173	−	14.9074i	−0.883009	−	1.01905i
$215$	−0.790216	−	5.49607i	−0.0538923	−	0.374829i
$216$	−6.54371	−	1.92141i	−0.445243	−	0.130735i
$217$	−3.26976	+	3.77350i	−0.221965	+	0.256162i
$218$	3.40214	+	2.18643i	0.230422	+	0.148083i
$219$	−23.7164	−	15.2416i	−1.60260	−	1.02993i
$220$	−0.898566	+	1.03700i	−0.0605813	+	0.0699145i
$221$	−21.3374	−	6.26523i	−1.43531	−	0.421445i
$222$	4.64438	+	32.3024i	0.311710	+	2.16799i
$223$	−11.1049	−	12.8158i	−0.743641	−	0.858208i	0.250295	−	0.968170i	$-0.419472\pi$
$223$	−11.1049	−	12.8158i	−0.743641	−	0.858208i	−0.993936	+	0.109962i	$0.964927\pi$
$224$	−3.59314	−	7.86788i	−0.240077	−	0.525695i
$225$	1.97931	−	0.581179i	0.131954	−	0.0387453i
$226$	0.978696	−	2.14305i	0.0651019	−	0.142553i
$227$	−2.89230	+	20.1164i	−0.191968	+	1.33517i	0.634821	+	0.772659i	$0.281074\pi$
$227$	−2.89230	+	20.1164i	−0.191968	+	1.33517i	−0.826790	+	0.562511i	$0.809835\pi$
$228$	−15.3559	+	9.86865i	−1.01697	+	0.653567i
$229$	6.88626			0.455057			0.227528	−	0.973771i	$-0.426936\pi$
$229$	6.88626			0.455057			0.227528	+	0.973771i	$0.426936\pi$
$230$	4.22499	−	9.11938i	0.278588	−	0.601314i
$231$	2.78219			0.183054
$232$	2.33444	−	1.50025i	0.153264	−	0.0984965i
$233$	0.805508	−	5.60243i	0.0527706	−	0.367027i	−0.946276	−	0.323361i	$-0.895187\pi$
$233$	0.805508	−	5.60243i	0.0527706	−	0.367027i	0.999046	−	0.0436661i	$-0.0139038\pi$
$234$	1.22817	−	2.68931i	0.0802878	−	0.175806i
$235$	12.5923	−	3.69744i	0.821432	−	0.241194i
$236$	2.35960	+	5.16681i	0.153597	+	0.336331i
$237$	12.9871	+	14.9879i	0.843600	+	0.973566i
$238$	2.84840	+	19.8110i	0.184634	+	1.28416i
$239$	19.2426	+	5.65013i	1.24470	+	0.365477i	0.836779	−	0.547541i	$-0.184436\pi$
$239$	19.2426	+	5.65013i	1.24470	+	0.365477i	0.407920	+	0.913018i	$0.366254\pi$
$240$	−7.24948	+	8.36635i	−0.467952	+	0.540046i
$241$	−11.7178	−	7.53057i	−0.754809	−	0.485087i	0.105778	−	0.994390i	$-0.466267\pi$
$241$	−11.7178	−	7.53057i	−0.754809	−	0.485087i	−0.860587	+	0.509303i	$0.829903\pi$
$242$	−1.49658	−	0.961792i	−0.0962037	−	0.0618263i
$243$	−3.83668	+	4.42777i	−0.246123	+	0.284041i
$244$	5.59768	+	1.64363i	0.358355	+	0.105222i
$245$	0.810157	+	5.63477i	0.0517590	+	0.359992i
$246$	5.49459	+	6.34110i	0.350323	+	0.404294i
$247$	−10.0252	−	21.9521i	−0.637889	−	1.39678i
$248$	4.83493	−	1.41966i	0.307018	−	0.0901487i
$249$	1.82498	−	3.99616i	0.115654	−	0.253246i
$250$	−2.56858	+	17.8649i	−0.162451	+	1.12987i
$251$	−5.30258	+	3.40776i	−0.334696	+	0.215096i	−0.697184	−	0.716892i	$-0.745564\pi$
$251$	−5.30258	+	3.40776i	−0.334696	+	0.215096i	0.362488	+	0.931989i	$0.381927\pi$
$252$	−0.979327			−0.0616918
$253$	4.59412	+	1.37624i	0.288830	+	0.0865235i
$254$	18.5411			1.16337
$255$	14.3110	−	9.19715i	0.896192	−	0.575948i
$256$	−2.89096	+	20.1070i	−0.180685	+	1.25669i
$257$	−0.656007	+	1.43646i	−0.0409206	+	0.0896037i	−0.928988	−	0.370109i	$-0.879320\pi$
$257$	−0.656007	+	1.43646i	−0.0409206	+	0.0896037i	0.888068	+	0.459713i	$0.152048\pi$
$258$	−15.2039	+	4.46427i	−0.946555	+	0.277934i
$259$	5.93710	+	13.0004i	0.368914	+	0.807808i
$260$	2.61492	+	3.01778i	0.162171	+	0.187155i
$261$	−0.151786	−	1.05569i	−0.00939530	−	0.0653458i
$262$	−2.87943	−	0.845478i	−0.177892	−	0.0522338i
$263$	−2.67058	+	3.08201i	−0.164675	+	0.190045i	−0.832089	−	0.554641i	$-0.812855\pi$
$263$	−2.67058	+	3.08201i	−0.164675	+	0.190045i	0.667415	+	0.744686i	$0.267401\pi$
$264$	−2.36208	−	1.51802i	−0.145376	−	0.0934276i
$265$	1.46882	+	0.943954i	0.0902289	+	0.0579866i
$266$	−14.2236	+	16.4149i	−0.872106	+	1.00646i
$267$	29.9428	+	8.79199i	1.83247	+	0.538061i
$268$	0.875647	+	6.09026i	0.0534887	+	0.372022i
$269$	11.0902	+	12.7988i	0.676181	+	0.780355i	0.985330	−	0.170659i	$-0.0545896\pi$
$269$	11.0902	+	12.7988i	0.676181	+	0.780355i	−0.309149	+	0.951014i	$0.600044\pi$
$270$	−3.99597	−	8.74994i	−0.243187	−	0.532505i
$271$	−18.9047	+	5.55093i	−1.14838	+	0.337195i	−0.799907	−	0.600124i	$-0.795118\pi$
$271$	−18.9047	+	5.55093i	−1.14838	+	0.337195i	−0.348473	+	0.937319i	$0.613300\pi$
$272$	15.7862	−	34.5670i	0.957181	−	2.09593i
$273$	1.15225	−	8.01405i	0.0697372	−	0.485033i
$274$	−27.3013	+	17.5455i	−1.64933	+	1.05996i
$275$	−3.61226			−0.217828
$276$	−10.1123	−	3.02929i	−0.608688	−	0.182342i
$277$	29.0173			1.74348			0.871740	−	0.489968i	$-0.162992\pi$
$277$	29.0173			1.74348			0.871740	+	0.489968i	$0.162992\pi$
$278$	32.4479	−	20.8530i	1.94610	−	1.25068i
$279$	0.275628	−	1.91704i	0.0165014	−	0.114770i
$280$	−1.07051	+	2.34409i	−0.0639753	+	0.140086i
$281$	−2.27945	+	0.669308i	−0.135981	+	0.0399276i	−0.349015	−	0.937117i	$-0.613484\pi$
$281$	−2.27945	+	0.669308i	−0.135981	+	0.0399276i	0.213034	+	0.977045i	$0.431666\pi$
$282$	−15.5584	−	34.0681i	−0.926488	−	2.02872i
$283$	11.6005	+	13.3877i	0.689578	+	0.795815i	0.987305	−	0.158836i	$-0.0507741\pi$
$283$	11.6005	+	13.3877i	0.689578	+	0.795815i	−0.297727	+	0.954651i	$0.596229\pi$
$284$	−0.206557	−	1.43664i	−0.0122569	−	0.0852488i
$285$	17.7132	+	5.20107i	1.04924	+	0.308085i
$286$	−3.39024	+	3.91254i	−0.200469	+	0.231354i
$287$	3.09121	+	1.98660i	0.182468	+	0.117265i
$288$	2.82245	+	1.81388i	0.166314	+	0.106884i
$289$	−27.1086	+	31.2849i	−1.59462	+	1.84029i
$290$	3.75539	+	1.10268i	0.220524	+	0.0647517i
$291$	−2.40614	−	16.7351i	−0.141050	−	0.981028i
$292$	−11.3794	−	13.1325i	−0.665927	−	0.768521i
$293$	−0.673311	−	1.47435i	−0.0393353	−	0.0861322i	0.888944	−	0.458015i	$-0.151440\pi$
$293$	−0.673311	−	1.47435i	−0.0393353	−	0.0861322i	−0.928280	+	0.371883i	$0.878712\pi$
$294$	15.5876	−	4.57693i	0.909087	−	0.266932i
$295$	2.38641	−	5.22552i	0.138942	−	0.304241i
$296$	2.05269	−	14.2768i	0.119310	−	0.829822i
$297$	3.86136	−	2.48155i	0.224059	−	0.143994i
$298$	−25.6861			−1.48796
$299$	5.86690	−	12.6633i	0.339292	−	0.732340i
$300$	7.95108			0.459056
$301$	−5.83788	+	3.75178i	−0.336490	+	0.216249i
$302$	−1.07626	+	7.48552i	−0.0619315	+	0.430743i
$303$	−1.48730	+	3.25673i	−0.0854431	+	0.187094i
$304$	39.5684	−	11.6183i	2.26940	−	0.666357i
$305$	−2.45107	−	5.36709i	−0.140348	−	0.307318i
$306$	−5.08401	−	5.86726i	−0.290633	−	0.335409i
$307$	−0.0945265	−	0.657446i	−0.00539491	−	0.0375224i	0.986946	−	0.161050i	$-0.0514882\pi$
$307$	−0.0945265	−	0.657446i	−0.00539491	−	0.0375224i	−0.992341	+	0.123528i	$0.960579\pi$
$308$	1.64542	+	0.483138i	0.0937563	+	0.0275293i
$309$	8.54698	−	9.86375i	0.486221	−	0.561129i
$310$	5.97906	+	3.84251i	0.339588	+	0.218240i
$311$	26.9576	+	17.3246i	1.52862	+	0.982387i	0.990191	+	0.139719i	$0.0446198\pi$
$311$	26.9576	+	17.3246i	1.52862	+	0.982387i	0.538433	+	0.842668i	$0.319017\pi$
$312$	−5.35089	+	6.17526i	−0.302935	+	0.349605i
$313$	−20.7739	−	6.09977i	−1.17421	−	0.344779i	−0.364271	−	0.931293i	$-0.618682\pi$
$313$	−20.7739	−	6.09977i	−1.17421	−	0.344779i	−0.809940	+	0.586513i	$0.800500\pi$
$314$	−3.78541	−	26.3281i	−0.213623	−	1.48578i
$315$	0.648609	+	0.748535i	0.0365450	+	0.0421752i
$316$	5.07799	+	11.1192i	0.285659	+	0.625506i
$317$	1.03240	−	0.303140i	0.0579853	−	0.0170260i	−0.252611	−	0.967568i	$-0.581289\pi$
$317$	1.03240	−	0.303140i	0.0579853	−	0.0170260i	0.310597	+	0.950542i	$0.399471\pi$
$318$	2.06987	−	4.53237i	0.116072	−	0.254163i
$319$	−0.265789	+	1.84860i	−0.0148813	+	0.103502i
$320$	−0.501236	+	0.322125i	−0.0280199	+	0.0180073i
$321$	20.9532			1.16949
$322$	−12.5608	−	0.0685661i	−0.699985	−	0.00382104i
$323$	−63.3714			−3.52608
$324$	−10.1781	+	6.54109i	−0.565452	+	0.363394i
$325$	−1.49602	+	10.4051i	−0.0829845	+	0.577170i
$326$	2.51570	−	5.50860i	0.139331	−	0.305093i
$327$	−4.12188	+	1.21029i	−0.227940	+	0.0669293i
$328$	−1.54051	−	3.37325i	−0.0850607	−	0.186257i
$329$	−10.7410	−	12.3958i	−0.592172	−	0.683403i
$330$	−0.563606	−	3.91997i	−0.0310255	−	0.215787i
$331$	−14.6531	−	4.30254i	−0.805408	−	0.236489i	−0.146986	−	0.989139i	$-0.546957\pi$
$331$	−14.6531	−	4.30254i	−0.805408	−	0.236489i	−0.658421	+	0.752650i	$0.728775\pi$
$332$	1.77326	−	2.04646i	0.0973205	−	0.112314i
$333$	−4.66365	−	2.99715i	−0.255567	−	0.164243i
$334$	26.4231	+	16.9811i	1.44581	+	0.929166i
$335$	4.07506	−	4.70287i	0.222645	−	0.256946i
$336$	13.2750	+	3.89788i	0.724208	+	0.212647i
$337$	1.64880	+	11.4676i	0.0898158	+	0.624682i	0.984157	+	0.177298i	$0.0567355\pi$
$337$	1.64880	+	11.4676i	0.0898158	+	0.624682i	−0.894342	+	0.447385i	$0.852355\pi$
$338$	−5.27888	−	6.09215i	−0.287133	−	0.331369i
$339$	1.03962	+	2.27645i	0.0564645	+	0.123640i
$340$	10.0608	−	2.95413i	0.545625	−	0.160210i
$341$	−1.40884	+	3.08493i	−0.0762930	+	0.167058i
$342$	1.19900	−	8.33921i	0.0648344	−	0.450933i
$343$	14.6551	−	9.41823i	0.791299	−	0.508537i
$344$	7.00343			0.377599
$345$	4.38198	+	9.73549i	0.235918	+	0.524141i
$346$	20.1885			1.08534
$347$	−0.134683	+	0.0865556i	−0.00723017	+	0.00464655i	−0.544251	−	0.838922i	$-0.683186\pi$
$347$	−0.134683	+	0.0865556i	−0.00723017	+	0.00464655i	0.537021	+	0.843569i	$0.319550\pi$
$348$	0.585038	−	4.06903i	0.0313613	−	0.218123i
$349$	−2.60585	+	5.70601i	−0.139488	+	0.305436i	−0.966464	−	0.256801i	$-0.917332\pi$
$349$	−2.60585	+	5.70601i	−0.139488	+	0.305436i	0.826977	+	0.562236i	$0.190059\pi$
$350$	9.07779	−	2.66548i	0.485228	−	0.142476i
$351$	−5.54887	−	12.1503i	−0.296177	−	0.648537i
$352$	−3.84728	−	4.44000i	−0.205061	−	0.236653i
$353$	−2.43319	−	16.9232i	−0.129506	−	0.900731i	−0.946182	−	0.323635i	$-0.895095\pi$
$353$	−2.43319	−	16.9232i	−0.129506	−	0.900731i	0.816676	−	0.577096i	$-0.195814\pi$
$354$	−15.7298	−	4.61869i	−0.836030	−	0.245481i
$355$	−0.961272	+	1.10937i	−0.0510190	+	0.0588791i
$356$	16.1817	+	10.3994i	0.857630	+	0.551165i
$357$	−17.8856	−	11.4944i	−0.946608	−	0.608348i
$358$	6.04043	−	6.97103i	0.319247	−	0.368430i
$359$	6.80814	+	1.99905i	0.359320	+	0.105506i	0.456409	−	0.889770i	$-0.349135\pi$
$359$	6.80814	+	1.99905i	0.359320	+	0.105506i	−0.0970898	+	0.995276i	$0.530953\pi$
$360$	−0.142255	−	0.989402i	−0.00749747	−	0.0521461i
$361$	−32.5930	−	37.6143i	−1.71542	−	1.97970i
$362$	6.70058	+	14.6722i	0.352175	+	0.771155i
$363$	1.81318	−	0.532398i	0.0951674	−	0.0279437i
$364$	2.07312	−	4.53951i	0.108661	−	0.237935i
$365$	−2.50107	+	17.3953i	−0.130912	+	0.910513i
$366$	−14.1650	+	9.10332i	−0.740419	+	0.475838i
$367$	3.72910			0.194658			0.0973288	−	0.995252i	$-0.468970\pi$
$367$	3.72910			0.194658			0.0973288	+	0.995252i	$0.468970\pi$
$368$	19.9923	+	13.0030i	1.04217	+	0.677830i
$369$	−1.42531			−0.0741985
$370$	17.1143	−	10.9987i	0.889729	−	0.571794i
$371$	0.310545	−	2.15989i	0.0161227	−	0.112136i
$372$	3.10105	−	6.79035i	0.160782	−	0.352063i
$373$	−23.9105	+	7.02077i	−1.23804	+	0.363521i	−0.834279	−	0.551343i	$-0.814116\pi$
$373$	−23.9105	+	7.02077i	−1.23804	+	0.363521i	−0.403762	+	0.914864i	$0.632297\pi$
$374$	5.64736	+	12.3660i	0.292018	+	0.639431i
$375$	−12.5551	−	14.4893i	−0.648341	−	0.748226i
$376$	2.35575	+	16.3846i	0.121488	+	0.844971i
$377$	5.21480	+	1.53120i	0.268576	+	0.0788611i
$378$	−7.87266	+	9.08554i	−0.404926	+	0.467310i
$379$	12.4080	+	7.97413i	0.637356	+	0.409604i	0.819026	−	0.573756i	$-0.194514\pi$
$379$	12.4080	+	7.97413i	0.637356	+	0.409604i	−0.181671	+	0.983359i	$0.558151\pi$
$380$	9.57260	+	6.15194i	0.491064	+	0.315588i
$381$	−12.8977	+	14.8847i	−0.660769	+	0.762568i
$382$	−25.8609	−	7.59344i	−1.32316	−	0.388514i
$383$	1.11335	+	7.74350i	0.0568894	+	0.395674i	0.998294	+	0.0583940i	$0.0185980\pi$
$383$	1.11335	+	7.74350i	0.0568894	+	0.395674i	−0.941404	+	0.337280i	$0.890493\pi$
$384$	−13.4272	−	15.4958i	−0.685202	−	0.790765i
$385$	−0.720481	−	1.57763i	−0.0367191	−	0.0804037i
$386$	−15.7937	+	4.63746i	−0.803881	+	0.236041i
$387$	1.11820	−	2.44851i	0.0568411	−	0.124465i
$388$	1.48309	−	10.3151i	0.0752927	−	0.523672i
$389$	9.23807	−	5.93695i	0.468389	−	0.301015i	−0.285074	−	0.958505i	$-0.592018\pi$
$389$	9.23807	−	5.93695i	0.468389	−	0.301015i	0.753463	+	0.657490i	$0.228382\pi$
$390$	−11.5248			−0.583583
$391$	−23.8481	−	27.8276i	−1.20605	−	1.40730i
$392$	−7.18016			−0.362653
$393$	2.68176	−	1.72346i	0.135277	−	0.0869371i
$394$	−0.656287	+	4.56458i	−0.0330633	+	0.229960i
$395$	5.13568	−	11.2456i	0.258404	−	0.565826i
$396$	−0.638238	+	0.187404i	−0.0320727	+	0.00941738i
$397$	14.8000	+	32.4074i	0.742789	+	1.62648i	0.778911	+	0.627134i	$0.215772\pi$
$397$	14.8000	+	32.4074i	0.742789	+	1.62648i	−0.0361218	+	0.999347i	$0.511500\pi$
$398$	17.3948	+	20.0747i	0.871924	+	1.00625i
$399$	−3.28351	−	22.8373i	−0.164381	−	1.14330i
$400$	−17.2356	−	5.06082i	−0.861779	−	0.253041i
$401$	1.42252	−	1.64168i	0.0710372	−	0.0819814i	−0.719118	−	0.694887i	$-0.755454\pi$
$401$	1.42252	−	1.64168i	0.0710372	−	0.0819814i	0.790156	+	0.612906i	$0.210000\pi$
$402$	−14.9393	−	9.60091i	−0.745105	−	0.478850i
$403$	8.30263	+	5.33578i	0.413583	+	0.265794i
$404$	−1.44515	+	1.66779i	−0.0718989	+	0.0829758i
$405$	11.7406	+	3.44735i	0.583394	+	0.171300i
$406$	−0.696140	−	4.84176i	−0.0345488	−	0.240292i
$407$	6.35703	+	7.33641i	0.315106	+	0.363652i
$408$	8.91336	+	19.5175i	0.441277	+	0.966262i
$409$	6.95024	−	2.04077i	0.343667	−	0.100910i	−0.105344	−	0.994436i	$-0.533594\pi$
$409$	6.95024	−	2.04077i	0.343667	−	0.100910i	0.449011	+	0.893526i	$0.351776\pi$
$410$	2.17282	−	4.75780i	0.107308	−	0.234971i
$411$	4.90607	−	34.1224i	0.241998	−	1.68314i
$412$	6.76766	−	4.34931i	0.333419	−	0.214275i
$413$	−7.17954			−0.353282
$414$	4.11312	−	2.61173i	0.202149	−	0.128359i
$415$	−2.73861			−0.134433
$416$	−14.3827	+	9.24321i	−0.705171	+	0.453186i
$417$	−5.83092	+	40.5549i	−0.285541	+	1.98598i
$418$	−6.12853	+	13.4196i	−0.299756	+	0.656375i
$419$	2.59616	−	0.762301i	0.126831	−	0.0372409i	−0.217701	−	0.976015i	$-0.569856\pi$
$419$	2.59616	−	0.762301i	0.126831	−	0.0372409i	0.344532	+	0.938775i	$0.388038\pi$
$420$	1.58588	+	3.47259i	0.0773828	+	0.169445i
$421$	13.3894	+	15.4522i	0.652559	+	0.753093i	0.981543	−	0.191242i	$-0.0612517\pi$
$421$	13.3894	+	15.4522i	0.652559	+	0.753093i	−0.328984	+	0.944336i	$0.606706\pi$
$422$	−3.97103	−	27.6191i	−0.193306	−	1.34448i
$423$	6.10444	+	1.79242i	0.296808	+	0.0871506i
$424$	−1.44213	+	1.66431i	−0.0700362	+	0.0808261i
$425$	23.2219	+	14.9238i	1.12643	+	0.723910i
$426$	3.52405	+	2.26477i	0.170741	+	0.109728i
$427$	−4.82897	+	5.57293i	−0.233690	+	0.269693i
$428$	12.3919	+	3.63860i	0.598987	+	0.175879i
$429$	−0.782634	−	5.44334i	−0.0377859	−	0.262807i
$430$	6.46870	+	7.46528i	0.311948	+	0.360008i
$431$	−0.944404	−	2.06796i	−0.0454903	−	0.0996099i	0.885522	−	0.464597i	$-0.153801\pi$
$431$	−0.944404	−	2.06796i	−0.0454903	−	0.0996099i	−0.931013	+	0.364987i	$0.881073\pi$
$432$	21.9008	−	6.43066i	1.05370	−	0.309395i
$433$	−4.26410	+	9.33707i	−0.204919	+	0.448711i	−0.983990	−	0.178226i	$-0.942964\pi$
$433$	−4.26410	+	9.33707i	−0.204919	+	0.448711i	0.779070	+	0.626937i	$0.215692\pi$
$434$	1.26412	−	8.79216i	0.0606798	−	0.422037i
$435$	−3.49758	+	2.24776i	−0.167696	+	0.107772i
$436$	−2.64789			−0.126811
$437$	5.87480	−	39.3347i	0.281030	−	1.88163i
$438$	50.1526			2.39639
$439$	4.51128	−	2.89922i	0.215312	−	0.138372i	−0.428540	−	0.903523i	$-0.640972\pi$
$439$	4.51128	−	2.89922i	0.215312	−	0.138372i	0.643851	+	0.765151i	$0.277335\pi$
$440$	−0.249099	+	1.73252i	−0.0118753	+	0.0825948i
$441$	−1.14641	+	2.51029i	−0.0545911	+	0.119538i
$442$	37.9590	−	11.1458i	1.80552	−	0.530150i
$443$	−1.36700	−	2.99331i	−0.0649481	−	0.142217i	0.874374	−	0.485252i	$-0.161272\pi$
$443$	−1.36700	−	2.99331i	−0.0649481	−	0.142217i	−0.939322	+	0.343035i	$0.888545\pi$
$444$	−13.9927	−	16.1484i	−0.664064	−	0.766370i
$445$	−2.76856	−	19.2558i	−0.131243	−	0.912812i
$446$	28.9455	+	8.49916i	1.37061	+	0.402447i
$447$	17.8679	−	20.6207i	0.845124	−	0.975325i
$448$	0.626433	+	0.402584i	0.0295962	+	0.0190203i
$449$	−15.1318	−	9.72464i	−0.714116	−	0.458934i	0.132470	−	0.991187i	$-0.457709\pi$
$449$	−15.1318	−	9.72464i	−0.714116	−	0.458934i	−0.846585	+	0.532253i	$0.821346\pi$
$450$	−2.40322	+	2.77347i	−0.113289	+	0.130743i
$451$	2.39473	+	0.703156i	0.112763	+	0.0331103i
$452$	0.219528	+	1.52685i	0.0103257	+	0.0718171i
$453$	−5.26067	−	6.07114i	−0.247168	−	0.285247i
$454$	−15.0192	−	32.8875i	−0.704887	−	1.54349i
$455$	−4.84274	+	1.42196i	−0.227031	+	0.0666624i
$456$	−9.67281	+	21.1805i	−0.452971	+	0.991867i
$457$	3.24864	−	22.5948i	0.151965	−	1.05694i	−0.760956	−	0.648803i	$-0.775270\pi$
$457$	3.24864	−	22.5948i	0.151965	−	1.05694i	0.912921	−	0.408136i	$-0.133821\pi$
$458$	−10.3058	+	6.62315i	−0.481559	+	0.309479i
$459$	−35.0756			−1.63719
$460$	0.900946	+	6.51862i	0.0420068	+	0.303932i
$461$	32.0936			1.49475			0.747375	−	0.664403i	$-0.231314\pi$
$461$	32.0936			1.49475			0.747375	+	0.664403i	$0.231314\pi$
$462$	−4.16376	+	2.67589i	−0.193716	+	0.124493i
$463$	−4.21845	+	29.3399i	−0.196048	+	1.36354i	0.619566	+	0.784945i	$0.287309\pi$
$463$	−4.21845	+	29.3399i	−0.196048	+	1.36354i	−0.815613	+	0.578597i	$0.803600\pi$
$464$	−3.85811	+	8.44808i	−0.179108	+	0.392192i
$465$	−7.24394	+	2.12701i	−0.335930	+	0.0986378i
$466$	4.18287	+	9.15920i	0.193768	+	0.424292i
$467$	27.6524	+	31.9126i	1.27960	+	1.47674i	0.800946	+	0.598737i	$0.204331\pi$
$467$	27.6524	+	31.9126i	1.27960	+	1.47674i	0.478656	+	0.878002i	$0.341124\pi$
$468$	0.275486	+	1.91605i	0.0127344	+	0.0885694i
$469$	−7.46209	−	2.19107i	−0.344567	−	0.101174i
$470$	−15.2892	+	17.6447i	−0.705239	+	0.813889i
$471$	23.7693	+	15.2756i	1.09523	+	0.703862i
$472$	6.09544	+	3.91730i	0.280566	+	0.180309i
$473$	−3.08667	+	3.56221i	−0.141925	+	0.163791i
$474$	−33.8513	−	9.93965i	−1.55484	−	0.456543i
$475$	4.26316	+	29.6509i	0.195607	+	1.36048i
$476$	−8.58172	−	9.90383i	−0.393342	−	0.453941i
$477$	0.351612	+	0.769923i	0.0160992	+	0.0352524i
$478$	−34.2323	+	10.0515i	−1.56575	+	0.459745i
$479$	−9.12919	+	19.9901i	−0.417123	+	0.913373i	0.578120	+	0.815952i	$0.303787\pi$
$479$	−9.12919	+	19.9901i	−0.417123	+	0.913373i	−0.995243	+	0.0974210i	$0.968941\pi$
$480$	1.86127	−	12.9454i	0.0849548	−	0.590873i
$481$	23.7652	−	15.2730i	1.08360	−	0.696387i
$482$	24.7794			1.12867
$483$	8.79266	−	10.0360i	0.400080	−	0.456656i
$484$	1.16479			0.0529449
$485$	−8.86650	+	5.69815i	−0.402607	+	0.258740i
$486$	1.48330	−	10.3166i	0.0672839	−	0.467970i
$487$	9.19688	−	20.1384i	0.416750	−	0.912556i	−0.578543	−	0.815652i	$-0.696379\pi$
$487$	9.19688	−	20.1384i	0.416750	−	0.912556i	0.995294	−	0.0969045i	$-0.0308941\pi$
$488$	7.14052	−	2.09664i	0.323236	−	0.0949107i
$489$	2.67230	+	5.85152i	0.120846	+	0.264615i
$490$	−6.63194	−	7.65366i	−0.299600	−	0.345757i
$491$	0.169571	+	1.17940i	0.00765265	+	0.0532254i	0.993290	−	0.115651i	$-0.0368953\pi$
$491$	0.169571	+	1.17940i	0.00765265	+	0.0532254i	−0.985637	+	0.168876i	$0.945986\pi$
$492$	−5.27112	−	1.54774i	−0.237641	−	0.0697776i
$493$	9.34603	−	10.7859i	0.420924	−	0.485772i
$494$	36.1169	+	23.2109i	1.62498	+	1.04431i
$495$	0.565945	+	0.363711i	0.0254373	+	0.0163476i
$496$	−11.0442	+	12.7457i	−0.495898	+	0.572297i
$497$	1.76024	+	0.516853i	0.0789576	+	0.0231840i
$498$	1.11224	+	7.73581i	0.0498408	+	0.346650i
$499$	−12.3501	−	14.2528i	−0.552868	−	0.638044i	0.408681	−	0.912677i	$-0.365989\pi$
$499$	−12.3501	−	14.2528i	−0.552868	−	0.638044i	−0.961549	+	0.274633i	$0.911444\pi$
$500$	−4.90908	−	10.7494i	−0.219541	−	0.480727i
$501$	−32.0130	+	9.39987i	−1.43024	+	0.419955i
$502$	4.65817	−	10.2000i	0.207904	−	0.455247i
$503$	−5.25654	+	36.5601i	−0.234378	+	1.63013i	0.444428	+	0.895814i	$0.353407\pi$
$503$	−5.25654	+	36.5601i	−0.234378	+	1.63013i	−0.678806	+	0.734318i	$0.737502\pi$
$504$	−1.05094	+	0.675395i	−0.0468124	+	0.0300845i
$505$	2.23188			0.0993173
$506$	−8.19912	+	2.35894i	−0.364495	+	0.104868i
$507$	8.56288			0.380291
$508$	−10.2126	+	6.56326i	−0.453112	+	0.291197i
$509$	2.93369	−	20.4043i	0.130034	−	0.904404i	−0.815472	−	0.578797i	$-0.803522\pi$
$509$	2.93369	−	20.4043i	0.130034	−	0.904404i	0.945505	−	0.325607i	$-0.105569\pi$
$510$	−12.5718	+	27.5285i	−0.556691	+	1.21898i
$511$	21.0742	−	6.18793i	0.932266	−	0.273738i
$512$	−5.99763	−	13.1330i	−0.265060	−	0.580401i
$513$	−24.9267	−	28.7669i	−1.10054	−	1.27009i
$514$	−0.399806	−	2.78071i	−0.0176347	−	0.122652i
$515$	−7.80656	−	2.29221i	−0.343998	−	0.101007i
$516$	6.79419	−	7.84091i	0.299097	−	0.345177i
$517$	−9.37210	−	6.02308i	−0.412185	−	0.264895i
$518$	−21.3891	−	13.7459i	−0.939781	−	0.603961i
$519$	−14.0437	+	16.2073i	−0.616448	+	0.711419i
$520$	4.88735	+	1.43505i	0.214324	+	0.0629313i
$521$	−0.929359	−	6.46384i	−0.0407160	−	0.283186i	−1.00000		0.000741672i	$-0.999764\pi$
$521$	−0.929359	−	6.46384i	−0.0407160	−	0.283186i	0.959284	−	0.282444i	$-0.0911452\pi$
$522$	1.24252	+	1.43394i	0.0543835	+	0.0627619i
$523$	6.62775	+	14.5127i	0.289811	+	0.634598i	0.997403	−	0.0720234i	$-0.0229456\pi$
$523$	6.62775	+	14.5127i	0.289811	+	0.634598i	−0.707592	+	0.706622i	$0.750218\pi$
$524$	1.88531	−	0.553576i	0.0823600	−	0.0241831i
$525$	−4.17492	+	9.14179i	−0.182208	+	0.398980i
$526$	1.03247	−	7.18100i	0.0450179	−	0.313107i
$527$	21.8021	−	14.0113i	0.949713	−	0.610344i
$528$	9.39733			0.408966
$529$	19.4834	−	12.2228i	0.847106	−	0.531424i
$530$	−3.10609			−0.134920
$531$	2.34277	−	1.50561i	0.101668	−	0.0653379i
$532$	2.02389	−	14.0764i	0.0877466	−	0.610291i
$533$	3.01721	−	6.60678i	0.130690	−	0.286171i
$534$	−53.2678	+	15.6408i	−2.30512	+	0.676845i
$535$	−5.42608	−	11.8815i	−0.234590	−	0.513681i
$536$	5.13984	+	5.93169i	0.222007	+	0.256210i
$537$	1.39443	+	9.69846i	0.0601740	+	0.418520i
$538$	−28.9071	−	8.48789i	−1.24627	−	0.365939i
$539$	3.16457	−	3.65211i	0.136308	−	0.157307i
$540$	5.29836	+	3.40505i	0.228005	+	0.146530i
$541$	26.0066	+	16.7134i	1.11811	+	0.718565i	0.963045	−	0.269339i	$-0.0868053\pi$
$541$	26.0066	+	16.7134i	1.11811	+	0.718565i	0.155064	+	0.987904i	$0.450442\pi$
$542$	22.9536	−	26.4898i	0.985940	−	1.13783i
$543$	−16.4399	−	4.82719i	−0.705504	−	0.207155i
$544$	6.38920	+	44.4379i	0.273935	+	1.90526i
$545$	1.75370	+	2.02388i	0.0751204	+	0.0866936i
$546$	5.98343	+	13.1019i	0.256067	+	0.560708i
$547$	−24.4926	+	7.19169i	−1.04723	+	0.307494i	−0.759698	−	0.650276i	$-0.774653\pi$
$547$	−24.4926	+	7.19169i	−1.04723	+	0.307494i	−0.287532	+	0.957771i	$0.592835\pi$
$548$	8.82700	−	19.3284i	0.377071	−	0.825670i
$549$	0.407064	−	2.83119i	0.0173731	−	0.120832i
$550$	5.40603	−	3.47425i	0.230514	−	0.148142i
$551$	15.4878			0.659802
$552$	−12.9409	+	3.72317i	−0.550799	+	0.158469i
$553$	−15.4507			−0.657032
$554$	−43.4266	+	27.9086i	−1.84502	+	1.18572i
$555$	−3.07545	+	21.3902i	−0.130546	+	0.907965i
$556$	−10.4910	+	22.9721i	−0.444917	+	0.974233i
$557$	7.10371	−	2.08584i	0.300994	−	0.0883798i	−0.127748	−	0.991807i	$-0.540775\pi$
$557$	7.10371	−	2.08584i	0.300994	−	0.0883798i	0.428742	+	0.903427i	$0.358957\pi$
$558$	1.43129	+	3.13409i	0.0605914	+	0.132677i
$559$	8.98255	+	10.3664i	0.379922	+	0.438453i
$560$	−1.22743	−	8.53694i	−0.0518682	−	0.360752i
$561$	−13.8558	−	4.06844i	−0.584994	−	0.171770i
$562$	2.76764	−	3.19403i	0.116746	−	0.134732i
$563$	−27.1951	−	17.4772i	−1.14614	−	0.736576i	−0.177269	−	0.984162i	$-0.556726\pi$
$563$	−27.1951	−	17.4772i	−1.14614	−	0.736576i	−0.968866	+	0.247586i	$0.920363\pi$
$564$	20.6293	+	13.2576i	0.868649	+	0.558247i
$565$	1.02164	−	1.17903i	0.0429805	−	0.0496022i
$566$	−30.2372	−	8.87844i	−1.27096	−	0.373189i
$567$	−2.17636	−	15.1369i	−0.0913986	−	0.635691i
$568$	−1.21244	−	1.39923i	−0.0508730	−	0.0587105i
$569$	5.24883	+	11.4933i	0.220043	+	0.481826i	0.987171	−	0.159668i	$-0.0510423\pi$
$569$	5.24883	+	11.4933i	0.220043	+	0.481826i	−0.767128	+	0.641494i	$0.778315\pi$
$570$	−31.5115	+	9.25262i	−1.31987	+	0.387550i
$571$	1.98264	−	4.34137i	0.0829708	−	0.181681i	−0.863599	−	0.504179i	$-0.831795\pi$
$571$	1.98264	−	4.34137i	0.0829708	−	0.181681i	0.946570	+	0.322498i	$0.104523\pi$
$572$	0.482399	−	3.35516i	0.0201701	−	0.140286i
$573$	24.0855	−	15.4788i	1.00619	−	0.646636i
$574$	−6.53693			−0.272846
$575$	−11.4160	+	13.0303i	−0.476079	+	0.543402i
$576$	−0.288838			−0.0120349
$577$	−28.5933	+	18.3758i	−1.19036	+	0.764995i	−0.977262	−	0.212037i	$-0.931990\pi$
$577$	−28.5933	+	18.3758i	−1.19036	+	0.764995i	−0.213094	+	0.977032i	$0.568354\pi$
$578$	10.4805	−	72.8931i	0.435929	−	3.03196i
$579$	7.26361	−	15.9051i	0.301865	−	0.660993i
$580$	−2.45884	+	0.721980i	−0.102098	+	0.0299786i
$581$	1.42183	+	3.11336i	0.0589872	+	0.129164i
$582$	19.6966	+	22.7311i	0.816452	+	0.942236i
$583$	−0.210930	−	1.46705i	−0.00873583	−	0.0607590i
$584$	−21.2683	−	6.24493i	−0.880088	−	0.258417i
$585$	1.28205	−	1.47957i	0.0530063	−	0.0611725i
$586$	2.42568	+	1.55889i	0.100204	+	0.0643971i
$587$	−0.0900674	−	0.0578828i	−0.00371748	−	0.00238908i	0.538781	−	0.842446i	$-0.318885\pi$
$587$	−0.0900674	−	0.0578828i	−0.00371748	−	0.00238908i	−0.542498	+	0.840057i	$0.682521\pi$
$588$	−6.96564	+	8.03878i	−0.287258	+	0.331514i
$589$	26.9851	+	7.92353i	1.11190	+	0.326483i
$590$	1.45441	+	10.1156i	0.0598770	+	0.416454i
$591$	−3.20789	−	3.70210i	−0.131955	−	0.152284i
$592$	20.0536	+	43.9113i	0.824198	+	1.80474i
$593$	−37.4825	+	11.0058i	−1.53922	+	0.451956i	−0.937858	−	0.347020i	$-0.887194\pi$
$593$	−37.4825	+	11.0058i	−1.53922	+	0.451956i	−0.601363	+	0.798976i	$0.705376\pi$
$594$	−3.39210	+	7.42765i	−0.139179	+	0.304760i
$595$	−1.88617	+	13.1186i	−0.0773256	+	0.537811i
$596$	14.1482	−	9.09247i	0.579531	−	0.372442i
$597$	−28.2162			−1.15481
$598$	3.39922	+	24.5944i	0.139004	+	1.00574i
$599$	24.3793			0.996113			0.498056	−	0.867145i	$-0.334047\pi$
$599$	24.3793			0.996113			0.498056	+	0.867145i	$0.334047\pi$
$600$	8.53246	−	5.48348i	0.348336	−	0.223862i
$601$	−1.51222	+	10.5177i	−0.0616848	+	0.429027i	0.935455	+	0.353446i	$0.114990\pi$
$601$	−1.51222	+	10.5177i	−0.0616848	+	0.429027i	−0.997140	+	0.0755810i	$0.975919\pi$
$602$	5.12842	−	11.2297i	0.209019	−	0.457687i
$603$	2.89446	−	0.849890i	0.117871	−	0.0346102i
$604$	−2.05694	−	4.50408i	−0.0836958	−	0.183268i
$605$	−0.771441	−	0.890290i	−0.0313635	−	0.0361954i
$606$	−0.906440	−	6.30443i	−0.0368216	−	0.256100i
$607$	−15.4896	−	4.54817i	−0.628705	−	0.184604i	−0.0481693	−	0.998839i	$-0.515339\pi$
$607$	−15.4896	−	4.54817i	−0.628705	−	0.184604i	−0.580536	+	0.814235i	$0.697157\pi$
$608$	−31.9048	+	36.8201i	−1.29391	+	1.49325i
$609$	4.37120	+	2.80920i	0.177130	+	0.113834i
$610$	8.83023	+	5.67485i	0.357526	+	0.229768i
$611$	−21.2309	+	24.5017i	−0.858910	+	0.991235i
$612$	4.87724	+	1.43209i	0.197151	+	0.0578886i
$613$	−4.71464	−	32.7911i	−0.190423	−	1.32442i	−0.830892	−	0.556434i	$-0.812169\pi$
$613$	−4.71464	−	32.7911i	−0.190423	−	1.32442i	0.640469	−	0.767984i	$-0.278740\pi$
$614$	0.773793	+	0.893005i	0.0312277	+	0.0360387i
$615$	2.30808	+	5.05398i	0.0930706	+	0.203796i
$616$	2.09893	−	0.616300i	0.0845682	−	0.0248315i
$617$	13.5163	−	29.5965i	0.544145	−	1.19151i	−0.415318	−	0.909676i	$-0.636330\pi$
$617$	13.5163	−	29.5965i	0.544145	−	1.19151i	0.959463	−	0.281835i	$-0.0909432\pi$
$618$	−3.30435	+	22.9823i	−0.132921	+	0.924483i
$619$	13.4492	−	8.64328i	0.540569	−	0.347403i	−0.241692	−	0.970353i	$-0.577702\pi$
$619$	13.4492	−	8.64328i	0.540569	−	0.347403i	0.782262	+	0.622950i	$0.214066\pi$
$620$	−4.65351			−0.186889
$621$	3.25165	−	21.7714i	0.130484	−	0.873657i
$622$	−57.0068			−2.28576
$623$	−20.4533	+	13.1446i	−0.819446	+	0.526626i
$624$	3.89192	−	27.0689i	0.155801	−	1.08362i
$625$	2.53808	−	5.55762i	0.101523	−	0.222305i
$626$	36.9565	−	10.8514i	1.47708	−	0.433709i
$627$	−6.51004	−	14.2550i	−0.259986	−	0.569290i
$628$	11.4048	+	13.1618i	0.455099	+	0.525213i
$629$	−10.5572	−	73.4266i	−0.420941	−	2.92771i
$630$	−1.69063	−	0.496413i	−0.0673563	−	0.0197776i
$631$	1.20327	−	1.38865i	0.0479015	−	0.0552813i	−0.731293	−	0.682063i	$-0.761083\pi$
$631$	1.20327	−	1.38865i	0.0479015	−	0.0552813i	0.779195	+	0.626782i	$0.215628\pi$
$632$	13.1177	+	8.43024i	0.521794	+	0.335337i
$633$	24.9348	+	16.0246i	0.991071	+	0.636923i
$634$	−1.25351	+	1.44663i	−0.0497832	+	0.0574528i
$635$	11.7804	+	3.45903i	0.467490	+	0.137267i
$636$	0.464285	+	3.22918i	0.0184101	+	0.128045i
$637$	−9.20923	−	10.6280i	−0.364883	−	0.421097i
$638$	−1.38020	−	3.02221i	−0.0546426	−	0.119651i
$639$	−0.682777	+	0.200481i	−0.0270102	+	0.00793092i
$640$	−5.30972	+	11.6267i	−0.209885	+	0.459584i
$641$	−1.30958	+	9.10833i	−0.0517253	+	0.359758i	0.947477	+	0.319824i	$0.103624\pi$
$641$	−1.30958	+	9.10833i	−0.0517253	+	0.359758i	−0.999202	+	0.0399337i	$0.987285\pi$
$642$	−31.3581	+	20.1526i	−1.23760	+	0.795360i
$643$	−10.5860			−0.417470			−0.208735	−	0.977972i	$-0.566935\pi$
$643$	−10.5860			−0.417470			−0.208735	+	0.977972i	$0.566935\pi$
$644$	6.94287	−	4.40855i	0.273588	−	0.173721i
$645$	−10.4929			−0.413157
$646$	94.8402	−	60.9501i	3.73144	−	2.39805i
$647$	1.70646	−	11.8687i	0.0670881	−	0.466608i	−0.928389	−	0.371609i	$-0.878806\pi$
$647$	1.70646	−	11.8687i	0.0670881	−	0.466608i	0.995477	−	0.0949987i	$-0.0302847\pi$
$648$	−6.41129	+	14.0388i	−0.251859	+	0.551495i
$649$	−4.67898	+	1.37387i	−0.183666	+	0.0539293i
$650$	−7.76860	−	17.0109i	−0.304710	−	0.667221i
$651$	6.17895	+	7.13089i	0.242172	+	0.279482i
$652$	0.564288	+	3.92471i	0.0220992	+	0.153703i
$653$	3.80026	+	1.11586i	0.148716	+	0.0436669i	0.355243	−	0.934774i	$-0.384398\pi$
$653$	3.80026	+	1.11586i	0.148716	+	0.0436669i	−0.206527	+	0.978441i	$0.566216\pi$
$654$	5.00466	−	5.77568i	0.195698	−	0.225847i
$655$	−1.67176	−	1.07437i	−0.0653210	−	0.0419793i
$656$	10.4411	+	6.71009i	0.407657	+	0.261985i
$657$	−5.57910	+	6.43863i	−0.217662	+	0.251195i
$658$	27.9970	+	8.22065i	1.09144	+	0.320474i
$659$	5.43094	+	37.7730i	0.211559	+	1.47143i	0.767952	+	0.640508i	$0.221276\pi$
$659$	5.43094	+	37.7730i	0.211559	+	1.47143i	−0.556392	+	0.830920i	$0.687815\pi$
$660$	1.69805	+	1.95965i	0.0660963	+	0.0762792i
$661$	10.8793	+	23.8224i	0.423157	+	0.926585i	0.994388	+	0.105795i	$0.0337388\pi$
$661$	10.8793	+	23.8224i	0.423157	+	0.926585i	−0.571231	+	0.820789i	$0.693534\pi$
$662$	26.0677	−	7.65416i	1.01315	−	0.297487i
$663$	−17.4575	+	38.2266i	−0.677993	+	1.48460i
$664$	0.491582	−	3.41903i	0.0190771	−	0.132684i
$665$	−12.0996	+	7.77591i	−0.469201	+	0.301537i
$666$	9.86215			0.382150
$667$	5.82840	+	6.80099i	0.225676	+	0.263335i
$668$	−20.5652			−0.795690
$669$	−26.9583	+	17.3251i	−1.04227	+	0.669826i
$670$	−1.57546	+	10.9576i	−0.0608654	+	0.423328i
$671$	−2.08066	+	4.55601i	−0.0803230	+	0.175883i
$672$	−15.6831	+	4.60499i	−0.604990	+	0.177641i
$673$	−7.02508	−	15.3828i	−0.270797	−	0.592962i	0.724560	−	0.689211i	$-0.242043\pi$
$673$	−7.02508	−	15.3828i	−0.270797	−	0.592962i	−0.995357	+	0.0962489i	$0.969316\pi$
$674$	−13.4970	−	15.5764i	−0.519887	−	0.599981i
$675$	2.35962	+	16.4116i	0.0908220	+	0.631681i
$676$	5.06418	+	1.48698i	0.194776	+	0.0571915i
$677$	−33.2478	+	38.3700i	−1.27782	+	1.47468i	−0.473114	+	0.881001i	$0.656870\pi$
$677$	−33.2478	+	38.3700i	−1.27782	+	1.47468i	−0.804702	+	0.593678i	$0.797675\pi$
$678$	−3.74535	−	2.40699i	−0.143839	−	0.0924398i
$679$	11.0812	+	7.12143i	0.425256	+	0.273295i
$680$	8.75916	−	10.1086i	0.335899	−	0.387648i
$681$	36.8497	+	10.8200i	1.41208	+	0.414625i
$682$	−0.858622	−	5.97185i	−0.0328783	−	0.228674i
$683$	6.84431	+	7.89875i	0.261890	+	0.302237i	0.871432	−	0.490517i	$-0.163192\pi$
$683$	6.84431	+	7.89875i	0.261890	+	0.302237i	−0.609542	+	0.792754i	$0.708646\pi$
$684$	2.29153	+	5.01775i	0.0876187	+	0.191858i
$685$	−20.6196	+	6.05445i	−0.787833	+	0.231329i
$686$	−12.8741	+	28.1902i	−0.491534	+	1.07631i
$687$	1.85197	−	12.8807i	0.0706569	−	0.491429i
$688$	−19.7185	+	12.6723i	−0.751760	+	0.483127i
$689$	−4.31318			−0.164319
$690$	−15.9215	−	10.3554i	−0.606121	−	0.394222i
$691$	19.0341			0.724092			0.362046	−	0.932160i	$-0.382078\pi$
$691$	19.0341			0.724092			0.362046	+	0.932160i	$0.382078\pi$
$692$	−11.1200	+	7.14641i	−0.422720	+	0.271666i
$693$	0.119655	−	0.832218i	0.00454531	−	0.0316134i
$694$	0.118315	−	0.259074i	0.00449119	−	0.00983433i
$695$	24.5066	−	7.19578i	0.929588	−	0.272952i
$696$	−2.17840	−	4.77003i	−0.0825720	−	0.180808i
$697$	−12.4898	−	14.4140i	−0.473084	−	0.545968i
$698$	−1.58814	−	11.0458i	−0.0601121	−	0.418089i
$699$	−10.2627	−	3.01339i	−0.388170	−	0.113977i
$700$	−4.05660	+	4.68157i	−0.153325	+	0.176947i
$701$	−31.6648	−	20.3497i	−1.19596	−	0.768598i	−0.217709	−	0.976014i	$-0.569858\pi$
$701$	−31.6648	−	20.3497i	−1.19596	−	0.768598i	−0.978253	+	0.207416i	$0.933495\pi$
$702$	19.9904	+	12.8471i	0.754490	+	0.484881i
$703$	52.7177	−	60.8395i	1.98829	−	2.29460i
$704$	0.485292	+	0.142495i	0.0182901	+	0.00537047i
$705$	−3.52950	−	24.5482i	−0.132929	−	0.924540i
$706$	19.9181	+	22.9867i	0.749626	+	0.865114i
$707$	−1.15874	−	2.53729i	−0.0435789	−	0.0954244i
$708$	10.2991	−	3.02408i	0.387063	−	0.113652i
$709$	11.5330	−	25.2537i	0.433131	−	0.948424i	−0.559677	−	0.828711i	$-0.689075\pi$
$709$	11.5330	−	25.2537i	0.433131	−	0.948424i	0.992808	−	0.119714i	$-0.0381977\pi$
$710$	0.371638	−	2.58480i	0.0139473	−	0.0970057i
$711$	5.04177	−	3.24015i	0.189081	−	0.121515i
$712$	24.5369			0.919559
$713$	6.67570	+	14.8315i	0.250007	+	0.555443i
$714$	37.8225			1.41547
$715$	−2.88396	+	1.85341i	−0.107854	+	0.0693136i
$716$	−0.859496	+	5.97793i	−0.0321209	+	0.223406i
$717$	15.7436	−	34.4736i	0.587954	−	1.28744i
$718$	−12.1116	+	3.55628i	−0.452000	+	0.132719i
$719$	6.23559	+	13.6540i	0.232548	+	0.509210i	0.989548	−	0.144206i	$-0.0460628\pi$
$719$	6.23559	+	13.6540i	0.232548	+	0.509210i	−0.756999	+	0.653415i	$0.773335\pi$
$720$	2.19079	+	2.52831i	0.0816460	+	0.0942245i
$721$	1.44711	+	10.0649i	0.0538932	+	0.374835i
$722$	84.9550	+	24.9450i	3.16170	+	0.928358i
$723$	−17.2372	+	19.8928i	−0.641059	+	0.739822i
$724$	−8.88448	−	5.70971i	−0.330189	−	0.212200i
$725$	−5.67536	−	3.64733i	−0.210778	−	0.135459i
$726$	−2.20151	+	2.54068i	−0.0817057	+	0.0942934i
$727$	−37.5671	−	11.0307i	−1.39329	−	0.409106i	−0.502913	−	0.864337i	$-0.667738\pi$
$727$	−37.5671	−	11.0307i	−1.39329	−	0.409106i	−0.890373	+	0.455231i	$0.849557\pi$
$728$	−0.905972	−	6.30117i	−0.0335775	−	0.233537i
$729$	−13.1560	−	15.1829i	−0.487260	−	0.562328i
$730$	−12.9876	−	28.4390i	−0.480694	−	1.05257i
$731$	34.5601	−	10.1478i	1.27825	−	0.375328i
$732$	4.57982	−	10.0284i	0.169275	−	0.370660i
$733$	6.00202	−	41.7450i	0.221690	−	1.54189i	−0.509956	−	0.860201i	$-0.670338\pi$
$733$	6.00202	−	41.7450i	0.221690	−	1.54189i	0.731646	−	0.681685i	$-0.238753\pi$
$734$	−5.58089	+	3.58662i	−0.205995	+	0.132385i
$735$	10.7577			0.396803
$736$	−28.1749	−	0.153800i	−1.03854	−	0.00566913i
$737$	−5.28241			−0.194580
$738$	2.13308	−	1.37085i	0.0785199	−	0.0504616i
$739$	4.65423	−	32.3709i	0.171208	−	1.19078i	−0.705127	−	0.709081i	$-0.749110\pi$
$739$	4.65423	−	32.3709i	0.171208	−	1.19078i	0.876336	−	0.481700i	$-0.159981\pi$
$740$	−5.53336	+	12.1164i	−0.203410	+	0.445406i
$741$	−43.7575	+	12.8484i	−1.60747	+	0.471996i
$742$	1.61261	+	3.53112i	0.0592008	+	0.129632i
$743$	−3.00607	−	3.46919i	−0.110282	−	0.127272i	0.697925	−	0.716171i	$-0.254107\pi$
$743$	−3.00607	−	3.46919i	−0.110282	−	0.127272i	−0.808207	+	0.588899i	$0.799562\pi$
$744$	−1.35518	−	9.42551i	−0.0496834	−	0.345556i
$745$	−16.3200	−	4.79200i	−0.597920	−	0.175565i
$746$	29.0315	−	33.5041i	1.06292	−	1.22667i
$747$	−1.11686	−	0.717761i	−0.0408637	−	0.0262615i
$748$	−7.48799	−	4.81224i	−0.273788	−	0.175953i
$749$	−10.6902	+	12.3372i	−0.390612	+	0.450790i
$750$	32.7254	+	9.60904i	1.19496	+	0.350872i
$751$	−6.13003	−	42.6353i	−0.223688	−	1.55578i	−0.723915	−	0.689889i	$-0.757659\pi$
$751$	−6.13003	−	42.6353i	−0.223688	−	1.55578i	0.500227	−	0.865894i	$-0.333250\pi$
$752$	−36.2797	−	41.8690i	−1.32299	−	1.52681i
$753$	4.94814	+	10.8349i	0.180320	+	0.394847i
$754$	−9.27706	+	2.72399i	−0.337851	+	0.0992019i
$755$	−2.08031	+	4.55525i	−0.0757103	+	0.165783i
$756$	1.12021	−	7.79120i	0.0407415	−	0.283363i
$757$	−18.4039	+	11.8275i	−0.668900	+	0.429876i	−0.830529	−	0.556975i	$-0.811962\pi$
$757$	−18.4039	+	11.8275i	−0.668900	+	0.429876i	0.161629	+	0.986852i	$0.448325\pi$
$758$	−26.2390			−0.953043
$759$	3.80978	−	8.22316i	0.138286	−	0.298482i
$760$	14.5152			0.526523
$761$	6.61217	−	4.24938i	0.239691	−	0.154040i	−0.415281	−	0.909693i	$-0.636317\pi$
$761$	6.61217	−	4.24938i	0.239691	−	0.154040i	0.654972	+	0.755653i	$0.272680\pi$
$762$	4.98638	−	34.6810i	0.180638	−	1.25636i
$763$	1.39034	−	3.04443i	0.0503339	−	0.110216i
$764$	16.9324	−	4.97180i	0.612592	−	0.179873i
$765$	−2.13560	−	4.67632i	−0.0772129	−	0.169073i
$766$	−9.11385	−	10.5179i	−0.329297	−	0.380029i
$767$	2.01962	+	14.0467i	0.0729241	+	0.507199i
$768$	36.8326	+	10.8150i	1.32908	+	0.390254i
$769$	12.6007	−	14.5420i	0.454393	−	0.524398i	−0.481612	−	0.876385i	$-0.659948\pi$
$769$	12.6007	−	14.5420i	0.454393	−	0.524398i	0.936005	+	0.351987i	$0.114494\pi$
$770$	2.59561	+	1.66810i	0.0935394	+	0.0601141i
$771$	2.51046	+	1.61337i	0.0904119	+	0.0581042i
$772$	7.05776	−	8.14509i	0.254015	−	0.293148i
$773$	11.5613	+	3.39471i	0.415832	+	0.122099i	0.482955	−	0.875645i	$-0.339564\pi$
$773$	11.5613	+	3.39471i	0.415832	+	0.122099i	−0.0671224	+	0.997745i	$0.521382\pi$
$774$	0.681488	+	4.73985i	0.0244956	+	0.170370i
$775$	−8.02247	−	9.25842i	−0.288175	−	0.332572i
$776$	−5.52233	−	12.0922i	−0.198240	−	0.434085i
$777$	25.9139	−	7.60902i	0.929658	−	0.272972i
$778$	−8.11538	+	17.7702i	−0.290951	+	0.637093i
$779$	2.94555	−	20.4868i	0.105535	−	0.734015i
$780$	6.34799	−	4.07961i	0.227295	−	0.146073i
$781$	1.24607			0.0445880
$782$	62.4549	+	18.7093i	2.23338	+	0.669044i
$783$	8.57237			0.306351
$784$	20.2161	−	12.9921i	0.722003	−	0.464003i
$785$	2.50665	−	17.4341i	0.0894662	−	0.622251i
$786$	−2.35585	+	5.15859i	−0.0840303	+	0.184001i
$787$	−6.71433	+	1.97151i	−0.239340	+	0.0702766i	−0.399203	−	0.916863i	$-0.630713\pi$
$787$	−6.71433	+	1.97151i	−0.239340	+	0.0702766i	0.159863	+	0.987139i	$0.448895\pi$
$788$	−1.25430	−	2.74653i	−0.0446825	−	0.0978410i
$789$	5.04666	+	5.82416i	0.179666	+	0.207346i
$790$	3.12996	+	21.7693i	0.111359	+	0.774518i
$791$	−1.87078	−	0.549309i	−0.0665171	−	0.0195312i
$792$	−0.555663	+	0.641269i	−0.0197446	+	0.0227865i
$793$	12.2618	+	7.88020i	0.435430	+	0.279834i
$794$	−53.3185	−	34.2657i	−1.89220	−	1.21605i
$795$	2.16068	−	2.49356i	0.0766314	−	0.0884373i
$796$	−16.6874	−	4.89985i	−0.591468	−	0.173671i
$797$	−0.822263	−	5.71897i	−0.0291261	−	0.202576i	0.970062	−	0.242856i	$-0.0780842\pi$
$797$	−0.822263	−	5.71897i	−0.0291261	−	0.202576i	−0.999188	+	0.0402796i	$0.987175\pi$
$798$	26.8788	+	31.0198i	0.951499	+	1.09809i
$799$	35.3658	+	77.4403i	1.25115	+	2.73964i
$800$	20.3623	−	5.97890i	0.719915	−	0.211386i
$801$	3.91766	−	8.57848i	0.138424	−	0.303106i
$802$	−0.549961	+	3.82506i	−0.0194198	+	0.135068i
$803$	12.5501	−	8.06549i	0.442885	−	0.284625i
$804$	11.6273			0.410063
$805$	−7.96788	−	2.38690i	−0.280831	−	0.0841273i
$806$	−17.5574			−0.618434
$807$	26.9226	−	17.3021i	0.947720	−	0.609063i
$808$	−0.400623	+	2.78639i	−0.0140939	+	0.0980250i
$809$	4.97484	−	10.8934i	0.174906	−	0.382991i	−0.801794	−	0.597601i	$-0.796121\pi$
$809$	4.97484	−	10.8934i	0.174906	−	0.382991i	0.976700	+	0.214610i	$0.0688480\pi$
$810$	−20.8863	+	6.13278i	−0.733871	+	0.215484i
$811$	21.4509	+	46.9709i	0.753243	+	1.64937i	0.760448	+	0.649398i	$0.224979\pi$
$811$	21.4509	+	46.9709i	0.753243	+	1.64937i	−0.00720528	+	0.999974i	$0.502294\pi$
$812$	2.09735	+	2.42047i	0.0736024	+	0.0849417i
$813$	5.29881	+	36.8540i	0.185837	+	1.29253i
$814$	−16.5699	−	4.86536i	−0.580774	−	0.170531i
$815$	2.62607	−	3.03065i	0.0919872	−	0.106159i
$816$	−60.4119	−	38.8244i	−2.11484	−	1.35912i
$817$	32.8830	+	21.1326i	1.15043	+	0.739336i
$818$	−8.43877	+	9.73886i	−0.295055	+	0.340511i
$819$	−2.34764	−	0.689329i	−0.0820331	−	0.0240871i
$820$	0.487378	+	3.38979i	0.0170200	+	0.118377i
$821$	−9.87680	−	11.3984i	−0.344703	−	0.397808i	0.556754	−	0.830677i	$-0.312047\pi$
$821$	−9.87680	−	11.3984i	−0.344703	−	0.397808i	−0.901457	+	0.432869i	$0.857501\pi$
$822$	25.4764	+	55.7855i	0.888591	+	1.94574i
$823$	−21.9286	+	6.43882i	−0.764384	+	0.224443i	−0.640609	−	0.767867i	$-0.721318\pi$
$823$	−21.9286	+	6.43882i	−0.764384	+	0.224443i	−0.123775	+	0.992310i	$0.539500\pi$
$824$	4.26300	−	9.33467i	0.148509	−	0.325189i
$825$	−0.971469	+	6.75672i	−0.0338222	+	0.235239i
$826$	10.7447	−	6.90522i	0.373857	−	0.240263i
$827$	−34.3535			−1.19459			−0.597293	−	0.802023i	$-0.703757\pi$
$827$	−34.3535			−1.19459			−0.597293	+	0.802023i	$0.703757\pi$
$828$	−1.34104	+	2.89454i	−0.0466043	+	0.100592i
$829$	49.6108			1.72305			0.861526	−	0.507713i	$-0.169509\pi$
$829$	49.6108			1.72305			0.861526	+	0.507713i	$0.169509\pi$
$830$	4.09855	−	2.63398i	0.142263	−	0.0914267i
$831$	7.80381	−	54.2767i	0.270711	−	1.88284i
$832$	0.611438	−	1.33886i	0.0211978	−	0.0464167i
$833$	−35.4322	+	10.4038i	−1.22765	+	0.360472i
$834$	−30.2790	−	66.3017i	−1.04848	−	2.29584i
$835$	13.6203	+	15.7187i	0.471351	+	0.543968i
$836$	−1.37467	−	9.56106i	−0.0475441	−	0.330676i
$837$	14.9360	+	4.38561i	0.516264	+	0.151589i
$838$	−3.15218	+	3.63781i	−0.108890	+	0.125666i
$839$	32.8700	+	21.1243i	1.13480	+	0.729291i	0.966556	−	0.256455i	$-0.0825546\pi$
$839$	32.8700	+	21.1243i	1.13480	+	0.729291i	0.168242	+	0.985746i	$0.446191\pi$
$840$	4.09671	+	2.63280i	0.141350	+	0.0908402i
$841$	16.7068	−	19.2807i	0.576097	−	0.664852i
$842$	−34.9000	−	10.2476i	−1.20273	−	0.353155i
$843$	0.638909	+	4.44371i	0.0220052	+	0.153049i
$844$	11.9640	+	13.8072i	0.411818	+	0.475263i
$845$	−2.21746	−	4.85556i	−0.0762830	−	0.167036i
$846$	−10.8597	+	3.18870i	−0.373364	+	0.109630i
$847$	−0.611602	+	1.33922i	−0.0210149	+	0.0460162i
$848$	1.04892	−	7.29541i	0.0360201	−	0.250525i
$849$	28.1614	−	18.0982i	0.966496	−	0.621129i
$850$	−49.1069			−1.68435
$851$	46.5546	+	0.254130i	1.59587	+	0.00871146i
$852$	−2.74278			−0.0939659
$853$	25.1451	−	16.1598i	0.860953	−	0.553301i	−0.0340202	−	0.999421i	$-0.510831\pi$
$853$	25.1451	−	16.1598i	0.860953	−	0.553301i	0.894973	+	0.446120i	$0.147195\pi$
$854$	1.86693	−	12.9848i	0.0638851	−	0.444331i
$855$	2.31756	−	5.07476i	0.0792590	−	0.173553i
$856$	15.8074	−	4.64148i	0.540287	−	0.158642i
$857$	23.9497	+	52.4426i	0.818108	+	1.79141i	0.567630	+	0.823284i	$0.307860\pi$
$857$	23.9497	+	52.4426i	0.818108	+	1.79141i	0.250478	+	0.968122i	$0.419412\pi$
$858$	6.40663	+	7.39365i	0.218719	+	0.252415i
$859$	−0.240068	−	1.66971i	−0.00819103	−	0.0569699i	0.985316	−	0.170741i	$-0.0546161\pi$
$859$	−0.240068	−	1.66971i	−0.00819103	−	0.0569699i	−0.993507	+	0.113771i	$0.963707\pi$
$860$	−6.20561	−	1.82213i	−0.211610	−	0.0621342i
$861$	4.54726	−	5.24782i	0.154970	−	0.178845i
$862$	3.40232	+	2.18654i	0.115883	+	0.0744737i
$863$	−39.5133	−	25.3937i	−1.34505	−	0.864410i	−0.347730	−	0.937595i	$-0.613047\pi$
$863$	−39.5133	−	25.3937i	−1.34505	−	0.864410i	−0.997318	+	0.0731848i	$0.976684\pi$
$864$	−17.6591	+	20.3796i	−0.600773	+	0.693329i
$865$	12.8271	+	3.76637i	0.436133	+	0.128060i
$866$	−2.59877	−	18.0748i	−0.0883097	−	0.614207i
$867$	51.2278	+	59.1201i	1.73979	+	2.00782i
$868$	2.41599	+	5.29029i	0.0820042	+	0.179564i
$869$	−10.0694	+	2.95665i	−0.341581	+	0.100297i
$870$	3.07252	−	6.72788i	0.104168	−	0.228097i
$871$	−2.18772	+	15.2159i	−0.0741280	+	0.515571i
$872$	−2.84151	+	1.82613i	−0.0962257	+	0.0618405i
$873$	−5.10934			−0.172925
$874$	29.0397	+	64.5177i	0.982282	+	2.18234i
$875$	14.9368			0.504956
$876$	−27.6246	+	17.7532i	−0.933348	+	0.599826i
$877$	−6.96782	+	48.4622i	−0.235286	+	1.63645i	0.439359	+	0.898311i	$0.355205\pi$
$877$	−6.96782	+	48.4622i	−0.235286	+	1.63645i	−0.674646	+	0.738142i	$0.735704\pi$
$878$	−3.96303	+	8.67782i	−0.133746	+	0.292862i
$879$	−2.93883	+	0.862919i	−0.0991244	+	0.0291055i
$880$	−2.43355	−	5.32874i	−0.0820350	−	0.179632i
$881$	−9.37149	−	10.8153i	−0.315734	−	0.364376i	0.575594	−	0.817735i	$-0.304771\pi$
$881$	−9.37149	−	10.8153i	−0.315734	−	0.364376i	−0.891328	+	0.453360i	$0.850225\pi$
$882$	−0.698685	−	4.85946i	−0.0235260	−	0.163627i
$883$	−47.2786	−	13.8823i	−1.59105	−	0.467175i	−0.638015	−	0.770024i	$-0.720244\pi$
$883$	−47.2786	−	13.8823i	−1.59105	−	0.467175i	−0.953039	+	0.302849i	$0.902062\pi$
$884$	−16.9628	+	19.5761i	−0.570519	+	0.658414i
$885$	−9.13250	−	5.86910i	−0.306986	−	0.197288i
$886$	4.92477	+	3.16495i	0.165451	+	0.106329i
$887$	−10.6694	+	12.3131i	−0.358243	+	0.413435i	−0.906050	−	0.423170i	$-0.860917\pi$
$887$	−10.6694	+	12.3131i	−0.358243	+	0.413435i	0.547807	+	0.836605i	$0.315463\pi$
$888$	−26.1526	−	7.67911i	−0.877625	−	0.257694i
$889$	−2.18374	−	15.1882i	−0.0732402	−	0.509397i
$890$	22.6634	+	26.1550i	0.759680	+	0.876718i
$891$	−4.31496	−	9.44844i	−0.144557	−	0.316535i
$892$	−18.9520	+	5.56482i	−0.634561	+	0.186324i
$893$	−38.3791	+	84.0384i	−1.28431	+	2.81224i
$894$	−6.90793	+	48.0457i	−0.231036	+	1.60689i
$895$	5.13839	−	3.30224i	0.171757	−	0.110382i
$896$	15.9743			0.533665
$897$	−22.1089	−	14.3796i	−0.738194	−	0.480122i
$898$	31.9991			1.06782
$899$	−5.32836	+	3.42433i	−0.177711	+	0.114208i
$900$	0.341956	−	2.37836i	0.0113985	−	0.0792786i
$901$	−4.70502	+	10.3026i	−0.156747	+	0.343228i
$902$	−4.26019	+	1.25090i	−0.141849	+	0.0416506i
$903$	5.44766	+	11.9287i	0.181287	+	0.396963i
$904$	1.28858	+	1.48710i	0.0428575	+	0.0494602i
$905$	1.52006	+	10.5723i	0.0505286	+	0.351434i
$906$	13.7122	+	4.02626i	0.455557	+	0.133764i
$907$	6.45720	−	7.45200i	0.214408	−	0.247440i	−0.638350	−	0.769746i	$-0.720383\pi$
$907$	6.45720	−	7.45200i	0.214408	−	0.247440i	0.852758	+	0.522306i	$0.174928\pi$
$908$	19.9144	+	12.7982i	0.660882	+	0.424723i
$909$	0.910201	+	0.584951i	0.0301895	+	0.0194016i
$910$	5.87991	−	6.78578i	0.194917	−	0.224946i
$911$	−35.6460	−	10.4666i	−1.18100	−	0.346774i	−0.368443	−	0.929651i	$-0.620109\pi$
$911$	−35.6460	−	10.4666i	−1.18100	−	0.346774i	−0.812561	+	0.582877i	$0.801927\pi$
$912$	−11.0906	−	77.1371i	−0.367248	−	2.55426i
$913$	1.52239	+	1.75693i	0.0503838	+	0.0581460i
$914$	16.8696	+	36.9394i	0.557998	+	1.22185i
$915$	−10.6983	+	3.14130i	−0.353674	+	0.103848i
$916$	3.33206	−	7.29619i	0.110094	−	0.241073i
$917$	−0.353452	+	2.45831i	−0.0116720	+	0.0811806i
$918$	52.4933	−	33.7354i	1.73254	−	1.11343i
$919$	24.7268			0.815662			0.407831	−	0.913057i	$-0.366285\pi$
$919$	24.7268			0.815662			0.407831	+	0.913057i	$0.366285\pi$
$920$	5.46241	+	6.37393i	0.180090	+	0.210142i
$921$	−1.25517			−0.0413593
$922$	−48.0306	+	30.8674i	−1.58180	+	1.01656i
$923$	0.516063	−	3.58930i	0.0169864	−	0.118143i
$924$	1.34622	−	2.94781i	0.0442873	−	0.0969758i
$925$	−33.6455	+	9.87920i	−1.10626	+	0.324826i
$926$	−21.9057	−	47.9668i	−0.719865	−	1.57629i
$927$	−2.58290	−	2.98082i	−0.0848335	−	0.0979030i
$928$	−1.56150	−	10.8605i	−0.0512588	−	0.356513i
$929$	−47.7963	−	14.0343i	−1.56815	−	0.460449i	−0.621686	−	0.783267i	$-0.713552\pi$
$929$	−47.7963	−	14.0343i	−1.56815	−	0.460449i	−0.946461	+	0.322817i	$0.895370\pi$
$930$	8.79537	−	10.1504i	0.288412	−	0.332845i
$931$	−33.7128	−	21.6659i	−1.10489	−	0.710070i
$932$	−5.54617	−	3.56431i	−0.181671	−	0.116753i
$933$	39.6554	−	45.7648i	1.29826	−	1.49827i
$934$	−72.0773	−	21.1638i	−2.35844	−	0.692501i
$935$	1.28114	+	8.91049i	0.0418976	+	0.291404i
$936$	1.61704	+	1.86616i	0.0528546	+	0.0609974i
$937$	−1.20801	−	2.64517i	−0.0394640	−	0.0864140i	0.888873	−	0.458153i	$-0.151489\pi$
$937$	−1.20801	−	2.64517i	−0.0394640	−	0.0864140i	−0.928337	+	0.371739i	$0.878762\pi$
$938$	13.2749	−	3.89788i	0.433442	−	0.127270i
$939$	−16.9965	+	37.2170i	−0.554658	+	1.21453i
$940$	2.17551	−	15.1310i	0.0709573	−	0.493519i
$941$	−23.2360	+	14.9329i	−0.757472	+	0.486798i	−0.861488	−	0.507778i	$-0.830467\pi$
$941$	−23.2360	+	14.9329i	−0.757472	+	0.486798i	0.104016	+	0.994576i	$0.466831\pi$
$942$	−50.2645			−1.63771
$943$	10.1046	−	6.41618i	0.329052	−	0.208939i
$944$	−24.2502			−0.789276
$945$	−6.69701	+	4.30391i	−0.217854	+	0.140006i
$946$	1.19334	−	8.29987i	0.0387988	−	0.269852i
$947$	3.13507	−	6.86484i	0.101876	−	0.223077i	−0.851830	−	0.523819i	$-0.824507\pi$
$947$	3.13507	−	6.86484i	0.101876	−	0.223077i	0.953706	+	0.300741i	$0.0972341\pi$
$948$	22.1641	−	6.50798i	0.719858	−	0.211369i
$949$	−18.0349	−	39.4909i	−0.585437	−	1.28193i
$950$	−34.8982	−	40.2746i	−1.13225	−	1.30668i
$951$	−0.289371	−	2.01262i	−0.00938351	−	0.0652637i
$952$	−16.0394	−	4.70960i	−0.519840	−	0.152639i
$953$	9.87351	−	11.3946i	0.319834	−	0.369108i	−0.572952	−	0.819589i	$-0.694202\pi$
$953$	9.87351	−	11.3946i	0.319834	−	0.369108i	0.892786	+	0.450481i	$0.148747\pi$
$954$	−1.26672	−	0.814072i	−0.0410116	−	0.0263566i
$955$	−15.0145	−	9.64921i	−0.485856	−	0.312241i
$956$	15.2974	−	17.6541i	0.494753	−	0.570976i
$957$	3.38632	+	0.994314i	0.109464	+	0.0321416i
$958$	−5.56382	−	38.6972i	−0.179759	−	1.25025i
$959$	17.5881	+	20.2978i	0.567950	+	0.655449i
$960$	0.467732	+	1.02419i	0.0150960	+	0.0330556i
$961$	18.7086	−	5.49333i	0.603502	−	0.177204i
$962$	−20.8771	+	45.7144i	−0.673103	+	1.47389i
$963$	0.901145	−	6.26760i	0.0290390	−	0.201971i
$964$	−13.6488	+	8.77152i	−0.439597	+	0.282512i
$965$	−10.9000			−0.350882
$966$	−3.50630	+	23.4764i	−0.112813	+	0.755342i
$967$	−49.5086			−1.59209			−0.796044	−	0.605239i	$-0.793078\pi$
$967$	−49.5086			−1.59209			−0.796044	+	0.605239i	$0.793078\pi$
$968$	1.24996	−	0.803300i	0.0401752	−	0.0258190i
$969$	−17.0429	+	118.536i	−0.547496	+	3.80792i
$970$	7.78896	−	17.0554i	0.250089	−	0.547617i
$971$	40.6643	−	11.9401i	1.30498	−	0.383176i	0.445929	−	0.895068i	$-0.352873\pi$
$971$	40.6643	−	11.9401i	1.30498	−	0.383176i	0.859050	+	0.511892i	$0.171055\pi$
$972$	2.83489	+	6.20754i	0.0909292	+	0.199107i
$973$	−20.9037	−	24.1242i	−0.670142	−	0.773385i
$974$	5.60507	+	38.9841i	0.179598	+	1.24913i
$975$	19.0603	+	5.59661i	0.610418	+	0.179235i
$976$	−16.3107	+	18.8236i	−0.522093	+	0.602528i
$977$	−16.4118	−	10.5472i	−0.525061	−	0.337436i	0.251110	−	0.967959i	$-0.419204\pi$
$977$	−16.4118	−	10.5472i	−0.525061	−	0.337436i	−0.776171	+	0.630522i	$0.782841\pi$
$978$	−9.62725	−	6.18706i	−0.307846	−	0.197840i
$979$	−10.8143	+	12.4804i	−0.345628	+	0.398875i
$980$	6.36221	+	1.86811i	0.203233	+	0.0596747i
$981$	0.184755	+	1.28500i	0.00589879	+	0.0410270i
$982$	−1.38811	−	1.60196i	−0.0442964	−	0.0511207i
$983$	−21.0802	−	46.1593i	−0.672355	−	1.47225i	−0.870545	−	0.492089i	$-0.836233\pi$
$983$	−21.0802	−	46.1593i	−0.672355	−	1.47225i	0.198190	−	0.980164i	$-0.436494\pi$
$984$	−6.72395	+	1.97433i	−0.214352	+	0.0629394i
$985$	−1.26855	+	2.77773i	−0.0404193	+	0.0885060i
$986$	−3.61327	+	25.1309i	−0.115070	+	0.800330i
$987$	−26.0749	+	16.7573i	−0.829974	+	0.533392i
$988$	−28.1098			−0.894293
$989$	3.09485	+	22.3922i	0.0984105	+	0.712031i
$990$	−1.19679			−0.0380366
$991$	−16.1904	+	10.4050i	−0.514306	+	0.330525i	−0.771916	−	0.635725i	$-0.780701\pi$
$991$	−16.1904	+	10.4050i	−0.514306	+	0.330525i	0.257610	+	0.966249i	$0.417065\pi$
$992$	2.83553	−	19.7216i	0.0900283	−	0.626160i
$993$	−11.9886	+	26.2514i	−0.380448	+	0.833064i
$994$	−3.13144	+	0.919474i	−0.0993233	+	0.0291640i
$995$	7.30692	+	15.9999i	0.231645	+	0.507232i
$996$	−3.35099	−	3.86725i	−0.106180	−	0.122538i
$997$	0.955335	+	6.64450i	0.0302558	+	0.210434i	0.999341	−	0.0362918i	$-0.0115546\pi$
$997$	0.955335	+	6.64450i	0.0302558	+	0.210434i	−0.969085	+	0.246725i	$0.920645\pi$
$998$	32.1912	+	9.45219i	1.01899	+	0.299204i
$999$	29.1788	−	33.6742i	0.923178	−	1.06540i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	253.2.i.b.12.3	✓	120
23.2	even	11	inner	253.2.i.b.232.3	yes	120
23.5	odd	22		5819.2.a.t.1.12		60
23.18	even	11		5819.2.a.u.1.12		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.2.i.b.12.3	✓	120	1.1	even	1	trivial
253.2.i.b.232.3	yes	120	23.2	even	11	inner
5819.2.a.t.1.12		60	23.5	odd	22
5819.2.a.u.1.12		60	23.18	even	11

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:	\( N \)	\(=\)	\( 253 = 11 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	253.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.49658 + 0.961792i) q^{2} +(0.268936 - 1.87049i) q^{3} +(0.483871 - 1.05953i) q^{4} +(-1.13030 + 0.331887i) q^{5} +(1.39654 + 3.05800i) q^{6} +(0.964130 + 1.11267i) q^{7} +(-0.211455 - 1.47070i) q^{8} +(-0.547943 - 0.160891i) q^{9} +(1.37238 - 1.58381i) q^{10} +(0.841254 + 0.540641i) q^{11} +(-1.85171 - 1.19002i) q^{12} +(1.90572 - 2.19931i) q^{13} +(-2.51305 - 0.737898i) q^{14} +(0.316813 + 2.20348i) q^{15} +(3.25652 + 3.75823i) q^{16} +(-3.17449 - 6.95115i) q^{17} +(0.974783 - 0.286222i) q^{18} +(3.44496 - 7.54341i) q^{19} +(-0.195277 + 1.35818i) q^{20} +(2.34052 - 1.50416i) q^{21} -1.77899 q^{22} +(4.60887 - 1.32600i) q^{23} -2.80781 q^{24} +(-3.03883 + 1.95294i) q^{25} +(-0.736769 + 5.12434i) q^{26} +(1.90676 - 4.17522i) q^{27} +(1.64542 - 0.483138i) q^{28} +(0.775835 + 1.69884i) q^{29} +(-2.59343 - 2.99298i) q^{30} +(0.482647 + 3.35689i) q^{31} +(-5.63698 - 1.65517i) q^{32} +(1.23751 - 1.42816i) q^{33} +(11.4364 + 7.34975i) q^{34} +(-1.45904 - 0.937668i) q^{35} +(-0.435602 + 0.502711i) q^{36} +(9.31424 + 2.73491i) q^{37} +(2.09954 + 14.6026i) q^{38} +(-3.60129 - 4.15610i) q^{39} +(0.727117 + 1.59217i) q^{40} +(2.39473 - 0.703156i) q^{41} +(-2.05608 + 4.50220i) q^{42} +(-0.670798 + 4.66551i) q^{43} +(0.979883 - 0.629732i) q^{44} +0.672740 q^{45} +(-5.62220 + 6.41725i) q^{46} -11.1406 q^{47} +(7.90554 - 5.08058i) q^{48} +(0.687726 - 4.78324i) q^{49} +(2.66952 - 5.84544i) q^{50} +(-13.8558 + 4.06844i) q^{51} +(-1.40812 - 3.08334i) q^{52} +(-0.970593 - 1.12012i) q^{53} +(1.16208 + 8.08244i) q^{54} +(-1.13030 - 0.331887i) q^{55} +(1.43253 - 1.65323i) q^{56} +(-13.1834 - 8.47248i) q^{57} +(-2.79503 - 1.79626i) q^{58} +(-3.19344 + 3.68543i) q^{59} +(2.48795 + 0.730529i) q^{60} +(0.712803 + 4.95765i) q^{61} +(-3.95094 - 4.55963i) q^{62} +(-0.349271 - 0.764797i) q^{63} +(0.485292 - 0.142495i) q^{64} +(-1.42411 + 3.11838i) q^{65} +(-0.478434 + 3.32758i) q^{66} +(-4.44384 + 2.85588i) q^{67} -8.90099 q^{68} +(-1.24079 - 8.97748i) q^{69} +3.08541 q^{70} +(1.04826 - 0.673678i) q^{71} +(-0.120757 + 0.839884i) q^{72} +(6.19732 - 13.5702i) q^{73} +(-16.5699 + 4.86536i) q^{74} +(2.83570 + 6.20933i) q^{75} +(-6.32555 - 7.30007i) q^{76} +(0.209526 + 1.45728i) q^{77} +(9.38691 + 2.75625i) q^{78} +(-6.87244 + 7.93122i) q^{79} +(-4.92817 - 3.16714i) q^{80} +(-8.73818 - 5.61569i) q^{81} +(-2.90761 + 3.35556i) q^{82} +(2.23059 + 0.654959i) q^{83} +(-0.461194 - 3.20767i) q^{84} +(5.89514 + 6.80335i) q^{85} +(-3.48334 - 7.62746i) q^{86} +(3.38632 - 0.994314i) q^{87} +(0.617235 - 1.35156i) q^{88} +(-2.35018 + 16.3459i) q^{89} +(-1.00681 + 0.647036i) q^{90} +4.28446 q^{91} +(0.825160 - 5.52485i) q^{92} +6.40884 q^{93} +(16.6728 - 10.7150i) q^{94} +(-1.39029 + 9.66969i) q^{95} +(-4.61197 + 10.0988i) q^{96} +(8.58446 - 2.52063i) q^{97} +(3.57125 + 7.81994i) q^{98} +(-0.373975 - 0.431590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - q^{2} - 4 q^{3} - 19 q^{4} - 6 q^{5} - 25 q^{6} - 6 q^{8} - 26 q^{9} + 41 q^{10} - 12 q^{11} - 17 q^{12} - 18 q^{13} - 12 q^{14} + 19 q^{15} - 33 q^{16} - 10 q^{17} + 28 q^{18} + 28 q^{19} - 34 q^{20}+ \cdots - 26 q^{99}+O(q^{100}) \) 120 * q - q^2 - 4 * q^3 - 19 * q^4 - 6 * q^5 - 25 * q^6 - 6 * q^8 - 26 * q^9 + 41 * q^10 - 12 * q^11 - 17 * q^12 - 18 * q^13 - 12 * q^14 + 19 * q^15 - 33 * q^16 - 10 * q^17 + 28 * q^18 + 28 * q^19 - 34 * q^20 - 26 * q^21 + 10 * q^22 + 3 * q^23 + 108 * q^24 - 6 * q^25 - 26 * q^26 - 46 * q^27 - 3 * q^28 + 18 * q^29 + 16 * q^30 - 34 * q^31 - 63 * q^32 + 7 * q^33 - 24 * q^34 - 48 * q^35 - 122 * q^36 - 32 * q^37 + 143 * q^38 - 42 * q^39 + 8 * q^40 - 8 * q^41 + 174 * q^42 + 51 * q^43 - 19 * q^44 - 2 * q^45 - 67 * q^46 - 2 * q^47 - 111 * q^48 + 12 * q^49 - 113 * q^50 + 34 * q^51 + 127 * q^52 - 22 * q^53 - 27 * q^54 - 6 * q^55 + 191 * q^56 + 32 * q^57 - 71 * q^58 - 40 * q^59 + 12 * q^60 - 19 * q^61 + q^62 - 82 * q^63 - 6 * q^64 + 171 * q^65 - 3 * q^66 - 30 * q^67 - 152 * q^68 - 48 * q^69 + 86 * q^70 - 22 * q^71 - 130 * q^72 - 70 * q^73 - 27 * q^74 + 200 * q^75 + 4 * q^76 - 94 * q^78 - 6 * q^79 + 197 * q^80 + 4 * q^81 - 47 * q^82 + 50 * q^83 + 411 * q^84 - 98 * q^85 - 9 * q^86 - 72 * q^87 - 6 * q^88 - 41 * q^89 - 260 * q^90 + 30 * q^92 + 130 * q^93 + 33 * q^94 - 28 * q^95 - 265 * q^96 + 84 * q^97 - 117 * q^98 - 26 * q^99

Introduction

L-functions

Modular forms

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