LMFDB - Embedded newform 820.2.k.c.83.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(83,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.83"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [108] 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:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			83.20
Character	$\chi$	$=$	820.83
Dual form			820.2.k.c.247.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.238964 - 1.39388i) q^{2} +(-0.444020 + 0.444020i) q^{3} +(-1.88579 + 0.666174i) q^{4} +(1.32043 - 1.80457i) q^{5} +(0.725014 + 0.512805i) q^{6} +(-0.174110 - 0.174110i) q^{7} +(1.37920 + 2.46937i) q^{8} +2.60569i q^{9} +(-2.83089 - 1.40929i) q^{10} -3.21035i q^{11} +(0.541534 - 1.13312i) q^{12} +(-0.824514 - 0.824514i) q^{13} +(-0.201082 + 0.284294i) q^{14} +(0.214969 + 1.38756i) q^{15} +(3.11242 - 2.51253i) q^{16} +(2.09632 - 2.09632i) q^{17} +(3.63202 - 0.622667i) q^{18} -1.43141 q^{19} +(-1.28789 + 4.28268i) q^{20} +0.154617 q^{21} +(-4.47484 + 0.767159i) q^{22} +(4.09633 - 4.09633i) q^{23} +(-1.70884 - 0.484057i) q^{24} +(-1.51294 - 4.76561i) q^{25} +(-0.952242 + 1.34630i) q^{26} +(-2.48904 - 2.48904i) q^{27} +(0.444323 + 0.212348i) q^{28} -10.2809i q^{29} +(1.88272 - 0.631218i) q^{30} +9.15383i q^{31} +(-4.24592 - 3.73793i) q^{32} +(1.42546 + 1.42546i) q^{33} +(-3.42297 - 2.42107i) q^{34} +(-0.544093 + 0.0842940i) q^{35} +(-1.73585 - 4.91380i) q^{36} +(-3.35446 + 3.35446i) q^{37} +(0.342057 + 1.99522i) q^{38} +0.732201 q^{39} +(6.27729 + 0.771760i) q^{40} +1.00000 q^{41} +(-0.0369478 - 0.215517i) q^{42} +(6.42691 - 6.42691i) q^{43} +(2.13865 + 6.05405i) q^{44} +(4.70215 + 3.44063i) q^{45} +(-6.68867 - 4.73091i) q^{46} +(2.22800 + 2.22800i) q^{47} +(-0.266364 + 2.49759i) q^{48} -6.93937i q^{49} +(-6.28113 + 3.24767i) q^{50} +1.86162i q^{51} +(2.10413 + 1.00559i) q^{52} +(-7.48279 - 7.48279i) q^{53} +(-2.87462 + 4.06421i) q^{54} +(-5.79330 - 4.23903i) q^{55} +(0.189809 - 0.670075i) q^{56} +(0.635576 - 0.635576i) q^{57} +(-14.3303 + 2.45676i) q^{58} -4.94619 q^{59} +(-1.32974 - 2.47344i) q^{60} -13.2727 q^{61} +(12.7593 - 2.18744i) q^{62} +(0.453677 - 0.453677i) q^{63} +(-4.19560 + 6.81153i) q^{64} +(-2.57660 + 0.399182i) q^{65} +(1.64628 - 2.32755i) q^{66} +(-1.93499 - 1.93499i) q^{67} +(-2.55672 + 5.34975i) q^{68} +3.63770i q^{69} +(0.247514 + 0.738256i) q^{70} -14.6976i q^{71} +(-6.43443 + 3.59378i) q^{72} +(5.74025 + 5.74025i) q^{73} +(5.47730 + 3.87411i) q^{74} +(2.78780 + 1.44425i) q^{75} +(2.69935 - 0.953571i) q^{76} +(-0.558954 + 0.558954i) q^{77} +(-0.174970 - 1.02060i) q^{78} -7.25447 q^{79} +(-0.424309 - 8.93420i) q^{80} -5.60671 q^{81} +(-0.238964 - 1.39388i) q^{82} +(4.49891 - 4.49891i) q^{83} +(-0.291575 + 0.103002i) q^{84} +(-1.01492 - 6.55101i) q^{85} +(-10.4941 - 7.42253i) q^{86} +(4.56491 + 4.56491i) q^{87} +(7.92755 - 4.42772i) q^{88} +12.8980i q^{89} +(3.67217 - 7.37642i) q^{90} +0.287112i q^{91} +(-4.99596 + 10.4537i) q^{92} +(-4.06448 - 4.06448i) q^{93} +(2.57314 - 3.63797i) q^{94} +(-1.89008 + 2.58309i) q^{95} +(3.54499 - 0.225556i) q^{96} +(4.04246 - 4.04246i) q^{97} +(-9.67264 + 1.65826i) q^{98} +8.36519 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + 12 q^{2} - 4 q^{6} - 24 q^{8} + 4 q^{10} - 16 q^{13} + 52 q^{16} - 8 q^{17} + 18 q^{18} + 38 q^{20} + 72 q^{21} + 10 q^{22} - 12 q^{25} + 24 q^{26} - 58 q^{28} - 70 q^{30} - 38 q^{32} + 8 q^{33}+ \cdots + 122 q^{98}+O(q^{100}) $ 108 * q + 12 * q^2 - 4 * q^6 - 24 * q^8 + 4 * q^10 - 16 * q^13 + 52 * q^16 - 8 * q^17 + 18 * q^18 + 38 * q^20 + 72 * q^21 + 10 * q^22 - 12 * q^25 + 24 * q^26 - 58 * q^28 - 70 * q^30 - 38 * q^32 + 8 * q^33 + 72 * q^36 - 44 * q^37 + 56 * q^38 + 50 * q^40 + 108 * q^41 - 72 * q^42 - 4 * q^45 - 4 * q^46 - 94 * q^48 - 56 * q^50 - 50 * q^52 - 16 * q^53 - 32 * q^56 - 112 * q^57 + 68 * q^58 + 136 * q^60 + 8 * q^61 + 2 * q^62 - 48 * q^65 + 16 * q^66 - 16 * q^68 - 48 * q^70 - 42 * q^72 - 20 * q^73 - 12 * q^76 + 72 * q^77 + 100 * q^78 + 72 * q^80 - 52 * q^81 + 12 * q^82 - 32 * q^85 - 20 * q^86 - 38 * q^88 - 50 * q^90 + 8 * q^92 + 24 * q^93 + 44 * q^96 - 56 * q^97 + 122 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.238964	−	1.39388i	−0.168973	−	0.985621i
$2$	−0.238964	−	1.39388i	−0.168973	−	0.985621i
$3$	−0.444020	+	0.444020i	−0.256355	+	0.256355i	−0.823570	−	0.567215i	$-0.808021\pi$
$3$	−0.444020	+	0.444020i	−0.256355	+	0.256355i	0.567215	+	0.823570i	$0.308021\pi$
$4$	−1.88579	+	0.666174i	−0.942896	+	0.333087i
$5$	1.32043	−	1.80457i	0.590513	−	0.807028i
$5$	1.32043	−	1.80457i	0.590513	−	0.807028i
$6$	0.725014	+	0.512805i	0.295986	+	0.209352i
$7$	−0.174110	−	0.174110i	−0.0658074	−	0.0658074i	0.673437	−	0.739245i	$-0.264817\pi$
$7$	−0.174110	−	0.174110i	−0.0658074	−	0.0658074i	−0.739245	+	0.673437i	$0.764817\pi$
$8$	1.37920	+	2.46937i	0.487622	+	0.873055i
$9$			2.60569i			0.868564i
$10$	−2.83089	−	1.40929i	−0.895204	−	0.445656i
$11$		−	3.21035i		−	0.967957i	−0.875080	−	0.483979i	$-0.839191\pi$
$11$		−	3.21035i		−	0.967957i	0.875080	−	0.483979i	$-0.160809\pi$
$12$	0.541534	−	1.13312i	0.156328	−	0.327105i
$13$	−0.824514	−	0.824514i	−0.228679	−	0.228679i	0.583462	−	0.812141i	$-0.301698\pi$
$13$	−0.824514	−	0.824514i	−0.228679	−	0.228679i	−0.812141	+	0.583462i	$0.801698\pi$
$14$	−0.201082	+	0.284294i	−0.0537414	+	0.0759808i
$15$	0.214969	+	1.38756i	0.0555047	+	0.358267i
$16$	3.11242	−	2.51253i	0.778106	−	0.628133i
$17$	2.09632	−	2.09632i	0.508433	−	0.508433i	−0.405612	−	0.914045i	$-0.632942\pi$
$17$	2.09632	−	2.09632i	0.508433	−	0.508433i	0.914045	+	0.405612i	$0.132942\pi$
$18$	3.63202	−	0.622667i	0.856075	−	0.146764i
$19$	−1.43141			−0.328389			−0.164194	−	0.986428i	$-0.552502\pi$
$19$	−1.43141			−0.328389			−0.164194	+	0.986428i	$0.552502\pi$
$20$	−1.28789	+	4.28268i	−0.287982	+	0.957636i
$21$	0.154617			0.0337401
$22$	−4.47484	+	0.767159i	−0.954038	+	0.163559i
$23$	4.09633	−	4.09633i	0.854144	−	0.854144i	−0.136496	−	0.990641i	$-0.543584\pi$
$23$	4.09633	−	4.09633i	0.854144	−	0.854144i	0.990641	+	0.136496i	$0.0435841\pi$
$24$	−1.70884	−	0.484057i	−0.348816	−	0.0988077i
$25$	−1.51294	−	4.76561i	−0.302589	−	0.953121i
$26$	−0.952242	+	1.34630i	−0.186750	+	0.264031i
$27$	−2.48904	−	2.48904i	−0.479016	−	0.479016i
$28$	0.444323	+	0.212348i	0.0839691	+	0.0401299i
$29$		−	10.2809i		−	1.90911i	−0.298036	−	0.954555i	$-0.596332\pi$
$29$		−	10.2809i		−	1.90911i	0.298036	−	0.954555i	$-0.403668\pi$
$30$	1.88272	−	0.631218i	0.343736	−	0.115244i
$31$			9.15383i			1.64408i	0.569432	+	0.822038i	$0.307163\pi$
$31$			9.15383i			1.64408i	−0.569432	+	0.822038i	$0.692837\pi$
$32$	−4.24592	−	3.73793i	−0.750580	−	0.660780i
$33$	1.42546	+	1.42546i	0.248141	+	0.248141i
$34$	−3.42297	−	2.42107i	−0.587034	−	0.415211i
$35$	−0.544093	+	0.0842940i	−0.0919685	+	0.0142483i
$36$	−1.73585	−	4.91380i	−0.289308	−	0.818966i
$37$	−3.35446	+	3.35446i	−0.551469	+	0.551469i	−0.926865	−	0.375396i	$-0.877507\pi$
$37$	−3.35446	+	3.35446i	−0.551469	+	0.551469i	0.375396	+	0.926865i	$0.377507\pi$
$38$	0.342057	+	1.99522i	0.0554890	+	0.323667i
$39$	0.732201			0.117246
$40$	6.27729	+	0.771760i	0.992527	+	0.122026i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	−0.0369478	−	0.215517i	−0.00570117	−	0.0332549i
$43$	6.42691	−	6.42691i	0.980095	−	0.980095i	−0.0197110	−	0.999806i	$-0.506275\pi$
$43$	6.42691	−	6.42691i	0.980095	−	0.980095i	0.999806	+	0.0197110i	$0.00627461\pi$
$44$	2.13865	+	6.05405i	0.322414	+	0.912683i
$45$	4.70215	+	3.44063i	0.700956	+	0.512899i
$46$	−6.68867	−	4.73091i	−0.986190	−	0.697535i
$47$	2.22800	+	2.22800i	0.324987	+	0.324987i	0.850676	−	0.525690i	$-0.176193\pi$
$47$	2.22800	+	2.22800i	0.324987	+	0.324987i	−0.525690	+	0.850676i	$0.676193\pi$
$48$	−0.266364	+	2.49759i	−0.0384463	+	0.360496i
$49$		−	6.93937i		−	0.991339i
$50$	−6.28113	+	3.24767i	−0.888287	+	0.459290i
$51$			1.86162i			0.260679i
$52$	2.10413	+	1.00559i	0.291790	+	0.139450i
$53$	−7.48279	−	7.48279i	−1.02784	−	1.02784i	−0.999601	−	0.0282396i	$-0.991010\pi$
$53$	−7.48279	−	7.48279i	−1.02784	−	1.02784i	−0.0282396	−	0.999601i	$-0.508990\pi$
$54$	−2.87462	+	4.06421i	−0.391187	+	0.553069i
$55$	−5.79330	−	4.23903i	−0.781169	−	0.571591i
$56$	0.189809	−	0.670075i	0.0253644	−	0.0895426i
$57$	0.635576	−	0.635576i	0.0841841	−	0.0841841i
$58$	−14.3303	+	2.45676i	−1.88166	+	0.322588i
$59$	−4.94619			−0.643939			−0.321969	−	0.946750i	$-0.604345\pi$
$59$	−4.94619			−0.643939			−0.321969	+	0.946750i	$0.604345\pi$
$60$	−1.32974	−	2.47344i	−0.171669	−	0.319320i
$61$	−13.2727			−1.69940			−0.849700	−	0.527267i	$-0.823217\pi$
$61$	−13.2727			−1.69940			−0.849700	+	0.527267i	$0.823217\pi$
$62$	12.7593	−	2.18744i	1.62044	−	0.277805i
$63$	0.453677	−	0.453677i	0.0571579	−	0.0571579i
$64$	−4.19560	+	6.81153i	−0.524450	+	0.851441i
$65$	−2.57660	+	0.399182i	−0.319588	+	0.0495124i
$66$	1.64628	−	2.32755i	0.202643	−	0.286502i
$67$	−1.93499	−	1.93499i	−0.236397	−	0.236397i	0.578960	−	0.815356i	$-0.303459\pi$
$67$	−1.93499	−	1.93499i	−0.236397	−	0.236397i	−0.815356	+	0.578960i	$0.803459\pi$
$68$	−2.55672	+	5.34975i	−0.310047	+	0.648752i
$69$			3.63770i			0.437928i
$70$	0.247514	+	0.738256i	0.0295836	+	0.0882385i
$71$		−	14.6976i		−	1.74428i	−0.489254	−	0.872141i	$-0.662731\pi$
$71$		−	14.6976i		−	1.74428i	0.489254	−	0.872141i	$-0.337269\pi$
$72$	−6.43443	+	3.59378i	−0.758304	+	0.423531i
$73$	5.74025	+	5.74025i	0.671846	+	0.671846i	0.958141	−	0.286296i	$-0.0924240\pi$
$73$	5.74025	+	5.74025i	0.671846	+	0.671846i	−0.286296	+	0.958141i	$0.592424\pi$
$74$	5.47730	+	3.87411i	0.636723	+	0.450356i
$75$	2.78780	+	1.44425i	0.321907	+	0.166767i
$76$	2.69935	−	0.953571i	0.309637	−	0.109382i
$77$	−0.558954	+	0.558954i	−0.0636987	+	0.0636987i
$78$	−0.174970	−	1.02060i	−0.0198114	−	0.115560i
$79$	−7.25447			−0.816192			−0.408096	−	0.912939i	$-0.633807\pi$
$79$	−7.25447			−0.816192			−0.408096	+	0.912939i	$0.633807\pi$
$80$	−0.424309	−	8.93420i	−0.0474392	−	0.998874i
$81$	−5.60671			−0.622968
$82$	−0.238964	−	1.39388i	−0.0263892	−	0.153928i
$83$	4.49891	−	4.49891i	0.493819	−	0.493819i	−0.415688	−	0.909507i	$-0.636459\pi$
$83$	4.49891	−	4.49891i	0.493819	−	0.493819i	0.909507	+	0.415688i	$0.136459\pi$
$84$	−0.291575	+	0.103002i	−0.0318134	+	0.0112384i
$85$	−1.01492	−	6.55101i	−0.110083	−	0.710557i
$86$	−10.4941	−	7.42253i	−1.13161	−	0.800392i
$87$	4.56491	+	4.56491i	0.489410	+	0.489410i
$88$	7.92755	−	4.42772i	0.845080	−	0.471997i
$89$			12.8980i			1.36718i	0.729866	+	0.683591i	$0.239583\pi$
$89$			12.8980i			1.36718i	−0.729866	+	0.683591i	$0.760417\pi$
$90$	3.67217	−	7.37642i	0.387081	−	0.777543i
$91$			0.287112i			0.0300975i
$92$	−4.99596	+	10.4537i	−0.520865	+	1.08987i
$93$	−4.06448	−	4.06448i	−0.421467	−	0.421467i
$94$	2.57314	−	3.63797i	0.265400	−	0.375228i
$95$	−1.89008	+	2.58309i	−0.193918	+	0.265019i
$96$	3.54499	−	0.225556i	0.361809	−	0.0230207i
$97$	4.04246	−	4.04246i	0.410449	−	0.410449i	−0.471446	−	0.881895i	$-0.656268\pi$
$97$	4.04246	−	4.04246i	0.410449	−	0.410449i	0.881895	+	0.471446i	$0.156268\pi$
$98$	−9.67264	+	1.65826i	−0.977084	+	0.167510i
$99$	8.36519			0.840733
$100$	6.02782	+	7.97906i	0.602782	+	0.797906i
$101$	8.70498			0.866178			0.433089	−	0.901351i	$-0.357424\pi$
$101$	8.70498			0.866178			0.433089	+	0.901351i	$0.357424\pi$
$102$	2.59487	−	0.444860i	0.256930	−	0.0440477i
$103$	13.4957	−	13.4957i	1.32977	−	1.32977i	0.424196	−	0.905571i	$-0.360557\pi$
$103$	13.4957	−	13.4957i	1.32977	−	1.32977i	0.905571	−	0.424196i	$-0.139443\pi$
$104$	0.898860	−	3.17320i	0.0881405	−	0.311158i
$105$	0.204160	−	0.279016i	0.0199240	−	0.0272292i
$106$	−8.64198	+	12.2182i	−0.839384	+	1.18674i
$107$	11.6366	+	11.6366i	1.12496	+	1.12496i	0.990985	+	0.133971i	$0.0427729\pi$
$107$	11.6366	+	11.6366i	1.12496	+	1.12496i	0.133971	+	0.990985i	$0.457227\pi$
$108$	6.35194	+	3.03568i	0.611216	+	0.292108i
$109$			10.0792i			0.965412i	0.875783	+	0.482706i	$0.160346\pi$
$109$			10.0792i			0.965412i	−0.875783	+	0.482706i	$0.839654\pi$
$110$	−4.52431	+	9.08813i	−0.431376	+	0.866520i
$111$		−	2.97889i		−	0.282744i
$112$	−0.979361	−	0.104447i	−0.0925409	−	0.00986934i
$113$	5.37622	+	5.37622i	0.505752	+	0.505752i	0.913220	−	0.407467i	$-0.133588\pi$
$113$	5.37622	+	5.37622i	0.505752	+	0.505752i	−0.407467	+	0.913220i	$0.633588\pi$
$114$	−1.03780	−	0.734036i	−0.0971985	−	0.0687487i
$115$	−1.98321	−	12.8010i	−0.184935	−	1.19370i
$116$	6.84885	+	19.3876i	0.635900	+	1.80009i
$117$	2.14843	−	2.14843i	0.198622	−	0.198622i
$118$	1.18196	+	6.89438i	0.108808	+	0.634679i
$119$	−0.729982			−0.0669173
$120$	−3.12992	+	2.44456i	−0.285721	+	0.223157i
$121$	0.693650			0.0630591
$122$	3.17171	+	18.5006i	0.287153	+	1.67496i
$123$	−0.444020	+	0.444020i	−0.0400359	+	0.0400359i
$124$	−6.09805	−	17.2622i	−0.547621	−	1.55019i
$125$	−10.5976	−	3.56242i	−0.947878	−	0.318633i
$126$	−0.740783	−	0.523958i	−0.0659942	−	0.0466779i
$127$	7.84211	+	7.84211i	0.695875	+	0.695875i	0.963518	−	0.267643i	$-0.0862449\pi$
$127$	7.84211	+	7.84211i	0.695875	+	0.695875i	−0.267643	+	0.963518i	$0.586245\pi$
$128$	10.4970	+	4.22045i	0.927816	+	0.373038i
$129$			5.70735i			0.502504i
$130$	1.17213	+	3.49608i	0.102802	+	0.306626i
$131$			10.6008i			0.926199i	0.886306	+	0.463100i	$0.153263\pi$
$131$			10.6008i			0.926199i	−0.886306	+	0.463100i	$0.846737\pi$
$132$	−3.63772	−	1.73852i	−0.316623	−	0.151318i
$133$	0.249224	+	0.249224i	0.0216104	+	0.0216104i
$134$	−2.23475	+	3.15953i	−0.193053	+	0.272942i
$135$	−7.77824	+	1.20505i	−0.669444	+	0.103714i
$136$	8.06786	+	2.28535i	0.691814	+	0.195967i
$137$	2.60999	−	2.60999i	0.222986	−	0.222986i	−0.586768	−	0.809755i	$-0.699600\pi$
$137$	2.60999	−	2.60999i	0.222986	−	0.222986i	0.809755	+	0.586768i	$0.199600\pi$
$138$	5.07052	−	0.869281i	0.431631	−	0.0739982i
$139$	−9.94177			−0.843250			−0.421625	−	0.906770i	$-0.638540\pi$
$139$	−9.94177			−0.843250			−0.421625	+	0.906770i	$0.638540\pi$
$140$	0.969892	−	0.521422i	0.0819708	−	0.0440682i
$141$	−1.97855			−0.166624
$142$	−20.4866	+	3.51220i	−1.71920	+	0.294737i
$143$	−2.64698	+	2.64698i	−0.221351	+	0.221351i
$144$	6.54689	+	8.11002i	0.545574	+	0.675835i
$145$	−18.5525	−	13.5751i	−1.54070	−	1.12735i
$146$	6.62950	−	9.37292i	0.548661	−	0.775709i
$147$	3.08122	+	3.08122i	0.254135	+	0.254135i
$148$	4.09115	−	8.56046i	0.336291	−	0.703665i
$149$		−	4.13860i		−	0.339047i	−0.985526	−	0.169524i	$-0.945777\pi$
$149$		−	4.13860i		−	0.339047i	0.985526	−	0.169524i	$-0.0542229\pi$
$150$	1.34692	−	4.23098i	0.109975	−	0.345458i
$151$			1.97386i			0.160630i	0.996770	+	0.0803152i	$0.0255927\pi$
$151$			1.97386i			0.160630i	−0.996770	+	0.0803152i	$0.974407\pi$
$152$	−1.97421	−	3.53470i	−0.160130	−	0.286702i
$153$	5.46238	+	5.46238i	0.441607	+	0.441607i
$154$	0.912684	+	0.645544i	0.0735462	+	0.0520194i
$155$	16.5187	+	12.0870i	1.32682	+	0.970849i
$156$	−1.38078	+	0.487773i	−0.110551	+	0.0390531i
$157$	8.57021	−	8.57021i	0.683977	−	0.683977i	−0.276917	−	0.960894i	$-0.589313\pi$
$157$	8.57021	−	8.57021i	0.683977	−	0.683977i	0.960894	+	0.276917i	$0.0893127\pi$
$158$	1.73356	+	10.1118i	0.137915	+	0.804455i
$159$	6.64502			0.526984
$160$	−12.3518	+	2.72639i	−0.976495	+	0.215540i
$161$	−1.42642			−0.112418
$162$	1.33980	+	7.81508i	0.105265	+	0.614010i
$163$	−9.69093	+	9.69093i	−0.759052	+	0.759052i	−0.976150	−	0.217098i	$-0.930341\pi$
$163$	−9.69093	+	9.69093i	−0.759052	+	0.759052i	0.217098	+	0.976150i	$0.430341\pi$
$164$	−1.88579	+	0.666174i	−0.147256	+	0.0520195i
$165$	4.45455	−	0.690125i	0.346787	−	0.0537262i
$166$	−7.34601	−	5.19585i	−0.570161	−	0.403276i
$167$	15.6517	+	15.6517i	1.21117	+	1.21117i	0.970644	+	0.240522i	$0.0773188\pi$
$167$	15.6517	+	15.6517i	1.21117	+	1.21117i	0.240522	+	0.970644i	$0.422681\pi$
$168$	0.213247	+	0.381806i	0.0164524	+	0.0294570i
$169$		−	11.6404i		−	0.895412i
$170$	−8.88878	+	2.98013i	−0.681738	+	0.228566i
$171$		−	3.72983i		−	0.285227i
$172$	−7.83838	+	16.4013i	−0.597671	+	1.25058i
$173$	−4.88315	−	4.88315i	−0.371259	−	0.371259i	0.496677	−	0.867936i	$-0.334554\pi$
$173$	−4.88315	−	4.88315i	−0.371259	−	0.371259i	−0.867936	+	0.496677i	$0.834554\pi$
$174$	5.27208	−	7.45378i	0.399675	−	0.565069i
$175$	−0.566321	+	1.09316i	−0.0428098	+	0.0826350i
$176$	−8.06611	−	9.99197i	−0.608006	−	0.753173i
$177$	2.19621	−	2.19621i	0.165077	−	0.165077i
$178$	17.9782	−	3.08215i	1.34752	−	0.231017i
$179$	20.4713			1.53010			0.765049	−	0.643972i	$-0.222714\pi$
$179$	20.4713			1.53010			0.765049	+	0.643972i	$0.222714\pi$
$180$	−11.1593	−	3.35586i	−0.831768	−	0.250131i
$181$	6.56161			0.487721			0.243860	−	0.969810i	$-0.421586\pi$
$181$	6.56161			0.487721			0.243860	+	0.969810i	$0.421586\pi$
$182$	0.400199	−	0.0686095i	0.0296647	−	0.00508568i
$183$	5.89335	−	5.89335i	0.435649	−	0.435649i
$184$	15.7650	+	4.46570i	1.16221	+	0.329216i
$185$	1.62403	+	10.4827i	0.119401	+	0.770701i
$186$	−4.69413	+	6.63666i	−0.344190	+	0.486623i
$187$	−6.72994	−	6.72994i	−0.492142	−	0.492142i
$188$	−5.68577	−	2.71730i	−0.414678	−	0.198180i
$189$			0.866733i			0.0630455i
$190$	4.05217	+	2.01727i	0.293975	+	0.146348i
$191$			2.31236i			0.167317i	0.996494	+	0.0836583i	$0.0266604\pi$
$191$			2.31236i			0.167317i	−0.996494	+	0.0836583i	$0.973340\pi$
$192$	−1.16152	−	4.88738i	−0.0838257	−	0.352716i
$193$	15.8110	+	15.8110i	1.13810	+	1.13810i	0.988790	+	0.149312i	$0.0477059\pi$
$193$	15.8110	+	15.8110i	1.13810	+	1.13810i	0.149312	+	0.988790i	$0.452294\pi$
$194$	−6.60069	−	4.66869i	−0.473902	−	0.335192i
$195$	0.966818	−	1.32131i	0.0692352	−	0.0946208i
$196$	4.62283	+	13.0862i	0.330202	+	0.934729i
$197$	−5.48130	+	5.48130i	−0.390526	+	0.390526i	−0.874875	−	0.484349i	$-0.839057\pi$
$197$	−5.48130	+	5.48130i	−0.390526	+	0.390526i	0.484349	+	0.874875i	$0.339057\pi$
$198$	−1.99898	−	11.6601i	−0.142061	−	0.828644i
$199$	−9.94424			−0.704929			−0.352464	−	0.935825i	$-0.614656\pi$
$199$	−9.94424			−0.704929			−0.352464	+	0.935825i	$0.614656\pi$
$200$	9.68140	−	10.3088i	0.684578	−	0.728939i
$201$	1.71835			0.121203
$202$	−2.08018	−	12.1337i	−0.146361	−	0.853723i
$203$	−1.79000	+	1.79000i	−0.125633	+	0.125633i
$204$	−1.24016	−	3.51063i	−0.0868287	−	0.245793i
$205$	1.32043	−	1.80457i	0.0922226	−	0.126037i
$206$	−22.0363	−	15.5863i	−1.53534	−	1.08595i
$207$	10.6738	+	10.6738i	0.741879	+	0.741879i
$208$	−4.63785	−	0.494619i	−0.321577	−	0.0342957i
$209$			4.59534i			0.317866i
$210$	−0.437702	−	0.217899i	−0.0302043	−	0.0150365i
$211$		−	14.5655i		−	1.00273i	−0.865235	−	0.501367i	$-0.832831\pi$
$211$		−	14.5655i		−	1.00273i	0.865235	−	0.501367i	$-0.167169\pi$
$212$	19.0958	+	9.12615i	1.31151	+	0.626787i
$213$	6.52602	+	6.52602i	0.447155	+	0.447155i
$214$	13.4393	−	19.0008i	0.918693	−	1.29887i
$215$	−3.11154	−	20.0841i	−0.212205	−	1.36972i
$216$	2.71348	−	9.57925i	0.184629	−	0.651785i
$217$	1.59377	−	1.59377i	0.108192	−	0.108192i
$218$	14.0492	−	2.40857i	0.951530	−	0.163129i
$219$	−5.09757			−0.344462
$220$	13.7489	+	4.13459i	0.926950	+	0.278754i
$221$	−3.45690			−0.232536
$222$	−4.15221	+	0.711848i	−0.278678	+	0.0477761i
$223$	10.7555	−	10.7555i	0.720244	−	0.720244i	−0.248411	−	0.968655i	$-0.579908\pi$
$223$	10.7555	−	10.7555i	0.720244	−	0.720244i	0.968655	+	0.248411i	$0.0799083\pi$
$224$	0.0884455	+	1.39007i	0.00590951	+	0.0928779i
$225$	12.4177	−	3.94227i	0.827847	−	0.262818i
$226$	6.20907	−	8.77852i	0.413021	−	0.583938i
$227$	−4.19765	−	4.19765i	−0.278608	−	0.278608i	0.553945	−	0.832553i	$-0.313122\pi$
$227$	−4.19765	−	4.19765i	−0.278608	−	0.278608i	−0.832553	+	0.553945i	$0.813122\pi$
$228$	−0.775160	+	1.62197i	−0.0513362	+	0.107418i
$229$			14.8658i			0.982361i	0.871058	+	0.491180i	$0.163434\pi$
$229$			14.8658i			0.982361i	−0.871058	+	0.491180i	$0.836566\pi$
$230$	−17.3692	+	5.82334i	−1.14529	+	0.383980i
$231$		−	0.496373i		−	0.0326590i
$232$	25.3873	−	14.1794i	1.66676	−	0.930923i
$233$	−4.90678	−	4.90678i	−0.321454	−	0.321454i	0.527871	−	0.849325i	$-0.322990\pi$
$233$	−4.90678	−	4.90678i	−0.321454	−	0.321454i	−0.849325	+	0.527871i	$0.822990\pi$
$234$	−3.50805	−	2.48125i	−0.229328	−	0.162204i
$235$	6.96248	−	1.07867i	0.454182	−	0.0703645i
$236$	9.32748	−	3.29502i	0.607167	−	0.214488i
$237$	3.22113	−	3.22113i	0.209235	−	0.209235i
$238$	0.174440	+	1.01751i	0.0113072	+	0.0659551i
$239$	−22.9989			−1.48768			−0.743838	−	0.668360i	$-0.766997\pi$
$239$	−22.9989			−1.48768			−0.743838	+	0.668360i	$0.766997\pi$
$240$	4.15536	+	3.77856i	0.268228	+	0.243905i
$241$	8.19573			0.527934			0.263967	−	0.964532i	$-0.414969\pi$
$241$	8.19573			0.527934			0.263967	+	0.964532i	$0.414969\pi$
$242$	−0.165758	−	0.966863i	−0.0106553	−	0.0621523i
$243$	9.95661	−	9.95661i	0.638717	−	0.638717i
$244$	25.0296	−	8.84195i	1.60236	−	0.566048i
$245$	−12.5226	−	9.16294i	−0.800038	−	0.585398i
$246$	0.725014	+	0.512805i	0.0462252	+	0.0326952i
$247$	1.18022	+	1.18022i	0.0750956	+	0.0750956i
$248$	−22.6042	+	12.6250i	−1.43537	+	0.801688i
$249$			3.99521i			0.253186i
$250$	−2.43314	+	15.6231i	−0.153885	+	0.988089i
$251$			13.0361i			0.822829i	0.911448	+	0.411414i	$0.134965\pi$
$251$			13.0361i			0.822829i	−0.911448	+	0.411414i	$0.865035\pi$
$252$	−0.553313	+	1.15777i	−0.0348554	+	0.0729326i
$253$	−13.1507	−	13.1507i	−0.826775	−	0.826775i
$254$	9.05696	−	12.8049i	0.568284	−	0.803453i
$255$	3.35942	+	2.45813i	0.210375	+	0.153934i
$256$	3.37437	−	15.6401i	0.210898	−	0.977508i
$257$	−0.131158	+	0.131158i	−0.00818143	+	0.00818143i	−0.711186	−	0.703004i	$-0.751841\pi$
$257$	−0.131158	+	0.131158i	−0.00818143	+	0.00818143i	0.703004	+	0.711186i	$0.251841\pi$
$258$	7.95535	−	1.36385i	0.495278	−	0.0849098i
$259$	1.16809			0.0725815
$260$	4.59301	−	2.46924i	0.284847	−	0.153136i
$261$	26.7888			1.65818
$262$	14.7763	−	2.53322i	0.912881	−	0.156503i
$263$	−20.8537	+	20.8537i	−1.28589	+	1.28589i	−0.348632	+	0.937260i	$0.613354\pi$
$263$	−20.8537	+	20.8537i	−1.28589	+	1.28589i	−0.937260	+	0.348632i	$0.886646\pi$
$264$	−1.55399	+	5.48599i	−0.0956416	+	0.337639i
$265$	−23.3837	+	3.62274i	−1.43645	+	0.222543i
$266$	0.287832	−	0.406943i	0.0176481	−	0.0249513i
$267$	−5.72695	−	5.72695i	−0.350484	−	0.350484i
$268$	4.93803	+	2.35995i	0.301638	+	0.144157i
$269$		−	9.49122i		−	0.578690i	−0.957225	−	0.289345i	$-0.906563\pi$
$269$		−	9.49122i		−	0.578690i	0.957225	−	0.289345i	$-0.0934375\pi$
$270$	3.53841	+	10.5540i	0.215341	+	0.642293i
$271$		−	9.00575i		−	0.547060i	−0.961863	−	0.273530i	$-0.911809\pi$
$271$		−	9.00575i		−	0.547060i	0.961863	−	0.273530i	$-0.0881913\pi$
$272$	1.25757	−	11.7917i	0.0762513	−	0.714979i
$273$	−0.127483	−	0.127483i	−0.00771565	−	0.00771565i
$274$	−4.26170	−	3.01431i	−0.257459	−	0.182101i
$275$	−15.2993	+	4.85708i	−0.922580	+	0.292893i
$276$	−2.42334	−	6.85996i	−0.145868	−	0.412921i
$277$	−9.45911	+	9.45911i	−0.568343	+	0.568343i	−0.931664	−	0.363321i	$-0.881643\pi$
$277$	−9.45911	+	9.45911i	−0.568343	+	0.568343i	0.363321	+	0.931664i	$0.381643\pi$
$278$	2.37573	+	13.8576i	0.142487	+	0.831124i
$279$	−23.8521			−1.42799
$280$	−0.958568	−	1.22731i	−0.0572854	−	0.0733458i
$281$	2.20364			0.131458			0.0657290	−	0.997838i	$-0.479063\pi$
$281$	2.20364			0.131458			0.0657290	+	0.997838i	$0.479063\pi$
$282$	0.472802	+	2.75786i	0.0281550	+	0.164228i
$283$	5.88960	−	5.88960i	0.350100	−	0.350100i	−0.510046	−	0.860147i	$-0.670372\pi$
$283$	5.88960	−	5.88960i	0.350100	−	0.350100i	0.860147	+	0.510046i	$0.170372\pi$
$284$	9.79115	+	27.7166i	0.580998	+	1.64468i
$285$	−0.307709	−	1.98617i	−0.0182271	−	0.117651i
$286$	4.32210	+	3.05703i	0.255571	+	0.180766i
$287$	−0.174110	−	0.174110i	−0.0102774	−	0.0102774i
$288$	9.73991	−	11.0636i	0.573930	−	0.651927i
$289$			8.21085i			0.482991i
$290$	−14.4887	+	29.1040i	−0.850805	+	1.70904i
$291$			3.58986i			0.210441i
$292$	−14.6489	−	7.00091i	−0.857264	−	0.409697i
$293$	11.2673	+	11.2673i	0.658245	+	0.658245i	0.954965	−	0.296720i	$-0.0958928\pi$
$293$	11.2673	+	11.2673i	0.658245	+	0.658245i	−0.296720	+	0.954965i	$0.595893\pi$
$294$	3.55854	−	5.03114i	0.207538	−	0.293422i
$295$	−6.53108	+	8.92574i	−0.380254	+	0.519677i
$296$	−12.9099	−	3.65693i	−0.750371	−	0.212555i
$297$	−7.99069	+	7.99069i	−0.463667	+	0.463667i
$298$	−5.76870	+	0.988977i	−0.334172	+	0.0572899i
$299$	−6.75496			−0.390650
$300$	−6.21933	−	0.866388i	−0.359073	−	0.0500210i
$301$	−2.23798			−0.128995
$302$	2.75132	−	0.471682i	0.158321	−	0.0271423i
$303$	−3.86518	+	3.86518i	−0.222049	+	0.222049i
$304$	−4.45517	+	3.59647i	−0.255521	+	0.206272i
$305$	−17.5257	+	23.9516i	−1.00352	+	1.37146i
$306$	6.30858	−	8.91920i	0.360637	−	0.509877i
$307$	18.8034	+	18.8034i	1.07316	+	1.07316i	0.997103	+	0.0760615i	$0.0242345\pi$
$307$	18.8034	+	18.8034i	1.07316	+	1.07316i	0.0760615	+	0.997103i	$0.475765\pi$
$308$	0.681710	−	1.42643i	0.0388441	−	0.0812785i
$309$			11.9847i			0.681784i
$310$	12.9004	−	25.9134i	0.732692	−	1.47179i
$311$			18.5063i			1.04940i	0.851288	+	0.524698i	$0.175822\pi$
$311$			18.5063i			1.04940i	−0.851288	+	0.524698i	$0.824178\pi$
$312$	1.00985	+	1.80808i	0.0571717	+	0.102362i
$313$	4.23759	+	4.23759i	0.239523	+	0.239523i	0.816652	−	0.577130i	$-0.195827\pi$
$313$	4.23759	+	4.23759i	0.239523	+	0.239523i	−0.577130	+	0.816652i	$0.695827\pi$
$314$	−13.9938	−	9.89785i	−0.789716	−	0.558568i
$315$	−0.219644	−	1.41774i	−0.0123756	−	0.0798806i
$316$	13.6804	−	4.83274i	0.769584	−	0.271863i
$317$	19.5617	−	19.5617i	1.09869	−	1.09869i	0.104128	−	0.994564i	$-0.466795\pi$
$317$	19.5617	−	19.5617i	1.09869	−	1.09869i	0.994564	−	0.104128i	$-0.0332052\pi$
$318$	−1.58792	−	9.26234i	−0.0890462	−	0.519406i
$319$	−33.0052			−1.84794
$320$	6.75189	+	16.5654i	0.377442	+	0.926033i
$321$	−10.3338			−0.576776
$322$	0.340865	+	1.98826i	0.0189956	+	0.110802i
$323$	−3.00071	+	3.00071i	−0.166964	+	0.166964i
$324$	10.5731	−	3.73505i	0.587394	−	0.207503i
$325$	−2.68186	+	5.17675i	−0.148763	+	0.287154i
$326$	15.8238	+	11.1922i	0.876397	+	0.619878i
$327$	−4.47536	−	4.47536i	−0.247488	−	0.247488i
$328$	1.37920	+	2.46937i	0.0761537	+	0.136348i
$329$		−	0.775833i		−	0.0427730i
$330$	−2.02643	−	6.04419i	−0.111551	−	0.332722i
$331$		−	0.940233i		−	0.0516799i	−0.999666	−	0.0258399i	$-0.991774\pi$
$331$		−	0.940233i		−	0.0516799i	0.999666	−	0.0258399i	$-0.00822603\pi$
$332$	−5.48695	+	11.4811i	−0.301136	+	0.630105i
$333$	−8.74068	−	8.74068i	−0.478986	−	0.478986i
$334$	18.0764	−	25.5568i	0.989096	−	1.39840i
$335$	−6.04684	+	0.936810i	−0.330374	+	0.0511834i
$336$	0.481232	−	0.388479i	0.0262534	−	0.0211933i
$337$	−12.1329	+	12.1329i	−0.660920	+	0.660920i	−0.955597	−	0.294677i	$-0.904788\pi$
$337$	−12.1329	+	12.1329i	−0.660920	+	0.660920i	0.294677	+	0.955597i	$0.404788\pi$
$338$	−16.2252	+	2.78163i	−0.882536	+	0.151301i
$339$	−4.77430			−0.259304
$340$	6.27804	+	11.6777i	0.340475	+	0.633314i
$341$	29.3870			1.59140
$342$	−5.19892	+	0.891295i	−0.281126	+	0.0481957i
$343$	−2.42698	+	2.42698i	−0.131045	+	0.131045i
$344$	24.7344	+	7.00643i	1.33359	+	0.377761i
$345$	6.56449	+	4.80332i	0.353420	+	0.258602i
$346$	−5.63962	+	7.97342i	−0.303188	+	0.428653i
$347$	−4.80738	−	4.80738i	−0.258073	−	0.258073i	0.566197	−	0.824270i	$-0.308414\pi$
$347$	−4.80738	−	4.80738i	−0.258073	−	0.258073i	−0.824270	+	0.566197i	$0.808414\pi$
$348$	−11.6495	−	5.56744i	−0.624478	−	0.298446i
$349$		−	17.0655i		−	0.913498i	−0.889596	−	0.456749i	$-0.849014\pi$
$349$		−	17.0655i		−	0.913498i	0.889596	−	0.456749i	$-0.150986\pi$
$350$	1.65906	+	0.528157i	0.0886805	+	0.0282312i
$351$			4.10449i			0.219082i
$352$	−12.0001	+	13.6309i	−0.639606	+	0.726529i
$353$	−6.93155	−	6.93155i	−0.368929	−	0.368929i	0.498157	−	0.867087i	$-0.334010\pi$
$353$	−6.93155	−	6.93155i	−0.368929	−	0.368929i	−0.867087	+	0.498157i	$0.834010\pi$
$354$	−3.58606	−	2.53643i	−0.190597	−	0.134810i
$355$	−26.5228	−	19.4071i	−1.40768	−	1.03002i
$356$	−8.59229	−	24.3229i	−0.455390	−	1.28911i
$357$	0.324126	−	0.324126i	0.0171546	−	0.0171546i
$358$	−4.89192	−	28.5345i	−0.258546	−	1.50810i
$359$	−19.9093			−1.05077			−0.525387	−	0.850863i	$-0.676080\pi$
$359$	−19.9093			−1.05077			−0.525387	+	0.850863i	$0.676080\pi$
$360$	−2.01097	+	16.3567i	−0.105987	+	0.862073i
$361$	−16.9511			−0.892161
$362$	−1.56799	−	9.14609i	−0.0824118	−	0.480708i
$363$	−0.307994	+	0.307994i	−0.0161655	+	0.0161655i
$364$	−0.191267	−	0.541434i	−0.0100251	−	0.0283788i
$365$	17.9383	−	2.77910i	0.938932	−	0.145465i
$366$	−9.62292	−	6.80632i	−0.502998	−	0.355772i
$367$	−8.96172	−	8.96172i	−0.467798	−	0.467798i	0.433403	−	0.901200i	$-0.357313\pi$
$367$	−8.96172	−	8.96172i	−0.467798	−	0.467798i	−0.901200	+	0.433403i	$0.857313\pi$
$368$	2.45736	−	23.0417i	0.128099	−	1.20113i
$369$			2.60569i			0.135647i
$370$	14.2235	−	4.76869i	0.739443	−	0.247912i
$371$			2.60566i			0.135279i
$372$	10.3724	+	4.95712i	0.537785	+	0.257015i
$373$	3.37027	+	3.37027i	0.174506	+	0.174506i	0.788956	−	0.614450i	$-0.210622\pi$
$373$	3.37027	+	3.37027i	0.174506	+	0.174506i	−0.614450	+	0.788956i	$0.710622\pi$
$374$	−7.77250	+	10.9889i	−0.401906	+	0.568224i
$375$	6.28733	−	3.12376i	0.324676	−	0.161310i
$376$	−2.42890	+	8.57461i	−0.125261	+	0.442202i
$377$	−8.47672	+	8.47672i	−0.436573	+	0.436573i
$378$	1.20812	−	0.207118i	0.0621390	−	0.0106530i
$379$	8.37072			0.429975			0.214987	−	0.976617i	$-0.431029\pi$
$379$	8.37072			0.429975			0.214987	+	0.976617i	$0.431029\pi$
$380$	1.84351	−	6.13029i	0.0945701	−	0.314477i
$381$	−6.96410			−0.356782
$382$	3.22315	−	0.552572i	0.164911	−	0.0282720i
$383$	−3.93254	+	3.93254i	−0.200943	+	0.200943i	−0.800404	−	0.599461i	$-0.795382\pi$
$383$	−3.93254	+	3.93254i	−0.200943	+	0.200943i	0.599461	+	0.800404i	$0.295382\pi$
$384$	−6.53485	+	2.78693i	−0.333480	+	0.142220i
$385$	0.270613	+	1.74673i	0.0137917	+	0.0890216i
$386$	18.2604	−	25.8169i	0.929428	−	1.31405i
$387$	16.7466	+	16.7466i	0.851275	+	0.851275i
$388$	−4.93025	+	10.3162i	−0.250296	+	0.523726i
$389$			18.7369i			0.950000i	0.879986	+	0.475000i	$0.157552\pi$
$389$			18.7369i			0.950000i	−0.879986	+	0.475000i	$0.842448\pi$
$390$	−2.07278	−	1.03188i	−0.104959	−	0.0522513i
$391$		−	17.1745i		−	0.868551i
$392$	17.1359	−	9.57080i	0.865493	−	0.483398i
$393$	−4.70698	−	4.70698i	−0.237436	−	0.237436i
$394$	8.95010	+	6.33043i	0.450899	+	0.318922i
$395$	−9.57900	+	13.0912i	−0.481972	+	0.658690i
$396$	−15.7750	+	5.57267i	−0.792724	+	0.280037i
$397$	13.8702	−	13.8702i	0.696128	−	0.696128i	−0.267445	−	0.963573i	$-0.586179\pi$
$397$	13.8702	−	13.8702i	0.696128	−	0.696128i	0.963573	+	0.267445i	$0.0861794\pi$
$398$	2.37632	+	13.8611i	0.119114	+	0.694792i
$399$	−0.221320			−0.0110799
$400$	−16.6827	−	11.0313i	−0.834133	−	0.551563i
$401$	−6.71519			−0.335341			−0.167670	−	0.985843i	$-0.553624\pi$
$401$	−6.71519			−0.335341			−0.167670	+	0.985843i	$0.553624\pi$
$402$	−0.410623	−	2.39517i	−0.0204800	−	0.119460i
$403$	7.54746	−	7.54746i	0.375966	−	0.375966i
$404$	−16.4158	+	5.79903i	−0.816716	+	0.288513i
$405$	−7.40326	+	10.1177i	−0.367871	+	0.502753i
$406$	2.92279	+	2.06730i	0.145056	+	0.102598i
$407$	10.7690	+	10.7690i	0.533798	+	0.533798i
$408$	−4.59703	+	2.56755i	−0.227587	+	0.127113i
$409$			11.4935i			0.568315i	0.958778	+	0.284158i	$0.0917139\pi$
$409$			11.4935i			0.568315i	−0.958778	+	0.284158i	$0.908286\pi$
$410$	−2.83089	−	1.40929i	−0.139807	−	0.0695997i
$411$			2.31777i			0.114327i
$412$	−16.4595	+	34.4405i	−0.810903	+	1.69676i
$413$	0.861181	+	0.861181i	0.0423759	+	0.0423759i
$414$	12.3273	−	17.4286i	0.605854	−	0.856569i
$415$	−2.17811	−	14.0591i	−0.106919	−	0.690133i
$416$	0.418842	+	6.58280i	0.0205354	+	0.322748i
$417$	4.41434	−	4.41434i	0.216171	−	0.216171i
$418$	6.40535	−	1.09812i	0.313296	−	0.0537109i
$419$	−28.7599			−1.40501			−0.702506	−	0.711678i	$-0.747935\pi$
$419$	−28.7599			−1.40501			−0.702506	+	0.711678i	$0.747935\pi$
$420$	−0.199130	+	0.662173i	−0.00971653	+	0.0323107i
$421$	13.1093			0.638908			0.319454	−	0.947602i	$-0.396501\pi$
$421$	13.1093			0.638908			0.319454	+	0.947602i	$0.396501\pi$
$422$	−20.3026	+	3.48064i	−0.988315	+	0.169435i
$423$	−5.80547	+	5.80547i	−0.282272	+	0.282272i
$424$	8.15752	−	28.7981i	0.396164	−	1.39856i
$425$	−13.1619	−	6.81864i	−0.638445	−	0.330752i
$426$	7.53699	−	10.6560i	0.365168	−	0.516283i
$427$	2.31091	+	2.31091i	0.111833	+	0.111833i
$428$	−29.6963	−	14.1923i	−1.43543	−	0.686008i
$429$		−	2.35062i		−	0.113489i
$430$	−27.2512	+	9.13648i	−1.31417	+	0.440600i
$431$			23.4303i			1.12860i	0.825570	+	0.564299i	$0.190854\pi$
$431$			23.4303i			1.12860i	−0.825570	+	0.564299i	$0.809146\pi$
$432$	−14.0007	−	1.49316i	−0.673610	−	0.0718395i
$433$	0.585428	+	0.585428i	0.0281339	+	0.0281339i	0.721034	−	0.692900i	$-0.243667\pi$
$433$	0.585428	+	0.585428i	0.0281339	+	0.0281339i	−0.692900	+	0.721034i	$0.743667\pi$
$434$	−2.60238	−	1.84067i	−0.124918	−	0.0883550i
$435$	14.2653	−	2.21007i	0.683970	−	0.105965i
$436$	−6.71450	−	19.0073i	−0.321566	−	0.910283i
$437$	−5.86355	+	5.86355i	−0.280492	+	0.280492i
$438$	1.21814	+	7.10539i	0.0582048	+	0.339509i
$439$	15.7422			0.751333			0.375666	−	0.926755i	$-0.377414\pi$
$439$	15.7422			0.751333			0.375666	+	0.926755i	$0.377414\pi$
$440$	2.47762	−	20.1523i	0.118116	−	0.960723i
$441$	18.0819			0.861041
$442$	0.826075	+	4.81849i	0.0392924	+	0.229192i
$443$	−18.2559	+	18.2559i	−0.867365	+	0.867365i	−0.992180	−	0.124815i	$-0.960166\pi$
$443$	−18.2559	+	18.2559i	−0.867365	+	0.867365i	0.124815	+	0.992180i	$0.460166\pi$
$444$	1.98446	+	5.61757i	0.0941782	+	0.266598i
$445$	23.2753	+	17.0308i	1.10335	+	0.807339i
$446$	−17.5621	−	12.4217i	−0.831589	−	0.588185i
$447$	1.83762	+	1.83762i	0.0869164	+	0.0869164i
$448$	1.91645	−	0.455459i	0.0905438	−	0.0215184i
$449$			35.3802i			1.66969i	0.550483	+	0.834846i	$0.314444\pi$
$449$			35.3802i			1.66969i	−0.550483	+	0.834846i	$0.685556\pi$
$450$	−8.46243	−	16.3667i	−0.398923	−	0.771534i
$451$		−	3.21035i		−	0.151169i
$452$	−13.7199	−	6.55694i	−0.645331	−	0.308412i
$453$	−0.876433	−	0.876433i	−0.0411784	−	0.0411784i
$454$	−4.84793	+	6.85411i	−0.227525	+	0.321679i
$455$	0.518114	+	0.379111i	0.0242895	+	0.0177730i
$456$	2.44606	+	0.692886i	0.114547	+	0.0324474i
$457$	−25.4449	+	25.4449i	−1.19026	+	1.19026i	−0.213269	+	0.976993i	$0.568411\pi$
$457$	−25.4449	+	25.4449i	−1.19026	+	1.19026i	−0.976993	+	0.213269i	$0.931589\pi$
$458$	20.7211	−	3.55240i	0.968235	−	0.165993i
$459$	−10.4357			−0.487095
$460$	12.2676	+	22.8189i	0.571981	+	1.06394i
$461$	12.3168			0.573651			0.286826	−	0.957983i	$-0.407400\pi$
$461$	12.3168			0.573651			0.286826	+	0.957983i	$0.407400\pi$
$462$	−0.691884	+	0.118615i	−0.0321893	+	0.00551849i
$463$	17.2051	−	17.2051i	0.799588	−	0.799588i	−0.183442	−	0.983031i	$-0.558724\pi$
$463$	17.2051	−	17.2051i	0.799588	−	0.799588i	0.983031	+	0.183442i	$0.0587240\pi$
$464$	−25.8310	−	31.9984i	−1.19917	−	1.48549i
$465$	−12.7015	+	1.96779i	−0.589018	+	0.0912540i
$466$	−5.66690	+	8.01199i	−0.262514	+	0.371148i
$467$	−14.3518	−	14.3518i	−0.664121	−	0.664121i	0.292228	−	0.956349i	$-0.405603\pi$
$467$	−14.3518	−	14.3518i	−0.664121	−	0.664121i	−0.956349	+	0.292228i	$0.905603\pi$
$468$	−2.62026	+	5.48272i	−0.121122	+	0.253439i
$469$			0.673802i			0.0311133i
$470$	−3.16732	−	9.44709i	−0.146097	−	0.435762i
$471$			7.61068i			0.350682i
$472$	−6.82180	−	12.2140i	−0.313999	−	0.562194i
$473$	−20.6326	−	20.6326i	−0.948690	−	0.948690i
$474$	−5.25959	−	3.72013i	−0.241581	−	0.170871i
$475$	2.16565	+	6.82156i	0.0993668	+	0.312995i
$476$	1.37659	−	0.486295i	0.0630961	−	0.0222893i
$477$	19.4979	−	19.4979i	0.892746	−	0.892746i
$478$	5.49592	+	32.0577i	0.251377	+	1.46628i
$479$	−9.98039			−0.456016			−0.228008	−	0.973659i	$-0.573221\pi$
$479$	−9.98039			−0.456016			−0.228008	+	0.973659i	$0.573221\pi$
$480$	4.27387	−	6.69501i	0.195075	−	0.305584i
$481$	5.53159			0.252219
$482$	−1.95849	−	11.4239i	−0.0892067	−	0.520342i
$483$	0.633361	−	0.633361i	0.0288189	−	0.0288189i
$484$	−1.30808	+	0.462092i	−0.0594582	+	0.0210042i
$485$	−1.95712	−	12.6327i	−0.0888684	−	0.573620i
$486$	−16.2576	−	11.4990i	−0.737458	−	0.521606i
$487$	−22.3208	−	22.3208i	−1.01145	−	1.01145i	−0.999934	−	0.0115187i	$-0.996333\pi$
$487$	−22.3208	−	22.3208i	−1.01145	−	1.01145i	−0.0115187	−	0.999934i	$-0.503667\pi$
$488$	−18.3058	−	32.7753i	−0.828664	−	1.48367i
$489$		−	8.60593i		−	0.389174i
$490$	−9.77957	+	19.6446i	−0.441796	+	0.887451i
$491$			1.76687i			0.0797376i	0.999205	+	0.0398688i	$0.0126940\pi$
$491$			1.76687i			0.0797376i	−0.999205	+	0.0398688i	$0.987306\pi$
$492$	0.541534	−	1.13312i	0.0244143	−	0.0510851i
$493$	−21.5520	−	21.5520i	−0.970655	−	0.970655i
$494$	1.36305	−	1.92711i	0.0613267	−	0.0867050i
$495$	11.0456	−	15.0956i	0.496464	−	0.678495i
$496$	22.9993	+	28.4906i	1.03270	+	1.27927i
$497$	−2.55900	+	2.55900i	−0.114787	+	0.114787i
$498$	5.56883	−	0.954712i	0.249545	−	0.0427817i
$499$	−20.2452			−0.906301			−0.453151	−	0.891434i	$-0.649700\pi$
$499$	−20.2452			−0.906301			−0.453151	+	0.891434i	$0.649700\pi$
$500$	22.3581	−	0.341855i	0.999883	−	0.0152882i
$501$	−13.8993			−0.620977
$502$	18.1707	−	3.11515i	0.810997	−	0.139036i
$503$	19.0974	−	19.0974i	0.851512	−	0.851512i	−0.138807	−	0.990319i	$-0.544327\pi$
$503$	19.0974	−	19.0974i	0.851512	−	0.851512i	0.990319	+	0.138807i	$0.0443268\pi$
$504$	1.74601	+	0.494585i	0.0777735	+	0.0220306i
$505$	11.4943	−	15.7087i	0.511490	−	0.699030i
$506$	−15.1879	+	21.4730i	−0.675184	+	0.954590i
$507$	5.16855	+	5.16855i	0.229543	+	0.229543i
$508$	−20.0128	−	9.56438i	−0.887924	−	0.424351i
$509$		−	15.5738i		−	0.690296i	−0.938548	−	0.345148i	$-0.887829\pi$
$509$		−	15.5738i		−	0.690296i	0.938548	−	0.345148i	$-0.112171\pi$
$510$	2.62356	−	5.27003i	0.116173	−	0.233361i
$511$		−	1.99887i		−	0.0884248i
$512$	−22.6068	−	0.966026i	−0.999088	−	0.0426927i
$513$	3.56285	+	3.56285i	0.157303	+	0.157303i
$514$	0.214161	+	0.151477i	0.00944623	+	0.00668135i
$515$	−6.53382	−	42.1739i	−0.287914	−	1.85840i
$516$	−3.80209	−	10.7629i	−0.167378	−	0.473809i
$517$	7.15265	−	7.15265i	0.314573	−	0.314573i
$518$	−0.279131	−	1.62817i	−0.0122643	−	0.0715378i
$519$	4.33643			0.190348
$520$	−4.53939	−	5.81204i	−0.199065	−	0.254875i
$521$	31.9484			1.39969			0.699843	−	0.714297i	$-0.253253\pi$
$521$	31.9484			1.39969			0.699843	+	0.714297i	$0.253253\pi$
$522$	−6.40156	−	37.3403i	−0.280189	−	1.63434i
$523$	0.555159	−	0.555159i	0.0242754	−	0.0242754i	−0.694865	−	0.719140i	$-0.744536\pi$
$523$	0.555159	−	0.555159i	0.0242754	−	0.0242754i	0.719140	+	0.694865i	$0.244536\pi$
$524$	−7.06200	−	19.9910i	−0.308505	−	0.873309i
$525$	−0.233926	−	0.736841i	−0.0102094	−	0.0321584i
$526$	34.0507	+	24.0842i	1.48468	+	1.05012i
$527$	19.1894	+	19.1894i	0.835904	+	0.835904i
$528$	8.01814	+	0.855122i	0.348945	+	0.0372144i
$529$		−	10.5599i		−	0.459125i
$530$	10.6375	+	31.7283i	0.462065	+	1.37819i
$531$		−	12.8882i		−	0.559302i
$532$	−0.636010	−	0.303958i	−0.0275745	−	0.0131782i
$533$	−0.824514	−	0.824514i	−0.0357136	−	0.0357136i
$534$	−6.61413	+	9.35121i	−0.286222	+	0.404666i
$535$	36.3645	−	5.63379i	1.57217	−	0.243570i
$536$	2.10947	−	7.44695i	0.0911151	−	0.321659i
$537$	−9.08967	+	9.08967i	−0.392248	+	0.392248i
$538$	−13.2296	+	2.26806i	−0.570369	+	0.0977831i
$539$	−22.2778			−0.959573
$540$	13.8654	−	7.45413i	0.596670	−	0.320775i
$541$	27.4655			1.18084			0.590418	−	0.807098i	$-0.298963\pi$
$541$	27.4655			1.18084			0.590418	+	0.807098i	$0.298963\pi$
$542$	−12.5529	+	2.15205i	−0.539194	+	0.0924386i
$543$	−2.91349	+	2.91349i	−0.125030	+	0.125030i
$544$	−16.7368	+	1.06490i	−0.717582	+	0.0456574i
$545$	18.1886	+	13.3088i	0.779114	+	0.570088i
$546$	−0.147232	+	0.208160i	−0.00630096	+	0.00890844i
$547$	−13.9231	−	13.9231i	−0.595308	−	0.595308i	0.343752	−	0.939060i	$-0.388302\pi$
$547$	−13.9231	−	13.9231i	−0.595308	−	0.595308i	−0.939060	+	0.343752i	$0.888302\pi$
$548$	−3.18319	+	6.66060i	−0.135979	+	0.284527i
$549$		−	34.5847i		−	1.47604i
$550$	10.4262	+	20.1646i	0.444573	+	0.859823i
$551$			14.7162i			0.626930i
$552$	−8.98285	+	5.01713i	−0.382335	+	0.213543i
$553$	1.26308	+	1.26308i	0.0537114	+	0.0537114i
$554$	15.4452	+	10.9245i	0.656205	+	0.464136i
$555$	−5.37561	−	3.93341i	−0.228182	−	0.166964i
$556$	18.7481	−	6.62295i	0.795097	−	0.280876i
$557$	19.1303	−	19.1303i	0.810577	−	0.810577i	−0.174143	−	0.984720i	$-0.555716\pi$
$557$	19.1303	−	19.1303i	0.810577	−	0.810577i	0.984720	+	0.174143i	$0.0557155\pi$
$558$	5.69979	+	33.2469i	0.241292	+	1.40745i
$559$	−10.5982			−0.448254
$560$	−1.48166	+	1.62941i	−0.0626114	+	0.0688551i
$561$	5.97645			0.252326
$562$	−0.526591	−	3.07160i	−0.0222129	−	0.129568i
$563$	−7.52473	+	7.52473i	−0.317129	+	0.317129i	−0.847664	−	0.530534i	$-0.821991\pi$
$563$	−7.52473	+	7.52473i	−0.317129	+	0.317129i	0.530534	+	0.847664i	$0.321991\pi$
$564$	3.73113	−	1.31806i	0.157109	−	0.0555003i
$565$	16.8007	−	2.60286i	0.706810	−	0.109503i
$566$	−9.61679	−	6.80198i	−0.404224	−	0.285909i
$567$	0.976185	+	0.976185i	0.0409959	+	0.0409959i
$568$	36.2938	−	20.2709i	1.52285	−	0.850550i
$569$			28.7509i			1.20530i	0.798005	+	0.602651i	$0.205889\pi$
$569$			28.7509i			1.20530i	−0.798005	+	0.602651i	$0.794111\pi$
$570$	−2.69495	+	0.903534i	−0.112879	+	0.0378449i
$571$			31.6671i			1.32523i	0.748961	+	0.662614i	$0.230553\pi$
$571$			31.6671i			1.32523i	−0.748961	+	0.662614i	$0.769447\pi$
$572$	3.22830	−	6.75500i	0.134982	−	0.282441i
$573$	−1.02673	−	1.02673i	−0.0428924	−	0.0428924i
$574$	−0.201082	+	0.284294i	−0.00839300	+	0.0118662i
$575$	−25.7190	−	13.3240i	−1.07256	−	0.555649i
$576$	−17.7488	−	10.9324i	−0.739531	−	0.455519i
$577$	−33.3028	+	33.3028i	−1.38641	+	1.38641i	−0.553689	+	0.832723i	$0.686780\pi$
$577$	−33.3028	+	33.3028i	−1.38641	+	1.38641i	−0.832723	+	0.553689i	$0.813220\pi$
$578$	11.4449	−	1.96210i	0.476046	−	0.0816125i
$579$	−14.0408			−0.583516
$580$	44.0296	+	13.2407i	1.82823	+	0.549789i
$581$	−1.56661			−0.0649939
$582$	5.00383	−	0.857848i	0.207415	−	0.0355590i
$583$	−24.0224	+	24.0224i	−0.994906	+	0.994906i
$584$	−6.25785	+	22.0918i	−0.258952	+	0.914165i
$585$	−1.04015	−	6.71383i	−0.0430047	−	0.277583i
$586$	13.0128	−	18.3978i	0.537554	−	0.760005i
$587$	28.5386	+	28.5386i	1.17791	+	1.17791i	0.980275	+	0.197639i	$0.0633274\pi$
$587$	28.5386	+	28.5386i	1.17791	+	1.17791i	0.197639	+	0.980275i	$0.436673\pi$
$588$	−7.86316	−	3.75791i	−0.324271	−	0.154974i
$589$		−	13.1029i		−	0.539897i
$590$	14.0021	+	6.97060i	0.576457	+	0.286975i
$591$		−	4.86761i		−	0.200227i
$592$	−2.01231	+	18.8687i	−0.0827055	+	0.775497i
$593$	−17.1764	−	17.1764i	−0.705351	−	0.705351i	0.260203	−	0.965554i	$-0.416211\pi$
$593$	−17.1764	−	17.1764i	−0.705351	−	0.705351i	−0.965554	+	0.260203i	$0.916211\pi$
$594$	13.0475	+	9.22855i	0.535347	+	0.378652i
$595$	−0.963888	+	1.31730i	−0.0395156	+	0.0540042i
$596$	2.75703	+	7.80454i	0.112932	+	0.319686i
$597$	4.41544	−	4.41544i	0.180712	−	0.180712i
$598$	1.61419	+	9.41560i	0.0660093	+	0.385032i
$599$	35.1439			1.43594			0.717971	−	0.696073i	$-0.245071\pi$
$599$	35.1439			1.43594			0.717971	+	0.696073i	$0.245071\pi$
$600$	0.278558	+	8.87602i	0.0113721	+	0.362362i
$601$	15.9042			0.648744			0.324372	−	0.945930i	$-0.394847\pi$
$601$	15.9042			0.648744			0.324372	+	0.945930i	$0.394847\pi$
$602$	0.534797	+	3.11947i	0.0217967	+	0.127140i
$603$	5.04199	−	5.04199i	0.205326	−	0.205326i
$604$	−1.31493	−	3.72229i	−0.0535039	−	0.151458i
$605$	0.915914	−	1.25174i	0.0372372	−	0.0508904i
$606$	6.31124	+	4.46395i	0.256376	+	0.181336i
$607$	−14.0222	−	14.0222i	−0.569145	−	0.569145i	0.362744	−	0.931889i	$-0.381840\pi$
$607$	−14.0222	−	14.0222i	−0.569145	−	0.569145i	−0.931889	+	0.362744i	$0.881840\pi$
$608$	6.07767	+	5.35053i	0.246482	+	0.216993i
$609$		−	1.58959i		−	0.0644135i
$610$	37.5736	+	18.7051i	1.52131	+	0.757347i
$611$		−	3.67403i		−	0.148635i
$612$	−13.9398	−	6.66202i	−0.563483	−	0.269296i
$613$	9.95592	+	9.95592i	0.402116	+	0.402116i	0.878978	−	0.476862i	$-0.158226\pi$
$613$	9.95592	+	9.95592i	0.402116	+	0.402116i	−0.476862	+	0.878978i	$0.658226\pi$
$614$	21.7163	−	30.7029i	0.876397	−	1.23907i
$615$	0.214969	+	1.38756i	0.00866838	+	0.0559518i
$616$	−2.15118	−	0.609355i	−0.0866734	−	0.0245516i
$617$	13.6549	−	13.6549i	0.549727	−	0.549727i	−0.376635	−	0.926362i	$-0.622919\pi$
$617$	13.6549	−	13.6549i	0.549727	−	0.549727i	0.926362	+	0.376635i	$0.122919\pi$
$618$	16.7052	−	2.86391i	0.671981	−	0.115203i
$619$	29.4712			1.18455			0.592274	−	0.805737i	$-0.298230\pi$
$619$	29.4712			1.18455			0.592274	+	0.805737i	$0.298230\pi$
$620$	−39.2029	−	11.7892i	−1.57443	−	0.473464i
$621$	−20.3919			−0.818297
$622$	25.7955	−	4.42234i	1.03431	−	0.177320i
$623$	2.24566	−	2.24566i	0.0899706	−	0.0899706i
$624$	2.27892	−	1.83968i	0.0912298	−	0.0736460i
$625$	−20.4220	+	14.4202i	−0.816880	+	0.576807i
$626$	4.89405	−	6.91931i	0.195606	−	0.276551i
$627$	−2.04042	−	2.04042i	−0.0814866	−	0.0814866i
$628$	−10.4524	+	21.8709i	−0.417095	+	0.872743i
$629$			14.0641i			0.560771i
$630$	−1.92367	+	0.644947i	−0.0766408	+	0.0256953i
$631$		−	0.607461i		−	0.0241826i	−0.999927	−	0.0120913i	$-0.996151\pi$
$631$		−	0.607461i		−	0.0241826i	0.999927	−	0.0120913i	$-0.00384888\pi$
$632$	−10.0054	−	17.9140i	−0.397993	−	0.712580i
$633$	6.46739	+	6.46739i	0.257056	+	0.257056i
$634$	−31.9411	−	22.5920i	−1.26854	−	0.897244i
$635$	24.5066	−	3.79670i	0.972513	−	0.150667i
$636$	−12.5311	+	4.42674i	−0.496891	+	0.175532i
$637$	−5.72161	+	5.72161i	−0.226698	+	0.226698i
$638$	7.88706	+	46.0052i	0.312252	+	1.82136i
$639$	38.2974			1.51502
$640$	21.4767	−	13.3698i	0.848940	−	0.528490i
$641$	32.1254			1.26888			0.634439	−	0.772973i	$-0.281231\pi$
$641$	32.1254			1.26888			0.634439	+	0.772973i	$0.281231\pi$
$642$	2.46941	+	14.4040i	0.0974597	+	0.568482i
$643$	12.3190	−	12.3190i	0.485812	−	0.485812i	−0.421169	−	0.906982i	$-0.638380\pi$
$643$	12.3190	−	12.3190i	0.485812	−	0.485812i	0.906982	+	0.421169i	$0.138380\pi$
$644$	2.68994	−	0.950247i	0.105999	−	0.0374450i
$645$	10.2993	+	7.53614i	0.405535	+	0.296735i
$646$	4.89969	+	3.46556i	0.192776	+	0.136351i
$647$	6.50328	+	6.50328i	0.255670	+	0.255670i	0.823291	−	0.567620i	$-0.192136\pi$
$647$	6.50328	+	6.50328i	0.255670	+	0.255670i	−0.567620	+	0.823291i	$0.692136\pi$
$648$	−7.73279	−	13.8451i	−0.303773	−	0.543886i
$649$			15.8790i			0.623305i
$650$	7.85663	+	2.50113i	0.308162	+	0.0981025i
$651$			1.41533i			0.0554713i
$652$	11.8192	−	24.7309i	0.462877	−	0.968538i
$653$	−30.4496	−	30.4496i	−1.19159	−	1.19159i	−0.976622	−	0.214965i	$-0.931036\pi$
$653$	−30.4496	−	30.4496i	−1.19159	−	1.19159i	−0.214965	−	0.976622i	$-0.568964\pi$
$654$	−5.16866	+	7.30756i	−0.202110	+	0.285748i
$655$	19.1299	+	13.9976i	0.747469	+	0.546933i
$656$	3.11242	−	2.51253i	0.121520	−	0.0980979i
$657$	−14.9573	+	14.9573i	−0.583541	+	0.583541i
$658$	−1.08142	+	0.185396i	−0.0421580	+	0.00722750i
$659$	8.84426			0.344524			0.172262	−	0.985051i	$-0.444893\pi$
$659$	8.84426			0.344524			0.172262	+	0.985051i	$0.444893\pi$
$660$	−7.94062	+	4.26894i	−0.309088	+	0.166168i
$661$	−10.5395			−0.409938			−0.204969	−	0.978768i	$-0.565709\pi$
$661$	−10.5395			−0.409938			−0.204969	+	0.978768i	$0.565709\pi$
$662$	−1.31057	+	0.224682i	−0.0509368	+	0.00873252i
$663$	1.53493	−	1.53493i	0.0596117	−	0.0596117i
$664$	17.3144	+	4.90458i	0.671929	+	0.190335i
$665$	0.778823	−	0.120660i	0.0302015	−	0.00467898i
$666$	−10.0947	+	14.2722i	−0.391163	+	0.553035i
$667$	−42.1139	−	42.1139i	−1.63066	−	1.63066i
$668$	−39.9426	−	19.0891i	−1.54543	−	0.738580i
$669$			9.55134i			0.369276i
$670$	2.75078	+	8.20469i	0.106272	+	0.316975i
$671$			42.6101i			1.64495i
$672$	−0.656490	−	0.577946i	−0.0253246	−	0.0222948i
$673$	−5.01033	−	5.01033i	−0.193134	−	0.193134i	0.603915	−	0.797049i	$-0.293607\pi$
$673$	−5.01033	−	5.01033i	−0.193134	−	0.193134i	−0.797049	+	0.603915i	$0.793607\pi$
$674$	19.8111	+	14.0124i	0.763094	+	0.539739i
$675$	−8.09600	+	15.6276i	−0.311615	+	0.601505i
$676$	7.75450	+	21.9513i	0.298250	+	0.844280i
$677$	29.7725	−	29.7725i	1.14425	−	1.14425i	0.156584	−	0.987665i	$-0.449952\pi$
$677$	29.7725	−	29.7725i	1.14425	−	1.14425i	0.987665	−	0.156584i	$-0.0500481\pi$
$678$	1.14089	+	6.65479i	0.0438155	+	0.255576i
$679$	−1.40766			−0.0540212
$680$	14.7771	−	11.5414i	0.566676	−	0.442592i
$681$	3.72768			0.142845
$682$	−7.02245	−	40.9619i	−0.268903	−	1.56851i
$683$	7.93343	−	7.93343i	0.303564	−	0.303564i	−0.538842	−	0.842407i	$-0.681138\pi$
$683$	7.93343	−	7.93343i	0.303564	−	0.303564i	0.842407	+	0.538842i	$0.181138\pi$
$684$	2.48471	+	7.03368i	0.0950054	+	0.268939i
$685$	−1.26361	−	8.15621i	−0.0482799	−	0.311633i
$686$	3.96288	+	2.80296i	0.151304	+	0.107017i
$687$	−6.60072	−	6.60072i	−0.251833	−	0.251833i
$688$	3.85546	−	36.1511i	0.146988	−	1.37825i
$689$			12.3393i			0.470091i
$690$	5.12657	−	10.2979i	0.195165	−	0.392035i
$691$			36.1365i			1.37470i	0.726327	+	0.687349i	$0.241226\pi$
$691$			36.1365i			1.37470i	−0.726327	+	0.687349i	$0.758774\pi$
$692$	12.4616	+	5.95558i	0.473720	+	0.226397i
$693$	−1.45646	−	1.45646i	−0.0553264	−	0.0553264i
$694$	−5.55210	+	7.84969i	−0.210755	+	0.297970i
$695$	−13.1274	+	17.9406i	−0.497950	+	0.680526i
$696$	−4.97653	+	17.5684i	−0.188635	+	0.665928i
$697$	2.09632	−	2.09632i	0.0794040	−	0.0794040i
$698$	−23.7873	+	4.07806i	−0.900362	+	0.154357i
$699$	4.35741			0.164812
$700$	0.339730	−	2.43874i	0.0128406	−	0.0921756i
$701$	−23.1372			−0.873881			−0.436940	−	0.899490i	$-0.643938\pi$
$701$	−23.1372			−0.873881			−0.436940	+	0.899490i	$0.643938\pi$
$702$	5.72116	−	0.980827i	0.215931	−	0.0370189i
$703$	4.80162	−	4.80162i	0.181096	−	0.181096i
$704$	21.8674	+	13.4694i	0.824158	+	0.507645i
$705$	−2.61253	+	3.57043i	−0.0983936	+	0.134470i
$706$	−8.00534	+	11.3181i	−0.301285	+	0.425963i
$707$	−1.51562	−	1.51562i	−0.0570009	−	0.0570009i
$708$	−2.67853	+	5.60464i	−0.100665	+	0.210635i
$709$		−	12.7867i		−	0.480214i	−0.970746	−	0.240107i	$-0.922817\pi$
$709$		−	12.7867i		−	0.480214i	0.970746	−	0.240107i	$-0.0771825\pi$
$710$	−20.7131	+	41.6072i	−0.777349	+	1.56149i
$711$		−	18.9029i		−	0.708915i
$712$	−31.8499	+	17.7889i	−1.19362	+	0.666667i
$713$	37.4971	+	37.4971i	1.40428	+	1.40428i
$714$	−0.529247	−	0.374338i	−0.0198066	−	0.0140093i
$715$	1.28151	+	8.27180i	0.0479259	+	0.309348i
$716$	−38.6047	+	13.6375i	−1.44272	+	0.509656i
$717$	10.2120	−	10.2120i	0.381373	−	0.381373i
$718$	4.75762	+	27.7512i	0.177553	+	1.03567i
$719$	51.7741			1.93085			0.965424	−	0.260683i	$-0.0839478\pi$
$719$	51.7741			1.93085			0.965424	+	0.260683i	$0.0839478\pi$
$720$	23.2798	−	1.10562i	0.867586	−	0.0412040i
$721$	−4.69946			−0.175017
$722$	4.05070	+	23.6277i	0.150751	+	0.879332i
$723$	−3.63907	+	3.63907i	−0.135338	+	0.135338i
$724$	−12.3738	+	4.37118i	−0.459870	+	0.162453i
$725$	−48.9946	+	15.5544i	−1.81961	+	0.577675i
$726$	0.502906	+	0.355707i	0.0186646	+	0.0132015i
$727$	−10.3059	−	10.3059i	−0.382226	−	0.382226i	0.489677	−	0.871904i	$-0.337115\pi$
$727$	−10.3059	−	10.3059i	−0.382226	−	0.382226i	−0.871904	+	0.489677i	$0.837115\pi$
$728$	−0.708987	+	0.395986i	−0.0262768	+	0.0146762i
$729$		−	7.97829i		−	0.295492i
$730$	−8.16033	−	24.3397i	−0.302027	−	0.900851i
$731$		−	26.9458i		−	0.996626i
$732$	−7.18764	+	15.0396i	−0.265663	+	0.555881i
$733$	−2.85214	−	2.85214i	−0.105346	−	0.105346i	0.652469	−	0.757815i	$-0.273733\pi$
$733$	−2.85214	−	2.85214i	−0.105346	−	0.105346i	−0.757815	+	0.652469i	$0.773733\pi$
$734$	−10.3500	+	14.6331i	−0.382026	+	0.540117i
$735$	9.62880	−	1.49175i	0.355163	−	0.0550240i
$736$	−32.7045	+	2.08088i	−1.20550	+	0.0767023i
$737$	−6.21199	+	6.21199i	−0.228822	+	0.228822i
$738$	3.63202	−	0.622667i	0.133696	−	0.0229207i
$739$	−10.8253			−0.398216			−0.199108	−	0.979978i	$-0.563804\pi$
$739$	−10.8253			−0.398216			−0.199108	+	0.979978i	$0.563804\pi$
$740$	−10.0459	−	18.6862i	−0.369294	−	0.686920i
$741$	−1.04808			−0.0385023
$742$	3.63197	−	0.622659i	0.133334	−	0.0228585i
$743$	−2.81233	+	2.81233i	−0.103175	+	0.103175i	−0.756810	−	0.653635i	$-0.773243\pi$
$743$	−2.81233	+	2.81233i	−0.103175	+	0.103175i	0.653635	+	0.756810i	$0.273243\pi$
$744$	4.43098	−	15.6425i	0.162448	−	0.573481i
$745$	−7.46839	−	5.46472i	−0.273621	−	0.200212i
$746$	3.89237	−	5.50312i	0.142510	−	0.201484i
$747$	11.7228	+	11.7228i	0.428914	+	0.428914i
$748$	17.1746	+	8.20795i	0.627965	+	0.300112i
$749$		−	4.05211i		−	0.148061i
$750$	−5.85658	−	8.01731i	−0.213852	−	0.292751i
$751$		−	43.4783i		−	1.58654i	−0.608867	−	0.793272i	$-0.708376\pi$
$751$		−	43.4783i		−	1.58654i	0.608867	−	0.793272i	$-0.291624\pi$
$752$	12.5324	+	1.33656i	0.457009	+	0.0487393i
$753$	−5.78827	−	5.78827i	−0.210936	−	0.210936i
$754$	13.8411	+	9.78988i	0.504065	+	0.356526i
$755$	3.56197	+	2.60634i	0.129633	+	0.0948544i
$756$	−0.577395	−	1.63448i	−0.0209996	−	0.0594454i
$757$	21.7051	−	21.7051i	0.788887	−	0.788887i	−0.192425	−	0.981312i	$-0.561635\pi$
$757$	21.7051	−	21.7051i	0.788887	−	0.788887i	0.981312	+	0.192425i	$0.0616351\pi$
$758$	−2.00030	−	11.6678i	−0.0726543	−	0.423792i
$759$	11.6783			0.423896
$760$	−8.98541	−	1.10471i	−0.325935	−	0.0400720i
$761$	20.7761			0.753132			0.376566	−	0.926390i	$-0.377105\pi$
$761$	20.7761			0.753132			0.376566	+	0.926390i	$0.377105\pi$
$762$	1.66417	+	9.70711i	0.0602866	+	0.351651i
$763$	1.75489	−	1.75489i	0.0635312	−	0.0635312i
$764$	−1.54044	−	4.36063i	−0.0557310	−	0.157762i
$765$	17.0699	−	2.64457i	0.617164	−	0.0956146i
$766$	6.42122	+	4.54174i	0.232008	+	0.164100i
$767$	4.07820	+	4.07820i	0.147255	+	0.147255i
$768$	5.44624	+	8.44281i	0.196524	+	0.304654i
$769$			11.0693i			0.399169i	0.979881	+	0.199584i	$0.0639592\pi$
$769$			11.0693i			0.399169i	−0.979881	+	0.199584i	$0.936041\pi$
$770$	2.37006	−	0.794608i	0.0854111	−	0.0286357i
$771$		−	0.116474i		−	0.00419470i
$772$	−40.3492	−	19.2834i	−1.45220	−	0.694025i
$773$	−11.9761	−	11.9761i	−0.430750	−	0.430750i	0.458134	−	0.888883i	$-0.348518\pi$
$773$	−11.9761	−	11.9761i	−0.430750	−	0.430750i	−0.888883	+	0.458134i	$0.848518\pi$
$774$	19.3408	−	27.3445i	0.695192	−	0.982877i
$775$	43.6236	−	13.8492i	1.56700	−	0.497479i
$776$	15.5577	+	4.40696i	0.558489	+	0.158201i
$777$	−0.518654	+	0.518654i	−0.0186066	+	0.0186066i
$778$	26.1170	−	4.47745i	0.936339	−	0.160525i
$779$	−1.43141			−0.0512857
$780$	−0.942997	+	3.13578i	−0.0337647	+	0.112279i
$781$	−47.1844			−1.68839
$782$	−23.9391	+	4.10409i	−0.856062	+	0.146762i
$783$	−25.5895	+	25.5895i	−0.914493	+	0.914493i
$784$	−17.4354	−	21.5983i	−0.622693	−	0.771367i
$785$	−4.14920	−	26.7819i	−0.148091	−	0.955886i
$786$	−5.43615	+	7.68575i	−0.193901	+	0.274142i
$787$	5.47919	+	5.47919i	0.195312	+	0.195312i	0.797987	−	0.602675i	$-0.205898\pi$
$787$	5.47919	+	5.47919i	0.195312	+	0.195312i	−0.602675	+	0.797987i	$0.705898\pi$
$788$	6.68509	−	13.9881i	0.238147	−	0.498305i
$789$		−	18.5189i		−	0.659289i
$790$	20.5366	+	10.2236i	0.730658	+	0.363740i
$791$		−	1.87211i		−	0.0665645i
$792$	11.5373	+	20.6568i	0.409960	+	0.734006i
$793$	10.9435	+	10.9435i	0.388617	+	0.388617i
$794$	−22.6479	−	16.0189i	−0.803745	−	0.568491i
$795$	8.77426	−	11.9914i	0.311191	−	0.425291i
$796$	18.7528	−	6.62460i	0.664674	−	0.234803i
$797$	−24.4902	+	24.4902i	−0.867488	+	0.867488i	−0.992194	−	0.124706i	$-0.960201\pi$
$797$	−24.4902	+	24.4902i	−0.867488	+	0.867488i	0.124706	+	0.992194i	$0.460201\pi$
$798$	0.0528876	+	0.308494i	0.00187220	+	0.0109206i
$799$	9.34121			0.330468
$800$	−11.3897	+	25.8897i	−0.402686	+	0.915338i
$801$	−33.6081			−1.18749
$802$	1.60469	+	9.36016i	0.0566636	+	0.330519i
$803$	18.4282	−	18.4282i	0.650318	−	0.650318i
$804$	−3.24044	+	1.14472i	−0.114282	+	0.0403711i
$805$	−1.88349	+	2.57408i	−0.0663843	+	0.0907245i
$806$	−12.3238	−	8.71667i	−0.434088	−	0.307031i
$807$	4.21429	+	4.21429i	0.148350	+	0.148350i
$808$	12.0059	+	21.4958i	0.422367	+	0.756221i
$809$		−	12.9934i		−	0.456822i	−0.973565	−	0.228411i	$-0.926647\pi$
$809$		−	12.9934i		−	0.456822i	0.973565	−	0.228411i	$-0.0733531\pi$
$810$	15.8720	+	7.90147i	0.557684	+	0.277629i
$811$		−	31.6512i		−	1.11142i	−0.831375	−	0.555711i	$-0.812446\pi$
$811$		−	31.6512i		−	1.11142i	0.831375	−	0.555711i	$-0.187554\pi$
$812$	2.18312	−	4.56802i	0.0766124	−	0.160306i
$813$	3.99873	+	3.99873i	0.140242	+	0.140242i
$814$	12.4372	−	17.5840i	0.435925	−	0.616320i
$815$	4.69179	+	30.2841i	0.164346	+	1.06081i
$816$	4.67738	+	5.79415i	0.163741	+	0.202836i
$817$	−9.19957	+	9.19957i	−0.321852	+	0.321852i
$818$	16.0205	−	2.74653i	0.560143	−	0.0960301i
$819$	−0.748126			−0.0261416
$820$	−1.28789	+	4.28268i	−0.0449752	+	0.149558i
$821$	22.9741			0.801802			0.400901	−	0.916121i	$-0.368697\pi$
$821$	22.9741			0.801802			0.400901	+	0.916121i	$0.368697\pi$
$822$	3.23069	−	0.553865i	0.112683	−	0.0193183i
$823$	13.4369	−	13.4369i	0.468381	−	0.468381i	−0.433009	−	0.901390i	$-0.642548\pi$
$823$	13.4369	−	13.4369i	0.468381	−	0.468381i	0.901390	+	0.433009i	$0.142548\pi$
$824$	51.9390	+	14.7126i	1.80938	+	0.512536i
$825$	4.63654	−	8.94981i	0.161423	−	0.311593i
$826$	0.994590	−	1.40617i	0.0346062	−	0.0489270i
$827$	2.77222	+	2.77222i	0.0963996	+	0.0963996i	0.753662	−	0.657262i	$-0.228286\pi$
$827$	2.77222	+	2.77222i	0.0963996	+	0.0963996i	−0.657262	+	0.753662i	$0.728286\pi$
$828$	−27.2391	−	13.0179i	−0.946626	−	0.452405i
$829$			42.0604i			1.46082i	0.683010	+	0.730409i	$0.260671\pi$
$829$			42.0604i			1.46082i	−0.683010	+	0.730409i	$0.739329\pi$
$830$	−19.0762	+	6.39564i	−0.662143	+	0.221996i
$831$		−	8.40006i		−	0.291395i
$832$	9.07553	−	2.15687i	0.314637	−	0.0747759i
$833$	−14.5472	−	14.5472i	−0.504030	−	0.504030i
$834$	−7.20792	−	5.09818i	−0.249590	−	0.176536i
$835$	48.9116	−	7.57766i	1.69265	−	0.262236i
$836$	−3.06130	−	8.66586i	−0.105877	−	0.299715i
$837$	22.7842	−	22.7842i	0.787539	−	0.787539i
$838$	6.87258	+	40.0877i	0.237409	+	1.38481i
$839$	9.55496			0.329874			0.164937	−	0.986304i	$-0.447258\pi$
$839$	9.55496			0.329874			0.164937	+	0.986304i	$0.447258\pi$
$840$	0.970573	+	0.119327i	0.0334879	+	0.00411717i
$841$	−76.6962			−2.64470
$842$	−3.13265	−	18.2728i	−0.107958	−	0.629721i
$843$	−0.978458	+	0.978458i	−0.0336999	+	0.0336999i
$844$	9.70319	+	27.4676i	0.333997	+	0.945473i
$845$	−21.0058	−	15.3702i	−0.722623	−	0.528752i
$846$	9.47943	+	6.70482i	0.325909	+	0.230517i
$847$	−0.120771	−	0.120771i	−0.00414975	−	0.00414975i
$848$	−42.0904	−	4.48887i	−1.44539	−	0.154148i
$849$			5.23020i			0.179500i
$850$	−6.35913	+	19.9755i	−0.218116	+	0.685153i
$851$			27.4819i			0.942069i
$852$	−16.6542	−	7.95925i	−0.570563	−	0.272679i
$853$	17.7565	+	17.7565i	0.607969	+	0.607969i	0.942415	−	0.334446i	$-0.108549\pi$
$853$	17.7565	+	17.7565i	0.607969	+	0.607969i	−0.334446	+	0.942415i	$0.608549\pi$
$854$	2.66891	−	3.77336i	0.0913281	−	0.129122i
$855$	−6.73073	−	4.92496i	−0.230186	−	0.168430i
$856$	−12.6859	+	44.7845i	−0.433596	+	1.53070i
$857$	12.6998	−	12.6998i	0.433819	−	0.433819i	−0.456107	−	0.889925i	$-0.650756\pi$
$857$	12.6998	−	12.6998i	0.433819	−	0.433819i	0.889925	+	0.456107i	$0.150756\pi$
$858$	−3.27648	+	0.561714i	−0.111857	+	0.0191766i
$859$	1.28821			0.0439532			0.0219766	−	0.999758i	$-0.493004\pi$
$859$	1.28821			0.0439532			0.0219766	+	0.999758i	$0.493004\pi$
$860$	19.2472	+	35.8016i	0.656324	+	1.22082i
$861$	0.154617			0.00526932
$862$	32.6590	−	5.59901i	1.11237	−	0.190703i
$863$	−2.72289	+	2.72289i	−0.0926882	+	0.0926882i	−0.751931	−	0.659242i	$-0.770877\pi$
$863$	−2.72289	+	2.72289i	−0.0926882	+	0.0926882i	0.659242	+	0.751931i	$0.270877\pi$
$864$	1.26440	+	19.8721i	0.0430157	+	0.676063i
$865$	−15.2598	+	2.36414i	−0.518850	+	0.0803832i
$866$	0.676119	−	0.955912i	0.0229755	−	0.0324832i
$867$	−3.64578	−	3.64578i	−0.123817	−	0.123817i
$868$	−1.94380	+	4.06726i	−0.0659767	+	0.138052i
$869$			23.2894i			0.790039i
$870$	−6.48946	−	19.3560i	−0.220013	−	0.656230i
$871$			3.19085i			0.108118i
$872$	−24.8893	+	13.9012i	−0.842857	+	0.470756i
$873$	10.5334	+	10.5334i	0.356501	+	0.356501i
$874$	9.57425	+	6.77189i	0.323854	+	0.229063i
$875$	1.22489	+	2.46540i	0.0414090	+	0.0833458i
$876$	9.61296	−	3.39587i	0.324792	−	0.114736i
$877$	−14.8823	+	14.8823i	−0.502539	+	0.502539i	−0.912226	−	0.409687i	$-0.865638\pi$
$877$	−14.8823	+	14.8823i	−0.502539	+	0.502539i	0.409687	+	0.912226i	$0.365638\pi$
$878$	−3.76181	−	21.9427i	−0.126955	−	0.740529i
$879$	−10.0058			−0.337488
$880$	−28.6819	+	1.36218i	−0.966867	+	0.0459191i
$881$	14.2219			0.479146			0.239573	−	0.970878i	$-0.422993\pi$
$881$	14.2219			0.479146			0.239573	+	0.970878i	$0.422993\pi$
$882$	−4.32092	−	25.2039i	−0.145493	−	0.848660i
$883$	−10.7554	+	10.7554i	−0.361948	+	0.361948i	−0.864530	−	0.502582i	$-0.832384\pi$
$883$	−10.7554	+	10.7554i	−0.361948	+	0.361948i	0.502582	+	0.864530i	$0.332384\pi$
$884$	6.51899	−	2.30289i	0.219257	−	0.0774547i
$885$	−1.06328	−	6.86313i	−0.0357416	−	0.230702i
$886$	29.8090	+	21.0840i	1.00145	+	0.708331i
$887$	−28.8889	−	28.8889i	−0.969993	−	0.969993i	0.0295696	−	0.999563i	$-0.490586\pi$
$887$	−28.8889	−	28.8889i	−0.969993	−	0.969993i	−0.999563	+	0.0295696i	$0.990586\pi$
$888$	7.35599	−	4.10849i	0.246851	−	0.137872i
$889$		−	2.73078i		−	0.0915874i
$890$	18.1769	−	36.5127i	0.609292	−	1.22391i
$891$			17.9995i			0.603007i
$892$	−13.1176	+	27.4478i	−0.439211	+	0.919019i
$893$	−3.18919	−	3.18919i	−0.106722	−	0.106722i
$894$	2.12229	−	3.00054i	0.0709801	−	0.100353i
$895$	27.0309	−	36.9419i	0.903543	−	1.23483i
$896$	−1.09282	−	2.56246i	−0.0365085	−	0.0856058i
$897$	2.99934	−	2.99934i	0.100145	−	0.100145i
$898$	49.3156	−	8.45459i	1.64568	−	0.282133i
$899$	94.1094			3.13872
$900$	−20.7910	+	15.7066i	−0.693033	+	0.523555i
$901$	−31.3727			−1.04518
$902$	−4.47484	+	0.767159i	−0.148996	+	0.0255436i
$903$	0.993707	−	0.993707i	0.0330685	−	0.0330685i
$904$	−5.86099	+	20.6908i	−0.194934	+	0.688165i
$905$	8.66413	−	11.8409i	0.288005	−	0.393604i
$906$	−1.01220	+	1.43108i	−0.0336282	+	0.0475443i
$907$	3.58310	+	3.58310i	0.118975	+	0.118975i	0.764087	−	0.645113i	$-0.223190\pi$
$907$	3.58310	+	3.58310i	0.118975	+	0.118975i	−0.645113	+	0.764087i	$0.723190\pi$
$908$	10.7123	+	5.11954i	0.355499	+	0.169898i
$909$			22.6825i			0.752331i
$910$	0.404623	−	0.812781i	0.0134131	−	0.0269434i
$911$		−	27.5406i		−	0.912462i	−0.889861	−	0.456231i	$-0.849199\pi$
$911$		−	27.5406i		−	0.912462i	0.889861	−	0.456231i	$-0.150801\pi$
$912$	0.381277	−	3.57509i	0.0126254	−	0.118383i
$913$	−14.4431	−	14.4431i	−0.477996	−	0.477996i
$914$	41.5475	+	29.3867i	1.37427	+	0.972025i
$915$	−2.85322	−	18.4167i	−0.0943246	−	0.608838i
$916$	−9.90322	−	28.0338i	−0.327212	−	0.926264i
$917$	1.84571	−	1.84571i	0.0609507	−	0.0609507i
$918$	2.49375	+	14.5460i	0.0823060	+	0.480091i
$919$	−53.7650			−1.77354			−0.886772	−	0.462207i	$-0.847058\pi$
$919$	−53.7650			−1.77354			−0.886772	+	0.462207i	$0.847058\pi$
$920$	28.8753	−	22.5525i	0.951989	−	0.743533i
$921$	−16.6981			−0.550222
$922$	−2.94328	−	17.1681i	−0.0969317	−	0.565402i
$923$	−12.1184	+	12.1184i	−0.398881	+	0.398881i
$924$	0.330671	+	0.936057i	0.0108783	+	0.0307940i
$925$	21.0611	+	10.9109i	0.692485	+	0.358749i
$926$	−28.0932	−	19.8704i	−0.923200	−	0.652982i
$927$	35.1655	+	35.1655i	1.15499	+	1.15499i
$928$	−38.4292	+	43.6518i	−1.26150	+	1.43294i
$929$		−	32.4323i		−	1.06407i	−0.846723	−	0.532034i	$-0.821428\pi$
$929$		−	32.4323i		−	1.06407i	0.846723	−	0.532034i	$-0.178572\pi$
$930$	5.77806	+	17.2341i	0.189470	+	0.565129i
$931$			9.93312i			0.325545i
$932$	12.5219	+	5.98439i	0.410169	+	0.196025i
$933$	−8.21716	−	8.21716i	−0.269018	−	0.269018i
$934$	−16.5751	+	23.4342i	−0.542353	+	0.766790i
$935$	−21.0310	+	3.25825i	−0.687788	+	0.106556i
$936$	8.26839	+	2.34215i	0.270261	+	0.0765557i
$937$	−6.15885	+	6.15885i	−0.201201	+	0.201201i	−0.800514	−	0.599314i	$-0.795440\pi$
$937$	−6.15885	+	6.15885i	−0.201201	+	0.201201i	0.599314	+	0.800514i	$0.295440\pi$
$938$	0.939198	−	0.161015i	0.0306659	−	0.00525731i
$939$	−3.76314			−0.122806
$940$	−12.4112	+	6.67237i	−0.404809	+	0.217629i
$941$	−16.5330			−0.538960			−0.269480	−	0.963006i	$-0.586852\pi$
$941$	−16.5330			−0.538960			−0.269480	+	0.963006i	$0.586852\pi$
$942$	10.6084	−	1.81868i	0.345639	−	0.0592558i
$943$	4.09633	−	4.09633i	0.133395	−	0.133395i
$944$	−15.3946	+	12.4275i	−0.501053	+	0.404479i
$945$	1.56408	+	1.14446i	0.0508795	+	0.0372292i
$946$	−23.8289	+	33.6898i	−0.774745	+	1.09535i
$947$	15.8010	+	15.8010i	0.513463	+	0.513463i	0.915586	−	0.402123i	$-0.131728\pi$
$947$	15.8010	+	15.8010i	0.513463	+	0.513463i	−0.402123	+	0.915586i	$0.631728\pi$
$948$	−3.92855	+	8.22021i	−0.127593	+	0.266980i
$949$		−	9.46583i		−	0.307274i
$950$	8.99091	−	4.64876i	0.291704	−	0.150826i
$951$			17.3715i			0.563310i
$952$	−1.00679	−	1.80260i	−0.0326303	−	0.0584225i
$953$	−15.2139	−	15.2139i	−0.492827	−	0.492827i	0.416369	−	0.909196i	$-0.363303\pi$
$953$	−15.2139	−	15.2139i	−0.492827	−	0.492827i	−0.909196	+	0.416369i	$0.863303\pi$
$954$	−31.8369	−	22.5184i	−1.03076	−	0.729059i
$955$	4.17282	+	3.05331i	0.135029	+	0.0988027i
$956$	43.3712	−	15.3213i	1.40272	−	0.495526i
$957$	14.6550	−	14.6550i	0.473727	−	0.473727i
$958$	2.38496	+	13.9114i	0.0770544	+	0.449458i
$959$	−0.908850			−0.0293483
$960$	−10.3533	−	4.35738i	−0.334152	−	0.140634i
$961$	−52.7927			−1.70299
$962$	−1.32185	−	7.71036i	−0.0426182	−	0.248592i
$963$	−30.3215	+	30.3215i	−0.977097	+	0.977097i
$964$	−15.4555	+	5.45979i	−0.497787	+	0.175848i
$965$	49.4094	−	7.65479i	1.59054	−	0.246416i
$966$	−1.03418	−	0.731477i	−0.0332741	−	0.0235349i
$967$	−7.70992	−	7.70992i	−0.247934	−	0.247934i	0.572188	−	0.820122i	$-0.306095\pi$
$967$	−7.70992	−	7.70992i	−0.247934	−	0.247934i	−0.820122	+	0.572188i	$0.806095\pi$
$968$	0.956683	+	1.71288i	0.0307490	+	0.0550540i
$969$		−	2.66475i		−	0.0856041i
$970$	−17.1407	+	5.74675i	−0.550355	+	0.184517i
$971$			19.4308i			0.623563i	0.950154	+	0.311781i	$0.100926\pi$
$971$			19.4308i			0.623563i	−0.950154	+	0.311781i	$0.899074\pi$
$972$	−12.1433	+	25.4089i	−0.389495	+	0.814992i
$973$	1.73096	+	1.73096i	0.0554920	+	0.0554920i
$974$	−25.7786	+	36.4464i	−0.826000	+	1.16782i
$975$	−1.10778	−	3.48938i	−0.0354773	−	0.111750i
$976$	−41.3104	+	33.3482i	−1.32231	+	1.06745i
$977$	18.4063	−	18.4063i	0.588869	−	0.588869i	−0.348456	−	0.937325i	$-0.613294\pi$
$977$	18.4063	−	18.4063i	0.588869	−	0.588869i	0.937325	+	0.348456i	$0.113294\pi$
$978$	−11.9956	+	2.05651i	−0.383578	+	0.0657599i
$979$	41.4070			1.32337
$980$	29.7191	+	8.93717i	0.949342	+	0.285488i
$981$	−26.2633			−0.838522
$982$	2.46280	−	0.422218i	0.0785910	−	0.0134735i
$983$	7.65464	−	7.65464i	0.244145	−	0.244145i	−0.574417	−	0.818563i	$-0.694771\pi$
$983$	7.65464	−	7.65464i	0.244145	−	0.244145i	0.818563	+	0.574417i	$0.194771\pi$
$984$	−1.70884	−	0.484057i	−0.0544759	−	0.0154312i
$985$	2.65373	+	17.1290i	0.0845549	+	0.545777i
$986$	−24.8907	+	35.1911i	−0.792683	+	1.12071i
$987$	0.344485	+	0.344485i	0.0109651	+	0.0109651i
$988$	−3.01188	−	1.43942i	−0.0958208	−	0.0457940i
$989$		−	52.6535i		−	1.67428i
$990$	−23.6809	−	11.7890i	−0.752628	−	0.374677i
$991$			6.71556i			0.213327i	0.994295	+	0.106663i	$0.0340167\pi$
$991$			6.71556i			0.213327i	−0.994295	+	0.106663i	$0.965983\pi$
$992$	34.2164	−	38.8665i	1.08637	−	1.23401i
$993$	0.417482	+	0.417482i	0.0132484	+	0.0132484i
$994$	4.17844	+	2.95542i	0.132532	+	0.0937402i
$995$	−13.1306	+	17.9451i	−0.416270	+	0.568897i
$996$	−2.66150	−	7.53413i	−0.0843330	−	0.238728i
$997$	38.3857	−	38.3857i	1.21569	−	1.21569i	0.246562	−	0.969127i	$-0.420699\pi$
$997$	38.3857	−	38.3857i	1.21569	−	1.21569i	0.969127	−	0.246562i	$-0.0793008\pi$
$998$	4.83789	+	28.2194i	0.153141	+	0.893269i
$999$	16.6987			0.528325

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.k.c.83.20	✓	108
4.3	odd	2	inner	820.2.k.c.83.51	yes	108
5.2	odd	4	inner	820.2.k.c.247.51	yes	108
20.7	even	4	inner	820.2.k.c.247.20	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.k.c.83.20	✓	108	1.1	even	1	trivial
820.2.k.c.83.51	yes	108	4.3	odd	2	inner
820.2.k.c.247.20	yes	108	20.7	even	4	inner
820.2.k.c.247.51	yes	108	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.238964 - 1.39388i) q^{2} +(-0.444020 + 0.444020i) q^{3} +(-1.88579 + 0.666174i) q^{4} +(1.32043 - 1.80457i) q^{5} +(0.725014 + 0.512805i) q^{6} +(-0.174110 - 0.174110i) q^{7} +(1.37920 + 2.46937i) q^{8} +2.60569i q^{9} +(-2.83089 - 1.40929i) q^{10} -3.21035i q^{11} +(0.541534 - 1.13312i) q^{12} +(-0.824514 - 0.824514i) q^{13} +(-0.201082 + 0.284294i) q^{14} +(0.214969 + 1.38756i) q^{15} +(3.11242 - 2.51253i) q^{16} +(2.09632 - 2.09632i) q^{17} +(3.63202 - 0.622667i) q^{18} -1.43141 q^{19} +(-1.28789 + 4.28268i) q^{20} +0.154617 q^{21} +(-4.47484 + 0.767159i) q^{22} +(4.09633 - 4.09633i) q^{23} +(-1.70884 - 0.484057i) q^{24} +(-1.51294 - 4.76561i) q^{25} +(-0.952242 + 1.34630i) q^{26} +(-2.48904 - 2.48904i) q^{27} +(0.444323 + 0.212348i) q^{28} -10.2809i q^{29} +(1.88272 - 0.631218i) q^{30} +9.15383i q^{31} +(-4.24592 - 3.73793i) q^{32} +(1.42546 + 1.42546i) q^{33} +(-3.42297 - 2.42107i) q^{34} +(-0.544093 + 0.0842940i) q^{35} +(-1.73585 - 4.91380i) q^{36} +(-3.35446 + 3.35446i) q^{37} +(0.342057 + 1.99522i) q^{38} +0.732201 q^{39} +(6.27729 + 0.771760i) q^{40} +1.00000 q^{41} +(-0.0369478 - 0.215517i) q^{42} +(6.42691 - 6.42691i) q^{43} +(2.13865 + 6.05405i) q^{44} +(4.70215 + 3.44063i) q^{45} +(-6.68867 - 4.73091i) q^{46} +(2.22800 + 2.22800i) q^{47} +(-0.266364 + 2.49759i) q^{48} -6.93937i q^{49} +(-6.28113 + 3.24767i) q^{50} +1.86162i q^{51} +(2.10413 + 1.00559i) q^{52} +(-7.48279 - 7.48279i) q^{53} +(-2.87462 + 4.06421i) q^{54} +(-5.79330 - 4.23903i) q^{55} +(0.189809 - 0.670075i) q^{56} +(0.635576 - 0.635576i) q^{57} +(-14.3303 + 2.45676i) q^{58} -4.94619 q^{59} +(-1.32974 - 2.47344i) q^{60} -13.2727 q^{61} +(12.7593 - 2.18744i) q^{62} +(0.453677 - 0.453677i) q^{63} +(-4.19560 + 6.81153i) q^{64} +(-2.57660 + 0.399182i) q^{65} +(1.64628 - 2.32755i) q^{66} +(-1.93499 - 1.93499i) q^{67} +(-2.55672 + 5.34975i) q^{68} +3.63770i q^{69} +(0.247514 + 0.738256i) q^{70} -14.6976i q^{71} +(-6.43443 + 3.59378i) q^{72} +(5.74025 + 5.74025i) q^{73} +(5.47730 + 3.87411i) q^{74} +(2.78780 + 1.44425i) q^{75} +(2.69935 - 0.953571i) q^{76} +(-0.558954 + 0.558954i) q^{77} +(-0.174970 - 1.02060i) q^{78} -7.25447 q^{79} +(-0.424309 - 8.93420i) q^{80} -5.60671 q^{81} +(-0.238964 - 1.39388i) q^{82} +(4.49891 - 4.49891i) q^{83} +(-0.291575 + 0.103002i) q^{84} +(-1.01492 - 6.55101i) q^{85} +(-10.4941 - 7.42253i) q^{86} +(4.56491 + 4.56491i) q^{87} +(7.92755 - 4.42772i) q^{88} +12.8980i q^{89} +(3.67217 - 7.37642i) q^{90} +0.287112i q^{91} +(-4.99596 + 10.4537i) q^{92} +(-4.06448 - 4.06448i) q^{93} +(2.57314 - 3.63797i) q^{94} +(-1.89008 + 2.58309i) q^{95} +(3.54499 - 0.225556i) q^{96} +(4.04246 - 4.04246i) q^{97} +(-9.67264 + 1.65826i) q^{98} +8.36519 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 12 q^{2} - 4 q^{6} - 24 q^{8} + 4 q^{10} - 16 q^{13} + 52 q^{16} - 8 q^{17} + 18 q^{18} + 38 q^{20} + 72 q^{21} + 10 q^{22} - 12 q^{25} + 24 q^{26} - 58 q^{28} - 70 q^{30} - 38 q^{32} + 8 q^{33}+ \cdots + 122 q^{98}+O(q^{100}) \) 108 * q + 12 * q^2 - 4 * q^6 - 24 * q^8 + 4 * q^10 - 16 * q^13 + 52 * q^16 - 8 * q^17 + 18 * q^18 + 38 * q^20 + 72 * q^21 + 10 * q^22 - 12 * q^25 + 24 * q^26 - 58 * q^28 - 70 * q^30 - 38 * q^32 + 8 * q^33 + 72 * q^36 - 44 * q^37 + 56 * q^38 + 50 * q^40 + 108 * q^41 - 72 * q^42 - 4 * q^45 - 4 * q^46 - 94 * q^48 - 56 * q^50 - 50 * q^52 - 16 * q^53 - 32 * q^56 - 112 * q^57 + 68 * q^58 + 136 * q^60 + 8 * q^61 + 2 * q^62 - 48 * q^65 + 16 * q^66 - 16 * q^68 - 48 * q^70 - 42 * q^72 - 20 * q^73 - 12 * q^76 + 72 * q^77 + 100 * q^78 + 72 * q^80 - 52 * q^81 + 12 * q^82 - 32 * q^85 - 20 * q^86 - 38 * q^88 - 50 * q^90 + 8 * q^92 + 24 * q^93 + 44 * q^96 - 56 * q^97 + 122 * q^98

Introduction

L-functions

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