LMFDB - Embedded newform 600.2.bq.a.67.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [600,2,Mod(67,600)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("600.67"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(600, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 10, 0, 13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.bq (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$60$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			67.15
Character	$\chi$	$=$	600.67
Dual form			600.2.bq.a.403.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.05549 - 0.941247i) q^{2} +(0.156434 - 0.987688i) q^{3} +(0.228107 + 1.98695i) q^{4} +(-1.03358 - 1.98285i) q^{5} +(-1.09477 + 0.895249i) q^{6} +(-3.05339 + 3.05339i) q^{7} +(1.62945 - 2.31190i) q^{8} +(-0.951057 - 0.309017i) q^{9} +(-0.775421 + 3.06573i) q^{10} +(-1.89568 - 5.83431i) q^{11} +(1.99817 + 0.0855290i) q^{12} +(3.50842 - 1.78763i) q^{13} +(6.09681 - 0.348819i) q^{14} +(-2.12013 + 0.710672i) q^{15} +(-3.89593 + 0.906473i) q^{16} +(0.774890 + 4.89246i) q^{17} +(0.712967 + 1.22134i) q^{18} +(-2.77265 + 3.81623i) q^{19} +(3.70406 - 2.50598i) q^{20} +(2.53814 + 3.49345i) q^{21} +(-3.49066 + 7.94234i) q^{22} +(-2.52893 + 4.96331i) q^{23} +(-2.02854 - 1.97105i) q^{24} +(-2.86341 + 4.09889i) q^{25} +(-5.38569 - 1.41547i) q^{26} +(-0.453990 + 0.891007i) q^{27} +(-6.76343 - 5.37043i) q^{28} +(-4.90352 + 3.56261i) q^{29} +(2.90669 + 1.24546i) q^{30} +(3.46448 - 4.76844i) q^{31} +(4.96532 + 2.71027i) q^{32} +(-6.05903 + 0.959656i) q^{33} +(3.78713 - 5.89330i) q^{34} +(9.21036 + 2.89849i) q^{35} +(0.397059 - 1.96019i) q^{36} +(0.842170 + 1.65285i) q^{37} +(6.51852 - 1.41823i) q^{38} +(-1.21678 - 3.74487i) q^{39} +(-6.26834 - 0.841407i) q^{40} +(-0.573072 + 1.76373i) q^{41} +(0.609227 - 6.07632i) q^{42} +(-6.82342 + 6.82342i) q^{43} +(11.1601 - 5.09747i) q^{44} +(0.370261 + 2.20520i) q^{45} +(7.34096 - 2.85836i) q^{46} +(-0.583483 + 3.68397i) q^{47} +(0.285854 + 3.98977i) q^{48} -11.6464i q^{49} +(6.88036 - 1.63115i) q^{50} +4.95345 q^{51} +(4.35222 + 6.56328i) q^{52} +(0.991395 + 0.157022i) q^{53} +(1.31784 - 0.513129i) q^{54} +(-9.60923 + 9.78910i) q^{55} +(2.08381 + 12.0345i) q^{56} +(3.33551 + 3.33551i) q^{57} +(8.52890 + 0.855129i) q^{58} +(-4.87832 - 1.58506i) q^{59} +(-1.89568 - 4.05048i) q^{60} +(0.213065 - 0.0692289i) q^{61} +(-8.14500 + 1.77210i) q^{62} +(3.84750 - 1.96040i) q^{63} +(-2.68980 - 7.53425i) q^{64} +(-7.17085 - 5.10902i) q^{65} +(7.29850 + 4.69014i) q^{66} +(-0.0981466 - 0.619673i) q^{67} +(-9.54432 + 2.65567i) q^{68} +(4.50659 + 3.27423i) q^{69} +(-6.99322 - 11.7285i) q^{70} +(-4.15707 - 5.72172i) q^{71} +(-2.26411 + 1.69522i) q^{72} +(2.39485 + 1.22024i) q^{73} +(0.666843 - 2.53725i) q^{74} +(3.60049 + 3.46936i) q^{75} +(-8.21512 - 4.63861i) q^{76} +(23.6027 + 12.0262i) q^{77} +(-2.24055 + 5.09796i) q^{78} +(-5.32568 + 3.86934i) q^{79} +(5.82418 + 6.78815i) q^{80} +(0.809017 + 0.587785i) q^{81} +(2.26498 - 1.32220i) q^{82} +(-9.06800 + 1.43623i) q^{83} +(-6.36235 + 5.84004i) q^{84} +(8.90012 - 6.59326i) q^{85} +(13.6246 - 0.779507i) q^{86} +(2.75167 + 5.40046i) q^{87} +(-16.5773 - 5.12406i) q^{88} +(9.54984 - 3.10293i) q^{89} +(1.68483 - 2.67607i) q^{90} +(-5.25425 + 16.1709i) q^{91} +(-10.4387 - 3.89270i) q^{92} +(-4.16777 - 4.16777i) q^{93} +(4.08338 - 3.33918i) q^{94} +(10.4328 + 1.55337i) q^{95} +(3.45365 - 4.48021i) q^{96} +(-8.99587 - 1.42481i) q^{97} +(-10.9621 + 12.2926i) q^{98} +6.13455i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 12 q^{8} - 8 q^{10} + 8 q^{12} - 8 q^{17} + 20 q^{20} + 28 q^{22} + 8 q^{25} - 4 q^{28} - 8 q^{30} - 20 q^{32} + 48 q^{35} + 20 q^{38} - 108 q^{40} - 20 q^{42} + 32 q^{43} - 140 q^{44} - 16 q^{48}+ \cdots - 192 q^{98}+O(q^{100}) $ 480 * q + 12 * q^8 - 8 * q^10 + 8 * q^12 - 8 * q^17 + 20 * q^20 + 28 * q^22 + 8 * q^25 - 4 * q^28 - 8 * q^30 - 20 * q^32 + 48 * q^35 + 20 * q^38 - 108 * q^40 - 20 * q^42 + 32 * q^43 - 140 * q^44 - 16 * q^48 + 124 * q^50 - 132 * q^52 + 152 * q^58 - 20 * q^60 + 116 * q^62 - 60 * q^64 + 8 * q^65 - 48 * q^67 - 72 * q^68 - 4 * q^70 - 12 * q^72 + 40 * q^73 + 24 * q^78 - 76 * q^80 + 120 * q^81 - 64 * q^82 - 80 * q^83 - 80 * q^84 - 132 * q^88 + 200 * q^89 - 48 * q^90 - 216 * q^92 - 40 * q^94 + 20 * q^96 - 56 * q^97 - 192 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{13}{20}\right)$

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 $

$2$	−1.05549	−	0.941247i	−0.746342	−	0.665562i
$2$	−1.05549	−	0.941247i	−0.746342	−	0.665562i
$3$	0.156434	−	0.987688i	0.0903175	−	0.570242i
$3$	0.156434	−	0.987688i	0.0903175	−	0.570242i
$4$	0.228107	+	1.98695i	0.114053	+	0.993475i
$5$	−1.03358	−	1.98285i	−0.462233	−	0.886759i
$5$	−1.03358	−	1.98285i	−0.462233	−	0.886759i
$6$	−1.09477	+	0.895249i	−0.446939	+	0.365484i
$7$	−3.05339	+	3.05339i	−1.15407	+	1.15407i	−0.168345	+	0.985728i	$0.553842\pi$
$7$	−3.05339	+	3.05339i	−1.15407	+	1.15407i	−0.985728	+	0.168345i	$0.946158\pi$
$8$	1.62945	−	2.31190i	0.576097	−	0.817382i
$9$	−0.951057	−	0.309017i	−0.317019	−	0.103006i
$10$	−0.775421	+	3.06573i	−0.245210	+	0.969470i
$11$	−1.89568	−	5.83431i	−0.571569	−	1.75911i	−0.647574	−	0.762002i	$-0.724216\pi$
$11$	−1.89568	−	5.83431i	−0.571569	−	1.75911i	0.0760048	−	0.997107i	$-0.475784\pi$
$12$	1.99817	+	0.0855290i	0.576822	+	0.0246901i
$13$	3.50842	−	1.78763i	0.973061	−	0.495799i	0.106197	−	0.994345i	$-0.466132\pi$
$13$	3.50842	−	1.78763i	0.973061	−	0.495799i	0.866863	+	0.498546i	$0.166132\pi$
$14$	6.09681	−	0.348819i	1.62944	−	0.0932258i
$15$	−2.12013	+	0.710672i	−0.547415	+	0.183495i
$16$	−3.89593	+	0.906473i	−0.973984	+	0.226618i
$17$	0.774890	+	4.89246i	0.187938	+	1.18660i	0.883605	+	0.468232i	$0.155109\pi$
$17$	0.774890	+	4.89246i	0.187938	+	1.18660i	−0.695667	+	0.718364i	$0.744891\pi$
$18$	0.712967	+	1.22134i	0.168048	+	0.287873i
$19$	−2.77265	+	3.81623i	−0.636090	+	0.875503i	−0.998400	−	0.0565547i	$-0.981988\pi$
$19$	−2.77265	+	3.81623i	−0.636090	+	0.875503i	0.362309	+	0.932058i	$0.381988\pi$
$20$	3.70406	−	2.50598i	0.828253	−	0.560354i
$21$	2.53814	+	3.49345i	0.553868	+	0.762334i
$22$	−3.49066	+	7.94234i	−0.744211	+	1.69331i
$23$	−2.52893	+	4.96331i	−0.527319	+	1.03492i	0.461686	+	0.887043i	$0.347245\pi$
$23$	−2.52893	+	4.96331i	−0.527319	+	1.03492i	−0.989005	+	0.147879i	$0.952755\pi$
$24$	−2.02854	−	1.97105i	−0.414074	−	0.402338i
$25$	−2.86341	+	4.09889i	−0.572682	+	0.819778i
$26$	−5.38569	−	1.41547i	−1.05622	−	0.277597i
$27$	−0.453990	+	0.891007i	−0.0873705	+	0.171474i
$28$	−6.76343	−	5.37043i	−1.27817	−	1.01492i
$29$	−4.90352	+	3.56261i	−0.910560	+	0.661561i	−0.941156	−	0.337971i	$-0.890259\pi$
$29$	−4.90352	+	3.56261i	−0.910560	+	0.661561i	0.0305963	+	0.999532i	$0.490259\pi$
$30$	2.90669	+	1.24546i	0.530686	+	0.227389i
$31$	3.46448	−	4.76844i	0.622238	−	0.856438i	−0.375275	−	0.926913i	$-0.622452\pi$
$31$	3.46448	−	4.76844i	0.622238	−	0.856438i	0.997513	+	0.0704758i	$0.0224518\pi$
$32$	4.96532	+	2.71027i	0.877754	+	0.479112i
$33$	−6.05903	+	0.959656i	−1.05474	+	0.167055i
$34$	3.78713	−	5.89330i	0.649488	−	1.01069i
$35$	9.21036	+	2.89849i	1.55684	+	0.489934i
$36$	0.397059	−	1.96019i	0.0661765	−	0.326698i
$37$	0.842170	+	1.65285i	0.138452	+	0.271727i	0.949813	−	0.312818i	$-0.101273\pi$
$37$	0.842170	+	1.65285i	0.138452	+	0.271727i	−0.811361	+	0.584545i	$0.801273\pi$
$38$	6.51852	−	1.41823i	1.05744	−	0.230067i
$39$	−1.21678	−	3.74487i	−0.194841	−	0.599659i
$40$	−6.26834	−	0.841407i	−0.991111	−	0.133038i
$41$	−0.573072	+	1.76373i	−0.0894988	+	0.275449i	−0.985781	−	0.168035i	$-0.946258\pi$
$41$	−0.573072	+	1.76373i	−0.0894988	+	0.275449i	0.896282	+	0.443484i	$0.146258\pi$
$42$	0.609227	−	6.07632i	0.0940058	−	0.937596i
$43$	−6.82342	+	6.82342i	−1.04056	+	1.04056i	−0.0414200	+	0.999142i	$0.513188\pi$
$43$	−6.82342	+	6.82342i	−1.04056	+	1.04056i	−0.999142	+	0.0414200i	$0.986812\pi$
$44$	11.1601	−	5.09747i	1.68244	−	0.768472i
$45$	0.370261	+	2.20520i	0.0551953	+	0.328732i
$46$	7.34096	−	2.85836i	1.08237	−	0.421442i
$47$	−0.583483	+	3.68397i	−0.0851098	+	0.537362i	0.907887	+	0.419216i	$0.137695\pi$
$47$	−0.583483	+	3.68397i	−0.0851098	+	0.537362i	−0.992996	+	0.118146i	$0.962305\pi$
$48$	0.285854	+	3.98977i	0.0412595	+	0.575874i
$49$		−	11.6464i		−	1.66377i
$50$	6.88036	−	1.63115i	0.973030	−	0.230679i
$51$	4.95345			0.693621
$52$	4.35222	+	6.56328i	0.603545	+	0.910163i
$53$	0.991395	+	0.157022i	0.136179	+	0.0215686i	0.224152	−	0.974554i	$-0.428039\pi$
$53$	0.991395	+	0.157022i	0.136179	+	0.0215686i	−0.0879730	+	0.996123i	$0.528039\pi$
$54$	1.31784	−	0.513129i	0.179335	−	0.0698280i
$55$	−9.60923	+	9.78910i	−1.29571	+	1.31996i
$56$	2.08381	+	12.0345i	0.278461	+	1.60818i
$57$	3.33551	+	3.33551i	0.441799	+	0.441799i
$58$	8.52890	+	0.855129i	1.11990	+	0.112284i
$59$	−4.87832	−	1.58506i	−0.635103	−	0.206357i	−0.0262686	−	0.999655i	$-0.508363\pi$
$59$	−4.87832	−	1.58506i	−0.635103	−	0.206357i	−0.608834	+	0.793298i	$0.708363\pi$
$60$	−1.89568	−	4.05048i	−0.244732	−	0.522915i
$61$	0.213065	−	0.0692289i	0.0272801	−	0.00886386i	−0.295345	−	0.955391i	$-0.595435\pi$
$61$	0.213065	−	0.0692289i	0.0272801	−	0.00886386i	0.322625	+	0.946527i	$0.395435\pi$
$62$	−8.14500	+	1.77210i	−1.03442	+	0.225057i
$63$	3.84750	−	1.96040i	0.484739	−	0.246987i
$64$	−2.68980	−	7.53425i	−0.336226	−	0.941781i
$65$	−7.17085	−	5.10902i	−0.889435	−	0.633695i
$66$	7.29850	+	4.69014i	0.898383	+	0.577316i
$67$	−0.0981466	−	0.619673i	−0.0119905	−	0.0757051i	0.980967	−	0.194172i	$-0.0622020\pi$
$67$	−0.0981466	−	0.619673i	−0.0119905	−	0.0757051i	−0.992958	+	0.118467i	$0.962202\pi$
$68$	−9.54432	+	2.65567i	−1.15742	+	0.322047i
$69$	4.50659	+	3.27423i	0.542530	+	0.394171i
$70$	−6.99322	−	11.7285i	−0.835850	−	1.40183i
$71$	−4.15707	−	5.72172i	−0.493354	−	0.679043i	0.487649	−	0.873040i	$-0.337855\pi$
$71$	−4.15707	−	5.72172i	−0.493354	−	0.679043i	−0.981002	+	0.193997i	$0.937855\pi$
$72$	−2.26411	+	1.69522i	−0.266828	+	0.199784i
$73$	2.39485	+	1.22024i	0.280296	+	0.142818i	0.588487	−	0.808506i	$-0.299724\pi$
$73$	2.39485	+	1.22024i	0.280296	+	0.142818i	−0.308191	+	0.951324i	$0.599724\pi$
$74$	0.666843	−	2.53725i	0.0775189	−	0.294950i
$75$	3.60049	+	3.46936i	0.415749	+	0.400608i
$76$	−8.21512	−	4.63861i	−0.942339	−	0.532086i
$77$	23.6027	+	12.0262i	2.68978	+	1.37051i
$78$	−2.24055	+	5.09796i	−0.253693	+	0.577230i
$79$	−5.32568	+	3.86934i	−0.599186	+	0.435334i	−0.845590	−	0.533833i	$-0.820751\pi$
$79$	−5.32568	+	3.86934i	−0.599186	+	0.435334i	0.246404	+	0.969167i	$0.420751\pi$
$80$	5.82418	+	6.78815i	0.651163	+	0.758938i
$81$	0.809017	+	0.587785i	0.0898908	+	0.0653095i
$82$	2.26498	−	1.32220i	0.250125	−	0.146012i
$83$	−9.06800	+	1.43623i	−0.995343	+	0.157647i	−0.632796	−	0.774319i	$-0.718093\pi$
$83$	−9.06800	+	1.43623i	−0.995343	+	0.157647i	−0.362547	+	0.931966i	$0.618093\pi$
$84$	−6.36235	+	5.84004i	−0.694189	+	0.637201i
$85$	8.90012	−	6.59326i	0.965353	−	0.715140i
$86$	13.6246	−	0.779507i	1.46917	−	0.0840564i
$87$	2.75167	+	5.40046i	0.295010	+	0.578990i
$88$	−16.5773	−	5.12406i	−1.76714	−	0.546227i
$89$	9.54984	−	3.10293i	1.01228	−	0.328910i	0.244519	−	0.969645i	$-0.421370\pi$
$89$	9.54984	−	3.10293i	1.01228	−	0.328910i	0.767763	+	0.640734i	$0.221370\pi$
$90$	1.68483	−	2.67607i	0.177597	−	0.282082i
$91$	−5.25425	+	16.1709i	−0.550795	+	1.69517i
$92$	−10.4387	−	3.89270i	−1.08831	−	0.405842i
$93$	−4.16777	−	4.16777i	−0.432178	−	0.432178i
$94$	4.08338	−	3.33918i	0.421169	−	0.344410i
$95$	10.4328	+	1.55337i	1.07038	+	0.159372i
$96$	3.45365	−	4.48021i	0.352486	−	0.457260i
$97$	−8.99587	−	1.42481i	−0.913392	−	0.144667i	−0.317989	−	0.948094i	$-0.603008\pi$
$97$	−8.99587	−	1.42481i	−0.913392	−	0.144667i	−0.595403	+	0.803427i	$0.703008\pi$
$98$	−10.9621	+	12.2926i	−1.10734	+	1.24174i
$99$			6.13455i			0.616546i
$100$	−8.79745	−	4.75447i	−0.879745	−	0.475447i
$101$		−	10.7575i		−	1.07041i	−0.844723	−	0.535203i	$-0.820235\pi$
$101$		−	10.7575i		−	1.07041i	0.844723	−	0.535203i	$-0.179765\pi$
$102$	−5.22830	−	4.66242i	−0.517679	−	0.461648i
$103$	13.2684	+	2.10151i	1.30738	+	0.207068i	0.770959	−	0.636884i	$-0.219777\pi$
$103$	13.2684	+	2.10151i	1.30738	+	0.207068i	0.536418	+	0.843953i	$0.319777\pi$
$104$	1.58396	−	11.0240i	0.155320	−	1.08099i
$105$	4.30362	−	8.64354i	0.419991	−	0.843523i
$106$	−0.898608	−	1.09888i	−0.0872806	−	0.106733i
$107$	−3.45864	−	3.45864i	−0.334359	−	0.334359i	0.519880	−	0.854239i	$-0.325977\pi$
$107$	−3.45864	−	3.45864i	−0.334359	−	0.334359i	−0.854239	+	0.519880i	$0.825977\pi$
$108$	−1.87394	−	0.698812i	−0.180320	−	0.0672432i
$109$	0.820468	−	2.52514i	0.0785866	−	0.241865i	−0.904043	−	0.427441i	$-0.859415\pi$
$109$	0.820468	−	2.52514i	0.0785866	−	0.241865i	0.982630	+	0.185576i	$0.0594152\pi$
$110$	19.3564	−	1.28761i	1.84556	−	0.122769i
$111$	1.76425	−	0.573238i	0.167455	−	0.0544094i
$112$	9.12800	−	14.6636i	0.862515	−	1.38558i
$113$	−5.59229	−	10.9755i	−0.526079	−	1.03249i	−0.989252	−	0.146220i	$-0.953289\pi$
$113$	−5.59229	−	10.9755i	−0.526079	−	1.03249i	0.463173	−	0.886268i	$-0.346711\pi$
$114$	−0.381048	−	6.66012i	−0.0356884	−	0.623778i
$115$	12.4554	−	0.115495i	1.16147	−	0.0107700i
$116$	−8.19726	−	8.93038i	−0.761096	−	0.829165i
$117$	−3.88911	+	0.615975i	−0.359549	+	0.0569469i
$118$	3.65707	+	6.26471i	0.336660	+	0.576714i
$119$	−17.3046	−	12.5726i	−1.58631	−	1.15252i
$120$	−1.81163	+	6.05954i	−0.165379	+	0.553158i
$121$	−21.5463	+	15.6543i	−1.95876	+	1.42312i
$122$	−0.290049	−	0.127476i	−0.0262598	−	0.0115412i
$123$	1.65237	+	0.841925i	0.148989	+	0.0759138i
$124$	10.2649	+	5.79603i	0.921817	+	0.520498i
$125$	11.0871	+	1.44118i	0.991657	+	0.128903i
$126$	−5.90620	−	1.55227i	−0.526166	−	0.138287i
$127$	−7.63293	−	3.88917i	−0.677313	−	0.345108i	0.0812630	−	0.996693i	$-0.474105\pi$
$127$	−7.63293	−	3.88917i	−0.677313	−	0.345108i	−0.758576	+	0.651584i	$0.774105\pi$
$128$	−4.25254	+	10.4841i	−0.375875	+	0.926670i
$129$	5.67199	+	7.80683i	0.499391	+	0.687353i
$130$	2.75989	+	12.1420i	0.242059	+	1.06493i
$131$	−4.80563	−	3.49150i	−0.419870	−	0.305054i	0.357715	−	0.933831i	$-0.383556\pi$
$131$	−4.80563	−	3.49150i	−0.419870	−	0.305054i	−0.777586	+	0.628777i	$0.783556\pi$
$132$	−3.28889	−	11.8201i	−0.286261	−	1.02881i
$133$	−3.18645	−	20.1184i	−0.276300	−	1.74449i
$134$	−0.479673	+	0.746437i	−0.0414375	+	0.0644824i
$135$	2.23597	−	0.0207335i	0.192442	−	0.00178446i
$136$	12.5735	+	6.18054i	1.07817	+	0.529977i
$137$	6.87890	−	3.50497i	0.587704	−	0.299450i	−0.134739	−	0.990881i	$-0.543019\pi$
$137$	6.87890	−	3.50497i	0.587704	−	0.299450i	0.722442	+	0.691431i	$0.243019\pi$
$138$	−1.67479	−	7.69773i	−0.142568	−	0.655274i
$139$	−1.65335	+	0.537207i	−0.140236	+	0.0455653i	−0.378294	−	0.925686i	$-0.623489\pi$
$139$	−1.65335	+	0.537207i	−0.140236	+	0.0455653i	0.238058	+	0.971251i	$0.423489\pi$
$140$	−3.65821	+	18.9617i	−0.309175	+	1.60255i
$141$	3.54733	+	1.15260i	0.298739	+	0.0970663i
$142$	−0.997816	+	9.95203i	−0.0837349	+	0.835156i
$143$	−17.0804	−	17.0804i	−1.42834	−	1.42834i
$144$	3.98537	+	0.341803i	0.332114	+	0.0284836i
$145$	12.1323	+	6.04069i	1.00754	+	0.501652i
$146$	−1.37919	−	3.54209i	−0.114143	−	0.293146i
$147$	−11.5030	−	1.82190i	−0.948752	−	0.150268i
$148$	−3.09203	+	2.05038i	−0.254163	+	0.168540i
$149$	−12.4430			−1.01937			−0.509686	−	0.860361i	$-0.670238\pi$
$149$	−12.4430			−1.01937			−0.509686	+	0.860361i	$0.670238\pi$
$150$	−0.534740	−	7.05082i	−0.0436613	−	0.575697i
$151$			3.71698i			0.302484i	0.988497	+	0.151242i	$0.0483273\pi$
$151$			3.71698i			0.302484i	−0.988497	+	0.151242i	$0.951673\pi$
$152$	4.30487	+	12.6285i	0.349171	+	1.02430i
$153$	0.774890	−	4.89246i	0.0626461	−	0.395532i
$154$	−13.5927	−	34.9094i	−1.09533	−	2.81308i
$155$	−13.0359	−	1.94096i	−1.04707	−	0.155902i
$156$	7.16331	−	3.27192i	0.573524	−	0.261963i
$157$	0.428812	−	0.428812i	0.0342229	−	0.0342229i	−0.689788	−	0.724011i	$-0.742296\pi$
$157$	0.428812	−	0.428812i	0.0342229	−	0.0342229i	0.724011	+	0.689788i	$0.242296\pi$
$158$	9.26320	+	0.928752i	0.736940	+	0.0738875i
$159$	0.310177	−	0.954625i	0.0245986	−	0.0757067i
$160$	0.241983	−	12.6468i	0.0191305	−	0.999817i
$161$	−7.43311	−	22.8768i	−0.585811	−	1.80294i
$162$	−0.300656	−	1.38188i	−0.0236218	−	0.108571i
$163$	−8.60779	−	16.8937i	−0.674214	−	1.32322i	−0.933903	−	0.357528i	$-0.883620\pi$
$163$	−8.60779	−	16.8937i	−0.674214	−	1.32322i	0.259688	−	0.965693i	$-0.416380\pi$
$164$	−3.63517	−	0.736345i	−0.283859	−	0.0574989i
$165$	8.16537	+	11.0223i	0.635673	+	0.858083i
$166$	10.9230	+	7.01931i	0.847790	+	0.544804i
$167$	−20.1134	+	3.18566i	−1.55643	+	0.246514i	−0.874543	−	0.484948i	$-0.838838\pi$
$167$	−20.1134	+	3.18566i	−1.55643	+	0.246514i	−0.681882	+	0.731462i	$0.738838\pi$
$168$	12.2123	−	0.175545i	0.942200	−	0.0135436i
$169$	1.47218	−	2.02629i	0.113245	−	0.155868i
$170$	−15.5999	−	1.41811i	−1.19645	−	0.108764i
$171$	3.81623	−	2.77265i	0.291834	−	0.212030i
$172$	−15.1143	−	12.0013i	−1.15245	−	0.915092i
$173$	−6.34046	+	12.4439i	−0.482056	+	0.946089i	0.514036	+	0.857769i	$0.328150\pi$
$173$	−6.34046	+	12.4439i	−0.482056	+	0.946089i	−0.996092	+	0.0883201i	$0.971850\pi$
$174$	2.17882	−	8.29012i	0.165176	−	0.628473i
$175$	−3.77240	−	21.2586i	−0.285167	−	1.60700i
$176$	12.6741	+	21.0117i	0.955346	+	1.58382i
$177$	−2.32868	+	4.57030i	−0.175035	+	0.343525i
$178$	−13.0004	−	5.71366i	−0.974419	−	0.428257i
$179$	−3.76347	−	5.17997i	−0.281295	−	0.387169i	0.644868	−	0.764294i	$-0.276913\pi$
$179$	−3.76347	−	5.17997i	−0.281295	−	0.387169i	−0.926162	+	0.377125i	$0.876913\pi$
$180$	−4.29716	+	1.23871i	−0.320291	+	0.0923281i
$181$	−1.53004	+	2.10592i	−0.113727	+	0.156531i	−0.862086	−	0.506763i	$-0.830842\pi$
$181$	−1.53004	+	2.10592i	−0.113727	+	0.156531i	0.748359	+	0.663294i	$0.230842\pi$
$182$	20.7666	−	12.1226i	1.53932	−	0.898590i
$183$	−0.0350459	−	0.221271i	−0.00259067	−	0.0163568i
$184$	7.35394	+	13.9341i	0.542140	+	1.02724i
$185$	2.40691	−	3.37826i	0.176959	−	0.248375i
$186$	0.476126	+	8.32193i	0.0349112	+	0.610194i
$187$	27.0752	−	13.7955i	1.97993	−	1.00883i
$188$	−7.45295	−	0.319014i	−0.543562	−	0.0232665i
$189$	−1.33438	−	4.10680i	−0.0970619	−	0.298726i
$190$	−9.54957	−	11.4594i	−0.692799	−	0.831352i
$191$	11.2931	+	3.66934i	0.817137	+	0.265504i	0.687618	−	0.726073i	$-0.258657\pi$
$191$	11.2931	+	3.66934i	0.817137	+	0.265504i	0.129519	+	0.991577i	$0.458657\pi$
$192$	−7.86227	+	1.47807i	−0.567411	+	0.106671i
$193$	9.10782	−	9.10782i	0.655595	−	0.655595i	−0.298740	−	0.954335i	$-0.596566\pi$
$193$	9.10782	−	9.10782i	0.655595	−	0.655595i	0.954335	+	0.298740i	$0.0965662\pi$
$194$	8.15393	+	9.97120i	0.585418	+	0.715891i
$195$	−6.16788	+	6.28334i	−0.441691	+	0.449959i
$196$	23.1408	−	2.65662i	1.65291	−	0.189759i
$197$	−0.700395	+	4.42212i	−0.0499011	+	0.315063i	0.950094	+	0.311963i	$0.100987\pi$
$197$	−0.700395	+	4.42212i	−0.0499011	+	0.315063i	−0.999995	+	0.00309960i	$0.999013\pi$
$198$	5.77413	−	6.47494i	0.410350	−	0.460154i
$199$	−21.1680			−1.50056			−0.750281	−	0.661119i	$-0.770082\pi$
$199$	−21.1680			−1.50056			−0.750281	+	0.661119i	$0.770082\pi$
$200$	4.81046	+	13.2989i	0.340151	+	0.940371i
$201$	−0.627398			−0.0442532
$202$	−10.1254	+	11.3544i	−0.712422	+	0.798890i
$203$	4.09430	−	25.8504i	0.287364	−	1.81434i
$204$	1.12991	+	9.84225i	0.0791098	+	0.689095i
$205$	4.08954	−	0.686649i	0.285626	−	0.0479577i
$206$	−12.0266	−	14.7070i	−0.837934	−	1.02468i
$207$	3.93891	−	3.93891i	0.273773	−	0.273773i
$208$	−12.0481	+	10.1448i	−0.835388	+	0.703413i
$209$	27.5211	+	8.94216i	1.90368	+	0.618542i
$210$	−12.6781	+	5.07238i	−0.874874	+	0.350027i
$211$	7.74774	+	23.8451i	0.533376	+	1.64156i	0.747131	+	0.664677i	$0.231431\pi$
$211$	7.74774	+	23.8451i	0.533376	+	1.64156i	−0.213755	+	0.976887i	$0.568569\pi$
$212$	−0.0858500	+	2.00567i	−0.00589620	+	0.137750i
$213$	−6.30158	+	3.21082i	−0.431777	+	0.220002i
$214$	0.395114	+	6.90598i	0.0270094	+	0.472083i
$215$	20.5824	+	6.47726i	1.40371	+	0.441746i
$216$	1.32017	+	2.50143i	0.0898261	+	0.170201i
$217$	3.98152	+	25.1383i	0.270283	+	1.70650i
$218$	−3.24278	+	1.89299i	−0.219628	+	0.128210i
$219$	1.57985	−	2.17448i	0.106757	−	0.146938i
$220$	−21.6424	−	16.8601i	−1.45913	−	1.13671i
$221$	11.4645	+	15.7796i	0.771189	+	1.06145i
$222$	−2.40170	−	1.05555i	−0.161191	−	0.0708436i
$223$	−6.35108	+	12.4647i	−0.425300	+	0.834698i	0.574568	+	0.818457i	$0.305170\pi$
$223$	−6.35108	+	12.4647i	−0.425300	+	0.834698i	−0.999868	+	0.0162414i	$0.994830\pi$
$224$	−23.4366	+	6.88557i	−1.56592	+	0.460062i
$225$	3.98989	−	3.01343i	0.265993	−	0.200895i
$226$	−4.42806	+	16.8482i	−0.294550	+	1.12073i
$227$	−2.05770	+	4.03847i	−0.136575	+	0.268043i	−0.949157	−	0.314804i	$-0.898061\pi$
$227$	−2.05770	+	4.03847i	−0.136575	+	0.268043i	0.812582	+	0.582847i	$0.198061\pi$
$228$	−5.86663	+	7.38834i	−0.388527	+	0.489305i
$229$	8.32107	−	6.04561i	0.549872	−	0.399505i	−0.277866	−	0.960620i	$-0.589627\pi$
$229$	8.32107	−	6.04561i	0.549872	−	0.399505i	0.827738	+	0.561115i	$0.189627\pi$
$230$	−13.2552	−	11.6017i	−0.874022	−	0.764993i
$231$	15.5704	−	21.4308i	1.02446	−	1.41004i
$232$	0.246401	+	17.1416i	0.0161770	+	1.12540i
$233$	−12.9275	+	2.04752i	−0.846912	+	0.134138i	−0.564784	−	0.825239i	$-0.691040\pi$
$233$	−12.9275	+	2.04752i	−0.846912	+	0.134138i	−0.282128	+	0.959377i	$0.591040\pi$
$234$	4.68469	+	3.01046i	0.306248	+	0.196800i
$235$	7.90784	−	2.65073i	0.515851	−	0.172914i
$236$	2.03666	−	10.0545i	0.132575	−	0.654494i
$237$	2.98858	+	5.86541i	0.194129	+	0.381000i
$238$	6.43094	+	29.5581i	0.416856	+	1.91597i
$239$	3.91809	+	12.0587i	0.253440	+	0.780009i	0.994133	+	0.108165i	$0.0344975\pi$
$239$	3.91809	+	12.0587i	0.253440	+	0.780009i	−0.740693	+	0.671844i	$0.765502\pi$
$240$	7.61568	−	4.69057i	0.491590	−	0.302775i
$241$	3.06322	−	9.42761i	0.197319	−	0.607286i	−0.802623	−	0.596487i	$-0.796563\pi$
$241$	3.06322	−	9.42761i	0.197319	−	0.607286i	0.999942	−	0.0107986i	$-0.00343736\pi$
$242$	37.4765	+	3.75749i	2.40908	+	0.241541i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	0.186156	+	0.407557i	0.0119174	+	0.0260912i
$245$	−23.0931	+	12.0375i	−1.47536	+	0.769049i
$246$	−0.951597	−	2.44393i	−0.0606716	−	0.155819i
$247$	−2.90563	+	18.3454i	−0.184881	+	1.16729i
$248$	−5.37900	−	15.7795i	−0.341567	−	1.00200i
$249$			9.18104i			0.581825i
$250$	−10.3458	−	11.9568i	−0.654323	−	0.756215i
$251$	17.5195			1.10582			0.552912	−	0.833240i	$-0.313517\pi$
$251$	17.5195			1.10582			0.552912	+	0.833240i	$0.313517\pi$
$252$	4.77285	+	7.19760i	0.300661	+	0.453406i
$253$	33.7515	+	5.34572i	2.12194	+	0.336082i
$254$	4.39579	+	11.2894i	0.275816	+	0.708363i
$255$	−5.11980	−	9.82196i	−0.320614	−	0.615075i
$256$	14.3566	−	7.06312i	0.897288	−	0.441445i
$257$	−8.19492	−	8.19492i	−0.511185	−	0.511185i	0.403704	−	0.914889i	$-0.367722\pi$
$257$	−8.19492	−	8.19492i	−0.511185	−	0.511185i	−0.914889	+	0.403704i	$0.867722\pi$
$258$	1.36144	−	13.5788i	0.0847596	−	0.845377i
$259$	−7.61828	−	2.47533i	−0.473377	−	0.153809i
$260$	8.51563	−	15.4135i	0.528117	−	0.955906i
$261$	5.76443	−	1.87298i	0.356809	−	0.115934i
$262$	1.78592	+	8.20852i	0.110335	+	0.507124i
$263$	8.35294	−	4.25603i	0.515064	−	0.262438i	−0.177081	−	0.984196i	$-0.556666\pi$
$263$	8.35294	−	4.25603i	0.515064	−	0.262438i	0.692146	+	0.721758i	$0.256666\pi$
$264$	−7.65423	+	15.5716i	−0.471085	+	0.958366i
$265$	−0.713339	−	2.12808i	−0.0438201	−	0.130727i
$266$	−15.5732	+	24.2340i	−0.954853	+	1.48588i
$267$	−1.57081	−	9.91768i	−0.0961317	−	0.606952i
$268$	1.20887	−	0.336364i	0.0738436	−	0.0205467i
$269$	−20.0906	−	14.5967i	−1.22495	−	0.889976i	−0.228446	−	0.973557i	$-0.573364\pi$
$269$	−20.0906	−	14.5967i	−1.22495	−	0.889976i	−0.996501	+	0.0835804i	$0.973364\pi$
$270$	−2.37956	−	2.08272i	−0.144815	−	0.126750i
$271$	−7.11677	−	9.79539i	−0.432313	−	0.595027i	0.536169	−	0.844110i	$-0.319871\pi$
$271$	−7.11677	−	9.79539i	−0.432313	−	0.595027i	−0.968482	+	0.249083i	$0.919871\pi$
$272$	−7.45381	−	18.3583i	−0.451953	−	1.11314i
$273$	15.1499	+	7.71925i	0.916912	+	0.467190i
$274$	−10.5596	−	2.77529i	−0.637931	−	0.167661i
$275$	29.3423	+	8.93583i	1.76941	+	0.538851i
$276$	−5.47775	+	9.70125i	−0.329722	+	0.583946i
$277$	−11.9237	−	6.07541i	−0.716424	−	0.365036i	0.0574737	−	0.998347i	$-0.481695\pi$
$277$	−11.9237	−	6.07541i	−0.716424	−	0.365036i	−0.773898	+	0.633311i	$0.781695\pi$
$278$	2.25074	+	0.989199i	0.134990	+	0.0593282i
$279$	−4.76844	+	3.46448i	−0.285479	+	0.207413i
$280$	21.7088	−	16.5705i	1.29735	−	0.990279i
$281$	11.8877	+	8.63689i	0.709158	+	0.515234i	0.882902	−	0.469557i	$-0.155586\pi$
$281$	11.8877	+	8.63689i	0.709158	+	0.515234i	−0.173744	+	0.984791i	$0.555586\pi$
$282$	−2.65929	−	4.55547i	−0.158358	−	0.271274i
$283$	27.0745	−	4.28818i	1.60941	−	0.254906i	0.714000	−	0.700146i	$-0.246882\pi$
$283$	27.0745	−	4.28818i	1.60941	−	0.254906i	0.895411	+	0.445241i	$0.146882\pi$
$284$	10.4205	−	9.56505i	0.618343	−	0.567581i
$285$	3.16629	−	10.0613i	0.187555	−	0.595983i
$286$	1.95127	+	34.1051i	0.115381	+	2.01668i
$287$	−3.63556	−	7.13518i	−0.214600	−	0.421176i
$288$	−3.88479	−	4.11199i	−0.228913	−	0.242301i
$289$	−7.16778	+	2.32895i	−0.421634	+	0.136997i
$290$	−7.11974	−	17.7954i	−0.418085	−	1.04498i
$291$	−2.81453	+	8.66223i	−0.164991	+	0.507789i
$292$	−1.87827	+	5.03679i	−0.109917	+	0.294756i
$293$	16.4593	+	16.4593i	0.961564	+	0.961564i	0.999288	−	0.0377244i	$-0.0120109\pi$
$293$	16.4593	+	16.4593i	0.961564	+	0.961564i	−0.0377244	+	0.999288i	$0.512011\pi$
$294$	10.4264	+	12.7502i	0.608081	+	0.743605i
$295$	1.89921	+	11.3113i	0.110576	+	0.658568i
$296$	5.19351	+	0.746218i	0.301866	+	0.0433730i
$297$	6.05903	+	0.959656i	0.351580	+	0.0556849i
$298$	13.1334	+	11.7120i	0.760800	+	0.678456i
$299$			21.9342i			1.26849i
$300$	−6.07215	+	7.94537i	−0.350576	+	0.458726i
$301$		−	41.6691i		−	2.40177i
$302$	3.49860	−	3.92323i	0.201322	−	0.225756i
$303$	−10.6250	−	1.68284i	−0.610391	−	0.0966764i
$304$	7.34277	−	17.3811i	0.421137	−	0.996876i
$305$	−0.357491	−	0.350922i	−0.0204699	−	0.0200937i
$306$	−5.42290	+	4.43457i	−0.310007	+	0.253507i
$307$	−13.0768	−	13.0768i	−0.746334	−	0.746334i	0.227455	−	0.973789i	$-0.426960\pi$
$307$	−13.0768	−	13.0768i	−0.746334	−	0.746334i	−0.973789	+	0.227455i	$0.926960\pi$
$308$	−18.5115	+	49.6406i	−1.05479	+	2.82853i
$309$	4.15128	−	12.7763i	0.236158	−	0.726820i
$310$	11.9323	+	14.3187i	0.677712	+	0.813248i
$311$	−18.7292	+	6.08550i	−1.06204	+	0.345077i	−0.787382	−	0.616466i	$-0.788564\pi$
$311$	−18.7292	+	6.08550i	−1.06204	+	0.345077i	−0.274656	+	0.961543i	$0.588564\pi$
$312$	−10.6405	−	3.28899i	−0.602398	−	0.186202i
$313$	1.55612	+	3.05406i	0.0879573	+	0.172626i	0.930795	−	0.365542i	$-0.119116\pi$
$313$	1.55612	+	3.05406i	0.0879573	+	0.172626i	−0.842837	+	0.538168i	$0.819116\pi$
$314$	−0.856224	+	0.0489875i	−0.0483195	+	0.00276452i
$315$	−7.86389	−	5.60279i	−0.443080	−	0.315681i
$316$	−8.90300	−	9.69924i	−0.500833	−	0.545625i
$317$	−16.4811	+	2.61036i	−0.925674	+	0.146612i	−0.601032	−	0.799225i	$-0.705244\pi$
$317$	−16.4811	+	2.61036i	−0.925674	+	0.146612i	−0.324641	+	0.945837i	$0.605244\pi$
$318$	−1.22593	+	0.715642i	−0.0687465	+	0.0401312i
$319$	30.0809	+	21.8550i	1.68421	+	1.22365i
$320$	−12.1592	+	13.1208i	−0.679718	+	0.733473i
$321$	−3.95710	+	2.87500i	−0.220864	+	0.160467i
$322$	−13.6871	+	31.1425i	−0.762754	+	1.73550i
$323$	−20.8193	−	10.6079i	−1.15842	−	0.590242i
$324$	−0.983357	+	1.74155i	−0.0546310	+	0.0967530i
$325$	−2.71875	+	19.4993i	−0.150809	+	1.08163i
$326$	−6.81578	+	25.9332i	−0.377491	+	1.43631i
$327$	−2.36570	−	1.20539i	−0.130824	−	0.0666580i
$328$	3.14379	+	4.19880i	0.173587	+	0.231840i
$329$	−9.46699	−	13.0302i	−0.521932	−	0.718378i
$330$	1.75625	−	19.3195i	0.0966781	−	1.06350i
$331$	−3.91697	−	2.84584i	−0.215296	−	0.156422i	0.474911	−	0.880034i	$-0.342480\pi$
$331$	−3.91697	−	2.84584i	−0.215296	−	0.156422i	−0.690207	+	0.723612i	$0.742480\pi$
$332$	−4.92219	−	17.6900i	−0.270140	−	0.970867i
$333$	−0.290192	−	1.83220i	−0.0159024	−	0.100404i
$334$	24.2280	+	15.5693i	1.32570	+	0.851915i
$335$	−1.12728	+	0.835094i	−0.0615898	+	0.0456261i
$336$	−13.0552	−	11.3095i	−0.712218	−	0.616985i
$337$	−14.2600	+	7.26583i	−0.776791	+	0.395795i	−0.796983	−	0.604001i	$-0.793572\pi$
$337$	−14.2600	+	7.26583i	−0.776791	+	0.395795i	0.0201922	+	0.999796i	$0.493572\pi$
$338$	−3.46111	+	0.753030i	−0.188259	+	0.0409595i
$339$	−11.7152	+	3.80650i	−0.636282	+	0.206741i
$340$	15.1307	+	16.1801i	0.820575	+	0.877490i
$341$	−34.3881	−	11.1734i	−1.86222	−	0.605072i
$342$	−6.63774	−	0.665516i	−0.358928	−	0.0359870i
$343$	14.1873	+	14.1873i	0.766040	+	0.766040i
$344$	4.65669	+	26.8935i	0.251072	+	1.45000i
$345$	1.83438	−	12.3201i	0.0987596	−	0.663292i
$346$	18.4050	−	7.16639i	0.989460	−	0.385267i
$347$	33.0692	+	5.23765i	1.77525	+	0.281172i	0.956235	−	0.292601i	$-0.0945208\pi$
$347$	33.0692	+	5.23765i	1.77525	+	0.281172i	0.819014	+	0.573773i	$0.194521\pi$
$348$	−10.1028	+	6.69932i	−0.541565	+	0.359121i
$349$	−10.2862			−0.550607			−0.275303	−	0.961357i	$-0.588778\pi$
$349$	−10.2862			−0.550607			−0.275303	+	0.961357i	$0.588778\pi$
$350$	−16.0279	+	25.9890i	−0.856727	+	1.38917i
$351$			3.93759i			0.210173i
$352$	6.39986	−	34.1070i	0.341114	−	1.81791i
$353$	−1.97390	+	12.4627i	−0.105060	+	0.663322i	0.877808	+	0.479012i	$0.159005\pi$
$353$	−1.97390	+	12.4627i	−0.105060	+	0.663322i	−0.982868	+	0.184310i	$0.940995\pi$
$354$	6.75968	−	2.63202i	0.359273	−	0.139891i
$355$	−7.04864	+	14.1567i	−0.374103	+	0.751361i
$356$	8.34375	+	18.2673i	0.442218	+	0.968163i
$357$	−15.1248	+	15.1248i	−0.800490	+	0.800490i
$358$	−0.903340	+	9.00974i	−0.0477430	+	0.476180i
$359$	7.02820	−	21.6306i	0.370934	−	1.14162i	−0.575247	−	0.817980i	$-0.695094\pi$
$359$	7.02820	−	21.6306i	0.370934	−	1.14162i	0.946181	−	0.323638i	$-0.104906\pi$
$360$	5.70153	+	2.73725i	0.300497	+	0.144266i
$361$	−1.00468	−	3.09210i	−0.0528781	−	0.162742i
$362$	3.59712	−	0.782623i	0.189061	−	0.0411338i
$363$	12.0910	+	23.7300i	0.634614	+	1.24550i
$364$	−33.3293	−	6.75123i	−1.74693	−	0.353861i
$365$	−0.0557276	−	6.00986i	−0.00291692	−	0.314570i
$366$	−0.171281	+	0.266536i	−0.00895298	+	0.0139321i
$367$	26.0922	−	4.13260i	1.36200	−	0.215720i	0.567697	−	0.823238i	$-0.307835\pi$
$367$	26.0922	−	4.13260i	1.36200	−	0.215720i	0.794306	+	0.607518i	$0.207835\pi$
$368$	5.35345	−	21.6292i	0.279068	−	1.12750i
$369$	1.09005	−	1.50032i	0.0567456	−	0.0781036i
$370$	−5.72024	+	1.30021i	−0.297381	+	0.0675949i
$371$	−3.50656	+	2.54767i	−0.182052	+	0.132268i
$372$	7.33045	−	9.23185i	0.380066	−	0.478649i
$373$	−0.367849	+	0.721944i	−0.0190465	+	0.0373808i	−0.900334	−	0.435200i	$-0.856678\pi$
$373$	−0.367849	+	0.721944i	−0.0190465	+	0.0373808i	0.881287	+	0.472581i	$0.156678\pi$
$374$	−41.5625	−	10.9235i	−2.14915	−	0.564840i
$375$	3.15783	−	10.7251i	0.163070	−	0.553843i
$376$	7.56623	+	7.35179i	0.390198	+	0.379139i
$377$	−10.8350	+	21.2648i	−0.558029	+	1.09519i
$378$	−2.45709	+	5.59066i	−0.126379	+	0.287553i
$379$	16.3610	+	22.5190i	0.840410	+	1.15673i	0.985895	+	0.167365i	$0.0535258\pi$
$379$	16.3610	+	22.5190i	0.840410	+	1.15673i	−0.145485	+	0.989360i	$0.546474\pi$
$380$	−0.706678	+	21.0838i	−0.0362518	+	1.08157i
$381$	−5.03534	+	6.93056i	−0.257969	+	0.355063i
$382$	−8.46592	−	14.5025i	−0.433154	−	0.742012i
$383$	−2.07096	−	13.0756i	−0.105821	−	0.668129i	−0.982388	−	0.186850i	$-0.940172\pi$
$383$	−2.07096	−	13.0756i	−0.105821	−	0.668129i	0.876567	−	0.481280i	$-0.159828\pi$
$384$	9.68976	+	5.84026i	0.494478	+	0.298034i
$385$	−0.549229	−	59.2307i	−0.0279913	−	3.01868i
$386$	−18.1859	+	1.04048i	−0.925638	+	0.0529588i
$387$	8.59801	−	4.38091i	0.437061	−	0.222694i
$388$	0.778999	−	18.1993i	0.0395477	−	0.923932i
$389$	−8.13527	−	25.0378i	−0.412475	−	1.26947i	−0.914490	−	0.404608i	$-0.867408\pi$
$389$	−8.13527	−	25.0378i	−0.412475	−	1.26947i	0.502015	−	0.864859i	$-0.332592\pi$
$390$	12.4243	−	0.826481i	0.629129	−	0.0418505i
$391$	−26.2425	−	8.52669i	−1.32714	−	0.431213i
$392$	−26.9254	−	18.9772i	−1.35994	−	0.958493i
$393$	−4.20028	+	4.20028i	−0.211876	+	0.211876i
$394$	4.90157	−	4.00825i	0.246937	−	0.201933i
$395$	13.1769	+	6.56077i	0.663000	+	0.330108i
$396$	−12.1890	+	1.39933i	−0.612523	+	0.0703191i
$397$	−1.17853	+	7.44092i	−0.0591485	+	0.373449i	0.940303	+	0.340338i	$0.110541\pi$
$397$	−1.17853	+	7.44092i	−0.0591485	+	0.373449i	−0.999452	+	0.0331110i	$0.989459\pi$
$398$	22.3426	+	19.9244i	1.11993	+	0.998718i
$399$	−20.3692			−1.01974
$400$	7.44013	−	18.5646i	0.372006	−	0.928230i
$401$	−15.6970			−0.783873			−0.391936	−	0.919992i	$-0.628195\pi$
$401$	−15.6970			−0.783873			−0.391936	+	0.919992i	$0.628195\pi$
$402$	0.662210	+	0.590536i	0.0330280	+	0.0294533i
$403$	3.63063	−	22.9229i	0.180855	−	1.14187i
$404$	21.3745	−	2.45385i	1.06342	−	0.122083i
$405$	0.329305	−	2.21169i	0.0163633	−	0.109900i
$406$	−28.6531	+	23.4310i	−1.42203	+	1.16286i
$407$	8.04676	−	8.04676i	0.398863	−	0.398863i
$408$	8.07138	−	11.4519i	0.399593	−	0.566953i
$409$	22.5692	+	7.33319i	1.11598	+	0.362603i	0.808231	−	0.588866i	$-0.200425\pi$
$409$	22.5692	+	7.33319i	1.11598	+	0.362603i	0.307746	+	0.951469i	$0.400425\pi$
$410$	−4.96277	−	3.12452i	−0.245094	−	0.154309i
$411$	−2.38572	−	7.34250i	−0.117679	−	0.362179i
$412$	−1.14898	+	26.8431i	−0.0566062	+	1.32246i
$413$	19.7352	−	10.0556i	0.971107	−	0.494804i
$414$	−7.86495	+	0.449980i	−0.386541	+	0.0221153i
$415$	12.2204	+	16.4960i	0.599874	+	0.809759i
$416$	22.2654	+	0.632598i	1.09165	+	0.0310157i
$417$	0.271952	+	1.71704i	0.0133175	+	0.0840836i
$418$	−20.6314	−	35.3425i	−1.00912	−	1.72866i
$419$	−5.11504	+	7.04024i	−0.249886	+	0.343938i	−0.915471	−	0.402383i	$-0.868182\pi$
$419$	−5.11504	+	7.04024i	−0.249886	+	0.343938i	0.665585	+	0.746322i	$0.268182\pi$
$420$	18.1560	+	6.57943i	0.885920	+	0.321043i
$421$	6.67806	+	9.19155i	0.325469	+	0.447969i	0.940127	−	0.340824i	$-0.110706\pi$
$421$	6.67806	+	9.19155i	0.325469	+	0.447969i	−0.614658	+	0.788793i	$0.710706\pi$
$422$	14.2665	−	32.4607i	0.694482	−	1.58016i
$423$	1.69333	−	3.32335i	0.0823327	−	0.161587i
$424$	1.97844	−	2.03615i	0.0960817	−	0.0988843i
$425$	−22.2725	−	10.8329i	−1.08037	−	0.525475i
$426$	9.67341	+	2.54237i	0.468678	+	0.123178i
$427$	−0.439187	+	0.861953i	−0.0212537	+	0.0417128i
$428$	6.08320	−	7.66107i	0.294042	−	0.370312i
$429$	−19.5421	+	14.1982i	−0.943502	+	0.685494i
$430$	−15.6278	−	26.2098i	−0.753638	−	1.26395i
$431$	−14.3062	+	19.6909i	−0.689107	+	0.948475i	−0.999998	−	0.00197063i	$-0.999373\pi$
$431$	−14.3062	+	19.6909i	−0.689107	+	0.948475i	0.310891	+	0.950446i	$0.399373\pi$
$432$	0.961044	−	3.88283i	0.0462383	−	0.186813i
$433$	25.0008	−	3.95973i	1.20146	−	0.190293i	0.476557	−	0.879144i	$-0.341885\pi$
$433$	25.0008	−	3.95973i	1.20146	−	0.190293i	0.724903	+	0.688851i	$0.241885\pi$
$434$	19.4589	−	30.2808i	0.934059	−	1.45352i
$435$	7.86424	−	11.0380i	0.377061	−	0.529231i
$436$	5.20448	+	1.05423i	0.249249	+	0.0504883i
$437$	−11.9293	−	23.4125i	−0.570655	−	1.11997i
$438$	−3.71424	+	0.808104i	−0.177473	+	0.0386127i
$439$	8.39811	+	25.8467i	0.400820	+	1.23360i	0.924335	+	0.381581i	$0.124620\pi$
$439$	8.39811	+	25.8467i	0.400820	+	1.23360i	−0.523515	+	0.852016i	$0.675380\pi$
$440$	6.97374	+	38.1664i	0.332460	+	1.81951i
$441$	−3.59893	+	11.0764i	−0.171378	+	0.527447i
$442$	2.75182	−	27.4461i	0.130891	−	1.30548i
$443$	−27.1261	+	27.1261i	−1.28880	+	1.28880i	−0.353282	+	0.935517i	$0.614934\pi$
$443$	−27.1261	+	27.1261i	−1.28880	+	1.28880i	−0.935517	+	0.353282i	$0.885066\pi$
$444$	1.54143	+	3.37471i	0.0731531	+	0.160157i
$445$	−16.0232	−	15.7288i	−0.759574	−	0.745616i
$446$	18.4359	−	7.17839i	0.872963	−	0.339907i
$447$	−1.94652	+	12.2898i	−0.0920671	+	0.581289i
$448$	31.2180	+	14.7920i	1.47491	+	0.698856i
$449$		−	27.4923i		−	1.29744i	−0.761026	−	0.648721i	$-0.775304\pi$
$449$		−	27.4923i		−	1.29744i	0.761026	−	0.648721i	$-0.224696\pi$
$450$	−7.04766	−	0.574835i	−0.332230	−	0.0270980i
$451$	11.3765			0.535700
$452$	20.5321	−	13.6152i	0.965749	−	0.640405i
$453$	3.67122	+	0.581464i	0.172489	+	0.0273196i
$454$	5.97308	−	2.32575i	0.280330	−	0.109153i
$455$	37.4952	−	6.29559i	1.75780	−	0.295142i
$456$	13.1464	−	2.27634i	0.615637	−	0.106599i
$457$	24.2037	+	24.2037i	1.13220	+	1.13220i	0.989810	+	0.142393i	$0.0454797\pi$
$457$	24.2037	+	24.2037i	1.13220	+	1.13220i	0.142393	+	0.989810i	$0.454520\pi$
$458$	−14.4732	−	1.45112i	−0.676288	−	0.0678064i
$459$	−4.71101	−	1.53070i	−0.219891	−	0.0714469i
$460$	3.07064	+	24.7219i	0.143169	+	1.15266i
$461$	4.37173	−	1.42046i	0.203612	−	0.0661575i	−0.205436	−	0.978671i	$-0.565861\pi$
$461$	4.37173	−	1.42046i	0.203612	−	0.0661575i	0.409047	+	0.912513i	$0.365861\pi$
$462$	−36.6060	+	7.96434i	−1.70307	+	0.370535i
$463$	19.6652	−	10.0199i	0.913919	−	0.465665i	0.0672205	−	0.997738i	$-0.478587\pi$
$463$	19.6652	−	10.0199i	0.913919	−	0.465665i	0.846698	+	0.532073i	$0.178587\pi$
$464$	15.8744	−	18.3246i	0.736949	−	0.850699i
$465$	−3.95634	+	12.5718i	−0.183471	+	0.583004i
$466$	15.5721	+	10.0069i	0.721363	+	0.463560i
$467$	−0.626657	−	3.95656i	−0.0289982	−	0.183088i	0.968938	−	0.247305i	$-0.0795449\pi$
$467$	−0.626657	−	3.95656i	−0.0289982	−	0.183088i	−0.997936	+	0.0642173i	$0.979545\pi$
$468$	−2.11104	−	7.58696i	−0.0975830	−	0.350707i
$469$	2.19178	+	1.59242i	0.101207	+	0.0735314i
$470$	−10.8416	−	4.64543i	−0.500087	−	0.214278i
$471$	−0.356452	−	0.490614i	−0.0164244	−	0.0226063i
$472$	−11.6135	+	8.69543i	−0.534553	+	0.400240i
$473$	52.7450	+	26.8749i	2.42522	+	1.23571i
$474$	2.36640	−	9.00386i	0.108692	−	0.413561i
$475$	−7.70306	−	22.2922i	−0.353441	−	1.02284i
$476$	21.0337	−	37.2513i	0.964080	−	1.70741i
$477$	−0.894350	−	0.455694i	−0.0409495	−	0.0208648i
$478$	7.21468	−	16.4156i	0.329992	−	0.750834i
$479$	23.0351	−	16.7360i	1.05250	−	0.764687i	0.0798152	−	0.996810i	$-0.474567\pi$
$479$	23.0351	−	16.7360i	1.05250	−	0.764687i	0.972687	+	0.232122i	$0.0745670\pi$
$480$	−12.4532	−	2.21740i	−0.568410	−	0.101210i
$481$	5.90937	+	4.29341i	0.269444	+	0.195763i
$482$	−12.1069	+	7.06748i	−0.551454	+	0.321915i
$483$	−23.7579	+	3.76288i	−1.08102	+	0.171217i
$484$	−36.0192	−	39.2406i	−1.63724	−	1.78367i
$485$	6.47280	+	19.3101i	0.293915	+	0.876828i
$486$	−1.41190	+	0.0807798i	−0.0640453	+	0.00366425i
$487$	6.83376	+	13.4120i	0.309667	+	0.607756i	0.992420	−	0.122893i	$-0.0392173\pi$
$487$	6.83376	+	13.4120i	0.309667	+	0.607756i	−0.682753	+	0.730650i	$0.739217\pi$
$488$	0.187127	−	0.605390i	0.00847084	−	0.0274047i
$489$	−18.0323	+	5.85905i	−0.815449	+	0.264956i
$490$	35.7048	+	9.03086i	1.61298	+	0.407972i
$491$	9.85489	−	30.3302i	0.444745	−	1.36878i	−0.438019	−	0.898966i	$-0.644320\pi$
$491$	9.85489	−	30.3302i	0.444745	−	1.36878i	0.882763	−	0.469818i	$-0.155680\pi$
$492$	−1.29595	+	3.47523i	−0.0584257	+	0.156675i
$493$	−21.2296	−	21.2296i	−0.956135	−	0.956135i
$494$	20.3344	−	16.6284i	0.914889	−	0.748149i
$495$	12.1639	−	6.34057i	0.546727	−	0.284988i
$496$	−9.17491	+	21.7180i	−0.411966	+	0.975167i
$497$	30.1638	+	4.77748i	1.35303	+	0.214299i
$498$	8.64163	−	9.69047i	0.387241	−	0.434240i
$499$		−	18.7164i		−	0.837862i	−0.908018	−	0.418931i	$-0.862405\pi$
$499$		−	18.7164i		−	0.837862i	0.908018	−	0.418931i	$-0.137595\pi$
$500$	−0.334509	+	22.3582i	−0.0149597	+	0.999888i
$501$			20.3642i			0.909804i
$502$	−18.4916	−	16.4902i	−0.825323	−	0.735995i
$503$	17.5075	+	2.77292i	0.780623	+	0.123638i	0.534013	−	0.845476i	$-0.320683\pi$
$503$	17.5075	+	2.77292i	0.780623	+	0.123638i	0.246610	+	0.969115i	$0.420683\pi$
$504$	1.73704	−	12.0894i	0.0773740	−	0.538505i
$505$	−21.3304	+	11.1187i	−0.949192	+	0.494777i
$506$	−30.5927	−	37.4109i	−1.36001	−	1.66312i
$507$	−1.77104	−	1.77104i	−0.0786546	−	0.0786546i
$508$	5.98647	−	16.0534i	0.265607	−	0.712254i
$509$	−5.66741	+	17.4425i	−0.251204	+	0.773125i	0.743350	+	0.668902i	$0.233236\pi$
$509$	−5.66741	+	17.4425i	−0.251204	+	0.773125i	−0.994554	+	0.104223i	$0.966764\pi$
$510$	−3.84101	+	15.1860i	−0.170083	+	0.672445i
$511$	−11.0383	+	3.58656i	−0.488305	+	0.158660i
$512$	−21.8014	−	6.05809i	−0.963493	−	0.267732i
$513$	−2.14153	−	4.20299i	−0.0945508	−	0.185566i
$514$	0.936186	+	16.3631i	0.0412934	+	0.721744i
$515$	−9.54704	−	28.4814i	−0.420693	−	1.25504i
$516$	−14.2180	+	13.0508i	−0.625911	+	0.574527i
$517$	22.5995	−	3.57941i	0.993925	−	0.157422i
$518$	5.71110	+	9.78336i	0.250931	+	0.429856i
$519$	11.2988	+	8.20905i	0.495962	+	0.360337i
$520$	−23.4961	+	8.25345i	−1.03037	+	0.361938i
$521$	−25.9177	+	18.8303i	−1.13548	+	0.824972i	−0.986483	−	0.163866i	$-0.947603\pi$
$521$	−25.9177	+	18.8303i	−1.13548	+	0.824972i	−0.148994	+	0.988838i	$0.547603\pi$
$522$	−7.84722	−	3.44885i	−0.343463	−	0.150952i
$523$	−17.4815	−	8.90727i	−0.764413	−	0.389488i	0.0278937	−	0.999611i	$-0.491120\pi$
$523$	−17.4815	−	8.90727i	−0.764413	−	0.389488i	−0.792307	+	0.610123i	$0.791120\pi$
$524$	5.84123	−	10.3450i	0.255175	−	0.451923i
$525$	−21.5870	+	0.400375i	−0.942135	+	0.0174738i
$526$	−12.8224	−	3.36999i	−0.559083	−	0.146939i
$527$	26.0140	+	13.2548i	1.13319	+	0.577388i
$528$	22.7357	−	9.23110i	0.989443	−	0.401732i
$529$	−4.71990	−	6.49639i	−0.205213	−	0.282452i
$530$	−1.25013	+	2.91759i	−0.0543023	+	0.126732i
$531$	4.14974	+	3.01497i	0.180084	+	0.130838i
$532$	39.2475	−	10.9205i	1.70159	−	0.473462i
$533$	1.14233	+	7.21236i	0.0494796	+	0.312402i
$534$	−7.67702	+	11.9465i	−0.332217	+	0.516976i
$535$	−3.28318	+	10.4328i	−0.141944	+	0.451047i
$536$	−1.59255	−	0.782819i	−0.0687877	−	0.0338126i
$537$	−5.70493	+	2.90681i	−0.246186	+	0.125438i
$538$	7.46630	+	34.3169i	0.321895	+	1.47951i
$539$	−67.9487	+	22.0779i	−2.92676	+	0.950961i
$540$	0.551237	+	4.43803i	0.0237214	+	0.190983i
$541$	−30.6377	−	9.95480i	−1.31722	−	0.427990i	−0.435680	−	0.900102i	$-0.643492\pi$
$541$	−30.6377	−	9.95480i	−1.31722	−	0.427990i	−0.881539	+	0.472111i	$0.843492\pi$
$542$	−1.70823	+	17.0375i	−0.0733747	+	0.731825i
$543$	1.84064	+	1.84064i	0.0789893	+	0.0789893i
$544$	−9.41230	+	26.3928i	−0.403549	+	1.13158i
$545$	−5.85500	+	0.983077i	−0.250801	+	0.0421104i
$546$	−8.72478	−	22.4073i	−0.373386	−	0.958946i
$547$	−45.7795	−	7.25076i	−1.95739	−	0.310020i	−0.999757	−	0.0220257i	$-0.992988\pi$
$547$	−45.7795	−	7.25076i	−1.95739	−	0.310020i	−0.957632	−	0.287994i	$-0.907012\pi$
$548$	8.53333	+	12.8685i	0.364526	+	0.549716i
$549$	−0.224030			−0.00956135
$550$	−22.5596	−	37.0500i	−0.961944	−	1.57982i
$551$		−	28.5908i		−	1.21801i
$552$	14.9130	−	5.08363i	0.634738	−	0.216373i
$553$	4.44680	−	28.0760i	0.189097	−	1.19391i
$554$	6.86681	+	17.6356i	0.291743	+	0.749267i
$555$	−2.96014	−	2.90575i	−0.125651	−	0.123342i
$556$	−1.44454	−	3.16259i	−0.0612623	−	0.134124i
$557$	−9.67756	+	9.67756i	−0.410051	+	0.410051i	−0.881756	−	0.471705i	$-0.843639\pi$
$557$	−9.67756	+	9.67756i	−0.410051	+	0.410051i	0.471705	+	0.881756i	$0.343639\pi$
$558$	8.29396	+	0.831574i	0.351111	+	0.0352033i
$559$	−11.7417	+	36.1372i	−0.496620	+	1.52844i
$560$	−38.5104	−	2.94338i	−1.62736	−	0.124381i
$561$	−9.39016	−	28.8999i	−0.396453	−	1.22016i
$562$	−4.41782	−	20.3054i	−0.186355	−	0.856530i
$563$	−8.83475	−	17.3392i	−0.372340	−	0.730759i	0.626474	−	0.779442i	$-0.284498\pi$
$563$	−8.83475	−	17.3392i	−0.372340	−	0.730759i	−0.998814	+	0.0486832i	$0.984498\pi$
$564$	−1.48098	+	7.31129i	−0.0623607	+	0.307861i
$565$	−15.9827	+	22.4328i	−0.672397	+	0.943755i
$566$	−32.6130	−	20.9577i	−1.37083	−	0.880916i
$567$	−4.26498	+	0.675507i	−0.179112	+	0.0283686i
$568$	−20.0018	+	0.287515i	−0.839256	+	0.0120639i
$569$	13.6031	−	18.7230i	0.570270	−	0.784910i	−0.422316	−	0.906448i	$-0.638783\pi$
$569$	13.6031	−	18.7230i	0.570270	−	0.784910i	0.992587	+	0.121539i	$0.0387829\pi$
$570$	−12.8122	+	7.63936i	−0.536644	+	0.319977i
$571$	32.4501	−	23.5764i	1.35800	−	0.986642i	0.359427	−	0.933173i	$-0.382972\pi$
$571$	32.4501	−	23.5764i	1.35800	−	0.986642i	0.998570	−	0.0534685i	$-0.0170277\pi$
$572$	30.0418	−	37.8341i	1.25611	−	1.58192i
$573$	5.39078	−	10.5800i	0.225203	−	0.441986i
$574$	−2.87869	+	10.9531i	−0.120154	+	0.457172i
$575$	−13.1027	−	24.5778i	−0.546420	−	1.02497i
$576$	0.229944	+	7.99669i	0.00958100	+	0.333196i
$577$	−1.92201	+	3.77216i	−0.0800143	+	0.157037i	−0.927547	−	0.373706i	$-0.878087\pi$
$577$	−1.92201	+	3.77216i	−0.0800143	+	0.157037i	0.847533	+	0.530743i	$0.178087\pi$
$578$	9.75762	+	4.28847i	0.405863	+	0.178377i
$579$	−7.57091	−	10.4205i	−0.314636	−	0.433060i
$580$	−9.23508	+	25.4843i	−0.383466	+	1.05818i
$581$	23.3028	−	32.0735i	0.966762	−	1.33063i
$582$	11.1240	−	6.49370i	0.461105	−	0.269173i
$583$	−0.963257	−	6.08176i	−0.0398940	−	0.251881i
$584$	6.72336	−	3.54836i	0.278214	−	0.146832i
$585$	5.24111	+	7.07488i	0.216693	+	0.292510i
$586$	−1.88031	−	32.8649i	−0.0776749	−	1.35764i
$587$	8.60125	−	4.38256i	0.355012	−	0.180888i	−0.267384	−	0.963590i	$-0.586159\pi$
$587$	8.60125	−	4.38256i	0.355012	−	0.180888i	0.622396	+	0.782702i	$0.286159\pi$
$588$	0.996105	−	23.2715i	0.0410787	−	0.959700i
$589$	8.59168	+	26.4425i	0.354014	+	1.08954i
$590$	8.64212	−	13.7265i	0.355791	−	0.565112i
$591$	4.25811	+	1.38354i	0.175155	+	0.0569114i
$592$	−4.77930	−	5.67600i	−0.196428	−	0.233282i
$593$	−33.0814	+	33.0814i	−1.35849	+	1.35849i	−0.482708	+	0.875782i	$0.660347\pi$
$593$	−33.0814	+	33.0814i	−1.35849	+	1.35849i	−0.875782	+	0.482708i	$0.839653\pi$
$594$	−5.49195	−	6.71595i	−0.225338	−	0.275559i
$595$	−7.04374	+	47.3074i	−0.288765	+	1.93941i
$596$	−2.83834	−	24.7236i	−0.116263	−	1.01272i
$597$	−3.31141	+	20.9074i	−0.135527	+	0.855684i
$598$	20.6455	−	23.1512i	0.844257	−	0.946725i
$599$	3.09819			0.126589			0.0632943	−	0.997995i	$-0.479839\pi$
$599$	3.09819			0.126589			0.0632943	+	0.997995i	$0.479839\pi$
$600$	13.8876	−	2.67084i	0.566961	−	0.109037i
$601$	−35.3961			−1.44384			−0.721919	−	0.691977i	$-0.756740\pi$
$601$	−35.3961			−1.44384			−0.721919	+	0.691977i	$0.756740\pi$
$602$	−39.2210	+	43.9813i	−1.59853	+	1.79254i
$603$	−0.0981466	+	0.619673i	−0.00399684	+	0.0252350i
$604$	−7.38546	+	0.847869i	−0.300510	+	0.0344993i
$605$	53.3102	+	26.5432i	2.16737	+	1.07913i
$606$	9.63060	+	11.7770i	0.391216	+	0.478407i
$607$	−20.2163	+	20.2163i	−0.820553	+	0.820553i	−0.986187	−	0.165634i	$-0.947033\pi$
$607$	−20.2163	+	20.2163i	−0.820553	+	0.820553i	0.165634	+	0.986187i	$0.447033\pi$
$608$	−24.1101	+	11.4342i	−0.977795	+	0.463718i
$609$	−24.8917	−	8.08779i	−1.00866	−	0.327734i
$610$	0.0470227	+	0.706881i	0.00190389	+	0.0286208i
$611$	4.53846	+	13.9680i	0.183607	+	0.565083i
$612$	9.89783	+	0.423664i	0.400096	+	0.0171256i
$613$	33.7457	−	17.1943i	1.36298	−	0.694472i	0.389026	−	0.921227i	$-0.372812\pi$
$613$	33.7457	−	17.1943i	1.36298	−	0.694472i	0.973952	+	0.226755i	$0.0728117\pi$
$614$	1.49390	+	26.1110i	0.0602887	+	1.05375i
$615$	−0.0384503	−	4.14661i	−0.00155046	−	0.167207i
$616$	66.2627	−	34.9711i	2.66980	−	1.40903i
$617$	1.98224	+	12.5154i	0.0798021	+	0.503851i	0.994920	+	0.100665i	$0.0320971\pi$
$617$	1.98224	+	12.5154i	0.0798021	+	0.503851i	−0.915118	+	0.403186i	$0.867903\pi$
$618$	−16.4073	+	9.57786i	−0.659998	+	0.385278i
$619$	−15.8578	+	21.8264i	−0.637379	+	0.877278i	−0.998472	−	0.0552522i	$-0.982404\pi$
$619$	−15.8578	+	21.8264i	−0.637379	+	0.877278i	0.361093	+	0.932530i	$0.382404\pi$
$620$	0.883006	−	26.3445i	0.0354624	−	1.05802i
$621$	−3.27423	−	4.50659i	−0.131390	−	0.180843i
$622$	25.4964	+	11.2057i	1.02231	+	0.449307i
$623$	−19.6849	+	38.6339i	−0.788661	+	1.54783i
$624$	8.13513	+	13.4868i	0.325666	+	0.539904i
$625$	−8.60177	−	23.4736i	−0.344071	−	0.938944i
$626$	1.23216	−	4.68822i	0.0492471	−	0.187379i
$627$	13.1373	−	25.7834i	0.524654	−	1.02969i
$628$	0.949843	+	0.754213i	0.0379029	+	0.0300964i
$629$	−7.43393	+	5.40106i	−0.296410	+	0.215354i
$630$	3.02663	+	13.3155i	0.120584	+	0.530504i
$631$	24.0127	−	33.0507i	0.955932	−	1.31573i	0.00709014	−	0.999975i	$-0.497743\pi$
$631$	24.0127	−	33.0507i	0.955932	−	1.31573i	0.948842	−	0.315752i	$-0.102257\pi$
$632$	0.267615	+	18.6174i	0.0106451	+	0.740559i
$633$	24.7635	−	3.92216i	0.984262	−	0.155892i
$634$	19.8526	+	12.7576i	0.788449	+	0.506671i
$635$	0.177616	+	19.1548i	0.00704849	+	0.760134i
$636$	1.96755	+	0.398549i	0.0780183	+	0.0158035i
$637$	−20.8194	−	40.8604i	−0.824896	−	1.61895i
$638$	−11.1790	−	51.3813i	−0.442580	−	2.03420i
$639$	2.18550	+	6.72628i	0.0864571	+	0.266088i
$640$	25.1837	−	2.40401i	0.995475	−	0.0950268i
$641$	1.70828	−	5.25755i	0.0674731	−	0.207661i	−0.911635	−	0.411000i	$-0.865180\pi$
$641$	1.70828	−	5.25755i	0.0674731	−	0.207661i	0.979108	+	0.203340i	$0.0651795\pi$
$642$	6.88276	+	0.690083i	0.271641	+	0.0272354i
$643$	−34.2132	+	34.2132i	−1.34924	+	1.34924i	−0.462748	+	0.886490i	$0.653137\pi$
$643$	−34.2132	+	34.2132i	−1.34924	+	1.34924i	−0.886490	+	0.462748i	$0.846863\pi$
$644$	43.7594	−	19.9876i	1.72436	−	0.787620i
$645$	9.61731	−	19.3157i	0.378681	−	0.760557i
$646$	11.9898	+	30.7926i	0.471731	+	1.21152i
$647$	4.06904	−	25.6909i	0.159971	−	1.01001i	−0.768835	−	0.639447i	$-0.779163\pi$
$647$	4.06904	−	25.6909i	0.159971	−	1.01001i	0.928806	−	0.370567i	$-0.120837\pi$
$648$	2.67715	−	0.912605i	0.105169	−	0.0358505i
$649$			31.4664i			1.23516i
$650$	21.2233	−	18.0223i	0.832446	−	0.706892i
$651$	25.4517			0.997530
$652$	31.6035	−	20.9568i	1.23769	−	0.820733i
$653$	−38.6219	−	6.11710i	−1.51139	−	0.239381i	−0.654968	−	0.755656i	$-0.727318\pi$
$653$	−38.6219	−	6.11710i	−1.51139	−	0.239381i	−0.856422	+	0.516276i	$0.827318\pi$
$654$	1.36240	+	3.49898i	0.0532742	+	0.136821i
$655$	−1.95610	+	13.1376i	−0.0764312	+	0.513329i
$656$	0.633874	−	7.39086i	0.0247486	−	0.288565i
$657$	−1.90056	−	1.90056i	−0.0741481	−	0.0741481i
$658$	−2.27235	+	22.6640i	−0.0885854	+	0.883534i
$659$	39.9221	+	12.9715i	1.55514	+	0.505297i	0.955506	−	0.294973i	$-0.0953107\pi$
$659$	39.9221	+	12.9715i	1.55514	+	0.505297i	0.599639	+	0.800270i	$0.295311\pi$
$660$	−20.0381	+	18.7384i	−0.779983	+	0.729392i
$661$	−14.0571	+	4.56742i	−0.546757	+	0.177652i	−0.569354	−	0.822093i	$-0.692807\pi$
$661$	−14.0571	+	4.56742i	−0.546757	+	0.177652i	0.0225971	+	0.999745i	$0.492807\pi$
$662$	1.45567	+	6.69058i	0.0565761	+	0.260037i
$663$	17.3788	−	8.85493i	0.674936	−	0.343897i
$664$	−11.4554	+	23.3046i	−0.444556	+	0.904394i
$665$	−36.5984	+	27.1124i	−1.41923	+	1.05137i
$666$	−1.41826	+	2.20701i	−0.0549564	+	0.0855198i
$667$	−5.28169	−	33.3473i	−0.204508	−	1.29121i
$668$	−10.9178	−	39.2377i	−0.422420	−	1.51815i
$669$	11.3177	+	8.22280i	0.437568	+	0.317912i
$670$	1.97586	+	0.179616i	0.0763341	+	0.00693917i
$671$	−0.807806	−	1.11185i	−0.0311850	−	0.0429225i
$672$	3.13451	+	24.2252i	0.120916	+	0.934507i
$673$	−33.0550	−	16.8424i	−1.27418	−	0.649225i	−0.319702	−	0.947518i	$-0.603583\pi$
$673$	−33.0550	−	16.8424i	−1.27418	−	0.649225i	−0.954474	+	0.298293i	$0.903583\pi$
$674$	21.8902	+	5.75319i	0.843178	+	0.221605i
$675$	−2.35218	−	4.41217i	−0.0905353	−	0.169825i
$676$	4.36194	+	2.46294i	0.167767	+	0.0947286i
$677$	−2.85945	−	1.45696i	−0.109898	−	0.0559956i	0.398178	−	0.917308i	$-0.369643\pi$
$677$	−2.85945	−	1.45696i	−0.109898	−	0.0559956i	−0.508075	+	0.861313i	$0.669643\pi$
$678$	15.9481	+	7.00919i	0.612483	+	0.269186i
$679$	31.8184	−	23.1174i	1.22108	−	0.887165i
$680$	−0.740719	−	31.3196i	−0.0284053	−	1.20105i
$681$	3.66685	+	2.66412i	0.140514	+	0.102089i
$682$	25.7793	+	44.1611i	0.987140	+	1.69101i
$683$	15.6314	−	2.47577i	0.598119	−	0.0947327i	0.149968	−	0.988691i	$-0.452083\pi$
$683$	15.6314	−	2.47577i	0.598119	−	0.0947327i	0.448150	+	0.893958i	$0.352083\pi$
$684$	6.37963	+	6.95020i	0.243931	+	0.265747i
$685$	−14.0598	−	10.0172i	−0.537196	−	0.382736i
$686$	−1.62075	−	28.3282i	−0.0618806	−	1.08158i
$687$	−4.66948	−	9.16436i	−0.178152	−	0.349642i
$688$	20.3984	−	32.7688i	0.777680	−	1.24930i
$689$	3.75893	−	1.22135i	0.143204	−	0.0465297i
$690$	−13.5324	+	11.2771i	−0.515171	+	0.429312i
$691$	8.64567	−	26.6086i	0.328897	−	1.01224i	−0.640754	−	0.767746i	$-0.721378\pi$
$691$	8.64567	−	26.6086i	0.328897	−	1.01224i	0.969651	−	0.244494i	$-0.0786218\pi$
$692$	−26.1716	−	9.75965i	−0.994895	−	0.371006i
$693$	−18.7312	−	18.7312i	−0.711539	−	0.711539i
$694$	−29.9742	−	36.6546i	−1.13781	−	1.39139i
$695$	2.77408	+	2.72311i	0.105227	+	0.103293i
$696$	16.9691	+	2.43816i	0.643210	+	0.0924183i
$697$	−9.07307	−	1.43703i	−0.343667	−	0.0544315i
$698$	10.8569	+	9.68184i	0.410941	+	0.366463i
$699$			13.0887i			0.495060i
$700$	41.3793	−	12.3448i	1.56399	−	0.466590i
$701$			33.3680i			1.26029i	0.776477	+	0.630146i	$0.217005\pi$
$701$			33.3680i			1.26029i	−0.776477	+	0.630146i	$0.782995\pi$
$702$	3.70625	−	4.15608i	0.139883	−	0.156861i
$703$	−8.64271	−	1.36887i	−0.325966	−	0.0516279i
$704$	−38.8581	+	29.9757i	−1.46452	+	1.12975i
$705$	−1.38103	−	8.22515i	−0.0520127	−	0.309777i
$706$	13.8139	−	11.2963i	0.519893	−	0.425141i
$707$	32.8467	+	32.8467i	1.23533	+	1.23533i
$708$	−9.61214	−	3.58446i	−0.361246	−	0.134712i
$709$	1.14957	−	3.53802i	0.0431731	−	0.132873i	−0.927147	−	0.374699i	$-0.877746\pi$
$709$	1.14957	−	3.53802i	0.0431731	−	0.132873i	0.970320	+	0.241826i	$0.0777462\pi$
$710$	20.7647	−	8.30773i	0.779287	−	0.311784i
$711$	6.26072	−	2.03423i	0.234795	−	0.0762896i
$712$	8.38728	−	27.1344i	0.314327	−	1.01690i
$713$	14.9058	+	29.2544i	0.558228	+	1.09558i
$714$	30.2002	−	1.72786i	1.13022	−	0.0646634i
$715$	−16.2139	+	51.5220i	−0.606366	+	1.92681i
$716$	9.43386	−	8.65940i	0.352560	−	0.323617i
$717$	12.5231	−	1.98347i	0.467684	−	0.0740739i
$718$	−27.7779	+	16.2155i	−1.03666	+	0.605158i
$719$	5.82305	+	4.23069i	0.217163	+	0.157778i	0.691049	−	0.722808i	$-0.257149\pi$
$719$	5.82305	+	4.23069i	0.217163	+	0.157778i	−0.473886	+	0.880586i	$0.657149\pi$
$720$	−3.44147	−	8.25568i	−0.128256	−	0.307671i
$721$	−46.9304	+	34.0970i	−1.74778	+	1.26984i
$722$	−1.85000	+	4.20933i	−0.0688498	+	0.156655i
$723$	−8.83235	−	4.50031i	−0.328479	−	0.167368i
$724$	−4.53336	−	2.55973i	−0.168481	−	0.0951317i
$725$	−0.561978	−	30.3002i	−0.0208713	−	1.12532i
$726$	9.57384	−	36.4273i	0.355319	−	1.35194i
$727$	−24.6378	−	12.5536i	−0.913764	−	0.465586i	−0.0671198	−	0.997745i	$-0.521381\pi$
$727$	−24.6378	−	12.5536i	−0.913764	−	0.465586i	−0.846645	+	0.532159i	$0.821381\pi$
$728$	28.8241	+	38.4970i	1.06829	+	1.42679i
$729$	−0.587785	−	0.809017i	−0.0217698	−	0.0299636i
$730$	−5.59794	+	6.39578i	−0.207189	+	0.236718i
$731$	−38.6707	−	28.0959i	−1.43029	−	1.03917i
$732$	0.431661	−	0.120108i	0.0159546	−	0.00443932i
$733$	2.76403	+	17.4514i	0.102092	+	0.644582i	0.984671	+	0.174419i	$0.0558048\pi$
$733$	2.76403	+	17.4514i	0.102092	+	0.644582i	−0.882580	+	0.470163i	$0.844195\pi$
$734$	−31.4298	−	20.1973i	−1.16010	−	0.745497i
$735$	8.27677	+	24.6919i	0.305293	+	0.910773i
$736$	−26.0089	+	17.7904i	−0.958700	+	0.655762i
$737$	−3.42931	+	1.74732i	−0.126320	+	0.0643634i
$738$	−2.56270	+	0.557566i	−0.0943345	+	0.0205243i
$739$	33.6371	−	10.9294i	1.23736	−	0.402043i	0.383986	−	0.923339i	$-0.374551\pi$
$739$	33.6371	−	10.9294i	1.23736	−	0.402043i	0.853376	+	0.521296i	$0.174551\pi$
$740$	7.26146	+	4.01180i	0.266937	+	0.147477i
$741$	17.6650	+	5.73971i	0.648940	+	0.210854i
$742$	6.09912	+	0.611513i	0.223906	+	0.0224494i
$743$	18.6309	+	18.6309i	0.683503	+	0.683503i	0.960788	−	0.277285i	$-0.0894346\pi$
$743$	18.6309	+	18.6309i	0.683503	+	0.683503i	−0.277285	+	0.960788i	$0.589435\pi$
$744$	−16.4267	+	2.84433i	−0.602230	+	0.104278i
$745$	12.8609	+	24.6727i	0.471187	+	0.903937i
$746$	1.06779	−	0.415766i	0.0390945	−	0.0152223i
$747$	9.06800	+	1.43623i	0.331781	+	0.0525489i
$748$	33.5870	+	50.6502i	1.22806	+	1.85195i
$749$	21.1211			0.771750
$750$	−13.4280	+	8.34792i	−0.490323	+	0.304823i
$751$			2.89670i			0.105702i	0.998602	+	0.0528511i	$0.0168309\pi$
$751$			2.89670i			0.105702i	−0.998602	+	0.0528511i	$0.983169\pi$
$752$	−1.06620	−	14.8814i	−0.0388805	−	0.542669i
$753$	2.74066	−	17.3038i	0.0998752	−	0.630587i
$754$	31.4516	−	12.2464i	1.14540	−	0.445986i
$755$	7.37023	−	3.84181i	0.268230	−	0.139818i
$756$	7.85563	−	3.58814i	0.285706	−	0.130499i
$757$	22.2796	−	22.2796i	0.809764	−	0.809764i	−0.174834	−	0.984598i	$-0.555939\pi$
$757$	22.2796	−	22.2796i	0.809764	−	0.809764i	0.984598	+	0.174834i	$0.0559388\pi$
$758$	3.92712	−	39.1684i	0.142639	−	1.42266i
$759$	10.5598	−	32.4997i	0.383297	−	1.17967i
$760$	20.5909	−	21.5885i	0.746911	−	0.783097i
$761$	−0.200292	−	0.616434i	−0.00726056	−	0.0223457i	0.947361	−	0.320169i	$-0.103740\pi$
$761$	−0.200292	−	0.616434i	−0.00726056	−	0.0223457i	−0.954621	+	0.297823i	$0.903740\pi$
$762$	11.8381	−	2.57561i	0.428850	−	0.0933045i
$763$	5.20503	+	10.2155i	0.188435	+	0.369824i
$764$	−4.71476	+	23.2757i	−0.170574	+	0.842086i
$765$	−10.5019	+	3.52028i	−0.379699	+	0.127276i
$766$	−10.1215	+	15.7504i	−0.365703	+	0.569084i
$767$	−19.9487	+	3.15956i	−0.720305	+	0.114085i
$768$	−4.73029	−	15.2848i	−0.170690	−	0.551542i
$769$	0.693436	−	0.954432i	0.0250059	−	0.0344177i	−0.796331	−	0.604861i	$-0.793229\pi$
$769$	0.693436	−	0.954432i	0.0250059	−	0.0344177i	0.821337	+	0.570443i	$0.193229\pi$
$770$	−55.1710	+	63.0342i	−1.98823	+	2.27159i
$771$	−9.37599	+	6.81206i	−0.337668	+	0.245330i
$772$	20.1743	+	16.0192i	0.726090	+	0.576544i
$773$	−5.21978	+	10.2444i	−0.187743	+	0.368466i	−0.965623	−	0.259947i	$-0.916295\pi$
$773$	−5.21978	+	10.2444i	−0.187743	+	0.368466i	0.777880	+	0.628412i	$0.216295\pi$
$774$	−13.1986	−	3.46887i	−0.474414	−	0.124686i
$775$	9.62510	+	27.8545i	0.345744	+	1.00056i
$776$	−17.9523	+	18.4759i	−0.644450	+	0.663248i
$777$	−3.63661	+	7.13726i	−0.130463	+	0.256048i
$778$	−14.9801	+	34.0844i	−0.537062	+	1.22198i
$779$	−5.14188	−	7.07720i	−0.184227	−	0.253567i
$780$	−13.8916	−	10.8220i	−0.497399	−	0.387490i
$781$	−25.5018	+	35.1002i	−0.912525	+	1.25598i
$782$	19.6729	+	33.7005i	0.703500	+	1.20513i
$783$	−0.948162	−	5.98646i	−0.0338845	−	0.213939i
$784$	10.5571	+	45.3736i	0.377041	+	1.62049i
$785$	−1.29349	−	0.407058i	−0.0461665	−	0.0145285i
$786$	8.38684	−	0.479839i	0.299149	−	0.0171153i
$787$	−4.22211	+	2.15127i	−0.150502	+	0.0766847i	−0.527620	−	0.849481i	$-0.676915\pi$
$787$	−4.22211	+	2.15127i	−0.150502	+	0.0766847i	0.377117	+	0.926165i	$0.376915\pi$
$788$	−8.94629	−	0.382934i	−0.318698	−	0.0136415i
$789$	−2.89695	−	8.91589i	−0.103134	−	0.317414i
$790$	−7.73271	−	19.3275i	−0.275117	−	0.687641i
$791$	50.5879	+	16.4370i	1.79870	+	0.584433i
$792$	14.1825	+	9.99593i	0.503953	+	0.355190i
$793$	0.623765	−	0.623765i	0.0221505	−	0.0221505i
$794$	8.24767	−	6.74451i	0.292699	−	0.239354i
$795$	−2.21348	+	0.371651i	−0.0785039	+	0.0131811i
$796$	−4.82857	−	42.0598i	−0.171144	−	1.49077i
$797$	−5.38394	+	33.9929i	−0.190709	+	1.20409i	0.687634	+	0.726058i	$0.258649\pi$
$797$	−5.38394	+	33.9929i	−0.190709	+	1.20409i	−0.878343	+	0.478031i	$0.841351\pi$
$798$	21.4995	+	19.1725i	0.761072	+	0.678698i
$799$	−18.4758			−0.653627
$800$	−25.3268	+	12.5917i	−0.895439	+	0.445184i
$801$	−10.0413			−0.354792
$802$	16.5680	+	14.7748i	0.585037	+	0.521716i
$803$	2.57937	−	16.2855i	0.0910239	−	0.574702i
$804$	−0.143114	−	1.24661i	−0.00504723	−	0.0439644i
$805$	−37.6785	+	38.3838i	−1.32799	+	1.35285i
$806$	−25.4082	+	20.7775i	−0.894966	+	0.731856i
$807$	−17.5599	+	17.5599i	−0.618136	+	0.618136i
$808$	−24.8702	−	17.5287i	−0.874931	−	0.616657i
$809$	16.4461	+	5.34366i	0.578214	+	0.187873i	0.583500	−	0.812113i	$-0.301683\pi$
$809$	16.4461	+	5.34366i	0.578214	+	0.187873i	−0.00528640	+	0.999986i	$0.501683\pi$
$810$	−2.42932	+	2.02445i	−0.0853577	+	0.0711319i
$811$	−10.3410	−	31.8265i	−0.363123	−	1.11758i	−0.951148	−	0.308736i	$-0.900094\pi$
$811$	−10.3410	−	31.8265i	−0.363123	−	1.11758i	0.588025	−	0.808843i	$-0.299906\pi$
$812$	52.2974	+	2.23852i	1.83528	+	0.0785566i
$813$	−10.7881	+	5.49681i	−0.378355	+	0.192782i
$814$	−16.0672	+	0.919261i	−0.563156	+	0.0322201i
$815$	−24.6009	+	34.5291i	−0.861733	+	1.20950i
$816$	−19.2983	+	4.49017i	−0.675576	+	0.157187i
$817$	−7.12076	−	44.9587i	−0.249124	−	1.57291i
$818$	−16.9192	−	28.9833i	−0.591566	−	1.01338i
$819$	9.99417	−	13.7558i	0.349225	−	0.480666i
$820$	2.29719	+	7.96908i	0.0802213	+	0.278292i
$821$	23.8737	+	32.8593i	0.833197	+	1.14680i	0.987320	+	0.158746i	$0.0507450\pi$
$821$	23.8737	+	32.8593i	0.833197	+	1.14680i	−0.154122	+	0.988052i	$0.549255\pi$
$822$	−4.39301	+	9.99548i	−0.153224	+	0.348632i
$823$	17.1119	−	33.5840i	0.596483	−	1.17066i	−0.373532	−	0.927617i	$-0.621853\pi$
$823$	17.1119	−	33.5840i	0.596483	−	1.17066i	0.970015	−	0.243046i	$-0.0781466\pi$
$824$	26.4787	−	27.2510i	0.922429	−	0.949335i
$825$	13.4160	−	27.5832i	0.467084	−	0.960322i
$826$	−30.2951	−	7.96217i	−1.05410	−	0.277039i
$827$	16.3209	−	32.0315i	0.567532	−	1.11384i	−0.411742	−	0.911301i	$-0.635079\pi$
$827$	16.3209	−	32.0315i	0.567532	−	1.11384i	0.979273	−	0.202543i	$-0.0649206\pi$
$828$	8.72490	+	6.92792i	0.303211	+	0.240762i
$829$	2.84873	−	2.06973i	0.0989406	−	0.0718845i	−0.537215	−	0.843445i	$-0.680524\pi$
$829$	2.84873	−	2.06973i	0.0989406	−	0.0718845i	0.636156	+	0.771561i	$0.280524\pi$
$830$	2.62842	−	28.9138i	0.0912336	−	1.00361i
$831$	−7.86589	+	10.8265i	−0.272865	+	0.375566i
$832$	−22.9054	−	21.6249i	−0.794102	−	0.749710i
$833$	56.9796	−	9.02468i	1.97422	−	0.312686i
$834$	1.32911	−	2.06828i	0.0460234	−	0.0716188i
$835$	27.1056	+	36.5894i	0.938029	+	1.26623i
$836$	−11.4899	+	56.7229i	−0.397385	+	1.96180i
$837$	2.67587	+	5.25170i	0.0924917	+	0.181525i
$838$	12.0255	−	2.61637i	0.415413	−	0.0903811i
$839$	−4.86469	−	14.9720i	−0.167948	−	0.516890i	0.831294	−	0.555833i	$-0.187601\pi$
$839$	−4.86469	−	14.9720i	−0.167948	−	0.516890i	−0.999241	+	0.0389437i	$0.987601\pi$
$840$	−12.9705	−	24.0338i	−0.447525	−	0.829243i
$841$	2.39077	−	7.35803i	0.0824403	−	0.253725i
$842$	1.60292	−	15.9873i	0.0552404	−	0.550958i
$843$	10.3902	−	10.3902i	0.357857	−	0.357857i
$844$	−45.6117	+	20.8336i	−1.57002	+	0.717122i
$845$	−5.53945	−	0.824786i	−0.190563	−	0.0283735i
$846$	−4.91539	+	1.91391i	−0.168995	+	0.0658017i
$847$	17.9906	−	113.588i	0.618165	−	3.90294i
$848$	−4.00474	+	0.286927i	−0.137524	+	0.00985311i
$849$		−	27.4120i		−	0.940776i
$850$	13.3119	+	32.3979i	0.456593	+	1.11124i
$851$	−10.3334			−0.354225
$852$	−7.81716	−	11.7885i	−0.267812	−	0.403868i
$853$	−17.1124	−	2.71034i	−0.585918	−	0.0928003i	−0.143564	−	0.989641i	$-0.545856\pi$
$853$	−17.1124	−	2.71034i	−0.585918	−	0.0928003i	−0.442354	+	0.896841i	$0.645856\pi$
$854$	1.27487	−	0.496397i	0.0436251	−	0.0169863i
$855$	−9.44216	−	4.70125i	−0.322915	−	0.160779i
$856$	−13.6317	+	2.36037i	−0.465922	+	0.0806758i
$857$	−25.4107	−	25.4107i	−0.868014	−	0.868014i	0.124238	−	0.992252i	$-0.460351\pi$
$857$	−25.4107	−	25.4107i	−0.868014	−	0.868014i	−0.992252	+	0.124238i	$0.960351\pi$
$858$	33.9904	+	3.40797i	1.16041	+	0.116346i
$859$	2.60701	+	0.847069i	0.0889501	+	0.0289016i	0.353154	−	0.935565i	$-0.385109\pi$
$859$	2.60701	+	0.847069i	0.0889501	+	0.0289016i	−0.264204	+	0.964467i	$0.585109\pi$
$860$	−8.17500	+	42.3737i	−0.278765	+	1.44493i
$861$	−7.61606	+	2.47461i	−0.259555	+	0.0843344i
$862$	33.6340	−	7.31773i	1.14558	−	0.249243i
$863$	−12.9308	+	6.58858i	−0.440170	+	0.224278i	−0.660008	−	0.751258i	$-0.729447\pi$
$863$	−12.9308	+	6.58858i	−0.440170	+	0.224278i	0.219838	+	0.975536i	$0.429447\pi$
$864$	−4.66908	+	3.19370i	−0.158845	+	0.108652i
$865$	31.2277	−	0.289566i	1.06177	−	0.00984552i
$866$	−30.1151	−	19.3525i	−1.02335	−	0.657623i
$867$	1.17899	+	7.44386i	0.0400406	+	0.252807i
$868$	−49.0404	+	13.6453i	−1.66454	+	0.463152i
$869$	32.6707	+	23.7367i	1.10828	+	0.805211i
$870$	−18.6901	+	4.24827i	−0.633653	+	0.144030i
$871$	−1.45209	−	1.99862i	−0.0492020	−	0.0677208i
$872$	−4.50098	−	6.01143i	−0.152422	−	0.203573i
$873$	8.11529	+	4.13495i	0.274661	+	0.139947i
$874$	−9.44578	+	35.9400i	−0.319508	+	1.21569i
$875$	−38.2536	+	29.4527i	−1.29321	+	0.995682i
$876$	4.68096	+	2.64307i	0.158155	+	0.0893011i
$877$	14.6233	+	7.45095i	0.493794	+	0.251601i	0.683110	−	0.730316i	$-0.260627\pi$
$877$	14.6233	+	7.45095i	0.493794	+	0.251601i	−0.189316	+	0.981916i	$0.560627\pi$
$878$	15.4641	−	35.1856i	0.521887	−	1.18746i
$879$	18.8315	−	13.6819i	0.635170	−	0.461478i
$880$	28.5634	−	46.8482i	0.962871	−	1.57925i
$881$	3.19329	+	2.32006i	0.107585	+	0.0781648i	0.640277	−	0.768144i	$-0.278820\pi$
$881$	3.19329	+	2.32006i	0.107585	+	0.0781648i	−0.532692	+	0.846309i	$0.678820\pi$
$882$	14.2242	−	8.30349i	0.478955	−	0.279593i
$883$	15.1808	−	2.40440i	0.510874	−	0.0809145i	0.104325	−	0.994543i	$-0.466732\pi$
$883$	15.1808	−	2.40440i	0.510874	−	0.0809145i	0.406549	+	0.913629i	$0.366732\pi$
$884$	−28.7381	+	26.3789i	−0.966567	+	0.887219i
$885$	11.4691	−	0.106350i	0.385530	−	0.00357491i
$886$	54.1636	−	3.09888i	1.81966	−	0.104109i
$887$	10.0920	+	19.8066i	0.338855	+	0.665041i	0.996061	−	0.0886703i	$-0.0282618\pi$
$887$	10.0920	+	19.8066i	0.338855	+	0.665041i	−0.657206	+	0.753711i	$0.728262\pi$
$888$	1.54947	−	5.01283i	0.0519969	−	0.168220i
$889$	35.1815	−	11.4312i	1.17995	−	0.383389i
$890$	2.10762	+	31.6834i	0.0706476	+	1.06203i
$891$	1.89568	−	5.83431i	0.0635077	−	0.195457i
$892$	−26.2155	−	9.77600i	−0.877758	−	0.327325i
$893$	−12.4411	−	12.4411i	−0.416325	−	0.416325i
$894$	13.6223	−	11.1396i	0.455598	−	0.372564i
$895$	−6.38125	+	12.8163i	−0.213302	+	0.428403i
$896$	−19.0273	−	44.9967i	−0.635658	−	1.50323i
$897$	21.6641	+	3.43126i	0.723344	+	0.114566i
$898$	−25.8771	+	29.0178i	−0.863529	+	0.968336i
$899$			35.7247i			1.19149i
$900$	6.89766	+	7.24033i	0.229922	+	0.241344i
$901$			4.97204i			0.165643i
$902$	−12.0078	−	10.7081i	−0.399815	−	0.356542i
$903$	−41.1561	−	6.51849i	−1.36959	−	0.216922i
$904$	−34.4866	−	4.95514i	−1.14701	−	0.164805i
$905$	5.75714	+	0.857198i	0.191374	+	0.0284942i
$906$	−3.32763	−	4.06926i	−0.110553	−	0.135192i
$907$	−9.60174	−	9.60174i	−0.318821	−	0.318821i	0.529493	−	0.848314i	$-0.322382\pi$
$907$	−9.60174	−	9.60174i	−0.318821	−	0.318821i	−0.848314	+	0.529493i	$0.822382\pi$
$908$	−8.49361	−	3.16735i	−0.281870	−	0.105112i
$909$	−3.32424	+	10.2309i	−0.110258	+	0.339339i
$910$	−45.5015	−	28.6474i	−1.50836	−	0.949651i
$911$	19.9132	−	6.47020i	0.659754	−	0.214367i	0.0400442	−	0.999198i	$-0.487250\pi$
$911$	19.9132	−	6.47020i	0.659754	−	0.214367i	0.619710	+	0.784831i	$0.287250\pi$
$912$	−16.0185	−	9.97137i	−0.530424	−	0.330185i
$913$	25.5695	+	50.1829i	0.846225	+	1.66081i
$914$	−2.76503	−	48.3284i	−0.0914591	−	1.59856i
$915$	−0.402526	+	0.298193i	−0.0133071	+	0.00985797i
$916$	13.9104	+	15.1545i	0.459613	+	0.500719i
$917$	25.3344	−	4.01257i	0.836615	−	0.132507i
$918$	3.53164	+	6.04986i	0.116562	+	0.199675i
$919$	10.2401	+	7.43983i	0.337788	+	0.245417i	0.743728	−	0.668482i	$-0.233056\pi$
$919$	10.2401	+	7.43983i	0.337788	+	0.245417i	−0.405940	+	0.913900i	$0.633056\pi$
$920$	20.0284	−	28.9838i	0.660316	−	0.955569i
$921$	−14.9615	+	10.8702i	−0.492998	+	0.358184i
$922$	−5.95131	−	2.61560i	−0.195996	−	0.0861402i
$923$	−24.8131	−	12.6429i	−0.816732	−	0.416146i
$924$	46.1336	+	26.0490i	1.51768	+	0.856951i
$925$	−9.18633	−	1.28083i	−0.302045	−	0.0421134i
$926$	−30.1876	−	7.93392i	−0.992025	−	0.260725i
$927$	−11.9696	−	6.09883i	−0.393134	−	0.200312i
$928$	−34.0032	+	4.39969i	−1.11621	+	0.144427i
$929$	3.33647	+	4.59226i	0.109466	+	0.150667i	0.860235	−	0.509898i	$-0.170317\pi$
$929$	3.33647	+	4.59226i	0.109466	+	0.150667i	−0.750769	+	0.660565i	$0.770317\pi$
$930$	16.0091	−	9.54550i	0.524958	−	0.313009i
$931$	44.4453	+	32.2914i	1.45664	+	1.05831i
$932$	−7.01718	−	25.2193i	−0.229855	−	0.826086i
$933$	3.08068	+	19.4506i	0.100857	+	0.636785i
$934$	−3.06267	+	4.76593i	−0.100214	+	0.155946i
$935$	−55.3389	−	39.4273i	−1.80978	−	1.28941i
$936$	−4.91303	+	9.99496i	−0.160587	+	0.326695i
$937$	5.78989	−	2.95010i	0.189148	−	0.0963755i	−0.356852	−	0.934161i	$-0.616150\pi$
$937$	5.78989	−	2.95010i	0.189148	−	0.0963755i	0.546000	+	0.837785i	$0.316150\pi$
$938$	−0.814535	−	3.74380i	−0.0265955	−	0.122239i
$939$	3.25989	−	1.05920i	0.106383	−	0.0345658i
$940$	7.07069	+	15.1078i	0.230621	+	0.492763i
$941$	−27.8544	−	9.05046i	−0.908029	−	0.295036i	−0.182482	−	0.983209i	$-0.558413\pi$
$941$	−27.8544	−	9.05046i	−0.908029	−	0.295036i	−0.725547	+	0.688173i	$0.758413\pi$
$942$	−0.0855587	+	0.853346i	−0.00278765	+	0.0278035i
$943$	−7.30470	−	7.30470i	−0.237874	−	0.237874i
$944$	20.4424	+	1.75323i	0.665344	+	0.0570629i
$945$	−6.76399	+	6.89060i	−0.220033	+	0.224151i
$946$	−30.3757	−	78.0122i	−0.987599	−	2.53639i
$947$	23.1546	+	3.66732i	0.752422	+	0.119172i	0.520853	−	0.853646i	$-0.325614\pi$
$947$	23.1546	+	3.66732i	0.752422	+	0.119172i	0.231569	+	0.972818i	$0.425614\pi$
$948$	−10.9726	+	7.27609i	−0.356372	+	0.236317i
$949$	10.5835			0.343554
$950$	−12.8520	+	30.7796i	−0.416975	+	0.998624i
$951$			16.6866i			0.541100i
$952$	−57.2636	+	19.5204i	−1.85592	+	0.632659i
$953$	−8.98804	+	56.7483i	−0.291151	+	1.83826i	0.215992	+	0.976395i	$0.430701\pi$
$953$	−8.98804	+	56.7483i	−0.291151	+	1.83826i	−0.507143	+	0.861862i	$0.669299\pi$
$954$	0.515054	+	1.32278i	0.0166755	+	0.0428267i
$955$	−4.39656	−	26.1850i	−0.142269	−	0.847328i
$956$	−23.0662	+	10.5357i	−0.746014	+	0.340749i
$957$	26.2917	−	26.2917i	0.849889	−	0.849889i
$958$	−40.0660	−	4.01712i	−1.29447	−	0.129787i
$959$	−10.3019	+	31.7060i	−0.332666	+	1.02384i
$960$	11.0571	+	14.0620i	0.356867	+	0.453850i
$961$	−1.15592	−	3.55757i	−0.0372878	−	0.114760i
$962$	−2.19611	−	10.0938i	−0.0708053	−	0.325438i
$963$	2.22058	+	4.35814i	0.0715572	+	0.140439i
$964$	19.4309	+	3.93595i	0.625828	+	0.126769i
$965$	−27.4731	−	8.64577i	−0.884392	−	0.278317i
$966$	28.6180	+	18.3904i	0.920768	+	0.591701i
$967$	−56.0768	+	8.88169i	−1.80331	+	0.285616i	−0.965510	−	0.260364i	$-0.916157\pi$
$967$	−56.0768	+	8.88169i	−1.80331	+	0.285616i	−0.837798	+	0.545980i	$0.816157\pi$
$968$	1.08270	+	75.3210i	0.0347993	+	2.42091i
$969$	−13.7342	+	18.9035i	−0.441206	+	0.607268i
$970$	11.3437	−	26.4741i	0.364223	−	0.850033i
$971$	−42.7569	+	31.0647i	−1.37213	+	0.996914i	−0.374568	+	0.927199i	$0.622209\pi$
$971$	−42.7569	+	31.0647i	−1.37213	+	0.996914i	−0.997567	+	0.0697149i	$0.977791\pi$
$972$	1.56628	+	1.24369i	0.0502385	+	0.0398914i
$973$	3.40803	−	6.68864i	0.109256	−	0.214428i
$974$	5.41107	−	20.5885i	0.173382	−	0.659697i
$975$	18.8340	+	5.73565i	0.603169	+	0.183688i
$976$	−0.767332	+	0.462849i	−0.0245617	+	0.0148154i
$977$	−1.12497	+	2.20787i	−0.0359908	+	0.0706360i	−0.908302	−	0.418316i	$-0.862621\pi$
$977$	−1.12497	+	2.20787i	−0.0359908	+	0.0706360i	0.872311	+	0.488952i	$0.162621\pi$
$978$	24.5477	+	10.7887i	0.784949	+	0.344985i
$979$	−36.2069	−	49.8346i	−1.15718	−	1.59272i
$980$	−29.1856	−	43.1390i	−0.932301	−	1.37802i
$981$	−1.56062	+	2.14801i	−0.0498269	+	0.0685808i
$982$	−38.9499	+	22.7373i	−1.24294	+	0.725576i
$983$	4.51844	+	28.5283i	0.144116	+	0.909913i	0.948724	+	0.316106i	$0.102376\pi$
$983$	4.51844	+	28.5283i	0.144116	+	0.909913i	−0.804608	+	0.593807i	$0.797624\pi$
$984$	4.63890	−	2.44825i	0.147883	−	0.0780474i
$985$	9.49233	−	3.18185i	0.302451	−	0.101382i
$986$	2.42527	+	42.3900i	0.0772364	+	1.34997i
$987$	−14.3507	+	7.31206i	−0.456789	+	0.232746i
$988$	−37.1142	−	1.58862i	−1.18076	−	0.0505409i
$989$	−16.6108	−	51.1227i	−0.528192	−	1.62561i
$990$	−18.8069	−	4.75686i	−0.597723	−	0.151183i
$991$	13.8124	+	4.48792i	0.438765	+	0.142564i	0.520066	−	0.854126i	$-0.325907\pi$
$991$	13.8124	+	4.48792i	0.438765	+	0.142564i	−0.0813006	+	0.996690i	$0.525907\pi$
$992$	30.1260	−	14.2872i	0.956502	−	0.453619i
$993$	−3.42355	+	3.42355i	−0.108643	+	0.108643i
$994$	−27.3407	−	33.4342i	−0.867195	−	1.06047i
$995$	21.8789	+	41.9731i	0.693609	+	1.33064i
$996$	−18.2423	+	2.09426i	−0.578028	+	0.0663590i
$997$	−3.83172	+	24.1925i	−0.121352	+	0.766185i	0.849691	+	0.527280i	$0.176788\pi$
$997$	−3.83172	+	24.1925i	−0.121352	+	0.766185i	−0.971043	+	0.238904i	$0.923212\pi$
$998$	−17.6168	+	19.7549i	−0.557649	+	0.625332i
$999$	−1.85504			−0.0586908

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.bq.a.67.15	✓	480
8.3	odd	2	inner	600.2.bq.a.67.58	yes	480
25.3	odd	20	inner	600.2.bq.a.403.58	yes	480
200.3	even	20	inner	600.2.bq.a.403.15	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.bq.a.67.15	✓	480	1.1	even	1	trivial
600.2.bq.a.67.58	yes	480	8.3	odd	2	inner
600.2.bq.a.403.15	yes	480	200.3	even	20	inner
600.2.bq.a.403.58	yes	480	25.3	odd	20	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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.bq (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05549 - 0.941247i) q^{2} +(0.156434 - 0.987688i) q^{3} +(0.228107 + 1.98695i) q^{4} +(-1.03358 - 1.98285i) q^{5} +(-1.09477 + 0.895249i) q^{6} +(-3.05339 + 3.05339i) q^{7} +(1.62945 - 2.31190i) q^{8} +(-0.951057 - 0.309017i) q^{9} +(-0.775421 + 3.06573i) q^{10} +(-1.89568 - 5.83431i) q^{11} +(1.99817 + 0.0855290i) q^{12} +(3.50842 - 1.78763i) q^{13} +(6.09681 - 0.348819i) q^{14} +(-2.12013 + 0.710672i) q^{15} +(-3.89593 + 0.906473i) q^{16} +(0.774890 + 4.89246i) q^{17} +(0.712967 + 1.22134i) q^{18} +(-2.77265 + 3.81623i) q^{19} +(3.70406 - 2.50598i) q^{20} +(2.53814 + 3.49345i) q^{21} +(-3.49066 + 7.94234i) q^{22} +(-2.52893 + 4.96331i) q^{23} +(-2.02854 - 1.97105i) q^{24} +(-2.86341 + 4.09889i) q^{25} +(-5.38569 - 1.41547i) q^{26} +(-0.453990 + 0.891007i) q^{27} +(-6.76343 - 5.37043i) q^{28} +(-4.90352 + 3.56261i) q^{29} +(2.90669 + 1.24546i) q^{30} +(3.46448 - 4.76844i) q^{31} +(4.96532 + 2.71027i) q^{32} +(-6.05903 + 0.959656i) q^{33} +(3.78713 - 5.89330i) q^{34} +(9.21036 + 2.89849i) q^{35} +(0.397059 - 1.96019i) q^{36} +(0.842170 + 1.65285i) q^{37} +(6.51852 - 1.41823i) q^{38} +(-1.21678 - 3.74487i) q^{39} +(-6.26834 - 0.841407i) q^{40} +(-0.573072 + 1.76373i) q^{41} +(0.609227 - 6.07632i) q^{42} +(-6.82342 + 6.82342i) q^{43} +(11.1601 - 5.09747i) q^{44} +(0.370261 + 2.20520i) q^{45} +(7.34096 - 2.85836i) q^{46} +(-0.583483 + 3.68397i) q^{47} +(0.285854 + 3.98977i) q^{48} -11.6464i q^{49} +(6.88036 - 1.63115i) q^{50} +4.95345 q^{51} +(4.35222 + 6.56328i) q^{52} +(0.991395 + 0.157022i) q^{53} +(1.31784 - 0.513129i) q^{54} +(-9.60923 + 9.78910i) q^{55} +(2.08381 + 12.0345i) q^{56} +(3.33551 + 3.33551i) q^{57} +(8.52890 + 0.855129i) q^{58} +(-4.87832 - 1.58506i) q^{59} +(-1.89568 - 4.05048i) q^{60} +(0.213065 - 0.0692289i) q^{61} +(-8.14500 + 1.77210i) q^{62} +(3.84750 - 1.96040i) q^{63} +(-2.68980 - 7.53425i) q^{64} +(-7.17085 - 5.10902i) q^{65} +(7.29850 + 4.69014i) q^{66} +(-0.0981466 - 0.619673i) q^{67} +(-9.54432 + 2.65567i) q^{68} +(4.50659 + 3.27423i) q^{69} +(-6.99322 - 11.7285i) q^{70} +(-4.15707 - 5.72172i) q^{71} +(-2.26411 + 1.69522i) q^{72} +(2.39485 + 1.22024i) q^{73} +(0.666843 - 2.53725i) q^{74} +(3.60049 + 3.46936i) q^{75} +(-8.21512 - 4.63861i) q^{76} +(23.6027 + 12.0262i) q^{77} +(-2.24055 + 5.09796i) q^{78} +(-5.32568 + 3.86934i) q^{79} +(5.82418 + 6.78815i) q^{80} +(0.809017 + 0.587785i) q^{81} +(2.26498 - 1.32220i) q^{82} +(-9.06800 + 1.43623i) q^{83} +(-6.36235 + 5.84004i) q^{84} +(8.90012 - 6.59326i) q^{85} +(13.6246 - 0.779507i) q^{86} +(2.75167 + 5.40046i) q^{87} +(-16.5773 - 5.12406i) q^{88} +(9.54984 - 3.10293i) q^{89} +(1.68483 - 2.67607i) q^{90} +(-5.25425 + 16.1709i) q^{91} +(-10.4387 - 3.89270i) q^{92} +(-4.16777 - 4.16777i) q^{93} +(4.08338 - 3.33918i) q^{94} +(10.4328 + 1.55337i) q^{95} +(3.45365 - 4.48021i) q^{96} +(-8.99587 - 1.42481i) q^{97} +(-10.9621 + 12.2926i) q^{98} +6.13455i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 12 q^{8} - 8 q^{10} + 8 q^{12} - 8 q^{17} + 20 q^{20} + 28 q^{22} + 8 q^{25} - 4 q^{28} - 8 q^{30} - 20 q^{32} + 48 q^{35} + 20 q^{38} - 108 q^{40} - 20 q^{42} + 32 q^{43} - 140 q^{44} - 16 q^{48}+ \cdots - 192 q^{98}+O(q^{100}) \) 480 * q + 12 * q^8 - 8 * q^10 + 8 * q^12 - 8 * q^17 + 20 * q^20 + 28 * q^22 + 8 * q^25 - 4 * q^28 - 8 * q^30 - 20 * q^32 + 48 * q^35 + 20 * q^38 - 108 * q^40 - 20 * q^42 + 32 * q^43 - 140 * q^44 - 16 * q^48 + 124 * q^50 - 132 * q^52 + 152 * q^58 - 20 * q^60 + 116 * q^62 - 60 * q^64 + 8 * q^65 - 48 * q^67 - 72 * q^68 - 4 * q^70 - 12 * q^72 + 40 * q^73 + 24 * q^78 - 76 * q^80 + 120 * q^81 - 64 * q^82 - 80 * q^83 - 80 * q^84 - 132 * q^88 + 200 * q^89 - 48 * q^90 - 216 * q^92 - 40 * q^94 + 20 * q^96 - 56 * q^97 - 192 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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