LMFDB - Embedded newform 51.3.j.a.37.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [51,3,Mod(7,51)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(51, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 11])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("51.7"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	51.j (of order $16$, 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:	$1.38964934824$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			37.4
Character	$\chi$	$=$	51.37
Dual form			51.3.j.a.40.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.495155 + 0.205100i) q^{2} +(1.69877 + 0.337906i) q^{3} +(-2.62531 + 2.62531i) q^{4} +(3.55986 + 5.32771i) q^{5} +(-0.910460 + 0.181102i) q^{6} +(3.48700 - 5.21867i) q^{7} +(1.58189 - 3.81901i) q^{8} +(2.77164 + 1.14805i) q^{9} +(-2.85540 - 1.90792i) q^{10} +(2.24337 + 11.2782i) q^{11} +(-5.34692 + 3.57269i) q^{12} +(-16.7380 - 16.7380i) q^{13} +(-0.656259 + 3.29924i) q^{14} +(4.24712 + 10.2534i) q^{15} -12.6356i q^{16} +(5.36442 - 16.1314i) q^{17} -1.60786 q^{18} +(6.69526 - 2.77327i) q^{19} +(-23.3327 - 4.64115i) q^{20} +(7.68704 - 7.68704i) q^{21} +(-3.42397 - 5.12434i) q^{22} +(-17.8153 + 3.54368i) q^{23} +(3.97773 - 5.95309i) q^{24} +(-6.14476 + 14.8348i) q^{25} +(11.7209 + 4.85495i) q^{26} +(4.32044 + 2.88683i) q^{27} +(4.54617 + 22.8551i) q^{28} +(24.4257 - 16.3208i) q^{29} +(-4.20597 - 4.20597i) q^{30} +(-3.99140 + 20.0661i) q^{31} +(8.91910 + 21.5326i) q^{32} +19.9171i q^{33} +(0.652335 + 9.08781i) q^{34} +40.2168 q^{35} +(-10.2904 + 4.26243i) q^{36} +(49.2580 + 9.79803i) q^{37} +(-2.74640 + 2.74640i) q^{38} +(-22.7781 - 34.0899i) q^{39} +(25.9779 - 5.16732i) q^{40} +(-17.1040 + 25.5980i) q^{41} +(-2.22967 + 5.38289i) q^{42} +(-57.3648 - 23.7613i) q^{43} +(-35.4983 - 23.7192i) q^{44} +(3.75017 + 18.8534i) q^{45} +(8.09453 - 5.40859i) q^{46} +(-23.0234 - 23.0234i) q^{47} +(4.26964 - 21.4649i) q^{48} +(3.67618 + 8.87508i) q^{49} -8.60581i q^{50} +(14.5638 - 25.5909i) q^{51} +87.8850 q^{52} +(-7.98943 + 3.30933i) q^{53} +(-2.73138 - 0.543305i) q^{54} +(-52.1008 + 52.1008i) q^{55} +(-14.4141 - 21.5723i) q^{56} +(12.3108 - 2.44877i) q^{57} +(-8.74715 + 13.0910i) q^{58} +(-21.0823 + 50.8972i) q^{59} +(-38.0685 - 15.7685i) q^{60} +(-13.8629 - 9.26287i) q^{61} +(-2.13920 - 10.7545i) q^{62} +(15.6560 - 10.4610i) q^{63} +(26.9061 + 26.9061i) q^{64} +(29.5902 - 148.760i) q^{65} +(-4.08500 - 9.86205i) q^{66} +1.37885i q^{67} +(28.2668 + 56.4334i) q^{68} -31.4615 q^{69} +(-19.9136 + 8.24846i) q^{70} +(-80.9852 - 16.1090i) q^{71} +(8.76884 - 8.76884i) q^{72} +(-63.6984 - 95.3314i) q^{73} +(-26.4000 + 5.25128i) q^{74} +(-15.4513 + 23.1245i) q^{75} +(-10.2965 + 24.8579i) q^{76} +(66.6797 + 27.6196i) q^{77} +(18.2706 + 12.2080i) q^{78} +(6.44381 + 32.3952i) q^{79} +(67.3186 - 44.9808i) q^{80} +(6.36396 + 6.36396i) q^{81} +(3.21900 - 16.1830i) q^{82} +(52.5138 + 126.780i) q^{83} +40.3618i q^{84} +(105.040 - 28.8455i) q^{85} +33.2779 q^{86} +(47.0086 - 19.4716i) q^{87} +(46.6203 + 9.27335i) q^{88} +(-95.1227 + 95.1227i) q^{89} +(-5.72375 - 8.56619i) q^{90} +(-145.715 + 28.9846i) q^{91} +(37.4675 - 56.0740i) q^{92} +(-13.5610 + 32.7390i) q^{93} +(16.1223 + 6.67806i) q^{94} +(38.6093 + 25.7979i) q^{95} +(7.87550 + 39.5928i) q^{96} +(46.1775 - 30.8548i) q^{97} +(-3.64056 - 3.64056i) q^{98} +(-6.73011 + 33.8345i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{10} - 80 q^{11} - 48 q^{13} - 64 q^{14} + 16 q^{17} + 48 q^{19} + 224 q^{20} + 192 q^{22} + 112 q^{23} - 144 q^{24} + 80 q^{25} - 368 q^{26} - 240 q^{28} - 160 q^{29} - 192 q^{30} - 64 q^{31}+ \cdots + 240 q^{99}+O(q^{100}) $ 48 * q - 48 * q^10 - 80 * q^11 - 48 * q^13 - 64 * q^14 + 16 * q^17 + 48 * q^19 + 224 * q^20 + 192 * q^22 + 112 * q^23 - 144 * q^24 + 80 * q^25 - 368 * q^26 - 240 * q^28 - 160 * q^29 - 192 * q^30 - 64 * q^31 - 80 * q^32 + 16 * q^34 + 128 * q^35 + 48 * q^36 + 128 * q^37 + 400 * q^38 + 192 * q^39 + 128 * q^40 + 320 * q^41 + 432 * q^42 - 112 * q^43 + 704 * q^44 + 96 * q^45 + 80 * q^46 - 32 * q^49 + 128 * q^52 - 336 * q^53 - 608 * q^55 - 880 * q^56 - 752 * q^58 - 512 * q^59 - 400 * q^61 - 560 * q^62 + 160 * q^64 - 240 * q^65 - 208 * q^68 - 240 * q^69 + 80 * q^70 - 160 * q^71 - 288 * q^72 + 544 * q^73 - 48 * q^74 - 288 * q^75 + 496 * q^76 + 512 * q^77 - 384 * q^78 + 608 * q^79 + 816 * q^80 + 1184 * q^82 + 976 * q^83 - 32 * q^85 + 128 * q^86 + 144 * q^87 - 448 * q^88 + 240 * q^89 + 48 * q^90 - 640 * q^91 + 1280 * q^92 + 288 * q^93 - 32 * q^94 + 704 * q^95 + 768 * q^96 + 288 * q^97 + 1008 * q^98 + 240 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$1$	$e\left(\frac{1}{16}\right)$

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 $

$2$	−0.495155	+	0.205100i	−0.247578	+	0.102550i	−0.503022	−	0.864274i	$-0.667778\pi$
$2$	−0.495155	+	0.205100i	−0.247578	+	0.102550i	0.255444	+	0.966824i	$0.417778\pi$
$3$	1.69877	+	0.337906i	0.566257	+	0.112635i
$3$	1.69877	+	0.337906i	0.566257	+	0.112635i
$4$	−2.62531	+	2.62531i	−0.656329	+	0.656329i
$5$	3.55986	+	5.32771i	0.711972	+	1.06554i	0.994341	+	0.106235i	$0.0338797\pi$
$5$	3.55986	+	5.32771i	0.711972	+	1.06554i	−0.282369	+	0.959306i	$0.591120\pi$
$6$	−0.910460	+	0.181102i	−0.151743	+	0.0301836i
$7$	3.48700	−	5.21867i	0.498143	−	0.745524i	−0.494158	−	0.869372i	$-0.664524\pi$
$7$	3.48700	−	5.21867i	0.498143	−	0.745524i	0.992301	+	0.123848i	$0.0395236\pi$
$8$	1.58189	−	3.81901i	0.197736	−	0.477377i
$9$	2.77164	+	1.14805i	0.307960	+	0.127561i
$10$	−2.85540	−	1.90792i	−0.285540	−	0.190792i
$11$	2.24337	+	11.2782i	0.203943	+	1.02529i	0.938114	+	0.346325i	$0.112571\pi$
$11$	2.24337	+	11.2782i	0.203943	+	1.02529i	−0.734172	+	0.678964i	$0.762429\pi$
$12$	−5.34692	+	3.57269i	−0.445576	+	0.297725i
$13$	−16.7380	−	16.7380i	−1.28754	−	1.28754i	−0.936278	−	0.351261i	$-0.885753\pi$
$13$	−16.7380	−	16.7380i	−1.28754	−	1.28754i	−0.351261	−	0.936278i	$-0.614247\pi$
$14$	−0.656259	+	3.29924i	−0.0468756	+	0.235660i
$15$	4.24712	+	10.2534i	0.283141	+	0.683563i
$16$		−	12.6356i		−	0.789723i
$17$	5.36442	−	16.1314i	0.315554	−	0.948908i
$17$	5.36442	−	16.1314i	0.315554	−	0.948908i
$18$	−1.60786			−0.0893254
$19$	6.69526	−	2.77327i	0.352382	−	0.145961i	−0.199469	−	0.979904i	$-0.563922\pi$
$19$	6.69526	−	2.77327i	0.352382	−	0.145961i	0.551851	+	0.833943i	$0.313922\pi$
$20$	−23.3327	−	4.64115i	−1.16663	−	0.232058i
$21$	7.68704	−	7.68704i	0.366049	−	0.366049i
$22$	−3.42397	−	5.12434i	−0.155635	−	0.232924i
$23$	−17.8153	+	3.54368i	−0.774578	+	0.154073i	−0.566525	−	0.824044i	$-0.691713\pi$
$23$	−17.8153	+	3.54368i	−0.774578	+	0.154073i	−0.208053	+	0.978118i	$0.566713\pi$
$24$	3.97773	−	5.95309i	0.165739	−	0.248046i
$25$	−6.14476	+	14.8348i	−0.245791	+	0.593391i
$26$	11.7209	+	4.85495i	0.450803	+	0.186729i
$27$	4.32044	+	2.88683i	0.160016	+	0.106920i
$28$	4.54617	+	22.8551i	0.162363	+	0.816254i
$29$	24.4257	−	16.3208i	0.842267	−	0.562785i	−0.0579037	−	0.998322i	$-0.518442\pi$
$29$	24.4257	−	16.3208i	0.842267	−	0.562785i	0.900171	+	0.435537i	$0.143442\pi$
$30$	−4.20597	−	4.20597i	−0.140199	−	0.140199i
$31$	−3.99140	+	20.0661i	−0.128755	+	0.647295i	0.861469	+	0.507810i	$0.169545\pi$
$31$	−3.99140	+	20.0661i	−0.128755	+	0.647295i	−0.990224	+	0.139485i	$0.955455\pi$
$32$	8.91910	+	21.5326i	0.278722	+	0.672894i
$33$			19.9171i			0.603548i
$34$	0.652335	+	9.08781i	0.0191863	+	0.267288i
$35$	40.2168			1.14905
$36$	−10.2904	+	4.26243i	−0.285845	+	0.118401i
$37$	49.2580	+	9.79803i	1.33130	+	0.264812i	0.808928	−	0.587907i	$-0.200048\pi$
$37$	49.2580	+	9.79803i	1.33130	+	0.264812i	0.522370	+	0.852719i	$0.325048\pi$
$38$	−2.74640	+	2.74640i	−0.0722736	+	0.0722736i
$39$	−22.7781	−	34.0899i	−0.584055	−	0.874100i
$40$	25.9779	−	5.16732i	0.649447	−	0.129183i
$41$	−17.1040	+	25.5980i	−0.417171	+	0.624341i	−0.979229	−	0.202757i	$-0.935010\pi$
$41$	−17.1040	+	25.5980i	−0.417171	+	0.624341i	0.562058	+	0.827098i	$0.310010\pi$
$42$	−2.22967	+	5.38289i	−0.0530873	+	0.128164i
$43$	−57.3648	−	23.7613i	−1.33406	−	0.552588i	−0.402253	−	0.915529i	$-0.631773\pi$
$43$	−57.3648	−	23.7613i	−1.33406	−	0.552588i	−0.931812	+	0.362941i	$0.881773\pi$
$44$	−35.4983	−	23.7192i	−0.806780	−	0.539073i
$45$	3.75017	+	18.8534i	0.0833371	+	0.418964i
$46$	8.09453	−	5.40859i	0.175968	−	0.117578i
$47$	−23.0234	−	23.0234i	−0.489860	−	0.489860i	0.418402	−	0.908262i	$-0.362590\pi$
$47$	−23.0234	−	23.0234i	−0.489860	−	0.489860i	−0.908262	+	0.418402i	$0.862590\pi$
$48$	4.26964	−	21.4649i	0.0889508	−	0.447186i
$49$	3.67618	+	8.87508i	0.0750241	+	0.181124i
$50$		−	8.60581i		−	0.172116i
$51$	14.5638	−	25.5909i	0.285565	−	0.501783i
$52$	87.8850			1.69010
$53$	−7.98943	+	3.30933i	−0.150744	+	0.0624402i	−0.456780	−	0.889580i	$-0.650997\pi$
$53$	−7.98943	+	3.30933i	−0.150744	+	0.0624402i	0.306036	+	0.952020i	$0.400997\pi$
$54$	−2.73138	−	0.543305i	−0.0505811	−	0.0100612i
$55$	−52.1008	+	52.1008i	−0.947286	+	0.947286i
$56$	−14.4141	−	21.5723i	−0.257395	−	0.385219i
$57$	12.3108	−	2.44877i	0.215979	−	0.0429609i
$58$	−8.74715	+	13.0910i	−0.150813	+	0.225708i
$59$	−21.0823	+	50.8972i	−0.357328	+	0.862665i	0.638346	+	0.769749i	$0.279619\pi$
$59$	−21.0823	+	50.8972i	−0.357328	+	0.862665i	−0.995674	+	0.0929158i	$0.970381\pi$
$60$	−38.0685	−	15.7685i	−0.634475	−	0.262808i
$61$	−13.8629	−	9.26287i	−0.227260	−	0.151850i	0.436728	−	0.899594i	$-0.356137\pi$
$61$	−13.8629	−	9.26287i	−0.227260	−	0.151850i	−0.663988	+	0.747743i	$0.731137\pi$
$62$	−2.13920	−	10.7545i	−0.0345033	−	0.173460i
$63$	15.6560	−	10.4610i	0.248508	−	0.166048i
$64$	26.9061	+	26.9061i	0.420408	+	0.420408i
$65$	29.5902	−	148.760i	0.455234	−	2.28862i
$66$	−4.08500	−	9.86205i	−0.0618939	−	0.149425i
$67$			1.37885i			0.0205799i	0.999947	+	0.0102900i	$0.00327545\pi$
$67$			1.37885i			0.0205799i	−0.999947	+	0.0102900i	$0.996725\pi$
$68$	28.2668	+	56.4334i	0.415688	+	0.829902i
$69$	−31.4615			−0.455964
$70$	−19.9136	+	8.24846i	−0.284479	+	0.117835i
$71$	−80.9852	−	16.1090i	−1.14064	−	0.226887i	−0.411602	−	0.911364i	$-0.635031\pi$
$71$	−80.9852	−	16.1090i	−1.14064	−	0.226887i	−0.729034	+	0.684477i	$0.760031\pi$
$72$	8.76884	−	8.76884i	0.121789	−	0.121789i
$73$	−63.6984	−	95.3314i	−0.872581	−	1.30591i	−0.951064	−	0.308994i	$-0.900008\pi$
$73$	−63.6984	−	95.3314i	−0.872581	−	1.30591i	0.0784829	−	0.996915i	$-0.474992\pi$
$74$	−26.4000	+	5.25128i	−0.356756	+	0.0709632i
$75$	−15.4513	+	23.1245i	−0.206017	+	0.308327i
$76$	−10.2965	+	24.8579i	−0.135480	+	0.327077i
$77$	66.6797	+	27.6196i	0.865970	+	0.358697i
$78$	18.2706	+	12.2080i	0.234238	+	0.156513i
$79$	6.44381	+	32.3952i	0.0815673	+	0.410066i	0.999898	+	0.0142534i	$0.00453714\pi$
$79$	6.44381	+	32.3952i	0.0815673	+	0.410066i	−0.918331	+	0.395813i	$0.870463\pi$
$80$	67.3186	−	44.9808i	0.841482	−	0.562261i
$81$	6.36396	+	6.36396i	0.0785674	+	0.0785674i
$82$	3.21900	−	16.1830i	0.0392561	−	0.197354i
$83$	52.5138	+	126.780i	0.632697	+	1.52747i	0.836219	+	0.548395i	$0.184761\pi$
$83$	52.5138	+	126.780i	0.632697	+	1.52747i	−0.203522	+	0.979070i	$0.565239\pi$
$84$			40.3618i			0.480497i
$85$	105.040	−	28.8455i	1.23577	−	0.339359i
$86$	33.2779			0.386953
$87$	47.0086	−	19.4716i	0.540329	−	0.223812i
$88$	46.6203	+	9.27335i	0.529776	+	0.105379i
$89$	−95.1227	+	95.1227i	−1.06879	+	1.06879i	−0.0713428	+	0.997452i	$0.522728\pi$
$89$	−95.1227	+	95.1227i	−1.06879	+	1.06879i	−0.997452	+	0.0713428i	$0.977272\pi$
$90$	−5.72375	−	8.56619i	−0.0635972	−	0.0951799i
$91$	−145.715	+	28.9846i	−1.60127	+	0.318512i
$92$	37.4675	−	56.0740i	0.407255	−	0.609500i
$93$	−13.5610	+	32.7390i	−0.145817	+	0.352033i
$94$	16.1223	+	6.67806i	0.171514	+	0.0710432i
$95$	38.6093	+	25.7979i	0.406414	+	0.271557i
$96$	7.87550	+	39.5928i	0.0820364	+	0.412425i
$97$	46.1775	−	30.8548i	0.476057	−	0.318091i	−0.294290	−	0.955716i	$-0.595083\pi$
$97$	46.1775	−	30.8548i	0.476057	−	0.318091i	0.770347	+	0.637625i	$0.220083\pi$
$98$	−3.64056	−	3.64056i	−0.0371486	−	0.0371486i
$99$	−6.73011	+	33.8345i	−0.0679809	+	0.341763i
$100$	−22.8140	−	55.0779i	−0.228140	−	0.550779i
$101$		−	82.1962i		−	0.813824i	−0.913467	−	0.406912i	$-0.866606\pi$
$101$		−	82.1962i		−	0.813824i	0.913467	−	0.406912i	$-0.133394\pi$
$102$	−1.96266	+	15.6585i	−0.0192418	+	0.153515i
$103$	16.5114			0.160305			0.0801526	−	0.996783i	$-0.474459\pi$
$103$	16.5114			0.160305			0.0801526	+	0.996783i	$0.474459\pi$
$104$	−90.4002	+	37.4450i	−0.869233	+	0.360048i
$105$	68.3190	+	13.5895i	0.650657	+	0.129424i
$106$	3.27727	−	3.27727i	0.0309176	−	0.0309176i
$107$	34.4817	+	51.6054i	0.322258	+	0.482294i	0.956862	−	0.290544i	$-0.0938364\pi$
$107$	34.4817	+	51.6054i	0.322258	+	0.482294i	−0.634603	+	0.772838i	$0.718836\pi$
$108$	−18.9213	+	3.76369i	−0.175198	+	0.0348490i
$109$	39.8838	−	59.6904i	0.365907	−	0.547618i	−0.602139	−	0.798391i	$-0.705685\pi$
$109$	39.8838	−	59.6904i	0.365907	−	0.547618i	0.968046	+	0.250773i	$0.0806848\pi$
$110$	15.1121	−	36.4838i	0.137383	−	0.331671i
$111$	80.3672	+	33.2892i	0.724029	+	0.299903i
$112$	−65.9408	−	44.0603i	−0.588758	−	0.393395i
$113$	12.6224	+	63.4570i	0.111702	+	0.561566i	0.995586	+	0.0938584i	$0.0299201\pi$
$113$	12.6224	+	63.4570i	0.111702	+	0.561566i	−0.883883	+	0.467708i	$0.845080\pi$
$114$	−5.59352	+	3.73747i	−0.0490660	+	0.0327848i
$115$	−82.2996	−	82.2996i	−0.715649	−	0.715649i
$116$	−21.2781	+	106.972i	−0.183432	+	0.922176i
$117$	−27.1756	−	65.6077i	−0.232270	−	0.560750i
$118$		−	29.5260i		−	0.250221i
$119$	−65.4788	−	84.2455i	−0.550242	−	0.707945i
$120$	45.8765			0.382304
$121$	−10.3753	+	4.29758i	−0.0857461	+	0.0355172i
$122$	8.76409	+	1.74329i	0.0718368	+	0.0142892i
$123$	−37.7055	+	37.7055i	−0.306549	+	0.306549i
$124$	−42.2012	−	63.1586i	−0.340333	−	0.509344i
$125$	56.2016	−	11.1792i	0.449613	−	0.0894336i
$126$	−5.60660	+	8.39087i	−0.0444968	+	0.0665942i
$127$	−36.9000	+	89.0846i	−0.290551	+	0.701453i	−0.999995	−	0.00330943i	$-0.998947\pi$
$127$	−36.9000	+	89.0846i	−0.290551	+	0.701453i	0.709443	+	0.704763i	$0.248947\pi$
$128$	−104.972	−	43.4807i	−0.820091	−	0.339693i
$129$	−89.4205	−	59.7489i	−0.693182	−	0.463170i
$130$	15.8589	+	79.7283i	0.121992	+	0.613295i
$131$	104.315	−	69.7011i	0.796299	−	0.532070i	−0.0895839	−	0.995979i	$-0.528554\pi$
$131$	104.315	−	69.7011i	0.796299	−	0.532070i	0.885883	+	0.463910i	$0.153554\pi$
$132$	−52.2886	−	52.2886i	−0.396126	−	0.396126i
$133$	8.87363	−	44.6107i	0.0667190	−	0.335419i
$134$	−0.282803	−	0.682747i	−0.00211047	−	0.00509513i
$135$			33.2947i			0.246628i
$136$	−53.1202	−	46.0049i	−0.390590	−	0.338271i
$137$	20.2525			0.147828			0.0739141	−	0.997265i	$-0.476451\pi$
$137$	20.2525			0.147828			0.0739141	+	0.997265i	$0.476451\pi$
$138$	15.5783	−	6.45276i	0.112887	−	0.0467591i
$139$	−111.076	−	22.0944i	−0.799110	−	0.158953i	−0.221387	−	0.975186i	$-0.571058\pi$
$139$	−111.076	−	22.0944i	−0.799110	−	0.158953i	−0.577723	+	0.816233i	$0.696058\pi$
$140$	−105.582	+	105.582i	−0.754155	+	0.754155i
$141$	−31.3317	−	46.8912i	−0.222211	−	0.332562i
$142$	43.4042	−	8.63363i	0.305663	−	0.0608002i
$143$	151.225	−	226.324i	1.05752	−	1.58268i
$144$	14.5063	−	35.0212i	0.100738	−	0.243203i
$145$	173.904	+	72.0336i	1.19934	+	0.496783i
$146$	51.0931	+	34.1393i	0.349953	+	0.233831i
$147$	3.24604	+	16.3189i	0.0220819	+	0.111013i
$148$	−155.041	+	103.595i	−1.04757	+	0.699965i
$149$	38.0492	+	38.0492i	0.255364	+	0.255364i	0.823165	−	0.567802i	$-0.192206\pi$
$149$	38.0492	+	38.0492i	0.255364	+	0.255364i	−0.567802	+	0.823165i	$0.692206\pi$
$150$	2.90796	−	14.6193i	0.0193864	−	0.0974620i
$151$	−16.7446	−	40.4251i	−0.110891	−	0.267716i	0.858685	−	0.512503i	$-0.171282\pi$
$151$	−16.7446	−	40.4251i	−0.110891	−	0.267716i	−0.969577	+	0.244788i	$0.921282\pi$
$152$		−	29.9563i		−	0.197081i
$153$	33.3879	−	38.5519i	0.218222	−	0.251973i
$154$	−38.6816			−0.251179
$155$	−121.115	+	50.1676i	−0.781389	+	0.323662i
$156$	149.296	+	29.6969i	0.957028	+	0.190365i
$157$	209.426	−	209.426i	1.33392	−	1.33392i	0.432098	−	0.901827i	$-0.357773\pi$
$157$	209.426	−	209.426i	1.33392	−	1.33392i	0.901827	−	0.432098i	$-0.142227\pi$
$158$	−9.83496	−	14.7191i	−0.0622466	−	0.0931586i
$159$	−14.6904	+	2.92211i	−0.0923927	+	0.0183781i
$160$	−82.9687	+	124.171i	−0.518555	+	0.776072i
$161$	−43.6287	+	105.329i	−0.270985	+	0.654217i
$162$	−4.45640	−	1.84590i	−0.0275086	−	0.0113945i
$163$	248.529	+	166.062i	1.52472	+	1.01878i	0.984120	+	0.177504i	$0.0568022\pi$
$163$	248.529	+	166.062i	1.52472	+	1.01878i	0.540599	+	0.841281i	$0.318198\pi$
$164$	−22.2993	−	112.106i	−0.135971	−	0.683574i
$165$	−106.112	+	70.9020i	−0.643105	+	0.429709i
$166$	−52.0050	−	52.0050i	−0.313283	−	0.313283i
$167$	−30.7855	+	154.769i	−0.184345	+	0.926763i	0.772245	+	0.635325i	$0.219134\pi$
$167$	−30.7855	+	154.769i	−0.184345	+	0.926763i	−0.956590	+	0.291438i	$0.905866\pi$
$168$	−17.1969	−	41.5169i	−0.102362	−	0.247124i
$169$			391.321i			2.31551i
$170$	−46.0949	+	35.8268i	−0.271147	+	0.210746i
$171$	21.7407			0.127139
$172$	212.981	−	88.2198i	1.23826	−	0.512906i
$173$	−227.985	−	45.3491i	−1.31783	−	0.262133i	−0.514412	−	0.857543i	$-0.671990\pi$
$173$	−227.985	−	45.3491i	−1.31783	−	0.262133i	−0.803422	+	0.595410i	$0.796990\pi$
$174$	−19.2829	+	19.2829i	−0.110821	+	0.110821i
$175$	55.9910	+	83.7964i	0.319948	+	0.478836i
$176$	142.506	−	28.3463i	0.809695	−	0.161058i
$177$	−53.0125	+	79.3388i	−0.299506	+	0.448242i
$178$	27.5909	−	66.6102i	0.155005	−	0.374215i
$179$	−128.996	−	53.4319i	−0.720649	−	0.298503i	−0.00794580	−	0.999968i	$-0.502529\pi$
$179$	−128.996	−	53.4319i	−0.720649	−	0.298503i	−0.712703	+	0.701466i	$0.752529\pi$
$180$	−59.3414	−	39.6507i	−0.329674	−	0.220281i
$181$	−12.8881	−	64.7927i	−0.0712048	−	0.357971i	0.928713	−	0.370800i	$-0.120916\pi$
$181$	−12.8881	−	64.7927i	−0.0712048	−	0.357971i	−0.999918	+	0.0128288i	$0.995916\pi$
$182$	66.2071	−	44.2382i	0.363775	−	0.243067i
$183$	−20.4198	−	20.4198i	−0.111584	−	0.111584i
$184$	−14.6484	+	73.6425i	−0.0796109	+	0.400231i
$185$	123.151	+	297.312i	0.665679	+	1.60709i
$186$		−	18.9923i		−	0.102109i
$187$	193.968	+	24.3122i	1.03726	+	0.130012i
$188$	120.887			0.643018
$189$	30.1308	−	12.4806i	0.159422	−	0.0660348i
$190$	−24.4088	−	4.85521i	−0.128467	−	0.0255537i
$191$	248.510	−	248.510i	1.30110	−	1.30110i	0.373449	−	0.927651i	$-0.378175\pi$
$191$	248.510	−	248.510i	1.30110	−	1.30110i	0.927651	−	0.373449i	$-0.121825\pi$
$192$	36.6155	+	54.7990i	0.190706	+	0.285412i
$193$	19.5873	−	3.89615i	0.101488	−	0.0201873i	−0.144085	−	0.989565i	$-0.546024\pi$
$193$	19.5873	−	3.89615i	0.101488	−	0.0201873i	0.245573	+	0.969378i	$0.421024\pi$
$194$	−16.5367	+	24.7490i	−0.0852409	+	0.127572i
$195$	100.534	−	242.710i	0.515559	−	1.24467i
$196$	−32.9510	−	13.6488i	−0.168117	−	0.0696365i
$197$	−241.780	−	161.552i	−1.22731	−	0.820061i	−0.238777	−	0.971075i	$-0.576746\pi$
$197$	−241.780	−	161.552i	−1.22731	−	0.820061i	−0.988532	+	0.151013i	$0.951746\pi$
$198$	−3.60702	−	18.1337i	−0.0182173	−	0.0915844i
$199$	−39.3307	+	26.2799i	−0.197642	+	0.132060i	−0.650453	−	0.759546i	$-0.725421\pi$
$199$	−39.3307	+	26.2799i	−0.197642	+	0.132060i	0.452812	+	0.891606i	$0.350421\pi$
$200$	46.9339	+	46.9339i	0.234669	+	0.234669i
$201$	−0.465923	+	2.34235i	−0.00231803	+	0.0116535i
$202$	16.8584	+	40.6999i	0.0834576	+	0.201485i
$203$		−	184.380i		−	0.908278i
$204$	28.9496	+	105.419i	0.141910	+	0.516759i
$205$	−197.266			−0.962275
$206$	−8.17572	+	3.38650i	−0.0396880	+	0.0164393i
$207$	−53.4459	−	10.6310i	−0.258193	−	0.0513577i
$208$	−211.494	+	211.494i	−1.01680	+	1.01680i
$209$	46.2974	+	69.2889i	0.221518	+	0.331526i
$210$	−36.6158	+	7.28333i	−0.174361	+	0.0346825i
$211$	−156.591	+	234.355i	−0.742139	+	1.11069i	0.247747	+	0.968825i	$0.420310\pi$
$211$	−156.591	+	234.355i	−0.742139	+	1.11069i	−0.989886	+	0.141864i	$0.954690\pi$
$212$	12.2867	−	29.6628i	0.0579563	−	0.139919i
$213$	−132.132	−	54.7308i	−0.620337	−	0.256952i
$214$	−27.6581	−	18.4805i	−0.129243	−	0.0863576i
$215$	−77.6175	−	390.210i	−0.361012	−	1.81493i
$216$	17.8593	−	11.9332i	0.0826819	−	0.0552463i
$217$	90.8005	+	90.8005i	0.418436	+	0.418436i
$218$	−7.50620	+	37.7362i	−0.0344321	+	0.173102i
$219$	−75.9959	−	183.470i	−0.347013	−	0.837764i
$220$		−	273.562i		−	1.24346i
$221$	−359.797	+	180.218i	−1.62804	+	0.815467i
$222$	−46.6219			−0.210009
$223$	−14.9693	+	6.20048i	−0.0671268	+	0.0278048i	−0.415994	−	0.909367i	$-0.636566\pi$
$223$	−14.9693	+	6.20048i	−0.0671268	+	0.0278048i	0.348867	+	0.937172i	$0.386566\pi$
$224$	143.473	+	28.5385i	0.640502	+	0.127404i
$225$	−34.0621	+	34.0621i	−0.151387	+	0.151387i
$226$	−19.2651	−	28.8322i	−0.0852437	−	0.127576i
$227$	173.599	−	34.5309i	0.764752	−	0.152119i	0.202723	−	0.979236i	$-0.435021\pi$
$227$	173.599	−	34.5309i	0.764752	−	0.152119i	0.562029	+	0.827117i	$0.310021\pi$
$228$	−25.8909	+	38.7485i	−0.113557	+	0.169950i
$229$	109.856	−	265.215i	0.479720	−	1.15815i	−0.480021	−	0.877257i	$-0.659371\pi$
$229$	109.856	−	265.215i	0.479720	−	1.15815i	0.959740	−	0.280889i	$-0.0906291\pi$
$230$	57.6308	+	23.8714i	0.250569	+	0.103789i
$231$	103.941	+	69.4509i	0.449960	+	0.300653i
$232$	−23.6904	−	119.100i	−0.102114	−	0.513361i
$233$	−120.073	+	80.2303i	−0.515335	+	0.344336i	−0.785888	−	0.618369i	$-0.787794\pi$
$233$	−120.073	+	80.2303i	−0.515335	+	0.344336i	0.270552	+	0.962705i	$0.412794\pi$
$234$	26.9123	+	26.9123i	0.115010	+	0.115010i
$235$	40.7019	−	204.622i	0.173199	−	0.870732i
$236$	−78.2735	−	188.969i	−0.331667	−	0.800716i
$237$			57.2095i			0.241390i
$238$	49.7009	+	28.2849i	0.208828	+	0.118844i
$239$	−148.134			−0.619809			−0.309905	−	0.950768i	$-0.600297\pi$
$239$	−148.134			−0.619809			−0.309905	+	0.950768i	$0.600297\pi$
$240$	129.558	−	53.6647i	0.539826	−	0.223603i
$241$	31.7629	+	6.31803i	0.131796	+	0.0262159i	0.260548	−	0.965461i	$-0.416097\pi$
$241$	31.7629	+	6.31803i	0.131796	+	0.0262159i	−0.128751	+	0.991677i	$0.541097\pi$
$242$	4.25594	−	4.25594i	0.0175865	−	0.0175865i
$243$	8.66048	+	12.9613i	0.0356398	+	0.0533388i
$244$	60.7123	−	12.0764i	0.248821	−	0.0494936i
$245$	−34.1971	+	51.1796i	−0.139580	+	0.208896i
$246$	10.9367	−	26.4035i	0.0444581	−	0.107331i
$247$	−158.484	−	65.6463i	−0.641636	−	0.265774i
$248$	70.3189	+	46.9856i	0.283544	+	0.189458i
$249$	46.3693	+	233.114i	0.186222	+	0.936202i
$250$	−25.5357	+	17.0624i	−0.102143	+	0.0682496i
$251$	241.835	+	241.835i	0.963486	+	0.963486i	0.999356	−	0.0358707i	$-0.0114204\pi$
$251$	241.835	+	241.835i	0.963486	+	0.963486i	−0.0358707	+	0.999356i	$0.511420\pi$
$252$	−13.6385	+	68.5654i	−0.0541210	+	0.272085i
$253$	−79.9326	−	192.974i	−0.315939	−	0.762744i
$254$		−	51.6789i		−	0.203460i
$255$	188.186	−	13.5082i	0.737984	−	0.0529735i
$256$	−91.3087			−0.356675
$257$	−236.109	+	97.7996i	−0.918713	+	0.380543i	−0.791385	−	0.611318i	$-0.790640\pi$
$257$	−236.109	+	97.7996i	−0.918713	+	0.380543i	−0.127327	+	0.991861i	$0.540640\pi$
$258$	56.5315	+	11.2448i	0.219115	+	0.0435846i
$259$	222.896	−	222.896i	0.860600	−	0.860600i
$260$	312.858	+	468.225i	1.20330	+	1.80087i
$261$	86.4364	−	17.1933i	0.331174	−	0.0658746i
$262$	−37.3565	+	55.9079i	−0.142582	+	0.213389i
$263$	−145.488	+	351.238i	−0.553185	+	1.33551i	0.361890	+	0.932221i	$0.382132\pi$
$263$	−145.488	+	351.238i	−0.553185	+	1.33551i	−0.915074	+	0.403285i	$0.867868\pi$
$264$	76.0636	+	31.5066i	0.288120	+	0.119343i
$265$	−46.0724	−	30.7846i	−0.173858	−	0.116168i
$266$	4.75584	+	23.9092i	0.0178791	+	0.0898843i
$267$	−193.734	+	129.449i	−0.725596	+	0.484828i
$268$	−3.61992	−	3.61992i	−0.0135072	−	0.0135072i
$269$	43.6093	−	219.239i	0.162116	−	0.815014i	−0.811062	−	0.584961i	$-0.801110\pi$
$269$	43.6093	−	219.239i	0.162116	−	0.815014i	0.973178	−	0.230053i	$-0.0738901\pi$
$270$	−6.82876	−	16.4861i	−0.0252917	−	0.0610595i
$271$			46.2263i			0.170577i	0.996356	+	0.0852885i	$0.0271812\pi$
$271$			46.2263i			0.170577i	−0.996356	+	0.0852885i	$0.972819\pi$
$272$	−203.830	−	67.7825i	−0.749374	−	0.249200i
$273$	−257.331			−0.942605
$274$	−10.0281	+	4.15378i	−0.0365990	+	0.0151598i
$275$	−181.094	−	36.0219i	−0.658525	−	0.130989i
$276$	82.5964	−	82.5964i	0.299262	−	0.299262i
$277$	117.184	+	175.378i	0.423046	+	0.633133i	0.980371	−	0.197162i	$-0.0631724\pi$
$277$	117.184	+	175.378i	0.423046	+	0.633133i	−0.557325	+	0.830294i	$0.688172\pi$
$278$	59.5316	−	11.8416i	0.214142	−	0.0425956i
$279$	−34.0997	+	51.0338i	−0.122221	+	0.182917i
$280$	63.6184	−	153.588i	0.227208	−	0.548530i
$281$	364.197	+	150.855i	1.29607	+	0.536852i	0.920790	−	0.390058i	$-0.127545\pi$
$281$	364.197	+	150.855i	1.29607	+	0.536852i	0.375284	+	0.926910i	$0.377545\pi$
$282$	25.1315	+	16.7923i	0.0891187	+	0.0595472i
$283$	−5.36585	−	26.9760i	−0.0189606	−	0.0953214i	0.970146	−	0.242521i	$-0.0779742\pi$
$283$	−5.36585	−	26.9760i	−0.0189606	−	0.0953214i	−0.989107	+	0.147199i	$0.952974\pi$
$284$	254.903	−	170.320i	0.897544	−	0.599720i
$285$	56.8711	+	56.8711i	0.199548	+	0.199548i
$286$	−28.4607	+	143.082i	−0.0995130	+	0.500285i
$287$	73.9456	+	178.520i	0.257650	+	0.622022i
$288$			69.9202i			0.242779i
$289$	−231.446	−	173.072i	−0.800851	−	0.598864i
$290$	−100.884			−0.347875
$291$	88.8711	−	36.8116i	0.305399	−	0.126500i
$292$	417.503	+	83.0466i	1.42981	+	0.284406i
$293$	318.093	−	318.093i	1.08564	−	1.08564i	0.0896705	−	0.995971i	$-0.471419\pi$
$293$	318.093	−	318.093i	1.08564	−	1.08564i	0.995971	−	0.0896705i	$-0.0285814\pi$
$294$	−4.95431	−	7.41464i	−0.0168514	−	0.0252199i
$295$	−346.216	+	68.8666i	−1.17361	+	0.233446i
$296$	115.339	−	172.618i	0.389660	−	0.583168i
$297$	−22.8658	+	55.2030i	−0.0769893	+	0.185869i
$298$	−26.6442	−	11.0364i	−0.0894100	−	0.0370348i
$299$	357.506	+	238.878i	1.19567	+	0.798924i
$300$	−20.1446	−	101.274i	−0.0671486	−	0.337579i
$301$	−324.033	+	216.512i	−1.07652	+	0.719310i
$302$	16.5824	+	16.5824i	0.0549085	+	0.0549085i
$303$	27.7746	−	139.632i	0.0916654	−	0.460833i
$304$	−35.0418	−	84.5984i	−0.115269	−	0.278284i
$305$		−	106.832i		−	0.350268i
$306$	−8.62523	+	25.9370i	−0.0281870	+	0.0847615i
$307$	−381.605			−1.24301			−0.621507	−	0.783409i	$-0.713479\pi$
$307$	−381.605			−1.24301			−0.621507	+	0.783409i	$0.713479\pi$
$308$	−247.565	+	102.545i	−0.803784	+	0.332938i
$309$	28.0491	+	5.57932i	0.0907738	+	0.0180560i
$310$	49.6815	−	49.6815i	0.160263	−	0.160263i
$311$	−27.7066	−	41.4659i	−0.0890888	−	0.133331i	0.784248	−	0.620447i	$-0.213049\pi$
$311$	−27.7066	−	41.4659i	−0.0890888	−	0.133331i	−0.873337	+	0.487116i	$0.838049\pi$
$312$	−166.222	+	33.0636i	−0.532763	+	0.105973i
$313$	149.214	−	223.315i	0.476722	−	0.713465i	−0.512694	−	0.858571i	$-0.671352\pi$
$313$	149.214	−	223.315i	0.476722	−	0.713465i	0.989416	+	0.145106i	$0.0463524\pi$
$314$	−60.7452	+	146.652i	−0.193456	+	0.467044i
$315$	111.466	+	46.1709i	0.353861	+	0.146574i
$316$	−101.965	−	68.1306i	−0.322673	−	0.215603i
$317$	−23.6483	−	118.888i	−0.0746002	−	0.375041i	0.925392	−	0.379012i	$-0.123736\pi$
$317$	−23.6483	−	118.888i	−0.0746002	−	0.375041i	−0.999992	+	0.00397098i	$0.998736\pi$
$318$	6.67473	−	4.45991i	0.0209897	−	0.0140249i
$319$	238.864	+	238.864i	0.748791	+	0.748791i
$320$	−47.5659	+	239.130i	−0.148643	+	0.747280i
$321$	41.1386	+	99.3173i	0.128158	+	0.309400i
$322$		−	61.1024i		−	0.189759i
$323$	−8.82056	−	122.881i	−0.0273082	−	0.380437i
$324$	−33.4148			−0.103132
$325$	351.155	−	145.453i	1.08048	−	0.447549i
$326$	−157.120	−	31.2531i	−0.481963	−	0.0958684i
$327$	87.9232	−	87.9232i	0.268878	−	0.268878i
$328$	70.7024	+	105.814i	0.215556	+	0.322602i
$329$	−200.434	+	39.8688i	−0.609223	+	0.121182i
$330$	38.0001	−	56.8712i	0.115152	−	0.172337i
$331$	79.5190	−	191.976i	0.240239	−	0.579988i	−0.757068	−	0.653337i	$-0.773369\pi$
$331$	79.5190	−	191.976i	0.240239	−	0.579988i	0.997306	+	0.0733489i	$0.0233687\pi$
$332$	−470.702	−	194.971i	−1.41778	−	0.587262i
$333$	125.277	+	83.7073i	0.376207	+	0.251373i
$334$	−16.4996	−	82.9490i	−0.0494000	−	0.248350i
$335$	−7.34613	+	4.90852i	−0.0219287	+	0.0146523i
$336$	−97.1301	−	97.1301i	−0.289078	−	0.289078i
$337$	−52.5791	+	264.333i	−0.156021	+	0.784372i	0.820950	+	0.571000i	$0.193444\pi$
$337$	−52.5791	+	264.333i	−0.156021	+	0.784372i	−0.976971	+	0.213371i	$0.931556\pi$
$338$	−80.2600	−	193.765i	−0.237456	−	0.573269i
$339$			112.064i			0.330572i
$340$	−200.035	+	351.492i	−0.588337	+	1.03380i
$341$	−235.264			−0.689923
$342$	−10.7650	+	4.45902i	−0.0314767	+	0.0130381i
$343$	360.771	+	71.7618i	1.05181	+	0.209218i
$344$	−181.489	+	181.489i	−0.527585	+	0.527585i
$345$	−111.999	−	167.618i	−0.324633	−	0.485848i
$346$	122.189	−	24.3049i	0.353148	−	0.0702455i
$347$	55.8712	−	83.6171i	0.161012	−	0.240971i	−0.742188	−	0.670192i	$-0.766212\pi$
$347$	55.8712	−	83.6171i	0.161012	−	0.240971i	0.903200	+	0.429221i	$0.141212\pi$
$348$	−72.2933	+	174.531i	−0.207739	+	0.501527i
$349$	44.8108	+	18.5612i	0.128398	+	0.0531841i	0.445957	−	0.895054i	$-0.352863\pi$
$349$	44.8108	+	18.5612i	0.128398	+	0.0531841i	−0.317560	+	0.948238i	$0.602863\pi$
$350$	−44.9109	−	30.0085i	−0.128317	−	0.0857385i
$351$	−23.9958	−	120.635i	−0.0683642	−	0.343690i
$352$	−222.840	+	148.897i	−0.633068	+	0.423003i
$353$	74.5877	+	74.5877i	0.211297	+	0.211297i	0.804818	−	0.593521i	$-0.202263\pi$
$353$	74.5877	+	74.5877i	0.211297	+	0.211297i	−0.593521	+	0.804818i	$0.702263\pi$
$354$	9.97703	−	50.1579i	0.0281837	−	0.141689i
$355$	−202.472	−	488.811i	−0.570344	−	1.37693i
$356$		−	499.454i		−	1.40296i
$357$	−82.7664	−	165.239i	−0.231839	−	0.462855i
$358$	74.8320			0.209028
$359$	449.007	−	185.985i	1.25072	−	0.518063i	0.343668	−	0.939091i	$-0.388331\pi$
$359$	449.007	−	185.985i	1.25072	−	0.518063i	0.907048	+	0.421028i	$0.138331\pi$
$360$	77.9336	+	15.5020i	0.216482	+	0.0430610i
$361$	−218.130	+	218.130i	−0.604238	+	0.604238i
$362$	19.6706	+	29.4391i	0.0543387	+	0.0813236i
$363$	−19.0774	+	3.79473i	−0.0525548	+	0.0104538i
$364$	306.455	−	458.643i	0.841910	−	1.26001i
$365$	281.140	−	678.733i	0.770247	−	1.85954i
$366$	14.2991	+	5.92288i	0.0390686	+	0.0161827i
$367$	−103.367	−	69.0676i	−0.281654	−	0.188195i	0.406717	−	0.913554i	$-0.366674\pi$
$367$	−103.367	−	69.0676i	−0.281654	−	0.188195i	−0.688371	+	0.725359i	$0.741674\pi$
$368$	44.7764	+	225.106i	0.121675	+	0.611702i
$369$	−76.7939	+	51.3121i	−0.208114	+	0.139057i
$370$	−121.957	−	121.957i	−0.329615	−	0.329615i
$371$	−10.5889	+	53.2338i	−0.0285414	+	0.143487i
$372$	−50.3485	−	121.552i	−0.135345	−	0.326753i
$373$			260.189i			0.697557i	0.937205	+	0.348778i	$0.113403\pi$
$373$			260.189i			0.697557i	−0.937205	+	0.348778i	$0.886597\pi$
$374$	−101.031	+	27.7445i	−0.270135	+	0.0741831i
$375$	99.2511			0.264670
$376$	−124.347	+	51.5063i	−0.330710	+	0.136985i
$377$	−682.015	−	135.661i	−1.80906	−	0.359844i
$378$	−12.3597	+	12.3597i	−0.0326975	+	0.0326975i
$379$	−6.57751	−	9.84394i	−0.0173549	−	0.0259734i	0.822691	−	0.568489i	$-0.192472\pi$
$379$	−6.57751	−	9.84394i	−0.0173549	−	0.0259734i	−0.840046	+	0.542516i	$0.817472\pi$
$380$	−169.089	+	33.6340i	−0.444972	+	0.0885104i
$381$	−92.7869	+	138.865i	−0.243535	+	0.364476i
$382$	−72.0817	+	174.021i	−0.188695	+	0.455551i
$383$	247.581	+	102.551i	0.646426	+	0.267758i	0.681714	−	0.731619i	$-0.261235\pi$
$383$	247.581	+	102.551i	0.646426	+	0.267758i	−0.0352880	+	0.999377i	$0.511235\pi$
$384$	−163.630	−	109.334i	−0.426120	−	0.284725i
$385$	90.2211	+	453.572i	0.234340	+	1.17811i
$386$	−8.89964	+	5.94655i	−0.0230561	+	0.0154056i
$387$	−131.715	−	131.715i	−0.340350	−	0.340350i
$388$	−40.2269	+	202.234i	−0.103678	+	0.521222i
$389$	168.418	+	406.597i	0.432951	+	1.04524i	0.978331	+	0.207048i	$0.0663856\pi$
$389$	168.418	+	406.597i	0.432951	+	1.04524i	−0.545379	+	0.838189i	$0.683614\pi$
$390$			140.799i			0.361023i
$391$	−38.4041	+	306.396i	−0.0982202	+	0.783621i
$392$	39.7093			0.101299
$393$	200.760	−	83.1575i	0.510839	−	0.211597i
$394$	152.853	+	30.4043i	0.387952	+	0.0771684i
$395$	−149.653	+	149.653i	−0.378869	+	0.378869i
$396$	−71.1577	−	106.495i	−0.179691	−	0.268927i
$397$	588.293	−	117.019i	1.48185	−	0.294757i	0.613096	−	0.790008i	$-0.289924\pi$
$397$	588.293	−	117.019i	1.48185	−	0.294757i	0.868750	+	0.495251i	$0.164924\pi$
$398$	14.0848	−	21.0794i	0.0353889	−	0.0529632i
$399$	30.1485	−	72.7849i	0.0755601	−	0.182418i
$400$	187.446	+	77.6426i	0.468615	+	0.194107i
$401$	378.869	+	253.152i	0.944811	+	0.631302i	0.929595	−	0.368582i	$-0.120157\pi$
$401$	378.869	+	253.152i	0.944811	+	0.631302i	0.0152153	+	0.999884i	$0.495157\pi$
$402$	−0.249713	−	1.25539i	−0.000621176	−	0.00312286i
$403$	402.675	−	269.059i	0.999194	−	0.667640i
$404$	215.791	+	215.791i	0.534136	+	0.534136i
$405$	−11.2505	+	56.5601i	−0.0277790	+	0.139655i
$406$	37.8164	+	91.2969i	0.0931439	+	0.224869i
$407$			577.522i			1.41897i
$408$	−74.6937	−	96.1014i	−0.183073	−	0.235543i
$409$	540.999			1.32274			0.661368	−	0.750061i	$-0.269976\pi$
$409$	540.999			1.32274			0.661368	+	0.750061i	$0.269976\pi$
$410$	97.6775	−	40.4594i	0.238238	−	0.0986814i
$411$	34.4043	+	6.84344i	0.0837087	+	0.0166507i
$412$	−43.3477	+	43.3477i	−0.105213	+	0.105213i
$413$	192.102	+	287.500i	0.465137	+	0.696127i
$414$	28.6444	−	5.69773i	0.0691895	−	0.0137626i
$415$	−488.503	+	731.096i	−1.17711	+	1.76168i
$416$	211.125	−	509.701i	0.507512	−	1.22524i
$417$	−181.227	−	75.0667i	−0.434597	−	0.180016i
$418$	−37.1356	−	24.8132i	−0.0888410	−	0.0593617i
$419$	−149.197	−	750.063i	−0.356078	−	1.79013i	−0.579039	−	0.815300i	$-0.696572\pi$
$419$	−149.197	−	750.063i	−0.356078	−	1.79013i	0.222961	−	0.974827i	$-0.428428\pi$
$420$	−215.036	+	143.682i	−0.511990	+	0.342101i
$421$	−150.559	−	150.559i	−0.357621	−	0.357621i	0.505314	−	0.862935i	$-0.331377\pi$
$421$	−150.559	−	150.559i	−0.357621	−	0.357621i	−0.862935	+	0.505314i	$0.831377\pi$
$422$	29.4707	−	148.159i	0.0698358	−	0.351088i
$423$	−37.3805	−	90.2446i	−0.0883701	−	0.213344i
$424$			35.7467i			0.0843083i
$425$	206.343	+	178.704i	0.485513	+	0.420480i
$426$	76.6511			0.179932
$427$	−96.6797	+	40.0460i	−0.226416	+	0.0937846i
$428$	−226.006	−	44.9553i	−0.528051	−	0.105036i
$429$	333.372	−	333.372i	0.777091	−	0.777091i
$430$	118.465	+	177.295i	0.275499	+	0.412314i
$431$	−137.151	+	27.2810i	−0.318216	+	0.0632970i	−0.351614	−	0.936145i	$-0.614367\pi$
$431$	−137.151	+	27.2810i	−0.318216	+	0.0632970i	0.0333983	+	0.999442i	$0.489367\pi$
$432$	36.4767	−	54.5913i	0.0844368	−	0.126369i
$433$	−61.4414	+	148.333i	−0.141897	+	0.342570i	−0.978811	−	0.204764i	$-0.934357\pi$
$433$	−61.4414	+	148.333i	−0.141897	+	0.342570i	0.836914	+	0.547334i	$0.184357\pi$
$434$	−63.5836	−	26.3372i	−0.146506	−	0.0606847i
$435$	271.083	+	181.132i	0.623179	+	0.416395i
$436$	51.9984	+	261.414i	0.119262	+	0.599572i
$437$	−109.450	+	73.1324i	−0.250459	+	0.167351i
$438$	75.2595	+	75.2595i	0.171825	+	0.171825i
$439$	56.4305	−	283.695i	0.128543	−	0.646230i	−0.861761	−	0.507315i	$-0.830638\pi$
$439$	56.4305	−	283.695i	0.128543	−	0.646230i	0.990304	−	0.138916i	$-0.0443618\pi$
$440$	116.556	+	281.391i	0.264900	+	0.639525i
$441$			28.8190i			0.0653491i
$442$	141.193	−	163.030i	0.319441	−	0.368847i
$443$	320.942			0.724475			0.362237	−	0.932086i	$-0.382013\pi$
$443$	320.942			0.724475			0.362237	+	0.932086i	$0.382013\pi$
$444$	−298.384	+	123.595i	−0.672036	+	0.278366i
$445$	−845.409	−	168.162i	−1.89980	−	0.377893i
$446$	6.14040	−	6.14040i	0.0137677	−	0.0137677i
$447$	51.7798	+	77.4939i	0.115838	+	0.173364i
$448$	234.236	−	46.5924i	0.522847	−	0.104001i
$449$	−98.0551	+	146.750i	−0.218386	+	0.326837i	−0.924445	−	0.381316i	$-0.875471\pi$
$449$	−98.0551	+	146.750i	−0.218386	+	0.326837i	0.706059	+	0.708153i	$0.250471\pi$
$450$	9.87990	−	23.8522i	0.0219553	−	0.0530049i
$451$	−327.069	−	135.477i	−0.725209	−	0.300391i
$452$	−199.732	−	133.457i	−0.441886	−	0.295259i
$453$	−14.7854	−	74.3310i	−0.0326388	−	0.164086i
$454$	−78.8761	+	52.7033i	−0.173736	+	0.116087i
$455$	−673.148	−	673.148i	−1.47945	−	1.47945i
$456$	10.1224	−	50.8888i	0.0221983	−	0.111598i
$457$	48.4868	+	117.057i	0.106098	+	0.256143i	0.968009	−	0.250917i	$-0.0807321\pi$
$457$	48.4868	+	117.057i	0.106098	+	0.256143i	−0.861911	+	0.507060i	$0.830732\pi$
$458$			153.854i			0.335926i
$459$	69.7453	−	54.2088i	0.151951	−	0.118102i
$460$	432.125			0.939402
$461$	−387.047	+	160.320i	−0.839582	+	0.347766i	−0.760689	−	0.649117i	$-0.775139\pi$
$461$	−387.047	+	160.320i	−0.839582	+	0.347766i	−0.0788932	+	0.996883i	$0.525139\pi$
$462$	−65.7112	−	13.0708i	−0.142232	−	0.0282917i
$463$	103.023	−	103.023i	0.222511	−	0.222511i	−0.587044	−	0.809555i	$-0.699708\pi$
$463$	103.023	−	103.023i	0.222511	−	0.222511i	0.809555	+	0.587044i	$0.199708\pi$
$464$	−206.222	−	308.633i	−0.444444	−	0.665158i
$465$	−222.699	+	44.2976i	−0.478923	+	0.0952637i
$466$	42.9996	−	64.3535i	0.0922739	−	0.138098i
$467$	−245.852	+	593.540i	−0.526450	+	1.27096i	0.407384	+	0.913257i	$0.366441\pi$
$467$	−245.852	+	593.540i	−0.526450	+	1.27096i	−0.933834	+	0.357706i	$0.883559\pi$
$468$	243.585	+	100.896i	0.520482	+	0.215591i
$469$	7.19578	+	4.80807i	0.0153428	+	0.0102517i
$470$	21.8143	+	109.668i	0.0464133	+	0.233336i
$471$	426.533	−	285.000i	0.905591	−	0.605097i
$472$	161.027	+	161.027i	0.341160	+	0.341160i
$473$	139.294	−	700.276i	0.294490	−	1.48050i
$474$	−11.7337	−	28.3276i	−0.0247546	−	0.0597628i
$475$			116.364i			0.244976i
$476$	393.073	+	49.2684i	0.825784	+	0.103505i
$477$	−25.9431			−0.0543880
$478$	73.3495	−	30.3824i	0.153451	−	0.0635615i
$479$	550.248	+	109.451i	1.14874	+	0.228499i	0.732508	−	0.680758i	$-0.238350\pi$
$479$	550.248	+	109.451i	1.14874	+	0.228499i	0.416234	+	0.909257i	$0.363350\pi$
$480$	−182.903	+	182.903i	−0.381048	+	0.381048i
$481$	−660.481	−	988.480i	−1.37314	−	2.05505i
$482$	−17.0234	+	3.38616i	−0.0353182	+	0.00702523i
$483$	−109.706	+	164.187i	−0.227135	+	0.339932i
$484$	15.9559	−	38.5208i	0.0329666	−	0.0795885i
$485$	328.771	+	136.181i	0.677878	+	0.280786i
$486$	−6.94666	−	4.64161i	−0.0142935	−	0.00955063i
$487$	−71.7615	−	360.770i	−0.147354	−	0.740800i	−0.981831	−	0.189757i	$-0.939230\pi$
$487$	−71.7615	−	360.770i	−0.147354	−	0.740800i	0.834477	−	0.551043i	$-0.185770\pi$
$488$	−57.3045	+	38.2897i	−0.117427	+	0.0784624i
$489$	366.080	+	366.080i	0.748631	+	0.748631i
$490$	6.43595	−	32.3557i	0.0131346	−	0.0660321i
$491$	20.5037	+	49.5003i	0.0417591	+	0.100815i	0.943383	−	0.331706i	$-0.107624\pi$
$491$	20.5037	+	49.5003i	0.0417591	+	0.100815i	−0.901624	+	0.432521i	$0.857624\pi$
$492$		−	197.978i		−	0.402394i
$493$	−132.247	−	481.574i	−0.268250	−	0.976823i
$494$	91.9384			0.186110
$495$	−204.219	+	84.5902i	−0.412563	+	0.170889i
$496$	253.547	+	50.4337i	0.511184	+	0.101681i
$497$	−366.463	+	366.463i	−0.737350	+	0.737350i
$498$	−70.7718	−	105.917i	−0.142112	−	0.212686i
$499$	−473.710	+	94.2268i	−0.949319	+	0.188831i	−0.645381	−	0.763861i	$-0.723301\pi$
$499$	−473.710	+	94.2268i	−0.949319	+	0.188831i	−0.303938	+	0.952692i	$0.598301\pi$
$500$	−118.198	+	176.896i	−0.236396	+	0.353792i
$501$	−104.595	+	252.515i	−0.208773	+	0.504022i
$502$	−169.346	−	70.1455i	−0.337343	−	0.139732i
$503$	−586.741	−	392.048i	−1.16648	−	0.779419i	−0.187280	−	0.982307i	$-0.559967\pi$
$503$	−586.741	−	392.048i	−1.16648	−	0.779419i	−0.979202	+	0.202888i	$0.934967\pi$
$504$	−15.1847	−	76.3386i	−0.0301284	−	0.151465i
$505$	437.917	−	292.607i	0.867162	−	0.579419i
$506$	79.1581	+	79.1581i	0.156439	+	0.156439i
$507$	−132.230	+	664.765i	−0.260808	+	1.31117i
$508$	−137.001	−	330.749i	−0.269687	−	0.651081i
$509$		−	383.508i		−	0.753454i	−0.926324	−	0.376727i	$-0.877049\pi$
$509$		−	383.508i		−	0.753454i	0.926324	−	0.376727i	$-0.122951\pi$
$510$	−90.4108	+	45.2857i	−0.177276	+	0.0887954i
$511$	−719.619			−1.40826
$512$	465.099	−	192.650i	0.908396	−	0.376270i
$513$	36.9324	+	7.34632i	0.0719930	+	0.0143203i
$514$	96.8520	−	96.8520i	0.188428	−	0.188428i
$515$	58.7784	+	87.9680i	0.114133	+	0.170812i
$516$	391.616	−	77.8974i	0.758947	−	0.150964i
$517$	208.012	−	311.312i	0.402345	−	0.602151i
$518$	−64.6520	+	156.084i	−0.124811	+	0.301320i
$519$	−371.971	−	154.075i	−0.716707	−	0.296870i
$520$	−521.308	−	348.327i	−1.00252	−	0.669860i
$521$	15.7696	+	79.2789i	0.0302679	+	0.152167i	0.992964	−	0.118419i	$-0.0377826\pi$
$521$	15.7696	+	79.2789i	0.0302679	+	0.152167i	−0.962696	+	0.270586i	$0.912783\pi$
$522$	−39.2731	+	26.2415i	−0.0752358	+	0.0502710i
$523$	−315.384	−	315.384i	−0.603029	−	0.603029i	0.338087	−	0.941115i	$-0.390220\pi$
$523$	−315.384	−	315.384i	−0.603029	−	0.603029i	−0.941115	+	0.338087i	$0.890220\pi$
$524$	−90.8726	+	456.847i	−0.173421	+	0.871846i
$525$	66.8004	+	161.270i	0.127239	+	0.307182i
$526$		−	203.757i		−	0.387371i
$527$	302.284	+	172.030i	0.573594	+	0.326433i
$528$	251.664			0.476636
$529$	−183.905	+	76.1761i	−0.347647	+	0.144000i
$530$	29.1269	+	5.79370i	0.0549564	+	0.0109315i
$531$	−116.865	+	116.865i	−0.220085	+	0.220085i
$532$	93.8211	+	140.413i	0.176355	+	0.263935i
$533$	714.746	−	142.172i	1.34099	−	0.266739i
$534$	69.3785	−	103.832i	0.129922	−	0.194443i
$535$	−152.189	+	367.416i	−0.284465	+	0.686759i
$536$	5.26586	+	2.18119i	0.00982436	+	0.00406939i
$537$	−201.080	−	134.357i	−0.374450	−	0.250200i
$538$	23.3725	+	117.502i	0.0434433	+	0.218404i
$539$	−91.8478	+	61.3707i	−0.170404	+	0.113860i
$540$	−87.4092	−	87.4092i	−0.161869	−	0.161869i
$541$	−61.6576	+	309.974i	−0.113970	+	0.572965i	0.881028	+	0.473065i	$0.156852\pi$
$541$	−61.6576	+	309.974i	−0.113970	+	0.572965i	−0.994997	+	0.0999000i	$0.968148\pi$
$542$	−9.48103	−	22.8892i	−0.0174927	−	0.0422311i
$543$		−	114.423i		−	0.210724i
$544$	395.198	−	28.3678i	0.726467	−	0.0521467i
$545$	459.994			0.844025
$546$	127.419	−	52.7787i	0.233368	−	0.0966642i
$547$	364.390	+	72.4818i	0.666162	+	0.132508i	0.516577	−	0.856241i	$-0.327206\pi$
$547$	364.390	+	72.4818i	0.666162	+	0.132508i	0.149585	+	0.988749i	$0.452206\pi$
$548$	−53.1691	+	53.1691i	−0.0970239	+	0.0970239i
$549$	−27.7886	−	41.5886i	−0.0506168	−	0.0757534i
$550$	97.0579	−	19.3060i	0.176469	−	0.0351019i
$551$	118.275	−	177.011i	0.214655	−	0.321254i
$552$	−49.7686	+	120.152i	−0.0901604	+	0.217667i
$553$	191.530	+	79.3342i	0.346346	+	0.143461i
$554$	−93.9941	−	62.8049i	−0.169664	−	0.113366i
$555$	108.741	+	546.678i	0.195930	+	0.985005i
$556$	349.615	−	233.605i	0.628804	−	0.420153i
$557$	−216.299	−	216.299i	−0.388329	−	0.388329i	0.485762	−	0.874091i	$-0.338542\pi$
$557$	−216.299	−	216.299i	−0.388329	−	0.388329i	−0.874091	+	0.485762i	$0.838542\pi$
$558$	6.41761	−	32.2635i	0.0115011	−	0.0578199i
$559$	562.456	+	1357.89i	1.00618	+	2.42914i
$560$		−	508.162i		−	0.907432i
$561$	321.291	+	106.844i	0.572711	+	0.190452i
$562$	−211.275			−0.375933
$563$	−671.729	+	278.239i	−1.19312	+	0.494209i	−0.888771	−	0.458351i	$-0.848440\pi$
$563$	−671.729	+	278.239i	−1.19312	+	0.494209i	−0.304354	+	0.952559i	$0.598440\pi$
$564$	205.360	+	40.8486i	0.364113	+	0.0724266i
$565$	−293.146	+	293.146i	−0.518843	+	0.518843i
$566$	8.18970	+	12.2568i	0.0144694	+	0.0216551i
$567$	55.4025	−	11.0203i	0.0977117	−	0.0194361i
$568$	−189.630	+	283.801i	−0.333855	+	0.499649i
$569$	−278.428	+	672.184i	−0.489328	+	1.18134i	0.465731	+	0.884926i	$0.345791\pi$
$569$	−278.428	+	672.184i	−0.489328	+	1.18134i	−0.955059	+	0.296416i	$0.904209\pi$
$570$	−39.8243	−	16.4958i	−0.0698672	−	0.0289399i
$571$	611.373	+	408.507i	1.07071	+	0.715423i	0.960442	−	0.278479i	$-0.0898303\pi$
$571$	611.373	+	408.507i	1.07071	+	0.715423i	0.110264	+	0.993902i	$0.464830\pi$
$572$	197.159	+	991.183i	0.344683	+	1.73284i
$573$	506.134	−	338.188i	0.883306	−	0.590206i
$574$	−73.2291	−	73.2291i	−0.127577	−	0.127577i
$575$	56.9011	−	286.061i	0.0989584	−	0.497497i
$576$	43.6844	+	105.464i	0.0758410	+	0.183096i
$577$		−	418.939i		−	0.726064i	−0.931777	−	0.363032i	$-0.881741\pi$
$577$		−	418.939i		−	0.726064i	0.931777	−	0.363032i	$-0.118259\pi$
$578$	150.099	+	38.2278i	0.259686	+	0.0661380i
$579$	34.5908			0.0597423
$580$	−645.664	+	267.443i	−1.11321	+	0.461109i
$581$	844.737	+	168.029i	1.45394	+	0.289206i
$582$	−36.4549	+	36.4549i	−0.0626373	+	0.0626373i
$583$	−55.2465	−	82.6822i	−0.0947624	−	0.141822i
$584$	−464.836	+	92.4615i	−0.795951	+	0.158325i
$585$	252.797	−	378.338i	0.432132	−	0.646732i
$586$	−92.2646	+	222.746i	−0.157448	+	0.380113i
$587$	−103.393	−	42.8269i	−0.176138	−	0.0729589i	0.292872	−	0.956152i	$-0.405389\pi$
$587$	−103.393	−	42.8269i	−0.176138	−	0.0729589i	−0.469010	+	0.883193i	$0.655389\pi$
$588$	−51.3642	−	34.3204i	−0.0873540	−	0.0583681i
$589$	28.9253	+	145.417i	0.0491092	+	0.246888i
$590$	157.306	−	105.109i	0.266620	−	0.178150i
$591$	−356.139	−	356.139i	−0.602604	−	0.602604i
$592$	123.804	−	622.403i	0.209128	−	1.05136i
$593$	−265.651	−	641.339i	−0.447978	−	1.08152i	−0.973078	−	0.230475i	$-0.925972\pi$
$593$	−265.651	−	641.339i	−0.447978	−	1.08152i	0.525100	−	0.851041i	$-0.324028\pi$
$594$		−	32.0238i		−	0.0539122i
$595$	215.740	−	648.754i	0.362588	−	1.09034i
$596$	−199.782			−0.335205
$597$	−75.6939	+	31.3534i	−0.126790	+	0.0525183i
$598$	−226.015	−	44.9572i	−0.377952	−	0.0751793i
$599$	−54.0124	+	54.0124i	−0.0901709	+	0.0901709i	−0.750753	−	0.660583i	$-0.770309\pi$
$599$	−54.0124	+	54.0124i	−0.0901709	+	0.0901709i	0.660583	+	0.750753i	$0.270309\pi$
$600$	63.8706	+	95.5891i	0.106451	+	0.159315i
$601$	27.4805	−	5.46622i	0.0457247	−	0.00909520i	−0.172175	−	0.985066i	$-0.555079\pi$
$601$	27.4805	−	5.46622i	0.0457247	−	0.00909520i	0.217900	+	0.975971i	$0.430079\pi$
$602$	116.040	−	173.666i	0.192758	−	0.288483i
$603$	−1.58299	+	3.82168i	−0.00262520	+	0.00633778i
$604$	150.088	+	62.1687i	0.248491	+	0.102928i
$605$	−59.8307	−	39.9776i	−0.0988938	−	0.0660787i
$606$	14.8859	+	74.8363i	0.0245641	+	0.123492i
$607$	134.622	−	89.9515i	0.221783	−	0.148190i	−0.439716	−	0.898137i	$-0.644921\pi$
$607$	134.622	−	89.9515i	0.221783	−	0.148190i	0.661498	+	0.749947i	$0.269921\pi$
$608$	119.431	+	119.431i	0.196433	+	0.196433i
$609$	62.3033	−	313.220i	0.102304	−	0.514318i
$610$	21.9112	+	52.8983i	0.0359200	+	0.0867186i
$611$			770.732i			1.26143i
$612$	13.5569	+	188.865i	0.0221519	+	0.308602i
$613$	−205.487			−0.335215			−0.167608	−	0.985854i	$-0.553604\pi$
$613$	−205.487			−0.335215			−0.167608	+	0.985854i	$0.553604\pi$
$614$	188.954	−	78.2673i	0.307742	−	0.127471i
$615$	−335.110	−	66.6576i	−0.544895	−	0.108386i
$616$	210.960	−	210.960i	0.342467	−	0.342467i
$617$	−558.899	−	836.451i	−0.905833	−	1.35567i	−0.934454	−	0.356084i	$-0.884112\pi$
$617$	−558.899	−	836.451i	−0.905833	−	1.35567i	0.0286214	−	0.999590i	$-0.490888\pi$
$618$	−15.0330	+	2.99025i	−0.0243252	+	0.00483859i
$619$	276.892	−	414.398i	0.447321	−	0.669463i	−0.537455	−	0.843292i	$-0.680614\pi$
$619$	276.892	−	414.398i	0.447321	−	0.669463i	0.984776	+	0.173830i	$0.0556142\pi$
$620$	186.260	−	449.672i	0.300419	−	0.725277i
$621$	−87.1999	−	36.1194i	−0.140419	−	0.0581633i
$622$	22.2237	+	14.8494i	0.0357295	+	0.0238737i
$623$	164.721	+	828.107i	0.264399	+	1.32922i
$624$	−430.745	+	287.815i	−0.690297	+	0.461241i
$625$	543.480	+	543.480i	0.869569	+	0.869569i
$626$	−28.0823	+	141.179i	−0.0448599	+	0.225526i
$627$	55.2354	+	133.350i	0.0880947	+	0.212680i
$628$			1099.62i			1.75099i
$629$	422.297	−	742.042i	0.671378	−	1.17972i
$630$	−64.6628			−0.102639
$631$	−207.851	+	86.0948i	−0.329400	+	0.136442i	−0.541253	−	0.840860i	$-0.682050\pi$
$631$	−207.851	+	86.0948i	−0.329400	+	0.136442i	0.211854	+	0.977301i	$0.432050\pi$
$632$	133.911	+	26.6366i	0.211885	+	0.0421465i
$633$	−345.203	+	345.203i	−0.545344	+	0.545344i
$634$	36.0935	+	54.0177i	0.0569298	+	0.0852015i
$635$	−605.975	+	120.536i	−0.954292	+	0.189820i
$636$	30.8956	−	46.2385i	0.0485780	−	0.0727020i
$637$	87.0192	−	210.083i	0.136608	−	0.329801i
$638$	−167.266	−	69.2839i	−0.262173	−	0.108595i
$639$	−205.968	−	137.623i	−0.322328	−	0.215373i
$640$	−142.032	−	714.043i	−0.221925	−	1.11569i
$641$	−2.54624	+	1.70135i	−0.00397230	+	0.00265420i	−0.557555	−	0.830140i	$-0.688260\pi$
$641$	−2.54624	+	1.70135i	−0.00397230	+	0.00265420i	0.553582	+	0.832794i	$0.313260\pi$
$642$	−40.7400	−	40.7400i	−0.0634579	−	0.0634579i
$643$	173.781	−	873.656i	0.270266	−	1.35872i	−0.572264	−	0.820069i	$-0.693935\pi$
$643$	173.781	−	873.656i	0.270266	−	1.35872i	0.842530	−	0.538649i	$-0.181065\pi$
$644$	−161.983	−	391.060i	−0.251526	−	0.607237i
$645$		−	689.104i		−	1.06838i
$646$	29.5705	+	59.0361i	0.0457747	+	0.0913872i
$647$	392.063			0.605970			0.302985	−	0.952995i	$-0.402017\pi$
$647$	392.063			0.605970			0.302985	+	0.952995i	$0.402017\pi$
$648$	34.3711	−	14.2370i	0.0530418	−	0.0219707i
$649$	−621.324	−	123.589i	−0.957356	−	0.190430i
$650$	−144.044	+	144.044i	−0.221606	+	0.221606i
$651$	123.567	+	184.931i	0.189811	+	0.284073i
$652$	−1088.43	+	216.503i	−1.66937	+	0.332059i
$653$	−447.801	+	670.182i	−0.685760	+	1.02631i	0.311347	+	0.950296i	$0.399220\pi$
$653$	−447.801	+	670.182i	−0.685760	+	1.02631i	−0.997107	+	0.0760156i	$0.975780\pi$
$654$	−25.5026	+	61.5687i	−0.0389948	+	0.0941418i
$655$	742.694	+	307.634i	1.13388	+	0.469670i
$656$	323.445	+	216.119i	0.493056	+	0.329450i
$657$	−67.1037	−	337.353i	−0.102137	−	0.513475i
$658$	91.0690	−	60.8504i	0.138403	−	0.0924778i
$659$	−565.122	−	565.122i	−0.857544	−	0.857544i	0.133504	−	0.991048i	$-0.457377\pi$
$659$	−565.122	−	565.122i	−0.857544	−	0.857544i	−0.991048	+	0.133504i	$0.957377\pi$
$660$	92.4382	−	464.718i	0.140058	−	0.704119i
$661$	285.848	+	690.099i	0.432448	+	1.04402i	0.978495	+	0.206268i	$0.0661320\pi$
$661$	285.848	+	690.099i	0.432448	+	1.04402i	−0.546047	+	0.837755i	$0.683868\pi$
$662$			111.367i			0.168229i
$663$	−672.110	+	184.571i	−1.01374	+	0.278388i
$664$	567.244			0.854283
$665$	269.262	−	111.532i	0.404905	−	0.167717i
$666$	−79.1999	−	15.7538i	−0.118919	−	0.0236544i
$667$	−377.316	+	377.316i	−0.565691	+	0.565691i
$668$	−325.497	−	487.140i	−0.487270	−	0.729251i
$669$	−27.5245	+	5.47497i	−0.0411428	+	0.00818382i
$670$	2.63074	−	3.93717i	0.00392647	−	0.00587638i
$671$	73.3688	−	177.128i	0.109343	−	0.263976i
$672$	234.084	+	96.9606i	0.348339	+	0.144287i
$673$	213.585	+	142.713i	0.317363	+	0.212055i	0.704040	−	0.710160i	$-0.251377\pi$
$673$	213.585	+	142.713i	0.317363	+	0.212055i	−0.386678	+	0.922215i	$0.626377\pi$
$674$	−28.1799	−	141.670i	−0.0418100	−	0.210193i
$675$	−69.3735	+	46.3539i	−0.102776	+	0.0686725i
$676$	−1027.34	−	1027.34i	−1.51974	−	1.51974i
$677$	−74.1983	+	373.020i	−0.109599	+	0.550990i	0.886499	+	0.462731i	$0.153130\pi$
$677$	−74.1983	+	373.020i	−0.109599	+	0.550990i	−0.996098	+	0.0882591i	$0.971870\pi$
$678$	−22.9843	−	55.4891i	−0.0339002	−	0.0818424i
$679$		−	348.576i		−	0.513367i
$680$	56.0000	−	446.780i	0.0823530	−	0.657029i
$681$	306.573			0.450180
$682$	116.492	−	48.2526i	0.170810	−	0.0707517i
$683$	−146.312	−	29.1032i	−0.214219	−	0.0426108i	0.0868139	−	0.996225i	$-0.472331\pi$
$683$	−146.312	−	29.1032i	−0.214219	−	0.0426108i	−0.301033	+	0.953614i	$0.597331\pi$
$684$	−57.0761	+	57.0761i	−0.0834447	+	0.0834447i
$685$	72.0959	+	107.899i	0.105250	+	0.157517i
$686$	−193.356	+	38.4609i	−0.281860	+	0.0560655i
$687$	276.238	−	413.419i	0.402093	−	0.601774i
$688$	−300.237	+	724.837i	−0.436391	+	1.05354i
$689$	189.119	+	78.3355i	0.274483	+	0.113694i
$690$	89.8351	+	60.0259i	0.130196	+	0.0869940i
$691$	161.575	+	812.293i	0.233828	+	1.17553i	0.902070	+	0.431589i	$0.142047\pi$
$691$	161.575	+	812.293i	0.233828	+	1.17553i	−0.668242	+	0.743944i	$0.732953\pi$
$692$	717.588	−	479.477i	1.03698	−	0.692886i
$693$	153.103	+	153.103i	0.220928	+	0.220928i
$694$	−10.5150	+	52.8626i	−0.0151513	+	0.0761710i
$695$	−277.703	−	670.435i	−0.399573	−	0.964654i
$696$		−	210.328i		−	0.302196i
$697$	321.179	+	413.231i	0.460802	+	0.592870i
$698$	−25.9952			−0.0372424
$699$	−231.087	+	95.7194i	−0.330597	+	0.136938i
$700$	−366.986	−	72.9980i	−0.524265	−	0.104283i
$701$	197.792	−	197.792i	0.282158	−	0.282158i	−0.551811	−	0.833969i	$-0.686063\pi$
$701$	197.792	−	197.792i	0.282158	−	0.282158i	0.833969	+	0.551811i	$0.186063\pi$
$702$	36.6240	+	54.8117i	0.0521709	+	0.0780793i
$703$	356.968	−	71.0053i	0.507778	−	0.101003i
$704$	−243.092	+	363.812i	−0.345301	+	0.516779i
$705$	138.286	−	333.852i	0.196151	−	0.473549i
$706$	−52.2305	−	21.6346i	−0.0739808	−	0.0306439i
$707$	−428.955	−	286.618i	−0.606725	−	0.405401i
$708$	−69.1149	−	347.464i	−0.0976199	−	0.490768i
$709$	−588.890	+	393.484i	−0.830592	+	0.554984i	−0.896603	−	0.442835i	$-0.853973\pi$
$709$	−588.890	+	393.484i	−0.830592	+	0.554984i	0.0660110	+	0.997819i	$0.478973\pi$
$710$	200.510	+	200.510i	0.282409	+	0.282409i
$711$	−19.3314	+	97.1857i	−0.0271891	+	0.136689i
$712$	212.802	+	513.748i	0.298879	+	0.721557i
$713$		−	371.628i		−	0.521218i
$714$	74.8728	+	64.8438i	0.104864	+	0.0908176i
$715$	1744.12			2.43934
$716$	478.931	−	198.380i	0.668898	−	0.277067i
$717$	−251.646	−	50.0555i	−0.350971	−	0.0698125i
$718$	−184.183	+	184.183i	−0.256522	+	0.256522i
$719$	−234.756	−	351.338i	−0.326504	−	0.488648i	0.631510	−	0.775367i	$-0.282435\pi$
$719$	−234.756	−	351.338i	−0.326504	−	0.488648i	−0.958015	+	0.286719i	$0.907435\pi$
$720$	238.223	−	47.3855i	0.330865	−	0.0658132i
$721$	57.5754	−	86.1677i	0.0798549	−	0.119511i
$722$	63.2698	−	152.747i	0.0876313	−	0.211561i
$723$	51.8229	+	21.4658i	0.0716776	+	0.0296898i
$724$	203.937	+	136.266i	0.281680	+	0.188213i
$725$	92.0243	+	462.638i	0.126930	+	0.638121i
$726$	8.66797	−	5.79175i	0.0119394	−	0.00797762i
$727$	434.163	+	434.163i	0.597198	+	0.597198i	0.939566	−	0.342368i	$-0.111229\pi$
$727$	434.163	+	434.163i	0.597198	+	0.597198i	−0.342368	+	0.939566i	$0.611229\pi$
$728$	−119.813	+	602.340i	−0.164578	+	0.827390i
$729$	10.3325	+	24.9447i	0.0141735	+	0.0342178i
$730$			393.740i			0.539370i
$731$	−691.032	+	797.910i	−0.945325	+	1.09153i
$732$	107.217			0.146471
$733$	865.897	−	358.666i	1.18131	−	0.489313i	0.296391	−	0.955067i	$-0.404217\pi$
$733$	865.897	−	358.666i	1.18131	−	0.489313i	0.884914	+	0.465754i	$0.154217\pi$
$734$	65.3485	+	12.9986i	0.0890307	+	0.0177093i
$735$	−75.3870	+	75.3870i	−0.102567	+	0.102567i
$736$	−235.201	−	352.003i	−0.319567	−	0.478266i
$737$	−15.5510	+	3.09328i	−0.0211004	+	0.00419712i
$738$	27.5008	−	41.1579i	0.0372640	−	0.0557695i
$739$	125.045	−	301.885i	0.169208	−	0.408505i	−0.816414	−	0.577467i	$-0.804041\pi$
$739$	125.045	−	301.885i	0.169208	−	0.408505i	0.985623	+	0.168962i	$0.0540414\pi$
$740$	−1103.85	−	457.228i	−1.49168	−	0.617876i
$741$	−247.046	−	165.071i	−0.333395	−	0.222768i
$742$	−5.67513	−	28.5308i	−0.00764842	−	0.0384512i
$743$	−154.735	+	103.391i	−0.208257	+	0.139153i	−0.655325	−	0.755347i	$-0.727468\pi$
$743$	−154.735	+	103.391i	−0.208257	+	0.139153i	0.447068	+	0.894500i	$0.352468\pi$
$744$	103.579	+	103.579i	0.139219	+	0.139219i
$745$	−67.2652	+	338.165i	−0.0902888	+	0.453913i
$746$	−53.3647	−	128.834i	−0.0715345	−	0.172700i
$747$			411.676i			0.551106i
$748$	−573.053	+	445.399i	−0.766114	+	0.595453i
$749$	389.549			0.520093
$750$	−49.1447	+	20.3564i	−0.0655263	+	0.0271419i
$751$	−561.969	−	111.783i	−0.748295	−	0.148845i	−0.193810	−	0.981039i	$-0.562085\pi$
$751$	−561.969	−	111.783i	−0.748295	−	0.148845i	−0.554485	+	0.832194i	$0.687085\pi$
$752$	−290.914	+	290.914i	−0.386854	+	0.386854i
$753$	329.104	+	492.539i	0.437058	+	0.654103i
$754$	365.527	−	72.7079i	0.484784	−	0.0964296i
$755$	155.764	−	233.118i	0.206311	−	0.308766i
$756$	−46.3373	+	111.868i	−0.0612928	+	0.147974i
$757$	−299.760	−	124.165i	−0.395985	−	0.164022i	0.175800	−	0.984426i	$-0.443749\pi$
$757$	−299.760	−	124.165i	−0.395985	−	0.164022i	−0.571785	+	0.820404i	$0.693749\pi$
$758$	5.27588	+	3.52523i	0.00696027	+	0.00465070i
$759$	−70.5798	−	354.829i	−0.0929905	−	0.467495i
$760$	159.598	−	106.640i	0.209998	−	0.140316i
$761$	279.900	+	279.900i	0.367806	+	0.367806i	0.866676	−	0.498871i	$-0.166252\pi$
$761$	279.900	+	279.900i	0.367806	+	0.367806i	−0.498871	+	0.866676i	$0.666252\pi$
$762$	17.4626	−	87.7906i	0.0229168	−	0.115211i
$763$	−172.429	−	416.281i	−0.225988	−	0.545584i
$764$			1304.83i			1.70790i
$765$	324.249	+	40.6419i	0.423855	+	0.0531266i
$766$	−143.625			−0.187499
$767$	1204.79	−	499.042i	1.57079	−	0.650641i
$768$	−155.113	−	30.8538i	−0.201969	−	0.0401742i
$769$	−163.217	+	163.217i	−0.212246	+	0.212246i	−0.805221	−	0.592975i	$-0.797953\pi$
$769$	−163.217	+	163.217i	−0.212246	+	0.212246i	0.592975	+	0.805221i	$0.297953\pi$
$770$	−137.701	−	206.084i	−0.178833	−	0.267642i
$771$	−434.142	+	86.3562i	−0.563090	+	0.112006i
$772$	−41.1941	+	61.6513i	−0.0533602	+	0.0798592i
$773$	−146.571	+	353.855i	−0.189614	+	0.457768i	−0.989885	−	0.141870i	$-0.954689\pi$
$773$	−146.571	+	353.855i	−0.189614	+	0.457768i	0.800272	+	0.599638i	$0.204689\pi$
$774$	92.2344	+	38.2047i	0.119166	+	0.0493601i
$775$	−273.150	−	182.513i	−0.352452	−	0.235501i
$776$	−44.7874	−	225.161i	−0.0577157	−	0.290157i
$777$	453.966	−	303.330i	0.584255	−	0.390387i
$778$	−166.786	−	166.786i	−0.214378	−	0.214378i
$779$	−43.5258	+	218.819i	−0.0558740	+	0.280897i
$780$	373.258	+	901.124i	0.478536	+	1.15529i
$781$		−	949.504i		−	1.21575i
$782$	−43.8258	−	159.590i	−0.0560433	−	0.204080i
$783$	152.645			0.194949
$784$	112.142	−	46.4506i	0.143038	−	0.0592482i
$785$	1861.29	+	370.233i	2.37107	+	0.471635i
$786$	−82.3517	+	82.3517i	−0.104773	+	0.104773i
$787$	239.352	+	358.216i	0.304133	+	0.455166i	0.951783	−	0.306771i	$-0.0992485\pi$
$787$	239.352	+	358.216i	0.304133	+	0.455166i	−0.647651	+	0.761937i	$0.724248\pi$
$788$	1058.87	−	210.623i	1.34375	−	0.267288i
$789$	−365.836	+	547.512i	−0.463670	+	0.693931i
$790$	43.4077	−	104.796i	0.0549465	−	0.132653i
$791$	375.175	+	155.403i	0.474305	+	0.196464i
$792$	118.568	+	79.2248i	0.149707	+	0.100031i
$793$	76.9947	+	387.079i	0.0970930	+	0.488119i
$794$	−267.296	+	178.601i	−0.336645	+	0.224939i
$795$	−67.8641	−	67.8641i	−0.0853636	−	0.0853636i
$796$	34.2623	−	172.248i	0.0430431	−	0.216392i
$797$	−118.715	−	286.603i	−0.148952	−	0.359602i	0.831739	−	0.555167i	$-0.187346\pi$
$797$	−118.715	−	286.603i	−0.148952	−	0.359602i	−0.980691	+	0.195565i	$0.937346\pi$
$798$			42.2233i			0.0529114i
$799$	−494.908	+	247.893i	−0.619409	+	0.310254i
$800$	−374.237			−0.467797
$801$	−372.851	+	154.440i	−0.465483	+	0.192809i
$802$	−239.521	−	47.6436i	−0.298654	−	0.0594060i
$803$	932.266	−	932.266i	1.16098	−	1.16098i
$804$	−4.92622	−	7.37261i	−0.00612714	−	0.00916992i
$805$	−716.473	+	142.515i	−0.890029	+	0.177038i
$806$	−144.203	+	215.815i	−0.178912	+	0.267760i
$807$	148.164	−	357.700i	0.183599	−	0.443247i
$808$	−313.908	−	130.025i	−0.388500	−	0.160922i
$809$	−124.164	−	82.9635i	−0.153478	−	0.102551i	0.476460	−	0.879196i	$-0.341920\pi$
$809$	−124.164	−	82.9635i	−0.153478	−	0.102551i	−0.629938	+	0.776645i	$0.716920\pi$
$810$	−6.02974	−	30.3135i	−0.00744412	−	0.0374241i
$811$	1041.11	−	695.646i	1.28373	−	0.857763i	0.288711	−	0.957416i	$-0.406773\pi$
$811$	1041.11	−	695.646i	1.28373	−	0.857763i	0.995022	+	0.0996528i	$0.0317732\pi$
$812$	484.056	+	484.056i	0.596129	+	0.596129i
$813$	−15.6202	+	78.5279i	−0.0192130	+	0.0965903i
$814$	−118.450	−	285.963i	−0.145516	−	0.351306i
$815$			1915.25i			2.35000i
$816$	−323.356	−	184.022i	−0.396269	−	0.225518i
$817$	−449.969			−0.550757
$818$	−267.879	+	110.959i	−0.327480	+	0.135647i
$819$	−437.146	−	86.9538i	−0.533756	−	0.106171i
$820$	517.886	−	517.886i	0.631569	−	0.631569i
$821$	−623.156	−	932.618i	−0.759020	−	1.13595i	−0.986753	−	0.162230i	$-0.948131\pi$
$821$	−623.156	−	932.618i	−0.759020	−	1.13595i	0.227733	−	0.973724i	$-0.426869\pi$
$822$	−18.4391	+	3.66776i	−0.0224319	+	0.00446199i
$823$	440.786	−	659.683i	0.535584	−	0.801559i	−0.460711	−	0.887550i	$-0.652406\pi$
$823$	440.786	−	659.683i	0.535584	−	0.801559i	0.996296	+	0.0859913i	$0.0274057\pi$
$824$	26.1192	−	63.0574i	0.0316981	−	0.0765259i
$825$	−295.465	−	122.386i	−0.358140	−	0.148346i
$826$	−154.087	−	102.957i	−0.186545	−	0.124646i
$827$	−7.49045	−	37.6570i	−0.00905737	−	0.0455345i	0.975992	−	0.217805i	$-0.0698897\pi$
$827$	−7.49045	−	37.6570i	−0.00905737	−	0.0455345i	−0.985050	+	0.172271i	$0.944890\pi$
$828$	168.222	−	112.402i	0.203167	−	0.135752i
$829$	365.421	+	365.421i	0.440798	+	0.440798i	0.892280	−	0.451482i	$-0.149105\pi$
$829$	365.421	+	365.421i	0.440798	+	0.440798i	−0.451482	+	0.892280i	$0.649105\pi$
$830$	91.9369	−	462.198i	0.110767	−	0.556865i
$831$	139.807	+	337.523i	0.168239	+	0.406165i
$832$		−	900.709i		−	1.08258i
$833$	162.888	−	11.6923i	0.195544	−	0.0140364i
$834$	105.132			0.126057
$835$	−934.158	+	386.941i	−1.11875	+	0.463402i
$836$	−303.450	−	60.3600i	−0.362979	−	0.0722010i
$837$	−75.1721	+	75.1721i	−0.0898114	+	0.0898114i
$838$	227.714	+	340.798i	0.271735	+	0.406680i
$839$	−924.310	+	183.857i	−1.10168	+	0.219138i	−0.712256	−	0.701920i	$-0.752326\pi$
$839$	−924.310	+	183.857i	−1.10168	+	0.219138i	−0.389425	+	0.921058i	$0.627326\pi$
$840$	159.971	−	239.414i	0.190442	−	0.285017i
$841$	8.41291	−	20.3106i	0.0100035	−	0.0241505i
$842$	105.430	+	43.6703i	0.125213	+	0.0518650i
$843$	567.712	+	379.333i	0.673442	+	0.449980i
$844$	−204.155	−	1026.36i	−0.241890	−	1.21606i
$845$	−2084.84	+	1393.05i	−2.46727	+	1.64858i
$846$	37.0184	+	37.0184i	0.0437569	+	0.0437569i
$847$	−13.7510	+	69.1308i	−0.0162349	+	0.0816184i
$848$	41.8153	+	100.951i	0.0493105	+	0.119046i
$849$		−	47.6391i		−	0.0561120i
$850$	−138.824	−	46.1652i	−0.163322	−	0.0543120i
$851$	−912.267			−1.07199
$852$	490.573	−	203.202i	0.575790	−	0.238500i
$853$	−957.807	−	190.520i	−1.12287	−	0.223352i	−0.401470	−	0.915872i	$-0.631500\pi$
$853$	−957.807	−	190.520i	−1.12287	−	0.223352i	−0.721399	+	0.692520i	$0.756500\pi$
$854$	39.6580	−	39.6580i	0.0464380	−	0.0464380i
$855$	77.3938	+	115.828i	0.0905191	+	0.135471i
$856$	251.628	−	50.0519i	0.293958	−	0.0584719i
$857$	199.400	−	298.424i	0.232673	−	0.348219i	−0.696700	−	0.717363i	$-0.745349\pi$
$857$	199.400	−	298.424i	0.232673	−	0.348219i	0.929372	+	0.369144i	$0.120349\pi$
$858$	−96.6964	+	233.446i	−0.112700	+	0.272081i
$859$	−1086.63	−	450.098i	−1.26500	−	0.523979i	−0.353558	−	0.935413i	$-0.615028\pi$
$859$	−1086.63	−	450.098i	−1.26500	−	0.523979i	−0.911440	+	0.411433i	$0.865028\pi$
$860$	1228.19	+	820.652i	1.42813	+	0.954247i
$861$	65.2933	+	328.252i	0.0758343	+	0.381245i
$862$	62.3157	−	41.6380i	0.0722920	−	0.0483040i
$863$	−1041.77	−	1041.77i	−1.20715	−	1.20715i	−0.971945	−	0.235208i	$-0.924423\pi$
$863$	−1041.77	−	1041.77i	−1.20715	−	1.20715i	−0.235208	−	0.971945i	$-0.575577\pi$
$864$	−23.6265	+	118.778i	−0.0273455	+	0.137475i
$865$	−569.989	−	1376.07i	−0.658946	−	1.59084i
$866$		−	86.0494i		−	0.0993642i
$867$	−334.691	−	372.216i	−0.386034	−	0.429315i
$868$	−476.760			−0.549262
$869$	−350.904	+	145.349i	−0.403802	+	0.167260i
$870$	−171.378	−	34.0893i	−0.196987	−	0.0391831i
$871$	23.0792	−	23.0792i	0.0264974	−	0.0264974i
$872$	−164.867	−	246.740i	−0.189067	−	0.282959i
$873$	163.410	−	32.5043i	0.187183	−	0.0372329i
$874$	39.1955	−	58.6602i	0.0448461	−	0.0671170i
$875$	137.635	−	332.279i	0.157297	−	0.379748i
$876$	681.180	+	282.154i	0.777603	+	0.322094i
$877$	−14.2326	−	9.50992i	−0.0162287	−	0.0108437i	0.547429	−	0.836852i	$-0.315606\pi$
$877$	−14.2326	−	9.50992i	−0.0162287	−	0.0108437i	−0.563658	+	0.826008i	$0.690606\pi$
$878$	30.2440	+	152.047i	0.0344465	+	0.173174i
$879$	647.853	−	432.881i	0.737034	−	0.492470i
$880$	658.323	+	658.323i	0.748094	+	0.748094i
$881$	155.647	−	782.491i	0.176671	−	0.888185i	−0.786148	−	0.618038i	$-0.787928\pi$
$881$	155.647	−	782.491i	0.176671	−	0.888185i	0.962819	−	0.270147i	$-0.0870722\pi$
$882$	−5.91077	−	14.2699i	−0.00670155	−	0.0161790i
$883$		−	731.139i		−	0.828017i	−0.910273	−	0.414009i	$-0.864128\pi$
$883$		−	731.139i		−	0.828017i	0.910273	−	0.414009i	$-0.135872\pi$
$884$	471.452	−	1417.71i	0.533317	−	1.60375i
$885$	−611.411			−0.690860
$886$	−158.916	+	65.8253i	−0.179364	+	0.0742949i
$887$	1377.66	+	274.034i	1.55317	+	0.308944i	0.895742	−	0.444575i	$-0.146645\pi$
$887$	1377.66	+	274.034i	1.55317	+	0.308944i	0.657426	+	0.753519i	$0.271645\pi$
$888$	254.264	−	254.264i	0.286333	−	0.286333i
$889$	336.232	+	503.207i	0.378214	+	0.566037i
$890$	453.099	−	90.1270i	0.509100	−	0.101266i
$891$	−57.4972	+	86.0506i	−0.0645311	+	0.0965776i
$892$	23.0209	−	55.5773i	0.0258081	−	0.0623064i
$893$	−217.998	−	90.2976i	−0.244118	−	0.101117i
$894$	−41.5331	−	27.7515i	−0.0464576	−	0.0310419i
$895$	−174.538	−	877.464i	−0.195015	−	0.980406i
$896$	−592.948	+	396.195i	−0.661772	+	0.442182i
$897$	526.603	+	526.603i	0.587071	+	0.587071i
$898$	18.4541	−	92.7751i	0.0205502	−	0.103313i
$899$	230.002	+	555.273i	0.255842	+	0.617656i
$900$		−	178.848i		−	0.198720i
$901$	10.5255	+	146.634i	0.0116821	+	0.162745i
$902$	189.736			0.210351
$903$	−623.619	+	258.311i	−0.690608	+	0.286059i
$904$	262.310	+	52.1768i	0.290166	+	0.0577177i
$905$	299.317	−	299.317i	0.330737	−	0.330737i
$906$	22.5664	+	33.7729i	0.0249077	+	0.0372770i
$907$	1659.57	−	330.109i	1.82973	−	0.363957i	0.844553	−	0.535472i	$-0.179866\pi$
$907$	1659.57	−	330.109i	1.82973	−	0.363957i	0.985181	+	0.171516i	$0.0548664\pi$
$908$	−365.097	+	546.406i	−0.402089	+	0.601769i
$909$	94.3653	−	227.818i	0.103812	−	0.250625i
$910$	471.376	+	195.250i	0.517995	+	0.214561i
$911$	−788.850	−	527.092i	−0.865916	−	0.578587i	0.0413495	−	0.999145i	$-0.486834\pi$
$911$	−788.850	−	527.092i	−0.865916	−	0.578587i	−0.907266	+	0.420558i	$0.861834\pi$
$912$	−30.9416	−	155.554i	−0.0339272	−	0.170564i
$913$	−1312.04	+	876.674i	−1.43706	+	0.960213i
$914$	−48.0170	−	48.0170i	−0.0525350	−	0.0525350i
$915$	36.0991	−	181.483i	0.0394526	−	0.198342i
$916$	407.868	+	984.680i	0.445270	+	1.07498i
$917$		−	787.434i		−	0.858707i
$918$	−23.4166	+	41.1465i	−0.0255082	+	0.0448219i
$919$	−866.632			−0.943016			−0.471508	−	0.881862i	$-0.656290\pi$
$919$	−866.632			−0.943016			−0.471508	+	0.881862i	$0.656290\pi$
$920$	−444.492	+	184.115i	−0.483143	+	0.200125i
$921$	−648.259	−	128.947i	−0.703865	−	0.140007i
$922$	158.767	−	158.767i	0.172198	−	0.172198i
$923$	1085.90	+	1625.16i	1.17649	+	1.76074i
$924$	−455.207	+	90.5464i	−0.492649	+	0.0979939i
$925$	−448.031	+	670.525i	−0.484357	+	0.724892i
$926$	−29.8823	+	72.1423i	−0.0322703	+	0.0779074i
$927$	45.7637	+	18.9559i	0.0493675	+	0.0204487i
$928$	569.284	+	380.384i	0.613453	+	0.409896i
$929$	11.1740	+	56.1754i	0.0120280	+	0.0604686i	0.986333	−	0.164763i	$-0.0526860\pi$
$929$	11.1740	+	56.1754i	0.0120280	+	0.0604686i	−0.974305	+	0.225232i	$0.927686\pi$
$930$	101.185	−	67.6098i	0.108801	−	0.0726987i
$931$	49.2259	+	49.2259i	0.0528743	+	0.0528743i
$932$	104.600	−	525.860i	0.112232	−	0.564227i
$933$	−33.0556	−	79.8032i	−0.0354293	−	0.0855340i
$934$		−	344.319i		−	0.368650i
$935$	560.969	+	1119.95i	0.599967	+	1.19781i
$936$	−293.546			−0.313617
$937$	−124.571	+	51.5988i	−0.132946	+	0.0550681i	−0.448165	−	0.893951i	$-0.647922\pi$
$937$	−124.571	+	51.5988i	−0.132946	+	0.0550681i	0.315218	+	0.949019i	$0.397922\pi$
$938$	−4.54916	−	0.904885i	−0.00484986	−	0.000964696i
$939$	328.940	−	328.940i	0.350309	−	0.350309i
$940$	430.342	+	644.052i	0.457811	+	0.685162i
$941$	238.649	−	47.4703i	0.253612	−	0.0504466i	−0.0666467	−	0.997777i	$-0.521230\pi$
$941$	238.649	−	47.4703i	0.253612	−	0.0504466i	0.320259	+	0.947330i	$0.396230\pi$
$942$	−152.747	+	228.602i	−0.162151	+	0.242677i
$943$	214.002	−	516.647i	0.226937	−	0.547876i
$944$	643.116	+	266.387i	0.681267	+	0.282190i
$945$	173.754	+	116.099i	0.183867	+	0.122856i
$946$	74.6547	+	375.315i	0.0789162	+	0.396738i
$947$	−84.5736	+	56.5103i	−0.0893069	+	0.0596730i	−0.599422	−	0.800433i	$-0.704603\pi$
$947$	−84.5736	+	56.5103i	−0.0893069	+	0.0596730i	0.510115	+	0.860106i	$0.329603\pi$
$948$	−150.193	−	150.193i	−0.158431	−	0.158431i
$949$	−529.473	+	2661.84i	−0.557927	+	2.80489i
$950$	−23.8662	−	57.6181i	−0.0251223	−	0.0606507i
$951$		−	209.954i		−	0.220772i
$952$	−425.315	+	116.798i	−0.446759	+	0.122687i
$953$	−1716.26			−1.80090			−0.900450	−	0.434959i	$-0.856763\pi$
$953$	−1716.26			−1.80090			−0.900450	+	0.434959i	$0.856763\pi$
$954$	12.8459	−	5.32093i	0.0134653	−	0.00557750i
$955$	2208.65	+	439.328i	2.31272	+	0.460029i
$956$	388.899	−	388.899i	0.406798	−	0.406798i
$957$	325.062	+	486.490i	0.339668	+	0.508349i
$958$	−294.907	+	58.6606i	−0.307836	+	0.0612323i
$959$	70.6204	−	105.691i	0.0736396	−	0.110209i
$960$	−161.607	+	390.154i	−0.168341	+	0.406410i
$961$	501.129	+	207.575i	0.521467	+	0.215999i
$962$	529.778	+	353.987i	0.550705	+	0.367969i
$963$	36.3250	+	182.618i	0.0377207	+	0.189635i
$964$	−99.9743	+	66.8007i	−0.103708	+	0.0692953i
$965$	90.4854	+	90.4854i	0.0937673	+	0.0937673i
$966$	20.6469	−	103.799i	0.0213736	−	0.107452i
$967$	−506.164	−	1221.99i	−0.523437	−	1.26369i	−0.935755	−	0.352650i	$-0.885281\pi$
$967$	−506.164	−	1221.99i	−0.523437	−	1.26369i	0.412318	−	0.911040i	$-0.364719\pi$
$968$			46.4216i			0.0479562i
$969$	26.5382	−	211.727i	0.0273872	−	0.218501i
$970$	−190.724			−0.196622
$971$	1195.67	−	495.263i	1.23138	−	0.510055i	0.330371	−	0.943851i	$-0.392826\pi$
$971$	1195.67	−	495.263i	1.23138	−	0.510055i	0.901011	+	0.433796i	$0.142826\pi$
$972$	−56.7640	−	11.2911i	−0.0583992	−	0.0116163i
$973$	−502.627	+	502.627i	−0.516574	+	0.516574i
$974$	109.527	+	163.919i	0.112451	+	0.168294i
$975$	645.682	−	128.434i	0.662238	−	0.131727i
$976$	−117.042	+	175.165i	−0.119920	+	0.179473i
$977$	−45.8334	+	110.652i	−0.0469124	+	0.113257i	−0.945599	−	0.325336i	$-0.894523\pi$
$977$	−45.8334	+	110.652i	−0.0469124	+	0.113257i	0.898686	+	0.438592i	$0.144523\pi$
$978$	−256.350	−	106.184i	−0.262116	−	0.108572i
$979$	−1286.21	−	859.416i	−1.31380	−	0.877851i
$980$	−44.5844	−	224.141i	−0.0454943	−	0.228715i
$981$	179.071	−	119.651i	0.182539	−	0.121969i
$982$	−20.3050	−	20.3050i	−0.0206772	−	0.0206772i
$983$	−35.6375	+	179.162i	−0.0362538	+	0.182260i	−0.994669	−	0.103116i	$-0.967119\pi$
$983$	−35.6375	+	179.162i	−0.0362538	+	0.182260i	0.958415	+	0.285377i	$0.0921187\pi$
$984$	84.3520	+	203.644i	0.0857236	+	0.206955i
$985$		−	1863.23i		−	1.89161i
$986$	164.254	+	211.330i	0.166586	+	0.214330i
$987$	−353.964			−0.358626
$988$	588.413	−	243.729i	0.595560	−	0.246689i
$989$	1106.17	+	220.031i	1.11848	+	0.222479i
$990$	83.7706	−	83.7706i	0.0846167	−	0.0846167i
$991$	1037.78	+	1553.14i	1.04720	+	1.56725i	0.801588	+	0.597877i	$0.203989\pi$
$991$	1037.78	+	1553.14i	1.04720	+	1.56725i	0.245612	+	0.969368i	$0.421011\pi$
$992$	−467.676	+	93.0266i	−0.471448	+	0.0937768i
$993$	199.954	−	299.253i	0.201364	−	0.301362i
$994$	106.294	−	256.618i	0.106936	−	0.258167i
$995$	−280.023	−	115.989i	−0.281430	−	0.116572i
$996$	−733.732	−	490.264i	−0.736679	−	0.492233i
$997$	14.2303	+	71.5408i	0.0142732	+	0.0717561i	0.987265	−	0.159082i	$-0.0508533\pi$
$997$	14.2303	+	71.5408i	0.0142732	+	0.0717561i	−0.972992	+	0.230838i	$0.925853\pi$
$998$	215.234	−	143.815i	0.215666	−	0.144103i
$999$	184.531	+	184.531i	0.184716	+	0.184716i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.3.j.a.37.4	✓	48
3.2	odd	2		153.3.p.c.37.3		48
17.6	odd	16	inner	51.3.j.a.40.4	yes	48
51.23	even	16		153.3.p.c.91.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.3.j.a.37.4	✓	48	1.1	even	1	trivial
51.3.j.a.40.4	yes	48	17.6	odd	16	inner
153.3.p.c.37.3		48	3.2	odd	2
153.3.p.c.91.3		48	51.23	even	16

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:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	51.j (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.495155 + 0.205100i) q^{2} +(1.69877 + 0.337906i) q^{3} +(-2.62531 + 2.62531i) q^{4} +(3.55986 + 5.32771i) q^{5} +(-0.910460 + 0.181102i) q^{6} +(3.48700 - 5.21867i) q^{7} +(1.58189 - 3.81901i) q^{8} +(2.77164 + 1.14805i) q^{9} +(-2.85540 - 1.90792i) q^{10} +(2.24337 + 11.2782i) q^{11} +(-5.34692 + 3.57269i) q^{12} +(-16.7380 - 16.7380i) q^{13} +(-0.656259 + 3.29924i) q^{14} +(4.24712 + 10.2534i) q^{15} -12.6356i q^{16} +(5.36442 - 16.1314i) q^{17} -1.60786 q^{18} +(6.69526 - 2.77327i) q^{19} +(-23.3327 - 4.64115i) q^{20} +(7.68704 - 7.68704i) q^{21} +(-3.42397 - 5.12434i) q^{22} +(-17.8153 + 3.54368i) q^{23} +(3.97773 - 5.95309i) q^{24} +(-6.14476 + 14.8348i) q^{25} +(11.7209 + 4.85495i) q^{26} +(4.32044 + 2.88683i) q^{27} +(4.54617 + 22.8551i) q^{28} +(24.4257 - 16.3208i) q^{29} +(-4.20597 - 4.20597i) q^{30} +(-3.99140 + 20.0661i) q^{31} +(8.91910 + 21.5326i) q^{32} +19.9171i q^{33} +(0.652335 + 9.08781i) q^{34} +40.2168 q^{35} +(-10.2904 + 4.26243i) q^{36} +(49.2580 + 9.79803i) q^{37} +(-2.74640 + 2.74640i) q^{38} +(-22.7781 - 34.0899i) q^{39} +(25.9779 - 5.16732i) q^{40} +(-17.1040 + 25.5980i) q^{41} +(-2.22967 + 5.38289i) q^{42} +(-57.3648 - 23.7613i) q^{43} +(-35.4983 - 23.7192i) q^{44} +(3.75017 + 18.8534i) q^{45} +(8.09453 - 5.40859i) q^{46} +(-23.0234 - 23.0234i) q^{47} +(4.26964 - 21.4649i) q^{48} +(3.67618 + 8.87508i) q^{49} -8.60581i q^{50} +(14.5638 - 25.5909i) q^{51} +87.8850 q^{52} +(-7.98943 + 3.30933i) q^{53} +(-2.73138 - 0.543305i) q^{54} +(-52.1008 + 52.1008i) q^{55} +(-14.4141 - 21.5723i) q^{56} +(12.3108 - 2.44877i) q^{57} +(-8.74715 + 13.0910i) q^{58} +(-21.0823 + 50.8972i) q^{59} +(-38.0685 - 15.7685i) q^{60} +(-13.8629 - 9.26287i) q^{61} +(-2.13920 - 10.7545i) q^{62} +(15.6560 - 10.4610i) q^{63} +(26.9061 + 26.9061i) q^{64} +(29.5902 - 148.760i) q^{65} +(-4.08500 - 9.86205i) q^{66} +1.37885i q^{67} +(28.2668 + 56.4334i) q^{68} -31.4615 q^{69} +(-19.9136 + 8.24846i) q^{70} +(-80.9852 - 16.1090i) q^{71} +(8.76884 - 8.76884i) q^{72} +(-63.6984 - 95.3314i) q^{73} +(-26.4000 + 5.25128i) q^{74} +(-15.4513 + 23.1245i) q^{75} +(-10.2965 + 24.8579i) q^{76} +(66.6797 + 27.6196i) q^{77} +(18.2706 + 12.2080i) q^{78} +(6.44381 + 32.3952i) q^{79} +(67.3186 - 44.9808i) q^{80} +(6.36396 + 6.36396i) q^{81} +(3.21900 - 16.1830i) q^{82} +(52.5138 + 126.780i) q^{83} +40.3618i q^{84} +(105.040 - 28.8455i) q^{85} +33.2779 q^{86} +(47.0086 - 19.4716i) q^{87} +(46.6203 + 9.27335i) q^{88} +(-95.1227 + 95.1227i) q^{89} +(-5.72375 - 8.56619i) q^{90} +(-145.715 + 28.9846i) q^{91} +(37.4675 - 56.0740i) q^{92} +(-13.5610 + 32.7390i) q^{93} +(16.1223 + 6.67806i) q^{94} +(38.6093 + 25.7979i) q^{95} +(7.87550 + 39.5928i) q^{96} +(46.1775 - 30.8548i) q^{97} +(-3.64056 - 3.64056i) q^{98} +(-6.73011 + 33.8345i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{10} - 80 q^{11} - 48 q^{13} - 64 q^{14} + 16 q^{17} + 48 q^{19} + 224 q^{20} + 192 q^{22} + 112 q^{23} - 144 q^{24} + 80 q^{25} - 368 q^{26} - 240 q^{28} - 160 q^{29} - 192 q^{30} - 64 q^{31}+ \cdots + 240 q^{99}+O(q^{100}) \) 48 * q - 48 * q^10 - 80 * q^11 - 48 * q^13 - 64 * q^14 + 16 * q^17 + 48 * q^19 + 224 * q^20 + 192 * q^22 + 112 * q^23 - 144 * q^24 + 80 * q^25 - 368 * q^26 - 240 * q^28 - 160 * q^29 - 192 * q^30 - 64 * q^31 - 80 * q^32 + 16 * q^34 + 128 * q^35 + 48 * q^36 + 128 * q^37 + 400 * q^38 + 192 * q^39 + 128 * q^40 + 320 * q^41 + 432 * q^42 - 112 * q^43 + 704 * q^44 + 96 * q^45 + 80 * q^46 - 32 * q^49 + 128 * q^52 - 336 * q^53 - 608 * q^55 - 880 * q^56 - 752 * q^58 - 512 * q^59 - 400 * q^61 - 560 * q^62 + 160 * q^64 - 240 * q^65 - 208 * q^68 - 240 * q^69 + 80 * q^70 - 160 * q^71 - 288 * q^72 + 544 * q^73 - 48 * q^74 - 288 * q^75 + 496 * q^76 + 512 * q^77 - 384 * q^78 + 608 * q^79 + 816 * q^80 + 1184 * q^82 + 976 * q^83 - 32 * q^85 + 128 * q^86 + 144 * q^87 - 448 * q^88 + 240 * q^89 + 48 * q^90 - 640 * q^91 + 1280 * q^92 + 288 * q^93 - 32 * q^94 + 704 * q^95 + 768 * q^96 + 288 * q^97 + 1008 * q^98 + 240 * q^99

Introduction

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