LMFDB - Embedded newform 285.2.bi.a.23.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,2,Mod(17,285)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 9, 20]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("285.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	285.bi (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.27573645761$
Analytic rank:	$0$
Dimension:	$432$
Relative dimension:	$36$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			23.13
Character	$\chi$	$=$	285.23
Dual form			285.2.bi.a.62.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.425015 - 0.911447i) q^{2} +(-1.70872 + 0.283348i) q^{3} +(0.635477 - 0.757331i) q^{4} +(0.685416 - 2.12843i) q^{5} +(0.984487 + 1.43698i) q^{6} +(-0.0170740 - 0.0637212i) q^{7} +(-2.90316 - 0.777900i) q^{8} +(2.83943 - 0.968323i) q^{9} +O(q^{10})$	\(q+(-0.425015 - 0.911447i) q^{2} +(-1.70872 + 0.283348i) q^{3} +(0.635477 - 0.757331i) q^{4} +(0.685416 - 2.12843i) q^{5} +(0.984487 + 1.43698i) q^{6} +(-0.0170740 - 0.0637212i) q^{7} +(-2.90316 - 0.777900i) q^{8} +(2.83943 - 0.968323i) q^{9} +(-2.23126 + 0.279893i) q^{10} +(-0.508093 + 0.293348i) q^{11} +(-0.871261 + 1.47413i) q^{12} +(-0.808532 + 0.566140i) q^{13} +(-0.0508218 + 0.0426446i) q^{14} +(-0.568097 + 3.83109i) q^{15} +(0.181526 + 1.02948i) q^{16} +(-1.25813 - 2.69807i) q^{17} +(-2.08937 - 2.17644i) q^{18} +(-1.84387 - 3.94970i) q^{19} +(-1.17636 - 1.87165i) q^{20} +(0.0472300 + 0.104044i) q^{21} +(0.483318 + 0.338423i) q^{22} +(-3.65422 + 0.319702i) q^{23} +(5.18110 + 0.506606i) q^{24} +(-4.06041 - 2.91772i) q^{25} +(0.859645 + 0.496316i) q^{26} +(-4.57741 + 2.45914i) q^{27} +(-0.0591082 - 0.0275626i) q^{28} +(-2.64543 + 0.962857i) q^{29} +(3.73329 - 1.11048i) q^{30} +(-1.34144 + 2.32345i) q^{31} +(-4.06287 + 2.84486i) q^{32} +(0.785068 - 0.645215i) q^{33} +(-1.92442 + 2.29344i) q^{34} +(-0.147329 - 0.00733468i) q^{35} +(1.07105 - 2.76573i) q^{36} +(4.97782 - 4.97782i) q^{37} +(-2.81627 + 3.35927i) q^{38} +(1.22114 - 1.19647i) q^{39} +(-3.64558 + 5.64598i) q^{40} +(9.04391 - 1.59469i) q^{41} +(0.0747568 - 0.0872677i) q^{42} +(8.99006 + 0.786528i) q^{43} +(-0.100720 + 0.571210i) q^{44} +(-0.114815 - 6.70722i) q^{45} +(1.84449 + 3.19475i) q^{46} +(2.88314 + 1.34443i) q^{47} +(-0.601879 - 1.70766i) q^{48} +(6.05841 - 3.49782i) q^{49} +(-0.933612 + 4.94092i) q^{50} +(2.91428 + 4.25375i) q^{51} +(-0.0850473 + 0.972095i) q^{52} +(0.904964 - 0.0791740i) q^{53} +(4.18684 + 3.12690i) q^{54} +(0.276114 + 1.28250i) q^{55} +0.198275i q^{56} +(4.26979 + 6.22647i) q^{57} +(2.00194 + 2.00194i) q^{58} +(-7.64934 - 2.78413i) q^{59} +(2.54039 + 2.86481i) q^{60} +(-0.829391 - 0.695941i) q^{61} +(2.68784 + 0.235155i) q^{62} +(-0.110183 - 0.164399i) q^{63} +(6.13035 + 3.53936i) q^{64} +(0.650807 + 2.10894i) q^{65} +(-0.921745 - 0.441322i) q^{66} +(-0.965016 + 2.06948i) q^{67} +(-2.84285 - 0.761738i) q^{68} +(6.15343 - 1.58170i) q^{69} +(0.0559318 + 0.137400i) q^{70} +(4.86122 + 5.79338i) q^{71} +(-8.99658 + 0.602408i) q^{72} +(8.16451 - 11.6601i) q^{73} +(-6.65267 - 2.42138i) q^{74} +(7.76482 + 3.83505i) q^{75} +(-4.16297 - 1.11352i) q^{76} +(0.0273677 + 0.0273677i) q^{77} +(-1.60952 - 0.604485i) q^{78} +(6.16710 - 1.08743i) q^{79} +(2.31561 + 0.319261i) q^{80} +(7.12470 - 5.49897i) q^{81} +(-5.29727 - 7.56529i) q^{82} +(-0.451231 - 1.68402i) q^{83} +(0.108809 + 0.0303485i) q^{84} +(-6.60499 + 0.828539i) q^{85} +(-3.10403 - 8.52825i) q^{86} +(4.24746 - 2.39483i) q^{87} +(1.70327 - 0.456390i) q^{88} +(-0.572351 + 3.24596i) q^{89} +(-6.06448 + 2.95532i) q^{90} +(0.0498800 + 0.0418543i) q^{91} +(-2.08005 + 2.97062i) q^{92} +(1.63380 - 4.35022i) q^{93} -3.19924i q^{94} +(-9.67047 + 1.21735i) q^{95} +(6.13622 - 6.01226i) q^{96} +(-13.4682 + 6.28032i) q^{97} +(-5.76300 - 4.03529i) q^{98} +(-1.15864 + 1.32494i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 432 q - 12 q^{3} - 24 q^{6} - 12 q^{7}+O(q^{10}) $ 432 * q - 12 * q^3 - 24 * q^6 - 12 * q^7	$ 432 q - 12 q^{3} - 24 q^{6} - 12 q^{7} - 24 q^{10} - 6 q^{12} - 24 q^{13} + 6 q^{15} - 108 q^{16} + 24 q^{18} - 24 q^{21} - 72 q^{22} - 6 q^{27} - 72 q^{28} - 6 q^{30} - 24 q^{31} - 102 q^{33} - 24 q^{36} - 48 q^{37} - 24 q^{40} + 24 q^{42} - 36 q^{43} + 12 q^{45} - 24 q^{46} - 156 q^{48} - 72 q^{51} - 48 q^{52} + 12 q^{55} - 90 q^{57} + 96 q^{58} + 132 q^{60} - 24 q^{61} + 18 q^{63} - 72 q^{66} - 120 q^{67} + 24 q^{70} + 168 q^{72} - 24 q^{73} - 192 q^{75} - 168 q^{76} - 6 q^{78} + 72 q^{81} - 312 q^{82} + 42 q^{87} - 204 q^{88} + 156 q^{90} + 72 q^{91} + 138 q^{93} + 240 q^{96} - 48 q^{97}+O(q^{100}) $ 432 * q - 12 * q^3 - 24 * q^6 - 12 * q^7 - 24 * q^10 - 6 * q^12 - 24 * q^13 + 6 * q^15 - 108 * q^16 + 24 * q^18 - 24 * q^21 - 72 * q^22 - 6 * q^27 - 72 * q^28 - 6 * q^30 - 24 * q^31 - 102 * q^33 - 24 * q^36 - 48 * q^37 - 24 * q^40 + 24 * q^42 - 36 * q^43 + 12 * q^45 - 24 * q^46 - 156 * q^48 - 72 * q^51 - 48 * q^52 + 12 * q^55 - 90 * q^57 + 96 * q^58 + 132 * q^60 - 24 * q^61 + 18 * q^63 - 72 * q^66 - 120 * q^67 + 24 * q^70 + 168 * q^72 - 24 * q^73 - 192 * q^75 - 168 * q^76 - 6 * q^78 + 72 * q^81 - 312 * q^82 + 42 * q^87 - 204 * q^88 + 156 * q^90 + 72 * q^91 + 138 * q^93 + 240 * q^96 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/285\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$211$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−0.425015	−	0.911447i	−0.300531	−	0.644491i	0.696819	−	0.717247i	$-0.254598\pi$
$2$	−0.425015	−	0.911447i	−0.300531	−	0.644491i	−0.997350	+	0.0727566i	$0.976820\pi$
$3$	−1.70872	+	0.283348i	−0.986528	+	0.163591i
$3$	−1.70872	+	0.283348i	−0.986528	+	0.163591i
$4$	0.635477	−	0.757331i	0.317738	−	0.378666i
$5$	0.685416	−	2.12843i	0.306527	−	0.951862i
$5$	0.685416	−	2.12843i	0.306527	−	0.951862i
$6$	0.984487	+	1.43698i	0.401915	+	0.586644i
$7$	−0.0170740	−	0.0637212i	−0.00645338	−	0.0240844i	0.962624	−	0.270841i	$-0.0873018\pi$
$7$	−0.0170740	−	0.0637212i	−0.00645338	−	0.0240844i	−0.969077	+	0.246757i	$0.920635\pi$
$8$	−2.90316	−	0.777900i	−1.02642	−	0.275029i
$9$	2.83943	−	0.968323i	0.946476	−	0.322774i
$10$	−2.23126	+	0.279893i	−0.705587	+	0.0885098i
$11$	−0.508093	+	0.293348i	−0.153196	+	0.0884476i	−0.574638	−	0.818407i	$-0.694857\pi$
$11$	−0.508093	+	0.293348i	−0.153196	+	0.0884476i	0.421443	+	0.906855i	$0.361524\pi$
$12$	−0.871261	+	1.47413i	−0.251511	+	0.425544i
$13$	−0.808532	+	0.566140i	−0.224246	+	0.157019i	−0.680301	−	0.732933i	$-0.738151\pi$
$13$	−0.808532	+	0.566140i	−0.224246	+	0.157019i	0.456055	+	0.889952i	$0.349262\pi$
$14$	−0.0508218	+	0.0426446i	−0.0135827	+	0.0113972i
$15$	−0.568097	+	3.83109i	−0.146682	+	0.989184i
$16$	0.181526	+	1.02948i	0.0453815	+	0.257371i
$17$	−1.25813	−	2.69807i	−0.305141	−	0.654378i	0.692616	−	0.721306i	$-0.256458\pi$
$17$	−1.25813	−	2.69807i	−0.305141	−	0.654378i	−0.997758	+	0.0669282i	$0.978680\pi$
$18$	−2.08937	−	2.17644i	−0.492470	−	0.512991i
$19$	−1.84387	−	3.94970i	−0.423013	−	0.906124i
$19$	−1.84387	−	3.94970i	−0.423013	−	0.906124i
$20$	−1.17636	−	1.87165i	−0.263042	−	0.418514i
$21$	0.0472300	+	0.104044i	0.0103064	+	0.0227042i
$22$	0.483318	+	0.338423i	0.103044	+	0.0721520i
$23$	−3.65422	+	0.319702i	−0.761957	+	0.0666626i	−0.461509	−	0.887136i	$-0.652692\pi$
$23$	−3.65422	+	0.319702i	−0.761957	+	0.0666626i	−0.300448	+	0.953798i	$0.597136\pi$
$24$	5.18110	+	0.506606i	1.05759	+	0.103410i
$25$	−4.06041	−	2.91772i	−0.812082	−	0.583544i
$26$	0.859645	+	0.496316i	0.168590	+	0.0973356i
$27$	−4.57741	+	2.45914i	−0.880922	+	0.473261i
$28$	−0.0591082	−	0.0275626i	−0.0111704	−	0.00520885i
$29$	−2.64543	+	0.962857i	−0.491243	+	0.178798i	−0.575751	−	0.817625i	$-0.695290\pi$
$29$	−2.64543	+	0.962857i	−0.491243	+	0.178798i	0.0845080	+	0.996423i	$0.473068\pi$
$30$	3.73329	−	1.11048i	0.681602	−	0.202745i
$31$	−1.34144	+	2.32345i	−0.240931	+	0.417304i	−0.960980	−	0.276619i	$-0.910786\pi$
$31$	−1.34144	+	2.32345i	−0.240931	+	0.417304i	0.720049	+	0.693923i	$0.244119\pi$
$32$	−4.06287	+	2.84486i	−0.718222	+	0.502904i
$33$	0.785068	−	0.645215i	0.136663	−	0.112318i
$34$	−1.92442	+	2.29344i	−0.330036	+	0.393322i
$35$	−0.147329	−	0.00733468i	−0.0249031	−	0.00123979i
$36$	1.07105	−	2.76573i	0.178508	−	0.460956i
$37$	4.97782	−	4.97782i	0.818349	−	0.818349i	−0.167520	−	0.985869i	$-0.553576\pi$
$37$	4.97782	−	4.97782i	0.818349	−	0.818349i	0.985869	+	0.167520i	$0.0535757\pi$
$38$	−2.81627	+	3.35927i	−0.456860	+	0.544946i
$39$	1.22114	−	1.19647i	0.195538	−	0.191588i
$40$	−3.64558	+	5.64598i	−0.576416	+	0.892709i
$41$	9.04391	−	1.59469i	1.41242	−	0.249048i	0.585184	−	0.810900i	$-0.301022\pi$
$41$	9.04391	−	1.59469i	1.41242	−	0.249048i	0.827238	+	0.561852i	$0.189911\pi$
$42$	0.0747568	−	0.0872677i	0.0115352	−	0.0134657i
$43$	8.99006	+	0.786528i	1.37097	+	0.119944i	0.748727	−	0.662879i	$-0.230666\pi$
$43$	8.99006	+	0.786528i	1.37097	+	0.119944i	0.622244	+	0.782823i	$0.286221\pi$
$44$	−0.100720	+	0.571210i	−0.0151841	+	0.0861132i
$45$	−0.114815	−	6.70722i	−0.0171157	−	0.999854i
$46$	1.84449	+	3.19475i	0.271955	+	0.471040i
$47$	2.88314	+	1.34443i	0.420550	+	0.196105i	0.621361	−	0.783524i	$-0.286580\pi$
$47$	2.88314	+	1.34443i	0.420550	+	0.196105i	−0.200811	+	0.979630i	$0.564358\pi$
$48$	−0.601879	−	1.70766i	−0.0868737	−	0.246480i
$49$	6.05841	−	3.49782i	0.865487	−	0.499689i
$50$	−0.933612	+	4.94092i	−0.132033	+	0.698752i
$51$	2.91428	+	4.25375i	0.408081	+	0.595644i
$52$	−0.0850473	+	0.972095i	−0.0117939	+	0.134805i
$53$	0.904964	−	0.0791740i	0.124306	−	0.0108754i	−0.0248328	−	0.999692i	$-0.507905\pi$
$53$	0.904964	−	0.0791740i	0.124306	−	0.0108754i	0.149139	+	0.988816i	$0.452350\pi$
$54$	4.18684	+	3.12690i	0.569757	+	0.425517i
$55$	0.276114	+	1.28250i	0.0372312	+	0.172933i
$56$			0.198275i			0.0264956i
$57$	4.26979	+	6.22647i	0.565548	+	0.824716i
$58$	2.00194	+	2.00194i	0.262867	+	0.262867i
$59$	−7.64934	−	2.78413i	−0.995860	−	0.362463i	−0.207873	−	0.978156i	$-0.566654\pi$
$59$	−7.64934	−	2.78413i	−0.995860	−	0.362463i	−0.787986	+	0.615693i	$0.788876\pi$
$60$	2.54039	+	2.86481i	0.327964	+	0.369845i
$61$	−0.829391	−	0.695941i	−0.106193	−	0.0891062i	0.588145	−	0.808755i	$-0.299858\pi$
$61$	−0.829391	−	0.695941i	−0.106193	−	0.0891062i	−0.694338	+	0.719649i	$0.744303\pi$
$62$	2.68784	+	0.235155i	0.341356	+	0.0298647i
$63$	−0.110183	−	0.164399i	−0.0138818	−	0.0207123i
$64$	6.13035	+	3.53936i	0.766293	+	0.442420i
$65$	0.650807	+	2.10894i	0.0807227	+	0.261582i
$66$	−0.921745	−	0.441322i	−0.113459	−	0.0543230i
$67$	−0.965016	+	2.06948i	−0.117896	+	0.252828i	−0.956396	−	0.292073i	$-0.905655\pi$
$67$	−0.965016	+	2.06948i	−0.117896	+	0.252828i	0.838500	+	0.544901i	$0.183433\pi$
$68$	−2.84285	−	0.761738i	−0.344746	−	0.0923743i
$69$	6.15343	−	1.58170i	0.740786	−	0.190414i
$70$	0.0559318	+	0.137400i	0.00668513	+	0.0164224i
$71$	4.86122	+	5.79338i	0.576921	+	0.687547i	0.973036	−	0.230654i	$-0.0740864\pi$
$71$	4.86122	+	5.79338i	0.576921	+	0.687547i	−0.396115	+	0.918201i	$0.629642\pi$
$72$	−8.99658	+	0.602408i	−1.06026	+	0.0709944i
$73$	8.16451	−	11.6601i	0.955583	−	1.36471i	0.0245823	−	0.999698i	$-0.492174\pi$
$73$	8.16451	−	11.6601i	0.955583	−	1.36471i	0.931001	−	0.365017i	$-0.118937\pi$
$74$	−6.65267	−	2.42138i	−0.773358	−	0.281479i
$75$	7.76482	+	3.83505i	0.896604	+	0.442833i
$76$	−4.16297	−	1.11352i	−0.477525	−	0.127730i
$77$	0.0273677	+	0.0273677i	0.00311884	+	0.00311884i
$78$	−1.60952	−	0.604485i	−0.182242	−	0.0684445i
$79$	6.16710	−	1.08743i	0.693853	−	0.122345i	0.184410	−	0.982849i	$-0.440963\pi$
$79$	6.16710	−	1.08743i	0.693853	−	0.122345i	0.509443	+	0.860504i	$0.329852\pi$
$80$	2.31561	+	0.319261i	0.258893	+	0.0356944i
$81$	7.12470	−	5.49897i	0.791634	−	0.610996i
$82$	−5.29727	−	7.56529i	−0.584986	−	0.835446i
$83$	−0.451231	−	1.68402i	−0.0495290	−	0.184845i	0.936730	−	0.350054i	$-0.113837\pi$
$83$	−0.451231	−	1.68402i	−0.0495290	−	0.184845i	−0.986259	+	0.165209i	$0.947170\pi$
$84$	0.108809	+	0.0303485i	0.0118720	+	0.00331130i
$85$	−6.60499	+	0.828539i	−0.716412	+	0.0898677i
$86$	−3.10403	−	8.52825i	−0.334716	−	0.919625i
$87$	4.24746	−	2.39483i	0.455376	−	0.256752i
$88$	1.70327	−	0.456390i	0.181569	−	0.0486514i
$89$	−0.572351	+	3.24596i	−0.0606691	+	0.344072i	0.939330	+	0.343014i	$0.111448\pi$
$89$	−0.572351	+	3.24596i	−0.0606691	+	0.344072i	−0.999999	+	0.00105771i	$0.999663\pi$
$90$	−6.06448	+	2.95532i	−0.639252	+	0.311518i
$91$	0.0498800	+	0.0418543i	0.00522885	+	0.00438752i
$92$	−2.08005	+	2.97062i	−0.216860	+	0.309708i
$93$	1.63380	−	4.35022i	0.169418	−	0.451096i
$94$		−	3.19924i		−	0.329976i
$95$	−9.67047	+	1.21735i	−0.992170	+	0.124898i
$96$	6.13622	−	6.01226i	0.626275	−	0.613624i
$97$	−13.4682	+	6.28032i	−1.36749	+	0.637670i	−0.961143	−	0.276050i	$-0.910975\pi$
$97$	−13.4682	+	6.28032i	−1.36749	+	0.637670i	−0.406345	+	0.913720i	$0.633197\pi$
$98$	−5.76300	−	4.03529i	−0.582151	−	0.407626i
$99$	−1.15864	+	1.32494i	−0.116448	+	0.133161i
$100$	−4.78997	+	1.22093i	−0.478997	+	0.122093i
$101$	11.2928	+	1.99122i	1.12368	+	0.198134i	0.704454	−	0.709750i	$-0.251192\pi$
$101$	11.2928	+	1.99122i	1.12368	+	0.198134i	0.419221	+	0.907884i	$0.362303\pi$
$102$	2.63845	−	4.46412i	0.261246	−	0.442014i
$103$	−0.370212	+	1.38165i	−0.0364781	+	0.136138i	−0.981763	−	0.190107i	$-0.939117\pi$
$103$	−0.370212	+	1.38165i	−0.0364781	+	0.136138i	0.945285	+	0.326245i	$0.105783\pi$
$104$	2.78770	−	1.01464i	0.273356	−	0.0994936i
$105$	0.253822	−	0.0292124i	0.0247704	−	0.00285084i
$106$	−0.456786	−	0.791176i	−0.0443670	−	0.0768459i
$107$	12.0899	−	3.23947i	1.16877	−	0.313171i	0.378307	−	0.925680i	$-0.376506\pi$
$107$	12.0899	−	3.23947i	1.16877	−	0.313171i	0.790464	+	0.612509i	$0.209840\pi$
$108$	−1.04645	+	5.02934i	−0.100695	+	0.483948i
$109$	−10.1984	−	12.1540i	−0.976834	−	1.16415i	−0.986428	−	0.164192i	$-0.947498\pi$
$109$	−10.1984	−	12.1540i	−0.976834	−	1.16415i	0.00959413	−	0.999954i	$-0.496946\pi$
$110$	1.05158	−	0.796747i	0.100264	−	0.0759668i
$111$	−7.09524	+	9.91615i	−0.673450	+	0.941199i
$112$	0.0625007	−	0.0291445i	0.00590576	−	0.00275390i
$113$	13.8555	−	13.8555i	1.30341	−	1.30341i	0.377339	−	0.926075i	$-0.376839\pi$
$113$	13.8555	−	13.8555i	1.30341	−	1.30341i	0.926075	−	0.377339i	$-0.123161\pi$
$114$	3.86037	−	6.53803i	0.361557	−	0.612343i
$115$	−1.82420	+	7.99686i	−0.170107	+	0.745711i
$116$	−0.951905	+	2.61534i	−0.0883822	+	0.242828i
$117$	−1.74756	+	2.39043i	−0.161562	+	0.220996i
$118$	0.713494	+	8.15527i	0.0656824	+	0.750754i
$119$	−0.150443	+	0.126237i	−0.0137911	+	0.0115721i
$120$	4.62948	−	10.6804i	0.422612	−	0.974979i
$121$	−5.32789	+	9.22818i	−0.484354	+	0.838926i
$122$	−0.281811	+	1.05173i	−0.0255139	+	0.0952193i
$123$	−15.0016	+	5.28744i	−1.35265	+	0.476753i
$124$	0.907166	+	2.49242i	0.0814659	+	0.223826i
$125$	−8.99322	+	6.64244i	−0.804378	+	0.594118i
$126$	−0.103011	+	0.170298i	−0.00917696	+	0.0151714i
$127$	6.63731	+	9.47906i	0.588966	+	0.841131i	0.997430	−	0.0716434i	$-0.0228244\pi$
$127$	6.63731	+	9.47906i	0.588966	+	0.841131i	−0.408464	+	0.912774i	$0.633935\pi$
$128$	−0.244110	+	2.79019i	−0.0215765	+	0.246621i
$129$	−15.5843	+	1.20336i	−1.37212	+	0.105950i
$130$	1.64559	−	1.48951i	0.144328	−	0.130639i
$131$	3.21131	−	8.82300i	0.280573	−	0.770869i	−0.716721	−	0.697360i	$-0.754358\pi$
$131$	3.21131	−	8.82300i	0.280573	−	0.770869i	0.997295	−	0.0735091i	$-0.0234198\pi$
$132$	0.0102504	−	1.00458i	0.000892179	−	0.0874371i
$133$	−0.220197	+	0.184931i	−0.0190935	+	0.0160356i
$134$	2.29637			0.198376
$135$	2.09666	+	11.4282i	0.180452	+	0.983584i
$136$	1.55373	+	8.81163i	0.133231	+	0.755591i
$137$	1.26315	+	14.4379i	0.107918	+	1.23351i	0.836274	+	0.548311i	$0.184729\pi$
$137$	1.26315	+	14.4379i	0.107918	+	1.23351i	−0.728356	+	0.685199i	$0.759715\pi$
$138$	−4.05693	−	4.93629i	−0.345349	−	0.420205i
$139$	−22.9996	−	4.05545i	−1.95080	−	0.343979i	−0.999345	−	0.0361938i	$-0.988477\pi$
$139$	−22.9996	−	4.05545i	−1.95080	−	0.343979i	−0.951456	−	0.307785i	$-0.900412\pi$
$140$	−0.0991788	+	0.106916i	−0.00838214	+	0.00903603i
$141$	−5.30742	−	1.48032i	−0.446965	−	0.124665i
$142$	3.21427	−	6.89302i	0.269735	−	0.578449i
$143$	0.244733	−	0.524833i	0.0204656	−	0.0438887i
$144$	1.51230	+	2.74737i	0.126025	+	0.228948i
$145$	0.236152	+	6.29056i	0.0196114	+	0.522402i
$146$	−14.0976	−	2.48579i	−1.16673	−	0.205726i
$147$	−9.36101	+	7.69343i	−0.772083	+	0.634543i
$148$	−0.606572	−	6.93315i	−0.0498599	−	0.569902i
$149$	−0.136121	−	0.771979i	−0.0111514	−	0.0632430i	0.978724	−	0.205180i	$-0.0657780\pi$
$149$	−0.136121	−	0.771979i	−0.0111514	−	0.0632430i	−0.989876	+	0.141937i	$0.954667\pi$
$150$	0.195278	−	8.70718i	0.0159444	−	0.710938i
$151$	19.4382			1.58186			0.790928	−	0.611910i	$-0.209598\pi$
$151$	19.4382			1.58186			0.790928	+	0.611910i	$0.209598\pi$
$152$	2.28058	+	12.9010i	0.184979	+	1.04641i
$153$	−6.18497	−	6.44270i	−0.500025	−	0.520861i
$154$	0.0133125	−	0.0365759i	0.00107275	−	0.00294737i
$155$	4.02585	+	4.44770i	0.323364	+	0.357248i
$156$	−0.130119	−	1.68513i	−0.0104179	−	0.134919i
$157$	1.42721	−	16.3131i	0.113904	−	1.30193i	−0.697138	−	0.716937i	$-0.745543\pi$
$157$	1.42721	−	16.3131i	0.113904	−	1.30193i	0.811042	−	0.584989i	$-0.198901\pi$
$158$	−3.61224	−	5.15881i	−0.287374	−	0.410413i
$159$	−1.52389	+	0.391706i	−0.120853	+	0.0310643i
$160$	3.27031	+	10.5974i	0.258541	+	0.837802i
$161$	0.0827641	+	0.227392i	0.00652272	+	0.0179210i
$162$	−8.04012	−	4.15665i	−0.631692	−	0.326577i
$163$	−1.27030	+	4.74082i	−0.0994975	+	0.371330i	−0.997663	−	0.0683280i	$-0.978234\pi$
$163$	−1.27030	+	4.74082i	−0.0994975	+	0.371330i	0.898165	+	0.439658i	$0.144900\pi$
$164$	4.53949	−	7.86263i	0.354475	−	0.613968i
$165$	−0.835196	−	2.11320i	−0.0650199	−	0.164512i
$166$	−1.34311	+	1.12700i	−0.104246	+	0.0874725i
$167$	−1.95443	−	22.3392i	−0.151238	−	1.72866i	−0.570936	−	0.820995i	$-0.693419\pi$
$167$	−1.95443	−	22.3392i	−0.151238	−	1.72866i	0.419698	−	0.907664i	$-0.362136\pi$
$168$	−0.0561808	−	0.338796i	−0.00433444	−	0.0261387i
$169$	−4.11305	+	11.3005i	−0.316389	+	0.869271i
$170$	3.56239	+	5.66796i	0.273223	+	0.434713i
$171$	−9.06012	−	9.42943i	−0.692845	−	0.721087i
$172$	6.30863	−	6.30863i	0.481029	−	0.481029i
$173$	16.1857	−	7.54750i	1.23057	−	0.573825i	0.304984	−	0.952357i	$-0.401349\pi$
$173$	16.1857	−	7.54750i	1.23057	−	0.573825i	0.925588	+	0.378532i	$0.123571\pi$
$174$	−3.98799	−	2.85350i	−0.302329	−	0.216323i
$175$	−0.116593	+	0.308551i	−0.00881360	+	0.0233243i
$176$	−0.394229	−	0.469824i	−0.0297161	−	0.0354143i
$177$	13.8594	+	2.58987i	1.04174	+	0.194667i
$178$	3.20178	−	0.857915i	0.239984	−	0.0643035i
$179$	−1.89840	−	3.28812i	−0.141893	−	0.245766i	0.786316	−	0.617824i	$-0.211986\pi$
$179$	−1.89840	−	3.28812i	−0.141893	−	0.245766i	−0.928209	+	0.372058i	$0.878652\pi$
$180$	−5.15255	−	4.17533i	−0.384049	−	0.311211i
$181$	−17.5988	+	6.40544i	−1.30811	+	0.476112i	−0.899629	−	0.436655i	$-0.856163\pi$
$181$	−17.5988	+	6.40544i	−1.30811	+	0.476112i	−0.408479	+	0.912768i	$0.633941\pi$
$182$	0.0169483	−	0.0632517i	0.00125629	−	0.00468853i
$183$	1.61439	+	0.954161i	0.119339	+	0.0705336i
$184$	10.8575	+	1.91447i	0.800424	+	0.141136i
$185$	−7.18306	−	14.0068i	−0.528109	−	1.02980i
$186$	−4.65938	+	0.359779i	−0.341643	+	0.0263803i
$187$	1.43072	+	1.00180i	0.104625	+	0.0732589i
$188$	2.85035	−	1.32914i	0.207883	−	0.0969375i
$189$	0.234854	+	0.249691i	0.0170831	+	0.0181623i
$190$	5.21965	+	8.29673i	0.378673	+	0.601908i
$191$			17.7245i			1.28250i	0.767331	+	0.641251i	$0.221584\pi$
$191$			17.7245i			1.28250i	−0.767331	+	0.641251i	$0.778416\pi$
$192$	−11.4779	−	4.31074i	−0.828346	−	0.311101i
$193$	−1.41794	+	2.02503i	−0.102065	+	0.145765i	−0.866936	−	0.498419i	$-0.833914\pi$
$193$	−1.41794	+	2.02503i	−0.102065	+	0.145765i	0.764871	+	0.644184i	$0.222803\pi$
$194$	11.4484	+	9.60632i	0.821945	+	0.689694i
$195$	−1.70961	−	3.41918i	−0.122428	−	0.244853i
$196$	1.20096	−	6.81101i	0.0857832	−	0.486501i
$197$	3.02335	−	0.810103i	0.215404	−	0.0577174i	−0.149503	−	0.988761i	$-0.547767\pi$
$197$	3.02335	−	0.810103i	0.215404	−	0.0577174i	0.364907	+	0.931044i	$0.381101\pi$
$198$	1.70005	+	0.492920i	0.120817	+	0.0350303i
$199$	0.831624	+	2.28487i	0.0589522	+	0.161970i	0.965672	−	0.259763i	$-0.0836443\pi$
$199$	0.831624	+	2.28487i	0.0589522	+	0.161970i	−0.906720	+	0.421733i	$0.861422\pi$
$200$	9.51833	+	11.6292i	0.673048	+	0.822309i
$201$	1.06256	−	3.80960i	0.0749469	−	0.268708i
$202$	−2.98471	−	11.1391i	−0.210003	−	0.783744i
$203$	0.106523	+	0.152130i	0.00747642	+	0.0106774i
$204$	5.07346	+	0.496081i	0.355213	+	0.0347326i
$205$	2.80467	−	20.3423i	0.195887	−	1.42077i
$206$	1.41665	−	0.249793i	0.0987024	−	0.0174039i
$207$	−10.0663	+	4.44623i	−0.699657	+	0.309035i
$208$	−0.729602	−	0.729602i	−0.0505888	−	0.0505888i
$209$	2.09549	+	1.46592i	0.144948	+	0.101400i
$210$	−0.134504	−	0.218929i	−0.00928163	−	0.0151076i
$211$	−11.2010	−	4.07684i	−0.771111	−	0.280662i	−0.0736501	−	0.997284i	$-0.523465\pi$
$211$	−11.2010	−	4.07684i	−0.771111	−	0.280662i	−0.697461	+	0.716623i	$0.745687\pi$
$212$	0.515122	−	0.735671i	0.0353787	−	0.0505261i
$213$	−9.94799	−	8.52182i	−0.681625	−	0.583906i
$214$	−8.09097	−	9.64245i	−0.553088	−	0.659144i
$215$	7.83600	−	18.5956i	0.534411	−	1.26821i
$216$	15.2019	−	3.57851i	1.03436	−	0.243486i
$217$	0.170957	+	0.0458078i	0.0116053	+	0.00310964i
$218$	−6.74327	+	14.4610i	−0.456712	+	0.979422i
$219$	−10.6470	+	22.2373i	−0.719455	+	1.50265i
$220$	1.14674	+	0.605892i	0.0773135	+	0.0408492i
$221$	2.54472	+	1.46920i	0.171177	+	0.0988289i
$222$	12.0536	+	2.25242i	0.808987	+	0.151173i
$223$	15.6260	+	1.36709i	1.04639	+	0.0915474i	0.597364	−	0.801970i	$-0.296215\pi$
$223$	15.6260	+	1.36709i	1.04639	+	0.0915474i	0.449028	+	0.893518i	$0.351770\pi$
$224$	0.250647	+	0.210318i	0.0167471	+	0.0140525i
$225$	−14.3545	−	4.35286i	−0.956969	−	0.290191i
$226$	−18.5173	−	6.73976i	−1.23175	−	0.448322i
$227$	−4.63685	−	4.63685i	−0.307758	−	0.307758i	0.536281	−	0.844039i	$-0.319829\pi$
$227$	−4.63685	−	4.63685i	−0.307758	−	0.307758i	−0.844039	+	0.536281i	$0.819829\pi$
$228$	7.42885	+	0.723125i	0.491988	+	0.0478902i
$229$		−	3.64246i		−	0.240700i	−0.992732	−	0.120350i	$-0.961598\pi$
$229$		−	3.64246i		−	0.240700i	0.992732	−	0.120350i	$-0.0384017\pi$
$230$	8.06403	−	1.73613i	0.531726	−	0.114477i
$231$	−0.0545182	−	0.0390090i	−0.00358703	−	0.00256661i
$232$	8.42911	−	0.737451i	0.553398	−	0.0484161i
$233$	−1.50476	+	17.1995i	−0.0985800	+	1.12677i	0.772293	+	0.635267i	$0.219110\pi$
$233$	−1.50476	+	17.1995i	−0.0985800	+	1.12677i	−0.870873	+	0.491508i	$0.836446\pi$
$234$	2.92149	+	0.576840i	0.190984	+	0.0377092i
$235$	4.83768	−	5.21507i	0.315575	−	0.340193i
$236$	−6.96949	+	4.02384i	−0.453675	+	0.261929i
$237$	−10.2297	+	3.60554i	−0.664491	+	0.234205i
$238$	0.178998	+	0.0834683i	0.0116027	+	0.00541045i
$239$	9.36160	+	16.2148i	0.605552	+	1.04885i	0.991964	+	0.126520i	$0.0403809\pi$
$239$	9.36160	+	16.2148i	0.605552	+	1.04885i	−0.386412	+	0.922326i	$0.626286\pi$
$240$	−4.04718	+	0.110596i	−0.261244	+	0.00713892i
$241$	−0.0177680	+	0.100767i	−0.00114454	+	0.00649100i	−0.985375	−	0.170402i	$-0.945493\pi$
$241$	−0.0177680	+	0.100767i	−0.00114454	+	0.00649100i	0.984230	+	0.176893i	$0.0566046\pi$
$242$	10.6754	+	0.933980i	0.686243	+	0.0600385i
$243$	−10.6160	+	11.4149i	−0.681015	+	0.732269i
$244$	−1.05412	+	0.185869i	−0.0674829	+	0.0118991i
$245$	−3.29233	−	15.2924i	−0.210339	−	0.976992i
$246$	11.1951	+	11.4260i	0.713776	+	0.728493i
$247$	3.72691	+	2.14957i	0.237138	+	0.136774i
$248$	5.70184	−	5.70184i	0.362067	−	0.362067i
$249$	1.24819	+	2.74965i	0.0791007	+	0.174252i
$250$	9.87648	+	5.37371i	0.624644	+	0.339864i
$251$	−4.60466	+	5.48762i	−0.290644	+	0.346376i	−0.891532	−	0.452957i	$-0.850369\pi$
$251$	−4.60466	+	5.48762i	−0.290644	+	0.346376i	0.600889	+	0.799333i	$0.294814\pi$
$252$	−0.194523	−	0.0210262i	−0.0122538	−	0.00132453i
$253$	1.76290	−	1.23439i	0.110832	−	0.0776057i
$254$	5.81871	−	10.0783i	0.365098	−	0.632369i
$255$	11.0513	−	3.28725i	0.692059	−	0.205856i
$256$	15.9505	−	5.80551i	0.996906	−	0.362844i
$257$	−16.7291	−	7.80093i	−1.04354	−	0.486609i	−0.176211	−	0.984352i	$-0.556384\pi$
$257$	−16.7291	−	7.80093i	−1.04354	−	0.486609i	−0.867324	+	0.497744i	$0.834162\pi$
$258$	7.72037	+	13.6928i	0.480649	+	0.852479i
$259$	−0.402185	−	0.232201i	−0.0249905	−	0.0144283i
$260$	2.01074	+	0.847307i	0.124701	+	0.0525477i
$261$	−6.57914	+	5.29559i	−0.407239	+	0.327789i
$262$	−9.40655	+	0.822967i	−0.581139	+	0.0508430i
$263$	0.769790	+	0.539013i	0.0474673	+	0.0332370i	0.597069	−	0.802190i	$-0.296332\pi$
$263$	0.769790	+	0.539013i	0.0474673	+	0.0332370i	−0.549602	+	0.835427i	$0.685221\pi$
$264$	−2.78109	+	1.26246i	−0.171164	+	0.0776990i
$265$	0.451760	−	1.98042i	0.0277514	−	0.121656i
$266$	0.262142	+	0.122100i	0.0160730	+	0.00748643i
$267$	0.0582488	−	5.70861i	0.00356477	−	0.349361i
$268$	0.954040	+	2.04595i	0.0582773	+	0.124976i
$269$	5.19236	+	29.4473i	0.316584	+	1.79544i	0.563198	+	0.826322i	$0.309571\pi$
$269$	5.19236	+	29.4473i	0.316584	+	1.79544i	−0.246615	+	0.969114i	$0.579318\pi$
$270$	9.52510	−	6.76816i	0.579679	−	0.411897i
$271$	14.3089	−	12.0066i	0.869206	−	0.729350i	−0.0947248	−	0.995503i	$-0.530197\pi$
$271$	14.3089	−	12.0066i	0.869206	−	0.729350i	0.963931	+	0.266153i	$0.0857527\pi$
$272$	2.54924	−	1.78500i	0.154570	−	0.108231i
$273$	−0.0970902	−	0.0573838i	−0.00587617	−	0.00347302i
$274$	12.6225	−	7.28760i	0.762553	−	0.440260i
$275$	2.91897	+	0.291361i	0.176021	+	0.0175697i
$276$	2.71250	−	5.66532i	0.163273	−	0.341012i
$277$	16.4549	+	4.40909i	0.988681	+	0.264916i	0.716697	−	0.697385i	$-0.245653\pi$
$277$	16.4549	+	4.40909i	0.988681	+	0.264916i	0.271985	+	0.962302i	$0.412320\pi$
$278$	6.07884	+	22.6866i	0.364585	+	1.36065i
$279$	−1.55909	+	7.89622i	−0.0933400	+	0.472734i
$280$	0.422014	+	0.135901i	0.0252201	+	0.00812163i
$281$	−0.996027	+	1.18702i	−0.0594180	+	0.0708116i	−0.794935	−	0.606695i	$-0.792495\pi$
$281$	−0.996027	+	1.18702i	−0.0594180	+	0.0708116i	0.735517	+	0.677506i	$0.236939\pi$
$282$	0.906497	+	5.46659i	0.0539811	+	0.325531i
$283$	10.5356	+	22.5936i	0.626274	+	1.34305i	0.921782	+	0.387708i	$0.126733\pi$
$283$	10.5356	+	22.5936i	0.626274	+	1.34305i	−0.295509	+	0.955340i	$0.595489\pi$
$284$	7.47670			0.443660
$285$	16.1792	−	4.82022i	0.958371	−	0.285525i
$286$	−0.582373			−0.0344364
$287$	−0.256032	−	0.549062i	−0.0151131	−	0.0324101i
$288$	−8.78150	+	12.0119i	−0.517455	+	0.707810i
$289$	5.23070	−	6.23371i	0.307688	−	0.366689i
$290$	5.63314	−	2.88882i	0.330790	−	0.169637i
$291$	21.2338	−	14.5475i	1.24475	−	0.852789i
$292$	−3.64223	−	13.5930i	−0.213145	−	0.795469i
$293$	14.0476	+	3.76404i	0.820669	+	0.219898i	0.644639	−	0.764487i	$-0.277008\pi$
$293$	14.0476	+	3.76404i	0.820669	+	0.219898i	0.176030	+	0.984385i	$0.443674\pi$
$294$	10.9907	+	5.26224i	0.640992	+	0.306900i
$295$	−11.1688	+	14.3728i	−0.650273	+	0.836816i
$296$	−18.3237	+	10.5792i	−1.06504	+	0.614902i
$297$	1.60437	−	2.59224i	0.0930948	−	0.150417i
$298$	−0.645765	+	0.452170i	−0.0374082	+	0.0261935i
$299$	2.77355	−	2.32729i	0.160399	−	0.134590i
$300$	7.83876	−	3.44346i	0.452571	−	0.198808i
$301$	−0.103378	−	0.586287i	−0.00595862	−	0.0337930i
$302$	−8.26151	−	17.7169i	−0.475396	−	1.01949i
$303$	−19.8604	−	0.202649i	−1.14095	−	0.0116419i
$304$	3.73145	−	2.61521i	0.214013	−	0.149993i
$305$	−2.04974	+	1.28829i	−0.117368	+	0.0737672i
$306$	−3.24347	+	8.37552i	−0.185417	+	0.478797i
$307$	−9.91476	−	6.94239i	−0.565865	−	0.396223i	0.255344	−	0.966850i	$-0.417811\pi$
$307$	−9.91476	−	6.94239i	−0.565865	−	0.396223i	−0.821209	+	0.570627i	$0.806700\pi$
$308$	0.0381179	−	0.00333489i	0.00217197	−	0.000190023i
$309$	0.241100	−	2.46575i	0.0137157	−	0.140271i
$310$	2.34280	−	5.55969i	0.133062	−	0.315769i
$311$	−24.1228	−	13.9273i	−1.36788	−	0.789745i	−0.377221	−	0.926123i	$-0.623120\pi$
$311$	−24.1228	−	13.9273i	−1.36788	−	0.789745i	−0.990657	+	0.136379i	$0.956454\pi$
$312$	−4.47589	+	2.52362i	−0.253397	+	0.142872i
$313$	22.5824	+	10.5303i	1.27643	+	0.595210i	0.938278	−	0.345881i	$-0.112420\pi$
$313$	22.5824	+	10.5303i	1.27643	+	0.595210i	0.338153	+	0.941091i	$0.390198\pi$
$314$	−15.4751	+	5.63248i	−0.873310	+	0.317859i
$315$	−0.425432	+	0.121836i	−0.0239704	+	0.00686466i
$316$	3.09550	−	5.36157i	0.174136	−	0.301612i
$317$	−11.7562	+	8.23178i	−0.660294	+	0.462343i	−0.855075	−	0.518504i	$-0.826489\pi$
$317$	−11.7562	+	8.23178i	−0.660294	+	0.462343i	0.194781	+	0.980847i	$0.437600\pi$
$318$	1.00470	+	1.22247i	0.0563406	+	0.0685526i
$319$	1.06167	−	1.26525i	0.0594422	−	0.0708404i
$320$	11.7351	−	10.6221i	0.656012	−	0.593791i
$321$	−19.7403	+	8.96097i	−1.10179	+	0.500153i
$322$	0.172080	−	0.172080i	0.00958966	−	0.00958966i
$323$	−8.33674	+	9.94413i	−0.463869	+	0.553306i
$324$	0.363041	−	8.89023i	0.0201689	−	0.493901i
$325$	4.93481	+	0.0603073i	0.273734	+	0.00334525i
$326$	4.86090	−	0.857108i	0.269220	−	0.0474708i
$327$	20.8701	+	17.8781i	1.15412	+	0.988661i
$328$	−27.4965	−	2.40563i	−1.51824	−	0.132829i
$329$	0.0364419	−	0.206672i	0.00200911	−	0.0113942i
$330$	−1.57110	+	1.65938i	−0.0864862	+	0.0913458i
$331$	−4.16225	−	7.20922i	−0.228778	−	0.396255i	0.728668	−	0.684867i	$-0.240140\pi$
$331$	−4.16225	−	7.20922i	−0.228778	−	0.396255i	−0.957446	+	0.288612i	$0.906806\pi$
$332$	−1.56210	−	0.728421i	−0.0857316	−	0.0399773i
$333$	9.31403	−	18.9543i	0.510406	−	1.03869i
$334$	−19.5303	+	11.2758i	−1.06865	+	0.616987i
$335$	3.74331	+	3.47243i	0.204519	+	0.189719i
$336$	−0.0985379	+	0.0675092i	−0.00537568	+	0.00368293i
$337$	−2.29773	+	26.2632i	−0.125165	+	1.43065i	0.630755	+	0.775982i	$0.282745\pi$
$337$	−2.29773	+	26.2632i	−0.125165	+	1.43065i	−0.755920	+	0.654664i	$0.772810\pi$
$338$	12.0479	−	1.05406i	0.655321	−	0.0573332i
$339$	−19.7492	+	27.6010i	−1.07263	+	1.49908i
$340$	−3.56984	+	5.52868i	−0.193602	+	0.299835i
$341$		−	1.57404i		−	0.0852390i
$342$	−4.74374	+	12.2655i	−0.256512	+	0.663241i
$343$	−0.652857	−	0.652857i	−0.0352510	−	0.0352510i
$344$	−25.4877	−	9.27678i	−1.37421	−	0.500171i
$345$	0.851139	−	14.1813i	0.0458238	−	0.763493i
$346$	−13.7583	−	11.5446i	−0.739650	−	0.620640i
$347$	16.9006	+	1.47861i	0.907272	+	0.0793760i	0.531231	−	0.847227i	$-0.321730\pi$
$347$	16.9006	+	1.47861i	0.907272	+	0.0793760i	0.376041	+	0.926603i	$0.377285\pi$
$348$	0.885486	−	4.73859i	0.0474670	−	0.254015i
$349$	−22.2032	−	12.8190i	−1.18851	−	0.686186i	−0.230542	−	0.973062i	$-0.574050\pi$
$349$	−22.2032	−	12.8190i	−1.18851	−	0.686186i	−0.957968	+	0.286876i	$0.907383\pi$
$350$	0.330782	−	0.0248707i	0.0176810	−	0.00132939i
$351$	2.30876	−	4.57974i	0.123233	−	0.244449i
$352$	1.22979	−	2.63729i	0.0655478	−	0.140568i
$353$	−4.46337	−	1.19596i	−0.237561	−	0.0636543i	0.138074	−	0.990422i	$-0.455909\pi$
$353$	−4.46337	−	1.19596i	−0.237561	−	0.0636543i	−0.375635	+	0.926768i	$0.622575\pi$
$354$	−3.52994	−	13.7329i	−0.187614	−	0.729895i
$355$	15.6627	−	6.37588i	0.831292	−	0.338397i
$356$	2.09456	+	2.49619i	0.111011	+	0.132298i
$357$	0.221295	−	0.258330i	0.0117122	−	0.0136723i
$358$	−2.19010	+	3.12779i	−0.115751	+	0.165309i
$359$	−0.380206	−	0.138384i	−0.0200665	−	0.00730362i	0.331967	−	0.943291i	$-0.392288\pi$
$359$	−0.380206	−	0.138384i	−0.0200665	−	0.00730362i	−0.352034	+	0.935987i	$0.614510\pi$
$360$	−4.88422	+	19.5615i	−0.257421	+	1.03098i
$361$	−12.2003	+	14.5655i	−0.642120	+	0.766604i
$362$	13.3180	+	13.3180i	0.699977	+	0.699977i
$363$	6.48908	−	17.2780i	0.340588	−	0.906860i
$364$	0.0633952	−	0.0111783i	0.00332281	−	0.000585901i
$365$	−19.2216	−	25.3696i	−1.00611	−	1.32791i
$366$	0.183529	−	1.87696i	0.00959319	−	0.0981104i
$367$	7.28743	+	10.4075i	0.380401	+	0.543269i	0.963004	−	0.269488i	$-0.0868546\pi$
$367$	7.28743	+	10.4075i	0.380401	+	0.543269i	−0.582603	+	0.812757i	$0.697966\pi$
$368$	−0.992464	−	3.70393i	−0.0517358	−	0.193080i
$369$	24.1354	−	13.2854i	1.25644	−	0.691612i
$370$	−9.71357	+	12.5001i	−0.504985	+	0.649848i
$371$	−0.0204965	−	0.0563136i	−0.00106412	−	0.00292365i
$372$	−2.25631	−	4.00179i	−0.116984	−	0.207483i
$373$	−15.8371	+	4.24353i	−0.820012	+	0.219722i	−0.644352	−	0.764729i	$-0.722873\pi$
$373$	−15.8371	+	4.24353i	−0.820012	+	0.219722i	−0.175660	+	0.984451i	$0.556206\pi$
$374$	0.305011	−	1.72981i	0.0157718	−	0.0894461i
$375$	13.4848	−	13.8983i	0.696350	−	0.717703i
$376$	−7.32440	−	6.14590i	−0.377727	−	0.316951i
$377$	1.59380	−	2.27618i	0.0820849	−	0.117229i
$378$	0.127763	−	0.320179i	0.00657144	−	0.0164682i
$379$			12.6102i			0.647745i	0.946101	+	0.323872i	$0.104985\pi$
$379$			12.6102i			0.647745i	−0.946101	+	0.323872i	$0.895015\pi$
$380$	−5.22342	+	8.09735i	−0.267956	+	0.415385i
$381$	−14.0272	−	14.3164i	−0.718633	−	0.733450i
$382$	16.1550	−	7.53319i	0.826560	−	0.385431i
$383$	−25.0513	−	17.5411i	−1.28006	−	0.896308i	−0.282052	−	0.959399i	$-0.591015\pi$
$383$	−25.0513	−	17.5411i	−1.28006	−	0.896308i	−0.998008	+	0.0630913i	$0.979904\pi$
$384$	−0.373480	−	4.83682i	−0.0190591	−	0.246828i
$385$	0.0770084	−	0.0394919i	0.00392471	−	0.00201269i
$386$	2.44835	+	0.431710i	0.124618	+	0.0219735i
$387$	26.2882	−	6.47199i	1.33631	−	0.328990i
$388$	−3.80244	+	14.1909i	−0.193040	+	0.720433i
$389$	23.4551	−	8.53695i	1.18922	−	0.432841i	0.329770	−	0.944061i	$-0.393029\pi$
$389$	23.4551	−	8.53695i	1.18922	−	0.432841i	0.859449	+	0.511221i	$0.170807\pi$
$390$	−2.38979	+	3.01142i	−0.121012	+	0.152489i
$391$	5.46006	+	9.45710i	0.276127	+	0.478266i
$392$	−20.3095	+	5.44191i	−1.02578	+	0.274858i
$393$	−2.98724	+	15.9859i	−0.150686	+	0.806383i
$394$	−2.02333	−	2.41131i	−0.101934	−	0.121480i
$395$	1.91252	−	13.8716i	0.0962294	−	0.697954i
$396$	0.267129	+	1.71944i	0.0134238	+	0.0864051i
$397$	−8.32238	+	3.88079i	−0.417688	+	0.194771i	−0.620089	−	0.784532i	$-0.712903\pi$
$397$	−8.32238	+	3.88079i	−0.417688	+	0.194771i	0.202401	+	0.979303i	$0.435126\pi$
$398$	1.72908	−	1.72908i	0.0866711	−	0.0866711i
$399$	0.323855	−	0.378387i	0.0162130	−	0.0189431i
$400$	2.26668	−	4.70977i	0.113334	−	0.235489i
$401$	6.95700	−	19.1142i	0.347416	−	0.954518i	−0.635765	−	0.771883i	$-0.719315\pi$
$401$	6.95700	−	19.1142i	0.347416	−	0.954518i	0.983181	−	0.182635i	$-0.0584627\pi$
$402$	−3.92385	+	0.650672i	−0.195704	+	0.0324526i
$403$	−0.230798	−	2.63803i	−0.0114968	−	0.131410i
$404$	8.68432	−	7.28701i	0.432061	−	0.362542i
$405$	−6.82077	−	18.9335i	−0.338927	−	0.940813i
$406$	0.0933848	−	0.161747i	0.00463461	−	0.00802738i
$407$	−1.06896	+	3.98943i	−0.0529866	+	0.197749i
$408$	−5.15164	−	14.6163i	−0.255044	−	0.723617i
$409$	5.81415	+	15.9742i	0.287491	+	0.789875i	0.996416	+	0.0845911i	$0.0269584\pi$
$409$	5.81415	+	15.9742i	0.287491	+	0.789875i	−0.708925	+	0.705284i	$0.750819\pi$
$410$	−19.7330	+	6.08949i	−0.974543	+	0.300738i
$411$	−6.24930	−	24.3123i	−0.308255	−	1.19924i
$412$	0.811106	+	1.15838i	0.0399603	+	0.0570692i
$413$	−0.0468031	+	0.534962i	−0.00230303	+	0.0263238i
$414$	8.33084	+	7.28519i	0.409438	+	0.358048i
$415$	−3.89359	−	0.193840i	−0.191129	−	0.00951523i
$416$	1.67438	−	4.60031i	0.0820930	−	0.225549i
$417$	40.4489	+	0.412727i	1.98079	+	0.0202113i
$418$	0.445494	−	2.53297i	0.0217898	−	0.123892i
$419$	−37.7725			−1.84531			−0.922653	−	0.385631i	$-0.873984\pi$
$419$	−37.7725			−1.84531			−0.922653	+	0.385631i	$0.873984\pi$
$420$	0.139174	−	0.210791i	0.00679100	−	0.0102855i
$421$	−0.662996	−	3.76004i	−0.0323124	−	0.183253i	0.964380	−	0.264521i	$-0.0852140\pi$
$421$	−0.662996	−	3.76004i	−0.0323124	−	0.183253i	−0.996692	+	0.0812685i	$0.974103\pi$
$422$	1.04478	+	11.9419i	0.0508590	+	0.581321i
$423$	9.48832	+	1.02560i	0.461338	+	0.0498665i
$424$	−2.68885	−	0.474116i	−0.130582	−	0.0230251i
$425$	−2.76368	+	14.6261i	−0.134058	+	0.709472i
$426$	−3.53915	+	12.6890i	−0.171472	+	0.614783i
$427$	−0.0301852	+	0.0647323i	−0.00146076	+	0.00313262i
$428$	5.22947	−	11.2146i	0.252776	−	0.542080i
$429$	−0.269470	+	0.966135i	−0.0130101	+	0.0466454i
$430$	−20.2793	+	0.761301i	−0.977955	+	0.0367132i
$431$	−30.0487	−	5.29840i	−1.44740	−	0.255215i	−0.605927	−	0.795520i	$-0.707198\pi$
$431$	−30.0487	−	5.29840i	−1.44740	−	0.255215i	−0.841469	+	0.540305i	$0.818309\pi$
$432$	−3.36256	−	4.26597i	−0.161781	−	0.205247i
$433$	0.678346	+	7.75353i	0.0325992	+	0.372611i	0.994918	+	0.100687i	$0.0321042\pi$
$433$	0.678346	+	7.75353i	0.0325992	+	0.372611i	−0.962319	+	0.271923i	$0.912340\pi$
$434$	−0.0309079	−	0.175287i	−0.00148363	−	0.00841406i
$435$	−2.18593	−	10.6819i	−0.104807	−	0.512156i
$436$	−15.6855			−0.751200
$437$	8.00063	+	13.8436i	0.382722	+	0.662228i
$438$	24.7932	+	0.252982i	1.18466	+	0.0120879i
$439$	12.6284	−	34.6961i	0.602719	−	1.65596i	−0.143021	−	0.989720i	$-0.545682\pi$
$439$	12.6284	−	34.6961i	0.602719	−	1.65596i	0.745740	−	0.666237i	$-0.232096\pi$
$440$	0.196056	−	3.93811i	0.00934662	−	0.187742i
$441$	13.8154	−	15.7983i	0.657876	−	0.752301i
$442$	0.257550	−	2.94381i	0.0122504	−	0.140023i
$443$	−12.2871	−	17.5479i	−0.583780	−	0.833724i	0.413260	−	0.910613i	$-0.364390\pi$
$443$	−12.2871	−	17.5479i	−0.583780	−	0.833724i	−0.997040	+	0.0768891i	$0.975501\pi$
$444$	3.00096	+	11.6749i	0.142419	+	0.554067i
$445$	6.51650	+	3.44305i	0.308912	+	0.163216i
$446$	−5.39523	−	14.8233i	−0.255472	−	0.701903i
$447$	0.451331	+	1.28052i	0.0213472	+	0.0605667i
$448$	0.120862	−	0.451064i	0.00571021	−	0.0213108i
$449$	9.01379	−	15.6123i	0.425387	−	0.736792i	−0.571069	−	0.820902i	$-0.693471\pi$
$449$	9.01379	−	15.6123i	0.425387	−	0.736792i	0.996457	+	0.0841097i	$0.0268046\pi$
$450$	2.13349	+	14.9334i	0.100573	+	0.703969i
$451$	−4.12735	+	3.46326i	−0.194349	+	0.163079i
$452$	−1.68836	−	19.2980i	−0.0794137	−	0.907703i
$453$	−33.2143	+	5.50776i	−1.56054	+	0.258777i
$454$	−2.25551	+	6.19697i	−0.105856	+	0.290838i
$455$	0.123272	−	0.0774784i	0.00577910	−	0.00363224i
$456$	−7.55233	−	21.3979i	−0.353670	−	1.00205i
$457$	−7.85479	+	7.85479i	−0.367432	+	0.367432i	−0.866540	−	0.499108i	$-0.833661\pi$
$457$	−7.85479	+	7.85479i	−0.367432	+	0.367432i	0.499108	+	0.866540i	$0.333661\pi$
$458$	−3.31991	+	1.54810i	−0.155129	+	0.0723379i
$459$	12.3939	+	9.25625i	0.578497	+	0.432045i
$460$	4.89704	+	6.46334i	0.228326	+	0.301355i
$461$	13.1534	+	15.6756i	0.612615	+	0.730086i	0.979782	−	0.200069i	$-0.0641167\pi$
$461$	13.1534	+	15.6756i	0.612615	+	0.730086i	−0.367167	+	0.930155i	$0.619672\pi$
$462$	−0.0123836	+	0.0662699i	−0.000576139	+	0.00308315i
$463$	−20.7096	+	5.54912i	−0.962456	+	0.257889i	−0.705640	−	0.708571i	$-0.749340\pi$
$463$	−20.7096	+	5.54912i	−0.962456	+	0.257889i	−0.256817	+	0.966460i	$0.582674\pi$
$464$	−1.47146	−	2.54864i	−0.0683108	−	0.118318i
$465$	−8.13928	−	6.45914i	−0.377450	−	0.299536i
$466$	16.3160	−	5.93852i	0.755822	−	0.275097i
$467$	6.87379	−	25.6533i	0.318081	−	1.18709i	−0.603005	−	0.797737i	$-0.706030\pi$
$467$	6.87379	−	25.6533i	0.318081	−	1.18709i	0.921087	−	0.389358i	$-0.127303\pi$
$468$	0.699816	+	2.84255i	0.0323490	+	0.131397i
$469$	0.148347	+	0.0261575i	0.00685002	+	0.00120784i
$470$	−6.80934	−	2.19281i	−0.314092	−	0.101147i
$471$	2.18358	+	28.2788i	0.100614	+	1.30302i
$472$	20.0415	+	14.0332i	0.922485	+	0.645931i
$473$	−4.79851	+	2.23758i	−0.220636	+	0.102884i
$474$	7.63403	+	7.79143i	0.350643	+	0.357872i
$475$	−4.03725	+	21.4173i	−0.185242	+	0.982693i
$476$			0.194156i			0.00889910i
$477$	2.49291	−	1.10111i	0.114143	−	0.0504162i
$478$	10.8001	−	15.4241i	0.493985	−	0.705483i
$479$	1.13232	+	0.950129i	0.0517370	+	0.0434125i	0.668290	−	0.743901i	$-0.267027\pi$
$479$	1.13232	+	0.950129i	0.0517370	+	0.0434125i	−0.616552	+	0.787314i	$0.711471\pi$
$480$	−8.59080	−	17.1814i	−0.392114	−	0.784220i
$481$	−1.20658	+	6.84287i	−0.0550155	+	0.312008i
$482$	0.0993959	−	0.0266331i	0.00452736	−	0.00121310i
$483$	−0.205852	−	0.365098i	−0.00936657	−	0.0166125i
$484$	3.60304	+	9.89928i	0.163775	+	0.449967i
$485$	4.13589	+	32.9707i	0.187801	+	1.49712i
$486$	14.9161	+	4.82438i	0.676607	+	0.218838i
$487$	−4.55077	−	16.9837i	−0.206215	−	0.769605i	−0.989076	−	0.147408i	$-0.952907\pi$
$487$	−4.55077	−	16.9837i	−0.206215	−	0.769605i	0.782861	−	0.622197i	$-0.213760\pi$
$488$	1.86648	+	2.66561i	0.0844917	+	0.120667i
$489$	0.827280	−	8.46065i	0.0374109	−	0.382604i
$490$	−12.5389	+	9.50027i	−0.566449	+	0.429178i
$491$	23.2910	−	4.10683i	1.05111	−	0.185339i	0.378701	−	0.925519i	$-0.376371\pi$
$491$	23.2910	−	4.10683i	1.05111	−	0.185339i	0.672408	+	0.740180i	$0.265260\pi$
$492$	−5.52884	+	14.7213i	−0.249260	+	0.663686i
$493$	5.92615	+	5.92615i	0.266900	+	0.266900i
$494$	0.375228	−	4.31048i	0.0168823	−	0.193938i
$495$	2.02588	+	3.37421i	0.0910567	+	0.151660i
$496$	−2.63546	−	0.959231i	−0.118336	−	0.0430707i
$497$	0.286160	−	0.408679i	0.0128360	−	0.0183318i
$498$	1.97566	−	2.30630i	0.0885316	−	0.103348i
$499$	−2.89215	−	3.44673i	−0.129470	−	0.154297i	0.697415	−	0.716668i	$-0.254334\pi$
$499$	−2.89215	−	3.44673i	−0.129470	−	0.154297i	−0.826885	+	0.562371i	$0.809889\pi$
$500$	−0.684456	+	11.0320i	−0.0306098	+	0.493364i
$501$	9.66933	+	37.6176i	0.431994	+	1.68063i
$502$	6.95873	+	1.86459i	0.310583	+	0.0832205i
$503$	−13.4925	+	28.9348i	−0.601603	+	1.29014i	0.335813	+	0.941929i	$0.390989\pi$
$503$	−13.4925	+	28.9348i	−0.601603	+	1.29014i	−0.937416	+	0.348212i	$0.886789\pi$
$504$	0.191994	+	0.562987i	0.00855210	+	0.0250774i
$505$	11.9784	−	22.6711i	0.533034	−	1.00885i
$506$	−1.87434	−	1.08215i	−0.0833247	−	0.0481075i
$507$	3.82606	−	20.4748i	0.169921	−	0.909319i
$508$	11.3967	+	0.997078i	0.505645	+	0.0442382i
$509$	6.68019	+	5.60534i	0.296094	+	0.248452i	0.778716	−	0.627376i	$-0.215871\pi$
$509$	6.68019	+	5.60534i	0.296094	+	0.248452i	−0.482622	+	0.875829i	$0.660316\pi$
$510$	−7.69312	−	8.67554i	−0.340657	−	0.384159i
$511$	−0.882399	−	0.321167i	−0.0390350	−	0.0142076i
$512$	−8.10961	−	8.10961i	−0.358397	−	0.358397i
$513$	18.1530	+	13.5451i	0.801474	+	0.598029i
$514$			18.5632i			0.818790i
$515$	2.68699	+	1.73497i	0.118403	+	0.0764521i
$516$	−8.99213	+	12.5672i	−0.395856	+	0.553240i
$517$	−1.85929	+	0.162667i	−0.0817715	+	0.00715408i
$518$	−0.0407049	+	0.465259i	−0.00178847	+	0.0204423i
$519$	−25.5181	+	17.4827i	−1.12012	+	0.767406i
$520$	−0.248853	−	6.62886i	−0.0109129	−	0.290695i
$521$	−12.5229	+	7.23009i	−0.548638	+	0.316756i	−0.748572	−	0.663053i	$-0.769260\pi$
$521$	−12.5229	+	7.23009i	−0.548638	+	0.316756i	0.199935	+	0.979809i	$0.435927\pi$
$522$	7.62288	+	3.74584i	0.333645	+	0.163951i
$523$	−15.1477	−	7.06351i	−0.662365	−	0.308866i	0.0622090	−	0.998063i	$-0.480185\pi$
$523$	−15.1477	−	7.06351i	−0.662365	−	0.308866i	−0.724574	+	0.689197i	$0.757963\pi$
$524$	−4.64122	−	8.03883i	−0.202753	−	0.351178i
$525$	0.111797	−	0.560264i	0.00487922	−	0.0244519i
$526$	0.164110	−	0.930712i	0.00715552	−	0.0405810i
$527$	7.95654	+	0.696107i	0.346592	+	0.0303229i
$528$	0.806749	+	0.691092i	0.0351093	+	0.0300759i
$529$	−9.39950	+	1.65738i	−0.408674	+	0.0720602i
$530$	−1.99705	+	0.429951i	−0.0867463	+	0.0186759i
$531$	−24.4157	−	0.498311i	−1.05955	−	0.0216249i
$532$	0.000123760		0.284282i	5.36566e−6		0.0123252i
$533$	−6.40948	+	6.40948i	−0.277625	+	0.277625i
$534$	−5.22785	+	2.37315i	−0.226231	+	0.102696i
$535$	1.39161	−	27.9528i	0.0601646	−	1.20850i
$536$	4.41145	−	5.25736i	0.190546	−	0.227083i
$537$	4.17551	+	5.08057i	0.180187	+	0.219243i
$538$	24.6329	−	17.2481i	1.06200	−	0.743619i
$539$	−2.05216	+	3.55444i	−0.0883926	+	0.153101i
$540$	9.98732	+	5.67449i	0.429786	+	0.244191i
$541$	27.3566	−	9.95698i	1.17615	−	0.428084i	0.321310	−	0.946974i	$-0.395877\pi$
$541$	27.3566	−	9.95698i	1.17615	−	0.428084i	0.854841	+	0.518890i	$0.173654\pi$
$542$	−17.0249	−	7.93885i	−0.731283	−	0.341003i
$543$	28.2564	−	15.9317i	1.21260	−	0.683693i
$544$	12.7872	+	7.38272i	0.548249	+	0.316531i
$545$	−32.8592	+	13.3761i	−1.40753	+	0.572969i
$546$	−0.0110375	+	0.112882i	−0.000472362	+	0.00483089i
$547$	−28.5760	+	2.50008i	−1.22182	+	0.106896i	−0.679754	−	0.733440i	$-0.737914\pi$
$547$	−28.5760	+	2.50008i	−1.22182	+	0.106896i	−0.542067	+	0.840335i	$0.682358\pi$
$548$	11.7369	+	8.21830i	0.501378	+	0.351068i
$549$	−3.02889	−	1.17296i	−0.129270	−	0.0500606i
$550$	−0.975046	−	2.78432i	−0.0415761	−	0.118724i
$551$	8.68082	+	8.67326i	0.369815	+	0.369493i
$552$	−19.0948	−	0.194837i	−0.812729	−	0.00829282i
$553$	−0.174589	−	0.374408i	−0.00742430	−	0.0159215i
$554$	−2.97494	−	16.8717i	−0.126393	−	0.716811i
$555$	16.2426	+	21.8984i	0.689461	+	0.929535i
$556$	−17.6870	+	14.8412i	−0.750097	+	0.629406i
$557$	−22.7893	+	15.9572i	−0.965612	+	0.676129i	−0.946166	−	0.323682i	$-0.895079\pi$
$557$	−22.7893	+	15.9572i	−0.965612	+	0.676129i	−0.0194460	+	0.999811i	$0.506190\pi$
$558$	7.85963	−	1.93499i	0.332724	−	0.0819146i
$559$	−7.71403	+	4.45370i	−0.326269	+	0.188371i
$560$	−0.0191931	−	0.153004i	−0.000811055	−	0.00646561i
$561$	−2.72855	−	1.30640i	−0.115200	−	0.0551563i
$562$	1.50523	+	0.403326i	0.0634944	+	0.0170133i
$563$	−2.76576	−	10.3220i	−0.116563	−	0.435019i	0.882836	−	0.469681i	$-0.155631\pi$
$563$	−2.76576	−	10.3220i	−0.116563	−	0.435019i	−0.999399	+	0.0346623i	$0.988964\pi$
$564$	−4.49383	+	3.07877i	−0.189224	+	0.129639i
$565$	−19.9936	−	38.9872i	−0.841138	−	1.64020i
$566$	16.1151	−	19.2052i	0.677367	−	0.807255i
$567$	−0.472048	−	0.360105i	−0.0198242	−	0.0151230i
$568$	−9.60624	−	20.6007i	−0.403069	−	0.864384i
$569$	11.2807			0.472913			0.236456	−	0.971642i	$-0.424014\pi$
$569$	11.2807			0.472913			0.236456	+	0.971642i	$0.424014\pi$
$570$	−11.2698	−	12.6978i	−0.472039	−	0.531852i
$571$	6.72011			0.281228			0.140614	−	0.990065i	$-0.455092\pi$
$571$	6.72011			0.281228			0.140614	+	0.990065i	$0.455092\pi$
$572$	−0.241950	−	0.518863i	−0.0101164	−	0.0216948i
$573$	−5.02221	−	30.2862i	−0.209806	−	1.26522i
$574$	−0.391623	+	0.466719i	−0.0163460	+	0.0194805i
$575$	15.7704	+	9.36385i	0.657672	+	0.390499i
$576$	20.8339	+	4.11359i	0.868080	+	0.171400i
$577$	−6.24335	−	23.3005i	−0.259914	−	0.970012i	−0.965290	−	0.261179i	$-0.915889\pi$
$577$	−6.24335	−	23.3005i	−0.259914	−	0.970012i	0.705376	−	0.708833i	$-0.250778\pi$
$578$	−7.90482	−	2.11809i	−0.328797	−	0.0881010i
$579$	1.84907	−	3.86197i	0.0768446	−	0.160498i
$580$	4.91411	+	3.81866i	0.204047	+	0.158561i
$581$	−0.0996032	+	0.0575059i	−0.00413224	+	0.00238575i
$582$	−22.2840	−	13.1706i	−0.923700	−	0.545940i
$583$	−0.436580	+	0.305697i	−0.0180813	+	0.0126607i
$584$	−32.7733	+	27.5001i	−1.35617	+	1.13796i
$585$	3.89006	+	5.35800i	0.160834	+	0.221526i
$586$	−2.53971	−	14.4034i	−0.104915	−	0.595000i
$587$	4.71776	+	10.1173i	0.194723	+	0.417584i	0.979291	−	0.202458i	$-0.0648931\pi$
$587$	4.71776	+	10.1173i	0.194723	+	0.417584i	−0.784568	+	0.620043i	$0.787115\pi$
$588$	−0.122223	+	11.9784i	−0.00504041	+	0.493980i
$589$	11.6504	+	1.01417i	0.480046	+	0.0417880i
$590$	17.8469	+	4.07114i	0.734747	+	0.167606i
$591$	−4.93650	+	2.24090i	−0.203061	+	0.0921781i
$592$	6.02820	+	4.22099i	0.247757	+	0.173482i
$593$	13.5828	−	1.18834i	0.557778	−	0.0487992i	0.195218	−	0.980760i	$-0.437459\pi$
$593$	13.5828	−	1.18834i	0.557778	−	0.0487992i	0.362559	+	0.931961i	$0.381903\pi$
$594$	−3.04457	−	0.360555i	−0.124920	−	0.0147937i
$595$	0.165569	+	0.406731i	0.00678768	+	0.0166744i
$596$	−0.671146	−	0.387486i	−0.0274912	−	0.0158721i
$597$	−2.06842	−	3.66855i	−0.0846549	−	0.150144i
$598$	−3.30000	−	1.53882i	−0.134947	−	0.0629268i
$599$	33.2590	−	12.1053i	1.35892	−	0.494608i	0.443203	−	0.896421i	$-0.353842\pi$
$599$	33.2590	−	12.1053i	1.35892	−	0.494608i	0.915721	+	0.401814i	$0.131620\pi$
$600$	−19.5592	−	17.1740i	−0.798503	−	0.701126i
$601$	5.92752	−	10.2668i	0.241789	−	0.418790i	−0.719435	−	0.694560i	$-0.755599\pi$
$601$	5.92752	−	10.2668i	0.241789	−	0.418790i	0.961224	+	0.275769i	$0.0889326\pi$
$602$	−0.490432	+	0.343404i	−0.0199885	+	0.0139961i
$603$	−0.736165	+	6.81060i	−0.0299790	+	0.277349i
$604$	12.3525	−	14.7211i	0.502616	−	0.598994i
$605$	15.9897	+	17.6652i	0.650074	+	0.718192i
$606$	8.25626	+	18.1878i	0.335388	+	0.738830i
$607$	3.14252	−	3.14252i	0.127551	−	0.127551i	−0.640449	−	0.768000i	$-0.721252\pi$
$607$	3.14252	−	3.14252i	0.127551	−	0.127551i	0.768000	+	0.640449i	$0.221252\pi$
$608$	18.7277	+	10.8016i	0.759510	+	0.438063i
$609$	−0.225123	−	0.229764i	−0.00912243	−	0.00931051i
$610$	2.04538	+	1.32069i	0.0828149	+	0.0534731i
$611$	−3.09225	+	0.545247i	−0.125099	+	0.0220583i
$612$	−8.80966	+	0.589892i	−0.356110	+	0.0238450i
$613$	25.4430	+	2.22597i	1.02763	+	0.0899062i	0.588485	−	0.808508i	$-0.299725\pi$
$613$	25.4430	+	2.22597i	1.02763	+	0.0899062i	0.439148	+	0.898415i	$0.355280\pi$
$614$	−2.11370	+	11.9874i	−0.0853021	+	0.483772i
$615$	0.971571	+	35.5540i	0.0391775	+	1.43368i
$616$	−0.0581635	−	0.100742i	−0.00234347	−	0.00405901i
$617$	−28.0940	−	13.1004i	−1.13102	−	0.527404i	−0.235257	−	0.971933i	$-0.575593\pi$
$617$	−28.0940	−	13.1004i	−1.13102	−	0.527404i	−0.895764	+	0.444529i	$0.853371\pi$
$618$	−2.34987	+	0.828229i	−0.0945256	+	0.0333163i
$619$	−6.98820	+	4.03464i	−0.280879	+	0.162166i	−0.633821	−	0.773479i	$-0.718515\pi$
$619$	−6.98820	+	4.03464i	−0.280879	+	0.162166i	0.352942	+	0.935645i	$0.385181\pi$
$620$	5.92672	−	0.222493i	0.238023	−	0.00893555i
$621$	15.9406	−	10.4496i	0.639676	−	0.419329i
$622$	−2.44145	+	27.9060i	−0.0978934	+	1.11893i
$623$	0.216609	−	0.0189508i	0.00867826	−	0.000759250i
$624$	1.45341	+	1.03995i	0.0581832	+	0.0416314i
$625$	7.97385	+	23.6943i	0.318954	+	0.947770i
$626$		−	25.0582i		−	1.00153i
$627$	−3.99597	−	1.91109i	−0.159584	−	0.0763216i
$628$	−11.4475	−	11.4475i	−0.456803	−	0.456803i
$629$	−19.6933	−	7.16776i	−0.785222	−	0.285797i
$630$	0.291862	+	0.335977i	0.0116280	+	0.0133856i
$631$	25.0314	+	21.0039i	0.996486	+	0.836151i	0.986494	−	0.163799i	$-0.0523749\pi$
$631$	25.0314	+	21.0039i	0.996486	+	0.836151i	0.00999217	+	0.999950i	$0.496819\pi$
$632$	−18.7500	−	1.64041i	−0.745835	−	0.0652521i
$633$	20.2946	+	3.79238i	0.806637	+	0.150734i
$634$	12.4994	+	7.21653i	0.496414	+	0.286605i
$635$	24.7248	−	7.62994i	0.981175	−	0.302785i
$636$	−0.671747	+	1.40301i	−0.0266365	+	0.0556330i
$637$	−2.91816	+	6.25801i	−0.115622	+	0.247951i
$638$	−1.60444	−	0.429907i	−0.0635202	−	0.0170202i
$639$	19.4129	+	11.7426i	0.767964	+	0.464532i
$640$	5.77141	+	2.43202i	0.228135	+	0.0961338i
$641$	24.7099	+	29.4481i	0.975983	+	1.16313i	0.986595	+	0.163188i	$0.0521776\pi$
$641$	24.7099	+	29.4481i	0.975983	+	1.16313i	−0.0106119	+	0.999944i	$0.503378\pi$
$642$	16.5574	+	14.1837i	0.653467	+	0.559784i
$643$	2.78081	−	3.97141i	0.109664	−	0.156617i	−0.760568	−	0.649258i	$-0.775080\pi$
$643$	2.78081	−	3.97141i	0.109664	−	0.156617i	0.870233	+	0.492641i	$0.163968\pi$
$644$	0.224806	+	0.0818227i	0.00885860	+	0.00322427i
$645$	−8.12048	+	33.9949i	−0.319744	+	1.33855i
$646$	12.6068	+	3.37210i	0.496007	+	0.132673i
$647$	26.2550	+	26.2550i	1.03219	+	1.03219i	0.999464	+	0.0327256i	$0.0104188\pi$
$647$	26.2550	+	26.2550i	1.03219	+	1.03219i	0.0327256	+	0.999464i	$0.489581\pi$
$648$	−24.9618	+	10.4221i	−0.980592	+	0.409418i
$649$	4.70330	−	0.829318i	0.184621	−	0.0325536i
$650$	−2.04240	−	4.52345i	−0.0801095	−	0.177424i
$651$	−0.305097	−	0.0298322i	−0.0119577	−	0.00116922i
$652$	2.78313	+	3.97472i	0.108996	+	0.155662i
$653$	0.451964	+	1.68675i	0.0176867	+	0.0660077i	0.974205	−	0.225664i	$-0.0724552\pi$
$653$	0.451964	+	1.68675i	0.0176867	+	0.0660077i	−0.956518	+	0.291672i	$0.905788\pi$
$654$	7.42485	−	26.6204i	0.290335	−	1.04094i
$655$	−16.5780	−	12.8825i	−0.647757	−	0.503360i
$656$	3.28341	+	9.02110i	0.128196	+	0.352215i
$657$	11.8918	−	41.0140i	0.463942	−	1.60011i
$658$	−0.203859	+	0.0546239i	−0.00794726	+	0.00212946i
$659$	5.45283	−	30.9245i	0.212412	−	1.20465i	−0.672929	−	0.739707i	$-0.734964\pi$
$659$	5.45283	−	30.9245i	0.212412	−	1.20465i	0.885341	−	0.464942i	$-0.153925\pi$
$660$	−2.13114	−	0.710370i	−0.0829545	−	0.0276511i
$661$	17.3361	+	14.5467i	0.674296	+	0.565802i	0.914334	−	0.404962i	$-0.132715\pi$
$661$	17.3361	+	14.5467i	0.674296	+	0.565802i	−0.240037	+	0.970764i	$0.577160\pi$
$662$	−4.80181	+	6.85770i	−0.186628	+	0.266532i
$663$	−4.76451	−	1.78940i	−0.185038	−	0.0694945i
$664$			5.23998i			0.203351i
$665$	0.242685	+	0.595429i	0.00941094	+	0.0230898i
$666$	−21.2345	−	0.433384i	−0.822819	−	0.0167933i
$667$	9.35913	−	4.36423i	0.362387	−	0.168984i
$668$	−18.1602	−	12.7159i	−0.702638	−	0.491992i
$669$	−27.0877	+	2.09161i	−1.04727	+	0.0808662i
$670$	1.57397	−	4.88766i	0.0608078	−	0.188827i
$671$	0.625560	+	0.110303i	0.0241495	+	0.00425821i
$672$	−0.487879	−	0.288354i	−0.0188203	−	0.0111235i
$673$	3.37681	−	12.6024i	0.130166	−	0.485788i	−0.869805	−	0.493396i	$-0.835755\pi$
$673$	3.37681	−	12.6024i	0.130166	−	0.485788i	0.999971	+	0.00760864i	$0.00242193\pi$
$674$	24.9141	−	9.06798i	0.959654	−	0.349285i
$675$	25.7612	+	3.37048i	0.991549	+	0.129730i
$676$	5.94449	+	10.2962i	0.228634	+	0.396006i
$677$	2.62000	−	0.702026i	0.100695	−	0.0269811i	−0.208120	−	0.978103i	$-0.566734\pi$
$677$	2.62000	−	0.702026i	0.100695	−	0.0269811i	0.308815	+	0.951122i	$0.400068\pi$
$678$	33.5506	+	6.26949i	1.28850	+	0.240778i
$679$	0.630147	+	0.750979i	0.0241828	+	0.0288199i
$680$	19.8199	+	2.73264i	0.760057	+	0.104792i
$681$	9.23690	+	6.60922i	0.353959	+	0.253266i
$682$	−1.43465	+	0.668990i	−0.0549357	+	0.0256169i
$683$	−2.40175	+	2.40175i	−0.0919002	+	0.0919002i	−0.751562	−	0.659662i	$-0.770699\pi$
$683$	−2.40175	+	2.40175i	−0.0919002	+	0.0919002i	0.659662	+	0.751562i	$0.270699\pi$
$684$	−12.8987	+	0.869333i	−0.493194	+	0.0332398i
$685$	31.5957	+	7.20742i	1.20721	+	0.275381i
$686$	−0.317571	+	0.872519i	−0.0121249	+	0.0333129i
$687$	1.03208	+	6.22393i	0.0393764	+	0.237458i
$688$	0.822210	+	9.39790i	0.0313465	+	0.358292i
$689$	−0.686868	+	0.576351i	−0.0261676	+	0.0219572i
$690$	−13.2872	+	5.25148i	−0.505836	+	0.199920i
$691$	−3.27332	+	5.66955i	−0.124523	+	0.215680i	−0.921546	−	0.388268i	$-0.873073\pi$
$691$	−3.27332	+	5.66955i	−0.124523	+	0.215680i	0.797023	+	0.603948i	$0.206407\pi$
$692$	4.56965	−	17.0542i	0.173712	−	0.648302i
$693$	0.104209	+	0.0512078i	0.00395858	+	0.00194522i
$694$	−5.83533	−	16.0324i	−0.221506	−	0.608583i
$695$	−24.3960	+	46.1733i	−0.925394	+	1.75145i
$696$	−14.1940	+	3.64847i	−0.538022	+	0.138295i
$697$	−15.6810	−	22.3948i	−0.593960	−	0.848263i
$698$	−2.24717	+	25.6853i	−0.0850568	+	0.972203i
$699$	−2.30223	−	29.8154i	−0.0870783	−	1.12772i
$700$	0.159584	+	0.284377i	0.00603170	+	0.0107484i
$701$	−6.45104	+	17.7241i	−0.243652	+	0.669429i	0.756233	+	0.654302i	$0.227038\pi$
$701$	−6.45104	+	17.7241i	−0.243652	+	0.669429i	−0.999886	+	0.0151272i	$0.995185\pi$
$702$	−5.15545	−	0.157857i	−0.194580	−	0.00595794i
$703$	−28.8394	−	10.4825i	−1.08770	−	0.395353i
$704$	−4.15305			−0.156524
$705$	−6.78854	+	10.2818i	−0.255671	+	0.387236i
$706$	0.806947	+	4.57642i	0.0303699	+	0.172236i
$707$	−0.0659305	−	0.753589i	−0.00247957	−	0.0283416i
$708$	10.7687	−	8.85039i	0.404714	−	0.332618i
$709$	−3.65192	−	0.643932i	−0.137151	−	0.0241834i	0.104651	−	0.994509i	$-0.466627\pi$
$709$	−3.65192	−	0.643932i	−0.137151	−	0.0241834i	−0.241802	+	0.970326i	$0.577738\pi$
$710$	−12.4682	−	11.5659i	−0.467922	−	0.434061i
$711$	16.4581	−	9.05941i	0.617225	−	0.339754i
$712$	4.18666	−	8.97833i	0.156902	−	0.336477i
$713$	4.15912	−	8.91925i	0.155760	−	0.334029i
$714$	−0.329508	−	0.0919049i	−0.0123315	−	0.00343946i
$715$	−0.949324	−	0.880626i	−0.0355027	−	0.0329336i
$716$	−3.69659	−	0.651808i	−0.138148	−	0.0243592i
$717$	−20.5908	−	25.0539i	−0.768976	−	0.935654i
$718$	0.0354638	+	0.405353i	0.00132350	+	0.0151277i
$719$	0.276538	+	1.56832i	0.0103131	+	0.0584886i	0.989530	−	0.144327i	$-0.0461018\pi$
$719$	0.276538	+	1.56832i	0.0103131	+	0.0584886i	−0.979217	+	0.202816i	$0.934991\pi$
$720$	6.88414	−	1.33574i	0.256557	−	0.0497799i
$721$	0.0943614			0.00351420
$722$	18.4610	+	4.92938i	0.687046	+	0.183452i
$723$	0.00180827	−	0.177218i	6.72503e−5	−	0.00659079i
$724$	−6.33258	+	17.3986i	−0.235349	+	0.646615i
$725$	13.5509	+	3.80902i	0.503266	+	0.141463i
$726$	−18.5059	+	1.42896i	−0.686820	+	0.0530335i
$727$	−4.54603	+	51.9614i	−0.168603	+	1.92714i	0.168554	+	0.985692i	$0.446090\pi$
$727$	−4.54603	+	51.9614i	−0.168603	+	1.92714i	−0.337157	+	0.941448i	$0.609465\pi$
$728$	−0.112251	−	0.160312i	−0.00416031	−	0.00594154i
$729$	14.9053	−	22.5129i	0.552048	−	0.833812i
$730$	−14.9536	+	28.3020i	−0.553457	+	1.04750i
$731$	−9.18856	−	25.2454i	−0.339851	−	0.933733i
$732$	1.74852	−	0.616280i	0.0646272	−	0.0227784i
$733$	12.1880	−	45.4864i	0.450175	−	1.68008i	−0.251722	−	0.967800i	$-0.580997\pi$
$733$	12.1880	−	45.4864i	0.450175	−	1.68008i	0.701898	−	0.712278i	$-0.252336\pi$
$734$	6.38865	−	11.0655i	0.235809	−	0.408434i
$735$	9.95872	+	25.1974i	0.367333	+	0.929421i
$736$	13.9371	−	11.6946i	0.513729	−	0.431070i
$737$	−0.116760	−	1.33458i	−0.00430092	−	0.0491597i
$738$	−22.3669	−	16.3516i	−0.823335	−	0.601911i
$739$	11.4186	−	31.3724i	0.420041	−	1.15405i	−0.531642	−	0.846969i	$-0.678425\pi$
$739$	11.4186	−	31.3724i	0.420041	−	1.15405i	0.951683	−	0.307083i	$-0.0993530\pi$
$740$	−15.1725	−	3.46105i	−0.557751	−	0.127231i
$741$	−6.97731	−	2.61699i	−0.256318	−	0.0961377i
$742$	−0.0426155	+	0.0426155i	−0.00156447	+	0.00156447i
$743$	24.0314	−	11.2060i	0.881626	−	0.411109i	0.0715525	−	0.997437i	$-0.477205\pi$
$743$	24.0314	−	11.2060i	0.881626	−	0.411109i	0.810074	+	0.586328i	$0.199427\pi$
$744$	−8.12723	+	11.3584i	−0.297959	+	0.416421i
$745$	−1.73640	−	0.239404i	−0.0636168	−	0.00877108i
$746$	10.5987	+	12.6311i	0.388047	+	0.462457i
$747$	−2.91191	−	4.34470i	−0.106541	−	0.158964i
$748$	1.66788	−	0.446908i	0.0609839	−	0.0163406i
$749$	−0.412846	−	0.715070i	−0.0150851	−	0.0261281i
$750$	−18.3987	−	6.38368i	−0.671827	−	0.233099i
$751$	25.4861	−	9.27619i	0.930002	−	0.338493i	0.167792	−	0.985822i	$-0.446336\pi$
$751$	25.4861	−	9.27619i	0.930002	−	0.338493i	0.762210	+	0.647329i	$0.224114\pi$
$752$	−0.860707	+	3.21220i	−0.0313867	+	0.117137i
$753$	6.31316	−	10.6815i	0.230064	−	0.389256i
$754$	−2.75201	−	0.485253i	−0.100222	−	0.0176719i
$755$	13.3232	−	41.3727i	0.484882	−	1.50571i
$756$	0.338343	−	0.0191899i	0.0123054	−	0.000697928i
$757$	9.09976	+	6.37172i	0.330736	+	0.231584i	0.727135	−	0.686494i	$-0.240851\pi$
$757$	9.09976	+	6.37172i	0.330736	+	0.231584i	−0.396399	+	0.918078i	$0.629740\pi$
$758$	11.4936	−	5.35954i	0.417465	−	0.194667i
$759$	−2.66253	+	2.60874i	−0.0966437	+	0.0946914i
$760$	29.0219	+	3.98848i	1.05274	+	0.144677i
$761$			18.9197i			0.685838i	0.939365	+	0.342919i	$0.111416\pi$
$761$			18.9197i			0.685838i	−0.939365	+	0.342919i	$0.888584\pi$
$762$	−7.08687	+	18.8697i	−0.256730	+	0.683577i
$763$	−0.600341	+	0.857376i	−0.0217338	+	0.0310391i
$764$	13.4233	+	11.2635i	0.485640	+	0.407500i
$765$	−17.9521	+	8.74834i	−0.649059	+	0.316297i
$766$	−5.34062	+	30.2881i	−0.192964	+	1.09435i
$767$	7.76094	−	2.07954i	0.280231	−	0.0750878i
$768$	−25.6099	+	14.4395i	−0.924118	+	0.521041i
$769$	10.7826	+	29.6250i	0.388832	+	1.06831i	0.967528	+	0.252763i	$0.0813394\pi$
$769$	10.7826	+	29.6250i	0.388832	+	1.06831i	−0.578696	+	0.815543i	$0.696438\pi$
$770$	−0.0687245	−	0.0534044i	−0.00247666	−	0.00192456i
$771$	30.7958	+	8.58941i	1.10908	+	0.309340i
$772$	0.632549	+	2.36071i	0.0227659	+	0.0849636i
$773$	−14.5314	−	20.7530i	−0.522658	−	0.746433i	0.467862	−	0.883802i	$-0.345024\pi$
$773$	−14.5314	−	20.7530i	−0.522658	−	0.746433i	−0.990520	+	0.137368i	$0.956136\pi$
$774$	−17.0718	−	21.2096i	−0.613632	−	0.762365i
$775$	12.2260	−	5.52020i	0.439170	−	0.198292i
$776$	43.9858	−	7.75589i	1.57900	−	0.278420i
$777$	0.753013	+	0.282808i	0.0270142	+	0.0101457i
$778$	−17.7497	−	17.7497i	−0.636359	−	0.636359i
$779$	−22.9743	−	32.7804i	−0.823141	−	1.17448i
$780$	−3.67587	−	0.878068i	−0.131617	−	0.0314399i
$781$	−4.16942	−	1.51755i	−0.149194	−	0.0543021i
$782$	6.29904	−	8.99596i	0.225253	−	0.321695i
$783$	9.74140	−	10.9128i	0.348129	−	0.389993i
$784$	4.70072	+	5.60209i	0.167883	+	0.200075i
$785$	−33.7430	−	14.2190i	−1.20434	−	0.507497i
$786$	15.8399	−	4.07154i	0.564992	−	0.145227i
$787$	−33.6304	−	9.01123i	−1.19879	−	0.321216i	−0.396437	−	0.918062i	$-0.629754\pi$
$787$	−33.6304	−	9.01123i	−1.19879	−	0.321216i	−0.802356	+	0.596846i	$0.796420\pi$
$788$	1.30775	−	2.80448i	0.0465866	−	0.0999053i
$789$	−1.46808	−	0.702902i	−0.0522651	−	0.0250240i
$790$	−13.4560	+	4.15246i	−0.478745	+	0.147738i
$791$	−1.11946	−	0.646319i	−0.0398033	−	0.0229805i
$792$	4.39438	−	2.94520i	0.156148	−	0.104653i
$793$	1.06459	+	0.0931394i	0.0378047	+	0.00330748i
$794$	7.07427	+	5.93602i	0.251056	+	0.210661i
$795$	−0.210784	+	3.51198i	−0.00747573	+	0.124557i
$796$	2.25888	+	0.822165i	0.0800639	+	0.0291409i
$797$	−11.9662	−	11.9662i	−0.423865	−	0.423865i	0.462667	−	0.886532i	$-0.346893\pi$
$797$	−11.9662	−	11.9662i	−0.423865	−	0.423865i	−0.886532	+	0.462667i	$0.846893\pi$
$798$	−0.482523	−	0.134357i	−0.0170811	−	0.00475618i
$799$		−	9.47039i		−	0.335038i
$800$	24.7974	+	0.303044i	0.876721	+	0.0107142i
$801$	1.51799	+	9.77090i	0.0536356	+	0.345238i
$802$	−20.3784	+	1.78288i	−0.719587	+	0.0629557i
$803$	−0.727859	+	8.31947i	−0.0256856	+	0.293588i
$804$	−2.20990	−	3.22562i	−0.0779372	−	0.113759i
$805$	0.540716	−	0.0202989i	0.0190577	−	0.000715442i
$806$	−2.30633	+	1.33156i	−0.0812371	+	0.0469022i
$807$	−17.2161	−	48.8459i	−0.606036	−	1.71946i
$808$	−31.2358	−	14.5655i	−1.09887	−	0.512413i
$809$	8.19787	+	14.1991i	0.288222	+	0.499215i	0.973385	−	0.229174i	$-0.0736026\pi$
$809$	8.19787	+	14.1991i	0.288222	+	0.499215i	−0.685163	+	0.728389i	$0.740269\pi$
$810$	−14.3580	+	14.2638i	−0.504487	+	0.501178i
$811$	1.07338	−	6.08742i	0.0376913	−	0.213758i	−0.960145	−	0.279502i	$-0.909831\pi$
$811$	1.07338	−	6.08742i	0.0376913	−	0.213758i	0.997837	+	0.0657434i	$0.0209419\pi$
$812$	0.182905	+	0.0160021i	0.00641872	+	0.000561565i
$813$	−21.0479	+	24.5703i	−0.738181	+	0.861719i
$814$	4.09048	−	0.721262i	0.143371	−	0.0252802i
$815$	9.21981	+	5.95317i	0.322956	+	0.208531i
$816$	−3.85015	+	3.77237i	−0.134782	+	0.132060i
$817$	−13.4699	−	36.9583i	−0.471254	−	1.29301i
$818$	12.0886	−	12.0886i	0.422667	−	0.422667i
$819$	0.182159	+	0.0705423i	0.00636516	+	0.00246495i
$820$	−13.6236	−	15.0511i	−0.475757	−	0.525609i
$821$	−11.0749	+	13.1986i	−0.386517	+	0.460633i	−0.923860	−	0.382731i	$-0.874984\pi$
$821$	−11.0749	+	13.1986i	−0.386517	+	0.460633i	0.537343	+	0.843364i	$0.319428\pi$
$822$	−19.5033	+	16.0290i	−0.680257	+	0.559076i
$823$	−25.1983	+	17.6440i	−0.878357	+	0.615032i	−0.923352	−	0.383955i	$-0.874562\pi$
$823$	−25.1983	+	17.6440i	−0.878357	+	0.615032i	0.0449950	+	0.998987i	$0.485673\pi$
$824$	2.14957	−	3.72316i	0.0748838	−	0.129703i
$825$	−5.07025	+	0.329232i	−0.176524	+	0.0114624i
$826$	0.507482	−	0.184708i	0.0176575	−	0.00642682i
$827$	−7.65931	−	3.57160i	−0.266340	−	0.124197i	0.284861	−	0.958569i	$-0.408053\pi$
$827$	−7.65931	−	3.57160i	−0.266340	−	0.124197i	−0.551201	+	0.834372i	$0.685830\pi$
$828$	−3.02963	+	10.4490i	−0.105287	+	0.363128i
$829$	43.6718	+	25.2139i	1.51679	+	0.875717i	0.999806	+	0.0197192i	$0.00627722\pi$
$829$	43.6718	+	25.2139i	1.51679	+	0.875717i	0.516980	+	0.855997i	$0.327056\pi$
$830$	1.47816	+	3.63118i	0.0513076	+	0.126040i
$831$	−29.3661	−	2.87141i	−1.01870	−	0.0996081i
$832$	−6.96035	+	0.608952i	−0.241307	+	0.0211116i
$833$	−17.0596	−	11.9453i	−0.591081	−	0.413880i
$834$	−16.8152	−	37.0425i	−0.582263	−	1.28268i
$835$	−48.8870	−	11.1518i	−1.69180	−	0.385924i
$836$	2.44182	−	0.655424i	0.0844523	−	0.0226683i
$837$	0.426658	−	13.9342i	0.0147474	−	0.481635i
$838$	16.0539	+	34.4276i	0.554571	+	1.18928i
$839$	6.88135	+	39.0261i	0.237571	+	1.34733i	0.837132	+	0.547001i	$0.184231\pi$
$839$	6.88135	+	39.0261i	0.237571	+	1.34733i	−0.599561	+	0.800329i	$0.704658\pi$
$840$	−0.759609	−	0.112639i	−0.0262090	−	0.00388643i
$841$	−16.1441	+	13.5465i	−0.556693	+	0.467121i
$842$	−3.14529	+	2.20236i	−0.108394	+	0.0758982i
$843$	1.36559	−	2.31050i	0.0470334	−	0.0795779i
$844$	−10.2055	+	5.89216i	−0.351288	+	0.202816i
$845$	21.2332	+	16.4999i	0.730444	+	0.567614i
$846$	−3.09789	−	9.08400i	−0.106508	−	0.312314i
$847$	0.679000	+	0.181937i	0.0233307	+	0.00625144i
$848$	0.245783	+	0.917274i	0.00844022	+	0.0314993i
$849$	−24.4041	−	35.6208i	−0.837547	−	1.22250i
$850$	14.5056	−	3.69738i	0.497537	−	0.126819i
$851$	−16.5986	+	19.7815i	−0.568993	+	0.678100i
$852$	−12.7756	+	2.11851i	−0.437684	+	0.0725788i
$853$	1.47682	+	3.16705i	0.0505653	+	0.108438i	0.929967	−	0.367642i	$-0.119835\pi$
$853$	1.47682	+	3.16705i	0.0505653	+	0.108438i	−0.879402	+	0.476080i	$0.842057\pi$
$854$	0.0718292			0.00245795
$855$	−26.2798	+	12.8207i	−0.898751	+	0.438460i
$856$	−37.6188			−1.28578
$857$	9.71601	+	20.8361i	0.331893	+	0.711746i	0.999462	−	0.0328016i	$-0.0104430\pi$
$857$	9.71601	+	20.8361i	0.331893	+	0.711746i	−0.667569	+	0.744548i	$0.732665\pi$
$858$	0.995110	−	0.165014i	0.0339725	−	0.00563349i
$859$	18.2955	−	21.8038i	0.624235	−	0.743934i	−0.357557	−	0.933891i	$-0.616390\pi$
$859$	18.2955	−	21.8038i	0.624235	−	0.743934i	0.981792	+	0.189957i	$0.0608348\pi$
$860$	−9.10343	−	17.7515i	−0.310424	−	0.605321i
$861$	0.593061	+	0.865645i	0.0202115	+	0.0295011i
$862$	7.94195	+	29.6397i	0.270504	+	1.00953i
$863$	20.6033	+	5.52064i	0.701345	+	0.187925i	0.591833	−	0.806061i	$-0.298405\pi$
$863$	20.6033	+	5.52064i	0.701345	+	0.187925i	0.109512	+	0.993985i	$0.465071\pi$
$864$	11.6015	−	23.0132i	0.394692	−	0.782926i
$865$	−4.97039	−	39.6232i	−0.168998	−	1.34723i
$866$	6.77862	−	3.91364i	0.230347	−	0.132991i
$867$	−7.17148	+	12.1338i	−0.243556	+	0.412084i
$868$	0.143331	−	0.100361i	0.00486497	−	0.00340649i
$869$	−2.81447	+	2.36162i	−0.0954742	+	0.0801124i
$870$	−8.80691	+	6.53232i	−0.298582	+	0.221466i
$871$	−0.391371	−	2.21958i	−0.0132611	−	0.0752075i
$872$	20.1531	+	43.2185i	0.682471	+	1.46356i
$873$	−32.1606	+	30.8741i	−1.08847	+	1.04493i
$874$	9.21730	−	13.1759i	0.311780	−	0.445681i
$875$	0.576815	+	0.459646i	0.0194999	+	0.0155389i
$876$	10.0751	+	22.1945i	0.340405	+	0.749884i
$877$	−35.4614	−	24.8304i	−1.19745	−	0.838462i	−0.207271	−	0.978284i	$-0.566458\pi$
$877$	−35.4614	−	24.8304i	−1.19745	−	0.838462i	−0.990177	+	0.139822i	$0.955347\pi$
$878$	−36.9909	+	3.23629i	−1.24838	+	0.109219i
$879$	−25.0699	−	2.45133i	−0.845587	−	0.0826812i
$880$	−1.27020	+	0.517063i	−0.0428183	+	0.0174302i
$881$	−50.1750	−	28.9686i	−1.69044	−	0.975976i	−0.954159	−	0.299301i	$-0.903247\pi$
$881$	−50.1750	−	28.9686i	−1.69044	−	0.975976i	−0.736281	−	0.676676i	$-0.763420\pi$
$882$	−20.2711	−	5.87748i	−0.682563	−	0.197905i
$883$	−19.3578	−	9.02667i	−0.651441	−	0.303772i	0.0686613	−	0.997640i	$-0.478127\pi$
$883$	−19.3578	−	9.02667i	−0.651441	−	0.303772i	−0.720102	+	0.693868i	$0.755905\pi$
$884$	2.72978	−	0.993559i	0.0918125	−	0.0334170i
$885$	15.0118	−	27.7237i	0.504617	−	0.931921i
$886$	−10.7717	+	18.6572i	−0.361883	+	0.626801i
$887$	−2.75604	+	1.92980i	−0.0925388	+	0.0647964i	−0.618930	−	0.785446i	$-0.712434\pi$
$887$	−2.75604	+	1.92980i	−0.0925388	+	0.0647964i	0.526391	+	0.850242i	$0.323545\pi$
$888$	28.3124	−	23.2688i	0.950102	−	0.780850i
$889$	0.490692	−	0.584784i	0.0164573	−	0.0196130i
$890$	0.368544	−	7.40279i	0.0123536	−	0.248142i
$891$	−2.00690	+	4.88400i	−0.0672338	+	0.163620i
$892$	10.9653	−	10.9653i	0.367145	−	0.367145i
$893$	−0.00603666	−	13.8665i	−0.000202009	−	0.464025i
$894$	0.975308	−	0.955606i	0.0326192	−	0.0319602i
$895$	−8.29973	+	1.78687i	−0.277429	+	0.0597285i
$896$	0.181962	−	0.0320849i	0.00607894	−	0.00107188i
$897$	−4.07978	+	4.76256i	−0.136220	+	0.159017i
$898$	−18.0608	−	1.58012i	−0.602698	−	0.0527292i
$899$	1.31154	−	7.43814i	0.0437425	−	0.248076i
$900$	−12.4185	+	8.10500i	−0.413951	+	0.270167i
$901$	−1.35218	−	2.34204i	−0.0450476	−	0.0780248i
$902$	4.91076	+	2.28993i	0.163511	+	0.0762462i
$903$	0.342767	+	0.972506i	0.0114066	+	0.0323630i
$904$	−51.0029	+	29.4465i	−1.69633	+	0.979377i
$905$	1.57101	+	41.8482i	0.0522222	+	1.39108i
$906$	19.1366	+	27.9322i	0.635771	+	0.927986i
$907$	−4.18007	+	47.7784i	−0.138797	+	1.58645i	0.533257	+	0.845953i	$0.320968\pi$
$907$	−4.18007	+	47.7784i	−0.138797	+	1.58645i	−0.672054	+	0.740502i	$0.734588\pi$
$908$	−6.45824	+	0.565023i	−0.214324	+	0.0187509i
$909$	33.9932	−	5.28113i	1.12748	−	0.175164i
$910$	−0.123010	−	0.0794269i	−0.00407775	−	0.00263298i
$911$		−	42.4097i		−	1.40510i	−0.711636	−	0.702548i	$-0.752046\pi$
$911$		−	42.4097i		−	1.40510i	0.711636	−	0.702548i	$-0.247954\pi$
$912$	−5.63497	+	5.52595i	−0.186593	+	0.182983i
$913$	0.723269	+	0.723269i	0.0239367	+	0.0239367i
$914$	10.4976	+	3.82082i	0.347231	+	0.126382i
$915$	3.13739	−	2.78211i	0.103719	−	0.0919737i
$916$	−2.75855	−	2.31470i	−0.0911450	−	0.0764797i
$917$	−0.617042	−	0.0539842i	−0.0203765	−	0.00178272i
$918$	3.16899	−	15.2304i	0.104592	−	0.502679i
$919$	19.3544	+	11.1743i	0.638443	+	0.368605i	0.784015	−	0.620742i	$-0.213169\pi$
$919$	19.3544	+	11.1743i	0.638443	+	0.368605i	−0.145571	+	0.989348i	$0.546502\pi$
$920$	11.5167	−	21.7971i	0.379694	−	0.718631i
$921$	18.9086	+	9.05325i	0.623060	+	0.298315i
$922$	8.69710	−	18.6510i	0.286424	−	0.614238i
$923$	−7.21031	−	1.93200i	−0.237330	−	0.0635925i
$924$	−0.0641878	+	0.0164990i	−0.00211162	+	0.000542778i
$925$	−34.7359	+	5.68812i	−1.14211	+	0.187024i
$926$	13.8596	+	16.5172i	0.455455	+	0.542790i
$927$	0.286693	+	4.28158i	0.00941623	+	0.140625i
$928$	8.00885	−	11.4378i	0.262903	−	0.375465i
$929$	24.4689	+	8.90596i	0.802799	+	0.292195i	0.710646	−	0.703550i	$-0.248403\pi$
$929$	24.4689	+	8.90596i	0.802799	+	0.292195i	0.0921532	+	0.995745i	$0.470625\pi$
$930$	−2.42785	+	10.1638i	−0.0796124	+	0.333283i
$931$	−24.9863	−	17.4794i	−0.818892	−	0.572863i
$932$	12.0695	+	12.0695i	0.395348	+	0.395348i
$933$	45.1653	+	16.9627i	1.47865	+	0.555333i
$934$	−26.3031	+	4.63795i	−0.860665	+	0.151758i
$935$	3.11290	−	2.35853i	0.101803	−	0.0771323i
$936$	6.93297	−	5.58039i	0.226611	−	0.182401i
$937$	24.4511	+	34.9198i	0.798783	+	1.14078i	0.987324	+	0.158715i	$0.0507351\pi$
$937$	24.4511	+	34.9198i	0.798783	+	1.14078i	−0.188541	+	0.982065i	$0.560376\pi$
$938$	−0.0392084	−	0.146328i	−0.00128020	−	0.00477777i
$939$	−41.5707	−	11.5947i	−1.35661	−	0.378379i
$940$	−0.875302	−	6.97778i	−0.0285492	−	0.227590i
$941$	11.6320	+	31.9587i	0.379193	+	1.04183i	0.971691	+	0.236254i	$0.0759196\pi$
$941$	11.6320	+	31.9587i	0.379193	+	1.04183i	−0.592498	+	0.805572i	$0.701858\pi$
$942$	24.8466	−	14.0091i	0.809547	−	0.456443i
$943$	−32.5386	+	8.71869i	−1.05960	+	0.283920i
$944$	1.47767	−	8.38028i	0.0480940	−	0.272755i
$945$	0.692421	−	0.328728i	0.0225245	−	0.0106935i
$946$	4.07888	+	3.42258i	0.132616	+	0.111278i
$947$	10.5361	−	15.0471i	0.342377	−	0.488965i	−0.610629	−	0.791917i	$-0.709083\pi$
$947$	10.5361	−	15.0471i	0.342377	−	0.488965i	0.953006	+	0.302952i	$0.0979722\pi$
$948$	−3.77015	+	10.0385i	−0.122449	+	0.326036i
$949$			14.0498i			0.456077i
$950$	21.2366	−	5.42293i	0.689007	−	0.175943i
$951$	17.7556	−	17.3969i	0.575764	−	0.564132i
$952$	0.534959	−	0.249456i	0.0173381	−	0.00808491i
$953$	19.7334	+	13.8175i	0.639227	+	0.447591i	0.847728	−	0.530431i	$-0.177970\pi$
$953$	19.7334	+	13.8175i	0.639227	+	0.447591i	−0.208502	+	0.978022i	$0.566859\pi$
$954$	−2.06313	−	1.80417i	−0.0667961	−	0.0584122i
$955$	37.7254	+	12.1487i	1.22076	+	0.393122i
$956$	18.2290	+	3.21427i	0.589569	+	0.103957i
$957$	−1.45559	+	2.46278i	−0.0470525	+	0.0796103i
$958$	0.384740	−	1.43587i	0.0124304	−	0.0463908i
$959$	0.898431	−	0.327002i	0.0290119	−	0.0105595i
$960$	−17.0422	+	21.4752i	−0.550036	+	0.693110i
$961$	11.9011	+	20.6132i	0.383905	+	0.664943i
$962$	6.74973	−	1.80859i	0.217620	−	0.0583111i
$963$	31.1914	−	20.9051i	1.00513	−	0.673658i
$964$	0.0650232	+	0.0774916i	0.00209426	+	0.00249584i
$965$	3.33824	+	4.40596i	0.107462	+	0.141833i
$966$	−0.245278	+	0.342795i	−0.00789169	+	0.0110293i
$967$	49.7626	−	23.2047i	1.60026	−	0.746213i	0.601640	−	0.798767i	$-0.294514\pi$
$967$	49.7626	−	23.2047i	1.60026	−	0.746213i	0.998618	+	0.0525545i	$0.0167363\pi$
$968$	22.6463	−	22.6463i	0.727881	−	0.727881i
$969$	11.4275	−	19.3539i	0.367104	−	0.621737i
$970$	28.2933	−	17.7827i	0.908442	−	0.570968i
$971$	10.5519	−	28.9912i	0.338628	−	0.930372i	−0.647157	−	0.762357i	$-0.724042\pi$
$971$	10.5519	−	28.9912i	0.338628	−	0.930372i	0.985784	−	0.168015i	$-0.0537356\pi$
$972$	1.89869	+	15.2937i	0.0609006	+	0.490547i
$973$	0.134278	+	1.53481i	0.00430476	+	0.0492036i
$974$	−13.5456	+	11.3661i	−0.434029	+	0.364194i
$975$	−8.44927	+	1.29522i	−0.270593	+	0.0414802i
$976$	0.565905	−	0.980177i	0.0181142	−	0.0313747i
$977$	−8.01341	+	29.9064i	−0.256372	+	0.956792i	0.710951	+	0.703242i	$0.248265\pi$
$977$	−8.01341	+	29.9064i	−0.256372	+	0.956792i	−0.967322	+	0.253550i	$0.918402\pi$
$978$	−8.06305	+	2.84188i	−0.257828	+	0.0908734i
$979$	−0.661388	−	1.81715i	−0.0211381	−	0.0580764i
$980$	−13.6736	−	7.22454i	−0.436786	−	0.230780i
$981$	−40.7268	−	24.6351i	−1.30031	−	0.786539i
$982$	−13.6422	−	19.4831i	−0.435340	−	0.621730i
$983$	2.09845	−	23.9853i	0.0669300	−	0.765014i	−0.886368	−	0.462982i	$-0.846780\pi$
$983$	2.09845	−	23.9853i	0.0669300	−	0.765014i	0.953298	−	0.302032i	$-0.0976649\pi$
$984$	47.6653	−	3.68053i	1.51951	−	0.117331i
$985$	0.348004	−	6.99023i	0.0110883	−	0.222727i
$986$	2.88267	−	7.92007i	0.0918029	−	0.252226i
$987$	−0.00370873	+	0.363470i	−0.000118050	+	0.0115694i
$988$	3.99630	−	1.45651i	0.127139	−	0.0463376i
$989$	−33.1031			−1.05262
$990$	2.21438	−	3.28058i	0.0703778	−	0.104264i
$991$	6.30750	+	35.7716i	0.200364	+	1.13632i	0.904569	+	0.426327i	$0.140193\pi$
$991$	6.30750	+	35.7716i	0.200364	+	1.13632i	−0.704205	+	0.709997i	$0.748696\pi$
$992$	−1.15976	−	13.2561i	−0.0368224	−	0.420882i
$993$	9.15482	+	11.1392i	0.290519	+	0.353491i
$994$	−0.494112	−	0.0871253i	−0.0156723	−	0.00276345i
$995$	5.43318	−	0.203966i	0.172243	−	0.00646615i
$996$	2.87559	+	0.802047i	0.0911166	+	0.0254138i
$997$	−19.9816	+	42.8507i	−0.632824	+	1.35710i	0.284393	+	0.958708i	$0.408208\pi$
$997$	−19.9816	+	42.8507i	−0.632824	+	1.35710i	−0.917217	+	0.398388i	$0.869570\pi$
$998$	−1.91231	+	4.10095i	−0.0605330	+	0.129813i
$999$	−10.5444	+	35.0267i	−0.333609	+	1.10819i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.2.bi.a.23.13	✓	432
3.2	odd	2	inner	285.2.bi.a.23.24	yes	432
5.2	odd	4	inner	285.2.bi.a.137.24	yes	432
15.2	even	4	inner	285.2.bi.a.137.13	yes	432
19.5	even	9	inner	285.2.bi.a.233.13	yes	432
57.5	odd	18	inner	285.2.bi.a.233.24	yes	432
95.62	odd	36	inner	285.2.bi.a.62.24	yes	432
285.62	even	36	inner	285.2.bi.a.62.13	yes	432

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.bi.a.23.13	✓	432	1.1	even	1	trivial
285.2.bi.a.23.24	yes	432	3.2	odd	2	inner
285.2.bi.a.62.13	yes	432	285.62	even	36	inner
285.2.bi.a.62.24	yes	432	95.62	odd	36	inner
285.2.bi.a.137.13	yes	432	15.2	even	4	inner
285.2.bi.a.137.24	yes	432	5.2	odd	4	inner
285.2.bi.a.233.13	yes	432	19.5	even	9	inner
285.2.bi.a.233.24	yes	432	57.5	odd	18	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.bi (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.425015 - 0.911447i) q^{2} +(-1.70872 + 0.283348i) q^{3} +(0.635477 - 0.757331i) q^{4} +(0.685416 - 2.12843i) q^{5} +(0.984487 + 1.43698i) q^{6} +(-0.0170740 - 0.0637212i) q^{7} +(-2.90316 - 0.777900i) q^{8} +(2.83943 - 0.968323i) q^{9} +O(q^{10})\)	\(q+(-0.425015 - 0.911447i) q^{2} +(-1.70872 + 0.283348i) q^{3} +(0.635477 - 0.757331i) q^{4} +(0.685416 - 2.12843i) q^{5} +(0.984487 + 1.43698i) q^{6} +(-0.0170740 - 0.0637212i) q^{7} +(-2.90316 - 0.777900i) q^{8} +(2.83943 - 0.968323i) q^{9} +(-2.23126 + 0.279893i) q^{10} +(-0.508093 + 0.293348i) q^{11} +(-0.871261 + 1.47413i) q^{12} +(-0.808532 + 0.566140i) q^{13} +(-0.0508218 + 0.0426446i) q^{14} +(-0.568097 + 3.83109i) q^{15} +(0.181526 + 1.02948i) q^{16} +(-1.25813 - 2.69807i) q^{17} +(-2.08937 - 2.17644i) q^{18} +(-1.84387 - 3.94970i) q^{19} +(-1.17636 - 1.87165i) q^{20} +(0.0472300 + 0.104044i) q^{21} +(0.483318 + 0.338423i) q^{22} +(-3.65422 + 0.319702i) q^{23} +(5.18110 + 0.506606i) q^{24} +(-4.06041 - 2.91772i) q^{25} +(0.859645 + 0.496316i) q^{26} +(-4.57741 + 2.45914i) q^{27} +(-0.0591082 - 0.0275626i) q^{28} +(-2.64543 + 0.962857i) q^{29} +(3.73329 - 1.11048i) q^{30} +(-1.34144 + 2.32345i) q^{31} +(-4.06287 + 2.84486i) q^{32} +(0.785068 - 0.645215i) q^{33} +(-1.92442 + 2.29344i) q^{34} +(-0.147329 - 0.00733468i) q^{35} +(1.07105 - 2.76573i) q^{36} +(4.97782 - 4.97782i) q^{37} +(-2.81627 + 3.35927i) q^{38} +(1.22114 - 1.19647i) q^{39} +(-3.64558 + 5.64598i) q^{40} +(9.04391 - 1.59469i) q^{41} +(0.0747568 - 0.0872677i) q^{42} +(8.99006 + 0.786528i) q^{43} +(-0.100720 + 0.571210i) q^{44} +(-0.114815 - 6.70722i) q^{45} +(1.84449 + 3.19475i) q^{46} +(2.88314 + 1.34443i) q^{47} +(-0.601879 - 1.70766i) q^{48} +(6.05841 - 3.49782i) q^{49} +(-0.933612 + 4.94092i) q^{50} +(2.91428 + 4.25375i) q^{51} +(-0.0850473 + 0.972095i) q^{52} +(0.904964 - 0.0791740i) q^{53} +(4.18684 + 3.12690i) q^{54} +(0.276114 + 1.28250i) q^{55} +0.198275i q^{56} +(4.26979 + 6.22647i) q^{57} +(2.00194 + 2.00194i) q^{58} +(-7.64934 - 2.78413i) q^{59} +(2.54039 + 2.86481i) q^{60} +(-0.829391 - 0.695941i) q^{61} +(2.68784 + 0.235155i) q^{62} +(-0.110183 - 0.164399i) q^{63} +(6.13035 + 3.53936i) q^{64} +(0.650807 + 2.10894i) q^{65} +(-0.921745 - 0.441322i) q^{66} +(-0.965016 + 2.06948i) q^{67} +(-2.84285 - 0.761738i) q^{68} +(6.15343 - 1.58170i) q^{69} +(0.0559318 + 0.137400i) q^{70} +(4.86122 + 5.79338i) q^{71} +(-8.99658 + 0.602408i) q^{72} +(8.16451 - 11.6601i) q^{73} +(-6.65267 - 2.42138i) q^{74} +(7.76482 + 3.83505i) q^{75} +(-4.16297 - 1.11352i) q^{76} +(0.0273677 + 0.0273677i) q^{77} +(-1.60952 - 0.604485i) q^{78} +(6.16710 - 1.08743i) q^{79} +(2.31561 + 0.319261i) q^{80} +(7.12470 - 5.49897i) q^{81} +(-5.29727 - 7.56529i) q^{82} +(-0.451231 - 1.68402i) q^{83} +(0.108809 + 0.0303485i) q^{84} +(-6.60499 + 0.828539i) q^{85} +(-3.10403 - 8.52825i) q^{86} +(4.24746 - 2.39483i) q^{87} +(1.70327 - 0.456390i) q^{88} +(-0.572351 + 3.24596i) q^{89} +(-6.06448 + 2.95532i) q^{90} +(0.0498800 + 0.0418543i) q^{91} +(-2.08005 + 2.97062i) q^{92} +(1.63380 - 4.35022i) q^{93} -3.19924i q^{94} +(-9.67047 + 1.21735i) q^{95} +(6.13622 - 6.01226i) q^{96} +(-13.4682 + 6.28032i) q^{97} +(-5.76300 - 4.03529i) q^{98} +(-1.15864 + 1.32494i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q - 12 q^{3} - 24 q^{6} - 12 q^{7}+O(q^{10}) \) 432 * q - 12 * q^3 - 24 * q^6 - 12 * q^7	\( 432 q - 12 q^{3} - 24 q^{6} - 12 q^{7} - 24 q^{10} - 6 q^{12} - 24 q^{13} + 6 q^{15} - 108 q^{16} + 24 q^{18} - 24 q^{21} - 72 q^{22} - 6 q^{27} - 72 q^{28} - 6 q^{30} - 24 q^{31} - 102 q^{33} - 24 q^{36} - 48 q^{37} - 24 q^{40} + 24 q^{42} - 36 q^{43} + 12 q^{45} - 24 q^{46} - 156 q^{48} - 72 q^{51} - 48 q^{52} + 12 q^{55} - 90 q^{57} + 96 q^{58} + 132 q^{60} - 24 q^{61} + 18 q^{63} - 72 q^{66} - 120 q^{67} + 24 q^{70} + 168 q^{72} - 24 q^{73} - 192 q^{75} - 168 q^{76} - 6 q^{78} + 72 q^{81} - 312 q^{82} + 42 q^{87} - 204 q^{88} + 156 q^{90} + 72 q^{91} + 138 q^{93} + 240 q^{96} - 48 q^{97}+O(q^{100}) \) 432 * q - 12 * q^3 - 24 * q^6 - 12 * q^7 - 24 * q^10 - 6 * q^12 - 24 * q^13 + 6 * q^15 - 108 * q^16 + 24 * q^18 - 24 * q^21 - 72 * q^22 - 6 * q^27 - 72 * q^28 - 6 * q^30 - 24 * q^31 - 102 * q^33 - 24 * q^36 - 48 * q^37 - 24 * q^40 + 24 * q^42 - 36 * q^43 + 12 * q^45 - 24 * q^46 - 156 * q^48 - 72 * q^51 - 48 * q^52 + 12 * q^55 - 90 * q^57 + 96 * q^58 + 132 * q^60 - 24 * q^61 + 18 * q^63 - 72 * q^66 - 120 * q^67 + 24 * q^70 + 168 * q^72 - 24 * q^73 - 192 * q^75 - 168 * q^76 - 6 * q^78 + 72 * q^81 - 312 * q^82 + 42 * q^87 - 204 * q^88 + 156 * q^90 + 72 * q^91 + 138 * q^93 + 240 * q^96 - 48 * q^97

Introduction

L-functions

Modular forms

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