LMFDB - Embedded newform 150.2.l.a.113.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(17,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("150.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.l (of order $20$, degree $8$, 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:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			113.8
Character	$\chi$	$=$	150.113
Dual form			150.2.l.a.77.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.156434 + 0.987688i) q^{2} +(-0.282741 + 1.70882i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-0.103560 + 2.23367i) q^{5} +(-1.73201 - 0.0119417i) q^{6} +(2.28673 - 2.28673i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-2.84012 - 0.966305i) q^{9} +O(q^{10})$	\(q+(0.156434 + 0.987688i) q^{2} +(-0.282741 + 1.70882i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-0.103560 + 2.23367i) q^{5} +(-1.73201 - 0.0119417i) q^{6} +(2.28673 - 2.28673i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-2.84012 - 0.966305i) q^{9} +(-2.22237 + 0.247138i) q^{10} +(-2.43923 + 3.35732i) q^{11} +(-0.259151 - 1.71255i) q^{12} +(-2.10294 - 0.333073i) q^{13} +(2.61630 + 1.90085i) q^{14} +(-3.78765 - 0.808514i) q^{15} +(0.809017 - 0.587785i) q^{16} +(4.19457 - 2.13724i) q^{17} +(0.510116 - 2.95631i) q^{18} +(7.55516 + 2.45482i) q^{19} +(-0.591750 - 2.15635i) q^{20} +(3.26105 + 4.55415i) q^{21} +(-3.69756 - 1.88400i) q^{22} +(3.35168 - 0.530854i) q^{23} +(1.65093 - 0.523863i) q^{24} +(-4.97855 - 0.462637i) q^{25} -2.12915i q^{26} +(2.45425 - 4.58003i) q^{27} +(-1.46817 + 2.88144i) q^{28} +(0.0799714 + 0.246127i) q^{29} +(0.206041 - 3.86750i) q^{30} +(-0.605045 + 1.86214i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-5.04737 - 5.11745i) q^{33} +(2.76710 + 3.80859i) q^{34} +(4.87098 + 5.34460i) q^{35} +(2.99971 + 0.0413664i) q^{36} +(0.925865 - 5.84568i) q^{37} +(-1.24271 + 7.84617i) q^{38} +(1.16375 - 3.49937i) q^{39} +(2.03723 - 0.921792i) q^{40} +(-2.94138 - 4.04846i) q^{41} +(-3.98794 + 3.93333i) q^{42} +(6.41535 + 6.41535i) q^{43} +(1.28238 - 3.94676i) q^{44} +(2.45253 - 6.24381i) q^{45} +(1.04864 + 3.22737i) q^{46} +(1.85197 - 3.63470i) q^{47} +(0.775676 + 1.54865i) q^{48} -3.45825i q^{49} +(-0.321875 - 4.98963i) q^{50} +(2.46618 + 7.77205i) q^{51} +(2.10294 - 0.333073i) q^{52} +(-6.16604 - 3.14175i) q^{53} +(4.90757 + 1.70756i) q^{54} +(-7.24652 - 5.79612i) q^{55} +(-3.07564 - 0.999337i) q^{56} +(-6.33100 + 12.2163i) q^{57} +(-0.230586 + 0.117490i) q^{58} +(-5.82928 + 4.23522i) q^{59} +(3.85212 - 0.401506i) q^{60} +(-5.87923 - 4.27151i) q^{61} +(-1.93386 - 0.306293i) q^{62} +(-8.70425 + 4.28489i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(0.961755 - 4.66278i) q^{65} +(4.26487 - 5.78578i) q^{66} +(-1.94227 - 3.81192i) q^{67} +(-3.32883 + 3.32883i) q^{68} +(-0.0405238 + 5.87750i) q^{69} +(-4.51682 + 5.64709i) q^{70} +(10.3128 - 3.35084i) q^{71} +(0.428402 + 2.96925i) q^{72} +(0.126822 + 0.800725i) q^{73} +5.91855 q^{74} +(2.19820 - 8.37663i) q^{75} -7.94397 q^{76} +(2.09941 + 13.2551i) q^{77} +(3.63833 + 0.601998i) q^{78} +(-3.93956 + 1.28004i) q^{79} +(1.22914 + 1.86795i) q^{80} +(7.13251 + 5.48883i) q^{81} +(3.53849 - 3.53849i) q^{82} +(-5.20210 - 10.2097i) q^{83} +(-4.50875 - 3.32354i) q^{84} +(4.33950 + 9.59062i) q^{85} +(-5.33279 + 7.33995i) q^{86} +(-0.443197 + 0.0670665i) q^{87} +(4.09878 + 0.649183i) q^{88} +(-13.0522 - 9.48300i) q^{89} +(6.55059 + 1.44559i) q^{90} +(-5.57050 + 4.04720i) q^{91} +(-3.02359 + 1.54060i) q^{92} +(-3.01098 - 1.56041i) q^{93} +(3.87966 + 1.26058i) q^{94} +(-6.26567 + 16.6215i) q^{95} +(-1.40824 + 1.00839i) q^{96} +(0.292688 + 0.149132i) q^{97} +(3.41567 - 0.540989i) q^{98} +(10.1719 - 7.17812i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q + 4 * q^3 + 4 * q^7	$ 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) $ 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{19}{20}\right)$

Coefficient data

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

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

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

$2$	0.156434	+	0.987688i	0.110616	+	0.698401i
$2$	0.156434	+	0.987688i	0.110616	+	0.698401i
$3$	−0.282741	+	1.70882i	−0.163240	+	0.986586i
$3$	−0.282741	+	1.70882i	−0.163240	+	0.986586i
$4$	−0.951057	+	0.309017i	−0.475528	+	0.154508i
$5$	−0.103560	+	2.23367i	−0.0463134	+	0.998927i
$5$	−0.103560	+	2.23367i	−0.0463134	+	0.998927i
$6$	−1.73201	−	0.0119417i	−0.707090	−	0.00487519i
$7$	2.28673	−	2.28673i	0.864302	−	0.864302i	−0.127533	−	0.991834i	$-0.540706\pi$
$7$	2.28673	−	2.28673i	0.864302	−	0.864302i	0.991834	+	0.127533i	$0.0407057\pi$
$8$	−0.453990	−	0.891007i	−0.160510	−	0.315018i
$9$	−2.84012	−	0.966305i	−0.946705	−	0.322102i
$10$	−2.22237	+	0.247138i	−0.702775	+	0.0781518i
$11$	−2.43923	+	3.35732i	−0.735456	+	1.01227i	0.263411	+	0.964684i	$0.415153\pi$
$11$	−2.43923	+	3.35732i	−0.735456	+	1.01227i	−0.998867	+	0.0475851i	$0.984847\pi$
$12$	−0.259151	−	1.71255i	−0.0748105	−	0.494372i
$13$	−2.10294	−	0.333073i	−0.583250	−	0.0923778i	−0.142165	−	0.989843i	$-0.545406\pi$
$13$	−2.10294	−	0.333073i	−0.583250	−	0.0923778i	−0.441085	+	0.897465i	$0.645406\pi$
$14$	2.61630	+	1.90085i	0.699235	+	0.508024i
$15$	−3.78765	−	0.808514i	−0.977967	−	0.208757i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	4.19457	−	2.13724i	1.01733	−	0.518357i	0.135928	−	0.990719i	$-0.456598\pi$
$17$	4.19457	−	2.13724i	1.01733	−	0.518357i	0.881405	+	0.472361i	$0.156598\pi$
$18$	0.510116	−	2.95631i	0.120235	−	0.696809i
$19$	7.55516	+	2.45482i	1.73327	+	0.563175i	0.993916	−	0.110139i	$-0.0351295\pi$
$19$	7.55516	+	2.45482i	1.73327	+	0.563175i	0.739357	+	0.673313i	$0.235129\pi$
$20$	−0.591750	−	2.15635i	−0.132319	−	0.482174i
$21$	3.26105	+	4.55415i	0.711619	+	0.993797i
$22$	−3.69756	−	1.88400i	−0.788323	−	0.401671i
$23$	3.35168	−	0.530854i	0.698873	−	0.110691i	0.203120	−	0.979154i	$-0.434892\pi$
$23$	3.35168	−	0.530854i	0.698873	−	0.110691i	0.495754	+	0.868463i	$0.334892\pi$
$24$	1.65093	−	0.523863i	0.336995	−	0.106933i
$25$	−4.97855	−	0.462637i	−0.995710	−	0.0925275i
$26$		−	2.12915i		−	0.417561i
$27$	2.45425	−	4.58003i	0.472322	−	0.881426i
$28$	−1.46817	+	2.88144i	−0.277458	+	0.544542i
$29$	0.0799714	+	0.246127i	0.0148503	+	0.0457046i	0.958207	−	0.286075i	$-0.0923508\pi$
$29$	0.0799714	+	0.246127i	0.0148503	+	0.0457046i	−0.943357	+	0.331780i	$0.892351\pi$
$30$	0.206041	−	3.86750i	0.0376177	−	0.706105i
$31$	−0.605045	+	1.86214i	−0.108669	+	0.334450i	−0.990574	−	0.136978i	$-0.956261\pi$
$31$	−0.605045	+	1.86214i	−0.108669	+	0.334450i	0.881905	+	0.471427i	$0.156261\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−5.04737	−	5.11745i	−0.878634	−	0.890834i
$34$	2.76710	+	3.80859i	0.474555	+	0.653168i
$35$	4.87098	+	5.34460i	0.823346	+	0.903403i
$36$	2.99971	+	0.0413664i	0.499952	+	0.00689440i
$37$	0.925865	−	5.84568i	0.152211	−	0.961025i	−0.786817	−	0.617186i	$-0.788273\pi$
$37$	0.925865	−	5.84568i	0.152211	−	0.961025i	0.939029	−	0.343839i	$-0.111727\pi$
$38$	−1.24271	+	7.84617i	−0.201594	+	1.27282i
$39$	1.16375	−	3.49937i	0.186349	−	0.560347i
$40$	2.03723	−	0.921792i	0.322114	−	0.145748i
$41$	−2.94138	−	4.04846i	−0.459366	−	0.632264i	0.515011	−	0.857184i	$-0.327788\pi$
$41$	−2.94138	−	4.04846i	−0.459366	−	0.632264i	−0.974377	+	0.224920i	$0.927788\pi$
$42$	−3.98794	+	3.93333i	−0.615353	+	0.606925i
$43$	6.41535	+	6.41535i	0.978332	+	0.978332i	0.999770	−	0.0214378i	$-0.00682438\pi$
$43$	6.41535	+	6.41535i	0.978332	+	0.978332i	−0.0214378	+	0.999770i	$0.506824\pi$
$44$	1.28238	−	3.94676i	0.193326	−	0.594997i
$45$	2.45253	−	6.24381i	0.365601	−	0.930772i
$46$	1.04864	+	3.22737i	0.154613	+	0.475850i
$47$	1.85197	−	3.63470i	0.270138	−	0.530175i	−0.715590	−	0.698520i	$-0.753842\pi$
$47$	1.85197	−	3.63470i	0.270138	−	0.530175i	0.985728	+	0.168345i	$0.0538423\pi$
$48$	0.775676	+	1.54865i	0.111959	+	0.223529i
$49$		−	3.45825i		−	0.494035i
$50$	−0.321875	−	4.98963i	−0.0455201	−	0.705640i
$51$	2.46618	+	7.77205i	0.345334	+	1.08830i
$52$	2.10294	−	0.333073i	0.291625	−	0.0461889i
$53$	−6.16604	−	3.14175i	−0.846970	−	0.431553i	−0.0240506	−	0.999711i	$-0.507656\pi$
$53$	−6.16604	−	3.14175i	−0.846970	−	0.431553i	−0.822920	+	0.568158i	$0.807656\pi$
$54$	4.90757	+	1.70756i	0.667835	+	0.232370i
$55$	−7.24652	−	5.79612i	−0.977121	−	0.781549i
$56$	−3.07564	−	0.999337i	−0.411000	−	0.133542i
$57$	−6.33100	+	12.2163i	−0.838561	+	1.61809i
$58$	−0.230586	+	0.117490i	−0.0302775	+	0.0154271i
$59$	−5.82928	+	4.23522i	−0.758908	+	0.551379i	−0.898575	−	0.438820i	$-0.855397\pi$
$59$	−5.82928	+	4.23522i	−0.758908	+	0.551379i	0.139667	+	0.990198i	$0.455397\pi$
$60$	3.85212	−	0.401506i	0.497306	−	0.0518342i
$61$	−5.87923	−	4.27151i	−0.752758	−	0.546911i	0.143922	−	0.989589i	$-0.454029\pi$
$61$	−5.87923	−	4.27151i	−0.752758	−	0.546911i	−0.896681	+	0.442678i	$0.854029\pi$
$62$	−1.93386	−	0.306293i	−0.245600	−	0.0388993i
$63$	−8.70425	+	4.28489i	−1.09663	+	0.539846i
$64$	−0.587785	+	0.809017i	−0.0734732	+	0.101127i
$65$	0.961755	−	4.66278i	0.119291	−	0.578346i
$66$	4.26487	−	5.78578i	0.524969	−	0.712180i
$67$	−1.94227	−	3.81192i	−0.237286	−	0.465700i	0.741400	−	0.671064i	$-0.234162\pi$
$67$	−1.94227	−	3.81192i	−0.237286	−	0.465700i	−0.978686	+	0.205363i	$0.934162\pi$
$68$	−3.32883	+	3.32883i	−0.403680	+	0.403680i
$69$	−0.0405238	+	5.87750i	−0.00487849	+	0.707568i
$70$	−4.51682	+	5.64709i	−0.539863	+	0.674956i
$71$	10.3128	−	3.35084i	1.22391	−	0.397671i	0.375403	−	0.926862i	$-0.377504\pi$
$71$	10.3128	−	3.35084i	1.22391	−	0.397671i	0.848503	+	0.529191i	$0.177504\pi$
$72$	0.428402	+	2.96925i	0.0504876	+	0.349930i
$73$	0.126822	+	0.800725i	0.0148434	+	0.0937177i	0.993998	−	0.109399i	$-0.0348928\pi$
$73$	0.126822	+	0.800725i	0.0148434	+	0.0937177i	−0.979154	+	0.203117i	$0.934893\pi$
$74$	5.91855			0.688018
$75$	2.19820	−	8.37663i	0.253826	−	0.967250i
$76$	−7.94397			−0.911236
$77$	2.09941	+	13.2551i	0.239250	+	1.51056i
$78$	3.63833	+	0.601998i	0.411960	+	0.0681629i
$79$	−3.93956	+	1.28004i	−0.443235	+	0.144016i	−0.522128	−	0.852867i	$-0.674862\pi$
$79$	−3.93956	+	1.28004i	−0.443235	+	0.144016i	0.0788925	+	0.996883i	$0.474862\pi$
$80$	1.22914	+	1.86795i	0.137422	+	0.208843i
$81$	7.13251	+	5.48883i	0.792501	+	0.609870i
$82$	3.53849	−	3.53849i	0.390760	−	0.390760i
$83$	−5.20210	−	10.2097i	−0.571005	−	1.12066i	−0.978267	−	0.207349i	$-0.933517\pi$
$83$	−5.20210	−	10.2097i	−0.571005	−	1.12066i	0.407262	−	0.913311i	$-0.366483\pi$
$84$	−4.50875	−	3.32354i	−0.491945	−	0.362627i
$85$	4.33950	+	9.59062i	0.470685	+	1.04025i
$86$	−5.33279	+	7.33995i	−0.575049	+	0.791488i
$87$	−0.443197	+	0.0670665i	−0.0475157	+	0.00719029i
$88$	4.09878	+	0.649183i	0.436931	+	0.0692031i
$89$	−13.0522	−	9.48300i	−1.38353	−	1.00520i	−0.996540	−	0.0831132i	$-0.973514\pi$
$89$	−13.0522	−	9.48300i	−1.38353	−	1.00520i	−0.386993	−	0.922083i	$-0.626486\pi$
$90$	6.55059	+	1.44559i	0.690493	+	0.152378i
$91$	−5.57050	+	4.04720i	−0.583947	+	0.424262i
$92$	−3.02359	+	1.54060i	−0.315231	+	0.160618i
$93$	−3.01098	−	1.56041i	−0.312224	−	0.161807i
$94$	3.87966	+	1.26058i	0.400156	+	0.130019i
$95$	−6.26567	+	16.6215i	−0.642844	+	1.70533i
$96$	−1.40824	+	1.00839i	−0.143728	+	0.102918i
$97$	0.292688	+	0.149132i	0.0297179	+	0.0151420i	0.468786	−	0.883312i	$-0.344691\pi$
$97$	0.292688	+	0.149132i	0.0297179	+	0.0151420i	−0.439068	+	0.898454i	$0.644691\pi$
$98$	3.41567	−	0.540989i	0.345035	−	0.0546481i
$99$	10.1719	−	7.17812i	1.02231	−	0.721429i
$100$	4.87785	−	1.09846i	0.487785	−	0.109846i
$101$			1.17314i			0.116731i	0.998295	+	0.0583657i	$0.0185890\pi$
$101$			1.17314i			0.116731i	−0.998295	+	0.0583657i	$0.981411\pi$
$102$	−7.29056	+	3.65163i	−0.721873	+	0.361566i
$103$	4.46181	−	8.75679i	0.439635	−	0.862832i	−0.559780	−	0.828641i	$-0.689115\pi$
$103$	4.46181	−	8.75679i	0.439635	−	0.862832i	0.999415	−	0.0341911i	$-0.0108855\pi$
$104$	0.657944	+	2.02494i	0.0645168	+	0.198562i
$105$	−10.5102	+	6.81248i	−1.02569	+	0.664830i
$106$	2.13849	−	6.58160i	0.207709	−	0.639261i
$107$	−8.52875	−	8.52875i	−0.824506	−	0.824506i	0.162245	−	0.986751i	$-0.448127\pi$
$107$	−8.52875	−	8.52875i	−0.824506	−	0.824506i	−0.986751	+	0.162245i	$0.948127\pi$
$108$	−0.918829	+	5.11427i	−0.0884144	+	0.492121i
$109$	2.25230	+	3.10003i	0.215732	+	0.296929i	0.903144	−	0.429339i	$-0.141253\pi$
$109$	2.25230	+	3.10003i	0.215732	+	0.296929i	−0.687412	+	0.726268i	$0.741253\pi$
$110$	4.59116	−	8.06402i	0.437749	−	0.768874i
$111$	9.72743	+	3.23495i	0.923287	+	0.307048i
$112$	0.505897	−	3.19411i	0.0478027	−	0.301815i
$113$	−1.69932	+	10.7291i	−0.159858	+	1.00930i	0.769102	+	0.639126i	$0.220704\pi$
$113$	−1.69932	+	10.7291i	−0.159858	+	1.00930i	−0.928960	+	0.370179i	$0.879296\pi$
$114$	−13.0563	−	4.34200i	−1.22283	−	0.406665i
$115$	0.838652	+	7.54152i	0.0782047	+	0.703250i
$116$	−0.152115	−	0.209368i	−0.0141235	−	0.0194393i
$117$	5.65074	+	2.97805i	0.522411	+	0.275320i
$118$	−5.09498	−	5.09498i	−0.469031	−	0.469031i
$119$	4.70456	−	14.4791i	0.431266	−	1.32730i
$120$	0.999166	+	3.74188i	0.0912110	+	0.341585i
$121$	−1.92253	−	5.91693i	−0.174775	−	0.537903i
$122$	3.29921	−	6.47506i	0.298696	−	0.586224i
$123$	7.74973	−	3.88162i	0.698770	−	0.349994i
$124$		−	1.95797i		−	0.175831i
$125$	1.54896	−	11.0725i	0.138543	−	0.990356i
$126$	−5.59378	−	7.92678i	−0.498334	−	0.706173i
$127$	8.37033	−	1.32573i	0.742747	−	0.117640i	0.226418	−	0.974030i	$-0.427298\pi$
$127$	8.37033	−	1.32573i	0.742747	−	0.117640i	0.516328	+	0.856391i	$0.327298\pi$
$128$	−0.891007	−	0.453990i	−0.0787546	−	0.0401275i
$129$	−12.7766	+	9.14879i	−1.12491	+	0.805506i
$130$	4.75582	+	0.220495i	0.417113	+	0.0193387i
$131$	−1.25649	−	0.408257i	−0.109780	−	0.0356696i	0.253612	−	0.967306i	$-0.418381\pi$
$131$	−1.25649	−	0.408257i	−0.109780	−	0.0356696i	−0.363392	+	0.931636i	$0.618381\pi$
$132$	6.38171	+	3.30726i	0.555457	+	0.287860i
$133$	22.8901	−	11.6631i	1.98482	−	1.01132i
$134$	3.46115	−	2.51467i	0.298998	−	0.217235i
$135$	9.97610	+	5.95630i	0.858606	+	0.512637i
$136$	−3.80859	−	2.76710i	−0.326584	−	0.237277i
$137$	11.0215	+	1.74563i	0.941627	+	0.149139i	0.608331	−	0.793683i	$-0.291839\pi$
$137$	11.0215	+	1.74563i	0.941627	+	0.149139i	0.333296	+	0.942822i	$0.391839\pi$
$138$	−5.81148	+	0.879419i	−0.494706	+	0.0748611i
$139$	−8.50366	+	11.7043i	−0.721271	+	0.992744i	0.278210	+	0.960520i	$0.410259\pi$
$139$	−8.50366	+	11.7043i	−0.721271	+	0.992744i	−0.999481	+	0.0322239i	$0.989741\pi$
$140$	−6.28415	−	3.57781i	−0.531108	−	0.302380i
$141$	5.68741	+	4.19236i	0.478966	+	0.353060i
$142$	4.92286	+	9.66166i	0.413117	+	0.810788i
$143$	6.24779	−	6.24779i	0.522466	−	0.522466i
$144$	−2.86568	+	0.887621i	−0.238807	+	0.0739684i
$145$	−0.558047	+	0.153141i	−0.0463433	+	0.0127176i
$146$	−0.771027	+	0.250522i	−0.0638106	+	0.0207333i
$147$	5.90951	+	0.977787i	0.487408	+	0.0806465i
$148$	0.925865	+	5.84568i	0.0761057	+	0.480512i
$149$	−0.726481			−0.0595157			−0.0297578	−	0.999557i	$-0.509474\pi$
$149$	−0.726481			−0.0595157			−0.0297578	+	0.999557i	$0.509474\pi$
$150$	8.61737	+	0.860745i	0.703606	+	0.0702795i
$151$	6.70958			0.546018			0.273009	−	0.962012i	$-0.411981\pi$
$151$	6.70958			0.546018			0.273009	+	0.962012i	$0.411981\pi$
$152$	−1.24271	−	7.84617i	−0.100797	−	0.636408i
$153$	−13.9783	+	2.01678i	−1.13008	+	0.163047i
$154$	−12.7635	+	4.14712i	−1.02851	+	0.334184i
$155$	−4.09674	−	1.54431i	−0.329058	−	0.124042i
$156$	−0.0254258	+	3.68771i	−0.00203569	+	0.295253i
$157$	−3.31755	+	3.31755i	−0.264770	+	0.264770i	−0.826988	−	0.562219i	$-0.809948\pi$
$157$	−3.31755	+	3.31755i	−0.264770	+	0.264770i	0.562219	+	0.826988i	$0.309948\pi$
$158$	−1.88056	−	3.69082i	−0.149610	−	0.293626i
$159$	7.11207	−	9.64833i	0.564024	−	0.765162i
$160$	−1.65267	+	1.50621i	−0.130655	+	0.119077i
$161$	6.45046	−	8.87829i	0.508367	−	0.699708i
$162$	−4.30549	+	7.90334i	−0.338271	+	0.620945i
$163$	−2.78576	−	0.441222i	−0.218198	−	0.0345592i	0.0463782	−	0.998924i	$-0.485232\pi$
$163$	−2.78576	−	0.441222i	−0.218198	−	0.0345592i	−0.264576	+	0.964365i	$0.585232\pi$
$164$	4.04846	+	2.94138i	0.316132	+	0.229683i
$165$	11.9534	−	10.7442i	0.930571	−	0.836434i
$166$	9.27021	−	6.73520i	0.719508	−	0.522753i
$167$	−12.5922	+	6.41606i	−0.974416	+	0.496490i	−0.867316	−	0.497759i	$-0.834157\pi$
$167$	−12.5922	+	6.41606i	−0.974416	+	0.496490i	−0.107100	+	0.994248i	$0.534157\pi$
$168$	2.57729	−	4.97316i	0.198842	−	0.383687i
$169$	−8.05232	−	2.61636i	−0.619409	−	0.201258i
$170$	−8.79370	+	5.78638i	−0.674446	+	0.443795i
$171$	−19.0854	−	14.2726i	−1.45950	−	1.09145i
$172$	−8.08382	−	4.11891i	−0.616385	−	0.314064i
$173$	23.5254	−	3.72606i	1.78860	−	0.283287i	0.827902	−	0.560873i	$-0.189534\pi$
$173$	23.5254	−	3.72606i	1.78860	−	0.283287i	0.960701	+	0.277586i	$0.0895345\pi$
$174$	−0.135572	−	0.427249i	−0.0102777	−	0.0323897i
$175$	−12.4425	+	10.3267i	−0.940566	+	0.780622i
$176$			4.14987i			0.312808i
$177$	−5.58905	−	11.1586i	−0.420098	−	0.838735i
$178$	7.32443	−	14.3750i	0.548989	−	1.07745i
$179$	5.27300	+	16.2286i	0.394122	+	1.21298i	0.929643	+	0.368462i	$0.120116\pi$
$179$	5.27300	+	16.2286i	0.394122	+	1.21298i	−0.535520	+	0.844522i	$0.679884\pi$
$180$	−0.403049	+	6.69608i	−0.0300415	+	0.499097i
$181$	4.21277	−	12.9656i	0.313133	−	0.963723i	−0.663384	−	0.748279i	$-0.730880\pi$
$181$	4.21277	−	12.9656i	0.313133	−	0.963723i	0.976516	−	0.215444i	$-0.0691198\pi$
$182$	−4.86879	−	4.86879i	−0.360899	−	0.360899i
$183$	8.96153	−	8.83880i	0.662456	−	0.653383i
$184$	−1.99462	−	2.74537i	−0.147046	−	0.202391i
$185$	12.9614	+	2.67346i	0.952944	+	0.196556i
$186$	1.07018	−	3.21801i	0.0784694	−	0.235956i
$187$	−3.05614	+	19.2957i	−0.223487	+	1.41104i
$188$	−0.638146	+	4.02909i	−0.0465415	+	0.293852i
$189$	−4.86106	−	16.0855i	−0.353590	−	1.17005i
$190$	−17.3970	−	3.58835i	−1.26211	−	0.260326i
$191$	−2.54587	−	3.50409i	−0.184213	−	0.253547i	0.706916	−	0.707297i	$-0.250086\pi$
$191$	−2.54587	−	3.50409i	−0.184213	−	0.253547i	−0.891129	+	0.453750i	$0.850086\pi$
$192$	−1.21627	−	1.23316i	−0.0877768	−	0.0889956i
$193$	−3.55219	−	3.55219i	−0.255692	−	0.255692i	0.567607	−	0.823299i	$-0.307869\pi$
$193$	−3.55219	−	3.55219i	−0.255692	−	0.255692i	−0.823299	+	0.567607i	$0.807869\pi$
$194$	−0.101509	+	0.312414i	−0.00728794	+	0.0224300i
$195$	7.69591	+	2.96182i	0.551115	+	0.212100i
$196$	1.06866	+	3.28899i	0.0763326	+	0.234928i
$197$	−5.35950	+	10.5186i	−0.381849	+	0.749421i	−0.999309	−	0.0371819i	$-0.988162\pi$
$197$	−5.35950	+	10.5186i	−0.381849	+	0.749421i	0.617460	+	0.786603i	$0.288162\pi$
$198$	8.68098	+	8.92375i	0.616931	+	0.634184i
$199$			21.2504i			1.50640i	0.657791	+	0.753200i	$0.271491\pi$
$199$			21.2504i			1.50640i	−0.657791	+	0.753200i	$0.728509\pi$
$200$	1.84800	+	4.64595i	0.130673	+	0.328519i
$201$	7.06304	−	2.24120i	0.498188	−	0.158082i
$202$	−1.15869	+	0.183519i	−0.0815254	+	0.0129124i
$203$	0.745698	+	0.379952i	0.0523377	+	0.0266674i
$204$	−4.74717	−	6.62956i	−0.332368	−	0.464162i
$205$	9.34753	−	6.15081i	0.652860	−	0.429591i
$206$	9.34696	+	3.03701i	0.651234	+	0.211599i
$207$	−10.0321	−	1.73106i	−0.697281	−	0.120317i
$208$	−1.89709	+	0.966615i	−0.131539	+	0.0670227i
$209$	−26.6704	+	19.3772i	−1.84483	+	1.34035i
$210$	−8.37276	−	9.31508i	−0.577775	−	0.642801i
$211$	−13.9066	−	10.1037i	−0.957368	−	0.695568i	−0.00482966	−	0.999988i	$-0.501537\pi$
$211$	−13.9066	−	10.1037i	−0.957368	−	0.695568i	−0.952538	+	0.304420i	$0.901537\pi$
$212$	6.83510	+	1.08257i	0.469437	+	0.0743515i
$213$	2.81012	+	18.5701i	0.192546	+	1.27240i
$214$	7.08956	−	9.75794i	0.484632	−	0.667039i
$215$	−14.9941	+	13.6654i	−1.02259	+	0.931973i
$216$	−5.19504	−	0.107469i	−0.353478	−	0.00731232i
$217$	2.87463	+	5.64177i	0.195142	+	0.382988i
$218$	−2.70953	+	2.70953i	−0.183512	+	0.183512i
$219$	−1.40415	−	0.00968123i	−0.0948837	−	0.000654197i
$220$	8.68295	+	3.27314i	0.585405	+	0.220675i
$221$	−9.53279	+	3.09739i	−0.641245	+	0.208353i
$222$	−1.67342	+	10.1137i	−0.112312	+	0.678789i
$223$	1.41010	+	8.90303i	0.0944273	+	0.596191i	0.988844	+	0.148956i	$0.0475912\pi$
$223$	1.41010	+	8.90303i	0.0944273	+	0.596191i	−0.894417	+	0.447235i	$0.852409\pi$
$224$	3.23392			0.216075
$225$	13.6926	+	6.12474i	0.912841	+	0.408316i
$226$	−10.8628			−0.722582
$227$	−0.146769	−	0.926664i	−0.00974142	−	0.0615049i	0.982339	−	0.187111i	$-0.0599124\pi$
$227$	−0.146769	−	0.926664i	−0.00974142	−	0.0615049i	−0.992080	+	0.125606i	$0.959912\pi$
$228$	2.24608	−	13.5748i	0.148751	−	0.899013i
$229$	12.7060	−	4.12842i	0.839634	−	0.272814i	0.142536	−	0.989790i	$-0.454474\pi$
$229$	12.7060	−	4.12842i	0.839634	−	0.272814i	0.697098	+	0.716976i	$0.254474\pi$
$230$	−7.31747	+	2.00808i	−0.482500	+	0.132409i
$231$	−23.2442	−	0.160262i	−1.52936	−	0.0105445i
$232$	0.182994	−	0.182994i	0.0120142	−	0.0120142i
$233$	7.94675	+	15.5964i	0.520609	+	1.02175i	0.990303	+	0.138924i	$0.0443643\pi$
$233$	7.94675	+	15.5964i	0.520609	+	1.02175i	−0.469694	+	0.882829i	$0.655636\pi$
$234$	−2.05741	+	6.04704i	−0.134497	+	0.395307i
$235$	7.92692	+	4.51310i	0.517095	+	0.294402i
$236$	4.23522	−	5.82928i	0.275689	−	0.379454i
$237$	−1.07348	−	7.09391i	−0.0697302	−	0.460799i
$238$	15.0368	+	2.38160i	0.974693	+	0.154376i
$239$	22.7805	+	16.5510i	1.47354	+	1.07059i	0.979567	+	0.201119i	$0.0644576\pi$
$239$	22.7805	+	16.5510i	1.47354	+	1.07059i	0.493978	+	0.869474i	$0.335542\pi$
$240$	−3.53951	+	1.57222i	−0.228474	+	0.101487i
$241$	−24.2497	+	17.6185i	−1.56206	+	1.13491i	−0.627771	+	0.778398i	$0.716032\pi$
$241$	−24.2497	+	17.6185i	−1.56206	+	1.13491i	−0.934293	+	0.356507i	$0.883968\pi$
$242$	5.54333	−	2.82447i	0.356339	−	0.181564i
$243$	−11.3961	+	10.6362i	−0.731058	+	0.682315i
$244$	6.91145	+	2.24567i	0.442460	+	0.143764i
$245$	7.72457	+	0.358136i	0.493505	+	0.0228805i
$246$	5.04615	+	7.04710i	0.321731	+	0.449307i
$247$	−15.0704	−	7.67876i	−0.958908	−	0.488588i
$248$	1.93386	−	0.306293i	0.122800	−	0.0194496i
$249$	18.9174	−	6.00274i	1.19884	−	0.380408i
$250$	11.1785	−	0.202237i	0.706991	−	0.0127906i
$251$		−	4.80121i		−	0.303050i	−0.988453	−	0.151525i	$-0.951582\pi$
$251$		−	4.80121i		−	0.303050i	0.988453	−	0.151525i	$-0.0484184\pi$
$252$	6.95412	−	6.76494i	0.438069	−	0.426151i
$253$	−6.39328	+	12.5475i	−0.401942	+	0.788856i
$254$	2.61882	+	8.05989i	0.164319	+	0.505722i
$255$	−17.6156	+	4.70376i	−1.10313	+	0.294561i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−1.72232	−	1.72232i	−0.107435	−	0.107435i	0.651346	−	0.758781i	$-0.274205\pi$
$257$	−1.72232	−	1.72232i	−0.107435	−	0.107435i	−0.758781	+	0.651346i	$0.774205\pi$
$258$	−11.0348	−	11.1881i	−0.686999	−	0.696539i
$259$	−11.2503	−	15.4847i	−0.699059	−	0.962172i
$260$	0.526194	+	4.73176i	0.0326332	+	0.293451i
$261$	0.0107053	−	0.776305i	0.000662643	−	0.0480521i
$262$	0.206673	−	1.30488i	0.0127683	−	0.0806159i
$263$	1.32670	−	8.37644i	0.0818077	−	0.516514i	−0.912423	−	0.409249i	$-0.865791\pi$
$263$	1.32670	−	8.37644i	0.0818077	−	0.516514i	0.994230	−	0.107265i	$-0.0342092\pi$
$264$	−2.26823	+	6.82052i	−0.139600	+	0.419774i
$265$	7.65619	−	13.4475i	0.470316	−	0.826075i
$266$	15.1003	+	20.7838i	0.925859	+	1.27434i
$267$	19.8951	−	19.6226i	1.21756	−	1.20089i
$268$	3.02516	+	3.02516i	0.184791	+	0.184791i
$269$	9.64838	−	29.6947i	0.588272	−	1.81052i	0.00255910	−	0.999997i	$-0.499185\pi$
$269$	9.64838	−	29.6947i	0.588272	−	1.81052i	0.585713	−	0.810519i	$-0.300815\pi$
$270$	−4.32236	+	10.7850i	−0.263051	+	0.656357i
$271$	−4.41195	−	13.5786i	−0.268007	−	0.824840i	−0.990985	−	0.133969i	$-0.957228\pi$
$271$	−4.41195	−	13.5786i	−0.268007	−	0.824840i	0.722979	−	0.690870i	$-0.242772\pi$
$272$	2.13724	−	4.19457i	0.129589	−	0.254333i
$273$	−5.34092	−	10.6633i	−0.323247	−	0.645371i
$274$			11.1588i			0.674130i
$275$	13.6971	−	15.5861i	0.825964	−	0.939876i
$276$	−1.77771	−	5.60236i	−0.107005	−	0.337222i
$277$	−1.01738	+	0.161137i	−0.0611283	+	0.00968177i	−0.186924	−	0.982374i	$-0.559852\pi$
$277$	−1.01738	+	0.161137i	−0.0611283	+	0.00968177i	0.125795	+	0.992056i	$0.459852\pi$
$278$	−12.8904	−	6.56801i	−0.773118	−	0.393923i
$279$	3.51779	−	4.70402i	0.210604	−	0.281623i
$280$	2.55070	−	6.76647i	0.152433	−	0.404374i
$281$	9.41859	+	3.06028i	0.561866	+	0.182561i	0.576160	−	0.817337i	$-0.304550\pi$
$281$	9.41859	+	3.06028i	0.561866	+	0.182561i	−0.0142948	+	0.999898i	$0.504550\pi$
$282$	−3.25104	+	6.27321i	−0.193596	+	0.373564i
$283$	−20.4282	+	10.4087i	−1.21433	+	0.618733i	−0.939430	−	0.342740i	$-0.888645\pi$
$283$	−20.4282	+	10.4087i	−1.21433	+	0.618733i	−0.274901	+	0.961473i	$0.588645\pi$
$284$	−8.77260	+	6.37367i	−0.520558	+	0.378208i
$285$	−26.6316	−	15.4065i	−1.57752	−	0.912600i
$286$	7.14824	+	5.19350i	0.422684	+	0.307098i
$287$	−15.9839	−	2.53160i	−0.943498	−	0.149435i
$288$	−1.32498	−	2.69155i	−0.0780754	−	0.158601i
$289$	3.03429	−	4.17635i	0.178488	−	0.245667i
$290$	−0.238553	−	0.527220i	−0.0140083	−	0.0309594i
$291$	−0.337594	+	0.457984i	−0.0197901	+	0.0268475i
$292$	−0.368053	−	0.722344i	−0.0215387	−	0.0422720i
$293$	−15.8273	+	15.8273i	−0.924643	+	0.924643i	−0.997353	−	0.0727102i	$-0.976835\pi$
$293$	−15.8273	+	15.8273i	−0.924643	+	0.924643i	0.0727102	+	0.997353i	$0.476835\pi$
$294$	−0.0412974	+	5.98972i	−0.00240852	+	0.349327i
$295$	−8.85640	−	13.4593i	−0.515640	−	0.783630i
$296$	−5.62888	+	1.82893i	−0.327172	+	0.106305i
$297$	9.39009	+	19.4115i	0.544869	+	1.12637i
$298$	−0.113647	−	0.717537i	−0.00658338	−	0.0415658i
$299$	−7.22519			−0.417844
$300$	0.497907	+	8.64593i	0.0287466	+	0.499173i
$301$	29.3403			1.69115
$302$	1.04961	+	6.62697i	0.0603982	+	0.381339i
$303$	−2.00468	−	0.331694i	−0.115166	−	0.0190553i
$304$	7.55516	−	2.45482i	0.433318	−	0.140794i
$305$	10.1500	−	12.6899i	0.581187	−	0.726621i
$306$	−4.17864	−	13.4907i	−0.238877	−	0.771213i
$307$	17.9634	−	17.9634i	1.02523	−	1.02523i	0.0255531	−	0.999673i	$-0.491865\pi$
$307$	17.9634	−	17.9634i	1.02523	−	1.02523i	0.999673	−	0.0255531i	$-0.00813470\pi$
$308$	−6.09271	−	11.9576i	−0.347165	−	0.681349i
$309$	13.7022	+	10.1003i	0.779492	+	0.574587i
$310$	0.884428	−	4.28788i	0.0502322	−	0.243535i
$311$	−0.0645141	+	0.0887961i	−0.00365826	+	0.00503516i	−0.810842	−	0.585265i	$-0.800991\pi$
$311$	−0.0645141	+	0.0887961i	−0.00365826	+	0.00503516i	0.807184	+	0.590300i	$0.200991\pi$
$312$	−3.64629	+	0.551773i	−0.206430	+	0.0312380i
$313$	−23.8631	−	3.77954i	−1.34882	−	0.213633i	−0.560122	−	0.828410i	$-0.689246\pi$
$313$	−23.8631	−	3.77954i	−1.34882	−	0.213633i	−0.788701	+	0.614778i	$0.789246\pi$
$314$	−3.79569	−	2.75773i	−0.214203	−	0.155628i
$315$	−8.66962	−	19.8861i	−0.488478	−	1.12046i
$316$	3.35119	−	2.43478i	0.188519	−	0.136967i
$317$	−15.5247	+	7.91021i	−0.871951	+	0.444281i	−0.831906	−	0.554916i	$-0.812750\pi$
$317$	−15.5247	+	7.91021i	−0.871951	+	0.444281i	−0.0400453	+	0.999198i	$0.512750\pi$
$318$	10.6421	+	5.51518i	0.596780	+	0.309276i
$319$	−1.02139	−	0.331871i	−0.0571871	−	0.0185812i
$320$	−1.74620	−	1.39670i	−0.0976158	−	0.0780779i
$321$	16.9855	−	12.1627i	0.948039	−	0.678853i
$322$	9.77806	+	4.98217i	0.544910	+	0.277646i
$323$	36.9372	−	5.85028i	2.05524	−	0.325518i
$324$	−8.47956	−	3.01612i	−0.471087	−	0.167562i
$325$	10.3155	+	2.63112i	0.572201	+	0.145948i
$326$		−	2.82049i		−	0.156212i
$327$	−5.93421	+	2.97227i	−0.328162	+	0.164367i
$328$	−2.27185	+	4.45875i	−0.125442	+	0.246193i
$329$	−4.07661	−	12.5465i	−0.224751	−	0.691712i
$330$	12.4818	+	10.1255i	0.687102	+	0.557389i
$331$	−6.00597	+	18.4845i	−0.330118	+	1.01600i	0.638959	+	0.769240i	$0.279365\pi$
$331$	−6.00597	+	18.4845i	−0.330118	+	1.01600i	−0.969077	+	0.246758i	$0.920635\pi$
$332$	8.10246	+	8.10246i	0.444680	+	0.444680i
$333$	−8.27828	+	15.7078i	−0.453647	+	0.860779i
$334$	−8.30693	−	11.4335i	−0.454535	−	0.625613i
$335$	8.71571	−	3.94363i	0.476190	−	0.215463i
$336$	5.31511	+	1.76759i	0.289963	+	0.0964299i
$337$	1.59645	−	10.0796i	0.0869642	−	0.549070i	−0.905285	−	0.424805i	$-0.860343\pi$
$337$	1.59645	−	10.0796i	0.0869642	−	0.549070i	0.992249	−	0.124265i	$-0.0396574\pi$
$338$	1.32448	−	8.36247i	0.0720425	−	0.454858i
$339$	−17.8535	−	5.93736i	−0.969671	−	0.322473i
$340$	−7.09077	−	7.78024i	−0.384551	−	0.421943i
$341$	−4.77593	−	6.57351i	−0.258631	−	0.355976i
$342$	11.1112	−	21.0832i	0.600826	−	1.14005i
$343$	8.09903	+	8.09903i	0.437306	+	0.437306i
$344$	2.80361	−	8.62863i	0.151161	−	0.465225i
$345$	−13.1242	−	0.699191i	−0.706583	−	0.0376432i
$346$	7.36036	+	22.6529i	0.395696	+	1.21783i
$347$	0.353015	−	0.692830i	0.0189508	−	0.0371931i	−0.881337	−	0.472488i	$-0.843356\pi$
$347$	0.353015	−	0.692830i	0.0189508	−	0.0371931i	0.900288	+	0.435295i	$0.143356\pi$
$348$	0.400781	−	0.200739i	0.0214841	−	0.0107608i
$349$		−	17.4564i		−	0.934420i	−0.884146	−	0.467210i	$-0.845259\pi$
$349$		−	17.4564i		−	0.934420i	0.884146	−	0.467210i	$-0.154741\pi$
$350$	−12.1460	−	10.6739i	−0.649229	−	0.570543i
$351$	−6.68663	+	8.81407i	−0.356906	+	0.470460i
$352$	−4.09878	+	0.649183i	−0.218466	+	0.0346016i
$353$	−17.8715	−	9.10601i	−0.951207	−	0.484664i	−0.0916989	−	0.995787i	$-0.529230\pi$
$353$	−17.8715	−	9.10601i	−0.951207	−	0.484664i	−0.859508	+	0.511123i	$0.829230\pi$
$354$	10.1469	−	7.26583i	0.539304	−	0.386175i
$355$	6.41666	+	23.3824i	0.340561	+	1.24101i
$356$	15.3438	+	4.98551i	0.813220	+	0.264231i
$357$	23.4120	+	12.1331i	1.23910	+	0.642150i
$358$	−15.2039	+	7.74680i	−0.803553	+	0.409431i
$359$	8.90157	−	6.46737i	0.469807	−	0.341335i	−0.327559	−	0.944831i	$-0.606226\pi$
$359$	8.90157	−	6.46737i	0.469807	−	0.341335i	0.797366	+	0.603496i	$0.206226\pi$
$360$	−6.67670	+	0.649411i	−0.351893	+	0.0342270i
$361$	35.6830	+	25.9252i	1.87805	+	1.36449i
$362$	13.4650	+	2.13264i	0.707703	+	0.112089i
$363$	10.6545	−	1.61229i	0.559218	−	0.0846233i
$364$	4.04720	−	5.57050i	0.212131	−	0.291973i
$365$	−1.80169	+	0.200356i	−0.0943046	+	0.0104871i
$366$	10.1319	+	7.46851i	0.529602	+	0.390385i
$367$	−2.78767	−	5.47112i	−0.145515	−	0.285590i	0.806732	−	0.590917i	$-0.201234\pi$
$367$	−2.78767	−	5.47112i	−0.145515	−	0.285590i	−0.952247	+	0.305327i	$0.901234\pi$
$368$	2.39954	−	2.39954i	0.125085	−	0.125085i
$369$	4.44181	+	14.3404i	0.231231	+	0.746530i
$370$	−0.612925	+	13.2201i	−0.0318645	+	0.687279i
$371$	−21.2844	+	6.91571i	−1.10503	+	0.359046i
$372$	3.34581	+	0.553597i	0.173472	+	0.0287026i
$373$	−0.780034	−	4.92494i	−0.0403886	−	0.255004i	0.959230	−	0.282627i	$-0.0912060\pi$
$373$	−0.780034	−	4.92494i	−0.0403886	−	0.255004i	−0.999618	+	0.0276236i	$0.991206\pi$
$374$	−19.5363			−1.01020
$375$	18.4830	+	5.77754i	0.954456	+	0.298351i
$376$	−4.07932			−0.210375
$377$	−0.0861969	−	0.544226i	−0.00443937	−	0.0280291i
$378$	15.1270	−	7.31754i	0.778049	−	0.376373i
$379$	12.3464	−	4.01158i	0.634190	−	0.206061i	0.0257600	−	0.999668i	$-0.491799\pi$
$379$	12.3464	−	4.01158i	0.634190	−	0.206061i	0.608430	+	0.793607i	$0.291799\pi$
$380$	0.822677	−	17.7442i	0.0422025	−	0.910258i
$381$	−0.101202	+	14.6782i	−0.00518475	+	0.751987i
$382$	3.06269	−	3.06269i	0.156701	−	0.156701i
$383$	−10.6277	−	20.8580i	−0.543049	−	1.06579i	−0.985607	−	0.169054i	$-0.945929\pi$
$383$	−10.6277	−	20.8580i	−0.543049	−	1.06579i	0.442558	−	0.896740i	$-0.354071\pi$
$384$	1.02771	−	1.39421i	0.0524451	−	0.0711478i
$385$	−29.8250	+	3.31668i	−1.52002	+	0.169033i
$386$	2.95277	−	4.06414i	0.150292	−	0.206859i
$387$	−12.0212	−	24.4195i	−0.611070	−	1.24131i
$388$	−0.324447	−	0.0513873i	−0.0164713	−	0.00260880i
$389$	13.2509	+	9.62737i	0.671849	+	0.488127i	0.870644	−	0.491914i	$-0.163703\pi$
$389$	13.2509	+	9.62737i	0.671849	+	0.488127i	−0.198794	+	0.980041i	$0.563703\pi$
$390$	−1.72145	+	8.06449i	−0.0871690	+	0.408361i
$391$	12.9243	−	9.39005i	0.653610	−	0.474875i
$392$	−3.08132	+	1.57001i	−0.155630	+	0.0792975i
$393$	1.05290	−	2.03168i	0.0531116	−	0.102484i
$394$	−11.2275	−	3.64805i	−0.565635	−	0.183786i
$395$	−2.45121	−	8.93224i	−0.123334	−	0.449430i
$396$	−7.45588	+	9.97009i	−0.374672	+	0.501016i
$397$	−9.95826	−	5.07399i	−0.499791	−	0.254656i	0.185874	−	0.982574i	$-0.440488\pi$
$397$	−9.95826	−	5.07399i	−0.499791	−	0.254656i	−0.685665	+	0.727918i	$0.740488\pi$
$398$	−20.9888	+	3.32429i	−1.05207	+	0.166632i
$399$	13.4581	+	42.4127i	0.673749	+	2.12329i
$400$	−4.29966	+	2.55204i	−0.214983	+	0.127602i
$401$		−	1.92108i		−	0.0959344i	−0.998849	−	0.0479672i	$-0.984726\pi$
$401$		−	1.92108i		−	0.0959344i	0.998849	−	0.0479672i	$-0.0152743\pi$
$402$	3.31851	+	6.62548i	0.165512	+	0.330449i
$403$	1.89260	−	3.71444i	0.0942771	−	0.185029i
$404$	−0.362519	−	1.11572i	−0.0180360	−	0.0555091i
$405$	−12.9989	+	15.3632i	−0.645919	+	0.763406i
$406$	−0.258621	+	0.795954i	−0.0128352	+	0.0395026i
$407$	17.3674	+	17.3674i	0.860870	+	0.860870i
$408$	5.80532	−	5.72582i	0.287406	−	0.283470i
$409$	17.6951	+	24.3552i	0.874965	+	1.20429i	0.977790	+	0.209586i	$0.0672117\pi$
$409$	17.6951	+	24.3552i	0.874965	+	1.20429i	−0.102825	+	0.994699i	$0.532788\pi$
$410$	7.53736	+	8.27025i	0.372244	+	0.408439i
$411$	−6.09918	+	18.3401i	−0.300850	+	0.904651i
$412$	−1.53743	+	9.70698i	−0.0757439	+	0.478228i
$413$	−3.64518	+	23.0148i	−0.179368	+	1.13248i
$414$	0.140375	−	10.1794i	0.00689906	−	0.500291i
$415$	23.3438	−	10.5625i	1.14590	−	0.518490i
$416$	−1.25148	−	1.72252i	−0.0613591	−	0.0844535i
$417$	−17.5962	−	17.8405i	−0.861687	−	0.873652i
$418$	−23.3108	−	23.3108i	−1.14017	−	1.14017i
$419$	−3.90949	+	12.0322i	−0.190991	+	0.587809i	0.809009	+	0.587796i	$0.200004\pi$
$419$	−3.90949	+	12.0322i	−0.190991	+	0.587809i	−1.00000		1.33744e-5i	$0.999996\pi$
$420$	7.89060	−	9.72687i	0.385022	−	0.474623i
$421$	1.01762	+	3.13191i	0.0495958	+	0.152640i	0.972787	−	0.231700i	$-0.0744289\pi$
$421$	1.01762	+	3.13191i	0.0495958	+	0.152640i	−0.923191	+	0.384340i	$0.874429\pi$
$422$	7.80385	−	15.3159i	0.379886	−	0.745567i
$423$	−8.77203	+	8.53339i	−0.426511	+	0.414908i
$424$			6.92030i			0.336080i
$425$	−21.8717	+	8.69980i	−1.06093	+	0.422002i
$426$	−17.9019	+	5.68053i	−0.867350	+	0.275222i
$427$	−23.2120	+	3.67642i	−1.12331	+	0.177914i
$428$	10.7469	+	5.47580i	0.519469	+	0.264683i
$429$	8.90983	+	12.4428i	0.430171	+	0.600746i
$430$	−15.8428	−	12.6718i	−0.764006	−	0.611089i
$431$	−20.9947	−	6.82158i	−1.01128	−	0.328584i	−0.243914	−	0.969797i	$-0.578432\pi$
$431$	−20.9947	−	6.82158i	−1.01128	−	0.328584i	−0.767363	+	0.641213i	$0.778432\pi$
$432$	−0.706538	−	5.14789i	−0.0339933	−	0.247678i
$433$	4.32426	−	2.20332i	0.207811	−	0.105885i	−0.346988	−	0.937870i	$-0.612795\pi$
$433$	4.32426	−	2.20332i	0.207811	−	0.105885i	0.554798	+	0.831985i	$0.312795\pi$
$434$	−5.12262	+	3.72180i	−0.245894	+	0.178652i
$435$	−0.103907	−	0.996900i	−0.00498196	−	0.0477977i
$436$	−3.10003	−	2.25230i	−0.148465	−	0.107866i
$437$	26.6256	+	4.21709i	1.27368	+	0.201731i
$438$	−0.210095	−	1.38838i	−0.0100387	−	0.0663392i
$439$	18.6603	−	25.6837i	0.890609	−	1.22582i	−0.0827589	−	0.996570i	$-0.526373\pi$
$439$	18.6603	−	25.6837i	0.890609	−	1.22582i	0.973368	−	0.229249i	$-0.0736269\pi$
$440$	−1.87453	+	9.08808i	−0.0893647	+	0.433257i
$441$	−3.34172	+	9.82182i	−0.159129	+	0.467706i
$442$	−4.55051	−	8.93089i	−0.216446	−	0.424799i
$443$	7.52521	−	7.52521i	0.357533	−	0.357533i	−0.505370	−	0.862903i	$-0.668644\pi$
$443$	7.52521	−	7.52521i	0.357533	−	0.357533i	0.862903	+	0.505370i	$0.168644\pi$
$444$	−10.2510	−	0.0706778i	−0.486490	−	0.00335422i
$445$	22.5336	−	28.1723i	1.06819	−	1.33549i
$446$	−8.57283	+	2.78548i	−0.405935	+	0.131896i
$447$	0.205406	−	1.24142i	0.00971536	−	0.0587173i
$448$	0.505897	+	3.19411i	0.0239014	+	0.150907i
$449$	−25.0738			−1.18331			−0.591654	−	0.806192i	$-0.701525\pi$
$449$	−25.0738			−1.18331			−0.591654	+	0.806192i	$0.701525\pi$
$450$	−3.90734	+	14.4822i	−0.184194	+	0.682695i
$451$	20.7667			0.977865
$452$	−1.69932	−	10.7291i	−0.0799291	−	0.504652i
$453$	−1.89707	+	11.4654i	−0.0891321	+	0.538694i
$454$	0.892296	−	0.289924i	0.0418775	−	0.0136068i
$455$	−8.46323	−	12.8618i	−0.396762	−	0.602969i
$456$	13.7590	+	0.0948648i	0.644326	+	0.00444245i
$457$	2.79354	−	2.79354i	0.130676	−	0.130676i	−0.638744	−	0.769420i	$-0.720546\pi$
$457$	2.79354	−	2.79354i	0.130676	−	0.130676i	0.769420	+	0.638744i	$0.220546\pi$
$458$	6.06524	+	11.9037i	0.283410	+	0.556224i
$459$	0.505929	−	24.4566i	0.0236147	−	1.14154i
$460$	−3.12806	−	6.91325i	−0.145847	−	0.322332i
$461$	1.72146	−	2.36939i	0.0801764	−	0.110353i	−0.767045	−	0.641593i	$-0.778274\pi$
$461$	1.72146	−	2.36939i	0.0801764	−	0.110353i	0.847221	+	0.531240i	$0.178274\pi$
$462$	−3.47790	−	22.9831i	−0.161807	−	1.06927i
$463$	−29.8805	−	4.73261i	−1.38867	−	0.219943i	−0.583077	−	0.812417i	$-0.698151\pi$
$463$	−29.8805	−	4.73261i	−1.38867	−	0.219943i	−0.805589	+	0.592474i	$0.798151\pi$
$464$	0.209368	+	0.152115i	0.00971966	+	0.00706175i
$465$	3.79726	−	6.56394i	0.176094	−	0.304395i
$466$	−14.1612	+	10.2887i	−0.656006	+	0.476616i
$467$	−29.7766	+	15.1719i	−1.37790	+	0.702073i	−0.976838	−	0.213980i	$-0.931357\pi$
$467$	−29.7766	+	15.1719i	−1.37790	+	0.702073i	−0.401057	+	0.916053i	$0.631357\pi$
$468$	−6.29444	−	1.08611i	−0.290961	−	0.0502057i
$469$	−13.1583	−	4.27538i	−0.607593	−	0.197419i
$470$	−3.21749	+	8.53533i	−0.148412	+	0.393705i
$471$	−4.73109	−	6.60710i	−0.217997	−	0.304439i
$472$	6.42005	+	3.27118i	0.295507	+	0.150568i
$473$	−37.1869	+	5.88983i	−1.70986	+	0.270815i
$474$	6.83864	−	2.17000i	0.314109	−	0.0996713i
$475$	−36.4781	−	15.7168i	−1.67373	−	0.721134i
$476$			15.2243i			0.697803i
$477$	14.4764	+	14.8812i	0.662827	+	0.681364i
$478$	−12.7835	+	25.0891i	−0.584706	+	1.14755i
$479$	5.54891	+	17.0778i	0.253536	+	0.780303i	0.994115	+	0.108334i	$0.0345515\pi$
$479$	5.54891	+	17.0778i	0.253536	+	0.780303i	−0.740579	+	0.671970i	$0.765448\pi$
$480$	−2.10657	−	3.24998i	−0.0961512	−	0.148341i
$481$	−3.89408	+	11.9847i	−0.177555	+	0.546457i
$482$	−21.1951	−	21.1951i	−0.965408	−	0.965408i
$483$	13.3476	+	13.5329i	0.607336	+	0.615769i
$484$	3.65686	+	5.03324i	0.166221	+	0.228784i
$485$	−0.363422	+	0.638323i	−0.0165021	+	0.0289848i
$486$	−12.2880	−	9.59189i	−0.557396	−	0.435097i
$487$	−4.63925	+	29.2911i	−0.210225	+	1.32731i	0.626388	+	0.779511i	$0.284532\pi$
$487$	−4.63925	+	29.2911i	−0.210225	+	1.32731i	−0.836613	+	0.547794i	$0.815468\pi$
$488$	−1.13683	+	7.17766i	−0.0514619	+	0.324917i
$489$	1.54162	−	4.63561i	0.0697143	−	0.209630i
$490$	0.854663	+	7.68550i	0.0386097	+	0.347195i
$491$	−3.11567	−	4.28835i	−0.140608	−	0.193531i	0.732905	−	0.680331i	$-0.238164\pi$
$491$	−3.11567	−	4.28835i	−0.140608	−	0.193531i	−0.873513	+	0.486800i	$0.838164\pi$
$492$	−6.17095	+	6.08644i	−0.278208	+	0.274398i
$493$	0.861478	+	0.861478i	0.0387990	+	0.0387990i
$494$	5.22669	−	16.0861i	0.235160	−	0.723748i
$495$	14.9801	+	23.4640i	0.673308	+	1.05463i
$496$	0.605045	+	1.86214i	0.0271673	+	0.0836124i
$497$	15.9201	−	31.2450i	0.714116	−	1.40153i
$498$	8.88817	+	17.7454i	0.398288	+	0.795191i
$499$		−	6.85423i		−	0.306837i	−0.988161	−	0.153419i	$-0.950972\pi$
$499$		−	6.85423i		−	0.306837i	0.988161	−	0.153419i	$-0.0490283\pi$
$500$	1.94845	+	11.0092i	0.0871374	+	0.492349i
$501$	−7.40354	−	23.3319i	−0.330766	−	1.04239i
$502$	4.74210	−	0.751075i	0.211650	−	0.0335221i
$503$	15.5468	+	7.92150i	0.693198	+	0.353202i	0.764833	−	0.644229i	$-0.222822\pi$
$503$	15.5468	+	7.92150i	0.693198	+	0.353202i	−0.0716346	+	0.997431i	$0.522822\pi$
$504$	7.76951	+	5.81024i	0.346082	+	0.258809i
$505$	−2.62040	−	0.121490i	−0.116606	−	0.00540623i
$506$	−13.3932	−	4.35170i	−0.595399	−	0.193457i
$507$	6.74759	−	13.0202i	0.299671	−	0.578247i
$508$	−7.55098	+	3.84742i	−0.335021	+	0.170702i
$509$	15.1140	−	10.9809i	0.669914	−	0.486721i	−0.200082	−	0.979779i	$-0.564121\pi$
$509$	15.1140	−	10.9809i	0.669914	−	0.486721i	0.869997	+	0.493058i	$0.164121\pi$
$510$	−7.40153	−	16.6629i	−0.327745	−	0.737844i
$511$	2.12105	+	1.54103i	0.0938296	+	0.0681712i
$512$	0.987688	+	0.156434i	0.0436501	+	0.00691349i
$513$	29.7854	−	28.5781i	1.31506	−	1.26175i
$514$	1.43168	−	1.97054i	0.0631489	−	0.0869170i
$515$	19.0977	+	10.8731i	0.841545	+	0.479124i
$516$	9.32409	−	12.6492i	0.410470	−	0.556849i
$517$	7.68544	+	15.0835i	0.338005	+	0.663373i
$518$	13.5341	−	13.5341i	0.594655	−	0.594655i
$519$	−0.284436	+	41.2541i	−0.0124853	+	1.81085i
$520$	−4.59119	+	1.25993i	−0.201337	+	0.0552514i
$521$	39.6353	−	12.8783i	1.73645	−	0.564208i	0.742096	−	0.670294i	$-0.233832\pi$
$521$	39.6353	−	12.8783i	1.73645	−	0.564208i	0.994357	+	0.106086i	$0.0338320\pi$
$522$	0.768422	−	0.110867i	0.0336329	−	0.00485253i
$523$	−0.235880	−	1.48929i	−0.0103143	−	0.0651221i	0.981994	−	0.188910i	$-0.0604956\pi$
$523$	−0.235880	−	1.48929i	−0.0103143	−	0.0651221i	−0.992309	+	0.123788i	$0.960496\pi$
$524$	1.32115			0.0577146
$525$	−14.1284	−	24.1818i	−0.616613	−	1.05538i
$526$	8.48086			0.369783
$527$	1.44193	+	9.10399i	0.0628115	+	0.396576i
$528$	−7.09137	−	1.17334i	−0.308612	−	0.0510630i
$529$	−10.9224	+	3.54889i	−0.474885	+	0.154299i
$530$	14.4797	+	5.45827i	0.628956	+	0.237092i
$531$	20.6483	−	6.39566i	0.896062	−	0.277548i
$532$	−18.1657	+	18.1657i	−0.787583	+	0.787583i
$533$	4.83711	+	9.49337i	0.209519	+	0.411203i
$534$	22.4933	+	16.5805i	0.973382	+	0.717509i
$535$	19.9336	−	18.1672i	0.861807	−	0.785435i
$536$	−2.51467	+	3.46115i	−0.108617	+	0.149499i
$537$	−29.2226	+	4.42210i	−1.26105	+	0.190828i
$538$	30.8384	+	4.88432i	1.32954	+	0.210578i
$539$	11.6104	+	8.43547i	0.500096	+	0.363341i
$540$	−11.3284	−	2.58199i	−0.487498	−	0.111111i
$541$	5.13325	−	3.72953i	0.220696	−	0.160345i	−0.471944	−	0.881629i	$-0.656448\pi$
$541$	5.13325	−	3.72953i	0.220696	−	0.160345i	0.692640	+	0.721284i	$0.256448\pi$
$542$	12.7212	−	6.48178i	0.546423	−	0.278416i
$543$	20.9647	+	10.8647i	0.899680	+	0.466251i
$544$	4.47727	+	1.45475i	0.191961	+	0.0623720i
$545$	−7.15769	+	4.70986i	−0.306602	+	0.201748i
$546$	9.69648	−	6.94327i	0.414971	−	0.297145i
$547$	38.9139	+	19.8276i	1.66384	+	0.847769i	0.994491	+	0.104820i	$0.0334268\pi$
$547$	38.9139	+	19.8276i	1.66384	+	0.847769i	0.669349	+	0.742948i	$0.266573\pi$
$548$	−11.0215	+	1.74563i	−0.470813	+	0.0745695i
$549$	12.5701	+	17.8127i	0.536479	+	0.760228i
$550$	17.5369	+	11.0902i	0.747776	+	0.472889i
$551$			2.05584i			0.0875819i
$552$	5.25529	−	2.63222i	0.223680	−	0.112035i
$553$	−6.08160	+	11.9358i	−0.258616	+	0.507562i
$554$	−0.318306	−	0.979644i	−0.0135235	−	0.0416211i
$555$	−8.23317	+	21.3928i	−0.349479	+	0.908076i
$556$	4.47064	−	13.7592i	0.189597	−	0.583520i
$557$	−20.2280	−	20.2280i	−0.857087	−	0.857087i	0.133907	−	0.990994i	$-0.457248\pi$
$557$	−20.2280	−	20.2280i	−0.857087	−	0.857087i	−0.990994	+	0.133907i	$0.957248\pi$
$558$	5.19641	+	2.73861i	0.219982	+	0.115934i
$559$	−11.3543	−	15.6279i	−0.480237	−	0.660989i
$560$	7.08218	+	1.46079i	0.299277	+	0.0617295i
$561$	−32.1088	−	10.6781i	−1.35563	−	0.450829i
$562$	−1.54922	+	9.78136i	−0.0653497	+	0.412602i
$563$	5.05943	−	31.9440i	0.213230	−	1.34628i	−0.616166	−	0.787616i	$-0.711315\pi$
$563$	5.05943	−	31.9440i	0.213230	−	1.34628i	0.829396	−	0.558662i	$-0.188685\pi$
$564$	−6.70455	−	2.22966i	−0.282313	−	0.0938857i
$565$	−23.7892	−	4.90681i	−1.00082	−	0.206431i
$566$	−13.4762	−	18.5484i	−0.566448	−	0.779649i
$567$	28.8616	−	3.75864i	1.21207	−	0.157848i
$568$	−7.66753	−	7.66753i	−0.321723	−	0.321723i
$569$	6.31946	−	19.4493i	0.264925	−	0.815356i	−0.726785	−	0.686865i	$-0.758986\pi$
$569$	6.31946	−	19.4493i	0.264925	−	0.815356i	0.991711	−	0.128492i	$-0.0410135\pi$
$570$	11.0507	−	28.7138i	0.462863	−	1.20269i
$571$	4.67018	+	14.3733i	0.195441	+	0.601505i	0.999971	+	0.00759356i	$0.00241713\pi$
$571$	4.67018	+	14.3733i	0.195441	+	0.601505i	−0.804530	+	0.593912i	$0.797583\pi$
$572$	−4.01133	+	7.87267i	−0.167722	+	0.329173i
$573$	6.70768	−	3.35968i	0.280217	−	0.140353i
$574$		−	16.1831i		−	0.675470i
$575$	−16.9321	+	1.09227i	−0.706117	+	0.0455508i
$576$	2.45113	−	1.72972i	0.102131	−	0.0720717i
$577$	−11.1059	+	1.75900i	−0.462343	+	0.0732279i	−0.383261	−	0.923640i	$-0.625199\pi$
$577$	−11.1059	+	1.75900i	−0.462343	+	0.0732279i	−0.0790822	+	0.996868i	$0.525199\pi$
$578$	4.59960	+	2.34361i	0.191318	+	0.0974814i
$579$	7.07439	−	5.06570i	0.294002	−	0.210523i
$580$	0.483411	−	0.318092i	0.0200726	−	0.0132080i
$581$	−35.2426	−	11.4510i	−1.46211	−	0.475068i
$582$	−0.505157	−	0.261793i	−0.0209394	−	0.0108517i
$583$	25.5883	−	13.0379i	1.05976	−	0.539973i
$584$	0.655875	−	0.476521i	0.0271403	−	0.0197186i
$585$	−7.23716	+	12.3135i	−0.299220	+	0.509100i
$586$	−18.1084	−	13.1565i	−0.748052	−	0.543491i
$587$	3.10689	+	0.492083i	0.128235	+	0.0203104i	0.220222	−	0.975450i	$-0.429322\pi$
$587$	3.10689	+	0.492083i	0.128235	+	0.0203104i	−0.0919870	+	0.995760i	$0.529322\pi$
$588$	−5.92243	+	0.896209i	−0.244237	+	0.0369590i
$589$	−9.14242	+	12.5835i	−0.376707	+	0.518493i
$590$	11.9081	−	10.8529i	0.490250	−	0.446805i
$591$	−16.4591	−	12.1325i	−0.677035	−	0.499063i
$592$	−2.68697	−	5.27347i	−0.110434	−	0.216738i
$593$	6.10055	−	6.10055i	0.250519	−	0.250519i	−0.570664	−	0.821184i	$-0.693314\pi$
$593$	6.10055	−	6.10055i	0.250519	−	0.250519i	0.821184	+	0.570664i	$0.193314\pi$
$594$	−17.7035	+	12.3111i	−0.726385	+	0.505131i
$595$	31.8544	+	12.0079i	1.30590	+	0.492275i
$596$	0.690925	−	0.224495i	0.0283014	−	0.00919568i
$597$	−36.3131	−	6.00835i	−1.48619	−	0.245905i
$598$	−1.13027	−	7.13624i	−0.0462201	−	0.291822i
$599$	−9.03274			−0.369068			−0.184534	−	0.982826i	$-0.559078\pi$
$599$	−9.03274			−0.369068			−0.184534	+	0.982826i	$0.559078\pi$
$600$	−8.46159	+	1.84430i	−0.345443	+	0.0752931i
$601$	−26.1467			−1.06654			−0.533272	−	0.845944i	$-0.679038\pi$
$601$	−26.1467			−1.06654			−0.533272	+	0.845944i	$0.679038\pi$
$602$	4.58984	+	28.9791i	0.187068	+	1.18110i
$603$	1.83280	+	12.7031i	0.0746373	+	0.517311i
$604$	−6.38119	+	2.07337i	−0.259647	+	0.0843644i
$605$	13.4156	−	3.68153i	0.545420	−	0.149676i
$606$	0.0140093	−	2.03188i	0.000569088	−	0.0825397i
$607$	2.58049	−	2.58049i	0.104739	−	0.104739i	−0.652795	−	0.757534i	$-0.726404\pi$
$607$	2.58049	−	2.58049i	0.104739	−	0.104739i	0.757534	+	0.652795i	$0.226404\pi$
$608$	3.60649	+	7.07813i	0.146262	+	0.287056i
$609$	−0.860108	+	1.16683i	−0.0348533	+	0.0472825i
$610$	14.1215	+	8.03989i	0.571762	+	0.325526i
$611$	−5.10520	+	7.02671i	−0.206534	+	0.284270i
$612$	12.6709	−	6.23760i	0.512192	−	0.252140i
$613$	−17.4916	−	2.77040i	−0.706479	−	0.111895i	−0.207152	−	0.978309i	$-0.566419\pi$
$613$	−17.4916	−	2.77040i	−0.706479	−	0.111895i	−0.499327	+	0.866414i	$0.666419\pi$
$614$	20.5524	+	14.9322i	0.829426	+	0.602613i
$615$	7.86769	+	17.7123i	0.317256	+	0.714230i
$616$	10.8573	−	7.88829i	0.437453	−	0.317828i
$617$	30.3282	−	15.4530i	1.22097	−	0.622115i	0.279802	−	0.960058i	$-0.409731\pi$
$617$	30.3282	−	15.4530i	1.22097	−	0.622115i	0.941167	+	0.337943i	$0.109731\pi$
$618$	−7.83246	+	15.1136i	−0.315068	+	0.607957i
$619$	−19.0736	−	6.19740i	−0.766634	−	0.249095i	−0.100511	−	0.994936i	$-0.532048\pi$
$619$	−19.0736	−	6.19740i	−0.766634	−	0.249095i	−0.666124	+	0.745841i	$0.732048\pi$
$620$	4.37345	+	0.202767i	0.175642	+	0.00814331i
$621$	5.79455	−	16.6536i	0.232527	−	0.668287i
$622$	−0.0977951	−	0.0498291i	−0.00392122	−	0.00199796i
$623$	−51.5319	+	8.16185i	−2.06458	+	0.326998i
$624$	−1.11538	−	3.51508i	−0.0446511	−	0.140716i
$625$	24.5719	+	4.60653i	0.982877	+	0.184261i
$626$		−	24.1606i		−	0.965650i
$627$	−25.5713	−	51.0536i	−1.02122	−	2.03888i
$628$	2.13000	−	4.18036i	0.0849962	−	0.166815i
$629$	−8.61003	−	26.4990i	−0.343304	−	1.05658i
$630$	18.2851	−	11.6738i	0.728495	−	0.465094i
$631$	6.17329	−	18.9994i	0.245755	−	0.756356i	−0.749756	−	0.661714i	$-0.769829\pi$
$631$	6.17329	−	18.9994i	0.245755	−	0.756356i	0.995511	−	0.0946420i	$-0.0301706\pi$
$632$	2.92905	+	2.92905i	0.116511	+	0.116511i
$633$	21.1974	−	20.9071i	0.842519	−	0.830981i
$634$	−10.2414	−	14.0961i	−0.406738	−	0.559827i
$635$	2.09441	+	18.8338i	0.0831141	+	0.747398i
$636$	−3.78248	+	11.3739i	−0.149985	+	0.451003i
$637$	−1.15185	+	7.27248i	−0.0456379	+	0.288146i
$638$	0.168004	−	1.06074i	0.00665134	−	0.0419949i
$639$	−32.5275	−	0.448558i	−1.28677	−	0.0177447i
$640$	1.10634	−	1.94320i	0.0437318	−	0.0768116i
$641$	10.5427	+	14.5108i	0.416411	+	0.573140i	0.964767	−	0.263104i	$-0.0847463\pi$
$641$	10.5427	+	14.5108i	0.416411	+	0.573140i	−0.548357	+	0.836245i	$0.684746\pi$
$642$	14.6700	+	14.8737i	0.578980	+	0.587019i
$643$	15.8850	+	15.8850i	0.626441	+	0.626441i	0.947171	−	0.320729i	$-0.103928\pi$
$643$	15.8850	+	15.8850i	0.626441	+	0.626441i	−0.320729	+	0.947171i	$0.603928\pi$
$644$	−3.39121	+	10.4371i	−0.133632	+	0.411278i
$645$	−19.1122	−	29.4860i	−0.752543	−	1.16101i
$646$	11.5565	+	35.5673i	0.454685	+	1.39938i
$647$	2.64083	−	5.18292i	0.103822	−	0.203762i	−0.833252	−	0.552894i	$-0.813524\pi$
$647$	2.64083	−	5.18292i	0.103822	−	0.203762i	0.937074	+	0.349132i	$0.113524\pi$
$648$	1.65249	−	8.84699i	0.0649161	−	0.347543i
$649$		−	29.9014i		−	1.17373i
$650$	−0.985026	+	10.6001i	−0.0386359	+	0.415770i
$651$	−10.4535	+	3.31705i	−0.409706	+	0.130006i
$652$	2.78576	−	0.441222i	0.109099	−	0.0172796i
$653$	43.3609	+	22.0935i	1.69684	+	0.864586i	0.987096	+	0.160131i	$0.0511917\pi$
$653$	43.3609	+	22.0935i	1.69684	+	0.864586i	0.709749	+	0.704455i	$0.248808\pi$
$654$	−3.86399	−	5.39618i	−0.151094	−	0.211007i
$655$	1.04203	−	2.76430i	0.0407156	−	0.108010i
$656$	−4.75925	−	1.54638i	−0.185818	−	0.0603758i
$657$	0.413554	−	2.39670i	0.0161343	−	0.0935041i
$658$	11.7543	−	5.98913i	0.458231	−	0.233480i
$659$	7.82256	−	5.68342i	0.304724	−	0.221395i	−0.424906	−	0.905238i	$-0.639693\pi$
$659$	7.82256	−	5.68342i	0.304724	−	0.221395i	0.729629	+	0.683843i	$0.239693\pi$
$660$	−8.04822	+	13.9121i	−0.313277	+	0.541529i
$661$	−18.4358	−	13.3944i	−0.717069	−	0.520981i	0.168377	−	0.985723i	$-0.446147\pi$
$661$	−18.4358	−	13.3944i	−0.717069	−	0.520981i	−0.885447	+	0.464741i	$0.846147\pi$
$662$	−19.1964	−	3.04042i	−0.746090	−	0.118169i
$663$	−2.59757	−	17.1656i	−0.100881	−	0.666655i
$664$	−6.73520	+	9.27021i	−0.261377	+	0.359754i
$665$	23.6810	+	52.3368i	0.918309	+	2.02953i
$666$	−16.8094	−	5.71912i	−0.651350	−	0.221612i
$667$	0.398696	+	0.782485i	0.0154376	+	0.0302979i
$668$	9.99325	−	9.99325i	0.386650	−	0.386650i
$669$	−15.6123	−	0.107643i	−0.603608	−	0.00416171i
$670$	5.25851	+	7.99149i	0.203154	+	0.308738i
$671$	28.6816	−	9.31923i	1.10724	−	0.359765i
$672$	−0.914361	+	5.52618i	−0.0352722	+	0.213177i
$673$	−2.98296	−	18.8337i	−0.114985	−	0.725985i	−0.976059	−	0.217506i	$-0.930208\pi$
$673$	−2.98296	−	18.8337i	−0.114985	−	0.725985i	0.861074	−	0.508479i	$-0.169792\pi$
$674$	10.2052			0.393091
$675$	−14.3375	+	21.6665i	−0.551851	+	0.833942i
$676$	8.46671			0.325643
$677$	2.13887	+	13.5043i	0.0822035	+	0.519012i	0.994089	+	0.108568i	$0.0346265\pi$
$677$	2.13887	+	13.5043i	0.0822035	+	0.519012i	−0.911886	+	0.410445i	$0.865374\pi$
$678$	3.07135	−	18.5625i	0.117955	−	0.712890i
$679$	1.01032	−	0.328273i	0.0387725	−	0.0125980i
$680$	6.57521	−	8.22057i	0.252148	−	0.315245i
$681$	1.62500	+	0.0112039i	0.0622701	+	0.000429335i
$682$	5.74546	−	5.74546i	0.220005	−	0.220005i
$683$	10.3197	+	20.2536i	0.394874	+	0.774984i	0.999773	−	0.0213182i	$-0.00678632\pi$
$683$	10.3197	+	20.2536i	0.394874	+	0.774984i	−0.604898	+	0.796303i	$0.706786\pi$
$684$	22.5618	+	7.67629i	0.862672	+	0.293510i
$685$	−5.04054	+	24.4375i	−0.192589	+	0.933709i
$686$	−6.73235	+	9.26628i	−0.257042	+	0.353788i
$687$	3.46222	+	22.8795i	0.132092	+	0.872906i
$688$	8.96098	+	1.41928i	0.341634	+	0.0541095i
$689$	11.9204	+	8.66065i	0.454130	+	0.329945i
$690$	−1.36249	−	13.0720i	−0.0518693	−	0.497642i
$691$	−1.73154	+	1.25804i	−0.0658711	+	0.0478581i	−0.620234	−	0.784417i	$-0.712962\pi$
$691$	−1.73154	+	1.25804i	−0.0658711	+	0.0478581i	0.554362	+	0.832275i	$0.312962\pi$
$692$	−21.2226	+	10.8134i	−0.806761	+	0.411065i
$693$	6.84594	−	39.6748i	0.260056	−	1.50712i
$694$	0.739524	+	0.240286i	0.0280720	+	0.00912113i
$695$	−25.2628	−	20.2065i	−0.958274	−	0.766474i
$696$	0.260964	+	0.364444i	0.00989181	+	0.0138142i
$697$	−20.9904	−	10.6951i	−0.795067	−	0.405107i
$698$	17.2415	−	2.73078i	0.652600	−	0.103362i
$699$	−28.8982	+	9.16982i	−1.09303	+	0.346834i
$700$	8.64242	−	13.6662i	0.326653	−	0.516533i
$701$			41.0774i			1.55147i	0.631057	+	0.775736i	$0.282621\pi$
$701$			41.0774i			1.55147i	−0.631057	+	0.775736i	$0.717379\pi$
$702$	−9.75157	−	5.22548i	−0.368049	−	0.197223i
$703$	21.3452	−	41.8923i	0.805049	−	1.58000i
$704$	−1.28238	−	3.94676i	−0.0483315	−	0.148749i
$705$	−9.95332	+	12.2696i	−0.374864	+	0.462101i
$706$	6.19817	−	19.0760i	0.233271	−	0.717935i
$707$	2.68264	+	2.68264i	0.100891	+	0.100891i
$708$	8.76371	+	8.88540i	0.329360	+	0.333934i
$709$	8.41710	+	11.5851i	0.316111	+	0.435089i	0.937275	−	0.348591i	$-0.113340\pi$
$709$	8.41710	+	11.5851i	0.316111	+	0.435089i	−0.621164	+	0.783681i	$0.713340\pi$
$710$	−22.0908	+	9.99548i	−0.829051	+	0.375124i
$711$	12.4257	+	0.171352i	0.466001	+	0.00642620i
$712$	−2.52383	+	15.9348i	−0.0945844	+	0.597182i
$713$	−1.03939	+	6.56247i	−0.0389256	+	0.245767i
$714$	−8.32124	+	25.0218i	−0.311415	+	0.936418i
$715$	13.3085	+	14.6025i	0.497709	+	0.546103i
$716$	−10.0298	−	13.8049i	−0.374833	−	0.515913i
$717$	−34.7235	+	34.2480i	−1.29677	+	1.27902i
$718$	7.78025	+	7.78025i	0.290357	+	0.290357i
$719$	−1.52577	+	4.69583i	−0.0569015	+	0.175125i	−0.975468	−	0.220142i	$-0.929348\pi$
$719$	−1.52577	+	4.69583i	−0.0569015	+	0.175125i	0.918566	+	0.395267i	$0.129348\pi$
$720$	−1.68588	−	6.49290i	−0.0628291	−	0.241976i
$721$	−9.82145	−	30.2273i	−0.365770	−	1.12572i
$722$	−20.0240	+	39.2993i	−0.745216	+	1.46257i
$723$	−23.2504	−	46.4198i	−0.864690	−	1.72637i
$724$			13.6328i			0.506659i
$725$	−0.284274	−	1.26235i	−0.0105577	−	0.0468826i
$726$	3.25918	+	10.2711i	0.120959	+	0.381198i
$727$	11.2362	−	1.77964i	0.416729	−	0.0660033i	0.0554505	−	0.998461i	$-0.482340\pi$
$727$	11.2362	−	1.77964i	0.416729	−	0.0660033i	0.361278	+	0.932458i	$0.382340\pi$
$728$	6.13504	+	3.12596i	0.227380	+	0.115856i
$729$	−14.9533	−	22.4811i	−0.553825	−	0.832633i
$730$	−0.479735	−	1.74816i	−0.0177558	−	0.0647024i
$731$	40.6208	+	13.1985i	1.50242	+	0.488165i
$732$	−5.79158	+	11.1755i	−0.214063	+	0.413057i
$733$	−41.0960	+	20.9395i	−1.51792	+	0.773417i	−0.996790	−	0.0800619i	$-0.974488\pi$
$733$	−41.0960	+	20.9395i	−1.51792	+	0.773417i	−0.521127	+	0.853479i	$0.674488\pi$
$734$	4.96767	−	3.60922i	0.183360	−	0.133219i
$735$	−2.79604	+	13.0986i	−0.103134	+	0.483150i
$736$	2.74537	+	1.99462i	0.101196	+	0.0735228i
$737$	17.5355	+	2.77735i	0.645928	+	0.102305i
$738$	−13.4690	+	6.63045i	−0.495799	+	0.244070i
$739$	−22.5951	+	31.0995i	−0.831175	+	1.14401i	0.156528	+	0.987674i	$0.449970\pi$
$739$	−22.5951	+	31.0995i	−0.831175	+	1.14401i	−0.987703	+	0.156341i	$0.950030\pi$
$740$	−13.1532	+	1.46270i	−0.483521	+	0.0537698i
$741$	17.3826	−	23.5815i	0.638567	−	0.866288i
$742$	−10.1602	−	19.9405i	−0.372992	−	0.732038i
$743$	−16.0682	+	16.0682i	−0.589485	+	0.589485i	−0.937492	−	0.348007i	$-0.886859\pi$
$743$	−16.0682	+	16.0682i	−0.589485	+	0.589485i	0.348007	+	0.937492i	$0.386859\pi$
$744$	−0.0233815	+	3.39122i	−0.000857208	+	0.124328i
$745$	0.0752344	−	1.62272i	0.00275637	−	0.0594518i
$746$	4.74228	−	1.54086i	0.173627	−	0.0564149i
$747$	4.90889	+	34.0235i	0.179607	+	1.24486i
$748$	−3.05614	−	19.2957i	−0.111744	−	0.705522i
$749$	−39.0059			−1.42524
$750$	−2.81503	+	19.1592i	−0.102790	+	0.699596i
$751$	−3.78871			−0.138252			−0.0691261	−	0.997608i	$-0.522021\pi$
$751$	−3.78871			−0.138252			−0.0691261	+	0.997608i	$0.522021\pi$
$752$	−0.638146	−	4.02909i	−0.0232708	−	0.146926i
$753$	8.20440	+	1.35750i	0.298985	+	0.0494700i
$754$	0.524041	−	0.170271i	0.0190845	−	0.00620092i
$755$	−0.694844	+	14.9870i	−0.0252879	+	0.545432i
$756$	9.59383	+	13.7961i	0.348924	+	0.501758i
$757$	−28.0026	+	28.0026i	−1.01777	+	1.01777i	−0.0179316	+	0.999839i	$0.505708\pi$
$757$	−28.0026	+	28.0026i	−1.01777	+	1.01777i	−0.999839	+	0.0179316i	$0.994292\pi$
$758$	5.89359	+	11.5668i	0.214065	+	0.420126i
$759$	−19.6338	−	14.4726i	−0.712661	−	0.525324i
$760$	17.6544	−	1.96326i	0.640394	−	0.0712147i
$761$	−2.20853	+	3.03978i	−0.0800592	+	0.110192i	−0.847168	−	0.531325i	$-0.821694\pi$
$761$	−2.20853	+	3.03978i	−0.0800592	+	0.110192i	0.767109	+	0.641517i	$0.221694\pi$
$762$	−14.5133	+	2.19622i	−0.525762	+	0.0795607i
$763$	12.2393	+	1.93852i	0.443094	+	0.0701791i
$764$	3.50409	+	2.54587i	0.126774	+	0.0921064i
$765$	−3.05722	−	31.4317i	−0.110534	−	1.13642i
$766$	18.9387	−	13.7597i	0.684282	−	0.497160i
$767$	13.6693	−	6.96484i	0.493569	−	0.251486i
$768$	1.53781	+	0.796956i	0.0554910	+	0.0287577i
$769$	−26.5144	−	8.61506i	−0.956135	−	0.310667i	−0.210929	−	0.977501i	$-0.567649\pi$
$769$	−26.5144	−	8.61506i	−0.956135	−	0.310667i	−0.745206	+	0.666834i	$0.767649\pi$
$770$	−7.94150	−	28.9389i	−0.286192	−	1.04289i
$771$	3.43010	−	2.45616i	0.123532	−	0.0884564i
$772$	4.47602	+	2.28065i	0.161095	+	0.0820823i
$773$	−27.7544	+	4.39587i	−0.998258	+	0.158108i	−0.634118	−	0.773236i	$-0.718637\pi$
$773$	−27.7544	+	4.39587i	−0.998258	+	0.158108i	−0.364139	+	0.931344i	$0.618637\pi$
$774$	22.2384	−	15.6932i	0.799342	−	0.564081i
$775$	3.87374	−	8.99082i	0.139149	−	0.322960i
$776$		−	0.328491i		−	0.0117921i
$777$	29.6414	−	14.8465i	1.06338	−	0.532616i
$778$	−7.43594	+	14.5938i	−0.266591	+	0.523215i
$779$	−12.2844	−	37.8074i	−0.440133	−	1.35459i
$780$	−8.23450	−	0.438692i	−0.294842	−	0.0157077i
$781$	−13.9055	+	42.7968i	−0.497579	+	1.53139i
$782$	11.2963	+	11.2963i	0.403953	+	0.403953i
$783$	1.32354	+	0.237787i	0.0472994	+	0.00849780i
$784$	−2.03271	−	2.79778i	−0.0725966	−	0.0999207i
$785$	−7.06675	−	7.75388i	−0.252223	−	0.276748i
$786$	2.17137	+	0.722110i	0.0774503	+	0.0257568i
$787$	5.04761	−	31.8694i	0.179928	−	1.13602i	−0.718054	−	0.695987i	$-0.754967\pi$
$787$	5.04761	−	31.8694i	0.179928	−	1.13602i	0.897982	−	0.440033i	$-0.145033\pi$
$788$	1.84676	−	11.6600i	0.0657881	−	0.415370i
$789$	13.9387	+	4.63545i	0.496231	+	0.165026i
$790$	8.43881	−	3.81834i	0.300239	−	0.135850i
$791$	20.6486	+	28.4203i	0.734178	+	1.01051i
$792$	−11.0137	−	5.80442i	−0.391355	−	0.206251i
$793$	10.9409	+	10.9409i	0.388524	+	0.388524i
$794$	3.45370	−	10.6294i	0.122567	−	0.377223i
$795$	20.8146	+	16.8852i	0.738219	+	0.598856i
$796$	−6.56673	−	20.2103i	−0.232752	−	0.716336i
$797$	19.5331	−	38.3358i	0.691897	−	1.35792i	−0.231030	−	0.972947i	$-0.574209\pi$
$797$	19.5331	−	38.3358i	0.691897	−	1.35792i	0.922926	−	0.384977i	$-0.125791\pi$
$798$	−39.7852	+	19.9272i	−1.40838	+	0.705417i
$799$		−	19.2041i		−	0.679393i
$800$	−3.19323	−	3.84750i	−0.112898	−	0.136030i
$801$	27.9064	+	39.5452i	0.986023	+	1.39726i
$802$	1.89743	−	0.300524i	0.0670007	−	0.0106119i
$803$	−2.99763	−	1.52737i	−0.105784	−	0.0538998i
$804$	−6.02478	+	4.31411i	−0.212478	+	0.152147i
$805$	19.1632	+	15.3276i	0.675413	+	0.540228i
$806$	3.96477	+	1.28823i	0.139653	+	0.0453761i
$807$	48.0148	+	24.8832i	1.69020	+	0.875930i
$808$	1.04527	−	0.532593i	0.0367726	−	0.0187366i
$809$	−41.5683	+	30.2011i	−1.46146	+	1.06181i	−0.478483	+	0.878097i	$0.658813\pi$
$809$	−41.5683	+	30.2011i	−1.46146	+	1.06181i	−0.982979	+	0.183718i	$0.941187\pi$
$810$	−17.2076	−	10.4355i	−0.604612	−	0.366666i
$811$	−8.15608	−	5.92574i	−0.286399	−	0.208081i	0.435305	−	0.900283i	$-0.356641\pi$
$811$	−8.15608	−	5.92574i	−0.286399	−	0.208081i	−0.721704	+	0.692202i	$0.756641\pi$
$812$	−0.826612	−	0.130923i	−0.0290084	−	0.00459448i
$813$	24.4507	−	3.70000i	0.857525	−	0.129765i
$814$	−14.4367	+	19.8704i	−0.506007	+	0.696459i
$815$	1.27404	−	6.17678i	0.0446276	−	0.216363i
$816$	6.56348	+	4.83813i	0.229768	+	0.169369i
$817$	32.7205	+	64.2176i	1.14475	+	2.24669i
$818$	−21.2872	+	21.2872i	−0.744290	+	0.744290i
$819$	19.7317	−	6.11173i	0.689481	−	0.213561i
$820$	−6.98933	+	8.73832i	−0.244078	+	0.305155i
$821$	−48.8450	+	15.8707i	−1.70470	+	0.553891i	−0.989437	−	0.144964i	$-0.953693\pi$
$821$	−48.8450	+	15.8707i	−1.70470	+	0.553891i	−0.715264	+	0.698855i	$0.753693\pi$
$822$	−19.0684	−	3.15506i	−0.665088	−	0.110045i
$823$	−1.24703	−	7.87346i	−0.0434689	−	0.274452i	0.956375	−	0.292143i	$-0.0943683\pi$
$823$	−1.24703	−	7.87346i	−0.0434689	−	0.274452i	−0.999843	+	0.0176915i	$0.994368\pi$
$824$	−9.82797			−0.342374
$825$	22.7611	+	27.8126i	0.792439	+	0.968311i
$826$	−23.3017			−0.810768
$827$	0.742663	+	4.68899i	0.0258249	+	0.163052i	0.997230	−	0.0743745i	$-0.0236960\pi$
$827$	0.742663	+	4.68899i	0.0258249	+	0.163052i	−0.971405	+	0.237427i	$0.923696\pi$
$828$	10.0760	−	1.45376i	0.350167	−	0.0505218i
$829$	−29.4902	+	9.58196i	−1.02424	+	0.332795i	−0.772510	−	0.635003i	$-0.780999\pi$
$829$	−29.4902	+	9.58196i	−1.02424	+	0.332795i	−0.251729	+	0.967798i	$0.580999\pi$
$830$	14.0842	+	21.4041i	0.488869	+	0.742946i
$831$	0.0123007	−	1.78407i	0.000426706	−	0.0618888i
$832$	1.50554	−	1.50554i	0.0521952	−	0.0521952i
$833$	−7.39111	−	14.5059i	−0.256087	−	0.502598i
$834$	14.8682	−	20.1704i	0.514843	−	0.698443i
$835$	−13.0273	−	28.7913i	−0.450828	−	0.996364i
$836$	19.3772	−	26.6704i	0.670174	−	0.922416i
$837$	7.04370	+	7.34128i	0.243466	+	0.253752i
$838$	−12.4956	−	1.97911i	−0.431653	−	0.0683672i
$839$	21.8902	+	15.9042i	0.755734	+	0.549073i	0.897599	−	0.440813i	$-0.145310\pi$
$839$	21.8902	+	15.9042i	0.755734	+	0.549073i	−0.141865	+	0.989886i	$0.545310\pi$
$840$	10.8415	+	6.27184i	0.374067	+	0.216399i
$841$	23.4073	−	17.0064i	0.807149	−	0.586428i
$842$	−2.93416	+	1.49503i	−0.101118	+	0.0515222i
$843$	−7.89249	+	15.2294i	−0.271832	+	0.524528i
$844$	16.3481	+	5.31184i	0.562727	+	0.182841i
$845$	6.67797	−	17.7153i	0.229729	−	0.609423i
$846$	−9.80058	−	7.32912i	−0.336951	−	0.251980i
$847$	−17.9267	−	9.13411i	−0.615969	−	0.313852i
$848$	−6.83510	+	1.08257i	−0.234718	+	0.0371757i
$849$	−12.0107	−	37.8511i	−0.412205	−	1.29904i
$850$	−12.0142	−	20.2414i	−0.412083	−	0.694276i
$851$		−	20.0844i		−	0.688483i
$852$	−8.41106	−	16.7929i	−0.288158	−	0.575314i
$853$	5.33449	−	10.4695i	0.182650	−	0.358470i	−0.781468	−	0.623945i	$-0.785529\pi$
$853$	5.33449	−	10.4695i	0.182650	−	0.358470i	0.964118	+	0.265475i	$0.0855289\pi$
$854$	−7.26231	−	22.3511i	−0.248511	−	0.764839i
$855$	33.8567	−	41.1525i	1.15787	−	1.40738i
$856$	−3.72720	+	11.4711i	−0.127393	+	0.392076i
$857$	−16.7084	−	16.7084i	−0.570749	−	0.570749i	0.361588	−	0.932338i	$-0.382235\pi$
$857$	−16.7084	−	16.7084i	−0.570749	−	0.570749i	−0.932338	+	0.361588i	$0.882235\pi$
$858$	−10.8958	+	10.7466i	−0.371978	+	0.366884i
$859$	17.7522	+	24.4338i	0.605698	+	0.833672i	0.996215	−	0.0869239i	$-0.0277037\pi$
$859$	17.7522	+	24.4338i	0.605698	+	0.833672i	−0.390517	+	0.920596i	$0.627704\pi$
$860$	10.0374	−	17.6300i	0.342274	−	0.601179i
$861$	8.84533	−	26.5977i	0.301448	−	0.906448i
$862$	3.45331	−	21.8033i	0.117620	−	0.742624i
$863$	5.92575	−	37.4137i	0.201715	−	1.27358i	−0.654145	−	0.756369i	$-0.726971\pi$
$863$	5.92575	−	37.4137i	0.201715	−	1.27358i	0.855860	−	0.517208i	$-0.173029\pi$
$864$	4.97399	−	1.50315i	0.169218	−	0.0511381i
$865$	5.88649	+	52.9338i	0.200147	+	1.79980i
$866$	2.85266	+	3.92635i	0.0969372	+	0.133423i
$867$	6.27870	+	6.36588i	0.213236	+	0.216197i
$868$	−4.47733	−	4.47733i	−0.151971	−	0.151971i
$869$	5.31201	−	16.3487i	0.180197	−	0.554591i
$870$	0.968372	−	0.258577i	0.0328309	−	0.00876659i
$871$	2.81483	+	8.66316i	0.0953769	+	0.293540i
$872$	1.73962	−	3.41420i	0.0589111	−	0.115620i
$873$	−0.687160	−	0.706377i	−0.0232568	−	0.0239072i
$874$			26.9575i			0.911852i
$875$	−21.7778	−	28.8619i	−0.736224	−	0.975710i
$876$	1.33842	−	0.424699i	0.0452209	−	0.0143492i
$877$	22.7610	−	3.60498i	0.768583	−	0.121732i	0.240183	−	0.970728i	$-0.422792\pi$
$877$	22.7610	−	3.60498i	0.768583	−	0.121732i	0.528399	+	0.848996i	$0.322792\pi$
$878$	28.2867	+	14.4128i	0.954628	+	0.486407i
$879$	−22.5710	−	31.5211i	−0.761301	−	1.06318i
$880$	−9.26944	−	0.429761i	−0.312473	−	0.0144872i
$881$	17.8899	+	5.81277i	0.602725	+	0.195837i	0.594456	−	0.804129i	$-0.297368\pi$
$881$	17.8899	+	5.81277i	0.602725	+	0.195837i	0.00826973	+	0.999966i	$0.497368\pi$
$882$	−10.2237	−	1.76411i	−0.344248	−	0.0594005i
$883$	−1.53112	+	0.780142i	−0.0515261	+	0.0262539i	−0.479564	−	0.877507i	$-0.659205\pi$
$883$	−1.53112	+	0.780142i	−0.0515261	+	0.0262539i	0.428038	+	0.903761i	$0.359205\pi$
$884$	8.10908	−	5.89159i	0.272738	−	0.198156i
$885$	25.5035	−	11.3285i	0.857292	−	0.380803i
$886$	8.60976	+	6.25536i	0.289251	+	0.210153i
$887$	9.35284	+	1.48134i	0.314038	+	0.0497387i	0.311464	−	0.950258i	$-0.399181\pi$
$887$	9.35284	+	1.48134i	0.314038	+	0.0497387i	0.00257386	+	0.999997i	$0.499181\pi$
$888$	−1.53380	−	10.1358i	−0.0514710	−	0.340136i
$889$	16.1091	−	22.1722i	0.540281	−	0.743633i
$890$	31.3505	+	17.8490i	1.05087	+	0.598301i
$891$	−35.8256	+	10.5576i	−1.20020	+	0.353691i
$892$	−4.09227	−	8.03154i	−0.137019	−	0.268916i
$893$	22.9145	−	22.9145i	0.766804	−	0.766804i
$894$	1.25827	+	0.00867545i	0.0420829	+	0.000290150i
$895$	−36.7954	+	10.0975i	−1.22994	+	0.337522i
$896$	−3.07564	+	0.999337i	−0.102750	+	0.0333855i
$897$	2.04286	−	12.3465i	0.0682090	−	0.412239i
$898$	−3.92241	−	24.7651i	−0.130893	−	0.826423i
$899$	−0.506708			−0.0168997
$900$	−14.9151	−	1.59372i	−0.497170	−	0.0531242i
$901$	−32.5786			−1.08535
$902$	3.24862	+	20.5110i	0.108167	+	0.682942i
$903$	−8.29571	+	50.1373i	−0.276064	+	1.66846i
$904$	10.3311	−	3.35679i	0.343608	−	0.111645i
$905$	28.5245	+	10.7526i	0.948187	+	0.357430i
$906$	−11.6211	−	0.0801240i	−0.386084	−	0.00266194i
$907$	−31.9675	+	31.9675i	−1.06146	+	1.06146i	−0.0634811	+	0.997983i	$0.520220\pi$
$907$	−31.9675	+	31.9675i	−1.06146	+	1.06146i	−0.997983	+	0.0634811i	$0.979780\pi$
$908$	0.425941	+	0.835956i	0.0141353	+	0.0277422i
$909$	1.13361	−	3.33184i	0.0375994	−	0.110510i
$910$	11.3795	−	10.3711i	0.377226	−	0.343797i
$911$	0.323364	−	0.445072i	0.0107135	−	0.0147459i	−0.803627	−	0.595134i	$-0.797099\pi$
$911$	0.323364	−	0.445072i	0.0107135	−	0.0147459i	0.814340	+	0.580388i	$0.197099\pi$
$912$	2.05869	+	13.6045i	0.0681700	+	0.450489i
$913$	46.9663	+	7.43873i	1.55436	+	0.246186i
$914$	3.19615	+	2.32214i	0.105719	+	0.0768095i
$915$	18.8149	+	20.9324i	0.622002	+	0.692005i
$916$	−10.8083	+	7.85272i	−0.357118	+	0.259461i
$917$	−3.80682	+	1.93967i	−0.125712	+	0.0640535i
$918$	24.2346	−	3.32615i	0.799862	−	0.109779i
$919$	26.9142	+	8.74495i	0.887817	+	0.288469i	0.717199	−	0.696868i	$-0.245424\pi$
$919$	26.9142	+	8.74495i	0.887817	+	0.288469i	0.170618	+	0.985337i	$0.445424\pi$
$920$	6.33880	−	4.17102i	0.208984	−	0.137514i
$921$	25.6172	+	35.7752i	0.844116	+	1.17883i
$922$	2.60951	+	1.32961i	0.0859397	+	0.0437885i
$923$	−22.8033	+	3.61169i	−0.750579	+	0.118880i
$924$	22.1561	−	7.03043i	0.728881	−	0.231284i
$925$	−7.31390	+	28.6747i	−0.240480	+	0.942818i
$926$		−	30.2530i		−	0.994175i
$927$	−21.1338	+	20.5588i	−0.694124	+	0.675240i
$928$	−0.117490	+	0.230586i	−0.00385678	+	0.00756936i
$929$	8.51025	+	26.1919i	0.279212	+	0.859327i	0.988074	+	0.153980i	$0.0492091\pi$
$929$	8.51025	+	26.1919i	0.279212	+	0.859327i	−0.708862	+	0.705348i	$0.750791\pi$
$930$	7.07715	+	2.72369i	0.232069	+	0.0893132i
$931$	8.48938	−	26.1276i	0.278228	−	0.856298i
$932$	−12.3774	−	12.3774i	−0.405434	−	0.405434i
$933$	−0.133496	−	0.135349i	−0.00437045	−	0.00443113i
$934$	−19.6432	−	27.0366i	−0.642745	−	0.884663i
$935$	−42.7838	−	8.82468i	−1.39918	−	0.288598i
$936$	0.0880754	−	6.38685i	0.00287883	−	0.208761i
$937$	5.87766	−	37.1101i	0.192015	−	1.21233i	−0.683794	−	0.729675i	$-0.739671\pi$
$937$	5.87766	−	37.1101i	0.192015	−	1.21233i	0.875809	−	0.482658i	$-0.160329\pi$
$938$	2.16434	−	13.6651i	0.0706681	−	0.446181i
$939$	13.2056	−	39.7091i	0.430949	−	1.29586i
$940$	−8.93357	−	1.84266i	−0.291381	−	0.0601009i
$941$	−12.4653	−	17.1570i	−0.406358	−	0.559304i	0.555968	−	0.831204i	$-0.312348\pi$
$941$	−12.4653	−	17.1570i	−0.406358	−	0.559304i	−0.962325	+	0.271900i	$0.912348\pi$
$942$	5.78565	−	5.70642i	0.188507	−	0.185925i
$943$	−12.0077	−	12.0077i	−0.391025	−	0.391025i
$944$	−2.22659	+	6.85273i	−0.0724693	+	0.223037i
$945$	36.4330	−	9.19218i	1.18517	−	0.299022i
$946$	−11.6346	−	35.8077i	−0.378274	−	1.16421i
$947$	−15.8634	+	31.1336i	−0.515490	+	1.01171i	0.475744	+	0.879584i	$0.342179\pi$
$947$	−15.8634	+	31.1336i	−0.515490	+	1.01171i	−0.991234	+	0.132122i	$0.957821\pi$
$948$	3.21308	+	6.41499i	0.104356	+	0.208349i
$949$		−	1.72612i		−	0.0560321i
$950$	9.81683	−	38.4876i	0.318500	−	1.24870i
$951$	−9.12765	−	28.7653i	−0.295984	−	0.932780i
$952$	−15.0368	+	2.38160i	−0.487346	+	0.0771881i
$953$	−38.7848	−	19.7619i	−1.25636	−	0.640150i	−0.306220	−	0.951961i	$-0.599064\pi$
$953$	−38.7848	−	19.7619i	−1.25636	−	0.640150i	−0.950144	+	0.311811i	$0.899064\pi$
$954$	−12.4334	+	16.6261i	−0.402546	+	0.538289i
$955$	8.09063	−	5.32375i	0.261807	−	0.172273i
$956$	−26.7800	−	8.70136i	−0.866128	−	0.281422i
$957$	0.855897	−	1.65154i	0.0276672	−	0.0533868i
$958$	−15.9995	+	8.15214i	−0.516920	+	0.263384i
$959$	29.1949	−	21.2113i	0.942751	−	0.684949i
$960$	2.88043	−	2.58904i	0.0929654	−	0.0835610i
$961$	21.9781	+	15.9680i	0.708970	+	0.515097i
$962$	−12.4464	−	1.97131i	−0.401287	−	0.0635576i
$963$	15.9813	+	32.4640i	0.514989	+	1.04614i
$964$	17.6185	−	24.2497i	0.567453	−	0.781032i
$965$	8.30228	−	7.56655i	0.267260	−	0.243576i
$966$	−11.2783	+	15.3003i	−0.362873	+	0.492278i
$967$	−22.2871	−	43.7408i	−0.716704	−	1.40661i	−0.905393	−	0.424574i	$-0.860424\pi$
$967$	−22.2871	−	43.7408i	−0.716704	−	1.40661i	0.188689	−	0.982037i	$-0.439576\pi$
$968$	−4.39921	+	4.39921i	−0.141396	+	0.141396i
$969$	−0.446593	+	64.7731i	−0.0143466	+	2.08081i
$970$	−0.687316	−	0.259092i	−0.0220684	−	0.00831893i
$971$	33.3615	−	10.8398i	1.07062	−	0.347866i	0.279892	−	0.960032i	$-0.409701\pi$
$971$	33.3615	−	10.8398i	1.07062	−	0.347866i	0.790730	+	0.612166i	$0.209701\pi$
$972$	7.55152	−	13.6372i	0.242215	−	0.437415i
$973$	7.31895	+	46.2101i	0.234635	+	1.48143i
$974$	−29.6562			−0.950246
$975$	−7.41271	+	16.8834i	−0.237397	+	0.540701i
$976$	−7.26713			−0.232615
$977$	−1.87057	−	11.8103i	−0.0598448	−	0.377845i	−0.999374	−	0.0353765i	$-0.988737\pi$
$977$	−1.87057	−	11.8103i	−0.0598448	−	0.377845i	0.939529	−	0.342469i	$-0.111263\pi$
$978$	4.81970	+	0.797467i	0.154117	+	0.0255002i
$979$	63.6748	−	20.6892i	2.03506	−	0.661230i
$980$	−7.45718	+	2.04642i	−0.238211	+	0.0653704i
$981$	−3.40123	−	10.9809i	−0.108593	−	0.350592i
$982$	3.74816	−	3.74816i	0.119609	−	0.119609i
$983$	13.2156	+	25.9371i	0.421512	+	0.827264i	0.999934	+	0.0115261i	$0.00366897\pi$
$983$	13.2156	+	25.9371i	0.421512	+	0.827264i	−0.578421	+	0.815738i	$0.696331\pi$
$984$	−6.97685	−	5.14285i	−0.222414	−	0.163948i
$985$	−22.9401	−	13.0607i	−0.730932	−	0.416147i
$986$	−0.716107	+	0.985637i	−0.0228055	+	0.0313891i
$987$	22.5923	−	3.41877i	0.719122	−	0.108821i
$988$	16.7057	+	2.64592i	0.531479	+	0.0841780i
$989$	24.9078	+	18.0966i	0.792023	+	0.575438i
$990$	−20.8317	+	18.4663i	−0.662075	+	0.586897i
$991$	−15.9396	+	11.5808i	−0.506337	+	0.367875i	−0.811432	−	0.584447i	$-0.801312\pi$
$991$	−15.9396	+	11.5808i	−0.506337	+	0.367875i	0.305095	+	0.952322i	$0.401312\pi$
$992$	−1.74456	+	0.888898i	−0.0553898	+	0.0282225i
$993$	−29.8884	−	15.4894i	−0.948481	−	0.491542i
$994$	33.3508	+	10.8363i	1.05782	+	0.343708i
$995$	−47.4663	−	2.20069i	−1.50478	−	0.0697666i
$996$	−16.1365	+	11.5547i	−0.511305	+	0.366126i
$997$	0.834811	+	0.425357i	0.0264387	+	0.0134712i	0.467160	−	0.884173i	$-0.345277\pi$
$997$	0.834811	+	0.425357i	0.0264387	+	0.0134712i	−0.440721	+	0.897644i	$0.645277\pi$
$998$	6.76984	−	1.07224i	0.214296	−	0.0339411i
$999$	−24.5011	−	18.5873i	−0.775180	−	0.588076i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.l.a.113.8	yes	80
3.2	odd	2	inner	150.2.l.a.113.2	yes	80
5.2	odd	4		750.2.l.c.707.5		80
5.3	odd	4		750.2.l.a.707.6		80
5.4	even	2		750.2.l.b.293.3		80
15.2	even	4		750.2.l.c.707.9		80
15.8	even	4		750.2.l.a.707.2		80
15.14	odd	2		750.2.l.b.293.9		80
25.2	odd	20	inner	150.2.l.a.77.2	✓	80
25.11	even	5		750.2.l.c.593.9		80
25.14	even	10		750.2.l.a.593.2		80
25.23	odd	20		750.2.l.b.407.9		80
75.2	even	20	inner	150.2.l.a.77.8	yes	80
75.11	odd	10		750.2.l.c.593.5		80
75.14	odd	10		750.2.l.a.593.6		80
75.23	even	20		750.2.l.b.407.3		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.77.2	✓	80	25.2	odd	20	inner
150.2.l.a.77.8	yes	80	75.2	even	20	inner
150.2.l.a.113.2	yes	80	3.2	odd	2	inner
150.2.l.a.113.8	yes	80	1.1	even	1	trivial
750.2.l.a.593.2		80	25.14	even	10
750.2.l.a.593.6		80	75.14	odd	10
750.2.l.a.707.2		80	15.8	even	4
750.2.l.a.707.6		80	5.3	odd	4
750.2.l.b.293.3		80	5.4	even	2
750.2.l.b.293.9		80	15.14	odd	2
750.2.l.b.407.3		80	75.23	even	20
750.2.l.b.407.9		80	25.23	odd	20
750.2.l.c.593.5		80	75.11	odd	10
750.2.l.c.593.9		80	25.11	even	5
750.2.l.c.707.5		80	5.2	odd	4
750.2.l.c.707.9		80	15.2	even	4

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.156434 + 0.987688i) q^{2} +(-0.282741 + 1.70882i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-0.103560 + 2.23367i) q^{5} +(-1.73201 - 0.0119417i) q^{6} +(2.28673 - 2.28673i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-2.84012 - 0.966305i) q^{9} +O(q^{10})\)	\(q+(0.156434 + 0.987688i) q^{2} +(-0.282741 + 1.70882i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-0.103560 + 2.23367i) q^{5} +(-1.73201 - 0.0119417i) q^{6} +(2.28673 - 2.28673i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-2.84012 - 0.966305i) q^{9} +(-2.22237 + 0.247138i) q^{10} +(-2.43923 + 3.35732i) q^{11} +(-0.259151 - 1.71255i) q^{12} +(-2.10294 - 0.333073i) q^{13} +(2.61630 + 1.90085i) q^{14} +(-3.78765 - 0.808514i) q^{15} +(0.809017 - 0.587785i) q^{16} +(4.19457 - 2.13724i) q^{17} +(0.510116 - 2.95631i) q^{18} +(7.55516 + 2.45482i) q^{19} +(-0.591750 - 2.15635i) q^{20} +(3.26105 + 4.55415i) q^{21} +(-3.69756 - 1.88400i) q^{22} +(3.35168 - 0.530854i) q^{23} +(1.65093 - 0.523863i) q^{24} +(-4.97855 - 0.462637i) q^{25} -2.12915i q^{26} +(2.45425 - 4.58003i) q^{27} +(-1.46817 + 2.88144i) q^{28} +(0.0799714 + 0.246127i) q^{29} +(0.206041 - 3.86750i) q^{30} +(-0.605045 + 1.86214i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-5.04737 - 5.11745i) q^{33} +(2.76710 + 3.80859i) q^{34} +(4.87098 + 5.34460i) q^{35} +(2.99971 + 0.0413664i) q^{36} +(0.925865 - 5.84568i) q^{37} +(-1.24271 + 7.84617i) q^{38} +(1.16375 - 3.49937i) q^{39} +(2.03723 - 0.921792i) q^{40} +(-2.94138 - 4.04846i) q^{41} +(-3.98794 + 3.93333i) q^{42} +(6.41535 + 6.41535i) q^{43} +(1.28238 - 3.94676i) q^{44} +(2.45253 - 6.24381i) q^{45} +(1.04864 + 3.22737i) q^{46} +(1.85197 - 3.63470i) q^{47} +(0.775676 + 1.54865i) q^{48} -3.45825i q^{49} +(-0.321875 - 4.98963i) q^{50} +(2.46618 + 7.77205i) q^{51} +(2.10294 - 0.333073i) q^{52} +(-6.16604 - 3.14175i) q^{53} +(4.90757 + 1.70756i) q^{54} +(-7.24652 - 5.79612i) q^{55} +(-3.07564 - 0.999337i) q^{56} +(-6.33100 + 12.2163i) q^{57} +(-0.230586 + 0.117490i) q^{58} +(-5.82928 + 4.23522i) q^{59} +(3.85212 - 0.401506i) q^{60} +(-5.87923 - 4.27151i) q^{61} +(-1.93386 - 0.306293i) q^{62} +(-8.70425 + 4.28489i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(0.961755 - 4.66278i) q^{65} +(4.26487 - 5.78578i) q^{66} +(-1.94227 - 3.81192i) q^{67} +(-3.32883 + 3.32883i) q^{68} +(-0.0405238 + 5.87750i) q^{69} +(-4.51682 + 5.64709i) q^{70} +(10.3128 - 3.35084i) q^{71} +(0.428402 + 2.96925i) q^{72} +(0.126822 + 0.800725i) q^{73} +5.91855 q^{74} +(2.19820 - 8.37663i) q^{75} -7.94397 q^{76} +(2.09941 + 13.2551i) q^{77} +(3.63833 + 0.601998i) q^{78} +(-3.93956 + 1.28004i) q^{79} +(1.22914 + 1.86795i) q^{80} +(7.13251 + 5.48883i) q^{81} +(3.53849 - 3.53849i) q^{82} +(-5.20210 - 10.2097i) q^{83} +(-4.50875 - 3.32354i) q^{84} +(4.33950 + 9.59062i) q^{85} +(-5.33279 + 7.33995i) q^{86} +(-0.443197 + 0.0670665i) q^{87} +(4.09878 + 0.649183i) q^{88} +(-13.0522 - 9.48300i) q^{89} +(6.55059 + 1.44559i) q^{90} +(-5.57050 + 4.04720i) q^{91} +(-3.02359 + 1.54060i) q^{92} +(-3.01098 - 1.56041i) q^{93} +(3.87966 + 1.26058i) q^{94} +(-6.26567 + 16.6215i) q^{95} +(-1.40824 + 1.00839i) q^{96} +(0.292688 + 0.149132i) q^{97} +(3.41567 - 0.540989i) q^{98} +(10.1719 - 7.17812i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q + 4 * q^3 + 4 * q^7	\( 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) \) 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Introduction

L-functions

Modular forms

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