LMFDB - Embedded newform 360.2.bo.a.43.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(43,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 8, 9]))

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

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

chi := DirichletCharacter("360.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bo (of order $12$, degree $4$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$272$
Relative dimension:	$68$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			43.5
Character	$\chi$	$=$	360.43
Dual form			360.2.bo.a.67.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37266 - 0.340317i) q^{2} +(-1.62317 - 0.604421i) q^{3} +(1.76837 + 0.934277i) q^{4} +(1.13051 - 1.92924i) q^{5} +(2.02236 + 1.38205i) q^{6} +(3.44877 - 0.924095i) q^{7} +(-2.10941 - 1.88425i) q^{8} +(2.26935 + 1.96215i) q^{9} +O(q^{10})$	\(q+(-1.37266 - 0.340317i) q^{2} +(-1.62317 - 0.604421i) q^{3} +(1.76837 + 0.934277i) q^{4} +(1.13051 - 1.92924i) q^{5} +(2.02236 + 1.38205i) q^{6} +(3.44877 - 0.924095i) q^{7} +(-2.10941 - 1.88425i) q^{8} +(2.26935 + 1.96215i) q^{9} +(-2.20835 + 2.26345i) q^{10} +(-2.54379 + 4.40598i) q^{11} +(-2.30566 - 2.58533i) q^{12} +(1.78469 + 0.478207i) q^{13} +(-5.04846 + 0.0947893i) q^{14} +(-3.00107 + 2.44817i) q^{15} +(2.25425 + 3.30429i) q^{16} +(3.48816 - 3.48816i) q^{17} +(-2.44728 - 3.46566i) q^{18} -0.267684i q^{19} +(3.80159 - 2.35539i) q^{20} +(-6.15647 - 0.584545i) q^{21} +(4.99118 - 5.18220i) q^{22} +(2.42625 + 0.650112i) q^{23} +(2.28505 + 4.33342i) q^{24} +(-2.44390 - 4.36203i) q^{25} +(-2.28703 - 1.26378i) q^{26} +(-2.49757 - 4.55655i) q^{27} +(6.96205 + 1.58796i) q^{28} +(2.25790 - 3.91080i) q^{29} +(4.95260 - 2.33918i) q^{30} +(6.25338 - 3.61039i) q^{31} +(-1.96981 - 5.30282i) q^{32} +(6.79207 - 5.61413i) q^{33} +(-5.97513 + 3.60096i) q^{34} +(2.11606 - 7.69819i) q^{35} +(2.17986 + 5.59001i) q^{36} +(0.459741 + 0.459741i) q^{37} +(-0.0910975 + 0.367438i) q^{38} +(-2.60782 - 1.85492i) q^{39} +(-6.01986 + 1.93940i) q^{40} +(-1.01420 - 1.75664i) q^{41} +(8.25179 + 2.89753i) q^{42} +(-6.17228 + 1.65386i) q^{43} +(-8.61477 + 5.41479i) q^{44} +(6.35098 - 2.15989i) q^{45} +(-3.10916 - 1.71808i) q^{46} +(-12.3810 + 3.31749i) q^{47} +(-1.66185 - 6.72594i) q^{48} +(4.97788 - 2.87398i) q^{49} +(1.87017 + 6.81927i) q^{50} +(-7.77019 + 3.55356i) q^{51} +(2.70922 + 2.51304i) q^{52} +(6.27784 - 6.27784i) q^{53} +(1.87764 + 7.10454i) q^{54} +(5.62440 + 9.88857i) q^{55} +(-9.01609 - 4.54903i) q^{56} +(-0.161794 + 0.434497i) q^{57} +(-4.43023 + 4.59978i) q^{58} +(12.0393 - 6.95090i) q^{59} +(-7.59428 + 1.52544i) q^{60} +(3.24440 + 1.87316i) q^{61} +(-9.81241 + 2.82769i) q^{62} +(9.63968 + 4.66991i) q^{63} +(0.899232 + 7.94930i) q^{64} +(2.94018 - 2.90248i) q^{65} +(-11.2338 + 5.39481i) q^{66} +(-10.9536 - 2.93500i) q^{67} +(9.42726 - 2.90945i) q^{68} +(-3.54527 - 2.52172i) q^{69} +(-5.52445 + 9.84683i) q^{70} +5.77252i q^{71} +(-1.08982 - 8.41500i) q^{72} +(1.30545 + 1.30545i) q^{73} +(-0.474609 - 0.787525i) q^{74} +(1.33037 + 8.55746i) q^{75} +(0.250091 - 0.473364i) q^{76} +(-4.70141 + 17.5459i) q^{77} +(2.94838 + 3.43365i) q^{78} +(0.436342 - 0.755767i) q^{79} +(8.92321 - 0.613464i) q^{80} +(1.29991 + 8.90563i) q^{81} +(0.794330 + 2.75642i) q^{82} +(0.471936 - 0.126455i) q^{83} +(-10.3408 - 6.78554i) q^{84} +(-2.78609 - 10.6729i) q^{85} +(9.03526 - 0.169645i) q^{86} +(-6.02872 + 4.98316i) q^{87} +(13.6679 - 4.50089i) q^{88} +12.5274i q^{89} +(-9.45275 + 0.803436i) q^{90} +6.59690 q^{91} +(3.68312 + 3.41643i) q^{92} +(-12.3325 + 2.08060i) q^{93} +(18.1239 - 0.340292i) q^{94} +(-0.516426 - 0.302619i) q^{95} +(-0.00779747 + 9.79796i) q^{96} +(-2.34140 - 8.73824i) q^{97} +(-7.81098 + 2.25093i) q^{98} +(-14.4180 + 5.00741i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8}+O(q^{10}) $ 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8	$ 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8} - 8 q^{10} - 8 q^{11} - 10 q^{12} - 4 q^{16} - 16 q^{17} + 20 q^{18} + 14 q^{20} + 6 q^{22} - 4 q^{25} - 48 q^{26} - 8 q^{27} + 8 q^{28} - 34 q^{30} - 22 q^{32} + 4 q^{33} - 16 q^{35} - 8 q^{36} - 26 q^{38} - 2 q^{40} - 8 q^{41} - 66 q^{42} - 4 q^{43} - 40 q^{46} - 38 q^{48} - 42 q^{50} - 16 q^{51} + 14 q^{52} + 24 q^{56} + 16 q^{57} + 6 q^{58} + 14 q^{60} - 76 q^{62} - 4 q^{65} - 44 q^{66} - 4 q^{67} - 46 q^{68} + 18 q^{70} + 38 q^{72} - 16 q^{73} - 120 q^{75} - 38 q^{78} + 92 q^{80} - 32 q^{81} - 4 q^{83} - 40 q^{86} - 42 q^{88} - 14 q^{90} - 32 q^{91} + 52 q^{92} + 108 q^{96} - 4 q^{97} - 140 q^{98}+O(q^{100}) $ 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8 - 8 * q^10 - 8 * q^11 - 10 * q^12 - 4 * q^16 - 16 * q^17 + 20 * q^18 + 14 * q^20 + 6 * q^22 - 4 * q^25 - 48 * q^26 - 8 * q^27 + 8 * q^28 - 34 * q^30 - 22 * q^32 + 4 * q^33 - 16 * q^35 - 8 * q^36 - 26 * q^38 - 2 * q^40 - 8 * q^41 - 66 * q^42 - 4 * q^43 - 40 * q^46 - 38 * q^48 - 42 * q^50 - 16 * q^51 + 14 * q^52 + 24 * q^56 + 16 * q^57 + 6 * q^58 + 14 * q^60 - 76 * q^62 - 4 * q^65 - 44 * q^66 - 4 * q^67 - 46 * q^68 + 18 * q^70 + 38 * q^72 - 16 * q^73 - 120 * q^75 - 38 * q^78 + 92 * q^80 - 32 * q^81 - 4 * q^83 - 40 * q^86 - 42 * q^88 - 14 * q^90 - 32 * q^91 + 52 * q^92 + 108 * q^96 - 4 * q^97 - 140 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.37266	−	0.340317i	−0.970614	−	0.240641i
$2$	−1.37266	−	0.340317i	−0.970614	−	0.240641i
$3$	−1.62317	−	0.604421i	−0.937137	−	0.348962i
$3$	−1.62317	−	0.604421i	−0.937137	−	0.348962i
$4$	1.76837	+	0.934277i	0.884184	+	0.467138i
$5$	1.13051	−	1.92924i	0.505578	−	0.862781i
$5$	1.13051	−	1.92924i	0.505578	−	0.862781i
$6$	2.02236	+	1.38205i	0.825624	+	0.564221i
$7$	3.44877	−	0.924095i	1.30351	−	0.349275i	0.460735	−	0.887538i	$-0.347586\pi$
$7$	3.44877	−	0.924095i	1.30351	−	0.349275i	0.842777	+	0.538263i	$0.180919\pi$
$8$	−2.10941	−	1.88425i	−0.745790	−	0.666182i
$9$	2.26935	+	1.96215i	0.756451	+	0.654051i
$10$	−2.20835	+	2.26345i	−0.698342	+	0.715765i
$11$	−2.54379	+	4.40598i	−0.766983	+	1.32845i	0.172209	+	0.985060i	$0.444909\pi$
$11$	−2.54379	+	4.40598i	−0.766983	+	1.32845i	−0.939192	+	0.343393i	$0.888424\pi$
$12$	−2.30566	−	2.58533i	−0.665588	−	0.746319i
$13$	1.78469	+	0.478207i	0.494985	+	0.132631i	0.497672	−	0.867366i	$-0.334188\pi$
$13$	1.78469	+	0.478207i	0.494985	+	0.132631i	−0.00268658	+	0.999996i	$0.500855\pi$
$14$	−5.04846	+	0.0947893i	−1.34926	+	0.0253335i
$15$	−3.00107	+	2.44817i	−0.774874	+	0.632116i
$16$	2.25425	+	3.30429i	0.563564	+	0.826073i
$17$	3.48816	−	3.48816i	0.846003	−	0.846003i	−0.143628	−	0.989632i	$-0.545877\pi$
$17$	3.48816	−	3.48816i	0.846003	−	0.846003i	0.989632	+	0.143628i	$0.0458770\pi$
$18$	−2.44728	−	3.46566i	−0.576831	−	0.816864i
$19$		−	0.267684i		−	0.0614110i	−0.999528	−	0.0307055i	$-0.990225\pi$
$19$		−	0.267684i		−	0.0614110i	0.999528	−	0.0307055i	$-0.00977540\pi$
$20$	3.80159	−	2.35539i	0.850062	−	0.526682i
$21$	−6.15647	−	0.584545i	−1.34345	−	0.127558i
$22$	4.99118	−	5.18220i	1.06412	−	1.10485i
$23$	2.42625	+	0.650112i	0.505908	+	0.135558i	0.502741	−	0.864437i	$-0.332325\pi$
$23$	2.42625	+	0.650112i	0.505908	+	0.135558i	0.00316765	+	0.999995i	$0.498992\pi$
$24$	2.28505	+	4.33342i	0.466434	+	0.884556i
$25$	−2.44390	−	4.36203i	−0.488781	−	0.872407i
$26$	−2.28703	−	1.26378i	−0.448523	−	0.247847i
$27$	−2.49757	−	4.55655i	−0.480658	−	0.876908i
$28$	6.96205	+	1.58796i	1.31570	+	0.300097i
$29$	2.25790	−	3.91080i	0.419281	−	0.726216i	−0.576586	−	0.817036i	$-0.695615\pi$
$29$	2.25790	−	3.91080i	0.419281	−	0.726216i	0.995867	+	0.0908199i	$0.0289488\pi$
$30$	4.95260	−	2.33918i	0.904217	−	0.427074i
$31$	6.25338	−	3.61039i	1.12314	−	0.648445i	0.180939	−	0.983494i	$-0.442086\pi$
$31$	6.25338	−	3.61039i	1.12314	−	0.648445i	0.942201	+	0.335049i	$0.108753\pi$
$32$	−1.96981	−	5.30282i	−0.348216	−	0.937414i
$33$	6.79207	−	5.61413i	1.18235	−	0.977294i
$34$	−5.97513	+	3.60096i	−1.02473	+	0.617560i
$35$	2.11606	−	7.69819i	0.357680	−	1.30123i
$36$	2.17986	+	5.59001i	0.363309	+	0.931669i
$37$	0.459741	+	0.459741i	0.0755810	+	0.0755810i	0.743887	−	0.668306i	$-0.232980\pi$
$37$	0.459741	+	0.459741i	0.0755810	+	0.0755810i	−0.668306	+	0.743887i	$0.732980\pi$
$38$	−0.0910975	+	0.367438i	−0.0147780	+	0.0596064i
$39$	−2.60782	−	1.85492i	−0.417585	−	0.297024i
$40$	−6.01986	+	1.93940i	−0.951824	+	0.306646i
$41$	−1.01420	−	1.75664i	−0.158391	−	0.274342i	0.775897	−	0.630859i	$-0.217297\pi$
$41$	−1.01420	−	1.75664i	−0.158391	−	0.274342i	−0.934289	+	0.356517i	$0.883964\pi$
$42$	8.25179	+	2.89753i	1.27328	+	0.447099i
$43$	−6.17228	+	1.65386i	−0.941264	+	0.252211i	−0.696651	−	0.717410i	$-0.745328\pi$
$43$	−6.17228	+	1.65386i	−0.941264	+	0.252211i	−0.244613	+	0.969621i	$0.578661\pi$
$44$	−8.61477	+	5.41479i	−1.29873	+	0.816310i
$45$	6.35098	−	2.15989i	0.946748	−	0.321977i
$46$	−3.10916	−	1.71808i	−0.458421	−	0.253316i
$47$	−12.3810	+	3.31749i	−1.80596	+	0.483905i	−0.994883	−	0.101037i	$-0.967784\pi$
$47$	−12.3810	+	3.31749i	−1.80596	+	0.483905i	−0.811075	+	0.584942i	$0.801117\pi$
$48$	−1.66185	−	6.72594i	−0.239868	−	0.970806i
$49$	4.97788	−	2.87398i	0.711125	−	0.410568i
$50$	1.87017	+	6.81927i	0.264481	+	0.964391i
$51$	−7.77019	+	3.55356i	−1.08804	+	0.497598i
$52$	2.70922	+	2.51304i	0.375701	+	0.348497i
$53$	6.27784	−	6.27784i	0.862327	−	0.862327i	−0.129281	−	0.991608i	$-0.541267\pi$
$53$	6.27784	−	6.27784i	0.862327	−	0.862327i	0.991608	+	0.129281i	$0.0412669\pi$
$54$	1.87764	+	7.10454i	0.255514	+	0.966805i
$55$	5.62440	+	9.88857i	0.758394	+	1.33337i
$56$	−9.01609	−	4.54903i	−1.20483	−	0.607890i
$57$	−0.161794	+	0.434497i	−0.0214301	+	0.0575505i
$58$	−4.43023	+	4.59978i	−0.581718	+	0.603980i
$59$	12.0393	−	6.95090i	1.56738	−	0.904930i	0.570912	−	0.821012i	$-0.306590\pi$
$59$	12.0393	−	6.95090i	1.56738	−	0.904930i	0.996473	−	0.0839182i	$-0.0267435\pi$
$60$	−7.59428	+	1.52544i	−0.980417	+	0.196933i
$61$	3.24440	+	1.87316i	0.415403	+	0.239833i	0.693109	−	0.720833i	$-0.256241\pi$
$61$	3.24440	+	1.87316i	0.415403	+	0.239833i	−0.277706	+	0.960666i	$0.589574\pi$
$62$	−9.81241	+	2.82769i	−1.24618	+	0.359117i
$63$	9.63968	+	4.66991i	1.21449	+	0.588354i
$64$	0.899232	+	7.94930i	0.112404	+	0.993663i
$65$	2.94018	−	2.90248i	0.364685	−	0.360008i
$66$	−11.2338	+	5.39481i	−1.38278	+	0.664055i
$67$	−10.9536	−	2.93500i	−1.33819	−	0.358567i	−0.482428	−	0.875936i	$-0.660245\pi$
$67$	−10.9536	−	2.93500i	−1.33819	−	0.358567i	−0.855763	+	0.517368i	$0.826912\pi$
$68$	9.42726	−	2.90945i	1.14322	−	0.352822i
$69$	−3.54527	−	2.52172i	−0.426801	−	0.303579i
$70$	−5.52445	+	9.84683i	−0.660298	+	1.17692i
$71$			5.77252i			0.685072i	0.939505	+	0.342536i	$0.111286\pi$
$71$			5.77252i			0.685072i	−0.939505	+	0.342536i	$0.888714\pi$
$72$	−1.08982	−	8.41500i	−0.128436	−	0.991718i
$73$	1.30545	+	1.30545i	0.152791	+	0.152791i	0.779363	−	0.626572i	$-0.215543\pi$
$73$	1.30545	+	1.30545i	0.152791	+	0.152791i	−0.626572	+	0.779363i	$0.715543\pi$
$74$	−0.474609	−	0.787525i	−0.0551722	−	0.0915479i
$75$	1.33037	+	8.55746i	0.153617	+	0.988130i
$76$	0.250091	−	0.473364i	0.0286874	−	0.0542986i
$77$	−4.70141	+	17.5459i	−0.535776	+	1.99954i
$78$	2.94838	+	3.43365i	0.333838	+	0.388784i
$79$	0.436342	−	0.755767i	0.0490923	−	0.0850304i	−0.840435	−	0.541912i	$-0.817700\pi$
$79$	0.436342	−	0.755767i	0.0490923	−	0.0850304i	0.889527	+	0.456882i	$0.151034\pi$
$80$	8.92321	−	0.613464i	0.997645	−	0.0685874i
$81$	1.29991	+	8.90563i	0.144435	+	0.989514i
$82$	0.794330	+	2.75642i	0.0877191	+	0.304395i
$83$	0.471936	−	0.126455i	0.0518017	−	0.0138802i	−0.232825	−	0.972519i	$-0.574797\pi$
$83$	0.471936	−	0.126455i	0.0518017	−	0.0138802i	0.284627	+	0.958638i	$0.408130\pi$
$84$	−10.3408	−	6.78554i	−1.12827	−	0.740363i
$85$	−2.78609	−	10.6729i	−0.302194	−	1.15764i
$86$	9.03526	−	0.169645i	0.974297	−	0.0182933i
$87$	−6.02872	+	4.98316i	−0.646346	+	0.534251i
$88$	13.6679	−	4.50089i	1.45700	−	0.479797i
$89$			12.5274i			1.32790i	0.747775	+	0.663952i	$0.231122\pi$
$89$			12.5274i			1.32790i	−0.747775	+	0.663952i	$0.768878\pi$
$90$	−9.45275	+	0.803436i	−0.996407	+	0.0846895i
$91$	6.59690			0.691543
$92$	3.68312	+	3.41643i	0.383992	+	0.356187i
$93$	−12.3325	+	2.08060i	−1.27882	+	0.215748i
$94$	18.1239	−	0.340292i	1.86934	−	0.0350984i
$95$	−0.516426	−	0.302619i	−0.0529842	−	0.0310481i
$96$	−0.00779747	+	9.79796i	−0.000795826	+	1.00000i
$97$	−2.34140	−	8.73824i	−0.237734	−	0.887234i	−0.976898	−	0.213708i	$-0.931446\pi$
$97$	−2.34140	−	8.73824i	−0.237734	−	0.887234i	0.739164	−	0.673526i	$-0.235221\pi$
$98$	−7.81098	+	2.25093i	−0.789028	+	0.227378i
$99$	−14.4180	+	5.00741i	−1.44906	+	0.503263i
$100$	−0.246379	−	9.99696i	−0.0246379	−	0.999696i
$101$	−2.71741	−	1.56890i	−0.270392	−	0.156111i	0.358674	−	0.933463i	$-0.383229\pi$
$101$	−2.71741	−	1.56890i	−0.270392	−	0.156111i	−0.629066	+	0.777352i	$0.716562\pi$
$102$	11.8751	−	2.23348i	1.17581	−	0.221148i
$103$	5.16742	+	1.38461i	0.509161	+	0.136429i	0.504248	−	0.863559i	$-0.331770\pi$
$103$	5.16742	+	1.38461i	0.509161	+	0.136429i	0.00491264	+	0.999988i	$0.498436\pi$
$104$	−2.86359	−	4.37154i	−0.280798	−	0.428665i
$105$	−8.08767	+	11.2165i	−0.789276	+	1.09461i
$106$	−10.7538	+	6.48085i	−1.04450	+	0.629476i
$107$	−0.319046	+	0.319046i	−0.0308434	+	0.0308434i	−0.722360	−	0.691517i	$-0.756943\pi$
$107$	−0.319046	+	0.319046i	−0.0308434	+	0.0308434i	0.691517	+	0.722360i	$0.256943\pi$
$108$	−0.159558	−	10.3911i	−0.0153534	−	0.999882i
$109$	−6.45000			−0.617798			−0.308899	−	0.951095i	$-0.599961\pi$
$109$	−6.45000			−0.617798			−0.308899	+	0.951095i	$0.599961\pi$
$110$	−4.35511	−	15.4877i	−0.415244	−	1.47669i
$111$	−0.468361	−	1.02411i	−0.0444548	−	0.0972047i
$112$	10.8279	+	9.31259i	1.02314	+	0.879957i
$113$	−3.65055	+	13.6240i	−0.343415	+	1.28164i	0.551038	+	0.834480i	$0.314232\pi$
$113$	−3.65055	+	13.6240i	−0.343415	+	1.28164i	−0.894453	+	0.447162i	$0.852435\pi$
$114$	0.369954	−	0.541353i	0.0346494	−	0.0507024i
$115$	3.99712	−	3.94586i	0.372733	−	0.367953i
$116$	7.64656	−	4.80623i	0.709965	−	0.446247i
$117$	3.11178	+	4.58706i	0.287684	+	0.424074i
$118$	−18.8913	+	5.44401i	−1.73909	+	0.501162i
$119$	8.80647	−	15.2533i	0.807288	−	1.39826i
$120$	10.9435	+	0.490559i	0.998997	+	0.0447817i
$121$	−7.44177	−	12.8895i	−0.676525	−	1.17178i
$122$	−3.81598	−	3.67532i	−0.345483	−	0.332748i
$123$	0.584464	+	3.46433i	0.0526994	+	0.312368i
$124$	14.4314	−	0.542115i	1.29598	−	0.0486834i
$125$	−11.1782	−	0.216443i	−0.999813	−	0.0193592i
$126$	−11.6427	−	9.69074i	−1.03722	−	0.863319i
$127$	−2.35806	−	2.35806i	−0.209244	−	0.209244i	0.594702	−	0.803946i	$-0.297270\pi$
$127$	−2.35806	−	2.35806i	−0.209244	−	0.209244i	−0.803946	+	0.594702i	$0.797270\pi$
$128$	1.47095	−	11.2177i	0.130015	−	0.991512i
$129$	11.0183	+	1.04616i	0.970106	+	0.0921096i
$130$	−5.02363	+	2.98351i	−0.440601	+	0.261671i
$131$	7.71421	+	13.3614i	0.673994	+	1.16739i	0.976762	+	0.214327i	$0.0687559\pi$
$131$	7.71421	+	13.3614i	0.673994	+	1.16739i	−0.302768	+	0.953064i	$0.597911\pi$
$132$	17.2560	−	3.58217i	1.50194	−	0.311788i
$133$	−0.247366	−	0.923181i	−0.0214493	−	0.0800499i
$134$	14.0366	+	7.75643i	1.21258	+	0.670053i
$135$	−11.6142	−	0.332800i	−0.999590	−	0.0286429i
$136$	−13.9305	+	0.785412i	−1.19453	+	0.0673485i
$137$	2.51915	+	9.40158i	0.215225	+	0.803231i	0.986087	+	0.166229i	$0.0531591\pi$
$137$	2.51915	+	9.40158i	0.215225	+	0.803231i	−0.770862	+	0.637002i	$0.780174\pi$
$138$	4.00826	+	4.66797i	0.341206	+	0.397364i
$139$	1.74068	−	1.00498i	0.147642	−	0.0852413i	−0.424359	−	0.905494i	$-0.639501\pi$
$139$	1.74068	−	1.00498i	0.147642	−	0.0852413i	0.572001	+	0.820253i	$0.306167\pi$
$140$	10.9342	−	11.6362i	0.924110	−	0.983442i
$141$	22.1016	+	2.09851i	1.86129	+	0.176726i
$142$	1.96449	−	7.92369i	0.164856	−	0.664941i
$143$	−6.64686	+	6.64686i	−0.555839	+	0.555839i
$144$	−1.36783	+	11.9218i	−0.113985	+	0.993482i
$145$	−4.99228	−	8.77720i	−0.414586	−	0.728907i
$146$	−1.34767	−	2.23620i	−0.111534	−	0.185069i
$147$	−9.81702	+	1.65622i	−0.809694	+	0.136603i
$148$	0.383467	+	1.24252i	0.0315208	+	0.102134i
$149$	5.04979	+	8.74650i	0.413695	+	0.716541i	0.995290	−	0.0969373i	$-0.0309046\pi$
$149$	5.04979	+	8.74650i	0.413695	+	0.716541i	−0.581595	+	0.813478i	$0.697571\pi$
$150$	1.08611	−	12.1992i	0.0886809	−	0.996060i
$151$	−12.9877	−	7.49844i	−1.05692	−	0.610214i	−0.132343	−	0.991204i	$-0.542250\pi$
$151$	−12.9877	−	7.49844i	−1.05692	−	0.610214i	−0.924579	+	0.380990i	$0.875583\pi$
$152$	−0.504383	+	0.564656i	−0.0409109	+	0.0457997i
$153$	14.7602	−	1.07156i	1.19329	−	0.0866305i
$154$	12.4246	−	22.4845i	1.00120	−	1.81185i
$155$	0.104198	−	16.1458i	0.00836940	−	1.29686i
$156$	−2.87858	−	5.71660i	−0.230471	−	0.457694i
$157$	−0.235114	+	0.877458i	−0.0187642	+	0.0700288i	−0.974673	−	0.223635i	$-0.928208\pi$
$157$	−0.235114	+	0.877458i	−0.0187642	+	0.0700288i	0.955909	+	0.293663i	$0.0948745\pi$
$158$	−0.856148	+	0.888913i	−0.0681115	+	0.0707181i
$159$	−13.9844	+	6.39553i	−1.10904	+	0.507199i
$160$	−12.4573	−	2.19465i	−0.984834	−	0.173502i
$161$	8.96835			0.706805
$162$	1.24640	−	12.6667i	0.0979267	−	0.995194i
$163$	13.3113	+	13.3113i	1.04262	+	1.04262i	0.999050	+	0.0435674i	$0.0138723\pi$
$163$	13.3113	+	13.3113i	1.04262	+	1.04262i	0.0435674	+	0.999050i	$0.486128\pi$
$164$	−0.152286	−	4.05394i	−0.0118916	−	0.316559i
$165$	−3.15249	−	19.4503i	−0.245421	−	1.51421i
$166$	−0.690840	+	0.0129711i	−0.0536196	+	0.00100676i
$167$	5.46054	−	20.3790i	0.422549	−	1.57697i	−0.346669	−	0.937988i	$-0.612687\pi$
$167$	5.46054	−	20.3790i	0.422549	−	1.57697i	0.769218	−	0.638987i	$-0.220646\pi$
$168$	11.8851	+	12.8334i	0.916956	+	0.990115i
$169$	−8.30188	−	4.79309i	−0.638606	−	0.368699i
$170$	0.192184	+	15.5983i	0.0147399	+	1.19634i
$171$	0.525237	−	0.607470i	0.0401659	−	0.0464544i
$172$	−12.4600	−	2.84199i	−0.950069	−	0.216700i
$173$	3.18196	+	11.8753i	0.241920	+	0.902859i	0.974906	+	0.222615i	$0.0714593\pi$
$173$	3.18196	+	11.8753i	0.241920	+	0.902859i	−0.732986	+	0.680244i	$0.761874\pi$
$174$	9.97121	−	4.78849i	0.755915	−	0.363014i
$175$	−12.4594	−	12.7852i	−0.941842	−	0.966474i
$176$	−20.2930	+	1.52677i	−1.52964	+	0.115084i
$177$	−23.7431	+	4.00567i	−1.78464	+	0.301085i
$178$	4.26329	−	17.1958i	0.319547	−	1.28888i
$179$			1.81651i			0.135772i	0.997693	+	0.0678862i	$0.0216255\pi$
$179$			1.81651i			0.135772i	−0.997693	+	0.0678862i	$0.978375\pi$
$180$	13.2488	+	2.11409i	0.987507	+	0.157575i
$181$		−	3.39261i		−	0.252171i	−0.992019	−	0.126085i	$-0.959759\pi$
$181$		−	3.39261i		−	0.252171i	0.992019	−	0.126085i	$-0.0402414\pi$
$182$	−9.05528	−	2.24504i	−0.671222	−	0.166413i
$183$	−4.13404	−	5.00143i	−0.305597	−	0.369716i
$184$	−3.89299	−	5.94301i	−0.286995	−	0.438124i
$185$	1.40669	−	0.367209i	0.103422	−	0.0269977i
$186$	17.6363	+	1.34100i	1.29316	+	0.0983272i
$187$	6.49561	+	24.2419i	0.475006	+	1.77275i
$188$	−24.9937	−	5.70076i	−1.82285	−	0.415771i
$189$	−12.8242	−	13.4065i	−0.932826	−	0.975178i
$190$	0.605889	+	0.591140i	0.0439558	+	0.0428858i
$191$	8.00326	+	4.62068i	0.579095	+	0.334341i	0.760774	−	0.649017i	$-0.224820\pi$
$191$	8.00326	+	4.62068i	0.579095	+	0.334341i	−0.181678	+	0.983358i	$0.558153\pi$
$192$	3.34511	−	13.4466i	0.241413	−	0.970422i
$193$	−4.99989	+	18.6598i	−0.359900	+	1.34317i	0.514305	+	0.857608i	$0.328050\pi$
$193$	−4.99989	+	18.6598i	−0.359900	+	1.34317i	−0.874205	+	0.485558i	$0.838617\pi$
$194$	0.240170	+	12.7914i	0.0172432	+	0.918370i
$195$	−6.52673	+	2.93410i	−0.467389	+	0.210116i
$196$	11.4878	−	0.431540i	0.820558	−	0.0308243i
$197$	11.4401	+	11.4401i	0.815075	+	0.815075i	0.985390	−	0.170315i	$-0.0544784\pi$
$197$	11.4401	+	11.4401i	0.815075	+	0.815075i	−0.170315	+	0.985390i	$0.554478\pi$
$198$	21.4950	−	1.96677i	1.52758	−	0.139772i
$199$	14.1836			1.00545			0.502726	−	0.864446i	$-0.332330\pi$
$199$	14.1836			1.00545			0.502726	+	0.864446i	$0.332330\pi$
$200$	−3.06394	+	13.8062i	−0.216654	+	0.976249i
$201$	16.0055	+	11.3846i	1.12894	+	0.803005i
$202$	3.19615	+	3.07834i	0.224880	+	0.216591i
$203$	4.17303	−	15.5739i	0.292889	−	1.09308i
$204$	−17.0606	−	0.975507i	−1.19448	−	0.0682992i
$205$	−4.53554	−	0.0292704i	−0.316776	−	0.00204434i
$206$	−6.62189	−	3.65915i	−0.461369	−	0.254945i
$207$	4.23040	+	6.23601i	0.294033	+	0.433433i
$208$	2.44302	+	6.97515i	0.169393	+	0.483639i
$209$	1.17941	+	0.680933i	0.0815816	+	0.0471011i
$210$	14.9187	−	12.6440i	1.02949	−	0.872517i
$211$	−10.4741	−	18.1417i	−0.721069	−	1.24893i	−0.960572	−	0.278033i	$-0.910318\pi$
$211$	−10.4741	−	18.1417i	−0.721069	−	1.24893i	0.239503	−	0.970896i	$-0.423016\pi$
$212$	16.9668	−	5.23629i	1.16528	−	0.359630i
$213$	3.48903	−	9.36977i	0.239064	−	0.642006i
$214$	0.546518	−	0.329364i	0.0373592	−	0.0225149i
$215$	−3.78713	+	13.7775i	−0.258280	+	0.939617i
$216$	−3.31724	+	14.3177i	−0.225710	+	0.974195i
$217$	18.2301	−	18.2301i	1.23754	−	1.23754i
$218$	8.85363	+	2.19505i	0.599644	+	0.148667i
$219$	−1.32993	−	2.90801i	−0.0898680	−	0.196505i
$220$	0.707346	+	22.7414i	0.0476893	+	1.53322i
$221$	7.89336	−	4.55724i	0.530965	−	0.306553i
$222$	0.294374	+	1.56515i	0.0197571	+	0.105046i
$223$	3.45399	+	12.8905i	0.231296	+	0.863209i	0.979784	+	0.200060i	$0.0641138\pi$
$223$	3.45399	+	12.8905i	0.231296	+	0.863209i	−0.748487	+	0.663149i	$0.769220\pi$
$224$	−11.6937	−	16.4679i	−0.781320	−	1.10031i
$225$	3.01290	−	14.6943i	0.200860	−	0.979620i
$226$	9.64745	−	17.4588i	0.641739	−	1.16134i
$227$	1.42039	+	5.30095i	0.0942743	+	0.351836i	0.996908	−	0.0785722i	$-0.0250361\pi$
$227$	1.42039	+	5.30095i	0.0942743	+	0.351836i	−0.902634	+	0.430409i	$0.858369\pi$
$228$	−0.692051	+	0.617190i	−0.0458322	+	0.0408744i
$229$	3.35248	+	5.80666i	0.221538	+	0.383715i	0.955275	−	0.295718i	$-0.0955590\pi$
$229$	3.35248	+	5.80666i	0.221538	+	0.383715i	−0.733737	+	0.679433i	$0.762226\pi$
$230$	−6.82951	+	4.05601i	−0.450324	+	0.267446i
$231$	18.2363	−	25.6383i	1.19986	−	1.68688i
$232$	−12.1317	+	3.99504i	−0.796488	+	0.262287i
$233$	−10.8668	−	10.8668i	−0.711909	−	0.711909i	0.255025	−	0.966934i	$-0.417916\pi$
$233$	−10.8668	−	10.8668i	−0.711909	−	0.711909i	−0.966934	+	0.255025i	$0.917916\pi$
$234$	−2.71035	−	7.35545i	−0.177181	−	0.480841i
$235$	−7.59663	+	27.6364i	−0.495550	+	1.80280i
$236$	27.7840	−	1.04371i	1.80858	−	0.0679395i
$237$	−1.16506	+	0.963003i	−0.0756787	+	0.0625538i
$238$	−17.2792	+	17.9405i	−1.12004	+	1.16291i
$239$	5.52601	+	9.57132i	0.357448	+	0.619117i	0.987534	−	0.157408i	$-0.0503137\pi$
$239$	5.52601	+	9.57132i	0.357448	+	0.619117i	−0.630086	+	0.776525i	$0.716980\pi$
$240$	−14.8547	−	4.39762i	−0.958864	−	0.283865i
$241$	−10.0632	+	17.4300i	−0.648230	+	1.12277i	0.335315	+	0.942106i	$0.391157\pi$
$241$	−10.0632	+	17.4300i	−0.648230	+	1.12277i	−0.983545	+	0.180662i	$0.942176\pi$
$242$	5.82847	+	20.2254i	0.374668	+	1.30014i
$243$	3.27277	−	15.2410i	0.209948	−	0.977713i
$244$	3.98725	+	6.34360i	0.255258	+	0.406107i
$245$	0.0829449	−	12.8526i	0.00529915	−	0.821120i
$246$	0.376703	−	4.95424i	0.0240177	−	0.315871i
$247$	0.128009	−	0.477734i	0.00814499	−	0.0303975i
$248$	−19.9938	−	4.16711i	−1.26961	−	0.264612i
$249$	−0.842463	−	0.0799902i	−0.0533890	−	0.00506918i
$250$	15.2702	+	4.10125i	0.965774	+	0.259386i
$251$	−15.7647			−0.995062			−0.497531	−	0.867446i	$-0.665760\pi$
$251$	−15.7647			−0.995062			−0.497531	+	0.867446i	$0.665760\pi$
$252$	12.6835	+	17.2643i	0.798987	+	1.08755i
$253$	−9.03626	+	9.03626i	−0.568105	+	0.568105i
$254$	2.43432	+	4.03930i	0.152743	+	0.253448i
$255$	−1.92861	+	19.0079i	−0.120774	+	1.19032i
$256$	−5.83667	+	14.8974i	−0.364792	+	0.931089i
$257$	−16.9754	−	4.54855i	−1.05890	−	0.283731i	−0.312973	−	0.949762i	$-0.601325\pi$
$257$	−16.9754	−	4.54855i	−1.05890	−	0.283731i	−0.745924	+	0.666031i	$0.767992\pi$
$258$	−14.7683	−	5.18573i	−0.919433	−	0.322850i
$259$	2.01039	+	1.16070i	0.124919	+	0.0721222i
$260$	7.91105	−	2.38571i	0.490622	−	0.147955i
$261$	12.7975	−	4.44463i	0.792148	−	0.275116i
$262$	−6.04184	−	20.9659i	−0.373266	−	1.29528i
$263$	−4.33870	−	16.1923i	−0.267536	−	0.998457i	−0.960680	−	0.277658i	$-0.910442\pi$
$263$	−4.33870	−	16.1923i	−0.267536	−	0.998457i	0.693144	−	0.720799i	$-0.256225\pi$
$264$	−24.9057	−	0.955431i	−1.53284	−	0.0588027i
$265$	−5.01429	−	19.2086i	−0.308025	−	1.17997i
$266$	0.0253736	+	1.35139i	0.00155575	+	0.0828592i
$267$	7.57183	−	20.3341i	0.463388	−	1.24443i
$268$	−16.6278	−	15.4238i	−1.01571	−	0.942160i
$269$	−22.5794			−1.37669			−0.688344	−	0.725384i	$-0.741662\pi$
$269$	−22.5794			−1.37669			−0.688344	+	0.725384i	$0.741662\pi$
$270$	15.8290	+	4.40933i	0.963323	+	0.268343i
$271$		−	0.0153675i		−	0.000933507i	−1.00000		0.000466754i	$-0.999851\pi$
$271$		−	0.0153675i		−	0.000933507i	1.00000		0.000466754i	$-0.000148572\pi$
$272$	19.3891	+	3.66269i	1.17564	+	0.222083i
$273$	−10.7079	−	3.98730i	−0.648071	−	0.241323i
$274$	−0.258402	−	13.7624i	−0.0156106	−	0.831420i
$275$	25.4358	+	0.328317i	1.53384	+	0.0197983i
$276$	−3.91337	−	7.77159i	−0.235557	−	0.467795i
$277$	6.37310	−	1.70767i	0.382923	−	0.102604i	−0.0622223	−	0.998062i	$-0.519819\pi$
$277$	6.37310	−	1.70767i	0.382923	−	0.102604i	0.445145	+	0.895458i	$0.353152\pi$
$278$	−2.73136	+	0.787110i	−0.163816	+	0.0472077i
$279$	21.2752	+	4.07684i	1.27372	+	0.244074i
$280$	−18.9689	+	12.2515i	−1.13361	+	0.732165i
$281$	−6.66545	+	11.5449i	−0.397628	+	0.688711i	−0.993433	−	0.114418i	$-0.963500\pi$
$281$	−6.66545	+	11.5449i	−0.397628	+	0.688711i	0.595805	+	0.803129i	$0.296833\pi$
$282$	−29.6238	−	10.4021i	−1.76407	−	0.619436i
$283$	−2.30180	+	8.59043i	−0.136828	+	0.510648i	0.863156	+	0.504937i	$0.168484\pi$
$283$	−2.30180	+	8.59043i	−0.136828	+	0.510648i	−0.999984	+	0.00571072i	$0.998182\pi$
$284$	−5.39313	+	10.2079i	−0.320023	+	0.605730i
$285$	0.655337	+	0.803340i	0.0388188	+	0.0475858i
$286$	11.3859	−	6.86182i	0.673262	−	0.405748i
$287$	−5.12104	−	5.12104i	−0.302286	−	0.302286i
$288$	5.93474	−	15.8990i	0.349708	−	0.936859i
$289$		−	7.33454i		−	0.431443i
$290$	3.86564	+	13.7470i	0.226998	+	0.807254i
$291$	−1.48108	+	15.5988i	−0.0868223	+	0.914420i
$292$	1.08887	+	3.52817i	0.0637211	+	0.206471i
$293$	13.3995	+	3.59040i	0.782810	+	0.209753i	0.628023	−	0.778195i	$-0.283864\pi$
$293$	13.3995	+	3.59040i	0.782810	+	0.209753i	0.154787	+	0.987948i	$0.450531\pi$
$294$	14.0390	+	1.06748i	0.818773	+	0.0622567i
$295$	0.200607	−	31.0847i	0.0116798	−	1.80982i
$296$	−0.103518	−	1.83605i	−0.00601685	−	0.106718i
$297$	26.4294	+	0.586652i	1.53359	+	0.0340410i
$298$	−3.95505	−	13.7245i	−0.229110	−	0.795037i
$299$	4.01923	+	2.32050i	0.232438	+	0.134198i
$300$	−5.64246	+	16.3757i	−0.325767	+	0.945450i
$301$	−19.7585	+	11.4075i	−1.13886	+	0.657520i
$302$	15.2758	+	14.7127i	0.879021	+	0.846621i
$303$	3.46254	+	4.18904i	0.198918	+	0.240654i
$304$	0.884506	−	0.603428i	0.0507299	−	0.0346090i
$305$	7.28158	−	4.14160i	0.416942	−	0.237147i
$306$	−20.6253	−	3.55226i	−1.17907	−	0.203069i
$307$	4.74940	−	4.74940i	0.271062	−	0.271062i	−0.558465	−	0.829528i	$-0.688610\pi$
$307$	4.74940	−	4.74940i	0.271062	−	0.271062i	0.829528	+	0.558465i	$0.188610\pi$
$308$	−24.7066	+	26.6352i	−1.40779	+	1.51768i
$309$	−7.55071	−	5.37074i	−0.429545	−	0.305531i
$310$	−5.63772	+	22.1272i	−0.320201	+	1.25674i
$311$	−7.10052	+	4.09949i	−0.402634	+	0.232461i	−0.687620	−	0.726071i	$-0.741344\pi$
$311$	−7.10052	+	4.09949i	−0.402634	+	0.232461i	0.284986	+	0.958532i	$0.408011\pi$
$312$	2.00585	+	8.82656i	0.113559	+	0.499705i
$313$	−24.7057	+	6.61987i	−1.39645	+	0.374177i	−0.877068	−	0.480367i	$-0.840504\pi$
$313$	−24.7057	+	6.61987i	−1.39645	+	0.374177i	−0.519380	+	0.854544i	$0.673837\pi$
$314$	0.621345	−	1.12443i	0.0350645	−	0.0634555i
$315$	19.9071	−	13.3179i	1.12164	−	0.750376i
$316$	1.47771	−	0.928810i	0.0831276	−	0.0522497i
$317$	−3.92486	+	1.05166i	−0.220442	+	0.0590673i	−0.367350	−	0.930083i	$-0.619735\pi$
$317$	−3.92486	+	1.05166i	−0.220442	+	0.0590673i	0.146907	+	0.989150i	$0.453068\pi$
$318$	21.3723	−	4.01972i	1.19850	−	0.225415i
$319$	11.4873	+	19.8965i	0.643163	+	1.11399i
$320$	16.3527	+	7.25191i	0.914142	+	0.405394i
$321$	0.710704	−	0.325028i	0.0396676	−	0.0181413i
$322$	−12.3105	−	3.05208i	−0.686035	−	0.170086i
$323$	−0.933726	−	0.933726i	−0.0519539	−	0.0519539i
$324$	−6.02159	+	16.9629i	−0.334533	+	0.942384i
$325$	−2.27567	−	8.95359i	−0.126231	−	0.496656i
$326$	−13.7417	−	22.8018i	−0.761084	−	1.26288i
$327$	10.4694	+	3.89851i	0.578961	+	0.215588i
$328$	−1.17059	+	5.61649i	−0.0646349	+	0.310119i
$329$	−39.6336	+	22.8825i	−2.18507	+	1.26155i
$330$	−2.29200	+	27.7714i	−0.126170	+	1.52877i
$331$	4.23030	−	7.32709i	0.232518	−	0.402733i	−0.726030	−	0.687663i	$-0.758637\pi$
$331$	4.23030	−	7.32709i	0.232518	−	0.402733i	0.958549	+	0.284929i	$0.0919702\pi$
$332$	0.952701	+	0.217300i	0.0522862	+	0.0119259i
$333$	0.141232	+	1.94540i	0.00773947	+	0.106607i
$334$	−14.4308	+	26.1150i	−0.789616	+	1.42895i
$335$	−18.0454	+	17.8140i	−0.985925	+	0.973281i
$336$	−11.9468	−	21.6605i	−0.651749	−	1.18168i
$337$	1.71698	+	0.460062i	0.0935296	+	0.0250612i	0.305280	−	0.952263i	$-0.401250\pi$
$337$	1.71698	+	0.460062i	0.0935296	+	0.0250612i	−0.211751	+	0.977324i	$0.567916\pi$
$338$	9.76445	+	9.40454i	0.531116	+	0.511540i
$339$	14.1601	−	19.9077i	0.769072	−	1.08124i
$340$	5.04458	−	21.4766i	0.273581	−	1.16473i
$341$			36.7363i			1.98938i
$342$	−0.927702	+	0.655100i	−0.0501644	+	0.0354237i
$343$	−3.16100	+	3.16100i	−0.170678	+	0.170678i
$344$	16.1362	+	8.14143i	0.870003	+	0.438957i
$345$	−8.87295	+	3.98885i	−0.477703	+	0.214752i
$346$	−0.326391	−	17.3835i	−0.0175469	−	0.934543i
$347$	−8.65088	−	2.31800i	−0.464404	−	0.124437i	0.0190275	−	0.999819i	$-0.493943\pi$
$347$	−8.65088	−	2.31800i	−0.464404	−	0.124437i	−0.483431	+	0.875382i	$0.660610\pi$
$348$	−15.3166	+	3.17958i	−0.821058	+	0.170443i
$349$	−13.5687	+	23.5016i	−0.726313	+	1.25801i	0.232118	+	0.972688i	$0.425434\pi$
$349$	−13.5687	+	23.5016i	−0.726313	+	1.25801i	−0.958431	+	0.285324i	$0.907899\pi$
$350$	12.7514	+	21.7899i	0.681592	+	1.16472i
$351$	−2.27843	−	9.32640i	−0.121614	−	0.497806i
$352$	28.3749	+	4.81033i	1.51239	+	0.256391i
$353$	−7.06345	+	1.89265i	−0.375950	+	0.100735i	−0.441846	−	0.897091i	$-0.645676\pi$
$353$	−7.06345	+	1.89265i	−0.375950	+	0.100735i	0.0658961	+	0.997826i	$0.479009\pi$
$354$	33.9543	+	2.58177i	1.80465	+	0.137219i
$355$	11.1366	+	6.52588i	0.591067	+	0.346358i
$356$	−11.7041	+	22.1531i	−0.620315	+	1.17411i
$357$	−23.5138	+	19.4358i	−1.24448	+	1.02865i
$358$	0.618189	−	2.49344i	0.0326723	−	0.131783i
$359$	9.40665			0.496464			0.248232	−	0.968701i	$-0.420150\pi$
$359$	9.40665			0.496464			0.248232	+	0.968701i	$0.420150\pi$
$360$	−17.4666	−	7.41071i	−0.920569	−	0.390579i
$361$	18.9283			0.996229
$362$	−1.15456	+	4.65689i	−0.0606825	+	0.244761i
$363$	4.28856	+	25.4198i	0.225091	+	1.33420i
$364$	11.6658	+	6.16333i	0.611452	+	0.323046i
$365$	3.99434	−	1.04270i	0.209074	−	0.0545774i
$366$	3.97254	+	8.27213i	0.207648	+	0.432391i
$367$	−28.0207	+	7.50813i	−1.46267	+	0.391921i	−0.900411	−	0.435040i	$-0.856734\pi$
$367$	−28.0207	+	7.50813i	−1.46267	+	0.391921i	−0.562259	+	0.826961i	$0.690068\pi$
$368$	3.32123	+	9.48256i	0.173131	+	0.494313i
$369$	1.14523	−	5.97646i	0.0596183	−	0.311122i
$370$	−2.05587	+	0.0253300i	−0.106880	+	0.00131684i
$371$	15.8495	−	27.4521i	0.822864	−	1.42524i
$372$	−23.7522	−	7.84268i	−1.23150	−	0.406624i
$373$	17.9995	+	4.82295i	0.931979	+	0.249723i	0.692698	−	0.721228i	$-0.256422\pi$
$373$	17.9995	+	4.82295i	0.931979	+	0.249723i	0.239280	+	0.970950i	$0.423088\pi$
$374$	−0.666289	−	35.4864i	−0.0344530	−	1.83496i
$375$	18.0134	+	7.10768i	0.930205	+	0.367039i
$376$	32.3676	+	16.3310i	1.66923	+	0.842205i
$377$	5.89983	−	5.89983i	0.303857	−	0.303857i
$378$	13.0408	+	22.7668i	0.670747	+	1.17100i
$379$		−	18.2204i		−	0.935920i	−0.883750	−	0.467960i	$-0.844989\pi$
$379$		−	18.2204i		−	0.935920i	0.883750	−	0.467960i	$-0.155011\pi$
$380$	−0.630502	−	1.01763i	−0.0323441	−	0.0522032i
$381$	2.40227	+	5.25280i	0.123072	+	0.269109i
$382$	−9.41322	−	9.06625i	−0.481622	−	0.463870i
$383$	−22.9271	−	6.14329i	−1.17152	−	0.313907i	−0.379961	−	0.925003i	$-0.624063\pi$
$383$	−22.9271	−	6.14329i	−1.17152	−	0.313907i	−0.791557	+	0.611095i	$0.790729\pi$
$384$	−9.16779	+	17.3191i	−0.467842	+	0.883812i
$385$	28.5352	+	28.9059i	1.45429	+	1.47318i
$386$	13.2134	−	23.9120i	0.672544	−	1.21709i
$387$	−17.2522	−	8.35778i	−0.876979	−	0.424850i
$388$	4.02347	−	17.6400i	0.204261	−	0.895533i
$389$	8.02989	−	13.9082i	0.407132	−	0.705173i	−0.587435	−	0.809271i	$-0.699862\pi$
$389$	8.02989	−	13.9082i	0.407132	−	0.705173i	0.994567	+	0.104098i	$0.0331956\pi$
$390$	9.95748	−	1.80636i	0.504217	−	0.0914684i
$391$	10.7309	−	6.19546i	0.542683	−	0.313318i
$392$	−15.9157	−	3.31714i	−0.803863	−	0.167541i
$393$	−4.44556	−	26.3504i	−0.224249	−	1.32920i
$394$	−11.8101	−	19.5966i	−0.594983	−	0.987263i
$395$	−0.964765	−	1.69621i	−0.0485426	−	0.0853455i
$396$	−30.1746	−	4.61543i	−1.51633	−	0.231934i
$397$	22.6532	+	22.6532i	1.13693	+	1.13693i	0.988997	+	0.147937i	$0.0472632\pi$
$397$	22.6532	+	22.6532i	1.13693	+	1.13693i	0.147937	+	0.988997i	$0.452737\pi$
$398$	−19.4693	−	4.82694i	−0.975906	−	0.241953i
$399$	−0.156473	+	1.64799i	−0.00783347	+	0.0825027i
$400$	8.90424	−	17.9085i	0.445212	−	0.895425i
$401$	−12.0764	−	20.9170i	−0.603069	−	1.04455i	−0.992354	−	0.123428i	$-0.960611\pi$
$401$	−12.0764	−	20.9170i	−0.603069	−	1.04455i	0.389285	−	0.921117i	$-0.372722\pi$
$402$	−18.0957	−	21.0740i	−0.902531	−	1.05108i
$403$	12.8869	−	3.45303i	0.641941	−	0.172008i
$404$	−3.33960	−	5.31320i	−0.166151	−	0.264342i
$405$	18.6506	+	7.56004i	0.926757	+	0.375661i
$406$	−11.0282	+	19.9575i	−0.547321	+	0.990475i
$407$	−3.19510	+	0.856124i	−0.158375	+	0.0424365i
$408$	23.0863	+	7.14504i	1.14294	+	0.353732i
$409$	10.2081	−	5.89365i	0.504758	−	0.291422i	−0.225918	−	0.974146i	$-0.572538\pi$
$409$	10.2081	−	5.89365i	0.504758	−	0.291422i	0.730676	+	0.682724i	$0.239205\pi$
$410$	6.21578	+	1.58370i	0.306975	+	0.0782134i
$411$	1.59351	−	16.7830i	0.0786021	−	0.827843i
$412$	7.84430	+	7.27629i	0.386461	+	0.358477i
$413$	35.0975	−	35.0975i	1.72703	−	1.72703i
$414$	−3.68466	−	9.99957i	−0.181091	−	0.491452i
$415$	0.289566	−	1.05343i	0.0142142	−	0.0517110i
$416$	−0.979662	−	10.4059i	−0.0480319	−	0.510190i
$417$	−3.43284	+	0.579151i	−0.168107	+	0.0283611i
$418$	−1.38719	−	1.33606i	−0.0678498	−	0.0653489i
$419$	7.69693	−	4.44382i	0.376020	−	0.217095i	−0.300065	−	0.953919i	$-0.597009\pi$
$419$	7.69693	−	4.44382i	0.376020	−	0.217095i	0.676085	+	0.736824i	$0.263675\pi$
$420$	−24.7813	+	12.2787i	−1.20920	+	0.599140i
$421$	−31.3701	−	18.1115i	−1.52888	−	0.882702i	−0.999409	−	0.0343770i	$-0.989055\pi$
$421$	−31.3701	−	18.1115i	−1.52888	−	0.882702i	−0.529476	−	0.848325i	$-0.677611\pi$
$422$	8.20344	+	28.4669i	0.399337	+	1.38575i
$423$	−34.6063	−	16.7649i	−1.68262	−	0.815138i
$424$	−25.0715	+	1.41355i	−1.21758	+	0.0686480i
$425$	−23.7402	−	6.69074i	−1.15157	−	0.324549i
$426$	−7.97793	+	11.6741i	−0.386532	+	0.565612i
$427$	12.9202	+	3.46195i	0.625251	+	0.167535i
$428$	−0.862269	+	0.266114i	−0.0416793	+	0.0128631i
$429$	14.8065	−	6.77148i	0.714864	−	0.326930i
$430$	9.88714	−	17.6229i	0.476800	−	0.849853i
$431$		−	5.20304i		−	0.250622i	−0.992118	−	0.125311i	$-0.960007\pi$
$431$		−	5.20304i		−	0.250622i	0.992118	−	0.125311i	$-0.0399928\pi$
$432$	9.42599	−	18.5243i	0.453508	−	0.891252i
$433$	−16.6989	−	16.6989i	−0.802500	−	0.802500i	0.180986	−	0.983486i	$-0.442071\pi$
$433$	−16.6989	−	16.6989i	−0.802500	−	0.802500i	−0.983486	+	0.180986i	$0.942071\pi$
$434$	−31.2277	+	18.8196i	−1.49898	+	0.903372i
$435$	2.79818	+	17.2643i	0.134163	+	0.827761i
$436$	−11.4060	−	6.02609i	−0.546247	−	0.288597i
$437$	0.174025	−	0.649469i	0.00832473	−	0.0310683i
$438$	0.835885	+	4.44429i	0.0399401	+	0.212356i
$439$	13.3662	−	23.1510i	0.637936	−	1.10494i	−0.347949	−	0.937513i	$-0.613122\pi$
$439$	13.3662	−	23.1510i	0.637936	−	1.10494i	0.985885	−	0.167424i	$-0.0535448\pi$
$440$	6.76834	−	31.4568i	0.322668	−	1.49964i
$441$	16.9357	+	3.24529i	0.806464	+	0.154537i
$442$	−12.3858	+	3.56927i	−0.589131	+	0.169773i
$443$	−11.8069	+	3.16364i	−0.560961	+	0.150309i	−0.528148	−	0.849153i	$-0.677113\pi$
$443$	−11.8069	+	3.16364i	−0.560961	+	0.150309i	−0.0328131	+	0.999462i	$0.510447\pi$
$444$	0.128572	−	2.24859i	0.00610177	−	0.106713i
$445$	24.1683	+	14.1623i	1.14569	+	0.671359i
$446$	−0.354294	−	18.8696i	−0.0167763	−	0.893503i
$447$	−2.91010	−	17.2492i	−0.137643	−	0.815861i
$448$	10.4472	+	26.5843i	0.493582	+	1.25599i
$449$			0.467894i			0.0220813i	0.999939	+	0.0110406i	$0.00351442\pi$
$449$			0.467894i			0.0220813i	−0.999939	+	0.0110406i	$0.996486\pi$
$450$	−9.13639	+	19.1449i	−0.430694	+	0.902498i
$451$	10.3197			0.485934
$452$	−19.1841	+	20.6817i	−0.902346	+	0.972786i
$453$	16.5490	+	20.0212i	0.777539	+	0.940680i
$454$	−0.145696	−	7.75976i	−0.00683787	−	0.364184i
$455$	7.45785	−	12.7270i	0.349629	−	0.596650i
$456$	1.15999	−	0.611673i	0.0543214	−	0.0286442i
$457$	4.85993	+	18.1375i	0.227338	+	0.848437i	0.981454	+	0.191696i	$0.0613988\pi$
$457$	4.85993	+	18.1375i	0.227338	+	0.848437i	−0.754116	+	0.656741i	$0.771934\pi$
$458$	−2.62569	−	9.11145i	−0.122691	−	0.425750i
$459$	−24.6059	−	7.18203i	−1.14851	−	0.335228i
$460$	10.7549	−	3.24332i	0.501450	−	0.151220i
$461$	24.0301	+	13.8738i	1.11919	+	0.646166i	0.941194	−	0.337865i	$-0.109705\pi$
$461$	24.0301	+	13.8738i	1.11919	+	0.646166i	0.177997	+	0.984031i	$0.443038\pi$
$462$	−33.7573	+	28.9865i	−1.57053	+	1.34857i
$463$	1.63210	+	0.437319i	0.0758501	+	0.0203240i	0.296545	−	0.955019i	$-0.404166\pi$
$463$	1.63210	+	0.437319i	0.0758501	+	0.0203240i	−0.220694	+	0.975343i	$0.570832\pi$
$464$	18.0123	−	1.35518i	0.836199	−	0.0629125i
$465$	−9.92799	+	26.1444i	−0.460400	+	1.21242i
$466$	11.2182	+	18.6146i	0.519675	+	0.862303i
$467$	−16.7541	+	16.7541i	−0.775287	+	0.775287i	−0.979025	−	0.203738i	$-0.934691\pi$
$467$	−16.7541	+	16.7541i	−0.775287	+	0.775287i	0.203738	+	0.979025i	$0.434691\pi$
$468$	1.21719	+	11.0189i	0.0562648	+	0.509348i
$469$	−40.4885			−1.86959
$470$	19.8327	−	35.3500i	0.914814	−	1.63057i
$471$	0.911984	−	1.28215i	0.0420220	−	0.0590786i
$472$	−38.4931	−	8.02272i	−1.77179	−	0.369276i
$473$	8.41415	−	31.4020i	0.386883	−	1.44387i
$474$	1.92695	−	0.925382i	0.0885078	−	0.0425042i
$475$	−1.16765	+	0.654195i	−0.0535753	+	0.0300165i
$476$	29.8238	−	18.7457i	1.36697	−	0.859208i
$477$	26.5647	−	1.92854i	1.21631	−	0.0883020i
$478$	−4.32802	−	15.0187i	−0.197959	−	0.686941i
$479$	−0.360334	+	0.624117i	−0.0164641	+	0.0285166i	−0.874140	−	0.485674i	$-0.838574\pi$
$479$	−0.360334	+	0.624117i	−0.0164641	+	0.0285166i	0.857676	+	0.514191i	$0.171908\pi$
$480$	18.8938	+	11.0917i	0.862378	+	0.506265i
$481$	0.600646	+	1.04035i	0.0273871	+	0.0474358i
$482$	19.7451	−	20.5008i	0.899365	−	0.933784i
$483$	−14.5571	−	5.42065i	−0.662373	−	0.246648i
$484$	−1.11741	−	29.7461i	−0.0507915	−	1.35210i
$485$	−19.5051	−	5.36153i	−0.885681	−	0.243454i
$486$	−9.67916	+	19.8069i	−0.439056	+	0.898460i
$487$	0.798221	+	0.798221i	0.0361709	+	0.0361709i	0.724961	−	0.688790i	$-0.241858\pi$
$487$	0.798221	+	0.798221i	0.0361709	+	0.0361709i	−0.688790	+	0.724961i	$0.741858\pi$
$488$	−3.31429	−	10.0645i	−0.150031	−	0.455599i
$489$	−13.5608	−	29.6520i	−0.613241	−	1.34091i
$490$	−4.48780	+	17.6139i	−0.202738	+	0.795715i
$491$	−1.09664	−	1.89944i	−0.0494909	−	0.0857207i	0.840219	−	0.542248i	$-0.182427\pi$
$491$	−1.09664	−	1.89944i	−0.0494909	−	0.0857207i	−0.889710	+	0.456527i	$0.849093\pi$
$492$	−2.20310	+	6.67227i	−0.0993233	+	0.300809i
$493$	−5.76557	−	21.5174i	−0.259668	−	0.969095i
$494$	−0.338293	+	0.612201i	−0.0152205	+	0.0275442i
$495$	−6.63915	+	33.4766i	−0.298408	+	1.50466i
$496$	26.0265	+	12.5242i	1.16862	+	0.562355i
$497$	5.33436	+	19.9081i	0.239279	+	0.893000i
$498$	1.12919	+	0.396504i	0.0506002	+	0.0177678i
$499$	2.31044	−	1.33393i	0.103429	−	0.0597150i	−0.447393	−	0.894337i	$-0.647647\pi$
$499$	2.31044	−	1.33393i	0.103429	−	0.0597150i	0.550822	+	0.834622i	$0.314314\pi$
$500$	−19.5650	−	10.8263i	−0.874975	−	0.484168i
$501$	−21.1809	+	29.7781i	−0.946291	+	1.33039i
$502$	21.6396	+	5.36501i	0.965821	+	0.239452i
$503$	27.9859	−	27.9859i	1.24783	−	1.24783i	0.291150	−	0.956677i	$-0.405962\pi$
$503$	27.9859	−	27.9859i	1.24783	−	1.24783i	0.956677	−	0.291150i	$-0.0940380\pi$
$504$	−11.5348	−	28.0143i	−0.513800	−	1.24786i
$505$	−6.09883	+	3.46887i	−0.271394	+	0.154363i
$506$	15.4789	−	9.32849i	0.688120	−	0.414702i
$507$	10.5783	+	12.7978i	0.469799	+	0.568371i
$508$	−1.96684	−	6.37301i	−0.0872645	−	0.282757i
$509$	−10.3867	−	17.9903i	−0.460382	−	0.797405i	0.538598	−	0.842563i	$-0.318954\pi$
$509$	−10.3867	−	17.9903i	−0.460382	−	0.797405i	−0.998980	+	0.0451578i	$0.985621\pi$
$510$	9.11601	−	25.4349i	0.403664	−	1.12628i
$511$	5.70856	+	3.29584i	0.252532	+	0.145799i
$512$	13.0816	−	18.4627i	0.578130	−	0.815945i
$513$	−1.21972	+	0.668561i	−0.0538518	+	0.0295177i
$514$	21.7535	+	12.0206i	0.959504	+	0.530207i
$515$	8.51304	−	8.40387i	0.375129	−	0.370319i
$516$	18.5070	+	12.1441i	0.814724	+	0.534615i
$517$	16.8780	−	62.9895i	0.742293	−	2.77028i
$518$	−2.36456	−	2.27741i	−0.103893	−	0.100063i
$519$	2.01278	−	21.1988i	0.0883513	−	0.930523i
$520$	−11.6710	+	0.582489i	−0.511809	+	0.0255439i
$521$	−2.16941			−0.0950434			−0.0475217	−	0.998870i	$-0.515132\pi$
$521$	−2.16941			−0.0950434			−0.0475217	+	0.998870i	$0.515132\pi$
$522$	−19.0792	+	1.74572i	−0.835074	+	0.0764082i
$523$	0.198517	+	0.198517i	0.00868053	+	0.00868053i	0.711434	−	0.702753i	$-0.248046\pi$
$523$	0.198517	+	0.198517i	0.00868053	+	0.00868053i	−0.702753	+	0.711434i	$0.748046\pi$
$524$	1.15832	+	30.8351i	0.0506015	+	1.34704i
$525$	12.4960	+	28.2833i	0.545371	+	1.23439i
$526$	0.445043	+	23.7029i	0.0194048	+	1.03350i
$527$	9.21917	−	34.4064i	0.401593	−	1.49877i
$528$	33.8618	+	9.78730i	1.47364	+	0.425938i
$529$	−14.4545	−	8.34533i	−0.628458	−	0.362840i
$530$	0.345885	+	28.0732i	0.0150243	+	1.21942i
$531$	40.9601	+	7.84893i	1.77752	+	0.340614i
$532$	0.425073	−	1.86363i	0.0184292	−	0.0807987i
$533$	−0.969995	−	3.62007i	−0.0420151	−	0.156803i
$534$	−17.3136	+	25.3349i	−0.749231	+	1.09635i
$535$	0.254831	+	0.976200i	0.0110173	+	0.0422048i
$536$	17.5753	+	26.8303i	0.759138	+	1.15889i
$537$	1.09794	−	2.94850i	0.0473794	−	0.127237i
$538$	30.9937	+	7.68414i	1.33623	+	0.331287i
$539$			29.2432i			1.25960i
$540$	−20.2272	−	11.4394i	−0.870441	−	0.492272i
$541$			4.88647i			0.210086i	0.994468	+	0.105043i	$0.0334980\pi$
$541$			4.88647i			0.210086i	−0.994468	+	0.105043i	$0.966502\pi$
$542$	−0.00522981	+	0.0210942i	−0.000224640	+	0.000906075i
$543$	−2.05056	+	5.50678i	−0.0879982	+	0.236319i
$544$	−25.3681	−	11.6261i	−1.08765	−	0.498463i
$545$	−7.29178	+	12.4436i	−0.312345	+	0.533024i
$546$	13.3413	+	9.11727i	0.570955	+	0.390183i
$547$	9.93198	+	37.0667i	0.424661	+	1.58486i	0.764662	+	0.644431i	$0.222906\pi$
$547$	9.93198	+	37.0667i	0.424661	+	1.58486i	−0.340001	+	0.940425i	$0.610427\pi$
$548$	−4.32890	+	18.9790i	−0.184921	+	0.810744i
$549$	3.68727	+	10.6169i	0.157369	+	0.453117i
$550$	−34.8029	−	9.10691i	−1.48400	−	0.388320i
$551$	−1.04686	−	0.604404i	−0.0445977	−	0.0257485i
$552$	2.72690	+	11.9995i	0.116065	+	0.510733i
$553$	0.806443	−	3.00969i	0.0342935	−	0.127985i
$554$	−9.32923	+	0.175165i	−0.396361	+	0.00744203i
$555$	−2.50524	−	0.254192i	−0.106342	−	0.0107898i
$556$	4.01709	−	0.150902i	0.170362	−	0.00639967i
$557$	−28.8184	−	28.8184i	−1.22107	−	1.22107i	−0.967251	−	0.253823i	$-0.918312\pi$
$557$	−28.8184	−	28.8184i	−1.22107	−	1.22107i	−0.253823	−	0.967251i	$-0.581688\pi$
$558$	−27.8162	−	12.8364i	−1.17755	−	0.543409i
$559$	−11.8065			−0.499363
$560$	30.2072	−	10.3616i	1.27649	−	0.437857i
$561$	4.10886	−	43.2748i	0.173476	−	1.82706i
$562$	13.0783	−	13.5788i	0.551675	−	0.572788i
$563$	−9.86777	+	36.8270i	−0.415877	+	1.55207i	0.367195	+	0.930144i	$0.380318\pi$
$563$	−9.86777	+	36.8270i	−0.415877	+	1.55207i	−0.783072	+	0.621931i	$0.786349\pi$
$564$	37.1233	+	24.3600i	1.56317	+	1.02574i
$565$	22.1570	+	22.4449i	0.932153	+	0.944263i
$566$	6.08305	−	11.0084i	0.255690	−	0.462716i
$567$	12.7127	+	29.5122i	0.533885	+	1.23940i
$568$	10.8769	−	12.1766i	0.456383	−	0.510920i
$569$	39.4195	+	22.7588i	1.65255	+	0.954100i	0.976019	+	0.217686i	$0.0698508\pi$
$569$	39.4195	+	22.7588i	1.65255	+	0.954100i	0.676531	+	0.736414i	$0.263483\pi$
$570$	−0.626162	−	1.32573i	−0.0262270	−	0.0555288i
$571$	−12.5819	−	21.7925i	−0.526537	−	0.911989i	−0.999522	−	0.0309185i	$-0.990157\pi$
$571$	−12.5819	−	21.7925i	−0.526537	−	0.911989i	0.472985	−	0.881071i	$-0.343177\pi$
$572$	−17.9641	+	5.54410i	−0.751117	+	0.231810i
$573$	−10.1978	−	12.3375i	−0.426019	−	0.515406i
$574$	5.28665	+	8.77221i	0.220661	+	0.366145i
$575$	−3.09372	−	12.1722i	−0.129017	−	0.507616i
$576$	−13.5571	+	19.8042i	−0.564878	+	0.825175i
$577$	−12.2839	+	12.2839i	−0.511383	+	0.511383i	−0.914950	−	0.403567i	$-0.867770\pi$
$577$	−12.2839	+	12.2839i	−0.511383	+	0.511383i	0.403567	+	0.914950i	$0.367770\pi$
$578$	−2.49607	+	10.0678i	−0.103823	+	0.418765i
$579$	19.3941	−	27.2660i	0.805990	−	1.13314i
$580$	−0.627848	−	20.1855i	−0.0260700	−	0.838157i
$581$	1.51074	−	0.872227i	0.0626761	−	0.0361861i
$582$	7.34156	−	20.9078i	0.304317	−	0.866656i
$583$	11.6905	+	43.6295i	0.484171	+	1.80695i
$584$	−0.293942	−	5.21352i	−0.0121634	−	0.215737i
$585$	12.3674	−	0.817653i	0.511330	−	0.0338058i
$586$	−17.1711	−	9.48847i	−0.709331	−	0.391965i
$587$	−7.53084	−	28.1055i	−0.310831	−	1.16004i	−0.927808	−	0.373057i	$-0.878310\pi$
$587$	−7.53084	−	28.1055i	−0.310831	−	1.16004i	0.616977	−	0.786981i	$-0.288357\pi$
$588$	−18.9075	−	6.24301i	−0.779731	−	0.257457i
$589$	−0.966444	−	1.67393i	−0.0398216	−	0.0689731i
$590$	−10.8540	+	42.6003i	−0.446853	+	1.75383i
$591$	−11.6546	−	25.4839i	−0.479406	−	1.04827i
$592$	−0.482745	+	2.55549i	−0.0198407	+	0.105030i
$593$	16.8874	+	16.8874i	0.693482	+	0.693482i	0.962996	−	0.269514i	$-0.0868632\pi$
$593$	16.8874	+	16.8874i	0.693482	+	0.693482i	−0.269514	+	0.962996i	$0.586863\pi$
$594$	−36.0788	−	9.79964i	−1.48033	−	0.402084i
$595$	−19.4713	−	34.2337i	−0.798247	−	1.40344i
$596$	0.758247	+	20.1849i	0.0310590	+	0.826807i
$597$	−23.0225	−	8.57289i	−0.942246	−	0.350865i
$598$	−4.72731	−	4.55306i	−0.193314	−	0.186189i
$599$	12.7234	+	22.0376i	0.519866	+	0.900434i	0.999733	+	0.0230927i	$0.00735130\pi$
$599$	12.7234	+	22.0376i	0.519866	+	0.900434i	−0.479868	+	0.877341i	$0.659315\pi$
$600$	13.3181	−	20.5579i	0.543708	−	0.839274i
$601$	7.77634	−	13.4690i	0.317203	−	0.549413i	−0.662700	−	0.748885i	$-0.730590\pi$
$601$	7.77634	−	13.4690i	0.317203	−	0.549413i	0.979903	+	0.199472i	$0.0639228\pi$
$602$	31.0037	−	8.93450i	1.26362	−	0.364143i
$603$	−19.0986	−	28.1531i	−0.777754	−	1.14648i
$604$	−15.9614	−	25.3941i	−0.649459	−	1.03327i
$605$	−33.2799	−	0.214774i	−1.35302	−	0.00873182i
$606$	−3.32727	−	6.92848i	−0.135161	−	0.281450i
$607$	−10.9530	+	40.8770i	−0.444567	+	1.65915i	0.272510	+	0.962153i	$0.412146\pi$
$607$	−10.9530	+	40.8770i	−0.444567	+	1.65915i	−0.717077	+	0.696994i	$0.754520\pi$
$608$	−1.41948	+	0.527287i	−0.0575675	+	0.0213843i
$609$	−16.1867	+	22.7569i	−0.655920	+	0.922155i
$610$	−11.4046	+	3.20694i	−0.461757	+	0.129845i
$611$	−23.6828			−0.958103
$612$	27.1026	+	11.8952i	1.09556	+	0.480834i
$613$	3.28119	−	3.28119i	0.132526	−	0.132526i	−0.637732	−	0.770258i	$-0.720127\pi$
$613$	3.28119	−	3.28119i	0.132526	−	0.132526i	0.770258	+	0.637732i	$0.220127\pi$
$614$	−8.13559	+	4.90299i	−0.328326	+	0.197868i
$615$	7.34426	+	2.78889i	0.296149	+	0.112459i
$616$	42.9780	−	28.1529i	1.73163	−	1.13431i
$617$	−6.24499	−	1.67334i	−0.251414	−	0.0673661i	0.130911	−	0.991394i	$-0.458210\pi$
$617$	−6.24499	−	1.67334i	−0.251414	−	0.0673661i	−0.382325	+	0.924028i	$0.624876\pi$
$618$	8.53677	+	9.94182i	0.343399	+	0.399919i
$619$	−11.5290	−	6.65625i	−0.463388	−	0.267537i	0.250080	−	0.968225i	$-0.419543\pi$
$619$	−11.5290	−	6.65625i	−0.463388	−	0.267537i	−0.713468	+	0.700688i	$0.752877\pi$
$620$	15.2689	−	28.4544i	0.613214	−	1.14276i
$621$	−3.09748	−	12.6790i	−0.124297	−	0.508792i
$622$	11.1417	−	3.21076i	0.446741	−	0.128740i
$623$	11.5765	+	43.2042i	0.463804	+	1.73094i
$624$	0.250491	−	12.7984i	0.0100277	−	0.512348i
$625$	−13.0547	+	21.3208i	−0.522186	+	0.852831i
$626$	36.1652	−	0.679035i	1.44545	−	0.0271397i
$627$	−1.50281	−	1.81813i	−0.0600166	−	0.0726091i
$628$	−1.23556	+	1.33201i	−0.0493041	+	0.0531529i
$629$	3.20730			0.127884
$630$	−31.8579	+	11.5061i	−1.26925	+	0.458414i
$631$			10.0713i			0.400933i	0.979701	+	0.200466i	$0.0642458\pi$
$631$			10.0713i			0.400933i	−0.979701	+	0.200466i	$0.935754\pi$
$632$	−2.34448	+	0.772047i	−0.0932583	+	0.0307104i
$633$	6.03605	+	35.7779i	0.239911	+	1.42204i
$634$	5.74538	−	0.107875i	0.228178	−	0.00428425i
$635$	−7.21507	+	1.88345i	−0.286321	+	0.0747426i
$636$	−30.7048	−	1.75567i	−1.21753	−	0.0696170i
$637$	10.2583	−	2.74871i	0.406450	−	0.108908i
$638$	−8.99693	−	31.2204i	−0.356192	−	1.23603i
$639$	−11.3266	+	13.0999i	−0.448072	+	0.518223i
$640$	−19.9786	−	15.5195i	−0.789725	−	0.613461i
$641$	3.99496	−	6.91947i	0.157791	−	0.273303i	−0.776281	−	0.630388i	$-0.782896\pi$
$641$	3.99496	−	6.91947i	0.157791	−	0.273303i	0.934072	+	0.357085i	$0.116229\pi$
$642$	−1.08616	+	0.204287i	−0.0428675	+	0.00806255i
$643$	−1.88977	+	7.05271i	−0.0745251	+	0.278132i	−0.993125	−	0.117057i	$-0.962654\pi$
$643$	−1.88977	+	7.05271i	−0.0745251	+	0.278132i	0.918600	+	0.395188i	$0.129321\pi$
$644$	15.8593	+	8.37891i	0.624946	+	0.330175i
$645$	14.4745	−	20.0742i	0.569935	−	0.790420i
$646$	0.963921	+	1.59945i	0.0379250	+	0.0629294i
$647$	−20.6523	−	20.6523i	−0.811927	−	0.811927i	0.172995	−	0.984923i	$-0.444655\pi$
$647$	−20.6523	−	20.6523i	−0.811927	−	0.811927i	−0.984923	+	0.172995i	$0.944655\pi$
$648$	14.0383	−	21.2350i	0.551478	−	0.834189i
$649$			70.7266i			2.77626i
$650$	0.0766475	+	13.0646i	0.00300636	+	0.512437i
$651$	−40.6092	+	18.5719i	−1.59160	+	0.727890i
$652$	11.1028	+	35.9756i	0.434820	+	1.40891i
$653$	−31.9369	−	8.55748i	−1.24979	−	0.334880i	−0.427534	−	0.903999i	$-0.640618\pi$
$653$	−31.9369	−	8.55748i	−1.24979	−	0.334880i	−0.822255	+	0.569119i	$0.807284\pi$
$654$	−13.0442	−	8.91425i	−0.510069	−	0.348575i
$655$	34.4983	+	0.222637i	1.34796	+	0.00869915i
$656$	3.51820	−	7.31113i	0.137363	−	0.285452i
$657$	0.401033	+	5.52402i	0.0156458	+	0.215513i
$658$	62.1906	−	17.9218i	2.42444	−	0.698664i
$659$	−25.3884	−	14.6580i	−0.988991	−	0.570994i	−0.0840182	−	0.996464i	$-0.526775\pi$
$659$	−25.3884	−	14.6580i	−0.988991	−	0.570994i	−0.904972	+	0.425470i	$0.860109\pi$
$660$	12.5972	−	37.3406i	0.490346	−	1.45348i
$661$	−31.4846	+	18.1777i	−1.22461	+	0.707029i	−0.965897	−	0.258926i	$-0.916632\pi$
$661$	−31.4846	+	18.1777i	−1.22461	+	0.707029i	−0.258713	+	0.965954i	$0.583298\pi$
$662$	−8.30028	+	8.61793i	−0.322599	+	0.334945i
$663$	−15.5667	+	2.62625i	−0.604562	+	0.101995i
$664$	−1.23378	−	0.622498i	−0.0478799	−	0.0241576i
$665$	−2.06068	−	0.566437i	−0.0799098	−	0.0219655i
$666$	0.468189	−	2.71843i	0.0181420	−	0.105337i
$667$	8.02069	−	8.02069i	0.310562	−	0.310562i
$668$	28.6959	−	30.9359i	1.11028	−	1.19695i
$669$	2.18485	−	23.0111i	0.0844714	−	0.889659i
$670$	30.8325	−	18.3113i	1.19116	−	0.707427i
$671$	−16.5062	+	9.52985i	−0.637214	+	0.367896i
$672$	9.02735	+	33.7981i	0.348238	+	1.30379i
$673$	26.4189	−	7.07891i	1.01837	−	0.272872i	0.289249	−	0.957254i	$-0.406595\pi$
$673$	26.4189	−	7.07891i	1.01837	−	0.272872i	0.729124	+	0.684382i	$0.239928\pi$
$674$	−2.20025	−	1.21582i	−0.0847505	−	0.0468318i
$675$	−13.7720	+	22.0303i	−0.530084	+	0.847945i
$676$	−10.2027	−	16.2322i	−0.392412	−	0.624316i
$677$	8.39531	−	2.24952i	0.322658	−	0.0864559i	−0.0938546	−	0.995586i	$-0.529919\pi$
$677$	8.39531	−	2.24952i	0.322658	−	0.0864559i	0.416512	+	0.909130i	$0.363252\pi$
$678$	−26.2119	+	22.5074i	−1.00666	+	0.864393i
$679$	−16.1499	−	27.9725i	−0.619777	−	1.07349i
$680$	−14.2333	+	27.7632i	−0.545823	+	1.06467i
$681$	0.898479	−	9.46285i	0.0344298	−	0.362617i
$682$	12.5020	−	50.4263i	0.478726	−	1.93092i
$683$	23.0167	+	23.0167i	0.880709	+	0.880709i	0.993607	−	0.112897i	$-0.0360131\pi$
$683$	23.0167	+	23.0167i	0.880709	+	0.880709i	−0.112897	+	0.993607i	$0.536013\pi$
$684$	1.49636	−	0.583513i	0.0572147	−	0.0223112i
$685$	20.9858	+	5.76853i	0.801825	+	0.220404i
$686$	5.41471	−	3.26322i	0.206735	−	0.124591i
$687$	−1.93197	−	11.4515i	−0.0737093	−	0.436902i
$688$	−19.3787	−	16.6668i	−0.738807	−	0.635416i
$689$	14.2061	−	8.20191i	0.541210	−	0.312468i
$690$	13.5370	−	2.45570i	0.515344	−	0.0934870i
$691$	−14.1588	+	24.5238i	−0.538628	+	0.932931i	0.460350	+	0.887737i	$0.347724\pi$
$691$	−14.1588	+	24.5238i	−0.538628	+	0.932931i	−0.998978	+	0.0451936i	$0.985610\pi$
$692$	−5.46788	+	23.9727i	−0.207858	+	0.911304i
$693$	−45.0969	+	30.5930i	−1.71309	+	1.16213i
$694$	11.0858	+	6.12586i	0.420812	+	0.232534i
$695$	0.0290044	−	4.49431i	0.00110020	−	0.170479i
$696$	22.1065	+	0.848051i	0.837946	+	0.0321453i
$697$	−9.66515	−	2.58977i	−0.366094	−	0.0980945i
$698$	26.6231	−	27.6420i	1.00770	−	1.04626i
$699$	11.0706	+	24.2068i	0.418727	+	0.915586i
$700$	−10.0878	−	34.2495i	−0.381285	−	1.29451i
$701$		−	49.4383i		−	1.86726i	−0.358239	−	0.933630i	$-0.616623\pi$
$701$		−	49.4383i		−	1.86726i	0.358239	−	0.933630i	$-0.383377\pi$
$702$	−0.0464298	+	13.5773i	−0.00175238	+	0.512443i
$703$	0.123066	−	0.123066i	0.00464150	−	0.00464150i
$704$	−37.3119	−	16.2594i	−1.40625	−	0.612798i
$705$	29.0346	−	40.2669i	1.09351	−	1.51654i
$706$	10.3398	−	0.194139i	0.389143	−	0.00730651i
$707$	−10.8215	−	2.89962i	−0.406985	−	0.109051i
$708$	−45.7289	−	15.0991i	−1.71860	−	0.567459i
$709$	−3.09402	+	5.35900i	−0.116198	+	0.201261i	−0.918258	−	0.395982i	$-0.870404\pi$
$709$	−3.09402	+	5.35900i	−0.116198	+	0.201261i	0.802060	+	0.597244i	$0.203737\pi$
$710$	−13.0658	−	12.7477i	−0.490350	−	0.478414i
$711$	2.47314	−	0.858931i	0.0927502	−	0.0322124i
$712$	23.6047	−	26.4255i	0.884625	−	0.990337i
$713$	17.5194	−	4.69431i	0.656107	−	0.175803i
$714$	38.8906	−	18.6765i	1.45545	−	0.698951i
$715$	5.30904	+	20.3377i	0.198547	+	0.760587i
$716$	−1.69712	+	3.21226i	−0.0634245	+	0.120048i
$717$	−3.18453	−	18.8759i	−0.118929	−	0.704934i
$718$	−12.9121	−	3.20124i	−0.481875	−	0.119469i
$719$	35.5397			1.32541			0.662703	−	0.748882i	$-0.269409\pi$
$719$	35.5397			1.32541			0.662703	+	0.748882i	$0.269409\pi$
$720$	21.4536	+	16.1165i	0.799529	+	0.600628i
$721$	19.1007			0.711349
$722$	−25.9821	−	6.44164i	−0.966954	−	0.239733i
$723$	26.8694	−	22.2095i	0.999284	−	0.825979i
$724$	3.16964	−	5.99939i	0.117799	−	0.222966i
$725$	−22.5771	−	0.291418i	−0.838493	−	0.0108230i
$726$	2.76409	−	36.3522i	0.102585	−	1.34916i
$727$	4.67222	−	1.25192i	0.173283	−	0.0464311i	−0.171134	−	0.985248i	$-0.554743\pi$
$727$	4.67222	−	1.25192i	0.173283	−	0.0464311i	0.344417	+	0.938817i	$0.388076\pi$
$728$	−13.9156	−	12.4302i	−0.515746	−	0.460694i
$729$	−14.5242	+	22.7606i	−0.537935	+	0.842986i
$730$	−5.83771	+	0.0719254i	−0.216063	+	0.00266208i
$731$	−15.7610	+	27.2988i	−0.582941	+	1.00968i
$732$	−2.63778	−	12.7067i	−0.0974952	−	0.469653i
$733$	10.1983	+	2.73262i	0.376682	+	0.100932i	0.442192	−	0.896920i	$-0.354201\pi$
$733$	10.1983	+	2.73262i	0.376682	+	0.100932i	−0.0655103	+	0.997852i	$0.520868\pi$
$734$	41.0180	−	0.770149i	1.51400	−	0.0284267i
$735$	−7.90298	+	20.8117i	−0.291506	+	0.767652i
$736$	−1.33183	−	14.1466i	−0.0490919	−	0.521449i
$737$	40.7952	−	40.7952i	1.50271	−	1.50271i
$738$	−3.60590	+	7.81388i	−0.132735	+	0.287633i
$739$			27.1417i			0.998425i	0.866480	+	0.499213i	$0.166377\pi$
$739$			27.1417i			0.998425i	−0.866480	+	0.499213i	$0.833623\pi$
$740$	2.83062	+	0.664878i	0.104056	+	0.0244414i
$741$	−0.496532	+	0.698072i	−0.0182406	+	0.0256443i
$742$	−31.0983	+	32.2885i	−1.14166	+	1.18535i
$743$	−47.9760	−	12.8551i	−1.76007	−	0.471609i	−0.773341	−	0.633991i	$-0.781416\pi$
$743$	−47.9760	−	12.8551i	−1.76007	−	0.471609i	−0.986728	+	0.162382i	$0.948082\pi$
$744$	29.9346	+	18.8486i	1.09746	+	0.691022i
$745$	22.5829	+	0.145740i	0.827373	+	0.00533951i
$746$	−23.0658	−	12.7458i	−0.844498	−	0.466657i
$747$	1.31911	+	0.639040i	0.0482638	+	0.0233812i
$748$	−11.1620	+	48.9374i	−0.408125	+	1.78933i
$749$	−0.805488	+	1.39515i	−0.0294319	+	0.0509775i
$750$	−22.3073	−	15.8867i	−0.814546	−	0.580099i
$751$	−9.13682	+	5.27515i	−0.333407	+	0.192493i	−0.657353	−	0.753583i	$-0.728324\pi$
$751$	−9.13682	+	5.27515i	−0.333407	+	0.192493i	0.323946	+	0.946076i	$0.394991\pi$
$752$	−38.8719	−	33.4320i	−1.41751	−	1.21914i
$753$	25.5888	+	9.52854i	0.932509	+	0.347239i
$754$	−10.1062	+	6.09062i	−0.368048	+	0.221807i
$755$	−29.1489	+	16.5792i	−1.06084	+	0.603381i
$756$	−10.1526	−	35.6890i	−0.369247	−	1.29800i
$757$	20.4882	+	20.4882i	0.744657	+	0.744657i	0.973470	−	0.228813i	$-0.0734845\pi$
$757$	20.4882	+	20.4882i	0.744657	+	0.744657i	−0.228813	+	0.973470i	$0.573484\pi$
$758$	−6.20072	+	25.0104i	−0.225220	+	0.908417i
$759$	20.1291	−	9.20568i	0.730639	−	0.334145i
$760$	0.519146	+	1.61142i	0.0188314	+	0.0584524i
$761$	3.34630	+	5.79596i	0.121303	+	0.210103i	0.920282	−	0.391256i	$-0.127959\pi$
$761$	3.34630	+	5.79596i	0.121303	+	0.210103i	−0.798979	+	0.601359i	$0.794626\pi$
$762$	−1.50988	−	8.02782i	−0.0546971	−	0.290817i
$763$	−22.2446	+	5.96041i	−0.805307	+	0.215781i
$764$	9.83571	+	15.6483i	0.355844	+	0.566136i
$765$	14.6192	−	29.6873i	0.528558	−	1.07335i
$766$	29.3803	+	16.2351i	1.06155	+	0.586598i
$767$	24.8104	−	6.64794i	0.895853	−	0.240043i
$768$	18.4782	−	20.6532i	0.666775	−	0.745259i
$769$	28.4627	−	16.4330i	1.02639	−	0.592588i	0.110443	−	0.993882i	$-0.464773\pi$
$769$	28.4627	−	16.4330i	1.02639	−	0.592588i	0.915949	+	0.401295i	$0.131440\pi$
$770$	−29.3319	−	49.3889i	−1.05705	−	1.77985i
$771$	24.8047	+	17.6433i	0.893320	+	0.635410i
$772$	−26.2751	+	28.3262i	−0.945662	+	1.01948i
$773$	7.27459	−	7.27459i	0.261649	−	0.261649i	−0.564075	−	0.825724i	$-0.690767\pi$
$773$	7.27459	−	7.27459i	0.261649	−	0.261649i	0.825724	+	0.564075i	$0.190767\pi$
$774$	20.8370	+	17.3436i	0.748972	+	0.623402i
$775$	−31.0313	−	18.4540i	−1.11468	−	0.662887i
$776$	−11.5260	+	22.8443i	−0.413760	+	0.820064i
$777$	−2.56165	−	3.09913i	−0.0918986	−	0.111181i
$778$	−15.7555	+	16.3584i	−0.564861	+	0.586479i
$779$	−0.470226	+	0.271485i	−0.0168476	+	0.00972696i
$780$	−14.2829	−	0.909196i	−0.511411	−	0.0325544i
$781$	−25.4336	−	14.6841i	−0.910086	−	0.525439i
$782$	−16.8382	+	4.85234i	−0.602132	+	0.173519i
$783$	−23.4590	−	0.520719i	−0.838356	−	0.0186090i
$784$	20.7179	+	9.96967i	0.739924	+	0.356060i
$785$	1.42703	+	1.44556i	0.0509327	+	0.0515944i
$786$	−2.86529	+	37.6830i	−0.102201	+	1.34411i
$787$	11.9886	+	3.21234i	0.427347	+	0.114507i	0.466081	−	0.884742i	$-0.345666\pi$
$787$	11.9886	+	3.21234i	0.427347	+	0.114507i	−0.0387333	+	0.999250i	$0.512332\pi$
$788$	9.54211	+	30.9186i	0.339924	+	1.10143i
$789$	−2.74449	+	28.9052i	−0.0977063	+	1.02905i
$790$	0.747041	+	2.65664i	0.0265785	+	0.0945188i
$791$			50.3596i			1.79058i
$792$	39.8486	+	16.6043i	1.41596	+	0.590009i
$793$	4.89451	+	4.89451i	0.173809	+	0.173809i
$794$	−23.3858	−	38.8044i	−0.829932	−	1.37712i
$795$	−3.47102	+	34.2095i	−0.123105	+	1.21329i
$796$	25.0819	+	13.2514i	0.889005	+	0.469685i
$797$	−10.3877	+	38.7675i	−0.367952	+	1.37322i	0.495423	+	0.868652i	$0.335013\pi$
$797$	−10.3877	+	38.7675i	−0.367952	+	1.37322i	−0.863375	+	0.504563i	$0.831654\pi$
$798$	0.775624	−	2.20887i	0.0274568	−	0.0781933i
$799$	−31.6151	+	54.7589i	−1.11846	+	1.93723i
$800$	−18.3170	+	21.5519i	−0.647605	+	0.761976i
$801$	−24.5807	+	28.4291i	−0.868517	+	1.00449i
$802$	9.45838	+	32.8217i	0.333987	+	1.15897i
$803$	−9.07259	+	2.43099i	−0.320165	+	0.0857878i
$804$	17.6673	+	35.0857i	0.623078	+	1.23738i
$805$	10.1388	−	17.3021i	0.357345	−	0.609817i
$806$	−18.8644	+	0.354195i	−0.664469	+	0.0124760i
$807$	36.6501	+	13.6474i	1.29014	+	0.480412i
$808$	2.77595	+	8.42972i	0.0976574	+	0.296556i
$809$		−	20.0665i		−	0.705501i	−0.935717	−	0.352750i	$-0.885247\pi$
$809$		−	20.0665i		−	0.705501i	0.935717	−	0.352750i	$-0.114753\pi$
$810$	−23.0281	−	16.7245i	−0.809124	−	0.587638i
$811$	−12.8210			−0.450207			−0.225103	−	0.974335i	$-0.572272\pi$
$811$	−12.8210			−0.450207			−0.225103	+	0.974335i	$0.572272\pi$
$812$	21.9298	−	23.6417i	0.769586	−	0.829661i
$813$	−0.00928841	+	0.0249440i	−0.000325759	+	0.000874824i
$814$	4.67712	−	0.0878172i	0.163933	−	0.00307799i
$815$	40.7290	−	10.6321i	1.42668	−	0.372425i
$816$	−29.2580	−	17.6643i	−1.02423	−	0.618376i
$817$	0.442712	+	1.65222i	0.0154885	+	0.0578040i
$818$	−16.0179	+	4.61597i	−0.560054	+	0.161393i
$819$	14.9707	+	12.9441i	0.523118	+	0.452305i
$820$	−7.99316	−	4.28921i	−0.279133	−	0.149786i
$821$	34.0779	+	19.6749i	1.18933	+	0.686659i	0.958154	−	0.286253i	$-0.0924099\pi$
$821$	34.0779	+	19.6749i	1.18933	+	0.686659i	0.231174	+	0.972912i	$0.425743\pi$
$822$	−7.89887	+	22.4949i	−0.275505	+	0.784601i
$823$	0.903765	+	0.242163i	0.0315033	+	0.00844128i	0.274536	−	0.961577i	$-0.411476\pi$
$823$	0.903765	+	0.242163i	0.0315033	+	0.00844128i	−0.243033	+	0.970018i	$0.578142\pi$
$824$	−8.29128	−	12.6574i	−0.288840	−	0.440941i
$825$	−41.0882	−	15.9068i	−1.43051	−	0.553805i
$826$	−60.1211	+	36.2325i	−2.09188	+	1.26069i
$827$	1.79823	−	1.79823i	0.0625307	−	0.0625307i	−0.675150	−	0.737681i	$-0.735921\pi$
$827$	1.79823	−	1.79823i	0.0625307	−	0.0625307i	0.737681	+	0.675150i	$0.235921\pi$
$828$	1.65475	+	14.9799i	0.0575064	+	0.520588i
$829$	54.2952			1.88575			0.942875	−	0.333147i	$-0.108111\pi$
$829$	54.2952			1.88575			0.942875	+	0.333147i	$0.108111\pi$
$830$	−0.755976	+	1.34746i	−0.0262403	+	0.0467710i
$831$	−11.3768	−	1.08020i	−0.394656	−	0.0374718i
$832$	−2.19656	+	14.6171i	−0.0761520	+	0.506756i
$833$	7.33874	−	27.3885i	0.254272	−	0.948956i
$834$	4.90920	+	0.373279i	0.169992	+	0.0129256i
$835$	−33.1427	−	33.5733i	−1.14695	−	1.16185i
$836$	1.44945	+	2.30604i	0.0501304	+	0.0797560i
$837$	−32.0692	−	19.4766i	−1.10847	−	0.673209i
$838$	−12.0775	+	3.48044i	−0.417212	+	0.120230i
$839$	−19.7009	+	34.1230i	−0.680151	+	1.17806i	0.294784	+	0.955564i	$0.404752\pi$
$839$	−19.7009	+	34.1230i	−0.680151	+	1.17806i	−0.974935	+	0.222491i	$0.928581\pi$
$840$	38.1948	−	8.42097i	1.31785	−	0.290551i
$841$	4.30379	+	7.45438i	0.148406	+	0.257047i
$842$	36.8967	+	35.5367i	1.27154	+	1.22467i
$843$	17.7971	−	14.7106i	0.612966	−	0.506660i
$844$	−1.57273	−	41.8670i	−0.0541358	−	1.44112i
$845$	−18.6323	+	10.5977i	−0.640972	+	0.364571i
$846$	41.7972	+	34.7896i	1.43702	+	1.19609i
$847$	−37.5761	−	37.5761i	−1.29113	−	1.29113i
$848$	34.8956	+	6.59195i	1.19832	+	0.226369i
$849$	8.92844	−	12.5525i	0.306423	−	0.430799i
$850$	30.3102	+	17.2633i	1.03963	+	0.592126i
$851$	0.816565	+	1.41433i	0.0279915	+	0.0484827i
$852$	14.9239	−	13.3095i	0.511283	−	0.455976i
$853$	−4.86878	−	18.1706i	−0.166704	−	0.622148i	−0.997817	−	0.0660438i	$-0.978962\pi$
$853$	−4.86878	−	18.1706i	−0.166704	−	0.622148i	0.831113	−	0.556104i	$-0.187704\pi$
$854$	−16.5568	−	9.14902i	−0.566561	−	0.313073i
$855$	−0.578168	−	1.70006i	−0.0197729	−	0.0581407i
$856$	1.27416	−	0.0718381i	0.0435500	−	0.00245538i
$857$	−1.73320	−	6.46839i	−0.0592050	−	0.220956i	0.929985	−	0.367599i	$-0.119820\pi$
$857$	−1.73320	−	6.46839i	−0.0592050	−	0.220956i	−0.989190	+	0.146643i	$0.953153\pi$
$858$	−22.6287	+	4.25601i	−0.772530	+	0.145298i
$859$	−18.9821	+	10.9593i	−0.647662	+	0.373928i	−0.787560	−	0.616238i	$-0.788656\pi$
$859$	−18.9821	+	10.9593i	−0.647662	+	0.373928i	0.139898	+	0.990166i	$0.455323\pi$
$860$	−19.5690	+	20.8255i	−0.667298	+	0.710142i
$861$	5.21705	+	11.4076i	0.177797	+	0.388769i
$862$	−1.77068	+	7.14199i	−0.0603098	+	0.243257i
$863$	−18.4126	+	18.4126i	−0.626773	+	0.626773i	−0.947255	−	0.320482i	$-0.896155\pi$
$863$	−18.4126	+	18.4126i	−0.626773	+	0.626773i	0.320482	+	0.947255i	$0.396155\pi$
$864$	−19.2428	+	22.2197i	−0.654653	+	0.755930i
$865$	26.5074	+	7.28630i	0.901279	+	0.247742i
$866$	17.2390	+	28.6048i	0.585804	+	0.972032i
$867$	−4.43314	+	11.9052i	−0.150557	+	0.404321i
$868$	49.2695	−	15.2056i	1.67232	−	0.516111i
$869$	2.21993	+	3.84503i	0.0753059	+	0.130434i
$870$	2.03440	−	24.6502i	0.0689726	−	0.835721i
$871$	−18.1452	−	10.4761i	−0.614827	−	0.354971i
$872$	13.6057	+	12.1534i	0.460747	+	0.411566i
$873$	11.8323	−	24.4243i	0.400462	−	0.826638i
$874$	−0.459902	+	0.832274i	−0.0155564	+	0.0281521i
$875$	−38.7512	+	9.58330i	−1.31003	+	0.323975i
$876$	0.365085	−	6.38495i	0.0123351	−	0.215727i
$877$	−7.14653	+	26.6712i	−0.241321	+	0.900622i	0.733876	+	0.679284i	$0.237709\pi$
$877$	−7.14653	+	26.6712i	−0.241321	+	0.900622i	−0.975197	+	0.221339i	$0.928957\pi$
$878$	−26.2259	+	27.2296i	−0.885082	+	0.918954i
$879$	−19.5796	−	13.9268i	−0.660404	−	0.469738i
$880$	−19.9959	+	40.8760i	−0.674061	+	1.37793i
$881$	−51.5933			−1.73822			−0.869111	−	0.494618i	$-0.835308\pi$
$881$	−51.5933			−1.73822			−0.869111	+	0.494618i	$0.835308\pi$
$882$	−22.1425	−	10.2182i	−0.745577	−	0.344064i
$883$	−18.6778	−	18.6778i	−0.628558	−	0.628558i	0.319147	−	0.947705i	$-0.396604\pi$
$883$	−18.6778	−	18.6778i	−0.628558	−	0.628558i	−0.947705	+	0.319147i	$0.896604\pi$
$884$	18.2161	−	0.684288i	0.612674	−	0.0230151i
$885$	−19.1139	+	50.3345i	−0.642505	+	1.69197i
$886$	17.2834	−	0.324511i	0.580647	−	0.0109022i
$887$	−0.184302	+	0.687826i	−0.00618827	+	0.0230949i	−0.968951	−	0.247253i	$-0.920472\pi$
$887$	−0.184302	+	0.687826i	−0.00618827	+	0.0230949i	0.962763	+	0.270348i	$0.0871388\pi$
$888$	−0.941719	+	3.04279i	−0.0316020	+	0.102109i
$889$	−10.3115	−	5.95334i	−0.345836	−	0.199669i
$890$	−28.3551	−	27.6649i	−0.950466	−	0.927330i
$891$	−42.5447	−	16.9267i	−1.42530	−	0.567065i
$892$	−5.93533	+	26.0221i	−0.198730	+	0.871283i
$893$	0.888038	+	3.31420i	0.0297171	+	0.110906i
$894$	−1.87564	+	24.6676i	−0.0627308	+	0.825009i
$895$	3.50448	+	2.05358i	0.117142	+	0.0686436i
$896$	−5.29325	−	40.0465i	−0.176835	−	1.33786i
$897$	−5.12132	−	6.19587i	−0.170996	−	0.206874i
$898$	0.159232	−	0.642258i	0.00531365	−	0.0214324i
$899$		−	32.6076i		−	1.08752i
$900$	19.0564	−	23.1701i	0.635215	−	0.772335i
$901$		−	43.7962i		−	1.45906i
$902$	−14.1653	−	3.51195i	−0.471654	−	0.116935i
$903$	38.9663	−	6.57396i	1.29672	−	0.218768i
$904$	33.3716	−	21.8602i	1.10992	−	0.727059i
$905$	−6.54515	−	3.83537i	−0.217568	−	0.127492i
$906$	−15.9025	−	33.1142i	−0.528324	−	1.10014i
$907$	−11.3206	−	42.2489i	−0.375893	−	1.40285i	−0.852035	−	0.523484i	$-0.824632\pi$
$907$	−11.3206	−	42.2489i	−0.375893	−	1.40285i	0.476142	−	0.879368i	$-0.342035\pi$
$908$	−2.44079	+	10.7011i	−0.0810004	+	0.355127i
$909$	−3.08834	−	8.89235i	−0.102434	−	0.294941i
$910$	−14.5683	+	14.9317i	−0.482934	+	0.494982i
$911$	−21.8229	−	12.5995i	−0.723026	−	0.417439i	0.0928397	−	0.995681i	$-0.470406\pi$
$911$	−21.8229	−	12.5995i	−0.723026	−	0.417439i	−0.815865	+	0.578242i	$0.803739\pi$
$912$	−1.80043	+	0.444852i	−0.0596181	+	0.0147305i
$913$	−0.643350	+	2.40102i	−0.0212918	+	0.0794620i
$914$	−0.498509	−	26.5505i	−0.0164892	−	0.878212i
$915$	−14.3225	+	2.32138i	−0.473487	+	0.0767423i
$916$	0.503389	+	13.4005i	0.0166324	+	0.442764i
$917$	38.9517	+	38.9517i	1.28630	+	1.28630i
$918$	31.3313	+	18.2323i	1.03409	+	0.601754i
$919$	24.5666			0.810378			0.405189	−	0.914233i	$-0.367206\pi$
$919$	24.5666			0.810378			0.405189	+	0.914233i	$0.367206\pi$
$920$	−15.8665	+	0.791881i	−0.523104	+	0.0261076i
$921$	−10.5797	+	4.83844i	−0.348613	+	0.159432i
$922$	−28.2635	−	27.2217i	−0.930810	−	0.896501i
$923$	−2.76046	+	10.3022i	−0.0908617	+	0.339100i
$924$	56.2018	−	28.3003i	1.84890	−	0.931011i
$925$	0.881843	−	3.12897i	0.0289948	−	0.102880i
$926$	−2.09148	−	1.15572i	−0.0687304	−	0.0379793i
$927$	9.00989	+	13.2814i	0.295923	+	0.436219i
$928$	−25.1859	−	4.26970i	−0.826766	−	0.140160i
$929$	13.4364	+	7.75751i	0.440834	+	0.254515i	0.703951	−	0.710248i	$-0.251417\pi$
$929$	13.4364	+	7.75751i	0.440834	+	0.254515i	−0.263117	+	0.964764i	$0.584751\pi$
$930$	22.5251	−	32.5086i	0.738627	−	1.06600i
$931$	−0.769319	−	1.33250i	−0.0252134	−	0.0436709i
$932$	−9.06393	−	29.3692i	−0.296899	−	0.962019i
$933$	14.0032	−	2.36246i	0.458443	−	0.0773434i
$934$	28.6993	−	17.2959i	0.939070	−	0.565939i
$935$	54.1117	+	14.8741i	1.76964	+	0.486436i
$936$	2.07913	−	15.5394i	0.0679584	−	0.507920i
$937$	0.145787	−	0.145787i	0.00476266	−	0.00476266i	−0.704721	−	0.709484i	$-0.748928\pi$
$937$	0.145787	−	0.145787i	0.00476266	−	0.00476266i	0.709484	+	0.704721i	$0.248928\pi$
$938$	55.5768	+	13.7789i	1.81465	+	0.449898i
$939$	44.1027	+	4.18746i	1.43924	+	0.136653i
$940$	−39.2536	+	41.7739i	−1.28031	+	1.36252i
$941$	−13.4925	+	7.78989i	−0.439843	+	0.253943i	−0.703531	−	0.710665i	$-0.748394\pi$
$941$	−13.4925	+	7.78989i	−0.439843	+	0.253943i	0.263688	+	0.964608i	$0.415061\pi$
$942$	−1.68818	+	1.44959i	−0.0550038	+	0.0472303i
$943$	−1.31869	−	4.92140i	−0.0429423	−	0.160263i
$944$	50.1074	+	24.1123i	1.63086	+	0.784788i
$945$	−40.3622	+	9.58485i	−1.31298	+	0.311795i
$946$	−22.2364	+	40.2407i	−0.722967	+	1.30834i
$947$	0.810932	+	3.02644i	0.0263518	+	0.0983461i	0.977849	−	0.209310i	$-0.0671219\pi$
$947$	0.810932	+	3.02644i	0.0263518	+	0.0983461i	−0.951497	+	0.307657i	$0.900455\pi$
$948$	−2.95996	+	0.614458i	−0.0961351	+	0.0199567i
$949$	1.70555	+	2.95411i	0.0553646	+	0.0958943i
$950$	1.82541	−	0.500614i	0.0592242	−	0.0162421i
$951$	7.00635	+	0.665240i	0.227197	+	0.0215719i
$952$	−47.3174	+	15.5818i	−1.53356	+	0.505010i
$953$	9.08162	+	9.08162i	0.294183	+	0.294183i	0.838730	−	0.544547i	$-0.183299\pi$
$953$	9.08162	+	9.08162i	0.294183	+	0.294183i	−0.544547	+	0.838730i	$0.683299\pi$
$954$	−37.1205	−	6.39319i	−1.20182	−	0.206987i
$955$	17.9621	−	10.2165i	0.581241	−	0.330597i
$956$	0.829753	+	22.0884i	0.0268361	+	0.714391i
$957$	−6.61989	−	39.2385i	−0.213991	−	1.26840i
$958$	0.707013	−	0.734070i	0.0228425	−	0.0237167i
$959$	17.3759	+	30.0959i	0.561097	+	0.971849i
$960$	−22.1599	−	21.6550i	−0.715209	−	0.698911i
$961$	10.5698	−	18.3074i	0.340962	−	0.590563i
$962$	−0.470432	−	1.63245i	−0.0151673	−	0.0526324i
$963$	−1.35005	+	0.0980107i	−0.0435046	+	0.00315835i
$964$	−34.0800	+	21.4209i	−1.09764	+	0.689921i
$965$	30.3468	+	30.7411i	0.976899	+	0.989590i
$966$	18.1372	+	12.3947i	0.583555	+	0.398794i
$967$	12.3431	−	46.0650i	0.396926	−	1.48135i	−0.421548	−	0.906806i	$-0.638513\pi$
$967$	12.3431	−	46.0650i	0.396926	−	1.48135i	0.818474	−	0.574543i	$-0.194820\pi$
$968$	−8.58929	+	41.2114i	−0.276070	+	1.32459i
$969$	0.951231	+	2.07996i	0.0305579	+	0.0668178i
$970$	24.9492	+	13.9975i	0.801070	+	0.449431i
$971$	12.6987			0.407519			0.203760	−	0.979021i	$-0.434684\pi$
$971$	12.6987			0.407519			0.203760	+	0.979021i	$0.434684\pi$
$972$	20.0268	−	23.8941i	0.642360	−	0.766403i
$973$	5.07449	−	5.07449i	0.162681	−	0.162681i
$974$	−0.824035	−	1.36733i	−0.0264038	−	0.0438121i
$975$	−1.71794	+	15.9086i	−0.0550182	+	0.509484i
$976$	1.12426	+	14.9430i	0.0359866	+	0.478314i
$977$	46.9616	+	12.5833i	1.50243	+	0.402576i	0.913914	−	0.405908i	$-0.133045\pi$
$977$	46.9616	+	12.5833i	1.50243	+	0.402576i	0.588519	+	0.808483i	$0.299711\pi$
$978$	8.52325	+	45.3170i	0.272543	+	1.44908i
$979$	−55.1956	−	31.8672i	−1.76406	−	1.01848i
$980$	12.1545	−	22.6506i	0.388262	−	0.723546i
$981$	−14.6373	−	12.6559i	−0.467334	−	0.404071i
$982$	0.858903	+	2.98049i	0.0274087	+	0.0951113i
$983$	−1.84803	−	6.89693i	−0.0589429	−	0.219978i	0.930172	−	0.367125i	$-0.119658\pi$
$983$	−1.84803	−	6.89693i	−0.0589429	−	0.219978i	−0.989115	+	0.147147i	$0.952991\pi$
$984$	5.29478	−	8.40898i	0.168791	−	0.268068i
$985$	35.0038	−	9.13755i	1.11532	−	0.291147i
$986$	0.591405	+	31.4981i	0.0188342	+	1.00310i
$987$	78.1627	−	13.1867i	2.48795	−	0.419739i
$988$	0.672702	−	0.725215i	0.0214015	−	0.0230722i
$989$	−16.0507			−0.510383
$990$	20.5059	−	43.6924i	0.651721	−	1.38864i
$991$			25.5946i			0.813038i	0.913642	+	0.406519i	$0.133257\pi$
$991$			25.5946i			0.813038i	−0.913642	+	0.406519i	$0.866743\pi$
$992$	−31.4632	−	26.0487i	−0.998957	−	0.827048i
$993$	−11.2951	+	9.33622i	−0.358440	+	0.296276i
$994$	−0.547173	−	29.1423i	−0.0173553	−	0.924339i
$995$	16.0347	−	27.3636i	0.508335	−	0.867485i
$996$	−1.41505	−	0.928546i	−0.0448377	−	0.0294221i
$997$	42.9326	−	11.5037i	1.35969	−	0.364327i	0.495986	−	0.868330i	$-0.334807\pi$
$997$	42.9326	−	11.5037i	1.35969	−	0.364327i	0.863702	+	0.504003i	$0.168140\pi$
$998$	−3.62540	+	1.04475i	−0.114760	+	0.0330709i
$999$	0.946595	−	3.24307i	0.0299489	−	0.102606i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bo.a.43.5	✓	272
5.2	odd	4	inner	360.2.bo.a.187.39	yes	272
8.3	odd	2	inner	360.2.bo.a.43.52	yes	272
9.4	even	3	inner	360.2.bo.a.283.50	yes	272
40.27	even	4	inner	360.2.bo.a.187.50	yes	272
45.22	odd	12	inner	360.2.bo.a.67.52	yes	272
72.67	odd	6	inner	360.2.bo.a.283.39	yes	272
360.67	even	12	inner	360.2.bo.a.67.5	yes	272

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bo.a.43.5	✓	272	1.1	even	1	trivial
360.2.bo.a.43.52	yes	272	8.3	odd	2	inner
360.2.bo.a.67.5	yes	272	360.67	even	12	inner
360.2.bo.a.67.52	yes	272	45.22	odd	12	inner
360.2.bo.a.187.39	yes	272	5.2	odd	4	inner
360.2.bo.a.187.50	yes	272	40.27	even	4	inner
360.2.bo.a.283.39	yes	272	72.67	odd	6	inner
360.2.bo.a.283.50	yes	272	9.4	even	3	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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37266 - 0.340317i) q^{2} +(-1.62317 - 0.604421i) q^{3} +(1.76837 + 0.934277i) q^{4} +(1.13051 - 1.92924i) q^{5} +(2.02236 + 1.38205i) q^{6} +(3.44877 - 0.924095i) q^{7} +(-2.10941 - 1.88425i) q^{8} +(2.26935 + 1.96215i) q^{9} +O(q^{10})\)	\(q+(-1.37266 - 0.340317i) q^{2} +(-1.62317 - 0.604421i) q^{3} +(1.76837 + 0.934277i) q^{4} +(1.13051 - 1.92924i) q^{5} +(2.02236 + 1.38205i) q^{6} +(3.44877 - 0.924095i) q^{7} +(-2.10941 - 1.88425i) q^{8} +(2.26935 + 1.96215i) q^{9} +(-2.20835 + 2.26345i) q^{10} +(-2.54379 + 4.40598i) q^{11} +(-2.30566 - 2.58533i) q^{12} +(1.78469 + 0.478207i) q^{13} +(-5.04846 + 0.0947893i) q^{14} +(-3.00107 + 2.44817i) q^{15} +(2.25425 + 3.30429i) q^{16} +(3.48816 - 3.48816i) q^{17} +(-2.44728 - 3.46566i) q^{18} -0.267684i q^{19} +(3.80159 - 2.35539i) q^{20} +(-6.15647 - 0.584545i) q^{21} +(4.99118 - 5.18220i) q^{22} +(2.42625 + 0.650112i) q^{23} +(2.28505 + 4.33342i) q^{24} +(-2.44390 - 4.36203i) q^{25} +(-2.28703 - 1.26378i) q^{26} +(-2.49757 - 4.55655i) q^{27} +(6.96205 + 1.58796i) q^{28} +(2.25790 - 3.91080i) q^{29} +(4.95260 - 2.33918i) q^{30} +(6.25338 - 3.61039i) q^{31} +(-1.96981 - 5.30282i) q^{32} +(6.79207 - 5.61413i) q^{33} +(-5.97513 + 3.60096i) q^{34} +(2.11606 - 7.69819i) q^{35} +(2.17986 + 5.59001i) q^{36} +(0.459741 + 0.459741i) q^{37} +(-0.0910975 + 0.367438i) q^{38} +(-2.60782 - 1.85492i) q^{39} +(-6.01986 + 1.93940i) q^{40} +(-1.01420 - 1.75664i) q^{41} +(8.25179 + 2.89753i) q^{42} +(-6.17228 + 1.65386i) q^{43} +(-8.61477 + 5.41479i) q^{44} +(6.35098 - 2.15989i) q^{45} +(-3.10916 - 1.71808i) q^{46} +(-12.3810 + 3.31749i) q^{47} +(-1.66185 - 6.72594i) q^{48} +(4.97788 - 2.87398i) q^{49} +(1.87017 + 6.81927i) q^{50} +(-7.77019 + 3.55356i) q^{51} +(2.70922 + 2.51304i) q^{52} +(6.27784 - 6.27784i) q^{53} +(1.87764 + 7.10454i) q^{54} +(5.62440 + 9.88857i) q^{55} +(-9.01609 - 4.54903i) q^{56} +(-0.161794 + 0.434497i) q^{57} +(-4.43023 + 4.59978i) q^{58} +(12.0393 - 6.95090i) q^{59} +(-7.59428 + 1.52544i) q^{60} +(3.24440 + 1.87316i) q^{61} +(-9.81241 + 2.82769i) q^{62} +(9.63968 + 4.66991i) q^{63} +(0.899232 + 7.94930i) q^{64} +(2.94018 - 2.90248i) q^{65} +(-11.2338 + 5.39481i) q^{66} +(-10.9536 - 2.93500i) q^{67} +(9.42726 - 2.90945i) q^{68} +(-3.54527 - 2.52172i) q^{69} +(-5.52445 + 9.84683i) q^{70} +5.77252i q^{71} +(-1.08982 - 8.41500i) q^{72} +(1.30545 + 1.30545i) q^{73} +(-0.474609 - 0.787525i) q^{74} +(1.33037 + 8.55746i) q^{75} +(0.250091 - 0.473364i) q^{76} +(-4.70141 + 17.5459i) q^{77} +(2.94838 + 3.43365i) q^{78} +(0.436342 - 0.755767i) q^{79} +(8.92321 - 0.613464i) q^{80} +(1.29991 + 8.90563i) q^{81} +(0.794330 + 2.75642i) q^{82} +(0.471936 - 0.126455i) q^{83} +(-10.3408 - 6.78554i) q^{84} +(-2.78609 - 10.6729i) q^{85} +(9.03526 - 0.169645i) q^{86} +(-6.02872 + 4.98316i) q^{87} +(13.6679 - 4.50089i) q^{88} +12.5274i q^{89} +(-9.45275 + 0.803436i) q^{90} +6.59690 q^{91} +(3.68312 + 3.41643i) q^{92} +(-12.3325 + 2.08060i) q^{93} +(18.1239 - 0.340292i) q^{94} +(-0.516426 - 0.302619i) q^{95} +(-0.00779747 + 9.79796i) q^{96} +(-2.34140 - 8.73824i) q^{97} +(-7.81098 + 2.25093i) q^{98} +(-14.4180 + 5.00741i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8}+O(q^{10}) \) 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8	\( 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8} - 8 q^{10} - 8 q^{11} - 10 q^{12} - 4 q^{16} - 16 q^{17} + 20 q^{18} + 14 q^{20} + 6 q^{22} - 4 q^{25} - 48 q^{26} - 8 q^{27} + 8 q^{28} - 34 q^{30} - 22 q^{32} + 4 q^{33} - 16 q^{35} - 8 q^{36} - 26 q^{38} - 2 q^{40} - 8 q^{41} - 66 q^{42} - 4 q^{43} - 40 q^{46} - 38 q^{48} - 42 q^{50} - 16 q^{51} + 14 q^{52} + 24 q^{56} + 16 q^{57} + 6 q^{58} + 14 q^{60} - 76 q^{62} - 4 q^{65} - 44 q^{66} - 4 q^{67} - 46 q^{68} + 18 q^{70} + 38 q^{72} - 16 q^{73} - 120 q^{75} - 38 q^{78} + 92 q^{80} - 32 q^{81} - 4 q^{83} - 40 q^{86} - 42 q^{88} - 14 q^{90} - 32 q^{91} + 52 q^{92} + 108 q^{96} - 4 q^{97} - 140 q^{98}+O(q^{100}) \) 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8 - 8 * q^10 - 8 * q^11 - 10 * q^12 - 4 * q^16 - 16 * q^17 + 20 * q^18 + 14 * q^20 + 6 * q^22 - 4 * q^25 - 48 * q^26 - 8 * q^27 + 8 * q^28 - 34 * q^30 - 22 * q^32 + 4 * q^33 - 16 * q^35 - 8 * q^36 - 26 * q^38 - 2 * q^40 - 8 * q^41 - 66 * q^42 - 4 * q^43 - 40 * q^46 - 38 * q^48 - 42 * q^50 - 16 * q^51 + 14 * q^52 + 24 * q^56 + 16 * q^57 + 6 * q^58 + 14 * q^60 - 76 * q^62 - 4 * q^65 - 44 * q^66 - 4 * q^67 - 46 * q^68 + 18 * q^70 + 38 * q^72 - 16 * q^73 - 120 * q^75 - 38 * q^78 + 92 * q^80 - 32 * q^81 - 4 * q^83 - 40 * q^86 - 42 * q^88 - 14 * q^90 - 32 * q^91 + 52 * q^92 + 108 * q^96 - 4 * q^97 - 140 * q^98

Introduction

L-functions

Modular forms

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