LMFDB - Embedded newform 51.2.i.a.41.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [51,2,Mod(5,51)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("51.5"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(51, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	51.i (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.407237050309$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			41.1
Character	$\chi$	$=$	51.41
Dual form			51.2.i.a.5.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.88095 - 0.779115i) q^{2} +(1.10321 + 1.33527i) q^{3} +(1.51674 + 1.51674i) q^{4} +(2.03727 - 0.405238i) q^{5} +(-1.03475 - 3.37109i) q^{6} +(0.388855 - 1.95490i) q^{7} +(-0.112963 - 0.272718i) q^{8} +(-0.565877 + 2.94615i) q^{9} +(-4.14772 - 0.825033i) q^{10} +(-1.30817 - 1.95782i) q^{11} +(-0.351977 + 3.69852i) q^{12} +(-4.24491 + 4.24491i) q^{13} +(-2.25451 + 3.37411i) q^{14} +(2.78862 + 2.27324i) q^{15} -3.68900i q^{16} +(-4.01006 - 0.958875i) q^{17} +(3.35977 - 5.10067i) q^{18} +(1.93477 - 4.67096i) q^{19} +(3.70464 + 2.47536i) q^{20} +(3.03931 - 1.63744i) q^{21} +(0.935240 + 4.70177i) q^{22} +(0.734889 - 0.491037i) q^{23} +(0.239529 - 0.451700i) q^{24} +(-0.633157 + 0.262262i) q^{25} +(11.2917 - 4.67719i) q^{26} +(-4.55817 + 2.49461i) q^{27} +(3.55487 - 2.37529i) q^{28} +(-0.0116792 - 0.0587151i) q^{29} +(-3.47415 - 6.44850i) q^{30} +(2.44942 + 1.63665i) q^{31} +(-3.10008 + 7.48426i) q^{32} +(1.17103 - 3.90663i) q^{33} +(6.79564 + 4.92789i) q^{34} -4.14024i q^{35} +(-5.32682 + 3.61024i) q^{36} +(-1.52979 + 2.28949i) q^{37} +(-7.27842 + 7.27842i) q^{38} +(-10.3511 - 0.985083i) q^{39} +(-0.340652 - 0.509822i) q^{40} +(3.25313 + 0.647088i) q^{41} +(-6.99253 + 0.711965i) q^{42} +(-2.53831 - 6.12803i) q^{43} +(0.985341 - 4.95364i) q^{44} +(0.0410472 + 6.23140i) q^{45} +(-1.76486 + 0.351053i) q^{46} +(5.76615 + 5.76615i) q^{47} +(4.92580 - 4.06972i) q^{48} +(2.79671 + 1.15844i) q^{49} +1.39527 q^{50} +(-3.14356 - 6.41233i) q^{51} -12.8768 q^{52} +(1.75216 + 0.725770i) q^{53} +(10.5173 - 1.14089i) q^{54} +(-3.45848 - 3.45848i) q^{55} +(-0.577063 + 0.114785i) q^{56} +(8.37143 - 2.56958i) q^{57} +(-0.0237779 + 0.119540i) q^{58} +(-3.54618 - 8.56124i) q^{59} +(0.781708 + 7.67751i) q^{60} +(5.30616 + 1.05546i) q^{61} +(-3.33210 - 4.98684i) q^{62} +(5.53939 + 2.25186i) q^{63} +(6.44515 - 6.44515i) q^{64} +(-6.92782 + 10.3682i) q^{65} +(-5.24636 + 6.43581i) q^{66} +7.09503i q^{67} +(-4.62784 - 7.53656i) q^{68} +(1.46640 + 0.439558i) q^{69} +(-3.22572 + 7.78759i) q^{70} +(-0.742386 - 0.496046i) q^{71} +(0.867389 - 0.178482i) q^{72} +(-0.551496 - 2.77256i) q^{73} +(4.66124 - 3.11454i) q^{74} +(-1.04869 - 0.556105i) q^{75} +(10.0192 - 4.15007i) q^{76} +(-4.33604 + 1.79604i) q^{77} +(18.7024 + 9.91759i) q^{78} +(-3.30560 + 2.20873i) q^{79} +(-1.49492 - 7.51548i) q^{80} +(-8.35957 - 3.33431i) q^{81} +(-5.61482 - 3.75170i) q^{82} +(1.44855 - 3.49712i) q^{83} +(7.09339 + 2.12627i) q^{84} +(-8.55813 - 0.328458i) q^{85} +13.5041i q^{86} +(0.0655159 - 0.0803696i) q^{87} +(-0.386156 + 0.577923i) q^{88} +(2.00979 - 2.00979i) q^{89} +(4.77777 - 11.7529i) q^{90} +(6.64775 + 9.94906i) q^{91} +(1.85941 + 0.369859i) q^{92} +(0.516848 + 5.07620i) q^{93} +(-6.35335 - 15.3383i) q^{94} +(2.04880 - 10.3000i) q^{95} +(-13.4135 + 4.11723i) q^{96} +(18.4735 - 3.67461i) q^{97} +(-4.35792 - 4.35792i) q^{98} +(6.50828 - 2.74618i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} + 16 q^{12} - 16 q^{13} + 16 q^{15} + 16 q^{18} - 16 q^{19} + 16 q^{21} - 16 q^{22} + 16 q^{24} + 16 q^{25} - 8 q^{27} + 32 q^{28} - 8 q^{30}+ \cdots - 64 q^{99}+O(q^{100}) $ 32 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 + 16 * q^12 - 16 * q^13 + 16 * q^15 + 16 * q^18 - 16 * q^19 + 16 * q^21 - 16 * q^22 + 16 * q^24 + 16 * q^25 - 8 * q^27 + 32 * q^28 - 8 * q^30 + 16 * q^31 + 96 * q^34 + 8 * q^36 + 16 * q^37 - 24 * q^39 + 16 * q^40 - 56 * q^42 + 16 * q^43 - 40 * q^45 - 32 * q^46 - 64 * q^48 - 48 * q^49 - 40 * q^51 - 96 * q^52 - 24 * q^54 - 48 * q^55 + 8 * q^57 - 48 * q^58 + 32 * q^60 - 32 * q^61 + 64 * q^63 + 16 * q^64 + 72 * q^66 + 80 * q^69 + 48 * q^70 + 64 * q^72 + 48 * q^73 + 88 * q^75 + 48 * q^76 + 96 * q^78 + 16 * q^79 + 48 * q^81 + 112 * q^82 - 56 * q^87 + 16 * q^88 - 88 * q^90 + 16 * q^91 - 72 * q^93 - 48 * q^94 - 112 * q^96 - 16 * q^97 - 64 * q^99

Character values

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

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{11}{16}\right)$

Coefficient data

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

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

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

$2$	−1.88095	−	0.779115i	−1.33003	−	0.550917i	−0.399367	−	0.916791i	$-0.630770\pi$
$2$	−1.88095	−	0.779115i	−1.33003	−	0.550917i	−0.930665	+	0.365874i	$0.880770\pi$
$3$	1.10321	+	1.33527i	0.636936	+	0.770917i
$3$	1.10321	+	1.33527i	0.636936	+	0.770917i
$4$	1.51674	+	1.51674i	0.758368	+	0.758368i
$5$	2.03727	−	0.405238i	0.911094	−	0.181228i	0.282777	−	0.959186i	$-0.408744\pi$
$5$	2.03727	−	0.405238i	0.911094	−	0.181228i	0.628316	+	0.777958i	$0.283744\pi$
$6$	−1.03475	−	3.37109i	−0.422433	−	1.37624i
$7$	0.388855	−	1.95490i	0.146973	−	0.738885i	−0.835057	−	0.550163i	$-0.814566\pi$
$7$	0.388855	−	1.95490i	0.146973	−	0.738885i	0.982031	−	0.188722i	$-0.0604344\pi$
$8$	−0.112963	−	0.272718i	−0.0399386	−	0.0964202i
$9$	−0.565877	+	2.94615i	−0.188626	+	0.982049i
$10$	−4.14772	−	0.825033i	−1.31163	−	0.260898i
$11$	−1.30817	−	1.95782i	−0.394429	−	0.590304i	0.580106	−	0.814541i	$-0.303011\pi$
$11$	−1.30817	−	1.95782i	−0.394429	−	0.590304i	−0.974535	+	0.224237i	$0.928011\pi$
$12$	−0.351977	+	3.69852i	−0.101607	+	1.06767i
$13$	−4.24491	+	4.24491i	−1.17733	+	1.17733i	−0.196905	+	0.980423i	$0.563089\pi$
$13$	−4.24491	+	4.24491i	−1.17733	+	1.17733i	−0.980423	+	0.196905i	$0.936911\pi$
$14$	−2.25451	+	3.37411i	−0.602543	+	0.901770i
$15$	2.78862	+	2.27324i	0.720020	+	0.586947i
$16$		−	3.68900i		−	0.922250i
$17$	−4.01006	−	0.958875i	−0.972582	−	0.232561i
$17$	−4.01006	−	0.958875i	−0.972582	−	0.232561i
$18$	3.35977	−	5.10067i	0.791906	−	1.20224i
$19$	1.93477	−	4.67096i	0.443868	−	1.07159i	−0.530712	−	0.847552i	$-0.678076\pi$
$19$	1.93477	−	4.67096i	0.443868	−	1.07159i	0.974580	−	0.224039i	$-0.0719244\pi$
$20$	3.70464	+	2.47536i	0.828382	+	0.553507i
$21$	3.03931	−	1.63744i	0.663231	−	0.357318i
$22$	0.935240	+	4.70177i	0.199394	+	1.00242i
$23$	0.734889	−	0.491037i	0.153235	−	0.102388i	−0.476589	−	0.879126i	$-0.658127\pi$
$23$	0.734889	−	0.491037i	0.153235	−	0.102388i	0.629824	+	0.776738i	$0.283127\pi$
$24$	0.239529	−	0.451700i	0.0488937	−	0.0922028i
$25$	−0.633157	+	0.262262i	−0.126631	+	0.0524525i
$26$	11.2917	−	4.67719i	2.21449	−	0.917273i
$27$	−4.55817	+	2.49461i	−0.877221	+	0.480087i
$28$	3.55487	−	2.37529i	0.671806	−	0.448887i
$29$	−0.0116792	−	0.0587151i	−0.00216877	−	0.0109031i	0.979686	−	0.200539i	$-0.0642693\pi$
$29$	−0.0116792	−	0.0587151i	−0.00216877	−	0.0109031i	−0.981855	+	0.189636i	$0.939269\pi$
$30$	−3.47415	−	6.44850i	−0.634290	−	1.17733i
$31$	2.44942	+	1.63665i	0.439930	+	0.293952i	0.755741	−	0.654870i	$-0.227277\pi$
$31$	2.44942	+	1.63665i	0.439930	+	0.293952i	−0.315812	+	0.948822i	$0.602277\pi$
$32$	−3.10008	+	7.48426i	−0.548022	+	1.32304i
$33$	1.17103	−	3.90663i	0.203850	−	0.680057i
$34$	6.79564	+	4.92789i	1.16544	+	0.845126i
$35$		−	4.14024i		−	0.699829i
$36$	−5.32682	+	3.61024i	−0.887803	+	0.601707i
$37$	−1.52979	+	2.28949i	−0.251496	+	0.376390i	−0.935640	−	0.352957i	$-0.885176\pi$
$37$	−1.52979	+	2.28949i	−0.251496	+	0.376390i	0.684144	+	0.729347i	$0.260176\pi$
$38$	−7.27842	+	7.27842i	−1.18072	+	1.18072i
$39$	−10.3511	−	0.985083i	−1.65750	−	0.157740i
$40$	−0.340652	−	0.509822i	−0.0538618	−	0.0806099i
$41$	3.25313	+	0.647088i	0.508054	+	0.101058i	0.442460	−	0.896788i	$-0.354106\pi$
$41$	3.25313	+	0.647088i	0.508054	+	0.101058i	0.0655937	+	0.997846i	$0.479106\pi$
$42$	−6.99253	+	0.711965i	−1.07897	+	0.109859i
$43$	−2.53831	−	6.12803i	−0.387089	−	0.934515i	−0.990554	−	0.137126i	$-0.956214\pi$
$43$	−2.53831	−	6.12803i	−0.387089	−	0.934515i	0.603465	−	0.797390i	$-0.293786\pi$
$44$	0.985341	−	4.95364i	0.148546	−	0.746790i
$45$	0.0410472	+	6.23140i	0.00611895	+	0.928923i
$46$	−1.76486	+	0.351053i	−0.260215	+	0.0517599i
$47$	5.76615	+	5.76615i	0.841080	+	0.841080i	0.988999	−	0.147919i	$-0.0472576\pi$
$47$	5.76615	+	5.76615i	0.841080	+	0.841080i	−0.147919	+	0.988999i	$0.547258\pi$
$48$	4.92580	−	4.06972i	0.710978	−	0.587414i
$49$	2.79671	+	1.15844i	0.399530	+	0.165491i
$50$	1.39527			0.197321
$51$	−3.14356	−	6.41233i	−0.440187	−	0.897906i
$52$	−12.8768			−1.78570
$53$	1.75216	+	0.725770i	0.240678	+	0.0996922i	0.499762	−	0.866163i	$-0.333421\pi$
$53$	1.75216	+	0.725770i	0.240678	+	0.0996922i	−0.259084	+	0.965855i	$0.583421\pi$
$54$	10.5173	−	1.14089i	1.43122	−	0.155256i
$55$	−3.45848	−	3.45848i	−0.466341	−	0.466341i
$56$	−0.577063	+	0.114785i	−0.0771133	+	0.0153388i
$57$	8.37143	−	2.56958i	1.10882	−	0.340350i
$58$	−0.0237779	+	0.119540i	−0.00312219	+	0.0156963i
$59$	−3.54618	−	8.56124i	−0.461674	−	1.11458i	−0.967710	−	0.252067i	$-0.918890\pi$
$59$	−3.54618	−	8.56124i	−0.461674	−	1.11458i	0.506036	−	0.862512i	$-0.331110\pi$
$60$	0.781708	+	7.67751i	0.100918	+	0.991162i
$61$	5.30616	+	1.05546i	0.679385	+	0.135138i	0.522708	−	0.852512i	$-0.324922\pi$
$61$	5.30616	+	1.05546i	0.679385	+	0.135138i	0.156677	+	0.987650i	$0.449922\pi$
$62$	−3.33210	−	4.98684i	−0.423177	−	0.633330i
$63$	5.53939	+	2.25186i	0.697898	+	0.283708i
$64$	6.44515	−	6.44515i	0.805644	−	0.805644i
$65$	−6.92782	+	10.3682i	−0.859291	+	1.28602i
$66$	−5.24636	+	6.43581i	−0.645782	+	0.792194i
$67$			7.09503i			0.866796i	0.901203	+	0.433398i	$0.142685\pi$
$67$			7.09503i			0.866796i	−0.901203	+	0.433398i	$0.857315\pi$
$68$	−4.62784	−	7.53656i	−0.561208	−	0.913942i
$69$	1.46640	+	0.439558i	0.176534	+	0.0529166i
$70$	−3.22572	+	7.78759i	−0.385548	+	0.930795i
$71$	−0.742386	−	0.496046i	−0.0881050	−	0.0588699i	0.510737	−	0.859737i	$-0.329372\pi$
$71$	−0.742386	−	0.496046i	−0.0881050	−	0.0588699i	−0.598842	+	0.800867i	$0.704372\pi$
$72$	0.867389	−	0.178482i	0.102223	−	0.0210343i
$73$	−0.551496	−	2.77256i	−0.0645477	−	0.324503i	0.934998	−	0.354654i	$-0.115401\pi$
$73$	−0.551496	−	2.77256i	−0.0645477	−	0.324503i	−0.999545	+	0.0301507i	$0.990401\pi$
$74$	4.66124	−	3.11454i	0.541858	−	0.362058i
$75$	−1.04869	−	0.556105i	−0.121093	−	0.0642135i
$76$	10.0192	−	4.15007i	1.14928	−	0.476046i
$77$	−4.33604	+	1.79604i	−0.494137	+	0.204678i
$78$	18.7024	+	9.91759i	2.11763	+	1.12295i
$79$	−3.30560	+	2.20873i	−0.371909	+	0.248502i	−0.727452	−	0.686158i	$-0.759296\pi$
$79$	−3.30560	+	2.20873i	−0.371909	+	0.248502i	0.355543	+	0.934660i	$0.384296\pi$
$80$	−1.49492	−	7.51548i	−0.167137	−	0.840256i
$81$	−8.35957	−	3.33431i	−0.928841	−	0.370479i
$82$	−5.61482	−	3.75170i	−0.620053	−	0.414306i
$83$	1.44855	−	3.49712i	0.159000	−	0.383859i	−0.824224	−	0.566264i	$-0.808388\pi$
$83$	1.44855	−	3.49712i	0.159000	−	0.383859i	0.983223	+	0.182405i	$0.0583882\pi$
$84$	7.09339	+	2.12627i	0.773952	+	0.231995i
$85$	−8.55813	−	0.328458i	−0.928260	−	0.0356263i
$86$			13.5041i			1.45619i
$87$	0.0655159	−	0.0803696i	0.00702404	−	0.00861653i
$88$	−0.386156	+	0.577923i	−0.0411643	+	0.0616068i
$89$	2.00979	−	2.00979i	0.213037	−	0.213037i	−0.592519	−	0.805556i	$-0.701867\pi$
$89$	2.00979	−	2.00979i	0.213037	−	0.213037i	0.805556	+	0.592519i	$0.201867\pi$
$90$	4.77777	−	11.7529i	0.503621	−	1.23887i
$91$	6.64775	+	9.94906i	0.696873	+	1.04294i
$92$	1.85941	+	0.369859i	0.193856	+	0.0385604i
$93$	0.516848	+	5.07620i	0.0535947	+	0.526377i
$94$	−6.35335	−	15.3383i	−0.655298	−	1.58203i
$95$	2.04880	−	10.3000i	0.210203	−	1.05676i
$96$	−13.4135	+	4.11723i	−1.36901	+	0.420213i
$97$	18.4735	−	3.67461i	1.87570	−	0.373100i	0.880758	−	0.473566i	$-0.157033\pi$
$97$	18.4735	−	3.67461i	1.87570	−	0.373100i	0.994940	+	0.100466i	$0.0320334\pi$
$98$	−4.35792	−	4.35792i	−0.440216	−	0.440216i
$99$	6.50828	−	2.74618i	0.654107	−	0.276002i
$100$	−1.35812	−	0.562550i	−0.135812	−	0.0562550i
$101$	−3.48372			−0.346643			−0.173321	−	0.984865i	$-0.555450\pi$
$101$	−3.48372			−0.346643			−0.173321	+	0.984865i	$0.555450\pi$
$102$	0.916937	+	14.5105i	0.0907902	+	1.43675i
$103$	−3.80817			−0.375230			−0.187615	−	0.982243i	$-0.560076\pi$
$103$	−3.80817			−0.375230			−0.187615	+	0.982243i	$0.560076\pi$
$104$	1.63718	+	0.678143i	0.160539	+	0.0664974i
$105$	5.52833	−	4.56754i	0.539510	−	0.445746i
$106$	−2.73027	−	2.73027i	−0.265188	−	0.265188i
$107$	3.93543	−	0.782805i	0.380452	−	0.0756766i	−0.00115968	−	0.999999i	$-0.500369\pi$
$107$	3.93543	−	0.782805i	0.380452	−	0.0756766i	0.381612	+	0.924323i	$0.375369\pi$
$108$	−10.6972	−	3.12988i	−1.02934	−	0.301173i
$109$	−2.89730	+	14.5657i	−0.277511	+	1.39514i	0.550689	+	0.834711i	$0.314365\pi$
$109$	−2.89730	+	14.5657i	−0.277511	+	1.39514i	−0.828200	+	0.560433i	$0.810635\pi$
$110$	3.81067	+	9.19977i	0.363333	+	0.877163i
$111$	−4.74476	+	0.483102i	−0.450352	+	0.0458540i
$112$	−7.21164	−	1.43449i	−0.681436	−	0.135546i
$113$	3.69755	+	5.53377i	0.347836	+	0.520573i	0.963597	−	0.267360i	$-0.0861513\pi$
$113$	3.69755	+	5.53377i	0.347836	+	0.520573i	−0.615761	+	0.787933i	$0.711151\pi$
$114$	−17.7482	−	1.68905i	−1.66227	−	0.158194i
$115$	1.29818	−	1.29818i	0.121056	−	0.121056i
$116$	0.0713412	−	0.106770i	0.00662386	−	0.00991331i
$117$	−10.1040	−	14.9082i	−0.934119	−	1.37827i
$118$			18.8661i			1.73677i
$119$	−3.43384	+	7.46642i	−0.314780	+	0.684445i
$120$	0.304939	−	1.01730i	0.0278370	−	0.0928663i
$121$	2.08778	−	5.04035i	0.189798	−	0.458214i
$122$	−9.15830	−	6.11938i	−0.829153	−	0.554023i
$123$	2.72484	+	5.05767i	0.245690	+	0.456035i
$124$	1.23276	+	6.19750i	0.110705	+	0.556552i
$125$	−9.81919	+	6.56097i	−0.878255	+	0.586831i
$126$	−8.66486	−	8.55146i	−0.771927	−	0.761824i
$127$	3.25107	−	1.34664i	0.288486	−	0.119495i	−0.233748	−	0.972297i	$-0.575099\pi$
$127$	3.25107	−	1.34664i	0.288486	−	0.119495i	0.522234	+	0.852803i	$0.325099\pi$
$128$	−2.17601	+	0.901332i	−0.192334	+	0.0796672i
$129$	5.38227	−	10.1498i	0.473883	−	0.893640i
$130$	21.1089	−	14.1045i	1.85137	−	1.23705i
$131$	4.01054	+	20.1623i	0.350402	+	1.76159i	0.606640	+	0.794977i	$0.292517\pi$
$131$	4.01054	+	20.1623i	0.350402	+	1.76159i	−0.256237	+	0.966614i	$0.582483\pi$
$132$	7.70147	−	4.14919i	0.670327	−	0.361141i
$133$	−8.37893	−	5.59862i	−0.726546	−	0.485462i
$134$	5.52784	−	13.3454i	0.477533	−	1.15287i
$135$	−8.27531	+	6.92933i	−0.712225	+	0.596381i
$136$	0.191487	+	1.20193i	0.0164199	+	0.103065i
$137$		−	13.4046i		−	1.14524i	−0.819822	−	0.572618i	$-0.805928\pi$
$137$		−	13.4046i		−	1.14524i	0.819822	−	0.572618i	$-0.194072\pi$
$138$	−2.41575	−	1.96928i	−0.205643	−	0.167636i
$139$	−0.0563146	+	0.0842808i	−0.00477654	+	0.00714860i	−0.833850	−	0.551991i	$-0.813868\pi$
$139$	−0.0563146	+	0.0842808i	−0.00477654	+	0.00714860i	0.829074	+	0.559139i	$0.188868\pi$
$140$	6.27966	−	6.27966i	0.530728	−	0.530728i
$141$	−1.33811	+	14.0606i	−0.112689	+	1.18412i
$142$	1.00991	+	1.51144i	0.0847500	+	0.126837i
$143$	13.8638	+	2.75769i	1.15935	+	0.230610i
$144$	10.8683	+	2.08752i	0.905695	+	0.173960i
$145$	−0.0475872	−	0.114886i	−0.00395190	−	0.00954073i
$146$	−1.12280	+	5.64471i	−0.0929239	+	0.467160i
$147$	1.53853	+	5.01235i	0.126895	+	0.413412i
$148$	−5.79285	+	1.15227i	−0.476169	+	0.0947159i
$149$	9.82755	+	9.82755i	0.805104	+	0.805104i	0.983888	−	0.178784i	$-0.0572163\pi$
$149$	9.82755	+	9.82755i	0.805104	+	0.805104i	−0.178784	+	0.983888i	$0.557216\pi$
$150$	1.53927	+	1.86306i	0.125681	+	0.152118i
$151$	4.63104	+	1.91824i	0.376869	+	0.156104i	0.563074	−	0.826407i	$-0.309619\pi$
$151$	4.63104	+	1.91824i	0.376869	+	0.156104i	−0.186205	+	0.982511i	$0.559619\pi$
$152$	−1.49241			−0.121050
$153$	5.09419	−	11.2716i	0.411840	−	0.911256i
$154$	9.55519			0.769979
$155$	5.65337	+	2.34170i	0.454089	+	0.188090i
$156$	−14.2058	−	17.1940i	−1.13737	−	1.37662i
$157$	−8.48035	−	8.48035i	−0.676806	−	0.676806i	0.282470	−	0.959276i	$-0.408846\pi$
$157$	−8.48035	−	8.48035i	−0.676806	−	0.676806i	−0.959276	+	0.282470i	$0.908846\pi$
$158$	7.93852	−	1.57907i	0.631555	−	0.125624i
$159$	0.963899	+	3.14028i	0.0764422	+	0.249040i
$160$	−3.28279	+	16.5037i	−0.259527	+	1.30473i
$161$	−0.674165	−	1.62758i	−0.0531317	−	0.128271i
$162$	13.1261	+	12.7847i	1.03128	+	1.00446i
$163$	−11.3986	−	2.26731i	−0.892803	−	0.177590i	−0.272690	−	0.962102i	$-0.587913\pi$
$163$	−11.3986	−	2.26731i	−0.892803	−	0.177590i	−0.620113	+	0.784512i	$0.712913\pi$
$164$	3.95268	+	5.91560i	0.308652	+	0.461931i
$165$	0.802581	−	8.43340i	0.0624809	−	0.656539i
$166$	−5.44932	+	5.44932i	−0.422949	+	0.422949i
$167$	8.95841	−	13.4072i	0.693223	−	1.03748i	−0.303196	−	0.952928i	$-0.598054\pi$
$167$	8.95841	−	13.4072i	0.693223	−	1.03748i	0.996419	−	0.0845529i	$-0.0269462\pi$
$168$	−0.789888	−	0.643902i	−0.0609412	−	0.0496781i
$169$		−	23.0386i		−	1.77220i
$170$	15.8415	+	7.28558i	1.21499	+	0.558778i
$171$	12.6665	+	8.34332i	0.968630	+	0.638029i
$172$	5.44465	−	13.1446i	0.415151	−	1.00226i
$173$	−15.1405	−	10.1166i	−1.15111	−	0.769149i	−0.174607	−	0.984638i	$-0.555866\pi$
$173$	−15.1405	−	10.1166i	−1.15111	−	0.769149i	−0.976506	+	0.215489i	$0.930866\pi$
$174$	−0.185849	+	0.100127i	−0.0140892	+	0.00759059i
$175$	0.266492	+	1.33974i	0.0201449	+	0.101275i
$176$	−7.22239	+	4.82584i	−0.544408	+	0.363762i
$177$	7.51938	−	14.1799i	0.565191	−	1.06583i
$178$	−5.34616	+	2.21445i	−0.400712	+	0.165980i
$179$	−17.7630	+	7.35767i	−1.32767	+	0.549938i	−0.929989	−	0.367587i	$-0.880184\pi$
$179$	−17.7630	+	7.35767i	−1.32767	+	0.549938i	−0.397679	+	0.917525i	$0.630184\pi$
$180$	−9.38914	+	9.51366i	−0.699825	+	0.709106i
$181$	2.91194	−	1.94570i	0.216443	−	0.144623i	−0.442623	−	0.896708i	$-0.645952\pi$
$181$	2.91194	−	1.94570i	0.216443	−	0.144623i	0.659066	+	0.752085i	$0.270952\pi$
$182$	−4.75262	−	23.8930i	−0.352288	−	1.77107i
$183$	4.44446	+	8.24954i	0.328544	+	0.609823i
$184$	−0.216930	−	0.144948i	−0.0159923	−	0.0106857i
$185$	−2.18880	+	5.28424i	−0.160924	+	0.388505i
$186$	2.98278	−	9.95076i	0.218708	−	0.729625i
$187$	3.36854	+	9.10533i	0.246332	+	0.665848i
$188$			17.4915i			1.27570i
$189$	3.10425	+	9.88083i	0.225801	+	0.718725i
$190$	−11.8786	+	17.7776i	−0.861764	+	1.28972i
$191$	6.08578	−	6.08578i	0.440352	−	0.440352i	−0.451778	−	0.892130i	$-0.649210\pi$
$191$	6.08578	−	6.08578i	0.440352	−	0.440352i	0.892130	+	0.451778i	$0.149210\pi$
$192$	15.7163	+	1.49568i	1.13423	+	0.107941i
$193$	−5.97920	−	8.94851i	−0.430392	−	0.644128i	0.551365	−	0.834264i	$-0.314107\pi$
$193$	−5.97920	−	8.94851i	−0.430392	−	0.644128i	−0.981758	+	0.190136i	$0.939107\pi$
$194$	−37.6106	−	7.48122i	−2.70029	−	0.537120i
$195$	−21.4872	+	2.18778i	−1.53873	+	0.156670i
$196$	2.48483	+	5.99892i	0.177488	+	0.428494i
$197$	−4.95440	+	24.9075i	−0.352987	+	1.77458i	0.241422	+	0.970420i	$0.422386\pi$
$197$	−4.95440	+	24.9075i	−0.352987	+	1.77458i	−0.594408	+	0.804163i	$0.702614\pi$
$198$	−14.3813	+	0.0947319i	−1.02204	+	0.00673231i
$199$	−23.7232	+	4.71884i	−1.68169	+	0.334510i	−0.941276	−	0.337637i	$-0.890372\pi$
$199$	−23.7232	+	4.71884i	−1.68169	+	0.334510i	−0.740418	+	0.672147i	$0.765372\pi$
$200$	0.143047	+	0.143047i	0.0101150	+	0.0101150i
$201$	−9.47376	+	7.82727i	−0.668227	+	0.552093i
$202$	6.55269	+	2.71422i	0.461046	+	0.190972i
$203$	−0.119324			−0.00837490
$204$	4.95787	−	14.4938i	0.347120	−	1.01477i
$205$	6.88972			0.481199
$206$	7.16297	+	2.96700i	0.499068	+	0.206721i
$207$	1.03081	+	2.44296i	0.0716463	+	0.169797i
$208$	15.6595	+	15.6595i	1.08579	+	1.08579i
$209$	−11.6759	+	2.32248i	−0.807639	+	0.160649i
$210$	−13.9571	+	4.28410i	−0.963134	+	0.295631i
$211$	2.14574	−	10.7873i	0.147719	−	0.742631i	−0.833921	−	0.551884i	$-0.813909\pi$
$211$	2.14574	−	10.7873i	0.147719	−	0.742631i	0.981639	−	0.190747i	$-0.0610910\pi$
$212$	1.55677	+	3.75837i	0.106919	+	0.258126i
$213$	−0.156649	−	1.53852i	−0.0107334	−	0.105418i
$214$	−8.01223	−	1.59373i	−0.547705	−	0.108945i
$215$	−7.65453	−	11.4558i	−0.522034	−	0.781280i
$216$	1.19523	+	0.961294i	0.0813251	+	0.0654078i
$217$	4.15197	−	4.15197i	0.281854	−	0.281854i
$218$	16.7980	−	25.1401i	1.13771	−	1.70270i
$219$	3.09369	−	3.79509i	0.209052	−	0.256449i
$220$		−	10.4912i		−	0.707316i
$221$	21.0927	−	12.9520i	1.41885	−	0.871246i
$222$	9.30104	+	2.78802i	0.624245	+	0.187120i
$223$	3.85027	−	9.29537i	0.257833	−	0.622464i	−0.740962	−	0.671547i	$-0.765630\pi$
$223$	3.85027	−	9.29537i	0.257833	−	0.622464i	0.998795	+	0.0490833i	$0.0156300\pi$
$224$	13.4255	+	8.97065i	0.897031	+	0.599377i
$225$	−0.414374	−	2.01378i	−0.0276249	−	0.134252i
$226$	−2.64346	−	13.2895i	−0.175840	−	0.884008i
$227$	1.50999	−	1.00895i	0.100222	−	0.0669661i	−0.504449	−	0.863441i	$-0.668305\pi$
$227$	1.50999	−	1.00895i	0.100222	−	0.0669661i	0.604671	+	0.796475i	$0.293305\pi$
$228$	16.5946	+	8.79987i	1.09901	+	0.582786i
$229$	1.66699	−	0.690491i	0.110158	−	0.0456290i	−0.326924	−	0.945051i	$-0.606012\pi$
$229$	1.66699	−	0.690491i	0.110158	−	0.0456290i	0.437082	+	0.899422i	$0.356012\pi$
$230$	−3.45324	+	1.43038i	−0.227700	+	0.0943163i
$231$	−7.18174	−	3.80836i	−0.472523	−	0.250572i
$232$	−0.0146933	+	0.00981777i	−0.000964664	+	0.000644568i
$233$	0.271493	+	1.36489i	0.0177861	+	0.0894166i	0.988659	−	0.150179i	$-0.0479851\pi$
$233$	0.271493	+	1.36489i	0.0177861	+	0.0894166i	−0.970873	+	0.239596i	$0.922985\pi$
$234$	7.38996	+	35.9138i	0.483097	+	2.34776i
$235$	14.0839	+	9.41054i	0.918730	+	0.613876i
$236$	7.60652	−	18.3638i	0.495143	−	1.19538i
$237$	−6.59600	−	1.97718i	−0.428456	−	0.128431i
$238$	12.2761	−	11.3686i	0.795740	−	0.736917i
$239$		−	8.01035i		−	0.518146i	−0.965858	−	0.259073i	$-0.916583\pi$
$239$		−	8.01035i		−	0.518146i	0.965858	−	0.259073i	$-0.0834171\pi$
$240$	8.38597	−	10.2872i	0.541312	−	0.664038i
$241$	−9.62530	+	14.4053i	−0.620020	+	0.927925i	0.379976	+	0.924996i	$0.375932\pi$
$241$	−9.62530	+	14.4053i	−0.620020	+	0.927925i	−0.999996	+	0.00292882i	$0.999068\pi$
$242$	−7.85403	+	7.85403i	−0.504876	+	0.504876i
$243$	−4.77012	−	14.8407i	−0.306003	−	0.952031i
$244$	6.44719	+	9.64891i	0.412739	+	0.617708i
$245$	6.16709	+	1.22671i	0.394001	+	0.0783717i
$246$	−1.18477	−	11.6362i	−0.0755383	−	0.741896i
$247$	11.6149	+	28.0408i	0.739036	+	1.78419i
$248$	0.169649	−	0.852883i	0.0107727	−	0.0541581i
$249$	6.26764	−	1.92383i	0.397196	−	0.121918i
$250$	23.5811	−	4.69058i	1.49140	−	0.296658i
$251$	−15.7099	−	15.7099i	−0.991603	−	0.991603i	0.00836189	−	0.999965i	$-0.497338\pi$
$251$	−15.7099	−	15.7099i	−0.991603	−	0.991603i	−0.999965	+	0.00836189i	$0.997338\pi$
$252$	4.98632	+	11.8173i	0.314109	+	0.744418i
$253$	−1.92272	−	0.796417i	−0.120880	−	0.0500703i
$254$	−7.16429			−0.449527
$255$	−9.00279	−	11.7897i	−0.563777	−	0.738303i
$256$	−13.4344			−0.839653
$257$	−16.5305	−	6.84714i	−1.03114	−	0.427113i	−0.198017	−	0.980199i	$-0.563450\pi$
$257$	−16.5305	−	6.84714i	−1.03114	−	0.427113i	−0.833124	+	0.553086i	$0.813450\pi$
$258$	−18.0316	+	14.8978i	−1.12260	+	0.927499i
$259$	3.88088	+	3.88088i	0.241146	+	0.241146i
$260$	−26.2335	+	5.21818i	−1.62694	+	0.323618i
$261$	0.179592	−	0.00118300i	0.0111165	−	7.32259e-5i
$262$	8.16515	−	41.0490i	0.504445	−	2.53601i
$263$	2.97552	+	7.18354i	0.183478	+	0.442956i	0.988679	−	0.150047i	$-0.0479424\pi$
$263$	2.97552	+	7.18354i	0.183478	+	0.442956i	−0.805201	+	0.593003i	$0.797942\pi$
$264$	−1.19769	+	0.121946i	−0.0737127	+	0.00750528i
$265$	3.86374	+	0.768545i	0.237347	+	0.0472113i
$266$	11.3984	+	17.0589i	0.698879	+	1.04595i
$267$	4.90081	+	0.466396i	0.299925	+	0.0285429i
$268$	−10.7613	+	10.7613i	−0.657350	+	0.657350i
$269$	−6.79874	+	10.1750i	−0.414527	+	0.620383i	−0.978705	−	0.205270i	$-0.934193\pi$
$269$	−6.79874	+	10.1750i	−0.414527	+	0.620383i	0.564179	+	0.825653i	$0.309193\pi$
$270$	20.9642	−	6.58630i	1.27584	−	0.400829i
$271$			1.34760i			0.0818610i	0.999162	+	0.0409305i	$0.0130322\pi$
$271$			1.34760i			0.0818610i	−0.999162	+	0.0409305i	$0.986968\pi$
$272$	−3.53729	+	14.7931i	−0.214480	+	0.896963i
$273$	−5.95082	+	19.8524i	−0.360160	+	1.20152i
$274$	−10.4437	+	25.2134i	−0.630930	+	1.52320i
$275$	1.34174	+	0.896522i	0.0809099	+	0.0540623i
$276$	1.55745	+	2.89083i	0.0937472	+	0.174008i
$277$	3.28766	+	16.5282i	0.197536	+	0.993081i	0.944574	+	0.328299i	$0.106475\pi$
$277$	3.28766	+	16.5282i	0.197536	+	0.993081i	−0.747038	+	0.664782i	$0.768525\pi$
$278$	0.171589	−	0.114652i	0.0102912	−	0.00687639i
$279$	−6.20789	+	6.29022i	−0.371657	+	0.376586i
$280$	−1.12912	+	0.467695i	−0.0674776	+	0.0279501i
$281$	4.14660	−	1.71758i	0.247365	−	0.102462i	−0.255556	−	0.966794i	$-0.582259\pi$
$281$	4.14660	−	1.71758i	0.247365	−	0.102462i	0.502921	+	0.864332i	$0.332259\pi$
$282$	13.4717	−	25.4048i	0.802230	−	1.51283i
$283$	4.58733	−	3.06516i	0.272688	−	0.182205i	−0.411706	−	0.911317i	$-0.635067\pi$
$283$	4.58733	−	3.06516i	0.272688	−	0.182205i	0.684394	+	0.729112i	$0.260067\pi$
$284$	−0.373632	−	1.87837i	−0.0221710	−	0.111461i
$285$	16.0135	−	8.62735i	0.948561	−	0.511040i
$286$	−23.9286	−	15.9886i	−1.41493	−	0.945425i
$287$	2.52999	−	6.10794i	0.149341	−	0.360540i
$288$	−20.2955	−	13.3685i	−1.19592	−	0.787744i
$289$	15.1611	+	7.69029i	0.891830	+	0.452370i
$290$			0.253170i			0.0148666i
$291$	25.2866	+	20.6132i	1.48233	+	1.20837i
$292$	3.36876	−	5.04171i	0.197142	−	0.295044i
$293$	17.1538	−	17.1538i	1.00214	−	1.00214i	0.00213730	−	0.999998i	$-0.499320\pi$
$293$	17.1538	−	17.1538i	1.00214	−	1.00214i	0.999998	−	0.00213730i	$-0.000680326\pi$
$294$	1.01131	−	10.6267i	0.0589806	−	0.619759i
$295$	−10.6939	−	16.0045i	−0.622621	−	0.931818i
$296$	0.797195	+	0.158572i	0.0463360	+	0.00921681i
$297$	10.8469	+	5.66069i	0.629398	+	0.328467i
$298$	−10.8283	−	26.1419i	−0.627269	−	1.51436i
$299$	−1.03513	+	5.20395i	−0.0598631	+	0.300952i
$300$	−0.747125	−	2.43405i	−0.0431353	−	0.140530i
$301$	−12.9667	+	2.57925i	−0.747391	+	0.148665i
$302$	−7.21623	−	7.21623i	−0.415247	−	0.415247i
$303$	−3.84325	−	4.65169i	−0.220789	−	0.267233i
$304$	−17.2312	−	7.13738i	−0.988275	−	0.409357i
$305$	11.2378			0.643474
$306$	−18.3638	+	17.2324i	−1.04979	+	0.985109i
$307$	−21.5715			−1.23115			−0.615575	−	0.788078i	$-0.711076\pi$
$307$	−21.5715			−1.23115			−0.615575	+	0.788078i	$0.711076\pi$
$308$	−9.30075	−	3.85250i	−0.529959	−	0.219516i
$309$	−4.20119	−	5.08492i	−0.238997	−	0.289271i
$310$	−8.80924	−	8.80924i	−0.500331	−	0.500331i
$311$	28.4123	−	5.65155i	1.61111	−	0.320470i	0.694268	−	0.719717i	$-0.255728\pi$
$311$	28.4123	−	5.65155i	1.61111	−	0.320470i	0.916844	+	0.399247i	$0.130728\pi$
$312$	0.900645	+	2.93421i	0.0509890	+	0.166117i
$313$	−2.17257	+	10.9222i	−0.122801	+	0.617361i	0.869543	+	0.493857i	$0.164413\pi$
$313$	−2.17257	+	10.9222i	−0.122801	+	0.617361i	−0.992344	+	0.123504i	$0.960587\pi$
$314$	9.34394	+	22.5583i	0.527309	+	1.27304i
$315$	12.1978	+	2.34287i	0.687266	+	0.132006i
$316$	−8.36379	−	1.66366i	−0.470500	−	0.0935882i
$317$	6.07417	+	9.09064i	0.341159	+	0.510581i	0.961888	−	0.273445i	$-0.0881630\pi$
$317$	6.07417	+	9.09064i	0.341159	+	0.510581i	−0.620728	+	0.784026i	$0.713163\pi$
$318$	0.633593	−	6.65770i	0.0355301	−	0.373345i
$319$	−0.0996751	+	0.0996751i	−0.00558074	+	0.00558074i
$320$	10.5187	−	15.7423i	0.588012	−	0.880022i
$321$	5.38684	+	4.39125i	0.300664	+	0.245096i
$322$			3.58665i			0.199876i
$323$	−12.2374	+	16.8756i	−0.680908	+	0.938984i
$324$	−7.62198	−	17.7365i	−0.423444	−	0.985363i
$325$	1.57442	−	3.80098i	0.0873329	−	0.210840i
$326$	19.6736	+	13.1455i	1.08962	+	0.728061i
$327$	−22.6455	+	12.2003i	−1.25230	+	0.674679i
$328$	−0.191012	−	0.960283i	−0.0105469	−	0.0530228i
$329$	13.5145	−	9.03009i	0.745077	−	0.497845i
$330$	−8.08020	+	15.2375i	−0.444800	+	0.838796i
$331$	10.9585	−	4.53916i	0.602334	−	0.249495i	−0.0606127	−	0.998161i	$-0.519305\pi$
$331$	10.9585	−	4.53916i	0.602334	−	0.249495i	0.662947	+	0.748666i	$0.269305\pi$
$332$	7.50129	−	3.10713i	0.411687	−	0.170526i
$333$	−5.87951	−	5.80256i	−0.322195	−	0.317978i
$334$	−27.2961	+	18.2386i	−1.49357	+	0.997974i
$335$	2.87517	+	14.4545i	0.157087	+	0.789732i
$336$	−6.04050	−	11.2120i	−0.329536	−	0.611665i
$337$	19.3446	+	12.9256i	1.05377	+	0.704103i	0.956671	−	0.291172i	$-0.0940451\pi$
$337$	19.3446	+	12.9256i	1.05377	+	0.704103i	0.0970945	+	0.995275i	$0.469045\pi$
$338$	−17.9497	+	43.3344i	−0.976335	+	2.35708i
$339$	−3.30991	+	11.0421i	−0.179769	+	0.599724i
$340$	−12.4822	−	13.4786i	−0.676945	−	0.730980i
$341$		−	6.93655i		−	0.375635i
$342$	−17.3246	−	25.5620i	−0.936808	−	1.38223i
$343$	11.1037	−	16.6179i	0.599543	−	0.897280i
$344$	−1.38448	+	1.38448i	−0.0746464	+	0.0746464i
$345$	3.16557	+	0.301258i	0.170429	+	0.0162192i
$346$	20.5966	+	30.8250i	1.10728	+	1.65716i
$347$	−28.6483	−	5.69850i	−1.53792	−	0.305912i	−0.647863	−	0.761757i	$-0.724337\pi$
$347$	−28.6483	−	5.69850i	−1.53792	−	0.305912i	−0.890059	+	0.455845i	$0.849337\pi$
$348$	0.221270	−	0.0225292i	0.0118613	−	0.00120769i
$349$	−4.16097	−	10.0455i	−0.222732	−	0.537722i	0.772527	−	0.634982i	$-0.218992\pi$
$349$	−4.16097	−	10.0455i	−0.222732	−	0.537722i	−0.995259	+	0.0972594i	$0.968992\pi$
$350$	0.542557	−	2.72762i	0.0290009	−	0.145797i
$351$	8.75965	−	29.9384i	0.467556	−	1.59800i
$352$	18.7082	−	3.72130i	0.997153	−	0.198346i
$353$	−17.9892	−	17.9892i	−0.957468	−	0.957468i	0.0416640	−	0.999132i	$-0.486734\pi$
$353$	−17.9892	−	17.9892i	−0.957468	−	0.957468i	−0.999132	+	0.0416640i	$0.986734\pi$
$354$	−25.1913	+	20.8132i	−1.33890	+	1.10621i
$355$	−1.71345	−	0.709736i	−0.0909407	−	0.0376689i
$356$	6.09664			0.323121
$357$	−13.7579	+	3.65190i	−0.728145	+	0.193279i
$358$	39.1437			2.06881
$359$	13.3198	+	5.51725i	0.702993	+	0.291189i	0.705402	−	0.708808i	$-0.250767\pi$
$359$	13.3198	+	5.51725i	0.702993	+	0.291189i	−0.00240862	+	0.999997i	$0.500767\pi$
$360$	1.69478	−	0.715114i	0.0893226	−	0.0376898i
$361$	−4.63947	−	4.63947i	−0.244183	−	0.244183i
$362$	−6.99314	+	1.39102i	−0.367551	+	0.0731104i
$363$	9.03347	−	2.77280i	0.474134	−	0.145534i
$364$	−5.00722	+	25.1730i	−0.262449	+	1.31942i
$365$	−2.24709	−	5.42495i	−0.117618	−	0.283955i
$366$	−1.93247	−	18.9797i	−0.101012	−	0.992085i
$367$	34.1345	+	6.78978i	1.78181	+	0.354424i	0.972490	−	0.232947i	$-0.0748368\pi$
$367$	34.1345	+	6.78978i	1.78181	+	0.354424i	0.809318	+	0.587370i	$0.199837\pi$
$368$	−1.81143	−	2.71100i	−0.0944276	−	0.141321i
$369$	−3.74729	+	9.21803i	−0.195076	+	0.479871i
$370$	8.23406	−	8.23406i	0.428068	−	0.428068i
$371$	2.10015	−	3.14309i	0.109034	−	0.163181i
$372$	−6.91533	+	8.48318i	−0.358543	+	0.439832i
$373$			28.1519i			1.45765i	0.684699	+	0.728826i	$0.259934\pi$
$373$			28.1519i			1.45765i	−0.684699	+	0.728826i	$0.740066\pi$
$374$	0.758042	−	19.7511i	0.0391974	−	1.02131i
$375$	−19.5932	−	5.87314i	−1.01179	−	0.303288i
$376$	0.921168	−	2.22390i	0.0475056	−	0.114689i
$377$	0.298818	+	0.199664i	0.0153899	+	0.0102832i
$378$	1.85936	−	21.0039i	0.0956351	−	1.08032i
$379$	−2.74737	−	13.8119i	−0.141123	−	0.709472i	−0.984948	−	0.172853i	$-0.944701\pi$
$379$	−2.74737	−	13.8119i	−0.141123	−	0.709472i	0.843825	−	0.536619i	$-0.180299\pi$
$380$	18.7299	−	12.5149i	0.960825	−	0.642003i
$381$	5.38472	+	2.85543i	0.275868	+	0.146288i
$382$	−16.1886	+	6.70552i	−0.828279	+	0.343084i
$383$	−15.0509	+	6.23429i	−0.769065	+	0.318557i	−0.732494	−	0.680774i	$-0.761644\pi$
$383$	−15.0509	+	6.23429i	−0.769065	+	0.318557i	−0.0365717	+	0.999331i	$0.511644\pi$
$384$	−3.60410	−	1.91120i	−0.183921	−	0.0975304i
$385$	−8.10584	+	5.41615i	−0.413112	+	0.276032i
$386$	4.27466	+	21.4902i	0.217575	+	1.09382i
$387$	19.4904	−	4.01053i	0.990755	−	0.203867i
$388$	33.5928	+	22.4460i	1.70542	+	1.13952i
$389$	1.24058	−	2.99501i	0.0628997	−	0.151853i	−0.889304	−	0.457316i	$-0.848811\pi$
$389$	1.24058	−	2.99501i	0.0628997	−	0.151853i	0.952204	+	0.305462i	$0.0988110\pi$
$390$	42.1208	+	12.6259i	2.13287	+	0.639335i
$391$	−3.41779	+	1.26442i	−0.172845	+	0.0639445i
$392$		−	0.893573i		−	0.0451322i
$393$	−22.4977	+	27.5983i	−1.13486	+	1.39215i
$394$	28.7248	−	42.9896i	1.44713	−	2.16579i
$395$	−5.83933	+	5.83933i	−0.293809	+	0.293809i
$396$	14.0366	+	5.70611i	0.705365	+	0.286743i
$397$	−9.87912	−	14.7851i	−0.495819	−	0.742045i	0.496190	−	0.868214i	$-0.334732\pi$
$397$	−9.87912	−	14.7851i	−0.495819	−	0.742045i	−0.992009	+	0.126169i	$0.959732\pi$
$398$	48.2987	+	9.60721i	2.42099	+	0.481566i
$399$	−1.76802	−	17.3645i	−0.0885118	−	0.869315i
$400$	0.967485	+	2.33572i	0.0483743	+	0.116786i
$401$	2.86708	−	14.4138i	0.143175	−	0.719791i	−0.840780	−	0.541377i	$-0.817903\pi$
$401$	2.86708	−	14.4138i	0.143175	−	0.719791i	0.983955	−	0.178414i	$-0.0570967\pi$
$402$	23.9180	−	7.34155i	1.19292	−	0.366163i
$403$	−17.3450	+	3.45014i	−0.864018	+	0.171864i
$404$	−5.28388	−	5.28388i	−0.262883	−	0.262883i
$405$	−18.3819	−	3.40528i	−0.913402	−	0.169210i
$406$	0.224442	+	0.0929671i	0.0111389	+	0.00461388i
$407$	6.48364			0.321382
$408$	−1.39365	+	1.58166i	−0.0689959	+	0.0783040i
$409$	−3.98334			−0.196964			−0.0984819	−	0.995139i	$-0.531399\pi$
$409$	−3.98334			−0.196964			−0.0984819	+	0.995139i	$0.531399\pi$
$410$	−12.9592	−	5.36788i	−0.640010	−	0.265101i
$411$	17.8988	−	14.7881i	0.882881	−	0.729441i
$412$	−5.77599	−	5.77599i	−0.284562	−	0.284562i
$413$	−18.1154	+	3.60337i	−0.891399	+	0.177310i
$414$	−0.0355587	−	5.39820i	−0.00174761	−	0.265307i
$415$	1.53393	−	7.71158i	0.0752976	−	0.378547i
$416$	−18.6104	−	44.9296i	−0.912452	−	2.20285i
$417$	−0.174664	+	0.0177839i	−0.00855333	+	0.000870883i
$418$	23.7712	+	4.72840i	1.16269	+	0.231273i
$419$	−5.48388	−	8.20720i	−0.267905	−	0.400948i	0.672987	−	0.739654i	$-0.265011\pi$
$419$	−5.48388	−	8.20720i	−0.267905	−	0.400948i	−0.940892	+	0.338706i	$0.890011\pi$
$420$	15.3128	+	1.45727i	0.747187	+	0.0711075i
$421$	1.66544	−	1.66544i	0.0811686	−	0.0811686i	−0.665357	−	0.746525i	$-0.731721\pi$
$421$	1.66544	−	1.66544i	0.0811686	−	0.0811686i	0.746525	+	0.665357i	$0.231721\pi$
$422$	−12.4406	+	18.6187i	−0.605599	+	0.906343i
$423$	−20.2509	+	13.7250i	−0.984631	+	0.667333i
$424$		−	0.559831i		−	0.0271878i
$425$	2.79047	−	0.444568i	0.135358	−	0.0215647i
$426$	−0.904037	+	3.01593i	−0.0438007	+	0.146122i
$427$	4.12665	−	9.96262i	0.199703	−	0.482125i
$428$	7.15631	+	4.78170i	0.345914	+	0.231132i
$429$	11.6124	+	21.5542i	0.560652	+	1.04065i
$430$	5.47239	+	27.5115i	0.263902	+	1.32672i
$431$	−17.1107	+	11.4330i	−0.824191	+	0.550707i	−0.894629	−	0.446809i	$-0.852560\pi$
$431$	−17.1107	+	11.4330i	−0.824191	+	0.550707i	0.0704381	+	0.997516i	$0.477560\pi$
$432$	9.20261	+	16.8151i	0.442761	+	0.809017i
$433$	−8.90305	+	3.68777i	−0.427853	+	0.177223i	−0.586210	−	0.810159i	$-0.699381\pi$
$433$	−8.90305	+	3.68777i	−0.427853	+	0.177223i	0.158356	+	0.987382i	$0.449381\pi$
$434$	−11.0445	+	4.57479i	−0.530153	+	0.219597i
$435$	0.100905	−	0.190284i	0.00483800	−	0.00912342i
$436$	−26.4868	+	17.6979i	−1.26849	+	0.847577i
$437$	−0.871769	−	4.38268i	−0.0417024	−	0.209652i
$438$	−8.77589	+	4.72804i	−0.419328	+	0.225914i
$439$	−32.3786	−	21.6347i	−1.54534	−	1.03257i	−0.977880	−	0.209168i	$-0.932924\pi$
$439$	−32.3786	−	21.6347i	−1.54534	−	1.03257i	−0.567465	−	0.823398i	$-0.692076\pi$
$440$	−0.552506	+	1.33387i	−0.0263397	+	0.0635897i
$441$	−4.99552	+	7.58399i	−0.237882	+	0.361142i
$442$	−49.7654	+	7.92844i	−2.36710	+	0.377118i
$443$		−	13.1202i		−	0.623358i	−0.950187	−	0.311679i	$-0.899109\pi$
$443$		−	13.1202i		−	0.623358i	0.950187	−	0.311679i	$-0.100891\pi$
$444$	−7.92929	−	6.46381i	−0.376307	−	0.306759i
$445$	3.28003	−	4.90892i	0.155489	−	0.232705i
$446$	−14.4843	+	14.4843i	−0.685852	+	0.685852i
$447$	−2.28060	+	23.9642i	−0.107869	+	1.13347i
$448$	−10.0934	−	15.1059i	−0.476870	−	0.713686i
$449$	20.7822	+	4.13384i	0.980774	+	0.195088i	0.659341	−	0.751844i	$-0.270835\pi$
$449$	20.7822	+	4.13384i	0.980774	+	0.195088i	0.321433	+	0.946932i	$0.395835\pi$
$450$	−0.789550	+	4.11067i	−0.0372198	+	0.193779i
$451$	−2.98877	−	7.21554i	−0.140736	−	0.339766i
$452$	−2.78507	+	14.0015i	−0.130998	+	0.658574i
$453$	2.54763	+	8.29989i	0.119698	+	0.389963i
$454$	−3.62631	+	0.721317i	−0.170191	+	0.0338531i
$455$	17.5750	+	17.5750i	0.823927	+	0.823927i
$456$	−1.64643	−	1.99277i	−0.0771014	−	0.0933199i
$457$	−12.9893	−	5.38033i	−0.607612	−	0.251681i	0.0575953	−	0.998340i	$-0.481657\pi$
$457$	−12.9893	−	5.38033i	−0.607612	−	0.251681i	−0.665207	+	0.746659i	$0.731657\pi$
$458$	−3.67350			−0.171651
$459$	20.6705	−	5.63280i	0.964819	−	0.262917i
$460$	3.93799			0.183610
$461$	−23.3686	−	9.67958i	−1.08838	−	0.450823i	−0.234940	−	0.972010i	$-0.575489\pi$
$461$	−23.3686	−	9.67958i	−1.08838	−	0.450823i	−0.853443	+	0.521187i	$0.825489\pi$
$462$	10.5413	+	12.7587i	0.490427	+	0.593590i
$463$	0.372140	+	0.372140i	0.0172948	+	0.0172948i	0.715701	−	0.698406i	$-0.246107\pi$
$463$	0.372140	+	0.372140i	0.0172948	+	0.0172948i	−0.698406	+	0.715701i	$0.746107\pi$
$464$	−0.216600	+	0.0430844i	−0.0100554	+	0.00200014i
$465$	3.11003	+	10.1321i	0.144224	+	0.469866i
$466$	0.552739	−	2.77880i	0.0256051	−	0.128726i
$467$	−5.76357	−	13.9145i	−0.266706	−	0.643886i	0.732618	−	0.680640i	$-0.238298\pi$
$467$	−5.76357	−	13.9145i	−0.266706	−	0.643886i	−0.999324	+	0.0367542i	$0.988298\pi$
$468$	7.28670	−	37.9370i	0.336828	−	1.75364i
$469$	13.8701	+	2.75894i	0.640462	+	0.127396i
$470$	−19.1591	−	28.6737i	−0.883745	−	1.32262i
$471$	1.96797	−	20.6791i	0.0906792	−	0.952843i
$472$	−1.93421	+	1.93421i	−0.0890293	+	0.0890293i
$473$	−8.67701	+	12.9861i	−0.398969	+	0.597100i
$474$	10.8663	+	8.85801i	0.499106	+	0.406862i
$475$			3.46487i			0.158979i
$476$	−16.5328	+	6.11636i	−0.757780	+	0.280343i
$477$	−3.12973	+	4.75144i	−0.143301	+	0.217553i
$478$	−6.24098	+	15.0671i	−0.285456	+	0.689151i
$479$	8.39525	+	5.60953i	0.383589	+	0.256306i	0.732382	−	0.680894i	$-0.238408\pi$
$479$	8.39525	+	5.60953i	0.383589	+	0.256306i	−0.348793	+	0.937200i	$0.613408\pi$
$480$	−25.6584	+	13.8236i	−1.17114	+	0.630956i
$481$	−3.22487	−	16.2125i	−0.147042	−	0.739228i
$482$	29.3281	−	19.5964i	1.33586	−	0.892591i
$483$	1.42951	−	2.69574i	0.0650450	−	0.122661i
$484$	10.8115	−	4.47827i	0.491432	−	0.203558i
$485$	36.1464	−	14.9723i	1.64132	−	0.679858i
$486$	−2.59025	+	31.6310i	−0.117496	+	1.43481i
$487$	−3.66950	+	2.45188i	−0.166281	+	0.111105i	−0.635926	−	0.771750i	$-0.719382\pi$
$487$	−3.66950	+	2.45188i	−0.166281	+	0.111105i	0.469645	+	0.882855i	$0.344382\pi$
$488$	−0.311559	−	1.56631i	−0.0141036	−	0.0709036i
$489$	−9.54747	−	17.7214i	−0.431752	−	0.801390i
$490$	−10.6442	−	7.11225i	−0.480858	−	0.321299i
$491$	−14.6134	+	35.2798i	−0.659492	+	1.59216i	0.139096	+	0.990279i	$0.455580\pi$
$491$	−14.6134	+	35.2798i	−0.659492	+	1.59216i	−0.798589	+	0.601877i	$0.794420\pi$
$492$	−3.53830	+	11.8040i	−0.159519	+	0.532166i
$493$	−0.00946634	+	0.246650i	−0.000426342	+	0.0111086i
$494$		−	61.7926i		−	2.78018i
$495$	12.1463	−	8.23211i	0.545933	−	0.370006i
$496$	6.03761	−	9.03592i	0.271097	−	0.405725i
$497$	−1.25840	+	1.25840i	−0.0564471	+	0.0564471i
$498$	−13.2880	−	1.26458i	−0.595450	−	0.0566672i
$499$	−7.24621	−	10.8447i	−0.324385	−	0.485477i	0.633056	−	0.774106i	$-0.281800\pi$
$499$	−7.24621	−	10.8447i	−0.324385	−	0.485477i	−0.957441	+	0.288630i	$0.906800\pi$
$500$	−24.8444	−	4.94186i	−1.11108	−	0.221007i
$501$	27.7852	−	2.82903i	1.24135	−	0.126392i
$502$	17.3098	+	41.7895i	0.772573	+	1.86516i
$503$	−0.728223	+	3.66103i	−0.0324699	+	0.163237i	−0.993618	−	0.112795i	$-0.964020\pi$
$503$	−0.728223	+	3.66103i	−0.0324699	+	0.163237i	0.961148	+	0.276032i	$0.0890196\pi$
$504$	−0.0116268	−	1.76507i	−0.000517897	−	0.0786223i
$505$	−7.09726	+	1.41173i	−0.315824	+	0.0628213i
$506$	2.99604	+	2.99604i	0.133190	+	0.133190i
$507$	30.7627	−	25.4163i	1.36622	−	1.12878i
$508$	6.97351	+	2.88852i	0.309400	+	0.128158i
$509$	40.1261			1.77856			0.889279	−	0.457364i	$-0.151207\pi$
$509$	40.1261			1.77856			0.889279	+	0.457364i	$0.151207\pi$
$510$	7.74823	+	29.1901i	0.343098	+	1.29256i
$511$	−5.63453			−0.249257
$512$	29.6215	+	12.2696i	1.30910	+	0.542246i
$513$	2.83317	+	26.1175i	0.125088	+	1.15312i
$514$	25.7582	+	25.7582i	1.13615	+	1.13615i
$515$	−7.75825	+	1.54321i	−0.341870	+	0.0680021i
$516$	23.5581	−	7.23107i	1.03709	−	0.318330i
$517$	3.74596	−	18.8322i	0.164747	−	0.828239i
$518$	−4.27608	−	10.3234i	−0.187880	−	0.453583i
$519$	−3.19478	−	31.3773i	−0.140235	−	1.37731i
$520$	3.61019	+	0.718111i	0.158317	+	0.0314912i
$521$	9.04943	+	13.5434i	0.396463	+	0.593348i	0.974972	−	0.222328i	$-0.0713654\pi$
$521$	9.04943	+	13.5434i	0.396463	+	0.593348i	−0.578509	+	0.815676i	$0.696365\pi$
$522$	−0.338726	−	0.137698i	−0.0148256	−	0.00602687i
$523$	12.6275	−	12.6275i	0.552161	−	0.552161i	−0.374903	−	0.927064i	$-0.622324\pi$
$523$	12.6275	−	12.6275i	0.552161	−	0.552161i	0.927064	+	0.374903i	$0.122324\pi$
$524$	−24.4980	+	36.6639i	−1.07020	+	1.60167i
$525$	−1.49492	+	1.83385i	−0.0652437	+	0.0800358i
$526$		−	15.8301i		−	0.690227i
$527$	−8.25299	−	8.91176i	−0.359506	−	0.388202i
$528$	−14.4116	−	4.31992i	−0.627183	−	0.188000i
$529$	−8.50277	+	20.5275i	−0.369686	+	0.892501i
$530$	−6.66871	−	4.45589i	−0.289670	−	0.193551i
$531$	27.2294	−	5.60297i	1.18165	−	0.243148i
$532$	−4.21700	−	21.2003i	−0.182830	−	0.919148i
$533$	−16.5561	+	11.0624i	−0.717124	+	0.479167i
$534$	−8.85480	−	4.69556i	−0.383185	−	0.203197i
$535$	7.70029	−	3.18957i	0.332913	−	0.137897i
$536$	1.93494	−	0.801478i	0.0835766	−	0.0346186i
$537$	−29.4207	−	15.6013i	−1.26960	−	0.673247i
$538$	20.7156	−	13.8417i	0.893113	−	0.596759i
$539$	−1.39057	−	6.99088i	−0.0598962	−	0.301119i
$540$	−23.0614	−	2.04150i	−0.992405	−	0.0878521i
$541$	23.5252	+	15.7191i	1.01143	+	0.675815i	0.946710	−	0.322089i	$-0.104385\pi$
$541$	23.5252	+	15.7191i	1.01143	+	0.675815i	0.0647190	+	0.997904i	$0.479385\pi$
$542$	1.04994	−	2.53477i	0.0450986	−	0.108878i
$543$	5.81049	+	1.74172i	0.249352	+	0.0747442i
$544$	19.6080	−	27.0397i	0.840684	−	1.15932i
$545$			30.8484i			1.32140i
$546$	26.6605	−	32.7049i	1.14096	−	1.39964i
$547$	−17.7662	+	26.5890i	−0.759629	+	1.13687i	0.227001	+	0.973894i	$0.427108\pi$
$547$	−17.7662	+	26.5890i	−0.759629	+	1.13687i	−0.986631	+	0.162971i	$0.947892\pi$
$548$	20.3313	−	20.3313i	0.868510	−	0.868510i
$549$	−6.11218	+	15.0355i	−0.260861	+	0.641698i
$550$	−1.82525	−	2.73168i	−0.0778290	−	0.116479i
$551$	−0.296852	−	0.0590476i	−0.0126463	−	0.00251551i
$552$	−0.0457739	−	0.449566i	−0.00194827	−	0.0191348i
$553$	3.03246	+	7.32101i	0.128953	+	0.311321i
$554$	6.69342	−	33.6501i	0.284376	−	1.42966i
$555$	−9.47057	+	2.90696i	−0.402003	+	0.123394i
$556$	−0.213246	+	0.0424173i	−0.00904365	+	0.00179889i
$557$	−4.85771	−	4.85771i	−0.205828	−	0.205828i	0.596664	−	0.802491i	$-0.296493\pi$
$557$	−4.85771	−	4.85771i	−0.205828	−	0.205828i	−0.802491	+	0.596664i	$0.796493\pi$
$558$	16.5775	−	6.99492i	0.701783	−	0.296119i
$559$	36.7879	+	15.2380i	1.55596	+	0.644500i
$560$	−15.2734			−0.645417
$561$	−8.44186	+	14.5430i	−0.356416	+	0.614004i
$562$	−9.13772			−0.385452
$563$	−10.7792	−	4.46490i	−0.454290	−	0.188173i	0.143792	−	0.989608i	$-0.454070\pi$
$563$	−10.7792	−	4.46490i	−0.454290	−	0.188173i	−0.598082	+	0.801435i	$0.704070\pi$
$564$	−23.3558	+	19.2967i	−0.983456	+	0.812537i
$565$	9.77538	+	9.77538i	0.411253	+	0.411253i
$566$	−11.0166	+	2.19135i	−0.463064	+	0.0921092i
$567$	−9.76892	+	15.0456i	−0.410256	+	0.631856i
$568$	−0.0514182	+	0.258497i	−0.00215746	+	0.0108463i
$569$	16.5175	+	39.8769i	0.692452	+	1.67173i	0.739782	+	0.672847i	$0.234929\pi$
$569$	16.5175	+	39.8769i	0.692452	+	1.67173i	−0.0473304	+	0.998879i	$0.515071\pi$
$570$	−36.8424	+	3.75121i	−1.54316	+	0.157121i
$571$	−9.09986	−	1.81007i	−0.380817	−	0.0757493i	0.000969942	−	1.00000i	$-0.499691\pi$
$571$	−9.09986	−	1.81007i	−0.380817	−	0.0757493i	−0.381787	+	0.924250i	$0.624691\pi$
$572$	16.8451	+	25.2105i	0.704329	+	1.05410i
$573$	14.8400	+	1.41228i	0.619950	+	0.0589988i
$574$	−9.51757	+	9.51757i	−0.397256	+	0.397256i
$575$	−0.336520	+	0.503637i	−0.0140338	+	0.0210031i
$576$	15.3412	+	22.6355i	0.639217	+	0.943147i
$577$		−	16.0098i		−	0.666496i	−0.942839	−	0.333248i	$-0.891855\pi$
$577$		−	16.0098i		−	0.666496i	0.942839	−	0.333248i	$-0.108145\pi$
$578$	−22.5257	−	26.2773i	−0.936945	−	1.09299i
$579$	5.35236	−	17.8559i	0.222437	−	0.742065i
$580$	0.102074	−	0.246428i	0.00423839	−	0.0102324i
$581$	−6.27326	−	4.19166i	−0.260259	−	0.173899i
$582$	−31.5028	−	58.4736i	−1.30583	−	2.42381i
$583$	−0.871206	−	4.37985i	−0.0360817	−	0.181395i
$584$	−0.693826	+	0.463600i	−0.0287107	+	0.0191839i
$585$	−26.6260	−	26.2775i	−1.10085	−	1.08644i
$586$	−45.6302	+	18.9006i	−1.88497	+	0.780778i
$587$	26.6989	−	11.0590i	1.10198	−	0.456455i	0.243812	−	0.969823i	$-0.421602\pi$
$587$	26.6989	−	11.0590i	1.10198	−	0.456455i	0.858169	+	0.513367i	$0.171602\pi$
$588$	−5.26888	+	9.93595i	−0.217285	+	0.409752i
$589$	12.3838	−	8.27460i	0.510266	−	0.340949i
$590$	7.64527	+	38.4354i	0.314751	+	1.58236i
$591$	−38.7239	+	20.8626i	−1.59289	+	0.858173i
$592$	8.44594	+	5.64340i	0.347126	+	0.231942i
$593$	15.8785	−	38.3341i	0.652052	−	1.57419i	−0.157744	−	0.987480i	$-0.550422\pi$
$593$	15.8785	−	38.3341i	0.652052	−	1.57419i	0.809795	−	0.586712i	$-0.199578\pi$
$594$	−15.9921	−	19.0984i	−0.656162	−	0.783618i
$595$	−3.96997	+	16.6026i	−0.162753	+	0.680641i
$596$			29.8116i			1.22113i
$597$	−32.4725	−	26.4710i	−1.32901	−	1.08339i
$598$	6.00150	−	8.98188i	0.245419	−	0.367296i
$599$	−21.9297	+	21.9297i	−0.896025	+	0.896025i	−0.995082	−	0.0990569i	$-0.968417\pi$
$599$	−21.9297	+	21.9297i	−0.896025	+	0.896025i	0.0990569	+	0.995082i	$0.468417\pi$
$600$	−0.0331958	+	0.348816i	−0.00135521	+	0.0142404i
$601$	−3.23917	−	4.84775i	−0.132128	−	0.197744i	0.759506	−	0.650500i	$-0.225441\pi$
$601$	−3.23917	−	4.84775i	−0.132128	−	0.197744i	−0.891634	+	0.452756i	$0.850441\pi$
$602$	26.3993	+	5.25115i	1.07596	+	0.214021i
$603$	−20.9030	−	4.01491i	−0.851236	−	0.163500i
$604$	4.11461	+	9.93354i	0.167421	+	0.404190i
$605$	2.21083	−	11.1146i	0.0898830	−	0.451873i
$606$	3.60476	+	11.7439i	0.146434	+	0.477065i
$607$	32.9476	−	6.55369i	1.33730	−	0.266006i	0.525927	−	0.850530i	$-0.323719\pi$
$607$	32.9476	−	6.55369i	1.33730	−	0.266006i	0.811377	+	0.584524i	$0.198719\pi$
$608$	28.9607	+	28.9607i	1.17451	+	1.17451i
$609$	−0.131639	−	0.159329i	−0.00533427	−	0.00645635i
$610$	−21.1377	−	8.75552i	−0.855841	−	0.354501i
$611$	−48.9537			−1.98045
$612$	24.8226	−	9.36953i	1.00339	−	0.378741i
$613$	38.7828			1.56642			0.783210	−	0.621757i	$-0.213581\pi$
$613$	38.7828			1.56642			0.783210	+	0.621757i	$0.213581\pi$
$614$	40.5749	+	16.8067i	1.63747	+	0.678262i
$615$	7.60078	+	9.19962i	0.306493	+	0.370964i
$616$	0.979626	+	0.979626i	0.0394702	+	0.0394702i
$617$	33.4612	−	6.65584i	1.34710	−	0.267954i	0.531737	−	0.846910i	$-0.321540\pi$
$617$	33.4612	−	6.65584i	1.34710	−	0.267954i	0.815359	+	0.578956i	$0.196540\pi$
$618$	3.94049	+	12.8377i	0.158510	+	0.516407i
$619$	−2.31092	+	11.6178i	−0.0928839	+	0.466959i	0.906148	+	0.422961i	$0.139009\pi$
$619$	−2.31092	+	11.6178i	−0.0928839	+	0.466959i	−0.999032	+	0.0439976i	$0.985991\pi$
$620$	5.02292	+	12.1264i	0.201725	+	0.487008i
$621$	−2.12480	+	4.07149i	−0.0852655	+	0.163383i
$622$	−57.8452	−	11.5061i	−2.31938	−	0.461354i
$623$	−3.14743	−	4.71046i	−0.126099	−	0.188721i
$624$	−3.63397	+	38.1852i	−0.145475	+	1.52863i
$625$	−14.9226	+	14.9226i	−0.596903	+	0.596903i
$626$	12.5962	−	18.8515i	0.503444	−	0.753457i
$627$	−15.9820	−	13.0283i	−0.638261	−	0.520299i
$628$		−	25.7249i		−	1.02654i
$629$	8.32988	−	7.71412i	0.332134	−	0.307582i
$630$	−21.1180	−	13.9103i	−0.841362	−	0.554198i
$631$	−12.5910	+	30.3974i	−0.501240	+	1.21010i	0.447568	+	0.894250i	$0.352290\pi$
$631$	−12.5910	+	30.3974i	−0.501240	+	1.21010i	−0.948809	+	0.315851i	$0.897710\pi$
$632$	0.975771	+	0.651990i	0.0388141	+	0.0259348i
$633$	16.7712	−	9.03552i	0.666594	−	0.359130i
$634$	−4.34256	−	21.8315i	−0.172465	−	0.867040i
$635$	6.07759	−	4.06092i	0.241182	−	0.161153i
$636$	−3.30100	+	6.22496i	−0.130893	+	0.246836i
$637$	−16.7893	+	6.95434i	−0.665215	+	0.275541i
$638$	0.265142	−	0.109825i	0.0104971	−	0.00434803i
$639$	1.88152	−	1.90648i	0.0744319	−	0.0754190i
$640$	−4.06785	+	2.71805i	−0.160796	+	0.107441i
$641$	−4.61604	−	23.2064i	−0.182322	−	0.916597i	−0.958284	−	0.285817i	$-0.907735\pi$
$641$	−4.61604	−	23.2064i	−0.182322	−	0.916597i	0.775962	−	0.630780i	$-0.217265\pi$
$642$	−6.71108	−	12.4567i	−0.264865	−	0.491626i
$643$	−37.0269	−	24.7406i	−1.46020	−	0.975672i	−0.995945	−	0.0899696i	$-0.971323\pi$
$643$	−37.0269	−	24.7406i	−1.46020	−	0.975672i	−0.464253	−	0.885703i	$-0.653677\pi$
$644$	1.44608	−	3.49114i	0.0569834	−	0.137570i
$645$	6.85205	−	22.8589i	0.269799	−	0.900070i
$646$	36.1660	−	22.2078i	1.42293	−	0.873754i
$647$			35.4575i			1.39398i	0.717081	+	0.696990i	$0.245478\pi$
$647$			35.4575i			1.39398i	−0.717081	+	0.696990i	$0.754522\pi$
$648$	0.0349984	+	2.65646i	0.00137487	+	0.104355i
$649$	−12.1223	+	18.1424i	−0.475843	+	0.712150i
$650$	−5.92280	+	5.92280i	−0.232311	+	0.232311i
$651$	10.1245	+	0.963515i	0.396809	+	0.0377631i
$652$	−13.8497	−	20.7275i	−0.542395	−	0.811752i
$653$	−19.1428	−	3.80775i	−0.749117	−	0.149009i	−0.194255	−	0.980951i	$-0.562229\pi$
$653$	−19.1428	−	3.80775i	−0.749117	−	0.149009i	−0.554862	+	0.831943i	$0.687229\pi$
$654$	52.1004	−	5.30476i	2.03729	−	0.207432i
$655$	16.3411	+	39.4508i	0.638498	+	1.54147i
$656$	2.38711	−	12.0008i	0.0932009	−	0.468552i
$657$	8.48044	−	0.0558619i	0.330853	−	0.00217938i
$658$	−32.4555	+	6.45581i	−1.26525	+	0.251673i
$659$	9.54185	+	9.54185i	0.371698	+	0.371698i	0.868095	−	0.496398i	$-0.165344\pi$
$659$	9.54185	+	9.54185i	0.371698	+	0.371698i	−0.496398	+	0.868095i	$0.665344\pi$
$660$	14.0085	−	11.5739i	0.545282	−	0.450515i
$661$	3.15244	+	1.30578i	0.122616	+	0.0507890i	0.443148	−	0.896449i	$-0.353862\pi$
$661$	3.15244	+	1.30578i	0.122616	+	0.0507890i	−0.320532	+	0.947238i	$0.603862\pi$
$662$	−24.1489			−0.938575
$663$	40.5639	+	13.8757i	1.57537	+	0.538886i
$664$	−1.11736			−0.0433620
$665$	−19.3389	−	8.01043i	−0.749930	−	0.310631i
$666$	6.53820	+	15.4951i	0.253350	+	0.600424i
$667$	−0.0374142	−	0.0374142i	−0.00144868	−	0.00144868i
$668$	33.9228	−	6.74765i	1.31251	−	0.261075i
$669$	16.6594	−	5.11356i	0.644091	−	0.197702i
$670$	5.85363	−	29.4282i	0.226146	−	1.13691i
$671$	−4.87497	−	11.7692i	−0.188196	−	0.454346i
$672$	2.83289	+	27.8231i	0.109281	+	1.07330i
$673$	10.7113	+	2.13061i	0.412890	+	0.0821289i	0.397165	−	0.917747i	$-0.369994\pi$
$673$	10.7113	+	2.13061i	0.412890	+	0.0821289i	0.0157255	+	0.999876i	$0.494994\pi$
$674$	−26.3156	−	39.3841i	−1.01364	−	1.51702i
$675$	2.23180	−	2.77492i	0.0859019	−	0.106807i
$676$	34.9435	−	34.9435i	1.34398	−	1.34398i
$677$	−8.78236	+	13.1437i	−0.337533	+	0.505154i	−0.960945	−	0.276739i	$-0.910746\pi$
$677$	−8.78236	+	13.1437i	−0.337533	+	0.505154i	0.623412	+	0.781894i	$0.285746\pi$
$678$	14.8288	−	18.1908i	0.569498	−	0.698614i
$679$		−	37.5428i		−	1.44076i
$680$	0.877178	+	2.37106i	0.0336383	+	0.0909258i
$681$	3.01305	+	0.903171i	0.115460	+	0.0346096i
$682$	−5.40437	+	13.0473i	−0.206944	+	0.499607i
$683$	23.8160	+	15.9134i	0.911295	+	0.608908i	0.920369	−	0.391051i	$-0.127888\pi$
$683$	23.8160	+	15.9134i	0.911295	+	0.608908i	−0.00907414	+	0.999959i	$0.502888\pi$
$684$	6.55711	+	31.8663i	0.250717	+	1.21844i
$685$	−5.43206	−	27.3088i	−0.207549	−	1.04342i
$686$	−33.8327	+	22.6063i	−1.29174	+	0.863112i
$687$	2.76103	+	1.46413i	0.105340	+	0.0558600i
$688$	−22.6063	+	9.36383i	−0.861857	+	0.356993i
$689$	−10.5186	+	4.35695i	−0.400727	+	0.165987i
$690$	−5.71956	−	3.03299i	−0.217740	−	0.115464i
$691$	−19.3217	+	12.9103i	−0.735032	+	0.491133i	−0.865869	−	0.500271i	$-0.833234\pi$
$691$	−19.3217	+	12.9103i	−0.735032	+	0.491133i	0.130837	+	0.991404i	$0.458234\pi$
$692$	−7.62001	−	38.3084i	−0.289669	−	1.45627i
$693$	−2.83775	−	13.7909i	−0.107797	−	0.523874i
$694$	49.4462	+	33.0389i	1.87695	+	1.25414i
$695$	−0.0805742	+	0.194523i	−0.00305635	+	0.00737869i
$696$	−0.0293191	−	0.00878851i	−0.00111134	−	0.000333127i
$697$	−12.4248	−	5.71421i	−0.470622	−	0.216441i
$698$			22.1369i			0.837895i
$699$	−1.52297	+	1.86826i	−0.0576042	+	0.0706642i
$700$	−1.62784	+	2.43624i	−0.0615266	+	0.0920811i
$701$	−13.2794	+	13.2794i	−0.501558	+	0.501558i	−0.911922	−	0.410364i	$-0.865402\pi$
$701$	−13.2794	+	13.2794i	−0.501558	+	0.501558i	0.410364	+	0.911922i	$0.365402\pi$
$702$	−39.8019	+	49.4879i	−1.50223	+	1.86780i
$703$	7.73433	+	11.5752i	0.291706	+	0.436568i
$704$	−21.0498	−	4.18706i	−0.793344	−	0.157806i
$705$	2.97181	+	29.1875i	0.111925	+	1.09926i
$706$	19.8211	+	47.8524i	0.745977	+	1.80095i
$707$	−1.35466	+	6.81034i	−0.0509472	+	0.256129i
$708$	32.9121	−	10.1023i	1.23691	−	0.379666i
$709$	−19.7635	+	3.93121i	−0.742235	+	0.147640i	−0.551702	−	0.834041i	$-0.686022\pi$
$709$	−19.7635	+	3.93121i	−0.742235	+	0.147640i	−0.190533	+	0.981681i	$0.561022\pi$
$710$	2.66995	+	2.66995i	0.100202	+	0.100202i
$711$	−4.63669	−	10.9887i	−0.173889	−	0.412107i
$712$	−0.775137	−	0.321072i	−0.0290495	−	0.0120327i
$713$	2.60371			0.0975097
$714$	28.7231	+	3.84994i	1.07494	+	0.144080i
$715$	29.3619			1.09807
$716$	−38.1014	−	15.7821i	−1.42392	−	0.589806i
$717$	10.6960	−	8.83706i	0.399448	−	0.330026i
$718$	−20.7553	−	20.7553i	−0.774582	−	0.774582i
$719$	25.0780	−	4.98832i	0.935252	−	0.186033i	0.296138	−	0.955145i	$-0.404301\pi$
$719$	25.0780	−	4.98832i	0.935252	−	0.186033i	0.639114	+	0.769112i	$0.279301\pi$
$720$	22.9876	−	0.151423i	0.856699	−	0.00564320i
$721$	−1.48082	+	7.44460i	−0.0551488	+	0.277252i
$722$	5.11193	+	12.3413i	0.190246	+	0.459295i
$723$	−29.8536	+	3.03963i	−1.11027	+	0.113045i
$724$	7.36776	+	1.46554i	0.273821	+	0.0544663i
$725$	0.0227935	+	0.0341129i	0.000846530	+	0.00126692i
$726$	−19.1518	−	1.82262i	−0.710791	−	0.0676438i
$727$	−17.6366	+	17.6366i	−0.654107	+	0.654107i	−0.953979	−	0.299872i	$-0.903056\pi$
$727$	−17.6366	+	17.6366i	−0.654107	+	0.654107i	0.299872	+	0.953979i	$0.403056\pi$
$728$	1.96233	−	2.93684i	0.0727288	−	0.108846i
$729$	14.5539	−	22.7417i	0.539032	−	0.842285i
$730$			11.9548i			0.442467i
$731$	4.30276	+	27.0077i	0.159143	+	0.998914i
$732$	−5.77129	+	19.2535i	−0.213313	+	0.711628i
$733$	18.5044	−	44.6736i	0.683476	−	1.65006i	−0.0740508	−	0.997254i	$-0.523593\pi$
$733$	18.5044	−	44.6736i	0.683476	−	1.65006i	0.757527	−	0.652804i	$-0.226407\pi$
$734$	−58.9153	−	39.3659i	−2.17460	−	1.45302i
$735$	5.16558	+	9.58803i	0.190535	+	0.353660i
$736$	1.39683	+	7.02235i	0.0514879	+	0.258847i
$737$	13.8908	−	9.28151i	0.511673	−	0.341889i
$738$	14.2304	−	14.4191i	0.523827	−	0.530774i
$739$	18.8828	−	7.82153i	0.694617	−	0.287720i	−0.00730558	−	0.999973i	$-0.502325\pi$
$739$	18.8828	−	7.82153i	0.694617	−	0.287720i	0.701922	+	0.712254i	$0.252325\pi$
$740$	−11.3346	+	4.69496i	−0.416669	+	0.172590i
$741$	−24.6283	+	46.4437i	−0.904744	+	1.70615i
$742$	−6.39910	+	4.27574i	−0.234918	+	0.156968i
$743$	−9.42343	−	47.3748i	−0.345712	−	1.73801i	−0.627573	−	0.778558i	$-0.715952\pi$
$743$	−9.42343	−	47.3748i	−0.345712	−	1.73801i	0.281861	−	0.959455i	$-0.409048\pi$
$744$	1.32598	−	0.714378i	0.0486129	−	0.0261904i
$745$	24.0038	+	16.0389i	0.879433	+	0.587618i
$746$	21.9336	−	52.9523i	0.803045	−	1.93872i
$747$	9.48333	+	6.24660i	0.346977	+	0.228551i
$748$	−8.70120	+	18.9196i	−0.318147	+	0.691768i
$749$		−	7.99778i		−	0.292233i
$750$	32.2780	+	26.3125i	1.17863	+	0.960795i
$751$	6.36250	−	9.52215i	0.232171	−	0.347468i	−0.697031	−	0.717041i	$-0.745496\pi$
$751$	6.36250	−	9.52215i	0.232171	−	0.347468i	0.929202	+	0.369573i	$0.120496\pi$
$752$	21.2713	−	21.2713i	0.775686	−	0.775686i
$753$	3.64568	−	38.3083i	0.132856	−	1.39603i
$754$	−0.406500	−	0.608370i	−0.0148039	−	0.0221555i
$755$	10.2120	+	2.03130i	0.371653	+	0.0739264i
$756$	−10.2783	+	19.6950i	−0.373818	+	0.716299i
$757$	−13.3441	−	32.2155i	−0.484999	−	1.17089i	−0.957207	−	0.289405i	$-0.906543\pi$
$757$	−13.3441	−	32.2155i	−0.484999	−	1.17089i	0.472207	−	0.881488i	$-0.343457\pi$
$758$	−5.59343	+	28.1201i	−0.203163	+	1.02137i
$759$	−1.05773	−	3.44596i	−0.0383930	−	0.125080i
$760$	−3.04044	+	0.604781i	−0.110288	+	0.0219377i
$761$	18.9898	+	18.9898i	0.688381	+	0.688381i	0.961874	−	0.273493i	$-0.0881789\pi$
$761$	18.9898	+	18.9898i	0.688381	+	0.688381i	−0.273493	+	0.961874i	$0.588179\pi$
$762$	−7.90368	−	9.56624i	−0.286320	−	0.346548i
$763$	27.3480	+	11.3279i	0.990063	+	0.410098i
$764$	18.4611			0.667898
$765$	5.81053	−	25.0276i	0.210080	−	0.904876i
$766$	33.1672			1.19838
$767$	51.3950	+	21.2885i	1.85576	+	0.768683i
$768$	−14.8209	−	17.9386i	−0.534805	−	0.647303i
$769$	−3.12150	−	3.12150i	−0.112564	−	0.112564i	0.648581	−	0.761145i	$-0.275363\pi$
$769$	−3.12150	−	3.12150i	−0.112564	−	0.112564i	−0.761145	+	0.648581i	$0.775363\pi$
$770$	19.4665	−	3.87212i	0.701523	−	0.139542i
$771$	−9.09372	−	29.6264i	−0.327502	−	1.06697i
$772$	4.50366	−	22.6414i	0.162090	−	0.814882i
$773$	−10.5772	−	25.5356i	−0.380436	−	0.918453i	−0.991881	−	0.127167i	$-0.959412\pi$
$773$	−10.5772	−	25.5356i	−0.380436	−	0.918453i	0.611446	−	0.791286i	$-0.290588\pi$
$774$	−39.7852	−	7.64168i	−1.43005	−	0.274675i
$775$	−1.98010	−	0.393867i	−0.0711274	−	0.0141481i
$776$	−3.08896	−	4.62295i	−0.110887	−	0.165954i
$777$	−0.900604	+	9.46341i	−0.0323090	+	0.339498i
$778$	−4.66692	+	4.66692i	−0.167317	+	0.167317i
$779$	9.31659	−	13.9433i	0.333802	−	0.499569i
$780$	−35.9086	−	29.2721i	−1.28574	−	1.04811i
$781$			2.10237i			0.0752287i
$782$	7.41381	+	0.284540i	0.265117	+	0.0101751i
$783$	0.199707	+	0.238499i	0.00713694	+	0.00852325i
$784$	4.27347	−	10.3171i	0.152624	−	0.368467i
$785$	−20.7133	−	13.8402i	−0.739289	−	0.493977i
$786$	63.8192	−	34.3828i	2.27636	−	1.22639i
$787$	6.32596	+	31.8028i	0.225496	+	1.13365i	0.913155	+	0.407612i	$0.133638\pi$
$787$	6.32596	+	31.8028i	0.225496	+	1.13365i	−0.687659	+	0.726034i	$0.741362\pi$
$788$	−45.2926	+	30.2635i	−1.61348	+	1.07809i
$789$	−6.30933	+	11.8980i	−0.224618	+	0.423581i
$790$	15.5330	−	6.43398i	0.552639	−	0.228911i
$791$	12.2558	−	5.07652i	0.435766	−	0.180500i
$792$	−1.48413	−	1.46470i	−0.0527362	−	0.0520460i
$793$	−27.0045	+	18.0439i	−0.958960	+	0.640756i
$794$	7.06280	+	35.5071i	0.250649	+	1.26010i
$795$	3.23628	+	6.00698i	0.114779	+	0.213046i
$796$	−43.1391	−	28.8246i	−1.52903	−	1.02166i
$797$	−12.9695	+	31.3112i	−0.459404	+	1.10910i	0.509235	+	0.860627i	$0.329928\pi$
$797$	−12.9695	+	31.3112i	−0.459404	+	1.10910i	−0.968639	+	0.248472i	$0.920072\pi$
$798$	−10.2034	+	34.0393i	−0.361197	+	1.20498i
$799$	−17.5936	−	28.6516i	−0.622416	−	1.01362i
$800$		−	5.55174i		−	0.196284i
$801$	4.78384	+	7.05842i	0.169029	+	0.249397i
$802$	−16.6228	+	24.8778i	−0.586973	+	0.878467i
$803$	−4.70671	+	4.70671i	−0.166096	+	0.166096i
$804$	−26.2411	−	2.49729i	−0.925452	−	0.0880725i
$805$	−2.03301	−	3.04262i	−0.0716542	−	0.107238i
$806$	35.3132	+	7.02423i	1.24385	+	0.247418i
$807$	−21.0868	+	2.14702i	−0.742291	+	0.0755785i
$808$	0.393532	+	0.950071i	0.0138444	+	0.0334234i
$809$	−3.43987	+	17.2934i	−0.120939	+	0.608004i	0.872012	+	0.489484i	$0.162815\pi$
$809$	−3.43987	+	17.2934i	−0.120939	+	0.608004i	−0.992952	+	0.118520i	$0.962185\pi$
$810$	31.9222	+	20.7267i	1.12163	+	0.728263i
$811$	−2.34514	+	0.466478i	−0.0823490	+	0.0163802i	−0.236093	−	0.971730i	$-0.575867\pi$
$811$	−2.34514	+	0.466478i	−0.0823490	+	0.0163802i	0.153744	+	0.988111i	$0.450867\pi$
$812$	−0.180983	−	0.180983i	−0.00635126	−	0.00635126i
$813$	−1.79941	+	1.48668i	−0.0631080	+	0.0521402i
$814$	−12.1954	−	5.05150i	−0.427448	−	0.177055i
$815$	−24.1407			−0.845612
$816$	−23.6551	+	11.5966i	−0.828094	+	0.405962i
$817$	−33.5348			−1.17323
$818$	7.49247	+	3.10348i	0.261968	+	0.108511i
$819$	−33.0732	+	13.9553i	−1.15567	+	0.487638i
$820$	10.4499	+	10.4499i	0.364926	+	0.364926i
$821$	−45.7670	+	9.10361i	−1.59728	+	0.317718i	−0.911882	−	0.410453i	$-0.865371\pi$
$821$	−45.7670	+	9.10361i	−1.59728	+	0.317718i	−0.685396	+	0.728171i	$0.740371\pi$
$822$	−45.1883	+	13.8704i	−1.57612	+	0.483786i
$823$	−9.41661	+	47.3405i	−0.328242	+	1.65019i	0.366125	+	0.930566i	$0.380684\pi$
$823$	−9.41661	+	47.3405i	−0.328242	+	1.65019i	−0.694368	+	0.719620i	$0.744316\pi$
$824$	0.430183	+	1.03855i	0.0149861	+	0.0361797i
$825$	0.283118	+	2.78063i	0.00985690	+	0.0968091i
$826$	36.8815	+	7.33619i	1.28327	+	0.255259i
$827$	−17.9442	−	26.8554i	−0.623982	−	0.933855i	−0.999974	−	0.00723238i	$-0.997698\pi$
$827$	−17.9442	−	26.8554i	−0.623982	−	0.933855i	0.375992	−	0.926623i	$-0.377302\pi$
$828$	−2.14185	+	5.26879i	−0.0744346	+	0.183103i
$829$	−2.76317	+	2.76317i	−0.0959688	+	0.0959688i	−0.753461	−	0.657492i	$-0.771617\pi$
$829$	−2.76317	+	2.76317i	−0.0959688	+	0.0959688i	0.657492	+	0.753461i	$0.271617\pi$
$830$	−8.89345	+	13.3100i	−0.308696	+	0.461996i
$831$	−18.4426	+	22.6239i	−0.639765	+	0.784813i
$832$			54.7182i			1.89701i
$833$	−10.1042	−	7.32709i	−0.350089	−	0.253869i
$834$	0.342390	+	0.102633i	0.0118560	+	0.00355387i
$835$	12.8176	−	30.9444i	0.443570	−	1.07087i
$836$	−21.2319	−	14.1867i	−0.734319	−	0.490656i
$837$	−15.2477	−	1.34979i	−0.527038	−	0.0466557i
$838$	3.92054	+	19.7099i	0.135433	+	0.680867i
$839$	−15.4135	+	10.2990i	−0.532134	+	0.355561i	−0.792425	−	0.609970i	$-0.791182\pi$
$839$	−15.4135	+	10.2990i	−0.532134	+	0.355561i	0.260291	+	0.965530i	$0.416182\pi$
$840$	−1.87015	−	0.991708i	−0.0645262	−	0.0342172i
$841$	26.7892	−	11.0964i	0.923765	−	0.382636i
$842$	−4.43018	+	1.83504i	−0.152674	+	0.0632396i
$843$	6.86797	+	3.64197i	0.236545	+	0.125436i
$844$	19.6161	−	13.1070i	0.675213	−	0.451163i
$845$	−9.33610	−	46.9357i	−0.321172	−	1.61464i
$846$	48.7842	−	10.0383i	1.67724	−	0.345123i
$847$	−9.04157	−	6.04138i	−0.310672	−	0.207584i
$848$	2.67737	−	6.46373i	0.0919411	−	0.221965i
$849$	9.15357	+	2.74382i	0.314150	+	0.0941675i
$850$	−5.59511	−	1.33789i	−0.191911	−	0.0458892i
$851$			2.43371i			0.0834264i
$852$	2.09594	−	2.57113i	0.0718057	−	0.0880855i
$853$	20.6014	−	30.8322i	0.705378	−	1.05567i	−0.289752	−	0.957102i	$-0.593573\pi$
$853$	20.6014	−	30.8322i	0.705378	−	1.05567i	0.995130	−	0.0985712i	$-0.0314272\pi$
$854$	−15.5241	+	15.5241i	−0.531222	+	0.531222i
$855$	29.1860	+	11.8646i	0.998142	+	0.405762i
$856$	−0.658043	−	0.984832i	−0.0224915	−	0.0336609i
$857$	−48.2422	−	9.59597i	−1.64792	−	0.327792i	−0.718139	−	0.695900i	$-0.755006\pi$
$857$	−48.2422	−	9.59597i	−1.64792	−	0.327792i	−0.929783	+	0.368108i	$0.880006\pi$
$858$	−5.04913	−	49.5898i	−0.172375	−	1.69297i
$859$	−10.7823	−	26.0307i	−0.367887	−	0.888157i	−0.994096	−	0.108502i	$-0.965395\pi$
$859$	−10.7823	−	26.0307i	−0.367887	−	0.888157i	0.626209	−	0.779655i	$-0.284605\pi$
$860$	5.76554	−	28.9853i	0.196603	−	0.988392i
$861$	10.9468	−	3.36009i	0.373067	−	0.114512i
$862$	41.0919	−	8.17368i	1.39959	−	0.278397i
$863$	5.07346	+	5.07346i	0.172702	+	0.172702i	0.788166	−	0.615463i	$-0.211031\pi$
$863$	5.07346	+	5.07346i	0.172702	+	0.172702i	−0.615463	+	0.788166i	$0.711031\pi$
$864$	−4.53958	−	41.8480i	−0.154440	−	1.42370i
$865$	−34.9449	−	14.4747i	−1.18816	−	0.492153i
$866$	19.6194			0.666694
$867$	6.45724	+	28.7281i	0.219299	+	0.975658i
$868$	12.5949			0.427498
$869$	8.64858	+	3.58236i	0.293383	+	0.121523i
$870$	−0.338049	+	0.279298i	−0.0114609	+	0.00946909i
$871$	−30.1178	−	30.1178i	−1.02050	−	1.02050i
$872$	4.29962	−	0.855247i	0.145603	−	0.0289623i
$873$	0.372207	+	56.5050i	0.0125973	+	1.91240i
$874$	−1.77486	+	8.92281i	−0.0600354	+	0.301818i
$875$	9.00784	+	21.7469i	0.304521	+	0.735178i
$876$	10.4485	−	1.06384i	0.353021	−	0.0359439i
$877$	23.3238	+	4.63939i	0.787588	+	0.156661i	0.572469	−	0.819927i	$-0.305986\pi$
$877$	23.3238	+	4.63939i	0.787588	+	0.156661i	0.215120	+	0.976588i	$0.430986\pi$
$878$	44.0465	+	65.9203i	1.48650	+	2.22470i
$879$	41.8290	+	3.98074i	1.41086	+	0.134267i
$880$	−12.7583	+	12.7583i	−0.430083	+	0.430083i
$881$	10.9801	−	16.4329i	0.369930	−	0.553639i	−0.599071	−	0.800696i	$-0.704463\pi$
$881$	10.9801	−	16.4329i	0.369930	−	0.553639i	0.969001	+	0.247056i	$0.0794633\pi$
$882$	15.3051	−	10.3730i	0.515350	−	0.349278i
$883$		−	1.29910i		−	0.0437182i	−0.999761	−	0.0218591i	$-0.993041\pi$
$883$		−	1.29910i		−	0.0437182i	0.999761	−	0.0218591i	$-0.00695852\pi$
$884$	51.6368	+	12.3473i	1.73673	+	0.415284i
$885$	9.57275	−	31.9354i	0.321785	−	1.07350i
$886$	−10.2221	+	24.6784i	−0.343419	+	0.829087i
$887$	−3.55045	−	2.37234i	−0.119213	−	0.0796553i	0.494535	−	0.869158i	$-0.335339\pi$
$887$	−3.55045	−	2.37234i	−0.119213	−	0.0796553i	−0.613747	+	0.789503i	$0.710339\pi$
$888$	0.667734	+	1.23941i	0.0224077	+	0.0415917i
$889$	−1.36835	−	6.87918i	−0.0458931	−	0.230720i
$890$	−9.99419	+	6.67790i	−0.335006	+	0.223844i
$891$	4.40777	+	20.7284i	0.147666	+	0.694426i
$892$	19.9385	−	8.25878i	0.667589	−	0.276525i
$893$	38.0897	−	15.7773i	1.27462	−	0.527966i
$894$	22.9606	−	43.2986i	0.767916	−	1.44812i
$895$	−33.2064	+	22.1878i	−1.10997	+	0.741656i
$896$	0.915867	+	4.60437i	0.0305970	+	0.153821i
$897$	−8.09062	+	4.35885i	−0.270138	+	0.145538i
$898$	−35.8696	−	23.9673i	−1.19698	−	0.799799i
$899$	0.0674890	−	0.162933i	0.00225089	−	0.00543412i
$900$	2.42588	−	3.68287i	0.0808627	−	0.122762i
$901$	−6.33035	−	4.59049i	−0.210895	−	0.152931i
$902$			15.9007i			0.529434i
$903$	−17.7490	−	14.4686i	−0.590648	−	0.481486i
$904$	1.09147	−	1.63350i	0.0363017	−	0.0543293i
$905$	5.14393	−	5.14393i	0.170990	−	0.170990i
$906$	1.67461	−	17.5966i	0.0556353	−	0.584607i
$907$	30.0777	+	45.0145i	0.998715	+	1.49468i	0.863806	+	0.503825i	$0.168074\pi$
$907$	30.0777	+	45.0145i	0.998715	+	1.49468i	0.134910	+	0.990858i	$0.456926\pi$
$908$	3.82057	+	0.759958i	0.126790	+	0.0252201i
$909$	1.97136	−	10.2635i	0.0653857	−	0.340420i
$910$	−19.3647	−	46.7505i	−0.641934	−	1.54977i
$911$	10.7023	−	53.8041i	0.354583	−	1.78261i	−0.231994	−	0.972717i	$-0.574525\pi$
$911$	10.7023	−	53.8041i	0.354583	−	1.78261i	0.586577	−	0.809893i	$-0.300475\pi$
$912$	−9.47920	−	30.8822i	−0.313888	−	1.02261i
$913$	−8.74168	+	1.73883i	−0.289307	+	0.0575468i
$914$	20.2402	+	20.2402i	0.669488	+	0.669488i
$915$	12.3976	+	15.0054i	0.409851	+	0.496065i
$916$	3.57568	+	1.48110i	0.118144	+	0.0489368i
$917$	40.9750			1.35311
$918$	−43.2688	−	5.50971i	−1.42808	−	0.181848i
$919$	8.09126			0.266906			0.133453	−	0.991055i	$-0.457393\pi$
$919$	8.09126			0.266906			0.133453	+	0.991055i	$0.457393\pi$
$920$	−0.500682	−	0.207389i	−0.0165070	−	0.00683743i
$921$	−23.7978	−	28.8037i	−0.784164	−	0.949115i
$922$	36.4136	+	36.4136i	1.19922	+	1.19922i
$923$	5.25704	−	1.04569i	0.173037	−	0.0344193i
$924$	−5.11652	−	16.6691i	−0.168321	−	0.548372i
$925$	0.368150	−	1.85082i	0.0121047	−	0.0608544i
$926$	−0.410037	−	0.989916i	−0.0134746	−	0.0325307i
$927$	2.15495	−	11.2194i	0.0707780	−	0.368494i
$928$	0.475645	+	0.0946117i	0.0156138	+	0.00310578i
$929$	4.95694	+	7.41858i	0.162632	+	0.243396i	0.903831	−	0.427889i	$-0.140743\pi$
$929$	4.95694	+	7.41858i	0.162632	+	0.243396i	−0.741199	+	0.671285i	$0.765743\pi$
$930$	2.04429	−	21.4811i	0.0670349	−	0.704393i
$931$	10.8220	−	10.8220i	0.354677	−	0.354677i
$932$	−1.65839	+	2.48195i	−0.0543223	+	0.0812991i
$933$	38.8909	+	31.7031i	1.27323	+	1.03791i
$934$			30.6629i			1.00332i
$935$	10.5524	+	17.1849i	0.345102	+	0.562007i
$936$	−2.92435	+	4.43963i	−0.0955854	+	0.145114i
$937$	8.51098	−	20.5473i	0.278042	−	0.671252i	−0.721740	−	0.692165i	$-0.756657\pi$
$937$	8.51098	−	20.5473i	0.278042	−	0.671252i	0.999781	+	0.0209128i	$0.00665724\pi$
$938$	−23.9394	−	15.9958i	−0.781650	−	0.522282i
$939$	−16.9809	+	9.14851i	−0.554150	+	0.298550i
$940$	7.08820	+	35.6348i	0.231192	+	1.16228i
$941$	33.0806	−	22.1038i	1.07840	−	0.720563i	0.116286	−	0.993216i	$-0.462901\pi$
$941$	33.0806	−	22.1038i	1.07840	−	0.720563i	0.962112	+	0.272653i	$0.0879012\pi$
$942$	−19.8130	+	37.3631i	−0.645544	+	1.21735i
$943$	2.70843	−	1.12187i	0.0881987	−	0.0365331i
$944$	−31.5824	+	13.0819i	−1.02792	+	0.425778i
$945$	10.3283	+	18.8719i	0.335979	+	0.613904i
$946$	26.4386	−	17.6657i	0.859594	−	0.574363i
$947$	1.22705	+	6.16877i	0.0398736	+	0.200458i	0.995587	−	0.0938399i	$-0.0299142\pi$
$947$	1.22705	+	6.16877i	0.0398736	+	0.200458i	−0.955714	+	0.294298i	$0.904914\pi$
$948$	−7.00554	−	13.0033i	−0.227529	−	0.422326i
$949$	14.1103	+	9.42821i	0.458040	+	0.306053i
$950$	2.69953	−	6.51724i	0.0875843	−	0.211447i
$951$	−5.43738	+	18.1395i	−0.176319	+	0.588213i
$952$	2.42412	+	0.0930369i	0.0785662	+	0.00301534i
$953$			45.4373i			1.47186i	0.677058	+	0.735930i	$0.263255\pi$
$953$			45.4373i			1.47186i	−0.677058	+	0.735930i	$0.736745\pi$
$954$	9.58878	−	6.49879i	0.310448	−	0.210406i
$955$	9.93218	−	14.8646i	0.321398	−	0.481006i
$956$	12.1496	−	12.1496i	0.392946	−	0.392946i
$957$	−0.243055	−	0.0231308i	−0.00785685	−	0.000747713i
$958$	−11.4206	−	17.0921i	−0.368982	−	0.552221i
$959$	−26.2048	−	5.21246i	−0.846197	−	0.168319i
$960$	32.6245	−	3.32176i	1.05295	−	0.107209i
$961$	−8.54214	−	20.6226i	−0.275553	−	0.665244i
$962$	−6.56560	+	33.0075i	−0.211683	+	1.06420i
$963$	0.0792916	+	12.0373i	0.00255513	+	0.387897i
$964$	−36.4480	+	7.24997i	−1.17391	+	0.233506i
$965$	−15.8075	−	15.8075i	−0.508862	−	0.508862i
$966$	−4.78913	+	3.95681i	−0.154088	+	0.127308i
$967$	−30.2049	−	12.5113i	−0.971323	−	0.402335i	−0.160119	−	0.987098i	$-0.551188\pi$
$967$	−30.2049	−	12.5113i	−0.971323	−	0.402335i	−0.811204	+	0.584763i	$0.801188\pi$
$968$	−1.61044			−0.0517614
$969$	−36.0338	+	2.27703i	−1.15757	+	0.0731486i
$970$	−79.6546			−2.55755
$971$	−22.2614	−	9.22099i	−0.714403	−	0.295916i	−0.00427801	−	0.999991i	$-0.501362\pi$
$971$	−22.2614	−	9.22099i	−0.714403	−	0.295916i	−0.710125	+	0.704075i	$0.751362\pi$
$972$	15.2744	−	29.7444i	0.489927	−	0.954053i
$973$	0.142863	+	0.142863i	0.00457997	+	0.00457997i
$974$	8.81244	−	1.75290i	0.282369	−	0.0561667i
$975$	6.81223	−	2.09099i	0.218166	−	0.0669653i
$976$	3.89360	−	19.5744i	0.124631	−	0.626562i
$977$	16.3952	+	39.5815i	0.524529	+	1.26633i	0.935063	+	0.354481i	$0.115342\pi$
$977$	16.3952	+	39.5815i	0.524529	+	1.26633i	−0.410534	+	0.911845i	$0.634658\pi$
$978$	4.15129	+	40.7717i	0.132744	+	1.30373i
$979$	−6.56395	−	1.30565i	−0.209785	−	0.0417288i
$980$	7.49325	+	11.2144i	0.239363	+	0.358232i
$981$	−41.2733	−	16.7783i	−1.31775	−	0.535690i
$982$	54.9740	−	54.9740i	1.75429	−	1.75429i
$983$	20.8744	−	31.2407i	0.665790	−	0.996425i	−0.332782	−	0.943004i	$-0.607987\pi$
$983$	20.8744	−	31.2407i	0.665790	−	0.996425i	0.998572	−	0.0534211i	$-0.0170126\pi$
$984$	1.07151	−	1.31444i	0.0341585	−	0.0419029i
$985$			52.7509i			1.68078i
$986$	0.209974	−	0.456560i	0.00668694	−	0.0145398i
$987$	26.9668	+	8.08340i	0.858363	+	0.257298i
$988$	−24.9138	+	60.1471i	−0.792612	+	1.91354i
$989$	−4.87446	−	3.25701i	−0.154999	−	0.103567i
$990$	−29.2602	+	6.02085i	−0.929951	+	0.191355i
$991$	−2.99298	−	15.0467i	−0.0950750	−	0.477974i	−0.998760	−	0.0497773i	$-0.984149\pi$
$991$	−2.99298	−	15.0467i	−0.0950750	−	0.477974i	0.903685	−	0.428197i	$-0.140851\pi$
$992$	−19.8425	+	13.2584i	−0.630001	+	0.420953i
$993$	18.1505	+	9.62491i	0.575988	+	0.305437i
$994$	3.34743	−	1.38655i	0.106174	−	0.0439788i
$995$	−46.4183	+	19.2271i	−1.47156	+	0.609539i
$996$	12.4243	+	6.58842i	0.393679	+	0.208762i
$997$	31.0246	−	20.7300i	0.982558	−	0.656524i	0.0430578	−	0.999073i	$-0.486290\pi$
$997$	31.0246	−	20.7300i	0.982558	−	0.656524i	0.939500	+	0.342548i	$0.111290\pi$
$998$	5.18048	+	26.0440i	0.163985	+	0.824409i
$999$	1.26166	−	14.2521i	0.0399172	−	0.450917i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.2.i.a.41.1	yes	32
3.2	odd	2	inner	51.2.i.a.41.4	yes	32
4.3	odd	2		816.2.cj.c.449.2		32
12.11	even	2		816.2.cj.c.449.4		32
17.2	even	8		867.2.i.g.827.4		32
17.3	odd	16		867.2.i.d.131.1		32
17.4	even	4		867.2.i.c.503.4		32
17.5	odd	16	inner	51.2.i.a.5.4	yes	32
17.6	odd	16		867.2.i.f.65.1		32
17.7	odd	16		867.2.i.b.224.4		32
17.8	even	8		867.2.i.b.329.1		32
17.9	even	8		867.2.i.i.329.1		32
17.10	odd	16		867.2.i.i.224.4		32
17.11	odd	16		867.2.i.g.65.1		32
17.12	odd	16		867.2.i.h.158.4		32
17.13	even	4		867.2.i.d.503.4		32
17.14	odd	16		867.2.i.c.131.1		32
17.15	even	8		867.2.i.f.827.4		32
17.16	even	2		867.2.i.h.653.1		32
51.2	odd	8		867.2.i.g.827.1		32
51.5	even	16	inner	51.2.i.a.5.1	✓	32
51.8	odd	8		867.2.i.b.329.4		32
51.11	even	16		867.2.i.g.65.4		32
51.14	even	16		867.2.i.c.131.4		32
51.20	even	16		867.2.i.d.131.4		32
51.23	even	16		867.2.i.f.65.4		32
51.26	odd	8		867.2.i.i.329.4		32
51.29	even	16		867.2.i.h.158.1		32
51.32	odd	8		867.2.i.f.827.1		32
51.38	odd	4		867.2.i.c.503.1		32
51.41	even	16		867.2.i.b.224.1		32
51.44	even	16		867.2.i.i.224.1		32
51.47	odd	4		867.2.i.d.503.1		32
51.50	odd	2		867.2.i.h.653.4		32
68.39	even	16		816.2.cj.c.209.4		32
204.107	odd	16		816.2.cj.c.209.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.i.a.5.1	✓	32	51.5	even	16	inner
51.2.i.a.5.4	yes	32	17.5	odd	16	inner
51.2.i.a.41.1	yes	32	1.1	even	1	trivial
51.2.i.a.41.4	yes	32	3.2	odd	2	inner
816.2.cj.c.209.2		32	204.107	odd	16
816.2.cj.c.209.4		32	68.39	even	16
816.2.cj.c.449.2		32	4.3	odd	2
816.2.cj.c.449.4		32	12.11	even	2
867.2.i.b.224.1		32	51.41	even	16
867.2.i.b.224.4		32	17.7	odd	16
867.2.i.b.329.1		32	17.8	even	8
867.2.i.b.329.4		32	51.8	odd	8
867.2.i.c.131.1		32	17.14	odd	16
867.2.i.c.131.4		32	51.14	even	16
867.2.i.c.503.1		32	51.38	odd	4
867.2.i.c.503.4		32	17.4	even	4
867.2.i.d.131.1		32	17.3	odd	16
867.2.i.d.131.4		32	51.20	even	16
867.2.i.d.503.1		32	51.47	odd	4
867.2.i.d.503.4		32	17.13	even	4
867.2.i.f.65.1		32	17.6	odd	16
867.2.i.f.65.4		32	51.23	even	16
867.2.i.f.827.1		32	51.32	odd	8
867.2.i.f.827.4		32	17.15	even	8
867.2.i.g.65.1		32	17.11	odd	16
867.2.i.g.65.4		32	51.11	even	16
867.2.i.g.827.1		32	51.2	odd	8
867.2.i.g.827.4		32	17.2	even	8
867.2.i.h.158.1		32	51.29	even	16
867.2.i.h.158.4		32	17.12	odd	16
867.2.i.h.653.1		32	17.16	even	2
867.2.i.h.653.4		32	51.50	odd	2
867.2.i.i.224.1		32	51.44	even	16
867.2.i.i.224.4		32	17.10	odd	16
867.2.i.i.329.1		32	17.9	even	8
867.2.i.i.329.4		32	51.26	odd	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	51.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.88095 - 0.779115i) q^{2} +(1.10321 + 1.33527i) q^{3} +(1.51674 + 1.51674i) q^{4} +(2.03727 - 0.405238i) q^{5} +(-1.03475 - 3.37109i) q^{6} +(0.388855 - 1.95490i) q^{7} +(-0.112963 - 0.272718i) q^{8} +(-0.565877 + 2.94615i) q^{9} +(-4.14772 - 0.825033i) q^{10} +(-1.30817 - 1.95782i) q^{11} +(-0.351977 + 3.69852i) q^{12} +(-4.24491 + 4.24491i) q^{13} +(-2.25451 + 3.37411i) q^{14} +(2.78862 + 2.27324i) q^{15} -3.68900i q^{16} +(-4.01006 - 0.958875i) q^{17} +(3.35977 - 5.10067i) q^{18} +(1.93477 - 4.67096i) q^{19} +(3.70464 + 2.47536i) q^{20} +(3.03931 - 1.63744i) q^{21} +(0.935240 + 4.70177i) q^{22} +(0.734889 - 0.491037i) q^{23} +(0.239529 - 0.451700i) q^{24} +(-0.633157 + 0.262262i) q^{25} +(11.2917 - 4.67719i) q^{26} +(-4.55817 + 2.49461i) q^{27} +(3.55487 - 2.37529i) q^{28} +(-0.0116792 - 0.0587151i) q^{29} +(-3.47415 - 6.44850i) q^{30} +(2.44942 + 1.63665i) q^{31} +(-3.10008 + 7.48426i) q^{32} +(1.17103 - 3.90663i) q^{33} +(6.79564 + 4.92789i) q^{34} -4.14024i q^{35} +(-5.32682 + 3.61024i) q^{36} +(-1.52979 + 2.28949i) q^{37} +(-7.27842 + 7.27842i) q^{38} +(-10.3511 - 0.985083i) q^{39} +(-0.340652 - 0.509822i) q^{40} +(3.25313 + 0.647088i) q^{41} +(-6.99253 + 0.711965i) q^{42} +(-2.53831 - 6.12803i) q^{43} +(0.985341 - 4.95364i) q^{44} +(0.0410472 + 6.23140i) q^{45} +(-1.76486 + 0.351053i) q^{46} +(5.76615 + 5.76615i) q^{47} +(4.92580 - 4.06972i) q^{48} +(2.79671 + 1.15844i) q^{49} +1.39527 q^{50} +(-3.14356 - 6.41233i) q^{51} -12.8768 q^{52} +(1.75216 + 0.725770i) q^{53} +(10.5173 - 1.14089i) q^{54} +(-3.45848 - 3.45848i) q^{55} +(-0.577063 + 0.114785i) q^{56} +(8.37143 - 2.56958i) q^{57} +(-0.0237779 + 0.119540i) q^{58} +(-3.54618 - 8.56124i) q^{59} +(0.781708 + 7.67751i) q^{60} +(5.30616 + 1.05546i) q^{61} +(-3.33210 - 4.98684i) q^{62} +(5.53939 + 2.25186i) q^{63} +(6.44515 - 6.44515i) q^{64} +(-6.92782 + 10.3682i) q^{65} +(-5.24636 + 6.43581i) q^{66} +7.09503i q^{67} +(-4.62784 - 7.53656i) q^{68} +(1.46640 + 0.439558i) q^{69} +(-3.22572 + 7.78759i) q^{70} +(-0.742386 - 0.496046i) q^{71} +(0.867389 - 0.178482i) q^{72} +(-0.551496 - 2.77256i) q^{73} +(4.66124 - 3.11454i) q^{74} +(-1.04869 - 0.556105i) q^{75} +(10.0192 - 4.15007i) q^{76} +(-4.33604 + 1.79604i) q^{77} +(18.7024 + 9.91759i) q^{78} +(-3.30560 + 2.20873i) q^{79} +(-1.49492 - 7.51548i) q^{80} +(-8.35957 - 3.33431i) q^{81} +(-5.61482 - 3.75170i) q^{82} +(1.44855 - 3.49712i) q^{83} +(7.09339 + 2.12627i) q^{84} +(-8.55813 - 0.328458i) q^{85} +13.5041i q^{86} +(0.0655159 - 0.0803696i) q^{87} +(-0.386156 + 0.577923i) q^{88} +(2.00979 - 2.00979i) q^{89} +(4.77777 - 11.7529i) q^{90} +(6.64775 + 9.94906i) q^{91} +(1.85941 + 0.369859i) q^{92} +(0.516848 + 5.07620i) q^{93} +(-6.35335 - 15.3383i) q^{94} +(2.04880 - 10.3000i) q^{95} +(-13.4135 + 4.11723i) q^{96} +(18.4735 - 3.67461i) q^{97} +(-4.35792 - 4.35792i) q^{98} +(6.50828 - 2.74618i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} + 16 q^{12} - 16 q^{13} + 16 q^{15} + 16 q^{18} - 16 q^{19} + 16 q^{21} - 16 q^{22} + 16 q^{24} + 16 q^{25} - 8 q^{27} + 32 q^{28} - 8 q^{30}+ \cdots - 64 q^{99}+O(q^{100}) \) 32 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 + 16 * q^12 - 16 * q^13 + 16 * q^15 + 16 * q^18 - 16 * q^19 + 16 * q^21 - 16 * q^22 + 16 * q^24 + 16 * q^25 - 8 * q^27 + 32 * q^28 - 8 * q^30 + 16 * q^31 + 96 * q^34 + 8 * q^36 + 16 * q^37 - 24 * q^39 + 16 * q^40 - 56 * q^42 + 16 * q^43 - 40 * q^45 - 32 * q^46 - 64 * q^48 - 48 * q^49 - 40 * q^51 - 96 * q^52 - 24 * q^54 - 48 * q^55 + 8 * q^57 - 48 * q^58 + 32 * q^60 - 32 * q^61 + 64 * q^63 + 16 * q^64 + 72 * q^66 + 80 * q^69 + 48 * q^70 + 64 * q^72 + 48 * q^73 + 88 * q^75 + 48 * q^76 + 96 * q^78 + 16 * q^79 + 48 * q^81 + 112 * q^82 - 56 * q^87 + 16 * q^88 - 88 * q^90 + 16 * q^91 - 72 * q^93 - 48 * q^94 - 112 * q^96 - 16 * q^97 - 64 * q^99

Introduction

L-functions

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