LMFDB - Embedded newform 720.2.cq.a.173.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(173,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2, 9]))

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

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

chi := DirichletCharacter("720.173");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.cq (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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$560$
Relative dimension:	$140$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			173.8
Character	$\chi$	$=$	720.173
Dual form			720.2.cq.a.437.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40148 + 0.189382i) q^{2} +(-1.35263 + 1.08184i) q^{3} +(1.92827 - 0.530828i) q^{4} +(2.05945 + 0.871024i) q^{5} +(1.69080 - 1.77234i) q^{6} +(-2.15913 + 0.578537i) q^{7} +(-2.60189 + 1.10912i) q^{8} +(0.659238 - 2.92667i) q^{9} +O(q^{10})$	\(q+(-1.40148 + 0.189382i) q^{2} +(-1.35263 + 1.08184i) q^{3} +(1.92827 - 0.530828i) q^{4} +(2.05945 + 0.871024i) q^{5} +(1.69080 - 1.77234i) q^{6} +(-2.15913 + 0.578537i) q^{7} +(-2.60189 + 1.10912i) q^{8} +(0.659238 - 2.92667i) q^{9} +(-3.05122 - 0.830698i) q^{10} +(1.41594 - 0.379400i) q^{11} +(-2.03397 + 2.80410i) q^{12} +(-1.91938 + 1.10816i) q^{13} +(2.91641 - 1.21971i) q^{14} +(-3.72799 + 1.04982i) q^{15} +(3.43644 - 2.04716i) q^{16} +(-4.64939 - 4.64939i) q^{17} +(-0.369647 + 4.22651i) q^{18} +(-5.78840 + 5.78840i) q^{19} +(4.43353 + 0.586357i) q^{20} +(2.29463 - 3.11839i) q^{21} +(-1.91255 + 0.799874i) q^{22} +(0.278722 - 1.04021i) q^{23} +(2.31951 - 4.31507i) q^{24} +(3.48263 + 3.58765i) q^{25} +(2.48010 - 1.91655i) q^{26} +(2.27449 + 4.67191i) q^{27} +(-3.85628 + 2.26170i) q^{28} +(-1.00329 + 0.268830i) q^{29} +(5.02587 - 2.17731i) q^{30} +(0.389919 + 0.675359i) q^{31} +(-4.42840 + 3.51984i) q^{32} +(-1.50480 + 2.04501i) q^{33} +(7.39651 + 5.63549i) q^{34} +(-4.95053 - 0.689190i) q^{35} +(-0.282373 - 5.99335i) q^{36} -2.88249i q^{37} +(7.01608 - 9.20852i) q^{38} +(1.39737 - 3.57540i) q^{39} +(-6.32453 + 0.0178649i) q^{40} +(-2.69916 - 4.67508i) q^{41} +(-2.62530 + 4.80491i) q^{42} +(-4.29906 + 7.44619i) q^{43} +(2.52892 - 1.48321i) q^{44} +(3.90687 - 5.45311i) q^{45} +(-0.193626 + 1.51061i) q^{46} +(-0.779697 + 0.208919i) q^{47} +(-2.43355 + 6.48674i) q^{48} +(-1.73504 + 1.00172i) q^{49} +(-5.56026 - 4.36846i) q^{50} +(11.3188 + 1.25902i) q^{51} +(-3.11284 + 3.15569i) q^{52} -6.25687i q^{53} +(-4.07241 - 6.11682i) q^{54} +(3.24652 + 0.451965i) q^{55} +(4.97616 - 3.90003i) q^{56} +(1.56745 - 14.0917i) q^{57} +(1.35517 - 0.566764i) q^{58} +(-6.11658 - 1.63893i) q^{59} +(-6.63129 + 4.00325i) q^{60} +(0.525959 - 0.140930i) q^{61} +(-0.674363 - 0.872656i) q^{62} +(0.269809 + 6.70046i) q^{63} +(5.53970 - 5.77164i) q^{64} +(-4.91809 + 0.610358i) q^{65} +(1.72165 - 3.15102i) q^{66} +(-4.82293 - 8.35356i) q^{67} +(-11.4333 - 6.49724i) q^{68} +(0.748328 + 1.70855i) q^{69} +(7.06857 + 0.0283408i) q^{70} -14.6020 q^{71} +(1.53077 + 8.34606i) q^{72} +(1.91839 - 1.91839i) q^{73} +(0.545891 + 4.03974i) q^{74} +(-8.59200 - 1.08513i) q^{75} +(-8.08894 + 14.2342i) q^{76} +(-2.83770 + 1.63835i) q^{77} +(-1.28127 + 5.27547i) q^{78} +(-14.2083 - 8.20319i) q^{79} +(8.86029 - 1.22279i) q^{80} +(-8.13081 - 3.85874i) q^{81} +(4.66818 + 6.04084i) q^{82} +(6.15721 - 10.6646i) q^{83} +(2.76933 - 7.23114i) q^{84} +(-5.52543 - 13.6249i) q^{85} +(4.61485 - 11.2498i) q^{86} +(1.06625 - 1.44903i) q^{87} +(-3.26332 + 2.55761i) q^{88} -4.04817i q^{89} +(-4.44266 + 8.38229i) q^{90} +(3.50309 - 3.50309i) q^{91} +(-0.0147191 - 2.15375i) q^{92} +(-1.25805 - 0.491683i) q^{93} +(1.05316 - 0.440456i) q^{94} +(-16.9627 + 6.87906i) q^{95} +(2.18208 - 9.55188i) q^{96} +(3.18808 + 11.8981i) q^{97} +(2.24190 - 1.73248i) q^{98} +(-0.176938 - 4.39411i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 560 q - 6 q^{2} - 6 q^{5} - 8 q^{6}+O(q^{10}) $ 560 * q - 6 * q^2 - 6 * q^5 - 8 * q^6	$ 560 q - 6 q^{2} - 6 q^{5} - 8 q^{6} - 12 q^{11} - 10 q^{12} - 8 q^{15} - 4 q^{16} + 20 q^{18} - 6 q^{20} - 8 q^{21} + 6 q^{22} - 24 q^{24} + 8 q^{28} + 28 q^{30} - 8 q^{31} + 54 q^{32} - 8 q^{33} - 12 q^{34} + 8 q^{36} - 18 q^{38} - 24 q^{39} + 8 q^{40} - 46 q^{42} - 4 q^{43} - 14 q^{45} - 40 q^{46} - 12 q^{47} - 22 q^{48} - 6 q^{50} - 8 q^{51} - 18 q^{52} + 24 q^{54} - 12 q^{56} + 24 q^{57} - 10 q^{58} - 88 q^{60} - 4 q^{61} + 20 q^{63} - 24 q^{64} - 12 q^{65} + 24 q^{66} - 4 q^{67} - 30 q^{68} + 12 q^{69} + 2 q^{70} - 22 q^{72} + 24 q^{74} - 66 q^{75} + 8 q^{76} - 12 q^{77} - 122 q^{78} - 16 q^{81} - 12 q^{84} - 12 q^{85} - 12 q^{86} + 12 q^{87} - 10 q^{88} - 94 q^{90} - 16 q^{91} - 120 q^{92} - 12 q^{95} + 48 q^{96} - 4 q^{97} + 32 q^{99}+O(q^{100}) $ 560 * q - 6 * q^2 - 6 * q^5 - 8 * q^6 - 12 * q^11 - 10 * q^12 - 8 * q^15 - 4 * q^16 + 20 * q^18 - 6 * q^20 - 8 * q^21 + 6 * q^22 - 24 * q^24 + 8 * q^28 + 28 * q^30 - 8 * q^31 + 54 * q^32 - 8 * q^33 - 12 * q^34 + 8 * q^36 - 18 * q^38 - 24 * q^39 + 8 * q^40 - 46 * q^42 - 4 * q^43 - 14 * q^45 - 40 * q^46 - 12 * q^47 - 22 * q^48 - 6 * q^50 - 8 * q^51 - 18 * q^52 + 24 * q^54 - 12 * q^56 + 24 * q^57 - 10 * q^58 - 88 * q^60 - 4 * q^61 + 20 * q^63 - 24 * q^64 - 12 * q^65 + 24 * q^66 - 4 * q^67 - 30 * q^68 + 12 * q^69 + 2 * q^70 - 22 * q^72 + 24 * q^74 - 66 * q^75 + 8 * q^76 - 12 * q^77 - 122 * q^78 - 16 * q^81 - 12 * q^84 - 12 * q^85 - 12 * q^86 + 12 * q^87 - 10 * q^88 - 94 * q^90 - 16 * q^91 - 120 * q^92 - 12 * q^95 + 48 * q^96 - 4 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.40148	+	0.189382i	−0.990993	+	0.133913i
$2$	−1.40148	+	0.189382i	−0.990993	+	0.133913i
$3$	−1.35263	+	1.08184i	−0.780944	+	0.624602i
$3$	−1.35263	+	1.08184i	−0.780944	+	0.624602i
$4$	1.92827	−	0.530828i	0.964134	−	0.265414i
$5$	2.05945	+	0.871024i	0.921012	+	0.389534i
$5$	2.05945	+	0.871024i	0.921012	+	0.389534i
$6$	1.69080	−	1.77234i	0.690267	−	0.723554i
$7$	−2.15913	+	0.578537i	−0.816075	+	0.218667i	−0.642630	−	0.766177i	$-0.722157\pi$
$7$	−2.15913	+	0.578537i	−0.816075	+	0.218667i	−0.173445	+	0.984844i	$0.555490\pi$
$8$	−2.60189	+	1.10912i	−0.919908	+	0.392134i
$9$	0.659238	−	2.92667i	0.219746	−	0.975557i
$10$	−3.05122	−	0.830698i	−0.964880	−	0.262690i
$11$	1.41594	−	0.379400i	0.426922	−	0.114393i	−0.0389589	−	0.999241i	$-0.512404\pi$
$11$	1.41594	−	0.379400i	0.426922	−	0.114393i	0.465881	+	0.884847i	$0.345737\pi$
$12$	−2.03397	+	2.80410i	−0.587157	+	0.809473i
$13$	−1.91938	+	1.10816i	−0.532341	+	0.307347i	−0.741969	−	0.670434i	$-0.766108\pi$
$13$	−1.91938	+	1.10816i	−0.532341	+	0.307347i	0.209628	+	0.977781i	$0.432775\pi$
$14$	2.91641	−	1.21971i	0.779442	−	0.325980i
$15$	−3.72799	+	1.04982i	−0.962562	+	0.271062i
$16$	3.43644	−	2.04716i	0.859111	−	0.511790i
$17$	−4.64939	−	4.64939i	−1.12764	−	1.12764i	−0.990560	−	0.137082i	$-0.956228\pi$
$17$	−4.64939	−	4.64939i	−1.12764	−	1.12764i	−0.137082	−	0.990560i	$-0.543772\pi$
$18$	−0.369647	+	4.22651i	−0.0871266	+	0.996197i
$19$	−5.78840	+	5.78840i	−1.32795	+	1.32795i	−0.420793	+	0.907157i	$0.638248\pi$
$19$	−5.78840	+	5.78840i	−1.32795	+	1.32795i	−0.907157	+	0.420793i	$0.861752\pi$
$20$	4.43353	+	0.586357i	0.991367	+	0.131113i
$21$	2.29463	−	3.11839i	0.500729	−	0.680488i
$22$	−1.91255	+	0.799874i	−0.407758	+	0.170534i
$23$	0.278722	−	1.04021i	0.0581176	−	0.216898i	−0.930760	−	0.365631i	$-0.880853\pi$
$23$	0.278722	−	1.04021i	0.0581176	−	0.216898i	0.988877	+	0.148734i	$0.0475197\pi$
$24$	2.31951	−	4.31507i	0.473469	−	0.880811i
$25$	3.48263	+	3.58765i	0.696527	+	0.717531i
$26$	2.48010	−	1.91655i	0.486388	−	0.375866i
$27$	2.27449	+	4.67191i	0.437725	+	0.899109i
$28$	−3.85628	+	2.26170i	−0.728769	+	0.427422i
$29$	−1.00329	+	0.268830i	−0.186306	+	0.0499206i	−0.350766	−	0.936463i	$-0.614079\pi$
$29$	−1.00329	+	0.268830i	−0.186306	+	0.0499206i	0.164460	+	0.986384i	$0.447412\pi$
$30$	5.02587	−	2.17731i	0.917594	−	0.397520i
$31$	0.389919	+	0.675359i	0.0700315	+	0.121298i	0.898915	−	0.438123i	$-0.144357\pi$
$31$	0.389919	+	0.675359i	0.0700315	+	0.121298i	−0.828883	+	0.559421i	$0.811023\pi$
$32$	−4.42840	+	3.51984i	−0.782837	+	0.622227i
$33$	−1.50480	+	2.04501i	−0.261952	+	0.355991i
$34$	7.39651	+	5.63549i	1.26849	+	0.966479i
$35$	−4.95053	−	0.689190i	−0.836793	−	0.116494i
$36$	−0.282373	−	5.99335i	−0.0470621	−	0.998892i
$37$		−	2.88249i		−	0.473878i	−0.971525	−	0.236939i	$-0.923856\pi$
$37$		−	2.88249i		−	0.473878i	0.971525	−	0.236939i	$-0.0761442\pi$
$38$	7.01608	−	9.20852i	1.13816	−	1.49382i
$39$	1.39737	−	3.57540i	0.223759	−	0.572522i
$40$	−6.32453	+	0.0178649i	−0.999996	+	0.00282469i
$41$	−2.69916	−	4.67508i	−0.421538	−	0.730125i	0.574552	−	0.818468i	$-0.305176\pi$
$41$	−2.69916	−	4.67508i	−0.421538	−	0.730125i	−0.996090	+	0.0883429i	$0.971843\pi$
$42$	−2.62530	+	4.80491i	−0.405093	+	0.741413i
$43$	−4.29906	+	7.44619i	−0.655600	+	1.13553i	0.326143	+	0.945321i	$0.394251\pi$
$43$	−4.29906	+	7.44619i	−0.655600	+	1.13553i	−0.981743	+	0.190212i	$0.939082\pi$
$44$	2.52892	−	1.48321i	0.381249	−	0.223602i
$45$	3.90687	−	5.45311i	0.582401	−	0.812901i
$46$	−0.193626	+	1.51061i	−0.0285486	+	0.222727i
$47$	−0.779697	+	0.208919i	−0.113730	+	0.0304740i	−0.315235	−	0.949014i	$-0.602083\pi$
$47$	−0.779697	+	0.208919i	−0.113730	+	0.0304740i	0.201505	+	0.979488i	$0.435417\pi$
$48$	−2.43355	+	6.48674i	−0.351252	+	0.936281i
$49$	−1.73504	+	1.00172i	−0.247862	+	0.143103i
$50$	−5.56026	−	4.36846i	−0.786340	−	0.617794i
$51$	11.3188	+	1.25902i	1.58495	+	0.176298i
$52$	−3.11284	+	3.15569i	−0.431674	+	0.437615i
$53$		−	6.25687i		−	0.859447i	−0.902960	−	0.429724i	$-0.858611\pi$
$53$		−	6.25687i		−	0.859447i	0.902960	−	0.429724i	$-0.141389\pi$
$54$	−4.07241	−	6.11682i	−0.554185	−	0.832393i
$55$	3.24652	+	0.451965i	0.437761	+	0.0609429i
$56$	4.97616	−	3.90003i	0.664967	−	0.521164i
$57$	1.56745	−	14.0917i	0.207614	−	1.86649i
$58$	1.35517	−	0.566764i	0.177943	−	0.0744198i
$59$	−6.11658	−	1.63893i	−0.796311	−	0.213371i	−0.162347	−	0.986734i	$-0.551906\pi$
$59$	−6.11658	−	1.63893i	−0.796311	−	0.213371i	−0.633964	+	0.773363i	$0.718573\pi$
$60$	−6.63129	+	4.00325i	−0.856096	+	0.516817i
$61$	0.525959	−	0.140930i	0.0673421	−	0.0180443i	−0.224991	−	0.974361i	$-0.572235\pi$
$61$	0.525959	−	0.140930i	0.0673421	−	0.0180443i	0.292333	+	0.956317i	$0.405569\pi$
$62$	−0.674363	−	0.872656i	−0.0856441	−	0.110827i
$63$	0.269809	+	6.70046i	0.0339927	+	0.844179i
$64$	5.53970	−	5.77164i	0.692462	−	0.721454i
$65$	−4.91809	+	0.610358i	−0.610015	+	0.0757056i
$66$	1.72165	−	3.15102i	0.211920	−	0.387863i
$67$	−4.82293	−	8.35356i	−0.589214	−	1.02055i	−0.994336	−	0.106286i	$-0.966104\pi$
$67$	−4.82293	−	8.35356i	−0.589214	−	1.02055i	0.405121	−	0.914263i	$-0.367229\pi$
$68$	−11.4333	−	6.49724i	−1.38649	−	0.787906i
$69$	0.748328	+	1.70855i	0.0900881	+	0.205685i
$70$	7.06857	+	0.0283408i	0.844856	+	0.00338738i
$71$	−14.6020			−1.73294			−0.866471	−	0.499227i	$-0.833617\pi$
$71$	−14.6020			−1.73294			−0.866471	+	0.499227i	$0.833617\pi$
$72$	1.53077	+	8.34606i	0.180403	+	0.983593i
$73$	1.91839	−	1.91839i	0.224531	−	0.224531i	−0.585872	−	0.810403i	$-0.699248\pi$
$73$	1.91839	−	1.91839i	0.224531	−	0.224531i	0.810403	+	0.585872i	$0.199248\pi$
$74$	0.545891	+	4.03974i	0.0634585	+	0.469610i
$75$	−8.59200	−	1.08513i	−0.992119	−	0.125300i
$76$	−8.08894	+	14.2342i	−0.927865	+	1.63278i
$77$	−2.83770	+	1.63835i	−0.323386	+	0.186707i
$78$	−1.28127	+	5.27547i	−0.145075	+	0.597329i
$79$	−14.2083	−	8.20319i	−1.59856	−	0.922932i	−0.991764	−	0.128077i	$-0.959120\pi$
$79$	−14.2083	−	8.20319i	−1.59856	−	0.922932i	−0.606800	−	0.794855i	$-0.707547\pi$
$80$	8.86029	−	1.22279i	0.990611	−	0.136712i
$81$	−8.13081	−	3.85874i	−0.903424	−	0.428749i
$82$	4.66818	+	6.04084i	0.515515	+	0.667099i
$83$	6.15721	−	10.6646i	0.675841	−	1.17059i	−0.300381	−	0.953819i	$-0.597114\pi$
$83$	6.15721	−	10.6646i	0.675841	−	1.17059i	0.976222	−	0.216772i	$-0.0695528\pi$
$84$	2.76933	−	7.23114i	0.302159	−	0.788982i
$85$	−5.52543	−	13.6249i	−0.599317	−	1.47783i
$86$	4.61485	−	11.2498i	0.497632	−	1.21310i
$87$	1.06625	−	1.44903i	0.114314	−	0.155352i
$88$	−3.26332	+	2.55761i	−0.347872	+	0.272642i
$89$		−	4.04817i		−	0.429105i	−0.976712	−	0.214553i	$-0.931171\pi$
$89$		−	4.04817i		−	0.429105i	0.976712	−	0.214553i	$-0.0688294\pi$
$90$	−4.44266	+	8.38229i	−0.468297	+	0.883571i
$91$	3.50309	−	3.50309i	0.367223	−	0.367223i
$92$	−0.0147191	−	2.15375i	−0.00153458	−	0.224544i
$93$	−1.25805	−	0.491683i	−0.130454	−	0.0509852i
$94$	1.05316	−	0.440456i	0.108625	−	0.0454295i
$95$	−16.9627	+	6.87906i	−1.74034	+	0.705776i
$96$	2.18208	−	9.55188i	0.222708	−	0.974885i
$97$	3.18808	+	11.8981i	0.323701	+	1.20807i	0.915612	+	0.402064i	$0.131707\pi$
$97$	3.18808	+	11.8981i	0.323701	+	1.20807i	−0.591911	+	0.806003i	$0.701626\pi$
$98$	2.24190	−	1.73248i	0.226466	−	0.175006i
$99$	−0.176938	−	4.39411i	−0.0177830	−	0.441624i
$100$	8.61988	+	5.06928i	0.861988	+	0.506928i
$101$	7.81109	−	2.09298i	0.777233	−	0.208259i	0.151668	−	0.988431i	$-0.451535\pi$
$101$	7.81109	−	2.09298i	0.777233	−	0.208259i	0.625564	+	0.780173i	$0.284869\pi$
$102$	−16.1015	+	0.379095i	−1.59428	+	0.0375360i
$103$	1.04194	+	0.279188i	0.102666	+	0.0275092i	0.309786	−	0.950806i	$-0.399743\pi$
$103$	1.04194	+	0.279188i	0.102666	+	0.0275092i	−0.207120	+	0.978315i	$0.566409\pi$
$104$	3.76495	−	5.01213i	0.369183	−	0.491480i
$105$	7.44185	−	4.42347i	0.726251	−	0.431687i
$106$	1.18494	+	8.76885i	0.115091	+	0.851706i
$107$	6.67047			0.644858			0.322429	−	0.946594i	$-0.395501\pi$
$107$	6.67047			0.644858			0.322429	+	0.946594i	$0.395501\pi$
$108$	6.86580	+	7.80133i	0.660662	+	0.750683i
$109$	−7.66567	+	7.66567i	−0.734238	+	0.734238i	−0.971456	−	0.237219i	$-0.923764\pi$
$109$	−7.66567	+	7.66567i	−0.734238	+	0.734238i	0.237219	+	0.971456i	$0.423764\pi$
$110$	−4.63551	−	0.0185857i	−0.441979	−	0.00177208i
$111$	3.11840	+	3.89895i	0.295985	+	0.370072i
$112$	−6.23537	+	6.40820i	−0.589187	+	0.605518i
$113$	3.08414	+	0.826393i	0.290131	+	0.0777405i	0.400949	−	0.916100i	$-0.368680\pi$
$113$	3.08414	+	0.826393i	0.290131	+	0.0777405i	−0.110818	+	0.993841i	$0.535347\pi$
$114$	0.471966	+	20.0460i	0.0442037	+	1.87748i
$115$	1.48006	−	1.89947i	0.138016	−	0.177127i
$116$	−1.79191	+	1.05095i	−0.166374	+	0.0975784i
$117$	1.97788	+	6.34794i	0.182855	+	0.586867i
$118$	8.88262	+	1.13855i	0.817712	+	0.104812i
$119$	12.7285	+	7.34879i	1.16682	+	0.673663i
$120$	8.53545	−	6.86630i	0.779176	−	0.626805i
$121$	−7.66534	+	4.42558i	−0.696849	+	0.402326i
$122$	−0.710429	+	0.297117i	−0.0643192	+	0.0268997i
$123$	8.70867	+	3.40361i	0.785235	+	0.306893i
$124$	1.11037	+	1.09529i	0.0997140	+	0.0983603i
$125$	4.04736	+	10.4220i	0.362007	+	0.932175i
$126$	−1.64708	−	9.33944i	−0.146733	−	0.832023i
$127$	0.459934	−	0.459934i	0.0408126	−	0.0408126i	−0.686406	−	0.727219i	$-0.740813\pi$
$127$	0.459934	−	0.459934i	0.0408126	−	0.0408126i	0.727219	+	0.686406i	$0.240813\pi$
$128$	−6.67071	+	9.13793i	−0.589613	+	0.807686i
$129$	−2.24054	−	14.7229i	−0.197269	−	1.29628i
$130$	6.77700	−	1.78680i	0.594382	−	0.156713i
$131$	17.2549	+	4.62344i	1.50757	+	0.403952i	0.915627	−	0.402028i	$-0.131695\pi$
$131$	17.2549	+	4.62344i	1.50757	+	0.403952i	0.591942	+	0.805980i	$0.298361\pi$
$132$	−1.81611	+	4.74212i	−0.158072	+	0.412749i
$133$	9.14911	−	15.8467i	0.793328	−	1.37408i
$134$	8.34123	+	10.7939i	0.720572	+	0.932454i
$135$	0.614840	+	11.6027i	0.0529170	+	0.998599i
$136$	17.2539	+	6.94047i	1.47951	+	0.595140i
$137$	5.00297	+	18.6713i	0.427433	+	1.59520i	0.758553	+	0.651612i	$0.225907\pi$
$137$	5.00297	+	18.6713i	0.427433	+	1.59520i	−0.331120	+	0.943589i	$0.607427\pi$
$138$	−1.37233	−	2.25277i	−0.116821	−	0.191769i
$139$	1.11900	−	4.17616i	0.0949123	−	0.354217i	−0.902094	−	0.431540i	$-0.857970\pi$
$139$	1.11900	−	4.17616i	0.0949123	−	0.354217i	0.997006	+	0.0773224i	$0.0246371\pi$
$140$	−9.91180	+	1.29894i	−0.837700	+	0.109781i
$141$	0.828627	−	1.12610i	0.0697830	−	0.0948347i
$142$	20.4644	−	2.76536i	1.71733	−	0.232064i
$143$	−2.29730	+	2.29730i	−0.192110	+	0.192110i
$144$	−3.72593	−	11.4069i	−0.310494	−	0.950575i
$145$	−2.30038	−	0.320247i	−0.191036	−	0.0265951i
$146$	−2.32527	+	3.05189i	−0.192441	+	0.252576i
$147$	1.26316	−	3.23200i	0.104184	−	0.266571i
$148$	−1.53011	−	5.55821i	−0.125774	−	0.456882i
$149$	−2.38624	−	0.639392i	−0.195489	−	0.0523811i	0.159746	−	0.987158i	$-0.448932\pi$
$149$	−2.38624	−	0.639392i	−0.195489	−	0.0523811i	−0.355235	+	0.934777i	$0.615599\pi$
$150$	12.2470	−	0.106391i	0.999962	−	0.00868678i
$151$	−3.29560	−	1.90272i	−0.268192	−	0.154841i	0.359874	−	0.933001i	$-0.382820\pi$
$151$	−3.29560	−	1.90272i	−0.268192	−	0.154841i	−0.628066	+	0.778160i	$0.716153\pi$
$152$	8.64075	−	21.4808i	0.700858	−	1.74233i
$153$	−16.6723	+	10.5422i	−1.34787	+	0.852285i
$154$	3.66670	−	2.83352i	0.295471	−	0.228331i
$155$	0.214762	+	1.73049i	0.0172501	+	0.138997i
$156$	0.796588	−	7.63609i	0.0637781	−	0.611377i
$157$	11.4340	+	19.8043i	0.912532	+	1.58055i	0.810475	+	0.585773i	$0.199209\pi$
$157$	11.4340	+	19.8043i	0.912532	+	1.58055i	0.102056	+	0.994779i	$0.467458\pi$
$158$	21.4662	+	8.80577i	1.70776	+	0.700550i
$159$	6.76894	+	8.46326i	0.536812	+	0.671180i
$160$	−12.1859	+	3.39169i	−0.963381	+	0.268136i
$161$			2.40719i			0.189713i
$162$	12.1259	+	3.86811i	0.952702	+	0.303907i
$163$		−	2.73827i		−	0.214478i	−0.994233	−	0.107239i	$-0.965799\pi$
$163$		−	2.73827i		−	0.214478i	0.994233	−	0.107239i	$-0.0342009\pi$
$164$	−7.68637	−	7.58202i	−0.600205	−	0.592057i
$165$	−4.88031	+	2.90088i	−0.379931	+	0.225833i
$166$	−6.60949	+	16.1122i	−0.512996	+	1.25055i
$167$	−21.5525	−	5.77498i	−1.66778	−	0.446881i	−0.703271	−	0.710922i	$-0.748278\pi$
$167$	−21.5525	−	5.77498i	−1.66778	−	0.446881i	−0.964512	+	0.264041i	$0.914945\pi$
$168$	−2.51170	+	10.6587i	−0.193782	+	0.822339i
$169$	−4.04398	+	7.00438i	−0.311075	+	0.538798i
$170$	10.3241	+	18.0485i	0.791820	+	1.38426i
$171$	13.1248	+	20.7567i	1.00368	+	1.58730i
$172$	−4.33709	+	16.6403i	−0.330700	+	1.26881i
$173$	−5.19025	+	8.98978i	−0.394608	+	0.683480i	−0.993051	−	0.117685i	$-0.962453\pi$
$173$	−5.19025	+	8.98978i	−0.394608	+	0.683480i	0.598443	+	0.801165i	$0.295786\pi$
$174$	−1.21990	+	2.23271i	−0.0924807	+	0.169261i
$175$	−9.59505	−	5.73138i	−0.725318	−	0.433252i
$176$	4.08911	−	4.20244i	0.308228	−	0.316771i
$177$	10.0466	−	4.40029i	0.755145	−	0.330746i
$178$	0.766651	+	5.67342i	0.0574629	+	0.425241i
$179$	−0.761132	−	0.761132i	−0.0568897	−	0.0568897i	0.678090	−	0.734979i	$-0.262808\pi$
$179$	−0.761132	−	0.761132i	−0.0568897	−	0.0568897i	−0.734979	+	0.678090i	$0.762808\pi$
$180$	4.63882	−	12.5889i	0.345758	−	0.938324i
$181$	11.4768	−	11.4768i	0.853064	−	0.853064i	−0.137445	−	0.990509i	$-0.543889\pi$
$181$	11.4768	−	11.4768i	0.853064	−	0.853064i	0.990509	+	0.137445i	$0.0438891\pi$
$182$	−4.24607	+	5.57292i	−0.314740	+	0.413092i
$183$	−0.558966	+	0.759631i	−0.0413199	+	0.0561536i
$184$	0.428510	+	3.01564i	0.0315901	+	0.222316i
$185$	2.51072	−	5.93633i	0.184592	−	0.436447i
$186$	1.85624	+	0.450831i	0.136106	+	0.0330565i
$187$	−8.34723	−	4.81928i	−0.610410	−	0.352420i
$188$	−1.39256	+	0.816737i	−0.101563	+	0.0595667i
$189$	−7.61379	−	8.77138i	−0.553822	−	0.638024i
$190$	22.4701	−	12.8533i	1.63015	−	0.932474i
$191$	22.1330	+	12.7785i	1.60149	+	0.924619i	0.991190	+	0.132446i	$0.0422831\pi$
$191$	22.1330	+	12.7785i	1.60149	+	0.924619i	0.610297	+	0.792173i	$0.291050\pi$
$192$	−1.24918	+	13.8000i	−0.0901521	+	0.995928i
$193$	4.73852	−	17.6844i	0.341086	−	1.27295i	−0.556032	−	0.831161i	$-0.687677\pi$
$193$	4.73852	−	17.6844i	0.341086	−	1.27295i	0.897119	−	0.441790i	$-0.145656\pi$
$194$	−6.72130	−	16.0711i	−0.482561	−	1.15384i
$195$	5.99207	−	6.14619i	0.429101	−	0.440138i
$196$	−2.81387	+	2.85260i	−0.200991	+	0.203757i
$197$	−19.6027			−1.39663			−0.698317	−	0.715789i	$-0.746067\pi$
$197$	−19.6027			−1.39663			−0.698317	+	0.715789i	$0.746067\pi$
$198$	1.08014	+	6.12473i	0.0767621	+	0.435265i
$199$	−7.28635			−0.516515			−0.258258	−	0.966076i	$-0.583148\pi$
$199$	−7.28635			−0.516515			−0.258258	+	0.966076i	$0.583148\pi$
$200$	−13.0406	−	5.47203i	−0.922109	−	0.386931i
$201$	15.5609	+	6.08166i	1.09758	+	0.428967i
$202$	−10.5507	+	4.41253i	−0.742343	+	0.310465i
$203$	2.01070	−	1.16088i	0.141124	−	0.0814778i
$204$	22.4940	−	3.58062i	1.57490	−	0.250694i
$205$	−1.48666	−	11.9791i	−0.103833	−	0.836657i
$206$	−1.51313	−	0.193950i	−0.105425	−	0.0135131i
$207$	−2.86059	−	1.50147i	−0.198825	−	0.104359i
$208$	−4.32728	+	7.73740i	−0.300043	+	0.536492i
$209$	−5.99991	+	10.3921i	−0.415022	+	0.718840i
$210$	−9.59185	+	7.60874i	−0.661901	+	0.525053i
$211$	−4.95012	+	18.4741i	−0.340781	+	1.27181i	0.556684	+	0.830724i	$0.312073\pi$
$211$	−4.95012	+	18.4741i	−0.340781	+	1.27181i	−0.897465	+	0.441086i	$0.854593\pi$
$212$	−3.32132	−	12.0649i	−0.228110	−	0.828623i
$213$	19.7512	−	15.7971i	1.35333	−	1.08240i
$214$	−9.34850	+	1.26327i	−0.639050	+	0.0863551i
$215$	−15.3395	+	11.5904i	−1.04614	+	0.790461i
$216$	−11.0997	−	9.63311i	−0.755238	−	0.655450i
$217$	−1.23261	−	1.23261i	−0.0836748	−	0.0836748i
$218$	9.29151	−	12.1950i	0.629300	−	0.825949i
$219$	−0.519487	+	4.67028i	−0.0351036	+	0.315589i
$220$	6.50008	−	0.851835i	0.438235	−	0.0574307i
$221$	14.0762	+	3.77171i	0.946867	+	0.253712i
$222$	−5.10875	−	4.87372i	−0.342877	−	0.327103i
$223$	−3.77576	+	1.01171i	−0.252844	+	0.0677493i	−0.383015	−	0.923742i	$-0.625114\pi$
$223$	−3.77576	+	1.01171i	−0.252844	+	0.0677493i	0.130171	+	0.991492i	$0.458447\pi$
$224$	7.52513	−	10.1618i	0.502794	−	0.678964i
$225$	12.7958	−	7.82741i	0.853051	−	0.521827i
$226$	−4.47885	−	0.574089i	−0.297929	−	0.0381878i
$227$	9.72719	+	5.61599i	0.645616	+	0.372747i	0.786775	−	0.617240i	$-0.211749\pi$
$227$	9.72719	+	5.61599i	0.645616	+	0.372747i	−0.141159	+	0.989987i	$0.545083\pi$
$228$	−4.45781	−	28.0047i	−0.295226	−	1.85465i
$229$	4.20912	−	15.7087i	0.278147	−	1.03806i	−0.675557	−	0.737308i	$-0.736097\pi$
$229$	4.20912	−	15.7087i	0.278147	−	1.03806i	0.953703	−	0.300749i	$-0.0972367\pi$
$230$	−1.71454	+	2.94236i	−0.113053	+	0.194013i
$231$	2.06594	−	5.28603i	0.135929	−	0.347795i
$232$	2.31228	−	1.81224i	0.151809	−	0.118979i
$233$	−8.36652	−	8.36652i	−0.548109	−	0.548109i	0.377784	−	0.925894i	$-0.376686\pi$
$233$	−8.36652	−	8.36652i	−0.548109	−	0.548109i	−0.925894	+	0.377784i	$0.876686\pi$
$234$	−3.97414	−	8.52191i	−0.259797	−	0.557095i
$235$	−1.78772	−	0.248877i	−0.116618	−	0.0162350i
$236$	−12.6644	+	0.0865510i	−0.824382	+	0.00563399i
$237$	28.0933	−	4.27526i	1.82485	−	0.277708i
$238$	−19.2304	−	7.88861i	−1.24652	−	0.511343i
$239$	−9.16156	−	15.8683i	−0.592612	−	1.02643i	−0.993879	−	0.110473i	$-0.964763\pi$
$239$	−9.16156	−	15.8683i	−0.592612	−	1.02643i	0.401267	−	0.915961i	$-0.368570\pi$
$240$	−10.6619	+	11.2394i	−0.688221	+	0.725501i
$241$	−5.48403	+	9.49861i	−0.353257	+	0.611859i	−0.986818	−	0.161833i	$-0.948259\pi$
$241$	−5.48403	+	9.49861i	−0.353257	+	0.611859i	0.633561	+	0.773693i	$0.281593\pi$
$242$	9.90466	−	7.65403i	0.636696	−	0.492019i
$243$	15.1726	−	3.57678i	0.973320	−	0.229451i
$244$	0.939380	−	0.550945i	0.0601377	−	0.0352707i
$245$	−4.44574	+	0.551736i	−0.284028	+	0.0352491i
$246$	−12.8496	−	3.12081i	−0.819259	−	0.198976i
$247$	4.69570	−	17.5246i	0.298780	−	1.11506i
$248$	−1.76358	−	1.32474i	−0.111988	−	0.0841214i
$249$	3.20895	+	21.0864i	0.203359	+	1.33630i
$250$	−7.64602	−	13.8397i	−0.483577	−	0.875302i
$251$	−0.464950	−	0.464950i	−0.0293474	−	0.0293474i	0.692281	−	0.721628i	$-0.256606\pi$
$251$	−0.464950	−	0.464950i	−0.0293474	−	0.0293474i	−0.721628	+	0.692281i	$0.756606\pi$
$252$	4.07706	+	12.7771i	0.256831	+	0.804880i
$253$		−	1.57862i		−	0.0992467i
$254$	−0.557484	+	0.731690i	−0.0349796	+	0.0459103i
$255$	22.2139	+	12.4518i	1.39109	+	0.779765i
$256$	7.61827	−	14.0699i	0.476142	−	0.879368i
$257$	−6.90170	+	25.7575i	−0.430516	+	1.60671i	0.321057	+	0.947060i	$0.395962\pi$
$257$	−6.90170	+	25.7575i	−0.430516	+	1.60671i	−0.751574	+	0.659649i	$0.770705\pi$
$258$	5.92831	+	20.2094i	0.369081	+	1.25818i
$259$	1.66763	+	6.22367i	0.103621	+	0.386720i
$260$	−9.15941	+	3.78760i	−0.568043	+	0.234897i
$261$	0.125373	+	3.11352i	0.00776037	+	0.192722i
$262$	−25.0580	−	3.21187i	−1.54809	−	0.198430i
$263$	8.20381	−	2.19821i	0.505869	−	0.135547i	0.00314640	−	0.999995i	$-0.498998\pi$
$263$	8.20381	−	2.19821i	0.505869	−	0.135547i	0.502722	+	0.864448i	$0.332332\pi$
$264$	1.64716	−	6.98991i	0.101375	−	0.430199i
$265$	5.44989	−	12.8857i	0.334784	−	0.791561i
$266$	−9.82117	+	23.9415i	−0.602175	+	1.46795i
$267$	4.37948	+	5.47570i	0.268020	+	0.335107i
$268$	−13.7342	−	13.5478i	−0.838950	−	0.827561i
$269$	3.78103	+	3.78103i	0.230534	+	0.230534i	0.812915	−	0.582382i	$-0.197879\pi$
$269$	3.78103	+	3.78103i	0.230534	+	0.230534i	−0.582382	+	0.812915i	$0.697879\pi$
$270$	−3.05902	−	16.1444i	−0.186166	−	0.982518i
$271$	−9.93541			−0.603533			−0.301767	−	0.953382i	$-0.597576\pi$
$271$	−9.93541			−0.603533			−0.301767	+	0.953382i	$0.597576\pi$
$272$	−25.4954	−	6.45931i	−1.54588	−	0.391653i
$273$	−0.948610	+	8.52818i	−0.0574125	+	0.516149i
$274$	−10.5476	−	25.2200i	−0.637201	−	1.52359i
$275$	6.29236	+	3.75859i	0.379443	+	0.226652i
$276$	2.34992	+	2.89731i	0.141449	+	0.174398i
$277$	−21.2228	−	12.2530i	−1.27516	−	0.736211i	−0.299202	−	0.954190i	$-0.596720\pi$
$277$	−21.2228	−	12.2530i	−1.27516	−	0.736211i	−0.975954	+	0.217978i	$0.930054\pi$
$278$	−0.777361	+	6.06471i	−0.0466230	+	0.363737i
$279$	2.23360	−	0.695942i	0.133722	−	0.0416650i
$280$	13.6452	−	3.69755i	0.815454	−	0.220971i
$281$	−5.85897	+	10.1480i	−0.349517	+	0.605381i	−0.986164	−	0.165775i	$-0.946988\pi$
$281$	−5.85897	+	10.1480i	−0.349517	+	0.605381i	0.636647	+	0.771155i	$0.280321\pi$
$282$	−0.948038	+	1.73513i	−0.0564548	+	0.103325i
$283$	15.2788	+	26.4637i	0.908231	+	1.57310i	0.816520	+	0.577317i	$0.195900\pi$
$283$	15.2788	+	26.4637i	0.908231	+	1.57310i	0.0917107	+	0.995786i	$0.470766\pi$
$284$	−28.1566	+	7.75117i	−1.67079	+	0.459947i
$285$	15.5023	−	27.6558i	0.918278	−	1.63819i
$286$	2.78454	−	3.65467i	0.164653	−	0.216105i
$287$	8.53255	+	8.53255i	0.503660	+	0.503660i
$288$	7.38206	+	15.2809i	0.434992	+	0.900434i
$289$			26.2336i			1.54315i
$290$	3.28457	+	0.0131692i	0.192877	+	0.000773322i
$291$	−17.1841	−	12.6447i	−1.00735	−	0.741248i
$292$	2.68084	−	4.71752i	0.156884	−	0.276072i
$293$	−4.29905	+	2.48206i	−0.251153	+	0.145003i	−0.620292	−	0.784371i	$-0.712986\pi$
$293$	−4.29905	+	2.48206i	−0.251153	+	0.145003i	0.369139	+	0.929374i	$0.379653\pi$
$294$	−1.15821	+	4.76879i	−0.0675481	+	0.278121i
$295$	−11.1692	−	8.70298i	−0.650297	−	0.506707i
$296$	3.19703	+	7.49993i	0.185824	+	0.435924i
$297$	4.99306	+	5.75220i	0.289727	+	0.333776i
$298$	3.46535	+	0.444181i	0.200743	+	0.0257307i
$299$	0.617735	+	2.30542i	0.0357245	+	0.133326i
$300$	−17.1437	+	2.46846i	−0.989792	+	0.142517i
$301$	4.97433	−	18.5645i	0.286716	−	1.07004i
$302$	4.97904	+	2.04248i	0.286512	+	0.117532i
$303$	−8.30128	+	11.2814i	−0.476896	+	0.648099i
$304$	−8.04172	+	31.7413i	−0.461224	+	1.82049i
$305$	1.20594	+	0.167885i	0.0690518	+	0.00961305i
$306$	21.3693	−	17.9320i	1.22160	−	1.02511i
$307$	9.85920			0.562694			0.281347	−	0.959606i	$-0.409219\pi$
$307$	9.85920			0.562694			0.281347	+	0.959606i	$0.409219\pi$
$308$	−4.60217	+	4.66551i	−0.262233	+	0.265842i
$309$	−1.71141	+	0.749579i	−0.0973585	+	0.0426421i
$310$	−0.628709	−	2.38457i	−0.0357082	−	0.135435i
$311$	14.2751	+	24.7252i	0.809465	+	1.40203i	0.913235	+	0.407433i	$0.133576\pi$
$311$	14.2751	+	24.7252i	0.809465	+	1.40203i	−0.103770	+	0.994601i	$0.533091\pi$
$312$	0.329738	+	10.8527i	0.0186678	+	0.614411i
$313$	4.95494	+	18.4921i	0.280070	+	1.04523i	0.952367	+	0.304954i	$0.0986410\pi$
$313$	4.95494	+	18.4921i	0.280070	+	1.04523i	−0.672297	+	0.740281i	$0.734692\pi$
$314$	−19.7750	−	25.5898i	−1.11597	−	1.44412i
$315$	−5.28061	+	14.0342i	−0.297529	+	0.790740i
$316$	−31.7520	−	8.27577i	−1.78619	−	0.465548i
$317$	−26.9859	−	15.5803i	−1.51568	−	0.875079i	−0.999831	−	0.0184012i	$-0.994142\pi$
$317$	−26.9859	−	15.5803i	−1.51568	−	0.875079i	−0.515851	−	0.856678i	$-0.672524\pi$
$318$	−11.0893	−	10.5791i	−0.621857	−	0.593248i
$319$	−1.31860	+	0.761296i	−0.0738276	+	0.0426244i
$320$	16.4359	−	7.06116i	0.918797	−	0.394731i
$321$	−9.02270	+	7.21639i	−0.503598	+	0.402780i
$322$	−0.455878	−	3.37362i	−0.0254051	−	0.188004i
$323$	53.8250			2.99490
$324$	−17.7267	−	3.12463i	−0.984818	−	0.173591i
$325$	−10.6602	−	3.02678i	−0.591321	−	0.167896i
$326$	0.518578	+	3.83761i	0.0287214	+	0.212546i
$327$	2.07580	−	18.6619i	0.114792	−	1.03200i
$328$	12.2082	+	9.17036i	0.674083	+	0.506349i
$329$	1.56260	−	0.902168i	0.0861489	−	0.0497381i
$330$	6.29026	−	4.98975i	0.346267	−	0.274677i
$331$	1.15114	+	4.29613i	0.0632726	+	0.236136i	0.990319	−	0.138810i	$-0.0443278\pi$
$331$	1.15114	+	4.29613i	0.0632726	+	0.236136i	−0.927046	+	0.374946i	$0.877661\pi$
$332$	6.21168	−	23.8326i	0.340910	−	1.30799i
$333$	−8.43609	−	1.90024i	−0.462295	−	0.104133i
$334$	31.2990	+	4.01183i	1.71260	+	0.219518i
$335$	−2.65641	−	21.4046i	−0.145135	−	1.16946i
$336$	1.50152	−	15.4136i	0.0819147	−	0.840882i
$337$	29.6691	+	7.94982i	1.61618	+	0.433054i	0.949876	−	0.312625i	$-0.101208\pi$
$337$	29.6691	+	7.94982i	1.61618	+	0.433054i	0.666304	+	0.745680i	$0.267875\pi$
$338$	4.34104	−	10.5823i	0.236121	−	0.575603i
$339$	−5.06574	+	2.21874i	−0.275133	+	0.120506i
$340$	−17.8870	−	23.3394i	−0.970058	−	1.26576i
$341$	0.808333	+	0.808333i	0.0437737	+	0.0437737i
$342$	−22.3250	−	26.6044i	−1.20720	−	1.43860i
$343$	14.2308	−	14.2308i	0.768391	−	0.768391i
$344$	2.92696	−	24.1424i	0.157811	−	1.30167i
$345$	0.0529524	+	4.17048i	0.00285086	+	0.224531i
$346$	5.57151	−	13.5819i	0.299526	−	0.730167i
$347$	4.39067	+	7.60487i	0.235704	+	0.408251i	0.959477	−	0.281787i	$-0.0909272\pi$
$347$	4.39067	+	7.60487i	0.235704	+	0.408251i	−0.723773	+	0.690038i	$0.757594\pi$
$348$	1.28683	−	3.36011i	0.0689815	−	0.180121i
$349$	5.26215	+	19.6386i	0.281676	+	1.05123i	0.951234	+	0.308470i	$0.0998170\pi$
$349$	5.26215	+	19.6386i	0.281676	+	1.05123i	−0.669558	+	0.742760i	$0.733516\pi$
$350$	14.5327	+	6.21527i	0.776803	+	0.332220i
$351$	−9.54281	−	6.44669i	−0.509358	−	0.344099i
$352$	−4.93492	+	6.66402i	−0.263032	+	0.355194i
$353$	1.31532	+	4.90885i	0.0700075	+	0.261272i	0.992055	−	0.125805i	$-0.0401515\pi$
$353$	1.31532	+	4.90885i	0.0700075	+	0.261272i	−0.922047	+	0.387077i	$0.873485\pi$
$354$	−13.2467	+	8.06954i	−0.704053	+	0.428891i
$355$	−30.0721	−	12.7187i	−1.59606	−	0.675040i
$356$	−2.14888	−	7.80597i	−0.113891	−	0.413715i
$357$	−25.1672	+	3.82997i	−1.33199	+	0.202704i
$358$	1.21085	+	0.922563i	0.0639955	+	0.0487590i
$359$		−	18.3813i		−	0.970128i	−0.874479	−	0.485064i	$-0.838796\pi$
$359$		−	18.3813i		−	0.970128i	0.874479	−	0.485064i	$-0.161204\pi$
$360$	−4.11708	+	18.5216i	−0.216989	+	0.976174i
$361$		−	48.0111i		−	2.52690i
$362$	−13.9110	+	18.2580i	−0.731144	+	0.959617i
$363$	5.58061	−	14.2789i	0.292906	−	0.749447i
$364$	4.89536	−	8.61444i	0.256587	−	0.451519i
$365$	5.62180	−	2.27986i	0.294258	−	0.119333i
$366$	0.639516	−	1.17046i	0.0334281	−	0.0611811i
$367$	5.49141	+	20.4942i	0.286649	+	1.06979i	0.947626	+	0.319383i	$0.103476\pi$
$367$	5.49141	+	20.4942i	0.286649	+	1.06979i	−0.660977	+	0.750407i	$0.729858\pi$
$368$	−1.17165	−	4.14519i	−0.0610767	−	0.216083i
$369$	−15.4618	+	4.81756i	−0.804910	+	0.250792i
$370$	−2.39448	+	8.79510i	−0.124483	+	0.457236i
$371$	3.61983	+	13.5094i	0.187932	+	0.701373i
$372$	−2.68686	−	0.280290i	−0.139307	−	0.0145323i
$373$	−8.44164	−	14.6214i	−0.437092	−	0.757065i	0.560372	−	0.828241i	$-0.310658\pi$
$373$	−8.44164	−	14.6214i	−0.437092	−	0.757065i	−0.997464	+	0.0711759i	$0.977325\pi$
$374$	12.6111	+	5.17328i	0.652106	+	0.267504i
$375$	−16.7496	−	9.71860i	−0.864945	−	0.501866i
$376$	1.79697	−	1.40836i	0.0926717	−	0.0726308i
$377$	1.62779	−	1.62779i	0.0838354	−	0.0838354i
$378$	12.3317	+	10.8510i	0.634273	+	0.558113i
$379$	13.2084	+	13.2084i	0.678469	+	0.678469i	0.959654	−	0.281185i	$-0.0907274\pi$
$379$	13.2084	+	13.2084i	0.678469	+	0.678469i	−0.281185	+	0.959654i	$0.590727\pi$
$380$	−29.0571	+	22.2690i	−1.49060	+	1.14237i
$381$	−0.124547	+	1.11970i	−0.00638072	+	0.0573639i
$382$	−33.4389	−	13.7172i	−1.71088	−	0.701831i
$383$	−27.2178	−	7.29299i	−1.39077	−	0.372655i	−0.515746	−	0.856742i	$-0.672485\pi$
$383$	−27.2178	−	7.29299i	−1.39077	−	0.372655i	−0.875020	+	0.484087i	$0.839152\pi$
$384$	−0.862765	−	19.5769i	−0.0440278	−	0.999030i
$385$	−7.27114	+	0.902382i	−0.370572	+	0.0459896i
$386$	−3.29182	+	25.6816i	−0.167549	+	1.30716i
$387$	18.9584	+	17.4907i	0.963712	+	0.889104i
$388$	12.4633	+	21.2504i	0.632729	+	1.07882i
$389$	3.93727	+	14.6941i	0.199627	+	0.745020i	0.991020	+	0.133712i	$0.0426896\pi$
$389$	3.93727	+	14.6941i	0.199627	+	0.745020i	−0.791393	+	0.611308i	$0.790644\pi$
$390$	−7.23377	+	9.74853i	−0.366296	+	0.493636i
$391$	−6.13220	+	3.54043i	−0.310119	+	0.179047i
$392$	3.40334	−	4.53074i	0.171895	−	0.228837i
$393$	−28.3414	+	12.4133i	−1.42964	+	0.626167i
$394$	27.4727	−	3.71239i	1.38405	−	0.187028i
$395$	−22.1161	−	29.2699i	−1.11278	−	1.47273i
$396$	−2.67370	−	8.37910i	−0.134359	−	0.421065i
$397$	−5.64875			−0.283503			−0.141751	−	0.989902i	$-0.545273\pi$
$397$	−5.64875			−0.283503			−0.141751	+	0.989902i	$0.545273\pi$
$398$	10.2116	−	1.37990i	0.511863	−	0.0691682i
$399$	4.76825	+	31.3327i	0.238711	+	1.56860i
$400$	19.3124	+	5.19926i	0.965619	+	0.259963i
$401$	4.25898	−	2.45892i	0.212683	−	0.122793i	−0.389874	−	0.920868i	$-0.627482\pi$
$401$	4.25898	−	2.45892i	0.212683	−	0.122793i	0.602558	+	0.798075i	$0.294148\pi$
$402$	−22.9600	−	5.57635i	−1.14514	−	0.278123i
$403$	−1.49681	−	0.864182i	−0.0745612	−	0.0430480i
$404$	13.9509	−	8.18217i	0.694082	−	0.407078i
$405$	−13.3839	−	15.0290i	−0.665052	−	0.746797i
$406$	−2.59810	+	2.00774i	−0.128942	+	0.0996423i
$407$	−1.09362	−	4.08143i	−0.0542085	−	0.202309i
$408$	−30.8468	+	9.27812i	−1.52714	+	0.459336i
$409$	15.2552	+	26.4227i	0.754319	+	1.30652i	0.945712	+	0.325005i	$0.105366\pi$
$409$	15.2552	+	26.4227i	0.754319	+	1.30652i	−0.191393	+	0.981513i	$0.561301\pi$
$410$	4.35215	+	16.5069i	0.214937	+	0.815217i
$411$	−26.9666	−	19.8431i	−1.33017	−	0.978786i
$412$	2.15735	−	0.0147437i	0.106285	−	0.000726372i
$413$	14.1547			0.696506
$414$	4.29341	+	1.56253i	0.211009	+	0.0767941i
$415$	21.9696	−	16.6001i	1.07844	−	0.814866i
$416$	4.59925	−	11.6633i	0.225497	−	0.571839i
$417$	3.00435	+	6.85940i	0.147124	+	0.335906i
$418$	6.44064	−	15.7006i	0.315022	−	0.767942i
$419$	0.388961	−	1.45162i	0.0190020	−	0.0709163i	−0.955774	−	0.294103i	$-0.904979\pi$
$419$	0.388961	−	1.45162i	0.0190020	−	0.0709163i	0.974776	+	0.223186i	$0.0716459\pi$
$420$	12.0018	−	12.4800i	0.585628	−	0.608961i
$421$	1.79941	+	6.71550i	0.0876980	+	0.327293i	0.995811	−	0.0914309i	$-0.0291441\pi$
$421$	1.79941	+	6.71550i	0.0876980	+	0.327293i	−0.908113	+	0.418724i	$0.862477\pi$
$422$	3.43882	−	26.8285i	0.167399	−	1.30599i
$423$	0.0974322	+	2.41964i	0.00473732	+	0.117647i
$424$	6.93964	+	16.2797i	0.337019	+	0.790613i
$425$	0.488287	−	32.8725i	0.0236854	−	1.59455i
$426$	−24.6892	+	25.8798i	−1.19619	+	1.25388i
$427$	−1.05408	+	0.608574i	−0.0510105	+	0.0294510i
$428$	12.8625	−	3.54087i	0.621730	−	0.171155i
$429$	0.622091	−	5.59271i	0.0300348	−	0.270019i
$430$	19.3029	−	19.1487i	0.930869	−	0.923434i
$431$		−	6.93010i		−	0.333811i	−0.985973	−	0.166906i	$-0.946623\pi$
$431$		−	6.93010i		−	0.333811i	0.985973	−	0.166906i	$-0.0533775\pi$
$432$	17.3803	+	11.3985i	0.836209	+	0.548410i
$433$	−13.5818	−	13.5818i	−0.652699	−	0.652699i	0.300943	−	0.953642i	$-0.402699\pi$
$433$	−13.5818	−	13.5818i	−0.652699	−	0.652699i	−0.953642	+	0.300943i	$0.902699\pi$
$434$	1.96090	+	1.49403i	0.0941263	+	0.0717160i
$435$	3.45802	−	2.05547i	0.165800	−	0.0985520i
$436$	−10.7123	+	18.8506i	−0.513027	+	0.902781i
$437$	4.40777	+	7.63448i	0.210852	+	0.365207i
$438$	−0.156419	−	6.64367i	−0.00747401	−	0.317447i
$439$	−10.3987	+	18.0110i	−0.496302	+	0.859620i	−0.999991	−	0.00426498i	$-0.998642\pi$
$439$	−10.3987	+	18.0110i	−0.496302	+	0.859620i	0.503689	+	0.863885i	$0.331976\pi$
$440$	−8.94838	+	2.42482i	−0.426597	+	0.115599i
$441$	1.78791	+	5.73825i	0.0851388	+	0.273250i
$442$	−20.4417	−	2.62018i	−0.972315	−	0.124629i
$443$	−21.6818	−	12.5180i	−1.03013	−	0.594749i	−0.113111	−	0.993582i	$-0.536082\pi$
$443$	−21.6818	−	12.5180i	−1.03013	−	0.594749i	−0.917023	+	0.398834i	$0.869415\pi$
$444$	8.08278	+	5.86289i	0.383592	+	0.278241i
$445$	3.52606	−	8.33699i	0.167151	−	0.395211i
$446$	5.10004	−	2.13295i	0.241494	−	0.100998i
$447$	3.91944	−	1.71667i	0.185383	−	0.0811959i
$448$	−8.62182	+	15.6666i	−0.407343	+	0.740179i
$449$	−16.2299			−0.765937			−0.382969	−	0.923761i	$-0.625098\pi$
$449$	−16.2299			−0.765937			−0.382969	+	0.923761i	$0.625098\pi$
$450$	−16.4506	+	13.3932i	−0.775488	+	0.631362i
$451$	−5.59557	−	5.59557i	−0.263485	−	0.263485i
$452$	6.38572	−	0.0436413i	0.300359	−	0.00205271i
$453$	6.51618	−	0.991640i	0.306157	−	0.0465913i
$454$	−14.6960	−	6.02853i	−0.689717	−	0.282933i
$455$	10.2657	−	4.16315i	0.481263	−	0.195171i
$456$	11.5511	+	38.4036i	0.540929	+	1.79841i
$457$	25.6238	−	6.86587i	1.19863	−	0.321172i	0.396339	−	0.918104i	$-0.370281\pi$
$457$	25.6238	−	6.86587i	1.19863	−	0.321172i	0.802292	+	0.596932i	$0.203614\pi$
$458$	−2.92405	+	22.8124i	−0.136632	+	1.06596i
$459$	11.1465	−	32.2965i	0.520275	−	1.50747i
$460$	1.84565	−	4.44835i	0.0860541	−	0.207405i
$461$	4.87390	+	18.1896i	0.227000	+	0.847176i	0.981593	+	0.190983i	$0.0611675\pi$
$461$	4.87390	+	18.1896i	0.227000	+	0.847176i	−0.754593	+	0.656193i	$0.772166\pi$
$462$	−1.89429	+	7.79950i	−0.0881302	+	0.362866i
$463$	9.94857	−	37.1286i	0.462349	−	1.72551i	−0.203182	−	0.979141i	$-0.565128\pi$
$463$	9.94857	−	37.1286i	0.462349	−	1.72551i	0.665531	−	0.746370i	$-0.268205\pi$
$464$	−2.89741	+	2.97771i	−0.134509	+	0.138237i
$465$	−2.16262	−	2.10839i	−0.100289	−	0.0977741i
$466$	13.3099	+	10.1410i	0.616571	+	0.469773i
$467$			13.0750i			0.605040i	0.953143	+	0.302520i	$0.0978280\pi$
$467$			13.0750i			0.605040i	−0.953143	+	0.302520i	$0.902172\pi$
$468$	7.18355	+	11.1906i	0.332060	+	0.517287i
$469$	15.2462	+	15.2462i	0.704003	+	0.704003i
$470$	2.55257	+	0.0102343i	0.117741	+	0.000472074i
$471$	−36.8911	−	14.4181i	−1.69985	−	0.664353i
$472$	17.7325	−	2.51971i	0.816203	−	0.115979i
$473$	−3.26213	+	12.1744i	−0.149993	+	0.559780i
$474$	−38.5624	+	11.3120i	−1.77123	+	0.519579i
$475$	−40.9256	−	0.607908i	−1.87780	−	0.0278927i
$476$	28.4449	+	7.41381i	1.30377	+	0.339811i
$477$	−18.3118	−	4.12476i	−0.838440	−	0.188860i
$478$	15.8449	+	20.5040i	0.724727	+	0.937830i
$479$	4.80946	−	8.33023i	0.219750	−	0.380618i	−0.734982	−	0.678087i	$-0.762809\pi$
$479$	4.80946	−	8.33023i	0.219750	−	0.380618i	0.954731	+	0.297469i	$0.0961426\pi$
$480$	12.8138	−	17.7709i	0.584868	−	0.811129i
$481$	3.19425	+	5.53260i	0.145645	+	0.252265i
$482$	5.88686	−	14.3506i	0.268139	−	0.653654i
$483$	−2.60420	−	3.25605i	−0.118495	−	0.148155i
$484$	−12.4316	+	12.6027i	−0.565073	+	0.572850i
$485$	−3.79784	+	27.2803i	−0.172451	+	1.23874i
$486$	−20.5866	+	7.88618i	−0.933827	+	0.357725i
$487$	10.6422	+	10.6422i	0.482242	+	0.482242i	0.905847	−	0.423605i	$-0.139236\pi$
$487$	10.6422	+	10.6422i	0.482242	+	0.482242i	−0.423605	+	0.905847i	$0.639236\pi$
$488$	−1.21218	+	0.950038i	−0.0548728	+	0.0430062i
$489$	2.96237	+	3.70387i	0.133963	+	0.167495i
$490$	6.12610	−	1.61519i	0.276749	−	0.0729667i
$491$	−3.53518	+	13.1935i	−0.159541	+	0.595413i	0.839133	+	0.543926i	$0.183063\pi$
$491$	−3.53518	+	13.1935i	−0.159541	+	0.595413i	−0.998674	+	0.0514873i	$0.983604\pi$
$492$	18.5994	+	1.94027i	0.838525	+	0.0874740i
$493$	5.91457	+	3.41478i	0.266379	+	0.153794i
$494$	−3.26207	+	25.4496i	−0.146768	+	1.14503i
$495$	3.46298	−	9.20354i	0.155649	−	0.413668i
$496$	2.72250	+	1.52261i	0.122244	+	0.0683671i
$497$	31.5277	−	8.44782i	1.41421	−	0.378937i
$498$	−8.49066	−	28.9444i	−0.380475	−	1.29703i
$499$	−37.5672	−	10.0661i	−1.68174	−	0.450621i	−0.713502	−	0.700653i	$-0.752892\pi$
$499$	−37.5672	−	10.0661i	−1.68174	−	0.450621i	−0.968237	+	0.250032i	$0.919559\pi$
$500$	13.3367	+	17.9480i	0.596436	+	0.802661i
$501$	35.4003	−	15.5050i	1.58157	−	0.692711i
$502$	0.739670	+	0.563563i	0.0330131	+	0.0251531i
$503$	−6.54350	−	6.54350i	−0.291760	−	0.291760i	0.546015	−	0.837775i	$-0.316144\pi$
$503$	−6.54350	−	6.54350i	−0.291760	−	0.291760i	−0.837775	+	0.546015i	$0.816144\pi$
$504$	−8.13365	−	17.1346i	−0.362301	−	0.763237i
$505$	17.9095	+	2.49328i	0.796965	+	0.110950i
$506$	0.298961	+	2.21239i	0.0132904	+	0.0983528i
$507$	−2.10760	−	13.8493i	−0.0936020	−	0.615069i
$508$	0.642731	−	1.13102i	0.0285166	−	0.0501810i
$509$	1.07806	−	4.02338i	0.0477842	−	0.178333i	−0.937909	−	0.346880i	$-0.887241\pi$
$509$	1.07806	−	4.02338i	0.0477842	−	0.178333i	0.985694	+	0.168547i	$0.0539076\pi$
$510$	−33.4903	−	13.2441i	−1.48298	−	0.586457i
$511$	−3.03220	+	5.25193i	−0.134137	+	0.232332i
$512$	−8.01224	+	21.1614i	−0.354095	+	0.935210i
$513$	−40.2085	−	13.8772i	−1.77525	−	0.612694i
$514$	4.79456	−	37.4056i	0.211479	−	1.64989i
$515$	1.90265	+	1.48253i	0.0838407	+	0.0653281i
$516$	−12.1357	−	27.2003i	−0.534244	−	1.19743i
$517$	−1.02474	+	0.591634i	−0.0450680	+	0.0260200i
$518$	−3.51579	−	8.40650i	−0.154475	−	0.369361i
$519$	−2.70501	−	17.7749i	−0.118737	−	0.780232i
$520$	12.1194	−	7.04286i	0.531471	−	0.308850i
$521$	−33.5275			−1.46887			−0.734433	−	0.678681i	$-0.762552\pi$
$521$	−33.5275			−1.46887			−0.734433	+	0.678681i	$0.762552\pi$
$522$	−0.765351	−	4.33978i	−0.0334985	−	0.189947i
$523$	−7.73751			−0.338338			−0.169169	−	0.985587i	$-0.554108\pi$
$523$	−7.73751			−0.338338			−0.169169	+	0.985587i	$0.554108\pi$
$524$	35.7264	−	0.244161i	1.56071	−	0.0106662i
$525$	19.1790	−	2.62786i	0.837042	−	0.114689i
$526$	−11.0811	+	4.63439i	−0.483161	+	0.202069i
$527$	1.32712	−	4.95289i	0.0578104	−	0.215751i
$528$	−0.984686	+	10.1081i	−0.0428529	+	0.439900i
$529$	18.9142	+	10.9201i	0.822358	+	0.474789i
$530$	−5.19757	+	19.0911i	−0.225768	+	0.829264i
$531$	−8.82889	+	16.8208i	−0.383141	+	0.729959i
$532$	9.23005	−	35.4133i	0.400174	−	1.53536i
$533$	10.3614	+	5.98218i	0.448804	+	0.259117i
$534$	−7.17474	−	6.84466i	−0.310481	−	0.296197i
$535$	13.7375	+	5.81014i	0.593922	+	0.251194i
$536$	21.8139	+	16.3858i	0.942215	+	0.707761i
$537$	1.85296	+	0.206109i	0.0799610	+	0.00889425i
$538$	−6.01509	−	4.58297i	−0.259329	−	0.197586i
$539$	−2.07665	+	2.07665i	−0.0894478	+	0.0894478i
$540$	7.34460	+	22.0467i	0.316061	+	0.948739i
$541$	−11.0895	−	11.0895i	−0.476773	−	0.476773i	0.427325	−	0.904098i	$-0.359456\pi$
$541$	−11.0895	−	11.0895i	−0.476773	−	0.476773i	−0.904098	+	0.427325i	$0.859456\pi$
$542$	13.9242	−	1.88159i	0.598097	−	0.0808211i
$543$	−3.10783	+	27.9400i	−0.133370	+	1.19902i
$544$	36.9544	+	4.22421i	1.58441	+	0.181111i
$545$	−22.4640	+	9.11004i	−0.962252	+	0.390231i
$546$	−0.285630	−	12.1317i	−0.0122238	−	0.519189i
$547$	15.9692	−	27.6595i	0.682795	−	1.18264i	−0.291329	−	0.956623i	$-0.594098\pi$
$547$	15.9692	−	27.6595i	0.682795	−	1.18264i	0.974124	−	0.226013i	$-0.0725691\pi$
$548$	19.5583	+	33.3476i	0.835491	+	1.42454i
$549$	−0.0657247	−	1.63222i	−0.00280506	−	0.0696612i
$550$	−9.53040	−	4.07592i	−0.406377	−	0.173798i
$551$	4.25134	−	7.36353i	0.181113	−	0.313697i
$552$	−3.84206	−	3.61548i	−0.163529	−	0.153885i
$553$	35.4235	+	9.49171i	1.50636	+	0.403629i
$554$	32.0638	+	13.1531i	1.36226	+	0.558820i
$555$	3.02608	+	10.7459i	0.128450	+	0.456137i
$556$	−0.0590937	−	8.64676i	−0.00250613	−	0.366704i
$557$			4.01485i			0.170115i	0.996376	+	0.0850573i	$0.0271073\pi$
$557$			4.01485i			0.170115i	−0.996376	+	0.0850573i	$0.972893\pi$
$558$	−2.99854	+	1.39835i	−0.126938	+	0.0591969i
$559$		−	19.0561i		−	0.805988i
$560$	−18.4231	+	7.76617i	−0.778518	+	0.328181i
$561$	16.5044	−	2.51167i	0.696818	−	0.106043i
$562$	6.28935	−	15.3318i	0.265300	−	0.646733i
$563$	13.4214	+	23.2465i	0.565643	+	0.979723i	0.996990	+	0.0775363i	$0.0247054\pi$
$563$	13.4214	+	23.2465i	0.565643	+	0.979723i	−0.431346	+	0.902186i	$0.641961\pi$
$564$	1.00005	−	2.61128i	0.0421097	−	0.109955i
$565$	5.63181	+	4.38827i	0.236932	+	0.184616i
$566$	−26.4246	−	34.1947i	−1.11071	−	1.43731i
$567$	19.7879	+	3.62755i	0.831014	+	0.152343i
$568$	37.9929	−	16.1954i	1.59415	−	0.679545i
$569$	19.4820	+	11.2480i	0.816729	+	0.471539i	0.849287	−	0.527931i	$-0.177032\pi$
$569$	19.4820	+	11.2480i	0.816729	+	0.471539i	−0.0325580	+	0.999470i	$0.510365\pi$
$570$	−16.4886	+	41.6948i	−0.690632	+	1.74640i
$571$	−7.04471	−	1.88762i	−0.294812	−	0.0789946i	0.108382	−	0.994109i	$-0.465433\pi$
$571$	−7.04471	−	1.88762i	−0.294812	−	0.0789946i	−0.403193	+	0.915115i	$0.632100\pi$
$572$	−3.21034	+	5.64928i	−0.134231	+	0.236208i
$573$	−43.7621	+	6.65977i	−1.82819	+	0.278216i
$574$	−13.5741	−	10.3423i	−0.566571	−	0.431677i
$575$	4.70258	−	2.62269i	0.196111	−	0.109374i
$576$	−13.2397	−	20.0177i	−0.551654	−	0.834073i
$577$	17.6482	−	17.6482i	0.734705	−	0.734705i	−0.236843	−	0.971548i	$-0.576113\pi$
$577$	17.6482	−	17.6482i	0.734705	−	0.734705i	0.971548	+	0.236843i	$0.0761126\pi$
$578$	−4.96817	−	36.7657i	−0.206649	−	1.52925i
$579$	12.7222	+	29.0468i	0.528718	+	1.20715i
$580$	−4.60574	+	0.603582i	−0.191243	+	0.0250624i
$581$	−7.12435	+	26.5884i	−0.295568	+	1.10307i
$582$	26.4778	+	14.4669i	1.09754	+	0.599674i
$583$	−2.37386	−	8.85936i	−0.0983151	−	0.366917i
$584$	−2.86372	+	7.11919i	−0.118502	+	0.294594i
$585$	−1.45588	+	14.7960i	−0.0601930	+	0.611740i
$586$	5.55496	−	4.29271i	0.229473	−	0.177330i
$587$	14.0207	−	24.2846i	0.578697	−	1.00233i	−0.416932	−	0.908938i	$-0.636895\pi$
$587$	14.0207	−	24.2846i	0.578697	−	1.00233i	0.995629	−	0.0933954i	$-0.0297721\pi$
$588$	0.720080	−	6.90268i	0.0296956	−	0.284662i
$589$	−6.16625	−	1.65224i	−0.254076	−	0.0680795i
$590$	17.3016	+	10.0818i	0.712294	+	0.415060i
$591$	26.5153	−	21.2070i	1.09069	−	0.872340i
$592$	−5.90091	−	9.90550i	−0.242526	−	0.407114i
$593$	−2.70165	+	2.70165i	−0.110943	+	0.110943i	−0.760399	−	0.649456i	$-0.774997\pi$
$593$	−2.70165	+	2.70165i	−0.110943	+	0.110943i	0.649456	+	0.760399i	$0.274997\pi$
$594$	−8.08702	−	7.11597i	−0.331814	−	0.291972i
$595$	19.8126	+	26.2213i	0.812239	+	1.07497i
$596$	−4.94073	+	0.0337659i	−0.202380	+	0.00138311i
$597$	9.85576	−	7.88267i	0.403369	−	0.322616i
$598$	−1.30235	−	3.11400i	−0.0532569	−	0.127341i
$599$	30.9719	−	17.8816i	1.26548	−	0.730623i	0.291348	−	0.956617i	$-0.405896\pi$
$599$	30.9719	−	17.8816i	1.26548	−	0.730623i	0.974129	+	0.225994i	$0.0725629\pi$
$600$	23.5590	−	6.70620i	0.961793	−	0.273779i
$601$	34.0820	+	19.6773i	1.39023	+	0.802652i	0.993341	−	0.115213i	$-0.0367551\pi$
$601$	34.0820	+	19.6773i	1.39023	+	0.802652i	0.396893	+	0.917865i	$0.370088\pi$
$602$	−3.45563	+	26.9597i	−0.140841	+	1.09880i
$603$	−27.6276	+	8.60815i	−1.12508	+	0.350551i
$604$	−7.36482	−	1.91955i	−0.299670	−	0.0781054i
$605$	−19.6411	+	2.43756i	−0.798526	+	0.0991007i
$606$	9.49755	−	17.3827i	0.385812	−	0.706124i
$607$	−29.6614	−	7.94774i	−1.20392	−	0.322589i	−0.399545	−	0.916714i	$-0.630832\pi$
$607$	−29.6614	−	7.94774i	−1.20392	−	0.322589i	−0.804373	+	0.594125i	$0.797498\pi$
$608$	5.25906	−	46.0076i	0.213283	−	1.86585i
$609$	−1.46386	+	3.74551i	−0.0593185	+	0.151776i
$610$	−1.72189	−	0.00690376i	−0.0697171	−	0.000279525i
$611$	1.26502	−	1.26502i	0.0511773	−	0.0511773i
$612$	−26.5526	+	29.1783i	−1.07332	+	1.17946i
$613$	−43.6260			−1.76204			−0.881019	−	0.473081i	$-0.843142\pi$
$613$	−43.6260			−1.76204			−0.881019	+	0.473081i	$0.843142\pi$
$614$	−13.8174	+	1.86715i	−0.557626	+	0.0753522i
$615$	14.9704	+	14.5950i	0.603665	+	0.588528i
$616$	5.56627	−	7.41017i	0.224272	−	0.298564i
$617$	−16.7703	−	4.49358i	−0.675145	−	0.180905i	−0.0950739	−	0.995470i	$-0.530309\pi$
$617$	−16.7703	−	4.49358i	−0.675145	−	0.180905i	−0.580072	+	0.814566i	$0.696975\pi$
$618$	2.25654	−	1.37463i	0.0907713	−	0.0552956i
$619$	5.09110	−	1.36416i	0.204629	−	0.0548301i	−0.155049	−	0.987907i	$-0.549553\pi$
$619$	5.09110	−	1.36416i	0.204629	−	0.0548301i	0.359677	+	0.933077i	$0.382887\pi$
$620$	1.33271	+	3.22286i	0.0535231	+	0.129433i
$621$	5.49369	−	1.06377i	0.220454	−	0.0426876i
$622$	−24.6887	−	31.9483i	−0.989925	−	1.28101i
$623$	2.34202	+	8.74054i	0.0938310	+	0.350182i
$624$	−2.51742	−	15.1473i	−0.100777	−	0.606377i
$625$	−0.742535	+	24.9890i	−0.0297014	+	0.999559i
$626$	−10.4463	−	24.9778i	−0.417518	−	0.998315i
$627$	−3.12698	−	20.5477i	−0.124879	−	0.820597i
$628$	32.5605	+	32.1184i	1.29930	+	1.28167i
$629$	−13.4018	+	13.4018i	−0.534365	+	0.534365i
$630$	4.74281	−	20.6687i	0.188958	−	0.823461i
$631$		−	8.37151i		−	0.333265i	−0.986019	−	0.166632i	$-0.946711\pi$
$631$		−	8.37151i		−	0.333265i	0.986019	−	0.166632i	$-0.0532893\pi$
$632$	46.0670	+	5.58504i	1.83245	+	0.222161i
$633$	−13.2904	−	30.3440i	−0.528244	−	1.20606i
$634$	40.7708	+	16.7248i	1.61921	+	0.664228i
$635$	1.34782	−	0.546596i	0.0534867	−	0.0216910i
$636$	17.5449	+	12.7263i	0.695700	+	0.504630i
$637$	2.22013	−	3.84538i	0.0879648	−	0.152359i
$638$	1.70381	−	1.31666i	0.0674546	−	0.0521269i
$639$	−9.62621	+	42.7353i	−0.380807	+	1.69058i
$640$	−21.6973	+	13.0087i	−0.857662	+	0.514215i
$641$	−10.9054	−	6.29625i	−0.430738	−	0.248687i	0.268923	−	0.963162i	$-0.413332\pi$
$641$	−10.9054	−	6.29625i	−0.430738	−	0.248687i	−0.699661	+	0.714475i	$0.746666\pi$
$642$	11.2784	−	11.8223i	0.445125	−	0.466590i
$643$	2.51078	−	1.44960i	0.0990154	−	0.0571666i	−0.449675	−	0.893192i	$-0.648460\pi$
$643$	2.51078	−	1.44960i	0.0990154	−	0.0571666i	0.548690	+	0.836026i	$0.315127\pi$
$644$	1.27780	+	4.64171i	0.0503526	+	0.182909i
$645$	8.20970	−	32.2725i	0.323257	−	1.27073i
$646$	−75.4344	+	10.1935i	−2.96793	+	0.401057i
$647$	23.1875	−	23.1875i	0.911594	−	0.911594i	−0.0848039	−	0.996398i	$-0.527026\pi$
$647$	23.1875	−	23.1875i	0.911594	−	0.911594i	0.996398	+	0.0848039i	$0.0270264\pi$
$648$	25.4353	+	1.02197i	0.999194	+	0.0401469i
$649$	−9.28252			−0.364371
$650$	15.5132	+	2.22311i	0.608478	+	0.0871977i
$651$	3.00075	+	0.333781i	0.117609	+	0.0130819i
$652$	−1.45355	−	5.28011i	−0.0569254	−	0.206785i
$653$	−5.85460	−	10.1405i	−0.229108	−	0.396827i	0.728436	−	0.685114i	$-0.240248\pi$
$653$	−5.85460	−	10.1405i	−0.229108	−	0.396827i	−0.957544	+	0.288287i	$0.906914\pi$
$654$	0.625032	+	26.5473i	0.0244407	+	1.03808i
$655$	31.5084	+	24.5512i	1.23114	+	0.959294i
$656$	−18.8461	−	10.5400i	−0.735818	−	0.411519i
$657$	−4.34983	−	6.87919i	−0.169703	−	0.268383i
$658$	−2.01909	+	1.56029i	−0.0787124	+	0.0608266i
$659$	13.3128	−	3.56715i	0.518592	−	0.138956i	0.00997674	−	0.999950i	$-0.496824\pi$
$659$	13.3128	−	3.56715i	0.518592	−	0.138956i	0.508615	+	0.860994i	$0.330158\pi$
$660$	−7.87068	+	8.18427i	−0.306366	+	0.318572i
$661$	23.4882	+	6.29364i	0.913584	+	0.244794i	0.684841	−	0.728693i	$-0.259872\pi$
$661$	23.4882	+	6.29364i	0.913584	+	0.244794i	0.228743	+	0.973487i	$0.426538\pi$
$662$	−2.42691	−	5.80291i	−0.0943245	−	0.225537i
$663$	−23.1203	+	10.1265i	−0.897919	+	0.393280i
$664$	−4.19205	+	34.5772i	−0.162683	+	1.34186i
$665$	32.6450	−	24.6664i	1.26592	−	0.956520i
$666$	12.1829	+	1.06550i	0.472076	+	0.0412874i
$667$			1.11855i			0.0433106i
$668$	−44.6245	+	0.304973i	−1.72658	+	0.0117998i
$669$	4.01271	−	5.45325i	0.155140	−	0.210835i
$670$	7.77653	+	29.4949i	0.300434	+	1.13949i
$671$	0.691257	−	0.399098i	0.0266857	−	0.0154070i
$672$	0.814716	+	21.8862i	0.0314284	+	0.844278i
$673$	−8.64304	+	2.31590i	−0.333165	+	0.0892712i	−0.421523	−	0.906818i	$-0.638504\pi$
$673$	−8.64304	+	2.31590i	−0.333165	+	0.0892712i	0.0883588	+	0.996089i	$0.471838\pi$
$674$	−43.0861	−	5.52268i	−1.65962	−	0.212726i
$675$	−8.83998	+	24.4306i	−0.340251	+	0.940335i
$676$	−4.07976	+	15.6530i	−0.156914	+	0.602038i
$677$	−8.83626	+	15.3049i	−0.339605	+	0.588213i	−0.984358	−	0.176177i	$-0.943627\pi$
$677$	−8.83626	+	15.3049i	−0.339605	+	0.588213i	0.644753	+	0.764391i	$0.276960\pi$
$678$	6.67932	−	4.06887i	0.256518	−	0.156264i
$679$	−13.7670	−	23.8451i	−0.528328	−	0.915091i
$680$	29.4882	+	29.3221i	1.13082	+	1.12445i
$681$	−19.2329	+	2.92689i	−0.737008	+	0.112159i
$682$	−1.28594	−	0.979776i	−0.0492413	−	0.0375175i
$683$		−	14.4367i		−	0.552405i	−0.961099	−	0.276203i	$-0.910924\pi$
$683$		−	14.4367i		−	0.552405i	0.961099	−	0.276203i	$-0.0890761\pi$
$684$	36.3264	+	33.0574i	1.38897	+	1.26398i
$685$	−5.95985	+	42.8103i	−0.227714	+	1.63570i
$686$	−17.2491	+	22.6392i	−0.658572	+	0.864367i
$687$	11.3009	+	25.8017i	0.431155	+	0.984395i
$688$	0.470068	+	34.3893i	0.0179212	+	1.31108i
$689$	6.93359	+	12.0093i	0.264149	+	0.457519i
$690$	−0.864025	−	5.83480i	−0.0328929	−	0.222127i
$691$	−19.1210	+	5.12345i	−0.727396	+	0.194905i	−0.603469	−	0.797386i	$-0.706215\pi$
$691$	−19.1210	+	5.12345i	−0.727396	+	0.194905i	−0.123927	+	0.992291i	$0.539549\pi$
$692$	−5.23617	+	20.0898i	−0.199049	+	0.763701i
$693$	2.92419	+	9.38509i	0.111081	+	0.356510i
$694$	−7.59365	−	9.82653i	−0.288251	−	0.373010i
$695$	5.94206	−	7.62590i	0.225395	−	0.289267i
$696$	−1.16712	+	4.95282i	−0.0442396	+	0.187736i
$697$	−9.18682	+	34.2857i	−0.347976	+	1.29866i
$698$	−11.0940	−	26.5265i	−0.419913	−	1.00404i
$699$	20.3681	+	2.26559i	0.770392	+	0.0856925i
$700$	−21.5442	−	5.95832i	−0.814295	−	0.225203i
$701$	27.9884	−	27.9884i	1.05711	−	1.05711i	0.0588383	−	0.998268i	$-0.481260\pi$
$701$	27.9884	−	27.9884i	1.05711	−	1.05711i	0.998268	−	0.0588383i	$-0.0187396\pi$
$702$	14.5949	+	7.22764i	0.550849	+	0.272790i
$703$	16.6850	+	16.6850i	0.629286	+	0.629286i
$704$	5.65412	−	10.2741i	0.213098	−	0.387218i
$705$	2.68737	−	1.59739i	0.101212	−	0.0601610i
$706$	−2.77304	−	6.63053i	−0.104365	−	0.249543i
$707$	−15.6543	+	9.03802i	−0.588741	+	0.339910i
$708$	17.0367	−	13.8179i	0.640277	−	0.519310i
$709$	27.9392	−	7.48628i	1.04928	−	0.281153i	0.307325	−	0.951605i	$-0.400566\pi$
$709$	27.9392	−	7.48628i	1.04928	−	0.281153i	0.741953	+	0.670451i	$0.233900\pi$
$710$	44.5540	+	12.1299i	1.67208	+	0.455226i
$711$	−33.3747	+	36.1753i	−1.25165	+	1.35668i
$712$	4.48992	+	10.5329i	0.168267	+	0.394738i
$713$	0.811191	−	0.217358i	0.0303793	−	0.00814012i
$714$	34.5459	−	10.1338i	1.29285	−	0.379249i
$715$	−6.73216	+	2.73016i	−0.251768	+	0.102102i
$716$	−1.87170	−	1.06364i	−0.0699486	−	0.0397500i
$717$	29.5592	+	11.5526i	1.10391	+	0.431441i
$718$	3.48109	+	25.7610i	0.129913	+	0.961390i
$719$	−30.0959			−1.12239			−0.561193	−	0.827685i	$-0.689658\pi$
$719$	−30.0959			−1.12239			−0.561193	+	0.827685i	$0.689658\pi$
$720$	2.26234	−	26.7373i	0.0843123	−	0.996439i
$721$	−2.41122			−0.0897983
$722$	9.09244	+	67.2864i	0.338385	+	2.50414i
$723$	−2.85811	−	18.7810i	−0.106294	−	0.698473i
$724$	16.0382	−	28.2226i	0.596053	−	1.04888i
$725$	−4.45856	−	2.66322i	−0.165587	−	0.0989094i
$726$	−5.11693	+	21.0684i	−0.189907	+	0.781920i
$727$	−6.78971	+	1.81930i	−0.251816	+	0.0674740i	−0.382519	−	0.923948i	$-0.624943\pi$
$727$	−6.78971	+	1.81930i	−0.251816	+	0.0674740i	0.130703	+	0.991422i	$0.458277\pi$
$728$	−5.22931	+	13.0000i	−0.193811	+	0.481813i
$729$	−16.6534	+	21.2524i	−0.616793	+	0.787125i
$730$	−7.44705	+	4.25984i	−0.275628	+	0.157664i
$731$	54.6082	−	14.6322i	2.01976	−	0.541192i
$732$	−0.674602	+	1.76149i	−0.0249340	+	0.0651065i
$733$	−34.6563	+	20.0088i	−1.28006	+	0.739042i	−0.976859	−	0.213885i	$-0.931388\pi$
$733$	−34.6563	+	20.0088i	−1.28006	+	0.739042i	−0.303200	+	0.952927i	$0.598055\pi$
$734$	−11.5773	−	27.6822i	−0.427326	−	1.02177i
$735$	5.41656	−	5.55588i	0.199793	−	0.204932i
$736$	2.42707	+	5.58750i	0.0894629	+	0.205958i
$737$	−9.99832	−	9.99832i	−0.368293	−	0.368293i
$738$	20.7570	−	9.67989i	0.764076	−	0.356322i
$739$	4.51551	−	4.51551i	0.166106	−	0.166106i	−0.619159	−	0.785265i	$-0.712527\pi$
$739$	4.51551	−	4.51551i	0.166106	−	0.166106i	0.785265	+	0.619159i	$0.212527\pi$
$740$	1.69017	−	12.7796i	0.0621318	−	0.469787i
$741$	12.6073	+	28.7844i	0.463140	+	1.05742i
$742$	−7.63155	−	18.2476i	−0.280163	−	0.669890i
$743$	−1.45236	+	5.42029i	−0.0532820	+	0.198851i	−0.987436	−	0.158019i	$-0.949489\pi$
$743$	−1.45236	+	5.42029i	−0.0532820	+	0.198851i	0.934154	+	0.356870i	$0.116156\pi$
$744$	3.81865	−	0.116023i	0.139998	−	0.00425360i
$745$	−4.35742	−	3.39527i	−0.159643	−	0.124393i
$746$	14.5998	+	18.8928i	0.534536	+	0.691714i
$747$	−27.1527	−	25.0506i	−0.993465	−	0.916554i
$748$	−18.6539	−	4.86191i	−0.682055	−	0.177769i
$749$	−14.4024	+	3.85912i	−0.526253	+	0.141009i
$750$	25.3147	+	10.4483i	0.924361	+	0.381519i
$751$	−21.5087	−	37.2541i	−0.784863	−	1.35942i	−0.929081	−	0.369876i	$-0.879400\pi$
$751$	−21.5087	−	37.2541i	−0.784863	−	1.35942i	0.144218	−	0.989546i	$-0.453933\pi$
$752$	−2.25169	+	2.31410i	−0.0821108	+	0.0843866i
$753$	1.13191	+	0.125905i	0.0412491	+	0.00458823i
$754$	−1.97303	+	2.58958i	−0.0718536	+	0.0943069i
$755$	−5.12980	−	6.78909i	−0.186692	−	0.247080i
$756$	−19.3375	−	12.8720i	−0.703299	−	0.468149i
$757$			9.53743i			0.346644i	0.984865	+	0.173322i	$0.0554501\pi$
$757$			9.53743i			0.346644i	−0.984865	+	0.173322i	$0.944550\pi$
$758$	−21.0127	−	16.0098i	−0.763214	−	0.581502i
$759$	1.70781	+	2.13529i	0.0619896	+	0.0775061i
$760$	36.5055	−	36.7123i	1.32419	−	1.33170i
$761$	4.36810	+	7.56578i	0.158344	+	0.274259i	0.934272	−	0.356562i	$-0.116051\pi$
$761$	4.36810	+	7.56578i	0.158344	+	0.274259i	−0.775928	+	0.630822i	$0.782718\pi$
$762$	−0.0375015	−	1.59282i	−0.00135854	−	0.0577017i
$763$	12.1163	−	20.9861i	0.438640	−	0.759746i
$764$	49.4615	+	12.8915i	1.78946	+	0.466400i
$765$	−43.5181	+	7.18908i	−1.57340	+	0.259922i
$766$	39.5263	+	5.06639i	1.42814	+	0.183056i
$767$	13.5562	−	3.63239i	0.489488	−	0.131158i
$768$	4.91666	+	27.2732i	0.177415	+	0.984136i
$769$	−17.8438	+	10.3021i	−0.643464	+	0.371504i	−0.785948	−	0.618293i	$-0.787825\pi$
$769$	−17.8438	+	10.3021i	−0.643464	+	0.371504i	0.142484	+	0.989797i	$0.454491\pi$
$770$	10.0194	−	2.64169i	0.361075	−	0.0951998i
$771$	−18.5301	−	42.3070i	−0.667344	−	1.52365i
$772$	−0.250238	−	36.6156i	−0.00900627	−	1.31782i
$773$			20.9052i			0.751909i	0.926638	+	0.375954i	$0.122685\pi$
$773$			20.9052i			0.751909i	−0.926638	+	0.375954i	$0.877315\pi$
$774$	−29.8822	−	20.9225i	−1.07409	−	0.752042i
$775$	−1.06501	+	3.75092i	−0.0382563	+	0.134737i
$776$	−21.4915	−	27.4216i	−0.771499	−	0.984376i
$777$	−8.98871	−	6.61424i	−0.322468	−	0.237285i
$778$	−8.30078	−	19.8478i	−0.297597	−	0.711577i
$779$	42.6850	+	11.4374i	1.52935	+	0.409788i
$780$	8.29175	−	15.0323i	0.296892	−	0.538242i
$781$	−20.6756	+	5.54001i	−0.739831	+	0.198237i
$782$	7.92364	−	6.12315i	0.283349	−	0.218964i
$783$	−3.53792	−	4.07582i	−0.126435	−	0.145658i
$784$	−3.91166	+	6.99426i	−0.139702	+	0.249795i
$785$	6.29769	+	50.7451i	0.224774	+	1.81117i
$786$	37.3690	−	22.7642i	1.33291	−	0.811974i
$787$	14.9200	+	25.8421i	0.531840	+	0.921173i	0.999309	+	0.0371640i	$0.0118324\pi$
$787$	14.9200	+	25.8421i	0.531840	+	0.921173i	−0.467470	+	0.884009i	$0.654834\pi$
$788$	−37.7993	+	10.4057i	−1.34654	+	0.370686i
$789$	−8.71865	+	11.8486i	−0.310392	+	0.421821i
$790$	36.5384	+	36.8326i	1.29998	+	1.31044i
$791$	−7.13716			−0.253768
$792$	5.33398	+	11.2368i	0.189535	+	0.399281i
$793$	−0.853343	+	0.853343i	−0.0303031	+	0.0303031i
$794$	7.91659	−	1.06977i	0.280949	−	0.0379648i
$795$	6.56857	+	23.3255i	0.232963	+	0.827271i
$796$	−14.0500	+	3.86780i	−0.497990	+	0.137091i
$797$	−14.6022	+	8.43056i	−0.517235	+	0.298626i	−0.735803	−	0.677196i	$-0.763195\pi$
$797$	−14.6022	+	8.43056i	−0.517235	+	0.298626i	0.218568	+	0.975822i	$0.429862\pi$
$798$	−12.6164	−	43.0090i	−0.446617	−	1.52250i
$799$	4.59646	+	2.65377i	0.162611	+	0.0938835i
$800$	−28.0505	−	3.62923i	−0.991734	−	0.128313i
$801$	−11.8477	−	2.66871i	−0.418617	−	0.0942941i
$802$	−5.50318	+	4.25270i	−0.194324	+	0.150168i
$803$	1.98849	−	3.44417i	0.0701724	−	0.121542i
$804$	33.2339	+	3.46692i	1.17207	+	0.122269i
$805$	−2.09672	+	4.95748i	−0.0738997	+	0.174728i
$806$	2.26140	+	0.927662i	0.0796544	+	0.0326755i
$807$	−9.20483	−	1.02388i	−0.324025	−	0.0360421i
$808$	−18.0023	+	14.1092i	−0.633317	+	0.496358i
$809$		−	43.5717i		−	1.53190i	−0.642900	−	0.765950i	$-0.722269\pi$
$809$		−	43.5717i		−	1.53190i	0.642900	−	0.765950i	$-0.277731\pi$
$810$	21.6034	+	18.5281i	0.759068	+	0.651012i
$811$	0.980783	−	0.980783i	0.0344399	−	0.0344399i	−0.689677	−	0.724117i	$-0.742248\pi$
$811$	0.980783	−	0.980783i	0.0344399	−	0.0344399i	0.724117	+	0.689677i	$0.242248\pi$
$812$	3.26095	−	3.30583i	0.114437	−	0.116012i
$813$	13.4390	−	10.7485i	0.471325	−	0.376968i
$814$	2.30563	+	5.51292i	0.0808121	+	0.193228i
$815$	2.38510	−	5.63931i	0.0835463	−	0.197536i
$816$	41.4739	−	18.8449i	1.45188	−	0.659703i
$817$	−18.2168	−	67.9862i	−0.637327	−	2.37853i
$818$	−26.3837	−	34.1417i	−0.922485	−	1.19374i
$819$	−7.94302	−	12.5618i	−0.277552	−	0.438943i
$820$	−9.22554	−	22.3098i	−0.322170	−	0.779091i
$821$	11.9334	−	3.19755i	0.416480	−	0.111595i	−0.0444931	−	0.999010i	$-0.514167\pi$
$821$	11.9334	−	3.19755i	0.416480	−	0.111595i	0.460973	+	0.887414i	$0.347501\pi$
$822$	41.5510	+	22.7026i	1.44926	+	0.791844i
$823$	18.7299	+	5.01867i	0.652885	+	0.174940i	0.570033	−	0.821622i	$-0.306930\pi$
$823$	18.7299	+	5.01867i	0.652885	+	0.174940i	0.0828520	+	0.996562i	$0.473597\pi$
$824$	−3.02068	+	0.429226i	−0.105230	+	0.0149528i
$825$	−12.5775	+	1.72333i	−0.437891	+	0.0599987i
$826$	−19.8374	+	2.68064i	−0.690233	+	0.0932714i
$827$	−0.946998			−0.0329303			−0.0164652	−	0.999864i	$-0.505241\pi$
$827$	−0.946998			−0.0329303			−0.0164652	+	0.999864i	$0.505241\pi$
$828$	−6.31302	−	1.37675i	−0.219393	−	0.0478455i
$829$	28.0530	−	28.0530i	0.974321	−	0.974321i	−0.0253574	−	0.999678i	$-0.508072\pi$
$829$	28.0530	−	28.0530i	0.974321	−	0.974321i	0.999678	+	0.0253574i	$0.00807236\pi$
$830$	−27.6460	+	27.4252i	−0.959608	+	0.951944i
$831$	41.9625	−	6.38590i	1.45566	−	0.221525i
$832$	−4.23692	+	17.2168i	−0.146889	+	0.596886i
$833$	12.7242	+	3.40945i	0.440869	+	0.118131i
$834$	−5.50957	−	9.04431i	−0.190781	−	0.313179i
$835$	−39.3561	−	30.6660i	−1.36197	−	1.06124i
$836$	−6.05299	+	23.2238i	−0.209347	+	0.803211i
$837$	−2.26835	+	3.35776i	−0.0784056	+	0.116061i
$838$	−0.270208	+	2.10807i	−0.00933419	+	0.0728222i
$839$	−42.8889	−	24.7619i	−1.48069	−	0.854877i	−0.480930	−	0.876759i	$-0.659701\pi$
$839$	−42.8889	−	24.7619i	−1.48069	−	0.854877i	−0.999761	+	0.0218816i	$0.993034\pi$
$840$	−14.4567	+	19.7633i	−0.498805	+	0.681900i
$841$	−24.1804	+	13.9606i	−0.833808	+	0.481399i
$842$	−3.79363	−	9.07083i	−0.130737	−	0.312601i
$843$	−3.05352	−	20.0650i	−0.105169	−	0.691077i
$844$	0.261413	+	38.2507i	0.00899821	+	1.31664i
$845$	−14.4293	+	10.9027i	−0.496385	+	0.375065i
$846$	−0.594786	−	3.37262i	−0.0204491	−	0.115953i
$847$	13.9901	−	13.9901i	0.480706	−	0.480706i
$848$	−12.8088	−	21.5014i	−0.439857	−	0.738360i
$849$	−49.2961	−	19.2664i	−1.69184	−	0.661222i
$850$	5.54113	+	46.1625i	0.190059	+	1.58336i
$851$	−2.99838	−	0.803413i	−0.102783	−	0.0275406i
$852$	29.7001	−	40.9455i	1.01751	−	1.40277i
$853$	15.7991	−	27.3649i	0.540951	−	0.936955i	−0.457898	−	0.889005i	$-0.651398\pi$
$853$	15.7991	−	27.3649i	0.540951	−	0.936955i	0.998850	−	0.0479506i	$-0.0152690\pi$
$854$	1.36202	−	1.05253i	0.0466072	−	0.0360167i
$855$	8.95027	+	54.1793i	0.306093	+	1.85289i
$856$	−17.3558	+	7.39836i	−0.593210	+	0.252871i
$857$	−8.70946	−	32.5041i	−0.297509	−	1.11032i	−0.939204	−	0.343360i	$-0.888435\pi$
$857$	−8.70946	−	32.5041i	−0.297509	−	1.11032i	0.641694	−	0.766960i	$-0.278232\pi$
$858$	0.187314	+	7.95586i	0.00639479	+	0.271609i
$859$	4.40780	−	16.4501i	0.150392	−	0.561272i	−0.849064	−	0.528291i	$-0.822833\pi$
$859$	4.40780	−	16.4501i	0.150392	−	0.561272i	0.999456	−	0.0329812i	$-0.0105001\pi$
$860$	−23.4261	+	30.4921i	−0.798824	+	1.03977i
$861$	−20.7723	−	2.31055i	−0.707918	−	0.0787433i
$862$	1.31244	+	9.71237i	0.0447017	+	0.330804i
$863$	−17.1706	+	17.1706i	−0.584493	+	0.584493i	−0.936135	−	0.351641i	$-0.885624\pi$
$863$	−17.1706	+	17.1706i	−0.584493	+	0.584493i	0.351641	+	0.936135i	$0.385624\pi$
$864$	−26.5167	−	12.6832i	−0.902117	−	0.431491i
$865$	−18.5194	+	13.9931i	−0.629677	+	0.475781i
$866$	21.6067	+	16.4624i	0.734225	+	0.559415i
$867$	−28.3806	−	35.4845i	−0.963856	−	1.20512i
$868$	−3.03110	−	1.72249i	−0.102882	−	0.0584653i
$869$	−23.2305	−	6.22459i	−0.788040	−	0.211155i
$870$	−4.45707	+	3.53557i	−0.151109	+	0.119867i
$871$	18.5141	+	10.6891i	0.627326	+	0.362187i
$872$	11.4431	−	28.4474i	0.387512	−	0.963351i
$873$	36.9235	−	1.48680i	1.24967	−	0.0503207i
$874$	−7.62321	−	9.86478i	−0.257859	−	0.333681i
$875$	−14.7683	−	20.1610i	−0.499260	−	0.681566i
$876$	1.47741	+	9.28132i	0.0499170	+	0.313587i
$877$	24.6275	+	42.6561i	0.831613	+	1.44040i	0.896759	+	0.442520i	$0.145915\pi$
$877$	24.6275	+	42.6561i	0.831613	+	1.44040i	−0.0651458	+	0.997876i	$0.520751\pi$
$878$	11.1625	−	27.2114i	0.376717	−	0.918339i
$879$	3.12985	−	8.00821i	0.105567	−	0.270110i
$880$	12.0817	−	5.09299i	0.407275	−	0.171685i
$881$		−	24.8881i		−	0.838500i	−0.907871	−	0.419250i	$-0.862293\pi$
$881$		−	24.8881i		−	0.838500i	0.907871	−	0.419250i	$-0.137707\pi$
$882$	−3.59244	−	7.70342i	−0.120964	−	0.259388i
$883$			3.06585i			0.103174i	0.998669	+	0.0515870i	$0.0164280\pi$
$883$			3.06585i			0.103174i	−0.998669	+	0.0515870i	$0.983572\pi$
$884$	29.1448	−	0.199181i	0.980246	−	0.00669920i
$885$	24.5231	−	0.311369i	0.824335	−	0.0104666i
$886$	32.7572	+	13.4375i	1.10050	+	0.451443i
$887$	−24.6768	−	6.61212i	−0.828564	−	0.222013i	−0.180477	−	0.983579i	$-0.557764\pi$
$887$	−24.6768	−	6.61212i	−0.828564	−	0.222013i	−0.648087	+	0.761566i	$0.724431\pi$
$888$	−12.4381	−	6.68597i	−0.417397	−	0.224367i
$889$	−0.726969	+	1.25915i	−0.0243818	+	0.0422305i
$890$	−3.36281	+	12.3519i	−0.112722	+	0.414035i
$891$	−12.9768	−	2.37892i	−0.434738	−	0.0796968i
$892$	−6.74364	+	3.95514i	−0.225794	+	0.132428i
$893$	3.30389	−	5.72250i	0.110560	−	0.191496i
$894$	−5.16789	+	3.14815i	−0.172840	+	0.105290i
$895$	−0.904545	−	2.23047i	−0.0302356	−	0.0745565i
$896$	9.11630	−	23.5892i	0.304554	−	0.788061i
$897$	−3.32967	−	2.45010i	−0.111174	−	0.0818063i
$898$	22.7458	−	3.07365i	0.759039	−	0.102569i
$899$	−0.572758	−	0.572758i	−0.0191026	−	0.0191026i
$900$	20.5187	−	21.8857i	0.683956	−	0.729523i
$901$	−29.0906	+	29.0906i	−0.969149	+	0.969149i
$902$	8.90176	+	6.78236i	0.296396	+	0.225828i
$903$	13.3554	+	30.4924i	0.444438	+	1.01472i
$904$	−8.94117	+	1.27050i	−0.297379	+	0.0422563i
$905$	33.6324	−	13.6393i	1.11798	−	0.453385i
$906$	−8.94447	+	2.62381i	−0.297160	+	0.0871701i
$907$	35.5237	+	20.5096i	1.17954	+	0.681010i	0.955909	−	0.293663i	$-0.0948743\pi$
$907$	35.5237	+	20.5096i	1.17954	+	0.681010i	0.223635	+	0.974673i	$0.428208\pi$
$908$	21.7378	+	5.66568i	0.721393	+	0.188022i
$909$	−0.976087	−	24.2403i	−0.0323748	−	0.803999i
$910$	−13.5987	+	7.77869i	−0.450793	+	0.257861i
$911$	−34.5613	−	19.9540i	−1.14507	−	0.661105i	−0.197387	−	0.980326i	$-0.563246\pi$
$911$	−34.5613	−	19.9540i	−1.14507	−	0.661105i	−0.947681	+	0.319220i	$0.896579\pi$
$912$	−23.4615	−	51.6342i	−0.776889	−	1.70978i
$913$	4.67209	−	17.4365i	0.154624	−	0.577063i
$914$	−34.6109	+	14.4750i	−1.14483	+	0.478792i
$915$	−1.81282	+	1.07755i	−0.0599299	+	0.0356226i
$916$	−0.222281	−	32.5248i	−0.00734437	−	1.07465i
$917$	−39.9305			−1.31862
$918$	−9.50522	+	47.3737i	−0.313719	+	1.56356i
$919$	−9.59222			−0.316418			−0.158209	−	0.987406i	$-0.550572\pi$
$919$	−9.59222			−0.316418			−0.158209	+	0.987406i	$0.550572\pi$
$920$	−1.74420	+	6.58379i	−0.0575047	+	0.217061i
$921$	−13.3359	+	10.6661i	−0.439432	+	0.351460i
$922$	−10.2754	−	24.5693i	−0.338403	−	0.809147i
$923$	28.0269	−	16.1813i	0.922516	−	0.532615i
$924$	1.17771	−	11.2896i	0.0387439	−	0.371399i
$925$	10.3414	−	10.0386i	0.340022	−	0.330069i
$926$	−6.91120	+	53.9189i	−0.227116	+	1.77188i
$927$	1.50398	−	2.86538i	0.0493972	−	0.0941113i
$928$	3.49672	−	4.72191i	0.114785	−	0.155004i
$929$	20.3676	−	35.2777i	0.668238	−	1.15742i	−0.310158	−	0.950685i	$-0.600382\pi$
$929$	20.3676	−	35.2777i	0.668238	−	1.15742i	0.978396	−	0.206738i	$-0.0662847\pi$
$930$	3.43014	+	2.54529i	0.112479	+	0.0834634i
$931$	4.24470	−	15.8414i	0.139115	−	0.519183i
$932$	−20.5741	−	11.6917i	−0.673927	−	0.382975i
$933$	−46.0576	−	18.0007i	−1.50786	−	0.589317i
$934$	−2.47617	−	18.3243i	−0.0810229	−	0.599591i
$935$	−12.9930	−	17.1957i	−0.424915	−	0.562359i
$936$	−12.1869	−	14.3229i	−0.398340	−	0.468160i
$937$	−10.9489	−	10.9489i	−0.357684	−	0.357684i	0.505275	−	0.862959i	$-0.331391\pi$
$937$	−10.9489	−	10.9489i	−0.357684	−	0.357684i	−0.862959	+	0.505275i	$0.831391\pi$
$938$	−24.2545	−	18.4798i	−0.791938	−	0.603387i
$939$	−26.7077	−	19.6526i	−0.871574	−	0.641337i
$940$	−3.57931	+	0.469068i	−0.116744	+	0.0152993i
$941$	47.4727	+	12.7203i	1.54757	+	0.414669i	0.928701	−	0.370828i	$-0.120926\pi$
$941$	47.4727	+	12.7203i	1.54757	+	0.414669i	0.618865	+	0.785498i	$0.287593\pi$
$942$	54.4325	+	13.2202i	1.77351	+	0.430736i
$943$	−5.61536	+	1.50463i	−0.182861	+	0.0489975i
$944$	−24.3744	+	6.88952i	−0.793320	+	0.224235i
$945$	−8.04010	−	24.6960i	−0.261544	−	0.803360i
$946$	2.26618	−	17.6799i	0.0736797	−	0.574825i
$947$	−43.7582	−	25.2638i	−1.42195	−	0.820964i	−0.425486	−	0.904965i	$-0.639897\pi$
$947$	−43.7582	−	25.2638i	−1.42195	−	0.820964i	−0.996466	+	0.0840013i	$0.973230\pi$
$948$	51.9019	−	23.1566i	1.68570	−	0.752090i
$949$	−1.55625	+	5.80801i	−0.0505181	+	0.188536i
$950$	57.4714	−	6.89861i	1.86462	−	0.223820i
$951$	53.3576	−	8.12002i	1.73024	−	0.263310i
$952$	−41.2689	−	5.00333i	−1.33753	−	0.162159i
$953$	−33.1758	−	33.1758i	−1.07467	−	1.07467i	−0.996978	−	0.0776907i	$-0.975245\pi$
$953$	−33.1758	−	33.1758i	−1.07467	−	1.07467i	−0.0776907	−	0.996978i	$-0.524755\pi$
$954$	26.4447	+	2.31283i	0.856179	+	0.0748807i
$955$	34.4513	+	45.5950i	1.11482	+	1.47542i
$956$	−26.0893	−	25.7351i	−0.843788	−	0.832333i
$957$	0.959986	−	2.45627i	0.0310319	−	0.0794000i
$958$	−5.16275	+	12.5854i	−0.166801	+	0.406617i
$959$	−21.6041	−	37.4195i	−0.697634	−	1.20834i
$960$	−14.5928	+	27.3322i	−0.470979	+	0.882144i
$961$	15.1959	−	26.3201i	0.490191	−	0.849036i
$962$	−5.52443	−	7.14887i	−0.178115	−	0.230489i
$963$	4.39742	−	19.5223i	0.141705	−	0.629096i
$964$	−5.53254	+	21.2270i	−0.178191	+	0.683674i
$965$	25.1623	−	32.2927i	0.810002	−	1.03954i
$966$	4.26636	+	4.07008i	0.137268	+	0.130953i
$967$	−3.35798	+	12.5322i	−0.107985	+	0.403007i	−0.998667	−	0.0516210i	$-0.983561\pi$
$967$	−3.35798	+	12.5322i	−0.107985	+	0.403007i	0.890681	+	0.454628i	$0.150228\pi$
$968$	15.0359	−	20.0167i	0.483271	−	0.643361i
$969$	−72.8055	+	58.2301i	−2.33885	+	1.87062i
$970$	0.156175	−	38.9520i	0.00501447	−	1.25067i
$971$	3.46642	+	3.46642i	0.111243	+	0.111243i	0.760537	−	0.649294i	$-0.224936\pi$
$971$	3.46642	+	3.46642i	0.111243	+	0.111243i	−0.649294	+	0.760537i	$0.724936\pi$
$972$	27.3581	−	14.9510i	0.877512	−	0.479554i
$973$			9.66427i			0.309822i
$974$	−16.9302	−	12.8993i	−0.542477	−	0.413320i
$975$	17.6938	−	7.43850i	0.566656	−	0.238223i
$976$	1.51892	−	1.56102i	0.0486195	−	0.0499670i
$977$	−7.18243	+	26.8052i	−0.229786	+	0.857575i	0.750644	+	0.660707i	$0.229744\pi$
$977$	−7.18243	+	26.8052i	−0.229786	+	0.857575i	−0.980430	+	0.196867i	$0.936923\pi$
$978$	−4.85314	−	4.62987i	−0.155186	−	0.148047i
$979$	−1.53588	−	5.73197i	−0.0490868	−	0.183195i
$980$	−8.27970	+	3.42382i	−0.264485	+	0.109370i
$981$	17.3814	+	27.4884i	0.554945	+	0.877636i
$982$	2.45587	−	19.1598i	0.0783698	−	0.611415i
$983$	13.4971	−	3.61653i	0.430490	−	0.115349i	−0.0370663	−	0.999313i	$-0.511801\pi$
$983$	13.4971	−	3.61653i	0.430490	−	0.115349i	0.467556	+	0.883963i	$0.345135\pi$
$984$	−26.4341	+	0.803151i	−0.842687	+	0.0256035i
$985$	−40.3707	−	17.0744i	−1.28632	−	0.544036i
$986$	−8.93583	−	3.66562i	−0.284575	−	0.116737i
$987$	−1.13762	+	2.91079i	−0.0362110	+	0.0926514i
$988$	−0.247977	−	36.2848i	−0.00788920	−	1.15437i
$989$	6.54732	+	6.54732i	0.208193	+	0.208193i
$990$	−3.11030	+	13.5544i	−0.0988517	+	0.430786i
$991$	−35.5828			−1.13032			−0.565162	−	0.824980i	$-0.691186\pi$
$991$	−35.5828			−1.13032			−0.565162	+	0.824980i	$0.691186\pi$
$992$	−4.10387	−	1.61830i	−0.130298	−	0.0513812i
$993$	−6.20480	−	4.56573i	−0.196903	−	0.144889i
$994$	−42.5854	+	17.8102i	−1.35073	+	0.564905i
$995$	−15.0058	−	6.34659i	−0.475717	−	0.201200i
$996$	17.3810	+	38.9569i	0.550738	+	1.23440i
$997$	27.7959	+	16.0480i	0.880305	+	0.508245i	0.870759	−	0.491710i	$-0.163628\pi$
$997$	27.7959	+	16.0480i	0.880305	+	0.508245i	0.00954626	+	0.999954i	$0.496961\pi$
$998$	54.5559	+	6.99285i	1.72694	+	0.221355i
$999$	13.4667	−	6.55618i	0.426068	−	0.207428i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.cq.a.173.8	yes	560
5.2	odd	4		720.2.cm.a.317.65	yes	560
9.5	odd	6	inner	720.2.cq.a.653.55	yes	560
16.5	even	4		720.2.cm.a.533.19	yes	560
45.32	even	12		720.2.cm.a.77.19	✓	560
80.37	odd	4	inner	720.2.cq.a.677.55	yes	560
144.5	odd	12		720.2.cm.a.293.65	yes	560
720.437	even	12	inner	720.2.cq.a.437.8	yes	560

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.cm.a.77.19	✓	560	45.32	even	12
720.2.cm.a.293.65	yes	560	144.5	odd	12
720.2.cm.a.317.65	yes	560	5.2	odd	4
720.2.cm.a.533.19	yes	560	16.5	even	4
720.2.cq.a.173.8	yes	560	1.1	even	1	trivial
720.2.cq.a.437.8	yes	560	720.437	even	12	inner
720.2.cq.a.653.55	yes	560	9.5	odd	6	inner
720.2.cq.a.677.55	yes	560	80.37	odd	4	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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.cq (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40148 + 0.189382i) q^{2} +(-1.35263 + 1.08184i) q^{3} +(1.92827 - 0.530828i) q^{4} +(2.05945 + 0.871024i) q^{5} +(1.69080 - 1.77234i) q^{6} +(-2.15913 + 0.578537i) q^{7} +(-2.60189 + 1.10912i) q^{8} +(0.659238 - 2.92667i) q^{9} +O(q^{10})\)	\(q+(-1.40148 + 0.189382i) q^{2} +(-1.35263 + 1.08184i) q^{3} +(1.92827 - 0.530828i) q^{4} +(2.05945 + 0.871024i) q^{5} +(1.69080 - 1.77234i) q^{6} +(-2.15913 + 0.578537i) q^{7} +(-2.60189 + 1.10912i) q^{8} +(0.659238 - 2.92667i) q^{9} +(-3.05122 - 0.830698i) q^{10} +(1.41594 - 0.379400i) q^{11} +(-2.03397 + 2.80410i) q^{12} +(-1.91938 + 1.10816i) q^{13} +(2.91641 - 1.21971i) q^{14} +(-3.72799 + 1.04982i) q^{15} +(3.43644 - 2.04716i) q^{16} +(-4.64939 - 4.64939i) q^{17} +(-0.369647 + 4.22651i) q^{18} +(-5.78840 + 5.78840i) q^{19} +(4.43353 + 0.586357i) q^{20} +(2.29463 - 3.11839i) q^{21} +(-1.91255 + 0.799874i) q^{22} +(0.278722 - 1.04021i) q^{23} +(2.31951 - 4.31507i) q^{24} +(3.48263 + 3.58765i) q^{25} +(2.48010 - 1.91655i) q^{26} +(2.27449 + 4.67191i) q^{27} +(-3.85628 + 2.26170i) q^{28} +(-1.00329 + 0.268830i) q^{29} +(5.02587 - 2.17731i) q^{30} +(0.389919 + 0.675359i) q^{31} +(-4.42840 + 3.51984i) q^{32} +(-1.50480 + 2.04501i) q^{33} +(7.39651 + 5.63549i) q^{34} +(-4.95053 - 0.689190i) q^{35} +(-0.282373 - 5.99335i) q^{36} -2.88249i q^{37} +(7.01608 - 9.20852i) q^{38} +(1.39737 - 3.57540i) q^{39} +(-6.32453 + 0.0178649i) q^{40} +(-2.69916 - 4.67508i) q^{41} +(-2.62530 + 4.80491i) q^{42} +(-4.29906 + 7.44619i) q^{43} +(2.52892 - 1.48321i) q^{44} +(3.90687 - 5.45311i) q^{45} +(-0.193626 + 1.51061i) q^{46} +(-0.779697 + 0.208919i) q^{47} +(-2.43355 + 6.48674i) q^{48} +(-1.73504 + 1.00172i) q^{49} +(-5.56026 - 4.36846i) q^{50} +(11.3188 + 1.25902i) q^{51} +(-3.11284 + 3.15569i) q^{52} -6.25687i q^{53} +(-4.07241 - 6.11682i) q^{54} +(3.24652 + 0.451965i) q^{55} +(4.97616 - 3.90003i) q^{56} +(1.56745 - 14.0917i) q^{57} +(1.35517 - 0.566764i) q^{58} +(-6.11658 - 1.63893i) q^{59} +(-6.63129 + 4.00325i) q^{60} +(0.525959 - 0.140930i) q^{61} +(-0.674363 - 0.872656i) q^{62} +(0.269809 + 6.70046i) q^{63} +(5.53970 - 5.77164i) q^{64} +(-4.91809 + 0.610358i) q^{65} +(1.72165 - 3.15102i) q^{66} +(-4.82293 - 8.35356i) q^{67} +(-11.4333 - 6.49724i) q^{68} +(0.748328 + 1.70855i) q^{69} +(7.06857 + 0.0283408i) q^{70} -14.6020 q^{71} +(1.53077 + 8.34606i) q^{72} +(1.91839 - 1.91839i) q^{73} +(0.545891 + 4.03974i) q^{74} +(-8.59200 - 1.08513i) q^{75} +(-8.08894 + 14.2342i) q^{76} +(-2.83770 + 1.63835i) q^{77} +(-1.28127 + 5.27547i) q^{78} +(-14.2083 - 8.20319i) q^{79} +(8.86029 - 1.22279i) q^{80} +(-8.13081 - 3.85874i) q^{81} +(4.66818 + 6.04084i) q^{82} +(6.15721 - 10.6646i) q^{83} +(2.76933 - 7.23114i) q^{84} +(-5.52543 - 13.6249i) q^{85} +(4.61485 - 11.2498i) q^{86} +(1.06625 - 1.44903i) q^{87} +(-3.26332 + 2.55761i) q^{88} -4.04817i q^{89} +(-4.44266 + 8.38229i) q^{90} +(3.50309 - 3.50309i) q^{91} +(-0.0147191 - 2.15375i) q^{92} +(-1.25805 - 0.491683i) q^{93} +(1.05316 - 0.440456i) q^{94} +(-16.9627 + 6.87906i) q^{95} +(2.18208 - 9.55188i) q^{96} +(3.18808 + 11.8981i) q^{97} +(2.24190 - 1.73248i) q^{98} +(-0.176938 - 4.39411i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 560 q - 6 q^{2} - 6 q^{5} - 8 q^{6}+O(q^{10}) \) 560 * q - 6 * q^2 - 6 * q^5 - 8 * q^6	\( 560 q - 6 q^{2} - 6 q^{5} - 8 q^{6} - 12 q^{11} - 10 q^{12} - 8 q^{15} - 4 q^{16} + 20 q^{18} - 6 q^{20} - 8 q^{21} + 6 q^{22} - 24 q^{24} + 8 q^{28} + 28 q^{30} - 8 q^{31} + 54 q^{32} - 8 q^{33} - 12 q^{34} + 8 q^{36} - 18 q^{38} - 24 q^{39} + 8 q^{40} - 46 q^{42} - 4 q^{43} - 14 q^{45} - 40 q^{46} - 12 q^{47} - 22 q^{48} - 6 q^{50} - 8 q^{51} - 18 q^{52} + 24 q^{54} - 12 q^{56} + 24 q^{57} - 10 q^{58} - 88 q^{60} - 4 q^{61} + 20 q^{63} - 24 q^{64} - 12 q^{65} + 24 q^{66} - 4 q^{67} - 30 q^{68} + 12 q^{69} + 2 q^{70} - 22 q^{72} + 24 q^{74} - 66 q^{75} + 8 q^{76} - 12 q^{77} - 122 q^{78} - 16 q^{81} - 12 q^{84} - 12 q^{85} - 12 q^{86} + 12 q^{87} - 10 q^{88} - 94 q^{90} - 16 q^{91} - 120 q^{92} - 12 q^{95} + 48 q^{96} - 4 q^{97} + 32 q^{99}+O(q^{100}) \) 560 * q - 6 * q^2 - 6 * q^5 - 8 * q^6 - 12 * q^11 - 10 * q^12 - 8 * q^15 - 4 * q^16 + 20 * q^18 - 6 * q^20 - 8 * q^21 + 6 * q^22 - 24 * q^24 + 8 * q^28 + 28 * q^30 - 8 * q^31 + 54 * q^32 - 8 * q^33 - 12 * q^34 + 8 * q^36 - 18 * q^38 - 24 * q^39 + 8 * q^40 - 46 * q^42 - 4 * q^43 - 14 * q^45 - 40 * q^46 - 12 * q^47 - 22 * q^48 - 6 * q^50 - 8 * q^51 - 18 * q^52 + 24 * q^54 - 12 * q^56 + 24 * q^57 - 10 * q^58 - 88 * q^60 - 4 * q^61 + 20 * q^63 - 24 * q^64 - 12 * q^65 + 24 * q^66 - 4 * q^67 - 30 * q^68 + 12 * q^69 + 2 * q^70 - 22 * q^72 + 24 * q^74 - 66 * q^75 + 8 * q^76 - 12 * q^77 - 122 * q^78 - 16 * q^81 - 12 * q^84 - 12 * q^85 - 12 * q^86 + 12 * q^87 - 10 * q^88 - 94 * q^90 - 16 * q^91 - 120 * q^92 - 12 * q^95 + 48 * q^96 - 4 * q^97 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

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