LMFDB - Embedded newform 820.2.bw.a.11.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(11,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([20, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bw (of order $40$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [672,0,0,0,0,12,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$42$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			11.3
Character	$\chi$	$=$	820.11
Dual form			820.2.bw.a.671.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39175 - 0.251038i) q^{2} +(-0.0320264 + 0.0773185i) q^{3} +(1.87396 + 0.698766i) q^{4} +(-0.453990 + 0.891007i) q^{5} +(0.0639827 - 0.0995686i) q^{6} +(0.684981 + 2.85315i) q^{7} +(-2.43268 - 1.44295i) q^{8} +(2.11637 + 2.11637i) q^{9} +(0.855520 - 1.12609i) q^{10} +(3.14472 - 3.68199i) q^{11} +(-0.114044 + 0.122513i) q^{12} +(-0.274112 - 0.447310i) q^{13} +(-0.237077 - 4.14284i) q^{14} +(-0.0543517 - 0.0636376i) q^{15} +(3.02345 + 2.61892i) q^{16} +(-0.0922206 - 1.17177i) q^{17} +(-2.41418 - 3.47675i) q^{18} +(2.03814 + 1.24897i) q^{19} +(-1.47337 + 1.35248i) q^{20} +(-0.242539 - 0.0384144i) q^{21} +(-5.30099 + 4.33499i) q^{22} +(-0.892957 - 0.648771i) q^{23} +(0.189476 - 0.141879i) q^{24} +(-0.587785 - 0.809017i) q^{25} +(0.269205 + 0.691359i) q^{26} +(-0.463370 + 0.191934i) q^{27} +(-0.710058 + 5.82533i) q^{28} +(-0.661420 + 8.40414i) q^{29} +(0.0596687 + 0.102212i) q^{30} +(1.13657 - 3.49801i) q^{31} +(-3.55046 - 4.40389i) q^{32} +(0.183972 + 0.361066i) q^{33} +(-0.165811 + 1.65397i) q^{34} +(-2.85315 - 0.684981i) q^{35} +(2.48714 + 5.44483i) q^{36} +(2.54290 + 7.82623i) q^{37} +(-2.52305 - 2.24991i) q^{38} +(0.0433642 - 0.00686822i) q^{39} +(2.39009 - 1.51245i) q^{40} +(-6.21176 + 1.55370i) q^{41} +(0.327911 + 0.114350i) q^{42} +(0.382077 + 2.41234i) q^{43} +(8.46593 - 4.70248i) q^{44} +(-2.84651 + 0.924887i) q^{45} +(1.07991 + 1.12710i) q^{46} +(-0.189762 + 0.790414i) q^{47} +(-0.299321 + 0.149894i) q^{48} +(-1.43423 + 0.730778i) q^{49} +(0.614959 + 1.27351i) q^{50} +(0.0935534 + 0.0303973i) q^{51} +(-0.201110 - 1.02978i) q^{52} +(2.37886 + 0.187220i) q^{53} +(0.693080 - 0.150802i) q^{54} +(1.85301 + 4.47355i) q^{55} +(2.45061 - 7.92918i) q^{56} +(-0.161843 + 0.117586i) q^{57} +(3.03029 - 11.5305i) q^{58} +(8.44679 - 11.6260i) q^{59} +(-0.0573850 - 0.157233i) q^{60} +(-0.995078 + 6.28267i) q^{61} +(-2.45997 + 4.58305i) q^{62} +(-4.58865 + 7.48799i) q^{63} +(3.83582 + 7.02043i) q^{64} +(0.523001 - 0.0411610i) q^{65} +(-0.165403 - 0.548699i) q^{66} +(1.49032 - 1.27285i) q^{67} +(0.645978 - 2.26030i) q^{68} +(0.0787602 - 0.0482643i) q^{69} +(3.79893 + 1.66957i) q^{70} +(0.811324 + 0.692936i) q^{71} +(-2.09463 - 8.20224i) q^{72} +(-6.02934 + 6.02934i) q^{73} +(-1.57441 - 11.5305i) q^{74} +(0.0813767 - 0.0195368i) q^{75} +(2.94665 + 3.76470i) q^{76} +(12.6594 + 6.45026i) q^{77} +(-0.0620765 - 0.00132719i) q^{78} +(2.37199 + 0.982510i) q^{79} +(-3.70609 + 1.50495i) q^{80} +8.93701i q^{81} +(9.03529 - 0.602986i) q^{82} +6.72545i q^{83} +(-0.427666 - 0.241465i) q^{84} +(1.08593 + 0.449805i) q^{85} +(0.0738310 - 3.45330i) q^{86} +(-0.628613 - 0.320294i) q^{87} +(-12.9630 + 4.41944i) q^{88} +(3.00548 - 0.721551i) q^{89} +(4.19382 - 0.572634i) q^{90} +(1.08848 - 1.08848i) q^{91} +(-1.22003 - 1.83974i) q^{92} +(0.234061 + 0.199907i) q^{93} +(0.462525 - 1.05242i) q^{94} +(-2.03814 + 1.24897i) q^{95} +(0.454211 - 0.133475i) q^{96} +(-8.95591 + 7.64907i) q^{97} +(2.17955 - 0.657017i) q^{98} +(14.4478 - 1.13707i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q + 12 q^{6} + 100 q^{12} + 24 q^{14} + 32 q^{16} - 8 q^{17} - 40 q^{21} + 52 q^{22} - 24 q^{24} + 28 q^{28} + 12 q^{30} - 20 q^{32} + 40 q^{33} + 44 q^{34} + 36 q^{36} - 80 q^{37} + 52 q^{38} - 160 q^{42}+ \cdots - 116 q^{98}+O(q^{100}) $ 672 * q + 12 * q^6 + 100 * q^12 + 24 * q^14 + 32 * q^16 - 8 * q^17 - 40 * q^21 + 52 * q^22 - 24 * q^24 + 28 * q^28 + 12 * q^30 - 20 * q^32 + 40 * q^33 + 44 * q^34 + 36 * q^36 - 80 * q^37 + 52 * q^38 - 160 * q^42 + 24 * q^44 + 16 * q^46 + 40 * q^48 - 16 * q^49 - 64 * q^52 - 64 * q^54 + 68 * q^56 + 56 * q^58 + 36 * q^62 + 120 * q^64 + 8 * q^65 - 304 * q^68 + 104 * q^69 + 24 * q^70 - 40 * q^72 - 28 * q^74 - 24 * q^76 - 160 * q^77 - 128 * q^78 - 192 * q^82 - 204 * q^84 + 32 * q^85 - 168 * q^88 + 8 * q^89 + 48 * q^90 - 56 * q^92 - 356 * q^94 - 136 * q^96 - 116 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{3}{40}\right)$	$1$

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 $

$2$	−1.39175	−	0.251038i	−0.984119	−	0.177511i
$2$	−1.39175	−	0.251038i	−0.984119	−	0.177511i
$3$	−0.0320264	+	0.0773185i	−0.0184904	+	0.0446399i	−0.932855	−	0.360252i	$-0.882691\pi$
$3$	−0.0320264	+	0.0773185i	−0.0184904	+	0.0446399i	0.914365	+	0.404892i	$0.132691\pi$
$4$	1.87396	+	0.698766i	0.936980	+	0.349383i
$5$	−0.453990	+	0.891007i	−0.203031	+	0.398470i
$5$	−0.453990	+	0.891007i	−0.203031	+	0.398470i
$6$	0.0639827	−	0.0995686i	0.0261208	−	0.0406487i
$7$	0.684981	+	2.85315i	0.258899	+	1.07839i	0.938629	+	0.344928i	$0.112097\pi$
$7$	0.684981	+	2.85315i	0.258899	+	1.07839i	−0.679731	+	0.733462i	$0.737903\pi$
$8$	−2.43268	−	1.44295i	−0.860081	−	0.510158i
$9$	2.11637	+	2.11637i	0.705456	+	0.705456i
$10$	0.855520	−	1.12609i	0.270539	−	0.356102i
$11$	3.14472	−	3.68199i	0.948168	−	1.11016i	−0.0456293	−	0.998958i	$-0.514529\pi$
$11$	3.14472	−	3.68199i	0.948168	−	1.11016i	0.993798	−	0.111204i	$-0.0354707\pi$
$12$	−0.114044	+	0.122513i	−0.0329216	+	0.0353664i
$13$	−0.274112	−	0.447310i	−0.0760250	−	0.124062i	0.812368	−	0.583145i	$-0.198178\pi$
$13$	−0.274112	−	0.447310i	−0.0760250	−	0.124062i	−0.888393	+	0.459083i	$0.848178\pi$
$14$	−0.237077	−	4.14284i	−0.0633614	−	1.10722i
$15$	−0.0543517	−	0.0636376i	−0.0140335	−	0.0164312i
$16$	3.02345	+	2.61892i	0.755863	+	0.654730i
$17$	−0.0922206	−	1.17177i	−0.0223668	−	0.284197i	−0.997922	−	0.0644405i	$-0.979474\pi$
$17$	−0.0922206	−	1.17177i	−0.0223668	−	0.284197i	0.975555	−	0.219756i	$-0.0705263\pi$
$18$	−2.41418	−	3.47675i	−0.569027	−	0.819478i
$19$	2.03814	+	1.24897i	0.467581	+	0.286534i	0.736264	−	0.676695i	$-0.236588\pi$
$19$	2.03814	+	1.24897i	0.467581	+	0.286534i	−0.268683	+	0.963229i	$0.586588\pi$
$20$	−1.47337	+	1.35248i	−0.329454	+	0.302423i
$21$	−0.242539	−	0.0384144i	−0.0529264	−	0.00838271i
$22$	−5.30099	+	4.33499i	−1.13018	+	0.924222i
$23$	−0.892957	−	0.648771i	−0.186194	−	0.135278i	0.490783	−	0.871282i	$-0.336711\pi$
$23$	−0.892957	−	0.648771i	−0.186194	−	0.135278i	−0.676978	+	0.736004i	$0.736711\pi$
$24$	0.189476	−	0.141879i	0.0386767	−	0.0289608i
$25$	−0.587785	−	0.809017i	−0.117557	−	0.161803i
$26$	0.269205	+	0.691359i	0.0527954	+	0.135587i
$27$	−0.463370	+	0.191934i	−0.0891756	+	0.0369377i
$28$	−0.710058	+	5.82533i	−0.134188	+	1.10088i
$29$	−0.661420	+	8.40414i	−0.122823	+	1.56061i	0.559047	+	0.829136i	$0.311167\pi$
$29$	−0.661420	+	8.40414i	−0.122823	+	1.56061i	−0.681870	+	0.731474i	$0.738833\pi$
$30$	0.0596687	+	0.102212i	0.0108940	+	0.0186613i
$31$	1.13657	−	3.49801i	0.204135	−	0.628262i	−0.795613	−	0.605805i	$-0.792851\pi$
$31$	1.13657	−	3.49801i	0.204135	−	0.628262i	0.999748	−	0.0224569i	$-0.00714884\pi$
$32$	−3.55046	−	4.40389i	−0.627638	−	0.778506i
$33$	0.183972	+	0.361066i	0.0320255	+	0.0628535i
$34$	−0.165811	+	1.65397i	−0.0284364	+	0.283654i
$35$	−2.85315	−	0.684981i	−0.482271	−	0.115783i
$36$	2.48714	+	5.44483i	0.414524	+	0.907472i
$37$	2.54290	+	7.82623i	0.418049	+	1.28662i	0.909495	+	0.415715i	$0.136469\pi$
$37$	2.54290	+	7.82623i	0.418049	+	1.28662i	−0.491445	+	0.870908i	$0.663531\pi$
$38$	−2.52305	−	2.24991i	−0.409292	−	0.364984i
$39$	0.0433642	−	0.00686822i	0.00694383	−	0.00109979i
$40$	2.39009	−	1.51245i	0.377906	−	0.239139i
$41$	−6.21176	+	1.55370i	−0.970114	+	0.242648i
$41$	−6.21176	+	1.55370i	−0.970114	+	0.242648i
$42$	0.327911	+	0.114350i	0.0505978	+	0.0176446i
$43$	0.382077	+	2.41234i	0.0582662	+	0.367878i	0.999543	+	0.0302413i	$0.00962757\pi$
$43$	0.382077	+	2.41234i	0.0582662	+	0.367878i	−0.941276	+	0.337637i	$0.890372\pi$
$44$	8.46593	−	4.70248i	1.27629	−	0.708926i
$45$	−2.84651	+	0.924887i	−0.424332	+	0.137874i
$46$	1.07991	+	1.12710i	0.159224	+	0.166181i
$47$	−0.189762	+	0.790414i	−0.0276796	+	0.115294i	−0.984499	−	0.175388i	$-0.943882\pi$
$47$	−0.189762	+	0.790414i	−0.0276796	+	0.115294i	0.956820	+	0.290682i	$0.0938820\pi$
$48$	−0.299321	+	0.149894i	−0.0432033	+	0.0216354i
$49$	−1.43423	+	0.730778i	−0.204890	+	0.104397i
$50$	0.614959	+	1.27351i	0.0869683	+	0.180101i
$51$	0.0935534	+	0.0303973i	0.0131001	+	0.00425648i
$52$	−0.201110	−	1.02978i	−0.0278889	−	0.142805i
$53$	2.37886	+	0.187220i	0.326761	+	0.0257167i	0.240779	−	0.970580i	$-0.422597\pi$
$53$	2.37886	+	0.187220i	0.326761	+	0.0257167i	0.0859825	+	0.996297i	$0.472597\pi$
$54$	0.693080	−	0.150802i	0.0943162	−	0.0205215i
$55$	1.85301	+	4.47355i	0.249859	+	0.603214i
$56$	2.45061	−	7.92918i	0.327476	−	1.05958i
$57$	−0.161843	+	0.117586i	−0.0214366	+	0.0155746i
$58$	3.03029	−	11.5305i	0.397897	−	1.51402i
$59$	8.44679	−	11.6260i	1.09968	−	1.51358i	0.263869	−	0.964559i	$-0.415001\pi$
$59$	8.44679	−	11.6260i	1.09968	−	1.51358i	0.835810	−	0.549019i	$-0.184999\pi$
$60$	−0.0573850	−	0.157233i	−0.00740838	−	0.0202987i
$61$	−0.995078	+	6.28267i	−0.127407	+	0.804414i	0.838382	+	0.545083i	$0.183502\pi$
$61$	−0.995078	+	6.28267i	−0.127407	+	0.804414i	−0.965789	+	0.259331i	$0.916498\pi$
$62$	−2.45997	+	4.58305i	−0.312416	+	0.582048i
$63$	−4.58865	+	7.48799i	−0.578115	+	0.943398i
$64$	3.83582	+	7.02043i	0.479477	+	0.877554i
$65$	0.523001	−	0.0411610i	0.0648703	−	0.00510540i
$66$	−0.165403	−	0.548699i	−0.0203597	−	0.0675402i
$67$	1.49032	−	1.27285i	0.182071	−	0.155503i	−0.553741	−	0.832689i	$-0.686800\pi$
$67$	1.49032	−	1.27285i	0.182071	−	0.155503i	0.735813	+	0.677185i	$0.236800\pi$
$68$	0.645978	−	2.26030i	0.0783364	−	0.274102i
$69$	0.0787602	−	0.0482643i	0.00948162	−	0.00581034i
$70$	3.79893	+	1.66957i	0.454059	+	0.199552i
$71$	0.811324	+	0.692936i	0.0962864	+	0.0822364i	0.696288	−	0.717762i	$-0.254834\pi$
$71$	0.811324	+	0.692936i	0.0962864	+	0.0822364i	−0.600002	+	0.799999i	$0.704834\pi$
$72$	−2.09463	−	8.20224i	−0.246855	−	0.966643i
$73$	−6.02934	+	6.02934i	−0.705680	+	0.705680i	−0.965624	−	0.259943i	$-0.916296\pi$
$73$	−6.02934	+	6.02934i	−0.705680	+	0.705680i	0.259943	+	0.965624i	$0.416296\pi$
$74$	−1.57441	−	11.5305i	−0.183021	−	1.34040i
$75$	0.0813767	−	0.0195368i	0.00939657	−	0.00225592i
$76$	2.94665	+	3.76470i	0.338004	+	0.431841i
$77$	12.6594	+	6.45026i	1.44267	+	0.735076i
$78$	−0.0620765	−	0.00132719i	−0.00702878	−	0.000150274i
$79$	2.37199	+	0.982510i	0.266870	+	0.110541i	0.512106	−	0.858922i	$-0.328866\pi$
$79$	2.37199	+	0.982510i	0.266870	+	0.110541i	−0.245236	+	0.969463i	$0.578866\pi$
$80$	−3.70609	+	1.50495i	−0.414354	+	0.168259i
$81$			8.93701i			0.993002i
$82$	9.03529	−	0.602986i	0.997781	−	0.0665886i
$83$			6.72545i			0.738214i	0.929387	+	0.369107i	$0.120336\pi$
$83$			6.72545i			0.738214i	−0.929387	+	0.369107i	$0.879664\pi$
$84$	−0.427666	−	0.241465i	−0.0466622	−	0.0263460i
$85$	1.08593	+	0.449805i	0.117785	+	0.0487882i
$86$	0.0738310	−	3.45330i	0.00796140	−	0.372379i
$87$	−0.628613	−	0.320294i	−0.0673944	−	0.0343392i
$88$	−12.9630	+	4.41944i	−1.38186	+	0.471113i
$89$	3.00548	−	0.721551i	0.318580	−	0.0764842i	−0.0710018	−	0.997476i	$-0.522620\pi$
$89$	3.00548	−	0.721551i	0.318580	−	0.0764842i	0.389582	+	0.920992i	$0.372620\pi$
$90$	4.19382	−	0.572634i	0.442068	−	0.0603609i
$91$	1.08848	−	1.08848i	0.114104	−	0.114104i
$92$	−1.22003	−	1.83974i	−0.127197	−	0.191806i
$93$	0.234061	+	0.199907i	0.0242710	+	0.0207294i
$94$	0.462525	−	1.05242i	0.0477058	−	0.108549i
$95$	−2.03814	+	1.24897i	−0.209108	+	0.128142i
$96$	0.454211	−	0.133475i	0.0463577	−	0.0136228i
$97$	−8.95591	+	7.64907i	−0.909335	+	0.776646i	−0.975233	−	0.221181i	$-0.929009\pi$
$97$	−8.95591	+	7.64907i	−0.909335	+	0.776646i	0.0658976	+	0.997826i	$0.479009\pi$
$98$	2.17955	−	0.657017i	0.220168	−	0.0663687i
$99$	14.4478	−	1.13707i	1.45206	−	0.114280i
$100$	−0.536173	−	1.92679i	−0.0536173	−	0.192679i
$101$	1.64387	−	2.68256i	0.163572	−	0.266925i	−0.760344	−	0.649520i	$-0.774970\pi$
$101$	1.64387	−	2.68256i	0.163572	−	0.266925i	0.923916	+	0.382596i	$0.124970\pi$
$102$	−0.122572	−	0.0657911i	−0.0121365	−	0.00651429i
$103$	−1.68419	+	10.6336i	−0.165948	+	1.04776i	0.754331	+	0.656494i	$0.227961\pi$
$103$	−1.68419	+	10.6336i	−0.165948	+	1.04776i	−0.920279	+	0.391262i	$0.872039\pi$
$104$	0.0213815	+	1.48369i	0.00209663	+	0.145488i
$105$	0.144338	−	0.198664i	0.0140859	−	0.0193876i
$106$	−3.26379	−	0.857748i	−0.317007	−	0.0833119i
$107$	10.6753	−	7.75606i	1.03202	−	0.749807i	0.0633086	−	0.997994i	$-0.479835\pi$
$107$	10.6753	−	7.75606i	1.03202	−	0.749807i	0.968712	+	0.248187i	$0.0798348\pi$
$108$	−1.00245	+	0.0358897i	−0.0964611	+	0.00345349i
$109$	5.48561	+	13.2434i	0.525426	+	1.26849i	0.934491	+	0.355986i	$0.115855\pi$
$109$	5.48561	+	13.2434i	0.525426	+	1.26849i	−0.409065	+	0.912505i	$0.634145\pi$
$110$	−1.45590	−	6.69126i	−0.138815	−	0.637987i
$111$	−0.686552	−	0.0540328i	−0.0651647	−	0.00512857i
$112$	−5.40117	+	10.4203i	−0.510362	+	0.984624i
$113$	−7.38000	−	2.39791i	−0.694252	−	0.225576i	−0.0594274	−	0.998233i	$-0.518927\pi$
$113$	−7.38000	−	2.39791i	−0.694252	−	0.225576i	−0.634824	+	0.772657i	$0.718927\pi$
$114$	0.254764	−	0.123022i	0.0238608	−	0.0115220i
$115$	0.983453	−	0.501095i	0.0917075	−	0.0467273i
$116$	−7.11200	+	15.2868i	−0.660333	+	1.41935i
$117$	0.366551	−	1.52680i	0.0338877	−	0.141152i
$118$	−14.6744	+	14.0601i	−1.35089	+	1.29434i
$119$	3.28008	−	1.06576i	0.300685	−	0.0976983i
$120$	0.0403943	+	0.233236i	0.00368748	+	0.0212914i
$121$	−1.94703	−	12.2931i	−0.177003	−	1.11755i
$122$	2.96209	−	8.49413i	0.268175	−	0.769023i
$123$	0.0788103	−	0.530044i	0.00710608	−	0.0477925i
$124$	4.57419	−	5.76094i	0.410774	−	0.517348i
$125$	0.987688	−	0.156434i	0.0883415	−	0.0139919i
$126$	8.26604	−	9.26952i	0.736397	−	0.825795i
$127$	−1.81014	−	5.57105i	−0.160624	−	0.494351i	0.838063	−	0.545574i	$-0.183688\pi$
$127$	−1.81014	−	5.57105i	−0.160624	−	0.494351i	−0.998687	+	0.0512226i	$0.983688\pi$
$128$	−3.57612	−	10.7337i	−0.316087	−	0.948730i
$129$	−0.198755	−	0.0477169i	−0.0174994	−	0.00420124i
$130$	−0.738221	−	0.0740069i	−0.0647463	−	0.00649083i
$131$	4.79220	+	9.40523i	0.418697	+	0.821739i	0.999968	+	0.00802868i	$0.00255564\pi$
$131$	4.79220	+	9.40523i	0.418697	+	0.821739i	−0.581271	+	0.813710i	$0.697444\pi$
$132$	0.0924562	+	0.805177i	0.00804728	+	0.0700816i
$133$	−2.16742	+	6.67064i	−0.187939	+	0.578417i
$134$	−2.39369	+	1.39737i	−0.206783	+	0.120714i
$135$	0.0393510	−	0.500002i	0.00338679	−	0.0430333i
$136$	−1.46646	+	2.98362i	−0.125748	+	0.255843i
$137$	16.3599	−	6.77649i	1.39772	−	0.578955i	0.448562	−	0.893752i	$-0.351936\pi$
$137$	16.3599	−	6.77649i	1.39772	−	0.578955i	0.949159	+	0.314797i	$0.101936\pi$
$138$	−0.121731	+	0.0474003i	−0.0103624	+	0.00403498i
$139$	−0.942267	−	1.29692i	−0.0799220	−	0.110003i	0.767184	−	0.641427i	$-0.221657\pi$
$139$	−0.942267	−	1.29692i	−0.0799220	−	0.110003i	−0.847106	+	0.531424i	$0.821657\pi$
$140$	−4.86805	−	3.27731i	−0.411425	−	0.276983i
$141$	−0.0550363	−	0.0399862i	−0.00463489	−	0.00336744i
$142$	−0.955210	−	1.16807i	−0.0801595	−	0.0980222i
$143$	−2.50900	−	0.397386i	−0.209813	−	0.0332311i
$144$	0.856142	+	11.9413i	0.0713452	+	0.995111i
$145$	−7.18787	−	4.40473i	−0.596920	−	0.365793i
$146$	9.90495	−	6.87776i	0.819739	−	0.569208i
$147$	−0.0105694	−	0.134297i	−0.000871749	−	0.0110766i
$148$	−0.703416	+	16.4429i	−0.0578205	+	1.35160i
$149$	−0.430690	−	0.504273i	−0.0352835	−	0.0413117i	0.742484	−	0.669864i	$-0.233648\pi$
$149$	−0.430690	−	0.504273i	−0.0352835	−	0.0413117i	−0.777767	+	0.628553i	$0.783648\pi$
$150$	−0.118161	+	0.00676182i	−0.00964779	+	0.000552100i
$151$	−3.27841	−	5.34989i	−0.266794	−	0.435367i	0.690987	−	0.722867i	$-0.257176\pi$
$151$	−3.27841	−	5.34989i	−0.266794	−	0.435367i	−0.957781	+	0.287499i	$0.907176\pi$
$152$	−3.15593	−	5.97926i	−0.255979	−	0.484982i
$153$	2.28473	−	2.67508i	0.184710	−	0.216267i
$154$	−15.9995	−	12.1552i	−1.28927	−	0.979491i
$155$	2.60076	+	2.60076i	0.208898	+	0.208898i
$156$	0.0860621	+	0.0174307i	0.00689048	+	0.00139557i
$157$	−0.768540	−	3.20120i	−0.0613362	−	0.255484i	0.933274	−	0.359164i	$-0.116938\pi$
$157$	−0.768540	−	3.20120i	−0.0613362	−	0.255484i	−0.994611	+	0.103680i	$0.966938\pi$
$158$	−3.05458	−	1.96287i	−0.243009	−	0.156158i
$159$	−0.0906619	+	0.177934i	−0.00718996	+	0.0141111i
$160$	5.53577	−	1.16415i	0.437641	−	0.0920344i
$161$	1.23938	−	2.99214i	0.0976772	−	0.235814i
$162$	2.24353	−	12.4381i	0.176268	−	0.977232i
$163$	−13.5248			−1.05934			−0.529671	−	0.848203i	$-0.677685\pi$
$163$	−13.5248			−1.05934			−0.529671	+	0.848203i	$0.677685\pi$
$164$	−12.7263	−	1.42899i	−0.993755	−	0.111585i
$165$	−0.405234			−0.0315474
$166$	1.68834	−	9.36018i	0.131041	−	0.726491i
$167$	5.75185	−	13.8862i	0.445091	−	1.07455i	−0.529047	−	0.848593i	$-0.677450\pi$
$167$	5.75185	−	13.8862i	0.445091	−	1.07455i	0.974138	−	0.225953i	$-0.0725495\pi$
$168$	0.534589	+	0.443420i	0.0412444	+	0.0342106i
$169$	5.77693	−	11.3379i	0.444379	−	0.872143i
$170$	−1.39842	−	0.898627i	−0.107254	−	0.0689215i
$171$	1.67016	+	6.95673i	0.127721	+	0.531994i
$172$	−0.969663	+	4.78761i	−0.0739361	+	0.365052i
$173$	−16.1039	−	16.1039i	−1.22436	−	1.22436i	−0.966067	−	0.258292i	$-0.916840\pi$
$173$	−16.1039	−	16.1039i	−1.22436	−	1.22436i	−0.258292	−	0.966067i	$-0.583160\pi$
$174$	0.794469	+	0.603577i	0.0602285	+	0.0457570i
$175$	1.90563	−	2.23120i	0.144052	−	0.168663i
$176$	19.1507	−	2.89657i	1.44354	−	0.218337i
$177$	0.628386	+	1.02543i	0.0472324	+	0.0770763i
$178$	−4.36402	+	0.249733i	−0.327097	+	0.0187183i
$179$	−13.5556	−	15.8716i	−1.01319	−	1.18630i	−0.982403	−	0.186773i	$-0.940197\pi$
$179$	−13.5556	−	15.8716i	−1.01319	−	1.18630i	−0.0307919	−	0.999526i	$-0.509803\pi$
$180$	−5.98052	−	0.255842i	−0.445762	−	0.0190694i
$181$	−0.454904	−	5.78010i	−0.0338127	−	0.429631i	−0.990404	−	0.138200i	$-0.955868\pi$
$181$	−0.454904	−	5.78010i	−0.0338127	−	0.429631i	0.956592	−	0.291432i	$-0.0941316\pi$
$182$	−1.78815	+	1.24165i	−0.132547	+	0.0920372i
$183$	−0.453898	−	0.278149i	−0.0335531	−	0.0205614i
$184$	1.23613	+	2.86674i	0.0911289	+	0.211339i
$185$	−8.12767	−	1.28730i	−0.597558	−	0.0946439i
$186$	−0.275571	−	0.336980i	−0.0202059	−	0.0247085i
$187$	−4.60447	−	3.34534i	−0.336712	−	0.244636i
$188$	−0.907920	+	1.34860i	−0.0662168	+	0.0983571i
$189$	−0.865017	−	1.19059i	−0.0629207	−	0.0866029i
$190$	3.15012	−	1.22661i	0.228534	−	0.0889878i
$191$	−20.1492	+	8.34608i	−1.45795	+	0.603901i	−0.964074	−	0.265634i	$-0.914419\pi$
$191$	−20.1492	+	8.34608i	−1.45795	+	0.603901i	−0.493872	+	0.869535i	$0.664419\pi$
$192$	−0.665657	+	0.0717407i	−0.0480397	+	0.00517744i
$193$	1.71978	−	21.8519i	0.123792	−	1.57293i	−0.550734	−	0.834681i	$-0.685652\pi$
$193$	1.71978	−	21.8519i	0.123792	−	1.57293i	0.674527	−	0.738250i	$-0.264348\pi$
$194$	14.3846	−	8.39736i	1.03276	−	0.602895i
$195$	−0.0135673	+	0.0417559i	−0.000971575	+	0.00299020i
$196$	−3.19834	+	0.367256i	−0.228453	+	0.0262326i
$197$	4.83469	+	9.48862i	0.344458	+	0.676036i	0.996629	−	0.0820351i	$-0.0261420\pi$
$197$	4.83469	+	9.48862i	0.344458	+	0.676036i	−0.652172	+	0.758071i	$0.726142\pi$
$198$	−20.3933	−	2.04443i	−1.44929	−	0.145291i
$199$	−18.2970	−	4.39273i	−1.29704	−	0.311392i	−0.474580	−	0.880213i	$-0.657400\pi$
$199$	−18.2970	−	4.39273i	−1.29704	−	0.311392i	−0.822462	+	0.568821i	$0.807400\pi$
$200$	0.262523	+	2.81622i	0.0185632	+	0.199137i
$201$	0.0506855	+	0.155994i	0.00357508	+	0.0110030i
$202$	−2.96129	+	3.32079i	−0.208356	+	0.233650i
$203$	−24.4314	+	3.86955i	−1.71474	+	0.271589i
$204$	0.154075	+	0.122335i	0.0107874	+	0.00856519i
$205$	1.43572	−	6.24009i	0.100275	−	0.435827i
$206$	5.01341	−	14.3765i	0.349301	−	1.00166i
$207$	−0.516787	−	3.26286i	−0.0359192	−	0.226785i
$208$	0.342704	−	2.07030i	0.0237623	−	0.143549i
$209$	11.0081	−	3.57674i	0.761444	−	0.247408i
$210$	−0.250755	+	0.240257i	−0.0173037	+	0.0165793i
$211$	−5.62544	+	23.4316i	−0.387271	+	1.61310i	0.349485	+	0.936942i	$0.386357\pi$
$211$	−5.62544	+	23.4316i	−0.387271	+	1.61310i	−0.736756	+	0.676159i	$0.763643\pi$
$212$	4.32706	+	2.01311i	0.297184	+	0.138261i
$213$	−0.0795606	+	0.0405381i	−0.00545140	+	0.00277763i
$214$	−16.8045	+	8.11463i	−1.14873	+	0.554705i
$215$	−2.32287	−	0.754746i	−0.158418	−	0.0514732i
$216$	1.40418	+	0.201704i	0.0955422	+	0.0137242i
$217$	10.7589	+	0.846744i	0.730362	+	0.0574807i
$218$	−4.31002	−	19.8087i	−0.291911	−	1.34161i
$219$	−0.273082	−	0.659277i	−0.0184531	−	0.0445498i
$220$	0.346494	+	9.67808i	0.0233606	+	0.652496i
$221$	−0.498868	+	0.362449i	−0.0335575	+	0.0243809i
$222$	0.941948	+	0.247551i	0.0632194	+	0.0166145i
$223$	13.3020	−	18.3086i	0.890765	−	1.22603i	−0.0825561	−	0.996586i	$-0.526308\pi$
$223$	13.3020	−	18.3086i	0.890765	−	1.22603i	0.973321	−	0.229447i	$-0.0736916\pi$
$224$	10.1330	−	13.1466i	0.677038	−	0.878392i
$225$	0.468208	−	2.95615i	0.0312139	−	0.197076i
$226$	9.66918	+	5.18995i	0.643184	+	0.345231i
$227$	−8.91538	+	14.5486i	−0.591734	+	0.965623i	0.406905	+	0.913471i	$0.366608\pi$
$227$	−8.91538	+	14.5486i	−0.591734	+	0.965623i	−0.998639	+	0.0521521i	$0.983392\pi$
$228$	−0.385452	+	0.107261i	−0.0255272	+	0.00710351i
$229$	14.7287	−	1.15917i	0.973301	−	0.0766004i	0.418175	−	0.908367i	$-0.362670\pi$
$229$	14.7287	−	1.15917i	0.973301	−	0.0766004i	0.555126	+	0.831766i	$0.312670\pi$
$230$	−1.49452	+	0.450517i	−0.0985457	+	0.0297062i
$231$	−0.904159	+	0.772224i	−0.0594893	+	0.0508086i
$232$	13.7357	−	19.4902i	0.901795	−	1.27959i
$233$	−4.33291	+	2.65521i	−0.283858	+	0.173948i	−0.657138	−	0.753770i	$-0.728233\pi$
$233$	−4.33291	+	2.65521i	−0.283858	+	0.173948i	0.373280	+	0.927719i	$0.378233\pi$
$234$	−0.893432	+	2.03291i	−0.0584055	+	0.132895i
$235$	−0.618114	−	0.527919i	−0.0403213	−	0.0344376i
$236$	23.9528	−	15.8844i	1.55920	−	1.03398i
$237$	−0.151932	+	0.151932i	−0.00986907	+	0.00986907i
$238$	−4.83261	+	0.659856i	−0.313252	+	0.0427721i
$239$	−16.3962	+	3.93638i	−1.06058	+	0.254623i	−0.725966	−	0.687731i	$-0.758607\pi$
$239$	−16.3962	+	3.93638i	−1.06058	+	0.254623i	−0.334617	+	0.942354i	$0.608607\pi$
$240$	0.00233209	−	0.334748i	0.000150536	−	0.0216079i
$241$	−4.39900	−	2.24140i	−0.283364	−	0.144381i	0.306532	−	0.951860i	$-0.400831\pi$
$241$	−4.39900	−	2.24140i	−0.283364	−	0.144381i	−0.589896	+	0.807479i	$0.700831\pi$
$242$	−0.376237	+	17.5977i	−0.0241854	+	1.13123i
$243$	−2.08111	−	0.862022i	−0.133503	−	0.0552988i
$244$	−6.25485	+	11.0782i	−0.400426	+	0.709206i
$245$		−	1.60968i		−	0.102838i
$246$	−0.242746	+	0.717907i	−0.0154769	+	0.0457721i
$247$		−	1.25404i		−	0.0797925i
$248$	−7.81236	+	6.86952i	−0.496085	+	0.436215i
$249$	−0.520002	−	0.215392i	−0.0329538	−	0.0136499i
$250$	−1.41389	−	0.0302288i	−0.0894223	−	0.00191184i
$251$	−1.65138	−	0.841420i	−0.104234	−	0.0531100i	0.401096	−	0.916036i	$-0.368629\pi$
$251$	−1.65138	−	0.841420i	−0.104234	−	0.0531100i	−0.505330	+	0.862926i	$0.668629\pi$
$252$	−13.8313	+	10.8258i	−0.871290	+	0.681962i
$253$	−5.19687	+	1.24766i	−0.326724	+	0.0784396i
$254$	1.12073	+	8.20795i	0.0703210	+	0.515013i
$255$	−0.0695566	+	0.0695566i	−0.00435580	+	0.00435580i
$256$	2.28253	+	15.8364i	0.142658	+	0.989772i
$257$	−1.41977	−	1.21260i	−0.0885630	−	0.0756400i	0.604064	−	0.796936i	$-0.293547\pi$
$257$	−1.41977	−	1.21260i	−0.0885630	−	0.0756400i	−0.692627	+	0.721296i	$0.743547\pi$
$258$	0.264639	+	0.116305i	0.0164757	+	0.00724084i
$259$	−20.5876	+	12.6161i	−1.27925	+	0.783926i
$260$	1.00884	+	0.288321i	0.0625659	+	0.0178809i
$261$	−19.1861	+	16.3864i	−1.18759	+	1.01430i
$262$	−4.30850	−	14.2928i	−0.266180	−	0.883012i
$263$	10.9001	−	0.857858i	0.672130	−	0.0528978i	0.262198	−	0.965014i	$-0.415552\pi$
$263$	10.9001	−	0.857858i	0.672130	−	0.0528978i	0.409932	+	0.912116i	$0.365552\pi$
$264$	0.0734536	−	1.14382i	0.00452075	−	0.0703971i
$265$	−1.24679	+	2.03458i	−0.0765900	+	0.124983i
$266$	4.69110	−	8.73978i	0.287630	−	0.535870i
$267$	−0.0404653	+	0.255488i	−0.00247643	+	0.0156356i
$268$	3.68222	−	1.34389i	0.224927	−	0.0820911i
$269$	4.87370	−	6.70807i	0.297155	−	0.408998i	−0.634167	−	0.773196i	$-0.718657\pi$
$269$	4.87370	−	6.70807i	0.297155	−	0.408998i	0.931322	+	0.364198i	$0.118657\pi$
$270$	−0.180286	+	0.686001i	−0.0109719	+	0.0417487i
$271$	19.1159	−	13.8885i	1.16121	−	0.843666i	0.171276	−	0.985223i	$-0.445211\pi$
$271$	19.1159	−	13.8885i	1.16121	−	0.843666i	0.989930	+	0.141558i	$0.0452110\pi$
$272$	2.78996	−	3.78432i	0.169166	−	0.229458i
$273$	0.0492997	+	0.119020i	0.00298376	+	0.00720342i
$274$	−24.4701	+	5.32426i	−1.47829	+	0.321650i
$275$	−4.82721	−	0.379910i	−0.291092	−	0.0229094i
$276$	0.181319	−	0.0354105i	0.0109141	−	0.00213146i
$277$	15.4863	+	5.03179i	0.930479	+	0.302331i	0.734759	−	0.678329i	$-0.237295\pi$
$277$	15.4863	+	5.03179i	0.930479	+	0.302331i	0.195721	+	0.980660i	$0.437295\pi$
$278$	0.985828	+	2.04154i	0.0591260	+	0.122443i
$279$	9.80849	−	4.99768i	0.587219	−	0.299203i
$280$	5.95240	+	5.78328i	0.355724	+	0.345617i
$281$	5.44543	−	22.6818i	0.324847	−	1.35309i	−0.535998	−	0.844219i	$-0.680065\pi$
$281$	5.44543	−	22.6818i	0.324847	−	1.35309i	0.860845	−	0.508867i	$-0.169935\pi$
$282$	0.0665589	+	0.0694671i	0.00396353	+	0.00413671i
$283$	22.4372	−	7.29029i	1.33375	−	0.433363i	0.446558	−	0.894755i	$-0.352650\pi$
$283$	22.4372	−	7.29029i	1.33375	−	0.433363i	0.887196	+	0.461392i	$0.152650\pi$
$284$	1.03619	+	1.86546i	0.0614865	+	0.110695i
$285$	−0.0312945	−	0.197586i	−0.00185373	−	0.0117040i
$286$	3.39215	+	1.18292i	0.200582	+	0.0699474i
$287$	−8.68789	−	16.6588i	−0.512830	−	0.983341i
$288$	1.80619	−	16.8343i	0.106431	−	0.991972i
$289$	15.4262	−	2.44326i	0.907421	−	0.143721i
$290$	8.89799	+	7.93473i	0.522508	+	0.465943i
$291$	−0.304590	−	0.937430i	−0.0178554	−	0.0549531i
$292$	−15.5118	+	7.08564i	−0.907761	+	0.414656i
$293$	2.63900	+	0.633569i	0.154172	+	0.0370135i	0.309797	−	0.950803i	$-0.399739\pi$
$293$	2.63900	+	0.633569i	0.154172	+	0.0370135i	−0.155624	+	0.987816i	$0.549739\pi$
$294$	−0.0190036	+	0.189562i	−0.00110831	+	0.0110555i
$295$	6.52409	+	12.8042i	0.379847	+	0.745492i
$296$	5.10678	−	22.7079i	0.296826	−	1.31987i
$297$	−0.750468	+	2.30970i	−0.0435466	+	0.134023i
$298$	0.472823	+	0.809944i	0.0273899	+	0.0469188i
$299$	−0.0454317	+	0.577265i	−0.00262739	+	0.0333841i
$300$	0.166148	+	0.0202520i	0.00959257	+	0.00116925i
$301$	−6.62105	+	2.74253i	−0.381631	+	0.158077i
$302$	3.21972	+	8.26873i	0.185274	+	0.475812i
$303$	0.154764	+	0.213015i	0.00889097	+	0.0122374i
$304$	2.89125	+	9.11392i	0.165825	+	0.522719i
$305$	−5.14615	−	3.73889i	−0.294667	−	0.214088i
$306$	−3.85133	+	3.14950i	−0.220166	+	0.180045i
$307$	5.81094	+	0.920363i	0.331648	+	0.0525279i	0.320038	−	0.947405i	$-0.396304\pi$
$307$	5.81094	+	0.920363i	0.331648	+	0.0525279i	0.0116101	+	0.999933i	$0.496304\pi$
$308$	19.2159	+	20.9335i	1.09493	+	1.19279i
$309$	−0.768234	−	0.470774i	−0.0437033	−	0.0267814i
$310$	−2.96673	−	4.27251i	−0.168499	−	0.242662i
$311$	−1.17220	−	14.8942i	−0.0664693	−	0.844572i	−0.936295	−	0.351214i	$-0.885769\pi$
$311$	−1.17220	−	14.8942i	−0.0664693	−	0.844572i	0.869826	−	0.493359i	$-0.164231\pi$
$312$	−0.115401	−	0.0458640i	−0.00653332	−	0.00259654i
$313$	−18.1537	−	21.2553i	−1.02611	−	1.20142i	−0.979279	−	0.202515i	$-0.935088\pi$
$313$	−18.1537	−	21.2553i	−1.02611	−	1.20142i	−0.0468291	−	0.998903i	$-0.514912\pi$
$314$	0.265997	+	4.64822i	0.0150111	+	0.262314i
$315$	−4.58865	−	7.48799i	−0.258541	−	0.421901i
$316$	3.75847	+	3.49865i	0.211430	+	0.196814i
$317$	0.986570	−	1.15512i	0.0554113	−	0.0648783i	−0.732008	−	0.681296i	$-0.761417\pi$
$317$	0.986570	−	1.15512i	0.0554113	−	0.0648783i	0.787419	+	0.616418i	$0.211417\pi$
$318$	0.170847	−	0.224881i	0.00958064	−	0.0126107i
$319$	28.8640	+	28.8640i	1.61607	+	1.61607i
$320$	−7.99668	+	0.230528i	−0.447028	+	0.0128869i
$321$	0.257796	+	1.07380i	0.0143888	+	0.0599336i
$322$	−2.47606	+	3.85319i	−0.137985	+	0.214730i
$323$	1.27555	−	2.50342i	0.0709738	−	0.139294i
$324$	−6.24488	+	16.7476i	−0.346938	+	0.930423i
$325$	−0.200763	+	0.484684i	−0.0111363	+	0.0268854i
$326$	18.8232	+	3.39523i	1.04252	+	0.188044i
$327$	−1.19965			−0.0663407
$328$	17.3531	+	5.18358i	0.958165	+	0.286215i
$329$	−2.38515			−0.131498
$330$	0.563986	+	0.101729i	0.0310464	+	0.00560000i
$331$	8.99032	−	21.7045i	0.494153	−	1.19299i	−0.458436	−	0.888728i	$-0.651590\pi$
$331$	8.99032	−	21.7045i	0.494153	−	1.19299i	0.952588	−	0.304262i	$-0.0984099\pi$
$332$	−4.69952	+	12.6032i	−0.257920	+	0.691692i
$333$	−11.1815	+	21.9449i	−0.612741	+	1.20257i
$334$	−11.4911	+	17.8822i	−0.628766	+	0.978472i
$335$	0.457529	+	1.90574i	0.0249975	+	0.104122i
$336$	−0.632701	−	0.751334i	−0.0345167	−	0.0409886i
$337$	11.4237	+	11.4237i	0.622290	+	0.622290i	0.946116	−	0.323827i	$-0.104970\pi$
$337$	11.4237	+	11.4237i	0.622290	+	0.622290i	−0.323827	+	0.946116i	$0.604970\pi$
$338$	−10.8863	+	14.3293i	−0.592136	+	0.779410i
$339$	0.421757	−	0.493814i	0.0229067	−	0.0268203i
$340$	1.72067	+	1.60173i	0.0933166	+	0.0868657i
$341$	−9.30546	−	15.1851i	−0.503919	−	0.822321i
$342$	−0.578054	−	10.1013i	−0.0312576	−	0.546218i
$343$	10.2719	+	12.0269i	0.554633	+	0.649392i
$344$	2.55140	−	6.41975i	0.137562	−	0.346130i
$345$	0.00724744	+	0.0920874i	0.000390189	+	0.00495782i
$346$	18.3700	+	26.4554i	0.987578	+	1.42225i
$347$	24.2411	+	14.8550i	1.30133	+	0.797458i	0.988335	−	0.152296i	$-0.0486668\pi$
$347$	24.2411	+	14.8550i	1.30133	+	0.797458i	0.312998	+	0.949754i	$0.398667\pi$
$348$	−0.954185	−	1.03947i	−0.0511497	−	0.0557216i
$349$	−23.7374	−	3.75964i	−1.27063	−	0.201249i	−0.515540	−	0.856865i	$-0.672409\pi$
$349$	−23.7374	−	3.75964i	−1.27063	−	0.201249i	−0.755094	+	0.655617i	$0.772409\pi$
$350$	−3.21228	+	2.62690i	−0.171704	+	0.140414i
$351$	0.212869	+	0.154659i	0.0113621	+	0.00825507i
$352$	−27.3803	−	0.776252i	−1.45937	−	0.0413744i
$353$	−6.13557	−	8.44489i	−0.326564	−	0.449476i	0.613893	−	0.789389i	$-0.289602\pi$
$353$	−6.13557	−	8.44489i	−0.326564	−	0.449476i	−0.940457	+	0.339913i	$0.889602\pi$
$354$	−0.617137	−	1.58490i	−0.0328004	−	0.0842364i
$355$	−0.985744	+	0.408308i	−0.0523178	+	0.0216708i
$356$	6.13634	+	0.747966i	0.325225	+	0.0396421i
$357$	−0.0226459	+	0.287744i	−0.00119855	+	0.0152290i
$358$	14.8817	+	25.4923i	0.786524	+	1.34731i
$359$	−5.46054	+	16.8058i	−0.288196	+	0.886977i	0.697226	+	0.716851i	$0.254417\pi$
$359$	−5.46054	+	16.8058i	−0.288196	+	0.886977i	−0.985422	+	0.170126i	$0.945583\pi$
$360$	8.25919	+	1.85741i	0.435298	+	0.0978939i
$361$	−6.03175	−	11.8380i	−0.317460	−	0.623051i
$362$	−0.817909	+	8.15867i	−0.0429883	+	0.428810i
$363$	1.01284	+	0.243161i	0.0531603	+	0.0127627i
$364$	2.80037	−	1.27918i	0.146779	−	0.0670472i
$365$	−2.63492	−	8.10944i	−0.137918	−	0.424467i
$366$	0.561889	+	0.501061i	0.0293704	+	0.0261909i
$367$	−0.575588	+	0.0911642i	−0.0300455	+	0.00475873i	−0.171439	−	0.985195i	$-0.554842\pi$
$367$	−0.575588	+	0.0911642i	−0.0300455	+	0.00475873i	0.141394	+	0.989953i	$0.454842\pi$
$368$	−1.00073	−	4.30011i	−0.0521669	−	0.224159i
$369$	−16.4346	−	9.85817i	−0.855550	−	0.513196i
$370$	10.9886	+	3.83195i	0.571268	+	0.199214i
$371$	1.09531	+	6.91549i	0.0568655	+	0.359034i
$372$	0.298933	+	0.538172i	0.0154989	+	0.0279029i
$373$	31.6956	−	10.2985i	1.64114	−	0.533237i	0.664344	−	0.747427i	$-0.268711\pi$
$373$	31.6956	−	10.2985i	1.64114	−	0.533237i	0.976792	+	0.214190i	$0.0687111\pi$
$374$	5.56849	+	5.81179i	0.287940	+	0.300521i
$375$	−0.0195368	+	0.0813767i	−0.00100888	+	0.00420227i
$376$	1.60215	−	1.64900i	0.0826247	−	0.0850409i
$377$	3.94056	−	2.00782i	0.202949	−	0.103408i
$378$	0.905007	+	1.87417i	0.0465485	+	0.0963967i
$379$	0.414518	+	0.134685i	0.0212924	+	0.00691831i	0.319644	−	0.947538i	$-0.396437\pi$
$379$	0.414518	+	0.134685i	0.0212924	+	0.00691831i	−0.298351	+	0.954456i	$0.596437\pi$
$380$	−4.69213	+	0.916343i	−0.240701	+	0.0470074i
$381$	0.488718	+	0.0384630i	0.0250378	+	0.00197052i
$382$	30.1379	−	6.55747i	1.54199	−	0.335510i
$383$	3.77908	+	9.12350i	0.193102	+	0.466189i	0.990542	−	0.137209i	$-0.0438131\pi$
$383$	3.77908	+	9.12350i	0.193102	+	0.466189i	−0.797440	+	0.603398i	$0.793813\pi$
$384$	0.944441	+	0.0672597i	0.0481958	+	0.00343233i
$385$	−11.4945	+	8.35121i	−0.585812	+	0.425617i
$386$	−7.87915	+	29.9807i	−0.401038	+	1.52598i
$387$	−4.29678	+	5.91401i	−0.218418	+	0.300626i
$388$	−22.1279	+	8.07597i	−1.12338	+	0.409995i
$389$	−4.67122	+	29.4929i	−0.236840	+	1.49535i	0.526955	+	0.849893i	$0.323334\pi$
$389$	−4.67122	+	29.4929i	−0.236840	+	1.49535i	−0.763795	+	0.645458i	$0.776666\pi$
$390$	0.0293647	−	0.0547080i	0.00148694	−	0.00277025i
$391$	−0.677864	+	1.10617i	−0.0342811	+	0.0559416i
$392$	4.54349	+	0.291773i	0.229481	+	0.0147368i
$393$	−0.880676	+	0.0693107i	−0.0444242	+	0.00349626i
$394$	−4.34670	−	14.4195i	−0.218984	−	0.726445i
$395$	−1.95228	+	1.66741i	−0.0982300	+	0.0838963i
$396$	27.8692	+	7.96483i	1.40048	+	0.400248i
$397$	27.0460	−	16.5738i	1.35740	−	0.831815i	0.362430	−	0.932011i	$-0.381947\pi$
$397$	27.0460	−	16.5738i	1.35740	−	0.831815i	0.994968	+	0.100196i	$0.0319471\pi$
$398$	24.3622	+	10.7068i	1.22117	+	0.536685i
$399$	−0.446349	−	0.381218i	−0.0223454	−	0.0190848i
$400$	0.341609	−	3.98539i	0.0170804	−	0.199269i
$401$	−12.9143	+	12.9143i	−0.644911	+	0.644911i	−0.951759	−	0.306848i	$-0.900726\pi$
$401$	−12.9143	+	12.9143i	−0.644911	+	0.644911i	0.306848	+	0.951759i	$0.400726\pi$
$402$	−0.0313814	−	0.229829i	−0.00156516	−	0.0114628i
$403$	−1.87625	+	0.450447i	−0.0934625	+	0.0224384i
$404$	4.95503	−	3.87832i	0.246522	−	0.192954i
$405$	−7.96294	−	4.05732i	−0.395682	−	0.201610i
$406$	34.9738	+	0.747736i	1.73572	+	0.0371095i
$407$	36.8128	+	15.2484i	1.82474	+	0.755833i
$408$	−0.183723	−	0.208939i	−0.00909566	−	0.0103440i
$409$		−	18.1047i		−	0.895220i	−0.894229	−	0.447610i	$-0.852275\pi$
$409$		−	18.1047i		−	0.895220i	0.894229	−	0.447610i	$-0.147725\pi$
$410$	−3.56467	+	8.32425i	−0.176047	+	0.411105i
$411$			1.48195i			0.0730992i
$412$	−10.5865	+	18.7500i	−0.521559	+	0.923748i
$413$	38.9567	+	16.1364i	1.91693	+	0.794019i
$414$	−0.0998619	+	4.67084i	−0.00490794	+	0.229559i
$415$	−5.99242	−	3.05329i	−0.294156	−	0.149880i
$416$	−0.996684	+	2.79532i	−0.0488664	+	0.137052i
$417$	0.130453	−	0.0313191i	0.00638832	−	0.00153370i
$418$	−16.2184	+	2.21450i	−0.793269	+	0.108315i
$419$	16.6748	−	16.6748i	0.814618	−	0.814618i	−0.170704	−	0.985322i	$-0.554604\pi$
$419$	16.6748	−	16.6748i	0.814618	−	0.814618i	0.985322	+	0.170704i	$0.0546043\pi$
$420$	0.409303	−	0.271430i	0.0199720	−	0.0132444i
$421$	−13.6712	−	11.6763i	−0.666293	−	0.569068i	0.250654	−	0.968077i	$-0.419354\pi$
$421$	−13.6712	−	11.6763i	−0.666293	−	0.569068i	−0.916947	+	0.399009i	$0.869354\pi$
$422$	13.7115	−	31.1989i	0.667463	−	1.51874i
$423$	−2.07441	+	1.27120i	−0.100861	+	0.0618079i
$424$	−5.51684	−	3.88801i	−0.267922	−	0.188818i
$425$	−0.893779	+	0.763360i	−0.0433547	+	0.0370284i
$426$	0.120905	−	0.0364464i	0.00585788	−	0.00176583i
$427$	−18.6070	+	1.46440i	−0.900457	+	0.0708675i
$428$	25.4248	−	7.07501i	1.22895	−	0.341984i
$429$	0.111080	−	0.181265i	0.00536297	−	0.00875157i
$430$	3.04339	+	1.63355i	0.146765	+	0.0787767i
$431$	2.81823	−	17.7936i	0.135749	−	0.857088i	−0.822001	−	0.569487i	$-0.807142\pi$
$431$	2.81823	−	17.7936i	0.135749	−	0.857088i	0.957750	−	0.287602i	$-0.0928580\pi$
$432$	−1.90364	−	0.633224i	−0.0915887	−	0.0304660i
$433$	−2.36579	+	3.25623i	−0.113693	+	0.156484i	−0.862071	−	0.506788i	$-0.830833\pi$
$433$	−2.36579	+	3.25623i	−0.113693	+	0.156484i	0.748378	+	0.663272i	$0.230833\pi$
$434$	−14.7612	−	3.87935i	−0.708559	−	0.186215i
$435$	0.570769	−	0.414688i	0.0273663	−	0.0198828i
$436$	1.02575	+	28.6508i	0.0491247	+	1.37213i
$437$	−1.00967	−	2.43756i	−0.0482991	−	0.116604i
$438$	0.214559	+	0.986106i	0.0102520	+	0.0471180i
$439$	−14.1582	−	1.11428i	−0.675736	−	0.0531816i	−0.264052	−	0.964508i	$-0.585059\pi$
$439$	−14.1582	−	1.11428i	−0.675736	−	0.0531816i	−0.411684	+	0.911327i	$0.635059\pi$
$440$	1.94733	−	13.5565i	0.0928353	−	0.646280i
$441$	−4.58196	−	1.48877i	−0.218188	−	0.0708937i
$442$	0.785290	−	0.379205i	0.0373524	−	0.0180369i
$443$	−19.1753	+	9.77032i	−0.911048	+	0.464202i	−0.845699	−	0.533660i	$-0.820816\pi$
$443$	−19.1753	+	9.77032i	−0.911048	+	0.464202i	−0.0653490	+	0.997862i	$0.520816\pi$
$444$	−1.24882	−	0.580995i	−0.0592662	−	0.0275728i
$445$	−0.721551	+	3.00548i	−0.0342048	+	0.142473i
$446$	−23.1092	+	22.1417i	−1.09425	+	1.04844i
$447$	0.0527831	−	0.0171503i	0.00249656	−	0.000811180i
$448$	−17.4029	+	15.7530i	−0.822210	+	0.744261i
$449$	3.86530	+	24.4045i	0.182415	+	1.15172i	0.893649	+	0.448766i	$0.148136\pi$
$449$	3.86530	+	24.4045i	0.182415	+	1.15172i	−0.711235	+	0.702955i	$0.751864\pi$
$450$	−1.39373	+	3.99669i	−0.0657013	+	0.188406i
$451$	−13.8135	+	27.7576i	−0.650453	+	1.30706i
$452$	−12.1542	−	9.65047i	−0.571687	−	0.453920i
$453$	0.518641	−	0.0821447i	0.0243679	−	0.00385949i
$454$	16.0603	−	18.0099i	0.753745	−	0.845248i
$455$	0.475684	+	1.46401i	0.0223004	+	0.0686337i
$456$	0.563381	−	0.0525175i	0.0263827	−	0.00245936i
$457$	−8.60804	−	2.06661i	−0.402667	−	0.0966718i	0.0270530	−	0.999634i	$-0.491388\pi$
$457$	−8.60804	−	2.06661i	−0.402667	−	0.0966718i	−0.429720	+	0.902962i	$0.641388\pi$
$458$	−20.7897	−	2.08418i	−0.971441	−	0.0973872i
$459$	0.267636	+	0.525265i	0.0124922	+	0.0245172i
$460$	2.19310	−	0.251827i	0.102254	−	0.0117415i
$461$	−6.44415	+	19.8330i	−0.300134	+	0.923717i	0.681315	+	0.731991i	$0.261409\pi$
$461$	−6.44415	+	19.8330i	−0.300134	+	0.923717i	−0.981448	+	0.191726i	$0.938591\pi$
$462$	1.45222	−	0.847769i	0.0675636	−	0.0394418i
$463$	1.86045	−	23.6393i	0.0864625	−	1.09861i	−0.788699	−	0.614779i	$-0.789245\pi$
$463$	1.86045	−	23.6393i	0.0864625	−	1.09861i	0.875162	−	0.483831i	$-0.160755\pi$
$464$	−24.0095	+	23.6773i	−1.11461	+	1.09919i
$465$	−0.284380	+	0.117794i	−0.0131878	+	0.00546257i
$466$	6.69690	−	2.60767i	0.310228	−	0.120798i
$467$	−20.1506	−	27.7349i	−0.932457	−	1.28342i	−0.958893	−	0.283767i	$-0.908416\pi$
$467$	−20.1506	−	27.7349i	−0.932457	−	1.28342i	0.0264359	−	0.999651i	$-0.491584\pi$
$468$	1.75377	−	2.60502i	0.0810683	−	0.120417i
$469$	4.65248	+	3.38022i	0.214831	+	0.156084i
$470$	0.727735	+	0.889904i	0.0335679	+	0.0410482i
$471$	0.272126	+	0.0431005i	0.0125389	+	0.00198597i
$472$	−37.3240	+	16.0941i	−1.71798	+	0.740789i
$473$	10.0837	+	6.17932i	0.463651	+	0.284125i
$474$	0.249593	−	0.173312i	0.0114642	−	0.00796048i
$475$	−0.187547	−	2.38301i	−0.00860526	−	0.109340i
$476$	6.89146	+	0.294812i	0.315870	+	0.0135127i
$477$	4.63831	+	5.43077i	0.212374	+	0.248658i
$478$	23.8077	−	1.36241i	1.08894	−	0.0623151i
$479$	−1.36206	−	2.22269i	−0.0622343	−	0.101557i	0.820010	−	0.572350i	$-0.193968\pi$
$479$	−1.36206	−	2.22269i	−0.0622343	−	0.101557i	−0.882244	+	0.470793i	$0.843968\pi$
$480$	−0.0872801	+	0.465301i	−0.00398377	+	0.0212380i
$481$	2.80371	−	3.28273i	0.127838	−	0.149679i
$482$	5.55965	+	4.22380i	0.253235	+	0.192389i
$483$	0.191655	+	0.191655i	0.00872060	+	0.00872060i
$484$	4.94133	−	24.3973i	0.224606	−	1.10897i
$485$	−2.74947	−	11.4524i	−0.124847	−	0.520026i
$486$	2.67999	+	1.72216i	0.121567	+	0.0781188i
$487$	10.9950	−	21.5788i	0.498229	−	0.977829i	−0.495772	−	0.868453i	$-0.665115\pi$
$487$	10.9950	−	21.5788i	0.498229	−	0.977829i	0.994000	−	0.109376i	$-0.0348853\pi$
$488$	11.4863	−	13.8479i	0.519958	−	0.626863i
$489$	0.433149	−	1.04572i	0.0195877	−	0.0472889i
$490$	−0.404090	+	2.24027i	−0.0182549	+	0.101205i
$491$	−38.3276			−1.72970			−0.864850	−	0.502030i	$-0.832587\pi$
$491$	−38.3276			−1.72970			−0.864850	+	0.502030i	$0.832587\pi$
$492$	0.518064	−	0.938211i	0.0233561	−	0.0422978i
$493$	9.90875			0.446268
$494$	−0.314811	+	1.74531i	−0.0141640	+	0.0785253i
$495$	−5.54604	+	13.3893i	−0.249276	+	0.601806i
$496$	12.5974	−	7.59949i	0.565640	−	0.341227i
$497$	−1.42131	+	2.78948i	−0.0637545	+	0.125125i
$498$	0.669644	+	0.430313i	0.0300075	+	0.0192828i
$499$	4.89796	+	20.4015i	0.219263	+	0.913295i	0.968105	+	0.250546i	$0.0806102\pi$
$499$	4.89796	+	20.4015i	0.219263	+	0.913295i	−0.748842	+	0.662749i	$0.769390\pi$
$500$	1.96020	+	0.397011i	0.0876628	+	0.0177549i
$501$	0.889449	+	0.889449i	0.0397376	+	0.0397376i
$502$	2.08709	+	1.58561i	0.0931513	+	0.0707692i
$503$	8.58020	−	10.0461i	0.382572	−	0.447935i	−0.535388	−	0.844606i	$-0.679835\pi$
$503$	8.58020	−	10.0461i	0.382572	−	0.447935i	0.917961	+	0.396671i	$0.129835\pi$
$504$	21.9675	−	11.5947i	0.978508	−	0.516468i
$505$	1.64387	+	2.68256i	0.0731514	+	0.119372i
$506$	7.54597	−	0.431823i	0.335459	−	0.0191969i
$507$	0.691613	+	0.809774i	0.0307156	+	0.0359633i
$508$	0.500723	−	11.7048i	0.0222160	−	0.519316i
$509$	0.488199	+	6.20316i	0.0216390	+	0.274950i	0.998212	+	0.0597656i	$0.0190353\pi$
$509$	0.488199	+	6.20316i	0.0216390	+	0.274950i	−0.976573	+	0.215185i	$0.930965\pi$
$510$	0.114267	−	0.0793443i	0.00505983	−	0.00351343i
$511$	−21.3326	−	13.0726i	−0.943699	−	0.578299i
$512$	0.798803	−	22.6133i	0.0353024	−	0.999377i
$513$	−1.18413	−	0.187548i	−0.0522807	−	0.00828044i
$514$	1.67157	+	2.04406i	0.0737296	+	0.0901596i
$515$	−8.70997	−	6.32817i	−0.383807	−	0.278852i
$516$	−0.339116	−	0.228303i	−0.0149288	−	0.0100505i
$517$	2.31355	+	3.18433i	0.101750	+	0.140047i
$518$	31.8200	−	12.3902i	1.39809	−	0.544396i
$519$	1.76088	−	0.729382i	0.0772942	−	0.0320163i
$520$	−1.33168	−	0.654530i	−0.0583982	−	0.0287030i
$521$	2.17668	−	27.6574i	0.0953622	−	1.21169i	−0.744023	−	0.668154i	$-0.767085\pi$
$521$	2.17668	−	27.6574i	0.0953622	−	1.21169i	0.839385	−	0.543538i	$-0.182915\pi$
$522$	30.8159	−	17.9895i	1.34878	−	0.787378i
$523$	3.81320	−	11.7358i	0.166740	−	0.513172i	−0.832421	−	0.554144i	$-0.813046\pi$
$523$	3.81320	−	11.7358i	0.166740	−	0.513172i	0.999160	+	0.0409723i	$0.0130455\pi$
$524$	2.40834	+	20.9737i	0.105209	+	0.916238i
$525$	0.111483	+	0.218798i	0.00486552	+	0.00954911i
$526$	−15.3856	−	1.54241i	−0.670846	−	0.0672525i
$527$	−4.20370	−	1.00922i	−0.183116	−	0.0439623i
$528$	−0.389371	+	1.57347i	−0.0169452	+	0.0684767i
$529$	−6.73092	−	20.7157i	−0.292649	−	0.900680i
$530$	2.24599	−	2.51865i	0.0975595	−	0.109403i
$531$	42.4814	−	6.72840i	1.84354	−	0.291988i
$532$	−8.72287	+	10.9860i	−0.378185	+	0.476303i
$533$	2.39771	+	2.35270i	0.103856	+	0.101907i
$534$	0.120455	−	0.345418i	0.00521259	−	0.0149477i
$535$	2.06422	+	13.0329i	0.0892438	+	0.563463i
$536$	−5.46211	+	0.945987i	−0.235927	+	0.0408604i
$537$	1.66131	−	0.539791i	0.0716907	−	0.0232937i
$538$	−8.46697	+	8.11250i	−0.365037	+	0.349755i
$539$	−1.81954	+	7.57892i	−0.0783731	+	0.326447i
$540$	0.423126	−	0.909486i	0.0182085	−	0.0391381i
$541$	11.4286	−	5.82317i	0.491355	−	0.250358i	−0.190714	−	0.981646i	$-0.561080\pi$
$541$	11.4286	−	5.82317i	0.491355	−	0.250358i	0.682069	+	0.731288i	$0.261080\pi$
$542$	−30.0911	+	14.5306i	−1.29252	+	0.624141i
$543$	0.461478	+	0.149943i	0.0198039	+	0.00643468i
$544$	−4.83294	+	4.56646i	−0.207211	+	0.195785i
$545$	−14.2904	−	1.12468i	−0.612134	−	0.0481760i
$546$	−0.0387346	−	0.178023i	−0.00165769	−	0.00761867i
$547$	1.04718	+	2.52811i	0.0447741	+	0.108094i	0.944684	−	0.327981i	$-0.106368\pi$
$547$	1.04718	+	2.52811i	0.0447741	+	0.108094i	−0.899910	+	0.436075i	$0.856368\pi$
$548$	35.3930	−	1.26714i	1.51191	−	0.0541294i
$549$	−15.4024	+	11.1905i	−0.657358	+	0.477599i
$550$	6.62292	+	1.74055i	0.282402	+	0.0742175i
$551$	−11.8446	+	16.3027i	−0.504597	+	0.694518i
$552$	−0.261241	+	0.00376475i	−0.0111192	+	0.000160238i
$553$	−1.17848	+	7.44064i	−0.0501142	+	0.316408i
$554$	−20.2899	−	10.8907i	−0.862035	−	0.462700i
$555$	0.359832	−	0.587192i	0.0152740	−	0.0249249i
$556$	−0.859527	−	3.08880i	−0.0364521	−	0.130994i
$557$	14.9223	−	1.17441i	0.632277	−	0.0497613i	0.241729	−	0.970344i	$-0.422285\pi$
$557$	14.9223	−	1.17441i	0.632277	−	0.0497613i	0.390548	+	0.920582i	$0.372285\pi$
$558$	−14.9056	+	4.49324i	−0.631005	+	0.190214i
$559$	0.974332	−	0.832158i	0.0412098	−	0.0351965i
$560$	−6.83246	−	9.54318i	−0.288724	−	0.403273i
$561$	0.406122	−	0.248872i	0.0171465	−	0.0105074i
$562$	−13.2727	+	30.2006i	−0.559875	+	1.27393i
$563$	−21.4715	−	18.3384i	−0.904915	−	0.772870i	0.0695109	−	0.997581i	$-0.477856\pi$
$563$	−21.4715	−	18.3384i	−0.904915	−	0.772870i	−0.974425	+	0.224711i	$0.927856\pi$
$564$	−0.0751948	−	0.113390i	−0.00316627	−	0.00477458i
$565$	5.48700	−	5.48700i	0.230840	−	0.230840i
$566$	−33.0572	+	4.51371i	−1.38950	+	0.189725i
$567$	−25.4987	+	6.12169i	−1.07084	+	0.257087i
$568$	−0.973819	−	2.85638i	−0.0408605	−	0.119851i
$569$	6.72321	+	3.42564i	0.281851	+	0.143610i	0.589202	−	0.807986i	$-0.299442\pi$
$569$	6.72321	+	3.42564i	0.281851	+	0.143610i	−0.307350	+	0.951596i	$0.599442\pi$
$570$	−0.00604723	+	0.282847i	−0.000253291	+	0.0118472i
$571$	23.1783	+	9.60075i	0.969980	+	0.401779i	0.810705	−	0.585455i	$-0.199084\pi$
$571$	23.1783	+	9.60075i	0.969980	+	0.401779i	0.159275	+	0.987234i	$0.449084\pi$
$572$	−4.42408	−	2.49789i	−0.184980	−	0.104442i
$573$		−	1.82520i		−	0.0762489i
$574$	7.90941	+	25.3660i	0.330132	+	1.05876i
$575$			1.10376i			0.0460298i
$576$	−6.73982	+	22.9758i	−0.280826	+	0.957326i
$577$	29.4266	+	12.1889i	1.22505	+	0.507430i	0.899010	−	0.437927i	$-0.144287\pi$
$577$	29.4266	+	12.1889i	1.22505	+	0.507430i	0.326035	+	0.945358i	$0.394287\pi$
$578$	−22.0828	−	0.472126i	−0.918522	−	0.0196379i
$579$	1.63448	+	0.832807i	0.0679265	+	0.0346103i
$580$	−10.3919	−	13.2769i	−0.431500	−	0.551294i
$581$	−19.1887	+	4.60681i	−0.796083	+	0.191123i
$582$	0.188583	+	1.38114i	0.00781703	+	0.0572499i
$583$	8.17019	−	8.17019i	0.338375	−	0.338375i
$584$	23.3674	−	5.96742i	0.966951	−	0.246933i
$585$	1.19397	+	1.01975i	0.0493647	+	0.0421615i
$586$	−3.51380	−	1.54426i	−0.145154	−	0.0637929i
$587$	27.2838	−	16.7195i	1.12612	−	0.690089i	0.170698	−	0.985323i	$-0.445398\pi$
$587$	27.2838	−	16.7195i	1.12612	−	0.690089i	0.955425	+	0.295234i	$0.0953978\pi$
$588$	0.0740355	−	0.259053i	0.00305317	−	0.0106832i
$589$	6.68541	−	5.70988i	0.275468	−	0.235272i
$590$	−5.86558	−	19.4582i	−0.241482	−	0.801080i
$591$	−0.888484	+	0.0699252i	−0.0365473	+	0.00287634i
$592$	−12.8079	+	30.3219i	−0.526403	+	1.24622i
$593$	2.46113	−	4.01620i	0.101066	−	0.164925i	−0.798110	−	0.602512i	$-0.794167\pi$
$593$	2.46113	−	4.01620i	0.101066	−	0.164925i	0.899176	+	0.437586i	$0.144167\pi$
$594$	1.62429	−	3.02614i	0.0666454	−	0.124164i
$595$	−0.539524	+	3.40642i	−0.0221183	+	0.139650i
$596$	−0.454727	−	1.24594i	−0.0186263	−	0.0510357i
$597$	0.925627	−	1.27402i	0.0378834	−	0.0521420i
$598$	0.208145	−	0.792006i	0.00851169	−	0.0323875i
$599$	26.6826	−	19.3861i	1.09022	−	0.792093i	0.110786	−	0.993844i	$-0.464663\pi$
$599$	26.6826	−	19.3861i	1.09022	−	0.792093i	0.979437	+	0.201751i	$0.0646631\pi$
$600$	−0.226154	−	0.0698954i	−0.00923268	−	0.00285347i
$601$	0.418646	+	1.01070i	0.0170769	+	0.0412274i	0.932188	−	0.361974i	$-0.117897\pi$
$601$	0.418646	+	1.01070i	0.0170769	+	0.0412274i	−0.915111	+	0.403202i	$0.867897\pi$
$602$	9.90336	−	2.15479i	0.403631	−	0.0878228i
$603$	5.84788	+	0.460238i	0.238144	+	0.0187423i
$604$	−2.40530	−	12.3163i	−0.0978702	−	0.501144i
$605$	11.8372	+	3.84612i	0.481249	+	0.156367i
$606$	−0.161919	−	0.335316i	−0.00657751	−	0.0136213i
$607$	−39.4679	+	20.1099i	−1.60195	+	0.816235i	−0.602110	+	0.798413i	$0.705673\pi$
$607$	−39.4679	+	20.1099i	−1.60195	+	0.816235i	−0.999841	+	0.0178222i	$0.994327\pi$
$608$	−1.73598	−	13.4102i	−0.0704031	−	0.543853i
$609$	0.483260	−	2.01292i	0.0195827	−	0.0815678i
$610$	6.22357	+	6.49550i	0.251985	+	0.262995i
$611$	0.405576	−	0.131780i	0.0164079	−	0.00533124i
$612$	6.15075	−	3.41650i	0.248629	−	0.138104i
$613$	5.80176	+	36.6309i	0.234331	+	1.47951i	0.771606	+	0.636101i	$0.219454\pi$
$613$	5.80176	+	36.6309i	0.234331	+	1.47951i	−0.537275	+	0.843407i	$0.680546\pi$
$614$	−7.85636	−	2.73969i	−0.317057	−	0.110565i
$615$	0.436494	+	0.310855i	0.0176011	+	0.0125349i
$616$	−21.4887	−	33.9582i	−0.865805	−	1.36821i
$617$	−21.6425	+	3.42784i	−0.871294	+	0.137999i	−0.576042	−	0.817420i	$-0.695404\pi$
$617$	−21.6425	+	3.42784i	−0.871294	+	0.137999i	−0.295252	+	0.955419i	$0.595404\pi$
$618$	0.951010	+	0.848058i	0.0382552	+	0.0341139i
$619$	−8.66976	−	26.6828i	−0.348467	−	1.07247i	−0.959701	−	0.281022i	$-0.909327\pi$
$619$	−8.66976	−	26.6828i	−0.348467	−	1.07247i	0.611234	−	0.791450i	$-0.290673\pi$
$620$	3.05640	+	6.69104i	0.122748	+	0.268719i
$621$	0.538291	+	0.129232i	0.0216009	+	0.00518591i
$622$	−2.10759	+	21.0233i	−0.0845068	+	0.842959i
$623$	4.11739	+	8.08083i	0.164960	+	0.323752i
$624$	0.149097	+	0.0928016i	0.00596865	+	0.00371504i
$625$	−0.309017	+	0.951057i	−0.0123607	+	0.0380423i
$626$	19.9296	+	34.1394i	0.796548	+	1.36448i
$627$	−0.0760005	+	0.965678i	−0.00303517	+	0.0385655i
$628$	0.796676	−	6.53595i	0.0317908	−	0.260813i
$629$	8.93607	−	3.70144i	0.356304	−	0.147586i
$630$	4.50650	+	11.5734i	0.179543	+	0.461094i
$631$	15.5124	+	21.3510i	0.617538	+	0.849969i	0.997171	−	0.0751688i	$-0.0239496\pi$
$631$	15.5124	+	21.3510i	0.617538	+	0.849969i	−0.379632	+	0.925137i	$0.623950\pi$
$632$	−4.35257	−	5.81278i	−0.173136	−	0.231220i
$633$	−1.63154	−	1.18538i	−0.0648478	−	0.0471147i
$634$	−1.66304	+	1.35998i	−0.0660479	+	0.0540118i
$635$	5.78563	+	0.916354i	0.229596	+	0.0363644i
$636$	−0.294231	+	0.270090i	−0.0116670	+	0.0107098i
$637$	0.720025	+	0.441232i	0.0285284	+	0.0174822i
$638$	−32.9256	−	47.4176i	−1.30354	−	1.87728i
$639$	0.250552	+	3.18357i	0.00991169	+	0.125940i
$640$	11.1873	+	1.68663i	0.442216	+	0.0666699i
$641$	−1.95491	−	2.28890i	−0.0772142	−	0.0904062i	0.720454	−	0.693503i	$-0.243933\pi$
$641$	−1.95491	−	2.28890i	−0.0772142	−	0.0904062i	−0.797668	+	0.603096i	$0.793933\pi$
$642$	−0.0892249	−	1.55918i	−0.00352143	−	0.0615359i
$643$	11.4887	+	18.7478i	0.453069	+	0.739341i	0.994870	−	0.101166i	$-0.0322572\pi$
$643$	11.4887	+	18.7478i	0.453069	+	0.739341i	−0.541801	+	0.840507i	$0.682257\pi$
$644$	4.41336	−	4.74111i	0.173911	−	0.186826i
$645$	0.132749	−	0.155429i	0.00522698	−	0.00612001i
$646$	−2.40371	+	3.16393i	−0.0945728	+	0.124483i
$647$	24.4326	+	24.4326i	0.960546	+	0.960546i	0.999251	−	0.0387042i	$-0.0123230\pi$
$647$	24.4326	+	24.4326i	0.960546	+	0.960546i	−0.0387042	+	0.999251i	$0.512323\pi$
$648$	12.8956	−	21.7409i	0.506588	−	0.854061i
$649$	−16.2441	−	67.6616i	−0.637637	−	2.65595i
$650$	0.401086	−	0.624162i	0.0157319	−	0.0244816i
$651$	−0.410038	+	0.804744i	−0.0160706	+	0.0315404i
$652$	−25.3449	−	9.45065i	−0.992582	−	0.370116i
$653$	−1.16160	+	2.80436i	−0.0454571	+	0.109743i	−0.944977	−	0.327136i	$-0.893916\pi$
$653$	−1.16160	+	2.80436i	−0.0454571	+	0.109743i	0.899520	+	0.436879i	$0.143916\pi$
$654$	1.66961	+	0.301157i	0.0652871	+	0.0117762i
$655$	−10.5557			−0.412447
$656$	−22.8500	−	11.5706i	−0.892142	−	0.451754i
$657$	−25.5206			−0.995653
$658$	3.31955	+	0.598764i	0.129409	+	0.0233422i
$659$	7.90422	−	19.0825i	0.307905	−	0.743348i	−0.691868	−	0.722024i	$-0.743212\pi$
$659$	7.90422	−	19.0825i	0.307905	−	0.743348i	0.999773	−	0.0213236i	$-0.00678803\pi$
$660$	−0.759392	−	0.283164i	−0.0295593	−	0.0110221i
$661$	7.88647	−	15.4781i	0.306748	−	0.602027i	−0.685246	−	0.728312i	$-0.740305\pi$
$661$	7.88647	−	15.4781i	0.306748	−	0.602027i	0.991994	+	0.126285i	$0.0403053\pi$
$662$	−17.9610	+	27.9505i	−0.698073	+	1.08633i
$663$	−0.0120471	−	0.0501797i	−0.000467870	−	0.00194882i
$664$	9.70446	−	16.3608i	0.376606	−	0.634924i
$665$	−4.95959	−	4.95959i	−0.192325	−	0.192325i
$666$	21.0709	−	27.7349i	0.816479	−	1.07471i
$667$	6.04298	−	7.07543i	0.233985	−	0.273962i
$668$	20.4819	−	22.0030i	0.792469	−	0.851320i
$669$	0.989579	+	1.61485i	0.0382593	+	0.0624335i
$670$	−0.158354	−	2.76718i	−0.00611774	−	0.106906i
$671$	20.0035	+	23.4211i	0.772227	+	0.904162i
$672$	0.691951	+	1.20450i	0.0266926	+	0.0464648i
$673$	−1.60659	−	20.4136i	−0.0619294	−	0.786888i	−0.946959	−	0.321353i	$-0.895862\pi$
$673$	−1.60659	−	20.4136i	−0.0619294	−	0.786888i	0.885030	−	0.465534i	$-0.154138\pi$
$674$	−13.0312	−	18.7668i	−0.501944	−	0.722870i
$675$	0.427640	+	0.262058i	0.0164599	+	0.0100866i
$676$	18.7482	−	17.2100i	0.721086	−	0.661922i
$677$	−43.3275	−	6.86241i	−1.66521	−	0.263744i	−0.748454	−	0.663186i	$-0.769204\pi$
$677$	−43.3275	−	6.86241i	−1.66521	−	0.263744i	−0.916758	+	0.399443i	$0.869204\pi$
$678$	−0.710948	+	0.581391i	−0.0273038	+	0.0223282i
$679$	−27.9586	−	20.3131i	−1.07295	−	0.779546i
$680$	−1.99266	−	2.66116i	−0.0764151	−	0.102051i
$681$	−0.839347	−	1.15526i	−0.0321639	−	0.0442697i
$682$	9.13887	+	23.4700i	0.349945	+	0.898712i
$683$	34.6414	−	14.3489i	1.32552	−	0.549047i	0.396143	−	0.918189i	$-0.370348\pi$
$683$	34.6414	−	14.3489i	1.32552	−	0.549047i	0.929373	+	0.369142i	$0.120348\pi$
$684$	−1.73131	+	14.2037i	−0.0661982	+	0.543092i
$685$	−1.38934	+	17.6532i	−0.0530840	+	0.674496i
$686$	−11.2768	−	19.3171i	−0.430551	−	0.737532i
$687$	−0.382082	+	1.17593i	−0.0145773	+	0.0448644i
$688$	−5.16253	+	8.29422i	−0.196819	+	0.316214i
$689$	−0.568329	−	1.11541i	−0.0216516	−	0.0424937i
$690$	0.0130308	−	0.129982i	0.000496073	−	0.00494835i
$691$	−29.9036	−	7.17921i	−1.13759	−	0.273110i	−0.379453	−	0.925211i	$-0.623888\pi$
$691$	−29.9036	−	7.17921i	−1.13759	−	0.273110i	−0.758132	+	0.652101i	$0.773888\pi$
$692$	−18.9252	−	41.4310i	−0.719430	−	1.57497i
$693$	13.1407	+	40.4430i	0.499175	+	1.53630i
$694$	−30.0085	−	26.7599i	−1.13911	−	1.01579i
$695$	1.58334	−	0.250777i	0.0600596	−	0.00951251i
$696$	1.06704	+	1.68623i	0.0404462	+	0.0639162i
$697$	2.39344	+	7.13550i	0.0906581	+	0.270276i
$698$	32.0928	+	11.1915i	1.21473	+	0.423604i
$699$	−0.0665295	−	0.420051i	−0.00251638	−	0.0158878i
$700$	5.13016	−	2.84960i	0.193902	−	0.107705i
$701$	−18.8914	+	6.13820i	−0.713519	+	0.231836i	−0.643211	−	0.765689i	$-0.722398\pi$
$701$	−18.8914	+	6.13820i	−0.713519	+	0.231836i	−0.0703081	+	0.997525i	$0.522398\pi$
$702$	−0.257437	−	0.268685i	−0.00971632	−	0.0101409i
$703$	−4.59197	+	19.1269i	−0.173189	+	0.721386i
$704$	37.9118	+	7.95384i	1.42885	+	0.299772i
$705$	0.0606139	−	0.0308843i	0.00228285	−	0.00116317i
$706$	6.41922	+	13.2935i	0.241591	+	0.500306i
$707$	8.77977	+	2.85272i	0.330197	+	0.107288i
$708$	0.461033	+	2.36071i	0.0173267	+	0.0887211i
$709$	17.8834	+	1.40746i	0.671627	+	0.0528582i	0.409687	−	0.912226i	$-0.365638\pi$
$709$	17.8834	+	1.40746i	0.671627	+	0.0528582i	0.261940	+	0.965084i	$0.415638\pi$
$710$	1.47441	−	0.320806i	0.0553338	−	0.0120396i
$711$	2.94065	+	7.09935i	0.110283	+	0.266246i
$712$	−8.35250	−	2.58144i	−0.313023	−	0.0967435i
$713$	−3.28432	+	2.38620i	−0.122999	+	0.0893639i
$714$	0.103752	−	0.394783i	0.00388282	−	0.0147744i
$715$	1.49314	−	2.05512i	0.0558401	−	0.0768573i
$716$	−14.3122	−	39.2149i	−0.534871	−	1.46553i
$717$	0.220756	−	1.39380i	0.00824429	−	0.0520524i
$718$	11.8186	−	22.0188i	0.441067	−	0.821733i
$719$	−19.7107	+	32.1649i	−0.735083	+	1.19955i	0.238484	+	0.971146i	$0.423350\pi$
$719$	−19.7107	+	32.1649i	−0.735083	+	1.19955i	−0.973567	+	0.228400i	$0.926650\pi$
$720$	−11.0285	−	4.65842i	−0.411007	−	0.173609i
$721$	−31.4928	+	2.47854i	−1.17285	+	0.0923056i
$722$	5.42293	+	17.9897i	0.201821	+	0.669509i
$723$	0.314186	−	0.268340i	0.0116847	−	0.00997968i
$724$	3.18646	−	11.1495i	0.118424	−	0.414369i
$725$	7.18787	−	4.40473i	0.266951	−	0.163588i
$726$	−1.34858	−	0.592682i	−0.0500506	−	0.0219965i
$727$	−26.4826	−	22.6182i	−0.982184	−	0.838864i	0.00475024	−	0.999989i	$-0.498488\pi$
$727$	−26.4826	−	22.6182i	−0.982184	−	0.838864i	−0.986934	+	0.161124i	$0.948488\pi$
$728$	−4.21855	+	1.07730i	−0.156350	+	0.0399275i
$729$	−18.8250	+	18.8250i	−0.697221	+	0.697221i
$730$	1.63138	+	11.9478i	0.0603801	+	0.442208i
$731$	2.79148	−	0.670175i	0.103247	−	0.0247873i
$732$	−0.656226	−	0.838409i	−0.0242548	−	0.0309885i
$733$	30.7487	+	15.6673i	1.13573	+	0.578683i	0.917706	−	0.397260i	$-0.130039\pi$
$733$	30.7487	+	15.6673i	1.13573	+	0.578683i	0.218024	+	0.975943i	$0.430039\pi$
$734$	0.823963	+	0.0176162i	0.0304130	+	0.000650226i
$735$	0.124458	+	0.0515521i	0.00459070	+	0.00190153i
$736$	0.313285	+	6.23592i	0.0115479	+	0.229859i
$737$		−	9.49009i		−	0.349572i
$738$	20.3981	+	17.8459i	0.750866	+	0.656915i
$739$		−	4.58098i		−	0.168514i	−0.996444	−	0.0842570i	$-0.973148\pi$
$739$		−	4.58098i		−	0.168514i	0.996444	−	0.0842570i	$-0.0268517\pi$
$740$	−14.3314	−	8.09168i	−0.526833	−	0.297456i
$741$	0.0969604	+	0.0401623i	0.00356193	+	0.00147540i
$742$	0.211653	−	9.89963i	0.00777001	−	0.363427i
$743$	−40.1114	−	20.4378i	−1.47154	−	0.749789i	−0.479722	−	0.877421i	$-0.659262\pi$
$743$	−40.1114	−	20.4378i	−1.47154	−	0.749789i	−0.991822	+	0.127632i	$0.959262\pi$
$744$	−0.280940	−	0.824046i	−0.0102997	−	0.0302110i
$745$	0.644840	−	0.154812i	0.0236251	−	0.00567189i
$746$	−46.6978	+	6.37622i	−1.70973	+	0.233450i
$747$	−14.2335	+	14.2335i	−0.520778	+	0.520778i
$748$	−6.29098	−	9.48649i	−0.230021	−	0.346860i
$749$	29.4416	+	25.1455i	1.07577	+	0.918797i
$750$	0.0476191	−	0.108352i	0.00173880	−	0.00395645i
$751$	2.64281	−	1.61951i	0.0964374	−	0.0590969i	−0.473444	−	0.880824i	$-0.656989\pi$
$751$	2.64281	−	1.61951i	0.0964374	−	0.0590969i	0.569881	+	0.821727i	$0.306989\pi$
$752$	−2.64376	+	1.89281i	−0.0964082	+	0.0690236i
$753$	0.117945	−	0.100735i	0.00429816	−	0.00367098i
$754$	−5.98833	+	1.80516i	−0.218082	+	0.0657400i
$755$	6.25515	−	0.492291i	0.227648	−	0.0179163i
$756$	−0.789061	−	2.83557i	−0.0286979	−	0.103129i
$757$	−2.16109	+	3.52658i	−0.0785463	+	0.128176i	−0.889501	−	0.456933i	$-0.848948\pi$
$757$	−2.16109	+	3.52658i	−0.0785463	+	0.128176i	0.810955	+	0.585108i	$0.198948\pi$
$758$	−0.543097	−	0.291509i	−0.0197262	−	0.0105881i
$759$	0.0699699	−	0.441772i	0.00253975	−	0.0160353i
$760$	6.76032	−	0.0974231i	0.245223	−	0.00353391i
$761$	14.0743	−	19.3717i	0.510195	−	0.702223i	−0.473757	−	0.880655i	$-0.657103\pi$
$761$	14.0743	−	19.3717i	0.510195	−	0.702223i	0.983952	+	0.178433i	$0.0571027\pi$
$762$	−0.670520	−	0.176218i	−0.0242904	−	0.00638369i
$763$	−34.0280	+	24.7228i	−1.23190	+	0.895025i
$764$	−43.5908	+	1.56063i	−1.57706	+	0.0564617i
$765$	1.34627	+	3.25017i	0.0486743	+	0.117510i
$766$	−2.96920	−	13.6464i	−0.107282	−	0.493063i
$767$	−7.51580	−	0.591507i	−0.271380	−	0.0213581i
$768$	−1.29754	−	0.330699i	−0.0468211	−	0.0119331i
$769$	23.7255	+	7.70887i	0.855562	+	0.277989i	0.703774	−	0.710424i	$-0.251497\pi$
$769$	23.7255	+	7.70887i	0.855562	+	0.277989i	0.151788	+	0.988413i	$0.451497\pi$
$770$	18.0939	−	8.73729i	0.652060	−	0.314870i
$771$	0.139227	−	0.0709396i	0.00501413	−	0.00255483i
$772$	18.4921	−	39.7478i	0.665546	−	1.43055i
$773$	9.61970	−	40.0690i	0.345997	−	1.44118i	−0.479882	−	0.877333i	$-0.659321\pi$
$773$	9.61970	−	40.0690i	0.345997	−	1.44118i	0.825879	−	0.563847i	$-0.190679\pi$
$774$	7.46470	−	7.15220i	0.268313	−	0.257080i
$775$	−3.49801	+	1.13657i	−0.125652	+	0.0408269i
$776$	32.8240	−	5.68482i	1.17831	−	0.204073i
$777$	−0.316112	−	1.99585i	−0.0113404	−	0.0716007i
$778$	13.9050	−	39.8743i	0.498520	−	1.42956i
$779$	−14.6010	−	4.59166i	−0.523133	−	0.164513i
$780$	−0.0546022	+	0.0687685i	−0.00195507	+	0.00246231i
$781$	5.10277	−	0.808199i	0.182591	−	0.0289196i
$782$	1.22111	−	1.36935i	0.0436669	−	0.0489680i
$783$	−1.30656	−	4.02117i	−0.0466926	−	0.143705i
$784$	−6.25018	−	1.54667i	−0.223221	−	0.0552381i
$785$	3.20120	+	0.768540i	0.114256	+	0.0274304i
$786$	1.24308	+	0.124619i	0.0443393	+	0.00444503i
$787$	−20.6738	−	40.5747i	−0.736942	−	1.44633i	−0.888975	−	0.457955i	$-0.848582\pi$
$787$	−20.6738	−	40.5747i	−0.736942	−	1.44633i	0.152033	−	0.988375i	$-0.451418\pi$
$788$	2.42970	+	21.1596i	0.0865544	+	0.753780i
$789$	−0.282763	+	0.870256i	−0.0100666	+	0.0309819i
$790$	3.13568	−	1.83052i	0.111562	−	0.0651271i
$791$	1.78643	−	22.6988i	0.0635182	−	0.807075i
$792$	−36.7876	−	18.0813i	−1.30719	−	0.642491i
$793$	3.08307	−	1.27705i	0.109483	−	0.0453493i
$794$	−41.8020	+	16.2771i	−1.48350	+	0.577652i
$795$	−0.117381	−	0.161561i	−0.00416306	−	0.00572997i
$796$	−31.2184	−	21.0171i	−1.10651	−	0.744932i
$797$	25.8356	+	18.7707i	0.915144	+	0.664891i	0.942311	−	0.334740i	$-0.108648\pi$
$797$	25.8356	+	18.7707i	0.915144	+	0.664891i	−0.0271666	+	0.999631i	$0.508648\pi$
$798$	0.525508	+	0.642613i	0.0186028	+	0.0227482i
$799$	0.943686	+	0.149465i	0.0333852	+	0.00528770i
$800$	−1.47592	+	5.46092i	−0.0521816	+	0.193073i
$801$	7.88776	+	4.83362i	0.278700	+	0.170788i
$802$	21.2156	−	14.7316i	0.749147	−	0.520190i
$803$	3.23940	+	41.1605i	0.114316	+	1.45252i
$804$	−0.0140206	+	0.327744i	−0.000494470	+	0.0115586i
$805$	2.10335	+	2.46270i	0.0741332	+	0.0867988i
$806$	2.72435	−	0.155903i	0.0959612	−	0.00549144i
$807$	0.362571	+	0.591663i	0.0127631	+	0.0208275i
$808$	−7.86980	+	4.15377i	−0.276858	+	0.146129i
$809$	−35.7133	+	41.8150i	−1.25561	+	1.47014i	−0.433147	+	0.901323i	$0.642597\pi$
$809$	−35.7133	+	41.8150i	−1.25561	+	1.47014i	−0.822467	+	0.568812i	$0.807403\pi$
$810$	10.0639	+	7.64579i	0.353610	+	0.268646i
$811$	−0.384717	−	0.384717i	−0.0135092	−	0.0135092i	0.700320	−	0.713829i	$-0.253041\pi$
$811$	−0.384717	−	0.384717i	−0.0135092	−	0.0135092i	−0.713829	+	0.700320i	$0.753041\pi$
$812$	−48.4873	−	9.82042i	−1.70157	−	0.344629i
$813$	0.461626	+	1.92281i	0.0161899	+	0.0674359i
$814$	−47.4065	−	30.4634i	−1.66160	−	1.06774i
$815$	6.14012	−	12.0507i	0.215079	−	0.422116i
$816$	0.203246	+	0.336914i	0.00711504	+	0.0117943i
$817$	−2.23422	+	5.39388i	−0.0781654	+	0.188708i
$818$	−4.54497	+	25.1973i	−0.158911	+	0.881003i
$819$	4.60726			0.160991
$820$	7.05085	−	10.6904i	0.246226	−	0.373326i
$821$	−37.1895			−1.29792			−0.648961	−	0.760822i	$-0.724796\pi$
$821$	−37.1895			−1.29792			−0.648961	+	0.760822i	$0.724796\pi$
$822$	0.372026	−	2.06251i	0.0129759	−	0.0719383i
$823$	10.0685	−	24.3075i	0.350966	−	0.847307i	−0.645535	−	0.763731i	$-0.723366\pi$
$823$	10.0685	−	24.3075i	0.350966	−	0.847307i	0.996501	−	0.0835768i	$-0.0266344\pi$
$824$	19.4408	−	23.4378i	0.677251	−	0.816495i
$825$	0.183972	−	0.361066i	0.00640509	−	0.0125707i
$826$	−50.1673	−	32.2375i	−1.74554	−	1.12169i
$827$	4.07447	+	16.9714i	0.141683	+	0.590153i	0.997358	+	0.0726394i	$0.0231422\pi$
$827$	4.07447	+	16.9714i	0.141683	+	0.590153i	−0.855675	+	0.517513i	$0.826858\pi$
$828$	1.31154	−	6.47559i	0.0455792	−	0.225042i
$829$	13.0162	+	13.0162i	0.452070	+	0.452070i	0.896041	−	0.443971i	$-0.146431\pi$
$829$	13.0162	+	13.0162i	0.452070	+	0.452070i	−0.443971	+	0.896041i	$0.646431\pi$
$830$	7.57349	+	5.75376i	0.262880	+	0.199716i
$831$	−0.885020	+	1.03623i	−0.0307010	+	0.0359463i
$832$	2.08887	−	3.64019i	0.0724185	−	0.126201i
$833$	0.988573	+	1.61320i	0.0342520	+	0.0558942i
$834$	−0.189421	+	0.0108397i	−0.00655912	+	0.000375349i
$835$	9.76140	+	11.4291i	0.337807	+	0.395521i
$836$	23.1280	+	0.989398i	0.799898	+	0.0342191i
$837$	0.144734	+	1.83902i	0.00500274	+	0.0635659i
$838$	−27.3933	+	19.0212i	−0.946284	+	0.657078i
$839$	13.3591	+	8.18649i	0.461209	+	0.282629i	0.733630	−	0.679549i	$-0.237825\pi$
$839$	13.3591	+	8.18649i	0.461209	+	0.282629i	−0.272422	+	0.962178i	$0.587825\pi$
$840$	−0.637789	+	0.275014i	−0.0220058	+	0.00948887i
$841$	−41.5491	−	6.58074i	−1.43273	−	0.226922i
$842$	16.0957	+	19.6825i	0.554696	+	0.678304i
$843$	1.57933	+	1.14745i	0.0543950	+	0.0395203i
$844$	−26.9151	+	39.9791i	−0.926455	+	1.37614i
$845$	7.47944	+	10.2946i	0.257300	+	0.354144i
$846$	3.20619	−	1.24844i	0.110231	−	0.0429224i
$847$	33.7404	−	13.9757i	1.15933	−	0.480211i
$848$	6.70205	+	6.79609i	0.230149	+	0.233379i
$849$	−0.154908	+	1.96829i	−0.00531643	+	0.0675517i
$850$	1.43555	−	0.838037i	0.0492391	−	0.0287444i
$851$	2.80674	−	8.63824i	0.0962136	−	0.296115i
$852$	−0.177420	+	0.0203726i	−0.00607831	+	0.000697955i
$853$	−0.655389	−	1.28627i	−0.0224401	−	0.0440412i	0.879514	−	0.475872i	$-0.157868\pi$
$853$	−0.655389	−	1.28627i	−0.0224401	−	0.0440412i	−0.901954	+	0.431831i	$0.857868\pi$
$854$	26.2640	+	2.63298i	0.898737	+	0.0900986i
$855$	−6.95673	−	1.67016i	−0.237915	−	0.0571184i
$856$	−37.1611	+	3.46410i	−1.27014	+	0.118401i
$857$	−3.66878	−	11.2913i	−0.125323	−	0.385705i	0.868637	−	0.495450i	$-0.164997\pi$
$857$	−3.66878	−	11.2913i	−0.125323	−	0.385705i	−0.993960	+	0.109745i	$0.964997\pi$
$858$	−0.200100	+	0.224392i	−0.00683130	+	0.00766060i
$859$	−23.5511	+	3.73014i	−0.803555	+	0.127271i	−0.544684	−	0.838641i	$-0.683350\pi$
$859$	−23.5511	+	3.73014i	−0.803555	+	0.127271i	−0.258871	+	0.965912i	$0.583350\pi$
$860$	−3.82557	−	3.03750i	−0.130451	−	0.103578i
$861$	1.56628	−	0.138212i	0.0533787	−	0.00471027i
$862$	−8.38916	+	24.0569i	−0.285736	+	0.819380i
$863$	−0.0890348	−	0.562143i	−0.00303078	−	0.0191356i	0.986127	−	0.165995i	$-0.0530835\pi$
$863$	−0.0890348	−	0.562143i	−0.00303078	−	0.0191356i	−0.989157	+	0.146859i	$0.953084\pi$
$864$	2.49043	+	1.35918i	0.0847262	+	0.0462401i
$865$	21.6597	−	7.03767i	0.736453	−	0.239288i
$866$	4.11004	−	3.93797i	0.139665	−	0.133818i
$867$	−0.305134	+	1.27098i	−0.0103629	+	0.0431646i
$868$	19.5701	+	9.10471i	0.664251	+	0.309034i
$869$	11.0768	−	5.64393i	0.375756	−	0.191457i
$870$	−0.898472	+	0.433859i	−0.0304611	+	0.0147092i
$871$	−0.977873	−	0.317730i	−0.0331340	−	0.0107659i
$872$	5.76484	−	40.1324i	0.195222	−	1.35906i
$873$	−35.1423	−	2.76576i	−1.18939	−	0.0936066i
$874$	0.793294	+	3.64595i	0.0268336	+	0.123326i
$875$	1.12288	+	2.71087i	0.0379602	+	0.0916441i
$876$	−0.0510635	−	1.42628i	−0.00172528	−	0.0481895i
$877$	3.80496	−	2.76447i	0.128485	−	0.0933495i	−0.521687	−	0.853137i	$-0.674697\pi$
$877$	3.80496	−	2.76447i	0.128485	−	0.0933495i	0.650171	+	0.759788i	$0.274697\pi$
$878$	19.4251	+	5.10505i	0.655564	+	0.172287i
$879$	−0.133504	+	0.183753i	−0.00450299	+	0.00619784i
$880$	−6.11340	+	18.3785i	−0.206083	+	0.619538i
$881$	0.495560	−	3.12884i	0.0166958	−	0.105413i	−0.977933	−	0.208918i	$-0.933006\pi$
$881$	0.495560	−	3.12884i	0.0166958	−	0.105413i	0.994629	+	0.103505i	$0.0330057\pi$
$882$	6.00322	+	3.22224i	0.202139	+	0.108499i
$883$	28.8180	−	47.0267i	0.969803	−	1.58258i	0.167319	−	0.985903i	$-0.446489\pi$
$883$	28.8180	−	47.0267i	0.969803	−	1.58258i	0.802485	−	0.596672i	$-0.203511\pi$
$884$	−1.18813	+	0.330623i	−0.0399610	+	0.0111200i
$885$	−1.19895	+	0.0943593i	−0.0403022	+	0.00317185i
$886$	29.1401	−	8.78415i	0.978980	−	0.295109i
$887$	34.2871	−	29.2839i	1.15125	−	0.983257i	0.151260	−	0.988494i	$-0.451667\pi$
$887$	34.2871	−	29.2839i	1.15125	−	0.983257i	0.999986	+	0.00523650i	$0.00166684\pi$
$888$	1.59219	+	1.12210i	0.0534305	+	0.0376553i
$889$	14.6551	−	8.98069i	0.491518	−	0.301203i
$890$	1.75871	−	4.00175i	0.0589521	−	0.134139i
$891$	32.9060	+	28.1044i	1.10239	+	0.941533i
$892$	37.7208	−	25.0146i	1.26298	−	0.837550i
$893$	−1.37396	+	1.37396i	−0.0459780	+	0.0459780i
$894$	−0.0777665	+	0.0106184i	−0.00260090	+	0.000355133i
$895$	20.2958	−	4.87260i	0.678415	−	0.162873i
$896$	28.1752	−	17.5556i	0.941267	−	0.586490i
$897$	−0.0431783	−	0.0220004i	−0.00144168	−	0.000734573i
$898$	0.746915	−	34.9354i	0.0249249	−	1.16581i
$899$	28.6460	+	11.8656i	0.955399	+	0.395739i
$900$	2.94306	−	5.21253i	0.0981019	−	0.173751i
$901$		−	2.80475i		−	0.0934398i
$902$	26.1932	−	35.1641i	0.872140	−	1.17084i
$903$		−	0.599764i		−	0.0199589i
$904$	14.4931	+	16.4823i	0.482033	+	0.548192i
$905$	5.35663	+	2.21879i	0.178060	+	0.0737550i
$906$	−0.742442	−	0.0158733i	−0.0246660	−	0.000527356i
$907$	28.6724	+	14.6093i	0.952052	+	0.485094i	0.859794	−	0.510641i	$-0.170592\pi$
$907$	28.6724	+	14.6093i	0.952052	+	0.485094i	0.0922573	+	0.995735i	$0.470592\pi$
$908$	−26.8731	+	21.0337i	−0.891815	+	0.698027i
$909$	9.15632	−	2.19824i	0.303696	−	0.0729110i
$910$	−0.294515	−	2.15695i	−0.00976308	−	0.0715022i
$911$	−37.6218	+	37.6218i	−1.24647	+	1.24647i	−0.289197	+	0.957270i	$0.593388\pi$
$911$	−37.6218	+	37.6218i	−1.24647	+	1.24647i	−0.957270	+	0.289197i	$0.906612\pi$
$912$	−0.797272	−	0.0683384i	−0.0264003	−	0.00226291i
$913$	24.7631	+	21.1497i	0.819538	+	0.699952i
$914$	11.4615	+	5.03715i	0.379112	+	0.166614i
$915$	0.453898	−	0.278149i	0.0150054	−	0.00919533i
$916$	28.4110	+	8.11967i	0.938726	+	0.268282i
$917$	−23.5520	+	20.1153i	−0.777755	+	0.664265i
$918$	−0.240622	−	0.798226i	−0.00794170	−	0.0263454i
$919$	−1.73395	+	0.136465i	−0.0571979	+	0.00450157i	−0.107026	−	0.994256i	$-0.534133\pi$
$919$	−1.73395	+	0.136465i	−0.0571979	+	0.00450157i	0.0498279	+	0.998758i	$0.484133\pi$
$920$	−3.11547	−	0.200069i	−0.102714	−	0.00659608i
$921$	−0.257265	+	0.419818i	−0.00847716	+	0.0138335i
$922$	13.9475	−	25.9850i	0.459337	−	0.855770i
$923$	0.0875637	−	0.552856i	0.00288219	−	0.0181975i
$924$	−2.23396	+	0.815323i	−0.0734919	+	0.0268221i
$925$	4.83687	−	6.65739i	0.159035	−	0.218894i
$926$	−8.52364	+	32.4330i	−0.280104	+	1.06582i
$927$	−26.0689	+	18.9402i	−0.856216	+	0.622077i
$928$	39.3593	−	26.9257i	1.29203	−	0.883879i
$929$	20.9215	+	50.5090i	0.686413	+	1.65715i	0.751886	+	0.659293i	$0.229144\pi$
$929$	20.9215	+	50.5090i	0.686413	+	1.65715i	−0.0654726	+	0.997854i	$0.520856\pi$
$930$	0.425358	−	0.0925502i	0.0139480	−	0.00303484i
$931$	−3.83588	−	0.301890i	−0.125716	−	0.00989406i
$932$	−9.97506	+	1.94807i	−0.326744	+	0.0638111i
$933$	1.18914	+	0.386375i	0.0389307	+	0.0126493i
$934$	21.0821	+	43.6587i	0.689829	+	1.42856i
$935$	5.07111	−	2.58386i	0.165843	−	0.0845013i
$936$	−3.09478	+	3.18528i	−0.101156	+	0.104114i
$937$	3.60867	−	15.0312i	0.117890	−	0.491048i	−0.881917	−	0.471405i	$-0.843747\pi$
$937$	3.60867	−	15.0312i	0.117890	−	0.491048i	0.999807	−	0.0196428i	$-0.00625290\pi$
$938$	−5.62654	−	5.87239i	−0.183713	−	0.191740i
$939$	2.22482	−	0.722889i	0.0726044	−	0.0235906i
$940$	−0.789429	−	1.42122i	−0.0257483	−	0.0463550i
$941$	−1.47913	−	9.33884i	−0.0482182	−	0.304438i	0.951779	−	0.306784i	$-0.0992530\pi$
$941$	−1.47913	−	9.33884i	−0.0482182	−	0.304438i	−0.999997	+	0.00234669i	$0.999253\pi$
$942$	−0.367912	−	0.128299i	−0.0119872	−	0.00418021i
$943$	6.55484	+	2.64262i	0.213455	+	0.0860557i
$944$	55.9861	−	13.0292i	1.82219	−	0.424065i
$945$	1.45354	−	0.230217i	0.0472835	−	0.00748897i
$946$	−12.4828	−	11.1315i	−0.405852	−	0.361916i
$947$	−12.2038	−	37.5593i	−0.396569	−	1.22051i	−0.927733	−	0.373245i	$-0.878245\pi$
$947$	−12.2038	−	37.5593i	−0.396569	−	1.22051i	0.531164	−	0.847269i	$-0.321755\pi$
$948$	−0.390881	+	0.178550i	−0.0126952	+	0.00579904i
$949$	4.34970	+	1.04427i	0.141197	+	0.0338984i
$950$	−0.337207	+	3.36365i	−0.0109404	+	0.109131i
$951$	0.0577163	+	0.113275i	0.00187158	+	0.00367318i
$952$	−9.51721	−	2.14032i	−0.308455	−	0.0693682i
$953$	−10.6838	+	32.8812i	−0.346081	+	1.06513i	0.614922	+	0.788588i	$0.289188\pi$
$953$	−10.6838	+	32.8812i	−0.346081	+	1.06513i	−0.961003	+	0.276539i	$0.910812\pi$
$954$	−5.09207	−	8.72269i	−0.164862	−	0.282407i
$955$	1.71114	−	21.7421i	0.0553712	−	0.703558i
$956$	−33.4764	−	4.08049i	−1.08271	−	0.131972i
$957$	−3.15613	+	1.30731i	−0.102023	+	0.0422594i
$958$	1.33768	+	3.43536i	0.0432185	+	0.110991i
$959$	30.5406	+	42.0355i	0.986207	+	1.35740i
$960$	0.238281	−	0.625675i	0.00769047	−	0.0201936i
$961$	14.1352	+	10.2698i	0.455975	+	0.331285i
$962$	−4.72617	+	3.86491i	−0.152378	+	0.124610i
$963$	39.0076	+	6.17819i	1.25700	+	0.199089i
$964$	−6.67733	−	7.27417i	−0.215062	−	0.234285i
$965$	18.6894	+	11.4529i	0.601633	+	0.368681i
$966$	−0.218624	−	0.314849i	−0.00703411	−	0.0101301i
$967$	2.65844	+	33.7787i	0.0854896	+	1.08625i	0.878723	+	0.477331i	$0.158396\pi$
$967$	2.65844	+	33.7787i	0.0854896	+	1.08625i	−0.793234	+	0.608917i	$0.791604\pi$
$968$	−13.0018	+	32.7146i	−0.417892	+	1.05149i
$969$	0.152709	+	0.178799i	0.00490573	+	0.00574387i
$970$	0.951611	+	16.6291i	0.0305544	+	0.533929i
$971$	−16.3506	−	26.6818i	−0.524717	−	0.856260i	0.475002	−	0.879985i	$-0.342447\pi$
$971$	−16.3506	−	26.6818i	−0.524717	−	0.856260i	−0.999719	+	0.0237250i	$0.992447\pi$
$972$	−3.29756	−	3.06960i	−0.105769	−	0.0984575i
$973$	3.05487	−	3.57680i	0.0979347	−	0.114667i
$974$	−20.7194	+	27.2722i	−0.663891	+	0.873859i
$975$	−0.0310453	−	0.0310453i	−0.000994247	−	0.000994247i
$976$	−19.4624	+	16.3893i	−0.622976	+	0.524610i
$977$	1.49596	+	6.23113i	0.0478600	+	0.199351i	0.991178	−	0.132540i	$-0.0423133\pi$
$977$	1.49596	+	6.23113i	0.0478600	+	0.199351i	−0.943318	+	0.331891i	$0.892313\pi$
$978$	−0.865352	+	1.34664i	−0.0276709	+	0.0430609i
$979$	6.79463	−	13.3352i	0.217157	−	0.426195i
$980$	1.12479	−	3.01647i	0.0359300	−	0.0963576i
$981$	−16.4184	+	39.6376i	−0.524200	+	1.26553i
$982$	53.3426	+	9.62168i	1.70223	+	0.307040i
$983$	10.3634			0.330540			0.165270	−	0.986248i	$-0.447150\pi$
$983$	10.3634			0.330540			0.165270	+	0.986248i	$0.447150\pi$
$984$	−0.956544	+	1.17571i	−0.0304935	+	0.0374801i
$985$	−10.6493			−0.339316
$986$	−13.7905	−	2.48747i	−0.439181	−	0.0792172i
$987$	0.0763879	−	0.184417i	0.00243145	−	0.00587005i
$988$	0.876279	−	2.35002i	0.0278781	−	0.0747640i
$989$	1.22388	−	2.40200i	0.0389170	−	0.0763790i
$990$	11.0800	−	17.2424i	0.352144	−	0.547999i
$991$	−6.05824	−	25.2344i	−0.192446	−	0.801596i	−0.982149	−	0.188106i	$-0.939765\pi$
$991$	−6.05824	−	25.2344i	−0.192446	−	0.801596i	0.789703	−	0.613490i	$-0.210235\pi$
$992$	−19.4402	+	7.41419i	−0.617228	+	0.235401i
$993$	1.39024	+	1.39024i	0.0441178	+	0.0441178i
$994$	2.67838	−	3.52547i	0.0849530	−	0.111821i
$995$	12.2206	−	14.3085i	0.387420	−	0.453610i
$996$	−0.823955	−	0.766996i	−0.0261080	−	0.0243032i
$997$	6.02304	+	9.82870i	0.190751	+	0.311278i	0.933691	−	0.358081i	$-0.116569\pi$
$997$	6.02304	+	9.82870i	0.190751	+	0.311278i	−0.742939	+	0.669359i	$0.766569\pi$
$998$	−1.69522	−	29.6234i	−0.0536611	−	0.937712i
$999$	−2.68042	−	3.13837i	−0.0848048	−	0.0992936i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bw.a.11.3	✓	672
4.3	odd	2	inner	820.2.bw.a.11.7	yes	672
41.15	odd	40	inner	820.2.bw.a.671.7	yes	672
164.15	even	40	inner	820.2.bw.a.671.3	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bw.a.11.3	✓	672	1.1	even	1	trivial
820.2.bw.a.11.7	yes	672	4.3	odd	2	inner
820.2.bw.a.671.3	yes	672	164.15	even	40	inner
820.2.bw.a.671.7	yes	672	41.15	odd	40	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bw (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39175 - 0.251038i) q^{2} +(-0.0320264 + 0.0773185i) q^{3} +(1.87396 + 0.698766i) q^{4} +(-0.453990 + 0.891007i) q^{5} +(0.0639827 - 0.0995686i) q^{6} +(0.684981 + 2.85315i) q^{7} +(-2.43268 - 1.44295i) q^{8} +(2.11637 + 2.11637i) q^{9} +(0.855520 - 1.12609i) q^{10} +(3.14472 - 3.68199i) q^{11} +(-0.114044 + 0.122513i) q^{12} +(-0.274112 - 0.447310i) q^{13} +(-0.237077 - 4.14284i) q^{14} +(-0.0543517 - 0.0636376i) q^{15} +(3.02345 + 2.61892i) q^{16} +(-0.0922206 - 1.17177i) q^{17} +(-2.41418 - 3.47675i) q^{18} +(2.03814 + 1.24897i) q^{19} +(-1.47337 + 1.35248i) q^{20} +(-0.242539 - 0.0384144i) q^{21} +(-5.30099 + 4.33499i) q^{22} +(-0.892957 - 0.648771i) q^{23} +(0.189476 - 0.141879i) q^{24} +(-0.587785 - 0.809017i) q^{25} +(0.269205 + 0.691359i) q^{26} +(-0.463370 + 0.191934i) q^{27} +(-0.710058 + 5.82533i) q^{28} +(-0.661420 + 8.40414i) q^{29} +(0.0596687 + 0.102212i) q^{30} +(1.13657 - 3.49801i) q^{31} +(-3.55046 - 4.40389i) q^{32} +(0.183972 + 0.361066i) q^{33} +(-0.165811 + 1.65397i) q^{34} +(-2.85315 - 0.684981i) q^{35} +(2.48714 + 5.44483i) q^{36} +(2.54290 + 7.82623i) q^{37} +(-2.52305 - 2.24991i) q^{38} +(0.0433642 - 0.00686822i) q^{39} +(2.39009 - 1.51245i) q^{40} +(-6.21176 + 1.55370i) q^{41} +(0.327911 + 0.114350i) q^{42} +(0.382077 + 2.41234i) q^{43} +(8.46593 - 4.70248i) q^{44} +(-2.84651 + 0.924887i) q^{45} +(1.07991 + 1.12710i) q^{46} +(-0.189762 + 0.790414i) q^{47} +(-0.299321 + 0.149894i) q^{48} +(-1.43423 + 0.730778i) q^{49} +(0.614959 + 1.27351i) q^{50} +(0.0935534 + 0.0303973i) q^{51} +(-0.201110 - 1.02978i) q^{52} +(2.37886 + 0.187220i) q^{53} +(0.693080 - 0.150802i) q^{54} +(1.85301 + 4.47355i) q^{55} +(2.45061 - 7.92918i) q^{56} +(-0.161843 + 0.117586i) q^{57} +(3.03029 - 11.5305i) q^{58} +(8.44679 - 11.6260i) q^{59} +(-0.0573850 - 0.157233i) q^{60} +(-0.995078 + 6.28267i) q^{61} +(-2.45997 + 4.58305i) q^{62} +(-4.58865 + 7.48799i) q^{63} +(3.83582 + 7.02043i) q^{64} +(0.523001 - 0.0411610i) q^{65} +(-0.165403 - 0.548699i) q^{66} +(1.49032 - 1.27285i) q^{67} +(0.645978 - 2.26030i) q^{68} +(0.0787602 - 0.0482643i) q^{69} +(3.79893 + 1.66957i) q^{70} +(0.811324 + 0.692936i) q^{71} +(-2.09463 - 8.20224i) q^{72} +(-6.02934 + 6.02934i) q^{73} +(-1.57441 - 11.5305i) q^{74} +(0.0813767 - 0.0195368i) q^{75} +(2.94665 + 3.76470i) q^{76} +(12.6594 + 6.45026i) q^{77} +(-0.0620765 - 0.00132719i) q^{78} +(2.37199 + 0.982510i) q^{79} +(-3.70609 + 1.50495i) q^{80} +8.93701i q^{81} +(9.03529 - 0.602986i) q^{82} +6.72545i q^{83} +(-0.427666 - 0.241465i) q^{84} +(1.08593 + 0.449805i) q^{85} +(0.0738310 - 3.45330i) q^{86} +(-0.628613 - 0.320294i) q^{87} +(-12.9630 + 4.41944i) q^{88} +(3.00548 - 0.721551i) q^{89} +(4.19382 - 0.572634i) q^{90} +(1.08848 - 1.08848i) q^{91} +(-1.22003 - 1.83974i) q^{92} +(0.234061 + 0.199907i) q^{93} +(0.462525 - 1.05242i) q^{94} +(-2.03814 + 1.24897i) q^{95} +(0.454211 - 0.133475i) q^{96} +(-8.95591 + 7.64907i) q^{97} +(2.17955 - 0.657017i) q^{98} +(14.4478 - 1.13707i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q + 12 q^{6} + 100 q^{12} + 24 q^{14} + 32 q^{16} - 8 q^{17} - 40 q^{21} + 52 q^{22} - 24 q^{24} + 28 q^{28} + 12 q^{30} - 20 q^{32} + 40 q^{33} + 44 q^{34} + 36 q^{36} - 80 q^{37} + 52 q^{38} - 160 q^{42}+ \cdots - 116 q^{98}+O(q^{100}) \) 672 * q + 12 * q^6 + 100 * q^12 + 24 * q^14 + 32 * q^16 - 8 * q^17 - 40 * q^21 + 52 * q^22 - 24 * q^24 + 28 * q^28 + 12 * q^30 - 20 * q^32 + 40 * q^33 + 44 * q^34 + 36 * q^36 - 80 * q^37 + 52 * q^38 - 160 * q^42 + 24 * q^44 + 16 * q^46 + 40 * q^48 - 16 * q^49 - 64 * q^52 - 64 * q^54 + 68 * q^56 + 56 * q^58 + 36 * q^62 + 120 * q^64 + 8 * q^65 - 304 * q^68 + 104 * q^69 + 24 * q^70 - 40 * q^72 - 28 * q^74 - 24 * q^76 - 160 * q^77 - 128 * q^78 - 192 * q^82 - 204 * q^84 + 32 * q^85 - 168 * q^88 + 8 * q^89 + 48 * q^90 - 56 * q^92 - 356 * q^94 - 136 * q^96 - 116 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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