LMFDB - Embedded newform 820.2.bw.a.671.7

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)

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);

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")

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			671.7
Character	$\chi$	$=$	820.671
Dual form			820.2.bw.a.11.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.24606 - 0.668827i) q^{2} +(0.0320264 + 0.0773185i) q^{3} +(1.10534 + 1.66680i) q^{4} +(-0.453990 - 0.891007i) q^{5} +(0.0118059 - 0.117764i) q^{6} +(-0.684981 + 2.85315i) q^{7} +(-0.262523 - 2.81622i) q^{8} +(2.11637 - 2.11637i) q^{9} +(-0.0302288 + 1.41389i) q^{10} +(-3.14472 - 3.68199i) q^{11} +(-0.0934744 + 0.138845i) q^{12} +(-0.274112 + 0.447310i) q^{13} +(2.76179 - 3.09707i) q^{14} +(0.0543517 - 0.0636376i) q^{15} +(-1.55644 + 3.68476i) q^{16} +(-0.0922206 + 1.17177i) q^{17} +(-4.05261 + 1.22164i) q^{18} +(-2.03814 + 1.24897i) q^{19} +(0.983315 - 1.74158i) q^{20} +(-0.242539 + 0.0384144i) q^{21} +(1.45590 + 6.69126i) q^{22} +(0.892957 - 0.648771i) q^{23} +(0.209338 - 0.110491i) q^{24} +(-0.587785 + 0.809017i) q^{25} +(0.640734 - 0.374043i) q^{26} +(0.463370 + 0.191934i) q^{27} +(-5.51277 + 2.01198i) q^{28} +(-0.661420 - 8.40414i) q^{29} +(-0.110288 + 0.0429446i) q^{30} +(-1.13657 - 3.49801i) q^{31} +(4.40389 - 3.55046i) q^{32} +(0.183972 - 0.361066i) q^{33} +(0.898627 - 1.39842i) q^{34} +(2.85315 - 0.684981i) q^{35} +(5.86687 + 1.18825i) q^{36} +(2.54290 - 7.82623i) q^{37} +(3.37499 - 0.193136i) 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} +(2.66116 - 9.31147i) q^{44} +(-2.84651 - 0.924887i) q^{45} +(-1.54660 + 0.211176i) q^{46} +(0.189762 + 0.790414i) q^{47} +(-0.334748 - 0.00233209i) q^{48} +(-1.43423 - 0.730778i) q^{49} +(1.27351 - 0.614959i) q^{50} +(-0.0935534 + 0.0303973i) q^{51} +(-1.04856 + 0.0375406i) q^{52} +(2.37886 - 0.187220i) q^{53} +(-0.449017 - 0.549076i) q^{54} +(-1.85301 + 4.47355i) q^{55} +(8.21492 + 1.18004i) q^{56} +(-0.161843 - 0.117586i) q^{57} +(-4.79674 + 10.9145i) q^{58} +(-8.44679 - 11.6260i) q^{59} +(0.166148 + 0.0202520i) q^{60} +(-0.995078 - 6.28267i) q^{61} +(-0.923325 + 5.11891i) q^{62} +(4.58865 + 7.48799i) q^{63} +(-7.86216 + 1.47865i) q^{64} +(0.523001 + 0.0411610i) q^{65} +(-0.470732 + 0.326865i) q^{66} +(-1.49032 - 1.27285i) q^{67} +(-2.05505 + 1.14150i) q^{68} +(0.0787602 + 0.0482643i) q^{69} +(-4.01334 - 1.05474i) q^{70} +(-0.811324 + 0.692936i) q^{71} +(-6.51575 - 5.40456i) q^{72} +(-6.02934 - 6.02934i) q^{73} +(-8.40300 + 8.05121i) q^{74} +(-0.0813767 - 0.0195368i) q^{75} +(-4.33462 - 2.01663i) q^{76} +(12.6594 - 6.45026i) q^{77} +(0.0494408 + 0.0375614i) q^{78} +(-2.37199 + 0.982510i) q^{79} +(3.98976 - 0.286049i) q^{80} -8.93701i q^{81} +(6.70108 + 6.09061i) q^{82} +6.72545i q^{83} +(-0.332118 - 0.361803i) q^{84} +(1.08593 - 0.449805i) q^{85} +(2.08953 - 2.75038i) q^{86} +(0.628613 - 0.320294i) q^{87} +(-9.54373 + 9.82282i) q^{88} +(3.00548 + 0.721551i) q^{89} +(2.92834 + 3.05629i) q^{90} +(-1.08848 - 1.08848i) q^{91} +(2.06839 + 0.771267i) q^{92} +(0.234061 - 0.199907i) q^{93} +(0.292195 - 1.11182i) q^{94} +(2.03814 + 1.24897i) q^{95} +(0.415557 + 0.226794i) q^{96} +(-8.95591 - 7.64907i) q^{97} +(1.29838 + 1.86985i) 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 $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{37}{40}\right)$	$1$

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 $

$2$	−1.24606	−	0.668827i	−0.881099	−	0.472932i
$2$	−1.24606	−	0.668827i	−0.881099	−	0.472932i
$3$	0.0320264	+	0.0773185i	0.0184904	+	0.0446399i	0.932855	−	0.360252i	$-0.117309\pi$
$3$	0.0320264	+	0.0773185i	0.0184904	+	0.0446399i	−0.914365	+	0.404892i	$0.867309\pi$
$4$	1.10534	+	1.66680i	0.552671	+	0.833400i
$5$	−0.453990	−	0.891007i	−0.203031	−	0.398470i
$5$	−0.453990	−	0.891007i	−0.203031	−	0.398470i
$6$	0.0118059	−	0.117764i	0.00481972	−	0.0480769i
$7$	−0.684981	+	2.85315i	−0.258899	+	1.07839i	0.679731	+	0.733462i	$0.262097\pi$
$7$	−0.684981	+	2.85315i	−0.258899	+	1.07839i	−0.938629	+	0.344928i	$0.887903\pi$
$8$	−0.262523	−	2.81622i	−0.0928160	−	0.995683i
$9$	2.11637	−	2.11637i	0.705456	−	0.705456i
$10$	−0.0302288	+	1.41389i	−0.00955918	+	0.447111i
$11$	−3.14472	−	3.68199i	−0.948168	−	1.11016i	−0.993798	−	0.111204i	$-0.964529\pi$
$11$	−3.14472	−	3.68199i	−0.948168	−	1.11016i	0.0456293	−	0.998958i	$-0.485471\pi$
$12$	−0.0934744	+	0.138845i	−0.0269837	+	0.0400811i
$13$	−0.274112	+	0.447310i	−0.0760250	+	0.124062i	−0.888393	−	0.459083i	$-0.848178\pi$
$13$	−0.274112	+	0.447310i	−0.0760250	+	0.124062i	0.812368	+	0.583145i	$0.198178\pi$
$14$	2.76179	−	3.09707i	0.738120	−	0.827727i
$15$	0.0543517	−	0.0636376i	0.0140335	−	0.0164312i
$16$	−1.55644	+	3.68476i	−0.389110	+	0.921191i
$17$	−0.0922206	+	1.17177i	−0.0223668	+	0.284197i	0.975555	+	0.219756i	$0.0705263\pi$
$17$	−0.0922206	+	1.17177i	−0.0223668	+	0.284197i	−0.997922	+	0.0644405i	$0.979474\pi$
$18$	−4.05261	+	1.22164i	−0.955209	+	0.287944i
$19$	−2.03814	+	1.24897i	−0.467581	+	0.286534i	−0.736264	−	0.676695i	$-0.763412\pi$
$19$	−2.03814	+	1.24897i	−0.467581	+	0.286534i	0.268683	+	0.963229i	$0.413412\pi$
$20$	0.983315	−	1.74158i	0.219876	−	0.389429i
$21$	−0.242539	+	0.0384144i	−0.0529264	+	0.00838271i
$22$	1.45590	+	6.69126i	0.310399	+	1.42658i
$23$	0.892957	−	0.648771i	0.186194	−	0.135278i	−0.490783	−	0.871282i	$-0.663289\pi$
$23$	0.892957	−	0.648771i	0.186194	−	0.135278i	0.676978	+	0.736004i	$0.263289\pi$
$24$	0.209338	−	0.110491i	0.0427310	−	0.0225539i
$25$	−0.587785	+	0.809017i	−0.117557	+	0.161803i
$26$	0.640734	−	0.374043i	0.125658	−	0.0733558i
$27$	0.463370	+	0.191934i	0.0891756	+	0.0369377i
$28$	−5.51277	+	2.01198i	−1.04182	+	0.380229i
$29$	−0.661420	−	8.40414i	−0.122823	−	1.56061i	−0.681870	−	0.731474i	$-0.738833\pi$
$29$	−0.661420	−	8.40414i	−0.122823	−	1.56061i	0.559047	−	0.829136i	$-0.311167\pi$
$30$	−0.110288	+	0.0429446i	−0.0201358	+	0.00784057i
$31$	−1.13657	−	3.49801i	−0.204135	−	0.628262i	−0.999748	−	0.0224569i	$-0.992851\pi$
$31$	−1.13657	−	3.49801i	−0.204135	−	0.628262i	0.795613	−	0.605805i	$-0.207149\pi$
$32$	4.40389	−	3.55046i	0.778506	−	0.627638i
$33$	0.183972	−	0.361066i	0.0320255	−	0.0628535i
$34$	0.898627	−	1.39842i	0.154113	−	0.239828i
$35$	2.85315	−	0.684981i	0.482271	−	0.115783i
$36$	5.86687	+	1.18825i	0.977812	+	0.198042i
$37$	2.54290	−	7.82623i	0.418049	−	1.28662i	−0.491445	−	0.870908i	$-0.663531\pi$
$37$	2.54290	−	7.82623i	0.418049	−	1.28662i	0.909495	−	0.415715i	$-0.136469\pi$
$38$	3.37499	−	0.193136i	0.547496	−	0.0313308i
$39$	−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	0.941276	+	0.337637i	$0.109628\pi$
$43$	−0.382077	+	2.41234i	−0.0582662	+	0.367878i	−0.999543	+	0.0302413i	$0.990372\pi$
$44$	2.66116	−	9.31147i	0.401184	−	1.40376i
$45$	−2.84651	−	0.924887i	−0.424332	−	0.137874i
$46$	−1.54660	+	0.211176i	−0.228033	+	0.0311361i
$47$	0.189762	+	0.790414i	0.0276796	+	0.115294i	0.984499	−	0.175388i	$-0.0561180\pi$
$47$	0.189762	+	0.790414i	0.0276796	+	0.115294i	−0.956820	+	0.290682i	$0.906118\pi$
$48$	−0.334748	−	0.00233209i	−0.0483167	−	0.000336608i
$49$	−1.43423	−	0.730778i	−0.204890	−	0.104397i
$50$	1.27351	−	0.614959i	0.180101	−	0.0869683i
$51$	−0.0935534	+	0.0303973i	−0.0131001	+	0.00425648i
$52$	−1.04856	+	0.0375406i	−0.145410	+	0.00520594i
$53$	2.37886	−	0.187220i	0.326761	−	0.0257167i	0.0859825	−	0.996297i	$-0.472597\pi$
$53$	2.37886	−	0.187220i	0.326761	−	0.0257167i	0.240779	+	0.970580i	$0.422597\pi$
$54$	−0.449017	−	0.549076i	−0.0611035	−	0.0747198i
$55$	−1.85301	+	4.47355i	−0.249859	+	0.603214i
$56$	8.21492	+	1.18004i	1.09776	+	0.157689i
$57$	−0.161843	−	0.117586i	−0.0214366	−	0.0155746i
$58$	−4.79674	+	10.9145i	−0.629843	+	1.43314i
$59$	−8.44679	−	11.6260i	−1.09968	−	1.51358i	−0.835810	−	0.549019i	$-0.815001\pi$
$59$	−8.44679	−	11.6260i	−1.09968	−	1.51358i	−0.263869	−	0.964559i	$-0.584999\pi$
$60$	0.166148	+	0.0202520i	0.0214496	+	0.00261453i
$61$	−0.995078	−	6.28267i	−0.127407	−	0.804414i	−0.965789	−	0.259331i	$-0.916498\pi$
$61$	−0.995078	−	6.28267i	−0.127407	−	0.804414i	0.838382	−	0.545083i	$-0.183502\pi$
$62$	−0.923325	+	5.11891i	−0.117262	+	0.650103i
$63$	4.58865	+	7.48799i	0.578115	+	0.943398i
$64$	−7.86216	+	1.47865i	−0.982770	+	0.184831i
$65$	0.523001	+	0.0411610i	0.0648703	+	0.00510540i
$66$	−0.470732	+	0.326865i	−0.0579430	+	0.0402343i
$67$	−1.49032	−	1.27285i	−0.182071	−	0.155503i	0.553741	−	0.832689i	$-0.313200\pi$
$67$	−1.49032	−	1.27285i	−0.182071	−	0.155503i	−0.735813	+	0.677185i	$0.763200\pi$
$68$	−2.05505	+	1.14150i	−0.249211	+	0.138427i
$69$	0.0787602	+	0.0482643i	0.00948162	+	0.00581034i
$70$	−4.01334	−	1.05474i	−0.479686	−	0.126065i
$71$	−0.811324	+	0.692936i	−0.0962864	+	0.0822364i	−0.696288	−	0.717762i	$-0.745166\pi$
$71$	−0.811324	+	0.692936i	−0.0962864	+	0.0822364i	0.600002	+	0.799999i	$0.295166\pi$
$72$	−6.51575	−	5.40456i	−0.767888	−	0.636933i
$73$	−6.02934	−	6.02934i	−0.705680	−	0.705680i	0.259943	−	0.965624i	$-0.416296\pi$
$73$	−6.02934	−	6.02934i	−0.705680	−	0.705680i	−0.965624	+	0.259943i	$0.916296\pi$
$74$	−8.40300	+	8.05121i	−0.976829	+	0.935934i
$75$	−0.0813767	−	0.0195368i	−0.00939657	−	0.00225592i
$76$	−4.33462	−	2.01663i	−0.497215	−	0.231323i
$77$	12.6594	−	6.45026i	1.44267	−	0.735076i
$78$	0.0494408	+	0.0375614i	0.00559807	+	0.00425299i
$79$	−2.37199	+	0.982510i	−0.266870	+	0.110541i	−0.512106	−	0.858922i	$-0.671134\pi$
$79$	−2.37199	+	0.982510i	−0.266870	+	0.110541i	0.245236	+	0.969463i	$0.421134\pi$
$80$	3.98976	−	0.286049i	0.446069	−	0.0319812i
$81$		−	8.93701i		−	0.993002i
$82$	6.70108	+	6.09061i	0.740011	+	0.672595i
$83$			6.72545i			0.738214i	0.929387	+	0.369107i	$0.120336\pi$
$83$			6.72545i			0.738214i	−0.929387	+	0.369107i	$0.879664\pi$
$84$	−0.332118	−	0.361803i	−0.0362370	−	0.0394759i
$85$	1.08593	−	0.449805i	0.117785	−	0.0487882i
$86$	2.08953	−	2.75038i	0.225320	−	0.296581i
$87$	0.628613	−	0.320294i	0.0673944	−	0.0343392i
$88$	−9.54373	+	9.82282i	−1.01736	+	1.04712i
$89$	3.00548	+	0.721551i	0.318580	+	0.0764842i	0.389582	−	0.920992i	$-0.372620\pi$
$89$	3.00548	+	0.721551i	0.318580	+	0.0764842i	−0.0710018	+	0.997476i	$0.522620\pi$
$90$	2.92834	+	3.05629i	0.308674	+	0.322161i
$91$	−1.08848	−	1.08848i	−0.114104	−	0.114104i
$92$	2.06839	+	0.771267i	0.215645	+	0.0804101i
$93$	0.234061	−	0.199907i	0.0242710	−	0.0207294i
$94$	0.292195	−	1.11182i	0.0301376	−	0.114676i
$95$	2.03814	+	1.24897i	0.209108	+	0.128142i
$96$	0.415557	+	0.226794i	0.0424126	+	0.0231471i
$97$	−8.95591	−	7.64907i	−0.909335	−	0.776646i	0.0658976	−	0.997826i	$-0.479009\pi$
$97$	−8.95591	−	7.64907i	−0.909335	−	0.776646i	−0.975233	+	0.221181i	$0.929009\pi$
$98$	1.29838	+	1.86985i	0.131156	+	0.188883i
$99$	−14.4478	−	1.13707i	−1.45206	−	0.114280i
$100$	−1.99817	−	0.0854804i	−0.199817	−	0.00854804i
$101$	1.64387	+	2.68256i	0.163572	+	0.266925i	0.923916	−	0.382596i	$-0.124970\pi$
$101$	1.64387	+	2.68256i	0.163572	+	0.266925i	−0.760344	+	0.649520i	$0.774970\pi$
$102$	0.136904	+	0.0246941i	0.0135555	+	0.00244508i
$103$	1.68419	+	10.6336i	0.165948	+	1.04776i	0.920279	+	0.391262i	$0.127961\pi$
$103$	1.68419	+	10.6336i	0.165948	+	1.04776i	−0.754331	+	0.656494i	$0.772039\pi$
$104$	1.33168	+	0.654530i	0.130582	+	0.0641819i
$105$	0.144338	+	0.198664i	0.0140859	+	0.0193876i
$106$	−3.08942	−	1.35776i	−0.300071	−	0.131877i
$107$	−10.6753	−	7.75606i	−1.03202	−	0.749807i	−0.0633086	−	0.997994i	$-0.520165\pi$
$107$	−10.6753	−	7.75606i	−1.03202	−	0.749807i	−0.968712	+	0.248187i	$0.920165\pi$
$108$	0.192266	+	0.984497i	0.0185008	+	0.0947333i
$109$	5.48561	−	13.2434i	0.525426	−	1.26849i	−0.409065	−	0.912505i	$-0.634145\pi$
$109$	5.48561	−	13.2434i	0.525426	−	1.26849i	0.934491	−	0.355986i	$-0.115855\pi$
$110$	5.30099	−	4.33499i	0.505430	−	0.413325i
$111$	0.686552	−	0.0540328i	0.0651647	−	0.00512857i
$112$	−9.44706	−	6.96476i	−0.892663	−	0.658108i
$113$	−7.38000	+	2.39791i	−0.694252	+	0.225576i	−0.634824	−	0.772657i	$-0.718927\pi$
$113$	−7.38000	+	2.39791i	−0.694252	+	0.225576i	−0.0594274	+	0.998233i	$0.518927\pi$
$114$	0.123022	+	0.254764i	0.0115220	+	0.0238608i
$115$	−0.983453	−	0.501095i	−0.0917075	−	0.0467273i
$116$	13.2769	−	10.3919i	1.23273	−	0.964864i
$117$	0.366551	+	1.52680i	0.0338877	+	0.141152i
$118$	2.74944	+	20.1362i	0.253106	+	1.85368i
$119$	−3.28008	−	1.06576i	−0.300685	−	0.0976983i
$120$	−0.193486	−	0.136360i	−0.0176628	−	0.0124479i
$121$	−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
$126$	−0.709569	−	12.3995i	−0.0632134	−	1.10464i
$127$	1.81014	−	5.57105i	0.160624	−	0.494351i	−0.838063	−	0.545574i	$-0.816312\pi$
$127$	1.81014	−	5.57105i	0.160624	−	0.494351i	0.998687	+	0.0512226i	$0.0163118\pi$
$128$	10.7857	+	3.41594i	0.953330	+	0.301929i
$129$	−0.198755	+	0.0477169i	−0.0174994	+	0.00420124i
$130$	−0.624162	−	0.401086i	−0.0547426	−	0.0351776i
$131$	−4.79220	+	9.40523i	−0.418697	+	0.821739i	0.581271	+	0.813710i	$0.302556\pi$
$131$	−4.79220	+	9.40523i	−0.418697	+	0.821739i	−0.999968	+	0.00802868i	$0.997444\pi$
$132$	0.805177	−	0.0924562i	0.0700816	−	0.00804728i
$133$	−2.16742	−	6.67064i	−0.187939	−	0.578417i
$134$	1.00571	+	2.58282i	0.0868802	+	0.223121i
$135$	−0.0393510	−	0.500002i	−0.00338679	−	0.0430333i
$136$	3.32418	−	0.0479048i	0.285046	−	0.00410781i
$137$	16.3599	+	6.77649i	1.39772	+	0.578955i	0.949159	−	0.314797i	$-0.101936\pi$
$137$	16.3599	+	6.77649i	1.39772	+	0.578955i	0.448562	+	0.893752i	$0.351936\pi$
$138$	−0.0658597	−	0.112817i	−0.00560635	−	0.00960365i
$139$	0.942267	−	1.29692i	0.0799220	−	0.110003i	−0.767184	−	0.641427i	$-0.778343\pi$
$139$	0.942267	−	1.29692i	0.0799220	−	0.110003i	0.847106	+	0.531424i	$0.178343\pi$
$140$	4.29543	+	3.99849i	0.363030	+	0.337934i
$141$	−0.0550363	+	0.0399862i	−0.00463489	+	0.00336744i
$142$	1.47441	−	0.320806i	0.123730	−	0.0269214i
$143$	2.50900	−	0.397386i	0.209813	−	0.0332311i
$144$	4.50431	+	11.0923i	0.375360	+	0.924360i
$145$	−7.18787	+	4.40473i	−0.596920	+	0.365793i
$146$	3.48035	+	11.5455i	0.288035	+	0.955513i
$147$	0.0105694	−	0.134297i	0.000871749	−	0.0110766i
$148$	15.8555	−	4.41216i	1.30332	−	0.362677i
$149$	−0.430690	+	0.504273i	−0.0352835	+	0.0413117i	−0.777767	−	0.628553i	$-0.783648\pi$
$149$	−0.430690	+	0.504273i	−0.0352835	+	0.0413117i	0.742484	+	0.669864i	$0.233648\pi$
$150$	0.0883336	+	0.0787710i	0.00721241	+	0.00643162i
$151$	3.27841	−	5.34989i	0.266794	−	0.435367i	−0.690987	−	0.722867i	$-0.742824\pi$
$151$	3.27841	−	5.34989i	0.266794	−	0.435367i	0.957781	+	0.287499i	$0.0928239\pi$
$152$	4.05243	+	5.41195i	0.328696	+	0.438967i
$153$	2.28473	+	2.67508i	0.184710	+	0.216267i
$154$	−20.0885	−	0.429488i	−1.61877	−	0.0346092i
$155$	−2.60076	+	2.60076i	−0.208898	+	0.208898i
$156$	−0.0364843	−	0.0798712i	−0.00292108	−	0.00639481i
$157$	−0.768540	+	3.20120i	−0.0613362	+	0.255484i	−0.994611	−	0.103680i	$-0.966938\pi$
$157$	−0.768540	+	3.20120i	−0.0613362	+	0.255484i	0.933274	+	0.359164i	$0.116938\pi$
$158$	3.61277	+	0.362181i	0.287417	+	0.0288136i
$159$	0.0906619	+	0.177934i	0.00718996	+	0.0141111i
$160$	−5.16280	−	2.31202i	−0.408156	−	0.182782i
$161$	1.23938	+	2.99214i	0.0976772	+	0.235814i
$162$	−5.97732	+	11.1361i	−0.469622	+	0.874933i
$163$	13.5248			1.05934			0.529671	−	0.848203i	$-0.322315\pi$
$163$	13.5248			1.05934			0.529671	+	0.848203i	$0.322315\pi$
$164$	−4.27641	−	12.0711i	−0.333931	−	0.942597i
$165$	−0.405234			−0.0315474
$166$	4.49816	−	8.38033i	0.349125	−	0.650440i
$167$	−5.75185	−	13.8862i	−0.445091	−	1.07455i	−0.974138	−	0.225953i	$-0.927450\pi$
$167$	−5.75185	−	13.8862i	−0.445091	−	1.07455i	0.529047	−	0.848593i	$-0.322550\pi$
$168$	0.171856	+	0.672958i	0.0132589	+	0.0519198i
$169$	5.77693	+	11.3379i	0.444379	+	0.872143i
$170$	−1.65397	−	0.165811i	−0.126854	−	0.0127171i
$171$	−1.67016	+	6.95673i	−0.127721	+	0.531994i
$172$	−4.44321	+	2.02961i	−0.338792	+	0.154756i
$173$	−16.1039	+	16.1039i	−1.22436	+	1.22436i	−0.258292	+	0.966067i	$0.583160\pi$
$173$	−16.1039	+	16.1039i	−1.22436	+	1.22436i	−0.966067	+	0.258292i	$0.916840\pi$
$174$	−0.997512	−	0.0213267i	−0.0756212	−	0.00161677i
$175$	−1.90563	−	2.23120i	−0.144052	−	0.168663i
$176$	18.4618	−	5.85674i	1.39161	−	0.441469i
$177$	0.628386	−	1.02543i	0.0472324	−	0.0770763i
$178$	−3.26242	−	2.90924i	−0.244528	−	0.218057i
$179$	13.5556	−	15.8716i	1.01319	−	1.18630i	0.0307919	−	0.999526i	$-0.490197\pi$
$179$	13.5556	−	15.8716i	1.01319	−	1.18630i	0.982403	−	0.186773i	$-0.0598029\pi$
$180$	−1.60476	−	5.76687i	−0.119612	−	0.429837i
$181$	−0.454904	+	5.78010i	−0.0338127	+	0.429631i	0.956592	+	0.291432i	$0.0941316\pi$
$181$	−0.454904	+	5.78010i	−0.0338127	+	0.429631i	−0.990404	+	0.138200i	$0.955868\pi$
$182$	0.628311	+	2.08432i	0.0465735	+	0.154500i
$183$	0.453898	−	0.278149i	0.0335531	−	0.0205614i
$184$	−2.06150	−	2.34444i	−0.151976	−	0.172835i
$185$	−8.12767	+	1.28730i	−0.597558	+	0.0946439i
$186$	−0.425358	+	0.0925502i	−0.0311887	+	0.00678611i
$187$	4.60447	−	3.34534i	0.336712	−	0.244636i
$188$	−1.10771	+	1.18997i	−0.0807881	+	0.0867876i
$189$	−0.865017	+	1.19059i	−0.0629207	+	0.0866029i
$190$	−1.70430	−	2.91946i	−0.123643	−	0.211800i
$191$	20.1492	+	8.34608i	1.45795	+	0.603901i	0.964074	−	0.265634i	$-0.0855812\pi$
$191$	20.1492	+	8.34608i	1.45795	+	0.603901i	0.493872	+	0.869535i	$0.335581\pi$
$192$	−0.366123	−	0.560535i	−0.0264227	−	0.0404532i
$193$	1.71978	+	21.8519i	0.123792	+	1.57293i	0.674527	+	0.738250i	$0.264348\pi$
$193$	1.71978	+	21.8519i	0.123792	+	1.57293i	−0.550734	+	0.834681i	$0.685652\pi$
$194$	6.04372	+	15.5212i	0.433914	+	1.11436i
$195$	0.0135673	+	0.0417559i	0.000971575	+	0.00299020i
$196$	−0.367256	−	3.19834i	−0.0262326	−	0.228453i
$197$	4.83469	−	9.48862i	0.344458	−	0.676036i	−0.652172	−	0.758071i	$-0.726142\pi$
$197$	4.83469	−	9.48862i	0.344458	−	0.676036i	0.996629	+	0.0820351i	$0.0261420\pi$
$198$	17.2424	+	11.0800i	1.22536	+	0.787418i
$199$	18.2970	−	4.39273i	1.29704	−	0.311392i	0.474580	−	0.880213i	$-0.342600\pi$
$199$	18.2970	−	4.39273i	1.29704	−	0.311392i	0.822462	+	0.568821i	$0.192600\pi$
$200$	2.43268	+	1.44295i	0.172016	+	0.102032i
$201$	0.0506855	−	0.155994i	0.00357508	−	0.0110030i
$202$	−0.254202	−	4.44210i	−0.0178856	−	0.312545i
$203$	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
$208$	−1.22159	−	1.70625i	−0.0847023	−	0.118307i
$209$	11.0081	+	3.57674i	0.761444	+	0.247408i
$210$	−0.0469821	−	0.344085i	−0.00324207	−	0.0237441i
$211$	5.62544	+	23.4316i	0.387271	+	1.61310i	0.736756	+	0.676159i	$0.236357\pi$
$211$	5.62544	+	23.4316i	0.387271	+	1.61310i	−0.349485	+	0.936942i	$0.613643\pi$
$212$	2.94151	+	3.75814i	0.202024	+	0.258110i
$213$	−0.0795606	−	0.0405381i	−0.00545140	−	0.00277763i
$214$	8.11463	+	16.8045i	0.554705	+	1.14873i
$215$	2.32287	−	0.754746i	0.158418	−	0.0514732i
$216$	0.418883	−	1.35534i	0.0285014	−	0.0922190i
$217$	10.7589	−	0.846744i	0.730362	−	0.0574807i
$218$	−15.6930	+	12.8332i	−1.06286	+	0.869175i
$219$	0.273082	−	0.659277i	0.0184531	−	0.0445498i
$220$	−9.50472	+	1.85621i	−0.640808	+	0.125146i
$221$	−0.498868	−	0.362449i	−0.0335575	−	0.0243809i
$222$	−0.891625	−	0.391856i	−0.0598420	−	0.0262997i
$223$	−13.3020	−	18.3086i	−0.890765	−	1.22603i	−0.973321	−	0.229447i	$-0.926308\pi$
$223$	−13.3020	−	18.3086i	−0.890765	−	1.22603i	0.0825561	−	0.996586i	$-0.473692\pi$
$224$	7.11341	+	14.9970i	0.475284	+	1.00203i
$225$	0.468208	+	2.95615i	0.0312139	+	0.197076i
$226$	10.7997	+	1.94800i	0.718386	+	0.129579i
$227$	8.91538	+	14.5486i	0.591734	+	0.965623i	0.998639	+	0.0521521i	$0.0166081\pi$
$227$	8.91538	+	14.5486i	0.591734	+	0.965623i	−0.406905	+	0.913471i	$0.633392\pi$
$228$	0.0171002	−	0.399732i	0.00113249	−	0.0264729i
$229$	14.7287	+	1.15917i	0.973301	+	0.0766004i	0.555126	−	0.831766i	$-0.312670\pi$
$229$	14.7287	+	1.15917i	0.973301	+	0.0766004i	0.418175	+	0.908367i	$0.362670\pi$
$230$	0.890299	+	1.28216i	0.0587045	+	0.0845428i
$231$	0.904159	+	0.772224i	0.0594893	+	0.0508086i
$232$	−23.4943	+	4.06899i	−1.54247	+	0.267142i
$233$	−4.33291	−	2.65521i	−0.283858	−	0.173948i	0.373280	−	0.927719i	$-0.378233\pi$
$233$	−4.33291	−	2.65521i	−0.283858	−	0.173948i	−0.657138	+	0.753770i	$0.728233\pi$
$234$	0.564416	−	2.14764i	0.0368970	−	0.140396i
$235$	0.618114	−	0.527919i	0.0403213	−	0.0344376i
$236$	10.0416	−	26.9298i	0.653655	−	1.75298i
$237$	−0.151932	−	0.151932i	−0.00986907	−	0.00986907i
$238$	3.37437	+	3.52181i	0.218728	+	0.228285i
$239$	16.3962	+	3.93638i	1.06058	+	0.254623i	0.725966	−	0.687731i	$-0.241393\pi$
$239$	16.3962	+	3.93638i	1.06058	+	0.254623i	0.334617	+	0.942354i	$0.391393\pi$
$240$	0.149894	+	0.299321i	0.00967564	+	0.0193211i
$241$	−4.39900	+	2.24140i	−0.283364	+	0.144381i	−0.589896	−	0.807479i	$-0.700831\pi$
$241$	−4.39900	+	2.24140i	−0.283364	+	0.144381i	0.306532	+	0.951860i	$0.400831\pi$
$242$	10.6481	−	14.0157i	0.684484	−	0.900965i
$243$	2.08111	−	0.862022i	0.133503	−	0.0552988i
$244$	9.37206	−	8.60309i	0.599984	−	0.550757i
$245$			1.60968i			0.102838i
$246$	−0.256305	+	0.713178i	−0.0163414	+	0.0454706i
$247$		−	1.25404i		−	0.0797925i
$248$	−9.55279	+	4.11915i	−0.606603	+	0.261566i
$249$	−0.520002	+	0.215392i	−0.0329538	+	0.0136499i
$250$	−1.12609	−	0.855520i	−0.0712204	−	0.0541078i
$251$	1.65138	−	0.841420i	0.104234	−	0.0531100i	−0.401096	−	0.916036i	$-0.631371\pi$
$251$	1.65138	−	0.841420i	0.104234	−	0.0531100i	0.505330	+	0.862926i	$0.331371\pi$
$252$	−7.40896	+	15.9251i	−0.466721	+	1.00319i
$253$	−5.19687	−	1.24766i	−0.326724	−	0.0784396i
$254$	−5.98162	+	5.73120i	−0.375320	+	0.359608i
$255$	0.0695566	+	0.0695566i	0.00435580	+	0.00435580i
$256$	−11.1550	−	11.4702i	−0.697186	−	0.716890i
$257$	−1.41977	+	1.21260i	−0.0885630	+	0.0756400i	−0.692627	−	0.721296i	$-0.743547\pi$
$257$	−1.41977	+	1.21260i	−0.0885630	+	0.0756400i	0.604064	+	0.796936i	$0.293547\pi$
$258$	0.279575	+	0.0734745i	0.0174056	+	0.00457432i
$259$	20.5876	+	12.6161i	1.27925	+	0.783926i
$260$	0.509487	+	0.917234i	0.0315970	+	0.0568845i
$261$	−19.1861	−	16.3864i	−1.18759	−	1.01430i
$262$	12.2619	−	8.51435i	0.757540	−	0.526018i
$263$	−10.9001	−	0.857858i	−0.672130	−	0.0528978i	−0.262198	−	0.965014i	$-0.584448\pi$
$263$	−10.9001	−	0.857858i	−0.672130	−	0.0528978i	−0.409932	+	0.912116i	$0.634448\pi$
$264$	−1.06514	−	0.423318i	−0.0655547	−	0.0260534i
$265$	−1.24679	−	2.03458i	−0.0765900	−	0.124983i
$266$	−1.76076	+	9.76166i	−0.107959	+	0.598526i
$267$	0.0404653	+	0.255488i	0.00247643	+	0.0156356i
$268$	0.474279	−	3.89099i	0.0289712	−	0.237680i
$269$	4.87370	+	6.70807i	0.297155	+	0.408998i	0.931322	−	0.364198i	$-0.118657\pi$
$269$	4.87370	+	6.70807i	0.297155	+	0.408998i	−0.634167	+	0.773196i	$0.718657\pi$
$270$	−0.285381	+	0.649352i	−0.0173677	+	0.0395183i
$271$	−19.1159	−	13.8885i	−1.16121	−	0.843666i	−0.171276	−	0.985223i	$-0.554789\pi$
$271$	−19.1159	−	13.8885i	−1.16121	−	0.843666i	−0.989930	+	0.141558i	$0.954789\pi$
$272$	−4.17418	−	2.16361i	−0.253097	−	0.131188i
$273$	0.0492997	−	0.119020i	0.00298376	−	0.00720342i
$274$	−15.8532	−	19.3859i	−0.957724	−	1.17114i
$275$	4.82721	−	0.379910i	0.291092	−	0.0229094i
$276$	0.00660997	+	0.184626i	0.000397873	+	0.0111132i
$277$	15.4863	−	5.03179i	0.930479	−	0.302331i	0.195721	−	0.980660i	$-0.437295\pi$
$277$	15.4863	−	5.03179i	0.930479	−	0.302331i	0.734759	+	0.678329i	$0.237295\pi$
$278$	−2.04154	+	0.985828i	−0.122443	+	0.0591260i
$279$	−9.80849	−	4.99768i	−0.587219	−	0.299203i
$280$	−2.67808	−	7.85527i	−0.160046	−	0.469442i
$281$	5.44543	+	22.6818i	0.324847	+	1.35309i	0.860845	+	0.508867i	$0.169935\pi$
$281$	5.44543	+	22.6818i	0.324847	+	1.35309i	−0.535998	+	0.844219i	$0.680065\pi$
$282$	0.0953224	−	0.0130155i	0.00567637	−	0.000775064i
$283$	−22.4372	−	7.29029i	−1.33375	−	0.433363i	−0.446558	−	0.894755i	$-0.647350\pi$
$283$	−22.4372	−	7.29029i	−1.33375	−	0.433363i	−0.887196	+	0.461392i	$0.847350\pi$
$284$	−2.05177	−	0.586383i	−0.121750	−	0.0347954i
$285$	−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
$290$	11.9025	−	0.681129i	0.698941	−	0.0399973i
$291$	0.304590	−	0.937430i	0.0178554	−	0.0549531i
$292$	3.38522	−	16.7142i	0.198105	−	0.978123i
$293$	2.63900	−	0.633569i	0.154172	−	0.0370135i	−0.155624	−	0.987816i	$-0.549739\pi$
$293$	2.63900	−	0.633569i	0.154172	−	0.0370135i	0.309797	+	0.950803i	$0.399739\pi$
$294$	−0.102992	+	0.160273i	−0.00600659	+	0.00934732i
$295$	−6.52409	+	12.8042i	−0.379847	+	0.745492i
$296$	−22.7079	−	5.10678i	−1.31987	−	0.296826i
$297$	−0.750468	−	2.30970i	−0.0435466	−	0.134023i
$298$	0.873938	−	0.340299i	0.0506259	−	0.0197130i
$299$	0.0454317	+	0.577265i	0.00262739	+	0.0333841i
$300$	−0.0573850	−	0.157233i	−0.00331313	−	0.00907788i
$301$	−6.62105	−	2.74253i	−0.381631	−	0.158077i
$302$	−7.66325	+	4.47360i	−0.440971	+	0.257427i
$303$	−0.154764	+	0.213015i	−0.00889097	+	0.0122374i
$304$	−1.42993	−	9.45400i	−0.0820119	−	0.542224i
$305$	−5.14615	+	3.73889i	−0.294667	+	0.214088i
$306$	−1.05775	−	4.86140i	−0.0604678	−	0.277908i
$307$	−5.81094	+	0.920363i	−0.331648	+	0.0525279i	−0.320038	−	0.947405i	$-0.603696\pi$
$307$	−5.81094	+	0.920363i	−0.331648	+	0.0525279i	−0.0116101	+	0.999933i	$0.503696\pi$
$308$	24.7442	+	13.9709i	1.40993	+	0.796064i
$309$	−0.768234	+	0.470774i	−0.0437033	+	0.0267814i
$310$	4.98017	−	1.50125i	0.282854	−	0.0852653i
$311$	1.17220	−	14.8942i	0.0664693	−	0.844572i	−0.869826	−	0.493359i	$-0.835769\pi$
$311$	1.17220	−	14.8942i	0.0664693	−	0.844572i	0.936295	−	0.351214i	$-0.114231\pi$
$312$	−0.00795827	+	0.123926i	−0.000450548	+	0.00701593i
$313$	−18.1537	+	21.2553i	−1.02611	+	1.20142i	−0.0468291	+	0.998903i	$0.514912\pi$
$313$	−18.1537	+	21.2553i	−1.02611	+	1.20142i	−0.979279	+	0.202515i	$0.935088\pi$
$314$	3.09870	−	3.47487i	0.174870	−	0.196099i
$315$	4.58865	−	7.48799i	0.258541	−	0.421901i
$316$	−4.25950	−	2.86762i	−0.239616	−	0.161316i
$317$	0.986570	+	1.15512i	0.0554113	+	0.0648783i	0.787419	−	0.616418i	$-0.211417\pi$
$317$	0.986570	+	1.15512i	0.0554113	+	0.0648783i	−0.732008	+	0.681296i	$0.761417\pi$
$318$	0.00603669	−	0.282354i	0.000338521	−	0.0158336i
$319$	−28.8640	+	28.8640i	−1.61607	+	1.61607i
$320$	4.88683	+	6.33395i	0.273182	+	0.354078i
$321$	0.257796	−	1.07380i	0.0143888	−	0.0599336i
$322$	0.456873	−	4.55732i	0.0254605	−	0.253970i
$323$	−1.27555	−	2.50342i	−0.0709738	−	0.139294i
$324$	14.8962	−	9.87845i	0.827567	−	0.548803i
$325$	−0.200763	−	0.484684i	−0.0111363	−	0.0268854i
$326$	−16.8527	−	9.04573i	−0.933385	−	0.500996i
$327$	1.19965			0.0663407
$328$	−2.74483	+	17.9016i	−0.151558	+	0.988448i
$329$	−2.38515			−0.131498
$330$	0.504947	+	0.271031i	0.0277964	+	0.0149198i
$331$	−8.99032	−	21.7045i	−0.494153	−	1.19299i	−0.952588	−	0.304262i	$-0.901590\pi$
$331$	−8.99032	−	21.7045i	−0.494153	−	1.19299i	0.458436	−	0.888728i	$-0.348410\pi$
$332$	−11.2100	+	7.43392i	−0.615228	+	0.407989i
$333$	−11.1815	−	21.9449i	−0.612741	−	1.20257i
$334$	−2.12030	+	21.1500i	−0.116017	+	1.15728i
$335$	−0.457529	+	1.90574i	−0.0249975	+	0.104122i
$336$	0.235950	−	0.953489i	0.0128721	−	0.0520171i
$337$	11.4237	−	11.4237i	0.622290	−	0.622290i	−0.323827	−	0.946116i	$-0.604970\pi$
$337$	11.4237	−	11.4237i	0.622290	−	0.622290i	0.946116	+	0.323827i	$0.104970\pi$
$338$	0.384654	−	17.9914i	0.0209224	−	0.978605i
$339$	−0.421757	−	0.493814i	−0.0229067	−	0.0268203i
$340$	1.95005	+	1.31283i	0.105757	+	0.0711983i
$341$	−9.30546	+	15.1851i	−0.503919	+	0.822321i
$342$	6.73398	−	7.55147i	0.364132	−	0.408337i
$343$	−10.2719	+	12.0269i	−0.554633	+	0.649392i
$344$	6.89397	+	0.442716i	0.371698	+	0.0238697i
$345$	0.00724744	−	0.0920874i	0.000390189	−	0.00495782i
$346$	30.8372	−	9.29575i	1.65782	−	0.499743i
$347$	−24.2411	+	14.8550i	−1.30133	+	0.797458i	−0.988335	−	0.152296i	$-0.951333\pi$
$347$	−24.2411	+	14.8550i	−1.30133	+	0.797458i	−0.312998	+	0.949754i	$0.601333\pi$
$348$	1.22870	+	0.693737i	0.0658651	+	0.0371882i
$349$	−23.7374	+	3.75964i	−1.27063	+	0.201249i	−0.755094	−	0.655617i	$-0.772409\pi$
$349$	−23.7374	+	3.75964i	−1.27063	+	0.201249i	−0.515540	+	0.856865i	$0.672409\pi$
$350$	0.882241	+	4.05475i	0.0471578	+	0.216736i
$351$	−0.212869	+	0.154659i	−0.0113621	+	0.00825507i
$352$	−26.9218	−	5.04991i	−1.43493	−	0.269161i
$353$	−6.13557	+	8.44489i	−0.326564	+	0.449476i	−0.940457	−	0.339913i	$-0.889602\pi$
$353$	−6.13557	+	8.44489i	−0.326564	+	0.449476i	0.613893	+	0.789389i	$0.289602\pi$
$354$	−1.46885	+	0.857471i	−0.0780682	+	0.0455741i
$355$	0.985744	+	0.408308i	0.0523178	+	0.0216708i
$356$	2.11940	+	5.80708i	0.112328	+	0.307775i
$357$	−0.0226459	−	0.287744i	−0.00119855	−	0.0152290i
$358$	−27.5065	+	10.7106i	−1.45376	+	0.566074i
$359$	5.46054	+	16.8058i	0.288196	+	0.886977i	0.985422	+	0.170126i	$0.0544173\pi$
$359$	5.46054	+	16.8058i	0.288196	+	0.886977i	−0.697226	+	0.716851i	$0.745583\pi$
$360$	−1.85741	+	8.25919i	−0.0978939	+	0.435298i
$361$	−6.03175	+	11.8380i	−0.317460	+	0.623051i
$362$	4.43272	−	6.89811i	0.232979	−	0.362557i
$363$	−1.01284	+	0.243161i	−0.0531603	+	0.0127627i
$364$	0.611138	−	3.01743i	0.0320323	−	0.158156i
$365$	−2.63492	+	8.10944i	−0.137918	+	0.424467i
$366$	−0.751619	+	0.0430118i	−0.0392878	+	0.00224826i
$367$	0.575588	+	0.0911642i	0.0300455	+	0.00475873i	0.171439	−	0.985195i	$-0.445158\pi$
$367$	0.575588	+	0.0911642i	0.0300455	+	0.00475873i	−0.141394	+	0.989953i	$0.545158\pi$
$368$	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
$372$	0.591922	+	0.169167i	0.0306897	+	0.00877092i
$373$	31.6956	+	10.2985i	1.64114	+	0.533237i	0.976792	−	0.214190i	$-0.0687111\pi$
$373$	31.6956	+	10.2985i	1.64114	+	0.533237i	0.664344	+	0.747427i	$0.268711\pi$
$374$	−7.97491	+	1.08891i	−0.412373	+	0.0563063i
$375$	0.0195368	+	0.0813767i	0.00100888	+	0.00420227i
$376$	2.17616	−	0.741912i	0.112227	−	0.0382612i
$377$	3.94056	+	2.00782i	0.202949	+	0.103408i
$378$	1.87417	−	0.905007i	0.0963967	−	0.0465485i
$379$	−0.414518	+	0.134685i	−0.0212924	+	0.00691831i	−0.319644	−	0.947538i	$-0.603563\pi$
$379$	−0.414518	+	0.134685i	−0.0212924	+	0.00691831i	0.298351	+	0.954456i	$0.403563\pi$
$380$	0.171051	+	4.77771i	0.00877473	+	0.245091i
$381$	0.488718	−	0.0384630i	0.0250378	−	0.00197052i
$382$	−19.5251	−	23.8761i	−0.998990	−	1.22161i
$383$	−3.77908	+	9.12350i	−0.193102	+	0.466189i	−0.990542	−	0.137209i	$-0.956187\pi$
$383$	−3.77908	+	9.12350i	−0.193102	+	0.466189i	0.797440	+	0.603398i	$0.206187\pi$
$384$	0.0813115	+	0.943335i	0.00414941	+	0.0481394i
$385$	−11.4945	−	8.35121i	−0.585812	−	0.425617i
$386$	12.4722	−	28.3790i	0.634816	−	1.44445i
$387$	4.29678	+	5.91401i	0.218418	+	0.300626i
$388$	2.85013	−	23.3825i	0.144693	−	1.18707i
$389$	−4.67122	−	29.4929i	−0.236840	−	1.49535i	−0.763795	−	0.645458i	$-0.776666\pi$
$389$	−4.67122	−	29.4929i	−0.236840	−	1.49535i	0.526955	−	0.849893i	$-0.323334\pi$
$390$	0.0110218	−	0.0611046i	0.000558108	−	0.00309415i
$391$	0.677864	+	1.10617i	0.0342811	+	0.0559416i
$392$	−1.68151	+	4.23096i	−0.0849291	+	0.213696i
$393$	−0.880676	−	0.0693107i	−0.0444242	−	0.00349626i
$394$	−12.3706	+	8.58983i	−0.623220	+	0.432750i
$395$	1.95228	+	1.66741i	0.0982300	+	0.0838963i
$396$	−14.0745	−	25.3385i	−0.707271	−	1.27331i
$397$	27.0460	+	16.5738i	1.35740	+	0.831815i	0.994968	−	0.100196i	$-0.0319471\pi$
$397$	27.0460	+	16.5738i	1.35740	+	0.831815i	0.362430	+	0.932011i	$0.381947\pi$
$398$	−25.7372	−	6.76393i	−1.29009	−	0.339045i
$399$	0.446349	−	0.381218i	0.0223454	−	0.0190848i
$400$	−2.06618	−	3.42504i	−0.103309	−	0.171252i
$401$	−12.9143	−	12.9143i	−0.644911	−	0.644911i	0.306848	−	0.951759i	$-0.400726\pi$
$401$	−12.9143	−	12.9143i	−0.644911	−	0.644911i	−0.951759	+	0.306848i	$0.900726\pi$
$402$	−0.167490	+	0.160478i	−0.00835365	+	0.00800393i
$403$	1.87625	+	0.450447i	0.0934625	+	0.0224384i
$404$	−2.65425	+	5.70515i	−0.132054	+	0.283842i
$405$	−7.96294	+	4.05732i	−0.395682	+	0.201610i
$406$	−27.8549	−	21.1620i	−1.38242	−	1.05025i
$407$	−36.8128	+	15.2484i	−1.82474	+	0.755833i
$408$	0.110165	+	0.255487i	0.00545400	+	0.0126485i
$409$			18.1047i			0.895220i	0.894229	+	0.447610i	$0.147725\pi$
$409$			18.1047i			0.895220i	−0.894229	+	0.447610i	$0.852275\pi$
$410$	2.38454	−	8.73579i	0.117764	−	0.431430i
$411$			1.48195i			0.0730992i
$412$	−15.8624	+	14.5609i	−0.781485	+	0.717366i
$413$	38.9567	−	16.1364i	1.91693	−	0.794019i
$414$	−2.82624	+	3.72009i	−0.138902	+	0.182832i
$415$	5.99242	−	3.05329i	0.294156	−	0.149880i
$416$	0.380995	+	2.94313i	0.0186798	+	0.144299i
$417$	0.130453	+	0.0313191i	0.00638832	+	0.00153370i
$418$	−11.3245	−	11.8193i	−0.553900	−	0.578102i
$419$	−16.6748	−	16.6748i	−0.814618	−	0.814618i	0.170704	−	0.985322i	$-0.445396\pi$
$419$	−16.6748	−	16.6748i	−0.814618	−	0.814618i	−0.985322	+	0.170704i	$0.945396\pi$
$420$	−0.171591	+	0.460174i	−0.00837276	+	0.0224542i
$421$	−13.6712	+	11.6763i	−0.666293	+	0.569068i	−0.916947	−	0.399009i	$-0.869354\pi$
$421$	−13.6712	+	11.6763i	−0.666293	+	0.569068i	0.250654	+	0.968077i	$0.419354\pi$
$422$	8.66206	−	32.9597i	0.421663	−	1.60445i
$423$	2.07441	+	1.27120i	0.100861	+	0.0618079i
$424$	−1.15176	−	6.65024i	−0.0559344	−	0.322964i
$425$	−0.893779	−	0.763360i	−0.0433547	−	0.0370284i
$426$	0.0720244	+	0.103725i	0.00348959	+	0.00502551i
$427$	18.6070	+	1.46440i	0.900457	+	0.0708675i
$428$	1.12795	−	26.3667i	0.0545214	−	1.27448i
$429$	0.111080	+	0.181265i	0.00536297	+	0.00875157i
$430$	−3.39923	−	0.613137i	−0.163926	−	0.0295681i
$431$	−2.81823	−	17.7936i	−0.135749	−	0.857088i	−0.957750	−	0.287602i	$-0.907142\pi$
$431$	−2.81823	−	17.7936i	−0.135749	−	0.857088i	0.822001	−	0.569487i	$-0.192858\pi$
$432$	−1.42844	+	1.40867i	−0.0687258	+	0.0677749i
$433$	−2.36579	−	3.25623i	−0.113693	−	0.156484i	0.748378	−	0.663272i	$-0.230833\pi$
$433$	−2.36579	−	3.25623i	−0.113693	−	0.156484i	−0.862071	+	0.506788i	$0.830833\pi$
$434$	−13.9726	−	6.14075i	−0.670705	−	0.294765i
$435$	−0.570769	−	0.414688i	−0.0273663	−	0.0198828i
$436$	28.1376	−	5.49510i	1.34755	−	0.263168i
$437$	−1.00967	+	2.43756i	−0.0482991	+	0.116604i
$438$	−0.781219	+	0.638856i	−0.0373281	+	0.0305257i
$439$	14.1582	−	1.11428i	0.675736	−	0.0531816i	0.264052	−	0.964508i	$-0.414941\pi$
$439$	14.1582	−	1.11428i	0.675736	−	0.0531816i	0.411684	+	0.911327i	$0.364941\pi$
$440$	13.0850	+	4.04406i	0.623801	+	0.192793i
$441$	−4.58196	+	1.48877i	−0.218188	+	0.0708937i
$442$	0.379205	+	0.785290i	0.0180369	+	0.0373524i
$443$	19.1753	+	9.77032i	0.911048	+	0.464202i	0.845699	−	0.533660i	$-0.179184\pi$
$443$	19.1753	+	9.77032i	0.911048	+	0.464202i	0.0653490	+	0.997862i	$0.479184\pi$
$444$	0.848937	+	1.08462i	0.0402887	+	0.0514738i
$445$	−0.721551	−	3.00548i	−0.0342048	−	0.142473i
$446$	4.32980	+	31.7103i	0.205022	+	1.50153i
$447$	−0.0527831	−	0.0171503i	−0.00249656	−	0.000811180i
$448$	1.16663	−	23.4448i	0.0551182	−	1.10766i
$449$	3.86530	−	24.4045i	0.182415	−	1.15172i	−0.711235	−	0.702955i	$-0.751864\pi$
$449$	3.86530	−	24.4045i	0.182415	−	1.15172i	0.893649	−	0.448766i	$-0.148136\pi$
$450$	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
$454$	−1.37864	−	24.0913i	−0.0647026	−	1.13066i
$455$	−0.475684	+	1.46401i	−0.0223004	+	0.0686337i
$456$	−0.288659	+	0.486654i	−0.0135177	+	0.0227896i
$457$	−8.60804	+	2.06661i	−0.402667	+	0.0966718i	−0.429720	−	0.902962i	$-0.641388\pi$
$457$	−8.60804	+	2.06661i	−0.402667	+	0.0966718i	0.0270530	+	0.999634i	$0.491388\pi$
$458$	−17.5776	−	11.2954i	−0.821347	−	0.527798i
$459$	−0.267636	+	0.525265i	−0.0124922	+	0.0245172i
$460$	−0.251827	−	2.19310i	−0.0117415	−	0.102254i
$461$	−6.44415	−	19.8330i	−0.300134	−	0.923717i	−0.981448	−	0.191726i	$-0.938591\pi$
$461$	−6.44415	−	19.8330i	−0.300134	−	0.923717i	0.681315	−	0.731991i	$-0.261409\pi$
$462$	−0.610153	−	1.56697i	−0.0283869	−	0.0729018i
$463$	−1.86045	−	23.6393i	−0.0864625	−	1.09861i	−0.875162	−	0.483831i	$-0.839245\pi$
$463$	−1.86045	−	23.6393i	−0.0864625	−	1.09861i	0.788699	−	0.614779i	$-0.210755\pi$
$464$	31.9967	+	10.6434i	1.48541	+	0.494106i
$465$	−0.284380	−	0.117794i	−0.0131878	−	0.00546257i
$466$	3.62319	+	6.20652i	0.167841	+	0.287511i
$467$	20.1506	−	27.7349i	0.932457	−	1.28342i	−0.0264359	−	0.999651i	$-0.508416\pi$
$467$	20.1506	−	27.7349i	0.932457	−	1.28342i	0.958893	−	0.283767i	$-0.0915842\pi$
$468$	−2.13970	+	2.29860i	−0.0989076	+	0.106253i
$469$	4.65248	−	3.38022i	0.214831	−	0.156084i
$470$	−1.12329	+	0.244409i	−0.0518137	+	0.0112737i
$471$	−0.272126	+	0.0431005i	−0.0125389	+	0.00198597i
$472$	−30.5239	+	26.8401i	−1.40498	+	1.23542i
$473$	10.0837	−	6.17932i	0.463651	−	0.284125i
$474$	0.0877008	+	0.290934i	0.00402823	+	0.0133630i
$475$	0.187547	−	2.38301i	0.00860526	−	0.109340i
$476$	−1.84920	−	6.64527i	−0.0847577	−	0.304585i
$477$	4.63831	−	5.43077i	0.212374	−	0.248658i
$478$	−17.7979	−	15.8712i	−0.814058	−	0.725932i
$479$	1.36206	−	2.22269i	0.0622343	−	0.101557i	−0.820010	−	0.572350i	$-0.806032\pi$
$479$	1.36206	−	2.22269i	0.0622343	−	0.101557i	0.882244	+	0.470793i	$0.156032\pi$
$480$	0.0134163	−	0.473226i	0.000612369	−	0.0215997i
$481$	2.80371	+	3.28273i	0.127838	+	0.149679i
$482$	6.98054	+	0.149243i	0.317955	+	0.00679783i
$483$	−0.191655	+	0.191655i	−0.00872060	+	0.00872060i
$484$	−22.6422	+	10.3427i	−1.02919	+	0.470125i
$485$	−2.74947	+	11.4524i	−0.124847	+	0.520026i
$486$	−3.16973	−	0.317766i	−0.143782	−	0.0144142i
$487$	−10.9950	−	21.5788i	−0.498229	−	0.977829i	−0.994000	−	0.109376i	$-0.965115\pi$
$487$	−10.9950	−	21.5788i	−0.498229	−	0.977829i	0.495772	−	0.868453i	$-0.334885\pi$
$488$	−17.4321	+	4.45170i	−0.789116	+	0.201519i
$489$	0.433149	+	1.04572i	0.0195877	+	0.0472889i
$490$	1.07659	−	2.00576i	0.0486356	−	0.0906109i
$491$	38.3276			1.72970			0.864850	−	0.502030i	$-0.167413\pi$
$491$	38.3276			1.72970			0.864850	+	0.502030i	$0.167413\pi$
$492$	0.796365	−	0.717240i	0.0359029	−	0.0323357i
$493$	9.90875			0.446268
$494$	−0.838734	+	1.56261i	−0.0377364	+	0.0703051i
$495$	5.54604	+	13.3893i	0.249276	+	0.601806i
$496$	14.6584	+	1.25645i	0.658180	+	0.0564162i
$497$	−1.42131	−	2.78948i	−0.0637545	−	0.125125i
$498$	0.792015	+	0.0793997i	0.0354910	+	0.00355799i
$499$	−4.89796	+	20.4015i	−0.219263	+	0.913295i	0.748842	+	0.662749i	$0.230610\pi$
$499$	−4.89796	+	20.4015i	−0.219263	+	0.913295i	−0.968105	+	0.250546i	$0.919390\pi$
$500$	0.830988	+	1.81919i	0.0371629	+	0.0813567i
$501$	0.889449	−	0.889449i	0.0397376	−	0.0397376i
$502$	−2.62049	−	0.0560256i	−0.116958	−	0.00250055i
$503$	−8.58020	−	10.0461i	−0.382572	−	0.447935i	0.535388	−	0.844606i	$-0.320165\pi$
$503$	−8.58020	−	10.0461i	−0.382572	−	0.447935i	−0.917961	+	0.396671i	$0.870165\pi$
$504$	19.8832	−	14.8884i	0.885668	−	0.663182i
$505$	1.64387	−	2.68256i	0.0731514	−	0.119372i
$506$	5.64115	+	5.03047i	0.250780	+	0.223631i
$507$	−0.691613	+	0.809774i	−0.0307156	+	0.0359633i
$508$	11.2867	−	3.14077i	0.500764	−	0.139349i
$509$	0.488199	−	6.20316i	0.0216390	−	0.274950i	−0.976573	−	0.215185i	$-0.930965\pi$
$509$	0.488199	−	6.20316i	0.0216390	−	0.274950i	0.998212	−	0.0597656i	$-0.0190353\pi$
$510$	−0.0401505	−	0.133193i	−0.00177789	−	0.00589789i
$511$	21.3326	−	13.0726i	0.943699	−	0.578299i
$512$	6.22819	+	21.7534i	0.275250	+	0.961373i
$513$	−1.18413	+	0.187548i	−0.0522807	+	0.00828044i
$514$	2.58015	−	0.561393i	0.113805	−	0.0247620i
$515$	8.70997	−	6.32817i	0.383807	−	0.278852i
$516$	−0.299227	−	0.278541i	−0.0131727	−	0.0122621i
$517$	2.31355	−	3.18433i	0.101750	−	0.140047i
$518$	−17.2154	−	29.4900i	−0.756402	−	1.29571i
$519$	−1.76088	−	0.729382i	−0.0772942	−	0.0320163i
$520$	−0.0213815	−	1.48369i	−0.000937640	−	0.0650641i
$521$	2.17668	+	27.6574i	0.0953622	+	1.21169i	0.839385	+	0.543538i	$0.182915\pi$
$521$	2.17668	+	27.6574i	0.0953622	+	1.21169i	−0.744023	+	0.668154i	$0.767085\pi$
$522$	12.9473	+	33.2507i	0.566689	+	1.45534i
$523$	−3.81320	−	11.7358i	−0.166740	−	0.513172i	0.832421	−	0.554144i	$-0.186954\pi$
$523$	−3.81320	−	11.7358i	−0.166740	−	0.513172i	−0.999160	+	0.0409723i	$0.986954\pi$
$524$	−20.9737	+	2.40834i	−0.916238	+	0.105209i
$525$	0.111483	−	0.218798i	0.00486552	−	0.00954911i
$526$	13.0085	+	8.35924i	0.567196	+	0.364480i
$527$	4.20370	−	1.00922i	0.183116	−	0.0439623i
$528$	1.04410	+	1.23987i	0.0454387	+	0.0539585i
$529$	−6.73092	+	20.7157i	−0.292649	+	0.900680i
$530$	0.192799	+	3.36911i	0.00837465	+	0.146345i
$531$	−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
$536$	−3.19338	+	4.53121i	−0.137933	+	0.195718i
$537$	1.66131	+	0.539791i	0.0716907	+	0.0232937i
$538$	−1.58639	−	11.6183i	−0.0683943	−	0.500902i
$539$	1.81954	+	7.57892i	0.0783731	+	0.326447i
$540$	0.789906	−	0.618263i	0.0339922	−	0.0266058i
$541$	11.4286	+	5.82317i	0.491355	+	0.250358i	0.682069	−	0.731288i	$-0.261080\pi$
$541$	11.4286	+	5.82317i	0.491355	+	0.250358i	−0.190714	+	0.981646i	$0.561080\pi$
$542$	14.5306	+	30.0911i	0.624141	+	1.29252i
$543$	−0.461478	+	0.149943i	−0.0198039	+	0.00643468i
$544$	3.75420	+	5.48779i	0.160960	+	0.235287i
$545$	−14.2904	+	1.12468i	−0.612134	+	0.0481760i
$546$	−0.141034	+	0.115333i	−0.00603571	+	0.00493581i
$547$	−1.04718	+	2.52811i	−0.0447741	+	0.108094i	−0.944684	−	0.327981i	$-0.893632\pi$
$547$	−1.04718	+	2.52811i	−0.0447741	+	0.108094i	0.899910	+	0.436075i	$0.143632\pi$
$548$	6.78822	+	34.7590i	0.289978	+	1.48483i
$549$	−15.4024	−	11.1905i	−0.657358	−	0.477599i
$550$	−6.26910	−	2.75518i	−0.267315	−	0.117481i
$551$	11.8446	+	16.3027i	0.504597	+	0.694518i
$552$	0.115246	−	0.234477i	0.00490522	−	0.00997998i
$553$	−1.17848	−	7.44064i	−0.0501142	−	0.316408i
$554$	−22.6622	−	4.08770i	−0.962826	−	0.173670i
$555$	−0.359832	−	0.587192i	−0.0152740	−	0.0249249i
$556$	3.20323	+	0.137032i	0.135847	+	0.00581144i
$557$	14.9223	+	1.17441i	0.632277	+	0.0497613i	0.390548	−	0.920582i	$-0.372285\pi$
$557$	14.9223	+	1.17441i	0.632277	+	0.0497613i	0.241729	+	0.970344i	$0.422285\pi$
$558$	8.87941	+	12.7876i	0.375895	+	0.541342i
$559$	−0.974332	−	0.832158i	−0.0412098	−	0.0351965i
$560$	−1.91677	+	11.5793i	−0.0809983	+	0.489316i
$561$	0.406122	+	0.248872i	0.0171465	+	0.0105074i
$562$	8.38489	−	31.9050i	0.353695	−	1.34583i
$563$	21.4715	−	18.3384i	0.904915	−	0.772870i	−0.0695109	−	0.997581i	$-0.522144\pi$
$563$	21.4715	−	18.3384i	0.904915	−	0.772870i	0.974425	+	0.224711i	$0.0721439\pi$
$564$	−0.127483	−	0.0475360i	−0.00536799	−	0.00200163i
$565$	5.48700	+	5.48700i	0.230840	+	0.230840i
$566$	23.0822	+	24.0908i	0.970218	+	1.01261i
$567$	25.4987	+	6.12169i	1.07084	+	0.257087i
$568$	2.16445	+	2.10295i	0.0908183	+	0.0882379i
$569$	6.72321	−	3.42564i	0.281851	−	0.143610i	−0.307350	−	0.951596i	$-0.599442\pi$
$569$	6.72321	−	3.42564i	0.281851	−	0.143610i	0.589202	+	0.807986i	$0.299442\pi$
$570$	0.171146	−	0.225274i	0.00716850	−	0.00943567i
$571$	−23.1783	+	9.60075i	−0.969980	+	0.401779i	−0.810705	−	0.585455i	$-0.800916\pi$
$571$	−23.1783	+	9.60075i	−0.969980	+	0.401779i	−0.159275	+	0.987234i	$0.550916\pi$
$572$	3.43566	+	3.74275i	0.143652	+	0.156492i
$573$			1.82520i			0.0762489i
$574$	−21.9675	+	14.9473i	−0.916907	+	0.623887i
$575$			1.10376i			0.0460298i
$576$	−13.5099	+	19.7686i	−0.562911	+	0.823691i
$577$	29.4266	−	12.1889i	1.22505	−	0.507430i	0.326035	−	0.945358i	$-0.394287\pi$
$577$	29.4266	−	12.1889i	1.22505	−	0.507430i	0.899010	+	0.437927i	$0.144287\pi$
$578$	−17.5878	−	13.3619i	−0.731557	−	0.555781i
$579$	−1.63448	+	0.832807i	−0.0679265	+	0.0346103i
$580$	−15.2868	−	7.11200i	−0.634752	−	0.295310i
$581$	−19.1887	−	4.60681i	−0.796083	−	0.191123i
$582$	−1.00652	+	0.964379i	−0.0417214	+	0.0399748i
$583$	−8.17019	−	8.17019i	−0.338375	−	0.338375i
$584$	−15.3971	+	18.5628i	−0.637136	+	0.768133i
$585$	1.19397	−	1.01975i	0.0493647	−	0.0421615i
$586$	−3.71211	−	0.975571i	−0.153346	−	0.0403005i
$587$	−27.2838	−	16.7195i	−1.12612	−	0.690089i	−0.170698	−	0.985323i	$-0.554602\pi$
$587$	−27.2838	−	16.7195i	−1.12612	−	0.690089i	−0.955425	+	0.295234i	$0.904602\pi$
$588$	0.235529	−	0.130827i	0.00971305	−	0.00539521i
$589$	6.68541	+	5.70988i	0.275468	+	0.235272i
$590$	16.6932	−	11.5914i	0.687250	−	0.477210i
$591$	0.888484	+	0.0699252i	0.0365473	+	0.00287634i
$592$	24.8799	+	21.5510i	1.02256	+	0.885742i
$593$	2.46113	+	4.01620i	0.101066	+	0.164925i	0.899176	−	0.437586i	$-0.144167\pi$
$593$	2.46113	+	4.01620i	0.101066	+	0.164925i	−0.798110	+	0.602512i	$0.794167\pi$
$594$	−0.609662	+	3.37997i	−0.0250147	+	0.138682i
$595$	0.539524	+	3.40642i	0.0221183	+	0.139650i
$596$	−1.31658	−	0.160480i	−0.0539293	−	0.00657352i
$597$	0.925627	+	1.27402i	0.0378834	+	0.0521420i
$598$	0.329480	−	0.749694i	0.0134734	−	0.0306573i
$599$	−26.6826	−	19.3861i	−1.09022	−	0.792093i	−0.110786	−	0.993844i	$-0.535337\pi$
$599$	−26.6826	−	19.3861i	−1.09022	−	0.792093i	−0.979437	+	0.201751i	$0.935337\pi$
$600$	−0.0336566	+	0.234303i	−0.00137403	+	0.00956539i
$601$	0.418646	−	1.01070i	0.0170769	−	0.0412274i	−0.915111	−	0.403202i	$-0.867897\pi$
$601$	0.418646	−	1.01070i	0.0170769	−	0.0412274i	0.932188	+	0.361974i	$0.117897\pi$
$602$	6.41596	+	7.84570i	0.261495	+	0.319767i
$603$	−5.84788	+	0.460238i	−0.238144	+	0.0187423i
$604$	12.5410	−	0.448990i	0.510284	−	0.0182691i
$605$	11.8372	−	3.84612i	0.481249	−	0.156367i
$606$	0.335316	−	0.161919i	0.0136213	−	0.00657751i
$607$	39.4679	+	20.1099i	1.60195	+	0.816235i	0.999841	+	0.0178222i	$0.00567329\pi$
$607$	39.4679	+	20.1099i	1.60195	+	0.816235i	0.602110	+	0.798413i	$0.294327\pi$
$608$	−4.54132	+	12.7366i	−0.184175	+	0.516539i
$609$	0.483260	+	2.01292i	0.0195827	+	0.0815678i
$610$	8.91309	−	1.21701i	0.360880	−	0.0492754i
$611$	−0.405576	−	0.131780i	−0.0164079	−	0.00533124i
$612$	−1.93341	+	6.76507i	−0.0781535	+	0.273462i
$613$	5.80176	−	36.6309i	0.234331	−	1.47951i	−0.537275	−	0.843407i	$-0.680546\pi$
$613$	5.80176	−	36.6309i	0.234331	−	1.47951i	0.771606	−	0.636101i	$-0.219454\pi$
$614$	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	−0.295252	−	0.955419i	$-0.595404\pi$
$617$	−21.6425	−	3.42784i	−0.871294	−	0.137999i	−0.576042	+	0.817420i	$0.695404\pi$
$618$	1.27213	−	0.0727985i	0.0511727	−	0.00292839i
$619$	8.66976	−	26.6828i	0.348467	−	1.07247i	−0.611234	−	0.791450i	$-0.709327\pi$
$619$	8.66976	−	26.6828i	0.348467	−	1.07247i	0.959701	−	0.281022i	$-0.0906734\pi$
$620$	−7.20967	−	1.46022i	−0.289547	−	0.0586438i
$621$	0.538291	−	0.129232i	0.0216009	−	0.00518591i
$622$	−11.4223	+	17.7751i	−0.457991	+	0.712716i
$623$	−4.11739	+	8.08083i	−0.164960	+	0.323752i
$624$	0.0928016	−	0.149097i	0.00371504	−	0.00596865i
$625$	−0.309017	−	0.951057i	−0.0123607	−	0.0380423i
$626$	36.8367	−	14.3437i	1.47229	−	0.573289i
$627$	0.0760005	+	0.965678i	0.00303517	+	0.0385655i
$628$	−6.18526	+	2.25742i	−0.246819	+	0.0900807i
$629$	8.93607	+	3.70144i	0.356304	+	0.147586i
$630$	−10.7259	+	6.26149i	−0.427330	+	0.249464i
$631$	−15.5124	+	21.3510i	−0.617538	+	0.849969i	−0.997171	−	0.0751688i	$-0.976050\pi$
$631$	−15.5124	+	21.3510i	−0.617538	+	0.849969i	0.379632	+	0.925137i	$0.376050\pi$
$632$	3.38966	+	6.42210i	0.134834	+	0.255458i
$633$	−1.63154	+	1.18538i	−0.0648478	+	0.0471147i
$634$	−0.456749	−	2.09920i	−0.0181398	−	0.0833699i
$635$	−5.78563	+	0.916354i	−0.229596	+	0.0363644i
$636$	−0.196368	+	0.347793i	−0.00778650	+	0.0137909i
$637$	0.720025	−	0.441232i	0.0285284	−	0.0174822i
$638$	55.2714	−	16.6613i	2.18821	−	0.659628i
$639$	−0.250552	+	3.18357i	−0.00991169	+	0.125940i
$640$	−1.85298	−	11.1609i	−0.0732455	−	0.441175i
$641$	−1.95491	+	2.28890i	−0.0772142	+	0.0904062i	−0.797668	−	0.603096i	$-0.793933\pi$
$641$	−1.95491	+	2.28890i	−0.0772142	+	0.0904062i	0.720454	+	0.693503i	$0.243933\pi$
$642$	−1.03941	+	1.16560i	−0.0410224	+	0.0460025i
$643$	−11.4887	+	18.7478i	−0.453069	+	0.739341i	−0.994870	−	0.101166i	$-0.967743\pi$
$643$	−11.4887	+	18.7478i	−0.453069	+	0.739341i	0.541801	+	0.840507i	$0.317743\pi$
$644$	−3.61735	+	5.37314i	−0.142544	+	0.211731i
$645$	0.132749	+	0.155429i	0.00522698	+	0.00612001i
$646$	−0.0849323	+	3.97254i	−0.00334162	+	0.156297i
$647$	−24.4326	+	24.4326i	−0.960546	+	0.960546i	−0.999251	−	0.0387042i	$-0.987677\pi$
$647$	−24.4326	+	24.4326i	−0.960546	+	0.960546i	0.0387042	+	0.999251i	$0.487677\pi$
$648$	−25.1686	+	2.34618i	−0.988715	+	0.0921665i
$649$	−16.2441	+	67.6616i	−0.637637	+	2.65595i
$650$	−0.0740069	+	0.738221i	−0.00290279	+	0.0289554i
$651$	0.410038	+	0.804744i	0.0160706	+	0.0315404i
$652$	14.9495	+	22.5431i	0.585467	+	0.882855i
$653$	−1.16160	−	2.80436i	−0.0454571	−	0.109743i	0.899520	−	0.436879i	$-0.143916\pi$
$653$	−1.16160	−	2.80436i	−0.0454571	−	0.109743i	−0.944977	+	0.327136i	$0.893916\pi$
$654$	−1.49484	−	0.802357i	−0.0584527	−	0.0313746i
$655$	10.5557			0.412447
$656$	15.3933	−	20.4706i	0.601007	−	0.799244i
$657$	−25.5206			−0.995653
$658$	2.97205	+	1.59525i	0.115863	+	0.0621895i
$659$	−7.90422	−	19.0825i	−0.307905	−	0.743348i	−0.999773	−	0.0213236i	$-0.993212\pi$
$659$	−7.90422	−	19.0825i	−0.307905	−	0.743348i	0.691868	−	0.722024i	$-0.256788\pi$
$660$	−0.447922	−	0.675444i	−0.0174353	−	0.0262916i
$661$	7.88647	+	15.4781i	0.306748	+	0.602027i	0.991994	−	0.126285i	$-0.0403053\pi$
$661$	7.88647	+	15.4781i	0.306748	+	0.602027i	−0.685246	+	0.728312i	$0.740305\pi$
$662$	−3.31409	+	33.0582i	−0.128806	+	1.28484i
$663$	0.0120471	−	0.0501797i	0.000467870	−	0.00194882i
$664$	18.9403	−	1.76559i	0.735028	−	0.0685181i
$665$	−4.95959	+	4.95959i	−0.192325	+	0.192325i
$666$	−0.744514	+	34.8232i	−0.0288493	+	1.34937i
$667$	−6.04298	−	7.07543i	−0.233985	−	0.273962i
$668$	16.7877	−	24.9361i	0.649537	−	0.964809i
$669$	0.989579	−	1.61485i	0.0382593	−	0.0624335i
$670$	1.84472	−	2.06867i	0.0712678	−	0.0799196i
$671$	−20.0035	+	23.4211i	−0.772227	+	0.904162i
$672$	−0.931727	+	1.03030i	−0.0359422	+	0.0397446i
$673$	−1.60659	+	20.4136i	−0.0619294	+	0.786888i	0.885030	+	0.465534i	$0.154138\pi$
$673$	−1.60659	+	20.4136i	−0.0619294	+	0.786888i	−0.946959	+	0.321353i	$0.895862\pi$
$674$	−21.8751	+	6.59417i	−0.842599	+	0.253998i
$675$	−0.427640	+	0.262058i	−0.0164599	+	0.0100866i
$676$	−12.5125	+	22.1612i	−0.481249	+	0.852353i
$677$	−43.3275	+	6.86241i	−1.66521	+	0.263744i	−0.916758	−	0.399443i	$-0.869204\pi$
$677$	−43.3275	+	6.86241i	−1.66521	+	0.263744i	−0.748454	+	0.663186i	$0.769204\pi$
$678$	0.195259	+	0.897406i	0.00749889	+	0.0344647i
$679$	27.9586	−	20.3131i	1.07295	−	0.779546i
$680$	−1.55183	−	2.94012i	−0.0595100	−	0.112748i
$681$	−0.839347	+	1.15526i	−0.0321639	+	0.0442697i
$682$	21.7514	−	12.6979i	0.832904	−	0.486227i
$683$	−34.6414	−	14.3489i	−1.32552	−	0.549047i	−0.396143	−	0.918189i	$-0.629652\pi$
$683$	−34.6414	−	14.3489i	−1.32552	−	0.549047i	−0.929373	+	0.369142i	$0.879652\pi$
$684$	−13.4416	+	4.90573i	−0.513951	+	0.187575i
$685$	−1.38934	−	17.6532i	−0.0530840	−	0.674496i
$686$	20.8434	−	8.11611i	0.795805	−	0.309875i
$687$	0.382082	+	1.17593i	0.0145773	+	0.0448644i
$688$	−8.29422	−	5.16253i	−0.316214	−	0.196819i
$689$	−0.568329	+	1.11541i	−0.0216516	+	0.0424937i
$690$	−0.0706213	+	0.109899i	−0.00268851	+	0.00418380i
$691$	29.9036	−	7.17921i	1.13759	−	0.273110i	0.379453	−	0.925211i	$-0.376112\pi$
$691$	29.9036	−	7.17921i	1.13759	−	0.273110i	0.758132	+	0.652101i	$0.226112\pi$
$692$	−44.6423	−	9.04168i	−1.69705	−	0.343713i
$693$	13.1407	−	40.4430i	0.499175	−	1.53630i
$694$	40.1414	−	2.29711i	1.52375	−	0.0871972i
$695$	−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
$700$	1.61260	−	5.64254i	0.0609505	−	0.213268i
$701$	−18.8914	−	6.13820i	−0.713519	−	0.231836i	−0.0703081	−	0.997525i	$-0.522398\pi$
$701$	−18.8914	−	6.13820i	−0.713519	−	0.231836i	−0.643211	+	0.765689i	$0.722398\pi$
$702$	0.368688	−	0.0503415i	0.0139152	−	0.00190002i
$703$	4.59197	+	19.1269i	0.173189	+	0.721386i
$704$	30.1687	+	24.2985i	1.13702	+	0.915784i
$705$	0.0606139	+	0.0308843i	0.00228285	+	0.00116317i
$706$	13.2935	−	6.41922i	0.500306	−	0.241591i
$707$	−8.77977	+	2.85272i	−0.330197	+	0.107288i
$708$	2.40377	−	0.0860596i	0.0903393	−	0.00323432i
$709$	17.8834	−	1.40746i	0.671627	−	0.0528582i	0.261940	−	0.965084i	$-0.415638\pi$
$709$	17.8834	−	1.40746i	0.671627	−	0.0528582i	0.409687	+	0.912226i	$0.365638\pi$
$710$	−0.955210	−	1.16807i	−0.0358484	−	0.0438369i
$711$	−2.94065	+	7.09935i	−0.110283	+	0.266246i
$712$	1.24304	−	8.65350i	0.0465848	−	0.324304i
$713$	−3.28432	−	2.38620i	−0.122999	−	0.0893639i
$714$	−0.164232	+	0.373693i	−0.00614625	+	0.0139851i
$715$	−1.49314	−	2.05512i	−0.0558401	−	0.0768573i
$716$	41.4384	+	5.05098i	1.54862	+	0.188764i
$717$	0.220756	+	1.39380i	0.00824429	+	0.0520524i
$718$	4.43601	−	24.5932i	0.165550	−	0.917812i
$719$	19.7107	+	32.1649i	0.735083	+	1.19955i	0.973567	+	0.228400i	$0.0733496\pi$
$719$	19.7107	+	32.1649i	0.735083	+	1.19955i	−0.238484	+	0.971146i	$0.576650\pi$
$720$	7.83841	−	9.04918i	0.292120	−	0.337243i
$721$	−31.4928	−	2.47854i	−1.17285	−	0.0923056i
$722$	15.4335	−	10.7167i	0.574375	−	0.398833i
$723$	−0.314186	−	0.268340i	−0.0116847	−	0.00997968i
$724$	−10.1371	+	5.63075i	−0.376742	+	0.209265i
$725$	7.18787	+	4.40473i	0.266951	+	0.163588i
$726$	1.42469	+	0.374420i	0.0528754	+	0.0138960i
$727$	26.4826	−	22.6182i	0.982184	−	0.838864i	−0.00475024	−	0.999989i	$-0.501512\pi$
$727$	26.4826	−	22.6182i	0.982184	−	0.838864i	0.986934	+	0.161124i	$0.0515121\pi$
$728$	−2.77965	+	3.35116i	−0.103021	+	0.124202i
$729$	−18.8250	−	18.8250i	−0.697221	−	0.697221i
$730$	8.70708	−	8.34256i	0.322264	−	0.308772i
$731$	−2.79148	−	0.670175i	−0.103247	−	0.0247873i
$732$	0.965332	+	0.449108i	0.0356797	+	0.0165995i
$733$	30.7487	−	15.6673i	1.13573	−	0.578683i	0.218024	−	0.975943i	$-0.430039\pi$
$733$	30.7487	−	15.6673i	1.13573	−	0.578683i	0.917706	+	0.397260i	$0.130039\pi$
$734$	−0.656246	−	0.498565i	−0.0242225	−	0.0184024i
$735$	−0.124458	+	0.0515521i	−0.00459070	+	0.00190153i
$736$	1.62905	−	6.02752i	0.0600477	−	0.222177i
$737$			9.49009i			0.349572i
$738$	27.0719	−	1.29200i	0.996531	−	0.0475591i
$739$		−	4.58098i		−	0.168514i	−0.996444	−	0.0842570i	$-0.973148\pi$
$739$		−	4.58098i		−	0.168514i	0.996444	−	0.0842570i	$-0.0268517\pi$
$740$	−11.1295	−	12.1243i	−0.409129	−	0.445698i
$741$	0.0969604	−	0.0401623i	0.00356193	−	0.00147540i
$742$	5.99009	−	7.88456i	0.219903	−	0.289451i
$743$	40.1114	−	20.4378i	1.47154	−	0.749789i	0.479722	−	0.877421i	$-0.340738\pi$
$743$	40.1114	−	20.4378i	1.47154	−	0.749789i	0.991822	+	0.127632i	$0.0407377\pi$
$744$	−0.624428	−	0.606686i	−0.0228926	−	0.0222422i
$745$	0.644840	+	0.154812i	0.0236251	+	0.00567189i
$746$	−32.6068	−	34.0315i	−1.19382	−	1.24598i
$747$	14.2335	+	14.2335i	0.520778	+	0.520778i
$748$	10.6655	+	3.97698i	0.389970	+	0.145413i
$749$	29.4416	−	25.1455i	1.07577	−	0.918797i
$750$	0.0300828	−	0.114467i	0.00109847	−	0.00417975i
$751$	−2.64281	−	1.61951i	−0.0964374	−	0.0590969i	0.473444	−	0.880824i	$-0.343011\pi$
$751$	−2.64281	−	1.61951i	−0.0964374	−	0.0590969i	−0.569881	+	0.821727i	$0.693011\pi$
$752$	−3.20784	−	0.531006i	−0.116978	−	0.0193638i
$753$	0.117945	+	0.100735i	0.00429816	+	0.00367098i
$754$	−3.56730	−	5.13742i	−0.129914	−	0.187094i
$755$	−6.25515	−	0.492291i	−0.227648	−	0.0179163i
$756$	−2.94062	−	0.125798i	−0.106949	−	0.00457521i
$757$	−2.16109	−	3.52658i	−0.0785463	−	0.128176i	0.810955	−	0.585108i	$-0.198948\pi$
$757$	−2.16109	−	3.52658i	−0.0785463	−	0.128176i	−0.889501	+	0.456933i	$0.848948\pi$
$758$	0.606597	+	0.109415i	0.0220326	+	0.00397413i
$759$	−0.0699699	−	0.441772i	−0.00253975	−	0.0160353i
$760$	2.98232	−	6.06772i	0.108180	−	0.220099i
$761$	14.0743	+	19.3717i	0.510195	+	0.702223i	0.983952	−	0.178433i	$-0.0571027\pi$
$761$	14.0743	+	19.3717i	0.510195	+	0.702223i	−0.473757	+	0.880655i	$0.657103\pi$
$762$	−0.634698	−	0.278941i	−0.0229927	−	0.0101050i
$763$	34.0280	+	24.7228i	1.23190	+	0.895025i
$764$	8.36052	+	42.8100i	0.302473	+	1.54881i
$765$	1.34627	−	3.25017i	0.0486743	−	0.117510i
$766$	10.8110	−	8.84090i	0.390618	−	0.319435i
$767$	7.51580	−	0.591507i	0.271380	−	0.0213581i
$768$	0.529609	−	1.22984i	0.0191106	−	0.0443779i
$769$	23.7255	−	7.70887i	0.855562	−	0.277989i	0.151788	−	0.988413i	$-0.451497\pi$
$769$	23.7255	−	7.70887i	0.855562	−	0.277989i	0.703774	+	0.710424i	$0.251497\pi$
$770$	8.73729	+	18.0939i	0.314870	+	0.652060i
$771$	−0.139227	−	0.0709396i	−0.00501413	−	0.00255483i
$772$	−34.5217	+	27.0203i	−1.24246	+	0.972481i
$773$	9.61970	+	40.0690i	0.345997	+	1.44118i	0.825879	+	0.563847i	$0.190679\pi$
$773$	9.61970	+	40.0690i	0.345997	+	1.44118i	−0.479882	+	0.877333i	$0.659321\pi$
$774$	−1.39861	−	10.2430i	−0.0502718	−	0.368178i
$775$	3.49801	+	1.13657i	0.125652	+	0.0408269i
$776$	−19.1903	+	27.2299i	−0.688892	+	0.977495i
$777$	−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
$782$	−0.104822	−	1.83174i	−0.00374843	−	0.0655027i
$783$	1.30656	−	4.02117i	0.0466926	−	0.143705i
$784$	4.92504	−	4.14740i	0.175894	−	0.148121i
$785$	3.20120	−	0.768540i	0.114256	−	0.0274304i
$786$	1.05102	+	0.675385i	0.0374886	+	0.0240902i
$787$	20.6738	−	40.5747i	0.736942	−	1.44633i	−0.152033	−	0.988375i	$-0.548582\pi$
$787$	20.6738	−	40.5747i	0.736942	−	1.44633i	0.888975	−	0.457955i	$-0.151418\pi$
$788$	21.1596	−	2.42970i	0.753780	−	0.0865544i
$789$	−0.282763	−	0.870256i	−0.0100666	−	0.0309819i
$790$	−1.31746	−	3.38343i	−0.0468731	−	0.120377i
$791$	−1.78643	−	22.6988i	−0.0635182	−	0.807075i
$792$	0.590661	+	40.9867i	0.0209882	+	1.45640i
$793$	3.08307	+	1.27705i	0.109483	+	0.0453493i
$794$	−22.6160	−	38.7410i	−0.802610	−	1.37487i
$795$	0.117381	−	0.161561i	0.00416306	−	0.00572997i
$796$	27.5462	+	25.6420i	0.976351	+	0.908857i
$797$	25.8356	−	18.7707i	0.915144	−	0.664891i	−0.0271666	−	0.999631i	$-0.508648\pi$
$797$	25.8356	−	18.7707i	0.915144	−	0.664891i	0.942311	+	0.334740i	$0.108648\pi$
$798$	−0.811148	+	0.176491i	−0.0287143	+	0.00624772i
$799$	−0.943686	+	0.149465i	−0.0333852	+	0.00528770i
$800$	0.283836	+	5.64973i	0.0100351	+	0.199748i
$801$	7.88776	−	4.83362i	0.278700	−	0.170788i
$802$	7.45460	+	24.7295i	0.263231	+	0.873229i
$803$	−3.23940	+	41.1605i	−0.114316	+	1.45252i
$804$	0.316035	−	0.0879440i	0.0111457	−	0.00310154i
$805$	2.10335	−	2.46270i	0.0741332	−	0.0867988i
$806$	−2.03665	−	1.81617i	−0.0717379	−	0.0639718i
$807$	−0.362571	+	0.591663i	−0.0127631	+	0.0208275i
$808$	7.12311	−	5.33374i	0.250590	−	0.187640i
$809$	−35.7133	−	41.8150i	−1.25561	−	1.47014i	−0.822467	−	0.568812i	$-0.807403\pi$
$809$	−35.7133	−	41.8150i	−1.25561	−	1.47014i	−0.433147	−	0.901323i	$-0.642597\pi$
$810$	12.6360	+	0.270155i	0.443982	+	0.00949228i
$811$	0.384717	−	0.384717i	0.0135092	−	0.0135092i	−0.700320	−	0.713829i	$-0.746959\pi$
$811$	0.384717	−	0.384717i	0.0135092	−	0.0135092i	0.713829	+	0.700320i	$0.246959\pi$
$812$	20.5552	+	44.9993i	0.721347	+	1.57917i
$813$	0.461626	−	1.92281i	0.0161899	−	0.0674359i
$814$	56.0695	+	5.62099i	1.96524	+	0.197015i
$815$	−6.14012	−	12.0507i	−0.215079	−	0.422116i
$816$	0.0336033	−	0.392034i	0.00117635	−	0.0137239i
$817$	−2.23422	−	5.39388i	−0.0781654	−	0.188708i
$818$	12.1089	−	22.5596i	0.423378	−	0.788777i
$819$	−4.60726			−0.160991
$820$	−8.81401	+	9.29049i	−0.307799	+	0.324438i
$821$	−37.1895			−1.29792			−0.648961	−	0.760822i	$-0.724796\pi$
$821$	−37.1895			−1.29792			−0.648961	+	0.760822i	$0.724796\pi$
$822$	0.991169	−	1.84660i	0.0345710	−	0.0644077i
$823$	−10.0685	−	24.3075i	−0.350966	−	0.847307i	−0.996501	−	0.0835768i	$-0.973366\pi$
$823$	−10.0685	−	24.3075i	−0.350966	−	0.847307i	0.645535	−	0.763731i	$-0.276634\pi$
$824$	29.5043	−	7.53461i	1.02783	−	0.262481i
$825$	0.183972	+	0.361066i	0.00640509	+	0.0125707i
$826$	−59.3349	−	5.94834i	−2.06452	−	0.206969i
$827$	−4.07447	+	16.9714i	−0.141683	+	0.590153i	0.855675	+	0.517513i	$0.173142\pi$
$827$	−4.07447	+	16.9714i	−0.141683	+	0.590153i	−0.997358	+	0.0726394i	$0.976858\pi$
$828$	6.00977	−	2.74520i	0.208854	−	0.0954022i
$829$	13.0162	−	13.0162i	0.452070	−	0.452070i	−0.443971	−	0.896041i	$-0.646431\pi$
$829$	13.0162	−	13.0162i	0.452070	−	0.452070i	0.896041	+	0.443971i	$0.146431\pi$
$830$	−9.50905	−	0.203302i	−0.330064	−	0.00705672i
$831$	0.885020	+	1.03623i	0.0307010	+	0.0359463i
$832$	1.49370	−	3.92214i	0.0517847	−	0.135976i
$833$	0.988573	−	1.61320i	0.0342520	−	0.0558942i
$834$	−0.141606	−	0.126276i	−0.00490341	−	0.00437259i
$835$	−9.76140	+	11.4291i	−0.337807	+	0.395521i
$836$	6.20597	+	22.3018i	0.214638	+	0.771323i
$837$	0.144734	−	1.83902i	0.00500274	−	0.0635659i
$838$	9.62529	+	31.9304i	0.332500	+	1.10302i
$839$	−13.3591	+	8.18649i	−0.461209	+	0.282629i	−0.733630	−	0.679549i	$-0.762175\pi$
$839$	−13.3591	+	8.18649i	−0.461209	+	0.282629i	0.272422	+	0.962178i	$0.412175\pi$
$840$	0.521589	−	0.458641i	0.0179965	−	0.0158246i
$841$	−41.5491	+	6.58074i	−1.43273	+	0.226922i
$842$	24.8446	−	5.40573i	0.856200	−	0.186294i
$843$	−1.57933	+	1.14745i	−0.0543950	+	0.0395203i
$844$	−32.8378	+	35.2764i	−1.13032	+	1.21427i
$845$	7.47944	−	10.2946i	0.257300	−	0.354144i
$846$	−1.73463	−	2.97142i	−0.0596379	−	0.102159i
$847$	−33.7404	−	13.9757i	−1.15933	−	0.480211i
$848$	−3.01269	+	9.05693i	−0.103456	+	0.311016i
$849$	−0.154908	−	1.96829i	−0.00531643	−	0.0675517i
$850$	0.603149	+	1.54898i	0.0206878	+	0.0531295i
$851$	−2.80674	−	8.63824i	−0.0962136	−	0.296115i
$852$	−0.0203726	−	0.177420i	−0.000697955	−	0.00607831i
$853$	−0.655389	+	1.28627i	−0.0224401	+	0.0440412i	−0.901954	−	0.431831i	$-0.857868\pi$
$853$	−0.655389	+	1.28627i	−0.0224401	+	0.0440412i	0.879514	+	0.475872i	$0.157868\pi$
$854$	−22.2061	−	14.2696i	−0.759876	−	0.488296i
$855$	6.95673	−	1.67016i	0.237915	−	0.0571184i
$856$	−19.0402	+	32.1001i	−0.650782	+	1.09716i
$857$	−3.66878	+	11.2913i	−0.125323	+	0.385705i	−0.993960	−	0.109745i	$-0.964997\pi$
$857$	−3.66878	+	11.2913i	−0.125323	+	0.385705i	0.868637	+	0.495450i	$0.164997\pi$
$858$	−0.0171769	−	0.300161i	−0.000586409	−	0.0102473i
$859$	23.5511	+	3.73014i	0.803555	+	0.127271i	0.544684	−	0.838641i	$-0.316650\pi$
$859$	23.5511	+	3.73014i	0.803555	+	0.127271i	0.258871	+	0.965912i	$0.416650\pi$
$860$	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	$-0.946916\pi$
$863$	0.0890348	−	0.562143i	0.00303078	−	0.0191356i	0.989157	+	0.146859i	$0.0469165\pi$
$864$	2.72208	−	0.799917i	0.0926072	−	0.0272137i
$865$	21.6597	+	7.03767i	0.736453	+	0.239288i
$866$	0.770067	+	5.63977i	0.0261679	+	0.191647i
$867$	0.305134	+	1.27098i	0.0103629	+	0.0431646i
$868$	13.3036	+	16.9970i	0.451554	+	0.576915i
$869$	11.0768	+	5.64393i	0.375756	+	0.191457i
$870$	0.433859	+	0.898472i	0.0147092	+	0.0304611i
$871$	0.977873	−	0.317730i	0.0331340	−	0.0107659i
$872$	−38.7365	−	11.9720i	−1.31178	−	0.405422i
$873$	−35.1423	+	2.76576i	−1.18939	+	0.0936066i
$874$	2.88842	−	2.36206i	0.0977023	−	0.0798978i
$875$	−1.12288	+	2.71087i	−0.0379602	+	0.0916441i
$876$	1.40073	−	0.273554i	0.0473263	−	0.00924254i
$877$	3.80496	+	2.76447i	0.128485	+	0.0933495i	0.650171	−	0.759788i	$-0.274697\pi$
$877$	3.80496	+	2.76447i	0.128485	+	0.0933495i	−0.521687	+	0.853137i	$0.674697\pi$
$878$	−18.3873	−	8.08095i	−0.620542	−	0.272719i
$879$	0.133504	+	0.183753i	0.00450299	+	0.00619784i
$880$	−13.5999	−	13.7907i	−0.458452	−	0.464885i
$881$	0.495560	+	3.12884i	0.0166958	+	0.105413i	0.994629	−	0.103505i	$-0.0330057\pi$
$881$	0.495560	+	3.12884i	0.0166958	+	0.105413i	−0.977933	+	0.208918i	$0.933006\pi$
$882$	6.70513	+	1.20944i	0.225774	+	0.0407239i
$883$	−28.8180	−	47.0267i	−0.969803	−	1.58258i	−0.802485	−	0.596672i	$-0.796489\pi$
$883$	−28.8180	−	47.0267i	−0.969803	−	1.58258i	−0.167319	−	0.985903i	$-0.553511\pi$
$884$	0.0527102	−	1.23214i	0.00177283	−	0.0414414i
$885$	−1.19895	−	0.0943593i	−0.0403022	−	0.00317185i
$886$	−17.3590	−	24.9994i	−0.583187	−	0.839872i
$887$	−34.2871	−	29.2839i	−1.15125	−	0.983257i	−0.151260	−	0.988494i	$-0.548333\pi$
$887$	−34.2871	−	29.2839i	−1.15125	−	0.983257i	−0.999986	+	0.00523650i	$0.998333\pi$
$888$	−0.332404	−	1.91930i	−0.0111548	−	0.0644074i
$889$	14.6551	+	8.98069i	0.491518	+	0.301203i
$890$	−1.11105	+	4.22760i	−0.0372423	+	0.141710i
$891$	−32.9060	+	28.1044i	−1.10239	+	0.941533i
$892$	15.8135	−	42.4089i	0.529476	−	1.41996i
$893$	−1.37396	−	1.37396i	−0.0459780	−	0.0459780i
$894$	0.0543005	+	0.0566731i	0.00181608	+	0.00189543i
$895$	−20.2958	−	4.87260i	−0.678415	−	0.162873i
$896$	−17.1342	+	28.4334i	−0.572414	+	0.949893i
$897$	−0.0431783	+	0.0220004i	−0.00144168	+	0.000734573i
$898$	−21.1388	+	27.8243i	−0.705411	+	0.928510i
$899$	−28.6460	+	11.8656i	−0.955399	+	0.395739i
$900$	−4.40978	+	4.04796i	−0.146993	+	0.134932i
$901$			2.80475i			0.0934398i
$902$	1.35254	−	43.8266i	0.0450346	−	1.45927i
$903$		−	0.599764i		−	0.0199589i
$904$	8.69045	+	20.1542i	0.289040	+	0.670318i
$905$	5.35663	−	2.21879i	0.178060	−	0.0737550i
$906$	−0.591318	−	0.449239i	−0.0196452	−	0.0149249i
$907$	−28.6724	+	14.6093i	−0.952052	+	0.485094i	−0.859794	−	0.510641i	$-0.829408\pi$
$907$	−28.6724	+	14.6093i	−0.952052	+	0.485094i	−0.0922573	+	0.995735i	$0.529408\pi$
$908$	−14.3950	+	30.9413i	−0.477716	+	1.02682i
$909$	9.15632	+	2.19824i	0.303696	+	0.0729110i
$910$	1.57190	−	1.50609i	0.0521079	−	0.0499265i
$911$	37.6218	+	37.6218i	1.24647	+	1.24647i	0.957270	+	0.289197i	$0.0933881\pi$
$911$	37.6218	+	37.6218i	1.24647	+	1.24647i	0.289197	+	0.957270i	$0.406612\pi$
$912$	0.685175	−	0.413337i	0.0226884	−	0.0136870i
$913$	24.7631	−	21.1497i	0.819538	−	0.699952i
$914$	12.1084	+	3.18217i	0.400509	+	0.105257i
$915$	−0.453898	−	0.278149i	−0.0150054	−	0.00919533i
$916$	14.3481	+	25.8311i	0.474076	+	0.853483i
$917$	−23.5520	−	20.1153i	−0.777755	−	0.664265i
$918$	0.684802	−	0.475510i	0.0226018	−	0.0156942i
$919$	1.73395	+	0.136465i	0.0571979	+	0.00450157i	0.107026	−	0.994256i	$-0.465867\pi$
$919$	1.73395	+	0.136465i	0.0571979	+	0.00450157i	−0.0498279	+	0.998758i	$0.515867\pi$
$920$	−1.15301	+	2.90117i	−0.0380137	+	0.0956487i
$921$	−0.257265	−	0.419818i	−0.00847716	−	0.0138335i
$922$	−5.23507	+	29.0232i	−0.172408	+	0.955829i
$923$	−0.0875637	−	0.552856i	−0.00288219	−	0.0181975i
$924$	−0.287740	+	2.36062i	−0.00946593	+	0.0776588i
$925$	4.83687	+	6.65739i	0.159035	+	0.218894i
$926$	−13.4923	+	30.7003i	−0.443386	+	1.00888i
$927$	26.0689	+	18.9402i	0.856216	+	0.622077i
$928$	−32.7513	−	34.6626i	−1.07512	−	1.13786i
$929$	20.9215	−	50.5090i	0.686413	−	1.65715i	−0.0654726	−	0.997854i	$-0.520856\pi$
$929$	20.9215	−	50.5090i	0.686413	−	1.65715i	0.751886	−	0.659293i	$-0.229144\pi$
$930$	0.275571	+	0.336980i	0.00903634	+	0.0110500i
$931$	3.83588	−	0.301890i	0.125716	−	0.00989406i
$932$	−0.363640	−	10.1570i	−0.0119114	−	0.332703i
$933$	1.18914	−	0.386375i	0.0389307	−	0.0126493i
$934$	−43.6587	+	21.0821i	−1.42856	+	0.689829i
$935$	−5.07111	−	2.58386i	−0.165843	−	0.0845013i
$936$	4.20356	−	1.43311i	0.137398	−	0.0468426i
$937$	3.60867	+	15.0312i	0.117890	+	0.491048i	0.999807	+	0.0196428i	$0.00625290\pi$
$937$	3.60867	+	15.0312i	0.117890	+	0.491048i	−0.881917	+	0.471405i	$0.843747\pi$
$938$	−8.05806	+	1.10027i	−0.263105	+	0.0359249i
$939$	−2.22482	−	0.722889i	−0.0726044	−	0.0235906i
$940$	1.56316	+	0.446741i	0.0509847	+	0.0145711i
$941$	−1.47913	+	9.33884i	−0.0482182	+	0.304438i	−0.999997	−	0.00234669i	$-0.999253\pi$
$941$	−1.47913	+	9.33884i	−0.0482182	+	0.304438i	0.951779	+	0.306784i	$0.0992530\pi$
$942$	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
$946$	−16.6979	+	0.955544i	−0.542894	+	0.0310674i
$947$	12.2038	−	37.5593i	0.396569	−	1.22051i	−0.531164	−	0.847269i	$-0.678245\pi$
$947$	12.2038	−	37.5593i	0.396569	−	1.22051i	0.927733	−	0.373245i	$-0.121755\pi$
$948$	0.0853037	−	0.421178i	0.00277054	−	0.0136792i
$949$	4.34970	−	1.04427i	0.141197	−	0.0338984i
$950$	−1.82752	+	2.84395i	−0.0592926	+	0.0922698i
$951$	−0.0577163	+	0.113275i	−0.00187158	+	0.00367318i
$952$	−2.14032	+	9.51721i	−0.0693682	+	0.308455i
$953$	−10.6838	−	32.8812i	−0.346081	−	1.06513i	−0.961003	−	0.276539i	$-0.910812\pi$
$953$	−10.6838	−	32.8812i	−0.346081	−	1.06513i	0.614922	−	0.788588i	$-0.289188\pi$
$954$	−9.41187	+	3.66485i	−0.304721	+	0.118654i
$955$	−1.71114	−	21.7421i	−0.0553712	−	0.703558i
$956$	11.5622	+	31.6802i	0.373950	+	1.02461i
$957$	−3.15613	−	1.30731i	−0.102023	−	0.0422594i
$958$	−3.18381	+	1.85862i	−0.102864	+	0.0600493i
$959$	−30.5406	+	42.0355i	−0.986207	+	1.35740i
$960$	−0.333224	+	0.580696i	−0.0107548	+	0.0187419i
$961$	14.1352	−	10.2698i	0.455975	−	0.331285i
$962$	−1.29803	−	5.96568i	−0.0418500	−	0.192341i
$963$	−39.0076	+	6.17819i	−1.25700	+	0.199089i
$964$	−8.59836	−	4.85474i	−0.276935	−	0.156361i
$965$	18.6894	−	11.4529i	0.601633	−	0.368681i
$966$	0.366998	−	0.110630i	0.0118080	−	0.00355946i
$967$	−2.65844	+	33.7787i	−0.0854896	+	1.08625i	0.793234	+	0.608917i	$0.208396\pi$
$967$	−2.65844	+	33.7787i	−0.0854896	+	1.08625i	−0.878723	+	0.477331i	$0.841604\pi$
$968$	35.1311	+	2.25605i	1.12916	+	0.0725121i
$969$	0.152709	−	0.178799i	0.00490573	−	0.00574387i
$970$	11.0857	−	12.4315i	0.355940	−	0.399150i
$971$	16.3506	−	26.6818i	0.524717	−	0.856260i	−0.475002	−	0.879985i	$-0.657553\pi$
$971$	16.3506	−	26.6818i	0.524717	−	0.856260i	0.999719	+	0.0237250i	$0.00755262\pi$
$972$	3.73715	+	2.51596i	0.119869	+	0.0806994i
$973$	3.05487	+	3.57680i	0.0979347	+	0.114667i
$974$	−0.732094	+	34.2422i	−0.0234578	+	1.09719i
$975$	0.0310453	−	0.0310453i	0.000994247	−	0.000994247i
$976$	24.6989	+	6.11199i	0.790594	+	0.195640i
$977$	1.49596	−	6.23113i	0.0478600	−	0.199351i	−0.943318	−	0.331891i	$-0.892313\pi$
$977$	1.49596	−	6.23113i	0.0478600	−	0.199351i	0.991178	+	0.132540i	$0.0423133\pi$
$978$	0.159671	−	1.59273i	0.00510573	−	0.0509298i
$979$	−6.79463	−	13.3352i	−0.217157	−	0.426195i
$980$	−2.68301	+	1.77924i	−0.0857056	+	0.0568358i
$981$	−16.4184	−	39.6376i	−0.524200	−	1.26553i
$982$	−47.7586	−	25.6345i	−1.52404	−	0.818031i
$983$	−10.3634			−0.330540			−0.165270	−	0.986248i	$-0.552850\pi$
$983$	−10.3634			−0.330540			−0.165270	+	0.986248i	$0.552850\pi$
$984$	−1.47203	+	0.361096i	−0.0469266	+	0.0115113i
$985$	−10.6493			−0.339316
$986$	−12.3469	−	6.62724i	−0.393206	−	0.211054i
$987$	−0.0763879	−	0.184417i	−0.00243145	−	0.00587005i
$988$	2.09023	−	1.38614i	0.0664991	−	0.0440990i
$989$	1.22388	+	2.40200i	0.0389170	+	0.0763790i
$990$	2.04443	−	20.3933i	0.0649763	−	0.648141i
$991$	6.05824	−	25.2344i	0.192446	−	0.801596i	−0.789703	−	0.613490i	$-0.789765\pi$
$991$	6.05824	−	25.2344i	0.192446	−	0.801596i	0.982149	−	0.188106i	$-0.0602349\pi$
$992$	−17.4249	−	11.3695i	−0.553241	−	0.360983i
$993$	1.39024	−	1.39024i	0.0441178	−	0.0441178i
$994$	−0.0946374	+	4.42647i	−0.00300171	+	0.140399i
$995$	−12.2206	−	14.3085i	−0.387420	−	0.453610i
$996$	−0.933795	−	0.628658i	−0.0295884	−	0.0199198i
$997$	6.02304	−	9.82870i	0.190751	−	0.311278i	−0.742939	−	0.669359i	$-0.766569\pi$
$997$	6.02304	−	9.82870i	0.190751	−	0.311278i	0.933691	+	0.358081i	$0.116569\pi$
$998$	19.7482	−	22.1456i	0.625119	−	0.701007i
$999$	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.671.7	yes	672
4.3	odd	2	inner	820.2.bw.a.671.3	yes	672
41.11	odd	40	inner	820.2.bw.a.11.3	✓	672
164.11	even	40	inner	820.2.bw.a.11.7	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bw.a.11.3	✓	672	41.11	odd	40	inner
820.2.bw.a.11.7	yes	672	164.11	even	40	inner
820.2.bw.a.671.3	yes	672	4.3	odd	2	inner
820.2.bw.a.671.7	yes	672	1.1	even	1	trivial

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+(-1.24606 - 0.668827i) q^{2} +(0.0320264 + 0.0773185i) q^{3} +(1.10534 + 1.66680i) q^{4} +(-0.453990 - 0.891007i) q^{5} +(0.0118059 - 0.117764i) q^{6} +(-0.684981 + 2.85315i) q^{7} +(-0.262523 - 2.81622i) q^{8} +(2.11637 - 2.11637i) q^{9} +(-0.0302288 + 1.41389i) q^{10} +(-3.14472 - 3.68199i) q^{11} +(-0.0934744 + 0.138845i) q^{12} +(-0.274112 + 0.447310i) q^{13} +(2.76179 - 3.09707i) q^{14} +(0.0543517 - 0.0636376i) q^{15} +(-1.55644 + 3.68476i) q^{16} +(-0.0922206 + 1.17177i) q^{17} +(-4.05261 + 1.22164i) q^{18} +(-2.03814 + 1.24897i) q^{19} +(0.983315 - 1.74158i) q^{20} +(-0.242539 + 0.0384144i) q^{21} +(1.45590 + 6.69126i) q^{22} +(0.892957 - 0.648771i) q^{23} +(0.209338 - 0.110491i) q^{24} +(-0.587785 + 0.809017i) q^{25} +(0.640734 - 0.374043i) q^{26} +(0.463370 + 0.191934i) q^{27} +(-5.51277 + 2.01198i) q^{28} +(-0.661420 - 8.40414i) q^{29} +(-0.110288 + 0.0429446i) q^{30} +(-1.13657 - 3.49801i) q^{31} +(4.40389 - 3.55046i) q^{32} +(0.183972 - 0.361066i) q^{33} +(0.898627 - 1.39842i) q^{34} +(2.85315 - 0.684981i) q^{35} +(5.86687 + 1.18825i) q^{36} +(2.54290 - 7.82623i) q^{37} +(3.37499 - 0.193136i) 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} +(2.66116 - 9.31147i) q^{44} +(-2.84651 - 0.924887i) q^{45} +(-1.54660 + 0.211176i) q^{46} +(0.189762 + 0.790414i) q^{47} +(-0.334748 - 0.00233209i) q^{48} +(-1.43423 - 0.730778i) q^{49} +(1.27351 - 0.614959i) q^{50} +(-0.0935534 + 0.0303973i) q^{51} +(-1.04856 + 0.0375406i) q^{52} +(2.37886 - 0.187220i) q^{53} +(-0.449017 - 0.549076i) q^{54} +(-1.85301 + 4.47355i) q^{55} +(8.21492 + 1.18004i) q^{56} +(-0.161843 - 0.117586i) q^{57} +(-4.79674 + 10.9145i) q^{58} +(-8.44679 - 11.6260i) q^{59} +(0.166148 + 0.0202520i) q^{60} +(-0.995078 - 6.28267i) q^{61} +(-0.923325 + 5.11891i) q^{62} +(4.58865 + 7.48799i) q^{63} +(-7.86216 + 1.47865i) q^{64} +(0.523001 + 0.0411610i) q^{65} +(-0.470732 + 0.326865i) q^{66} +(-1.49032 - 1.27285i) q^{67} +(-2.05505 + 1.14150i) q^{68} +(0.0787602 + 0.0482643i) q^{69} +(-4.01334 - 1.05474i) q^{70} +(-0.811324 + 0.692936i) q^{71} +(-6.51575 - 5.40456i) q^{72} +(-6.02934 - 6.02934i) q^{73} +(-8.40300 + 8.05121i) q^{74} +(-0.0813767 - 0.0195368i) q^{75} +(-4.33462 - 2.01663i) q^{76} +(12.6594 - 6.45026i) q^{77} +(0.0494408 + 0.0375614i) q^{78} +(-2.37199 + 0.982510i) q^{79} +(3.98976 - 0.286049i) q^{80} -8.93701i q^{81} +(6.70108 + 6.09061i) q^{82} +6.72545i q^{83} +(-0.332118 - 0.361803i) q^{84} +(1.08593 - 0.449805i) q^{85} +(2.08953 - 2.75038i) q^{86} +(0.628613 - 0.320294i) q^{87} +(-9.54373 + 9.82282i) q^{88} +(3.00548 + 0.721551i) q^{89} +(2.92834 + 3.05629i) q^{90} +(-1.08848 - 1.08848i) q^{91} +(2.06839 + 0.771267i) q^{92} +(0.234061 - 0.199907i) q^{93} +(0.292195 - 1.11182i) q^{94} +(2.03814 + 1.24897i) q^{95} +(0.415557 + 0.226794i) q^{96} +(-8.95591 - 7.64907i) q^{97} +(1.29838 + 1.86985i) 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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