LMFDB - Embedded newform 820.2.bw.b.11.34

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 = [672,0,0,0,0,12,0,0,16] 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			11.34
Character	$\chi$	$=$	820.11
Dual form			820.2.bw.b.671.34

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.14905 - 0.824432i) q^{2} +(0.760926 - 1.83704i) q^{3} +(0.640623 - 1.89462i) q^{4} +(0.453990 - 0.891007i) q^{5} +(-0.640173 - 2.73818i) q^{6} +(0.369288 + 1.53819i) q^{7} +(-0.825882 - 2.70517i) q^{8} +(-0.674382 - 0.674382i) q^{9} +(-0.212917 - 1.39809i) q^{10} +(2.97155 - 3.47924i) q^{11} +(-2.99303 - 2.61852i) q^{12} +(-0.694833 - 1.13386i) q^{13} +(1.69247 + 1.46301i) q^{14} +(-1.29136 - 1.51199i) q^{15} +(-3.17920 - 2.42748i) q^{16} +(0.612824 + 7.78667i) q^{17} +(-1.33088 - 0.218915i) q^{18} +(-0.189408 - 0.116069i) q^{19} +(-1.39729 - 1.43094i) q^{20} +(3.10672 + 0.492057i) q^{21} +(0.546059 - 6.44766i) q^{22} +(-4.85718 - 3.52895i) q^{23} +(-5.59793 - 0.541254i) q^{24} +(-0.587785 - 0.809017i) q^{25} +(-1.73319 - 0.730022i) q^{26} +(3.75910 - 1.55707i) q^{27} +(3.15087 + 0.285741i) q^{28} +(-0.394065 + 5.00707i) q^{29} +(-2.73037 - 0.672709i) q^{30} +(-2.03933 + 6.27642i) q^{31} +(-5.65435 - 0.168255i) q^{32} +(-4.13037 - 8.10630i) q^{33} +(7.12375 + 8.44203i) q^{34} +(1.53819 + 0.369288i) q^{35} +(-1.70972 + 0.845675i) q^{36} +(-0.663202 - 2.04113i) q^{37} +(-0.313330 + 0.0227847i) q^{38} +(-2.61167 + 0.413648i) q^{39} +(-2.78526 - 0.492253i) q^{40} +(-0.182878 - 6.40051i) q^{41} +(3.97544 - 1.99589i) q^{42} +(1.57691 + 9.95621i) q^{43} +(-4.68821 - 7.85886i) q^{44} +(-0.907041 + 0.294716i) q^{45} +(-8.49052 - 0.0505157i) q^{46} +(0.184720 - 0.769413i) q^{47} +(-6.87852 + 3.99319i) q^{48} +(4.00738 - 2.04186i) q^{49} +(-1.34237 - 0.445010i) q^{50} +(14.7707 + 4.79930i) q^{51} +(-2.59337 + 0.590068i) q^{52} +(6.32005 + 0.497399i) q^{53} +(3.03569 - 4.88827i) q^{54} +(-1.75097 - 4.22721i) q^{55} +(3.85608 - 2.26935i) q^{56} +(-0.357349 + 0.259630i) q^{57} +(3.67519 + 6.07824i) q^{58} +(-3.71165 + 5.10865i) q^{59} +(-3.69193 + 1.47803i) q^{60} +(-0.117265 + 0.740384i) q^{61} +(2.83119 + 8.89320i) q^{62} +(0.788289 - 1.28637i) q^{63} +(-6.63584 + 4.46830i) q^{64} +(-1.32573 + 0.104337i) q^{65} +(-11.4291 - 5.90932i) q^{66} +(-2.25674 + 1.92744i) q^{67} +(15.1454 + 3.82725i) q^{68} +(-10.1788 + 6.23756i) q^{69} +(2.07191 - 0.843807i) q^{70} +(-3.14741 - 2.68814i) q^{71} +(-1.26735 + 2.38127i) q^{72} +(-8.46685 + 8.46685i) q^{73} +(-2.44482 - 1.79859i) q^{74} +(-1.93346 + 0.464182i) q^{75} +(-0.341247 + 0.284500i) q^{76} +(6.44910 + 3.28598i) q^{77} +(-2.65991 + 2.62845i) q^{78} +(-2.31353 - 0.958296i) q^{79} +(-3.60623 + 1.73064i) q^{80} -10.9516i q^{81} +(-5.48692 - 7.20373i) q^{82} +9.11427i q^{83} +(2.92250 - 5.57085i) q^{84} +(7.21619 + 2.98904i) q^{85} +(10.0202 + 10.1401i) q^{86} +(8.89832 + 4.53392i) q^{87} +(-11.8661 - 5.16510i) q^{88} +(7.63688 - 1.83345i) q^{89} +(-0.799261 + 1.08644i) q^{90} +(1.48751 - 1.48751i) q^{91} +(-9.79766 + 6.94181i) q^{92} +(9.97824 + 8.52222i) q^{93} +(-0.422077 - 1.03638i) q^{94} +(-0.189408 + 0.116069i) q^{95} +(-4.61164 + 10.2592i) q^{96} +(3.16973 - 2.70721i) q^{97} +(2.92129 - 5.65001i) q^{98} +(-4.35029 + 0.342376i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q + 12 q^{6} + 16 q^{9} - 124 q^{12} - 24 q^{14} - 32 q^{16} - 8 q^{17} + 40 q^{21} - 4 q^{22} - 24 q^{24} - 28 q^{28} - 12 q^{30} - 20 q^{32} + 40 q^{33} - 4 q^{34} - 60 q^{36} + 80 q^{37} - 172 q^{38}+ \cdots - 116 q^{98}+O(q^{100}) $ 672 * q + 12 * q^6 + 16 * q^9 - 124 * q^12 - 24 * q^14 - 32 * q^16 - 8 * q^17 + 40 * q^21 - 4 * q^22 - 24 * q^24 - 28 * q^28 - 12 * q^30 - 20 * q^32 + 40 * q^33 - 4 * q^34 - 60 * q^36 + 80 * q^37 - 172 * q^38 + 160 * q^42 - 24 * q^44 - 16 * q^46 + 40 * q^48 - 24 * q^52 - 64 * q^54 + 68 * q^56 - 112 * q^58 + 36 * q^62 - 120 * q^64 + 8 * q^65 + 144 * q^68 - 104 * q^69 + 24 * q^70 - 320 * q^72 - 92 * q^74 - 24 * q^76 + 160 * q^77 - 128 * q^78 - 192 * q^82 - 172 * q^84 - 32 * q^85 - 112 * q^88 + 8 * q^89 - 48 * q^90 + 24 * q^92 + 92 * q^94 + 56 * 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 $

$2$	1.14905	−	0.824432i	0.812500	−	0.582962i
$2$	1.14905	−	0.824432i	0.812500	−	0.582962i
$3$	0.760926	−	1.83704i	0.439321	−	1.06061i	−0.536863	−	0.843670i	$-0.680391\pi$
$3$	0.760926	−	1.83704i	0.439321	−	1.06061i	0.976184	−	0.216945i	$-0.0696093\pi$
$4$	0.640623	−	1.89462i	0.320312	−	0.947312i
$5$	0.453990	−	0.891007i	0.203031	−	0.398470i
$5$	0.453990	−	0.891007i	0.203031	−	0.398470i
$6$	−0.640173	−	2.73818i	−0.261349	−	1.11786i
$7$	0.369288	+	1.53819i	0.139578	+	0.581383i	0.997691	+	0.0679219i	$0.0216369\pi$
$7$	0.369288	+	1.53819i	0.139578	+	0.581383i	−0.858113	+	0.513461i	$0.828363\pi$
$8$	−0.825882	−	2.70517i	−0.291993	−	0.956420i
$9$	−0.674382	−	0.674382i	−0.224794	−	0.224794i
$10$	−0.212917	−	1.39809i	−0.0673304	−	0.442116i
$11$	2.97155	−	3.47924i	0.895956	−	1.04903i	−0.102568	−	0.994726i	$-0.532706\pi$
$11$	2.97155	−	3.47924i	0.895956	−	1.04903i	0.998524	−	0.0543042i	$-0.0172941\pi$
$12$	−2.99303	−	2.61852i	−0.864014	−	0.755901i
$13$	−0.694833	−	1.13386i	−0.192712	−	0.314478i	0.741660	−	0.670776i	$-0.234039\pi$
$13$	−0.694833	−	1.13386i	−0.192712	−	0.314478i	−0.934372	+	0.356298i	$0.884039\pi$
$14$	1.69247	+	1.46301i	0.452331	+	0.391005i
$15$	−1.29136	−	1.51199i	−0.333428	−	0.390394i
$16$	−3.17920	−	2.42748i	−0.794801	−	0.606870i
$17$	0.612824	+	7.78667i	0.148632	+	1.88855i	0.393993	+	0.919113i	$0.371093\pi$
$17$	0.612824	+	7.78667i	0.148632	+	1.88855i	−0.245361	+	0.969432i	$0.578907\pi$
$18$	−1.33088	−	0.218915i	−0.313691	−	0.0515988i
$19$	−0.189408	−	0.116069i	−0.0434532	−	0.0266281i	0.500602	−	0.865677i	$-0.333112\pi$
$19$	−0.189408	−	0.116069i	−0.0434532	−	0.0266281i	−0.544055	+	0.839049i	$0.683112\pi$
$20$	−1.39729	−	1.43094i	−0.312443	−	0.319968i
$21$	3.10672	+	0.492057i	0.677943	+	0.107376i
$22$	0.546059	−	6.44766i	0.116420	−	1.37464i
$23$	−4.85718	−	3.52895i	−1.01279	−	0.735837i	−0.0479997	−	0.998847i	$-0.515285\pi$
$23$	−4.85718	−	3.52895i	−1.01279	−	0.735837i	−0.964793	+	0.263010i	$0.915285\pi$
$24$	−5.59793	−	0.541254i	−1.14267	−	0.110483i
$25$	−0.587785	−	0.809017i	−0.117557	−	0.161803i
$26$	−1.73319	−	0.730022i	−0.339907	−	0.143169i
$27$	3.75910	−	1.55707i	0.723438	−	0.299658i
$28$	3.15087	+	0.285741i	0.595459	+	0.0540001i
$29$	−0.394065	+	5.00707i	−0.0731760	+	0.929789i	0.845295	+	0.534300i	$0.179425\pi$
$29$	−0.394065	+	5.00707i	−0.0731760	+	0.929789i	−0.918471	+	0.395489i	$0.870575\pi$
$30$	−2.73037	−	0.672709i	−0.498494	−	0.122819i
$31$	−2.03933	+	6.27642i	−0.366275	+	1.12728i	0.582904	+	0.812541i	$0.301916\pi$
$31$	−2.03933	+	6.27642i	−0.366275	+	1.12728i	−0.949179	+	0.314737i	$0.898084\pi$
$32$	−5.65435	−	0.168255i	−0.999558	−	0.0297436i
$33$	−4.13037	−	8.10630i	−0.719004	−	1.41113i
$34$	7.12375	+	8.44203i	1.22171	+	1.44780i
$35$	1.53819	+	0.369288i	0.260002	+	0.0624210i
$36$	−1.70972	+	0.845675i	−0.284954	+	0.140946i
$37$	−0.663202	−	2.04113i	−0.109030	−	0.335559i	0.881625	−	0.471950i	$-0.156450\pi$
$37$	−0.663202	−	2.04113i	−0.109030	−	0.335559i	−0.990655	+	0.136391i	$0.956450\pi$
$38$	−0.313330	+	0.0227847i	−0.0508289	+	0.00369617i
$39$	−2.61167	+	0.413648i	−0.418202	+	0.0662367i
$40$	−2.78526	−	0.492253i	−0.440389	−	0.0778320i
$41$	−0.182878	−	6.40051i	−0.0285608	−	0.999592i
$41$	−0.182878	−	6.40051i	−0.0285608	−	0.999592i
$42$	3.97544	−	1.99589i	0.613424	−	0.307972i
$43$	1.57691	+	9.95621i	0.240476	+	1.51831i	0.752072	+	0.659081i	$0.229055\pi$
$43$	1.57691	+	9.95621i	0.240476	+	1.51831i	−0.511596	+	0.859226i	$0.670945\pi$
$44$	−4.68821	−	7.85886i	−0.706774	−	1.18477i
$45$	−0.907041	+	0.294716i	−0.135214	+	0.0439336i
$46$	−8.49052	−	0.0505157i	−1.25186	−	0.00744814i
$47$	0.184720	−	0.769413i	0.0269441	−	0.112230i	−0.957277	−	0.289171i	$-0.906620\pi$
$47$	0.184720	−	0.769413i	0.0269441	−	0.112230i	0.984221	+	0.176941i	$0.0566202\pi$
$48$	−6.87852	+	3.99319i	−0.992828	+	0.576367i
$49$	4.00738	−	2.04186i	0.572482	−	0.291694i
$50$	−1.34237	−	0.445010i	−0.189840	−	0.0629340i
$51$	14.7707	+	4.79930i	2.06832	+	0.672037i
$52$	−2.59337	+	0.590068i	−0.359636	+	0.0818277i
$53$	6.32005	+	0.497399i	0.868126	+	0.0683230i	0.504695	−	0.863298i	$-0.331605\pi$
$53$	6.32005	+	0.497399i	0.868126	+	0.0683230i	0.363432	+	0.931621i	$0.381605\pi$
$54$	3.03569	−	4.88827i	0.413104	−	0.665209i
$55$	−1.75097	−	4.22721i	−0.236101	−	0.569997i
$56$	3.85608	−	2.26935i	0.515291	−	0.303255i
$57$	−0.357349	+	0.259630i	−0.0473321	+	0.0343888i
$58$	3.67519	+	6.07824i	0.482576	+	0.798112i
$59$	−3.71165	+	5.10865i	−0.483216	+	0.665090i	−0.979119	−	0.203288i	$-0.934837\pi$
$59$	−3.71165	+	5.10865i	−0.483216	+	0.665090i	0.495903	+	0.868378i	$0.334837\pi$
$60$	−3.69193	+	1.47803i	−0.476626	+	0.190813i
$61$	−0.117265	+	0.740384i	−0.0150143	+	0.0947964i	−0.994058	−	0.108856i	$-0.965281\pi$
$61$	−0.117265	+	0.740384i	−0.0150143	+	0.0947964i	0.979043	+	0.203652i	$0.0652813\pi$
$62$	2.83119	+	8.89320i	0.359561	+	1.12944i
$63$	0.788289	−	1.28637i	0.0993151	−	0.162067i
$64$	−6.63584	+	4.46830i	−0.829480	+	0.558537i
$65$	−1.32573	+	0.104337i	−0.164436	+	0.0129414i
$66$	−11.4291	−	5.90932i	−1.40682	−	0.727387i
$67$	−2.25674	+	1.92744i	−0.275705	+	0.235474i	−0.776539	−	0.630069i	$-0.783027\pi$
$67$	−2.25674	+	1.92744i	−0.275705	+	0.235474i	0.500834	+	0.865543i	$0.333027\pi$
$68$	15.1454	+	3.82725i	1.83665	+	0.464122i
$69$	−10.1788	+	6.23756i	−1.22538	+	0.750914i
$70$	2.07191	−	0.843807i	0.247641	−	0.100854i
$71$	−3.14741	−	2.68814i	−0.373528	−	0.319023i	0.442790	−	0.896625i	$-0.353989\pi$
$71$	−3.14741	−	2.68814i	−0.373528	−	0.319023i	−0.816319	+	0.577602i	$0.803989\pi$
$72$	−1.26735	+	2.38127i	−0.149359	+	0.280636i
$73$	−8.46685	+	8.46685i	−0.990970	+	0.990970i	−0.999960	−	0.00898942i	$-0.997139\pi$
$73$	−8.46685	+	8.46685i	−0.990970	+	0.990970i	0.00898942	+	0.999960i	$0.497139\pi$
$74$	−2.44482	−	1.79859i	−0.284205	−	0.209082i
$75$	−1.93346	+	0.464182i	−0.223256	+	0.0535991i
$76$	−0.341247	+	0.284500i	−0.0391437	+	0.0326344i
$77$	6.44910	+	3.28598i	0.734944	+	0.374472i
$78$	−2.65991	+	2.62845i	−0.301176	+	0.297613i
$79$	−2.31353	−	0.958296i	−0.260293	−	0.107817i	0.248721	−	0.968575i	$-0.419990\pi$
$79$	−2.31353	−	0.958296i	−0.260293	−	0.107817i	−0.509014	+	0.860758i	$0.669990\pi$
$80$	−3.60623	+	1.73064i	−0.403189	+	0.193491i
$81$		−	10.9516i		−	1.21684i
$82$	−5.48692	−	7.20373i	−0.605929	−	0.795518i
$83$			9.11427i			1.00042i	0.865904	+	0.500211i	$0.166744\pi$
$83$			9.11427i			1.00042i	−0.865904	+	0.500211i	$0.833256\pi$
$84$	2.92250	−	5.57085i	0.318871	−	0.607830i
$85$	7.21619	+	2.98904i	0.782706	+	0.324207i
$86$	10.0202	+	10.1401i	1.08050	+	1.09344i
$87$	8.89832	+	4.53392i	0.954000	+	0.486088i
$88$	−11.8661	−	5.16510i	−1.26493	−	0.550601i
$89$	7.63688	−	1.83345i	0.809507	−	0.194346i	0.192494	−	0.981298i	$-0.438342\pi$
$89$	7.63688	−	1.83345i	0.809507	−	0.194346i	0.617013	+	0.786953i	$0.288342\pi$
$90$	−0.799261	+	1.08644i	−0.0842495	+	0.114520i
$91$	1.48751	−	1.48751i	0.155934	−	0.155934i
$92$	−9.79766	+	6.94181i	−1.02148	+	0.723734i
$93$	9.97824	+	8.52222i	1.03470	+	0.883713i
$94$	−0.422077	−	1.03638i	−0.0435339	−	0.106895i
$95$	−0.189408	+	0.116069i	−0.0194328	+	0.0119085i
$96$	−4.61164	+	10.2592i	−0.470673	+	1.04708i
$97$	3.16973	−	2.70721i	0.321838	−	0.274875i	−0.473820	−	0.880622i	$-0.657125\pi$
$97$	3.16973	−	2.70721i	0.321838	−	0.274875i	0.795658	+	0.605746i	$0.207125\pi$
$98$	2.92129	−	5.65001i	0.295095	−	0.570737i
$99$	−4.35029	+	0.342376i	−0.437221	+	0.0344100i
$100$	−1.90933	+	0.595357i	−0.190933	+	0.0595357i
$101$	7.86924	−	12.8414i	0.783019	−	1.27777i	−0.173133	−	0.984898i	$-0.555389\pi$
$101$	7.86924	−	12.8414i	0.783019	−	1.27777i	0.956152	−	0.292872i	$-0.0946109\pi$
$102$	20.9290	−	6.66284i	2.07228	−	0.659719i
$103$	1.01368	−	6.40011i	0.0998807	−	0.630622i	−0.886066	−	0.463560i	$-0.846572\pi$
$103$	1.01368	−	6.40011i	0.0998807	−	0.630622i	0.985946	−	0.167062i	$-0.0534280\pi$
$104$	−2.49344	+	2.81608i	−0.244502	+	0.276139i
$105$	1.84885	−	2.54472i	0.180429	−	0.248339i
$106$	7.67212	−	4.63892i	0.745182	−	0.450572i
$107$	12.9316	−	9.39533i	1.25014	−	0.908280i	0.251911	−	0.967750i	$-0.418941\pi$
$107$	12.9316	−	9.39533i	1.25014	−	0.908280i	0.998230	+	0.0594701i	$0.0189411\pi$
$108$	−0.541896	−	8.11957i	−0.0521439	−	0.781306i
$109$	−4.61338	−	11.1377i	−0.441882	−	1.06680i	−0.975288	−	0.220938i	$-0.929088\pi$
$109$	−4.61338	−	11.1377i	−0.441882	−	1.06680i	0.533406	−	0.845859i	$-0.320912\pi$
$110$	−5.49700	−	3.41372i	−0.524118	−	0.325485i
$111$	−4.25428	−	0.334819i	−0.403798	−	0.0317796i
$112$	2.55990	−	5.78667i	0.241887	−	0.546789i
$113$	13.3643	+	4.34233i	1.25721	+	0.408492i	0.860500	−	0.509451i	$-0.170152\pi$
$113$	13.3643	+	4.34233i	1.25721	+	0.408492i	0.396711	+	0.917944i	$0.370152\pi$
$114$	−0.196565	+	0.592937i	−0.0184100	+	0.0555337i
$115$	−5.34943	+	2.72567i	−0.498837	+	0.254170i
$116$	9.23407	+	3.95425i	0.857362	+	0.367143i
$117$	−0.296075	+	1.23324i	−0.0273721	+	0.114013i
$118$	−0.0531311	+	8.93009i	−0.00489111	+	0.822082i
$119$	−11.7511	+	3.81817i	−1.07722	+	0.350011i
$120$	−3.02367	+	4.74207i	−0.276022	+	0.432889i
$121$	−1.55421	−	9.81291i	−0.141292	−	0.892083i
$122$	0.475653	+	0.947414i	0.0430636	+	0.0857748i
$123$	−11.8971	−	4.53436i	−1.07273	−	0.408850i
$124$	10.5850	+	7.88459i	0.950562	+	0.708057i
$125$	−0.987688	+	0.156434i	−0.0883415	+	0.0139919i
$126$	−0.154743	−	2.12799i	−0.0137856	−	0.189577i
$127$	−3.36871	−	10.3678i	−0.298925	−	0.919997i	−0.981875	−	0.189531i	$-0.939303\pi$
$127$	−3.36871	−	10.3678i	−0.298925	−	0.919997i	0.682950	−	0.730465i	$-0.260697\pi$
$128$	−3.94109	+	10.6051i	−0.348346	+	0.937366i
$129$	19.4898	+	4.67910i	1.71599	+	0.411972i
$130$	−1.43731	+	1.21286i	−0.126060	+	0.106375i
$131$	8.19158	+	16.0769i	0.715701	+	1.40464i	0.906154	+	0.422947i	$0.139004\pi$
$131$	8.19158	+	16.0769i	0.715701	+	1.40464i	−0.190453	+	0.981696i	$0.560996\pi$
$132$	−18.0044	+	2.63241i	−1.56708	+	0.229122i
$133$	0.108591	−	0.334209i	0.00941605	−	0.0289796i
$134$	−1.00406	+	4.07526i	−0.0867378	+	0.352048i
$135$	0.319236	−	4.05627i	0.0274754	−	0.349108i
$136$	20.5581	−	8.08866i	1.76284	−	0.693597i
$137$	−0.214130	+	0.0886957i	−0.0182944	+	0.00757779i	−0.391812	−	0.920045i	$-0.628152\pi$
$137$	−0.214130	+	0.0886957i	−0.0182944	+	0.00757779i	0.373517	+	0.927623i	$0.378152\pi$
$138$	−6.55346	+	15.5590i	−0.557867	+	1.32447i
$139$	−7.60033	−	10.4610i	−0.644651	−	0.887286i	0.354202	−	0.935169i	$-0.384753\pi$
$139$	−7.60033	−	10.4610i	−0.644651	−	0.887286i	−0.998853	+	0.0478828i	$0.984753\pi$
$140$	1.68506	−	2.67773i	0.142414	−	0.226309i
$141$	−1.27288	−	0.924803i	−0.107196	−	0.0778825i
$142$	−5.83271	−	0.493978i	−0.489470	−	0.0414537i
$143$	−6.00972	−	0.951846i	−0.502558	−	0.0795974i
$144$	0.506948	+	3.78104i	0.0422456	+	0.315087i
$145$	4.28243	+	2.62428i	0.355636	+	0.217934i
$146$	−2.74848	+	16.7092i	−0.227465	+	1.38286i
$147$	−0.701658	−	8.91541i	−0.0578718	−	0.735331i
$148$	−4.29203	−	0.0510741i	−0.352803	−	0.00419827i
$149$	−3.44121	−	4.02914i	−0.281915	−	0.330080i	0.601322	−	0.799007i	$-0.294641\pi$
$149$	−3.44121	−	4.02914i	−0.281915	−	0.330080i	−0.883237	+	0.468926i	$0.844641\pi$
$150$	−1.83895	+	2.12737i	−0.150150	+	0.173699i
$151$	4.01089	+	6.54517i	0.326401	+	0.532638i	0.973182	−	0.230038i	$-0.0738850\pi$
$151$	4.01089	+	6.54517i	0.326401	+	0.532638i	−0.646780	+	0.762676i	$0.723885\pi$
$152$	−0.157558	+	0.608240i	−0.0127796	+	0.0493347i
$153$	4.83791	−	5.66446i	0.391122	−	0.457945i
$154$	10.1194	−	1.54110i	0.815445	−	0.124185i
$155$	4.66649	+	4.66649i	0.374822	+	0.374822i
$156$	−0.889389	+	5.21313i	−0.0712081	+	0.417384i
$157$	5.37112	+	22.3723i	0.428662	+	1.78551i	0.599683	+	0.800238i	$0.295294\pi$
$157$	5.37112	+	22.3723i	0.428662	+	1.78551i	−0.171021	+	0.985267i	$0.554706\pi$
$158$	−3.44841	+	0.806222i	−0.274341	+	0.0641395i
$159$	5.72284	−	11.2317i	0.453850	−	0.890732i
$160$	−2.71694	+	4.96168i	−0.214793	+	0.392255i
$161$	3.63451	−	8.77449i	0.286440	−	0.691527i
$162$	−9.02883	−	12.5839i	−0.709372	−	0.988684i
$163$	−0.486644			−0.0381169			−0.0190585	−	0.999818i	$-0.506067\pi$
$163$	−0.486644			−0.0381169			−0.0190585	+	0.999818i	$0.506067\pi$
$164$	−12.2437	−	3.75383i	−0.956074	−	0.293125i
$165$	−9.09791			−0.708272
$166$	7.51410	+	10.4727i	0.583207	+	0.812842i
$167$	−5.88196	+	14.2003i	−0.455160	+	1.09885i	0.515174	+	0.857085i	$0.327727\pi$
$167$	−5.88196	+	14.2003i	−0.455160	+	1.09885i	−0.970334	+	0.241768i	$0.922273\pi$
$168$	−1.23469	−	8.81058i	−0.0952586	−	0.679751i
$169$	5.09902	−	10.0074i	0.392232	−	0.769799i
$170$	10.7560	−	2.51470i	0.824949	−	0.192869i
$171$	0.0494582	+	0.206008i	0.00378216	+	0.0157538i
$172$	19.8735	+	3.39053i	1.51534	+	0.258525i
$173$	−2.79065	−	2.79065i	−0.212169	−	0.212169i	0.593019	−	0.805188i	$-0.297936\pi$
$173$	−2.79065	−	2.79065i	−0.212169	−	0.212169i	−0.805188	+	0.593019i	$0.797936\pi$
$174$	13.9625	−	2.12637i	1.05850	−	0.161200i
$175$	1.02736	−	1.20289i	0.0776614	−	0.0909298i
$176$	−17.8930	+	3.84783i	−1.34873	+	0.290041i
$177$	6.56050	+	10.7058i	0.493117	+	0.804694i
$178$	7.26358	−	8.40281i	0.544429	−	0.629817i
$179$	−4.32279	−	5.06133i	−0.323100	−	0.378302i	0.574955	−	0.818185i	$-0.305020\pi$
$179$	−4.32279	−	5.06133i	−0.323100	−	0.378302i	−0.898055	+	0.439884i	$0.855020\pi$
$180$	−0.0226964	+	1.90730i	−0.00169169	+	0.142162i
$181$	−1.72105	−	21.8680i	−0.127925	−	1.62544i	−0.641313	−	0.767279i	$-0.721610\pi$
$181$	−1.72105	−	21.8680i	−0.127925	−	1.62544i	0.513389	−	0.858156i	$-0.328390\pi$
$182$	0.482870	−	2.93557i	0.0357927	−	0.217599i
$183$	1.27088	+	0.778798i	0.0939464	+	0.0575704i
$184$	−5.53493	+	16.0540i	−0.408041	+	1.18352i
$185$	−2.11974	−	0.335735i	−0.155847	−	0.0246837i
$186$	18.4915	+	1.56606i	1.35586	+	0.114829i
$187$	28.9127	+	21.0063i	2.11431	+	1.53613i
$188$	−1.33941	−	0.842878i	−0.0976867	−	0.0614732i
$189$	3.78326	+	5.20721i	0.275192	+	0.378769i
$190$	−0.121948	+	0.289523i	−0.00884701	+	0.0210042i
$191$	−6.89217	+	2.85483i	−0.498700	+	0.206568i	−0.617832	−	0.786310i	$-0.711989\pi$
$191$	−6.89217	+	2.85483i	−0.498700	+	0.206568i	0.119132	+	0.992878i	$0.461989\pi$
$192$	3.15905	+	15.5903i	0.227985	+	1.12514i
$193$	−1.37718	+	17.4988i	−0.0991318	+	1.25959i	0.723223	+	0.690614i	$0.242660\pi$
$193$	−1.37718	+	17.4988i	−0.0991318	+	1.25959i	−0.822355	+	0.568974i	$0.807340\pi$
$194$	1.41027	−	5.72394i	0.101251	−	0.410955i
$195$	−0.817111	+	2.51481i	−0.0585145	+	0.180089i
$196$	−1.30134	−	8.90054i	−0.0929529	−	0.635753i
$197$	1.36433	+	2.67764i	0.0972043	+	0.190774i	0.934488	−	0.355994i	$-0.115858\pi$
$197$	1.36433	+	2.67764i	0.0972043	+	0.190774i	−0.837284	+	0.546769i	$0.815858\pi$
$198$	−4.71643	+	3.97993i	−0.335182	+	0.282841i
$199$	−23.0477	−	5.53326i	−1.63381	−	0.392242i	−0.690281	−	0.723542i	$-0.742513\pi$
$199$	−23.0477	−	5.53326i	−1.63381	−	0.392242i	−0.943526	+	0.331299i	$0.892513\pi$
$200$	−1.70308	+	2.25821i	−0.120426	+	0.159679i
$201$	1.82357	+	5.61237i	0.128625	+	0.395866i
$202$	−1.54475	−	21.2431i	−0.108689	−	1.49466i
$203$	−7.84737	+	1.24290i	−0.550777	+	0.0872345i
$204$	18.5553	−	24.9104i	1.29913	−	1.74408i
$205$	−5.78592	−	2.74283i	−0.404106	−	0.191567i
$206$	−4.11169	−	8.18975i	−0.286475	−	0.570607i
$207$	0.895736	+	5.65545i	0.0622579	+	0.393081i
$208$	−0.543419	+	5.29148i	−0.0376793	+	0.366898i
$209$	−0.966669	+	0.314090i	−0.0668659	+	0.0217260i
$210$	0.0264656	−	4.44826i	0.00182630	−	0.306959i
$211$	−0.177618	+	0.739833i	−0.0122277	+	0.0509322i	−0.978150	−	0.207899i	$-0.933337\pi$
$211$	−0.177618	+	0.739833i	−0.0122277	+	0.0509322i	0.965923	+	0.258831i	$0.0833374\pi$
$212$	4.99116	−	11.6555i	0.342794	−	0.800502i
$213$	−7.33316	+	3.73643i	−0.502460	+	0.256016i
$214$	7.11317	−	21.4569i	0.486246	−	1.46676i
$215$	9.58695	+	3.11499i	0.653824	+	0.212440i
$216$	−7.31670	−	8.88302i	−0.497838	−	0.604413i
$217$	−10.4074	−	0.819084i	−0.706504	−	0.0556030i
$218$	−14.4833	−	8.99432i	−0.980930	−	0.609172i
$219$	9.11128	+	21.9966i	0.615684	+	1.48639i
$220$	−9.13069	+	0.609377i	−0.615591	+	0.0410842i
$221$	8.40322	−	6.10530i	0.565262	−	0.410687i
$222$	−5.16440	+	3.12264i	−0.346612	+	0.209578i
$223$	−6.03934	+	8.31244i	−0.404424	+	0.556642i	−0.961847	−	0.273586i	$-0.911790\pi$
$223$	−6.03934	+	8.31244i	−0.404424	+	0.556642i	0.557423	+	0.830228i	$0.311790\pi$
$224$	−1.82927	−	8.75963i	−0.122223	−	0.585277i
$225$	−0.149195	+	0.941978i	−0.00994631	+	0.0627985i
$226$	18.9362	−	6.02843i	1.25962	−	0.401005i
$227$	−3.80169	+	6.20380i	−0.252327	+	0.411761i	−0.953574	−	0.301158i	$-0.902627\pi$
$227$	−3.80169	+	6.20380i	−0.252327	+	0.411761i	0.701247	+	0.712918i	$0.252627\pi$
$228$	0.262974	+	0.843368i	0.0174159	+	0.0558534i
$229$	−17.9582	+	1.41334i	−1.18671	+	0.0933965i	−0.656406	−	0.754408i	$-0.727924\pi$
$229$	−17.9582	+	1.41334i	−1.18671	+	0.0933965i	−0.530309	+	0.847805i	$0.677924\pi$
$230$	−3.89962	+	7.54217i	−0.257134	+	0.497316i
$231$	10.9438	−	9.34686i	0.720047	−	0.614978i
$232$	13.8704	−	3.06924i	0.910636	−	0.201505i
$233$	−17.9127	+	10.9769i	−1.17350	+	0.719124i	−0.965856	−	0.259080i	$-0.916581\pi$
$233$	−17.9127	+	10.9769i	−1.17350	+	0.719124i	−0.207647	+	0.978204i	$0.566581\pi$
$234$	0.676519	+	1.66115i	0.0442254	+	0.108593i
$235$	−0.601691	−	0.513892i	−0.0392500	−	0.0335226i
$236$	7.30121	+	10.3049i	0.475268	+	0.670793i
$237$	−3.52085	+	3.52085i	−0.228704	+	0.228704i
$238$	−10.3548	+	14.0752i	−0.671200	+	0.912363i
$239$	−0.385058	+	0.0924442i	−0.0249073	+	0.00597972i	−0.245880	−	0.969300i	$-0.579077\pi$
$239$	−0.385058	+	0.0924442i	−0.0249073	+	0.00597972i	0.220973	+	0.975280i	$0.429077\pi$
$240$	0.435173	+	7.94167i	0.0280903	+	0.512633i
$241$	23.2091	+	11.8256i	1.49503	+	0.761756i	0.994577	−	0.104007i	$-0.0331664\pi$
$241$	23.2091	+	11.8256i	1.49503	+	0.761756i	0.500454	+	0.865763i	$0.333166\pi$
$242$	−9.87594	−	9.99416i	−0.634850	−	0.642449i
$243$	−8.84118	−	3.66214i	−0.567162	−	0.234926i
$244$	1.32763	+	0.696481i	0.0849926	+	0.0445876i
$245$		−	4.49758i		−	0.287340i
$246$	−17.4087	+	4.59819i	−1.10994	+	0.293170i
$247$			0.295412i			0.0187966i
$248$	18.6630	+	0.333147i	1.18510	+	0.0211549i
$249$	16.7433	+	6.93529i	1.06106	+	0.439506i
$250$	−1.00593	+	0.994033i	−0.0636207	+	0.0628682i
$251$	17.2730	+	8.80104i	1.09026	+	0.555517i	0.904238	−	0.427028i	$-0.140440\pi$
$251$	17.2730	+	8.80104i	1.09026	+	0.555517i	0.186025	+	0.982545i	$0.440440\pi$
$252$	−1.93219	−	2.31759i	−0.121717	−	0.145994i
$253$	−26.7114	+	6.41285i	−1.67933	+	0.403172i
$254$	−12.4184	−	9.13587i	−0.779199	−	0.573235i
$255$	10.9820	−	10.9820i	0.687718	−	0.687718i
$256$	4.21467	+	15.4349i	0.263417	+	0.964682i
$257$	−12.2257	−	10.4417i	−0.762618	−	0.651337i	0.180583	−	0.983560i	$-0.442201\pi$
$257$	−12.2257	−	10.4417i	−0.762618	−	0.651337i	−0.943201	+	0.332223i	$0.892201\pi$
$258$	26.2524	−	10.6915i	1.63440	−	0.665627i
$259$	2.89474	−	1.77390i	0.179870	−	0.110225i
$260$	−0.651613	+	2.57860i	−0.0404113	+	0.159918i
$261$	3.64242	−	3.11092i	0.225460	−	0.192561i
$262$	22.6668	+	11.7197i	1.40036	+	0.724046i
$263$	−3.07309	+	0.241858i	−0.189495	+	0.0149136i	−0.172851	−	0.984948i	$-0.555298\pi$
$263$	−3.07309	+	0.241858i	−0.189495	+	0.0149136i	−0.0166436	+	0.999861i	$0.505298\pi$
$264$	−18.5177	+	17.8682i	−1.13968	+	1.09971i
$265$	3.31243	−	5.40539i	0.203481	−	0.332051i
$266$	−0.150756	−	0.473549i	−0.00924347	−	0.0290351i
$267$	2.44298	−	15.4244i	0.149508	−	0.943956i
$268$	2.20605	+	5.51045i	0.134756	+	0.336604i
$269$	−6.31171	+	8.68732i	−0.384832	+	0.529675i	−0.956857	−	0.290561i	$-0.906158\pi$
$269$	−6.31171	+	8.68732i	−0.384832	+	0.529675i	0.572025	+	0.820236i	$0.306158\pi$
$270$	−2.97731	−	4.92404i	−0.181193	−	0.299668i
$271$	17.6160	−	12.7988i	1.07010	−	0.777471i	0.0941673	−	0.995556i	$-0.469981\pi$
$271$	17.6160	−	12.7988i	1.07010	−	0.777471i	0.975930	+	0.218085i	$0.0699811\pi$
$272$	16.9537	−	26.2430i	1.02797	−	1.59122i
$273$	−1.60073	−	3.86450i	−0.0968805	−	0.233890i
$274$	−0.172923	+	0.278452i	−0.0104466	+	0.0168219i
$275$	−4.56140	−	0.358990i	−0.275063	−	0.0216479i
$276$	5.29708	+	23.2809i	0.318847	+	1.40134i
$277$	−15.5155	−	5.04129i	−0.932236	−	0.302902i	−0.196760	−	0.980452i	$-0.563042\pi$
$277$	−15.5155	−	5.04129i	−0.932236	−	0.302902i	−0.735477	+	0.677550i	$0.763042\pi$
$278$	−17.3575	−	5.75418i	−1.04103	−	0.345113i
$279$	5.60799	−	2.85741i	0.335741	−	0.171069i
$280$	−0.271383	−	4.46606i	−0.0162182	−	0.266898i
$281$	−1.94761	+	8.11238i	−0.116185	+	0.483944i	0.883689	+	0.468074i	$0.155052\pi$
$281$	−1.94761	+	8.11238i	−0.116185	+	0.483944i	−0.999874	+	0.0158701i	$0.994948\pi$
$282$	−2.22504	−	0.0132382i	−0.132499	−	0.000788326i
$283$	19.3492	−	6.28692i	1.15019	−	0.373719i	0.328974	−	0.944339i	$-0.393297\pi$
$283$	19.3492	−	6.28692i	1.15019	−	0.373719i	0.821214	+	0.570620i	$0.193297\pi$
$284$	−7.10931	+	4.24107i	−0.421860	+	0.251661i
$285$	0.0690984	+	0.436270i	0.00409303	+	0.0258424i
$286$	−7.69019	+	3.86089i	−0.454731	+	0.228299i
$287$	9.77770	−	2.64493i	0.577159	−	0.156125i
$288$	3.69972	+	3.92666i	0.218008	+	0.231381i
$289$	−43.4660	+	6.88434i	−2.55682	+	0.404961i
$290$	7.08425	−	0.515153i	0.416002	−	0.0302508i
$291$	−2.56131	−	7.88291i	−0.150147	−	0.462104i
$292$	10.6174	+	21.4656i	0.621339	+	1.25618i
$293$	11.0714	+	2.65801i	0.646798	+	0.155282i	0.543555	−	0.839374i	$-0.317078\pi$
$293$	11.0714	+	2.65801i	0.646798	+	0.155282i	0.103243	+	0.994656i	$0.467078\pi$
$294$	−8.15639	−	9.66577i	−0.475690	−	0.563719i
$295$	2.86679	+	5.62639i	0.166911	+	0.327581i
$296$	−4.97386	+	3.47980i	−0.289100	+	0.202259i
$297$	5.75293	−	17.7057i	0.333819	−	1.02739i
$298$	−7.27588	−	1.79263i	−0.421480	−	0.103844i
$299$	−0.626420	+	7.95942i	−0.0362268	+	0.460305i
$300$	−0.359167	+	3.96054i	−0.0207365	+	0.228662i
$301$	−14.7322	+	6.10230i	−0.849153	+	0.351730i
$302$	10.0048	+	4.21401i	0.575709	+	0.242489i
$303$	−17.6023	−	24.2275i	−1.01123	−	1.39183i
$304$	0.320410	+	0.828792i	0.0183768	+	0.0475345i
$305$	0.606449	+	0.440611i	0.0347252	+	0.0252293i
$306$	0.889025	−	10.4973i	0.0508222	−	0.600089i
$307$	−14.9376	−	2.36589i	−0.852536	−	0.135028i	−0.285153	−	0.958482i	$-0.592044\pi$
$307$	−14.9376	−	2.36589i	−0.852536	−	0.135028i	−0.567384	+	0.823454i	$0.692044\pi$
$308$	10.3571	−	10.1136i	0.590153	−	0.576273i
$309$	−10.9859	−	6.73218i	−0.624967	−	0.382980i
$310$	9.20923	+	1.51482i	0.523049	+	0.0860359i
$311$	1.77926	+	22.6077i	0.100893	+	1.28196i	0.813982	+	0.580890i	$0.197295\pi$
$311$	1.77926	+	22.6077i	0.100893	+	1.28196i	−0.713089	+	0.701073i	$0.752705\pi$
$312$	3.27592	+	6.72338i	0.185462	+	0.380636i
$313$	−15.3885	−	18.0176i	−0.869807	−	1.01841i	−0.999639	−	0.0268772i	$-0.991444\pi$
$313$	−15.3885	−	18.0176i	−0.869807	−	1.01841i	0.129832	−	0.991536i	$-0.458556\pi$
$314$	24.6161	+	21.2787i	1.38917	+	1.20083i
$315$	−0.788289	−	1.28637i	−0.0444151	−	0.0724788i
$316$	−3.29771	+	3.76937i	−0.185511	+	0.212043i
$317$	−17.7044	+	20.7292i	−0.994380	+	1.16427i	−0.00797001	+	0.999968i	$0.502537\pi$
$317$	−17.7044	+	20.7292i	−0.994380	+	1.16427i	−0.986410	+	0.164301i	$0.947463\pi$
$318$	−2.68396	−	17.6239i	−0.150509	−	0.988297i
$319$	16.2498	+	16.2498i	0.909815	+	0.909815i
$320$	0.968674	+	7.94114i	0.0541505	+	0.443923i
$321$	−7.41961	−	30.9049i	−0.414122	−	1.72494i
$322$	−3.05774	−	13.0787i	−0.170401	−	0.728849i
$323$	0.787720	−	1.54599i	0.0438299	−	0.0860211i
$324$	−20.7491	−	7.01584i	−1.15273	−	0.389769i
$325$	−0.508903	+	1.22860i	−0.0282289	+	0.0681505i
$326$	−0.559178	+	0.401205i	−0.0309700	+	0.0222207i
$327$	−23.9708			−1.32559
$328$	−17.1634	+	5.78079i	−0.947691	+	0.319191i
$329$	1.25172			0.0690096
$330$	−10.4539	+	7.50061i	−0.575470	+	0.412895i
$331$	4.49298	−	10.8470i	0.246957	−	0.596206i	−0.750986	−	0.660318i	$-0.770422\pi$
$331$	4.49298	−	10.8470i	0.246957	−	0.596206i	0.997943	+	0.0641121i	$0.0204215\pi$
$332$	17.2681	+	5.83882i	0.947712	+	0.320447i
$333$	−0.929247	+	1.82375i	−0.0509224	+	0.0999408i
$334$	4.94854	+	21.1661i	0.270772	+	1.15816i
$335$	0.692823	+	2.88581i	0.0378529	+	0.157669i
$336$	−8.68245	−	9.10586i	−0.473666	−	0.496765i
$337$	9.27236	+	9.27236i	0.505098	+	0.505098i	0.913018	−	0.407920i	$-0.133746\pi$
$337$	9.27236	+	9.27236i	0.505098	+	0.505098i	−0.407920	+	0.913018i	$0.633746\pi$
$338$	−2.39139	−	15.7028i	−0.130075	−	0.854118i
$339$	18.1463	−	21.2466i	0.985572	−	1.15396i
$340$	10.2860	−	11.7571i	0.557835	−	0.637619i
$341$	15.7772	+	25.7460i	0.854382	+	1.39423i
$342$	0.226670	+	0.195938i	0.0122569	+	0.0105951i
$343$	11.8122	+	13.8303i	0.637799	+	0.746766i
$344$	25.6308	−	12.4885i	1.38192	−	0.673332i
$345$	0.936641	+	11.9011i	0.0504270	+	0.640736i
$346$	−5.50728	−	0.905888i	−0.296073	−	0.0487008i
$347$	−19.2155	−	11.7753i	−1.03154	−	0.632129i	−0.0997079	−	0.995017i	$-0.531791\pi$
$347$	−19.2155	−	11.7753i	−1.03154	−	0.632129i	−0.931833	+	0.362888i	$0.881791\pi$
$348$	14.2906	−	13.9544i	0.766054	−	0.748037i
$349$	23.3331	+	3.69560i	1.24899	+	0.197821i	0.745692	−	0.666291i	$-0.232119\pi$
$349$	23.3331	+	3.69560i	1.24899	+	0.197821i	0.503300	+	0.864112i	$0.332119\pi$
$350$	0.188791	−	2.22917i	0.0100913	−	0.119154i
$351$	−4.37745	−	3.18040i	−0.233651	−	0.169757i
$352$	−17.3876	+	19.1729i	−0.926762	+	1.02192i
$353$	−8.21314	−	11.3044i	−0.437141	−	0.601674i	0.532432	−	0.846473i	$-0.321278\pi$
$353$	−8.21314	−	11.3044i	−0.437141	−	0.601674i	−0.969574	+	0.244799i	$0.921278\pi$
$354$	16.3645	+	6.89275i	0.869763	+	0.366345i
$355$	−3.82404	+	1.58397i	−0.202959	+	0.0840684i
$356$	1.41866	−	15.6436i	0.0751888	−	0.829107i
$357$	−1.92761	+	24.4926i	−0.102020	+	1.29628i
$358$	−9.13981	−	2.25187i	−0.483054	−	0.119015i
$359$	−5.92658	+	18.2401i	−0.312793	+	0.962678i	0.663860	+	0.747857i	$0.268917\pi$
$359$	−5.92658	+	18.2401i	−0.312793	+	0.962678i	−0.976653	+	0.214822i	$0.931083\pi$
$360$	1.54636	+	2.21030i	0.0815005	+	0.116493i
$361$	−8.60342	−	16.8852i	−0.452811	−	0.888692i
$362$	−20.0062	−	23.7085i	−1.05151	−	1.24609i
$363$	−19.2093	−	4.61175i	−1.00823	−	0.242054i
$364$	−1.86534	−	3.77121i	−0.0977704	−	0.197665i
$365$	3.70015	+	11.3879i	0.193675	+	0.596070i
$366$	2.10237	−	0.152880i	0.109893	−	0.00799118i
$367$	−36.1624	+	5.72756i	−1.88766	+	0.298976i	−0.989929	−	0.141562i	$-0.954787\pi$
$367$	−36.1624	+	5.72756i	−1.88766	+	0.298976i	−0.897734	+	0.440539i	$0.854787\pi$
$368$	6.87551	+	23.0100i	0.358411	+	1.19948i
$369$	−4.19306	+	4.43972i	−0.218282	+	0.231122i
$370$	−2.71248	+	1.36181i	−0.141015	+	0.0707971i
$371$	1.56882	+	9.90515i	0.0814492	+	0.514250i
$372$	22.5387	−	13.4455i	1.16858	−	0.697116i
$373$	0.0540662	−	0.0175672i	0.00279944	−	0.000909593i	−0.307617	−	0.951510i	$-0.599532\pi$
$373$	0.0540662	−	0.0175672i	0.00279944	−	0.000909593i	0.310416	+	0.950601i	$0.399532\pi$
$374$	50.5404	+	0.300699i	2.61338	+	0.0155488i
$375$	−0.464182	+	1.93346i	−0.0239702	+	0.0998433i
$376$	−2.23394	+	0.135747i	−0.115207	+	0.00700062i
$377$	5.95115	−	3.03226i	0.306500	−	0.156169i
$378$	8.64015	+	2.86430i	0.444401	+	0.147324i
$379$	−35.5669	−	11.5564i	−1.82695	−	0.593612i	−0.999485	−	0.0320970i	$-0.989781\pi$
$379$	−35.5669	−	11.5564i	−1.82695	−	0.593612i	−0.827466	−	0.561515i	$-0.810219\pi$
$380$	0.0985687	+	0.433214i	0.00505647	+	0.0222234i
$381$	−21.6095	−	1.70070i	−1.10709	−	0.0871296i
$382$	−5.56582	+	8.96247i	−0.284772	+	0.458560i
$383$	−6.77497	−	16.3562i	−0.346185	−	0.835765i	−0.997063	−	0.0765824i	$-0.975599\pi$
$383$	−6.77497	−	16.3562i	−0.346185	−	0.835765i	0.650878	−	0.759182i	$-0.274401\pi$
$384$	16.4831	+	15.3096i	0.841148	+	0.781266i
$385$	5.85566	−	4.25439i	0.298432	−	0.216824i
$386$	12.8441	+	21.2423i	0.653747	+	1.08121i
$387$	5.65084	−	7.77772i	0.287249	−	0.395364i
$388$	−3.09854	−	7.73975i	−0.157304	−	0.392926i
$389$	−4.59733	+	29.0264i	−0.233094	+	1.47170i	0.542282	+	0.840197i	$0.317561\pi$
$389$	−4.59733	+	29.0264i	−0.233094	+	1.47170i	−0.775376	+	0.631500i	$0.782439\pi$
$390$	1.13439	+	3.56329i	0.0574420	+	0.180434i
$391$	24.5022	−	39.9839i	1.23913	−	2.02207i
$392$	−8.83319	−	9.15428i	−0.446144	−	0.462361i
$393$	35.7670	−	2.81493i	1.80421	−	0.141994i
$394$	3.77521	+	1.95195i	0.190192	+	0.0983376i
$395$	−1.90417	+	1.62631i	−0.0958092	+	0.0818288i
$396$	−2.13823	+	8.46151i	−0.107450	+	0.425207i
$397$	24.7115	−	15.1432i	1.24023	−	0.760016i	0.261511	−	0.965201i	$-0.415779\pi$
$397$	24.7115	−	15.1432i	1.24023	−	0.760016i	0.978723	+	0.205184i	$0.0657794\pi$
$398$	−31.0447	+	12.6433i	−1.55613	+	0.633750i
$399$	−0.531325	−	0.453795i	−0.0265995	−	0.0227182i
$400$	−0.0951845	+	3.99887i	−0.00475923	+	0.199943i
$401$	−0.550242	+	0.550242i	−0.0274778	+	0.0274778i	−0.720712	−	0.693234i	$-0.756185\pi$
$401$	−0.550242	+	0.550242i	−0.0274778	+	0.0274778i	0.693234	+	0.720712i	$0.256185\pi$
$402$	6.72238	+	4.94547i	0.335282	+	0.246658i
$403$	8.53360	−	2.04874i	0.425089	−	0.102055i
$404$	−19.2885	−	23.1358i	−0.959637	−	1.15105i
$405$	−9.75793	−	4.97191i	−0.484875	−	0.247056i
$406$	−7.99232	+	7.89778i	−0.396652	+	0.391960i
$407$	−9.07231	−	3.75787i	−0.449698	−	0.186271i
$408$	0.784018	−	43.9209i	0.0388147	−	2.17441i
$409$		−	30.3998i		−	1.50317i	−0.659634	−	0.751587i	$-0.729289\pi$
$409$		−	30.3998i		−	1.50317i	0.659634	−	0.751587i	$-0.270711\pi$
$410$	−8.90958	+	1.61846i	−0.440013	+	0.0799301i
$411$			0.460857i			0.0227324i
$412$	−11.4764	−	6.02060i	−0.565403	−	0.296614i
$413$	−9.22877	−	3.82268i	−0.454118	−	0.188102i
$414$	5.69178	+	5.75992i	0.279736	+	0.283084i
$415$	8.12088	+	4.13779i	0.398638	+	0.203116i
$416$	3.73805	+	6.52818i	0.183273	+	0.320070i
$417$	−25.0005	+	6.00208i	−1.22428	+	0.293923i
$418$	−0.851803	+	1.15786i	−0.0416631	+	0.0566326i
$419$	13.5639	−	13.5639i	0.662642	−	0.662642i	−0.293360	−	0.956002i	$-0.594774\pi$
$419$	13.5639	−	13.5639i	0.662642	−	0.662642i	0.956002	+	0.293360i	$0.0947736\pi$
$420$	−3.63688	−	5.13308i	−0.177461	−	0.250469i
$421$	−27.3264	−	23.3390i	−1.33181	−	1.13747i	−0.979468	−	0.201601i	$-0.935386\pi$
$421$	−27.3264	−	23.3390i	−1.33181	−	1.13747i	−0.352341	−	0.935872i	$-0.614614\pi$
$422$	0.405850	+	0.996538i	0.0197565	+	0.0485107i
$423$	−0.643449	+	0.394306i	−0.0312856	+	0.0191718i
$424$	−3.87407	−	17.5076i	−0.188142	−	0.850243i
$425$	5.93934	−	5.07268i	0.288100	−	0.246061i
$426$	−5.34572	+	10.3390i	−0.259001	+	0.500928i
$427$	−1.18216	+	0.0930379i	−0.0572087	+	0.00450242i
$428$	−9.51636	−	30.5193i	−0.459990	−	1.47521i
$429$	−6.32153	+	10.3158i	−0.305206	+	0.498052i
$430$	13.5840	−	4.32452i	0.655077	−	0.208547i
$431$	−2.57675	+	16.2690i	−0.124118	+	0.783649i	0.844584	+	0.535423i	$0.179848\pi$
$431$	−2.57675	+	16.2690i	−0.124118	+	0.783649i	−0.968702	+	0.248226i	$0.920152\pi$
$432$	−15.7307	−	4.17490i	−0.756843	−	0.200865i
$433$	−9.10740	+	12.5353i	−0.437674	+	0.602406i	−0.969693	−	0.244326i	$-0.921433\pi$
$433$	−9.10740	+	12.5353i	−0.437674	+	0.602406i	0.532019	+	0.846732i	$0.321433\pi$
$434$	−12.6339	+	7.63907i	−0.606449	+	0.366687i
$435$	8.07951	−	5.87011i	0.387383	−	0.281450i
$436$	−24.0572	+	1.60556i	−1.15213	+	0.0768925i
$437$	0.510386	+	1.23218i	0.0244151	+	0.0589432i
$438$	28.6040	+	17.7635i	1.36675	+	0.848773i
$439$	35.4688	+	2.79145i	1.69283	+	0.133229i	0.887869	−	0.460097i	$-0.152185\pi$
$439$	35.4688	+	2.79145i	1.69283	+	0.133229i	0.804962	+	0.593326i	$0.202185\pi$
$440$	−9.98922	+	8.22784i	−0.476217	+	0.392247i
$441$	−4.07949	−	1.32551i	−0.194262	−	0.0631194i
$442$	4.62230	−	13.9432i	0.219861	−	0.663209i
$443$	6.99918	−	3.56626i	0.332541	−	0.169438i	−0.279745	−	0.960074i	$-0.590250\pi$
$443$	6.99918	−	3.56626i	0.332541	−	0.169438i	0.612286	+	0.790636i	$0.290250\pi$
$444$	−3.35974	+	7.84576i	−0.159446	+	0.372343i
$445$	1.83345	−	7.63688i	0.0869140	−	0.362023i
$446$	−0.0864511	+	14.5304i	−0.00409358	+	0.688035i
$447$	−10.0202	+	3.25576i	−0.473939	+	0.153992i
$448$	−9.32364	−	8.55712i	−0.440501	−	0.404286i
$449$	−1.49248	−	9.42314i	−0.0704344	−	0.444705i	−0.997552	−	0.0699339i	$-0.977721\pi$
$449$	−1.49248	−	9.42314i	−0.0704344	−	0.444705i	0.927117	−	0.374772i	$-0.122279\pi$
$450$	0.605165	+	1.20538i	0.0285277	+	0.0568221i
$451$	−22.8123	−	18.3832i	−1.07419	−	0.865630i
$452$	16.7886	−	22.5386i	0.789669	−	1.06013i
$453$	15.0757	−	2.38776i	0.708319	−	0.112187i
$454$	0.746283	+	10.2627i	0.0350248	+	0.481652i
$455$	−0.650066	−	2.00070i	−0.0304756	−	0.0937942i
$456$	0.997469	+	0.752266i	0.0467108	+	0.0352281i
$457$	−26.3023	−	6.31463i	−1.23037	−	0.295386i	−0.434399	−	0.900720i	$-0.643039\pi$
$457$	−26.3023	−	6.31463i	−1.23037	−	0.295386i	−0.795971	+	0.605335i	$0.793039\pi$
$458$	−19.4697	+	16.4294i	−0.909759	+	0.767693i
$459$	14.4280	+	28.3166i	0.673444	+	1.32171i
$460$	1.73715	+	11.8813i	0.0809952	+	0.553968i
$461$	−8.97677	+	27.6277i	−0.418090	+	1.28675i	0.491368	+	0.870952i	$0.336497\pi$
$461$	−8.97677	+	27.6277i	−0.418090	+	1.28675i	−0.909458	+	0.415796i	$0.863503\pi$
$462$	4.86906	−	19.7624i	0.226529	−	0.919430i
$463$	−0.202152	+	2.56859i	−0.00939482	+	0.119372i	−0.999826	−	0.0186321i	$-0.994069\pi$
$463$	−0.202152	+	2.56859i	−0.00939482	+	0.119372i	0.990432	+	0.138005i	$0.0440689\pi$
$464$	13.4074	−	14.9619i	0.622422	−	0.694589i
$465$	12.1234	−	5.02167i	0.562208	−	0.232874i
$466$	−11.5329	+	27.3809i	−0.534250	+	1.26839i
$467$	11.8997	+	16.3785i	0.550652	+	0.757907i	0.990100	−	0.140361i	$-0.0448262\pi$
$467$	11.8997	+	16.3785i	0.550652	+	0.757907i	−0.439449	+	0.898268i	$0.644826\pi$
$468$	2.14685	+	1.35099i	0.0992384	+	0.0624497i
$469$	−3.79817	−	2.75953i	−0.175383	−	0.127423i
$470$	−1.11504	−	0.0944340i	−0.0514330	−	0.00435591i
$471$	45.1858	+	7.15673i	2.08205	+	0.329765i
$472$	16.8851	+	5.82149i	0.777201	+	0.267956i
$473$	39.3259	+	24.0989i	1.80821	+	1.10807i
$474$	−1.14293	+	6.94834i	−0.0524963	+	0.319148i
$475$	0.0174291	+	0.221458i	0.000799703	+	0.0101612i
$476$	−0.294042	+	24.7099i	−0.0134774	+	1.13258i
$477$	−3.92669	−	4.59756i	−0.179791	−	0.210508i
$478$	−0.366236	+	0.423677i	−0.0167513	+	0.0193785i
$479$	−6.32865	−	10.3274i	−0.289163	−	0.471872i	0.674765	−	0.738032i	$-0.264245\pi$
$479$	−6.32865	−	10.3274i	−0.289163	−	0.471872i	−0.963929	+	0.266161i	$0.914245\pi$
$480$	7.04740	+	8.76659i	0.321668	+	0.400138i
$481$	−1.85355	+	2.17022i	−0.0845144	+	0.0989537i
$482$	36.4178	−	5.54612i	1.65879	−	0.252619i
$483$	−13.3535	−	13.3535i	−0.607604	−	0.607604i
$484$	−19.5874	−	3.34173i	−0.890338	−	0.151897i
$485$	−0.973111	−	4.05330i	−0.0441867	−	0.184051i
$486$	−13.1781	+	3.08098i	−0.597772	+	0.139756i
$487$	−2.03805	+	3.99989i	−0.0923527	+	0.181252i	−0.932562	−	0.361010i	$-0.882432\pi$
$487$	−2.03805	+	3.99989i	−0.0923527	+	0.181252i	0.840209	+	0.542262i	$0.182432\pi$
$488$	2.09971	−	0.294248i	0.0950493	−	0.0133200i
$489$	−0.370300	+	0.893984i	−0.0167456	+	0.0404274i
$490$	−3.70795	−	5.16794i	−0.167508	−	0.233464i
$491$	−16.0176			−0.722865			−0.361433	−	0.932398i	$-0.617712\pi$
$491$	−16.0176			−0.722865			−0.361433	+	0.932398i	$0.617712\pi$
$492$	−16.2125	+	19.6358i	−0.730916	+	0.885250i
$493$	−39.2299			−1.76683
$494$	0.243547	+	0.339443i	0.0109577	+	0.0152722i
$495$	−1.66993	+	4.03158i	−0.0750579	+	0.181206i
$496$	21.7193	−	15.0036i	0.975227	−	0.673680i
$497$	2.97258	−	5.83402i	0.133338	−	0.261692i
$498$	24.9565	−	5.83471i	1.11833	−	0.261460i
$499$	−3.53113	−	14.7082i	−0.158075	−	0.658430i	−0.993981	−	0.109557i	$-0.965057\pi$
$499$	−3.53113	−	14.7082i	−0.158075	−	0.658430i	0.835905	−	0.548874i	$-0.184943\pi$
$500$	−0.336352	+	1.97151i	−0.0150421	+	0.0881688i
$501$	21.6108	+	21.6108i	0.965499	+	0.965499i
$502$	27.1034	−	4.12761i	1.20968	−	0.184224i
$503$	2.08551	−	2.44182i	0.0929882	−	0.108875i	−0.711961	−	0.702219i	$-0.752193\pi$
$503$	2.08551	−	2.44182i	0.0929882	−	0.108875i	0.804949	+	0.593344i	$0.202193\pi$
$504$	−4.13088	−	1.07006i	−0.184004	−	0.0476643i
$505$	−7.86924	−	12.8414i	−0.350177	−	0.571436i
$506$	−25.4058	+	29.3904i	−1.12942	+	1.30656i
$507$	−14.5040	−	16.9820i	−0.644145	−	0.754196i
$508$	−21.8012	−	0.259429i	−0.967273	−	0.0115103i
$509$	0.463501	+	5.88933i	0.0205443	+	0.261040i	0.998608	+	0.0527363i	$0.0167943\pi$
$509$	0.463501	+	5.88933i	0.0205443	+	0.261040i	−0.978064	+	0.208304i	$0.933206\pi$
$510$	3.56493	−	21.6727i	0.157858	−	0.959684i
$511$	−16.1504	−	9.89696i	−0.714450	−	0.437816i
$512$	17.5679	+	14.2607i	0.776399	+	0.630242i
$513$	−0.892731	−	0.141395i	−0.0394150	−	0.00624273i
$514$	−22.6564	−	1.91879i	−0.999331	−	0.0846344i
$515$	−5.24234	−	3.80878i	−0.231005	−	0.167835i
$516$	21.3508	−	33.9284i	0.939916	−	1.49361i
$517$	−2.12807	−	2.92903i	−0.0935923	−	0.128819i
$518$	1.86373	−	4.42481i	0.0818878	−	0.194415i
$519$	−7.25000	+	3.00305i	−0.318240	+	0.131819i
$520$	1.37714	+	3.50014i	0.0603918	+	0.153492i
$521$	1.60778	−	20.4288i	0.0704382	−	0.895003i	−0.855616	−	0.517612i	$-0.826821\pi$
$521$	1.60778	−	20.4288i	0.0704382	−	0.895003i	0.926054	−	0.377391i	$-0.123179\pi$
$522$	1.62058	−	6.57753i	0.0709306	−	0.287891i
$523$	−6.98482	+	21.4971i	−0.305425	+	0.940001i	0.674093	+	0.738646i	$0.264534\pi$
$523$	−6.98482	+	21.4971i	−0.305425	+	0.940001i	−0.979518	+	0.201355i	$0.935466\pi$
$524$	35.7074	−	5.22074i	1.55988	−	0.228069i
$525$	−1.42800	−	2.80262i	−0.0623232	−	0.122316i
$526$	−3.33174	+	2.81146i	−0.145271	+	0.122586i
$527$	−50.1221	−	12.0333i	−2.18336	−	0.524177i
$528$	−6.54662	+	35.7980i	−0.284905	+	1.55791i
$529$	4.03135	+	12.4072i	0.175276	+	0.539444i
$530$	−0.650239	−	8.94193i	−0.0282446	−	0.388413i
$531$	5.94825	−	0.942111i	0.258132	−	0.0408841i
$532$	−0.563635	−	0.419842i	−0.0244367	−	0.0182024i
$533$	−7.13025	+	4.65465i	−0.308845	+	0.201615i
$534$	−9.90924	−	19.7374i	−0.428815	−	0.854121i
$535$	−2.50049	−	15.7875i	−0.108106	−	0.682553i
$536$	7.07785	+	4.51303i	0.305717	+	0.194933i
$537$	−12.5872	+	4.08982i	−0.543177	+	0.176489i
$538$	−0.0903500	+	15.1857i	−0.00389527	+	0.654703i
$539$	4.80401	−	20.0101i	0.206923	−	0.861897i
$540$	−7.48061	−	3.20338i	−0.321914	−	0.137851i
$541$	−13.6904	+	6.97559i	−0.588595	+	0.299904i	−0.722808	−	0.691048i	$-0.757149\pi$
$541$	−13.6904	+	6.97559i	−0.588595	+	0.299904i	0.134214	+	0.990952i	$0.457149\pi$
$542$	9.68992	−	29.2296i	0.416218	−	1.25552i
$543$	−41.4819	−	13.4783i	−1.78016	−	0.578409i
$544$	−2.15498	−	44.1317i	−0.0923939	−	1.89213i
$545$	−12.0182	−	0.945852i	−0.514802	−	0.0405158i
$546$	−5.02533	−	3.12081i	−0.215064	−	0.133558i
$547$	−12.6791	−	30.6102i	−0.542121	−	1.30880i	−0.923224	−	0.384263i	$-0.874455\pi$
$547$	−12.6791	−	30.6102i	−0.542121	−	1.30880i	0.381102	−	0.924533i	$-0.375545\pi$
$548$	0.0308682	+	0.462517i	0.00131862	+	0.0197578i
$549$	0.578383	−	0.420220i	0.0246848	−	0.0179345i
$550$	−5.53723	+	3.34807i	−0.236108	+	0.142762i
$551$	0.655806	−	0.902640i	0.0279383	−	0.0384538i
$552$	25.2801	+	22.3838i	1.07599	+	0.952717i
$553$	0.619687	−	3.91255i	0.0263518	−	0.166379i
$554$	−21.9843	+	6.99879i	−0.934022	+	0.297350i
$555$	−2.22973	+	3.63858i	−0.0946466	+	0.154449i
$556$	−24.6885	+	7.69823i	−1.04703	+	0.326478i
$557$	−10.5543	+	0.830643i	−0.447201	+	0.0351955i	−0.300061	−	0.953920i	$-0.597007\pi$
$557$	−10.5543	+	0.830643i	−0.447201	+	0.0351955i	−0.147140	+	0.989116i	$0.547007\pi$
$558$	4.08811	−	7.90671i	0.173063	−	0.334718i
$559$	10.1933	−	8.70590i	0.431131	−	0.368220i
$560$	−3.99379	−	4.90798i	−0.168769	−	0.207400i
$561$	60.5899	−	37.1295i	2.55811	−	1.56761i
$562$	4.45021	+	10.9272i	0.187721	+	0.460935i
$563$	17.0787	+	14.5866i	0.719783	+	0.614752i	0.931995	−	0.362471i	$-0.118067\pi$
$563$	17.0787	+	14.5866i	0.719783	+	0.614752i	−0.212212	+	0.977224i	$0.568067\pi$
$564$	−2.56759	+	1.81918i	−0.108115	+	0.0766015i
$565$	9.93633	−	9.93633i	0.418024	−	0.418024i
$566$	17.0500	−	23.1760i	0.716664	−	0.974162i
$567$	16.8457	−	4.04428i	0.707451	−	0.169844i
$568$	−4.67247	+	10.7343i	−0.196053	+	0.450403i
$569$	17.0485	+	8.68665i	0.714710	+	0.364163i	0.773232	−	0.634123i	$-0.218639\pi$
$569$	17.0485	+	8.68665i	0.714710	+	0.364163i	−0.0585218	+	0.998286i	$0.518639\pi$
$570$	0.439072	+	0.444328i	0.0183907	+	0.0186109i
$571$	−2.20177	−	0.912004i	−0.0921413	−	0.0381662i	0.336137	−	0.941813i	$-0.390880\pi$
$571$	−2.20177	−	0.912004i	−0.0921413	−	0.0381662i	−0.428278	+	0.903647i	$0.640880\pi$
$572$	−5.65336	+	10.7764i	−0.236379	+	0.450583i
$573$			14.8335i			0.619678i
$574$	9.05448	−	11.1002i	0.377927	−	0.463314i
$575$			6.00381i			0.250376i
$576$	7.48842	+	1.46175i	0.312018	+	0.0609062i
$577$	10.8973	+	4.51382i	0.453661	+	0.187913i	0.597801	−	0.801645i	$-0.296041\pi$
$577$	10.8973	+	4.51382i	0.453661	+	0.187913i	−0.144139	+	0.989557i	$0.546041\pi$
$578$	−44.2688	+	43.7452i	−1.84134	+	1.81956i
$579$	31.0980	+	15.8452i	1.29239	+	0.658504i
$580$	7.71544	−	6.43242i	0.320366	−	0.267092i
$581$	−14.0195	+	3.36579i	−0.581628	+	0.139637i
$582$	−9.44199	−	6.94621i	−0.391383	−	0.287930i
$583$	20.5109	−	20.5109i	0.849476	−	0.849476i
$584$	29.8969	+	15.9116i	1.23714	+	0.658427i
$585$	0.964410	+	0.823684i	0.0398734	+	0.0340551i
$586$	14.9129	−	6.07344i	0.616047	−	0.250891i
$587$	−12.9091	+	7.91073i	−0.532817	+	0.326511i	−0.762748	−	0.646696i	$-0.776150\pi$
$587$	−12.9091	+	7.91073i	−0.532817	+	0.326511i	0.229930	+	0.973207i	$0.426150\pi$
$588$	−17.3409	−	4.38204i	−0.715125	−	0.180712i
$589$	1.11477	−	0.952100i	0.0459331	−	0.0392306i
$590$	7.93265	+	4.10152i	0.326582	+	0.168857i
$591$	5.95709	−	0.468833i	0.245042	−	0.0192852i
$592$	−2.84634	+	8.09907i	−0.116984	+	0.332870i
$593$	−11.1266	+	18.1569i	−0.456913	+	0.745615i	−0.995275	−	0.0970992i	$-0.969044\pi$
$593$	−11.1266	+	18.1569i	−0.456913	+	0.745615i	0.538361	+	0.842714i	$0.319044\pi$
$594$	−7.98676	−	25.0876i	−0.327701	−	1.02936i
$595$	−1.93288	+	12.2037i	−0.0792403	+	0.500304i
$596$	−9.83824	+	3.93865i	−0.402990	+	0.161333i
$597$	−27.7024	+	38.1291i	−1.13378	+	1.56052i
$598$	5.84222	+	9.66220i	0.238906	+	0.395117i
$599$	4.52191	−	3.28536i	0.184760	−	0.134236i	−0.491561	−	0.870843i	$-0.663573\pi$
$599$	4.52191	−	3.28536i	0.184760	−	0.134236i	0.676321	+	0.736607i	$0.263573\pi$
$600$	2.85250	+	4.84696i	0.116453	+	0.197876i
$601$	−6.06924	−	14.6524i	−0.247569	−	0.597685i	0.750427	−	0.660953i	$-0.229848\pi$
$601$	−6.06924	−	14.6524i	−0.247569	−	0.597685i	−0.997997	+	0.0632677i	$0.979848\pi$
$602$	−11.8971	+	19.1576i	−0.484891	+	0.780804i
$603$	2.82174	+	0.222076i	0.114910	+	0.00904362i
$604$	14.9701	−	3.40613i	0.609125	−	0.138594i
$605$	−9.44896	−	3.07015i	−0.384155	−	0.124820i
$606$	−40.1998	−	13.3266i	−1.63301	−	0.541358i
$607$	1.91027	−	0.973333i	0.0775356	−	0.0395064i	−0.414793	−	0.909916i	$-0.636146\pi$
$607$	1.91027	−	0.973333i	0.0775356	−	0.0395064i	0.492328	+	0.870410i	$0.336146\pi$
$608$	1.05145	+	0.688166i	0.0426419	+	0.0279088i
$609$	−3.68801	+	15.3617i	−0.149446	+	0.622486i
$610$	1.06009	+	0.00630720i	0.0429219	+	0.000255371i
$611$	−1.00076	+	0.325166i	−0.0404864	+	0.0131548i
$612$	−7.63276	−	12.7948i	−0.308536	−	0.517200i
$613$	−5.04617	−	31.8603i	−0.203813	−	1.28683i	−0.851272	−	0.524725i	$-0.824168\pi$
$613$	−5.04617	−	31.8603i	−0.203813	−	1.28683i	0.647459	−	0.762100i	$-0.275832\pi$
$614$	−19.1146	+	9.59655i	−0.771402	+	0.387285i
$615$	−9.44134	+	8.54188i	−0.380711	+	0.344442i
$616$	3.56293	−	20.1597i	0.143554	−	0.812259i
$617$	21.2840	−	3.37105i	0.856861	−	0.135714i	0.287480	−	0.957787i	$-0.407183\pi$
$617$	21.2840	−	3.37105i	0.856861	−	0.135714i	0.569382	+	0.822073i	$0.307183\pi$
$618$	−18.1736	+	1.32155i	−0.731048	+	0.0531604i
$619$	−0.233555	−	0.718808i	−0.00938736	−	0.0288913i	0.946253	−	0.323427i	$-0.104835\pi$
$619$	−0.233555	−	0.718808i	−0.00938736	−	0.0288913i	−0.955640	+	0.294536i	$0.904835\pi$
$620$	11.8307	−	5.85179i	0.475133	−	0.235013i
$621$	−23.7534	−	5.70270i	−0.953193	−	0.228841i
$622$	20.6829	+	24.5104i	0.829311	+	0.982778i
$623$	5.64041	+	11.0699i	0.225978	+	0.443507i
$624$	9.30715	+	5.02471i	0.372584	+	0.201149i
$625$	−0.309017	+	0.951057i	−0.0123607	+	0.0380423i
$626$	−32.5363	−	8.01632i	−1.30041	−	0.320396i
$627$	−0.158569	+	2.01481i	−0.00633263	+	0.0804636i
$628$	45.8280	+	4.15598i	1.82874	+	0.165842i
$629$	15.4872	−	6.41499i	0.617513	−	0.255782i
$630$	−1.96631	−	0.828211i	−0.0783396	−	0.0329967i
$631$	−6.64859	−	9.15100i	−0.264676	−	0.364296i	0.655907	−	0.754842i	$-0.272286\pi$
$631$	−6.64859	−	9.15100i	−0.264676	−	0.364296i	−0.920583	+	0.390546i	$0.872286\pi$
$632$	−0.681645	+	7.04993i	−0.0271144	+	0.280431i
$633$	1.22395	+	0.889250i	0.0486476	+	0.0353445i
$634$	−3.25341	+	38.4150i	−0.129209	+	1.52565i
$635$	−10.7672	−	1.70535i	−0.427282	−	0.0676749i
$636$	−17.6137	−	18.0379i	−0.698427	−	0.715250i
$637$	−5.09965	−	3.12507i	−0.202056	−	0.123820i
$638$	32.0687	+	5.27495i	1.26961	+	0.208837i
$639$	0.309721	+	3.93538i	0.0122524	+	0.155681i
$640$	7.65998	+	8.32614i	0.302787	+	0.329120i
$641$	−11.3910	−	13.3372i	−0.449919	−	0.526788i	0.488371	−	0.872636i	$-0.337591\pi$
$641$	−11.3910	−	13.3372i	−0.449919	−	0.526788i	−0.938290	+	0.345848i	$0.887591\pi$
$642$	−34.0045	−	29.3943i	−1.34205	−	1.16010i
$643$	13.9041	+	22.6894i	0.548323	+	0.894782i	0.999997	+	0.00259884i	$0.000827236\pi$
$643$	13.9041	+	22.6894i	0.548323	+	0.894782i	−0.451673	+	0.892183i	$0.649173\pi$
$644$	−14.2960	−	12.5072i	−0.563342	−	0.492852i
$645$	13.0173	−	15.2413i	0.512556	−	0.600126i
$646$	−0.369434	−	2.42584i	−0.0145352	−	0.0954432i
$647$	−27.9755	−	27.9755i	−1.09983	−	1.09983i	−0.994430	−	0.105402i	$-0.966387\pi$
$647$	−27.9755	−	27.9755i	−1.09983	−	1.09983i	−0.105402	−	0.994430i	$-0.533613\pi$
$648$	−29.6258	+	9.04471i	−1.16381	+	0.355310i
$649$	6.74486	+	28.0944i	0.264759	+	1.10280i
$650$	0.428144	+	1.83128i	0.0167932	+	0.0718286i
$651$	−9.42399	+	18.4956i	−0.369355	+	0.724901i
$652$	−0.311756	+	0.922008i	−0.0122093	+	0.0361086i
$653$	−0.593405	+	1.43261i	−0.0232217	+	0.0560622i	−0.935065	−	0.354476i	$-0.884659\pi$
$653$	−0.593405	+	1.43261i	−0.0232217	+	0.0560622i	0.911843	+	0.410538i	$0.134659\pi$
$654$	−27.5436	+	19.7623i	−1.07704	+	0.772767i
$655$	18.0435			0.705018
$656$	−14.9557	+	20.7925i	−0.583923	+	0.811809i
$657$	11.4198			0.445528
$658$	1.43829	−	1.03196i	0.0560703	−	0.0402299i
$659$	7.26630	−	17.5424i	0.283055	−	0.683355i	−0.716849	−	0.697228i	$-0.754416\pi$
$659$	7.26630	−	17.5424i	0.283055	−	0.683355i	0.999904	+	0.0138739i	$0.00441634\pi$
$660$	−5.82833	+	17.2371i	−0.226868	+	0.670954i
$661$	11.4001	−	22.3740i	0.443412	−	0.870246i	−0.555829	−	0.831297i	$-0.687599\pi$
$661$	11.4001	−	22.3740i	0.443412	−	0.870246i	0.999241	−	0.0389491i	$-0.0124010\pi$
$662$	−3.77998	−	16.1679i	−0.146913	−	0.628383i
$663$	−4.82144	−	20.0827i	−0.187249	−	0.779948i
$664$	24.6556	−	7.52732i	0.956823	−	0.292117i
$665$	−0.248483	−	0.248483i	−0.00963577	−	0.00963577i
$666$	0.435808	+	2.86168i	0.0168872	+	0.110888i
$667$	19.5837	−	22.9296i	0.758285	−	0.887838i
$668$	23.1361	+	20.2412i	0.895164	+	0.783154i
$669$	10.6748	+	17.4197i	0.412711	+	0.673483i
$670$	3.17524	+	2.74475i	0.122670	+	0.106039i
$671$	2.22751	+	2.60808i	0.0859922	+	0.100684i
$672$	−17.4837	−	3.30498i	−0.674449	−	0.127492i
$673$	2.67855	+	34.0342i	0.103251	+	1.31192i	0.802331	+	0.596880i	$0.203593\pi$
$673$	2.67855	+	34.0342i	0.103251	+	1.31192i	−0.699080	+	0.715043i	$0.746407\pi$
$674$	18.2988	+	3.00996i	0.704844	+	0.115939i
$675$	−3.46924	−	2.12595i	−0.133531	−	0.0818279i
$676$	−15.6937	−	16.0717i	−0.603604	−	0.618142i
$677$	24.4571	+	3.87363i	0.939964	+	0.148876i	0.607571	−	0.794265i	$-0.292144\pi$
$677$	24.4571	+	3.87363i	0.939964	+	0.148876i	0.332393	+	0.943141i	$0.392144\pi$
$678$	3.33460	−	39.3738i	0.128065	−	1.51214i
$679$	5.33475	+	3.87593i	0.204729	+	0.148744i
$680$	2.12613	−	21.9896i	0.0815335	−	0.843262i
$681$	8.50381	+	11.7045i	0.325867	+	0.448517i
$682$	39.3546	+	16.5762i	1.50697	+	0.634736i
$683$	11.9693	−	4.95783i	0.457991	−	0.189706i	−0.141746	−	0.989903i	$-0.545272\pi$
$683$	11.9693	−	4.95783i	0.457991	−	0.189706i	0.599737	+	0.800197i	$0.295272\pi$
$684$	0.421992	+	0.0382690i	0.0161353	+	0.00146325i
$685$	−0.0181847	+	0.231059i	−0.000694802	+	0.00882830i
$686$	24.9749	+	6.15333i	0.953547	+	0.234935i
$687$	−11.0685	+	34.0654i	−0.422291	+	1.29968i
$688$	19.1552	−	35.4807i	0.730285	−	1.35269i
$689$	−3.82740	−	7.51170i	−0.145812	−	0.286173i
$690$	10.8879	+	12.9028i	0.414497	+	0.491201i
$691$	24.9088	+	5.98008i	0.947576	+	0.227493i	0.677647	−	0.735387i	$-0.263000\pi$
$691$	24.9088	+	5.98008i	0.947576	+	0.227493i	0.269929	+	0.962880i	$0.413000\pi$
$692$	−7.07498	+	3.49947i	−0.268950	+	0.133030i
$693$	−2.13315	−	6.56516i	−0.0810317	−	0.249390i
$694$	−31.7874	+	2.31152i	−1.20663	+	0.0877440i
$695$	−12.7713	+	2.02277i	−0.484441	+	0.0767279i
$696$	4.91604	−	27.8159i	0.186342	−	1.05436i
$697$	49.7266	−	5.34640i	1.88353	−	0.202509i
$698$	29.8576	−	14.9901i	1.13013	−	0.567385i
$699$	6.53479	+	41.2591i	0.247169	+	1.56056i
$700$	−1.62087	−	2.71707i	−0.0612631	−	0.102695i
$701$	20.5656	−	6.68216i	0.776751	−	0.252382i	0.106298	−	0.994334i	$-0.466100\pi$
$701$	20.5656	−	6.68216i	0.776751	−	0.252382i	0.670452	+	0.741953i	$0.266100\pi$
$702$	−7.65193	−	0.0455264i	−0.288803	−	0.00171828i
$703$	−0.111296	+	0.463583i	−0.00419763	+	0.0174844i
$704$	−4.17246	+	36.3654i	−0.157255	+	1.37057i
$705$	−1.40188	+	0.714295i	−0.0527979	+	0.0269019i
$706$	−18.7570	−	6.21815i	−0.705930	−	0.234023i
$707$	22.6586	+	7.36224i	0.852166	+	0.276885i
$708$	24.4862	−	5.57132i	0.920248	−	0.209383i
$709$	−9.58597	−	0.754432i	−0.360009	−	0.0283333i	−0.102835	−	0.994698i	$-0.532791\pi$
$709$	−9.58597	−	0.754432i	−0.360009	−	0.0283333i	−0.257174	+	0.966365i	$0.582791\pi$
$710$	−3.08813	+	4.97272i	−0.115896	+	0.186623i
$711$	0.913946	+	2.20646i	0.0342757	+	0.0827487i
$712$	−11.2670	−	19.1448i	−0.422247	−	0.717482i
$713$	32.0546	−	23.2890i	1.20045	−	0.872180i
$714$	17.9776	+	29.7323i	0.672793	+	1.11270i
$715$	−3.57646	+	4.92257i	−0.133752	+	0.184094i
$716$	−12.3586	+	4.94765i	−0.461863	+	0.184902i
$717$	−0.123177	+	0.777710i	−0.00460013	+	0.0290441i
$718$	8.22783	+	25.8449i	0.307060	+	0.964522i
$719$	3.08197	−	5.02932i	0.114938	−	0.187562i	−0.789998	−	0.613109i	$-0.789918\pi$
$719$	3.08197	−	5.02932i	0.114938	−	0.187562i	0.904936	+	0.425548i	$0.139918\pi$
$720$	3.59908	+	1.26486i	0.134130	+	0.0471387i
$721$	10.2190	−	0.804249i	0.380574	−	0.0299518i
$722$	−23.8064	−	12.3089i	−0.885983	−	0.458091i
$723$	39.3846	−	33.6376i	1.46473	−	1.25100i
$724$	−42.5342	−	10.7484i	−1.58077	−	0.399461i
$725$	4.28243	−	2.62428i	0.159045	−	0.0974632i
$726$	−25.8745	+	10.5377i	−0.960294	+	0.391089i
$727$	33.6848	+	28.7695i	1.24930	+	1.06700i	0.995000	+	0.0998759i	$0.0318446\pi$
$727$	33.6848	+	28.7695i	1.24930	+	1.06700i	0.254299	+	0.967126i	$0.418155\pi$
$728$	−5.25247	−	2.79545i	−0.194670	−	0.103606i
$729$	9.77683	−	9.77683i	0.362105	−	0.362105i
$730$	13.6402	+	10.0347i	0.504846	+	0.371401i
$731$	−76.5593	+	18.3803i	−2.83165	+	0.679819i
$732$	2.28969	−	1.90893i	0.0846293	−	0.0705561i
$733$	−30.0627	−	15.3177i	−1.11039	−	0.565772i	−0.200114	−	0.979773i	$-0.564131\pi$
$733$	−30.0627	−	15.3177i	−1.11039	−	0.565772i	−0.910277	+	0.414000i	$0.864131\pi$
$734$	−36.8304	+	36.3947i	−1.35943	+	1.34335i
$735$	−8.26224	−	3.42233i	−0.304757	−	0.126235i
$736$	26.8705	+	20.7712i	0.990458	+	0.765636i
$737$			13.5792i			0.500198i
$738$	−1.15778	+	8.55834i	−0.0426184	+	0.315037i
$739$		−	10.4738i		−	0.385287i	−0.981269	−	0.192643i	$-0.938294\pi$
$739$		−	10.4738i		−	0.385287i	0.981269	−	0.192643i	$-0.0617060\pi$
$740$	−1.99405	+	3.80104i	−0.0733027	+	0.139729i
$741$	0.542683	+	0.224787i	0.0199360	+	0.00825775i
$742$	9.96878	+	10.0881i	0.365965	+	0.370346i
$743$	32.4439	+	16.5310i	1.19025	+	0.606463i	0.932998	−	0.359881i	$-0.117183\pi$
$743$	32.4439	+	16.5310i	1.19025	+	0.606463i	0.257253	+	0.966344i	$0.417183\pi$
$744$	14.8132	−	34.0311i	0.543077	−	1.24764i
$745$	−5.15227	+	1.23695i	−0.188765	+	0.0453184i
$746$	0.0476417	−	0.0647594i	0.00174429	−	0.00237101i
$747$	6.14650	−	6.14650i	0.224889	−	0.224889i
$748$	58.3213	−	41.3216i	2.13244	−	1.51087i
$749$	19.2273	+	16.4217i	0.702550	+	0.600035i
$750$	1.06064	+	2.60432i	0.0387290	+	0.0950964i
$751$	0.856707	−	0.524991i	0.0312617	−	0.0191572i	−0.506780	−	0.862075i	$-0.669164\pi$
$751$	0.856707	−	0.524991i	0.0312617	−	0.0191572i	0.538042	+	0.842918i	$0.319164\pi$
$752$	−2.45500	+	1.99772i	−0.0895245	+	0.0728492i
$753$	29.3113	−	25.0342i	1.06816	−	0.912299i
$754$	4.33826	−	8.39053i	0.157990	−	0.305565i
$755$	7.65269	−	0.602280i	0.278510	−	0.0219192i
$756$	12.2894	−	3.83200i	0.446960	−	0.139368i
$757$	5.22497	−	8.52638i	0.189905	−	0.309896i	−0.743490	−	0.668747i	$-0.766831\pi$
$757$	5.22497	−	8.52638i	0.189905	−	0.309896i	0.933395	+	0.358850i	$0.116831\pi$
$758$	−50.3956	+	16.0437i	−1.83045	+	0.582732i
$759$	−8.54478	+	53.9496i	−0.310156	+	1.95825i
$760$	0.470415	+	0.416520i	0.0170638	+	0.0151088i
$761$	18.8313	−	25.9191i	0.682634	−	0.939565i	−0.317328	−	0.948316i	$-0.602785\pi$
$761$	18.8313	−	25.9191i	0.682634	−	0.939565i	0.999962	+	0.00875065i	$0.00278546\pi$
$762$	−26.2324	+	15.8613i	−0.950300	+	0.574596i
$763$	15.4283	−	11.2093i	0.558541	−	0.405803i
$764$	0.993547	+	14.8870i	0.0359453	+	0.538591i
$765$	−2.85071	−	6.88222i	−0.103068	−	0.248827i
$766$	−21.2694	−	13.2086i	−0.768494	−	0.477246i
$767$	8.37150	+	0.658852i	0.302277	+	0.0237897i
$768$	31.5616	+	4.00232i	1.13888	+	0.144421i
$769$	0.125448	+	0.0407606i	0.00452378	+	0.00146987i	0.311278	−	0.950319i	$-0.399243\pi$
$769$	0.125448	+	0.0407606i	0.00452378	+	0.00146987i	−0.306754	+	0.951789i	$0.599243\pi$
$770$	3.22099	−	9.71610i	0.116076	−	0.350144i
$771$	−28.4847	+	14.5137i	−1.02585	+	0.522697i
$772$	32.2713	+	13.8194i	1.16147	+	0.497370i
$773$	7.49879	−	31.2347i	0.269713	−	1.12344i	−0.658854	−	0.752271i	$-0.728959\pi$
$773$	7.49879	−	31.2347i	0.269713	−	1.12344i	0.928567	−	0.371164i	$-0.121041\pi$
$774$	0.0808899	−	13.5957i	0.00290753	−	0.488688i
$775$	6.27642	−	2.03933i	0.225456	−	0.0732550i
$776$	−9.94127	−	6.33882i	−0.356871	−	0.227550i
$777$	−1.05604	−	6.66755i	−0.0378851	−	0.239197i
$778$	18.6477	+	37.1429i	0.668554	+	1.33164i
$779$	−0.708265	+	1.23353i	−0.0253762	+	0.0441960i
$780$	4.24116	+	3.15916i	0.151858	+	0.113116i
$781$	−18.7054	+	2.96264i	−0.669330	+	0.106012i
$782$	−4.80985	−	66.1438i	−0.172000	−	2.36530i
$783$	6.31502	+	19.4356i	0.225680	+	0.694573i
$784$	−17.6968	−	3.23634i	−0.632030	−	0.115584i
$785$	22.3723	+	5.37112i	0.798502	+	0.191703i
$786$	38.7773	−	32.7220i	1.38314	−	1.16715i
$787$	15.9115	+	31.2280i	0.567183	+	1.11316i	0.979373	+	0.202061i	$0.0647641\pi$
$787$	15.9115	+	31.2280i	0.567183	+	1.11316i	−0.412190	+	0.911098i	$0.635236\pi$
$788$	5.94715	−	0.869527i	0.211858	−	0.0309756i
$789$	−1.89410	+	5.82943i	−0.0674316	+	0.207533i
$790$	−0.847197	+	3.43857i	−0.0301419	+	0.122339i
$791$	−1.74407	+	22.1605i	−0.0620120	+	0.787937i
$792$	4.51901	+	11.4855i	0.160576	+	0.408120i
$793$	0.920975	−	0.381480i	0.0327048	−	0.0135468i
$794$	15.9101	−	37.7732i	0.564629	−	1.34052i
$795$	−7.40940	−	10.1982i	−0.262784	−	0.361692i
$796$	−25.2483	+	40.1220i	−0.894903	+	1.42209i
$797$	−10.8483	−	7.88174i	−0.384266	−	0.279186i	0.378836	−	0.925464i	$-0.376324\pi$
$797$	−10.8483	−	7.88174i	−0.384266	−	0.279186i	−0.763102	+	0.646278i	$0.776324\pi$
$798$	−0.984642	−	0.0833903i	−0.0348559	−	0.00295198i
$799$	6.10436	+	0.966836i	0.215957	+	0.0342042i
$800$	3.18742	+	4.67336i	0.112692	+	0.165228i
$801$	−6.38662	−	3.91372i	−0.225660	−	0.138285i
$802$	−0.178617	+	1.08589i	−0.00630720	+	0.0383442i
$803$	4.29852	+	54.6179i	0.151692	+	1.92742i
$804$	11.8015	+	0.140435i	0.416208	+	0.00495278i
$805$	−6.16809	−	7.22191i	−0.217397	−	0.254539i
$806$	8.11648	−	9.38948i	0.285891	−	0.330730i
$807$	11.1562	+	18.2053i	0.392717	+	0.640856i
$808$	−41.2373	−	10.6821i	−1.45072	−	0.375794i
$809$	−29.2470	+	34.2438i	−1.02827	+	1.20395i	−0.0495429	+	0.998772i	$0.515776\pi$
$809$	−29.2470	+	34.2438i	−1.02827	+	1.20395i	−0.978725	+	0.205175i	$0.934224\pi$
$810$	−15.3113	+	2.33178i	−0.537985	+	0.0819305i
$811$	−17.9942	−	17.9942i	−0.631863	−	0.631863i	0.316672	−	0.948535i	$-0.397435\pi$
$811$	−17.9942	−	17.9942i	−0.631863	−	0.631863i	−0.948535	+	0.316672i	$0.897435\pi$
$812$	−2.67238	+	15.6640i	−0.0937820	+	0.549700i
$813$	−10.1074	−	42.1002i	−0.354481	−	1.47652i
$814$	−13.5226	+	3.16152i	−0.473968	+	0.110811i
$815$	−0.220932	+	0.433603i	−0.00773890	+	0.0151885i
$816$	−35.3089	−	51.1136i	−1.23606	−	1.78933i
$817$	0.856931	−	2.06882i	0.0299802	−	0.0723787i
$818$	−25.0626	−	34.9308i	−0.876293	−	1.22133i
$819$	−2.00630			−0.0701058
$820$	−8.90322	+	9.20503i	−0.310914	+	0.321454i
$821$	49.9138			1.74200			0.871001	−	0.491281i	$-0.163471\pi$
$821$	49.9138			1.74200			0.871001	+	0.491281i	$0.163471\pi$
$822$	0.379945	+	0.529547i	0.0132521	+	0.0184701i
$823$	−1.66362	+	4.01633i	−0.0579901	+	0.140000i	−0.950219	−	0.311583i	$-0.899141\pi$
$823$	−1.66362	+	4.01633i	−0.0579901	+	0.140000i	0.892229	+	0.451584i	$0.149141\pi$
$824$	−18.1505	+	2.54357i	−0.632304	+	0.0886095i
$825$	−4.13037	+	8.10630i	−0.143801	+	0.282225i
$826$	−13.7558	+	3.21605i	−0.478627	+	0.111901i
$827$	−5.73900	−	23.9046i	−0.199565	−	0.831246i	−0.978850	−	0.204577i	$-0.934418\pi$
$827$	−5.73900	−	23.9046i	−0.199565	−	0.831246i	0.779286	−	0.626669i	$-0.215582\pi$
$828$	11.2888	+	1.92593i	0.392313	+	0.0669308i
$829$	−3.39041	−	3.39041i	−0.117754	−	0.117754i	0.645774	−	0.763528i	$-0.276535\pi$
$829$	−3.39041	−	3.39041i	−0.117754	−	0.117754i	−0.763528	+	0.645774i	$0.776535\pi$
$830$	12.7426	−	1.94059i	0.442302	−	0.0673588i
$831$	−21.0672	+	24.6665i	−0.730813	+	0.855673i
$832$	9.67724	+	4.41942i	0.335498	+	0.153216i
$833$	18.3551	+	29.9528i	0.635967	+	1.03780i
$834$	−23.7784	+	27.5079i	−0.823379	+	0.952519i
$835$	9.98222	+	11.6877i	0.345449	+	0.404469i
$836$	−0.0241885	+	2.03269i	−0.000836576	+	0.0703020i
$837$	2.10677	+	26.7690i	0.0728206	+	0.925273i
$838$	4.40307	−	26.7682i	0.152102	−	0.924691i
$839$	10.7282	+	6.57426i	0.370379	+	0.226969i	0.695215	−	0.718802i	$-0.255309\pi$
$839$	10.7282	+	6.57426i	0.370379	+	0.226969i	−0.324836	+	0.945770i	$0.605309\pi$
$840$	−8.41082	−	2.89980i	−0.290201	−	0.100053i
$841$	3.72751	+	0.590380i	0.128535	+	0.0203579i
$842$	−50.6408	−	4.28882i	−1.74520	−	0.147803i
$843$	13.4208	+	9.75075i	0.462236	+	0.335834i
$844$	1.28792	+	0.810474i	0.0443320	+	0.0278977i
$845$	−6.60174	−	9.08652i	−0.227107	−	0.312586i
$846$	−0.414275	+	0.983557i	−0.0142431	+	0.0338154i
$847$	14.5202	−	6.01447i	0.498920	−	0.206660i
$848$	−18.8853	−	16.9231i	−0.648524	−	0.581143i
$849$	3.17396	−	40.3290i	0.108930	−	1.38409i
$850$	2.64251	−	10.7253i	0.0906374	−	0.367876i
$851$	−3.98174	+	12.2545i	−0.136492	+	0.420080i
$852$	2.38134	+	16.2872i	0.0815834	+	0.557991i
$853$	17.7460	+	34.8285i	0.607611	+	1.19250i	0.965905	+	0.258895i	$0.0833584\pi$
$853$	17.7460	+	34.8285i	0.607611	+	1.19250i	−0.358294	+	0.933609i	$0.616642\pi$
$854$	−1.28165	+	1.08151i	−0.0438573	+	0.0370087i
$855$	0.206008	+	0.0494582i	0.00704533	+	0.00169144i
$856$	−36.0959	−	27.2226i	−1.23373	−	0.930448i
$857$	12.4646	+	38.3620i	0.425781	+	1.31042i	0.902244	+	0.431225i	$0.141919\pi$
$857$	12.4646	+	38.3620i	0.425781	+	1.31042i	−0.476463	+	0.879194i	$0.658081\pi$
$858$	1.24093	+	17.0650i	0.0423648	+	0.582591i
$859$	37.3685	−	5.91859i	1.27500	−	0.201940i	0.518013	−	0.855373i	$-0.326672\pi$
$859$	37.3685	−	5.91859i	1.27500	−	0.201940i	0.756984	+	0.653433i	$0.226672\pi$
$860$	12.0434	−	16.1681i	0.410675	−	0.551329i
$861$	2.58126	−	19.9746i	0.0879692	−	0.680733i
$862$	10.4519	+	20.8182i	0.355992	+	0.709071i
$863$	5.69492	+	35.9563i	0.193857	+	1.22397i	0.872173	+	0.489197i	$0.162710\pi$
$863$	5.69492	+	35.9563i	0.193857	+	1.22397i	−0.678316	+	0.734771i	$0.737290\pi$
$864$	−21.5172	+	8.17173i	−0.732031	+	0.278008i
$865$	−3.75341	+	1.21956i	−0.127620	+	0.0414662i
$866$	−0.130369	+	21.9121i	−0.00443013	+	0.744602i
$867$	−20.4276	+	85.0872i	−0.693758	+	2.88971i
$868$	−8.21911	+	19.1935i	−0.278975	+	0.651469i
$869$	−10.2089	+	5.20171i	−0.346314	+	0.176456i
$870$	4.44424	−	13.4060i	0.150674	−	0.454507i
$871$	3.75352	+	1.21959i	0.127183	+	0.0413243i
$872$	−26.3192	+	21.6784i	−0.891280	+	0.734122i
$873$	−3.96330	−	0.311918i	−0.134137	−	0.0105568i
$874$	1.60231	+	0.995057i	0.0541989	+	0.0336583i
$875$	−0.605368	−	1.46149i	−0.0204652	−	0.0494073i
$876$	47.5122	−	3.17094i	1.60529	−	0.107136i
$877$	−39.9166	+	29.0011i	−1.34789	+	0.979298i	−0.348775	+	0.937207i	$0.613402\pi$
$877$	−39.9166	+	29.0011i	−1.34789	+	0.979298i	−0.999114	+	0.0420916i	$0.986598\pi$
$878$	43.0567	−	26.0341i	1.45309	−	0.878607i
$879$	13.3074	−	18.3160i	0.448847	−	0.617784i
$880$	−4.69479	+	17.6896i	−0.158261	+	0.596317i
$881$	0.435632	−	2.75047i	0.0146768	−	0.0926657i	−0.979263	−	0.202595i	$-0.935062\pi$
$881$	0.435632	−	2.75047i	0.0146768	−	0.0926657i	0.993939	+	0.109929i	$0.0350625\pi$
$882$	−5.78033	+	1.84019i	−0.194634	+	0.0619625i
$883$	9.19276	−	15.0012i	0.309361	−	0.504831i	−0.659741	−	0.751493i	$-0.729334\pi$
$883$	9.19276	−	15.0012i	0.309361	−	0.504831i	0.969102	+	0.246662i	$0.0793338\pi$
$884$	−6.18395	−	19.8321i	−0.207989	−	0.667027i
$885$	12.5173	−	0.985133i	0.420765	−	0.0331149i
$886$	5.10226	−	9.86816i	0.171414	−	0.331527i
$887$	−21.1577	+	18.0704i	−0.710407	+	0.606745i	−0.929440	−	0.368972i	$-0.879710\pi$
$887$	−21.1577	+	18.0704i	−0.710407	+	0.606745i	0.219033	+	0.975717i	$0.429710\pi$
$888$	2.60779	+	11.7850i	0.0875117	+	0.395480i
$889$	14.7037	−	9.01045i	0.493147	−	0.302201i
$890$	−4.18936	−	10.2867i	−0.140428	−	0.344811i
$891$	−38.1032	−	32.5432i	−1.27650	−	1.09024i
$892$	11.8800	+	16.7674i	0.397772	+	0.561415i
$893$	−0.124293	+	0.124293i	−0.00415929	+	0.00415929i
$894$	−8.82954	+	12.0020i	−0.295304	+	0.401407i
$895$	−6.47218	+	1.55383i	−0.216341	+	0.0519389i
$896$	−17.7681	−	2.14583i	−0.593590	−	0.0716873i
$897$	14.1451	+	7.20729i	0.472291	+	0.240644i
$898$	−9.48367	−	9.59719i	−0.316474	−	0.320262i
$899$	−30.6228	−	12.6844i	−1.02133	−	0.423048i
$900$	1.68912	+	0.886121i	0.0563039	+	0.0295374i
$901$			49.5170i			1.64965i
$902$	−41.3682	−	2.31592i	−1.37741	−	0.0771116i
$903$			31.7071i			1.05515i
$904$	0.709368	−	39.7390i	0.0235932	−	1.32170i
$905$	−20.2659	−	8.39440i	−0.673660	−	0.279039i
$906$	15.3542	−	15.1726i	0.510109	−	0.504075i
$907$	−10.1724	−	5.18310i	−0.337769	−	0.172102i	0.276876	−	0.960906i	$-0.410701\pi$
$907$	−10.1724	−	5.18310i	−0.337769	−	0.172102i	−0.614645	+	0.788804i	$0.710701\pi$
$908$	9.31841	+	11.1771i	0.309242	+	0.370924i
$909$	−13.9669	+	3.35316i	−0.463253	+	0.111217i
$910$	−2.39640	−	1.76296i	−0.0794398	−	0.0584416i
$911$	22.9698	−	22.9698i	0.761024	−	0.761024i	−0.215483	−	0.976508i	$-0.569133\pi$
$911$	22.9698	−	22.9698i	0.761024	−	0.761024i	0.976508	+	0.215483i	$0.0691326\pi$
$912$	1.76633	+	0.0420438i	0.0584891	+	0.00139221i
$913$	31.7107	+	27.0835i	1.04947	+	0.896334i
$914$	−35.4286	+	14.4287i	−1.17187	+	0.477258i
$915$	1.27088	−	0.778798i	0.0420141	−	0.0257463i
$916$	−8.82671	+	34.9296i	−0.291643	+	1.15411i
$917$	−21.7043	+	18.5372i	−0.716739	+	0.612153i
$918$	39.9237	+	20.6422i	1.31768	+	0.681295i
$919$	−31.7765	+	2.50086i	−1.04821	+	0.0824958i	−0.590846	−	0.806784i	$-0.701206\pi$
$919$	−31.7765	+	2.50086i	−1.04821	+	0.0824958i	−0.457363	+	0.889280i	$0.651206\pi$
$920$	11.7914	+	12.2200i	0.388751	+	0.402882i
$921$	−15.7127	+	25.6408i	−0.517750	+	0.844892i
$922$	12.4624	+	39.1463i	0.410427	+	1.28921i
$923$	−0.861064	+	5.43654i	−0.0283423	+	0.178946i
$924$	−10.6980	−	26.7222i	−0.351937	−	0.879094i
$925$	−1.26149	+	1.73629i	−0.0414774	+	0.0570887i
$926$	1.88535	+	3.11809i	0.0619563	+	0.102467i
$927$	−4.99972	+	3.63251i	−0.164212	+	0.119307i
$928$	3.07065	−	28.2454i	0.100799	−	0.927201i
$929$	2.54328	+	6.14002i	0.0834422	+	0.201447i	0.960094	−	0.279679i	$-0.0902279\pi$
$929$	2.54328	+	6.14002i	0.0834422	+	0.201447i	−0.876651	+	0.481126i	$0.840228\pi$
$930$	9.79032	−	15.7650i	0.321037	−	0.516956i
$931$	−0.996027	−	0.0783890i	−0.0326435	−	0.00256910i
$932$	9.32187	+	40.9700i	0.305348	+	1.34202i
$933$	42.8850	+	13.9342i	1.40399	+	0.456185i
$934$	27.1763	+	9.00922i	0.889235	+	0.294791i
$935$	31.8429	−	16.2248i	1.04137	−	0.530606i
$936$	3.58064	−	0.217580i	0.117037	−	0.00711183i
$937$	11.9490	−	49.7713i	0.390358	−	1.62596i	−0.338272	−	0.941048i	$-0.609842\pi$
$937$	11.9490	−	49.7713i	0.390358	−	1.62596i	0.728629	−	0.684908i	$-0.240158\pi$
$938$	−6.63932	−	0.0395017i	−0.216782	−	0.00128978i
$939$	−44.8085	+	14.5591i	−1.46227	+	0.475120i
$940$	−1.35909	+	0.810766i	−0.0443286	+	0.0264443i
$941$	0.981052	+	6.19412i	0.0319814	+	0.201923i	0.998505	−	0.0546538i	$-0.0174055\pi$
$941$	0.981052	+	6.19412i	0.0319814	+	0.201923i	−0.966524	+	0.256576i	$0.917406\pi$
$942$	57.8209	−	29.0292i	1.88391	−	0.945823i
$943$	−21.6988	+	31.7338i	−0.706611	+	1.03340i
$944$	24.2013	−	7.23148i	0.787684	−	0.235365i
$945$	6.35723	−	1.00689i	0.206801	−	0.0327540i
$946$	65.0553	−	4.73069i	2.11513	−	0.153808i
$947$	−2.19347	−	6.75082i	−0.0712784	−	0.219372i	0.909071	−	0.416641i	$-0.136793\pi$
$947$	−2.19347	−	6.75082i	−0.0712784	−	0.219372i	−0.980349	+	0.197269i	$0.936793\pi$
$948$	4.41516	+	8.92624i	0.143398	+	0.289911i
$949$	15.4833	+	3.71722i	0.502610	+	0.120666i
$950$	0.202604	+	0.240097i	0.00657335	+	0.00778977i
$951$	24.6086	+	48.2971i	0.797989	+	1.56614i
$952$	20.0338	+	28.6353i	0.649299	+	0.928076i
$953$	16.5424	−	50.9124i	0.535862	−	1.64921i	−0.205916	−	0.978570i	$-0.566017\pi$
$953$	16.5424	−	50.9124i	0.535862	−	1.64921i	0.741779	−	0.670645i	$-0.233983\pi$
$954$	−8.30234	−	2.04553i	−0.268798	−	0.0662266i
$955$	−0.585308	+	7.43704i	−0.0189401	+	0.240657i
$956$	−0.0715300	+	0.788762i	−0.00231345	+	0.0255104i
$957$	42.2164	−	17.4866i	1.36466	−	0.565262i
$958$	−15.7862	−	6.64916i	−0.510028	−	0.214825i
$959$	−0.215507	−	0.296620i	−0.00695908	−	0.00957836i
$960$	15.3253	+	4.26313i	0.494621	+	0.137592i
$961$	−10.1550	−	7.37805i	−0.327581	−	0.238002i
$962$	−0.340612	+	4.02182i	−0.0109818	+	0.129669i
$963$	−15.0568	−	2.38477i	−0.485200	−	0.0768481i
$964$	37.2734	−	36.3968i	1.20050	−	1.17226i
$965$	14.9663	+	9.17135i	0.481782	+	0.295236i
$966$	−26.3528	−	4.33475i	−0.847888	−	0.139468i
$967$	−1.00548	−	12.7758i	−0.0323340	−	0.410843i	−0.991691	−	0.128646i	$-0.958937\pi$
$967$	−1.00548	−	12.7758i	−0.0323340	−	0.410843i	0.959357	−	0.282197i	$-0.0910631\pi$
$968$	−25.2619	+	12.3087i	−0.811950	+	0.395617i
$969$	−2.24064	−	2.62345i	−0.0719798	−	0.0842775i
$970$	−4.45982	−	3.85517i	−0.143196	−	0.123782i
$971$	26.0941	+	42.5818i	0.837401	+	1.36651i	0.928754	+	0.370696i	$0.120881\pi$
$971$	26.0941	+	42.5818i	0.837401	+	1.36651i	−0.0913533	+	0.995819i	$0.529119\pi$
$972$	−12.6022	+	14.4047i	−0.404217	+	0.462030i
$973$	13.2843	−	15.5539i	0.425874	−	0.498634i
$974$	0.955826	+	6.27630i	0.0306266	+	0.201106i
$975$	1.86975	+	1.86975i	0.0598799	+	0.0598799i
$976$	2.17008	−	2.06917i	0.0694625	−	0.0662326i
$977$	−10.4256	−	43.4258i	−0.333545	−	1.38931i	−0.847180	−	0.531305i	$-0.821702\pi$
$977$	−10.4256	−	43.4258i	−0.333545	−	1.38931i	0.513636	−	0.858008i	$-0.328298\pi$
$978$	0.311536	+	1.33252i	0.00996183	+	0.0426092i
$979$	16.3144	−	32.0187i	0.521409	−	1.02332i
$980$	−8.52123	−	2.88126i	−0.272201	−	0.0920384i
$981$	−4.39987	+	10.6222i	−0.140477	+	0.339142i
$982$	−18.4050	+	13.2054i	−0.587328	+	0.421403i
$983$	46.4885			1.48275			0.741376	−	0.671090i	$-0.234173\pi$
$983$	46.4885			1.48275			0.741376	+	0.671090i	$0.234173\pi$
$984$	−2.44056	+	35.9286i	−0.0778022	+	1.14536i
$985$	3.00519			0.0957533
$986$	−45.0770	+	32.3424i	−1.43555	+	1.02999i
$987$	0.952467	−	2.29946i	0.0303174	−	0.0731926i
$988$	0.559695	+	0.189248i	0.0178063	+	0.00602077i
$989$	27.4756	−	53.9239i	0.873674	−	1.71468i
$990$	1.40493	+	6.00922i	0.0446515	+	0.190986i
$991$	−2.96533	−	12.3515i	−0.0941967	−	0.392357i	0.905276	−	0.424824i	$-0.139664\pi$
$991$	−2.96533	−	12.3515i	−0.0941967	−	0.392357i	−0.999473	+	0.0324662i	$0.989664\pi$
$992$	12.5871	−	35.1459i	0.399642	−	1.11588i
$993$	−16.5076	−	16.5076i	−0.523852	−	0.523852i
$994$	−1.39411	−	9.15426i	−0.0442186	−	0.290355i
$995$	−15.3936	+	18.0236i	−0.488010	+	0.571386i
$996$	23.8659	−	27.2793i	0.756220	−	0.864378i
$997$	−15.8720	−	25.9007i	−0.502671	−	0.820284i	0.496180	−	0.868220i	$-0.334736\pi$
$997$	−15.8720	−	25.9007i	−0.502671	−	0.820284i	−0.998850	+	0.0479358i	$0.984736\pi$
$998$	−16.1834	−	13.9893i	−0.512276	−	0.442823i
$999$	−5.67121	−	6.64014i	−0.179429	−	0.210085i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bw.b.11.34	✓	672
4.3	odd	2	inner	820.2.bw.b.11.37	yes	672
41.15	odd	40	inner	820.2.bw.b.671.37	yes	672
164.15	even	40	inner	820.2.bw.b.671.34	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bw.b.11.34	✓	672	1.1	even	1	trivial
820.2.bw.b.11.37	yes	672	4.3	odd	2	inner
820.2.bw.b.671.34	yes	672	164.15	even	40	inner
820.2.bw.b.671.37	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+(1.14905 - 0.824432i) q^{2} +(0.760926 - 1.83704i) q^{3} +(0.640623 - 1.89462i) q^{4} +(0.453990 - 0.891007i) q^{5} +(-0.640173 - 2.73818i) q^{6} +(0.369288 + 1.53819i) q^{7} +(-0.825882 - 2.70517i) q^{8} +(-0.674382 - 0.674382i) q^{9} +(-0.212917 - 1.39809i) q^{10} +(2.97155 - 3.47924i) q^{11} +(-2.99303 - 2.61852i) q^{12} +(-0.694833 - 1.13386i) q^{13} +(1.69247 + 1.46301i) q^{14} +(-1.29136 - 1.51199i) q^{15} +(-3.17920 - 2.42748i) q^{16} +(0.612824 + 7.78667i) q^{17} +(-1.33088 - 0.218915i) q^{18} +(-0.189408 - 0.116069i) q^{19} +(-1.39729 - 1.43094i) q^{20} +(3.10672 + 0.492057i) q^{21} +(0.546059 - 6.44766i) q^{22} +(-4.85718 - 3.52895i) q^{23} +(-5.59793 - 0.541254i) q^{24} +(-0.587785 - 0.809017i) q^{25} +(-1.73319 - 0.730022i) q^{26} +(3.75910 - 1.55707i) q^{27} +(3.15087 + 0.285741i) q^{28} +(-0.394065 + 5.00707i) q^{29} +(-2.73037 - 0.672709i) q^{30} +(-2.03933 + 6.27642i) q^{31} +(-5.65435 - 0.168255i) q^{32} +(-4.13037 - 8.10630i) q^{33} +(7.12375 + 8.44203i) q^{34} +(1.53819 + 0.369288i) q^{35} +(-1.70972 + 0.845675i) q^{36} +(-0.663202 - 2.04113i) q^{37} +(-0.313330 + 0.0227847i) q^{38} +(-2.61167 + 0.413648i) q^{39} +(-2.78526 - 0.492253i) q^{40} +(-0.182878 - 6.40051i) q^{41} +(3.97544 - 1.99589i) q^{42} +(1.57691 + 9.95621i) q^{43} +(-4.68821 - 7.85886i) q^{44} +(-0.907041 + 0.294716i) q^{45} +(-8.49052 - 0.0505157i) q^{46} +(0.184720 - 0.769413i) q^{47} +(-6.87852 + 3.99319i) q^{48} +(4.00738 - 2.04186i) q^{49} +(-1.34237 - 0.445010i) q^{50} +(14.7707 + 4.79930i) q^{51} +(-2.59337 + 0.590068i) q^{52} +(6.32005 + 0.497399i) q^{53} +(3.03569 - 4.88827i) q^{54} +(-1.75097 - 4.22721i) q^{55} +(3.85608 - 2.26935i) q^{56} +(-0.357349 + 0.259630i) q^{57} +(3.67519 + 6.07824i) q^{58} +(-3.71165 + 5.10865i) q^{59} +(-3.69193 + 1.47803i) q^{60} +(-0.117265 + 0.740384i) q^{61} +(2.83119 + 8.89320i) q^{62} +(0.788289 - 1.28637i) q^{63} +(-6.63584 + 4.46830i) q^{64} +(-1.32573 + 0.104337i) q^{65} +(-11.4291 - 5.90932i) q^{66} +(-2.25674 + 1.92744i) q^{67} +(15.1454 + 3.82725i) q^{68} +(-10.1788 + 6.23756i) q^{69} +(2.07191 - 0.843807i) q^{70} +(-3.14741 - 2.68814i) q^{71} +(-1.26735 + 2.38127i) q^{72} +(-8.46685 + 8.46685i) q^{73} +(-2.44482 - 1.79859i) q^{74} +(-1.93346 + 0.464182i) q^{75} +(-0.341247 + 0.284500i) q^{76} +(6.44910 + 3.28598i) q^{77} +(-2.65991 + 2.62845i) q^{78} +(-2.31353 - 0.958296i) q^{79} +(-3.60623 + 1.73064i) q^{80} -10.9516i q^{81} +(-5.48692 - 7.20373i) q^{82} +9.11427i q^{83} +(2.92250 - 5.57085i) q^{84} +(7.21619 + 2.98904i) q^{85} +(10.0202 + 10.1401i) q^{86} +(8.89832 + 4.53392i) q^{87} +(-11.8661 - 5.16510i) q^{88} +(7.63688 - 1.83345i) q^{89} +(-0.799261 + 1.08644i) q^{90} +(1.48751 - 1.48751i) q^{91} +(-9.79766 + 6.94181i) q^{92} +(9.97824 + 8.52222i) q^{93} +(-0.422077 - 1.03638i) q^{94} +(-0.189408 + 0.116069i) q^{95} +(-4.61164 + 10.2592i) q^{96} +(3.16973 - 2.70721i) q^{97} +(2.92129 - 5.65001i) q^{98} +(-4.35029 + 0.342376i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q + 12 q^{6} + 16 q^{9} - 124 q^{12} - 24 q^{14} - 32 q^{16} - 8 q^{17} + 40 q^{21} - 4 q^{22} - 24 q^{24} - 28 q^{28} - 12 q^{30} - 20 q^{32} + 40 q^{33} - 4 q^{34} - 60 q^{36} + 80 q^{37} - 172 q^{38}+ \cdots - 116 q^{98}+O(q^{100}) \) 672 * q + 12 * q^6 + 16 * q^9 - 124 * q^12 - 24 * q^14 - 32 * q^16 - 8 * q^17 + 40 * q^21 - 4 * q^22 - 24 * q^24 - 28 * q^28 - 12 * q^30 - 20 * q^32 + 40 * q^33 - 4 * q^34 - 60 * q^36 + 80 * q^37 - 172 * q^38 + 160 * q^42 - 24 * q^44 - 16 * q^46 + 40 * q^48 - 24 * q^52 - 64 * q^54 + 68 * q^56 - 112 * q^58 + 36 * q^62 - 120 * q^64 + 8 * q^65 + 144 * q^68 - 104 * q^69 + 24 * q^70 - 320 * q^72 - 92 * q^74 - 24 * q^76 + 160 * q^77 - 128 * q^78 - 192 * q^82 - 172 * q^84 - 32 * q^85 - 112 * q^88 + 8 * q^89 - 48 * q^90 + 24 * q^92 + 92 * q^94 + 56 * q^96 - 116 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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