LMFDB - Embedded newform 213.2.n.a.11.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [213,2,Mod(11,213)] 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("213.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(213, base_ring=CyclotomicField(70)) chi = DirichletCharacter(H, H._module([35, 31])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 213 = 3 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	213.n (of order $70$, degree $24$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.70081356305$
Analytic rank:	$0$
Dimension:	$528$
Relative dimension:	$22$ over $\Q(\zeta_{70})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{70}]$

Embedding invariants

Embedding label			11.7
Character	$\chi$	$=$	213.11
Dual form			213.2.n.a.155.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.903072 - 0.485964i) q^{2} +(1.73064 - 0.0698660i) q^{3} +(-0.522416 - 0.791427i) q^{4} +(0.639254 - 0.207706i) q^{5} +(-1.59685 - 0.777935i) q^{6} +(-0.565283 - 3.11497i) q^{7} +(0.271029 + 3.01138i) q^{8} +(2.99024 - 0.241826i) q^{9} +(-0.678230 - 0.123081i) q^{10} +(-0.204948 - 0.179058i) q^{11} +(-0.959409 - 1.33318i) q^{12} +(-3.60077 - 4.12141i) q^{13} +(-1.00327 + 3.08774i) q^{14} +(1.09181 - 0.404127i) q^{15} +(0.473251 - 1.10723i) q^{16} +(3.51181 + 2.55148i) q^{17} +(-2.81792 - 1.23476i) q^{18} +(6.15106 + 1.69758i) q^{19} +(-0.498341 - 0.397414i) q^{20} +(-1.19593 - 5.35139i) q^{21} +(0.0980674 + 0.261300i) q^{22} +(-4.99559 - 2.40575i) q^{23} +(0.679447 + 5.19268i) q^{24} +(-3.67958 + 2.67337i) q^{25} +(1.24890 + 5.47177i) q^{26} +(5.15813 - 0.627430i) q^{27} +(-2.16995 + 2.07469i) q^{28} +(1.35336 - 3.60601i) q^{29} +(-1.18237 - 0.165623i) q^{30} +(2.69429 - 1.15159i) q^{31} +(3.76237 - 3.00039i) q^{32} +(-0.367202 - 0.295566i) q^{33} +(-1.93149 - 4.01078i) q^{34} +(-1.00836 - 1.87384i) q^{35} +(-1.75354 - 2.24022i) q^{36} +(-0.872484 + 0.420166i) q^{37} +(-4.72988 - 4.52223i) q^{38} +(-6.51959 - 6.88111i) q^{39} +(0.798739 + 1.86874i) q^{40} +(-2.02780 + 8.88436i) q^{41} +(-1.52057 + 5.41387i) q^{42} +(7.06959 + 7.39421i) q^{43} +(-0.0346429 + 0.255744i) q^{44} +(1.86129 - 0.775679i) q^{45} +(3.34227 + 4.60024i) q^{46} +(0.462907 + 10.3074i) q^{47} +(0.741670 - 1.94927i) q^{48} +(-2.82982 + 1.06205i) q^{49} +(4.62209 - 0.626104i) q^{50} +(6.25595 + 4.17034i) q^{51} +(-1.38070 + 5.00284i) q^{52} +(-3.03315 + 4.59502i) q^{53} +(-4.96307 - 1.94005i) q^{54} +(-0.168206 - 0.0718945i) q^{55} +(9.22714 - 2.54653i) q^{56} +(10.7639 + 2.50816i) q^{57} +(-2.97457 + 2.59880i) q^{58} +(-7.80062 + 4.66066i) q^{59} +(-0.890215 - 0.652963i) q^{60} +(-1.51754 + 8.36232i) q^{61} +(-2.99277 - 0.269354i) q^{62} +(-2.44361 - 9.17779i) q^{63} +(-7.22531 + 1.31120i) q^{64} +(-3.15785 - 1.88673i) q^{65} +(0.187975 + 0.445364i) q^{66} +(4.84978 - 3.20131i) q^{67} +(0.184683 - 4.11228i) q^{68} +(-8.81366 - 3.81447i) q^{69} +2.18224i q^{70} +(8.08549 + 2.37168i) q^{71} +(1.53867 + 8.93920i) q^{72} +(3.84742 - 7.14971i) q^{73} +(0.992101 + 0.0445553i) q^{74} +(-6.18126 + 4.88373i) q^{75} +(-1.86990 - 5.75496i) q^{76} +(-0.441906 + 0.739625i) q^{77} +(2.54368 + 9.38242i) q^{78} +(-2.40491 + 0.216446i) q^{79} +(0.0725499 - 0.806095i) q^{80} +(8.88304 - 1.44623i) q^{81} +(6.14872 - 7.03778i) q^{82} +(-4.25832 - 7.12723i) q^{83} +(-3.61046 + 3.74215i) q^{84} +(2.77490 + 0.901619i) q^{85} +(-2.79103 - 10.1131i) q^{86} +(2.09024 - 6.33526i) q^{87} +(0.483665 - 0.665707i) q^{88} +(-4.78435 - 3.15812i) q^{89} +(-2.05783 - 0.204027i) q^{90} +(-10.8026 + 13.5460i) q^{91} +(0.705803 + 5.21045i) q^{92} +(4.58239 - 2.18124i) q^{93} +(4.59100 - 9.53330i) q^{94} +(4.28469 - 0.192426i) q^{95} +(6.30168 - 5.45546i) q^{96} +(-1.66539 + 0.380113i) q^{97} +(3.07165 + 0.416083i) q^{98} +(-0.656145 - 0.485864i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 528 q - 20 q^{3} - 70 q^{4} - 30 q^{6} - 46 q^{7} - 26 q^{9} - 62 q^{10} - 55 q^{12} - 46 q^{13} - 22 q^{15} - 70 q^{16} - 18 q^{18} - 46 q^{19} - 2 q^{21} - 86 q^{22} - 13 q^{24} + 24 q^{25} + 7 q^{27}+ \cdots - 94 q^{99}+O(q^{100}) $ 528 * q - 20 * q^3 - 70 * q^4 - 30 * q^6 - 46 * q^7 - 26 * q^9 - 62 * q^10 - 55 * q^12 - 46 * q^13 - 22 * q^15 - 70 * q^16 - 18 * q^18 - 46 * q^19 - 2 * q^21 - 86 * q^22 - 13 * q^24 + 24 * q^25 + 7 * q^27 + 22 * q^28 - 55 * q^30 - 44 * q^31 - 28 * q^33 - 28 * q^34 + 8 * q^36 - 72 * q^37 - 144 * q^40 - 2 * q^42 - 76 * q^43 - 55 * q^45 - 30 * q^46 + 55 * q^48 - 72 * q^49 + 63 * q^51 + 78 * q^52 - 47 * q^54 - 70 * q^55 + 102 * q^57 - 166 * q^58 - 66 * q^60 - 74 * q^61 - 85 * q^63 + 58 * q^64 + 135 * q^66 + 52 * q^67 + 173 * q^69 + 154 * q^72 - 28 * q^73 + 127 * q^75 + 160 * q^76 + 184 * q^78 - 166 * q^79 + 102 * q^81 + 162 * q^82 + 168 * q^84 - 90 * q^85 + 87 * q^87 - 20 * q^88 + 60 * q^90 - 148 * q^91 + 5 * q^93 - 84 * q^94 + 120 * q^96 - 28 * q^97 - 94 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/213\mathbb{Z}\right)^\times$.

$n$	$7$	$143$
$\chi(n)$	$e\left(\frac{31}{70}\right)$	$-1$

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 $

$2$	−0.903072	−	0.485964i	−0.638568	−	0.343628i	0.122340	−	0.992488i	$-0.460960\pi$
$2$	−0.903072	−	0.485964i	−0.638568	−	0.343628i	−0.760908	+	0.648860i	$0.775246\pi$
$3$	1.73064	−	0.0698660i	0.999186	−	0.0403371i
$3$	1.73064	−	0.0698660i	0.999186	−	0.0403371i
$4$	−0.522416	−	0.791427i	−0.261208	−	0.395713i
$5$	0.639254	−	0.207706i	0.285883	−	0.0928891i	−0.162565	−	0.986698i	$-0.551977\pi$
$5$	0.639254	−	0.207706i	0.285883	−	0.0928891i	0.448448	+	0.893809i	$0.351977\pi$
$6$	−1.59685	−	0.777935i	−0.651909	−	0.317590i
$7$	−0.565283	−	3.11497i	−0.213657	−	1.17735i	−0.895233	−	0.445599i	$-0.852991\pi$
$7$	−0.565283	−	3.11497i	−0.213657	−	1.17735i	0.681576	−	0.731747i	$-0.261295\pi$
$8$	0.271029	+	3.01138i	0.0958233	+	1.06468i
$9$	2.99024	−	0.241826i	0.996746	−	0.0806086i
$10$	−0.678230	−	0.123081i	−0.214475	−	0.0389215i
$11$	−0.204948	−	0.179058i	−0.0617942	−	0.0539880i	0.626488	−	0.779431i	$-0.284492\pi$
$11$	−0.204948	−	0.179058i	−0.0617942	−	0.0539880i	−0.688282	+	0.725443i	$0.741635\pi$
$12$	−0.959409	−	1.33318i	−0.276957	−	0.384855i
$13$	−3.60077	−	4.12141i	−0.998674	−	1.14307i	−0.989706	−	0.143114i	$-0.954288\pi$
$13$	−3.60077	−	4.12141i	−0.998674	−	1.14307i	−0.00896755	−	0.999960i	$-0.502854\pi$
$14$	−1.00327	+	3.08774i	−0.268135	+	0.825234i
$15$	1.09181	−	0.404127i	0.281904	−	0.104345i
$16$	0.473251	−	1.10723i	0.118313	−	0.276806i
$17$	3.51181	+	2.55148i	0.851740	+	0.618825i	0.925625	−	0.378442i	$-0.123540\pi$
$17$	3.51181	+	2.55148i	0.851740	+	0.618825i	−0.0738856	+	0.997267i	$0.523540\pi$
$18$	−2.81792	−	1.23476i	−0.664189	−	0.291036i
$19$	6.15106	+	1.69758i	1.41115	+	0.389453i	0.886841	−	0.462075i	$-0.152895\pi$
$19$	6.15106	+	1.69758i	1.41115	+	0.389453i	0.524309	+	0.851528i	$0.324324\pi$
$20$	−0.498341	−	0.397414i	−0.111432	−	0.0888644i
$21$	−1.19593	−	5.35139i	−0.260974	−	1.16777i
$22$	0.0980674	+	0.261300i	0.0209080	+	0.0557093i
$23$	−4.99559	−	2.40575i	−1.04165	−	0.501633i	−0.166784	−	0.985993i	$-0.553338\pi$
$23$	−4.99559	−	2.40575i	−1.04165	−	0.501633i	−0.874869	+	0.484360i	$0.839053\pi$
$24$	0.679447	+	5.19268i	0.138692	+	1.05995i
$25$	−3.67958	+	2.67337i	−0.735916	+	0.534674i
$26$	1.24890	+	5.47177i	0.244929	+	1.07310i
$27$	5.15813	−	0.627430i	0.992683	−	0.120749i
$28$	−2.16995	+	2.07469i	−0.410083	+	0.392079i
$29$	1.35336	−	3.60601i	0.251312	−	0.669618i	−0.748666	−	0.662948i	$-0.769305\pi$
$29$	1.35336	−	3.60601i	0.251312	−	0.669618i	0.999978	−	0.00667079i	$-0.00212339\pi$
$30$	−1.18237	−	0.165623i	−0.215871	−	0.0302385i
$31$	2.69429	−	1.15159i	0.483909	−	0.206833i	−0.137221	−	0.990540i	$-0.543817\pi$
$31$	2.69429	−	1.15159i	0.483909	−	0.206833i	0.621129	+	0.783708i	$0.286674\pi$
$32$	3.76237	−	3.00039i	0.665099	−	0.530399i
$33$	−0.367202	−	0.295566i	−0.0639217	−	0.0514515i
$34$	−1.93149	−	4.01078i	−0.331248	−	0.687844i
$35$	−1.00836	−	1.87384i	−0.170444	−	0.316737i
$36$	−1.75354	−	2.24022i	−0.292256	−	0.373370i
$37$	−0.872484	+	0.420166i	−0.143436	+	0.0690749i	−0.504225	−	0.863572i	$-0.668222\pi$
$37$	−0.872484	+	0.420166i	−0.143436	+	0.0690749i	0.360789	+	0.932647i	$0.382507\pi$
$38$	−4.72988	−	4.52223i	−0.767289	−	0.733603i
$39$	−6.51959	−	6.88111i	−1.04397	−	1.10186i
$40$	0.798739	+	1.86874i	0.126292	+	0.295474i
$41$	−2.02780	+	8.88436i	−0.316689	+	1.38750i	0.526632	+	0.850093i	$0.323455\pi$
$41$	−2.02780	+	8.88436i	−0.316689	+	1.38750i	−0.843321	+	0.537411i	$0.819402\pi$
$42$	−1.52057	+	5.41387i	−0.234629	+	0.835379i
$43$	7.06959	+	7.39421i	1.07810	+	1.12761i	0.991332	+	0.131378i	$0.0419402\pi$
$43$	7.06959	+	7.39421i	1.07810	+	1.12761i	0.0867700	+	0.996228i	$0.472345\pi$
$44$	−0.0346429	+	0.255744i	−0.00522262	+	0.0385549i
$45$	1.86129	−	0.775679i	0.277465	−	0.115631i
$46$	3.34227	+	4.60024i	0.492791	+	0.678268i
$47$	0.462907	+	10.3074i	0.0675219	+	1.50349i	0.691685	+	0.722199i	$0.256869\pi$
$47$	0.462907	+	10.3074i	0.0675219	+	1.50349i	−0.624163	+	0.781294i	$0.714560\pi$
$48$	0.741670	−	1.94927i	0.107051	−	0.281353i
$49$	−2.82982	+	1.06205i	−0.404260	+	0.151721i
$50$	4.62209	−	0.626104i	0.653662	−	0.0885445i
$51$	6.25595	+	4.17034i	0.876008	+	0.583965i
$52$	−1.38070	+	5.00284i	−0.191468	+	0.693769i
$53$	−3.03315	+	4.59502i	−0.416635	+	0.631175i	−0.980922	−	0.194404i	$-0.937723\pi$
$53$	−3.03315	+	4.59502i	−0.416635	+	0.631175i	0.564287	+	0.825579i	$0.309151\pi$
$54$	−4.96307	−	1.94005i	−0.675388	−	0.264007i
$55$	−0.168206	−	0.0718945i	−0.0226808	−	0.00969425i
$56$	9.22714	−	2.54653i	1.23303	−	0.340294i
$57$	10.7639	+	2.50816i	1.42571	+	0.332214i
$58$	−2.97457	+	2.59880i	−0.390580	+	0.341239i
$59$	−7.80062	+	4.66066i	−1.01555	+	0.606766i	−0.921328	−	0.388785i	$-0.872895\pi$
$59$	−7.80062	+	4.66066i	−1.01555	+	0.606766i	−0.0942263	+	0.995551i	$0.530038\pi$
$60$	−0.890215	−	0.652963i	−0.114926	−	0.0842972i
$61$	−1.51754	+	8.36232i	−0.194301	+	1.07068i	0.728395	+	0.685157i	$0.240266\pi$
$61$	−1.51754	+	8.36232i	−0.194301	+	1.07068i	−0.922696	+	0.385528i	$0.874019\pi$
$62$	−2.99277	−	0.269354i	−0.380082	−	0.0342080i
$63$	−2.44361	−	9.17779i	−0.307866	−	1.15629i
$64$	−7.22531	+	1.31120i	−0.903164	+	0.163900i
$65$	−3.15785	−	1.88673i	−0.391683	−	0.234020i
$66$	0.187975	+	0.445364i	0.0231382	+	0.0548205i
$67$	4.84978	−	3.20131i	0.592495	−	0.391102i	−0.218774	−	0.975775i	$-0.570206\pi$
$67$	4.84978	−	3.20131i	0.592495	−	0.391102i	0.811269	+	0.584673i	$0.198777\pi$
$68$	0.184683	−	4.11228i	0.0223960	−	0.498687i
$69$	−8.81366	−	3.81447i	−1.06104	−	0.459208i
$70$			2.18224i			0.260827i
$71$	8.08549	+	2.37168i	0.959571	+	0.281466i
$71$	8.08549	+	2.37168i	0.959571	+	0.281466i
$72$	1.53867	+	8.93920i	0.181334	+	1.05350i
$73$	3.84742	−	7.14971i	0.450307	−	0.836810i	−0.549692	−	0.835367i	$-0.685255\pi$
$73$	3.84742	−	7.14971i	0.450307	−	0.836810i	0.999999	−	0.00144297i	$-0.000459311\pi$
$74$	0.992101	+	0.0445553i	0.115329	+	0.00517945i
$75$	−6.18126	+	4.88373i	−0.713750	+	0.563924i
$76$	−1.86990	−	5.75496i	−0.214492	−	0.660139i
$77$	−0.441906	+	0.739625i	−0.0503598	+	0.0842881i
$78$	2.54368	+	9.38242i	0.288015	+	1.06235i
$79$	−2.40491	+	0.216446i	−0.270574	+	0.0243521i	−0.224095	−	0.974567i	$-0.571943\pi$
$79$	−2.40491	+	0.216446i	−0.270574	+	0.0243521i	−0.0464784	+	0.998919i	$0.514800\pi$
$80$	0.0725499	−	0.806095i	0.00811133	−	0.0901242i
$81$	8.88304	−	1.44623i	0.987004	−	0.160693i
$82$	6.14872	−	7.03778i	0.679013	−	0.777193i
$83$	−4.25832	−	7.12723i	−0.467412	−	0.782315i	0.530447	−	0.847718i	$-0.322024\pi$
$83$	−4.25832	−	7.12723i	−0.467412	−	0.782315i	−0.997859	+	0.0654026i	$0.979167\pi$
$84$	−3.61046	+	3.74215i	−0.393934	+	0.408302i
$85$	2.77490	+	0.901619i	0.300980	+	0.0977944i
$86$	−2.79103	−	10.1131i	−0.300964	−	1.09052i
$87$	2.09024	−	6.33526i	0.224097	−	0.679211i
$88$	0.483665	−	0.665707i	0.0515588	−	0.0709646i
$89$	−4.78435	−	3.15812i	−0.507140	−	0.334760i	0.271284	−	0.962499i	$-0.412552\pi$
$89$	−4.78435	−	3.15812i	−0.507140	−	0.334760i	−0.778424	+	0.627739i	$0.783980\pi$
$90$	−2.05783	−	0.204027i	−0.216915	−	0.0215063i
$91$	−10.8026	+	13.5460i	−1.13242	+	1.42001i
$92$	0.705803	+	5.21045i	0.0735850	+	0.543227i
$93$	4.58239	−	2.18124i	0.475172	−	0.226184i
$94$	4.59100	−	9.53330i	0.473525	−	0.983285i
$95$	4.28469	−	0.192426i	0.439600	−	0.0197425i
$96$	6.30168	−	5.45546i	0.643163	−	0.556795i
$97$	−1.66539	+	0.380113i	−0.169094	+	0.0385947i	−0.306230	−	0.951958i	$-0.599068\pi$
$97$	−1.66539	+	0.380113i	−0.169094	+	0.0385947i	0.137135	+	0.990552i	$0.456210\pi$
$98$	3.07165	+	0.416083i	0.310284	+	0.0420308i
$99$	−0.656145	−	0.485864i	−0.0659450	−	0.0488312i
$100$	4.03805	+	1.51551i	0.403805	+	0.151551i
$101$	3.76928	+	0.860314i	0.375058	+	0.0856045i	0.405894	−	0.913920i	$-0.366960\pi$
$101$	3.76928	+	0.860314i	0.375058	+	0.0856045i	−0.0308367	+	0.999524i	$0.509817\pi$
$102$	−3.62294	−	6.80628i	−0.358724	−	0.673922i
$103$	−2.88736	−	3.62064i	−0.284500	−	0.356752i	0.618961	−	0.785422i	$-0.287554\pi$
$103$	−2.88736	−	3.62064i	−0.284500	−	0.356752i	−0.903461	+	0.428669i	$0.858982\pi$
$104$	11.4352	−	11.9603i	1.12132	−	1.17280i
$105$	−1.87602	−	3.17250i	−0.183081	−	0.309604i
$106$	4.97216	−	2.67563i	0.482939	−	0.259881i
$107$	−1.31054	+	0.705233i	−0.126695	+	0.0681774i	−0.535988	−	0.844225i	$-0.680061\pi$
$107$	−1.31054	+	0.705233i	−0.126695	+	0.0681774i	0.409293	+	0.912403i	$0.365775\pi$
$108$	−3.19126	−	3.75450i	−0.307079	−	0.361277i
$109$	5.55200	−	5.80693i	0.531785	−	0.556203i	−0.401260	−	0.915964i	$-0.631428\pi$
$109$	5.55200	−	5.80693i	0.531785	−	0.556203i	0.933044	+	0.359761i	$0.117142\pi$
$110$	0.116964	+	0.146668i	0.0111520	+	0.0139842i
$111$	−1.48060	+	0.788114i	−0.140532	+	0.0748045i
$112$	−3.71649	−	0.848264i	−0.351175	−	0.0801534i
$113$	−12.7906	−	4.80039i	−1.20324	−	0.451583i	−0.332394	−	0.943141i	$-0.607856\pi$
$113$	−12.7906	−	4.80039i	−1.20324	−	0.451583i	−0.870845	+	0.491558i	$0.836428\pi$
$114$	−8.50168	−	7.49590i	−0.796255	−	0.702056i
$115$	−3.69314	−	0.500270i	−0.344387	−	0.0466504i
$116$	−3.56090	+	0.812753i	−0.330622	+	0.0754622i
$117$	−11.7638	−	11.4532i	−1.08757	−	1.05885i
$118$	9.30943	−	0.418087i	0.857003	−	0.0384880i
$119$	5.96261	−	12.3815i	0.546591	−	1.13501i
$120$	1.51289	+	3.17832i	0.138108	+	0.290140i
$121$	−1.46662	−	10.8271i	−0.133329	−	0.984277i
$122$	5.43423	−	6.81430i	0.491992	−	0.616938i
$123$	−2.88868	+	15.5173i	−0.260463	+	1.39915i
$124$	−2.31894	−	1.53072i	−0.208247	−	0.137463i
$125$	−3.77232	+	5.19215i	−0.337406	+	0.464400i
$126$	−2.25332	+	9.47571i	−0.200741	+	0.844163i
$127$	−0.824436	−	2.98728i	−0.0731569	−	0.265078i	0.918229	−	0.396049i	$-0.129619\pi$
$127$	−0.824436	−	2.98728i	−0.0731569	−	0.265078i	−0.991386	+	0.130971i	$0.958190\pi$
$128$	−1.99127	−	0.647003i	−0.176005	−	0.0571875i
$129$	12.7515	+	12.3028i	1.12271	+	1.08320i
$130$	1.93488	+	3.23845i	0.169701	+	0.284031i
$131$	3.80518	−	4.35537i	0.332460	−	0.380531i	−0.562410	−	0.826859i	$-0.690126\pi$
$131$	3.80518	−	4.35537i	0.332460	−	0.380531i	0.894870	+	0.446328i	$0.147268\pi$
$132$	−0.0420866	+	0.445022i	−0.00366317	+	0.0387342i
$133$	1.81083	−	20.1200i	0.157019	−	1.74462i
$134$	−5.93542	+	0.534197i	−0.512742	+	0.0461476i
$135$	3.16704	−	1.47246i	0.272575	−	0.126729i
$136$	−6.73168	+	11.2669i	−0.577237	+	0.966131i
$137$	−4.01033	−	12.3425i	−0.342626	−	1.05449i	−0.962843	−	0.270063i	$-0.912955\pi$
$137$	−4.01033	−	12.3425i	−0.342626	−	1.05449i	0.620217	−	0.784430i	$-0.287045\pi$
$138$	6.10567	+	7.72785i	0.519749	+	0.657839i
$139$	6.23149	+	0.279856i	0.528548	+	0.0237371i	0.307540	−	0.951535i	$-0.400494\pi$
$139$	6.23149	+	0.279856i	0.528548	+	0.0237371i	0.221007	+	0.975272i	$0.429065\pi$
$140$	−0.956226	+	1.77697i	−0.0808159	+	0.150181i
$141$	1.52126	+	17.8061i	0.128114	+	1.49955i
$142$	−6.14923	−	6.07105i	−0.516032	−	0.509471i
$143$			1.48942i			0.124552i
$144$	1.14738	−	3.42531i	0.0956147	−	0.285443i
$145$	0.116149	−	2.58626i	0.00964564	−	0.214777i
$146$	−6.94900	+	4.58699i	−0.575103	+	0.379622i
$147$	−4.82321	+	2.03574i	−0.397811	+	0.167905i
$148$	0.788331	+	0.471006i	0.0648004	+	0.0387164i
$149$	9.88409	−	1.79370i	0.809737	−	0.146946i	0.242128	−	0.970244i	$-0.422155\pi$
$149$	9.88409	−	1.79370i	0.809737	−	0.146946i	0.567608	+	0.823299i	$0.307869\pi$
$150$	7.95543	−	1.40649i	0.649558	−	0.114839i
$151$	10.6764	+	0.960895i	0.868835	+	0.0781965i	0.515080	−	0.857142i	$-0.327762\pi$
$151$	10.6764	+	0.960895i	0.868835	+	0.0781965i	0.353754	+	0.935338i	$0.384905\pi$
$152$	−3.44496	+	18.9833i	−0.279423	+	1.53975i
$153$	11.1182	+	6.78029i	0.898850	+	0.548154i
$154$	0.758503	−	0.453185i	0.0611219	−	0.0365187i
$155$	1.48314	−	1.29578i	0.119129	−	0.104080i
$156$	−2.03996	+	8.75458i	−0.163327	+	0.700927i
$157$	−17.3351	+	4.78419i	−1.38349	+	0.381820i	−0.877028	−	0.480439i	$-0.840477\pi$
$157$	−17.3351	+	4.78419i	−1.38349	+	0.381820i	−0.506467	+	0.862260i	$0.669049\pi$
$158$	2.27699	+	0.973233i	0.181148	+	0.0774263i
$159$	−4.92825	+	8.16425i	−0.390836	+	0.647467i
$160$	1.78191	−	2.69948i	0.140872	−	0.213412i
$161$	−4.66991	+	16.9210i	−0.368040	+	1.33356i
$162$	−8.72484	−	3.01078i	−0.685488	−	0.236549i
$163$	−8.36368	+	1.13294i	−0.655094	+	0.0887385i	−0.454235	−	0.890882i	$-0.650087\pi$
$163$	−8.36368	+	1.13294i	−0.655094	+	0.0887385i	−0.200859	+	0.979620i	$0.564373\pi$
$164$	8.09067	−	3.03648i	0.631776	−	0.237109i
$165$	−0.296126	−	0.112672i	−0.0230534	−	0.00877148i
$166$	0.381996	+	8.50579i	0.0296486	+	0.660177i
$167$	13.6390	+	18.7725i	1.05542	+	1.45266i	0.884017	+	0.467455i	$0.154829\pi$
$167$	13.6390	+	18.7725i	1.05542	+	1.45266i	0.171400	+	0.985202i	$0.445171\pi$
$168$	15.7910	−	5.05179i	1.21830	−	0.389754i
$169$	−2.27547	+	16.7982i	−0.175036	+	1.29217i
$170$	−2.06778	−	2.16273i	−0.158591	−	0.165874i
$171$	18.8037	+	3.58870i	1.43795	+	0.274434i
$172$	2.15871	−	9.45792i	0.164600	−	0.721159i
$173$	−8.61199	−	20.1488i	−0.654758	−	1.53188i	−0.836168	−	0.548474i	$-0.815209\pi$
$173$	−8.61199	−	20.1488i	−0.654758	−	1.53188i	0.181410	−	0.983408i	$-0.441934\pi$
$174$	−4.96634	+	4.70541i	−0.376497	+	0.356716i
$175$	10.4075	+	9.95056i	0.786731	+	0.752191i
$176$	−0.295249	+	0.142185i	−0.0222553	+	0.0107176i
$177$	−13.1745	+	8.61092i	−0.990253	+	0.647237i
$178$	2.78588	+	5.17703i	0.208810	+	0.388035i
$179$	0.856646	+	1.77884i	0.0640287	+	0.132957i	0.930527	−	0.366223i	$-0.119349\pi$
$179$	0.856646	+	1.77884i	0.0640287	+	0.132957i	−0.866499	+	0.499180i	$0.833635\pi$
$180$	−1.58626	−	1.06785i	−0.118233	−	0.0795928i
$181$	−16.9252	+	13.4974i	−1.25804	+	1.00325i	−0.258734	+	0.965949i	$0.583305\pi$
$181$	−16.9252	+	13.4974i	−1.25804	+	1.00325i	−0.999304	+	0.0373033i	$0.988123\pi$
$182$	16.3384	−	6.98337i	1.21108	−	0.517642i
$183$	−2.04207	+	14.5782i	−0.150954	+	1.07765i
$184$	5.89068	−	15.6957i	0.434267	−	1.15710i
$185$	−0.470468	+	0.449813i	−0.0345895	+	0.0330709i
$186$	−5.19823	−	0.257063i	−0.381153	−	0.0188487i
$187$	−0.262877	−	1.15174i	−0.0192235	−	0.0842235i
$188$	7.91574	−	5.75112i	0.577315	−	0.419444i
$189$	−4.87023	−	15.7127i	−0.354257	−	1.14293i
$190$	−3.96289	−	1.90843i	−0.287499	−	0.138452i
$191$	−2.18264	−	5.81561i	−0.157930	−	0.420803i	0.833322	−	0.552788i	$-0.186436\pi$
$191$	−2.18264	−	5.81561i	−0.157930	−	0.420803i	−0.991252	+	0.131985i	$0.957865\pi$
$192$	−12.4128	+	2.77402i	−0.895818	+	0.200198i
$193$	−11.3239	−	9.03052i	−0.815113	−	0.650031i	0.124519	−	0.992217i	$-0.460261\pi$
$193$	−11.3239	−	9.03052i	−0.815113	−	0.650031i	−0.939632	+	0.342186i	$0.888833\pi$
$194$	1.68868	+	0.466047i	0.121240	+	0.0334602i
$195$	−5.59692	−	3.04462i	−0.400804	−	0.218030i
$196$	2.31888	+	1.68476i	0.165634	+	0.120340i
$197$	−1.81870	+	4.25507i	−0.129577	+	0.303161i	−0.971737	−	0.236068i	$-0.924141\pi$
$197$	−1.81870	+	4.25507i	−0.129577	+	0.303161i	0.842159	+	0.539229i	$0.181284\pi$
$198$	0.356434	+	0.757633i	0.0253306	+	0.0538426i
$199$	−5.29129	+	16.2849i	−0.375089	+	1.15441i	0.568329	+	0.822801i	$0.307590\pi$
$199$	−5.29129	+	16.2849i	−0.375089	+	1.15441i	−0.943418	+	0.331605i	$0.892410\pi$
$200$	−9.04782	−	10.3561i	−0.639777	−	0.732284i
$201$	8.16956	−	5.87915i	0.576236	−	0.414683i
$202$	−2.98585	−	2.60866i	−0.210084	−	0.183545i
$203$	−11.9976	−	2.17725i	−0.842067	−	0.152813i
$204$	0.0323110	−	7.12978i	0.00226222	−	0.499184i
$205$	0.549060	+	6.10055i	0.0383480	+	0.426081i
$206$	0.847998	+	4.67285i	0.0590828	+	0.325573i
$207$	−15.5198	−	5.98570i	−1.07870	−	0.416035i
$208$	−6.26740	+	2.03640i	−0.434566	+	0.141199i
$209$	−0.956683	−	1.44931i	−0.0661752	−	0.100251i
$210$	0.152464	+	3.77667i	0.0105210	+	0.260615i
$211$	6.85042	+	3.68637i	0.471602	+	0.253780i	0.692365	−	0.721548i	$-0.256569\pi$
$211$	6.85042	+	3.68637i	0.471602	+	0.253780i	−0.220763	+	0.975328i	$0.570855\pi$
$212$	5.22119			0.358593
$213$	14.1588	+	3.53962i	0.970144	+	0.242531i
$214$	1.52623			0.104331
$215$	6.05509	+	3.25838i	0.412954	+	0.222220i
$216$	3.28743	+	15.3631i	0.223682	+	1.04532i
$217$	−5.11021	−	7.74164i	−0.346904	−	0.525537i
$218$	−7.83581	+	2.54601i	−0.530708	+	0.172437i
$219$	6.15899	−	12.6424i	0.416186	−	0.854293i
$220$	0.0309741	+	0.170681i	0.00208827	+	0.0115073i
$221$	−2.12952	−	23.6609i	−0.143247	−	1.59161i
$222$	1.72008	+	0.00779514i	0.115444	+	0.000523176i
$223$	24.8728	+	4.51374i	1.66560	+	0.302262i	0.927891	−	0.372852i	$-0.121620\pi$
$223$	24.8728	+	4.51374i	1.66560	+	0.302262i	0.737713	+	0.675115i	$0.235906\pi$
$224$	−11.4729	−	10.0236i	−0.766566	−	0.669728i
$225$	−10.3563	+	8.88384i	−0.690422	+	0.592256i
$226$	9.21802	+	10.5509i	0.613173	+	0.701833i
$227$	5.22817	−	16.0907i	0.347006	−	1.06797i	−0.613495	−	0.789698i	$-0.710237\pi$
$227$	5.22817	−	16.0907i	0.347006	−	1.06797i	0.960501	−	0.278276i	$-0.0897630\pi$
$228$	−3.63820	−	9.82913i	−0.240946	−	0.650950i
$229$	1.52008	−	3.55640i	0.100450	−	0.235013i	−0.861764	−	0.507309i	$-0.830640\pi$
$229$	1.52008	−	3.55640i	0.100450	−	0.235013i	0.962214	+	0.272296i	$0.0877830\pi$
$230$	3.09206	+	2.24651i	0.203884	+	0.148131i
$231$	−0.713105	+	1.31090i	−0.0469189	+	0.0862509i
$232$	11.2259	+	3.09814i	0.737014	+	0.203403i
$233$	−7.42601	−	5.92204i	−0.486494	−	0.387966i	0.349299	−	0.937011i	$-0.386420\pi$
$233$	−7.42601	−	5.92204i	−0.486494	−	0.387966i	−0.835792	+	0.549046i	$0.814991\pi$
$234$	5.05771	+	16.0599i	0.330633	+	1.04987i
$235$	2.43683	+	6.49292i	0.158961	+	0.423551i
$236$	7.76374	+	3.73882i	0.505376	+	0.243376i
$237$	−4.14692	+	0.542612i	−0.269371	+	0.0352464i
$238$	−11.4016	+	8.28376i	−0.739057	+	0.536956i
$239$	2.43407	+	10.6643i	0.157447	+	0.689819i	0.990602	+	0.136779i	$0.0436751\pi$
$239$	2.43407	+	10.6643i	0.157447	+	0.689819i	−0.833155	+	0.553040i	$0.813468\pi$
$240$	0.0692392	−	1.40013i	0.00446937	−	0.0903780i
$241$	−3.20843	+	3.06757i	−0.206673	+	0.197600i	−0.787300	−	0.616570i	$-0.788522\pi$
$241$	−3.20843	+	3.06757i	−0.206673	+	0.197600i	0.580627	+	0.814170i	$0.302807\pi$
$242$	−3.93709	+	10.4903i	−0.253086	+	0.674344i
$243$	15.2723	−	3.12353i	0.979719	−	0.200375i
$244$	7.41095	−	3.16759i	0.474437	−	0.202784i
$245$	−1.58838	+	1.26669i	−0.101478	+	0.0809260i
$246$	10.1495	−	12.6095i	0.647111	−	0.803950i
$247$	−15.1521	−	31.4637i	−0.964105	−	2.00199i
$248$	4.19812	+	7.80142i	0.266581	+	0.495390i
$249$	−7.86758	−	12.0372i	−0.498588	−	0.762825i
$250$	5.92987	−	2.85567i	0.375038	−	0.180609i
$251$	5.83504	+	5.57887i	0.368305	+	0.352135i	0.852410	−	0.522875i	$-0.175140\pi$
$251$	5.83504	+	5.57887i	0.368305	+	0.352135i	−0.484105	+	0.875010i	$0.660855\pi$
$252$	−5.98696	+	6.72856i	−0.377143	+	0.423860i
$253$	0.593069	+	1.38755i	0.0372859	+	0.0872348i
$254$	−0.707183	+	3.09837i	−0.0443726	+	0.194409i
$255$	4.86535	+	1.36651i	0.304680	+	0.0855741i
$256$	11.6332	+	12.1674i	0.727077	+	0.760463i
$257$	1.36659	−	10.0886i	0.0852455	−	0.629308i	−0.897044	−	0.441941i	$-0.854290\pi$
$257$	1.36659	−	10.0886i	0.0852455	−	0.629308i	0.982290	−	0.187367i	$-0.0599955\pi$
$258$	−5.53683	−	17.3071i	−0.344708	−	1.07749i
$259$	1.80200	+	2.48025i	0.111971	+	0.154115i
$260$	0.156505	+	3.48486i	0.00970605	+	0.216122i
$261$	3.17483	−	11.1101i	0.196517	−	0.687697i
$262$	−5.55290	+	2.08404i	−0.343059	+	0.128752i
$263$	−15.7354	+	2.13151i	−0.970288	+	0.131434i	−0.602190	−	0.798353i	$-0.705705\pi$
$263$	−15.7354	+	2.13151i	−0.970288	+	0.131434i	−0.368098	+	0.929787i	$0.619991\pi$
$264$	0.790540	−	1.18589i	0.0486544	−	0.0729866i
$265$	−0.984537	+	3.56739i	−0.0604796	+	0.219143i
$266$	−11.4129	+	17.2898i	−0.699768	+	1.06010i
$267$	−8.50064	−	5.13131i	−0.520231	−	0.314031i
$268$	−5.06720	−	2.16583i	−0.309529	−	0.132299i
$269$	−29.1694	+	8.05026i	−1.77849	+	0.490833i	−0.991942	−	0.126693i	$-0.959564\pi$
$269$	−29.1694	+	8.05026i	−1.77849	+	0.490833i	−0.786551	+	0.617526i	$0.788135\pi$
$270$	−3.57563	−	0.209324i	−0.217606	−	0.0127391i
$271$	14.4453	−	12.6205i	0.877491	−	0.766641i	−0.0959962	−	0.995382i	$-0.530604\pi$
$271$	14.4453	−	12.6205i	0.877491	−	0.766641i	0.973487	+	0.228741i	$0.0734608\pi$
$272$	4.48703	−	2.68088i	0.272066	−	0.162552i
$273$	−17.7490	+	24.1981i	−1.07422	+	1.46453i
$274$	−2.37640	+	13.0951i	−0.143564	+	0.791102i
$275$	1.23281	+	0.110955i	0.0743414	+	0.00669085i
$276$	1.58552	+	8.96810i	0.0954373	+	0.539816i
$277$	−19.5011	+	3.53893i	−1.17171	+	0.212634i	−0.729309	−	0.684185i	$-0.760158\pi$
$277$	−19.5011	+	3.53893i	−1.17171	+	0.212634i	−0.442399	+	0.896818i	$0.645873\pi$
$278$	−5.49148	−	3.28101i	−0.329357	−	0.196782i
$279$	7.77808	−	4.09509i	0.465661	−	0.245167i
$280$	5.36956	−	3.54441i	0.320892	−	0.211819i
$281$	−0.760798	+	16.9405i	−0.0453854	+	1.01058i	0.839088	+	0.543995i	$0.183089\pi$
$281$	−0.760798	+	16.9405i	−0.0453854	+	1.01058i	−0.884474	+	0.466590i	$0.845482\pi$
$282$	7.27931	−	16.8195i	0.433477	−	1.00159i
$283$			12.7414i			0.757395i	0.925521	+	0.378697i	$0.123628\pi$
$283$			12.7414i			0.757395i	−0.925521	+	0.378697i	$0.876372\pi$
$284$	−2.34698	−	7.63807i	−0.139268	−	0.453236i
$285$	7.40182	−	0.632374i	0.438446	−	0.0374586i
$286$	0.723805	−	1.34506i	0.0427995	−	0.0795348i
$287$	28.8208	+	1.29434i	1.70124	+	0.0764026i
$288$	10.5248	−	9.88171i	0.620180	−	0.582285i
$289$	0.569480	+	1.75268i	0.0334988	+	0.103099i
$290$	−1.36172	+	2.27913i	−0.0799627	+	0.133835i
$291$	−2.85563	+	0.774193i	−0.167400	+	0.0453840i
$292$	−7.66843	+	0.690171i	−0.448761	+	0.0403892i
$293$	−0.888492	+	9.87195i	−0.0519062	+	0.576725i	0.927363	+	0.374163i	$0.122070\pi$
$293$	−0.888492	+	9.87195i	−0.0519062	+	0.576725i	−0.979269	+	0.202563i	$0.935073\pi$
$294$	5.34499	+	0.505487i	0.311726	+	0.0294806i
$295$	−4.01853	+	4.59958i	−0.233968	+	0.267798i
$296$	−1.50175	−	2.51350i	−0.0872874	−	0.146095i
$297$	−1.16950	−	0.795014i	−0.0678611	−	0.0461314i
$298$	−9.79772	−	3.18347i	−0.567567	−	0.184414i
$299$	8.07288	+	29.2514i	0.466867	+	1.69165i
$300$	7.09430	+	2.34067i	0.409589	+	0.135139i
$301$	19.0364	−	26.2014i	1.09724	−	1.51022i
$302$	−9.17461	−	6.05611i	−0.527940	−	0.348490i
$303$	6.58338	+	1.22555i	0.378206	+	0.0704061i
$304$	4.79060	−	6.00723i	0.274760	−	0.344538i
$305$	0.766814	+	5.66085i	0.0439076	+	0.324139i
$306$	−6.74553	−	11.5261i	−0.385616	−	0.658904i
$307$	8.41459	−	17.4731i	0.480246	−	0.997241i	−0.510292	−	0.860001i	$-0.670463\pi$
$307$	8.41459	−	17.4731i	0.480246	−	0.997241i	0.990538	−	0.137240i	$-0.0438231\pi$
$308$	0.816218	−	0.0366564i	0.0465083	−	0.00208869i
$309$	−5.24995	−	6.06430i	−0.298659	−	0.344986i
$310$	−1.96909	+	0.449431i	−0.111837	+	0.0255260i
$311$	−2.48700	−	0.336887i	−0.141025	−	0.0191031i	0.0633805	−	0.997989i	$-0.479812\pi$
$311$	−2.48700	−	0.336887i	−0.141025	−	0.0191031i	−0.204405	+	0.978886i	$0.565526\pi$
$312$	18.9547	−	21.4979i	1.07310	−	1.21708i
$313$	−31.0224	−	11.6429i	−1.75349	−	0.658096i	−1.00000		0.000635530i	$-0.999798\pi$
$313$	−31.0224	−	11.6429i	−1.75349	−	0.658096i	−0.753489	−	0.657460i	$-0.771631\pi$
$314$	17.9798	+	4.10378i	1.01466	+	0.231589i
$315$	−3.46837	−	5.35939i	−0.195421	−	0.301967i
$316$	1.42767	+	1.79024i	0.0803125	+	0.100709i
$317$	1.25175	−	1.30923i	0.0703054	−	0.0735337i	−0.686706	−	0.726935i	$-0.740944\pi$
$317$	1.25175	−	1.30923i	0.0703054	−	0.0735337i	0.757012	+	0.653401i	$0.226658\pi$
$318$	8.41809	−	4.97795i	0.472063	−	0.279150i
$319$	−0.923052	+	0.496715i	−0.0516810	+	0.0278107i
$320$	−4.34647	+	2.33893i	−0.242975	+	0.130750i
$321$	−2.21881	+	1.31207i	−0.123842	+	0.0732325i
$322$	12.4403	−	13.0115i	0.693269	−	0.725102i
$323$	17.2700	+	21.6559i	0.960929	+	1.20497i
$324$	−5.78523	−	6.27474i	−0.321402	−	0.348597i
$325$	24.2674	+	5.53887i	1.34611	+	0.307241i
$326$	8.10357	+	3.04132i	0.448815	+	0.168443i
$327$	9.20281	−	10.4376i	0.508916	−	0.577201i
$328$	−27.3038	−	3.69855i	−1.50760	−	0.204218i
$329$	31.8456	−	7.26855i	1.75571	−	0.400728i
$330$	0.212669	+	0.245657i	0.0117070	+	0.0135230i
$331$	−6.40432	+	0.287618i	−0.352013	+	0.0158089i	−0.220170	−	0.975462i	$-0.570661\pi$
$331$	−6.40432	+	0.287618i	−0.352013	+	0.0158089i	−0.131844	+	0.991271i	$0.542090\pi$
$332$	−3.41606	+	7.09353i	−0.187481	+	0.389308i
$333$	−2.50733	+	1.46739i	−0.137401	+	0.0804123i
$334$	−3.19425	−	23.5809i	−0.174782	−	1.29029i
$335$	2.43531	−	3.05378i	0.133055	−	0.166846i
$336$	−6.49117	−	1.20838i	−0.354123	−	0.0659228i
$337$	20.6308	+	13.6183i	1.12383	+	0.741835i	0.969234	−	0.246143i	$-0.0791632\pi$
$337$	20.6308	+	13.6183i	1.12383	+	0.741835i	0.154598	+	0.987977i	$0.450592\pi$
$338$	10.2182	−	14.0642i	0.555797	−	0.764989i
$339$	−22.4713	−	7.41413i	−1.22048	−	0.402680i
$340$	−0.736086	−	2.66715i	−0.0399199	−	0.144646i
$341$	−0.758392	−	0.246417i	−0.0410692	−	0.0133442i
$342$	−15.2371	−	12.3787i	−0.823926	−	0.669366i
$343$	−6.45841	−	10.8096i	−0.348721	−	0.583661i
$344$	−20.3507	+	23.2933i	−1.09724	+	1.25589i
$345$	−6.42646	−	0.607763i	−0.345989	−	0.0327209i
$346$	−2.01432	+	22.3809i	−0.108290	+	1.20320i
$347$	−26.4962	+	2.38470i	−1.42239	+	0.128018i	−0.773950	−	0.633247i	$-0.781722\pi$
$347$	−26.4962	+	2.38470i	−1.42239	+	0.128018i	−0.648442	+	0.761264i	$0.724579\pi$
$348$	−6.10586	+	1.65537i	−0.327309	+	0.0887371i
$349$	1.94741	−	3.25941i	0.104242	−	0.174472i	−0.801884	−	0.597480i	$-0.796169\pi$
$349$	1.94741	−	3.25941i	0.104242	−	0.174472i	0.906126	+	0.423008i	$0.139026\pi$
$350$	−4.56308	−	14.0437i	−0.243907	−	0.750668i
$351$	−21.1591	−	18.9996i	−1.12939	−	1.01412i
$352$	−1.30833	−	0.0587573i	−0.0697344	−	0.00313178i
$353$	16.7215	−	31.0737i	0.889995	−	1.65389i	0.142323	−	0.989820i	$-0.454543\pi$
$353$	16.7215	−	31.0737i	0.889995	−	1.65389i	0.747672	−	0.664068i	$-0.231171\pi$
$354$	16.0821	−	1.37397i	0.854753	−	0.0730258i
$355$	5.66130	−	0.163303i	0.300470	−	0.00866724i
$356$			5.43632i			0.288124i
$357$	9.45409	−	21.8445i	0.500363	−	1.15613i
$358$	0.0908405	−	2.02272i	0.00480107	−	0.106904i
$359$	−31.4090	+	20.7329i	−1.65771	+	1.09424i	−0.764461	+	0.644670i	$0.776995\pi$
$359$	−31.4090	+	20.7329i	−1.65771	+	1.09424i	−0.893244	+	0.449572i	$0.851576\pi$
$360$	2.84033	+	5.39483i	0.149699	+	0.284333i
$361$	18.6432	+	11.1388i	0.981222	+	0.586253i
$362$	21.8439	−	3.96408i	1.14809	−	0.208347i
$363$	−3.29464	−	18.6353i	−0.172924	−	0.978098i
$364$	16.3641	+	1.47280i	0.857714	+	0.0771957i
$365$	0.974442	−	5.36962i	0.0510046	−	0.281059i
$366$	8.92861	−	12.1728i	0.466706	−	0.636282i
$367$	2.33717	−	1.39640i	0.121999	−	0.0728913i	−0.450603	−	0.892724i	$-0.648791\pi$
$367$	2.33717	−	1.39640i	0.121999	−	0.0728913i	0.572602	+	0.819833i	$0.305934\pi$
$368$	−5.02787	+	4.39272i	−0.262096	+	0.228986i
$369$	−3.91513	+	27.0567i	−0.203813	+	1.40852i
$370$	0.643459	−	0.177583i	0.0334519	−	0.00923213i
$371$	16.0279	+	6.85066i	0.832128	+	0.355669i
$372$	−4.12020	−	2.48711i	−0.213623	−	0.128951i
$373$	1.33501	−	2.02245i	0.0691242	−	0.104719i	−0.798367	−	0.602171i	$-0.794303\pi$
$373$	1.33501	−	2.02245i	0.0691242	−	0.104719i	0.867491	+	0.497452i	$0.165731\pi$
$374$	−0.322307	+	1.16785i	−0.0166661	+	0.0603882i
$375$	−6.16577	+	9.24930i	−0.318399	+	0.477632i
$376$	−30.9141	+	4.18760i	−1.59427	+	0.215959i
$377$	−19.7350	+	7.40665i	−1.01640	+	0.381462i
$378$	−3.23765	+	16.5565i	−0.166527	+	0.851573i
$379$	1.23334	+	27.4625i	0.0633526	+	1.41066i	0.739137	+	0.673556i	$0.235234\pi$
$379$	1.23334	+	27.4625i	0.0633526	+	1.41066i	−0.675784	+	0.737100i	$0.736195\pi$
$380$	−2.39068	−	3.29049i	−0.122639	−	0.168799i
$381$	−1.63551	−	5.11231i	−0.0837898	−	0.261911i
$382$	−0.855099	+	6.31259i	−0.0437507	+	0.322980i
$383$	−6.72462	−	7.03341i	−0.343612	−	0.359390i	0.528295	−	0.849061i	$-0.322831\pi$
$383$	−6.72462	−	7.03341i	−0.343612	−	0.359390i	−0.871908	+	0.489670i	$0.837117\pi$
$384$	−3.49138	−	0.980607i	−0.178169	−	0.0500414i
$385$	−0.128865	+	0.564595i	−0.00656758	+	0.0287744i
$386$	5.83780	+	13.6582i	0.297136	+	0.695185i
$387$	22.9279	+	20.4008i	1.16549	+	1.03703i
$388$	1.17086	+	1.11945i	0.0594412	+	0.0568316i
$389$	8.52495	−	4.10540i	0.432232	−	0.208152i	−0.205100	−	0.978741i	$-0.565752\pi$
$389$	8.52495	−	4.10540i	0.432232	−	0.208152i	0.637332	+	0.770589i	$0.280038\pi$
$390$	3.57485	+	5.46941i	0.181019	+	0.276954i
$391$	−11.4054	−	21.1947i	−0.576793	−	1.07186i
$392$	−3.96520	−	8.23383i	−0.200273	−	0.415871i
$393$	6.28110	−	7.80344i	0.316840	−	0.393632i
$394$	3.71023	−	2.95881i	0.186919	−	0.149063i
$395$	−1.49239	+	0.637879i	−0.0750904	+	0.0320952i
$396$	−0.0417450	+	0.773114i	−0.00209776	+	0.0388504i
$397$	−4.33316	+	11.5457i	−0.217475	+	0.579460i	−0.999014	−	0.0443961i	$-0.985864\pi$
$397$	−4.33316	+	11.5457i	−0.217475	+	0.579460i	0.781539	+	0.623857i	$0.214435\pi$
$398$	12.6923	−	12.1351i	0.636207	−	0.608276i
$399$	1.72819	−	34.9469i	0.0865179	−	1.74954i
$400$	1.21866	+	5.33930i	0.0609330	+	0.266965i
$401$	−7.98375	+	5.80053i	−0.398689	+	0.289665i	−0.769007	−	0.639241i	$-0.779249\pi$
$401$	−7.98375	+	5.80053i	−0.398689	+	0.289665i	0.370318	+	0.928905i	$0.379249\pi$
$402$	−10.2348	+	1.33919i	−0.510463	+	0.0667926i
$403$	−14.4477	−	6.95765i	−0.719692	−	0.346585i
$404$	−1.28826	−	3.43255i	−0.0640933	−	0.170776i
$405$	5.37813	−	2.76957i	0.267241	−	0.137621i
$406$	9.77664	+	7.79661i	0.485207	+	0.386939i
$407$	0.254048	+	0.0701129i	0.0125927	+	0.00347537i
$408$	−10.8629	+	19.9693i	−0.537796	+	0.988629i
$409$	10.9462	+	7.95289i	0.541255	+	0.393245i	0.824551	−	0.565788i	$-0.191428\pi$
$409$	10.9462	+	7.95289i	0.541255	+	0.393245i	−0.283296	+	0.959033i	$0.591428\pi$
$410$	2.46881	−	5.77606i	0.121926	−	0.285259i
$411$	−7.80277	−	21.0803i	−0.384882	−	1.03981i
$412$	−1.35707	+	4.17662i	−0.0668578	+	0.205767i
$413$	18.9273	+	21.6641i	0.931354	+	1.06602i
$414$	11.1066	+	12.9476i	0.545861	+	0.636338i
$415$	−4.20252	−	3.67163i	−0.206294	−	0.180233i
$416$	−25.9133	−	4.70256i	−1.27050	−	0.230562i
$417$	10.8040	+	0.0489621i	0.529075	+	0.00239768i
$418$	0.159640	+	1.77375i	0.00780825	+	0.0867568i
$419$	1.98218	+	10.9227i	0.0968360	+	0.533610i	0.995483	+	0.0949382i	$0.0302653\pi$
$419$	1.98218	+	10.9227i	0.0968360	+	0.533610i	−0.898647	+	0.438672i	$0.855449\pi$
$420$	−1.53074	+	3.14210i	−0.0746922	+	0.153319i
$421$	30.3846	−	9.87257i	1.48086	−	0.481159i	0.546488	−	0.837467i	$-0.315965\pi$
$421$	30.3846	−	9.87257i	1.48086	−	0.481159i	0.934369	+	0.356308i	$0.115965\pi$
$422$	−4.39498	−	6.65811i	−0.213944	−	0.324112i
$423$	3.87681	+	30.7097i	0.188497	+	1.49316i
$424$	−14.6594	−	7.88858i	−0.711925	−	0.383103i
$425$	−19.7431			−0.957679
$426$	−11.0663	−	10.0772i	−0.536162	−	0.488241i
$427$	26.9062			1.30208
$428$	1.24279	+	0.668773i	0.0600724	+	0.0323264i
$429$	0.104060	+	2.57766i	0.00502406	+	0.124450i
$430$	−3.88472	−	5.88511i	−0.187338	−	0.283805i
$431$	25.0986	−	8.15503i	1.20896	−	0.392814i	0.365908	−	0.930651i	$-0.380758\pi$
$431$	25.0986	−	8.15503i	1.20896	−	0.392814i	0.843049	+	0.537837i	$0.180758\pi$
$432$	1.74638	−	6.00815i	0.0840229	−	0.289067i
$433$	−1.10131	−	6.06870i	−0.0529254	−	0.291643i	0.946601	−	0.322407i	$-0.104492\pi$
$433$	−1.10131	−	6.06870i	−0.0529254	−	0.291643i	−0.999527	+	0.0307636i	$0.990206\pi$
$434$	0.852733	+	9.47464i	0.0409325	+	0.454797i
$435$	0.0203207	−	4.48399i	0.000974305	−	0.214991i
$436$	−7.49621	−	1.36036i	−0.359003	−	0.0651495i
$437$	−26.6442	−	23.2784i	−1.27457	−	1.11355i
$438$	−11.7057	+	8.42394i	−0.559322	+	0.402511i
$439$	−1.39581	−	1.59764i	−0.0666185	−	0.0762510i	0.718797	−	0.695220i	$-0.244693\pi$
$439$	−1.39581	−	1.59764i	−0.0666185	−	0.0762510i	−0.785415	+	0.618970i	$0.787550\pi$
$440$	0.170913	−	0.526016i	0.00814796	−	0.0250768i
$441$	−8.20501	+	3.86011i	−0.390715	+	0.183815i
$442$	−9.57523	+	22.4024i	−0.455447	+	1.06557i
$443$	17.2539	+	12.5357i	0.819756	+	0.595587i	0.916642	−	0.399708i	$-0.130888\pi$
$443$	17.2539	+	12.5357i	0.819756	+	0.595587i	−0.0968868	+	0.995295i	$0.530888\pi$
$444$	1.39722	+	0.760064i	0.0663093	+	0.0360710i
$445$	−3.71438	−	1.02510i	−0.176078	−	0.0485946i
$446$	−20.2684	−	16.1635i	−0.959735	−	0.765363i
$447$	16.9805	−	3.79481i	0.803150	−	0.179488i
$448$	8.16869	+	21.7654i	0.385934	+	1.02832i
$449$	−0.564434	−	0.271817i	−0.0266373	−	0.0128278i	0.420518	−	0.907284i	$-0.361848\pi$
$449$	−0.564434	−	0.271817i	−0.0266373	−	0.0128278i	−0.447155	+	0.894456i	$0.647563\pi$
$450$	13.6697	−	2.98994i	0.644397	−	0.140947i
$451$	2.00641	−	1.45774i	0.0944781	−	0.0686424i
$452$	2.88286	+	12.6306i	0.135598	+	0.594095i
$453$	18.5442	+	0.917046i	0.871282	+	0.0430866i
$454$	−12.5409	+	11.9903i	−0.588573	+	0.562733i
$455$	−4.09201	+	10.9031i	−0.191837	+	0.511147i
$456$	−4.63570	+	33.0939i	−0.217087	+	1.54977i
$457$	7.39671	−	3.16150i	0.346003	−	0.147889i	−0.213005	−	0.977051i	$-0.568325\pi$
$457$	7.39671	−	3.16150i	0.346003	−	0.147889i	0.559008	+	0.829162i	$0.311182\pi$
$458$	−3.10102	+	2.47298i	−0.144901	+	0.115555i
$459$	19.7153	+	10.9575i	0.920230	+	0.511450i
$460$	1.53343	+	3.18420i	0.0714965	+	0.148464i
$461$	16.0524	+	29.8303i	0.747634	+	1.38934i	0.915005	+	0.403443i	$0.132187\pi$
$461$	16.0524	+	29.8303i	0.747634	+	1.38934i	−0.167371	+	0.985894i	$0.553528\pi$
$462$	1.28103	−	0.837294i	0.0595991	−	0.0389544i
$463$	−16.5840	+	7.98644i	−0.770725	+	0.371162i	−0.777555	−	0.628815i	$-0.783540\pi$
$463$	−16.5840	+	7.98644i	−0.770725	+	0.371162i	0.00683000	+	0.999977i	$0.497826\pi$
$464$	−3.35218	−	3.20502i	−0.155621	−	0.148789i
$465$	2.47626	−	2.34616i	0.114834	−	0.108800i
$466$	3.82832	+	8.95680i	0.177343	+	0.414916i
$467$	3.65595	−	16.0177i	0.169177	−	0.741213i	−0.817152	−	0.576423i	$-0.804448\pi$
$467$	3.65595	−	16.0177i	0.169177	−	0.741213i	0.986329	−	0.164790i	$-0.0526947\pi$
$468$	−2.91879	+	15.2936i	−0.134921	+	0.706945i
$469$	−12.7135	−	13.2972i	−0.587053	−	0.614010i
$470$	0.954687	−	7.04778i	0.0440364	−	0.325090i
$471$	−29.6666	+	9.49086i	−1.36697	+	0.437316i
$472$	−16.1492	−	22.2275i	−0.743328	−	1.02310i
$473$	−0.124908	−	2.78130i	−0.00574328	−	0.127884i
$474$	4.00865	+	1.52523i	0.184124	+	0.0700563i
$475$	−27.1716	+	10.1977i	−1.24672	+	0.467901i
$476$	−12.9140	+	1.74932i	−0.591912	+	0.0801799i
$477$	−7.95864	+	14.4737i	−0.364401	+	0.662705i
$478$	2.98435	−	10.8135i	0.136501	−	0.494600i
$479$	14.9263	−	22.6123i	0.681999	−	1.03318i	−0.314474	−	0.949266i	$-0.601828\pi$
$479$	14.9263	−	22.6123i	0.681999	−	1.03318i	0.996473	−	0.0839182i	$-0.0267435\pi$
$480$	2.89524	−	4.79632i	0.132149	−	0.218921i
$481$	4.87329	+	2.08295i	0.222203	+	0.0949741i
$482$	4.38817	−	1.21106i	0.199876	−	0.0551622i
$483$	−6.89973	+	29.6105i	−0.313948	+	1.34732i
$484$	−7.80263	+	6.81695i	−0.354665	+	0.309861i
$485$	−0.985653	+	0.588900i	−0.0447562	+	0.0267406i
$486$	−15.3099	−	4.60101i	−0.694472	−	0.208706i
$487$	1.84836	−	10.1853i	0.0837571	−	0.461540i	−0.914606	−	0.404346i	$-0.867499\pi$
$487$	1.84836	−	10.1853i	0.0837571	−	0.461540i	0.998363	−	0.0571936i	$-0.0182152\pi$
$488$	−25.5934	−	2.30345i	−1.15856	−	0.104272i
$489$	−14.3954	+	2.54504i	−0.650981	+	0.115091i
$490$	2.04999	−	0.372018i	0.0926091	−	0.0168061i
$491$	−30.0925	−	17.9794i	−1.35805	−	0.811400i	−0.365223	−	0.930920i	$-0.619007\pi$
$491$	−30.0925	−	17.9794i	−1.35805	−	0.811400i	−0.992832	+	0.119520i	$0.961864\pi$
$492$	13.7899	−	5.82032i	0.621697	−	0.262400i
$493$	13.9534	−	9.21055i	0.628429	−	0.414822i
$494$	−1.60676	+	35.7773i	−0.0722916	+	1.60970i
$495$	−0.520360	−	0.174305i	−0.0233885	−	0.00783443i
$496$		−	3.52818i		−	0.158420i
$497$	2.81710	−	26.5267i	0.126364	−	1.18988i
$498$	1.25536	+	14.6938i	0.0562541	+	0.658444i
$499$	−15.1097	+	28.0785i	−0.676403	+	1.25697i	0.278610	+	0.960404i	$0.410126\pi$
$499$	−15.1097	+	28.0785i	−0.676403	+	1.25697i	−0.955013	+	0.296563i	$0.904159\pi$
$500$	6.07992	+	0.273050i	0.271902	+	0.0122111i
$501$	24.9158	+	31.5355i	1.11315	+	1.40890i
$502$	−2.55833	−	7.87374i	−0.114184	−	0.351422i
$503$	−0.502722	+	0.841415i	−0.0224153	+	0.0375169i	−0.869451	−	0.494018i	$-0.835528\pi$
$503$	−0.502722	+	0.841415i	−0.0224153	+	0.0375169i	0.847036	+	0.531535i	$0.178385\pi$
$504$	26.9755	−	9.84609i	1.20159	−	0.438580i
$505$	2.58822	−	0.232944i	0.115174	−	0.0103659i
$506$	0.138717	−	1.54127i	0.00616672	−	0.0685179i
$507$	−2.76439	+	29.2306i	−0.122771	+	1.29818i
$508$	−1.93351	+	2.21308i	−0.0857857	+	0.0981897i
$509$	−10.8590	−	18.1749i	−0.481316	−	0.805587i	0.517426	−	0.855728i	$-0.326890\pi$
$509$	−10.8590	−	18.1749i	−0.481316	−	0.805587i	−0.998742	+	0.0501409i	$0.984033\pi$
$510$	−3.72968	−	3.59844i	−0.165153	−	0.159341i
$511$	−24.4460	−	7.94298i	−1.08143	−	0.351377i
$512$	−3.47870	−	12.6048i	−0.153738	−	0.557058i
$513$	32.7931	+	4.89701i	1.44785	+	0.216208i
$514$	−6.13681	+	8.44659i	−0.270683	+	0.372563i
$515$	−2.59779	−	1.71479i	−0.114472	−	0.0755625i
$516$	3.07516	−	16.5191i	0.135376	−	0.727212i
$517$	1.75075	−	2.19538i	0.0769981	−	0.0965526i
$518$	−0.422030	−	3.11555i	−0.0185429	−	0.136889i
$519$	−16.3120	−	34.2686i	−0.716016	−	1.50422i
$520$	4.82579	−	10.0208i	0.211625	−	0.439443i
$521$	30.5691	−	1.37286i	1.33926	−	0.0601461i	0.636335	−	0.771413i	$-0.280450\pi$
$521$	30.5691	−	1.37286i	1.33926	−	0.0601461i	0.702922	+	0.711267i	$0.251878\pi$
$522$	−8.26620	+	8.49036i	−0.361802	+	0.371613i
$523$	37.8649	−	8.64243i	1.65572	−	0.377907i	0.710334	−	0.703865i	$-0.248544\pi$
$523$	37.8649	−	8.64243i	1.65572	−	0.377907i	0.945384	+	0.325958i	$0.105687\pi$
$524$	−5.43484	−	0.736200i	−0.237422	−	0.0321610i
$525$	18.7068	+	16.4937i	0.816431	+	0.719845i
$526$	15.2461	+	5.72194i	0.664759	+	0.249488i
$527$	12.4001	+	2.83024i	0.540157	+	0.123287i
$528$	−0.501037	+	0.266698i	−0.0218048	+	0.0116066i
$529$	4.82803	+	6.05416i	0.209914	+	0.263224i
$530$	2.62273	−	2.74316i	0.113924	−	0.119155i
$531$	−22.1987	+	15.8229i	−0.963339	+	0.686654i
$532$	−16.8695	+	9.07785i	−0.731385	+	0.393575i
$533$	43.9177	−	23.6331i	1.90229	−	1.02367i
$534$	5.18306	+	8.76494i	0.224293	+	0.379296i
$535$	−0.691288	+	0.723031i	−0.0298870	+	0.0312594i
$536$	10.9548	+	13.7369i	0.473175	+	0.593343i
$537$	1.60683	+	3.01869i	0.0693397	+	0.130266i
$538$	30.2542	+	6.90533i	1.30435	+	0.297710i
$539$	0.770136	+	0.289037i	0.0331721	+	0.0124497i
$540$	−2.81986	−	1.73724i	−0.121347	−	0.0747588i
$541$	1.77500	+	0.240440i	0.0763133	+	0.0103373i	0.172290	−	0.985046i	$-0.444883\pi$
$541$	1.77500	+	0.240440i	0.0763133	+	0.0103373i	−0.0959771	+	0.995384i	$0.530598\pi$
$542$	−19.1783	+	4.37732i	−0.823777	+	0.188022i
$543$	−28.3484	+	24.5416i	−1.21655	+	1.05318i
$544$	20.8682	−	0.937190i	0.894715	−	0.0401817i
$545$	2.34300	−	4.86529i	0.100363	−	0.208406i
$546$	27.7880	−	13.2272i	1.18922	−	0.566072i
$547$	3.59253	+	26.5211i	0.153605	+	1.13396i	0.889523	+	0.456890i	$0.151037\pi$
$547$	3.59253	+	26.5211i	0.153605	+	1.13396i	−0.735918	+	0.677071i	$0.763249\pi$
$548$	−7.67315	+	9.62182i	−0.327781	+	0.411024i
$549$	−2.51557	+	25.3723i	−0.107362	+	1.08286i
$550$	−1.05940	−	0.699302i	−0.0451729	−	0.0298184i
$551$	14.4461	−	19.8833i	0.615424	−	0.847058i
$552$	9.09806	−	27.5751i	0.387239	−	1.17367i
$553$	2.03368	+	7.36886i	0.0864808	+	0.313356i
$554$	19.3307	+	6.28092i	0.821282	+	0.266851i
$555$	−0.782785	+	0.811335i	−0.0332274	+	0.0344393i
$556$	−3.03394	−	5.07797i	−0.128668	−	0.215354i
$557$	−16.7540	+	19.1765i	−0.709888	+	0.812533i	−0.989030	−	0.147717i	$-0.952807\pi$
$557$	−16.7540	+	19.1765i	−0.709888	+	0.812533i	0.279141	+	0.960250i	$0.409950\pi$
$558$	−9.01423	−	0.0817037i	−0.381603	−	0.00345879i
$559$	5.01863	−	55.7615i	0.212265	−	2.35846i
$560$	−2.55197	+	0.229682i	−0.107840	+	0.00970582i
$561$	−0.535413	−	1.97488i	−0.0226052	−	0.0833796i
$562$	8.91951	−	14.9288i	0.376247	−	0.629731i
$563$	−2.03394	−	6.25982i	−0.0857204	−	0.263820i	0.899004	−	0.437940i	$-0.144292\pi$
$563$	−2.03394	−	6.25982i	−0.0857204	−	0.263820i	−0.984724	+	0.174120i	$0.944292\pi$
$564$	13.2975	−	10.5062i	0.559926	−	0.442390i
$565$	−9.17352	−	0.411983i	−0.385933	−	0.0173323i
$566$	6.19183	−	11.5064i	0.260262	−	0.483648i
$567$	−9.52640	−	26.8528i	−0.400071	−	1.12771i
$568$	−4.95062	+	24.9913i	−0.207723	+	1.04861i
$569$		−	15.2722i		−	0.640245i	−0.947376	−	0.320123i	$-0.896276\pi$
$569$		−	15.2722i		−	0.640245i	0.947376	−	0.320123i	$-0.103724\pi$
$570$	−6.99168	−	3.02593i	−0.292849	−	0.126742i
$571$	−0.503748	+	11.2168i	−0.0210812	+	0.469409i	0.960490	+	0.278314i	$0.0897754\pi$
$571$	−0.503748	+	11.2168i	−0.0210812	+	0.469409i	−0.981571	+	0.191095i	$0.938796\pi$
$572$	1.17877	−	0.778098i	0.0492868	−	0.0325339i
$573$	−4.18367	−	9.91224i	−0.174775	−	0.414090i
$574$	−25.3982	−	15.1747i	−1.06010	−	0.633381i
$575$	24.8131	−	4.50292i	1.03478	−	0.187785i
$576$	−21.2883	+	5.66807i	−0.887013	+	0.236170i
$577$	−36.3893	−	3.27509i	−1.51491	−	0.136344i	−0.699248	−	0.714879i	$-0.746482\pi$
$577$	−36.3893	−	3.27509i	−1.51491	−	0.136344i	−0.815657	+	0.578535i	$0.803624\pi$
$578$	0.337457	−	1.85954i	0.0140364	−	0.0773468i
$579$	−20.2286	−	14.8374i	−0.840670	−	0.616623i
$580$	−2.10751	+	1.25918i	−0.0875095	+	0.0522845i
$581$	−19.7939	+	17.2934i	−0.821190	+	0.717452i
$582$	2.95507	+	0.688579i	0.122491	+	0.0285425i
$583$	1.44441	−	0.398633i	0.0598215	−	0.0165097i
$584$	22.5733	+	9.64828i	0.934088	+	0.399249i
$585$	−9.89898	−	4.87811i	−0.409273	−	0.201685i
$586$	5.59978	−	8.48330i	0.231325	−	0.350442i
$587$	−10.6687	+	38.6572i	−0.440345	+	1.59556i	0.320915	+	0.947108i	$0.396010\pi$
$587$	−10.6687	+	38.6572i	−0.440345	+	1.59556i	−0.761260	+	0.648447i	$0.775419\pi$
$588$	4.13086	+	2.75371i	0.170354	+	0.113561i
$589$	18.5277	−	2.50974i	0.763419	−	0.103412i
$590$	5.86425	−	2.20089i	0.241428	−	0.0906093i
$591$	−2.85024	+	7.49106i	−0.117243	+	0.308141i
$592$	0.0523148	+	1.16488i	0.00215013	+	0.0478763i
$593$	−14.9999	−	20.6456i	−0.615971	−	0.847812i	0.381080	−	0.924542i	$-0.375552\pi$
$593$	−14.9999	−	20.6456i	−0.615971	−	0.847812i	−0.997052	+	0.0767299i	$0.975552\pi$
$594$	0.669792	+	1.28629i	0.0274819	+	0.0527770i
$595$	1.23991	−	9.15339i	0.0508314	−	0.375252i
$596$	−6.58319	−	6.88548i	−0.269658	−	0.282040i
$597$	−8.01956	+	28.5530i	−0.328219	+	1.16860i
$598$	6.92474	−	30.3393i	0.283174	−	1.24067i
$599$	−8.13067	−	19.0226i	−0.332210	−	0.777244i	−0.999474	−	0.0324229i	$-0.989678\pi$
$599$	−8.13067	−	19.0226i	−0.332210	−	0.777244i	0.667264	−	0.744821i	$-0.267465\pi$
$600$	−16.3821	−	17.2905i	−0.668795	−	0.705881i
$601$	3.29374	+	3.14913i	0.134354	+	0.128456i	0.755249	−	0.655438i	$-0.227516\pi$
$601$	3.29374	+	3.14913i	0.134354	+	0.128456i	−0.620894	+	0.783894i	$0.713230\pi$
$602$	−29.9241	+	14.4107i	−1.21962	+	0.587336i
$603$	13.7278	−	10.7455i	0.559040	−	0.437590i
$604$	−4.81706	−	8.95159i	−0.196003	−	0.364235i
$605$	−3.18639	−	6.61661i	−0.129545	−	0.269004i
$606$	−5.34969	−	4.30605i	−0.217316	−	0.174921i
$607$	−13.7904	+	10.9975i	−0.559735	+	0.446374i	−0.862042	−	0.506837i	$-0.830815\pi$
$607$	−13.7904	+	10.9975i	−0.559735	+	0.446374i	0.302307	+	0.953211i	$0.402243\pi$
$608$	28.2360	−	12.0686i	1.14512	−	0.489448i
$609$	−20.9157	−	2.92981i	−0.847546	−	0.118722i
$610$	2.05848	−	5.48480i	0.0833453	−	0.222073i
$611$	40.8143	−	39.0225i	1.65117	−	1.57868i
$612$	−0.442210	−	12.3413i	−0.0178753	−	0.498869i
$613$	4.66634	+	20.4446i	0.188472	+	0.825749i	0.977423	+	0.211293i	$0.0677673\pi$
$613$	4.66634	+	20.4446i	0.188472	+	0.825749i	−0.788951	+	0.614456i	$0.789376\pi$
$614$	−16.0903	+	11.6903i	−0.649350	+	0.471780i
$615$	1.37645	+	10.5195i	0.0555037	+	0.424187i
$616$	−2.34706	−	1.13029i	−0.0945659	−	0.0455405i
$617$	12.9468	+	34.4965i	0.521217	+	1.38878i	0.888590	+	0.458703i	$0.151686\pi$
$617$	12.9468	+	34.4965i	0.521217	+	1.38878i	−0.367373	+	0.930074i	$0.619743\pi$
$618$	1.79405	+	8.02778i	0.0721674	+	0.322925i
$619$	−0.125557	−	0.100128i	−0.00504656	−	0.00402450i	0.620963	−	0.783840i	$-0.286742\pi$
$619$	−0.125557	−	0.100128i	−0.00504656	−	0.00402450i	−0.626010	+	0.779815i	$0.715313\pi$
$620$	−1.80033	−	0.496861i	−0.0723032	−	0.0199544i
$621$	−27.2774	−	9.27479i	−1.09460	−	0.372185i
$622$	2.08223	+	1.51283i	0.0834897	+	0.0606588i
$623$	−7.13293	+	16.6883i	−0.285775	+	0.668603i
$624$	−10.7043	+	3.96216i	−0.428517	+	0.158613i
$625$	5.69435	−	17.5254i	0.227774	−	0.701016i
$626$	22.3574	+	25.5901i	0.893582	+	1.02279i
$627$	−1.75693	−	2.44140i	−0.0701652	−	0.0975002i
$628$	12.8425	+	11.2201i	0.512471	+	0.447733i
$629$	−4.13605	−	0.750582i	−0.164915	−	0.0299277i
$630$	0.527722	+	6.52541i	0.0210249	+	0.259979i
$631$	−3.16956	−	35.2167i	−0.126178	−	1.40196i	−0.770616	−	0.637300i	$-0.780051\pi$
$631$	−3.16956	−	35.2167i	−0.126178	−	1.40196i	0.644438	−	0.764657i	$-0.277092\pi$
$632$	−1.30360	−	7.18344i	−0.0518545	−	0.285742i
$633$	12.1132	+	5.90117i	0.481455	+	0.234550i
$634$	−1.76666	+	0.574022i	−0.0701630	+	0.0227973i
$635$	−1.14750	−	1.73839i	−0.0455372	−	0.0689859i
$636$	9.03600	−	0.364783i	0.358301	−	0.0144646i
$637$	14.5667	+	7.83867i	0.577153	+	0.310579i
$638$	1.07497			0.0425584
$639$	24.7511	+	5.13659i	0.979137	+	0.203200i
$640$	−1.40731			−0.0556290
$641$	−18.0640	−	9.72067i	−0.713487	−	0.383944i	0.0764983	−	0.997070i	$-0.475626\pi$
$641$	−18.0640	−	9.72067i	−0.713487	−	0.383944i	−0.789985	+	0.613126i	$0.789912\pi$
$642$	2.64136	−	0.106632i	0.104246	−	0.00420841i
$643$	7.40117	+	11.2123i	0.291873	+	0.442169i	0.950694	−	0.310131i	$-0.100373\pi$
$643$	7.40117	+	11.2123i	0.291873	+	0.442169i	−0.658820	+	0.752300i	$0.728944\pi$
$644$	15.8314	−	5.14393i	0.623844	−	0.202699i
$645$	10.7068	+	5.21605i	0.421581	+	0.205382i
$646$	−5.07208	−	27.9494i	−0.199558	−	1.09966i
$647$	−3.30006	−	36.6667i	−0.129739	−	1.44152i	−0.752236	−	0.658894i	$-0.771024\pi$
$647$	−3.30006	−	36.6667i	−0.129739	−	1.44152i	0.622497	−	0.782622i	$-0.286118\pi$
$648$	6.76272	+	26.3582i	0.265665	+	1.03545i
$649$	2.43325	+	0.441570i	0.0955135	+	0.0173331i
$650$	−19.2235	−	16.7951i	−0.754008	−	0.658757i
$651$	−9.38482	−	13.0410i	−0.367820	−	0.511116i
$652$	5.26596	+	6.02737i	0.206231	+	0.236050i
$653$	−7.17375	+	22.0785i	−0.280731	+	0.864000i	0.706915	+	0.707298i	$0.250086\pi$
$653$	−7.17375	+	22.0785i	−0.280731	+	0.864000i	−0.987646	+	0.156702i	$0.949914\pi$
$654$	−13.3831	+	4.95368i	−0.523320	+	0.193704i
$655$	1.52784	−	3.57455i	0.0596975	−	0.139669i
$656$	8.87733	+	6.44976i	0.346602	+	0.251821i
$657$	9.77572	−	22.3097i	0.381387	−	0.870386i
$658$	−32.2911	−	8.91178i	−1.25884	−	0.347417i
$659$	−34.0759	−	27.1746i	−1.32741	−	1.05857i	−0.993242	−	0.116058i	$-0.962974\pi$
$659$	−34.0759	−	27.1746i	−1.32741	−	1.05857i	−0.334165	−	0.942514i	$-0.608454\pi$
$660$	0.0655298	+	0.293224i	0.00255074	+	0.0114137i
$661$	8.80448	+	23.4595i	0.342455	+	0.912467i	0.988777	+	0.149402i	$0.0477349\pi$
$661$	8.80448	+	23.4595i	0.342455	+	0.912467i	−0.646322	+	0.763065i	$0.723694\pi$
$662$	5.92333	+	2.85253i	0.230217	+	0.110867i
$663$	−5.33853	−	40.7998i	−0.207331	−	1.58453i
$664$	20.3087	−	14.7551i	0.788130	−	0.572610i
$665$	−3.02146	−	13.2379i	−0.117167	−	0.513343i
$666$	2.97739	−	0.106685i	0.115372	−	0.00413395i
$667$	−15.4360	+	14.7583i	−0.597683	+	0.571443i
$668$	7.73179	−	20.6013i	0.299152	−	0.797088i
$669$	43.3612	+	6.07391i	1.67644	+	0.234831i
$670$	−3.68328	+	1.57431i	−0.142298	+	0.0608209i
$671$	1.80836	−	1.44212i	0.0698108	−	0.0556723i
$672$	−20.5558	−	16.5456i	−0.792957	−	0.638262i
$673$	0.354613	+	0.736362i	0.0136693	+	0.0283847i	0.907692	−	0.419638i	$-0.137843\pi$
$673$	0.354613	+	0.736362i	0.0136693	+	0.0283847i	−0.894022	+	0.448022i	$0.852129\pi$
$674$	−12.0131	−	22.3241i	−0.462728	−	0.859892i
$675$	−17.3024	+	16.0983i	−0.665970	+	0.619623i
$676$	14.4833	−	6.97477i	0.557048	−	0.268260i
$677$	−5.52392	−	5.28140i	−0.212301	−	0.202981i	0.577419	−	0.816448i	$-0.304060\pi$
$677$	−5.52392	−	5.28140i	−0.212301	−	0.202981i	−0.789720	+	0.613467i	$0.789774\pi$
$678$	16.6902	+	17.6157i	0.640984	+	0.676528i
$679$	2.12545	+	4.97275i	0.0815674	+	0.190836i
$680$	−1.96304	+	8.60064i	−0.0752792	+	0.329820i
$681$	7.92390	−	28.2124i	0.303644	−	1.08110i
$682$	0.565133	+	0.591083i	0.0216401	+	0.0226337i
$683$	1.25917	−	9.29559i	0.0481809	−	0.355686i	−0.950770	−	0.309897i	$-0.899706\pi$
$683$	1.25917	−	9.29559i	0.0481809	−	0.355686i	0.998951	−	0.0457890i	$-0.0145802\pi$
$684$	−6.98314	−	16.7565i	−0.267007	−	0.640701i
$685$	−5.12724	−	7.05704i	−0.195902	−	0.269636i
$686$	0.579355	+	12.9004i	0.0221199	+	0.492538i
$687$	2.38224	−	6.26105i	0.0908880	−	0.238874i
$688$	11.5327	−	4.32831i	0.439682	−	0.165015i
$689$	29.8596	−	4.04476i	1.13756	−	0.154093i
$690$	5.50820	+	3.67188i	0.209694	+	0.139786i
$691$	1.14547	−	4.15050i	0.0435756	−	0.157893i	−0.938937	−	0.344089i	$-0.888188\pi$
$691$	1.14547	−	4.15050i	0.0435756	−	0.157893i	0.982512	+	0.186197i	$0.0596162\pi$
$692$	−11.4472	+	17.3418i	−0.435158	+	0.659236i
$693$	−1.14254	+	2.31852i	−0.0434016	+	0.0880733i
$694$	25.0869	+	10.7226i	0.952285	+	0.407026i
$695$	4.04163	−	1.11542i	0.153308	−	0.0423103i
$696$	19.6444	+	4.57746i	0.744618	+	0.173508i
$697$	−29.7895	+	26.0263i	−1.12836	+	0.985817i
$698$	−3.34260	+	1.99711i	−0.126519	+	0.0755917i
$699$	−13.2655	−	9.73011i	−0.501747	−	0.368026i
$700$	2.43811	−	13.4351i	0.0921518	−	0.507798i
$701$	−11.6818	−	1.05138i	−0.441215	−	0.0397101i	−0.133195	−	0.991090i	$-0.542524\pi$
$701$	−11.6818	−	1.05138i	−0.441215	−	0.0397101i	−0.308020	+	0.951380i	$0.599666\pi$
$702$	9.87513	+	27.4405i	0.372713	+	1.03568i
$703$	−6.07997	+	1.10335i	−0.229310	+	0.0416137i
$704$	1.71560	+	1.02502i	0.0646590	+	0.0386319i
$705$	4.67092	+	11.0667i	0.175917	+	0.416795i
$706$	−30.2014	+	19.9358i	−1.13665	+	0.750293i
$707$	0.549138	−	12.2275i	0.0206525	−	0.459863i
$708$	13.6975	+	5.92813i	0.514782	+	0.222793i
$709$			32.3807i			1.21608i	0.793905	+	0.608041i	$0.208044\pi$
$709$			32.3807i			1.21608i	−0.793905	+	0.608041i	$0.791956\pi$
$710$	−5.19192	−	2.60371i	−0.194849	−	0.0977155i
$711$	−7.13891	+	1.22879i	−0.267730	+	0.0460834i
$712$	8.21361	−	15.2634i	0.307818	−	0.572022i
$713$	−16.2300	−	0.728891i	−0.607819	−	0.0272972i
$714$	−19.1533	+	15.1328i	−0.716796	+	0.566331i
$715$	0.309362	+	0.952120i	0.0115695	+	0.0356073i
$716$	0.960298	−	1.60727i	0.0358880	−	0.0600664i
$717$	4.95757	+	18.2861i	0.185144	+	0.682907i
$718$	38.4401	−	3.45967i	1.43457	−	0.129114i
$719$	2.26953	−	25.2165i	0.0846390	−	0.940416i	−0.835672	−	0.549229i	$-0.814922\pi$
$719$	2.26953	−	25.2165i	0.0846390	−	0.940416i	0.920311	−	0.391188i	$-0.127936\pi$
$720$	0.0220067	−	2.42796i	0.000820141	−	0.0904848i
$721$	−9.64599	+	11.0407i	−0.359236	+	0.411178i
$722$	−11.4231	−	19.1191i	−0.425124	−	0.711538i
$723$	−5.33832	+	5.53303i	−0.198534	+	0.205776i
$724$	19.5242	+	6.34379i	0.725610	+	0.235765i
$725$	4.66041	+	16.8866i	0.173083	+	0.627153i
$726$	−6.08077	+	18.4301i	−0.225678	+	0.684004i
$727$	19.7304	−	27.1566i	0.731760	−	1.00718i	−0.267291	−	0.963616i	$-0.586128\pi$
$727$	19.7304	−	27.1566i	0.731760	−	1.00718i	0.999051	−	0.0435651i	$-0.0138716\pi$
$728$	−43.7201	−	28.8594i	−1.62037	−	1.06960i
$729$	26.2127	−	6.47273i	0.970839	−	0.239731i
$730$	−3.48943	+	4.37561i	−0.129150	+	0.161948i
$731$	5.96088	+	44.0050i	0.220471	+	1.62758i
$732$	12.6044	−	5.99973i	0.465871	−	0.221757i
$733$	−2.68480	+	5.57504i	−0.0991652	+	0.205919i	−0.944649	−	0.328082i	$-0.893598\pi$
$733$	−2.68480	+	5.57504i	−0.0991652	+	0.205919i	0.845484	+	0.534001i	$0.179312\pi$
$734$	−2.78923	+	0.125265i	−0.102952	+	0.00462360i
$735$	−2.66042	+	2.30316i	−0.0981311	+	0.0849535i
$736$	−26.0134	+	5.93740i	−0.958868	+	0.218855i
$737$	−1.56717	−	0.212288i	−0.0577276	−	0.00781973i
$738$	16.6842	−	22.5316i	0.614155	−	0.829398i
$739$	−42.3464	−	15.8929i	−1.55774	−	0.584628i	−0.583889	−	0.811833i	$-0.698470\pi$
$739$	−42.3464	−	15.8929i	−1.55774	−	0.584628i	−0.973847	+	0.227205i	$0.927041\pi$
$740$	0.601774	+	0.137351i	0.0221217	+	0.00504913i
$741$	−28.4211	−	53.3937i	−1.04407	−	1.96147i
$742$	−11.1452	−	13.9756i	−0.409153	−	0.513061i
$743$	11.8080	−	12.3502i	0.433193	−	0.453085i	−0.469778	−	0.882784i	$-0.655666\pi$
$743$	11.8080	−	12.3502i	0.433193	−	0.453085i	0.902972	+	0.429699i	$0.141380\pi$
$744$	7.81049	+	13.2081i	0.286347	+	0.484234i
$745$	5.94589	−	3.19962i	0.217840	−	0.117225i
$746$	−2.18845	+	1.17765i	−0.0801248	+	0.0431170i
$747$	−14.4569	−	20.2823i	−0.528952	−	0.742092i
$748$	−0.774186	+	0.809735i	−0.0283070	+	0.0296068i
$749$	2.93760	+	3.68364i	0.107338	+	0.134597i
$750$	10.0630	−	5.35644i	0.367447	−	0.195590i
$751$	−21.8196	−	4.98017i	−0.796207	−	0.181729i	−0.194980	−	0.980807i	$-0.562464\pi$
$751$	−21.8196	−	4.98017i	−0.796207	−	0.181729i	−0.601227	+	0.799078i	$0.705321\pi$
$752$	11.6317	+	4.36546i	0.424165	+	0.159192i
$753$	10.4881	+	9.24736i	0.382209	+	0.336992i
$754$	21.4214	+	2.90173i	0.780123	+	0.105675i
$755$	7.02453	−	1.60330i	0.255649	−	0.0583502i
$756$	−9.89119	+	12.0630i	−0.359739	+	0.438727i
$757$	−9.61033	+	0.431600i	−0.349293	+	0.0156868i	−0.218821	−	0.975765i	$-0.570221\pi$
$757$	−9.61033	+	0.431600i	−0.349293	+	0.0156868i	−0.130473	+	0.991452i	$0.541650\pi$
$758$	12.2320	−	25.4000i	0.444286	−	0.922569i
$759$	1.12333	+	2.35992i	0.0407744	+	0.0856598i
$760$	1.74074	+	12.8507i	0.0631434	+	0.466143i
$761$	13.6221	−	17.0816i	0.493803	−	0.619209i	−0.471016	−	0.882125i	$-0.656113\pi$
$761$	13.6221	−	17.0816i	0.493803	−	0.619209i	0.964819	+	0.262916i	$0.0846841\pi$
$762$	−1.00741	+	5.41158i	−0.0364946	+	0.196041i
$763$	−21.2268	−	14.0117i	−0.768463	−	0.507258i
$764$	−3.46239	+	4.76556i	−0.125265	+	0.172412i
$765$	8.51564	+	2.02501i	0.307884	+	0.0732145i
$766$	2.65484	+	9.61959i	0.0959232	+	0.347570i
$767$	47.2967	+	15.3676i	1.70779	+	0.554893i
$768$	20.9830	+	20.2446i	0.757160	+	0.730516i
$769$	0.280372	+	0.469264i	0.0101105	+	0.0169221i	0.863462	−	0.504413i	$-0.168291\pi$
$769$	0.280372	+	0.469264i	0.0101105	+	0.0169221i	−0.853352	+	0.521335i	$0.825434\pi$
$770$	0.390747	−	0.447246i	0.0140816	−	0.0161176i
$771$	1.66023	−	17.5552i	0.0597917	−	0.632234i
$772$	−1.23120	+	13.6797i	−0.0443118	+	0.492344i
$773$	15.6263	−	1.40639i	0.562040	−	0.0505845i	0.195023	−	0.980799i	$-0.437522\pi$
$773$	15.6263	−	1.40639i	0.562040	−	0.0505845i	0.367017	+	0.930214i	$0.380379\pi$
$774$	−10.7914	−	29.5655i	−0.387890	−	1.06271i
$775$	−6.83522	+	11.4402i	−0.245528	+	0.410945i
$776$	−1.59603	−	4.91209i	−0.0572943	−	0.176334i
$777$	3.29191	+	4.16652i	0.118097	+	0.149473i
$778$	−9.69371	−	0.435345i	−0.347536	−	0.0156079i
$779$	−27.5551	+	51.2059i	−0.987263	+	1.83464i
$780$	0.514328	+	6.02011i	0.0184159	+	0.215555i
$781$	−1.23244	−	1.93384i	−0.0441002	−	0.0691983i
$782$			24.6829i			0.882659i
$783$	4.71828	−	19.4494i	0.168617	−	0.695065i
$784$	−0.163287	+	3.63587i	−0.00583168	+	0.129852i
$785$	−10.0879	+	6.65893i	−0.360051	+	0.237668i
$786$	−9.46447	+	3.99468i	−0.337587	+	0.142486i
$787$	32.4029	+	19.3598i	1.15504	+	0.690103i	0.956999	−	0.290091i	$-0.0936856\pi$
$787$	32.4029	+	19.3598i	1.15504	+	0.690103i	0.198039	+	0.980194i	$0.436543\pi$
$788$	4.31769	−	0.783546i	0.153811	−	0.0279127i
$789$	−27.0835	+	4.78825i	−0.964196	+	0.170466i
$790$	1.65772	+	0.149198i	0.0589792	+	0.00530822i
$791$	−7.72275	+	42.5559i	−0.274589	+	1.51311i
$792$	1.28529	−	2.10759i	0.0456707	−	0.0748898i
$793$	39.9289	−	23.8564i	1.41792	−	0.847165i
$794$	9.52393	−	8.32081i	0.337992	−	0.295294i
$795$	−1.45464	+	6.24266i	−0.0515908	+	0.221404i
$796$	15.6526	−	4.31983i	0.554790	−	0.153112i
$797$	33.2743	+	14.2221i	1.17864	+	0.503773i	0.891016	−	0.453971i	$-0.149993\pi$
$797$	33.2743	+	14.2221i	1.17864	+	0.503773i	0.287620	+	0.957745i	$0.407136\pi$
$798$	−18.5436	+	30.7198i	−0.656437	+	1.08747i
$799$	−24.6736	+	37.3788i	−0.872888	+	1.32237i
$800$	−5.82278	+	21.0984i	−0.205866	+	0.745940i
$801$	−15.0701	−	8.28656i	−0.532474	−	0.292791i
$802$	10.0287	−	1.35849i	0.354127	−	0.0479698i
$803$	−2.06874	+	0.776409i	−0.0730041	+	0.0273989i
$804$	−8.92083	−	3.39424i	−0.314613	−	0.119706i
$805$	0.529346	+	11.7868i	0.0186570	+	0.415430i
$806$	9.66615	+	13.3043i	0.340476	+	0.468625i
$807$	−49.9194	+	15.9701i	−1.75725	+	0.562173i
$808$	−1.56915	+	11.5839i	−0.0552024	+	0.407521i
$809$	11.3036	+	11.8226i	0.397412	+	0.415660i	0.890977	−	0.454049i	$-0.150021\pi$
$809$	11.3036	+	11.8226i	0.397412	+	0.415660i	−0.493565	+	0.869709i	$0.664306\pi$
$810$	−6.20275	−	0.112451i	−0.217942	−	0.00395112i
$811$	−0.525019	+	2.30026i	−0.0184359	+	0.0807731i	−0.983309	−	0.181943i	$-0.941761\pi$
$811$	−0.525019	+	2.30026i	−0.0184359	+	0.0807731i	0.964873	+	0.262716i	$0.0846184\pi$
$812$	4.54462	+	10.6327i	0.159485	+	0.373133i
$813$	24.1179	−	22.8508i	0.845853	−	0.801412i
$814$	−0.195351	−	0.186775i	−0.00684707	−	0.00654647i
$815$	−5.11120	+	2.46142i	−0.179037	+	0.0862199i
$816$	7.57814	−	4.95313i	0.265288	−	0.173394i
$817$	30.9332	+	57.4835i	1.08221	+	2.01109i
$818$	−6.02040	−	12.5015i	−0.210498	−	0.437104i
$819$	−29.0266	+	43.1182i	−1.01427	+	1.50667i
$820$	4.54130	−	3.62157i	0.158589	−	0.126471i
$821$	−18.2448	+	7.79820i	−0.636748	+	0.272159i	−0.687089	−	0.726573i	$-0.741112\pi$
$821$	−18.2448	+	7.79820i	−0.636748	+	0.272159i	0.0503414	+	0.998732i	$0.483969\pi$
$822$	−3.19780	+	22.8289i	−0.111536	+	0.796249i
$823$	5.22319	−	13.9171i	0.182069	−	0.485121i	−0.813233	−	0.581938i	$-0.802295\pi$
$823$	5.22319	−	13.9171i	0.182069	−	0.485121i	0.995302	+	0.0968168i	$0.0308661\pi$
$824$	10.1206	−	9.67625i	0.352567	−	0.337088i
$825$	2.14131	+	0.105892i	0.0745508	+	0.00368668i
$826$	−6.56479	−	28.7622i	−0.228418	−	1.00077i
$827$	38.7270	−	28.1368i	1.34667	−	0.978413i	0.347500	−	0.937680i	$-0.387031\pi$
$827$	38.7270	−	28.1368i	1.34667	−	0.978413i	0.999170	−	0.0407326i	$-0.0129692\pi$
$828$	3.37054	+	15.4098i	0.117134	+	0.535527i
$829$	21.6965	+	10.4485i	0.753550	+	0.362891i	0.770898	−	0.636959i	$-0.219808\pi$
$829$	21.6965	+	10.4485i	0.753550	+	0.362891i	−0.0173476	+	0.999850i	$0.505522\pi$
$830$	2.01090	+	5.35802i	0.0697993	+	0.185980i
$831$	−33.5022	+	7.48708i	−1.16218	+	0.259724i
$832$	31.4207	+	25.0572i	1.08932	+	0.868701i
$833$	−12.6476	−	3.49052i	−0.438214	−	0.120939i
$834$	−9.73301	−	5.29458i	−0.337027	−	0.183336i
$835$	12.6179	+	9.16747i	0.436662	+	0.317253i
$836$	−0.647238	+	1.51429i	−0.0223852	+	0.0523728i
$837$	13.1750	−	7.63056i	0.455393	−	0.263751i
$838$	3.51800	−	10.8273i	0.121527	−	0.374022i
$839$	−10.9770	−	12.5642i	−0.378969	−	0.433765i	0.531680	−	0.846945i	$-0.321561\pi$
$839$	−10.9770	−	12.5642i	−0.378969	−	0.433765i	−0.910649	+	0.413180i	$0.864418\pi$
$840$	9.04514	−	6.50926i	0.312087	−	0.224591i
$841$	10.6674	+	9.31980i	0.367840	+	0.321372i
$842$	−32.2372	−	5.85019i	−1.11097	−	0.201611i
$843$	−0.133105	+	29.3711i	−0.00458437	+	1.01159i
$844$	−0.661280	−	7.34742i	−0.0227622	−	0.252909i
$845$	2.03448	+	11.2109i	0.0699883	+	0.385668i
$846$	11.4228	−	29.6171i	0.392723	−	1.01826i
$847$	−32.8968	+	10.6888i	−1.13035	+	0.367273i
$848$	3.65228	+	5.53297i	0.125420	+	0.190003i
$849$	0.890187	+	22.0507i	0.0305511	+	0.756778i
$850$	17.8294	+	9.59441i	0.611543	+	0.329085i
$851$	5.36939			0.184060
$852$	−4.59543	−	13.0548i	−0.157437	−	0.447250i
$853$	−47.1508			−1.61441			−0.807206	−	0.590270i	$-0.799021\pi$
$853$	−47.1508			−1.61441			−0.807206	+	0.590270i	$0.799021\pi$
$854$	−24.2982	−	13.0754i	−0.831467	−	0.447432i
$855$	12.7657	−	1.61155i	0.436578	−	0.0551138i
$856$	−2.47892	−	3.75540i	−0.0847277	−	0.128357i
$857$	−44.2039	+	14.3627i	−1.50998	+	0.490621i	−0.942909	−	0.333050i	$-0.891922\pi$
$857$	−44.2039	+	14.3627i	−1.50998	+	0.490621i	−0.567068	+	0.823671i	$0.691922\pi$
$858$	1.15867	−	2.37838i	0.0395565	−	0.0811965i
$859$	2.10594	+	11.6047i	0.0718538	+	0.395947i	0.999734	+	0.0230685i	$0.00734357\pi$
$859$	2.10594	+	11.6047i	0.0718538	+	0.395947i	−0.927880	+	0.372879i	$0.878371\pi$
$860$	−0.584506	−	6.49439i	−0.0199315	−	0.221457i
$861$	49.9688	+	0.226451i	1.70293	+	0.00771742i
$862$	−26.6289	−	4.83243i	−0.906983	−	0.164593i
$863$	−10.8681	−	9.49519i	−0.369955	−	0.323220i	0.452804	−	0.891610i	$-0.350424\pi$
$863$	−10.8681	−	9.49519i	−0.369955	−	0.323220i	−0.822759	+	0.568390i	$0.807566\pi$
$864$	17.5243	−	17.8370i	0.596187	−	0.606828i
$865$	−9.69027	−	11.0914i	−0.329479	−	0.377119i
$866$	−1.95461	+	6.01566i	−0.0664203	+	0.204421i
$867$	1.10802	+	2.99347i	0.0376303	+	0.101664i
$868$	−3.45728	+	8.08872i	−0.117348	+	0.274549i
$869$	0.531639	+	0.386258i	0.0180346	+	0.0131029i
$870$	−2.19741	+	4.03949i	−0.0744991	+	0.136952i
$871$	−30.6568	−	8.46075i	−1.03877	−	0.286682i
$872$	18.9916	+	15.1453i	0.643138	+	0.512885i
$873$	−4.88798	+	1.53936i	−0.165433	+	0.0520995i
$874$	12.7492	+	33.9701i	0.431248	+	1.14906i
$875$	18.3058	+	8.81560i	0.618849	+	0.298022i
$876$	−13.2231	+	1.73020i	−0.446766	+	0.0584580i
$877$	23.0411	−	16.7403i	0.778043	−	0.565281i	−0.126348	−	0.991986i	$-0.540326\pi$
$877$	23.0411	−	16.7403i	0.778043	−	0.565281i	0.904391	+	0.426705i	$0.140326\pi$
$878$	0.484126	+	2.12109i	0.0163384	+	0.0715834i
$879$	−0.847947	+	17.1469i	−0.0286005	+	0.578350i
$880$	−0.159207	+	0.152217i	−0.00536686	+	0.00513124i
$881$	11.9636	−	31.8769i	0.403064	−	1.07396i	−0.565402	−	0.824815i	$-0.691279\pi$
$881$	11.9636	−	31.8769i	0.403064	−	1.07396i	0.968466	−	0.249145i	$-0.0801495\pi$
$882$	9.28558	+	0.501383i	0.312662	+	0.0168825i
$883$	−27.2424	+	11.6440i	−0.916781	+	0.391851i	−0.799099	−	0.601200i	$-0.794689\pi$
$883$	−27.2424	+	11.6440i	−0.916781	+	0.391851i	−0.117683	+	0.993051i	$0.537547\pi$
$884$	−17.6134	+	14.0462i	−0.592402	+	0.472425i
$885$	−6.63329	+	8.24099i	−0.222976	+	0.277018i
$886$	−9.48960	−	19.7054i	−0.318809	−	0.662014i
$887$	11.0688	+	20.5693i	0.371655	+	0.690650i	0.995888	−	0.0905876i	$-0.0288745\pi$
$887$	11.0688	+	20.5693i	0.371655	+	0.690650i	−0.624234	+	0.781237i	$0.714589\pi$
$888$	−2.77460	−	4.24505i	−0.0931094	−	0.142455i
$889$	−8.83923	+	4.25675i	−0.296458	+	0.142767i
$890$	2.85619	+	2.73079i	0.0957396	+	0.0915364i
$891$	−2.07952	−	1.29418i	−0.0696667	−	0.0433565i
$892$	−9.42164	−	22.0430i	−0.315460	−	0.738055i
$893$	−14.6504	+	64.1874i	−0.490256	+	2.14795i
$894$	−17.1788	−	4.82492i	−0.574543	−	0.161369i
$895$	0.917091	+	0.959202i	0.0306550	+	0.0320626i
$896$	−0.889760	+	6.56848i	−0.0297248	+	0.219437i
$897$	16.0149	+	50.0597i	0.534723	+	1.67145i
$898$	0.377631	+	0.519765i	0.0126017	+	0.0173448i
$899$	−0.506322	−	11.2741i	−0.0168868	−	0.376014i
$900$	12.4412	+	3.55522i	0.414707	+	0.118507i
$901$	−22.3760	+	8.39784i	−0.745451	+	0.279772i
$902$	−2.52034	+	0.341403i	−0.0839182	+	0.0113675i
$903$	31.1146	−	46.6751i	1.03543	−	1.55325i
$904$	10.9892	−	39.8184i	0.365495	−	1.32434i
$905$	−8.01600	+	12.1437i	−0.266461	+	0.403671i
$906$	−16.3011	−	9.83996i	−0.541567	−	0.326911i
$907$	−25.8249	−	11.0381i	−0.857503	−	0.366514i	−0.0810657	−	0.996709i	$-0.525832\pi$
$907$	−25.8249	−	11.0381i	−0.857503	−	0.366514i	−0.776437	+	0.630194i	$0.782975\pi$
$908$	−15.4659	+	4.26830i	−0.513252	+	0.141649i
$909$	11.4791	+	1.66103i	0.380738	+	0.0550930i
$910$	8.99391	−	7.85774i	0.298145	−	0.260481i
$911$	−14.3955	+	8.60091i	−0.476944	+	0.284961i	−0.731184	−	0.682180i	$-0.761032\pi$
$911$	−14.3955	+	8.60091i	−0.476944	+	0.284961i	0.254240	+	0.967141i	$0.418175\pi$
$912$	7.87111	−	10.7311i	0.260639	−	0.355341i
$913$	−0.403451	+	2.22320i	−0.0133523	+	0.0735772i
$914$	−8.21613	−	0.739465i	−0.271766	−	0.0244593i
$915$	1.72258	+	9.74332i	0.0569468	+	0.322104i
$916$	−3.60874	+	0.654890i	−0.119236	+	0.0216382i
$917$	−15.7178	−	9.39097i	−0.519049	−	0.310117i
$918$	−12.4794	−	19.4763i	−0.411881	−	0.642813i
$919$	7.09799	−	4.68534i	0.234141	−	0.154555i	−0.428379	−	0.903599i	$-0.640915\pi$
$919$	7.09799	−	4.68534i	0.234141	−	0.154555i	0.662520	+	0.749044i	$0.269487\pi$
$920$	0.505554	−	11.2570i	0.0166676	−	0.371134i
$921$	13.3419	−	30.8275i	0.439629	−	1.01580i
$922$		−	34.7398i		−	1.14409i
$923$	−19.3393	−	41.8635i	−0.636562	−	1.37795i
$924$	1.41002	−	0.120465i	0.0463862	−	0.00396300i
$925$	2.08712	−	3.87851i	0.0686239	−	0.127525i
$926$	18.8577	+	0.846899i	0.619702	+	0.0278308i
$927$	−9.50947	−	10.1283i	−0.312332	−	0.332658i
$928$	−5.72759	−	17.6277i	−0.188017	−	0.578658i
$929$	9.64915	−	16.1500i	0.316578	−	0.529863i	−0.658256	−	0.752794i	$-0.728706\pi$
$929$	9.64915	−	16.1500i	0.316578	−	0.529863i	0.974834	+	0.222932i	$0.0715626\pi$
$930$	−3.37638	+	0.915377i	−0.110716	+	0.0300164i
$931$	−19.2093	+	1.72887i	−0.629560	+	0.0566615i
$932$	−0.807396	+	8.97091i	−0.0264471	+	0.293852i
$933$	−4.32765	−	0.409274i	−0.141681	−	0.0133990i
$934$	−11.0856	+	12.6885i	−0.362733	+	0.415181i
$935$	−0.407269	−	0.681653i	−0.0133191	−	0.0222924i
$936$	31.3017	−	38.5295i	1.02313	−	1.25938i
$937$	28.2401	+	9.17575i	0.922563	+	0.299759i	0.731518	−	0.681822i	$-0.238812\pi$
$937$	28.2401	+	9.17575i	0.922563	+	0.299759i	0.191045	+	0.981581i	$0.438812\pi$
$938$	5.01920	+	18.1866i	0.163883	+	0.593815i
$939$	−54.5021	−	17.9823i	−1.77861	−	0.586829i
$940$	3.86563	−	5.32058i	0.126083	−	0.173538i
$941$	−30.0096	−	19.8091i	−0.978284	−	0.645759i	−0.0427831	−	0.999084i	$-0.513622\pi$
$941$	−30.0096	−	19.8091i	−0.978284	−	0.645759i	−0.935501	+	0.353325i	$0.885051\pi$
$942$	31.4033	+	5.84599i	1.02318	+	0.190472i
$943$	31.5036	−	39.5043i	1.02590	−	1.28644i
$944$	1.46874	+	10.8427i	0.0478036	+	0.352900i
$945$	−6.37695	−	9.03285i	−0.207442	−	0.293839i
$946$	−1.23881	+	2.57241i	−0.0402771	+	0.0836363i
$947$	54.8829	−	2.46479i	1.78345	−	0.0800950i	0.871502	−	0.490392i	$-0.163146\pi$
$947$	54.8829	−	2.46479i	1.78345	−	0.0800950i	0.911952	+	0.410297i	$0.134575\pi$
$948$	2.59585	+	2.99851i	0.0843094	+	0.0973871i
$949$	−43.3206	+	9.88764i	−1.40625	+	0.320966i
$950$	29.4936	+	3.99518i	0.956899	+	0.129621i
$951$	2.07486	−	2.35326i	0.0672820	−	0.0763097i
$952$	38.9014	+	14.5999i	1.26080	+	0.473187i
$953$	13.8557	+	3.16247i	0.448830	+	0.102442i	0.440960	−	0.897527i	$-0.354638\pi$
$953$	13.8557	+	3.16247i	0.448830	+	0.102442i	0.00786940	+	0.999969i	$0.497495\pi$
$954$	14.2209	−	9.20318i	0.460419	−	0.297964i
$955$	−2.60320	−	3.26431i	−0.0842375	−	0.105630i
$956$	7.16845	−	7.49761i	0.231844	−	0.242490i
$957$	−1.56277	+	0.924126i	−0.0505171	+	0.0298728i
$958$	−24.4683	+	13.1669i	−0.790534	+	0.425405i
$959$	−36.1796	+	19.4691i	−1.16830	+	0.628689i
$960$	−7.35876	+	4.35152i	−0.237503	+	0.140445i
$961$	−15.4899	+	16.2012i	−0.499675	+	0.522619i
$962$	−3.38870	−	4.24929i	−0.109256	−	0.137003i
$963$	−3.74829	+	2.42574i	−0.120787	+	0.0781683i
$964$	4.10390	+	0.936687i	0.132178	+	0.0301687i
$965$	−9.11455	−	3.42075i	−0.293408	−	0.110118i
$966$	20.6206	−	23.3874i	0.663456	−	0.752476i
$967$	49.7563	+	6.73995i	1.60005	+	0.216742i	0.879238	−	0.476383i	$-0.158053\pi$
$967$	49.7563	+	6.73995i	1.60005	+	0.216742i	0.720817	+	0.693125i	$0.243767\pi$
$968$	32.2069	−	7.35101i	1.03517	−	0.236270i
$969$	31.4012	+	36.2720i	1.00875	+	1.16523i
$970$	1.17630	−	0.0528276i	0.0377687	−	0.00169619i
$971$	9.69185	−	20.1253i	0.311026	−	0.645852i	−0.685595	−	0.727983i	$-0.740458\pi$
$971$	9.69185	−	20.1253i	0.311026	−	0.645852i	0.996622	+	0.0821303i	$0.0261724\pi$
$972$	−10.4505	−	10.4551i	−0.335202	−	0.335348i
$973$	−2.65081	−	19.5691i	−0.0849811	−	0.627356i
$974$	−6.61889	+	8.29982i	−0.212083	+	0.265943i
$975$	42.3851	+	7.89034i	1.35741	+	0.252693i
$976$	8.54079	+	5.63773i	0.273384	+	0.180459i
$977$	−21.2988	+	29.3153i	−0.681410	+	0.937880i	−0.999950	−	0.0100296i	$-0.996807\pi$
$977$	−21.2988	+	29.3153i	−0.681410	+	0.937880i	0.318540	+	0.947909i	$0.396807\pi$
$978$	14.2369	+	4.69727i	0.455244	+	0.150202i
$979$	0.415058	+	1.50393i	0.0132653	+	0.0480657i
$980$	1.83229	+	0.595347i	0.0585304	+	0.0190177i
$981$	15.1975	−	18.7067i	0.485219	−	0.597260i
$982$	18.4383	+	30.8606i	0.588391	+	0.984800i
$983$	−5.97181	+	6.83529i	−0.190471	+	0.218012i	−0.840376	−	0.542004i	$-0.817666\pi$
$983$	−5.97181	+	6.83529i	−0.190471	+	0.218012i	0.649905	+	0.760016i	$0.274809\pi$
$984$	−47.5115	−	4.49326i	−1.51461	−	0.143240i
$985$	−0.278809	+	3.09783i	−0.00888360	+	0.0987049i
$986$	−17.0769	+	1.53695i	−0.543839	+	0.0489464i
$987$	54.6055	−	14.8042i	1.73811	−	0.471222i
$988$	−16.9855	+	28.4289i	−0.540380	+	0.904444i
$989$	−17.5282	−	53.9461i	−0.557363	−	1.71539i
$990$	0.385217	+	0.410286i	0.0122430	+	0.0130398i
$991$	36.2871	+	1.62966i	1.15270	+	0.0517677i	0.612994	−	0.790087i	$-0.289965\pi$
$991$	36.2871	+	1.62966i	1.15270	+	0.0517677i	0.539704	+	0.841855i	$0.318536\pi$
$992$	6.68168	−	12.4166i	0.212143	−	0.394229i
$993$	−11.0635	+	0.945208i	−0.351089	+	0.0299953i
$994$	−15.4351	+	22.5865i	−0.489570	+	0.716400i
$995$			11.5092i			0.364867i
$996$	−5.41639	+	12.5150i	−0.171625	+	0.396554i
$997$	2.16690	−	48.2497i	0.0686263	−	1.52808i	−0.609292	−	0.792946i	$-0.708546\pi$
$997$	2.16690	−	48.2497i	0.0686263	−	1.52808i	0.677918	−	0.735137i	$-0.262882\pi$
$998$	27.2903	−	18.0142i	0.863859	−	0.570228i
$999$	−4.23676	+	2.71470i	−0.134045	+	0.0858892i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	213.2.n.a.11.7	✓	528
3.2	odd	2	inner	213.2.n.a.11.16	yes	528
71.13	odd	70	inner	213.2.n.a.155.16	yes	528
213.155	even	70	inner	213.2.n.a.155.7	yes	528

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
213.2.n.a.11.7	✓	528	1.1	even	1	trivial
213.2.n.a.11.16	yes	528	3.2	odd	2	inner
213.2.n.a.155.7	yes	528	213.155	even	70	inner
213.2.n.a.155.16	yes	528	71.13	odd	70	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:	\( N \)	\(=\)	\( 213 = 3 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	213.n (of order \(70\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.903072 - 0.485964i) q^{2} +(1.73064 - 0.0698660i) q^{3} +(-0.522416 - 0.791427i) q^{4} +(0.639254 - 0.207706i) q^{5} +(-1.59685 - 0.777935i) q^{6} +(-0.565283 - 3.11497i) q^{7} +(0.271029 + 3.01138i) q^{8} +(2.99024 - 0.241826i) q^{9} +(-0.678230 - 0.123081i) q^{10} +(-0.204948 - 0.179058i) q^{11} +(-0.959409 - 1.33318i) q^{12} +(-3.60077 - 4.12141i) q^{13} +(-1.00327 + 3.08774i) q^{14} +(1.09181 - 0.404127i) q^{15} +(0.473251 - 1.10723i) q^{16} +(3.51181 + 2.55148i) q^{17} +(-2.81792 - 1.23476i) q^{18} +(6.15106 + 1.69758i) q^{19} +(-0.498341 - 0.397414i) q^{20} +(-1.19593 - 5.35139i) q^{21} +(0.0980674 + 0.261300i) q^{22} +(-4.99559 - 2.40575i) q^{23} +(0.679447 + 5.19268i) q^{24} +(-3.67958 + 2.67337i) q^{25} +(1.24890 + 5.47177i) q^{26} +(5.15813 - 0.627430i) q^{27} +(-2.16995 + 2.07469i) q^{28} +(1.35336 - 3.60601i) q^{29} +(-1.18237 - 0.165623i) q^{30} +(2.69429 - 1.15159i) q^{31} +(3.76237 - 3.00039i) q^{32} +(-0.367202 - 0.295566i) q^{33} +(-1.93149 - 4.01078i) q^{34} +(-1.00836 - 1.87384i) q^{35} +(-1.75354 - 2.24022i) q^{36} +(-0.872484 + 0.420166i) q^{37} +(-4.72988 - 4.52223i) q^{38} +(-6.51959 - 6.88111i) q^{39} +(0.798739 + 1.86874i) q^{40} +(-2.02780 + 8.88436i) q^{41} +(-1.52057 + 5.41387i) q^{42} +(7.06959 + 7.39421i) q^{43} +(-0.0346429 + 0.255744i) q^{44} +(1.86129 - 0.775679i) q^{45} +(3.34227 + 4.60024i) q^{46} +(0.462907 + 10.3074i) q^{47} +(0.741670 - 1.94927i) q^{48} +(-2.82982 + 1.06205i) q^{49} +(4.62209 - 0.626104i) q^{50} +(6.25595 + 4.17034i) q^{51} +(-1.38070 + 5.00284i) q^{52} +(-3.03315 + 4.59502i) q^{53} +(-4.96307 - 1.94005i) q^{54} +(-0.168206 - 0.0718945i) q^{55} +(9.22714 - 2.54653i) q^{56} +(10.7639 + 2.50816i) q^{57} +(-2.97457 + 2.59880i) q^{58} +(-7.80062 + 4.66066i) q^{59} +(-0.890215 - 0.652963i) q^{60} +(-1.51754 + 8.36232i) q^{61} +(-2.99277 - 0.269354i) q^{62} +(-2.44361 - 9.17779i) q^{63} +(-7.22531 + 1.31120i) q^{64} +(-3.15785 - 1.88673i) q^{65} +(0.187975 + 0.445364i) q^{66} +(4.84978 - 3.20131i) q^{67} +(0.184683 - 4.11228i) q^{68} +(-8.81366 - 3.81447i) q^{69} +2.18224i q^{70} +(8.08549 + 2.37168i) q^{71} +(1.53867 + 8.93920i) q^{72} +(3.84742 - 7.14971i) q^{73} +(0.992101 + 0.0445553i) q^{74} +(-6.18126 + 4.88373i) q^{75} +(-1.86990 - 5.75496i) q^{76} +(-0.441906 + 0.739625i) q^{77} +(2.54368 + 9.38242i) q^{78} +(-2.40491 + 0.216446i) q^{79} +(0.0725499 - 0.806095i) q^{80} +(8.88304 - 1.44623i) q^{81} +(6.14872 - 7.03778i) q^{82} +(-4.25832 - 7.12723i) q^{83} +(-3.61046 + 3.74215i) q^{84} +(2.77490 + 0.901619i) q^{85} +(-2.79103 - 10.1131i) q^{86} +(2.09024 - 6.33526i) q^{87} +(0.483665 - 0.665707i) q^{88} +(-4.78435 - 3.15812i) q^{89} +(-2.05783 - 0.204027i) q^{90} +(-10.8026 + 13.5460i) q^{91} +(0.705803 + 5.21045i) q^{92} +(4.58239 - 2.18124i) q^{93} +(4.59100 - 9.53330i) q^{94} +(4.28469 - 0.192426i) q^{95} +(6.30168 - 5.45546i) q^{96} +(-1.66539 + 0.380113i) q^{97} +(3.07165 + 0.416083i) q^{98} +(-0.656145 - 0.485864i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 528 q - 20 q^{3} - 70 q^{4} - 30 q^{6} - 46 q^{7} - 26 q^{9} - 62 q^{10} - 55 q^{12} - 46 q^{13} - 22 q^{15} - 70 q^{16} - 18 q^{18} - 46 q^{19} - 2 q^{21} - 86 q^{22} - 13 q^{24} + 24 q^{25} + 7 q^{27}+ \cdots - 94 q^{99}+O(q^{100}) \) 528 * q - 20 * q^3 - 70 * q^4 - 30 * q^6 - 46 * q^7 - 26 * q^9 - 62 * q^10 - 55 * q^12 - 46 * q^13 - 22 * q^15 - 70 * q^16 - 18 * q^18 - 46 * q^19 - 2 * q^21 - 86 * q^22 - 13 * q^24 + 24 * q^25 + 7 * q^27 + 22 * q^28 - 55 * q^30 - 44 * q^31 - 28 * q^33 - 28 * q^34 + 8 * q^36 - 72 * q^37 - 144 * q^40 - 2 * q^42 - 76 * q^43 - 55 * q^45 - 30 * q^46 + 55 * q^48 - 72 * q^49 + 63 * q^51 + 78 * q^52 - 47 * q^54 - 70 * q^55 + 102 * q^57 - 166 * q^58 - 66 * q^60 - 74 * q^61 - 85 * q^63 + 58 * q^64 + 135 * q^66 + 52 * q^67 + 173 * q^69 + 154 * q^72 - 28 * q^73 + 127 * q^75 + 160 * q^76 + 184 * q^78 - 166 * q^79 + 102 * q^81 + 162 * q^82 + 168 * q^84 - 90 * q^85 + 87 * q^87 - 20 * q^88 + 60 * q^90 - 148 * q^91 + 5 * q^93 - 84 * q^94 + 120 * q^96 - 28 * q^97 - 94 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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