LMFDB - Embedded newform 820.2.bw.a.11.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			11.10
Character	$\chi$	$=$	820.11
Dual form			820.2.bw.a.671.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.02336 - 0.976084i) q^{2} +(-0.470179 + 1.13511i) q^{3} +(0.0945183 + 1.99777i) q^{4} +(-0.453990 + 0.891007i) q^{5} +(1.58913 - 0.702691i) q^{6} +(0.644428 + 2.68423i) q^{7} +(1.85326 - 2.13668i) q^{8} +(1.05391 + 1.05391i) q^{9} +(1.33429 - 0.468685i) q^{10} +(-0.839506 + 0.982935i) q^{11} +(-2.31213 - 0.832019i) q^{12} +(1.80609 + 2.94728i) q^{13} +(1.96056 - 3.37595i) q^{14} +(-0.797936 - 0.934263i) q^{15} +(-3.98213 + 0.377651i) q^{16} +(-0.224143 - 2.84800i) q^{17} +(-0.0498207 - 2.10723i) q^{18} +(5.77889 + 3.54131i) q^{19} +(-1.82293 - 0.822750i) q^{20} +(-3.34991 - 0.530573i) q^{21} +(1.81854 - 0.186465i) q^{22} +(-2.31130 - 1.67926i) q^{23} +(1.55401 + 3.10829i) q^{24} +(-0.587785 - 0.809017i) q^{25} +(1.02851 - 4.77901i) q^{26} +(-5.09717 + 2.11132i) q^{27} +(-5.30156 + 1.54112i) q^{28} +(0.678920 - 8.62650i) q^{29} +(-0.0953464 + 1.73494i) q^{30} +(-1.98848 + 6.11991i) q^{31} +(4.44376 + 3.50043i) q^{32} +(-0.721024 - 1.41509i) q^{33} +(-2.55051 + 3.13330i) q^{34} +(-2.68423 - 0.644428i) q^{35} +(-2.00585 + 2.20507i) q^{36} +(-0.324687 - 0.999284i) q^{37} +(-2.45725 - 9.26470i) q^{38} +(-4.19468 + 0.664371i) q^{39} +(1.06244 + 2.62130i) q^{40} +(4.37897 + 4.67168i) q^{41} +(2.91026 + 3.81276i) q^{42} +(-1.11776 - 7.05726i) q^{43} +(-2.04302 - 1.58423i) q^{44} +(-1.41750 + 0.460575i) q^{45} +(0.726188 + 3.97451i) q^{46} +(-2.33917 + 9.74335i) q^{47} +(1.44364 - 4.69773i) q^{48} +(-0.552783 + 0.281657i) q^{49} +(-0.188155 + 1.40164i) q^{50} +(3.33819 + 1.08464i) q^{51} +(-5.71726 + 3.88672i) q^{52} +(-11.3872 - 0.896192i) q^{53} +(7.27704 + 2.81464i) q^{54} +(-0.494674 - 1.19425i) q^{55} +(6.92966 + 3.59765i) q^{56} +(-6.73689 + 4.89464i) q^{57} +(-9.11497 + 8.16530i) q^{58} +(-8.26946 + 11.3819i) q^{59} +(1.79102 - 1.68239i) q^{60} +(0.870975 - 5.49912i) q^{61} +(8.00847 - 4.32192i) q^{62} +(-2.14977 + 3.50810i) q^{63} +(-1.13084 - 7.91967i) q^{64} +(-3.44599 + 0.271205i) q^{65} +(-0.643382 + 2.15192i) q^{66} +(-3.13364 + 2.67638i) q^{67} +(5.66845 - 0.716972i) q^{68} +(2.99288 - 1.83404i) q^{69} +(2.11791 + 3.27952i) q^{70} +(4.53605 + 3.87415i) q^{71} +(4.20504 - 0.298702i) q^{72} +(-1.11577 + 1.11577i) q^{73} +(-0.643115 + 1.33955i) q^{74} +(1.19469 - 0.286820i) q^{75} +(-6.52849 + 11.8796i) q^{76} +(-3.17943 - 1.62000i) q^{77} +(4.94113 + 3.41447i) q^{78} +(0.233300 + 0.0966359i) q^{79} +(1.47136 - 3.71956i) q^{80} -2.30720i q^{81} +(0.0787056 - 9.05504i) q^{82} -3.93048i q^{83} +(0.743333 - 6.74247i) q^{84} +(2.63935 + 1.09325i) q^{85} +(-5.74462 + 8.31313i) q^{86} +(9.47283 + 4.82665i) q^{87} +(0.544398 + 3.61540i) q^{88} +(16.2443 - 3.89992i) q^{89} +(1.90017 + 0.912270i) q^{90} +(-6.74728 + 6.74728i) q^{91} +(3.13631 - 4.77616i) q^{92} +(-6.01184 - 5.13460i) q^{93} +(11.9041 - 7.68770i) q^{94} +(-5.77889 + 3.54131i) q^{95} +(-6.06274 + 3.39834i) q^{96} +(-9.39960 + 8.02802i) q^{97} +(0.840615 + 0.251327i) q^{98} +(-1.92069 + 0.151161i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q + 12 q^{6} + 100 q^{12} + 24 q^{14} + 32 q^{16} - 8 q^{17} - 40 q^{21} + 52 q^{22} - 24 q^{24} + 28 q^{28} + 12 q^{30} - 20 q^{32} + 40 q^{33} + 44 q^{34} + 36 q^{36} - 80 q^{37} + 52 q^{38} - 160 q^{42}+ \cdots - 116 q^{98}+O(q^{100}) $ 672 * q + 12 * q^6 + 100 * q^12 + 24 * q^14 + 32 * q^16 - 8 * q^17 - 40 * q^21 + 52 * q^22 - 24 * q^24 + 28 * q^28 + 12 * q^30 - 20 * q^32 + 40 * q^33 + 44 * q^34 + 36 * q^36 - 80 * q^37 + 52 * q^38 - 160 * q^42 + 24 * q^44 + 16 * q^46 + 40 * q^48 - 16 * q^49 - 64 * q^52 - 64 * q^54 + 68 * q^56 + 56 * q^58 + 36 * q^62 + 120 * q^64 + 8 * q^65 - 304 * q^68 + 104 * q^69 + 24 * q^70 - 40 * q^72 - 28 * q^74 - 24 * q^76 - 160 * q^77 - 128 * q^78 - 192 * q^82 - 204 * q^84 + 32 * q^85 - 168 * q^88 + 8 * q^89 + 48 * q^90 - 56 * q^92 - 356 * q^94 - 136 * q^96 - 116 * q^98

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.02336	−	0.976084i	−0.723623	−	0.690196i
$2$	−1.02336	−	0.976084i	−0.723623	−	0.690196i
$3$	−0.470179	+	1.13511i	−0.271458	+	0.655358i	−0.999546	−	0.0301259i	$-0.990409\pi$
$3$	−0.470179	+	1.13511i	−0.271458	+	0.655358i	0.728088	+	0.685484i	$0.240409\pi$
$4$	0.0945183	+	1.99777i	0.0472591	+	0.998883i
$5$	−0.453990	+	0.891007i	−0.203031	+	0.398470i
$5$	−0.453990	+	0.891007i	−0.203031	+	0.398470i
$6$	1.58913	−	0.702691i	0.648758	−	0.286872i
$7$	0.644428	+	2.68423i	0.243571	+	1.01455i	0.951350	+	0.308112i	$0.0996971\pi$
$7$	0.644428	+	2.68423i	0.243571	+	1.01455i	−0.707779	+	0.706434i	$0.750303\pi$
$8$	1.85326	−	2.13668i	0.655227	−	0.755432i
$9$	1.05391	+	1.05391i	0.351303	+	0.351303i
$10$	1.33429	−	0.468685i	0.421940	−	0.148211i
$11$	−0.839506	+	0.982935i	−0.253121	+	0.296366i	−0.872388	−	0.488814i	$-0.837430\pi$
$11$	−0.839506	+	0.982935i	−0.253121	+	0.296366i	0.619267	+	0.785180i	$0.287430\pi$
$12$	−2.31213	−	0.832019i	−0.667454	−	0.240183i
$13$	1.80609	+	2.94728i	0.500920	+	0.817427i	0.998757	−	0.0498435i	$-0.0158723\pi$
$13$	1.80609	+	2.94728i	0.500920	+	0.817427i	−0.497837	+	0.867271i	$0.665872\pi$
$14$	1.96056	−	3.37595i	0.523982	−	0.902259i
$15$	−0.797936	−	0.934263i	−0.206026	−	0.241226i
$16$	−3.98213	+	0.377651i	−0.995533	+	0.0944127i
$17$	−0.224143	−	2.84800i	−0.0543625	−	0.690742i	−0.962362	−	0.271770i	$-0.912391\pi$
$17$	−0.224143	−	2.84800i	−0.0543625	−	0.690742i	0.908000	−	0.418971i	$-0.137609\pi$
$18$	−0.0498207	−	2.10723i	−0.0117429	−	0.496678i
$19$	5.77889	+	3.54131i	1.32577	+	0.812431i	0.991508	−	0.130049i	$-0.0415136\pi$
$19$	5.77889	+	3.54131i	1.32577	+	0.812431i	0.334260	+	0.942481i	$0.391514\pi$
$20$	−1.82293	−	0.822750i	−0.407620	−	0.183973i
$21$	−3.34991	−	0.530573i	−0.731009	−	0.115780i
$22$	1.81854	−	0.186465i	0.387715	−	0.0397544i
$23$	−2.31130	−	1.67926i	−0.481940	−	0.350150i	0.320136	−	0.947371i	$-0.396271\pi$
$23$	−2.31130	−	1.67926i	−0.481940	−	0.350150i	−0.802076	+	0.597222i	$0.796271\pi$
$24$	1.55401	+	3.10829i	0.317212	+	0.634476i
$25$	−0.587785	−	0.809017i	−0.117557	−	0.161803i
$26$	1.02851	−	4.77901i	0.201708	−	0.937242i
$27$	−5.09717	+	2.11132i	−0.980950	+	0.406323i
$28$	−5.30156	+	1.54112i	−1.00190	+	0.291245i
$29$	0.678920	−	8.62650i	0.126072	−	1.60190i	−0.530532	−	0.847665i	$-0.678008\pi$
$29$	0.678920	−	8.62650i	0.126072	−	1.60190i	0.656604	−	0.754235i	$-0.271992\pi$
$30$	−0.0953464	+	1.73494i	−0.0174078	+	0.316755i
$31$	−1.98848	+	6.11991i	−0.357141	+	1.09917i	0.597616	+	0.801782i	$0.296115\pi$
$31$	−1.98848	+	6.11991i	−0.357141	+	1.09917i	−0.954758	+	0.297385i	$0.903885\pi$
$32$	4.44376	+	3.50043i	0.785553	+	0.618794i
$33$	−0.721024	−	1.41509i	−0.125514	−	0.246336i
$34$	−2.55051	+	3.13330i	−0.437409	+	0.537357i
$35$	−2.68423	−	0.644428i	−0.453718	−	0.108928i
$36$	−2.00585	+	2.20507i	−0.334308	+	0.367512i
$37$	−0.324687	−	0.999284i	−0.0533782	−	0.164281i	0.920814	−	0.390003i	$-0.127526\pi$
$37$	−0.324687	−	0.999284i	−0.0533782	−	0.164281i	−0.974192	+	0.225722i	$0.927526\pi$
$38$	−2.45725	−	9.26470i	−0.398618	−	1.50293i
$39$	−4.19468	+	0.664371i	−0.671686	+	0.106385i
$40$	1.06244	+	2.62130i	0.167986	+	0.414464i
$41$	4.37897	+	4.67168i	0.683880	+	0.729594i
$41$	4.37897	+	4.67168i	0.683880	+	0.729594i
$42$	2.91026	+	3.81276i	0.449064	+	0.588321i
$43$	−1.11776	−	7.05726i	−0.170457	−	1.07622i	−0.913458	−	0.406933i	$-0.866598\pi$
$43$	−1.11776	−	7.05726i	−0.170457	−	1.07622i	0.743001	−	0.669290i	$-0.233402\pi$
$44$	−2.04302	−	1.58423i	−0.307997	−	0.238832i
$45$	−1.41750	+	0.460575i	−0.211309	+	0.0686584i
$46$	0.726188	+	3.97451i	0.107071	+	0.586009i
$47$	−2.33917	+	9.74335i	−0.341203	+	1.42121i	0.493131	+	0.869955i	$0.335852\pi$
$47$	−2.33917	+	9.74335i	−0.341203	+	1.42121i	−0.834334	+	0.551259i	$0.814148\pi$
$48$	1.44364	−	4.69773i	0.208371	−	0.678059i
$49$	−0.552783	+	0.281657i	−0.0789689	+	0.0402367i
$50$	−0.188155	+	1.40164i	−0.0266091	+	0.198222i
$51$	3.33819	+	1.08464i	0.467440	+	0.151880i
$52$	−5.71726	+	3.88672i	−0.792841	+	0.538991i
$53$	−11.3872	−	0.896192i	−1.56415	−	0.123101i	−0.733421	−	0.679775i	$-0.762077\pi$
$53$	−11.3872	−	0.896192i	−1.56415	−	0.123101i	−0.830731	+	0.556673i	$0.812077\pi$
$54$	7.27704	+	2.81464i	0.990280	+	0.383024i
$55$	−0.494674	−	1.19425i	−0.0667018	−	0.161032i
$56$	6.92966	+	3.59765i	0.926014	+	0.480756i
$57$	−6.73689	+	4.89464i	−0.892323	+	0.648311i
$58$	−9.11497	+	8.16530i	−1.19685	+	1.07216i
$59$	−8.26946	+	11.3819i	−1.07659	+	1.48180i	−0.213375	+	0.976970i	$0.568445\pi$
$59$	−8.26946	+	11.3819i	−1.07659	+	1.48180i	−0.863218	+	0.504832i	$0.831555\pi$
$60$	1.79102	−	1.68239i	0.231220	−	0.217196i
$61$	0.870975	−	5.49912i	0.111517	−	0.704090i	−0.867059	−	0.498205i	$-0.833993\pi$
$61$	0.870975	−	5.49912i	0.111517	−	0.704090i	0.978576	−	0.205885i	$-0.0660074\pi$
$62$	8.00847	−	4.32192i	1.01708	−	0.548885i
$63$	−2.14977	+	3.50810i	−0.270845	+	0.441979i
$64$	−1.13084	−	7.91967i	−0.141355	−	0.989959i
$65$	−3.44599	+	0.271205i	−0.427422	+	0.0336389i
$66$	−0.643382	+	2.15192i	−0.0791949	+	0.264883i
$67$	−3.13364	+	2.67638i	−0.382835	+	0.326972i	−0.819951	−	0.572433i	$-0.806000\pi$
$67$	−3.13364	+	2.67638i	−0.382835	+	0.326972i	0.437117	+	0.899405i	$0.356000\pi$
$68$	5.66845	−	0.716972i	0.687401	−	0.0869457i
$69$	2.99288	−	1.83404i	0.360300	−	0.220792i
$70$	2.11791	+	3.27952i	0.253139	+	0.391978i
$71$	4.53605	+	3.87415i	0.538330	+	0.459777i	0.876564	−	0.481285i	$-0.159830\pi$
$71$	4.53605	+	3.87415i	0.538330	+	0.459777i	−0.338234	+	0.941062i	$0.609830\pi$
$72$	4.20504	−	0.298702i	0.495568	−	0.0352023i
$73$	−1.11577	+	1.11577i	−0.130590	+	0.130590i	−0.769381	−	0.638790i	$-0.779435\pi$
$73$	−1.11577	+	1.11577i	−0.130590	+	0.130590i	0.638790	+	0.769381i	$0.279435\pi$
$74$	−0.643115	+	1.33955i	−0.0747606	+	0.155719i
$75$	1.19469	−	0.286820i	0.137951	−	0.0331191i
$76$	−6.52849	+	11.8796i	−0.748869	+	1.36268i
$77$	−3.17943	−	1.62000i	−0.362330	−	0.184616i
$78$	4.94113	+	3.41447i	0.559473	+	0.386613i
$79$	0.233300	+	0.0966359i	0.0262483	+	0.0108724i	0.395769	−	0.918350i	$-0.370478\pi$
$79$	0.233300	+	0.0966359i	0.0262483	+	0.0108724i	−0.369521	+	0.929223i	$0.620478\pi$
$80$	1.47136	−	3.71956i	0.164503	−	0.415859i
$81$		−	2.30720i		−	0.256356i
$82$	0.0787056	−	9.05504i	0.00869158	−	0.999962i
$83$		−	3.93048i		−	0.431427i	−0.976457	−	0.215713i	$-0.930792\pi$
$83$		−	3.93048i		−	0.431427i	0.976457	−	0.215713i	$-0.0692077\pi$
$84$	0.743333	−	6.74247i	0.0811043	−	0.735664i
$85$	2.63935	+	1.09325i	0.286277	+	0.118580i
$86$	−5.74462	+	8.31313i	−0.619458	+	0.896428i
$87$	9.47283	+	4.82665i	1.01559	+	0.517471i
$88$	0.544398	+	3.61540i	0.0580331	+	0.385403i
$89$	16.2443	−	3.89992i	1.72190	−	0.413390i	0.752440	−	0.658660i	$-0.228877\pi$
$89$	16.2443	−	3.89992i	1.72190	−	0.413390i	0.969455	+	0.245270i	$0.0788765\pi$
$90$	1.90017	+	0.912270i	0.200296	+	0.0961617i
$91$	−6.74728	+	6.74728i	−0.707307	+	0.707307i
$92$	3.13631	−	4.77616i	0.326983	−	0.497949i
$93$	−6.01184	−	5.13460i	−0.623399	−	0.532433i
$94$	11.9041	−	7.68770i	1.22782	−	0.792926i
$95$	−5.77889	+	3.54131i	−0.592901	+	0.363330i
$96$	−6.06274	+	3.39834i	−0.618776	+	0.346842i
$97$	−9.39960	+	8.02802i	−0.954385	+	0.815122i	−0.982838	−	0.184473i	$-0.940942\pi$
$97$	−9.39960	+	8.02802i	−0.954385	+	0.815122i	0.0284523	+	0.999595i	$0.490942\pi$
$98$	0.840615	+	0.251327i	0.0849149	+	0.0253879i
$99$	−1.92069	+	0.151161i	−0.193036	+	0.0151923i
$100$	1.56067	−	1.25072i	0.156067	−	0.125072i
$101$	0.919474	−	1.50045i	0.0914911	−	0.149300i	−0.803620	−	0.595142i	$-0.797096\pi$
$101$	0.919474	−	1.50045i	0.0914911	−	0.149300i	0.895112	+	0.445842i	$0.147096\pi$
$102$	−2.35745	−	4.36833i	−0.233423	−	0.432529i
$103$	1.40493	−	8.87036i	0.138432	−	0.874023i	−0.816532	−	0.577300i	$-0.804106\pi$
$103$	1.40493	−	8.87036i	0.138432	−	0.874023i	0.954964	−	0.296723i	$-0.0958937\pi$
$104$	9.64456	+	1.60302i	0.945727	+	0.157189i
$105$	1.99357	−	2.74391i	0.194552	−	0.267778i
$106$	10.7784	+	12.0320i	1.04689	+	1.16865i
$107$	7.15787	−	5.20050i	0.691978	−	0.502751i	−0.185332	−	0.982676i	$-0.559336\pi$
$107$	7.15787	−	5.20050i	0.691978	−	0.502751i	0.877310	+	0.479925i	$0.159336\pi$
$108$	−4.69969	−	9.98339i	−0.452228	−	0.960652i
$109$	4.21931	+	10.1863i	0.404137	+	0.975673i	0.986651	+	0.162852i	$0.0520693\pi$
$109$	4.21931	+	10.1863i	0.404137	+	0.975673i	−0.582514	+	0.812821i	$0.697931\pi$
$110$	−0.659460	+	1.70499i	−0.0628770	+	0.162564i
$111$	1.28696	+	0.101286i	0.122153	+	0.00961365i
$112$	−3.57990	−	10.4456i	−0.338269	−	0.987017i
$113$	−8.56533	−	2.78304i	−0.805758	−	0.261807i	−0.122958	−	0.992412i	$-0.539238\pi$
$113$	−8.56533	−	2.78304i	−0.805758	−	0.261807i	−0.682800	+	0.730605i	$0.739238\pi$
$114$	11.6718	+	1.56681i	1.09317	+	0.146746i
$115$	2.54554	−	1.29702i	0.237373	−	0.120948i
$116$	17.2979	+	0.540961i	1.60607	+	0.0502270i
$117$	−1.20270	+	5.00961i	−0.111190	+	0.463139i
$118$	19.5723	−	3.57609i	1.80178	−	0.329206i
$119$	7.50026	−	2.43698i	0.687548	−	0.223398i
$120$	−3.47501	−	0.0264964i	−0.317224	−	0.00241878i
$121$	1.45939	+	9.21421i	0.132672	+	0.837656i
$122$	−6.25893	+	4.77742i	−0.566656	+	0.432527i
$123$	−7.36179	+	2.77410i	−0.663790	+	0.250132i
$124$	−12.4141	−	3.39407i	−1.11482	−	0.304796i
$125$	0.987688	−	0.156434i	0.0883415	−	0.0139919i
$126$	5.62419	−	1.49169i	0.501042	−	0.132890i
$127$	−1.00526	−	3.09388i	−0.0892026	−	0.274537i	0.896497	−	0.443050i	$-0.146104\pi$
$127$	−1.00526	−	3.09388i	−0.0892026	−	0.274537i	−0.985699	+	0.168513i	$0.946104\pi$
$128$	−6.57301	+	9.20845i	−0.580978	+	0.813919i
$129$	8.53634	+	2.04939i	0.751583	+	0.180439i
$130$	3.79120	+	3.08604i	0.332510	+	0.270663i
$131$	−8.12465	−	15.9455i	−0.709854	−	1.39317i	−0.910502	−	0.413504i	$-0.864305\pi$
$131$	−8.12465	−	15.9455i	−0.709854	−	1.39317i	0.200648	−	0.979663i	$-0.435695\pi$
$132$	2.75887	−	1.57419i	0.240129	−	0.137016i
$133$	−5.78162	+	17.7940i	−0.501330	+	1.54294i
$134$	5.81920	+	0.319804i	0.502702	+	0.0276268i
$135$	0.432869	−	5.50013i	0.0372555	−	0.473376i
$136$	−6.50067	−	4.79917i	−0.557428	−	0.411525i
$137$	9.17599	−	3.80082i	0.783958	−	0.324726i	0.0454461	−	0.998967i	$-0.485529\pi$
$137$	9.17599	−	3.80082i	0.783958	−	0.324726i	0.738511	+	0.674241i	$0.235529\pi$
$138$	−4.85295	−	1.04443i	−0.413111	−	0.0889074i
$139$	7.16657	+	9.86394i	0.607861	+	0.836649i	0.996399	−	0.0847837i	$-0.0270199\pi$
$139$	7.16657	+	9.86394i	0.607861	+	0.836649i	−0.388538	+	0.921433i	$0.627020\pi$
$140$	1.03371	−	5.42338i	0.0873641	−	0.458359i
$141$	−9.95998	−	7.23635i	−0.838781	−	0.609410i
$142$	−0.860497	−	8.39221i	−0.0722113	−	0.704258i
$143$	−4.41321	−	0.698983i	−0.369051	−	0.0584519i
$144$	−4.59481	−	3.79879i	−0.382901	−	0.316566i
$145$	7.37804	+	4.52127i	0.612713	+	0.375471i
$146$	2.23091	−	0.0527449i	0.184631	−	0.00436520i
$147$	−0.0598054	−	0.759900i	−0.00493267	−	0.0626755i
$148$	1.96565	−	0.743099i	0.161575	−	0.0610824i
$149$	−12.0418	−	14.0991i	−0.986500	−	1.15504i	−0.987908	−	0.155044i	$-0.950448\pi$
$149$	−12.0418	−	14.0991i	−0.986500	−	1.15504i	0.00140726	−	0.999999i	$-0.499552\pi$
$150$	−1.50255	−	0.872599i	−0.122683	−	0.0712474i
$151$	−3.77641	−	6.16254i	−0.307320	−	0.501501i	0.661275	−	0.750143i	$-0.270016\pi$
$151$	−3.77641	−	6.16254i	−0.307320	−	0.501501i	−0.968595	+	0.248643i	$0.920016\pi$
$152$	18.2764	−	5.78469i	1.48242	−	0.469200i
$153$	2.76530	−	3.23776i	0.223562	−	0.261757i
$154$	1.67243	+	4.76123i	0.134769	+	0.383671i
$155$	−4.55013	−	4.55013i	−0.365475	−	0.365475i
$156$	−1.72373	−	8.31718i	−0.138009	−	0.665908i
$157$	2.56319	+	10.6764i	0.204565	+	0.852073i	0.976351	+	0.216191i	$0.0693635\pi$
$157$	2.56319	+	10.6764i	0.204565	+	0.852073i	−0.771786	+	0.635882i	$0.780636\pi$
$158$	−0.144424	−	0.326613i	−0.0114898	−	0.0259840i
$159$	6.37130	−	12.5044i	0.505277	−	0.991662i
$160$	−5.13633	+	2.37026i	−0.406062	+	0.187386i
$161$	3.01806	−	7.28624i	0.237856	−	0.574236i
$162$	−2.25203	+	2.36109i	−0.176936	+	0.185505i
$163$	−14.4724			−1.13357			−0.566783	−	0.823867i	$-0.691812\pi$
$163$	−14.4724			−1.13357			−0.566783	+	0.823867i	$0.691812\pi$
$164$	−8.91903	+	9.18972i	−0.696459	+	0.717596i
$165$	1.58819			0.123641
$166$	−3.83648	+	4.02229i	−0.297769	+	0.312190i
$167$	0.792139	−	1.91239i	0.0612976	−	0.147985i	−0.890263	−	0.455447i	$-0.849479\pi$
$167$	0.792139	−	1.91239i	0.0612976	−	0.147985i	0.951561	+	0.307461i	$0.0994795\pi$
$168$	−7.34192	+	6.17440i	−0.566441	+	0.476365i
$169$	0.477416	−	0.936981i	0.0367243	−	0.0720755i
$170$	−1.63389	−	3.69501i	−0.125313	−	0.283394i
$171$	2.35820	+	9.82263i	0.180336	+	0.751155i
$172$	13.9931	−	2.90006i	1.06696	−	0.221128i
$173$	−4.20753	−	4.20753i	−0.319892	−	0.319892i	0.528833	−	0.848726i	$-0.322630\pi$
$173$	−4.20753	−	4.20753i	−0.319892	−	0.319892i	−0.848726	+	0.528833i	$0.822630\pi$
$174$	−4.98287	−	14.1857i	−0.377750	−	1.07541i
$175$	1.79281	−	2.09911i	0.135523	−	0.158678i
$176$	2.97182	−	4.23122i	0.224009	−	0.318940i
$177$	−9.03166	−	14.7383i	−0.678861	−	1.10780i
$178$	−20.4304	−	11.8648i	−1.53132	−	0.889306i
$179$	11.8082	+	13.8256i	0.882584	+	1.03337i	0.999192	+	0.0401948i	$0.0127979\pi$
$179$	11.8082	+	13.8256i	0.882584	+	1.03337i	−0.116608	+	0.993178i	$0.537202\pi$
$180$	−1.05410	−	2.78831i	−0.0785680	−	0.207828i
$181$	−0.813802	−	10.3403i	−0.0604895	−	0.768591i	−0.950115	−	0.311900i	$-0.899034\pi$
$181$	−0.813802	−	10.3403i	−0.0604895	−	0.768591i	0.889625	−	0.456691i	$-0.150966\pi$
$182$	13.4908	−	0.318960i	1.00000	−	0.0236429i
$183$	5.83261	+	3.57423i	0.431159	+	0.264214i
$184$	−7.87150	+	1.82642i	−0.580295	+	0.134645i
$185$	1.03777	+	0.164367i	0.0762986	+	0.0120845i
$186$	1.14046	+	11.1226i	0.0836224	+	0.815548i
$187$	2.98757	+	2.17060i	0.218473	+	0.158730i
$188$	−19.6860	−	3.75219i	−1.43575	−	0.273657i
$189$	−8.95202	−	12.3214i	−0.651164	−	0.896250i
$190$	9.37048	+	2.01666i	0.679806	+	0.146304i
$191$	10.2966	−	4.26501i	0.745039	−	0.308605i	0.0223235	−	0.999751i	$-0.492894\pi$
$191$	10.2966	−	4.26501i	0.745039	−	0.308605i	0.722716	+	0.691145i	$0.242894\pi$
$192$	9.52142	+	2.44003i	0.687149	+	0.176094i
$193$	0.371788	−	4.72402i	0.0267619	−	0.340042i	−0.968931	−	0.247331i	$-0.920447\pi$
$193$	0.371788	−	4.72402i	0.0267619	−	0.340042i	0.995693	−	0.0927115i	$-0.0295534\pi$
$194$	17.4552	+	0.959278i	1.25321	+	0.0688722i
$195$	1.31238	−	4.03910i	0.0939818	−	0.289246i
$196$	−0.614932	−	1.07771i	−0.0439237	−	0.0769791i
$197$	8.60621	+	16.8906i	0.613167	+	1.20341i	0.963732	+	0.266870i	$0.0859895\pi$
$197$	8.60621	+	16.8906i	0.613167	+	1.20341i	−0.350565	+	0.936538i	$0.614011\pi$
$198$	2.11309	+	1.72006i	0.150171	+	0.122239i
$199$	1.02600	+	0.246321i	0.0727313	+	0.0174612i	0.269648	−	0.962959i	$-0.413093\pi$
$199$	1.02600	+	0.246321i	0.0727313	+	0.0174612i	−0.196916	+	0.980420i	$0.563093\pi$
$200$	−2.81793	−	0.243409i	−0.199258	−	0.0172116i
$201$	−1.56462	−	4.81541i	−0.110360	−	0.339653i
$202$	−2.40551	+	0.638007i	−0.169251	+	0.0448900i
$203$	23.5931	−	3.73677i	1.65591	−	0.262270i
$204$	−1.85134	+	6.77144i	−0.129620	+	0.474095i
$205$	−6.15051	+	1.78079i	−0.429570	+	0.124376i
$206$	−10.0960	+	7.70622i	−0.703419	+	0.536917i
$207$	−0.666115	−	4.20569i	−0.0462982	−	0.292315i
$208$	−8.30514	−	11.0544i	−0.575858	−	0.766483i
$209$	−8.33229	+	2.70732i	−0.576356	+	0.187270i
$210$	−4.71842	+	0.862110i	−0.325602	+	0.0594912i
$211$	1.51689	−	6.31831i	0.104427	−	0.434970i	−0.895522	−	0.445016i	$-0.853198\pi$
$211$	1.51689	−	6.31831i	0.104427	−	0.434970i	0.999950	+	0.0100461i	$0.00319783\pi$
$212$	0.714083	−	22.8337i	0.0490434	−	1.56822i
$213$	−6.53035	+	3.32738i	−0.447452	+	0.227988i
$214$	−12.4012	−	1.66472i	−0.847728	−	0.113798i
$215$	6.79552	+	2.20800i	0.463451	+	0.150584i
$216$	−4.93517	+	14.8039i	−0.335796	+	1.00728i
$217$	−17.7087	−	1.39370i	−1.20214	−	0.0946108i
$218$	5.62485	−	14.5427i	0.380963	−	0.984953i
$219$	−0.741910	−	1.79113i	−0.0501336	−	0.121033i
$220$	2.33907	−	1.10112i	0.157700	−	0.0742376i
$221$	7.98902	−	5.80436i	0.537400	−	0.390444i
$222$	−1.21816	−	1.35983i	−0.0817573	−	0.0912661i
$223$	9.65617	−	13.2906i	0.646625	−	0.890003i	−0.352322	−	0.935879i	$-0.614608\pi$
$223$	9.65617	−	13.2906i	0.646625	−	0.890003i	0.998947	+	0.0458759i	$0.0146079\pi$
$224$	−6.53228	+	14.1839i	−0.436456	+	0.947700i
$225$	0.233158	−	1.47210i	0.0155439	−	0.0981401i
$226$	6.04890	+	11.2085i	0.402367	+	0.745581i
$227$	13.3136	−	21.7259i	0.883657	−	1.44200i	−0.0133149	−	0.999911i	$-0.504238\pi$
$227$	13.3136	−	21.7259i	0.883657	−	1.44200i	0.896972	−	0.442087i	$-0.145762\pi$
$228$	−10.4151	−	12.9961i	−0.689757	−	0.860688i
$229$	−24.6664	+	1.94129i	−1.63000	+	0.128284i	−0.860185	−	0.509983i	$-0.829652\pi$
$229$	−24.6664	+	1.94129i	−1.63000	+	0.128284i	−0.769815	+	0.638267i	$0.779652\pi$
$230$	−3.87100	−	1.15735i	−0.255246	−	0.0763135i
$231$	3.33379	−	2.84732i	0.219347	−	0.187340i
$232$	−17.1739	−	17.4378i	−1.12752	−	1.14485i
$233$	12.9392	−	7.92915i	0.847675	−	0.519456i	−0.0295345	−	0.999564i	$-0.509402\pi$
$233$	12.9392	−	7.92915i	0.847675	−	0.519456i	0.877209	+	0.480108i	$0.159402\pi$
$234$	6.12060	−	3.95268i	0.400116	−	0.258395i
$235$	−7.61943	−	6.50761i	−0.497037	−	0.424510i
$236$	−23.5201	−	15.4446i	−1.53103	−	1.00536i
$237$	−0.219385	+	0.219385i	−0.0142506	+	0.0142506i
$238$	−10.0541	−	4.82698i	−0.651713	−	0.312887i
$239$	4.47410	−	1.07414i	0.289405	−	0.0694801i	−0.0861433	−	0.996283i	$-0.527454\pi$
$239$	4.47410	−	1.07414i	0.289405	−	0.0694801i	0.375549	+	0.926803i	$0.377454\pi$
$240$	3.53031	+	3.41902i	0.227881	+	0.220697i
$241$	18.5450	+	9.44915i	1.19459	+	0.608673i	0.934172	−	0.356823i	$-0.116140\pi$
$241$	18.5450	+	9.44915i	1.19459	+	0.608673i	0.260416	+	0.965496i	$0.416140\pi$
$242$	7.50037	−	10.8539i	0.482142	−	0.697716i
$243$	−12.6726	−	5.24915i	−0.812946	−	0.336733i
$244$	11.0683	+	1.22024i	0.708574	+	0.0781176i
$245$		−	0.620402i		−	0.0396361i
$246$	10.2415	+	4.34683i	0.652973	+	0.277144i
$247$			23.4279i			1.49068i
$248$	9.39114	+	15.5905i	0.596338	+	0.990000i
$249$	4.46154	+	1.84803i	0.282739	+	0.117114i
$250$	−1.16345	−	0.803979i	−0.0735831	−	0.0508481i
$251$	−17.4289	−	8.88049i	−1.10011	−	0.560532i	−0.192899	−	0.981219i	$-0.561789\pi$
$251$	−17.4289	−	8.88049i	−1.10011	−	0.560532i	−0.907206	+	0.420687i	$0.861789\pi$
$252$	−7.21156	−	3.96315i	−0.454286	−	0.249655i
$253$	3.59096	−	0.862113i	0.225762	−	0.0542005i
$254$	−1.99115	+	4.14736i	−0.124936	+	0.260229i
$255$	−2.48193	+	2.48193i	−0.155425	+	0.155425i
$256$	15.7148	−	3.00771i	0.982172	−	0.187982i
$257$	13.5815	+	11.5997i	0.847189	+	0.723568i	0.962942	−	0.269710i	$-0.0869279\pi$
$257$	13.5815	+	11.5997i	0.847189	+	0.723568i	−0.115752	+	0.993278i	$0.536928\pi$
$258$	−6.73534	−	10.4294i	−0.419324	−	0.649309i
$259$	2.47308	−	1.51550i	0.153669	−	0.0941688i
$260$	−0.867514	−	6.85865i	−0.0538009	−	0.425355i
$261$	9.80705	−	8.37601i	0.607041	−	0.518462i
$262$	−7.24976	+	24.2483i	−0.447892	+	1.49807i
$263$	−2.66289	+	0.209574i	−0.164201	+	0.0129229i	−0.160293	−	0.987069i	$-0.551244\pi$
$263$	−2.66289	+	0.209574i	−0.164201	+	0.0129229i	−0.00390784	+	0.999992i	$0.501244\pi$
$264$	−4.35985	−	1.08193i	−0.268330	−	0.0665882i
$265$	5.96819	−	9.73921i	0.366623	−	0.598275i
$266$	23.2851	−	12.5663i	1.42770	−	0.770487i
$267$	−3.21090	+	20.2728i	−0.196504	+	1.24068i
$268$	−5.64296	−	6.00730i	−0.344699	−	0.366954i
$269$	−18.5936	+	25.5919i	−1.13367	+	1.56037i	−0.352776	+	0.935708i	$0.614762\pi$
$269$	−18.5936	+	25.5919i	−1.13367	+	1.56037i	−0.780897	+	0.624660i	$0.785238\pi$
$270$	−5.81157	+	5.20608i	−0.353681	+	0.316832i
$271$	5.20003	−	3.77805i	0.315880	−	0.229500i	−0.418536	−	0.908200i	$-0.637457\pi$
$271$	5.20003	−	3.77805i	0.315880	−	0.229500i	0.734415	+	0.678700i	$0.237457\pi$
$272$	1.96811	+	11.2565i	0.119334	+	0.682524i
$273$	−4.48649	−	10.8314i	−0.271535	−	0.655543i
$274$	−13.1002	−	5.06695i	−0.791414	−	0.306105i
$275$	1.28866	+	0.101420i	0.0777092	+	0.00611584i
$276$	3.94686	+	5.80571i	0.237573	+	0.349463i
$277$	−17.0000	−	5.52363i	−1.02143	−	0.331883i	−0.250034	−	0.968237i	$-0.580442\pi$
$277$	−17.0000	−	5.52363i	−1.02143	−	0.331883i	−0.771397	+	0.636354i	$0.780442\pi$
$278$	2.29408	−	17.0895i	0.137590	−	1.02496i
$279$	−8.54549	+	4.35414i	−0.511605	+	0.260676i
$280$	−6.35153	+	4.54107i	−0.379576	+	0.271381i
$281$	2.01587	−	8.39672i	0.120257	−	0.500906i	−0.879433	−	0.476022i	$-0.842078\pi$
$281$	2.01587	−	8.39672i	0.120257	−	0.500906i	0.999690	−	0.0248843i	$-0.00792174\pi$
$282$	3.12932	+	17.1271i	0.186349	+	1.01991i
$283$	3.42946	−	1.11430i	0.203860	−	0.0662382i	−0.205307	−	0.978698i	$-0.565819\pi$
$283$	3.42946	−	1.11430i	0.203860	−	0.0662382i	0.409167	+	0.912459i	$0.365819\pi$
$284$	−7.31091	+	9.42814i	−0.433822	+	0.559457i
$285$	−1.30267	−	8.22474i	−0.0771635	−	0.487191i
$286$	3.83402	+	5.02297i	0.226710	+	0.297015i
$287$	−9.71796	+	14.7647i	−0.573633	+	0.871535i
$288$	0.994188	+	8.37244i	0.0585831	+	0.493351i
$289$	8.72983	−	1.38267i	0.513520	−	0.0813335i
$290$	−3.13723	−	11.8285i	−0.184224	−	0.694591i
$291$	−4.69321	−	14.4442i	−0.275121	−	0.846735i
$292$	−2.33450	−	2.12358i	−0.136616	−	0.124273i
$293$	29.3005	+	7.03443i	1.71175	+	0.410956i	0.966672	−	0.256018i	$-0.0824106\pi$
$293$	29.3005	+	7.03443i	1.71175	+	0.410956i	0.745081	+	0.666974i	$0.232411\pi$
$294$	−0.680524	+	0.836024i	−0.0396890	+	0.0487579i
$295$	−6.38712	−	12.5354i	−0.371873	−	0.729841i
$296$	−2.73689	−	1.15818i	−0.159078	−	0.0673179i
$297$	2.20382	−	6.78265i	0.127878	−	0.393569i
$298$	−1.43889	+	26.1822i	−0.0833524	+	1.51669i
$299$	0.774814	−	9.84494i	0.0448086	−	0.569348i
$300$	0.685918	+	2.35960i	0.0396015	+	0.136232i
$301$	18.2230	−	7.54823i	1.05036	−	0.435073i
$302$	−2.15055	+	9.99258i	−0.123750	+	0.575008i
$303$	1.27086	+	1.74918i	0.0730088	+	0.100488i
$304$	−24.3497	−	11.9196i	−1.39655	−	0.683633i
$305$	4.50434	+	3.27259i	0.257918	+	0.187388i
$306$	−5.99022	+	0.614209i	−0.342438	+	0.0351120i
$307$	7.56560	+	1.19827i	0.431792	+	0.0683891i	0.368547	−	0.929609i	$-0.379855\pi$
$307$	7.56560	+	1.19827i	0.431792	+	0.0683891i	0.0632444	+	0.997998i	$0.479855\pi$
$308$	2.93587	−	6.50488i	0.167287	−	0.370650i
$309$	9.40829	+	5.76541i	0.535219	+	0.327983i
$310$	0.215095	+	9.09771i	0.0122166	+	0.516715i
$311$	1.74592	+	22.1840i	0.0990020	+	1.25794i	0.822962	+	0.568097i	$0.192320\pi$
$311$	1.74592	+	22.1840i	0.0990020	+	1.25794i	−0.723960	+	0.689842i	$0.757680\pi$
$312$	−6.35428	+	10.1940i	−0.359740	+	0.577119i
$313$	17.3656	+	20.3325i	0.981564	+	1.14926i	0.988794	+	0.149289i	$0.0476986\pi$
$313$	17.3656	+	20.3325i	0.981564	+	1.14926i	−0.00723004	+	0.999974i	$0.502301\pi$
$314$	7.79806	−	13.4277i	0.440070	−	0.757769i
$315$	−2.14977	−	3.50810i	−0.121126	−	0.197659i
$316$	−0.171005	+	0.475212i	−0.00961977	+	0.0267328i
$317$	−10.4504	+	12.2359i	−0.586955	+	0.687236i	−0.971817	−	0.235738i	$-0.924249\pi$
$317$	−10.4504	+	12.2359i	−0.586955	+	0.687236i	0.384861	+	0.922974i	$0.374249\pi$
$318$	−18.7255	+	6.57752i	−1.05007	+	0.368849i
$319$	7.90933	+	7.90933i	0.442838	+	0.442838i
$320$	7.56987	+	2.58787i	0.423169	+	0.144666i
$321$	2.53767	+	10.5702i	0.141639	+	0.589969i
$322$	−10.2005	+	4.51054i	−0.568454	+	0.251363i
$323$	8.79035	−	17.2520i	0.489108	−	0.959929i
$324$	4.60925	−	0.218073i	0.256070	−	0.0121152i
$325$	1.32280	−	3.19352i	0.0733758	−	0.177145i
$326$	14.8104	+	14.1263i	0.820274	+	0.782383i
$327$	−13.5465			−0.749121
$328$	18.0973	−	0.698632i	0.999256	−	0.0385755i
$329$	−27.6609			−1.52499
$330$	−1.62529	−	1.55021i	−0.0894691	−	0.0853362i
$331$	4.71537	−	11.3839i	0.259180	−	0.625716i	−0.739705	−	0.672932i	$-0.765035\pi$
$331$	4.71537	−	11.3839i	0.259180	−	0.625716i	0.998885	+	0.0472158i	$0.0150348\pi$
$332$	7.85218	−	0.371503i	0.430945	−	0.0203889i
$333$	0.710963	−	1.39534i	0.0389605	−	0.0764644i
$334$	−2.67730	+	1.18387i	−0.146495	+	0.0647783i
$335$	−0.962029	−	4.00714i	−0.0525613	−	0.218933i
$336$	13.5401	+	0.847717i	0.738675	+	0.0462468i
$337$	10.0752	+	10.0752i	0.548830	+	0.548830i	0.926102	−	0.377272i	$-0.123138\pi$
$337$	10.0752	+	10.0752i	0.548830	+	0.548830i	−0.377272	+	0.926102i	$0.623138\pi$
$338$	−1.40314	+	0.492868i	−0.0763207	+	0.0268085i
$339$	7.18631	−	8.41409i	0.390307	−	0.456990i
$340$	−1.93460	+	5.37613i	−0.104918	+	0.291561i
$341$	−4.34613	−	7.09224i	−0.235356	−	0.384067i
$342$	7.17443	−	12.3539i	0.387949	−	0.668020i
$343$	11.4374	+	13.3915i	0.617561	+	0.723071i
$344$	−17.1506	−	10.6907i	−0.924701	−	0.576401i
$345$	0.275401	+	3.49931i	0.0148271	+	0.188396i
$346$	0.198900	+	8.41270i	0.0106929	+	0.452270i
$347$	17.3383	+	10.6249i	0.930767	+	0.570375i	0.903188	−	0.429245i	$-0.141220\pi$
$347$	17.3383	+	10.6249i	0.930767	+	0.570375i	0.0275791	+	0.999620i	$0.491220\pi$
$348$	−8.74716	+	19.3807i	−0.468897	+	1.03891i
$349$	29.9787	+	4.74815i	1.60472	+	0.254163i	0.893586	−	0.448892i	$-0.148181\pi$
$349$	29.9787	+	4.74815i	1.60472	+	0.254163i	0.711135	+	0.703055i	$0.248181\pi$
$350$	−3.88359	+	0.398205i	−0.207586	+	0.0212849i
$351$	−15.4286	−	11.2095i	−0.823517	−	0.598320i
$352$	−7.17126	+	1.42930i	−0.382229	+	0.0761820i
$353$	9.80756	+	13.4989i	0.522004	+	0.718476i	0.985886	−	0.167421i	$-0.0535438\pi$
$353$	9.80756	+	13.4989i	0.522004	+	0.718476i	−0.463882	+	0.885897i	$0.653544\pi$
$354$	−5.14324	+	23.8982i	−0.273360	+	1.27018i
$355$	−5.51122	+	2.28282i	−0.292505	+	0.121160i
$356$	9.32651	+	32.0837i	0.494304	+	1.70043i
$357$	−0.760216	+	9.65946i	−0.0402349	+	0.511233i
$358$	1.41097	−	25.6743i	0.0745722	−	1.35693i
$359$	−8.19668	+	25.2268i	−0.432604	+	1.33142i	0.462917	+	0.886402i	$0.346803\pi$
$359$	−8.19668	+	25.2268i	−0.432604	+	1.33142i	−0.895522	+	0.445018i	$0.853197\pi$
$360$	−1.64290	+	3.88232i	−0.0865885	+	0.204616i
$361$	12.2289	+	24.0005i	0.643625	+	1.26318i
$362$	−9.26024	+	11.3762i	−0.486707	+	0.597920i
$363$	−11.1453	−	2.67576i	−0.584979	−	0.140441i
$364$	−14.1172	−	12.8417i	−0.739944	−	0.673090i
$365$	−0.487607	−	1.50070i	−0.0255225	−	0.0785503i
$366$	−2.48009	−	9.35083i	−0.129636	−	0.488776i
$367$	−1.40563	+	0.222630i	−0.0733733	+	0.0116212i	−0.193013	−	0.981196i	$-0.561826\pi$
$367$	−1.40563	+	0.222630i	−0.0733733	+	0.0116212i	0.119640	+	0.992817i	$0.461826\pi$
$368$	9.83809	+	5.81417i	0.512846	+	0.303085i
$369$	−0.308490	+	9.53855i	−0.0160593	+	0.496557i
$370$	−0.901576	−	1.18116i	−0.0468707	−	0.0614056i
$371$	−4.93264	−	31.1434i	−0.256090	−	1.61689i
$372$	9.68949	−	12.4956i	0.502377	−	0.647865i
$373$	11.2768	−	3.66407i	0.583893	−	0.189718i	−0.00215104	−	0.999998i	$-0.500685\pi$
$373$	11.2768	−	3.66407i	0.583893	−	0.189718i	0.586044	+	0.810279i	$0.300685\pi$
$374$	−0.938664	−	5.13742i	−0.0485372	−	0.265649i
$375$	−0.286820	+	1.19469i	−0.0148113	+	0.0616935i
$376$	16.4834	+	23.0551i	0.850065	+	1.18897i
$377$	26.6509	−	13.5793i	1.37259	−	0.699369i
$378$	−2.86562	+	21.3471i	−0.147391	+	1.09798i
$379$	18.6185	+	6.04951i	0.956367	+	0.310743i	0.745300	−	0.666729i	$-0.232306\pi$
$379$	18.6185	+	6.04951i	0.956367	+	0.310743i	0.211067	+	0.977472i	$0.432306\pi$
$380$	−7.62091	−	11.2101i	−0.390944	−	0.575068i
$381$	3.98456	+	0.313591i	0.204135	+	0.0160658i
$382$	−14.7002	−	5.68577i	−0.752125	−	0.290909i
$383$	3.52319	+	8.50574i	0.180027	+	0.434623i	0.987972	−	0.154635i	$-0.0494202\pi$
$383$	3.52319	+	8.50574i	0.180027	+	0.434623i	−0.807945	+	0.589258i	$0.799420\pi$
$384$	−7.36213	−	11.7907i	−0.375697	−	0.601693i
$385$	2.88686	−	2.09743i	0.147128	−	0.106895i
$386$	−4.99151	+	4.47146i	−0.254061	+	0.227591i
$387$	6.25969	−	8.61572i	0.318198	−	0.437962i
$388$	−16.9265	−	18.0194i	−0.859315	−	0.914797i
$389$	−2.65157	+	16.7413i	−0.134440	+	0.848820i	0.824635	+	0.565666i	$0.191381\pi$
$389$	−2.65157	+	16.7413i	−0.134440	+	0.848820i	−0.959074	+	0.283154i	$0.908619\pi$
$390$	−5.28554	+	2.85245i	−0.267644	+	0.144439i
$391$	−4.26447	+	6.95899i	−0.215664	+	0.351931i
$392$	−0.422639	+	1.70311i	−0.0213465	+	0.0860198i
$393$	21.9200	−	1.72514i	1.10572	−	0.0870219i
$394$	7.67947	−	25.6855i	0.386886	−	1.29402i
$395$	−0.192019	+	0.164000i	−0.00966153	+	0.00825173i
$396$	−0.483525	−	3.82279i	−0.0242980	−	0.192103i
$397$	−12.0517	+	7.38526i	−0.604855	+	0.370656i	−0.790954	−	0.611875i	$-0.790415\pi$
$397$	−12.0517	+	7.38526i	−0.604855	+	0.370656i	0.186099	+	0.982531i	$0.440415\pi$
$398$	−0.809535	−	1.25354i	−0.0405783	−	0.0628342i
$399$	−17.4798	−	14.9292i	−0.875085	−	0.747393i
$400$	2.64616	+	2.99964i	0.132308	+	0.149982i
$401$	17.2786	−	17.2786i	0.862851	−	0.862851i	−0.128818	−	0.991668i	$-0.541118\pi$
$401$	17.2786	−	17.2786i	0.862851	−	0.862851i	0.991668	+	0.128818i	$0.0411182\pi$
$402$	−3.09908	+	6.45508i	−0.154568	+	0.321950i
$403$	−21.6284	+	5.19252i	−1.07739	+	0.258658i
$404$	3.08445	+	1.69507i	0.153457	+	0.0843331i
$405$	2.05573	+	1.04745i	0.102150	+	0.0520481i
$406$	−27.7915	−	19.2048i	−1.37927	−	0.953116i
$407$	1.25481	+	0.519759i	0.0621986	+	0.0257635i
$408$	8.50408	−	5.12253i	0.421015	−	0.253603i
$409$			26.2043i			1.29572i	0.761760	+	0.647860i	$0.224336\pi$
$409$			26.2043i			1.29572i	−0.761760	+	0.647860i	$0.775664\pi$
$410$	8.03237	+	4.18103i	0.396691	+	0.206486i
$411$			12.2028i			0.601922i
$412$	17.8537	+	1.96830i	0.879588	+	0.0969713i
$413$	−35.8809	−	14.8623i	−1.76558	−	0.731328i
$414$	−3.42343	+	4.95410i	−0.168252	+	0.243481i
$415$	3.50209	+	1.78440i	0.171911	+	0.0875929i
$416$	−2.29087	+	19.4191i	−0.112319	+	0.952099i
$417$	−14.5663	+	3.49705i	−0.713313	+	0.171251i
$418$	11.1695	+	5.36246i	0.546317	+	0.262286i
$419$	4.30806	−	4.30806i	0.210462	−	0.210462i	−0.594002	−	0.804464i	$-0.702453\pi$
$419$	4.30806	−	4.30806i	0.210462	−	0.210462i	0.804464	+	0.594002i	$0.202453\pi$
$420$	5.67012	+	3.72333i	0.276674	+	0.181680i
$421$	5.84006	+	4.98788i	0.284627	+	0.243095i	0.780286	−	0.625423i	$-0.215073\pi$
$421$	5.84006	+	4.98788i	0.284627	+	0.243095i	−0.495659	+	0.868517i	$0.665073\pi$
$422$	−7.71952	+	4.98527i	−0.375781	+	0.242679i
$423$	−12.7339	+	7.80333i	−0.619142	+	0.379411i
$424$	−23.0183	+	22.6700i	−1.11787	+	1.10095i
$425$	−2.17233	+	1.85535i	−0.105374	+	0.0899976i
$426$	9.93069	+	2.96908i	0.481143	+	0.143852i
$427$	15.3222	−	1.20588i	0.741494	−	0.0583568i
$428$	11.0659	+	13.8082i	0.534892	+	0.667445i
$429$	2.86842	−	4.68084i	0.138489	−	0.225993i
$430$	−4.79905	−	8.89257i	−0.231431	−	0.428838i
$431$	−1.75437	+	11.0767i	−0.0845052	+	0.533545i	0.908726	+	0.417393i	$0.137056\pi$
$431$	−1.75437	+	11.0767i	−0.0845052	+	0.533545i	−0.993231	+	0.116152i	$0.962944\pi$
$432$	19.5003	−	10.3325i	0.938207	−	0.497122i
$433$	5.17691	−	7.12540i	0.248786	−	0.342425i	−0.666300	−	0.745684i	$-0.732123\pi$
$433$	5.17691	−	7.12540i	0.248786	−	0.342425i	0.915086	+	0.403259i	$0.132123\pi$
$434$	16.7619	+	18.7114i	0.804599	+	0.898178i
$435$	−8.60115	+	6.24910i	−0.412394	+	0.299622i
$436$	−19.9511	+	9.39199i	−0.955484	+	0.449795i
$437$	−7.40998	−	17.8893i	−0.354468	−	0.855761i
$438$	−0.989055	+	2.55713i	−0.0472589	+	0.122184i
$439$	−25.9903	−	2.04548i	−1.24045	−	0.0976254i	−0.558798	−	0.829304i	$-0.688737\pi$
$439$	−25.9903	−	2.04548i	−1.24045	−	0.0976254i	−0.681650	+	0.731679i	$0.738737\pi$
$440$	−3.46849	−	1.15629i	−0.165354	−	0.0551241i
$441$	−0.879422	−	0.285742i	−0.0418772	−	0.0136067i
$442$	−13.8412	−	1.85802i	−0.658357	−	0.0883772i
$443$	−15.6294	+	7.96355i	−0.742573	+	0.378360i	−0.783983	−	0.620782i	$-0.786815\pi$
$443$	−15.6294	+	7.96355i	−0.742573	+	0.378360i	0.0414099	+	0.999142i	$0.486815\pi$
$444$	−0.0807044	+	2.58062i	−0.00383006	+	0.122471i
$445$	−3.89992	+	16.2443i	−0.184874	+	0.770055i
$446$	−22.8544	+	4.17577i	−1.08219	+	0.197728i
$447$	21.6659	−	7.03966i	1.02476	−	0.332965i
$448$	20.5295	−	8.13910i	0.969928	−	0.384536i
$449$	2.87495	+	18.1517i	0.135677	+	0.856634i	0.957823	+	0.287357i	$0.0927767\pi$
$449$	2.87495	+	18.1517i	0.135677	+	0.856634i	−0.822146	+	0.569277i	$0.807223\pi$
$450$	−1.67550	+	1.27890i	−0.0789838	+	0.0602880i
$451$	−8.26814	+	0.382341i	−0.389331	+	0.0180037i
$452$	4.75029	−	17.3746i	0.223435	−	0.817231i
$453$	8.77077	−	1.38915i	0.412087	−	0.0652681i
$454$	−34.8309	+	9.23810i	−1.63470	+	0.433565i
$455$	−2.94867	−	9.07507i	−0.138236	−	0.425446i
$456$	−2.02693	+	23.4657i	−0.0949195	+	1.09888i
$457$	28.4330	+	6.82615i	1.33004	+	0.319314i	0.835332	−	0.549746i	$-0.185276\pi$
$457$	28.4330	+	6.82615i	1.33004	+	0.319314i	0.494706	+	0.869060i	$0.335276\pi$
$458$	27.1374	+	22.0898i	1.26805	+	1.03219i
$459$	7.15552	+	14.0435i	0.333991	+	0.655495i
$460$	2.83174	+	4.96280i	0.132030	+	0.231392i
$461$	−1.67107	+	5.14301i	−0.0778293	+	0.239534i	−0.982400	−	0.186790i	$-0.940192\pi$
$461$	−1.67107	+	5.14301i	−0.0778293	+	0.239534i	0.904571	+	0.426324i	$0.140192\pi$
$462$	−6.19088	−	0.340230i	−0.288026	−	0.0158289i
$463$	−0.103981	+	1.32120i	−0.00483239	+	0.0614013i	−0.998861	−	0.0477212i	$-0.984804\pi$
$463$	−0.103981	+	1.32120i	−0.00483239	+	0.0614013i	0.994028	+	0.109123i	$0.0348041\pi$
$464$	0.554253	+	34.6082i	0.0257306	+	1.60665i
$465$	7.30428	−	3.02553i	0.338728	−	0.140306i
$466$	−20.9809	−	4.51540i	−0.971923	−	0.209172i
$467$	17.6496	+	24.2926i	0.816727	+	1.12413i	0.990250	+	0.139298i	$0.0444847\pi$
$467$	17.6496	+	24.2926i	0.816727	+	1.12413i	−0.173524	+	0.984830i	$0.555515\pi$
$468$	−10.1217	−	1.92922i	−0.467876	−	0.0891780i
$469$	−9.20343	−	6.68668i	−0.424975	−	0.308762i
$470$	1.44542	+	14.0968i	0.0666723	+	0.650237i
$471$	−13.3241	−	2.11033i	−0.613944	−	0.0972391i
$472$	8.99413	+	38.7629i	0.413989	+	1.78421i
$473$	7.87520	+	4.82593i	0.362102	+	0.221896i
$474$	0.438648	−	0.0103709i	0.0201478	−	0.000476349i
$475$	−0.531767	−	6.75675i	−0.0243992	−	0.310021i
$476$	5.57743	+	14.7534i	0.255641	+	0.676222i
$477$	−11.0566	−	12.9456i	−0.506245	−	0.592737i
$478$	−5.62705	−	3.26787i	−0.257375	−	0.149469i
$479$	−9.05548	−	14.7772i	−0.413755	−	0.675187i	0.576082	−	0.817392i	$-0.304581\pi$
$479$	−9.05548	−	14.7772i	−0.413755	−	0.675187i	−0.989837	+	0.142205i	$0.954581\pi$
$480$	−0.275518	−	6.94476i	−0.0125756	−	0.316983i
$481$	2.35875	−	2.76174i	0.107550	−	0.125925i
$482$	−9.75498	−	27.7713i	−0.444327	−	1.26495i
$483$	6.85168	+	6.85168i	0.311762	+	0.311762i
$484$	−18.2699	+	3.78643i	−0.830450	+	0.172110i
$485$	−2.88569	−	12.0198i	−0.131032	−	0.545789i
$486$	7.84494	+	17.7412i	0.355854	+	0.804759i
$487$	−1.89877	+	3.72654i	−0.0860415	+	0.168866i	−0.930018	−	0.367515i	$-0.880209\pi$
$487$	−1.89877	+	3.72654i	−0.0860415	+	0.168866i	0.843976	+	0.536380i	$0.180209\pi$
$488$	−10.1357	−	12.0523i	−0.458824	−	0.545582i
$489$	6.80462	−	16.4278i	0.307716	−	0.742891i
$490$	−0.605565	+	0.634893i	−0.0273566	+	0.0286815i
$491$	13.7995			0.622764			0.311382	−	0.950285i	$-0.399208\pi$
$491$	13.7995			0.622764			0.311382	+	0.950285i	$0.399208\pi$
$492$	−6.23782	−	14.4449i	−0.281223	−	0.651227i
$493$	−24.7204			−1.11335
$494$	22.8676	−	23.9751i	1.02886	−	1.07869i
$495$	0.737287	−	1.77997i	0.0331386	−	0.0800037i
$496$	5.60720	−	25.1212i	0.251771	−	1.12798i
$497$	−7.47598	+	14.6724i	−0.335343	+	0.658148i
$498$	−2.76191	−	6.24604i	−0.123764	−	0.279892i
$499$	−5.24234	−	21.8359i	−0.234679	−	0.977510i	−0.957948	−	0.286943i	$-0.907361\pi$
$499$	−5.24234	−	21.8359i	−0.234679	−	0.977510i	0.723268	−	0.690567i	$-0.242639\pi$
$500$	0.405874	+	1.95838i	0.0181512	+	0.0875816i
$501$	1.79833	+	1.79833i	0.0803437	+	0.0803437i
$502$	9.16792	+	26.1000i	0.409184	+	1.16490i
$503$	11.2085	−	13.1235i	0.499763	−	0.585148i	−0.451986	−	0.892025i	$-0.649284\pi$
$503$	11.2085	−	13.1235i	0.499763	−	0.585148i	0.951749	+	0.306878i	$0.0992842\pi$
$504$	3.51163	+	11.0948i	0.156420	+	0.494202i
$505$	0.919474	+	1.50045i	0.0409161	+	0.0667689i
$506$	−4.51632	−	2.62283i	−0.200775	−	0.116599i
$507$	0.839109	+	0.982470i	0.0372661	+	0.0436330i
$508$	6.08583	−	2.30071i	0.270015	−	0.102077i
$509$	−3.27317	−	41.5895i	−0.145081	−	1.84342i	−0.452397	−	0.891817i	$-0.649431\pi$
$509$	−3.27317	−	41.5895i	−0.145081	−	1.84342i	0.307317	−	0.951607i	$-0.400569\pi$
$510$	4.96247	−	0.117327i	0.219742	−	0.00519531i
$511$	−3.71401	−	2.27595i	−0.164298	−	0.100682i
$512$	−19.0176	−	12.2610i	−0.840466	−	0.541864i
$513$	−36.9328	−	5.84958i	−1.63062	−	0.258265i
$514$	−2.57643	−	25.1273i	−0.113642	−	1.10832i
$515$	7.26572	+	5.27886i	0.320166	+	0.232614i
$516$	−3.28737	+	17.2473i	−0.144718	+	0.759270i
$517$	−7.61334	−	10.4789i	−0.334834	−	0.460860i
$518$	−4.01010	−	0.863031i	−0.176194	−	0.0379194i
$519$	6.75431	−	2.79773i	0.296481	−	0.122807i
$520$	−5.80684	+	7.86561i	−0.254647	+	0.344930i
$521$	1.96351	−	24.9487i	0.0860228	−	1.09302i	−0.790757	−	0.612130i	$-0.790313\pi$
$521$	1.96351	−	24.9487i	0.0860228	−	1.09302i	0.876780	−	0.480892i	$-0.159687\pi$
$522$	−18.2118	−	1.00086i	−0.797109	−	0.0438065i
$523$	11.0216	−	33.9209i	0.481940	−	1.48326i	−0.354425	−	0.935084i	$-0.615323\pi$
$523$	11.0216	−	33.9209i	0.481940	−	1.48326i	0.836365	−	0.548173i	$-0.184677\pi$
$524$	31.0875	−	17.7383i	1.35806	−	0.774901i
$525$	1.53978	+	3.02199i	0.0672016	+	0.131891i
$526$	2.92965	+	2.38474i	0.127739	+	0.103979i
$527$	17.8752	+	4.29146i	0.778656	+	0.186939i
$528$	3.40562	+	5.36278i	0.148211	+	0.233385i
$529$	−4.58518	−	14.1117i	−0.199356	−	0.613554i
$530$	−15.6139	+	4.14122i	−0.678224	+	0.179883i
$531$	−20.7108	+	3.28026i	−0.898771	+	0.142351i
$532$	−36.0947	−	9.86847i	−1.56490	−	0.427852i
$533$	−5.85990	+	21.3435i	−0.253821	+	0.924491i
$534$	23.0739	−	17.6122i	0.998504	−	0.762155i
$535$	1.38407	+	8.73869i	0.0598387	+	0.377806i
$536$	−0.0888721	+	11.6556i	−0.00383869	+	0.503446i
$537$	−21.2456	+	6.90310i	−0.916813	+	0.297891i
$538$	44.0078	−	8.04073i	1.89731	−	0.346660i
$539$	0.187214	−	0.779802i	0.00806387	−	0.0335885i
$540$	11.0289	+	0.344909i	0.474607	+	0.0148425i
$541$	−16.3303	+	8.32073i	−0.702096	+	0.357736i	−0.768317	−	0.640069i	$-0.778906\pi$
$541$	−16.3303	+	8.32073i	−0.702096	+	0.357736i	0.0662211	+	0.997805i	$0.478906\pi$
$542$	−9.00918	−	1.20938i	−0.386977	−	0.0519475i
$543$	12.1201	+	3.93805i	0.520123	+	0.168998i
$544$	8.97318	−	13.4404i	0.384722	−	0.576254i
$545$	−10.9916	−	0.865058i	−0.470829	−	0.0370550i
$546$	−5.98103	+	15.4635i	−0.255965	+	0.661778i
$547$	−2.19567	−	5.30081i	−0.0938800	−	0.226646i	0.869963	−	0.493117i	$-0.164143\pi$
$547$	−2.19567	−	5.30081i	−0.0938800	−	0.226646i	−0.963843	+	0.266470i	$0.914143\pi$
$548$	8.46044	+	17.9722i	0.361412	+	0.767735i
$549$	6.71349	−	4.87764i	0.286525	−	0.208173i
$550$	−1.21977	−	1.36163i	−0.0520110	−	0.0580601i
$551$	34.4725	−	47.4473i	1.46858	−	2.02132i
$552$	1.62782	−	9.79378i	0.0692848	−	0.416851i
$553$	−0.109049	+	0.688506i	−0.00463722	+	0.0292783i
$554$	12.0055	+	22.2461i	0.510066	+	0.945145i
$555$	−0.674515	+	1.10071i	−0.0286316	+	0.0467224i
$556$	−19.0285	+	15.2495i	−0.806987	+	0.646721i
$557$	33.0088	−	2.59785i	1.39863	−	0.110074i	0.643396	−	0.765533i	$-0.277525\pi$
$557$	33.0088	−	2.59785i	1.39863	−	0.110074i	0.755231	+	0.655459i	$0.227525\pi$
$558$	12.9951	+	3.88528i	0.550126	+	0.164477i
$559$	18.7809	−	16.0404i	0.794348	−	0.678437i
$560$	10.9323	+	1.55249i	0.461976	+	0.0656048i
$561$	−3.86856	+	2.37066i	−0.163331	+	0.100089i
$562$	−10.2589	+	6.62518i	−0.432744	+	0.279466i
$563$	−15.0774	−	12.8774i	−0.635438	−	0.542716i	0.272321	−	0.962206i	$-0.412209\pi$
$563$	−15.0774	−	12.8774i	−0.635438	−	0.542716i	−0.907760	+	0.419491i	$0.862209\pi$
$564$	13.5151	−	20.5817i	0.569089	−	0.866644i
$565$	6.36829	−	6.36829i	0.267916	−	0.267916i
$566$	−4.59721	−	2.20712i	−0.193235	−	0.0927721i
$567$	6.19308	−	1.48683i	0.260085	−	0.0624408i
$568$	16.6843	−	2.51229i	0.700059	−	0.105413i
$569$	−2.35275	−	1.19879i	−0.0986326	−	0.0502558i	0.403978	−	0.914769i	$-0.367627\pi$
$569$	−2.35275	−	1.19879i	−0.0986326	−	0.0502558i	−0.502611	+	0.864513i	$0.667627\pi$
$570$	−6.69494	+	9.68836i	−0.280420	+	0.405801i
$571$	36.8857	+	15.2785i	1.54362	+	0.639387i	0.982148	−	0.188110i	$-0.0602362\pi$
$571$	36.8857	+	15.2785i	1.54362	+	0.639387i	0.561469	+	0.827497i	$0.310236\pi$
$572$	0.979276	−	8.88262i	0.0409456	−	0.371401i
$573$			13.6932i			0.572041i
$574$	24.3566	−	5.62406i	1.01662	−	0.234744i
$575$			2.85693i			0.119142i
$576$	7.15480	−	9.53841i	0.298117	−	0.397434i
$577$	−8.53492	−	3.53528i	−0.355313	−	0.147176i	0.197885	−	0.980225i	$-0.436593\pi$
$577$	−8.53492	−	3.53528i	−0.355313	−	0.147176i	−0.553198	+	0.833050i	$0.686593\pi$
$578$	−10.2833	−	7.10609i	−0.427730	−	0.295574i
$579$	5.18749	+	2.64316i	0.215585	+	0.109846i
$580$	−8.33508	+	15.1669i	−0.346095	+	0.629773i
$581$	10.5503	−	2.53291i	0.437702	−	0.105083i
$582$	−9.29595	+	19.3626i	−0.385329	+	0.802604i
$583$	10.4405	−	10.4405i	0.432402	−	0.432402i
$584$	0.316233	+	4.45184i	0.0130858	+	0.184219i
$585$	−3.91758	−	3.34593i	−0.161972	−	0.138337i
$586$	−23.1187	−	35.7985i	−0.955023	−	1.47882i
$587$	−32.6238	+	19.9919i	−1.34653	+	0.825155i	−0.993866	−	0.110595i	$-0.964724\pi$
$587$	−32.6238	+	19.9919i	−1.34653	+	0.825155i	−0.352665	+	0.935750i	$0.614724\pi$
$588$	1.51245	−	0.191302i	0.0623723	−	0.00788914i
$589$	−33.1637	+	28.3244i	−1.36648	+	1.16709i
$590$	−5.69934	+	19.0626i	−0.234638	+	0.784795i
$591$	−23.2192	+	1.82739i	−0.955112	+	0.0751690i
$592$	1.67033	+	3.85666i	0.0686500	+	0.158508i
$593$	0.679084	−	1.10816i	0.0278866	−	0.0455068i	−0.838393	−	0.545066i	$-0.816505\pi$
$593$	0.679084	−	1.10816i	0.0278866	−	0.0455068i	0.866280	+	0.499559i	$0.166505\pi$
$594$	−8.87573	+	4.78996i	−0.364176	+	0.196534i
$595$	−1.23368	+	7.78915i	−0.0505759	+	0.319324i
$596$	27.0285	−	25.3893i	1.10713	−	1.03998i
$597$	−0.762007	+	1.04881i	−0.0311869	+	0.0429250i
$598$	−10.4024	+	9.31861i	−0.425386	+	0.381066i
$599$	−33.4876	+	24.3302i	−1.36827	+	0.994104i	−0.370396	+	0.928874i	$0.620778\pi$
$599$	−33.4876	+	24.3302i	−1.36827	+	0.994104i	−0.997870	+	0.0652298i	$0.979222\pi$
$600$	1.60123	−	3.08423i	0.0653699	−	0.125913i
$601$	1.04338	+	2.51895i	0.0425604	+	0.102750i	0.943730	−	0.330716i	$-0.107290\pi$
$601$	1.04338	+	2.51895i	0.0425604	+	0.102750i	−0.901170	+	0.433466i	$0.857290\pi$
$602$	−26.0164	−	10.0627i	−1.06035	−	0.410125i
$603$	−6.12322	−	0.481908i	−0.249357	−	0.0196248i
$604$	11.9544	−	8.12686i	0.486417	−	0.330677i
$605$	−8.87247	−	2.88284i	−0.360717	−	0.117204i
$606$	0.406812	−	3.03050i	0.0165256	−	0.123106i
$607$	−5.53459	+	2.82001i	−0.224642	+	0.114461i	−0.562690	−	0.826668i	$-0.690233\pi$
$607$	−5.53459	+	2.82001i	−0.224642	+	0.114461i	0.338048	+	0.941129i	$0.390233\pi$
$608$	13.2839	+	35.9653i	0.538734	+	1.45859i
$609$	−6.85130	+	28.5377i	−0.277629	+	1.15641i
$610$	−1.41522	−	7.74565i	−0.0573005	−	0.313612i
$611$	−32.9411	+	10.7032i	−1.33265	+	0.433006i
$612$	6.72965	+	5.21840i	0.272030	+	0.210941i
$613$	3.65506	+	23.0771i	0.147627	+	0.932077i	0.944638	+	0.328113i	$0.106413\pi$
$613$	3.65506	+	23.0771i	0.147627	+	0.932077i	−0.797012	+	0.603964i	$0.793587\pi$
$614$	−6.57270	−	8.61093i	−0.265252	−	0.347509i
$615$	0.870440	−	7.81881i	0.0350995	−	0.315285i
$616$	−9.35375	+	3.79115i	−0.376873	+	0.152750i
$617$	0.292663	−	0.0463532i	0.0117821	−	0.00186611i	−0.150541	−	0.988604i	$-0.548101\pi$
$617$	0.292663	−	0.0463532i	0.0117821	−	0.00186611i	0.162323	+	0.986738i	$0.448101\pi$
$618$	−4.00051	−	15.0834i	−0.160924	−	0.606742i
$619$	−12.4076	−	38.1866i	−0.498702	−	1.53485i	−0.811106	−	0.584899i	$-0.801134\pi$
$619$	−12.4076	−	38.1866i	−0.498702	−	1.53485i	0.312404	−	0.949949i	$-0.398866\pi$
$620$	8.66001	−	9.52015i	0.347794	−	0.382339i
$621$	15.3265	+	3.67958i	0.615033	+	0.147656i
$622$	19.8668	−	24.4063i	0.796585	−	0.978604i
$623$	20.9366	+	41.0904i	0.838807	+	1.64625i
$624$	16.4529	−	4.22974i	0.658641	−	0.169325i
$625$	−0.309017	+	0.951057i	−0.0123607	+	0.0380423i
$626$	2.07504	−	37.7578i	0.0829353	−	1.50910i
$627$	0.844549	−	10.7310i	0.0337280	−	0.428555i
$628$	−21.0868	+	6.12977i	−0.841454	+	0.244604i
$629$	−2.77319	+	1.14869i	−0.110574	+	0.0458013i
$630$	−1.22422	+	5.68840i	−0.0487743	+	0.226631i
$631$	1.31561	+	1.81078i	0.0523735	+	0.0720859i	0.834400	−	0.551159i	$-0.185814\pi$
$631$	1.31561	+	1.81078i	0.0523735	+	0.0720859i	−0.782027	+	0.623245i	$0.785814\pi$
$632$	0.638846	−	0.319396i	0.0254119	−	0.0127049i
$633$	6.45878	+	4.69258i	0.256714	+	0.186513i
$634$	22.6378	−	2.32117i	0.899062	−	0.0921856i
$635$	3.21305	+	0.508897i	0.127506	+	0.0201949i
$636$	25.5830	+	11.5465i	1.01443	+	0.457847i
$637$	−1.82850	−	1.12050i	−0.0724477	−	0.0443960i
$638$	−0.373893	−	15.8142i	−0.0148026	−	0.626092i
$639$	0.697579	+	8.86358i	0.0275958	+	0.350638i
$640$	−5.22070	−	10.0371i	−0.206366	−	0.396753i
$641$	−15.9516	−	18.6770i	−0.630052	−	0.737696i	0.349931	−	0.936775i	$-0.386205\pi$
$641$	−15.9516	−	18.6770i	−0.630052	−	0.737696i	−0.979983	+	0.199079i	$0.936205\pi$
$642$	7.72043	−	13.2940i	0.304701	−	0.524673i
$643$	24.1356	+	39.3857i	0.951814	+	1.55322i	0.827863	+	0.560930i	$0.189556\pi$
$643$	24.1356	+	39.3857i	0.951814	+	1.55322i	0.123950	+	0.992288i	$0.460444\pi$
$644$	14.8415	+	5.34069i	0.584835	+	0.210453i
$645$	−5.70144	+	6.67553i	−0.224494	+	0.262849i
$646$	−25.8351	+	9.07486i	−1.01647	+	0.357046i
$647$	7.12503	+	7.12503i	0.280114	+	0.280114i	0.833154	−	0.553041i	$-0.186533\pi$
$647$	7.12503	+	7.12503i	0.280114	+	0.280114i	−0.553041	+	0.833154i	$0.686533\pi$
$648$	−4.92977	−	4.27585i	−0.193660	−	0.167971i
$649$	−4.24545	−	17.6836i	−0.166648	−	0.694140i
$650$	−4.47085	+	1.97695i	−0.175361	+	0.0775423i
$651$	9.90827	−	19.4461i	0.388336	−	0.762152i
$652$	−1.36791	−	28.9125i	−0.0535714	−	1.13230i
$653$	−0.252453	+	0.609475i	−0.00987925	+	0.0238506i	−0.928742	−	0.370726i	$-0.879109\pi$
$653$	−0.252453	+	0.609475i	−0.00987925	+	0.0238506i	0.918863	+	0.394577i	$0.129109\pi$
$654$	13.8629	+	13.2225i	0.542081	+	0.517040i
$655$	17.8961			0.699258
$656$	−19.2019	−	16.9495i	−0.749709	−	0.661768i
$657$	−2.35183			−0.0917535
$658$	28.3069	+	26.9994i	1.10352	+	1.05254i
$659$	3.17571	−	7.66683i	0.123708	−	0.298657i	−0.849878	−	0.526980i	$-0.823324\pi$
$659$	3.17571	−	7.66683i	0.123708	−	0.298657i	0.973585	+	0.228323i	$0.0733242\pi$
$660$	0.150113	+	3.17284i	0.00584315	+	0.123502i
$661$	10.7521	−	21.1022i	0.418209	−	0.820781i	−0.581764	−	0.813358i	$-0.697637\pi$
$661$	10.7521	−	21.1022i	0.418209	−	0.820781i	0.999972	−	0.00742281i	$-0.00236277\pi$
$662$	−15.9372	+	7.04720i	−0.619415	+	0.273897i
$663$	2.83234	+	11.7975i	0.109999	+	0.458178i
$664$	−8.39820	−	7.28422i	−0.325914	−	0.282682i
$665$	−13.2298	−	13.2298i	−0.513029	−	0.513029i
$666$	−2.08954	+	0.733974i	−0.0809681	+	0.0284409i
$667$	−16.0553	+	18.7984i	−0.621664	+	0.727876i
$668$	3.89539	+	1.40175i	0.150717	+	0.0542354i
$669$	10.5462	+	17.2098i	0.407739	+	0.665369i
$670$	−2.92681	+	5.03976i	−0.113072	+	0.194703i
$671$	4.67409	+	5.47266i	0.180441	+	0.211270i
$672$	−13.0289	−	14.0838i	−0.502603	−	0.543296i
$673$	−1.34668	−	17.1112i	−0.0519107	−	0.659588i	−0.966742	−	0.255752i	$-0.917677\pi$
$673$	−1.34668	−	17.1112i	−0.0519107	−	0.659588i	0.914832	−	0.403835i	$-0.132323\pi$
$674$	−0.476277	−	20.1447i	−0.0183455	−	0.775946i
$675$	4.70413	+	2.88269i	0.181062	+	0.110955i
$676$	1.91699	+	0.865203i	0.0737305	+	0.0332770i
$677$	−39.2540	−	6.21722i	−1.50865	−	0.238947i	−0.653342	−	0.757063i	$-0.726634\pi$
$677$	−39.2540	−	6.21722i	−1.50865	−	0.238947i	−0.855310	+	0.518116i	$0.826634\pi$
$678$	−15.5670	+	1.59617i	−0.597848	+	0.0613005i
$679$	−27.6065	−	20.0573i	−1.05944	−	0.769727i
$680$	7.22733	−	3.61337i	0.277156	−	0.138566i
$681$	18.4015	+	25.3275i	0.705148	+	0.970554i
$682$	−2.47498	+	11.5001i	−0.0947721	+	0.440361i
$683$	17.7714	−	7.36117i	0.680005	−	0.281667i	−0.0158239	−	0.999875i	$-0.505037\pi$
$683$	17.7714	−	7.36117i	0.680005	−	0.281667i	0.695829	+	0.718207i	$0.255037\pi$
$684$	−19.4004	+	5.63956i	−0.741793	+	0.215634i
$685$	−0.779257	+	9.90140i	−0.0297739	+	0.378313i
$686$	1.36667	−	24.8681i	0.0521796	−	0.949468i
$687$	9.39404	−	28.9119i	0.358405	−	1.10306i
$688$	7.11625	+	27.6808i	0.271305	+	1.05532i
$689$	−17.9250	−	35.1798i	−0.682889	−	1.34024i
$690$	3.13378	−	3.84985i	0.119301	−	0.146561i
$691$	−36.8920	−	8.85699i	−1.40344	−	0.336936i	−0.540117	−	0.841590i	$-0.681620\pi$
$691$	−36.8920	−	8.85699i	−1.40344	−	0.336936i	−0.863322	+	0.504654i	$0.831620\pi$
$692$	8.00796	−	8.80334i	0.304417	−	0.334653i
$693$	−1.64350	−	5.05816i	−0.0624312	−	0.192144i
$694$	−7.37243	−	27.7967i	−0.279854	−	1.05515i
$695$	−12.0424	+	1.90733i	−0.456794	+	0.0723491i
$696$	27.8687	−	11.2954i	1.05636	−	0.428151i
$697$	12.3234	−	13.5184i	0.466784	−	0.512047i
$698$	−26.0443	−	34.1208i	−0.985790	−	1.29149i
$699$	2.91674	+	18.4156i	0.110321	+	0.696541i
$700$	4.36298	+	3.38320i	0.164905	+	0.127873i
$701$	−31.0013	+	10.0729i	−1.17090	+	0.380450i	−0.828980	−	0.559278i	$-0.811079\pi$
$701$	−31.0013	+	10.0729i	−1.17090	+	0.380450i	−0.341924	+	0.939728i	$0.611079\pi$
$702$	4.84751	+	26.5309i	0.182957	+	1.00135i
$703$	1.66244	−	6.92457i	0.0627002	−	0.261165i
$704$	8.73387	+	5.53707i	0.329170	+	0.208686i
$705$	10.9694	−	5.58917i	0.413130	−	0.210500i
$706$	3.13948	−	23.3872i	0.118156	−	0.880191i
$707$	4.62008	+	1.50116i	0.173756	+	0.0564568i
$708$	28.5901	−	19.4362i	1.07448	−	0.730456i
$709$	−15.4216	−	1.21371i	−0.579171	−	0.0455817i	−0.214510	−	0.976722i	$-0.568815\pi$
$709$	−15.4216	−	1.21371i	−0.579171	−	0.0455817i	−0.364662	+	0.931140i	$0.618815\pi$
$710$	7.86817	+	3.04327i	0.295287	+	0.114212i
$711$	0.144031	+	0.347722i	0.00540159	+	0.0130406i
$712$	21.7721	−	41.9366i	0.815944	−	1.57164i
$713$	14.8729	−	10.8058i	0.556994	−	0.404680i
$714$	10.2064	−	9.14304i	0.381966	−	0.342170i
$715$	2.62635	−	3.61486i	0.0982200	−	0.135188i
$716$	−26.5042	+	24.8967i	−0.990508	+	0.930434i
$717$	−0.884362	+	5.58364i	−0.0330271	+	0.208525i
$718$	33.0116	−	17.8154i	1.23198	−	0.664863i
$719$	−1.55055	+	2.53027i	−0.0578258	+	0.0943631i	−0.880247	−	0.474516i	$-0.842623\pi$
$719$	−1.55055	+	2.53027i	−0.0578258	+	0.0943631i	0.822421	+	0.568880i	$0.192623\pi$
$720$	5.47075	−	2.36939i	0.203883	−	0.0883020i
$721$	24.7155	−	1.94515i	0.920453	−	0.0724412i
$722$	10.9120	−	36.4975i	0.406103	−	1.35830i
$723$	−19.4453	+	16.6079i	−0.723179	+	0.617653i
$724$	20.5807	−	2.60314i	0.764874	−	0.0967449i
$725$	−7.37804	+	4.52127i	−0.274014	+	0.167916i
$726$	8.79389	+	13.6171i	0.326372	+	0.505376i
$727$	31.4519	+	26.8624i	1.16648	+	0.996272i	0.999948	+	0.0102371i	$0.00325864\pi$
$727$	31.4519	+	26.8624i	1.16648	+	0.996272i	0.166537	+	0.986035i	$0.446741\pi$
$728$	1.91233	+	26.9213i	0.0708758	+	0.997769i
$729$	16.8111	−	16.8111i	0.622632	−	0.622632i
$730$	−0.965815	+	2.01170i	−0.0357464	+	0.0744563i
$731$	−19.8486	+	4.76522i	−0.734125	+	0.176248i
$732$	−6.58918	+	11.9900i	−0.243543	+	0.443164i
$733$	−22.3786	−	11.4025i	−0.826573	−	0.421160i	−0.0110880	−	0.999939i	$-0.503530\pi$
$733$	−22.3786	−	11.4025i	−0.826573	−	0.421160i	−0.815485	+	0.578779i	$0.803530\pi$
$734$	1.65577	+	1.14418i	0.0611154	+	0.0422326i
$735$	0.704227	+	0.291700i	0.0259758	+	0.0107595i
$736$	−4.39275	−	15.5528i	−0.161919	−	0.573283i
$737$		−	5.32700i		−	0.196222i
$738$	9.62613	−	9.46023i	0.354343	−	0.348236i
$739$		−	11.7115i		−	0.430814i	−0.976524	−	0.215407i	$-0.930892\pi$
$739$		−	11.7115i		−	0.430814i	0.976524	−	0.215407i	$-0.0691078\pi$
$740$	−0.230278	+	2.08876i	−0.00846520	+	0.0767845i
$741$	−26.5933	−	11.0153i	−0.976929	−	0.404657i
$742$	−25.3508	+	36.6855i	−0.930657	+	1.34677i
$743$	−36.7549	−	18.7275i	−1.34841	−	0.687047i	−0.377388	−	0.926055i	$-0.623178\pi$
$743$	−36.7549	−	18.7275i	−1.34841	−	0.687047i	−0.971018	+	0.239008i	$0.923178\pi$
$744$	−22.1125	+	3.32966i	−0.810685	+	0.122071i
$745$	18.0292	−	4.32844i	0.660540	−	0.158582i
$746$	−15.1167	−	7.25750i	−0.553461	−	0.265716i
$747$	4.14237	−	4.14237i	0.151561	−	0.151561i
$748$	−4.05396	+	6.17362i	−0.148228	+	0.225730i
$749$	18.5721	+	15.8621i	0.678609	+	0.579587i
$750$	1.45964	−	0.942634i	0.0532984	−	0.0344201i
$751$	31.7191	−	19.4375i	1.15745	−	0.709284i	0.195013	−	0.980801i	$-0.437525\pi$
$751$	31.7191	−	19.4375i	1.15745	−	0.709284i	0.962434	+	0.271516i	$0.0875251\pi$
$752$	5.63531	−	39.6827i	0.205499	−	1.44708i
$753$	18.2751	−	15.6084i	0.665981	−	0.568802i
$754$	−40.5279	−	12.1170i	−1.47594	−	0.441276i
$755$	7.20532	−	0.567071i	0.262228	−	0.0206378i
$756$	23.7691	−	19.0486i	0.864475	−	0.692792i
$757$	7.38397	−	12.0495i	0.268375	−	0.437948i	−0.689855	−	0.723948i	$-0.742326\pi$
$757$	7.38397	−	12.0495i	0.268375	−	0.437948i	0.958230	+	0.286000i	$0.0923256\pi$
$758$	−13.1485	−	24.3640i	−0.477576	−	0.884941i
$759$	−0.709798	+	4.48149i	−0.0257640	+	0.162668i
$760$	−3.14314	+	18.9106i	−0.114014	+	0.685961i
$761$	5.68275	−	7.82163i	0.205999	−	0.283534i	−0.693499	−	0.720457i	$-0.743932\pi$
$761$	5.68275	−	7.82163i	0.205999	−	0.283534i	0.899499	+	0.436923i	$0.143932\pi$
$762$	−3.77153	−	4.21018i	−0.136628	−	0.152519i
$763$	−24.6234	+	17.8900i	−0.891428	+	0.647661i
$764$	9.49371	+	20.1672i	0.343470	+	0.729622i
$765$	1.62944	+	3.93381i	0.0589125	+	0.142227i
$766$	4.69684	−	12.1433i	0.169704	−	0.438757i
$767$	−48.4811	−	3.81555i	−1.75055	−	0.137771i
$768$	−3.97466	+	19.2522i	−0.143423	+	0.694703i
$769$	20.0708	+	6.52141i	0.723773	+	0.235168i	0.647658	−	0.761931i	$-0.275749\pi$
$769$	20.0708	+	6.52141i	0.723773	+	0.235168i	0.0761145	+	0.997099i	$0.475749\pi$
$770$	−5.00156	−	0.671404i	−0.180244	−	0.0241957i
$771$	−19.5527	+	9.96258i	−0.704172	+	0.358794i
$772$	9.47262	+	0.296240i	0.340927	+	0.0106619i
$773$	7.66251	−	31.9166i	0.275601	−	1.14796i	−0.647088	−	0.762416i	$-0.724013\pi$
$773$	7.66251	−	31.9166i	0.275601	−	1.14796i	0.922689	−	0.385546i	$-0.125987\pi$
$774$	−14.8156	+	2.70697i	−0.532535	+	0.0973001i
$775$	6.11991	−	1.98848i	0.219833	−	0.0714282i
$776$	−0.266579	+	34.9620i	−0.00956964	+	1.25506i
$777$	0.557478	+	3.51978i	0.0199994	+	0.126271i
$778$	19.0545	−	14.5442i	0.683136	−	0.521435i
$779$	8.76173	+	42.5044i	0.313921	+	1.52288i
$780$	8.19322	+	2.24007i	0.293364	+	0.0802072i
$781$	−7.61608	+	1.20627i	−0.272525	+	0.0431637i
$782$	11.1566	−	2.95904i	0.398960	−	0.105815i
$783$	14.7527	+	45.4041i	0.527218	+	1.62261i
$784$	2.09489	−	1.33035i	0.0748173	−	0.0475126i
$785$	−10.6764	−	2.56319i	−0.381059	−	0.0914841i
$786$	−24.1159	−	19.6303i	−0.860185	−	0.700191i
$787$	2.26957	+	4.45429i	0.0809015	+	0.158778i	0.927913	−	0.372796i	$-0.121601\pi$
$787$	2.26957	+	4.45429i	0.0809015	+	0.158778i	−0.847012	+	0.531574i	$0.821601\pi$
$788$	−32.9301	+	18.7897i	−1.17309	+	0.669354i
$789$	1.01415	−	3.12122i	0.0361045	−	0.111118i
$790$	0.356582	+	0.0195965i	0.0126866	+	0.000697214i
$791$	1.95061	−	24.7848i	0.0693556	−	0.881247i
$792$	−3.23655	+	4.38404i	−0.115006	+	0.155780i
$793$	17.7805	−	7.36492i	0.631404	−	0.261536i
$794$	19.5418	+	4.20567i	0.693512	+	0.149254i
$795$	8.24898	+	11.3537i	0.292561	+	0.402676i
$796$	−0.395116	+	2.07299i	−0.0140045	+	0.0734753i
$797$	12.6781	+	9.21119i	0.449082	+	0.326277i	0.789233	−	0.614094i	$-0.210478\pi$
$797$	12.6781	+	9.21119i	0.449082	+	0.326277i	−0.340151	+	0.940371i	$0.610478\pi$
$798$	3.31595	+	32.3396i	0.117383	+	1.14481i
$799$	28.2734	+	4.47806i	1.00024	+	0.158423i
$800$	0.219927	−	5.65258i	0.00777559	−	0.199849i
$801$	21.2302	+	13.0099i	0.750131	+	0.459681i
$802$	−34.5475	+	0.816799i	−1.21991	+	0.0288422i
$803$	−0.160033	−	2.03342i	−0.00564746	−	0.0717577i
$804$	9.47217	−	3.58089i	0.334058	−	0.126288i
$805$	5.12192	+	5.99699i	0.180524	+	0.211366i
$806$	27.2019	+	15.7974i	0.958147	+	0.556438i
$807$	−20.3074	−	33.1386i	−0.714854	−	1.16654i
$808$	−1.50195	−	4.74534i	−0.0528385	−	0.166941i
$809$	−22.7672	+	26.6570i	−0.800453	+	0.937210i	−0.999081	−	0.0428649i	$-0.986351\pi$
$809$	−22.7672	+	26.6570i	−0.800453	+	0.937210i	0.198628	+	0.980075i	$0.436351\pi$
$810$	−1.08135	−	3.07848i	−0.0379948	−	0.108167i
$811$	−9.44141	−	9.44141i	−0.331533	−	0.331533i	0.521636	−	0.853168i	$-0.325322\pi$
$811$	−9.44141	−	9.44141i	−0.331533	−	0.331533i	−0.853168	+	0.521636i	$0.825322\pi$
$812$	9.69517	+	46.7802i	0.340234	+	1.64166i
$813$	1.84356	+	7.67898i	0.0646565	+	0.269314i
$814$	−0.776788	−	1.75670i	−0.0272264	−	0.0615722i
$815$	6.57033	−	12.8950i	0.230149	−	0.451692i
$816$	−13.7027	−	3.05852i	−0.479691	−	0.107070i
$817$	18.5325	−	44.7415i	0.648371	−	1.56531i
$818$	25.5776	−	26.8163i	0.894300	−	0.937612i
$819$	−14.2220			−0.496958
$820$	−4.13894	−	12.1190i	−0.144538	−	0.423212i
$821$	−14.4351			−0.503788			−0.251894	−	0.967755i	$-0.581053\pi$
$821$	−14.4351			−0.503788			−0.251894	+	0.967755i	$0.581053\pi$
$822$	11.9110	−	12.4879i	0.415444	−	0.435564i
$823$	12.8032	−	30.9097i	0.446292	−	1.07744i	−0.527408	−	0.849612i	$-0.676836\pi$
$823$	12.8032	−	30.9097i	0.446292	−	1.07744i	0.973700	−	0.227832i	$-0.0731638\pi$
$824$	−16.3495	−	19.4410i	−0.569561	−	0.677259i
$825$	−0.721024	+	1.41509i	−0.0251028	+	0.0492671i
$826$	22.2120	+	50.2322i	0.772855	+	1.74780i
$827$	0.265305	+	1.10508i	0.00922557	+	0.0384272i	0.976793	−	0.214186i	$-0.0687099\pi$
$827$	0.265305	+	1.10508i	0.00922557	+	0.0384272i	−0.967567	+	0.252613i	$0.918710\pi$
$828$	8.33901	−	1.72826i	0.289801	−	0.0600610i
$829$	−11.7968	−	11.7968i	−0.409719	−	0.409719i	0.471922	−	0.881641i	$-0.343561\pi$
$829$	−11.7968	−	11.7968i	−0.409719	−	0.409719i	−0.881641	+	0.471922i	$0.843561\pi$
$830$	−1.84216	−	5.24441i	−0.0639422	−	0.182036i
$831$	14.2630	−	16.6998i	0.494777	−	0.579310i
$832$	21.2990	−	17.6366i	0.738412	−	0.611438i
$833$	0.926061	+	1.51119i	0.0320861	+	0.0523598i
$834$	18.3199	+	10.6392i	0.634366	+	0.368404i
$835$	1.34433	+	1.57401i	0.0465225	+	0.0544709i
$836$	−6.19615	−	16.3901i	−0.214298	−	0.566862i
$837$	−2.78545	−	35.3925i	−0.0962792	−	1.22334i
$838$	−8.61371	+	0.203652i	−0.297556	+	0.00703504i
$839$	−6.95384	−	4.26132i	−0.240073	−	0.147117i	0.397258	−	0.917707i	$-0.369962\pi$
$839$	−6.95384	−	4.26132i	−0.240073	−	0.147117i	−0.637331	+	0.770590i	$0.719962\pi$
$840$	−2.16827	−	9.34482i	−0.0748124	−	0.322427i
$841$	−45.3125	−	7.17680i	−1.56250	−	0.247476i
$842$	−1.10787	−	10.8048i	−0.0381797	−	0.372357i
$843$	8.58340	+	6.23621i	0.295628	+	0.214786i
$844$	12.7659	+	2.43320i	0.439419	+	0.0837541i
$845$	0.618114	+	0.850761i	0.0212638	+	0.0292671i
$846$	20.6480	+	4.44375i	0.709893	+	0.152779i
$847$	−23.7926	+	9.85523i	−0.817525	+	0.338630i
$848$	45.6838	−	0.731629i	1.56879	−	0.0251242i
$849$	−0.347605	+	4.41675i	−0.0119298	+	0.151582i
$850$	4.03405	+	0.221698i	0.138367	+	0.00760417i
$851$	−0.927607	+	2.85488i	−0.0317980	+	0.0978641i
$852$	−7.26457	−	12.7316i	−0.248880	−	0.436178i
$853$	15.2247	+	29.8801i	0.521282	+	1.02307i	0.990177	+	0.139820i	$0.0446524\pi$
$853$	15.2247	+	29.8801i	0.521282	+	1.02307i	−0.468895	+	0.883254i	$0.655348\pi$
$854$	−16.8571	−	13.7217i	−0.576839	−	0.469548i
$855$	−9.82263	−	2.35820i	−0.335927	−	0.0806489i
$856$	2.15359	−	24.9320i	0.0736080	−	0.852158i
$857$	17.2400	+	53.0593i	0.588908	+	1.81247i	0.582976	+	0.812489i	$0.301888\pi$
$857$	17.2400	+	53.0593i	0.588908	+	1.81247i	0.00593178	+	0.999982i	$0.498112\pi$
$858$	−7.50432	+	1.99035i	−0.256193	+	0.0679493i
$859$	54.7770	−	8.67583i	1.86897	−	0.296015i	0.883834	−	0.467801i	$-0.154954\pi$
$859$	54.7770	−	8.67583i	1.86897	−	0.296015i	0.985134	+	0.171786i	$0.0549537\pi$
$860$	−3.76876	+	13.7846i	−0.128514	+	0.470049i
$861$	−12.1905	−	17.9731i	−0.415450	−	0.612520i
$862$	12.6071	−	9.62298i	0.429400	−	0.327760i
$863$	1.54928	+	9.78177i	0.0527381	+	0.332975i	0.999924	+	0.0122917i	$0.00391267\pi$
$863$	1.54928	+	9.78177i	0.0527381	+	0.332975i	−0.947186	+	0.320684i	$0.896087\pi$
$864$	−30.0411	−	8.46007i	−1.02202	−	0.287818i
$865$	5.65911	−	1.83876i	0.192416	−	0.0625196i
$866$	−12.2528	+	2.23873i	−0.416368	+	0.0760751i
$867$	−2.53510	+	10.5594i	−0.0860965	+	0.358618i
$868$	1.11050	−	35.5095i	0.0376928	−	1.20527i
$869$	−0.290843	+	0.148192i	−0.00986619	+	0.00502707i
$870$	14.9017	+	2.00039i	0.505215	+	0.0678195i
$871$	−13.5477	−	4.40190i	−0.459045	−	0.149153i
$872$	29.5845	+	9.86258i	1.00186	+	0.333989i
$873$	−18.3671	−	1.44552i	−0.621633	−	0.0489235i
$874$	−9.87840	+	25.5399i	−0.334142	+	0.863900i
$875$	1.05640	+	2.55038i	0.0357129	+	0.0862185i
$876$	3.50813	−	1.65146i	0.118529	−	0.0557975i
$877$	−24.3009	+	17.6556i	−0.820583	+	0.596188i	−0.916879	−	0.399164i	$-0.869300\pi$
$877$	−24.3009	+	17.6556i	−0.820583	+	0.596188i	0.0962965	+	0.995353i	$0.469300\pi$
$878$	24.6008	+	27.4619i	0.830235	+	0.926796i
$879$	−21.7613	+	29.9519i	−0.733992	+	1.01025i
$880$	2.42087	+	4.56884i	0.0816074	+	0.154016i
$881$	−3.69224	+	23.3119i	−0.124395	+	0.785398i	0.844067	+	0.536237i	$0.180155\pi$
$881$	−3.69224	+	23.3119i	−0.124395	+	0.785398i	−0.968462	+	0.249161i	$0.919845\pi$
$882$	0.621055	+	1.15081i	0.0209120	+	0.0387496i
$883$	−2.35296	+	3.83968i	−0.0791833	+	0.129215i	−0.889781	−	0.456389i	$-0.849143\pi$
$883$	−2.35296	+	3.83968i	−0.0791833	+	0.129215i	0.810597	+	0.585604i	$0.199143\pi$
$884$	12.3509	+	15.4116i	0.415404	+	0.518347i
$885$	17.2322	−	1.35621i	0.579255	−	0.0455884i
$886$	23.7675	+	7.10601i	0.798485	+	0.238731i
$887$	14.2705	−	12.1881i	0.479156	−	0.409238i	−0.376794	−	0.926297i	$-0.622973\pi$
$887$	14.2705	−	12.1881i	0.479156	−	0.409238i	0.855949	+	0.517059i	$0.172973\pi$
$888$	2.60149	−	2.56212i	0.0873004	−	0.0859791i
$889$	7.65688	−	4.69214i	0.256803	−	0.157369i
$890$	19.8468	−	12.8171i	0.665268	−	0.429630i
$891$	2.26783	+	1.93691i	0.0759753	+	0.0648890i
$892$	27.4641	+	18.0346i	0.919567	+	0.603842i
$893$	−48.0220	+	48.0220i	−1.60700	+	1.60700i
$894$	−29.0432	−	13.9436i	−0.971350	−	0.466344i
$895$	−17.6795	+	4.24447i	−0.590960	+	0.141877i
$896$	−28.9535	−	11.7093i	−0.967267	−	0.391181i
$897$	10.8108	+	5.50839i	0.360963	+	0.183920i
$898$	14.7755	−	21.3819i	0.493066	−	0.713524i
$899$	51.4433	+	21.3085i	1.71573	+	0.710679i
$900$	2.96295	+	0.326654i	0.0987650	+	0.0108885i
$901$			32.6316i			1.08712i
$902$	8.83445	+	7.67913i	0.294155	+	0.255687i
$903$			24.2342i			0.806464i
$904$	−21.8203	+	13.1437i	−0.725732	+	0.437153i
$905$	9.58277	+	3.96931i	0.318542	+	0.131944i
$906$	−10.3316	−	7.13941i	−0.343243	−	0.237191i
$907$	40.8662	+	20.8224i	1.35694	+	0.691396i	0.972750	−	0.231858i	$-0.0744804\pi$
$907$	40.8662	+	20.8224i	1.35694	+	0.691396i	0.384191	+	0.923254i	$0.374480\pi$
$908$	44.6616	+	24.5440i	1.48215	+	0.814523i
$909$	2.55037	−	0.612290i	0.0845905	−	0.0203084i
$910$	−5.84050	+	12.1652i	−0.193611	+	0.403272i
$911$	3.25977	−	3.25977i	0.108001	−	0.108001i	−0.651041	−	0.759042i	$-0.725668\pi$
$911$	3.25977	−	3.25977i	0.108001	−	0.108001i	0.759042	+	0.651041i	$0.225668\pi$
$912$	24.9787	−	22.0353i	0.827129	−	0.729662i
$913$	3.86341	+	3.29967i	0.127860	+	0.109203i
$914$	−22.4342	−	34.7386i	−0.742056	−	1.14905i
$915$	−5.83261	+	3.57423i	−0.192820	+	0.118160i
$916$	−6.20966	−	49.0941i	−0.205173	−	1.62212i
$917$	37.5658	−	32.0842i	1.24053	−	1.05951i
$918$	6.38499	−	21.3559i	0.210736	−	0.704850i
$919$	8.48121	−	0.667486i	0.279769	−	0.0220183i	0.0622018	−	0.998064i	$-0.480188\pi$
$919$	8.48121	−	0.667486i	0.279769	−	0.0220183i	0.217568	+	0.976045i	$0.430188\pi$
$920$	1.94624	−	7.84273i	0.0641655	−	0.258567i
$921$	−4.91736	+	8.02441i	−0.162033	+	0.264413i
$922$	6.73011	−	3.63203i	0.221644	−	0.119615i
$923$	−3.22567	+	20.3661i	−0.106174	+	0.670357i
$924$	6.00338	+	6.39100i	0.197497	+	0.210248i
$925$	−0.617592	+	0.850042i	−0.0203063	+	0.0279492i
$926$	1.39601	−	1.25056i	0.0458758	−	0.0410961i
$927$	10.8292	−	7.86788i	0.355678	−	0.258415i
$928$	33.2134	−	35.9576i	1.09028	−	1.18037i
$929$	3.04661	+	7.35517i	0.0999560	+	0.241315i	0.965945	−	0.258748i	$-0.0833100\pi$
$929$	3.04661	+	7.35517i	0.0999560	+	0.241315i	−0.865989	+	0.500063i	$0.833310\pi$
$930$	−10.4281	−	4.03340i	−0.341949	−	0.132260i
$931$	−4.19190	−	0.329910i	−0.137384	−	0.0108124i
$932$	17.0636	+	25.1000i	0.558936	+	0.822179i
$933$	−26.0022	−	8.44864i	−0.851275	−	0.276596i
$934$	5.64979	−	42.0875i	0.184867	−	1.37715i
$935$	−3.29034	+	1.67651i	−0.107606	+	0.0548279i
$936$	8.47504	+	11.8539i	0.277015	+	0.387457i
$937$	−3.53083	+	14.7070i	−0.115347	+	0.480456i	0.884554	+	0.466437i	$0.154463\pi$
$937$	−3.53083	+	14.7070i	−0.115347	+	0.480456i	−0.999902	+	0.0140191i	$0.995537\pi$
$938$	2.89162	+	15.8262i	0.0944149	+	0.516743i
$939$	−31.2447	+	10.1520i	−1.01963	+	0.331298i
$940$	12.2805	−	15.8369i	0.400546	−	0.516543i
$941$	−2.80167	−	17.6890i	−0.0913317	−	0.576646i	−0.990334	−	0.138702i	$-0.955707\pi$
$941$	−2.80167	−	17.6890i	−0.0913317	−	0.576646i	0.899002	−	0.437944i	$-0.144293\pi$
$942$	11.5755	+	15.1651i	0.377149	+	0.494106i
$943$	−2.27616	−	18.1511i	−0.0741220	−	0.591081i
$944$	28.6317	−	48.4474i	0.931882	−	1.57683i
$945$	15.0426	−	2.38251i	0.489335	−	0.0775031i
$946$	−3.34863	−	12.6255i	−0.108873	−	0.410491i
$947$	7.00386	+	21.5557i	0.227595	+	0.700465i	0.998018	+	0.0629320i	$0.0200451\pi$
$947$	7.00386	+	21.5557i	0.227595	+	0.700465i	−0.770423	+	0.637533i	$0.779955\pi$
$948$	−0.459016	−	0.417545i	−0.0149082	−	0.0135612i
$949$	−5.30364	−	1.27329i	−0.172164	−	0.0413328i
$950$	−6.05097	+	7.43361i	−0.196319	+	0.241178i
$951$	−8.97554	−	17.6155i	−0.291052	−	0.571221i
$952$	8.69288	−	20.5421i	0.281738	−	0.665772i
$953$	17.6723	−	54.3896i	0.572460	−	1.76185i	−0.0722080	−	0.997390i	$-0.523005\pi$
$953$	17.6723	−	54.3896i	0.572460	−	1.76185i	0.644668	−	0.764462i	$-0.276995\pi$
$954$	−1.32116	+	24.0401i	−0.0427742	+	0.778326i
$955$	−0.874427	+	11.1107i	−0.0282958	+	0.359532i
$956$	2.56876	+	8.83667i	0.0830795	+	0.285798i
$957$	−12.6968	+	5.25918i	−0.410429	+	0.170005i
$958$	−5.15681	+	23.9613i	−0.166609	+	0.774153i
$959$	16.1155	+	22.1812i	0.520398	+	0.716267i
$960$	−6.49672	+	7.37589i	−0.209681	+	0.238056i
$961$	−8.41967	−	6.11725i	−0.271602	−	0.197331i
$962$	−5.10954	+	0.523908i	−0.164738	+	0.0168915i
$963$	13.0246	+	2.06289i	0.419711	+	0.0664758i
$964$	−17.1243	+	37.9417i	−0.551538	+	1.22202i
$965$	4.04034	+	2.47592i	0.130063	+	0.0797028i
$966$	−0.323895	−	13.6995i	−0.0104211	−	0.440775i
$967$	−2.31786	−	29.4512i	−0.0745373	−	0.947087i	−0.914538	−	0.404501i	$-0.867445\pi$
$967$	−2.31786	−	29.4512i	−0.0745373	−	0.947087i	0.840000	−	0.542586i	$-0.182555\pi$
$968$	22.3925	+	13.9581i	0.719722	+	0.448630i
$969$	15.4500	+	18.0896i	0.496324	+	0.581121i
$970$	−8.77921	+	15.1172i	−0.281883	+	0.485383i
$971$	−1.91024	−	3.11723i	−0.0613026	−	0.100037i	0.820520	−	0.571617i	$-0.193684\pi$
$971$	−1.91024	−	3.11723i	−0.0613026	−	0.100037i	−0.881823	+	0.471580i	$0.843684\pi$
$972$	9.28878	−	25.8130i	0.297938	−	0.827951i
$973$	−21.8588	+	25.5934i	−0.700761	+	0.820486i
$974$	5.58054	−	1.96023i	0.178812	−	0.0628097i
$975$	3.00306	+	3.00306i	0.0961748	+	0.0961748i
$976$	−1.39159	+	22.2272i	−0.0445438	+	0.711474i
$977$	−0.896201	−	3.73294i	−0.0286720	−	0.119427i	0.956199	−	0.292718i	$-0.0945599\pi$
$977$	−0.896201	−	3.73294i	−0.0286720	−	0.119427i	−0.984871	+	0.173291i	$0.944560\pi$
$978$	−22.9985	+	10.1696i	−0.735410	+	0.325189i
$979$	−9.80385	+	19.2411i	−0.313332	+	0.614949i
$980$	1.23942	−	0.0586394i	0.0395918	−	0.00187317i
$981$	−6.28868	+	15.1822i	−0.200782	+	0.484731i
$982$	−14.1219	−	13.4695i	−0.450646	−	0.429829i
$983$	−35.7906			−1.14154			−0.570771	−	0.821110i	$-0.693355\pi$
$983$	−35.7906			−1.14154			−0.570771	+	0.821110i	$0.693355\pi$
$984$	−7.71594	+	20.8709i	−0.245975	+	0.665341i
$985$	−18.9568			−0.604014
$986$	25.2978	+	24.1292i	0.805647	+	0.768432i
$987$	13.0056	−	31.3982i	0.413972	−	0.999416i
$988$	−46.8034	+	2.21436i	−1.48902	+	0.0704483i
$989$	−9.26750	+	18.1885i	−0.294689	+	0.578360i
$990$	−2.49191	+	1.10189i	−0.0791980	+	0.0350203i
$991$	4.41088	+	18.3726i	0.140116	+	0.583626i	0.997608	+	0.0691282i	$0.0220217\pi$
$991$	4.41088	+	18.3726i	0.140116	+	0.583626i	−0.857492	+	0.514498i	$0.827978\pi$
$992$	−30.2586	+	20.2349i	−0.960711	+	0.642458i
$993$	10.7049	+	10.7049i	0.339711	+	0.339711i
$994$	21.9721	−	7.71795i	0.696913	−	0.244798i
$995$	−0.685269	+	0.802347i	−0.0217245	+	0.0254361i
$996$	−3.27024	+	9.08779i	−0.103621	+	0.287958i
$997$	−8.36697	−	13.6536i	−0.264985	−	0.432415i	0.692280	−	0.721629i	$-0.256606\pi$
$997$	−8.36697	−	13.6536i	−0.264985	−	0.432415i	−0.957265	+	0.289213i	$0.906606\pi$
$998$	−15.9489	+	27.4629i	−0.504854	+	0.869323i
$999$	3.76479	+	4.40800i	0.119113	+	0.139463i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bw.a.11.10	✓	672
4.3	odd	2	inner	820.2.bw.a.11.15	yes	672
41.15	odd	40	inner	820.2.bw.a.671.15	yes	672
164.15	even	40	inner	820.2.bw.a.671.10	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bw.a.11.10	✓	672	1.1	even	1	trivial
820.2.bw.a.11.15	yes	672	4.3	odd	2	inner
820.2.bw.a.671.10	yes	672	164.15	even	40	inner
820.2.bw.a.671.15	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+(-1.02336 - 0.976084i) q^{2} +(-0.470179 + 1.13511i) q^{3} +(0.0945183 + 1.99777i) q^{4} +(-0.453990 + 0.891007i) q^{5} +(1.58913 - 0.702691i) q^{6} +(0.644428 + 2.68423i) q^{7} +(1.85326 - 2.13668i) q^{8} +(1.05391 + 1.05391i) q^{9} +(1.33429 - 0.468685i) q^{10} +(-0.839506 + 0.982935i) q^{11} +(-2.31213 - 0.832019i) q^{12} +(1.80609 + 2.94728i) q^{13} +(1.96056 - 3.37595i) q^{14} +(-0.797936 - 0.934263i) q^{15} +(-3.98213 + 0.377651i) q^{16} +(-0.224143 - 2.84800i) q^{17} +(-0.0498207 - 2.10723i) q^{18} +(5.77889 + 3.54131i) q^{19} +(-1.82293 - 0.822750i) q^{20} +(-3.34991 - 0.530573i) q^{21} +(1.81854 - 0.186465i) q^{22} +(-2.31130 - 1.67926i) q^{23} +(1.55401 + 3.10829i) q^{24} +(-0.587785 - 0.809017i) q^{25} +(1.02851 - 4.77901i) q^{26} +(-5.09717 + 2.11132i) q^{27} +(-5.30156 + 1.54112i) q^{28} +(0.678920 - 8.62650i) q^{29} +(-0.0953464 + 1.73494i) q^{30} +(-1.98848 + 6.11991i) q^{31} +(4.44376 + 3.50043i) q^{32} +(-0.721024 - 1.41509i) q^{33} +(-2.55051 + 3.13330i) q^{34} +(-2.68423 - 0.644428i) q^{35} +(-2.00585 + 2.20507i) q^{36} +(-0.324687 - 0.999284i) q^{37} +(-2.45725 - 9.26470i) q^{38} +(-4.19468 + 0.664371i) q^{39} +(1.06244 + 2.62130i) q^{40} +(4.37897 + 4.67168i) q^{41} +(2.91026 + 3.81276i) q^{42} +(-1.11776 - 7.05726i) q^{43} +(-2.04302 - 1.58423i) q^{44} +(-1.41750 + 0.460575i) q^{45} +(0.726188 + 3.97451i) q^{46} +(-2.33917 + 9.74335i) q^{47} +(1.44364 - 4.69773i) q^{48} +(-0.552783 + 0.281657i) q^{49} +(-0.188155 + 1.40164i) q^{50} +(3.33819 + 1.08464i) q^{51} +(-5.71726 + 3.88672i) q^{52} +(-11.3872 - 0.896192i) q^{53} +(7.27704 + 2.81464i) q^{54} +(-0.494674 - 1.19425i) q^{55} +(6.92966 + 3.59765i) q^{56} +(-6.73689 + 4.89464i) q^{57} +(-9.11497 + 8.16530i) q^{58} +(-8.26946 + 11.3819i) q^{59} +(1.79102 - 1.68239i) q^{60} +(0.870975 - 5.49912i) q^{61} +(8.00847 - 4.32192i) q^{62} +(-2.14977 + 3.50810i) q^{63} +(-1.13084 - 7.91967i) q^{64} +(-3.44599 + 0.271205i) q^{65} +(-0.643382 + 2.15192i) q^{66} +(-3.13364 + 2.67638i) q^{67} +(5.66845 - 0.716972i) q^{68} +(2.99288 - 1.83404i) q^{69} +(2.11791 + 3.27952i) q^{70} +(4.53605 + 3.87415i) q^{71} +(4.20504 - 0.298702i) q^{72} +(-1.11577 + 1.11577i) q^{73} +(-0.643115 + 1.33955i) q^{74} +(1.19469 - 0.286820i) q^{75} +(-6.52849 + 11.8796i) q^{76} +(-3.17943 - 1.62000i) q^{77} +(4.94113 + 3.41447i) q^{78} +(0.233300 + 0.0966359i) q^{79} +(1.47136 - 3.71956i) q^{80} -2.30720i q^{81} +(0.0787056 - 9.05504i) q^{82} -3.93048i q^{83} +(0.743333 - 6.74247i) q^{84} +(2.63935 + 1.09325i) q^{85} +(-5.74462 + 8.31313i) q^{86} +(9.47283 + 4.82665i) q^{87} +(0.544398 + 3.61540i) q^{88} +(16.2443 - 3.89992i) q^{89} +(1.90017 + 0.912270i) q^{90} +(-6.74728 + 6.74728i) q^{91} +(3.13631 - 4.77616i) q^{92} +(-6.01184 - 5.13460i) q^{93} +(11.9041 - 7.68770i) q^{94} +(-5.77889 + 3.54131i) q^{95} +(-6.06274 + 3.39834i) q^{96} +(-9.39960 + 8.02802i) q^{97} +(0.840615 + 0.251327i) q^{98} +(-1.92069 + 0.151161i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q + 12 q^{6} + 100 q^{12} + 24 q^{14} + 32 q^{16} - 8 q^{17} - 40 q^{21} + 52 q^{22} - 24 q^{24} + 28 q^{28} + 12 q^{30} - 20 q^{32} + 40 q^{33} + 44 q^{34} + 36 q^{36} - 80 q^{37} + 52 q^{38} - 160 q^{42}+ \cdots - 116 q^{98}+O(q^{100}) \) 672 * q + 12 * q^6 + 100 * q^12 + 24 * q^14 + 32 * q^16 - 8 * q^17 - 40 * q^21 + 52 * q^22 - 24 * q^24 + 28 * q^28 + 12 * q^30 - 20 * q^32 + 40 * q^33 + 44 * q^34 + 36 * q^36 - 80 * q^37 + 52 * q^38 - 160 * q^42 + 24 * q^44 + 16 * q^46 + 40 * q^48 - 16 * q^49 - 64 * q^52 - 64 * q^54 + 68 * q^56 + 56 * q^58 + 36 * q^62 + 120 * q^64 + 8 * q^65 - 304 * q^68 + 104 * q^69 + 24 * q^70 - 40 * q^72 - 28 * q^74 - 24 * q^76 - 160 * q^77 - 128 * q^78 - 192 * q^82 - 204 * q^84 + 32 * q^85 - 168 * q^88 + 8 * q^89 + 48 * q^90 - 56 * q^92 - 356 * q^94 - 136 * q^96 - 116 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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