LMFDB - Embedded newform 820.2.bw.b.11.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

sage:traces = [672,0,0,0,0,12,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

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

Embedding invariants

Embedding label			11.22
Character	$\chi$	$=$	820.11
Dual form			820.2.bw.b.671.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0619819 - 1.41285i) q^{2} +(0.411797 - 0.994165i) q^{3} +(-1.99232 - 0.175143i) q^{4} +(0.453990 - 0.891007i) q^{5} +(-1.37909 - 0.643429i) q^{6} +(-1.19934 - 4.99561i) q^{7} +(-0.370939 + 2.80400i) q^{8} +(1.30253 + 1.30253i) q^{9} +(-1.23072 - 0.696649i) q^{10} +(0.477372 - 0.558931i) q^{11} +(-0.994550 + 1.90857i) q^{12} +(-2.16365 - 3.53076i) q^{13} +(-7.13241 + 1.38486i) q^{14} +(-0.698856 - 0.818255i) q^{15} +(3.93865 + 0.697880i) q^{16} +(0.279049 + 3.54566i) q^{17} +(1.92102 - 1.75956i) q^{18} +(-4.60777 - 2.82364i) q^{19} +(-1.06055 + 1.69565i) q^{20} +(-5.46035 - 0.864834i) q^{21} +(-0.760100 - 0.709101i) q^{22} +(2.47563 + 1.79865i) q^{23} +(2.63488 + 1.52345i) q^{24} +(-0.587785 - 0.809017i) q^{25} +(-5.12256 + 2.83808i) q^{26} +(4.81381 - 1.99394i) q^{27} +(1.51452 + 10.1629i) q^{28} +(-0.241369 + 3.06688i) q^{29} +(-1.19939 + 0.936664i) q^{30} +(0.696155 - 2.14255i) q^{31} +(1.23013 - 5.52148i) q^{32} +(-0.359089 - 0.704753i) q^{33} +(5.02679 - 0.174490i) q^{34} +(-4.99561 - 1.19934i) q^{35} +(-2.36693 - 2.82319i) q^{36} +(-3.60495 - 11.0949i) q^{37} +(-4.27500 + 6.33509i) q^{38} +(-4.40114 + 0.697072i) q^{39} +(2.32998 + 1.60350i) q^{40} +(-0.416214 + 6.38958i) q^{41} +(-1.56033 + 7.66107i) q^{42} +(1.36490 + 8.61764i) q^{43} +(-1.04897 + 1.02996i) q^{44} +(1.75190 - 0.569228i) q^{45} +(2.69467 - 3.38622i) q^{46} +(-1.30774 + 5.44713i) q^{47} +(2.31573 - 3.62828i) q^{48} +(-17.2807 + 8.80495i) q^{49} +(-1.17946 + 0.780311i) q^{50} +(3.63988 + 1.18267i) q^{51} +(3.69229 + 7.41334i) q^{52} +(3.38052 + 0.266052i) q^{53} +(-2.51878 - 6.92480i) q^{54} +(-0.281289 - 0.679091i) q^{55} +(14.4526 - 1.50988i) q^{56} +(-4.70463 + 3.41811i) q^{57} +(4.31809 + 0.531110i) q^{58} +(0.840526 - 1.15688i) q^{59} +(1.24903 + 1.75262i) q^{60} +(-0.185238 + 1.16955i) q^{61} +(-2.98396 - 1.11637i) q^{62} +(4.94477 - 8.06913i) q^{63} +(-7.72481 - 2.08022i) q^{64} +(-4.12821 + 0.324897i) q^{65} +(-1.01797 + 0.463659i) q^{66} +(4.28308 - 3.65810i) q^{67} +(0.0650418 - 7.11294i) q^{68} +(2.80761 - 1.72050i) q^{69} +(-2.00413 + 6.98374i) q^{70} +(-9.85349 - 8.41568i) q^{71} +(-4.13546 + 3.16914i) q^{72} +(4.91542 - 4.91542i) q^{73} +(-15.8989 + 4.40559i) q^{74} +(-1.04634 + 0.251205i) q^{75} +(8.68559 + 6.43261i) q^{76} +(-3.36474 - 1.71442i) q^{77} +(0.712071 + 6.26138i) q^{78} +(0.821419 + 0.340243i) q^{79} +(2.40993 - 3.19253i) q^{80} -0.0806352i q^{81} +(9.00175 + 0.984089i) q^{82} -8.02077i q^{83} +(10.7273 + 2.67936i) q^{84} +(3.28589 + 1.36106i) q^{85} +(12.2601 - 1.39427i) q^{86} +(2.94959 + 1.50289i) q^{87} +(1.39017 + 1.54588i) q^{88} +(7.56287 - 1.81568i) q^{89} +(-0.695650 - 2.51047i) q^{90} +(-15.0434 + 15.0434i) q^{91} +(-4.61721 - 4.01706i) q^{92} +(-1.84337 - 1.57439i) q^{93} +(7.61494 + 2.18527i) q^{94} +(-4.60777 + 2.82364i) q^{95} +(-4.98270 - 3.49668i) q^{96} +(9.70012 - 8.28469i) q^{97} +(11.3690 + 24.9609i) q^{98} +(1.34982 - 0.106233i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q + 12 q^{6} + 16 q^{9} - 124 q^{12} - 24 q^{14} - 32 q^{16} - 8 q^{17} + 40 q^{21} - 4 q^{22} - 24 q^{24} - 28 q^{28} - 12 q^{30} - 20 q^{32} + 40 q^{33} - 4 q^{34} - 60 q^{36} + 80 q^{37} - 172 q^{38}+ \cdots - 116 q^{98}+O(q^{100}) $ 672 * q + 12 * q^6 + 16 * q^9 - 124 * q^12 - 24 * q^14 - 32 * q^16 - 8 * q^17 + 40 * q^21 - 4 * q^22 - 24 * q^24 - 28 * q^28 - 12 * q^30 - 20 * q^32 + 40 * q^33 - 4 * q^34 - 60 * q^36 + 80 * q^37 - 172 * q^38 + 160 * q^42 - 24 * q^44 - 16 * q^46 + 40 * q^48 - 24 * q^52 - 64 * q^54 + 68 * q^56 - 112 * q^58 + 36 * q^62 - 120 * q^64 + 8 * q^65 + 144 * q^68 - 104 * q^69 + 24 * q^70 - 320 * q^72 - 92 * q^74 - 24 * q^76 + 160 * q^77 - 128 * q^78 - 192 * q^82 - 172 * q^84 - 32 * q^85 - 112 * q^88 + 8 * q^89 - 48 * q^90 + 24 * q^92 + 92 * q^94 + 56 * q^96 - 116 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	0.0619819	−	1.41285i	0.0438278	−	0.999039i
$2$	0.0619819	−	1.41285i	0.0438278	−	0.999039i
$3$	0.411797	−	0.994165i	0.237751	−	0.573981i	−0.759299	−	0.650742i	$-0.774458\pi$
$3$	0.411797	−	0.994165i	0.237751	−	0.573981i	0.997050	+	0.0767610i	$0.0244578\pi$
$4$	−1.99232	−	0.175143i	−0.996158	−	0.0875714i
$5$	0.453990	−	0.891007i	0.203031	−	0.398470i
$5$	0.453990	−	0.891007i	0.203031	−	0.398470i
$6$	−1.37909	−	0.643429i	−0.563010	−	0.262679i
$7$	−1.19934	−	4.99561i	−0.453308	−	1.88816i	−0.459489	−	0.888184i	$-0.651967\pi$
$7$	−1.19934	−	4.99561i	−0.453308	−	1.88816i	0.00618030	−	0.999981i	$-0.498033\pi$
$8$	−0.370939	+	2.80400i	−0.131147	+	0.991363i
$9$	1.30253	+	1.30253i	0.434178	+	0.434178i
$10$	−1.23072	−	0.696649i	−0.389189	−	0.220300i
$11$	0.477372	−	0.558931i	0.143933	−	0.168524i	−0.683756	−	0.729710i	$-0.739655\pi$
$11$	0.477372	−	0.558931i	0.143933	−	0.168524i	0.827690	+	0.561186i	$0.189655\pi$
$12$	−0.994550	+	1.90857i	−0.287102	+	0.550956i
$13$	−2.16365	−	3.53076i	−0.600089	−	0.979256i	−0.998084	−	0.0618689i	$-0.980294\pi$
$13$	−2.16365	−	3.53076i	−0.600089	−	0.979256i	0.397995	−	0.917388i	$-0.369706\pi$
$14$	−7.13241	+	1.38486i	−1.90622	+	0.370119i
$15$	−0.698856	−	0.818255i	−0.180444	−	0.211272i
$16$	3.93865	+	0.697880i	0.984662	+	0.174470i
$17$	0.279049	+	3.54566i	0.0676794	+	0.859948i	0.933265	+	0.359188i	$0.116946\pi$
$17$	0.279049	+	3.54566i	0.0676794	+	0.859948i	−0.865586	+	0.500760i	$0.833054\pi$
$18$	1.92102	−	1.75956i	0.452790	−	0.414731i
$19$	−4.60777	−	2.82364i	−1.05709	−	0.647788i	−0.118550	−	0.992948i	$-0.537825\pi$
$19$	−4.60777	−	2.82364i	−1.05709	−	0.647788i	−0.938544	+	0.345160i	$0.887825\pi$
$20$	−1.06055	+	1.69565i	−0.237145	+	0.379160i
$21$	−5.46035	−	0.864834i	−1.19155	−	0.188722i
$22$	−0.760100	−	0.709101i	−0.162054	−	0.151181i
$23$	2.47563	+	1.79865i	0.516204	+	0.375044i	0.815172	−	0.579219i	$-0.196642\pi$
$23$	2.47563	+	1.79865i	0.516204	+	0.375044i	−0.298968	+	0.954263i	$0.596642\pi$
$24$	2.63488	+	1.52345i	0.537844	+	0.310973i
$25$	−0.587785	−	0.809017i	−0.117557	−	0.161803i
$26$	−5.12256	+	2.83808i	−1.00462	+	0.556594i
$27$	4.81381	−	1.99394i	0.926417	−	0.383735i
$28$	1.51452	+	10.1629i	0.286218	+	1.92061i
$29$	−0.241369	+	3.06688i	−0.0448210	+	0.569505i	0.932974	+	0.359943i	$0.117204\pi$
$29$	−0.241369	+	3.06688i	−0.0448210	+	0.569505i	−0.977795	+	0.209562i	$0.932796\pi$
$30$	−1.19939	+	0.936664i	−0.218978	+	0.171011i
$31$	0.696155	−	2.14255i	0.125033	−	0.384812i	−0.868874	−	0.495033i	$-0.835156\pi$
$31$	0.696155	−	2.14255i	0.125033	−	0.384812i	0.993907	+	0.110221i	$0.0351558\pi$
$32$	1.23013	−	5.52148i	0.217458	−	0.976070i
$33$	−0.359089	−	0.704753i	−0.0625094	−	0.122682i
$34$	5.02679	−	0.174490i	0.862088	−	0.0299247i
$35$	−4.99561	−	1.19934i	−0.844413	−	0.202726i
$36$	−2.36693	−	2.82319i	−0.394488	−	0.470531i
$37$	−3.60495	−	11.0949i	−0.592650	−	1.82399i	−0.566092	−	0.824342i	$-0.691545\pi$
$37$	−3.60495	−	11.0949i	−0.592650	−	1.82399i	−0.0265585	−	0.999647i	$-0.508455\pi$
$38$	−4.27500	+	6.33509i	−0.693496	+	1.02769i
$39$	−4.40114	+	0.697072i	−0.704747	+	0.111621i
$40$	2.32998	+	1.60350i	0.368402	+	0.253535i
$41$	−0.416214	+	6.38958i	−0.0650017	+	0.997885i
$41$	−0.416214	+	6.38958i	−0.0650017	+	0.997885i
$42$	−1.56033	+	7.66107i	−0.240764	+	1.18213i
$43$	1.36490	+	8.61764i	0.208145	+	1.31418i	0.841475	+	0.540296i	$0.181688\pi$
$43$	1.36490	+	8.61764i	0.208145	+	1.31418i	−0.633330	+	0.773882i	$0.718312\pi$
$44$	−1.04897	+	1.02996i	−0.158138	+	0.155272i
$45$	1.75190	−	0.569228i	0.261158	−	0.0848555i
$46$	2.69467	−	3.38622i	0.397308	−	0.499270i
$47$	−1.30774	+	5.44713i	−0.190753	+	0.794545i	0.792135	+	0.610345i	$0.208969\pi$
$47$	−1.30774	+	5.44713i	−0.190753	+	0.794545i	−0.982889	+	0.184200i	$0.941031\pi$
$48$	2.31573	−	3.62828i	0.334247	−	0.523697i
$49$	−17.2807	+	8.80495i	−2.46867	+	1.25785i
$50$	−1.17946	+	0.780311i	−0.166800	+	0.110353i
$51$	3.63988	+	1.18267i	0.509685	+	0.165607i
$52$	3.69229	+	7.41334i	0.512029	+	1.02805i
$53$	3.38052	+	0.266052i	0.464350	+	0.0365451i	0.308477	−	0.951232i	$-0.400181\pi$
$53$	3.38052	+	0.266052i	0.464350	+	0.0365451i	0.155873	+	0.987777i	$0.450181\pi$
$54$	−2.51878	−	6.92480i	−0.342763	−	0.942345i
$55$	−0.281289	−	0.679091i	−0.0379290	−	0.0915686i
$56$	14.4526	−	1.50988i	1.93131	−	0.201766i
$57$	−4.70463	+	3.41811i	−0.623143	+	0.452740i
$58$	4.31809	+	0.531110i	0.566994	+	0.0697381i
$59$	0.840526	−	1.15688i	0.109427	−	0.150614i	−0.750791	−	0.660540i	$-0.770327\pi$
$59$	0.840526	−	1.15688i	0.109427	−	0.150614i	0.860218	+	0.509926i	$0.170327\pi$
$60$	1.24903	+	1.75262i	0.161249	+	0.226263i
$61$	−0.185238	+	1.16955i	−0.0237173	+	0.149745i	−0.996705	−	0.0811118i	$-0.974153\pi$
$61$	−0.185238	+	1.16955i	−0.0237173	+	0.149745i	0.972988	+	0.230857i	$0.0741529\pi$
$62$	−2.98396	−	1.11637i	−0.378963	−	0.141778i
$63$	4.94477	−	8.06913i	0.622983	−	1.01662i
$64$	−7.72481	−	2.08022i	−0.965601	−	0.260028i
$65$	−4.12821	+	0.324897i	−0.512041	+	0.0402985i
$66$	−1.01797	+	0.463659i	−0.125303	+	0.0570725i
$67$	4.28308	−	3.65810i	0.523262	−	0.446908i	−0.348165	−	0.937433i	$-0.613195\pi$
$67$	4.28308	−	3.65810i	0.523262	−	0.446908i	0.871427	+	0.490526i	$0.163195\pi$
$68$	0.0650418	−	7.11294i	0.00788748	−	0.862571i
$69$	2.80761	−	1.72050i	0.337996	−	0.207124i
$70$	−2.00413	+	6.98374i	−0.239540	+	0.834716i
$71$	−9.85349	−	8.41568i	−1.16939	−	0.998757i	−0.999913	−	0.0132237i	$-0.995791\pi$
$71$	−9.85349	−	8.41568i	−1.16939	−	0.998757i	−0.169482	−	0.985533i	$-0.554209\pi$
$72$	−4.13546	+	3.16914i	−0.487369	+	0.373487i
$73$	4.91542	−	4.91542i	0.575306	−	0.575306i	−0.358300	−	0.933606i	$-0.616644\pi$
$73$	4.91542	−	4.91542i	0.575306	−	0.575306i	0.933606	+	0.358300i	$0.116644\pi$
$74$	−15.8989	+	4.40559i	−1.84821	+	0.512139i
$75$	−1.04634	+	0.251205i	−0.120821	+	0.0290067i
$76$	8.68559	+	6.43261i	0.996305	+	0.737871i
$77$	−3.36474	−	1.71442i	−0.383447	−	0.195376i
$78$	0.712071	+	6.26138i	0.0806261	+	0.708962i
$79$	0.821419	+	0.340243i	0.0924168	+	0.0382803i	0.428413	−	0.903583i	$-0.359073\pi$
$79$	0.821419	+	0.340243i	0.0924168	+	0.0382803i	−0.335996	+	0.941863i	$0.609073\pi$
$80$	2.40993	−	3.19253i	0.269438	−	0.356936i
$81$		−	0.0806352i		−	0.00895947i
$82$	9.00175	+	0.984089i	0.994077	+	0.108674i
$83$		−	8.02077i		−	0.880394i	−0.897901	−	0.440197i	$-0.854909\pi$
$83$		−	8.02077i		−	0.880394i	0.897901	−	0.440197i	$-0.145091\pi$
$84$	10.7273	+	2.67936i	1.17044	+	0.292343i
$85$	3.28589	+	1.36106i	0.356405	+	0.147628i
$86$	12.2601	−	1.39427i	1.32204	−	0.150348i
$87$	2.94959	+	1.50289i	0.316229	+	0.161127i
$88$	1.39017	+	1.54588i	0.148192	+	0.164791i
$89$	7.56287	−	1.81568i	0.801663	−	0.192462i	0.188143	−	0.982142i	$-0.439753\pi$
$89$	7.56287	−	1.81568i	0.801663	−	0.192462i	0.613520	+	0.789679i	$0.289753\pi$
$90$	−0.695650	−	2.51047i	−0.0733279	−	0.264626i
$91$	−15.0434	+	15.0434i	−1.57697	+	1.57697i
$92$	−4.61721	−	4.01706i	−0.481377	−	0.418808i
$93$	−1.84337	−	1.57439i	−0.191148	−	0.163256i
$94$	7.61494	+	2.18527i	0.785421	+	0.225393i
$95$	−4.60777	+	2.82364i	−0.472747	+	0.289700i
$96$	−4.98270	−	3.49668i	−0.508545	−	0.356878i
$97$	9.70012	−	8.28469i	0.984898	−	0.841182i	−0.00241033	−	0.999997i	$-0.500767\pi$
$97$	9.70012	−	8.28469i	0.984898	−	0.841182i	0.987308	+	0.158815i	$0.0507672\pi$
$98$	11.3690	+	24.9609i	1.14845	+	2.52143i
$99$	1.34982	−	0.106233i	0.135662	−	0.0106768i
$100$	1.02936	+	1.71476i	0.102936	+	0.171476i
$101$	2.70177	−	4.40888i	0.268836	−	0.438700i	−0.689524	−	0.724263i	$-0.742180\pi$
$101$	2.70177	−	4.40888i	0.268836	−	0.438700i	0.958360	+	0.285562i	$0.0921804\pi$
$102$	1.89654	−	5.06932i	0.187786	−	0.501937i
$103$	0.983316	−	6.20841i	0.0968890	−	0.611733i	−0.890690	−	0.454611i	$-0.849778\pi$
$103$	0.983316	−	6.20841i	0.0968890	−	0.611733i	0.987579	−	0.157122i	$-0.0502217\pi$
$104$	10.7028	−	4.75718i	1.04950	−	0.466480i
$105$	−3.24952	+	4.47258i	−0.317121	+	0.436479i
$106$	0.585424	−	4.75969i	0.0568614	−	0.462302i
$107$	−1.68436	+	1.22376i	−0.162833	+	0.118305i	−0.666218	−	0.745757i	$-0.732088\pi$
$107$	−1.68436	+	1.22376i	−0.162833	+	0.118305i	0.503385	+	0.864062i	$0.332088\pi$
$108$	−9.93985	+	3.12946i	−0.956462	+	0.301133i
$109$	2.11110	+	5.09664i	0.202206	+	0.488170i	0.992157	−	0.125002i	$-0.0398936\pi$
$109$	2.11110	+	5.09664i	0.202206	+	0.488170i	−0.789950	+	0.613171i	$0.789894\pi$
$110$	−0.976892	+	0.355329i	−0.0931430	+	0.0338793i
$111$	−12.5147	−	0.984925i	−1.18784	−	0.0934850i
$112$	−1.23745	−	20.5130i	−0.116928	−	1.93829i
$113$	2.99010	+	0.971541i	0.281285	+	0.0913949i	0.446262	−	0.894902i	$-0.352755\pi$
$113$	2.99010	+	0.971541i	0.281285	+	0.0913949i	−0.164977	+	0.986297i	$0.552755\pi$
$114$	4.53770	+	6.85882i	0.424994	+	0.642387i
$115$	2.72652	−	1.38923i	0.254249	−	0.129546i
$116$	1.01802	−	6.06792i	0.0945212	−	0.563392i
$117$	1.78070	−	7.41716i	0.164626	−	0.685717i
$118$	−1.58241	−	1.25925i	−0.145673	−	0.115923i
$119$	17.3781	−	5.64647i	1.59304	−	0.517611i
$120$	2.55362	−	1.65607i	0.233112	−	0.151178i
$121$	1.63626	+	10.3309i	0.148751	+	0.939176i
$122$	1.64092	+	0.334205i	0.148562	+	0.0302575i
$123$	6.18090	+	3.04499i	0.557313	+	0.274558i
$124$	−1.76221	+	4.14670i	−0.158251	+	0.372385i
$125$	−0.987688	+	0.156434i	−0.0883415	+	0.0139919i
$126$	−11.0940	−	7.48638i	−0.988334	−	0.666940i
$127$	−3.72564	−	11.4663i	−0.330597	−	1.01747i	−0.968851	−	0.247646i	$-0.920343\pi$
$127$	−3.72564	−	11.4663i	−0.330597	−	1.01747i	0.638254	−	0.769826i	$-0.279657\pi$
$128$	−3.41785	+	10.7851i	−0.302098	+	0.953277i
$129$	9.12942	+	2.19178i	0.803800	+	0.192975i
$130$	0.203158	+	5.85269i	0.0178181	+	0.513315i
$131$	−6.15725	−	12.0843i	−0.537962	−	1.05581i	−0.986762	−	0.162177i	$-0.948148\pi$
$131$	−6.15725	−	12.0843i	−0.537962	−	1.05581i	0.448800	−	0.893632i	$-0.351852\pi$
$132$	0.591987	+	1.46698i	0.0515259	+	0.127684i
$133$	−8.57955	+	26.4051i	−0.743941	+	2.28962i
$134$	−4.90288	−	6.27811i	−0.423545	−	0.542346i
$135$	0.408805	−	5.19436i	0.0351844	−	0.447060i
$136$	−10.0455	−	0.532768i	−0.861397	−	0.0456845i
$137$	10.1963	−	4.22346i	0.871132	−	0.360835i	0.0980809	−	0.995178i	$-0.468730\pi$
$137$	10.1963	−	4.22346i	0.871132	−	0.360835i	0.773051	+	0.634344i	$0.218730\pi$
$138$	−2.25680	−	4.07338i	−0.192112	−	0.346749i
$139$	3.27034	+	4.50123i	0.277386	+	0.381789i	0.924866	−	0.380293i	$-0.124177\pi$
$139$	3.27034	+	4.50123i	0.277386	+	0.381789i	−0.647480	+	0.762083i	$0.724177\pi$
$140$	9.74279	+	3.26441i	0.823416	+	0.275893i
$141$	4.87682	+	3.54322i	0.410702	+	0.298393i
$142$	−12.5009	+	13.3999i	−1.04905	+	1.12450i
$143$	−3.00632	−	0.476154i	−0.251401	−	0.0398180i
$144$	4.22121	+	6.03923i	0.351768	+	0.503269i
$145$	2.62303	+	1.60740i	0.217831	+	0.133487i
$146$	−6.64010	−	7.24943i	−0.549539	−	0.599967i
$147$	1.63744	+	20.8057i	0.135054	+	1.71603i
$148$	5.23901	+	22.7359i	0.430644	+	1.86888i
$149$	3.57097	+	4.18106i	0.292545	+	0.342526i	0.887141	−	0.461498i	$-0.152688\pi$
$149$	3.57097	+	4.18106i	0.292545	+	0.342526i	−0.594596	+	0.804025i	$0.702688\pi$
$150$	0.290062	+	1.49390i	0.0236834	+	0.121977i
$151$	−3.62465	−	5.91489i	−0.294970	−	0.481347i	0.670483	−	0.741925i	$-0.266087\pi$
$151$	−3.62465	−	5.91489i	−0.294970	−	0.481347i	−0.965453	+	0.260578i	$0.916087\pi$
$152$	9.62669	−	11.8728i	0.780828	−	0.963009i
$153$	−4.25486	+	4.98181i	−0.343985	+	0.402755i
$154$	−2.63078	+	4.64762i	−0.211994	+	0.374516i
$155$	−1.59297	−	1.59297i	−0.127951	−	0.127951i
$156$	8.89055	−	0.617960i	0.711814	−	0.0494764i
$157$	−1.33774	−	5.57209i	−0.106763	−	0.444702i	0.893225	−	0.449611i	$-0.148437\pi$
$157$	−1.33774	−	5.57209i	−0.106763	−	0.444702i	−0.999988	+	0.00490930i	$0.998437\pi$
$158$	0.531627	−	1.13946i	0.0422940	−	0.0906503i
$159$	1.65659	−	3.25123i	0.131376	−	0.257839i
$160$	−4.36121	−	3.60275i	−0.344784	−	0.284823i
$161$	6.01623	−	14.5245i	0.474145	−	1.14469i
$162$	−0.113926	−	0.00499792i	−0.00895086	−	0.000392674i
$163$	3.82938			0.299940			0.149970	−	0.988691i	$-0.452082\pi$
$163$	3.82938			0.299940			0.149970	+	0.988691i	$0.452082\pi$
$164$	1.94832	−	12.6572i	0.152138	−	0.988359i
$165$	−0.790962			−0.0615763
$166$	−11.3322	−	0.497142i	−0.879548	−	0.0385857i
$167$	5.62883	−	13.5892i	0.435572	−	1.05156i	−0.541889	−	0.840450i	$-0.682291\pi$
$167$	5.62883	−	13.5892i	0.435572	−	1.05156i	0.977461	−	0.211114i	$-0.0677092\pi$
$168$	4.45045	−	14.9900i	0.343360	−	1.15650i
$169$	−1.88299	+	3.69558i	−0.144846	+	0.284276i
$170$	2.12665	−	4.55812i	0.163106	−	0.349592i
$171$	−2.32388	−	9.67966i	−0.177712	−	0.740222i
$172$	−1.21000	−	17.4081i	−0.0922613	−	1.32736i
$173$	7.35818	+	7.35818i	0.559432	+	0.559432i	0.929146	−	0.369714i	$-0.120544\pi$
$173$	7.35818	+	7.35818i	0.559432	+	0.559432i	−0.369714	+	0.929146i	$0.620544\pi$
$174$	2.30619	−	4.07419i	0.174832	−	0.308863i
$175$	−3.33658	+	3.90664i	−0.252222	+	0.295314i
$176$	2.27027	−	1.86829i	0.171128	−	0.140827i
$177$	−0.804008	−	1.31202i	−0.0604330	−	0.0986176i
$178$	−2.09654	−	10.7978i	−0.157142	−	0.809328i
$179$	−17.0852	−	20.0042i	−1.27701	−	1.49518i	−0.777515	−	0.628864i	$-0.783520\pi$
$179$	−17.0852	−	20.0042i	−1.27701	−	1.49518i	−0.499492	−	0.866319i	$-0.666480\pi$
$180$	−3.59004	+	0.827249i	−0.267586	+	0.0616595i
$181$	−2.02008	−	25.6675i	−0.150151	−	1.90785i	−0.364678	−	0.931134i	$-0.618821\pi$
$181$	−2.02008	−	25.6675i	−0.150151	−	1.90785i	0.214527	−	0.976718i	$-0.431179\pi$
$182$	20.3217	+	22.1865i	1.50634	+	1.64457i
$183$	1.08644	+	0.665772i	0.0803121	+	0.0492153i
$184$	−5.96171	+	6.27446i	−0.439503	+	0.462559i
$185$	−11.5222	−	1.82494i	−0.847132	−	0.134172i
$186$	−2.33863	+	2.50683i	−0.171477	+	0.183810i
$187$	2.11499	+	1.53663i	0.154663	+	0.112369i
$188$	3.55946	−	10.6234i	0.259600	−	0.774788i
$189$	−15.7344	−	21.6565i	−1.14451	−	1.57528i
$190$	3.70380	+	6.68512i	0.268702	+	0.484990i
$191$	2.34837	−	0.972726i	0.169922	−	0.0703840i	−0.296101	−	0.955157i	$-0.595686\pi$
$191$	2.34837	−	0.972726i	0.169922	−	0.0703840i	0.466023	+	0.884773i	$0.345686\pi$
$192$	−5.24913	+	6.82310i	−0.378824	+	0.492415i
$193$	−0.493556	+	6.27123i	−0.0355270	+	0.451413i	0.953267	+	0.302128i	$0.0976970\pi$
$193$	−0.493556	+	6.27123i	−0.0355270	+	0.451413i	−0.988794	+	0.149285i	$0.952303\pi$
$194$	−11.1038	−	14.2184i	−0.797208	−	1.02082i
$195$	−1.37698	+	4.23791i	−0.0986076	+	0.303483i
$196$	35.9707	−	14.5157i	2.56934	−	1.03683i
$197$	1.07442	+	2.10867i	0.0765493	+	0.150236i	0.926109	−	0.377256i	$-0.123132\pi$
$197$	1.07442	+	2.10867i	0.0765493	+	0.150236i	−0.849560	+	0.527492i	$0.823132\pi$
$198$	−0.0664276	−	1.91368i	−0.00472080	−	0.136000i
$199$	18.0062	+	4.32290i	1.27642	+	0.306442i	0.814337	−	0.580392i	$-0.197101\pi$
$199$	18.0062	+	4.32290i	1.27642	+	0.306442i	0.462087	+	0.886835i	$0.347101\pi$
$200$	2.48651	−	1.34805i	0.175823	−	0.0953217i
$201$	−1.87299	−	5.76448i	−0.132111	−	0.406595i
$202$	−6.06165	−	4.09047i	−0.426496	−	0.287805i
$203$	15.6104	−	2.47245i	1.09564	−	0.173532i
$204$	−7.04465	−	2.99375i	−0.493224	−	0.209604i
$205$	5.50420	+	3.27166i	0.384430	+	0.228503i
$206$	−8.71064	−	1.77409i	−0.606899	−	0.123607i
$207$	0.881787	+	5.56738i	0.0612884	+	0.386960i
$208$	−6.05782	−	15.4164i	−0.420034	−	1.06893i
$209$	−3.77784	+	1.22750i	−0.261319	+	0.0849076i
$210$	6.11769	+	4.86832i	0.422161	+	0.335946i
$211$	1.59026	−	6.62392i	0.109478	−	0.456009i	−0.890521	−	0.454942i	$-0.849660\pi$
$211$	1.59026	−	6.62392i	0.109478	−	0.456009i	0.999999	−	0.00106767i	$-0.000339850\pi$
$212$	−6.68846	−	1.12213i	−0.459365	−	0.0770685i
$213$	−12.4242	+	6.33045i	−0.851292	+	0.433755i
$214$	1.62459	+	2.45560i	0.111055	+	0.167862i
$215$	8.29803	+	2.69619i	0.565921	+	0.183879i
$216$	3.80539	+	14.2375i	0.258924	+	0.968741i
$217$	−11.5383	−	0.908080i	−0.783268	−	0.0616445i
$218$	7.33166	−	2.66677i	0.496563	−	0.180617i
$219$	−2.86258	−	6.91088i	−0.193435	−	0.466994i
$220$	0.441478	+	1.40223i	0.0297645	+	0.0945384i
$221$	11.9151	−	8.65682i	0.801496	−	0.582321i
$222$	−2.16724	+	17.6203i	−0.145456	+	1.18260i
$223$	−14.4122	+	19.8367i	−0.965115	+	1.32837i	−0.0206389	+	0.999787i	$0.506570\pi$
$223$	−14.4122	+	19.8367i	−0.965115	+	1.32837i	−0.944476	+	0.328580i	$0.893430\pi$
$224$	−29.0585	+	0.476898i	−1.94156	+	0.0318641i
$225$	0.288162	−	1.81938i	0.0192108	−	0.121292i
$226$	1.55798	−	4.16435i	0.103635	−	0.277009i
$227$	2.57266	−	4.19819i	0.170753	−	0.278644i	−0.755804	−	0.654798i	$-0.772754\pi$
$227$	2.57266	−	4.19819i	0.170753	−	0.278644i	0.926557	+	0.376154i	$0.122754\pi$
$228$	9.97177	−	5.98598i	0.660396	−	0.396431i
$229$	25.5992	−	2.01470i	1.69164	−	0.133135i	0.804292	−	0.594235i	$-0.202545\pi$
$229$	25.5992	−	2.01470i	1.69164	−	0.133135i	0.887348	+	0.461100i	$0.152545\pi$
$230$	−1.79379	−	3.93828i	−0.118279	−	0.259682i
$231$	−3.09000	+	2.63911i	−0.203307	+	0.173641i
$232$	−8.50999	−	1.81442i	−0.558708	−	0.119123i
$233$	−16.0742	+	9.85028i	−1.05306	+	0.645314i	−0.937499	−	0.347987i	$-0.886865\pi$
$233$	−16.0742	+	9.85028i	−1.05306	+	0.645314i	−0.115557	+	0.993301i	$0.536865\pi$
$234$	−10.3690	−	2.97560i	−0.677843	−	0.194521i
$235$	4.25972	+	3.63815i	0.277874	+	0.237327i
$236$	−1.87721	+	2.15767i	−0.122196	+	0.140452i
$237$	0.676515	−	0.676515i	0.0439444	−	0.0439444i
$238$	−6.90052	−	24.9026i	−0.447294	−	1.61420i
$239$	22.7110	−	5.45244i	1.46905	−	0.352689i	0.581559	−	0.813504i	$-0.302443\pi$
$239$	22.7110	−	5.45244i	1.46905	−	0.352689i	0.887496	+	0.460815i	$0.152443\pi$
$240$	−2.18150	−	3.71054i	−0.140815	−	0.239514i
$241$	−11.3704	−	5.79351i	−0.732432	−	0.373193i	0.0476550	−	0.998864i	$-0.484825\pi$
$241$	−11.3704	−	5.79351i	−0.732432	−	0.373193i	−0.780087	+	0.625671i	$0.784825\pi$
$242$	14.6975	−	1.67147i	0.944793	−	0.107446i
$243$	14.3613	+	5.94863i	0.921275	+	0.381604i
$244$	0.573890	−	2.29766i	0.0367396	−	0.147093i
$245$			19.3946i			1.23907i
$246$	4.68524	−	8.54398i	0.298720	−	0.544744i
$247$			22.3783i			1.42390i
$248$	5.74946	+	2.74677i	0.365091	+	0.174420i
$249$	−7.97396	−	3.30292i	−0.505329	−	0.209314i
$250$	0.159800	+	1.40516i	0.0101067	+	0.0888699i
$251$	9.69709	+	4.94091i	0.612075	+	0.311868i	0.732408	−	0.680866i	$-0.238396\pi$
$251$	9.69709	+	4.94091i	0.612075	+	0.311868i	−0.120333	+	0.992734i	$0.538396\pi$
$252$	−11.2648	+	15.2102i	−0.709616	+	0.958154i
$253$	2.18712	−	0.525080i	0.137503	−	0.0330115i
$254$	−16.4312	+	4.55308i	−1.03098	+	0.285686i
$255$	2.70624	−	2.70624i	0.169471	−	0.169471i
$256$	15.0259	+	5.49741i	0.939120	+	0.343588i
$257$	−11.1642	−	9.53514i	−0.696405	−	0.594786i	0.229154	−	0.973390i	$-0.426404\pi$
$257$	−11.1642	−	9.53514i	−0.696405	−	0.594786i	−0.925559	+	0.378605i	$0.876404\pi$
$258$	3.66252	−	12.7627i	0.228019	−	0.794570i
$259$	−51.1023	+	31.3155i	−3.17534	+	1.94585i
$260$	8.28160	+	0.0757282i	0.513603	+	0.00469646i
$261$	−4.30910	+	3.68032i	−0.266727	+	0.227806i
$262$	−17.4550	+	7.95030i	−1.07837	+	0.491171i
$263$	−21.4514	+	1.68827i	−1.32275	+	0.104103i	−0.720083	−	0.693888i	$-0.755896\pi$
$263$	−21.4514	+	1.68827i	−1.32275	+	0.104103i	−0.602670	+	0.797991i	$0.705896\pi$
$264$	2.10933	−	0.745466i	0.129820	−	0.0458802i
$265$	1.77178	−	2.89128i	0.108839	−	0.177610i
$266$	36.7748	+	13.7583i	2.25481	+	0.843575i
$267$	1.30927	−	8.26643i	0.0801263	−	0.505897i
$268$	−9.17394	+	6.53793i	−0.560388	+	0.399368i
$269$	13.1807	−	18.1417i	0.803643	−	1.10612i	−0.188630	−	0.982048i	$-0.560405\pi$
$269$	13.1807	−	18.1417i	0.803643	−	1.10612i	0.992273	−	0.124072i	$-0.0395953\pi$
$270$	−7.31354	−	0.899539i	−0.445088	−	0.0547442i
$271$	−25.1653	+	18.2837i	−1.52868	+	1.11065i	−0.571719	+	0.820449i	$0.693723\pi$
$271$	−25.1653	+	18.2837i	−1.52868	+	1.11065i	−0.956965	+	0.290205i	$0.906277\pi$
$272$	−1.37536	+	14.1598i	−0.0833937	+	0.858567i
$273$	8.76077	+	21.1504i	0.530226	+	1.28008i
$274$	−5.33515	−	14.6677i	−0.322308	−	0.886110i
$275$	−0.732777	−	0.0576708i	−0.0441881	−	0.00347768i
$276$	−5.89497	+	2.93606i	−0.354836	+	0.176730i
$277$	18.4652	+	5.99970i	1.10946	+	0.360487i	0.805738	−	0.592272i	$-0.201769\pi$
$277$	18.4652	+	5.99970i	1.10946	+	0.360487i	0.303727	+	0.952759i	$0.401769\pi$
$278$	6.56229	−	4.34151i	0.393580	−	0.260387i
$279$	3.69750	−	1.88397i	0.221364	−	0.112790i
$280$	5.21602	−	13.5628i	0.311717	−	0.810533i
$281$	0.0633133	−	0.263719i	0.00377696	−	0.0157322i	−0.970450	−	0.241304i	$-0.922425\pi$
$281$	0.0633133	−	0.263719i	0.00377696	−	0.0157322i	0.974227	+	0.225572i	$0.0724250\pi$
$282$	5.30832	−	6.67062i	0.316106	−	0.397230i
$283$	−5.96964	+	1.93965i	−0.354858	+	0.115300i	−0.481021	−	0.876709i	$-0.659734\pi$
$283$	−5.96964	+	1.93965i	−0.354858	+	0.115300i	0.126163	+	0.992010i	$0.459734\pi$
$284$	18.1573	+	18.4925i	1.07744	+	1.09733i
$285$	0.909704	+	5.74365i	0.0538862	+	0.340224i
$286$	−0.859074	+	4.21798i	−0.0507981	+	0.249414i
$287$	32.4191	−	5.58404i	1.91364	−	0.329616i
$288$	8.79420	−	5.58963i	0.518203	−	0.329372i
$289$	4.29689	−	0.680560i	0.252758	−	0.0400330i
$290$	2.43360	−	3.60633i	0.142906	−	0.211771i
$291$	−4.24187	−	13.0551i	−0.248663	−	0.765305i
$292$	−10.6540	+	8.93216i	−0.623476	+	0.522715i
$293$	28.1347	+	6.75455i	1.64365	+	0.394605i	0.946597	−	0.322418i	$-0.104496\pi$
$293$	28.1347	+	6.75455i	1.64365	+	0.394605i	0.697050	+	0.717023i	$0.254496\pi$
$294$	29.4969	−	1.02389i	1.72030	−	0.0597147i
$295$	−0.649201	−	1.27413i	−0.0377979	−	0.0741826i
$296$	32.4473	−	5.99274i	1.88596	−	0.348321i
$297$	1.18350	−	3.64244i	0.0686736	−	0.211356i
$298$	6.12857	−	4.78611i	0.355019	−	0.277252i
$299$	0.994198	−	12.6325i	0.0574960	−	0.730556i
$300$	2.12865	−	0.317220i	0.122897	−	0.0183147i
$301$	41.4134	−	17.1540i	2.38703	−	0.988740i
$302$	−8.58154	+	4.75449i	−0.493812	+	0.273590i
$303$	−3.27058	−	4.50156i	−0.187890	−	0.258608i
$304$	−16.1778	−	14.3370i	−0.927861	−	0.822284i
$305$	0.957977	+	0.696011i	0.0548536	+	0.0398535i
$306$	6.77484	+	6.32029i	0.387292	+	0.361307i
$307$	−9.66309	−	1.53048i	−0.551502	−	0.0873493i	−0.125537	−	0.992089i	$-0.540065\pi$
$307$	−9.66309	−	1.53048i	−0.551502	−	0.0873493i	−0.425965	+	0.904740i	$0.640065\pi$
$308$	6.40335	+	4.00497i	0.364865	+	0.228205i
$309$	−5.76726	−	3.53418i	−0.328088	−	0.201053i
$310$	−2.34938	+	2.15191i	−0.133436	+	0.122220i
$311$	1.97817	+	25.1351i	0.112172	+	1.42528i	0.753215	+	0.657775i	$0.228502\pi$
$311$	1.97817	+	25.1351i	0.112172	+	1.42528i	−0.641043	+	0.767505i	$0.721498\pi$
$312$	−0.322035	−	12.5994i	−0.0182316	−	0.713298i
$313$	−17.2015	−	20.1404i	−0.972288	−	1.13840i	−0.990353	−	0.138566i	$-0.955751\pi$
$313$	−17.2015	−	20.1404i	−0.972288	−	1.13840i	0.0180649	−	0.999837i	$-0.494249\pi$
$314$	−7.95547	+	1.54467i	−0.448953	+	0.0871705i
$315$	−4.94477	−	8.06913i	−0.278606	−	0.454644i
$316$	−1.57694	−	0.821737i	−0.0887095	−	0.0462263i
$317$	−20.6738	+	24.2059i	−1.16116	+	1.35954i	−0.239801	+	0.970822i	$0.577082\pi$
$317$	−20.6738	+	24.2059i	−1.16116	+	1.35954i	−0.921356	+	0.388719i	$0.872918\pi$
$318$	−4.49084	−	2.54203i	−0.251834	−	0.142550i
$319$	1.59895	+	1.59895i	0.0895241	+	0.0895241i
$320$	−5.36048	+	5.93845i	−0.299660	+	0.331970i
$321$	0.523004	+	2.17847i	0.0291912	+	0.121590i
$322$	−20.1481	−	9.40031i	−1.12281	−	0.523859i
$323$	8.72588	−	17.1255i	0.485521	−	0.952888i
$324$	−0.0141227	+	0.160651i	−0.000784593	+	0.00892505i
$325$	−1.58468	+	3.82576i	−0.0879023	+	0.212215i
$326$	0.237352	−	5.41036i	0.0131457	−	0.299652i
$327$	5.93624			0.328275
$328$	−17.7620	−	3.53721i	−0.980742	−	0.195310i
$329$	28.7802			1.58670
$330$	−0.0490253	+	1.11751i	−0.00269876	+	0.0615172i
$331$	−5.75933	+	13.9043i	−0.316561	+	0.764247i	0.682870	+	0.730540i	$0.260731\pi$
$331$	−5.75933	+	13.9043i	−0.316561	+	0.764247i	−0.999432	+	0.0337072i	$0.989269\pi$
$332$	−1.40478	+	15.9799i	−0.0770973	+	0.877011i
$333$	9.75590	−	19.1470i	0.534620	−	1.04925i
$334$	−18.8507	−	8.79501i	−1.03146	−	0.481241i
$335$	−1.31491	−	5.47699i	−0.0718412	−	0.299240i
$336$	−20.9028	−	7.21695i	−1.14034	−	0.393717i
$337$	1.19763	+	1.19763i	0.0652393	+	0.0652393i	0.738974	−	0.673734i	$-0.235311\pi$
$337$	1.19763	+	1.19763i	0.0652393	+	0.0652393i	−0.673734	+	0.738974i	$0.735311\pi$
$338$	5.10461	+	2.88946i	0.277654	+	0.157166i
$339$	2.19718	−	2.57257i	0.119335	−	0.139723i
$340$	−6.30815	−	3.28716i	−0.342108	−	0.178271i
$341$	−0.865210	−	1.41189i	−0.0468537	−	0.0764584i
$342$	−13.8200	+	2.68334i	−0.747299	+	0.145098i
$343$	41.3555	+	48.4211i	2.23299	+	2.61449i
$344$	−24.6701	+	0.630560i	−1.33013	+	0.0339975i
$345$	−0.258353	−	3.28269i	−0.0139093	−	0.176734i
$346$	10.8521	−	9.93997i	0.583413	−	0.534376i
$347$	20.9468	+	12.8362i	1.12448	+	0.689083i	0.955046	−	0.296459i	$-0.0958057\pi$
$347$	20.9468	+	12.8362i	1.12448	+	0.689083i	0.169435	+	0.985541i	$0.445806\pi$
$348$	−5.61329	−	3.51083i	−0.300904	−	0.188200i
$349$	−23.7742	−	3.76546i	−1.27260	−	0.201560i	−0.516655	−	0.856193i	$-0.672823\pi$
$349$	−23.7742	−	3.76546i	−1.27260	−	0.201560i	−0.755947	+	0.654633i	$0.772823\pi$
$350$	5.31270	+	4.95625i	0.283976	+	0.264922i
$351$	−17.4555	−	12.6822i	−0.931708	−	0.676925i
$352$	−2.49890	−	3.32336i	−0.133192	−	0.177136i
$353$	11.0970	+	15.2738i	0.590636	+	0.812941i	0.994811	−	0.101741i	$-0.0324412\pi$
$353$	11.0970	+	15.2738i	0.590636	+	0.812941i	−0.404175	+	0.914682i	$0.632441\pi$
$354$	−1.90353	+	1.05463i	−0.101172	+	0.0560527i
$355$	−11.9718	+	4.95889i	−0.635398	+	0.263190i
$356$	−15.3856	+	2.29284i	−0.815437	+	0.121520i
$357$	1.54270	−	19.6019i	0.0816483	−	1.03744i
$358$	−29.3220	+	22.8990i	−1.54971	+	1.21025i
$359$	−8.41938	+	25.9122i	−0.444358	+	1.36759i	0.438828	+	0.898571i	$0.355394\pi$
$359$	−8.41938	+	25.9122i	−0.444358	+	1.36759i	−0.883186	+	0.469022i	$0.844606\pi$
$360$	0.946265	+	5.12348i	0.0498725	+	0.270031i
$361$	4.63274	+	9.09225i	0.243828	+	0.478540i
$362$	−36.3897	+	1.26315i	−1.91260	+	0.0663899i
$363$	10.9445	+	2.62753i	0.574435	+	0.137910i
$364$	32.6059	−	27.3364i	1.70901	−	1.43282i
$365$	−2.14812	−	6.61122i	−0.112437	−	0.346047i
$366$	1.00798	−	1.49372i	0.0526879	−	0.0780779i
$367$	21.0010	−	3.32624i	1.09625	−	0.173628i	0.417988	−	0.908453i	$-0.362735\pi$
$367$	21.0010	−	3.32624i	1.09625	−	0.173628i	0.678257	+	0.734824i	$0.262735\pi$
$368$	8.49538	+	8.81193i	0.442853	+	0.459354i
$369$	−8.86478	+	7.78051i	−0.461482	+	0.405037i
$370$	−3.29255	+	16.1661i	−0.171171	+	0.840437i
$371$	−2.72530	−	17.2068i	−0.141490	−	0.893335i
$372$	3.39683	+	3.45953i	0.176118	+	0.179368i
$373$	−15.7278	+	5.11027i	−0.814355	+	0.264600i	−0.686441	−	0.727185i	$-0.740828\pi$
$373$	−15.7278	+	5.11027i	−0.814355	+	0.264600i	−0.127914	+	0.991785i	$0.540828\pi$
$374$	2.30212	−	2.89293i	0.119040	−	0.149590i
$375$	−0.251205	+	1.04634i	−0.0129722	+	0.0540330i
$376$	−14.7886	−	5.68745i	−0.762666	−	0.293308i
$377$	11.3507	−	5.78345i	0.584588	−	0.297863i
$378$	−31.5727	+	20.8881i	−1.62393	+	1.07437i
$379$	19.9687	+	6.48821i	1.02572	+	0.333277i	0.773097	−	0.634288i	$-0.218706\pi$
$379$	19.9687	+	6.48821i	1.02572	+	0.333277i	0.252624	+	0.967565i	$0.418706\pi$
$380$	9.67467	−	4.81857i	0.496300	−	0.247188i
$381$	−12.9336	−	1.01790i	−0.662610	−	0.0521485i
$382$	−1.22876	−	3.37819i	−0.0628690	−	0.172843i
$383$	−1.45908	−	3.52253i	−0.0745554	−	0.179993i	0.882208	−	0.470860i	$-0.156056\pi$
$383$	−1.45908	−	3.52253i	−0.0745554	−	0.179993i	−0.956763	+	0.290867i	$0.906056\pi$
$384$	9.31470	+	7.83917i	0.475339	+	0.400041i
$385$	−3.05512	+	2.21967i	−0.155703	+	0.113125i
$386$	8.82974	+	1.08603i	0.449422	+	0.0552772i
$387$	−9.44694	+	13.0026i	−0.480215	+	0.660959i
$388$	−20.7767	+	14.8068i	−1.05478	+	0.751702i
$389$	−3.06263	+	19.3367i	−0.155281	+	0.980408i	0.779814	+	0.626011i	$0.215314\pi$
$389$	−3.06263	+	19.3367i	−0.155281	+	0.980408i	−0.935095	+	0.354396i	$0.884686\pi$
$390$	5.90220	+	2.20815i	0.298870	+	0.111814i
$391$	−5.68657	+	9.27963i	−0.287582	+	0.469291i
$392$	−18.2790	−	51.7211i	−0.923228	−	2.61231i
$393$	−14.5493	+	1.14506i	−0.733916	+	0.0577604i
$394$	3.04584	−	1.38730i	0.153447	−	0.0698912i
$395$	0.676075	−	0.577423i	0.0340170	−	0.0290533i
$396$	−2.70787	−	0.0247612i	−0.136076	−	0.00124430i
$397$	30.7744	−	18.8586i	1.54452	−	0.946485i	0.550798	−	0.834638i	$-0.314323\pi$
$397$	30.7744	−	18.8586i	1.54452	−	0.946485i	0.993725	−	0.111847i	$-0.0356767\pi$
$398$	7.22369	−	25.1722i	0.362091	−	1.26177i
$399$	22.7180	+	19.4030i	1.13732	+	0.971366i
$400$	−1.75048	−	3.59664i	−0.0875242	−	0.179832i
$401$	0.222087	−	0.222087i	0.0110905	−	0.0110905i	−0.701540	−	0.712630i	$-0.747504\pi$
$401$	0.222087	−	0.222087i	0.0110905	−	0.0110905i	0.712630	+	0.701540i	$0.247504\pi$
$402$	−8.26046	+	2.28897i	−0.411994	+	0.114164i
$403$	−9.07105	+	2.17777i	−0.451861	+	0.108482i
$404$	−6.15496	+	8.31069i	−0.306221	+	0.413473i
$405$	−0.0718465	−	0.0366076i	−0.00357008	−	0.00181905i
$406$	−2.52565	−	22.2085i	−0.125346	−	1.10219i
$407$	−7.92219	−	3.28148i	−0.392688	−	0.162657i
$408$	−4.66637	+	9.76751i	−0.231020	+	0.483564i
$409$			24.9255i			1.23248i	0.787557	+	0.616242i	$0.211346\pi$
$409$			24.9255i			1.23248i	−0.787557	+	0.616242i	$0.788654\pi$
$410$	4.96354	−	7.57385i	0.245132	−	0.374046i
$411$		−	11.8760i		−	0.585802i
$412$	−3.04644	+	12.1969i	−0.150087	+	0.600898i
$413$	−6.78743	−	2.81144i	−0.333987	−	0.138342i
$414$	7.92056	−	0.900760i	0.389274	−	0.0442699i
$415$	−7.14656	−	3.64135i	−0.350811	−	0.178747i
$416$	−22.1566	+	7.60329i	−1.08632	+	0.372782i
$417$	5.82168	−	1.39766i	0.285089	−	0.0684438i
$418$	1.50011	+	5.41362i	0.0733730	+	0.264789i
$419$	−3.59886	+	3.59886i	−0.175816	+	0.175816i	−0.789529	−	0.613713i	$-0.789675\pi$
$419$	−3.59886	+	3.59886i	−0.175816	+	0.175816i	0.613713	+	0.789529i	$0.289675\pi$
$420$	7.25741	−	8.34166i	0.354125	−	0.407031i
$421$	12.4441	+	10.6282i	0.606487	+	0.517989i	0.898814	−	0.438329i	$-0.144430\pi$
$421$	12.4441	+	10.6282i	0.606487	+	0.517989i	−0.292327	+	0.956318i	$0.594430\pi$
$422$	−9.26006	−	2.65737i	−0.450773	−	0.129359i
$423$	−8.79844	+	5.39169i	−0.427795	+	0.262153i
$424$	−1.99998	+	9.38027i	−0.0971274	+	0.455546i
$425$	2.70448	−	2.30984i	0.131186	−	0.112044i
$426$	8.17393	+	17.9460i	0.396028	+	0.869485i
$427$	6.06477	−	0.477308i	0.293495	−	0.0230985i
$428$	3.57010	−	2.14311i	0.172568	−	0.103591i
$429$	−1.71137	+	2.79270i	−0.0826256	+	0.134833i
$430$	4.32366	−	11.5568i	0.208505	−	0.557318i
$431$	−4.44652	+	28.0742i	−0.214182	+	1.35229i	0.612879	+	0.790176i	$0.290011\pi$
$431$	−4.44652	+	28.0742i	−0.214182	+	1.35229i	−0.827061	+	0.562112i	$0.809989\pi$
$432$	20.3514	−	4.49399i	0.979159	−	0.216217i
$433$	1.38752	−	1.90976i	0.0666800	−	0.0917771i	−0.774375	−	0.632727i	$-0.781935\pi$
$433$	1.38752	−	1.90976i	0.0666800	−	0.0917771i	0.841054	+	0.540950i	$0.181935\pi$
$434$	−1.99815	+	16.2456i	−0.0959142	+	0.779813i
$435$	2.67817	−	1.94580i	0.128408	−	0.0932942i
$436$	−3.31333	−	10.5239i	−0.158680	−	0.504002i
$437$	−6.32837	−	15.2780i	−0.302727	−	0.730847i
$438$	−9.94150	+	3.61606i	−0.475023	+	0.172782i
$439$	21.5311	+	1.69454i	1.02762	+	0.0808758i	0.581048	−	0.813870i	$-0.302643\pi$
$439$	21.5311	+	1.69454i	1.02762	+	0.0808758i	0.446577	+	0.894745i	$0.352643\pi$
$440$	2.00851	−	0.536832i	0.0957520	−	0.0255925i
$441$	−33.9774	−	11.0399i	−1.61797	−	0.525711i
$442$	−11.4923	−	17.3709i	−0.546634	−	0.826248i
$443$	−8.62465	+	4.39448i	−0.409769	+	0.208788i	−0.646710	−	0.762736i	$-0.723855\pi$
$443$	−8.62465	+	4.39448i	−0.409769	+	0.208788i	0.236940	+	0.971524i	$0.423855\pi$
$444$	24.7607	+	4.15414i	1.17509	+	0.197147i
$445$	1.81568	−	7.56287i	0.0860717	−	0.358514i
$446$	27.1331	+	21.5919i	1.28479	+	1.02241i
$447$	5.62718	−	1.82838i	0.266156	−	0.0864794i
$448$	−1.12732	+	41.0851i	−0.0532607	+	1.94109i
$449$	−0.555273	−	3.50586i	−0.0262050	−	0.165452i	0.971115	−	0.238611i	$-0.0766920\pi$
$449$	−0.555273	−	3.50586i	−0.0262050	−	0.165452i	−0.997320	+	0.0731590i	$0.976692\pi$
$450$	−2.55266	−	0.519899i	−0.120334	−	0.0245083i
$451$	3.37265	+	3.28284i	0.158812	+	0.154583i
$452$	−5.78706	−	2.45931i	−0.272200	−	0.115676i
$453$	−7.37299	+	1.16777i	−0.346413	+	0.0548665i
$454$	−5.77198	−	3.89500i	−0.270892	−	0.182801i
$455$	6.57419	+	20.2333i	0.308203	+	0.948550i
$456$	−7.83925	−	14.4597i	−0.367107	−	0.677137i
$457$	10.6832	+	2.56482i	0.499741	+	0.119977i	0.475476	−	0.879728i	$-0.342276\pi$
$457$	10.6832	+	2.56482i	0.499741	+	0.119977i	0.0242642	+	0.999706i	$0.492276\pi$
$458$	−1.25979	−	36.2928i	−0.0588661	−	1.69585i
$459$	8.41313	+	16.5117i	0.392691	+	0.770700i
$460$	−5.67540	+	2.29026i	−0.264617	+	0.106784i
$461$	−3.60249	+	11.0873i	−0.167785	+	0.516388i	−0.999231	−	0.0392177i	$-0.987513\pi$
$461$	−3.60249	+	11.0873i	−0.167785	+	0.516388i	0.831446	+	0.555605i	$0.187513\pi$
$462$	3.53716	+	4.52930i	0.164563	+	0.210722i
$463$	2.63371	−	33.4645i	0.122399	−	1.55523i	−0.562630	−	0.826709i	$-0.690210\pi$
$463$	2.63371	−	33.4645i	0.122399	−	1.55523i	0.685029	−	0.728516i	$-0.259790\pi$
$464$	−3.09098	+	11.9109i	−0.143495	+	0.552951i
$465$	−2.23966	+	0.927697i	−0.103862	+	0.0430209i
$466$	12.9207	+	23.3210i	0.598540	+	1.08033i
$467$	−0.379447	−	0.522264i	−0.0175587	−	0.0241675i	0.800147	−	0.599803i	$-0.204755\pi$
$467$	−0.379447	−	0.522264i	−0.0175587	−	0.0241675i	−0.817706	+	0.575636i	$0.804755\pi$
$468$	−4.84678	+	14.4655i	−0.224043	+	0.668666i
$469$	−23.4113	−	17.0093i	−1.08103	−	0.785417i
$470$	5.40420	−	5.79287i	0.249277	−	0.267205i
$471$	−6.09046	−	0.964634i	−0.280633	−	0.0444480i
$472$	2.93212	+	2.78597i	0.134962	+	0.128234i
$473$	5.46823	+	3.35094i	0.251430	+	0.154076i
$474$	−0.913886	−	0.997749i	−0.0419762	−	0.0458281i
$475$	0.424002	+	5.38746i	0.0194546	+	0.247194i
$476$	−35.6115	+	8.20592i	−1.63225	+	0.376118i
$477$	4.05669	+	4.74978i	0.185743	+	0.217477i
$478$	−6.29583	−	32.4253i	−0.287965	−	1.48310i
$479$	12.7025	+	20.7286i	0.580391	+	0.947112i	0.999237	+	0.0390548i	$0.0124347\pi$
$479$	12.7025	+	20.7286i	0.580391	+	0.947112i	−0.418846	+	0.908057i	$0.637565\pi$
$480$	−5.37766	+	2.85216i	−0.245456	+	0.130183i
$481$	−31.3735	+	36.7337i	−1.43051	+	1.67491i
$482$	−8.89014	+	15.7056i	−0.404935	+	0.715372i
$483$	−11.9622	−	11.9622i	−0.544301	−	0.544301i
$484$	−1.45056	−	20.8691i	−0.0659344	−	0.948594i
$485$	−2.97795	−	12.4040i	−0.135222	−	0.563238i
$486$	9.29468	−	19.9217i	0.421615	−	0.903665i
$487$	−15.8026	+	31.0144i	−0.716086	+	1.40540i	0.189778	+	0.981827i	$0.439223\pi$
$487$	−15.8026	+	31.0144i	−0.716086	+	1.40540i	−0.905863	+	0.423570i	$0.860777\pi$
$488$	−3.21069	−	0.953237i	−0.145341	−	0.0431510i
$489$	1.57693	−	3.80703i	0.0713110	−	0.172160i
$490$	27.4017	+	1.20211i	1.23788	+	0.0543059i
$491$	−18.9650			−0.855876			−0.427938	−	0.903808i	$-0.640760\pi$
$491$	−18.9650			−0.855876			−0.427938	+	0.903808i	$0.640760\pi$
$492$	−11.7810	−	7.14913i	−0.531129	−	0.322308i
$493$	−10.9415			−0.492778
$494$	31.6173	+	1.38705i	1.42253	+	0.0624063i
$495$	0.518151	−	1.25093i	0.0232891	−	0.0562250i
$496$	4.23715	−	7.95290i	0.190254	−	0.357096i
$497$	−30.2238	+	59.3175i	−1.35572	+	2.66075i
$498$	−5.16079	+	11.0613i	−0.231261	+	0.495670i
$499$	5.96539	+	24.8476i	0.267047	+	1.11233i	0.931134	+	0.364677i	$0.118821\pi$
$499$	5.96539	+	24.8476i	0.267047	+	1.11233i	−0.664087	+	0.747656i	$0.731179\pi$
$500$	1.99519	−	0.138680i	0.0892274	−	0.00620198i
$501$	−11.1920	−	11.1920i	−0.500020	−	0.500020i
$502$	7.58183	−	13.3943i	0.338394	−	0.597818i
$503$	−14.2513	+	16.6861i	−0.635433	+	0.743996i	−0.980917	−	0.194429i	$-0.937715\pi$
$503$	−14.2513	+	16.6861i	−0.635433	+	0.743996i	0.345484	+	0.938425i	$0.387715\pi$
$504$	20.7916	+	16.8583i	0.926133	+	0.750928i
$505$	−2.70177	−	4.40888i	−0.120227	−	0.196193i
$506$	−0.606300	−	3.12262i	−0.0269533	−	0.138817i
$507$	2.89861	+	3.39384i	0.128732	+	0.150726i
$508$	5.41440	+	23.4971i	0.240225	+	1.04251i
$509$	−3.22747	−	41.0089i	−0.143055	−	1.81769i	−0.481217	−	0.876601i	$-0.659805\pi$
$509$	−3.22747	−	41.0089i	−0.143055	−	1.81769i	0.338162	−	0.941088i	$-0.390195\pi$
$510$	−3.65578	−	3.99125i	−0.161881	−	0.176736i
$511$	−30.4508	−	18.6603i	−1.34706	−	0.825481i
$512$	8.69837	−	20.8887i	0.384417	−	0.923159i
$513$	−27.8111	−	4.40484i	−1.22789	−	0.194479i
$514$	−14.1637	+	15.1824i	−0.624736	+	0.669667i
$515$	−5.08532	−	3.69470i	−0.224086	−	0.162808i
$516$	−17.8048	−	5.96567i	−0.783813	−	0.262624i
$517$	2.42029	+	3.33124i	0.106444	+	0.146508i
$518$	41.0768	+	74.1410i	1.80481	+	3.25757i
$519$	10.3453	−	4.28517i	0.454109	−	0.188098i
$520$	0.620302	−	11.6960i	0.0272020	−	0.512904i
$521$	−3.47666	+	44.1752i	−0.152315	+	1.93535i	0.163529	+	0.986538i	$0.447712\pi$
$521$	−3.47666	+	44.1752i	−0.152315	+	1.93535i	−0.315844	+	0.948811i	$0.602288\pi$
$522$	4.93267	+	6.31625i	0.215897	+	0.276455i
$523$	4.71566	−	14.5133i	0.206201	−	0.634623i	−0.793461	−	0.608622i	$-0.791723\pi$
$523$	4.71566	−	14.5133i	0.206201	−	0.634623i	0.999662	−	0.0260010i	$-0.00827729\pi$
$524$	10.1507	+	25.1541i	0.443436	+	1.09886i
$525$	2.50985	+	4.92585i	0.109539	+	0.214982i
$526$	1.05567	+	30.4124i	0.0460295	+	1.32604i
$527$	7.79099	+	1.87045i	0.339381	+	0.0814781i
$528$	−0.922495	−	3.02638i	−0.0401464	−	0.131706i
$529$	−4.21380	−	12.9687i	−0.183209	−	0.563858i
$530$	−3.97514	−	2.68247i	−0.172669	−	0.116519i
$531$	2.60169	−	0.412068i	0.112904	−	0.0178822i
$532$	21.7178	−	51.1047i	0.941588	−	2.21567i
$533$	23.4606	−	12.3553i	1.01619	−	0.535167i
$534$	−11.5981	−	2.36218i	−0.501900	−	0.102222i
$535$	0.325693	+	2.05635i	0.0140810	+	0.0889036i
$536$	8.66853	+	13.3667i	0.374424	+	0.577353i
$537$	−26.9231	+	8.74784i	−1.16182	+	0.377497i
$538$	−24.8146	−	19.7469i	−1.06984	−	0.851350i
$539$	−3.32796	+	13.8620i	−0.143345	+	0.597077i
$540$	−1.72422	+	10.2772i	−0.0741988	+	0.442261i
$541$	3.44875	−	1.75723i	0.148274	−	0.0755491i	−0.378279	−	0.925691i	$-0.623484\pi$
$541$	3.44875	−	1.75723i	0.148274	−	0.0755491i	0.526553	+	0.850142i	$0.323484\pi$
$542$	24.2724	+	36.6882i	1.04259	+	1.57589i
$543$	−26.3496	−	8.56151i	−1.13077	−	0.367409i
$544$	19.9206	+	2.82084i	0.854087	+	0.120943i
$545$	5.49956	+	0.432825i	0.235575	+	0.0185402i
$546$	30.4254	−	11.0668i	1.30209	−	0.473613i
$547$	−6.31794	−	15.2528i	−0.270135	−	0.652165i	0.729353	−	0.684137i	$-0.239821\pi$
$547$	−6.31794	−	15.2528i	−0.270135	−	0.652165i	−0.999489	+	0.0319725i	$0.989821\pi$
$548$	−21.0540	+	6.62866i	−0.899384	+	0.283162i
$549$	−1.76465	+	1.28209i	−0.0753135	+	0.0547185i
$550$	−0.126899	+	1.03173i	−0.00541101	+	0.0439932i
$551$	9.77194	−	13.4499i	0.416299	−	0.572986i
$552$	3.78284	+	8.51072i	0.161008	+	0.362240i
$553$	0.714561	−	4.51156i	0.0303862	−	0.191851i
$554$	9.62121	−	25.7167i	0.408766	−	1.09260i
$555$	−6.55911	+	10.7035i	−0.278419	+	0.454338i
$556$	−5.72719	−	9.54065i	−0.242887	−	0.404614i
$557$	−21.7690	+	1.71326i	−0.922381	+	0.0725930i	−0.530749	−	0.847529i	$-0.678089\pi$
$557$	−21.7690	+	1.71326i	−0.922381	+	0.0725930i	−0.391632	+	0.920122i	$0.628089\pi$
$558$	−2.43260	−	5.34080i	−0.102980	−	0.226094i
$559$	27.4736	−	23.4647i	1.16201	−	0.992452i
$560$	−18.8390	−	8.21012i	−0.796092	−	0.346941i
$561$	2.39861	−	1.46987i	0.101269	−	0.0620579i
$562$	−0.368672	−	0.105798i	−0.0155515	−	0.00446283i
$563$	−14.0904	−	12.0343i	−0.593839	−	0.507187i	0.300971	−	0.953633i	$-0.402689\pi$
$563$	−14.0904	−	12.0343i	−0.593839	−	0.507187i	−0.894810	+	0.446447i	$0.852689\pi$
$564$	−9.09560	−	7.91335i	−0.382994	−	0.333212i
$565$	2.22312	−	2.22312i	0.0935276	−	0.0935276i
$566$	2.37044	+	8.55445i	0.0996369	+	0.359570i
$567$	−0.402823	+	0.0967091i	−0.0169170	+	0.00406140i
$568$	27.2526	−	24.5075i	1.14349	−	1.02831i
$569$	2.90569	+	1.48052i	0.121813	+	0.0620667i	0.513835	−	0.857889i	$-0.328224\pi$
$569$	2.90569	+	1.48052i	0.121813	+	0.0620667i	−0.392022	+	0.919956i	$0.628224\pi$
$570$	8.17132	−	0.929278i	0.342259	−	0.0389232i
$571$	10.5236	+	4.35903i	0.440400	+	0.182420i	0.591855	−	0.806045i	$-0.298396\pi$
$571$	10.5236	+	4.35903i	0.440400	+	0.182420i	−0.151455	+	0.988464i	$0.548396\pi$
$572$	5.90614	+	1.47518i	0.246948	+	0.0616806i
$573$		−	2.73523i		−	0.114266i
$574$	−5.88004	−	46.1495i	−0.245428	−	1.92624i
$575$		−	3.06004i		−	0.127613i
$576$	−7.35226	−	12.7714i	−0.306344	−	0.532141i
$577$	5.21987	+	2.16214i	0.217306	+	0.0900111i	0.488681	−	0.872463i	$-0.337478\pi$
$577$	5.21987	+	2.16214i	0.217306	+	0.0900111i	−0.271375	+	0.962474i	$0.587478\pi$
$578$	−0.695204	−	6.11306i	−0.0289167	−	0.254270i
$579$	6.03139	+	3.07315i	0.250656	+	0.127716i
$580$	−4.94438	−	3.66184i	−0.205304	−	0.152050i
$581$	−40.0687	+	9.61963i	−1.66233	+	0.399090i
$582$	−18.7079	+	5.18396i	−0.775468	+	0.214882i
$583$	1.76247	−	1.76247i	0.0729940	−	0.0729940i
$584$	11.9595	+	15.6061i	0.494887	+	0.645786i
$585$	−5.80032	−	4.95394i	−0.239814	−	0.204820i
$586$	11.2870	−	39.3316i	0.466263	−	1.62477i
$587$	23.0690	−	14.1367i	0.952160	−	0.583484i	0.0426156	−	0.999092i	$-0.486431\pi$
$587$	23.0690	−	14.1367i	0.952160	−	0.583484i	0.909544	+	0.415607i	$0.136431\pi$
$588$	0.381662	−	41.7383i	0.0157395	−	1.72126i
$589$	−9.25750	+	7.90666i	−0.381449	+	0.325788i
$590$	−1.84040	+	0.838254i	−0.0757679	+	0.0345104i
$591$	2.53881	−	0.199808i	0.104433	−	0.00821902i
$592$	−6.45573	−	46.2147i	−0.265329	−	1.89941i
$593$	16.4441	−	26.8343i	0.675277	−	1.10195i	−0.313069	−	0.949730i	$-0.601357\pi$
$593$	16.4441	−	26.8343i	0.675277	−	1.10195i	0.988346	−	0.152222i	$-0.0486428\pi$
$594$	−5.07288	−	1.89788i	−0.208143	−	0.0778709i
$595$	2.85843	−	18.0474i	0.117184	−	0.739872i
$596$	−6.38221	−	8.95543i	−0.261426	−	0.366829i
$597$	11.7126	−	16.1209i	0.479363	−	0.659786i
$598$	−17.7862	−	2.18764i	−0.727334	−	0.0894594i
$599$	35.5173	−	25.8048i	1.45120	−	1.05436i	0.465648	−	0.884970i	$-0.345821\pi$
$599$	35.5173	−	25.8048i	1.45120	−	1.05436i	0.985550	−	0.169387i	$-0.0541788\pi$
$600$	−0.316249	−	3.02713i	−0.0129108	−	0.123582i
$601$	5.21083	+	12.5801i	0.212554	+	0.513151i	0.993814	−	0.111054i	$-0.0354227\pi$
$601$	5.21083	+	12.5801i	0.212554	+	0.513151i	−0.781260	+	0.624206i	$0.785423\pi$
$602$	−21.6692	−	59.5744i	−0.883172	−	2.42807i
$603$	10.3436	+	0.814063i	0.421226	+	0.0331512i
$604$	6.18550	+	12.4192i	0.251684	+	0.505329i
$605$	9.94778	+	3.23223i	0.404435	+	0.131409i
$606$	−6.56277	+	4.34184i	−0.266594	+	0.176375i
$607$	11.2252	−	5.71954i	0.455618	−	0.232149i	−0.211092	−	0.977466i	$-0.567702\pi$
$607$	11.2252	−	5.71954i	0.455618	−	0.232149i	0.666710	+	0.745317i	$0.267702\pi$
$608$	−21.2588	+	21.9683i	−0.862160	+	0.890931i
$609$	3.97030	−	16.5375i	0.160885	−	0.670133i
$610$	1.04274	−	1.31034i	0.0422193	−	0.0530542i
$611$	22.0620	−	7.16837i	0.892532	−	0.290001i
$612$	9.34956	−	9.18013i	0.377934	−	0.371085i
$613$	0.665824	+	4.20385i	0.0268924	+	0.169792i	0.997479	−	0.0709596i	$-0.0226061\pi$
$613$	0.665824	+	4.20385i	0.0268924	+	0.169792i	−0.970587	+	0.240751i	$0.922606\pi$
$614$	−2.76129	+	13.5577i	−0.111436	+	0.547143i
$615$	5.51918	−	4.12483i	0.222555	−	0.166329i
$616$	6.05534	−	8.79877i	0.243977	−	0.354512i
$617$	−30.3624	+	4.80893i	−1.22234	+	0.193600i	−0.734060	−	0.679085i	$-0.762377\pi$
$617$	−30.3624	+	4.80893i	−1.22234	+	0.193600i	−0.488283	+	0.872685i	$0.662377\pi$
$618$	−5.35075	+	7.92924i	−0.215239	+	0.318961i
$619$	−6.95684	−	21.4110i	−0.279619	−	0.860579i	−0.987960	−	0.154709i	$-0.950556\pi$
$619$	−6.95684	−	21.4110i	−0.279619	−	0.860579i	0.708341	−	0.705870i	$-0.249444\pi$
$620$	2.89471	+	3.45271i	0.116254	+	0.138664i
$621$	15.5036	+	3.72208i	0.622137	+	0.149362i
$622$	35.6348	−	1.23695i	1.42883	−	0.0495973i
$623$	−18.1409	−	35.6036i	−0.726801	−	1.42643i
$624$	−17.8210	−	0.325944i	−0.713412	−	0.0130482i
$625$	−0.309017	+	0.951057i	−0.0123607	+	0.0380423i
$626$	−29.5217	+	23.0549i	−1.17992	+	0.921460i
$627$	−0.335370	+	4.26128i	−0.0133934	+	0.170179i
$628$	1.68929	+	11.3357i	0.0674101	+	0.452342i
$629$	38.3327	−	15.8779i	1.52843	−	0.633095i
$630$	−11.7070	+	6.48610i	−0.466418	+	0.258413i
$631$	−4.86810	−	6.70036i	−0.193796	−	0.266737i	0.701050	−	0.713112i	$-0.252715\pi$
$631$	−4.86810	−	6.70036i	−0.193796	−	0.266737i	−0.894846	+	0.446375i	$0.852715\pi$
$632$	−1.25874	+	2.17705i	−0.0500698	+	0.0865983i
$633$	−5.93040	−	4.30869i	−0.235712	−	0.171255i
$634$	32.9181	+	30.7094i	1.30734	+	1.21963i
$635$	−11.9080	−	1.88604i	−0.472554	−	0.0748452i
$636$	−3.86987	+	6.18734i	−0.153450	+	0.245344i
$637$	68.4776	+	41.9631i	2.71318	+	1.66264i
$638$	2.35819	−	2.15998i	0.0933617	−	0.0855144i
$639$	−1.87280	−	23.7962i	−0.0740869	−	0.941363i
$640$	8.05792	+	7.94166i	0.318517	+	0.313922i
$641$	24.5647	+	28.7616i	0.970247	+	1.13601i	0.990678	+	0.136222i	$0.0434961\pi$
$641$	24.5647	+	28.7616i	0.970247	+	1.13601i	−0.0204313	+	0.999791i	$0.506504\pi$
$642$	3.11027	−	0.603903i	0.122753	−	0.0238341i
$643$	8.10073	+	13.2192i	0.319462	+	0.521314i	0.971552	−	0.236827i	$-0.0761076\pi$
$643$	8.10073	+	13.2192i	0.319462	+	0.521314i	−0.652090	+	0.758142i	$0.726108\pi$
$644$	−14.5301	+	27.8836i	−0.572566	+	1.09877i
$645$	6.09756	−	7.13932i	0.240091	−	0.281111i
$646$	−23.6550	−	13.3899i	−0.930693	−	0.526817i
$647$	13.5357	+	13.5357i	0.532144	+	0.532144i	0.921210	−	0.389066i	$-0.127202\pi$
$647$	13.5357	+	13.5357i	0.532144	+	0.532144i	−0.389066	+	0.921210i	$0.627202\pi$
$648$	0.226101	+	0.0299107i	0.00888209	+	0.00117500i
$649$	−0.245375	−	1.02206i	−0.00963181	−	0.0401194i
$650$	5.30702	+	2.47605i	0.208158	+	0.0971188i
$651$	−5.65420	+	11.0970i	−0.221605	+	0.434925i
$652$	−7.62934	−	0.670688i	−0.298788	−	0.0262662i
$653$	17.3793	−	41.9573i	0.680103	−	1.64191i	−0.0837205	−	0.996489i	$-0.526680\pi$
$653$	17.3793	−	41.9573i	0.680103	−	1.64191i	0.763824	−	0.645425i	$-0.223320\pi$
$654$	0.367940	−	8.38705i	0.0143876	−	0.327960i
$655$	−13.5625			−0.529931
$656$	−6.09848	+	24.8759i	−0.238106	+	0.971239i
$657$	12.8050			0.499570
$658$	1.78385	−	40.6622i	0.0695417	−	1.58518i
$659$	2.29654	−	5.54435i	0.0894606	−	0.215977i	−0.872816	−	0.488049i	$-0.837709\pi$
$659$	2.29654	−	5.54435i	0.0894606	−	0.215977i	0.962277	+	0.272072i	$0.0877088\pi$
$660$	1.57585	+	0.138531i	0.0613398	+	0.00539233i
$661$	−16.2260	+	31.8452i	−0.631117	+	1.23864i	0.325018	+	0.945708i	$0.394630\pi$
$661$	−16.2260	+	31.8452i	−0.631117	+	1.23864i	−0.956134	+	0.292928i	$0.905370\pi$
$662$	19.2877	+	8.99891i	0.749638	+	0.349752i
$663$	−3.69971	−	15.4104i	−0.143685	−	0.598491i
$664$	22.4902	+	2.97521i	0.872790	+	0.115461i
$665$	19.6321	+	19.6321i	0.761301	+	0.761301i
$666$	−26.4473	−	14.9704i	−1.02481	−	0.580093i
$667$	−6.11377	+	7.15831i	−0.236726	+	0.277171i
$668$	−13.5945	+	26.0881i	−0.525986	+	1.00938i
$669$	13.7861	+	22.4968i	0.533001	+	0.869778i
$670$	−7.81970	+	1.51830i	−0.302101	+	0.0586571i
$671$	0.565269	+	0.661844i	0.0218220	+	0.0255502i
$672$	−11.4921	+	29.0854i	−0.443317	+	1.12199i
$673$	−2.02738	−	25.7603i	−0.0781498	−	0.992987i	−0.903562	−	0.428457i	$-0.859057\pi$
$673$	−2.02738	−	25.7603i	−0.0781498	−	0.992987i	0.825412	−	0.564530i	$-0.190943\pi$
$674$	1.76632	−	1.61785i	0.0680359	−	0.0623173i
$675$	−4.44262	−	2.72244i	−0.170996	−	0.104787i
$676$	4.39878	−	7.03298i	0.169184	−	0.270499i
$677$	−24.8055	−	3.92881i	−0.953354	−	0.150996i	−0.339667	−	0.940546i	$-0.610314\pi$
$677$	−24.8055	−	3.92881i	−0.953354	−	0.150996i	−0.613687	+	0.789549i	$0.710314\pi$
$678$	−3.49848	−	3.26375i	−0.134358	−	0.125344i
$679$	−53.0208	−	38.5219i	−2.03475	−	1.47833i
$680$	−5.03527	+	8.70876i	−0.193094	+	0.333966i
$681$	−3.11429	−	4.28645i	−0.119340	−	0.164257i
$682$	−2.04843	+	1.13490i	−0.0784384	+	0.0434577i
$683$	40.1385	−	16.6259i	1.53586	−	0.636173i	0.555168	−	0.831738i	$-0.312654\pi$
$683$	40.1385	−	16.6259i	1.53586	−	0.636173i	0.980691	+	0.195565i	$0.0626541\pi$
$684$	2.93458	+	19.6920i	0.112207	+	0.752941i
$685$	0.865909	−	11.0024i	0.0330847	−	0.420381i
$686$	70.9753	−	55.4281i	2.70985	−	2.11626i
$687$	8.53870	−	26.2794i	0.325772	−	1.00262i
$688$	−0.638213	+	34.8944i	−0.0243316	+	1.33034i
$689$	−6.37490	−	12.5114i	−0.242864	−	0.476648i
$690$	−4.65397	+	0.161548i	−0.177174	+	0.00615004i
$691$	−17.8568	−	4.28704i	−0.679305	−	0.163087i	−0.120912	−	0.992663i	$-0.538582\pi$
$691$	−17.8568	−	4.28704i	−0.679305	−	0.163087i	−0.558393	+	0.829577i	$0.688582\pi$
$692$	−13.3711	−	15.9486i	−0.508293	−	0.606273i
$693$	−2.14959	−	6.61577i	−0.0816563	−	0.251312i
$694$	19.4340	−	28.7991i	0.737704	−	1.09320i
$695$	5.49533	−	0.870374i	0.208450	−	0.0330152i
$696$	−5.30822	+	7.71316i	−0.201208	+	0.292367i
$697$	−22.7714	+	0.307255i	−0.862529	+	0.0116381i
$698$	−6.79361	+	33.3561i	−0.257142	+	1.26255i
$699$	3.17350	+	20.0367i	0.120033	+	0.757858i
$700$	7.33175	−	7.19888i	0.277114	−	0.272092i
$701$	38.8140	−	12.6114i	1.46598	−	0.476327i	0.536092	−	0.844160i	$-0.319900\pi$
$701$	38.8140	−	12.6114i	1.46598	−	0.476327i	0.929892	+	0.367833i	$0.119900\pi$
$702$	−19.0000	+	23.8761i	−0.717109	+	0.901144i
$703$	−14.7173	+	61.3018i	−0.555072	+	2.31204i
$704$	−4.85031	+	3.32459i	−0.182803	+	0.125300i
$705$	5.37106	−	2.73669i	0.202286	−	0.103070i
$706$	22.2674	−	14.7318i	0.838046	−	0.554439i
$707$	−25.2654	−	8.20923i	−0.950204	−	0.308740i
$708$	1.37205	+	2.75478i	0.0515647	+	0.103531i
$709$	12.6450	+	0.995181i	0.474892	+	0.0373748i	0.313647	−	0.949540i	$-0.398449\pi$
$709$	12.6450	+	0.995181i	0.474892	+	0.0373748i	0.161245	+	0.986914i	$0.448449\pi$
$710$	6.26415	+	17.2218i	0.235089	+	0.646322i
$711$	0.626748	+	1.51310i	0.0235049	+	0.0567458i
$712$	2.28581	+	21.8798i	0.0856645	+	0.819979i
$713$	5.57710	−	4.05200i	0.208864	−	0.151749i
$714$	−27.5989	−	3.39457i	−1.03286	−	0.127039i
$715$	−1.78910	+	2.46248i	−0.0669084	+	0.0920915i
$716$	30.5355	+	42.8470i	1.14117	+	1.60127i
$717$	3.93171	−	24.8238i	0.146832	−	0.927062i
$718$	36.0883	+	13.5014i	1.34680	+	0.503870i
$719$	−19.9666	+	32.5825i	−0.744627	+	1.21512i	0.225906	+	0.974149i	$0.427466\pi$
$719$	−19.9666	+	32.5825i	−0.744627	+	1.21512i	−0.970532	+	0.240971i	$0.922534\pi$
$720$	7.29739	−	1.01937i	0.271958	−	0.0379897i
$721$	−32.1942	+	2.53374i	−1.19897	+	0.0943613i
$722$	13.1332	−	5.98183i	0.488766	−	0.222621i
$723$	−10.4420	+	8.91831i	−0.388342	+	0.331675i
$724$	−0.470847	+	51.4916i	−0.0174989	+	1.91367i
$725$	2.62303	−	1.60740i	0.0974169	−	0.0596972i
$726$	4.39068	−	15.3001i	0.162953	−	0.567839i
$727$	−21.6962	−	18.5303i	−0.804669	−	0.687252i	0.148759	−	0.988873i	$-0.452472\pi$
$727$	−21.6962	−	18.5303i	−0.804669	−	0.687252i	−0.953428	+	0.301621i	$0.902472\pi$
$728$	−36.6014	−	47.7617i	−1.35654	−	1.77017i
$729$	11.9989	−	11.9989i	0.444403	−	0.444403i
$730$	−9.47384	+	2.62520i	−0.350642	+	0.0971630i
$731$	−30.1743	+	7.24421i	−1.11604	+	0.267937i
$732$	−2.04793	−	1.51671i	−0.0756937	−	0.0560593i
$733$	33.9649	+	17.3060i	1.25452	+	0.639210i	0.949689	−	0.313196i	$-0.101400\pi$
$733$	33.9649	+	17.3060i	1.25452	+	0.639210i	0.304832	+	0.952406i	$0.401400\pi$
$734$	−3.39781	−	29.8776i	−0.125415	−	1.10280i
$735$	19.2814	+	7.98662i	0.711205	+	0.294591i
$736$	12.9765	−	11.4566i	0.478322	−	0.422295i
$737$		−	4.14022i		−	0.152507i
$738$	10.4433	+	13.0069i	0.384422	+	0.478790i
$739$			5.20203i			0.191360i	0.995412	+	0.0956800i	$0.0305025\pi$
$739$			5.20203i			0.191360i	−0.995412	+	0.0956800i	$0.969497\pi$
$740$	22.6363	+	5.65390i	0.832128	+	0.207842i
$741$	22.2477	+	9.21531i	0.817290	+	0.338533i
$742$	−24.4797	+	2.78393i	−0.898678	+	0.102201i
$743$	−20.6073	−	10.4999i	−0.756007	−	0.385205i	0.0331066	−	0.999452i	$-0.489460\pi$
$743$	−20.6073	−	10.4999i	−0.756007	−	0.385205i	−0.789114	+	0.614247i	$0.789460\pi$
$744$	5.09835	−	4.58480i	0.186915	−	0.168087i
$745$	5.34654	−	1.28359i	0.195882	−	0.0470271i
$746$	6.24523	+	22.5378i	0.228654	+	0.825169i
$747$	10.4473	−	10.4473i	0.382247	−	0.382247i
$748$	−3.94460	−	3.43188i	−0.144229	−	0.125482i
$749$	8.13354	+	6.94670i	0.297193	+	0.253827i
$750$	1.46276	+	0.419771i	0.0534125	+	0.0153279i
$751$	9.59374	−	5.87905i	0.350081	−	0.214530i	−0.336329	−	0.941744i	$-0.609186\pi$
$751$	9.59374	−	5.87905i	0.350081	−	0.214530i	0.686410	+	0.727215i	$0.259186\pi$
$752$	−8.95217	+	20.5417i	−0.326452	+	0.749078i
$753$	8.90531	−	7.60585i	0.324527	−	0.277173i
$754$	−7.46763	−	16.3953i	−0.271955	−	0.597081i
$755$	−6.91576	+	0.544282i	−0.251690	+	0.0198085i
$756$	27.5549	+	45.9024i	1.00216	+	1.66945i
$757$	7.07626	−	11.5474i	0.257191	−	0.419697i	−0.697818	−	0.716275i	$-0.745845\pi$
$757$	7.07626	−	11.5474i	0.257191	−	0.419697i	0.955009	+	0.296578i	$0.0958455\pi$
$758$	10.4046	−	27.8107i	0.377912	−	1.01013i
$759$	0.378631	−	2.39058i	0.0137434	−	0.0867725i
$760$	−6.20829	−	13.9676i	−0.225198	−	0.506657i
$761$	27.3641	−	37.6634i	0.991948	−	1.36530i	0.0618100	−	0.998088i	$-0.480313\pi$
$761$	27.3641	−	37.6634i	0.991948	−	1.36530i	0.930138	−	0.367211i	$-0.119687\pi$
$762$	−2.23979	+	18.2102i	−0.0811392	+	0.659688i
$763$	22.9289	−	16.6588i	0.830083	−	0.603090i
$764$	−4.84906	+	1.52668i	−0.175433	+	0.0552333i
$765$	2.50715	+	6.05280i	0.0906463	+	0.218840i
$766$	−5.06725	+	1.84313i	−0.183087	+	0.0665951i
$767$	−5.90329	−	0.464599i	−0.213155	−	0.0167757i
$768$	11.6530	−	12.6744i	0.420490	−	0.457349i
$769$	−26.3605	−	8.56506i	−0.950585	−	0.308864i	−0.207632	−	0.978207i	$-0.566576\pi$
$769$	−26.3605	−	8.56506i	−0.950585	−	0.308864i	−0.742953	+	0.669343i	$0.766576\pi$
$770$	2.94671	+	4.45402i	0.106192	+	0.160512i
$771$	−14.0769	+	7.17253i	−0.506967	+	0.258312i
$772$	2.08168	−	12.4078i	0.0749213	−	0.446567i
$773$	0.798167	−	3.32461i	0.0287081	−	0.119578i	−0.956176	−	0.292793i	$-0.905415\pi$
$773$	0.798167	−	3.32461i	0.0287081	−	0.119578i	0.984884	+	0.173215i	$0.0554155\pi$
$774$	17.7852	+	14.1531i	0.639277	+	0.508722i
$775$	−2.14255	+	0.696155i	−0.0769625	+	0.0250066i
$776$	19.6321	+	30.2722i	0.704751	+	1.08671i
$777$	10.0890	+	63.6997i	0.361942	+	2.28521i
$778$	27.1301	+	5.52557i	0.972660	+	0.198101i
$779$	19.9597	−	28.2665i	0.715131	−	1.01275i
$780$	3.48562	−	8.20209i	0.124805	−	0.293682i
$781$	−9.40757	+	1.49001i	−0.336629	+	0.0533168i
$782$	12.7583	+	8.60946i	0.456236	+	0.307874i
$783$	4.95328	+	15.2446i	0.177016	+	0.544799i
$784$	−74.2074	+	22.6198i	−2.65026	+	0.807849i
$785$	−5.57209	−	1.33774i	−0.198877	−	0.0477460i
$786$	0.716003	+	20.6270i	0.0255390	+	0.735742i
$787$	14.6383	+	28.7293i	0.521799	+	1.02409i	0.990080	+	0.140508i	$0.0448735\pi$
$787$	14.6383	+	28.7293i	0.521799	+	1.02409i	−0.468281	+	0.883580i	$0.655126\pi$
$788$	−1.77127	−	4.38931i	−0.0630988	−	0.156363i
$789$	−7.15522	+	22.0215i	−0.254732	+	0.783986i
$790$	−0.773910	−	0.990985i	−0.0275345	−	0.0352577i
$791$	1.26730	−	16.1026i	0.0450600	−	0.572542i
$792$	−0.202823	+	3.82430i	−0.00720701	+	0.135890i
$793$	4.53018	−	1.87646i	0.160871	−	0.0666351i
$794$	−24.7370	−	44.6487i	−0.877883	−	1.58452i
$795$	−2.14479	−	2.95206i	−0.0760680	−	0.104699i
$796$	−35.1169	−	11.7662i	−1.24468	−	0.417043i
$797$	−1.86335	−	1.35380i	−0.0660031	−	0.0479541i	0.554294	−	0.832321i	$-0.312988\pi$
$797$	−1.86335	−	1.35380i	−0.0660031	−	0.0479541i	−0.620298	+	0.784367i	$0.712988\pi$
$798$	28.8218	−	30.8946i	1.02028	−	1.09366i
$799$	−19.6786	−	3.11678i	−0.696178	−	0.110264i
$800$	−5.19003	+	2.25025i	−0.183495	+	0.0795584i
$801$	12.2159	+	7.48590i	0.431627	+	0.264501i
$802$	−0.300012	−	0.327542i	−0.0105938	−	0.0115659i
$803$	−0.400896	−	5.09386i	−0.0141473	−	0.179758i
$804$	2.72199	+	11.8127i	0.0959971	+	0.416602i
$805$	−10.2101	−	11.9545i	−0.359858	−	0.421340i
$806$	2.51463	+	12.9511i	0.0885739	+	0.456181i
$807$	−12.6081	−	20.5745i	−0.443825	−	0.724257i
$808$	11.3603	+	9.21117i	0.399654	+	0.324048i
$809$	−11.7482	+	13.7553i	−0.413043	+	0.483611i	−0.927457	−	0.373931i	$-0.878010\pi$
$809$	−11.7482	+	13.7553i	−0.413043	+	0.483611i	0.514413	+	0.857542i	$0.328010\pi$
$810$	−0.0561744	+	0.0992397i	−0.00197377	+	0.00348693i
$811$	−18.9029	−	18.9029i	−0.663771	−	0.663771i	0.292496	−	0.956267i	$-0.405514\pi$
$811$	−18.9029	−	18.9029i	−0.663771	−	0.663771i	−0.956267	+	0.292496i	$0.905514\pi$
$812$	−31.5339	+	2.19185i	−1.10662	+	0.0769187i
$813$	7.81399	+	32.5476i	0.274049	+	1.14149i
$814$	−5.12728	+	10.9895i	−0.179711	+	0.385182i
$815$	1.73850	−	3.41200i	0.0608971	−	0.119517i
$816$	13.5108	+	7.19831i	0.472974	+	0.251991i
$817$	18.0440	−	43.5621i	0.631280	−	1.52404i
$818$	35.2160	+	1.54493i	1.23130	+	0.0540171i
$819$	−39.1889			−1.36937
$820$	−10.3931	−	7.48220i	−0.362943	−	0.261290i
$821$	−40.1741			−1.40209			−0.701044	−	0.713118i	$-0.747282\pi$
$821$	−40.1741			−1.40209			−0.701044	+	0.713118i	$0.747282\pi$
$822$	−16.7791	−	0.736100i	−0.585239	−	0.0256744i
$823$	−4.39793	+	10.6176i	−0.153302	+	0.370105i	−0.981808	−	0.189876i	$-0.939191\pi$
$823$	−4.39793	+	10.6176i	−0.153302	+	0.370105i	0.828506	+	0.559981i	$0.189191\pi$
$824$	17.0436	+	5.06016i	0.593743	+	0.176279i
$825$	−0.359089	+	0.704753i	−0.0125019	+	0.0245363i
$826$	−4.39286	+	9.41539i	−0.152847	+	0.327603i
$827$	1.82040	+	7.58252i	0.0633015	+	0.263670i	0.995042	−	0.0994548i	$-0.0317099\pi$
$827$	1.82040	+	7.58252i	0.0633015	+	0.263670i	−0.931741	+	0.363125i	$0.881710\pi$
$828$	−0.781711	−	11.2464i	−0.0271663	−	0.390840i
$829$	−4.67810	−	4.67810i	−0.162477	−	0.162477i	0.621186	−	0.783663i	$-0.286651\pi$
$829$	−4.67810	−	4.67810i	−0.162477	−	0.162477i	−0.783663	+	0.621186i	$0.786651\pi$
$830$	−5.58766	+	9.87135i	−0.193950	+	0.342639i
$831$	13.5686	−	15.8868i	0.470689	−	0.551106i
$832$	9.36903	+	31.7753i	0.324813	+	1.10161i
$833$	−36.0415	−	58.8144i	−1.24876	−	2.03780i
$834$	−1.61385	−	8.31182i	−0.0558832	−	0.287815i
$835$	−9.55263	−	11.1847i	−0.330582	−	0.387062i
$836$	7.74164	−	1.78390i	0.267750	−	0.0616974i
$837$	−0.920959	−	11.7019i	−0.0318330	−	0.404476i
$838$	4.86160	+	5.30772i	0.167941	+	0.183352i
$839$	−6.83532	−	4.18869i	−0.235981	−	0.144610i	0.399481	−	0.916742i	$-0.369190\pi$
$839$	−6.83532	−	4.18869i	−0.235981	−	0.144610i	−0.635462	+	0.772132i	$0.719190\pi$
$840$	−11.3357	−	10.7707i	−0.391120	−	0.371624i
$841$	19.2955	+	3.05610i	0.665361	+	0.105383i
$842$	15.7875	−	16.9229i	0.544072	−	0.583202i
$843$	−0.236108	−	0.171543i	−0.00813199	−	0.00590824i
$844$	−4.32844	+	12.9184i	−0.148991	+	0.444670i
$845$	2.43793	+	3.35552i	0.0838673	+	0.115433i
$846$	7.07233	+	12.7651i	0.243152	+	0.438873i
$847$	49.6469	−	20.5644i	1.70589	−	0.706602i
$848$	13.1290	+	3.40708i	0.450852	+	0.117000i
$849$	−0.529941	+	6.73354i	−0.0181875	+	0.231095i
$850$	−3.09584	−	3.96420i	−0.106186	−	0.135971i
$851$	11.0313	−	33.9508i	0.378148	−	1.16382i
$852$	25.8617	−	10.4362i	0.886006	−	0.357540i
$853$	−17.4612	−	34.2695i	−0.597860	−	1.17337i	−0.969524	−	0.244998i	$-0.921213\pi$
$853$	−17.4612	−	34.2695i	−0.597860	−	1.17337i	0.371664	−	0.928367i	$-0.378787\pi$
$854$	−0.298460	−	8.59822i	−0.0102131	−	0.294225i
$855$	−9.67966	−	2.32388i	−0.331037	−	0.0794750i
$856$	−2.80662	−	5.17687i	−0.0959283	−	0.176942i
$857$	15.4981	+	47.6983i	0.529405	+	1.62934i	0.755437	+	0.655221i	$0.227425\pi$
$857$	15.4981	+	47.6983i	0.529405	+	1.62934i	−0.226032	+	0.974120i	$0.572575\pi$
$858$	3.83960	+	2.59101i	0.131082	+	0.0884556i
$859$	20.6845	−	3.27610i	0.705745	−	0.111779i	0.206762	−	0.978391i	$-0.433707\pi$
$859$	20.6845	−	3.27610i	0.705745	−	0.111779i	0.498982	+	0.866612i	$0.333707\pi$
$860$	−16.0601	−	6.82501i	−0.547644	−	0.232731i
$861$	7.79860	−	34.5294i	0.265776	−	1.17676i
$862$	39.3892	+	8.02239i	1.34160	+	0.273244i
$863$	−8.55394	−	54.0075i	−0.291180	−	1.83844i	−0.506930	−	0.861987i	$-0.669220\pi$
$863$	−8.55394	−	54.0075i	−0.291180	−	1.83844i	0.215750	−	0.976449i	$-0.430780\pi$
$864$	−5.08793	−	29.0322i	−0.173095	−	0.987694i
$865$	9.89673	−	3.21564i	0.336499	−	0.109335i
$866$	−2.61221	−	2.07873i	−0.0887665	−	0.0706383i
$867$	1.09286	−	4.55207i	0.0371153	−	0.154596i
$868$	22.8288	+	3.83003i	0.774860	+	0.130000i
$869$	0.582295	−	0.296694i	0.0197530	−	0.0100647i
$870$	−2.58314	−	3.90447i	−0.0875767	−	0.132374i
$871$	−22.1830	−	7.20768i	−0.751641	−	0.244223i
$872$	−15.0741	+	4.02897i	−0.510472	+	0.136438i
$873$	23.4258	+	1.84365i	0.792843	+	0.0623981i
$874$	−21.9779	+	7.99410i	−0.743413	+	0.270405i
$875$	1.96606	+	4.74649i	0.0664650	+	0.160461i
$876$	4.49278	+	14.2700i	0.151797	+	0.482140i
$877$	29.8363	−	21.6773i	1.00750	−	0.731992i	0.0438168	−	0.999040i	$-0.486048\pi$
$877$	29.8363	−	21.6773i	1.00750	−	0.731992i	0.963683	+	0.267048i	$0.0860482\pi$
$878$	3.72867	−	30.3153i	0.125837	−	1.02309i
$879$	18.3009	−	25.1890i	0.617274	−	0.849605i
$880$	−0.633974	−	2.87101i	−0.0213713	−	0.0967817i
$881$	−3.20307	+	20.2234i	−0.107914	+	0.681343i	0.873120	+	0.487506i	$0.162093\pi$
$881$	−3.20307	+	20.2234i	−0.107914	+	0.681343i	−0.981034	+	0.193837i	$0.937907\pi$
$882$	−17.7038	+	47.3209i	−0.596118	+	1.59338i
$883$	−23.3271	+	38.0663i	−0.785018	+	1.28103i	0.170282	+	0.985395i	$0.445532\pi$
$883$	−23.3271	+	38.0663i	−0.785018	+	1.28103i	−0.955300	+	0.295638i	$0.904468\pi$
$884$	−25.2548	+	15.1603i	−0.849412	+	0.509896i
$885$	−1.53403	+	0.120731i	−0.0515659	+	0.00405833i
$886$	5.67418	+	12.4577i	0.190628	+	0.418526i
$887$	3.40630	−	2.90925i	0.114372	−	0.0976832i	−0.590423	−	0.807094i	$-0.701039\pi$
$887$	3.40630	−	2.90925i	0.114372	−	0.0976832i	0.704795	+	0.709411i	$0.251039\pi$
$888$	7.40390	−	34.7257i	0.248459	−	1.16532i
$889$	−52.8131	+	32.3639i	−1.77129	+	1.08545i
$890$	−10.5727	−	3.03406i	−0.354398	−	0.101702i
$891$	−0.0450695	−	0.0384930i	−0.00150989	−	0.00128956i
$892$	32.1880	−	36.9969i	1.07773	−	1.23875i
$893$	21.4065	−	21.4065i	0.716341	−	0.716341i
$894$	−2.23445	−	8.06371i	−0.0747313	−	0.269691i
$895$	−25.5804	+	6.14130i	−0.855057	+	0.205281i
$896$	57.9773	+	4.13926i	1.93689	+	0.138283i
$897$	−12.1494	−	6.19041i	−0.405656	−	0.206692i
$898$	−4.98768	+	0.567221i	−0.166441	+	0.0189284i
$899$	6.40290	+	2.65217i	0.213549	+	0.0884547i
$900$	−0.892761	+	3.57431i	−0.0297587	+	0.119144i
$901$			12.0604i			0.401790i
$902$	4.84723	−	4.56158i	0.161395	−	0.151884i
$903$		−	48.2357i		−	1.60518i
$904$	−3.83334	+	8.02384i	−0.127495	+	0.266869i
$905$	−23.7870	−	9.85291i	−0.790707	−	0.327522i
$906$	1.19289	+	10.4893i	0.0396312	+	0.348485i
$907$	20.2627	+	10.3244i	0.672813	+	0.342815i	0.756795	−	0.653652i	$-0.226764\pi$
$907$	20.2627	+	10.3244i	0.672813	+	0.342815i	−0.0839823	+	0.996467i	$0.526764\pi$
$908$	−5.86083	+	7.91355i	−0.194498	+	0.262620i
$909$	9.26186	−	2.22358i	0.307196	−	0.0737513i
$910$	28.9941	−	8.03427i	0.961147	−	0.266334i
$911$	−32.7273	+	32.7273i	−1.08430	+	1.08430i	−0.0882019	+	0.996103i	$0.528112\pi$
$911$	−32.7273	+	32.7273i	−1.08430	+	1.08430i	−0.996103	+	0.0882019i	$0.971888\pi$
$912$	−20.9153	+	10.1795i	−0.692575	+	0.337076i
$913$	−4.48306	−	3.82889i	−0.148368	−	0.126718i
$914$	4.28588	−	14.9349i	0.141764	−	0.494002i
$915$	1.08644	−	0.665772i	0.0359167	−	0.0220098i
$916$	−51.3545	−	0.469593i	−1.69680	−	0.0155158i
$917$	−52.9838	+	45.2524i	−1.74968	+	1.49437i
$918$	23.8501	−	10.8631i	0.787170	−	0.358536i
$919$	−18.1056	+	1.42494i	−0.597249	+	0.0470045i	−0.373481	−	0.927638i	$-0.621836\pi$
$919$	−18.1056	+	1.42494i	−0.597249	+	0.0470045i	−0.223768	+	0.974642i	$0.571836\pi$
$920$	2.88403	+	8.16047i	0.0950836	+	0.269043i
$921$	−5.50078	+	8.97646i	−0.181257	+	0.295784i
$922$	15.4415	+	5.77700i	0.508538	+	0.190255i
$923$	−8.39420	+	52.9989i	−0.276298	+	1.74448i
$924$	6.61848	−	4.71675i	0.217732	−	0.155170i
$925$	−6.85702	+	9.43788i	−0.225458	+	0.310316i
$926$	−47.1172	−	5.79524i	−1.54837	−	0.190443i
$927$	9.36747	−	6.80586i	0.307668	−	0.223534i
$928$	16.6368	+	5.10537i	0.546130	+	0.167592i
$929$	−1.31380	−	3.17179i	−0.0431043	−	0.104063i	0.900861	−	0.434108i	$-0.142936\pi$
$929$	−1.31380	−	3.17179i	−0.0431043	−	0.104063i	−0.943965	+	0.330045i	$0.892936\pi$
$930$	1.17188	+	3.22181i	0.0384276	+	0.105647i
$931$	104.487	+	8.22334i	3.42444	+	0.269509i
$932$	33.7501	−	16.8096i	1.10552	−	0.550617i
$933$	25.8030	+	8.38391i	0.844753	+	0.274477i
$934$	−0.761402	+	0.503732i	−0.0249138	+	0.0164826i
$935$	2.32933	−	1.18685i	0.0761773	−	0.0388143i
$936$	20.1372	+	7.74440i	0.658204	+	0.253134i
$937$	3.83570	−	15.9768i	0.125307	−	0.521940i	−0.874042	−	0.485851i	$-0.838510\pi$
$937$	3.83570	−	15.9768i	0.125307	−	0.521940i	0.999349	−	0.0360896i	$-0.0114902\pi$
$938$	−25.4828	+	32.0225i	−0.832042	+	1.04557i
$939$	−27.1064	+	8.80741i	−0.884585	+	0.287419i
$940$	−7.84952	−	7.99440i	−0.256023	−	0.260749i
$941$	−0.346804	−	2.18963i	−0.0113055	−	0.0713801i	0.981391	−	0.192022i	$-0.0615046\pi$
$941$	−0.346804	−	2.18963i	−0.0113055	−	0.0713801i	−0.992696	+	0.120642i	$0.961505\pi$
$942$	−1.74039	+	8.54514i	−0.0567048	+	0.278416i
$943$	−12.5230	+	15.0696i	−0.407805	+	0.490734i
$944$	4.11790	−	3.96998i	0.134026	−	0.129212i
$945$	−26.4393	+	4.18758i	−0.860072	+	0.136222i
$946$	5.07332	−	7.51812i	0.164948	−	0.244435i
$947$	−6.33673	−	19.5024i	−0.205916	−	0.633744i	−0.999675	−	0.0255114i	$-0.991879\pi$
$947$	−6.33673	−	19.5024i	−0.205916	−	0.633744i	0.793758	−	0.608233i	$-0.208121\pi$
$948$	−1.46632	+	1.22935i	−0.0476238	+	0.0399273i
$949$	−27.9904	−	6.71990i	−0.908607	−	0.218137i
$950$	7.63797	−	0.265129i	0.247809	−	0.00860191i
$951$	15.5513	+	30.5211i	0.504285	+	0.989715i
$952$	9.38650	+	50.8225i	0.304218	+	1.64717i
$953$	−13.4971	+	41.5399i	−0.437215	+	1.34561i	0.453585	+	0.891213i	$0.350145\pi$
$953$	−13.4971	+	41.5399i	−0.437215	+	1.34561i	−0.890800	+	0.454396i	$0.849855\pi$
$954$	6.96219	−	5.43712i	0.225409	−	0.176033i
$955$	0.199432	−	2.53402i	0.00645346	−	0.0819989i
$956$	−46.2025	+	6.88531i	−1.49430	+	0.222687i
$957$	2.24806	−	0.931179i	0.0726696	−	0.0301007i
$958$	30.0738	−	16.6620i	0.971639	−	0.538323i
$959$	−33.3277	−	45.8716i	−1.07621	−	1.48127i
$960$	3.69637	+	7.77464i	0.119300	+	0.250925i
$961$	20.9737	+	15.2383i	0.676570	+	0.491557i
$962$	49.9548	+	46.6031i	1.61061	+	1.50254i
$963$	−3.78792	−	0.599947i	−0.122064	−	0.0193330i
$964$	21.6387	+	13.5339i	0.696937	+	0.435899i
$965$	5.36363	+	3.28684i	0.172661	+	0.105807i
$966$	−17.6424	+	16.1595i	−0.567634	+	0.519923i
$967$	1.65818	+	21.0692i	0.0533235	+	0.677540i	0.964254	+	0.264980i	$0.0853653\pi$
$967$	1.65818	+	21.0692i	0.0533235	+	0.677540i	−0.910930	+	0.412560i	$0.864635\pi$
$968$	−29.5749	+	0.755923i	−0.950572	+	0.0242963i
$969$	−13.4323	−	15.7272i	−0.431507	−	0.505230i
$970$	−17.7097	+	3.43858i	−0.568624	+	0.110406i
$971$	14.8192	+	24.1828i	0.475571	+	0.776062i	0.997014	−	0.0772247i	$-0.0246059\pi$
$971$	14.8192	+	24.1828i	0.475571	+	0.776062i	−0.521443	+	0.853286i	$0.674606\pi$
$972$	−27.5703	−	14.3668i	−0.884318	−	0.460816i
$973$	18.5642	−	21.7358i	0.595140	−	0.696819i
$974$	42.8394	+	24.2492i	1.37266	+	0.776993i
$975$	3.15087	+	3.15087i	0.100909	+	0.100909i
$976$	−1.54579	+	4.47716i	−0.0494796	+	0.143310i
$977$	−7.41429	−	30.8827i	−0.237204	−	0.988026i	−0.956131	−	0.292940i	$-0.905366\pi$
$977$	−7.41429	−	30.8827i	−0.237204	−	0.988026i	0.718927	−	0.695086i	$-0.244634\pi$
$978$	−5.28105	−	2.46393i	−0.168869	−	0.0787879i
$979$	2.59546	−	5.09388i	0.0829513	−	0.162801i
$980$	3.39682	−	38.6401i	0.108507	−	1.23431i
$981$	−3.88877	+	9.38832i	−0.124159	+	0.299746i
$982$	−1.17548	+	26.7947i	−0.0375112	+	0.855054i
$983$	43.7923			1.39676			0.698379	−	0.715728i	$-0.253905\pi$
$983$	43.7923			1.39676			0.698379	+	0.715728i	$0.253905\pi$
$984$	−10.8309	+	16.2017i	−0.345276	+	0.516492i
$985$	2.36661			0.0754066
$986$	−0.678172	+	15.4587i	−0.0215974	+	0.492305i
$987$	11.8516	−	28.6122i	0.377240	−	0.910737i
$988$	3.91940	−	44.5847i	0.124693	−	1.41843i
$989$	−12.1211	+	23.7890i	−0.385429	+	0.756447i
$990$	−1.73526	−	0.809607i	−0.0551502	−	0.0257310i
$991$	−7.88333	−	32.8364i	−0.250422	−	1.04308i	−0.945880	−	0.324517i	$-0.894798\pi$
$991$	−7.88333	−	32.8364i	−0.250422	−	1.04308i	0.695458	−	0.718567i	$-0.255202\pi$
$992$	−10.9737	−	6.47941i	−0.348414	−	0.205722i
$993$	11.4514	+	11.4514i	0.363401	+	0.363401i
$994$	81.9337	+	46.3784i	2.59878	+	1.47103i
$995$	12.0264	−	14.0811i	0.381261	−	0.446400i
$996$	15.3082	+	7.97705i	0.485058	+	0.252763i
$997$	3.25571	+	5.31284i	0.103109	+	0.168259i	0.900034	−	0.435819i	$-0.143541\pi$
$997$	3.25571	+	5.31284i	0.103109	+	0.168259i	−0.796925	+	0.604079i	$0.793541\pi$
$998$	35.4758	−	6.88812i	1.12297	−	0.218040i
$999$	−39.4761	−	46.2206i	−1.24897	−	1.46236i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bw.b.11.22	✓	672
4.3	odd	2	inner	820.2.bw.b.11.27	yes	672
41.15	odd	40	inner	820.2.bw.b.671.27	yes	672
164.15	even	40	inner	820.2.bw.b.671.22	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bw.b.11.22	✓	672	1.1	even	1	trivial
820.2.bw.b.11.27	yes	672	4.3	odd	2	inner
820.2.bw.b.671.22	yes	672	164.15	even	40	inner
820.2.bw.b.671.27	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+(0.0619819 - 1.41285i) q^{2} +(0.411797 - 0.994165i) q^{3} +(-1.99232 - 0.175143i) q^{4} +(0.453990 - 0.891007i) q^{5} +(-1.37909 - 0.643429i) q^{6} +(-1.19934 - 4.99561i) q^{7} +(-0.370939 + 2.80400i) q^{8} +(1.30253 + 1.30253i) q^{9} +(-1.23072 - 0.696649i) q^{10} +(0.477372 - 0.558931i) q^{11} +(-0.994550 + 1.90857i) q^{12} +(-2.16365 - 3.53076i) q^{13} +(-7.13241 + 1.38486i) q^{14} +(-0.698856 - 0.818255i) q^{15} +(3.93865 + 0.697880i) q^{16} +(0.279049 + 3.54566i) q^{17} +(1.92102 - 1.75956i) q^{18} +(-4.60777 - 2.82364i) q^{19} +(-1.06055 + 1.69565i) q^{20} +(-5.46035 - 0.864834i) q^{21} +(-0.760100 - 0.709101i) q^{22} +(2.47563 + 1.79865i) q^{23} +(2.63488 + 1.52345i) q^{24} +(-0.587785 - 0.809017i) q^{25} +(-5.12256 + 2.83808i) q^{26} +(4.81381 - 1.99394i) q^{27} +(1.51452 + 10.1629i) q^{28} +(-0.241369 + 3.06688i) q^{29} +(-1.19939 + 0.936664i) q^{30} +(0.696155 - 2.14255i) q^{31} +(1.23013 - 5.52148i) q^{32} +(-0.359089 - 0.704753i) q^{33} +(5.02679 - 0.174490i) q^{34} +(-4.99561 - 1.19934i) q^{35} +(-2.36693 - 2.82319i) q^{36} +(-3.60495 - 11.0949i) q^{37} +(-4.27500 + 6.33509i) q^{38} +(-4.40114 + 0.697072i) q^{39} +(2.32998 + 1.60350i) q^{40} +(-0.416214 + 6.38958i) q^{41} +(-1.56033 + 7.66107i) q^{42} +(1.36490 + 8.61764i) q^{43} +(-1.04897 + 1.02996i) q^{44} +(1.75190 - 0.569228i) q^{45} +(2.69467 - 3.38622i) q^{46} +(-1.30774 + 5.44713i) q^{47} +(2.31573 - 3.62828i) q^{48} +(-17.2807 + 8.80495i) q^{49} +(-1.17946 + 0.780311i) q^{50} +(3.63988 + 1.18267i) q^{51} +(3.69229 + 7.41334i) q^{52} +(3.38052 + 0.266052i) q^{53} +(-2.51878 - 6.92480i) q^{54} +(-0.281289 - 0.679091i) q^{55} +(14.4526 - 1.50988i) q^{56} +(-4.70463 + 3.41811i) q^{57} +(4.31809 + 0.531110i) q^{58} +(0.840526 - 1.15688i) q^{59} +(1.24903 + 1.75262i) q^{60} +(-0.185238 + 1.16955i) q^{61} +(-2.98396 - 1.11637i) q^{62} +(4.94477 - 8.06913i) q^{63} +(-7.72481 - 2.08022i) q^{64} +(-4.12821 + 0.324897i) q^{65} +(-1.01797 + 0.463659i) q^{66} +(4.28308 - 3.65810i) q^{67} +(0.0650418 - 7.11294i) q^{68} +(2.80761 - 1.72050i) q^{69} +(-2.00413 + 6.98374i) q^{70} +(-9.85349 - 8.41568i) q^{71} +(-4.13546 + 3.16914i) q^{72} +(4.91542 - 4.91542i) q^{73} +(-15.8989 + 4.40559i) q^{74} +(-1.04634 + 0.251205i) q^{75} +(8.68559 + 6.43261i) q^{76} +(-3.36474 - 1.71442i) q^{77} +(0.712071 + 6.26138i) q^{78} +(0.821419 + 0.340243i) q^{79} +(2.40993 - 3.19253i) q^{80} -0.0806352i q^{81} +(9.00175 + 0.984089i) q^{82} -8.02077i q^{83} +(10.7273 + 2.67936i) q^{84} +(3.28589 + 1.36106i) q^{85} +(12.2601 - 1.39427i) q^{86} +(2.94959 + 1.50289i) q^{87} +(1.39017 + 1.54588i) q^{88} +(7.56287 - 1.81568i) q^{89} +(-0.695650 - 2.51047i) q^{90} +(-15.0434 + 15.0434i) q^{91} +(-4.61721 - 4.01706i) q^{92} +(-1.84337 - 1.57439i) q^{93} +(7.61494 + 2.18527i) q^{94} +(-4.60777 + 2.82364i) q^{95} +(-4.98270 - 3.49668i) q^{96} +(9.70012 - 8.28469i) q^{97} +(11.3690 + 24.9609i) q^{98} +(1.34982 - 0.106233i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q + 12 q^{6} + 16 q^{9} - 124 q^{12} - 24 q^{14} - 32 q^{16} - 8 q^{17} + 40 q^{21} - 4 q^{22} - 24 q^{24} - 28 q^{28} - 12 q^{30} - 20 q^{32} + 40 q^{33} - 4 q^{34} - 60 q^{36} + 80 q^{37} - 172 q^{38}+ \cdots - 116 q^{98}+O(q^{100}) \) 672 * q + 12 * q^6 + 16 * q^9 - 124 * q^12 - 24 * q^14 - 32 * q^16 - 8 * q^17 + 40 * q^21 - 4 * q^22 - 24 * q^24 - 28 * q^28 - 12 * q^30 - 20 * q^32 + 40 * q^33 - 4 * q^34 - 60 * q^36 + 80 * q^37 - 172 * q^38 + 160 * q^42 - 24 * q^44 - 16 * q^46 + 40 * q^48 - 24 * q^52 - 64 * q^54 + 68 * q^56 - 112 * q^58 + 36 * q^62 - 120 * q^64 + 8 * q^65 + 144 * q^68 - 104 * q^69 + 24 * q^70 - 320 * q^72 - 92 * q^74 - 24 * q^76 + 160 * q^77 - 128 * q^78 - 192 * q^82 - 172 * q^84 - 32 * q^85 - 112 * q^88 + 8 * q^89 - 48 * q^90 + 24 * q^92 + 92 * q^94 + 56 * q^96 - 116 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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