LMFDB - Embedded newform 820.2.bw.b.11.27

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			11.27
Character	$\chi$	$=$	820.11
Dual form			820.2.bw.b.671.27

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.495544 + 1.32455i) q^{2} +(-0.411797 + 0.994165i) q^{3} +(-1.50887 + 1.31275i) q^{4} +(0.453990 - 0.891007i) q^{5} +(-1.52089 - 0.0527928i) q^{6} +(1.19934 + 4.99561i) q^{7} +(-2.48651 - 1.34805i) q^{8} +(1.30253 + 1.30253i) q^{9} +(1.40516 + 0.159800i) q^{10} +(-0.477372 + 0.558931i) q^{11} +(-0.683740 - 2.04065i) q^{12} +(-2.16365 - 3.53076i) q^{13} +(-6.02262 + 4.06414i) q^{14} +(0.698856 + 0.818255i) q^{15} +(0.553387 - 3.96154i) q^{16} +(0.279049 + 3.54566i) q^{17} +(-1.07981 + 2.37073i) q^{18} +(4.60777 + 2.82364i) q^{19} +(0.484653 + 1.94039i) q^{20} +(-5.46035 - 0.864834i) q^{21} +(-0.976892 - 0.355329i) q^{22} +(-2.47563 - 1.79865i) q^{23} +(2.36412 - 1.91688i) q^{24} +(-0.587785 - 0.809017i) q^{25} +(3.60449 - 4.61552i) q^{26} +(-4.81381 + 1.99394i) q^{27} +(-8.36763 - 5.96331i) q^{28} +(-0.241369 + 3.06688i) q^{29} +(-0.737506 + 1.33115i) q^{30} +(-0.696155 + 2.14255i) q^{31} +(5.52148 - 1.23013i) q^{32} +(-0.359089 - 0.704753i) q^{33} +(-4.55812 + 2.12665i) q^{34} +(4.99561 + 1.19934i) q^{35} +(-3.67525 - 0.255458i) q^{36} +(-3.60495 - 11.0949i) q^{37} +(-1.45671 + 7.50246i) 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} +(-0.0134421 - 1.47002i) q^{44} +(1.75190 - 0.569228i) q^{45} +(1.15562 - 4.17040i) q^{46} +(1.30774 - 5.44713i) q^{47} +(3.71054 + 2.18150i) q^{48} +(-17.2807 + 8.80495i) q^{49} +(0.780311 - 1.17946i) q^{50} +(-3.63988 - 1.18267i) q^{51} +(7.89967 + 2.48713i) q^{52} +(3.38052 + 0.266052i) q^{53} +(-5.02653 - 5.38804i) q^{54} +(0.281289 + 0.679091i) q^{55} +(3.75217 - 14.0384i) q^{56} +(-4.70463 + 3.41811i) q^{57} +(-4.18185 + 1.20007i) q^{58} +(-0.840526 + 1.15688i) q^{59} +(-2.12865 - 0.317220i) q^{60} +(-0.185238 + 1.16955i) q^{61} +(-3.18289 + 0.139633i) q^{62} +(-4.94477 + 8.06913i) q^{63} +(4.36551 + 6.70391i) q^{64} +(-4.12821 + 0.324897i) q^{65} +(0.755536 - 0.824868i) q^{66} +(-4.28308 + 3.65810i) q^{67} +(-5.07560 - 4.98362i) q^{68} +(2.80761 - 1.72050i) q^{69} +(0.886960 + 7.21127i) q^{70} +(9.85349 + 8.41568i) q^{71} +(-1.48288 - 4.99465i) q^{72} +(4.91542 - 4.91542i) q^{73} +(12.9093 - 10.2730i) q^{74} +(1.04634 - 0.251205i) q^{75} +(-10.6593 + 1.78832i) q^{76} +(-3.36474 - 1.71442i) q^{77} +(3.10427 + 5.48411i) q^{78} +(-0.821419 - 0.340243i) q^{79} +(-3.27852 - 2.29157i) q^{80} -0.0806352i q^{81} +(-8.66958 + 2.61502i) q^{82} +8.02077i q^{83} +(9.37427 - 5.86314i) q^{84} +(3.28589 + 1.36106i) q^{85} +(10.7381 - 6.07830i) q^{86} +(-2.94959 - 1.50289i) q^{87} +(1.94046 - 0.746267i) q^{88} +(7.56287 - 1.81568i) q^{89} +(1.62212 + 2.03841i) q^{90} +(15.0434 - 15.0434i) q^{91} +(6.09657 - 0.535944i) q^{92} +(-1.84337 - 1.57439i) q^{93} +(7.86304 - 0.967125i) q^{94} +(4.60777 - 2.82364i) q^{95} +(-1.05078 + 5.99583i) q^{96} +(9.70012 - 8.28469i) q^{97} +(-20.2260 - 18.5259i) 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 $

$2$	0.495544	+	1.32455i	0.350403	+	0.936599i
$2$	0.495544	+	1.32455i	0.350403	+	0.936599i
$3$	−0.411797	+	0.994165i	−0.237751	+	0.573981i	−0.997050	−	0.0767610i	$-0.975542\pi$
$3$	−0.411797	+	0.994165i	−0.237751	+	0.573981i	0.759299	+	0.650742i	$0.225542\pi$
$4$	−1.50887	+	1.31275i	−0.754436	+	0.656374i
$5$	0.453990	−	0.891007i	0.203031	−	0.398470i
$5$	0.453990	−	0.891007i	0.203031	−	0.398470i
$6$	−1.52089	−	0.0527928i	−0.620899	−	0.0215526i
$7$	1.19934	+	4.99561i	0.453308	+	1.88816i	0.459489	+	0.888184i	$0.348033\pi$
$7$	1.19934	+	4.99561i	0.453308	+	1.88816i	−0.00618030	+	0.999981i	$0.501967\pi$
$8$	−2.48651	−	1.34805i	−0.879116	−	0.476609i
$9$	1.30253	+	1.30253i	0.434178	+	0.434178i
$10$	1.40516	+	0.159800i	0.444349	+	0.0505333i
$11$	−0.477372	+	0.558931i	−0.143933	+	0.168524i	−0.827690	−	0.561186i	$-0.810345\pi$
$11$	−0.477372	+	0.558931i	−0.143933	+	0.168524i	0.683756	+	0.729710i	$0.260345\pi$
$12$	−0.683740	−	2.04065i	−0.197379	−	0.589085i
$13$	−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	$-0.369706\pi$
$14$	−6.02262	+	4.06414i	−1.60961	+	1.08619i
$15$	0.698856	+	0.818255i	0.180444	+	0.211272i
$16$	0.553387	−	3.96154i	0.138347	−	0.990384i
$17$	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	$0.833054\pi$
$18$	−1.07981	+	2.37073i	−0.254513	+	0.558788i
$19$	4.60777	+	2.82364i	1.05709	+	0.647788i	0.938544	−	0.345160i	$-0.112175\pi$
$19$	4.60777	+	2.82364i	1.05709	+	0.647788i	0.118550	+	0.992948i	$0.462175\pi$
$20$	0.484653	+	1.94039i	0.108372	+	0.433884i
$21$	−5.46035	−	0.864834i	−1.19155	−	0.188722i
$22$	−0.976892	−	0.355329i	−0.208274	−	0.0757564i
$23$	−2.47563	−	1.79865i	−0.516204	−	0.375044i	0.298968	−	0.954263i	$-0.403358\pi$
$23$	−2.47563	−	1.79865i	−0.516204	−	0.375044i	−0.815172	+	0.579219i	$0.803358\pi$
$24$	2.36412	−	1.91688i	0.482575	−	0.391282i
$25$	−0.587785	−	0.809017i	−0.117557	−	0.161803i
$26$	3.60449	−	4.61552i	0.706898	−	0.905177i
$27$	−4.81381	+	1.99394i	−0.926417	+	0.383735i
$28$	−8.36763	−	5.96331i	−1.58133	−	1.12696i
$29$	−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	$0.932796\pi$
$30$	−0.737506	+	1.33115i	−0.134650	+	0.243034i
$31$	−0.696155	+	2.14255i	−0.125033	+	0.384812i	−0.993907	−	0.110221i	$-0.964844\pi$
$31$	−0.696155	+	2.14255i	−0.125033	+	0.384812i	0.868874	+	0.495033i	$0.164844\pi$
$32$	5.52148	−	1.23013i	0.976070	−	0.217458i
$33$	−0.359089	−	0.704753i	−0.0625094	−	0.122682i
$34$	−4.55812	+	2.12665i	−0.781712	+	0.364717i
$35$	4.99561	+	1.19934i	0.844413	+	0.202726i
$36$	−3.67525	−	0.255458i	−0.612542	−	0.0425763i
$37$	−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	$-0.508455\pi$
$38$	−1.45671	+	7.50246i	−0.236309	+	1.21706i
$39$	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	$-0.818312\pi$
$43$	−1.36490	−	8.61764i	−0.208145	−	1.31418i	0.633330	−	0.773882i	$-0.281688\pi$
$44$	−0.0134421	−	1.47002i	−0.00202648	−	0.221615i
$45$	1.75190	−	0.569228i	0.261158	−	0.0848555i
$46$	1.15562	−	4.17040i	0.170387	−	0.614892i
$47$	1.30774	−	5.44713i	0.190753	−	0.794545i	−0.792135	−	0.610345i	$-0.791031\pi$
$47$	1.30774	−	5.44713i	0.190753	−	0.794545i	0.982889	−	0.184200i	$-0.0589693\pi$
$48$	3.71054	+	2.18150i	0.535570	+	0.314873i
$49$	−17.2807	+	8.80495i	−2.46867	+	1.25785i
$50$	0.780311	−	1.17946i	0.110353	−	0.166800i
$51$	−3.63988	−	1.18267i	−0.509685	−	0.165607i
$52$	7.89967	+	2.48713i	1.09549	+	0.344903i
$53$	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	$0.450181\pi$
$54$	−5.02653	−	5.38804i	−0.684025	−	0.733220i
$55$	0.281289	+	0.679091i	0.0379290	+	0.0915686i
$56$	3.75217	−	14.0384i	0.501405	−	1.87597i
$57$	−4.70463	+	3.41811i	−0.623143	+	0.452740i
$58$	−4.18185	+	1.20007i	−0.549104	+	0.157577i
$59$	−0.840526	+	1.15688i	−0.109427	+	0.150614i	−0.860218	−	0.509926i	$-0.829673\pi$
$59$	−0.840526	+	1.15688i	−0.109427	+	0.150614i	0.750791	+	0.660540i	$0.229673\pi$
$60$	−2.12865	−	0.317220i	−0.274807	−	0.0409530i
$61$	−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	$0.0741529\pi$
$62$	−3.18289	+	0.139633i	−0.404227	+	0.0177334i
$63$	−4.94477	+	8.06913i	−0.622983	+	1.01662i
$64$	4.36551	+	6.70391i	0.545688	+	0.837988i
$65$	−4.12821	+	0.324897i	−0.512041	+	0.0402985i
$66$	0.755536	−	0.824868i	0.0930001	−	0.101534i
$67$	−4.28308	+	3.65810i	−0.523262	+	0.446908i	−0.871427	−	0.490526i	$-0.836805\pi$
$67$	−4.28308	+	3.65810i	−0.523262	+	0.446908i	0.348165	+	0.937433i	$0.386805\pi$
$68$	−5.07560	−	4.98362i	−0.615507	−	0.604353i
$69$	2.80761	−	1.72050i	0.337996	−	0.207124i
$70$	0.886960	+	7.21127i	0.106012	+	0.861912i
$71$	9.85349	+	8.41568i	1.16939	+	0.998757i	0.999913	+	0.0132237i	$0.00420935\pi$
$71$	9.85349	+	8.41568i	1.16939	+	0.998757i	0.169482	+	0.985533i	$0.445791\pi$
$72$	−1.48288	−	4.99465i	−0.174760	−	0.588625i
$73$	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	$0.116644\pi$
$74$	12.9093	−	10.2730i	1.50068	−	1.19421i
$75$	1.04634	−	0.251205i	0.120821	−	0.0290067i
$76$	−10.6593	+	1.78832i	−1.22270	+	0.205134i
$77$	−3.36474	−	1.71442i	−0.383447	−	0.195376i
$78$	3.10427	+	5.48411i	0.351489	+	0.620953i
$79$	−0.821419	−	0.340243i	−0.0924168	−	0.0382803i	0.335996	−	0.941863i	$-0.390927\pi$
$79$	−0.821419	−	0.340243i	−0.0924168	−	0.0382803i	−0.428413	+	0.903583i	$0.640927\pi$
$80$	−3.27852	−	2.29157i	−0.366550	−	0.256205i
$81$		−	0.0806352i		−	0.00895947i
$82$	−8.66958	+	2.61502i	−0.957395	+	0.288781i
$83$			8.02077i			0.880394i	0.897901	+	0.440197i	$0.145091\pi$
$83$			8.02077i			0.880394i	−0.897901	+	0.440197i	$0.854909\pi$
$84$	9.37427	−	5.86314i	1.02282	−	0.639721i
$85$	3.28589	+	1.36106i	0.356405	+	0.147628i
$86$	10.7381	−	6.07830i	1.15792	−	0.655440i
$87$	−2.94959	−	1.50289i	−0.316229	−	0.161127i
$88$	1.94046	−	0.746267i	0.206854	−	0.0795524i
$89$	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	$0.289753\pi$
$90$	1.62212	+	2.03841i	0.170986	+	0.214867i
$91$	15.0434	−	15.0434i	1.57697	−	1.57697i
$92$	6.09657	−	0.535944i	0.635612	−	0.0558761i
$93$	−1.84337	−	1.57439i	−0.191148	−	0.163256i
$94$	7.86304	−	0.967125i	0.811011	−	0.0997513i
$95$	4.60777	−	2.82364i	0.472747	−	0.289700i
$96$	−1.05078	+	5.99583i	−0.107245	+	0.611947i
$97$	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	$0.0507672\pi$
$98$	−20.2260	−	18.5259i	−2.04313	−	1.87140i
$99$	−1.34982	+	0.106233i	−0.135662	+	0.0106768i
$100$	1.94893	+	0.449089i	0.194893	+	0.0449089i
$101$	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	$0.0921804\pi$
$102$	−0.237217	−	5.40727i	−0.0234880	−	0.535399i
$103$	−0.983316	+	6.20841i	−0.0968890	+	0.611733i	0.890690	+	0.454611i	$0.150222\pi$
$103$	−0.983316	+	6.20841i	−0.0968890	+	0.611733i	−0.987579	+	0.157122i	$0.949778\pi$
$104$	0.620302	+	11.6960i	0.0608256	+	1.14689i
$105$	−3.24952	+	4.47258i	−0.317121	+	0.436479i
$106$	1.32280	+	4.60951i	0.128481	+	0.447715i
$107$	1.68436	−	1.22376i	0.162833	−	0.118305i	−0.503385	−	0.864062i	$-0.667912\pi$
$107$	1.68436	−	1.22376i	0.162833	−	0.118305i	0.666218	+	0.745757i	$0.267912\pi$
$108$	4.64587	−	9.32792i	0.447049	−	0.897579i
$109$	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	$0.789894\pi$
$110$	−0.760100	+	0.709101i	−0.0724727	+	0.0676102i
$111$	12.5147	+	0.984925i	1.18784	+	0.0934850i
$112$	20.4540	−	1.98672i	1.93272	−	0.187728i
$113$	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	$0.552755\pi$
$114$	−6.85882	−	4.53770i	−0.642387	−	0.424994i
$115$	−2.72652	+	1.38923i	−0.254249	+	0.129546i
$116$	−3.66184	−	4.94438i	−0.339994	−	0.459074i
$117$	1.78070	−	7.41716i	0.164626	−	0.685717i
$118$	−1.94887	−	0.540032i	−0.179408	−	0.0497140i
$119$	−17.3781	+	5.64647i	−1.59304	+	0.517611i
$120$	−0.634664	−	2.97670i	−0.0579366	−	0.271734i
$121$	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
$126$	−13.1383	−	2.55099i	−1.17046	−	0.227260i
$127$	3.72564	+	11.4663i	0.330597	+	1.01747i	0.968851	+	0.247646i	$0.0796571\pi$
$127$	3.72564	+	11.4663i	0.330597	+	1.01747i	−0.638254	+	0.769826i	$0.720343\pi$
$128$	−6.71636	+	9.10442i	−0.593648	+	0.804725i
$129$	9.12942	+	2.19178i	0.803800	+	0.192975i
$130$	−2.47605	−	5.30702i	−0.217164	−	0.465457i
$131$	6.15725	+	12.0843i	0.537962	+	1.05581i	0.986762	+	0.162177i	$0.0518515\pi$
$131$	6.15725	+	12.0843i	0.537962	+	1.05581i	−0.448800	+	0.893632i	$0.648148\pi$
$132$	1.46698	+	0.591987i	0.127684	+	0.0515259i
$133$	−8.57955	+	26.4051i	−0.743941	+	2.28962i
$134$	−6.96779	−	3.86041i	−0.601926	−	0.333489i
$135$	−0.408805	+	5.19436i	−0.0351844	+	0.447060i
$136$	4.08587	−	9.19250i	0.350361	−	0.788250i
$137$	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	$0.218730\pi$
$138$	3.67019	+	2.86623i	0.312427	+	0.243990i
$139$	−3.27034	−	4.50123i	−0.277386	−	0.381789i	0.647480	−	0.762083i	$-0.275823\pi$
$139$	−3.27034	−	4.50123i	−0.277386	−	0.381789i	−0.924866	+	0.380293i	$0.875823\pi$
$140$	−9.11217	+	4.74833i	−0.770119	+	0.401307i
$141$	4.87682	+	3.54322i	0.410702	+	0.298393i
$142$	−6.26415	+	17.2218i	−0.525676	+	1.44522i
$143$	3.00632	+	0.476154i	0.251401	+	0.0398180i
$144$	5.88084	−	4.43923i	0.490070	−	0.369936i
$145$	2.62303	+	1.60740i	0.217831	+	0.133487i
$146$	8.94653	+	4.07491i	0.740420	+	0.337242i
$147$	−1.63744	−	20.8057i	−0.135054	−	1.71603i
$148$	20.0042	+	12.0084i	1.64434	+	0.987083i
$149$	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	$0.702688\pi$
$150$	0.851244	+	1.26145i	0.0695038	+	0.102997i
$151$	3.62465	+	5.91489i	0.294970	+	0.481347i	0.965453	−	0.260578i	$-0.0839131\pi$
$151$	3.62465	+	5.91489i	0.294970	+	0.481347i	−0.670483	+	0.741925i	$0.733913\pi$
$152$	−7.65086	−	13.2325i	−0.620567	−	1.07330i
$153$	−4.25486	+	4.98181i	−0.343985	+	0.402755i
$154$	0.603459	−	5.30634i	0.0486281	−	0.427597i
$155$	1.59297	+	1.59297i	0.127951	+	0.127951i
$156$	−5.72568	+	6.82938i	−0.458421	+	0.546788i
$157$	−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	$0.998437\pi$
$158$	0.0436195	−	1.25662i	0.00347018	−	0.0999711i
$159$	−1.65659	+	3.25123i	−0.131376	+	0.257839i
$160$	1.41065	−	5.47814i	0.111522	−	0.433085i
$161$	6.01623	−	14.5245i	0.474145	−	1.14469i
$162$	0.106806	−	0.0399583i	0.00839143	−	0.00313942i
$163$	−3.82938			−0.299940			−0.149970	−	0.988691i	$-0.547918\pi$
$163$	−3.82938			−0.299940			−0.149970	+	0.988691i	$0.547918\pi$
$164$	−7.75990	−	10.1874i	−0.605946	−	0.795506i
$165$	−0.790962			−0.0615763
$166$	−10.6239	+	3.97465i	−0.824576	+	0.308492i
$167$	−5.62883	+	13.5892i	−0.435572	+	1.05156i	0.541889	+	0.840450i	$0.317709\pi$
$167$	−5.62883	+	13.5892i	−0.435572	+	1.05156i	−0.977461	+	0.211114i	$0.932291\pi$
$168$	12.4114	+	9.51126i	0.957560	+	0.733810i
$169$	−1.88299	+	3.69558i	−0.144846	+	0.284276i
$170$	−0.174490	+	5.02679i	−0.0133827	+	0.385537i
$171$	2.32388	+	9.67966i	0.177712	+	0.740222i
$172$	13.3722	+	11.2111i	1.01962	+	0.854842i
$173$	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	$0.620544\pi$
$174$	0.529003	−	4.65163i	0.0401036	−	0.352639i
$175$	3.33658	−	3.90664i	0.252222	−	0.295314i
$176$	1.95005	+	2.20043i	0.146991	+	0.165864i
$177$	−0.804008	−	1.31202i	−0.0604330	−	0.0986176i
$178$	6.15270	+	9.11766i	0.461165	+	0.683397i
$179$	17.0852	+	20.0042i	1.27701	+	1.49518i	0.777515	+	0.628864i	$0.216480\pi$
$179$	17.0852	+	20.0042i	1.27701	+	1.49518i	0.499492	+	0.866319i	$0.333520\pi$
$180$	−1.89614	+	3.15870i	−0.141330	+	0.235435i
$181$	−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	$-0.431179\pi$
$182$	27.3803	+	12.4710i	2.02957	+	0.924415i
$183$	−1.08644	−	0.665772i	−0.0803121	−	0.0492153i
$184$	3.73101	+	7.80964i	0.275054	+	0.575734i
$185$	−11.5222	−	1.82494i	−0.847132	−	0.134172i
$186$	1.17188	−	3.22181i	0.0859267	−	0.236235i
$187$	−2.11499	−	1.53663i	−0.154663	−	0.112369i
$188$	5.17749	+	9.93575i	0.377607	+	0.724639i
$189$	−15.7344	−	21.6565i	−1.14451	−	1.57528i
$190$	6.02341	+	4.70398i	0.436984	+	0.341263i
$191$	−2.34837	+	0.972726i	−0.169922	+	0.0703840i	−0.466023	−	0.884773i	$-0.654314\pi$
$191$	−2.34837	+	0.972726i	−0.169922	+	0.0703840i	0.296101	+	0.955157i	$0.404314\pi$
$192$	−8.46249	+	1.57939i	−0.610727	+	0.113983i
$193$	−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	$0.952303\pi$
$194$	15.7803	+	8.74288i	1.13296	+	0.627702i
$195$	1.37698	−	4.23791i	0.0986076	−	0.303483i
$196$	14.5157	−	35.9707i	1.03683	−	2.56934i
$197$	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	$0.823132\pi$
$198$	−0.809607	−	1.73526i	−0.0575362	−	0.123320i
$199$	−18.0062	−	4.32290i	−1.27642	−	0.306442i	−0.462087	−	0.886835i	$-0.652899\pi$
$199$	−18.0062	−	4.32290i	−1.27642	−	0.306442i	−0.814337	+	0.580392i	$0.802899\pi$
$200$	0.370939	+	2.80400i	0.0262293	+	0.198273i
$201$	−1.87299	−	5.76448i	−0.132111	−	0.406595i
$202$	7.17864	+	1.39383i	0.505087	+	0.0980696i
$203$	−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
$208$	−15.1846	+	6.61751i	−1.05286	+	0.458842i
$209$	−3.77784	+	1.22750i	−0.261319	+	0.0849076i
$210$	−7.53444	−	2.08779i	−0.519926	−	0.144071i
$211$	−1.59026	+	6.62392i	−0.109478	+	0.456009i	0.890521	+	0.454942i	$0.150340\pi$
$211$	−1.59026	+	6.62392i	−0.109478	+	0.456009i	−0.999999	+	0.00106767i	$0.999660\pi$
$212$	−5.45003	+	4.03633i	−0.374309	+	0.277216i
$213$	−12.4242	+	6.33045i	−0.851292	+	0.433755i
$214$	2.45560	+	1.62459i	0.167862	+	0.111055i
$215$	−8.29803	−	2.69619i	−0.565921	−	0.183879i
$216$	14.6575	+	1.53129i	0.997319	+	0.104191i
$217$	−11.5383	−	0.908080i	−0.783268	−	0.0616445i
$218$	−5.70462	+	5.32187i	−0.386365	+	0.360442i
$219$	2.86258	+	6.91088i	0.193435	+	0.466994i
$220$	−1.31590	−	0.655400i	−0.0887182	−	0.0441871i
$221$	11.9151	−	8.65682i	0.801496	−	0.582321i
$222$	4.89699	+	17.0644i	0.328664	+	1.14529i
$223$	14.4122	−	19.8367i	0.965115	−	1.32837i	0.0206389	−	0.999787i	$-0.493430\pi$
$223$	14.4122	−	19.8367i	0.965115	−	1.32837i	0.944476	−	0.328580i	$-0.106570\pi$
$224$	12.7674	+	26.1079i	0.853057	+	1.74440i
$225$	0.288162	−	1.81938i	0.0192108	−	0.121292i
$226$	0.194869	+	4.44198i	0.0129625	+	0.295476i
$227$	−2.57266	+	4.19819i	−0.170753	+	0.278644i	−0.926557	−	0.376154i	$-0.877246\pi$
$227$	−2.57266	+	4.19819i	−0.170753	+	0.278644i	0.755804	+	0.654798i	$0.227246\pi$
$228$	2.61156	−	11.3335i	0.172955	−	0.750578i
$229$	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	$0.152545\pi$
$230$	−3.19122	−	2.92299i	−0.210423	−	0.192736i
$231$	3.09000	−	2.63911i	0.203307	−	0.173641i
$232$	4.73448	−	7.30046i	0.310834	−	0.479299i
$233$	−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	$0.536865\pi$
$234$	10.7068	−	1.31690i	0.699927	−	0.0860885i
$235$	−4.25972	−	3.63815i	−0.277874	−	0.237327i
$236$	−0.250452	−	2.84899i	−0.0163030	−	0.185453i
$237$	0.676515	−	0.676515i	0.0439444	−	0.0439444i
$238$	−16.0906	−	20.2200i	−1.04300	−	1.31067i
$239$	−22.7110	+	5.45244i	−1.46905	+	0.352689i	−0.887496	−	0.460815i	$-0.847557\pi$
$239$	−22.7110	+	5.45244i	−1.46905	+	0.352689i	−0.581559	+	0.813504i	$0.697557\pi$
$240$	3.62828	−	2.31573i	0.234205	−	0.149480i
$241$	−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	$0.784825\pi$
$242$	−12.8730	+	7.28675i	−0.827509	+	0.468410i
$243$	−14.3613	−	5.94863i	−0.921275	−	0.381604i
$244$	−1.25582	−	2.00787i	−0.0803956	−	0.128540i
$245$			19.3946i			1.23907i
$246$	0.970338	−	9.69585i	0.0618665	−	0.618185i
$247$		−	22.3783i		−	1.42390i
$248$	4.61926	−	4.38902i	0.293324	−	0.278703i
$249$	−7.97396	−	3.30292i	−0.505329	−	0.209314i
$250$	−0.696649	−	1.23072i	−0.0440599	−	0.0778378i
$251$	−9.69709	−	4.94091i	−0.612075	−	0.311868i	0.120333	−	0.992734i	$-0.461604\pi$
$251$	−9.69709	−	4.94091i	−0.612075	−	0.311868i	−0.732408	+	0.680866i	$0.761604\pi$
$252$	−3.13171	−	18.6665i	−0.197279	−	1.17588i
$253$	2.18712	−	0.525080i	0.137503	−	0.0330115i
$254$	−13.3415	+	10.6169i	−0.837122	+	0.666162i
$255$	−2.70624	+	2.70624i	−0.169471	+	0.169471i
$256$	−15.3875	−	4.38452i	−0.961720	−	0.274033i
$257$	−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	$0.876404\pi$
$258$	1.62091	+	13.1785i	0.100913	+	0.820458i
$259$	51.1023	−	31.3155i	3.17534	−	1.94585i
$260$	5.80243	−	5.90952i	0.359851	−	0.366493i
$261$	−4.30910	+	3.68032i	−0.266727	+	0.227806i
$262$	−12.9551	+	14.1439i	−0.800367	+	0.873813i
$263$	21.4514	−	1.68827i	1.32275	−	0.104103i	0.602670	−	0.797991i	$-0.294104\pi$
$263$	21.4514	−	1.68827i	1.32275	−	0.104103i	0.720083	+	0.693888i	$0.244104\pi$
$264$	−0.0571628	+	2.23645i	−0.00351813	+	0.137644i
$265$	1.77178	−	2.89128i	0.108839	−	0.177610i
$266$	−39.2265	+	1.72087i	−2.40513	+	0.105513i
$267$	−1.30927	+	8.26643i	−0.0801263	+	0.505897i
$268$	1.66046	−	11.1422i	0.101429	−	0.680618i
$269$	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	$-0.0395953\pi$
$270$	−7.08278	+	2.03255i	−0.431044	+	0.123697i
$271$	25.1653	−	18.2837i	1.52868	−	1.11065i	0.571719	−	0.820449i	$-0.306277\pi$
$271$	25.1653	−	18.2837i	1.52868	−	1.11065i	0.956965	−	0.290205i	$-0.0937234\pi$
$272$	14.2007	+	0.856656i	0.861042	+	0.0519424i
$273$	8.76077	+	21.1504i	0.530226	+	1.28008i
$274$	10.6469	+	11.4127i	0.643205	+	0.689464i
$275$	0.732777	+	0.0576708i	0.0441881	+	0.00347768i
$276$	−1.97773	+	6.28170i	−0.119045	+	0.378114i
$277$	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	$0.401769\pi$
$278$	4.34151	−	6.56229i	0.260387	−	0.393580i
$279$	−3.69750	+	1.88397i	−0.221364	+	0.112790i
$280$	−10.8049	−	9.71653i	−0.645716	−	0.580674i
$281$	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	$0.0724250\pi$
$282$	−2.27649	+	8.21542i	−0.135563	+	0.489221i
$283$	5.96964	−	1.93965i	0.354858	−	0.115300i	−0.126163	−	0.992010i	$-0.540266\pi$
$283$	5.96964	−	1.93965i	0.354858	−	0.115300i	0.481021	+	0.876709i	$0.340266\pi$
$284$	−25.9153	+	0.236974i	−1.53779	+	0.0140618i
$285$	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
$290$	−0.829249	+	4.27087i	−0.0486952	+	0.250794i
$291$	4.24187	+	13.0551i	0.248663	+	0.765305i
$292$	−0.964030	+	13.8694i	−0.0564156	+	0.811647i
$293$	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	$0.254496\pi$
$294$	26.7468	−	12.4790i	1.55990	−	0.727792i
$295$	0.649201	+	1.27413i	0.0377979	+	0.0741826i
$296$	−5.99274	+	32.4473i	−0.348321	+	1.88596i
$297$	1.18350	−	3.64244i	0.0686736	−	0.211356i
$298$	−3.76846	+	6.80183i	−0.218301	+	0.394019i
$299$	−0.994198	+	12.6325i	−0.0574960	+	0.730556i
$300$	−1.24903	+	1.75262i	−0.0721128	+	0.101188i
$301$	41.4134	−	17.1540i	2.38703	−	0.988740i
$302$	−6.03840	+	7.73212i	−0.347471	+	0.444934i
$303$	3.27058	+	4.50156i	0.187890	+	0.258608i
$304$	13.7358	−	16.6913i	0.787804	−	0.957310i
$305$	0.957977	+	0.696011i	0.0548536	+	0.0398535i
$306$	−8.70713	−	3.16708i	−0.497754	−	0.181050i
$307$	9.66309	+	1.53048i	0.551502	+	0.0873493i	0.425965	−	0.904740i	$-0.359935\pi$
$307$	9.66309	+	1.53048i	0.551502	+	0.0873493i	0.125537	+	0.992089i	$0.459935\pi$
$308$	7.32755	−	1.83021i	0.417526	−	0.104286i
$309$	−5.76726	−	3.53418i	−0.328088	−	0.201053i
$310$	−1.32059	+	2.89936i	−0.0750043	+	0.164673i
$311$	−1.97817	−	25.1351i	−0.112172	−	1.42528i	−0.753215	−	0.657775i	$-0.771498\pi$
$311$	−1.97817	−	25.1351i	−0.112172	−	1.42528i	0.641043	−	0.767505i	$-0.278502\pi$
$312$	−11.8832	−	4.19969i	−0.672753	−	0.237761i
$313$	−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	$-0.494249\pi$
$314$	6.71761	−	4.53313i	0.379097	−	0.255819i
$315$	4.94477	+	8.06913i	0.278606	+	0.454644i
$316$	1.68607	−	0.564933i	0.0948488	−	0.0317800i
$317$	−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	$0.872918\pi$
$318$	−5.12733	−	0.583102i	−0.287527	−	0.0326988i
$319$	−1.59895	−	1.59895i	−0.0895241	−	0.0895241i
$320$	7.95512	−	0.846186i	0.444705	−	0.0473032i
$321$	0.523004	+	2.17847i	0.0291912	+	0.121590i
$322$	22.2197	+	0.771288i	1.23826	+	0.0429822i
$323$	−8.72588	+	17.1255i	−0.485521	+	0.952888i
$324$	0.105854	+	0.121668i	0.00588076	+	0.00675935i
$325$	−1.58468	+	3.82576i	−0.0879023	+	0.212215i
$326$	−1.89763	−	5.07221i	−0.105100	−	0.280924i
$327$	−5.93624			−0.328275
$328$	9.64842	−	15.3267i	0.532745	−	0.846276i
$329$	28.7802			1.58670
$330$	−0.391957	−	1.04767i	−0.0215765	−	0.0576723i
$331$	5.75933	−	13.9043i	0.316561	−	0.764247i	−0.682870	−	0.730540i	$-0.739269\pi$
$331$	5.75933	−	13.9043i	0.316561	−	0.764247i	0.999432	−	0.0337072i	$-0.0107314\pi$
$332$	−10.5292	−	12.1023i	−0.577867	−	0.664200i
$333$	9.75590	−	19.1470i	0.534620	−	1.04925i
$334$	−20.7889	−	0.721623i	−1.13752	−	0.0394855i
$335$	1.31491	+	5.47699i	0.0718412	+	0.299240i
$336$	−6.44776	+	21.1528i	−0.351754	+	1.15398i
$337$	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	$0.735311\pi$
$338$	−5.82810	−	0.662796i	−0.317007	−	0.0360514i
$339$	−2.19718	+	2.57257i	−0.119335	+	0.139723i
$340$	−6.74471	+	2.25988i	−0.365783	+	0.122559i
$341$	−0.865210	−	1.41189i	−0.0468537	−	0.0764584i
$342$	−11.6696	+	7.87480i	−0.631021	+	0.425820i
$343$	−41.3555	−	48.4211i	−2.23299	−	2.61449i
$344$	−8.22319	+	23.2678i	−0.443365	+	1.25452i
$345$	−0.258353	−	3.28269i	−0.0139093	−	0.176734i
$346$	−6.09998	+	13.3926i	−0.327937	+	0.719990i
$347$	−20.9468	−	12.8362i	−1.12448	−	0.689083i	−0.169435	−	0.985541i	$-0.554194\pi$
$347$	−20.9468	−	12.8362i	−1.12448	−	0.689083i	−0.955046	+	0.296459i	$0.904194\pi$
$348$	6.42347	−	1.60440i	0.344334	−	0.0860047i
$349$	−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	$0.772823\pi$
$350$	6.82796	+	2.48356i	0.364970	+	0.132752i
$351$	17.4555	+	12.6822i	0.931708	+	0.676925i
$352$	−1.94825	+	3.67336i	−0.103842	+	0.195791i
$353$	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	$0.632441\pi$
$354$	1.33942	−	1.71512i	0.0711893	−	0.0911573i
$355$	11.9718	−	4.95889i	0.635398	−	0.263190i
$356$	−9.02786	+	12.6678i	−0.478476	+	0.671391i
$357$	1.54270	−	19.6019i	0.0816483	−	1.03744i
$358$	−18.0301	+	32.5432i	−0.952920	+	1.71996i
$359$	8.41938	−	25.9122i	0.444358	−	1.36759i	−0.438828	−	0.898571i	$-0.644606\pi$
$359$	8.41938	−	25.9122i	0.444358	−	1.36759i	0.883186	−	0.469022i	$-0.155394\pi$
$360$	−5.12348	−	0.946265i	−0.270031	−	0.0498725i
$361$	4.63274	+	9.09225i	0.243828	+	0.478540i
$362$	32.9969	−	15.3951i	1.73428	−	0.809148i
$363$	−10.9445	−	2.62753i	−0.574435	−	0.137910i
$364$	−2.95036	+	42.4466i	−0.154641	+	2.22481i
$365$	−2.14812	−	6.61122i	−0.112437	−	0.346047i
$366$	0.343469	−	1.76897i	0.0179534	−	0.0924654i
$367$	−21.0010	+	3.32624i	−1.09625	+	0.173628i	−0.678257	−	0.734824i	$-0.737265\pi$
$367$	−21.0010	+	3.32624i	−1.09625	+	0.173628i	−0.417988	+	0.908453i	$0.637265\pi$
$368$	−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
$372$	4.84818	−	0.0443325i	0.251366	−	0.00229853i
$373$	−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	$0.540828\pi$
$374$	0.987273	−	3.56288i	0.0510507	−	0.184232i
$375$	0.251205	−	1.04634i	0.0129722	−	0.0540330i
$376$	−10.5947	+	11.7815i	−0.546381	+	0.607582i
$377$	11.3507	−	5.78345i	0.584588	−	0.297863i
$378$	20.8881	−	31.5727i	1.07437	−	1.62393i
$379$	−19.9687	−	6.48821i	−1.02572	−	0.333277i	−0.252624	−	0.967565i	$-0.581294\pi$
$379$	−19.9687	−	6.48821i	−1.02572	−	0.333277i	−0.773097	+	0.634288i	$0.781294\pi$
$380$	−3.24580	+	10.3094i	−0.166506	+	0.528859i
$381$	−12.9336	−	1.01790i	−0.662610	−	0.0521485i
$382$	−2.45215	−	2.62850i	−0.125463	−	0.134486i
$383$	1.45908	+	3.52253i	0.0745554	+	0.179993i	0.956763	−	0.290867i	$-0.0939438\pi$
$383$	1.45908	+	3.52253i	0.0745554	+	0.179993i	−0.882208	+	0.470860i	$0.843944\pi$
$384$	−6.28552	−	10.4263i	−0.320757	−	0.532067i
$385$	−3.05512	+	2.21967i	−0.155703	+	0.113125i
$386$	−8.55114	+	2.45393i	−0.435241	+	0.124902i
$387$	9.44694	−	13.0026i	0.480215	−	0.660959i
$388$	−3.76053	+	25.2343i	−0.190912	+	1.28108i
$389$	−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	$0.884686\pi$
$390$	6.29568	−	0.276191i	0.318794	−	0.0139855i
$391$	5.68657	−	9.27963i	0.287582	−	0.469291i
$392$	54.8382	+	1.40164i	2.76975	+	0.0707938i
$393$	−14.5493	+	1.14506i	−0.733916	+	0.0577604i
$394$	−2.26062	+	2.46806i	−0.113888	+	0.124339i
$395$	−0.676075	+	0.577423i	−0.0340170	+	0.0290533i
$396$	1.89725	−	1.93226i	0.0953402	−	0.0970999i
$397$	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	$-0.0356767\pi$
$398$	−3.19696	−	25.9923i	−0.160249	−	1.30288i
$399$	−22.7180	−	19.4030i	−1.13732	−	0.971366i
$400$	−3.53022	+	1.88083i	−0.176511	+	0.0940416i
$401$	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	$0.247504\pi$
$402$	6.70720	−	5.33743i	0.334525	−	0.266207i
$403$	9.07105	−	2.17777i	0.451861	−	0.108482i
$404$	1.71113	+	10.1992i	0.0851320	+	0.507428i
$405$	−0.0718465	−	0.0366076i	−0.00357008	−	0.00181905i
$406$	−11.0105	−	19.4516i	−0.546444	−	0.965367i
$407$	7.92219	+	3.28148i	0.392688	+	0.162657i
$408$	7.45631	+	7.84747i	0.369142	+	0.388508i
$409$			24.9255i			1.23248i	0.787557	+	0.616242i	$0.211346\pi$
$409$			24.9255i			1.23248i	−0.787557	+	0.616242i	$0.788654\pi$
$410$	−1.60590	+	8.91185i	−0.0793099	+	0.440125i
$411$			11.8760i			0.585802i
$412$	−6.66638	−	10.6585i	−0.328429	−	0.525109i
$413$	−6.78743	−	2.81144i	−0.333987	−	0.138342i
$414$	6.93732	−	3.92686i	0.340951	−	0.192994i
$415$	7.14656	+	3.64135i	0.350811	+	0.178747i
$416$	−16.2899	−	16.8335i	−0.798676	−	0.825328i
$417$	5.82168	−	1.39766i	0.285089	−	0.0684438i
$418$	−3.49797	−	4.39567i	−0.171091	−	0.214999i
$419$	3.59886	−	3.59886i	0.175816	−	0.175816i	−0.613713	−	0.789529i	$-0.710325\pi$
$419$	3.59886	−	3.59886i	0.175816	−	0.175816i	0.789529	+	0.613713i	$0.210325\pi$
$420$	−0.968262	−	11.0143i	−0.0472463	−	0.537445i
$421$	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	$0.594430\pi$
$422$	−9.56176	+	1.17606i	−0.465459	+	0.0572498i
$423$	8.79844	−	5.39169i	0.427795	−	0.262153i
$424$	−8.04705	−	5.21866i	−0.390799	−	0.253440i
$425$	2.70448	−	2.30984i	0.131186	−	0.112044i
$426$	−14.5417	−	13.3195i	−0.704550	−	0.645331i
$427$	−6.06477	+	0.477308i	−0.293495	+	0.0230985i
$428$	−0.934994	+	4.05763i	−0.0451947	+	0.196133i
$429$	−1.71137	+	2.79270i	−0.0826256	+	0.134833i
$430$	−0.540796	−	12.3272i	−0.0260795	−	0.594472i
$431$	4.44652	−	28.0742i	0.214182	−	1.35229i	−0.612879	−	0.790176i	$-0.709989\pi$
$431$	4.44652	−	28.0742i	0.214182	−	1.35229i	0.827061	−	0.562112i	$-0.190011\pi$
$432$	5.23518	+	20.1735i	0.251878	+	0.970597i
$433$	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	$0.181935\pi$
$434$	−4.51492	−	15.7330i	−0.216723	−	0.755208i
$435$	−2.67817	+	1.94580i	−0.128408	+	0.0932942i
$436$	−9.87598	−	4.91884i	−0.472974	−	0.235570i
$437$	−6.32837	−	15.2780i	−0.302727	−	0.730847i
$438$	−7.73528	+	7.21629i	−0.369606	+	0.344807i
$439$	−21.5311	−	1.69454i	−1.02762	−	0.0808758i	−0.446577	−	0.894745i	$-0.647357\pi$
$439$	−21.5311	−	1.69454i	−1.02762	−	0.0808758i	−0.581048	+	0.813870i	$0.697357\pi$
$440$	0.216022	−	2.06776i	0.0102985	−	0.0985767i
$441$	−33.9774	−	11.0399i	−1.61797	−	0.525711i
$442$	17.3709	+	11.4923i	0.826248	+	0.546634i
$443$	8.62465	−	4.39448i	0.409769	−	0.208788i	−0.236940	−	0.971524i	$-0.576145\pi$
$443$	8.62465	−	4.39448i	0.409769	−	0.208788i	0.646710	+	0.762736i	$0.276145\pi$
$444$	−20.1760	+	14.9425i	−0.957509	+	0.709138i
$445$	1.81568	−	7.56287i	0.0860717	−	0.358514i
$446$	33.4167	+	9.25976i	1.58233	+	0.438462i
$447$	−5.62718	+	1.82838i	−0.266156	+	0.0864794i
$448$	−28.2544	+	29.8487i	−1.33489	+	1.41022i
$449$	−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
$454$	−6.83559	−	1.32722i	−0.320810	−	0.0622897i
$455$	−6.57419	−	20.2333i	−0.308203	−	0.948550i
$456$	16.3059	−	2.15710i	0.763595	−	0.101015i
$457$	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	$0.492276\pi$
$458$	15.3541	+	32.9090i	0.717449	+	1.53774i
$459$	−8.41313	−	16.5117i	−0.392691	−	0.770700i
$460$	2.29026	−	5.67540i	0.106784	−	0.264617i
$461$	−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	$0.187513\pi$
$462$	5.02687	+	2.78507i	0.233871	+	0.129573i
$463$	−2.63371	+	33.4645i	−0.122399	+	1.55523i	0.562630	+	0.826709i	$0.309790\pi$
$463$	−2.63371	+	33.4645i	−0.122399	+	1.55523i	−0.685029	+	0.728516i	$0.740210\pi$
$464$	12.0160	+	2.65336i	0.557828	+	0.123179i
$465$	−2.23966	+	0.927697i	−0.103862	+	0.0430209i
$466$	−21.0127	−	16.4098i	−0.973394	−	0.760172i
$467$	0.379447	+	0.522264i	0.0175587	+	0.0241675i	0.817706	−	0.575636i	$-0.195245\pi$
$467$	0.379447	+	0.522264i	0.0175587	+	0.0241675i	−0.800147	+	0.599803i	$0.795245\pi$
$468$	7.05001	+	13.5292i	0.325887	+	0.625385i
$469$	−23.4113	−	17.0093i	−1.08103	−	0.785417i
$470$	2.70803	−	7.44509i	0.124912	−	0.343416i
$471$	6.09046	+	0.964634i	0.280633	+	0.0444480i
$472$	3.64952	−	1.74354i	0.167983	−	0.0802528i
$473$	5.46823	+	3.35094i	0.251430	+	0.154076i
$474$	1.23132	+	0.560835i	0.0565565	+	0.0257600i
$475$	−0.424002	−	5.38746i	−0.0194546	−	0.247194i
$476$	18.8089	−	31.3328i	0.862103	−	1.43614i
$477$	4.05669	+	4.74978i	0.185743	+	0.217477i
$478$	−18.4764	−	27.3800i	−0.845089	−	1.25233i
$479$	−12.7025	−	20.7286i	−0.580391	−	0.947112i	−0.999237	−	0.0390548i	$-0.987565\pi$
$479$	−12.7025	−	20.7286i	−0.580391	−	0.947112i	0.418846	−	0.908057i	$-0.362435\pi$
$480$	4.86528	+	3.65830i	0.222069	+	0.166978i
$481$	−31.3735	+	36.7337i	−1.43051	+	1.67491i
$482$	2.03926	−	17.9316i	0.0928858	−	0.816763i
$483$	11.9622	+	11.9622i	0.544301	+	0.544301i
$484$	−16.0308	−	13.4401i	−0.728674	−	0.610912i
$485$	−2.97795	−	12.4040i	−0.135222	−	0.563238i
$486$	0.762621	−	21.9700i	0.0345932	−	0.996580i
$487$	15.8026	−	31.0144i	0.716086	−	1.40540i	−0.189778	−	0.981827i	$-0.560777\pi$
$487$	15.8026	−	31.0144i	0.716086	−	1.40540i	0.905863	−	0.423570i	$-0.139223\pi$
$488$	2.03721	−	2.65838i	0.0922201	−	0.120339i
$489$	1.57693	−	3.80703i	0.0713110	−	0.172160i
$490$	−25.6891	+	9.61087i	−1.16052	+	0.434175i
$491$	18.9650			0.855876			0.427938	−	0.903808i	$-0.359240\pi$
$491$	18.9650			0.855876			0.427938	+	0.903808i	$0.359240\pi$
$492$	13.3235	−	3.51946i	0.600670	−	0.158670i
$493$	−10.9415			−0.492778
$494$	29.6412	−	11.0894i	1.33362	−	0.498937i
$495$	−0.518151	+	1.25093i	−0.0232891	+	0.0562250i
$496$	8.10253	+	3.94350i	0.363814	+	0.177068i
$497$	−30.2238	+	59.3175i	−1.35572	+	2.66075i
$498$	0.423439	−	12.1987i	0.0189747	−	0.546635i
$499$	−5.96539	−	24.8476i	−0.267047	−	1.11233i	−0.931134	−	0.364677i	$-0.881179\pi$
$499$	−5.96539	−	24.8476i	−0.267047	−	1.11233i	0.664087	−	0.747656i	$-0.268821\pi$
$500$	1.28494	−	1.53263i	0.0574641	−	0.0685411i
$501$	−11.1920	−	11.1920i	−0.500020	−	0.500020i
$502$	1.73915	−	15.2927i	0.0776223	−	0.682548i
$503$	14.2513	−	16.6861i	0.635433	−	0.743996i	−0.345484	−	0.938425i	$-0.612285\pi$
$503$	14.2513	−	16.6861i	0.635433	−	0.743996i	0.980917	+	0.194429i	$0.0622853\pi$
$504$	23.1729	−	13.3982i	1.03220	−	0.596803i
$505$	−2.70177	−	4.40888i	−0.120227	−	0.196193i
$506$	1.77931	+	2.63675i	0.0790999	+	0.117218i
$507$	−2.89861	−	3.39384i	−0.128732	−	0.150726i
$508$	−20.6739	−	12.4104i	−0.917256	−	0.550622i
$509$	−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	$-0.390195\pi$
$510$	−4.92561	−	2.24349i	−0.218110	−	0.0993433i
$511$	30.4508	+	18.6603i	1.34706	+	0.825481i
$512$	−1.81768	−	22.5543i	−0.0803308	−	0.996768i
$513$	−27.8111	−	4.40484i	−1.22789	−	0.194479i
$514$	7.09742	−	19.5127i	0.313054	−	0.860666i
$515$	5.08532	+	3.69470i	0.224086	+	0.162808i
$516$	−16.6524	+	8.67751i	−0.733080	+	0.382006i
$517$	2.42029	+	3.33124i	0.106444	+	0.146508i
$518$	66.8024	+	52.1693i	2.93513	+	2.29219i
$519$	−10.3453	+	4.28517i	−0.454109	+	0.188098i
$520$	10.7028	+	4.75718i	0.469350	+	0.208616i
$521$	−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	$0.602288\pi$
$522$	−7.01013	−	3.88386i	−0.306825	−	0.169992i
$523$	−4.71566	+	14.5133i	−0.206201	+	0.634623i	0.793461	+	0.608622i	$0.208277\pi$
$523$	−4.71566	+	14.5133i	−0.206201	+	0.634623i	−0.999662	+	0.0260010i	$0.991723\pi$
$524$	−25.1541	−	10.1507i	−1.09886	−	0.443436i
$525$	2.50985	+	4.92585i	0.109539	+	0.214982i
$526$	12.8663	+	27.5769i	0.560999	+	1.20241i
$527$	−7.79099	−	1.87045i	−0.339381	−	0.0814781i
$528$	−2.99062	+	1.03254i	−0.130150	+	0.0449357i
$529$	−4.21380	−	12.9687i	−0.183209	−	0.563858i
$530$	4.70764	+	0.914053i	0.204487	+	0.0397039i
$531$	−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
$536$	15.5812	−	3.32209i	0.673007	−	0.143492i
$537$	−26.9231	+	8.74784i	−1.16182	+	0.377497i
$538$	30.5613	+	8.46852i	1.31759	+	0.365104i
$539$	3.32796	−	13.8620i	0.143345	−	0.597077i
$540$	−6.20205	−	8.37429i	−0.266894	−	0.360372i
$541$	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	$0.323484\pi$
$542$	36.6882	+	24.2724i	1.57589	+	1.04259i
$543$	26.3496	+	8.56151i	1.13077	+	0.367409i
$544$	5.90238	+	19.2340i	0.253062	+	0.824652i
$545$	5.49956	+	0.432825i	0.235575	+	0.0185402i
$546$	−23.6734	+	22.0850i	−1.01313	+	0.945152i
$547$	6.31794	+	15.2528i	0.270135	+	0.652165i	0.999489	−	0.0319725i	$-0.0101789\pi$
$547$	6.31794	+	15.2528i	0.270135	+	0.652165i	−0.729353	+	0.684137i	$0.760179\pi$
$548$	−9.84063	+	19.7579i	−0.420371	+	0.844015i
$549$	−1.76465	+	1.28209i	−0.0753135	+	0.0547185i
$550$	0.286736	+	0.999179i	0.0122264	+	0.0426051i
$551$	−9.77194	+	13.4499i	−0.416299	+	0.572986i
$552$	−9.30048	+	0.493255i	−0.395855	+	0.0209943i
$553$	0.714561	−	4.51156i	0.0303862	−	0.191851i
$554$	1.20341	+	27.4312i	0.0511278	+	1.16544i
$555$	6.55911	−	10.7035i	0.278419	−	0.454338i
$556$	10.8435	+	2.49865i	0.459867	+	0.105967i
$557$	−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	$0.628089\pi$
$558$	−4.32769	−	3.96394i	−0.183206	−	0.167807i
$559$	−27.4736	+	23.4647i	−1.16201	+	0.992452i
$560$	7.51574	−	19.1266i	0.317598	−	0.808246i
$561$	2.39861	−	1.46987i	0.101269	−	0.0620579i
$562$	0.380684	−	0.0468227i	0.0160582	−	0.00197510i
$563$	14.0904	+	12.0343i	0.593839	+	0.507187i	0.894810	−	0.446447i	$-0.147311\pi$
$563$	14.0904	+	12.0343i	0.593839	+	0.507187i	−0.300971	+	0.953633i	$0.597311\pi$
$564$	−12.0098	+	1.05577i	−0.505706	+	0.0444561i
$565$	2.22312	−	2.22312i	0.0935276	−	0.0935276i
$566$	5.52739	+	6.94590i	0.232333	+	0.291958i
$567$	0.402823	−	0.0967091i	0.0169170	−	0.00406140i
$568$	−13.1561	−	34.2087i	−0.552016	−	1.43537i
$569$	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	$0.628224\pi$
$570$	−7.15695	+	4.05118i	−0.299772	+	0.169685i
$571$	−10.5236	−	4.35903i	−0.440400	−	0.182420i	0.151455	−	0.988464i	$-0.451604\pi$
$571$	−10.5236	−	4.35903i	−0.440400	−	0.182420i	−0.591855	+	0.806045i	$0.701604\pi$
$572$	−5.16122	+	3.22808i	−0.215801	+	0.134973i
$573$		−	2.73523i		−	0.114266i
$574$	−23.4614	−	40.1736i	−0.979261	−	1.67681i
$575$			3.06004i			0.127613i
$576$	−3.04584	+	14.4183i	−0.126910	+	0.600762i
$577$	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	$0.587478\pi$
$578$	3.03074	+	5.35420i	0.126062	+	0.222705i
$579$	−6.03139	−	3.07315i	−0.250656	−	0.127716i
$580$	−6.06792	+	1.01802i	−0.251957	+	0.0422712i
$581$	−40.0687	+	9.61963i	−1.66233	+	0.399090i
$582$	−15.1901	+	12.0880i	−0.629652	+	0.501062i
$583$	−1.76247	+	1.76247i	−0.0729940	+	0.0729940i
$584$	−18.8485	+	5.59601i	−0.779956	+	0.231565i
$585$	−5.80032	−	4.95394i	−0.239814	−	0.204820i
$586$	4.99526	+	40.6130i	0.206352	+	1.67771i
$587$	−23.0690	+	14.1367i	−0.952160	+	0.583484i	−0.909544	−	0.415607i	$-0.863569\pi$
$587$	−23.0690	+	14.1367i	−0.952160	+	0.583484i	−0.0426156	+	0.999092i	$0.513569\pi$
$588$	29.7833	+	29.2436i	1.22824	+	1.20599i
$589$	−9.25750	+	7.90666i	−0.381449	+	0.325788i
$590$	−1.36594	+	1.49129i	−0.0562349	+	0.0613953i
$591$	−2.53881	+	0.199808i	−0.104433	+	0.00821902i
$592$	−45.9478	+	8.14137i	−1.88844	+	0.334608i
$593$	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	$-0.0486428\pi$
$594$	5.41107	−	0.237384i	0.222019	−	0.00973997i
$595$	−2.85843	+	18.0474i	−0.117184	+	0.739872i
$596$	−10.8768	−	1.62091i	−0.445532	−	0.0663951i
$597$	11.7126	−	16.1209i	0.479363	−	0.659786i
$598$	−17.2250	+	4.94309i	−0.704385	+	0.202138i
$599$	−35.5173	+	25.8048i	−1.45120	+	1.05436i	−0.465648	+	0.884970i	$0.654179\pi$
$599$	−35.5173	+	25.8048i	−1.45120	+	1.05436i	−0.985550	+	0.169387i	$0.945821\pi$
$600$	−2.94039	−	0.785902i	−0.120041	−	0.0320843i
$601$	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	$0.785423\pi$
$602$	43.2436	+	46.3536i	1.76248	+	1.88923i
$603$	−10.3436	−	0.814063i	−0.421226	−	0.0331512i
$604$	−13.2339	−	4.16656i	−0.538479	−	0.169535i
$605$	9.94778	+	3.23223i	0.404435	+	0.131409i
$606$	−4.34184	+	6.56277i	−0.176375	+	0.266594i
$607$	−11.2252	+	5.71954i	−0.455618	+	0.232149i	−0.666710	−	0.745317i	$-0.732298\pi$
$607$	−11.2252	+	5.71954i	−0.455618	+	0.232149i	0.211092	+	0.977466i	$0.432298\pi$
$608$	28.9152	+	9.92256i	1.17266	+	0.402413i
$609$	3.97030	−	16.5375i	0.160885	−	0.670133i
$610$	−0.447182	+	1.61379i	−0.0181059	+	0.0653406i
$611$	−22.0620	+	7.16837i	−0.892532	+	0.290001i
$612$	−0.119811	−	13.1025i	−0.00484307	−	0.529636i
$613$	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	$0.662377\pi$
$618$	1.82327	−	9.39037i	0.0733427	−	0.377736i
$619$	6.95684	+	21.4110i	0.279619	+	0.860579i	0.987960	+	0.154709i	$0.0494439\pi$
$619$	6.95684	+	21.4110i	0.279619	+	0.860579i	−0.708341	+	0.705870i	$0.750556\pi$
$620$	−4.49477	−	0.312420i	−0.180514	−	0.0125471i
$621$	15.5036	+	3.72208i	0.622137	+	0.149362i
$622$	32.3124	−	15.0757i	1.29561	−	0.604482i
$623$	18.1409	+	35.6036i	0.726801	+	1.42643i
$624$	−0.325944	−	17.8210i	−0.0130482	−	0.713412i
$625$	−0.309017	+	0.951057i	−0.0123607	+	0.0380423i
$626$	18.1529	−	32.7648i	0.725535	−	1.30954i
$627$	0.335370	−	4.26128i	0.0133934	−	0.170179i
$628$	9.33323	+	6.65146i	0.372437	+	0.265422i
$629$	38.3327	−	15.8779i	1.52843	−	0.633095i
$630$	−8.23763	+	10.5482i	−0.328195	+	0.420251i
$631$	4.86810	+	6.70036i	0.193796	+	0.266737i	0.894846	−	0.446375i	$-0.147285\pi$
$631$	4.86810	+	6.70036i	0.193796	+	0.266737i	−0.701050	+	0.713112i	$0.747285\pi$
$632$	1.58380	+	1.95333i	0.0630004	+	0.0776995i
$633$	−5.93040	−	4.30869i	−0.235712	−	0.171255i
$634$	−42.3068	−	15.3884i	−1.68022	−	0.611152i
$635$	11.9080	+	1.88604i	0.472554	+	0.0748452i
$636$	−1.76847	−	7.08037i	−0.0701245	−	0.280755i
$637$	68.4776	+	41.9631i	2.71318	+	1.66264i
$638$	1.32554	−	2.91024i	0.0524787	−	0.115218i
$639$	1.87280	+	23.7962i	0.0740869	+	0.941363i
$640$	5.06293	+	10.1176i	0.200130	+	0.399935i
$641$	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	$0.506504\pi$
$642$	−2.62632	+	1.77227i	−0.103653	+	0.0699460i
$643$	−8.10073	−	13.2192i	−0.319462	−	0.521314i	0.652090	−	0.758142i	$-0.273892\pi$
$643$	−8.10073	−	13.2192i	−0.319462	−	0.521314i	−0.971552	+	0.236827i	$0.923892\pi$
$644$	9.98924	+	29.8133i	0.393631	+	1.17481i
$645$	6.09756	−	7.13932i	0.240091	−	0.281111i
$646$	−27.0077	−	3.07143i	−1.06260	−	0.120844i
$647$	−13.5357	−	13.5357i	−0.532144	−	0.532144i	0.389066	−	0.921210i	$-0.372798\pi$
$647$	−13.5357	−	13.5357i	−0.532144	−	0.532144i	−0.921210	+	0.389066i	$0.872798\pi$
$648$	−0.108701	+	0.200501i	−0.00427016	+	0.00787641i
$649$	−0.245375	−	1.02206i	−0.00963181	−	0.0401194i
$650$	−5.85269	−	0.203158i	−0.229562	−	0.00796852i
$651$	5.65420	−	11.0970i	0.221605	−	0.434925i
$652$	5.77804	−	5.02701i	0.226286	−	0.196873i
$653$	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	$-0.223320\pi$
$654$	−2.94167	−	7.86286i	−0.115028	−	0.307462i
$655$	13.5625			0.529931
$656$	25.0822	+	5.18476i	0.979297	+	0.202431i
$657$	12.8050			0.499570
$658$	14.2618	+	38.1208i	0.555985	+	1.48610i
$659$	−2.29654	+	5.54435i	−0.0894606	+	0.215977i	−0.962277	−	0.272072i	$-0.912291\pi$
$659$	−2.29654	+	5.54435i	−0.0894606	+	0.215977i	0.872816	+	0.488049i	$0.162291\pi$
$660$	1.19346	−	1.03833i	0.0464554	−	0.0404171i
$661$	−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	$0.905370\pi$
$662$	21.2709	+	0.738353i	0.826717	+	0.0286969i
$663$	3.69971	+	15.4104i	0.143685	+	0.598491i
$664$	10.8124	−	19.9438i	0.419603	−	0.773968i
$665$	19.6321	+	19.6321i	0.761301	+	0.761301i
$666$	30.1957	+	3.43399i	1.17006	+	0.133064i
$667$	6.11377	−	7.15831i	0.236726	−	0.277171i
$668$	−9.34601	−	27.8936i	−0.361608	−	1.07924i
$669$	13.7861	+	22.4968i	0.533001	+	0.869778i
$670$	−6.60296	+	4.45576i	−0.255095	+	0.172141i
$671$	−0.565269	−	0.661844i	−0.0218220	−	0.0255502i
$672$	−31.2131	+	1.94176i	−1.20407	+	0.0749049i
$673$	−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	$-0.190943\pi$
$674$	−0.992848	+	2.17981i	−0.0382431	+	0.0839631i
$675$	4.44262	+	2.72244i	0.170996	+	0.104787i
$676$	−2.01017	−	8.04806i	−0.0773144	−	0.309541i
$677$	−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	$0.710314\pi$
$678$	−4.49630	−	1.63546i	−0.172679	−	0.0628094i
$679$	53.0208	+	38.5219i	2.03475	+	1.47833i
$680$	−6.33563	−	7.81385i	−0.242960	−	0.299647i
$681$	−3.11429	−	4.28645i	−0.119340	−	0.164257i
$682$	1.44138	−	1.84567i	0.0551932	−	0.0706744i
$683$	−40.1385	+	16.6259i	−1.53586	+	0.636173i	−0.980691	−	0.195565i	$-0.937346\pi$
$683$	−40.1385	+	16.6259i	−1.53586	+	0.636173i	−0.555168	+	0.831738i	$0.687346\pi$
$684$	−16.2134	−	11.5547i	−0.619934	−	0.441805i
$685$	0.865909	−	11.0024i	0.0330847	−	0.420381i
$686$	43.6427	−	78.7723i	1.66629	−	3.00754i
$687$	−8.53870	+	26.2794i	−0.325772	+	1.00262i
$688$	−34.8944	+	0.638213i	−1.33034	+	0.0243316i
$689$	−6.37490	−	12.5114i	−0.242864	−	0.476648i
$690$	4.22006	−	1.96892i	0.160655	−	0.0749555i
$691$	17.8568	+	4.28704i	0.679305	+	0.163087i	0.558393	−	0.829577i	$-0.311418\pi$
$691$	17.8568	+	4.28704i	0.679305	+	0.163087i	0.120912	+	0.992663i	$0.461418\pi$
$692$	−20.7620	−	1.44311i	−0.789252	−	0.0548590i
$693$	−2.14959	−	6.61577i	−0.0816563	−	0.251312i
$694$	6.62214	−	34.1059i	0.251373	−	1.29464i
$695$	−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
$700$	0.0939534	+	10.2747i	0.00355111	+	0.388347i
$701$	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	$0.119900\pi$
$702$	−8.14822	+	29.4053i	−0.307535	+	1.10983i
$703$	14.7173	−	61.3018i	0.555072	−	2.31204i
$704$	−5.83099	−	0.760241i	−0.219764	−	0.0286526i
$705$	5.37106	−	2.73669i	0.202286	−	0.103070i
$706$	−14.7318	+	22.2674i	−0.554439	+	0.838046i
$707$	25.2654	+	8.20923i	0.950204	+	0.308740i
$708$	2.93550	+	0.924213i	0.110323	+	0.0347340i
$709$	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	$0.448449\pi$
$710$	12.5009	+	13.3999i	0.469149	+	0.502890i
$711$	−0.626748	−	1.51310i	−0.0235049	−	0.0567458i
$712$	−21.2528	−	5.68042i	−0.796483	−	0.212883i
$713$	5.57710	−	4.05200i	0.208864	−	0.151749i
$714$	26.7281	−	7.67020i	1.00028	−	0.287050i
$715$	1.78910	−	2.46248i	0.0669084	−	0.0920915i
$716$	−52.0398	−	7.75520i	−1.94482	−	0.289826i
$717$	3.93171	−	24.8238i	0.146832	−	0.927062i
$718$	38.4942	−	1.68874i	1.43659	−	0.0630232i
$719$	19.9666	−	32.5825i	0.744627	−	1.21512i	−0.225906	−	0.974149i	$-0.572534\pi$
$719$	19.9666	−	32.5825i	0.744627	−	1.21512i	0.970532	−	0.240971i	$-0.0774659\pi$
$720$	−1.28554	−	7.25523i	−0.0479091	−	0.270386i
$721$	−32.1942	+	2.53374i	−1.19897	+	0.0943613i
$722$	−9.74743	+	10.6419i	−0.362762	+	0.396051i
$723$	10.4420	−	8.91831i	0.388342	−	0.331675i
$724$	36.7430	+	36.0771i	1.36554	+	1.34080i
$725$	2.62303	−	1.60740i	0.0974169	−	0.0596972i
$726$	−1.94316	−	15.7986i	−0.0721176	−	0.586339i
$727$	21.6962	+	18.5303i	0.804669	+	0.687252i	0.953428	−	0.301621i	$-0.0975279\pi$
$727$	21.6962	+	18.5303i	0.804669	+	0.687252i	−0.148759	+	0.988873i	$0.547528\pi$
$728$	−57.6848	+	17.1263i	−2.13794	+	0.634742i
$729$	11.9989	−	11.9989i	0.444403	−	0.444403i
$730$	7.69241	−	6.12144i	0.284709	−	0.226565i
$731$	30.1743	−	7.24421i	1.11604	−	0.267937i
$732$	2.51329	−	0.421659i	0.0928940	−	0.0155850i
$733$	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	$0.401400\pi$
$734$	−14.8127	−	26.1686i	−0.546747	−	0.965902i
$735$	−19.2814	−	7.98662i	−0.711205	−	0.294591i
$736$	−15.8817	−	6.88587i	−0.585407	−	0.253816i
$737$		−	4.14022i		−	0.152507i
$738$	−14.6986	−	7.88626i	−0.541062	−	0.290297i
$739$		−	5.20203i		−	0.191360i	−0.995412	−	0.0956800i	$-0.969497\pi$
$739$		−	5.20203i		−	0.191360i	0.995412	−	0.0956800i	$-0.0305025\pi$
$740$	19.7813	−	12.3722i	0.727174	−	0.454811i
$741$	22.2477	+	9.21531i	0.817290	+	0.338533i
$742$	−21.4408	+	12.1365i	−0.787118	+	0.445547i
$743$	20.6073	+	10.4999i	0.756007	+	0.385205i	0.789114	−	0.614247i	$-0.210540\pi$
$743$	20.6073	+	10.4999i	0.756007	+	0.385205i	−0.0331066	+	0.999452i	$0.510540\pi$
$744$	2.46121	+	6.39969i	0.0902323	+	0.234624i
$745$	5.34654	−	1.28359i	0.195882	−	0.0470271i
$746$	−14.5626	−	18.2999i	−0.533176	−	0.670007i
$747$	−10.4473	+	10.4473i	−0.382247	+	0.382247i
$748$	5.20845	−	0.457870i	0.190440	−	0.0167414i
$749$	8.13354	+	6.94670i	0.297193	+	0.253827i
$750$	1.51042	−	0.185776i	0.0551527	−	0.00678358i
$751$	−9.59374	+	5.87905i	−0.350081	+	0.214530i	−0.686410	−	0.727215i	$-0.740814\pi$
$751$	−9.59374	+	5.87905i	−0.350081	+	0.214530i	0.336329	+	0.941744i	$0.390814\pi$
$752$	−20.8553	−	8.19502i	−0.760514	−	0.298842i
$753$	8.90531	−	7.60585i	0.324527	−	0.277173i
$754$	13.2852	+	12.1686i	0.483819	+	0.443153i
$755$	6.91576	−	0.544282i	0.251690	−	0.0198085i
$756$	52.1707	+	12.0216i	1.89743	+	0.437222i
$757$	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	$0.0958455\pi$
$758$	−1.30139	−	29.6647i	−0.0472686	−	1.07747i
$759$	−0.378631	+	2.39058i	−0.0137434	+	0.0867725i
$760$	−15.2637	+	0.809516i	−0.553673	+	0.0293642i
$761$	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	$-0.119687\pi$
$762$	−5.06093	−	17.6357i	−0.183338	−	0.638873i
$763$	−22.9289	+	16.6588i	−0.830083	+	0.603090i
$764$	2.26644	−	4.55053i	0.0819970	−	0.164632i
$765$	2.50715	+	6.05280i	0.0906463	+	0.218840i
$766$	−3.94273	+	3.67819i	−0.142457	+	0.132898i
$767$	5.90329	+	0.464599i	0.213155	+	0.0167757i
$768$	10.6955	−	13.4922i	0.385939	−	0.486858i
$769$	−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	$0.766576\pi$
$770$	−4.45402	−	2.94671i	−0.160512	−	0.106192i
$771$	14.0769	−	7.17253i	0.506967	−	0.258312i
$772$	−7.48782	−	10.1104i	−0.269493	−	0.363881i
$773$	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	$0.0554155\pi$
$774$	21.9040	+	6.06959i	0.787322	+	0.218167i
$775$	2.14255	−	0.696155i	0.0769625	−	0.0250066i
$776$	−35.2877	+	7.52372i	−1.26675	+	0.270086i
$777$	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
$782$	15.1093	+	2.93368i	0.540307	+	0.104908i
$783$	−4.95328	−	15.2446i	−0.177016	−	0.544799i
$784$	25.3182	+	73.3306i	0.904223	+	2.61895i
$785$	−5.57209	−	1.33774i	−0.198877	−	0.0477460i
$786$	−8.72651	−	18.7039i	−0.311264	−	0.667145i
$787$	−14.6383	−	28.7293i	−0.521799	−	1.02409i	−0.990080	−	0.140508i	$-0.955126\pi$
$787$	−14.6383	−	28.7293i	−0.521799	−	1.02409i	0.468281	−	0.883580i	$-0.344874\pi$
$788$	−4.38931	−	1.77127i	−0.156363	−	0.0630988i
$789$	−7.15522	+	22.0215i	−0.254732	+	0.783986i
$790$	−1.09985	−	0.609357i	−0.0391309	−	0.0216800i
$791$	−1.26730	+	16.1026i	−0.0450600	+	0.572542i
$792$	3.49955	+	1.55548i	0.124351	+	0.0552715i
$793$	4.53018	−	1.87646i	0.160871	−	0.0666351i
$794$	40.2293	+	31.4170i	1.42768	+	1.11495i
$795$	2.14479	+	2.95206i	0.0760680	+	0.104699i
$796$	32.8439	−	17.1149i	1.16412	−	0.606620i
$797$	−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	$0.712988\pi$
$798$	14.4425	−	39.7063i	0.511259	−	1.40559i
$799$	19.6786	+	3.11678i	0.696178	+	0.110264i
$800$	−4.24064	−	3.74392i	−0.149929	−	0.132368i
$801$	12.2159	+	7.48590i	0.431627	+	0.264501i
$802$	0.404220	+	0.184112i	0.0142735	+	0.00650121i
$803$	0.400896	+	5.09386i	0.0141473	+	0.179758i
$804$	10.3934	+	6.23909i	0.366547	+	0.220036i
$805$	−10.2101	−	11.9545i	−0.359858	−	0.421340i
$806$	7.37967	+	10.9359i	0.259938	+	0.385200i
$807$	12.6081	+	20.5745i	0.443825	+	0.724257i
$808$	−12.6614	+	7.32063i	−0.445426	+	0.257539i
$809$	−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	$0.328010\pi$
$810$	0.0128855	−	0.113305i	0.000452752	−	0.00398114i
$811$	18.9029	+	18.9029i	0.663771	+	0.663771i	0.956267	−	0.292496i	$-0.0944857\pi$
$811$	18.9029	+	18.9029i	0.663771	+	0.663771i	−0.292496	+	0.956267i	$0.594486\pi$
$812$	20.3084	−	24.2232i	0.712686	−	0.850066i
$813$	7.81399	+	32.5476i	0.274049	+	1.14149i
$814$	−0.420689	+	12.1195i	−0.0147452	+	0.424787i
$815$	−1.73850	+	3.41200i	−0.0608971	+	0.119517i
$816$	−6.69944	+	13.7650i	−0.234527	+	0.481873i
$817$	18.0440	−	43.5621i	0.631280	−	1.52404i
$818$	−33.0150	+	12.3517i	−1.15434	+	0.431866i
$819$	39.1889			1.36937
$820$	−12.6000	+	2.28912i	−0.440011	+	0.0799394i
$821$	−40.1741			−1.40209			−0.701044	−	0.713118i	$-0.747282\pi$
$821$	−40.1741			−1.40209			−0.701044	+	0.713118i	$0.747282\pi$
$822$	−15.7304	+	5.88511i	−0.548662	+	0.205267i
$823$	4.39793	−	10.6176i	0.153302	−	0.370105i	−0.828506	−	0.559981i	$-0.810809\pi$
$823$	4.39793	−	10.6176i	0.153302	−	0.370105i	0.981808	+	0.189876i	$0.0608086\pi$
$824$	10.8143	−	14.1117i	0.376734	−	0.491606i
$825$	−0.359089	+	0.704753i	−0.0125019	+	0.0245363i
$826$	0.360430	−	10.3835i	0.0125410	−	0.361288i
$827$	−1.82040	−	7.58252i	−0.0633015	−	0.263670i	0.931741	−	0.363125i	$-0.118290\pi$
$827$	−1.82040	−	7.58252i	−0.0633015	−	0.263670i	−0.995042	+	0.0994548i	$0.968290\pi$
$828$	8.63907	+	7.24290i	0.300229	+	0.251708i
$829$	−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	$0.786651\pi$
$830$	−1.28172	+	11.2704i	−0.0444892	+	0.391202i
$831$	−13.5686	+	15.8868i	−0.470689	+	0.551106i
$832$	14.2244	−	29.9185i	0.493144	−	1.03724i
$833$	−36.0415	−	58.8144i	−1.24876	−	2.03780i
$834$	4.73617	+	7.01851i	0.164000	+	0.243031i
$835$	9.55263	+	11.1847i	0.330582	+	0.387062i
$836$	4.08889	−	6.81149i	0.141417	−	0.235580i
$837$	−0.920959	−	11.7019i	−0.0318330	−	0.404476i
$838$	6.55026	+	2.98348i	0.226275	+	0.103062i
$839$	6.83532	+	4.18869i	0.235981	+	0.144610i	0.635462	−	0.772132i	$-0.280810\pi$
$839$	6.83532	+	4.18869i	0.235981	+	0.144610i	−0.399481	+	0.916742i	$0.630810\pi$
$840$	14.1092	−	6.74061i	0.486815	−	0.232573i
$841$	19.2955	+	3.05610i	0.665361	+	0.105383i
$842$	−7.91106	+	21.7496i	−0.272633	+	0.749540i
$843$	0.236108	+	0.171543i	0.00813199	+	0.00590824i
$844$	−6.29603	−	12.0823i	−0.216718	−	0.415888i
$845$	2.43793	+	3.35552i	0.0838673	+	0.115433i
$846$	11.5016	+	8.98216i	0.395433	+	0.308813i
$847$	−49.6469	+	20.5644i	−1.70589	+	0.706602i
$848$	2.92471	−	13.2448i	0.100435	−	0.454829i
$849$	−0.529941	+	6.73354i	−0.0181875	+	0.231095i
$850$	4.39969	+	2.43759i	0.150908	+	0.0836086i
$851$	−11.0313	+	33.9508i	−0.378148	+	1.16382i
$852$	10.4362	−	25.8617i	0.357540	−	0.886006i
$853$	−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	$-0.378787\pi$
$854$	−3.63758	−	7.79657i	−0.124475	−	0.266793i
$855$	9.67966	+	2.32388i	0.331037	+	0.0794750i
$856$	−5.83787	+	0.772287i	−0.199534	+	0.0263962i
$857$	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	$0.572575\pi$
$858$	−4.54713	−	0.882888i	−0.155236	−	0.0301413i
$859$	−20.6845	+	3.27610i	−0.705745	+	0.111779i	−0.498982	−	0.866612i	$-0.666293\pi$
$859$	−20.6845	+	3.27610i	−0.705745	+	0.111779i	−0.206762	+	0.978391i	$0.566293\pi$
$860$	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	$0.330780\pi$
$863$	8.55394	+	54.0075i	0.291180	+	1.83844i	−0.215750	+	0.976449i	$0.569220\pi$
$864$	−24.1265	+	16.9311i	−0.820802	+	0.576008i
$865$	9.89673	−	3.21564i	0.336499	−	0.109335i
$866$	3.21715	+	0.891472i	0.109323	+	0.0302934i
$867$	−1.09286	+	4.55207i	−0.0371153	+	0.154596i
$868$	18.6018	−	13.7766i	0.631387	−	0.467610i
$869$	0.582295	−	0.296694i	0.0197530	−	0.0100647i
$870$	−3.90447	−	2.58314i	−0.132374	−	0.0875767i
$871$	22.1830	+	7.20768i	0.751641	+	0.244223i
$872$	1.62127	−	15.5187i	0.0549030	−	0.525531i
$873$	23.4258	+	1.84365i	0.792843	+	0.0623981i
$874$	17.1005	−	15.9532i	0.578435	−	0.539625i
$875$	−1.96606	−	4.74649i	−0.0664650	−	0.160461i
$876$	−13.3915	−	6.66979i	−0.452457	−	0.225351i
$877$	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	$0.0860482\pi$
$878$	−8.42513	−	29.3588i	−0.284334	−	0.990811i
$879$	−18.3009	+	25.1890i	−0.617274	+	0.849605i
$880$	2.84591	−	0.738536i	0.0959355	−	0.0248960i
$881$	−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	$0.937907\pi$
$882$	−2.21436	−	50.4756i	−0.0745615	−	1.69960i
$883$	23.3271	−	38.0663i	0.785018	−	1.28103i	−0.170282	−	0.985395i	$-0.554468\pi$
$883$	23.3271	−	38.0663i	0.785018	−	1.28103i	0.955300	−	0.295638i	$-0.0955321\pi$
$884$	−6.61412	+	28.7035i	−0.222457	+	0.965405i
$885$	−1.53403	+	0.120731i	−0.0515659	+	0.00405833i
$886$	10.0946	+	9.24613i	0.339135	+	0.310630i
$887$	−3.40630	+	2.90925i	−0.114372	+	0.0976832i	−0.704795	−	0.709411i	$-0.748961\pi$
$887$	−3.40630	+	2.90925i	−0.114372	+	0.0976832i	0.590423	+	0.807094i	$0.298961\pi$
$888$	−29.7902	−	19.3195i	−0.999692	−	0.648318i
$889$	−52.8131	+	32.3639i	−1.77129	+	1.08545i
$890$	10.9172	−	1.34277i	0.365944	−	0.0450098i
$891$	0.0450695	+	0.0384930i	0.00150989	+	0.00128956i
$892$	4.29443	+	48.8507i	0.143788	+	1.63564i
$893$	21.4065	−	21.4065i	0.716341	−	0.716341i
$894$	−5.21030	−	6.54744i	−0.174259	−	0.218979i
$895$	25.5804	−	6.14130i	0.855057	−	0.205281i
$896$	−53.5374	−	22.6331i	−1.78856	−	0.756117i
$897$	−12.1494	−	6.19041i	−0.405656	−	0.206692i
$898$	4.36853	−	2.47280i	0.145780	−	0.0825183i
$899$	−6.40290	−	2.65217i	−0.213549	−	0.0884547i
$900$	1.95359	+	3.12350i	0.0651197	+	0.104117i
$901$			12.0604i			0.401790i
$902$	2.67700	−	6.09404i	0.0891343	−	0.202909i
$903$			48.2357i			1.60518i
$904$	−6.12523	−	6.44656i	−0.203722	−	0.214409i
$905$	−23.7870	−	9.85291i	−0.790707	−	0.327522i
$906$	−5.20041	−	9.18723i	−0.172772	−	0.305225i
$907$	−20.2627	−	10.3244i	−0.672813	−	0.342815i	0.0839823	−	0.996467i	$-0.473236\pi$
$907$	−20.2627	−	10.3244i	−0.672813	−	0.342815i	−0.756795	+	0.653652i	$0.773236\pi$
$908$	−1.62936	−	9.71178i	−0.0540722	−	0.322297i
$909$	9.26186	−	2.22358i	0.307196	−	0.0737513i
$910$	23.5422	−	18.7343i	0.780416	−	0.621037i
$911$	32.7273	−	32.7273i	1.08430	−	1.08430i	0.0882019	−	0.996103i	$-0.471888\pi$
$911$	32.7273	−	32.7273i	1.08430	−	1.08430i	0.996103	−	0.0882019i	$-0.0281121\pi$
$912$	10.9375	+	20.5291i	0.362177	+	0.679786i
$913$	−4.48306	−	3.82889i	−0.148368	−	0.126718i
$914$	1.89678	+	15.4215i	0.0627401	+	0.510097i
$915$	−1.08644	+	0.665772i	−0.0359167	+	0.0220098i
$916$	−35.9810	+	36.6452i	−1.18885	+	1.21079i
$917$	−52.9838	+	45.2524i	−1.74968	+	1.49437i
$918$	17.7015	−	19.3259i	0.584237	−	0.637850i
$919$	18.1056	−	1.42494i	0.597249	−	0.0470045i	0.223768	−	0.974642i	$-0.428164\pi$
$919$	18.1056	−	1.42494i	0.597249	−	0.0470045i	0.373481	+	0.927638i	$0.378164\pi$
$920$	8.65228	+	0.221149i	0.285257	+	0.00729107i
$921$	−5.50078	+	8.97646i	−0.181257	+	0.295784i
$922$	−16.4709	+	0.722578i	−0.542440	+	0.0237968i
$923$	8.39420	−	52.9989i	0.276298	−	1.74448i
$924$	−1.19793	+	8.03847i	−0.0394090	+	0.264446i
$925$	−6.85702	+	9.43788i	−0.225458	+	0.310316i
$926$	−45.6305	+	13.0946i	−1.49951	+	0.430317i
$927$	−9.36747	+	6.80586i	−0.307668	+	0.223534i
$928$	2.43994	+	17.2306i	0.0800950	+	0.565623i
$929$	−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	$0.892936\pi$
$930$	−2.33863	−	2.50683i	−0.0766868	−	0.0822022i
$931$	−104.487	−	8.22334i	−3.42444	−	0.269509i
$932$	11.3230	−	35.9642i	0.370896	−	1.17805i
$933$	25.8030	+	8.38391i	0.844753	+	0.274477i
$934$	−0.503732	+	0.761402i	−0.0164826	+	0.0249138i
$935$	−2.32933	+	1.18685i	−0.0761773	+	0.0388143i
$936$	−14.4265	+	16.0424i	−0.471544	+	0.524362i
$937$	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	$-0.0114902\pi$
$938$	10.9284	−	39.4383i	0.356824	−	1.28771i
$939$	27.1064	−	8.80741i	0.884585	−	0.287419i
$940$	11.2033	−	0.102445i	0.365413	−	0.00334139i
$941$	−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
$946$	−1.72874	+	8.90349i	−0.0562061	+	0.289478i
$947$	6.33673	+	19.5024i	0.205916	+	0.633744i	0.999675	+	0.0255114i	$0.00812140\pi$
$947$	6.33673	+	19.5024i	0.205916	+	0.633744i	−0.793758	+	0.608233i	$0.791879\pi$
$948$	−0.132681	+	1.90887i	−0.00430927	+	0.0619971i
$949$	−27.9904	−	6.71990i	−0.908607	−	0.218137i
$950$	6.92585	−	3.23134i	0.224704	−	0.104838i
$951$	−15.5513	−	30.5211i	−0.504285	−	0.989715i
$952$	50.8225	+	9.38650i	1.64717	+	0.304218i
$953$	−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	$0.849855\pi$
$954$	−4.28105	+	7.72702i	−0.138604	+	0.250172i
$955$	−0.199432	+	2.53402i	−0.00645346	+	0.0819989i
$956$	27.1104	−	38.0409i	0.876812	−	1.23033i
$957$	2.24806	−	0.931179i	0.0726696	−	0.0301007i
$958$	21.1614	−	27.0970i	0.683694	−	0.875464i
$959$	33.3277	+	45.8716i	1.07621	+	1.48127i
$960$	−2.43464	+	8.25716i	−0.0785778	+	0.266499i
$961$	20.9737	+	15.2383i	0.676570	+	0.491557i
$962$	−64.2027	−	23.3527i	−2.06998	−	0.752921i
$963$	3.78792	+	0.599947i	0.122064	+	0.0193330i
$964$	24.7619	−	6.18481i	0.797527	−	0.199199i
$965$	5.36363	+	3.28684i	0.172661	+	0.105807i
$966$	−9.91678	+	21.7724i	−0.319067	+	0.700517i
$967$	−1.65818	−	21.0692i	−0.0533235	−	0.677540i	−0.964254	−	0.264980i	$-0.914635\pi$
$967$	−1.65818	−	21.0692i	−0.0533235	−	0.677540i	0.910930	−	0.412560i	$-0.135365\pi$
$968$	9.85806	−	27.8938i	0.316850	−	0.896540i
$969$	−13.4323	−	15.7272i	−0.431507	−	0.505230i
$970$	14.9541	−	10.0912i	0.480147	−	0.324009i
$971$	−14.8192	−	24.1828i	−0.475571	−	0.776062i	0.521443	−	0.853286i	$-0.325394\pi$
$971$	−14.8192	−	24.1828i	−0.475571	−	0.776062i	−0.997014	+	0.0772247i	$0.975394\pi$
$972$	29.4783	−	9.87699i	0.945518	−	0.316805i
$973$	18.5642	−	21.7358i	0.595140	−	0.696819i
$974$	48.9111	+	5.56238i	1.56721	+	0.178230i
$975$	−3.15087	−	3.15087i	−0.100909	−	0.100909i
$976$	4.53069	+	1.38104i	0.145024	+	0.0442060i
$977$	−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	$-0.244634\pi$
$978$	5.82405	+	0.202164i	0.186233	+	0.00646448i
$979$	−2.59546	+	5.09388i	−0.0829513	+	0.162801i
$980$	−25.4602	−	29.2639i	−0.813296	−	0.934802i
$981$	−3.88877	+	9.38832i	−0.124159	+	0.299746i
$982$	9.39798	+	25.1201i	0.299901	+	0.801613i
$983$	−43.7923			−1.39676			−0.698379	−	0.715728i	$-0.746095\pi$
$983$	−43.7923			−1.39676			−0.698379	+	0.715728i	$0.746095\pi$
$984$	11.2641	+	15.9036i	0.359086	+	0.506988i
$985$	2.36661			0.0754066
$986$	−5.42198	−	14.4925i	−0.172671	−	0.461536i
$987$	−11.8516	+	28.6122i	−0.377240	+	0.910737i
$988$	29.3771	+	33.7660i	0.934609	+	1.07424i
$989$	−12.1211	+	23.7890i	−0.385429	+	0.756447i
$990$	−1.91368	−	0.0664276i	−0.0608208	−	0.00211121i
$991$	7.88333	+	32.8364i	0.250422	+	1.04308i	0.945880	+	0.324517i	$0.105202\pi$
$991$	7.88333	+	32.8364i	0.250422	+	1.04308i	−0.695458	+	0.718567i	$0.744798\pi$
$992$	−1.20821	+	12.6864i	−0.0383606	+	0.402793i
$993$	11.4514	+	11.4514i	0.363401	+	0.363401i
$994$	−93.5463	−	10.6385i	−2.96711	−	0.337432i
$995$	−12.0264	+	14.0811i	−0.381261	+	0.446400i
$996$	16.3676	−	5.48412i	0.518627	−	0.173771i
$997$	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	$0.793541\pi$
$998$	29.9558	−	20.2146i	0.948236	−	0.639881i
$999$	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.11.27	yes	672
4.3	odd	2	inner	820.2.bw.b.11.22	✓	672
41.15	odd	40	inner	820.2.bw.b.671.22	yes	672
164.15	even	40	inner	820.2.bw.b.671.27	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bw.b.11.22	✓	672	4.3	odd	2	inner
820.2.bw.b.11.27	yes	672	1.1	even	1	trivial
820.2.bw.b.671.22	yes	672	41.15	odd	40	inner
820.2.bw.b.671.27	yes	672	164.15	even	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+(0.495544 + 1.32455i) q^{2} +(-0.411797 + 0.994165i) q^{3} +(-1.50887 + 1.31275i) q^{4} +(0.453990 - 0.891007i) q^{5} +(-1.52089 - 0.0527928i) q^{6} +(1.19934 + 4.99561i) q^{7} +(-2.48651 - 1.34805i) q^{8} +(1.30253 + 1.30253i) q^{9} +(1.40516 + 0.159800i) q^{10} +(-0.477372 + 0.558931i) q^{11} +(-0.683740 - 2.04065i) q^{12} +(-2.16365 - 3.53076i) q^{13} +(-6.02262 + 4.06414i) q^{14} +(0.698856 + 0.818255i) q^{15} +(0.553387 - 3.96154i) q^{16} +(0.279049 + 3.54566i) q^{17} +(-1.07981 + 2.37073i) q^{18} +(4.60777 + 2.82364i) q^{19} +(0.484653 + 1.94039i) q^{20} +(-5.46035 - 0.864834i) q^{21} +(-0.976892 - 0.355329i) q^{22} +(-2.47563 - 1.79865i) q^{23} +(2.36412 - 1.91688i) q^{24} +(-0.587785 - 0.809017i) q^{25} +(3.60449 - 4.61552i) q^{26} +(-4.81381 + 1.99394i) q^{27} +(-8.36763 - 5.96331i) q^{28} +(-0.241369 + 3.06688i) q^{29} +(-0.737506 + 1.33115i) q^{30} +(-0.696155 + 2.14255i) q^{31} +(5.52148 - 1.23013i) q^{32} +(-0.359089 - 0.704753i) q^{33} +(-4.55812 + 2.12665i) q^{34} +(4.99561 + 1.19934i) q^{35} +(-3.67525 - 0.255458i) q^{36} +(-3.60495 - 11.0949i) q^{37} +(-1.45671 + 7.50246i) 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} +(-0.0134421 - 1.47002i) q^{44} +(1.75190 - 0.569228i) q^{45} +(1.15562 - 4.17040i) q^{46} +(1.30774 - 5.44713i) q^{47} +(3.71054 + 2.18150i) q^{48} +(-17.2807 + 8.80495i) q^{49} +(0.780311 - 1.17946i) q^{50} +(-3.63988 - 1.18267i) q^{51} +(7.89967 + 2.48713i) q^{52} +(3.38052 + 0.266052i) q^{53} +(-5.02653 - 5.38804i) q^{54} +(0.281289 + 0.679091i) q^{55} +(3.75217 - 14.0384i) q^{56} +(-4.70463 + 3.41811i) q^{57} +(-4.18185 + 1.20007i) q^{58} +(-0.840526 + 1.15688i) q^{59} +(-2.12865 - 0.317220i) q^{60} +(-0.185238 + 1.16955i) q^{61} +(-3.18289 + 0.139633i) q^{62} +(-4.94477 + 8.06913i) q^{63} +(4.36551 + 6.70391i) q^{64} +(-4.12821 + 0.324897i) q^{65} +(0.755536 - 0.824868i) q^{66} +(-4.28308 + 3.65810i) q^{67} +(-5.07560 - 4.98362i) q^{68} +(2.80761 - 1.72050i) q^{69} +(0.886960 + 7.21127i) q^{70} +(9.85349 + 8.41568i) q^{71} +(-1.48288 - 4.99465i) q^{72} +(4.91542 - 4.91542i) q^{73} +(12.9093 - 10.2730i) q^{74} +(1.04634 - 0.251205i) q^{75} +(-10.6593 + 1.78832i) q^{76} +(-3.36474 - 1.71442i) q^{77} +(3.10427 + 5.48411i) q^{78} +(-0.821419 - 0.340243i) q^{79} +(-3.27852 - 2.29157i) q^{80} -0.0806352i q^{81} +(-8.66958 + 2.61502i) q^{82} +8.02077i q^{83} +(9.37427 - 5.86314i) q^{84} +(3.28589 + 1.36106i) q^{85} +(10.7381 - 6.07830i) q^{86} +(-2.94959 - 1.50289i) q^{87} +(1.94046 - 0.746267i) q^{88} +(7.56287 - 1.81568i) q^{89} +(1.62212 + 2.03841i) q^{90} +(15.0434 - 15.0434i) q^{91} +(6.09657 - 0.535944i) q^{92} +(-1.84337 - 1.57439i) q^{93} +(7.86304 - 0.967125i) q^{94} +(4.60777 - 2.82364i) q^{95} +(-1.05078 + 5.99583i) q^{96} +(9.70012 - 8.28469i) q^{97} +(-20.2260 - 18.5259i) 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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