LMFDB - Embedded newform 603.2.e.a.202.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(202,603)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("603.202");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$33$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			202.8
Character	$\chi$	$=$	603.202
Dual form			603.2.e.a.403.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.884275 - 1.53161i) q^{2} +(-1.71455 + 0.245593i) q^{3} +(-0.563885 + 0.976678i) q^{4} +(-1.96647 + 3.40603i) q^{5} +(1.89229 + 2.40885i) q^{6} +(1.94697 + 3.37225i) q^{7} -1.54258 q^{8} +(2.87937 - 0.842165i) q^{9} +O(q^{10})$	\(q+(-0.884275 - 1.53161i) q^{2} +(-1.71455 + 0.245593i) q^{3} +(-0.563885 + 0.976678i) q^{4} +(-1.96647 + 3.40603i) q^{5} +(1.89229 + 2.40885i) q^{6} +(1.94697 + 3.37225i) q^{7} -1.54258 q^{8} +(2.87937 - 0.842165i) q^{9} +6.95560 q^{10} +(-1.70863 - 2.95943i) q^{11} +(0.726944 - 1.81305i) q^{12} +(-0.794579 + 1.37625i) q^{13} +(3.44331 - 5.96399i) q^{14} +(2.53512 - 6.32276i) q^{15} +(2.49184 + 4.31599i) q^{16} +1.12257 q^{17} +(-3.83602 - 3.66536i) q^{18} -5.52036 q^{19} +(-2.21773 - 3.84121i) q^{20} +(-4.16638 - 5.30373i) q^{21} +(-3.02179 + 5.23390i) q^{22} +(1.31436 - 2.27653i) q^{23} +(2.64484 - 0.378848i) q^{24} +(-5.23401 - 9.06557i) q^{25} +2.81051 q^{26} +(-4.72999 + 2.15109i) q^{27} -4.39146 q^{28} +(-4.22156 - 7.31196i) q^{29} +(-11.9257 + 1.70825i) q^{30} +(-0.536361 + 0.929005i) q^{31} +(2.86436 - 4.96121i) q^{32} +(3.65634 + 4.65446i) q^{33} +(-0.992662 - 1.71934i) q^{34} -15.3146 q^{35} +(-0.801109 + 3.28710i) q^{36} +11.7465 q^{37} +(4.88151 + 8.45503i) q^{38} +(1.02435 - 2.55480i) q^{39} +(3.03344 - 5.25408i) q^{40} +(-3.90184 + 6.75819i) q^{41} +(-4.43901 + 11.0712i) q^{42} +(-3.29435 - 5.70598i) q^{43} +3.85388 q^{44} +(-2.79376 + 11.4633i) q^{45} -4.64901 q^{46} +(0.625222 + 1.08292i) q^{47} +(-5.33236 - 6.78800i) q^{48} +(-4.08137 + 7.06913i) q^{49} +(-9.25661 + 16.0329i) q^{50} +(-1.92471 + 0.275696i) q^{51} +(-0.896103 - 1.55210i) q^{52} +2.26591 q^{53} +(7.47724 + 5.34235i) q^{54} +13.4399 q^{55} +(-3.00336 - 5.20197i) q^{56} +(9.46493 - 1.35576i) q^{57} +(-7.46604 + 12.9316i) q^{58} +(-1.66041 + 2.87592i) q^{59} +(4.74578 + 6.04130i) q^{60} +(-7.40341 - 12.8231i) q^{61} +1.89716 q^{62} +(8.44602 + 8.07027i) q^{63} -0.164172 q^{64} +(-3.12503 - 5.41271i) q^{65} +(3.89561 - 9.71592i) q^{66} +(-0.500000 + 0.866025i) q^{67} +(-0.633001 + 1.09639i) q^{68} +(-1.69443 + 4.22603i) q^{69} +(13.5423 + 23.4560i) q^{70} -5.84966 q^{71} +(-4.44166 + 1.29911i) q^{72} -7.21343 q^{73} +(-10.3871 - 17.9910i) q^{74} +(11.2004 + 14.2579i) q^{75} +(3.11285 - 5.39161i) q^{76} +(6.65328 - 11.5238i) q^{77} +(-4.81876 + 0.690242i) q^{78} +(-2.76106 - 4.78229i) q^{79} -19.6005 q^{80} +(7.58152 - 4.84980i) q^{81} +13.8012 q^{82} +(-5.82339 - 10.0864i) q^{83} +(7.52939 - 1.07851i) q^{84} +(-2.20750 + 3.82351i) q^{85} +(-5.82622 + 10.0913i) q^{86} +(9.03385 + 11.4999i) q^{87} +(2.63570 + 4.56516i) q^{88} +4.10251 q^{89} +(20.0277 - 5.85776i) q^{90} -6.18808 q^{91} +(1.48229 + 2.56741i) q^{92} +(0.691461 - 1.72455i) q^{93} +(1.10574 - 1.91519i) q^{94} +(10.8556 - 18.8025i) q^{95} +(-3.69265 + 9.20972i) q^{96} +(-3.99963 - 6.92756i) q^{97} +14.4362 q^{98} +(-7.41209 - 7.08234i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 7 q^{2} - 33 q^{4} - 18 q^{5} - 3 q^{6} + 36 q^{8} + 4 q^{9}+O(q^{10}) $ 66 * q - 7 * q^2 - 33 * q^4 - 18 * q^5 - 3 * q^6 + 36 * q^8 + 4 * q^9	\( 66 q - 7 q^{2} - 33 q^{4} - 18 q^{5} - 3 q^{6} + 36 q^{8} + 4 q^{9} - 8 q^{11} + q^{12} - 7 q^{14} + 3 q^{15} - 33 q^{16} + 66 q^{17} - 11 q^{18} - 29 q^{20} + q^{21} - 17 q^{23} + 47 q^{24} - 33 q^{25} + 60 q^{26} - 21 q^{27} - 54 q^{28} - 39 q^{29} - 34 q^{30} - 53 q^{32} + 8 q^{33} - 6 q^{34} + 62 q^{35} - 35 q^{36} + 24 q^{37} - 30 q^{38} - 5 q^{39} - 6 q^{40} - 38 q^{41} + 65 q^{42} + 22 q^{44} - 9 q^{45} + 12 q^{46} - 58 q^{47} - 59 q^{48} - 33 q^{49} - 31 q^{50} + 26 q^{51} + 9 q^{52} + 128 q^{53} - 22 q^{54} - 36 q^{55} - 32 q^{56} - 34 q^{57} + 3 q^{58} - 39 q^{59} + 127 q^{60} + 138 q^{62} - 35 q^{63} + 132 q^{64} - 28 q^{65} - 94 q^{66} - 33 q^{67} - 62 q^{68} + 60 q^{69} - 6 q^{70} + 42 q^{71} - 34 q^{72} - 25 q^{74} + 55 q^{75} - 6 q^{76} - 91 q^{77} + 125 q^{78} + 116 q^{80} - 90 q^{82} - 61 q^{83} - 26 q^{84} + 15 q^{85} - 47 q^{86} - q^{87} - 12 q^{88} + 110 q^{89} - 91 q^{90} + 36 q^{91} - 41 q^{92} - 11 q^{93} - 21 q^{94} - 6 q^{95} + 80 q^{96} - 12 q^{97} + 80 q^{98} - 38 q^{99}+O(q^{100}) \) 66 * q - 7 * q^2 - 33 * q^4 - 18 * q^5 - 3 * q^6 + 36 * q^8 + 4 * q^9 - 8 * q^11 + q^12 - 7 * q^14 + 3 * q^15 - 33 * q^16 + 66 * q^17 - 11 * q^18 - 29 * q^20 + q^21 - 17 * q^23 + 47 * q^24 - 33 * q^25 + 60 * q^26 - 21 * q^27 - 54 * q^28 - 39 * q^29 - 34 * q^30 - 53 * q^32 + 8 * q^33 - 6 * q^34 + 62 * q^35 - 35 * q^36 + 24 * q^37 - 30 * q^38 - 5 * q^39 - 6 * q^40 - 38 * q^41 + 65 * q^42 + 22 * q^44 - 9 * q^45 + 12 * q^46 - 58 * q^47 - 59 * q^48 - 33 * q^49 - 31 * q^50 + 26 * q^51 + 9 * q^52 + 128 * q^53 - 22 * q^54 - 36 * q^55 - 32 * q^56 - 34 * q^57 + 3 * q^58 - 39 * q^59 + 127 * q^60 + 138 * q^62 - 35 * q^63 + 132 * q^64 - 28 * q^65 - 94 * q^66 - 33 * q^67 - 62 * q^68 + 60 * q^69 - 6 * q^70 + 42 * q^71 - 34 * q^72 - 25 * q^74 + 55 * q^75 - 6 * q^76 - 91 * q^77 + 125 * q^78 + 116 * q^80 - 90 * q^82 - 61 * q^83 - 26 * q^84 + 15 * q^85 - 47 * q^86 - q^87 - 12 * q^88 + 110 * q^89 - 91 * q^90 + 36 * q^91 - 41 * q^92 - 11 * q^93 - 21 * q^94 - 6 * q^95 + 80 * q^96 - 12 * q^97 + 80 * q^98 - 38 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.884275	−	1.53161i	−0.625277	−	1.08301i	−0.988487	−	0.151304i	$-0.951653\pi$
$2$	−0.884275	−	1.53161i	−0.625277	−	1.08301i	0.363210	−	0.931707i	$-0.381681\pi$
$3$	−1.71455	+	0.245593i	−0.989896	+	0.141793i
$3$	−1.71455	+	0.245593i	−0.989896	+	0.141793i
$4$	−0.563885	+	0.976678i	−0.281943	+	0.488339i
$5$	−1.96647	+	3.40603i	−0.879432	+	1.52322i	−0.0274670	+	0.999623i	$0.508744\pi$
$5$	−1.96647	+	3.40603i	−0.879432	+	1.52322i	−0.851965	+	0.523598i	$0.824589\pi$
$6$	1.89229	+	2.40885i	0.772523	+	0.983409i
$7$	1.94697	+	3.37225i	0.735885	+	1.27459i	0.954334	+	0.298741i	$0.0965668\pi$
$7$	1.94697	+	3.37225i	0.735885	+	1.27459i	−0.218450	+	0.975848i	$0.570100\pi$
$8$	−1.54258			−0.545385
$9$	2.87937	−	0.842165i	0.959789	−	0.280722i
$10$	6.95560			2.19955
$11$	−1.70863	−	2.95943i	−0.515170	−	0.892301i	−0.999845	−	0.0176069i	$-0.994395\pi$
$11$	−1.70863	−	2.95943i	−0.515170	−	0.892301i	0.484675	−	0.874695i	$-0.338938\pi$
$12$	0.726944	−	1.81305i	0.209851	−	0.523382i
$13$	−0.794579	+	1.37625i	−0.220377	+	0.381703i	−0.954922	−	0.296856i	$-0.904062\pi$
$13$	−0.794579	+	1.37625i	−0.220377	+	0.381703i	0.734546	+	0.678559i	$0.237395\pi$
$14$	3.44331	−	5.96399i	0.920263	−	1.59394i
$15$	2.53512	−	6.32276i	0.654564	−	1.63253i
$16$	2.49184	+	4.31599i	0.622959	+	1.07900i
$17$	1.12257			0.272264			0.136132	−	0.990691i	$-0.456533\pi$
$17$	1.12257			0.272264			0.136132	+	0.990691i	$0.456533\pi$
$18$	−3.83602	−	3.66536i	−0.904159	−	0.863934i
$19$	−5.52036			−1.26646			−0.633228	−	0.773965i	$-0.718271\pi$
$19$	−5.52036			−1.26646			−0.633228	+	0.773965i	$0.718271\pi$
$20$	−2.21773	−	3.84121i	−0.495899	−	0.858922i
$21$	−4.16638	−	5.30373i	−0.909178	−	1.15737i
$22$	−3.02179	+	5.23390i	−0.644248	+	1.11587i
$23$	1.31436	−	2.27653i	0.274062	−	0.474690i	−0.695836	−	0.718201i	$-0.744966\pi$
$23$	1.31436	−	2.27653i	0.274062	−	0.474690i	0.969898	+	0.243511i	$0.0782992\pi$
$24$	2.64484	−	0.378848i	0.539875	−	0.0773320i
$25$	−5.23401	−	9.06557i	−1.04680	−	1.81311i
$26$	2.81051			0.551186
$27$	−4.72999	+	2.15109i	−0.910287	+	0.413977i
$28$	−4.39146			−0.829909
$29$	−4.22156	−	7.31196i	−0.783924	−	1.35780i	−0.929640	−	0.368470i	$-0.879882\pi$
$29$	−4.22156	−	7.31196i	−0.783924	−	1.35780i	0.145716	−	0.989327i	$-0.453452\pi$
$30$	−11.9257	+	1.70825i	−2.17733	+	0.311882i
$31$	−0.536361	+	0.929005i	−0.0963334	+	0.166854i	−0.910164	−	0.414247i	$-0.864045\pi$
$31$	−0.536361	+	0.929005i	−0.0963334	+	0.166854i	0.813831	+	0.581102i	$0.197378\pi$
$32$	2.86436	−	4.96121i	0.506352	−	0.877027i
$33$	3.65634	+	4.65446i	0.636488	+	0.810238i
$34$	−0.992662	−	1.71934i	−0.170240	−	0.294865i
$35$	−15.3146			−2.58864
$36$	−0.801109	+	3.28710i	−0.133518	+	0.547850i
$37$	11.7465			1.93111			0.965556	−	0.260196i	$-0.0837873\pi$
$37$	11.7465			1.93111			0.965556	+	0.260196i	$0.0837873\pi$
$38$	4.88151	+	8.45503i	0.791886	+	1.37159i
$39$	1.02435	−	2.55480i	0.164027	−	0.409095i
$40$	3.03344	−	5.25408i	0.479629	−	0.830742i
$41$	−3.90184	+	6.75819i	−0.609365	+	1.05545i	0.381980	+	0.924171i	$0.375242\pi$
$41$	−3.90184	+	6.75819i	−0.609365	+	1.05545i	−0.991345	+	0.131281i	$0.958091\pi$
$42$	−4.43901	+	11.0712i	−0.684955	+	1.70833i
$43$	−3.29435	−	5.70598i	−0.502384	−	0.870154i	−0.999996	−	0.00275447i	$-0.999123\pi$
$43$	−3.29435	−	5.70598i	−0.502384	−	0.870154i	0.497613	−	0.867399i	$-0.334210\pi$
$44$	3.85388			0.580994
$45$	−2.79376	+	11.4633i	−0.416469	+	1.70885i
$46$	−4.64901			−0.685459
$47$	0.625222	+	1.08292i	0.0911980	+	0.157960i	0.908015	−	0.418937i	$-0.137597\pi$
$47$	0.625222	+	1.08292i	0.0911980	+	0.157960i	−0.816818	+	0.576896i	$0.804264\pi$
$48$	−5.33236	−	6.78800i	−0.769660	−	0.979764i
$49$	−4.08137	+	7.06913i	−0.583052	+	1.00988i
$50$	−9.25661	+	16.0329i	−1.30908	+	2.26740i
$51$	−1.92471	+	0.275696i	−0.269513	+	0.0386052i
$52$	−0.896103	−	1.55210i	−0.124267	−	0.215237i
$53$	2.26591			0.311246			0.155623	−	0.987816i	$-0.450261\pi$
$53$	2.26591			0.311246			0.155623	+	0.987816i	$0.450261\pi$
$54$	7.47724	+	5.34235i	1.01752	+	0.727001i
$55$	13.4399			1.81223
$56$	−3.00336	−	5.20197i	−0.401341	−	0.695142i
$57$	9.46493	−	1.35576i	1.25366	−	0.179575i
$58$	−7.46604	+	12.9316i	−0.980339	+	1.69800i
$59$	−1.66041	+	2.87592i	−0.216168	+	0.374413i	−0.953633	−	0.300972i	$-0.902689\pi$
$59$	−1.66041	+	2.87592i	−0.216168	+	0.374413i	0.737466	+	0.675385i	$0.236022\pi$
$60$	4.74578	+	6.04130i	0.612678	+	0.779928i
$61$	−7.40341	−	12.8231i	−0.947910	−	1.64183i	−0.749817	−	0.661645i	$-0.769858\pi$
$61$	−7.40341	−	12.8231i	−0.947910	−	1.64183i	−0.198093	−	0.980183i	$-0.563475\pi$
$62$	1.89716			0.240940
$63$	8.44602	+	8.07027i	1.06410	+	1.01676i
$64$	−0.164172			−0.0205215
$65$	−3.12503	−	5.41271i	−0.387613	−	0.671365i
$66$	3.89561	−	9.71592i	0.479516	−	1.19595i
$67$	−0.500000	+	0.866025i	−0.0610847	+	0.105802i
$67$	−0.500000	+	0.866025i	−0.0610847	+	0.105802i
$68$	−0.633001	+	1.09639i	−0.0767627	+	0.132957i
$69$	−1.69443	+	4.22603i	−0.203985	+	0.508754i
$70$	13.5423	+	23.4560i	1.61862	+	2.80353i
$71$	−5.84966			−0.694227			−0.347113	−	0.937823i	$-0.612838\pi$
$71$	−5.84966			−0.694227			−0.347113	+	0.937823i	$0.612838\pi$
$72$	−4.44166	+	1.29911i	−0.523455	+	0.153101i
$73$	−7.21343			−0.844268			−0.422134	−	0.906533i	$-0.638719\pi$
$73$	−7.21343			−0.844268			−0.422134	+	0.906533i	$0.638719\pi$
$74$	−10.3871	−	17.9910i	−1.20748	−	2.09142i
$75$	11.2004	+	14.2579i	1.29331	+	1.64637i
$76$	3.11285	−	5.39161i	0.357068	−	0.618460i
$77$	6.65328	−	11.5238i	0.758212	−	1.31326i
$78$	−4.81876	+	0.690242i	−0.545617	+	0.0781545i
$79$	−2.76106	−	4.78229i	−0.310643	−	0.538050i	0.667859	−	0.744288i	$-0.267211\pi$
$79$	−2.76106	−	4.78229i	−0.310643	−	0.538050i	−0.978502	+	0.206238i	$0.933878\pi$
$80$	−19.6005			−2.19140
$81$	7.58152	−	4.84980i	0.842391	−	0.538867i
$82$	13.8012			1.52409
$83$	−5.82339	−	10.0864i	−0.639200	−	1.10713i	−0.985609	−	0.169043i	$-0.945932\pi$
$83$	−5.82339	−	10.0864i	−0.639200	−	1.10713i	0.346409	−	0.938084i	$-0.387401\pi$
$84$	7.52939	−	1.07851i	0.821524	−	0.117676i
$85$	−2.20750	+	3.82351i	−0.239437	+	0.414718i
$86$	−5.82622	+	10.0913i	−0.628258	+	1.08817i
$87$	9.03385	+	11.4999i	0.968530	+	1.23292i
$88$	2.63570	+	4.56516i	0.280966	+	0.486648i
$89$	4.10251			0.434865			0.217433	−	0.976075i	$-0.430232\pi$
$89$	4.10251			0.434865			0.217433	+	0.976075i	$0.430232\pi$
$90$	20.0277	−	5.85776i	2.11111	−	0.617462i
$91$	−6.18808			−0.648687
$92$	1.48229	+	2.56741i	0.154540	+	0.267671i
$93$	0.691461	−	1.72455i	0.0717012	−	0.178828i
$94$	1.10574	−	1.91519i	0.114048	−	0.197537i
$95$	10.8556	−	18.8025i	1.11376	−	1.92909i
$96$	−3.69265	+	9.20972i	−0.376879	+	0.939963i
$97$	−3.99963	−	6.92756i	−0.406100	−	0.703387i	0.588348	−	0.808608i	$-0.299778\pi$
$97$	−3.99963	−	6.92756i	−0.406100	−	0.703387i	−0.994449	+	0.105221i	$0.966445\pi$
$98$	14.4362			1.45828
$99$	−7.41209	−	7.08234i	−0.744943	−	0.711802i
$100$	11.8055			1.18055
$101$	7.52837	+	13.0395i	0.749101	+	1.29748i	0.948254	+	0.317513i	$0.102848\pi$
$101$	7.52837	+	13.0395i	0.749101	+	1.29748i	−0.199153	+	0.979968i	$0.563819\pi$
$102$	2.12423	+	2.70411i	0.210330	+	0.267746i
$103$	3.72515	−	6.45215i	0.367050	−	0.635749i	−0.622053	−	0.782975i	$-0.713701\pi$
$103$	3.72515	−	6.45215i	0.367050	−	0.635749i	0.989103	+	0.147226i	$0.0470344\pi$
$104$	1.22570	−	2.12298i	0.120190	−	0.208175i
$105$	26.2577	−	3.76117i	2.56249	−	0.367052i
$106$	−2.00369	−	3.47049i	−0.194615	−	0.337083i
$107$	−16.8888			−1.63270			−0.816352	−	0.577554i	$-0.804007\pi$
$107$	−16.8888			−1.63270			−0.816352	+	0.577554i	$0.804007\pi$
$108$	0.566253	−	5.83264i	0.0544877	−	0.561246i
$109$	−9.35514			−0.896059			−0.448030	−	0.894019i	$-0.647874\pi$
$109$	−9.35514			−0.896059			−0.448030	+	0.894019i	$0.647874\pi$
$110$	−11.8845	−	20.5846i	−1.13315	−	1.96267i
$111$	−20.1400	+	2.88486i	−1.91160	+	0.273819i
$112$	−9.70305	+	16.8062i	−0.916852	+	1.58803i
$113$	3.54132	−	6.13374i	0.333139	−	0.577014i	−0.649986	−	0.759946i	$-0.725225\pi$
$113$	3.54132	−	6.13374i	0.333139	−	0.577014i	0.983126	+	0.182932i	$0.0585588\pi$
$114$	−10.4461	−	13.2977i	−0.978367	−	1.24544i
$115$	5.16929	+	8.95347i	0.482038	+	0.834915i
$116$	9.52190			0.884086
$117$	−1.12886	+	4.63190i	−0.104363	+	0.428219i
$118$	5.87305			0.540658
$119$	2.18561	+	3.78559i	0.200355	+	0.347024i
$120$	−3.91062	+	9.75337i	−0.356989	+	0.890357i
$121$	−0.338814	+	0.586843i	−0.0308013	+	0.0533493i
$122$	−13.0933	+	22.6783i	−1.18541	+	2.05320i
$123$	5.03014	−	12.5455i	0.453552	−	1.13119i
$124$	−0.604892	−	1.04770i	−0.0543209	−	0.0940866i
$125$	21.5054			1.92350
$126$	4.89190	−	20.0723i	0.435805	−	1.78819i
$127$	−0.857131			−0.0760580			−0.0380290	−	0.999277i	$-0.512108\pi$
$127$	−0.857131			−0.0760580			−0.0380290	+	0.999277i	$0.512108\pi$
$128$	−5.58354	−	9.67098i	−0.493520	−	0.854802i
$129$	7.04968	+	8.97412i	0.620690	+	0.790127i
$130$	−5.52678	+	9.57266i	−0.484730	+	0.839578i
$131$	5.50131	−	9.52855i	0.480652	−	0.832513i	−0.519102	−	0.854712i	$-0.673733\pi$
$131$	5.50131	−	9.52855i	0.480652	−	0.832513i	0.999754	+	0.0221992i	$0.00706682\pi$
$132$	−6.60767	+	0.946487i	−0.575124	+	0.0823811i
$133$	−10.7480	−	18.6160i	−0.931966	−	1.61421i
$134$	1.76855			0.152779
$135$	1.97473	−	20.3405i	0.169957	−	1.75063i
$136$	−1.73166			−0.148488
$137$	8.73279	+	15.1256i	0.746093	+	1.29227i	0.949682	+	0.313214i	$0.101406\pi$
$137$	8.73279	+	15.1256i	0.746093	+	1.29227i	−0.203590	+	0.979056i	$0.565261\pi$
$138$	7.97097	−	1.14177i	0.678534	−	0.0971936i
$139$	−6.70872	+	11.6198i	−0.569026	+	0.985583i	0.427636	+	0.903951i	$0.359346\pi$
$139$	−6.70872	+	11.6198i	−0.569026	+	0.985583i	−0.996663	+	0.0816317i	$0.973987\pi$
$140$	8.63568	−	14.9574i	0.729848	−	1.26413i
$141$	−1.33793	−	1.70316i	−0.112674	−	0.143432i
$142$	5.17271	+	8.95939i	0.434084	+	0.751855i
$143$	5.43056			0.454126
$144$	10.8097	+	10.3288i	0.900807	+	0.860732i
$145$	33.2063			2.75763
$146$	6.37866	+	11.0482i	0.527901	+	0.914352i
$147$	5.26158	−	13.1227i	0.433967	−	1.08235i
$148$	−6.62367	+	11.4725i	−0.544463	+	0.943037i
$149$	−4.31054	+	7.46608i	−0.353133	+	0.611645i	−0.986797	−	0.161964i	$-0.948217\pi$
$149$	−4.31054	+	7.46608i	−0.353133	+	0.611645i	0.633663	+	0.773609i	$0.281550\pi$
$150$	11.9333	−	29.7626i	0.974354	−	2.43011i
$151$	−4.81009	−	8.33131i	−0.391439	−	0.677993i	0.601200	−	0.799098i	$-0.294689\pi$
$151$	−4.81009	−	8.33131i	−0.391439	−	0.677993i	−0.992640	+	0.121106i	$0.961356\pi$
$152$	8.51560			0.690707
$153$	3.23230	−	0.945390i	0.261316	−	0.0764302i
$154$	−23.5333			−1.89637
$155$	−2.10948	−	3.65372i	−0.169437	−	0.293474i
$156$	1.91760	+	2.44107i	0.153531	+	0.195442i
$157$	2.46730	−	4.27350i	0.196912	−	0.341062i	−0.750613	−	0.660742i	$-0.770242\pi$
$157$	2.46730	−	4.27350i	0.196912	−	0.341062i	0.947526	+	0.319679i	$0.103575\pi$
$158$	−4.88307	+	8.45772i	−0.388476	+	0.672860i
$159$	−3.88501	+	0.556492i	−0.308102	+	0.0441327i
$160$	11.2653	+	19.5122i	0.890604	+	1.54257i
$161$	10.2360			0.806713
$162$	−14.1322	−	7.32336i	−1.11033	−	0.575378i
$163$	21.4951			1.68363			0.841814	−	0.539768i	$-0.181488\pi$
$163$	21.4951			1.68363			0.841814	+	0.539768i	$0.181488\pi$
$164$	−4.40038	−	7.62168i	−0.343612	−	0.595153i
$165$	−23.0433	+	3.30074i	−1.79392	+	0.256962i
$166$	−10.2990	+	17.8383i	−0.799354	+	1.38452i
$167$	−1.96475	+	3.40305i	−0.152037	+	0.263336i	−0.931976	−	0.362519i	$-0.881917\pi$
$167$	−1.96475	+	3.40305i	−0.152037	+	0.263336i	0.779939	+	0.625855i	$0.215250\pi$
$168$	6.42698	+	8.18143i	0.495852	+	0.631211i
$169$	5.23729	+	9.07125i	0.402868	+	0.697788i
$170$	7.80816			0.598859
$171$	−15.8951	+	4.64905i	−1.21553	+	0.355522i
$172$	7.43054			0.566573
$173$	−1.73177	−	2.99952i	−0.131664	−	0.228049i	0.792654	−	0.609672i	$-0.208699\pi$
$173$	−1.73177	−	2.99952i	−0.131664	−	0.228049i	−0.924318	+	0.381622i	$0.875365\pi$
$174$	9.62500	−	24.0054i	0.729669	−	1.81985i
$175$	20.3809	−	35.3007i	1.54065	−	2.66849i
$176$	8.51524	−	14.7488i	0.641861	−	1.11174i
$177$	2.14056	−	5.33870i	0.160894	−	0.401281i
$178$	−3.62775	−	6.28344i	−0.271911	−	0.470964i
$179$	−8.07041			−0.603211			−0.301605	−	0.953433i	$-0.597523\pi$
$179$	−8.07041			−0.603211			−0.301605	+	0.953433i	$0.597523\pi$
$180$	−9.62059	−	9.19258i	−0.717076	−	0.685174i
$181$	−13.1221			−0.975358			−0.487679	−	0.873023i	$-0.662156\pi$
$181$	−13.1221			−0.975358			−0.487679	+	0.873023i	$0.662156\pi$
$182$	5.47196	+	9.47772i	0.405609	+	0.702535i
$183$	15.8428	+	20.1676i	1.17113	+	1.49083i
$184$	−2.02750	+	3.51174i	−0.149470	+	0.258889i
$185$	−23.0991	+	40.0089i	−1.69828	+	2.94151i
$186$	−3.25278	+	0.465931i	−0.238506	+	0.0341637i
$187$	−1.91806	−	3.32217i	−0.140262	−	0.242941i
$188$	−1.41021			−0.102850
$189$	−16.4631	−	11.7626i	−1.19752	−	0.855603i
$190$	−38.3974			−2.78564
$191$	1.83189	+	3.17292i	0.132551	+	0.229585i	0.924659	−	0.380796i	$-0.124350\pi$
$191$	1.83189	+	3.17292i	0.132551	+	0.229585i	−0.792108	+	0.610380i	$0.791017\pi$
$192$	0.281481	−	0.0403195i	0.0203141	−	0.00290981i
$193$	−4.92936	+	8.53791i	−0.354823	+	0.614572i	−0.987088	−	0.160181i	$-0.948792\pi$
$193$	−4.92936	+	8.53791i	−0.354823	+	0.614572i	0.632264	+	0.774753i	$0.282126\pi$
$194$	−7.07354	+	12.2517i	−0.507851	+	0.879623i
$195$	6.68735	+	8.51289i	0.478891	+	0.609620i
$196$	−4.60284	−	7.97236i	−0.328774	−	0.569454i
$197$	11.6893			0.832826			0.416413	−	0.909175i	$-0.363287\pi$
$197$	11.6893			0.832826			0.416413	+	0.909175i	$0.363287\pi$
$198$	−4.29305	+	17.6152i	−0.305094	+	1.25186i
$199$	−14.1519			−1.00320			−0.501602	−	0.865098i	$-0.667256\pi$
$199$	−14.1519			−1.00320			−0.501602	+	0.865098i	$0.667256\pi$
$200$	8.07389	+	13.9844i	0.570910	+	0.988845i
$201$	0.644585	−	1.60764i	0.0454655	−	0.113394i
$202$	13.3143	−	23.0610i	0.936791	−	1.62257i
$203$	16.4385	−	28.4723i	1.15376	−	1.99836i
$204$	0.816046	−	2.03528i	0.0571347	−	0.142498i
$205$	−15.3457	−	26.5795i	−1.07179	−	1.85640i
$206$	−13.1762			−0.918032
$207$	1.86730	−	7.66188i	0.129786	−	0.532537i
$208$	−7.91985			−0.549143
$209$	9.43223	+	16.3371i	0.652441	+	1.13006i
$210$	−28.9797	−	36.8906i	−1.99979	−	2.54569i
$211$	11.8874	−	20.5895i	0.818361	−	1.41744i	−0.0885282	−	0.996074i	$-0.528216\pi$
$211$	11.8874	−	20.5895i	0.818361	−	1.41744i	0.906889	−	0.421369i	$-0.138450\pi$
$212$	−1.27771	+	2.21306i	−0.0877536	+	0.151994i
$213$	10.0295	−	1.43664i	0.687212	−	0.0984368i
$214$	14.9344	+	25.8671i	1.02089	+	1.76824i
$215$	25.9130			1.76725
$216$	7.29640	−	3.31823i	0.496457	−	0.225777i
$217$	−4.17711			−0.283561
$218$	8.27251	+	14.3284i	0.560285	+	0.970443i
$219$	12.3678	−	1.77157i	0.835738	−	0.119712i
$220$	−7.57854	+	13.1264i	−0.510945	+	0.884982i
$221$	−0.891972	+	1.54494i	−0.0600005	+	0.103924i
$222$	22.2277	+	28.2955i	1.49183	+	1.89907i
$223$	−5.35134	−	9.26879i	−0.358352	−	0.620684i	0.629334	−	0.777135i	$-0.283328\pi$
$223$	−5.35134	−	9.26879i	−0.358352	−	0.620684i	−0.987686	+	0.156451i	$0.949995\pi$
$224$	22.3072			1.49047
$225$	−22.7053	−	21.6952i	−1.51369	−	1.44635i
$226$	−12.5260			−0.833217
$227$	−4.58965	−	7.94950i	−0.304626	−	0.527627i	0.672552	−	0.740050i	$-0.265198\pi$
$227$	−4.58965	−	7.94950i	−0.304626	−	0.527627i	−0.977178	+	0.212423i	$0.931865\pi$
$228$	−4.01299	+	10.0087i	−0.265767	+	0.662841i
$229$	−4.83413	+	8.37295i	−0.319448	+	0.553300i	−0.980373	−	0.197152i	$-0.936831\pi$
$229$	−4.83413	+	8.37295i	−0.319448	+	0.553300i	0.660925	+	0.750452i	$0.270164\pi$
$230$	9.14214	−	15.8347i	0.602815	−	1.04411i
$231$	−8.57722	+	21.3922i	−0.564339	+	1.40750i
$232$	6.51210	+	11.2793i	0.427541	+	0.740522i
$233$	−0.516910			−0.0338639			−0.0169320	−	0.999857i	$-0.505390\pi$
$233$	−0.516910			−0.0338639			−0.0169320	+	0.999857i	$0.505390\pi$
$234$	8.09248	−	2.36691i	0.529022	−	0.154730i
$235$	−4.91792			−0.320810
$236$	−1.87257	−	3.24338i	−0.121894	−	0.211126i
$237$	5.90847	+	7.52138i	0.383796	+	0.488566i
$238$	3.86536	−	6.69500i	0.250554	−	0.433973i
$239$	1.85264	−	3.20886i	0.119837	−	0.207564i	−0.799866	−	0.600179i	$-0.795096\pi$
$239$	1.85264	−	3.20886i	0.119837	−	0.207564i	0.919703	+	0.392615i	$0.128429\pi$
$240$	33.6060	−	4.81375i	2.16926	−	0.310726i
$241$	12.4536	+	21.5703i	0.802209	+	1.38947i	0.918159	+	0.396211i	$0.129675\pi$
$241$	12.4536	+	21.5703i	0.802209	+	1.38947i	−0.115951	+	0.993255i	$0.536992\pi$
$242$	1.19842			0.0770373
$243$	−11.8078	+	10.1772i	−0.757472	+	0.652868i
$244$	16.6987			1.06902
$245$	−16.0518	−	27.8025i	−1.02551	−	1.77624i
$246$	−23.6629	+	3.38948i	−1.50869	+	0.216106i
$247$	4.38636	−	7.59740i	0.279097	−	0.483411i
$248$	0.827382	−	1.43307i	0.0525388	−	0.0909998i
$249$	12.4616	+	15.8635i	0.789725	+	1.00531i
$250$	−19.0167	−	32.9379i	−1.20272	−	2.08317i
$251$	−8.95472			−0.565217			−0.282608	−	0.959235i	$-0.591200\pi$
$251$	−8.95472			−0.565217			−0.282608	+	0.959235i	$0.591200\pi$
$252$	−12.6446	+	3.69834i	−0.796538	+	0.232973i
$253$	−8.98298			−0.564755
$254$	0.757939	+	1.31279i	0.0475573	+	0.0823717i
$255$	2.84585	−	7.09774i	0.178214	−	0.444478i
$256$	−10.0389	+	17.3880i	−0.627434	+	1.08675i
$257$	−5.41843	+	9.38499i	−0.337992	+	0.585420i	−0.984055	−	0.177865i	$-0.943081\pi$
$257$	−5.41843	+	9.38499i	−0.337992	+	0.585420i	0.646063	+	0.763284i	$0.276414\pi$
$258$	7.51099	−	18.7329i	0.467614	−	1.16626i
$259$	22.8700	+	39.6121i	1.42108	+	2.46137i
$260$	7.04864			0.437138
$261$	−18.3133	−	17.4986i	−1.13356	−	1.08313i
$262$	−19.4587			−1.20216
$263$	3.55919	+	6.16470i	0.219469	+	0.380132i	0.954646	−	0.297744i	$-0.0962341\pi$
$263$	3.55919	+	6.16470i	0.219469	+	0.380132i	−0.735177	+	0.677876i	$0.762901\pi$
$264$	−5.64021	−	7.17989i	−0.347131	−	0.441892i
$265$	−4.45584	+	7.71774i	−0.273720	+	0.474097i
$266$	−19.0083	+	32.9233i	−1.16547	+	2.01866i
$267$	−7.03396	+	1.00755i	−0.430471	+	0.0616610i
$268$	−0.563885	−	0.976678i	−0.0344448	−	0.0596601i
$269$	5.42539			0.330792			0.165396	−	0.986227i	$-0.447110\pi$
$269$	5.42539			0.330792			0.165396	+	0.986227i	$0.447110\pi$
$270$	−32.8999	+	14.9621i	−2.00223	+	0.910565i
$271$	−15.9910			−0.971386			−0.485693	−	0.874129i	$-0.661433\pi$
$271$	−15.9910			−0.971386			−0.485693	+	0.874129i	$0.661433\pi$
$272$	2.79727	+	4.84501i	0.169609	+	0.293772i
$273$	10.6098	−	1.51975i	0.642133	−	0.0919795i
$274$	15.4444	−	26.7505i	0.933029	−	1.61605i
$275$	−17.8859	+	30.9794i	−1.07856	+	1.86813i
$276$	−3.17200	−	4.03791i	−0.190932	−	0.243053i
$277$	14.3898	+	24.9239i	0.864601	+	1.49753i	0.867443	+	0.497536i	$0.165762\pi$
$277$	14.3898	+	24.9239i	0.864601	+	1.49753i	−0.00284279	+	0.999996i	$0.500905\pi$
$278$	23.7294			1.42320
$279$	−0.762006	+	3.12665i	−0.0456201	+	0.187188i
$280$	23.6241			1.41181
$281$	−5.58019	−	9.66516i	−0.332886	−	0.576575i	0.650190	−	0.759771i	$-0.274689\pi$
$281$	−5.58019	−	9.66516i	−0.332886	−	0.576575i	−0.983076	+	0.183196i	$0.941356\pi$
$282$	−1.42548	+	3.55525i	−0.0848862	+	0.211712i
$283$	−12.3983	+	21.4745i	−0.737002	+	1.27652i	0.216837	+	0.976208i	$0.430426\pi$
$283$	−12.3983	+	21.4745i	−0.737002	+	1.27652i	−0.953839	+	0.300317i	$0.902908\pi$
$284$	3.29853	−	5.71323i	0.195732	−	0.339018i
$285$	−13.9947	+	34.9039i	−0.828977	+	2.06753i
$286$	−4.80211	−	8.31749i	−0.283955	−	0.491824i
$287$	−30.3870			−1.79369
$288$	4.06938	−	16.6974i	0.239791	−	0.983905i
$289$	−15.7398			−0.925873
$290$	−29.3635	−	50.8591i	−1.72428	−	2.98655i
$291$	8.55892	+	10.8954i	0.501733	+	0.638697i
$292$	4.06755	−	7.04520i	0.238035	−	0.412289i
$293$	−12.9683	+	22.4618i	−0.757618	+	1.31223i	0.186444	+	0.982466i	$0.440304\pi$
$293$	−12.9683	+	22.4618i	−0.757618	+	1.31223i	−0.944062	+	0.329768i	$0.893030\pi$
$294$	−24.7516	+	3.54544i	−1.44354	+	0.206774i
$295$	−6.53031	−	11.3108i	−0.380209	−	0.658542i
$296$	−18.1199			−1.05320
$297$	14.4478	+	10.3227i	0.838345	+	0.598982i
$298$	15.2468			0.883225
$299$	2.08872	+	3.61777i	0.120794	+	0.209221i
$300$	−20.2412	+	2.89936i	−1.16862	+	0.167394i
$301$	12.8280	−	22.2187i	0.739393	−	1.28067i
$302$	−8.50688	+	14.7343i	−0.489516	+	0.847867i
$303$	−16.1102	−	20.5080i	−0.925506	−	1.17815i
$304$	−13.7558	−	23.8258i	−0.788951	−	1.36650i
$305$	58.2344			3.33449
$306$	−4.30621	−	4.11463i	−0.246169	−	0.235218i
$307$	−10.1100			−0.577010			−0.288505	−	0.957478i	$-0.593158\pi$
$307$	−10.1100			−0.577010			−0.288505	+	0.957478i	$0.593158\pi$
$308$	7.50338	+	12.9962i	0.427544	+	0.740529i
$309$	−4.80236	+	11.9774i	−0.273196	+	0.681371i
$310$	−3.73072	+	6.46179i	−0.211890	+	0.367005i
$311$	−0.594305	+	1.02937i	−0.0337000	+	0.0583700i	−0.882383	−	0.470531i	$-0.844062\pi$
$311$	−0.594305	+	1.02937i	−0.0337000	+	0.0583700i	0.848684	+	0.528901i	$0.177396\pi$
$312$	−1.58014	+	3.94098i	−0.0894579	+	0.223114i
$313$	−15.2785	−	26.4631i	−0.863589	−	1.49578i	−0.868441	−	0.495792i	$-0.834878\pi$
$313$	−15.2785	−	26.4631i	−0.863589	−	1.49578i	0.00485223	−	0.999988i	$-0.498455\pi$
$314$	−8.72711			−0.492499
$315$	−44.0964	+	12.8974i	−2.48455	+	0.726688i
$316$	6.22768			0.350334
$317$	8.07009	+	13.9778i	0.453261	+	0.785072i	0.998586	−	0.0531529i	$-0.0169271\pi$
$317$	8.07009	+	13.9778i	0.453261	+	0.785072i	−0.545325	+	0.838225i	$0.683594\pi$
$318$	4.28775	+	5.45823i	0.240445	+	0.306082i
$319$	−14.4261	+	24.9868i	−0.807709	+	1.39899i
$320$	0.322839	−	0.559173i	0.0180472	−	0.0312587i
$321$	28.9567	−	4.14778i	1.61621	−	0.231507i
$322$	−9.05147	−	15.6776i	−0.504419	−	0.873679i
$323$	−6.19699			−0.344810
$324$	0.461590	+	10.1394i	0.0256439	+	0.563302i
$325$	16.6353			0.922763
$326$	−19.0076	−	32.9221i	−1.05273	−	1.82339i
$327$	16.0399	−	2.29756i	0.887006	−	0.127055i
$328$	6.01891	−	10.4251i	0.332339	−	0.575628i
$329$	−2.43457	+	4.21680i	−0.134222	+	0.232480i
$330$	25.4321	+	32.3746i	1.39999	+	1.78216i
$331$	−10.8812	−	18.8468i	−0.598084	−	1.03591i	−0.993104	−	0.117239i	$-0.962596\pi$
$331$	−10.8812	−	18.8468i	−0.598084	−	1.03591i	0.395020	−	0.918673i	$-0.370738\pi$
$332$	13.1349			0.720871
$333$	33.8225	−	9.89248i	1.85346	−	0.542105i
$334$	6.94953			0.380261
$335$	−1.96647	−	3.40603i	−0.107440	−	0.186091i
$336$	12.5089	−	31.1981i	0.682416	−	1.70199i
$337$	−9.83964	+	17.0428i	−0.535999	+	0.928378i	0.463115	+	0.886298i	$0.346732\pi$
$337$	−9.83964	+	17.0428i	−0.535999	+	0.928378i	−0.999114	+	0.0420798i	$0.986602\pi$
$338$	9.26241	−	16.0430i	0.503809	−	0.872622i
$339$	−4.56536	+	11.3863i	−0.247956	+	0.618421i
$340$	−2.48956	−	4.31204i	−0.135015	−	0.233853i
$341$	3.66577			0.198512
$342$	21.1762	+	20.2341i	1.14508	+	1.09414i
$343$	−4.52760			−0.244467
$344$	5.08180	+	8.80194i	0.273993	+	0.474569i
$345$	−11.0619	−	14.0816i	−0.595553	−	0.758129i
$346$	−3.06273	+	5.30480i	−0.164653	+	0.285188i
$347$	−14.5760	+	25.2463i	−0.782478	+	1.35529i	0.148016	+	0.988985i	$0.452711\pi$
$347$	−14.5760	+	25.2463i	−0.782478	+	1.35529i	−0.930494	+	0.366307i	$0.880622\pi$
$348$	−16.3258	+	2.33852i	−0.875154	+	0.125358i
$349$	4.43472	+	7.68116i	0.237385	+	0.411163i	0.959963	−	0.280126i	$-0.0903763\pi$
$349$	4.43472	+	7.68116i	0.237385	+	0.411163i	−0.722578	+	0.691289i	$0.757043\pi$
$350$	−72.0893			−3.85333
$351$	0.797916	−	8.21887i	0.0425896	−	0.438691i
$352$	−19.5765			−1.04343
$353$	11.2194	+	19.4326i	0.597150	+	1.03429i	0.993240	+	0.116083i	$0.0370337\pi$
$353$	11.2194	+	19.4326i	0.597150	+	1.03429i	−0.396089	+	0.918212i	$0.629633\pi$
$354$	−10.0696	+	1.44238i	−0.535196	+	0.0766618i
$355$	11.5032	−	19.9241i	0.610525	−	1.05746i
$356$	−2.31334	+	4.00683i	−0.122607	+	0.212362i
$357$	−4.67705	−	5.95381i	−0.247536	−	0.315109i
$358$	7.13646	+	12.3607i	0.377174	+	0.653284i
$359$	−17.2654			−0.911234			−0.455617	−	0.890176i	$-0.650581\pi$
$359$	−17.2654			−0.911234			−0.455617	+	0.890176i	$0.650581\pi$
$360$	4.30960	−	17.6831i	0.227136	−	0.931980i
$361$	11.4743			0.603913
$362$	11.6035	+	20.0979i	0.609869	+	1.05632i
$363$	0.436789	−	1.08938i	0.0229255	−	0.0571777i
$364$	3.48937	−	6.04376i	0.182892	−	0.316779i
$365$	14.1850	−	24.5691i	0.742477	−	1.28601i
$366$	16.8795	−	42.0987i	0.882306	−	2.20053i
$367$	2.96807	+	5.14084i	0.154932	+	0.268350i	0.933034	−	0.359788i	$-0.117151\pi$
$367$	2.96807	+	5.14084i	0.154932	+	0.268350i	−0.778102	+	0.628137i	$0.783818\pi$
$368$	13.1007			0.682919
$369$	−5.54333	+	22.7453i	−0.288574	+	1.18407i
$370$	81.7039			4.24759
$371$	4.41165	+	7.64120i	0.229041	+	0.396711i
$372$	1.29443	+	1.64778i	0.0671130	+	0.0854337i
$373$	1.09817	−	1.90208i	0.0568609	−	0.0984859i	−0.836194	−	0.548434i	$-0.815224\pi$
$373$	1.09817	−	1.90208i	0.0568609	−	0.0984859i	0.893055	+	0.449948i	$0.148558\pi$
$374$	−3.39218	+	5.87543i	−0.175405	+	0.303811i
$375$	−36.8721	+	5.28158i	−1.90407	+	0.272740i
$376$	−0.964456	−	1.67049i	−0.0497380	−	0.0861488i
$377$	13.4175			0.691034
$378$	−3.45777	+	35.6165i	−0.177848	+	1.83191i
$379$	−5.60517			−0.287918			−0.143959	−	0.989584i	$-0.545983\pi$
$379$	−5.60517			−0.287918			−0.143959	+	0.989584i	$0.545983\pi$
$380$	12.2426	+	21.2049i	0.628034	+	1.08779i
$381$	1.46959	−	0.210506i	0.0752896	−	0.0107845i
$382$	3.23979	−	5.61148i	0.165762	−	0.287108i
$383$	8.74100	−	15.1399i	0.446644	−	0.773611i	−0.551521	−	0.834161i	$-0.685952\pi$
$383$	8.74100	−	15.1399i	0.446644	−	0.773611i	0.998165	+	0.0605503i	$0.0192856\pi$
$384$	11.9484	+	15.2101i	0.609739	+	0.776187i
$385$	26.1670	+	45.3225i	1.33359	+	2.30985i
$386$	17.4357			0.887452
$387$	−14.2910	−	13.6552i	−0.726453	−	0.694134i
$388$	9.02132			0.457988
$389$	−2.31533	−	4.01027i	−0.117392	−	0.203329i	0.801342	−	0.598207i	$-0.204120\pi$
$389$	−2.31533	−	4.01027i	−0.117392	−	0.203329i	−0.918733	+	0.394879i	$0.870787\pi$
$390$	7.12496	−	17.7701i	0.360786	−	0.899826i
$391$	1.47546	−	2.55557i	0.0746172	−	0.129241i
$392$	6.29584	−	10.9047i	0.317988	−	0.550771i
$393$	−7.09213	+	17.6883i	−0.357750	+	0.892255i
$394$	−10.3365	−	17.9034i	−0.520747	−	0.901961i
$395$	21.7181			1.09276
$396$	11.0967	−	3.24560i	0.557632	−	0.163098i
$397$	−32.0225			−1.60717			−0.803583	−	0.595193i	$-0.797076\pi$
$397$	−32.0225			−1.60717			−0.803583	+	0.595193i	$0.797076\pi$
$398$	12.5142	+	21.6752i	0.627280	+	1.08648i
$399$	22.9999	+	29.2785i	1.15143	+	1.46576i
$400$	26.0846	−	45.1799i	1.30423	−	2.25899i
$401$	7.07924	−	12.2616i	0.353520	−	0.612315i	−0.633343	−	0.773871i	$-0.718318\pi$
$401$	7.07924	−	12.2616i	0.353520	−	0.612315i	0.986864	+	0.161556i	$0.0516512\pi$
$402$	−3.03227	+	0.434344i	−0.151236	+	0.0216631i
$403$	−0.852363	−	1.47634i	−0.0424592	−	0.0735416i
$404$	−16.9805			−0.844814
$405$	1.60973	+	35.3598i	0.0799881	+	1.75704i
$406$	−58.1446			−2.88567
$407$	−20.0704	−	34.7629i	−0.994852	−	1.72313i
$408$	2.96902	−	0.425284i	0.146988	−	0.0210547i
$409$	16.0063	−	27.7238i	0.791462	−	1.37085i	−0.133600	−	0.991035i	$-0.542654\pi$
$409$	16.0063	−	27.7238i	0.791462	−	1.37085i	0.925062	−	0.379817i	$-0.124013\pi$
$410$	−27.1397	+	47.0073i	−1.34033	+	2.32152i
$411$	−18.6876	−	23.7890i	−0.921790	−	1.17342i
$412$	4.20112	+	7.27654i	0.206974	+	0.358490i
$413$	−12.9311			−0.636297
$414$	−13.3862	+	3.91523i	−0.657896	+	0.192423i
$415$	45.8061			2.24853
$416$	4.55192	+	7.88415i	0.223176	+	0.386552i
$417$	8.64869	−	21.5704i	0.423528	−	1.05631i
$418$	16.6814	−	28.8930i	0.815913	−	1.41320i
$419$	11.8674	−	20.5549i	0.579760	−	1.00417i	−0.415746	−	0.909481i	$-0.636480\pi$
$419$	11.8674	−	20.5549i	0.579760	−	1.00417i	0.995506	−	0.0946935i	$-0.0301871\pi$
$420$	−11.1329	+	27.7662i	−0.543228	+	1.35485i
$421$	−7.38162	−	12.7853i	−0.359758	−	0.623120i	0.628162	−	0.778083i	$-0.283808\pi$
$421$	−7.38162	−	12.7853i	−0.359758	−	0.623120i	−0.987920	+	0.154963i	$0.950474\pi$
$422$	−42.0469			−2.04681
$423$	2.71224	+	2.59157i	0.131873	+	0.126007i
$424$	−3.49535			−0.169749
$425$	−5.87555	−	10.1767i	−0.285006	−	0.493645i
$426$	−11.0692	−	14.0909i	−0.536306	−	0.682709i
$427$	28.8284	−	49.9323i	1.39510	−	2.41639i
$428$	9.52336	−	16.4949i	0.460329	−	0.797313i
$429$	−9.31097	+	1.33371i	−0.449538	+	0.0643921i
$430$	−22.9142	−	39.6885i	−1.10502	−	1.91395i
$431$	−34.3670			−1.65540			−0.827700	−	0.561171i	$-0.810351\pi$
$431$	−34.3670			−1.65540			−0.827700	+	0.561171i	$0.810351\pi$
$432$	−21.0704	−	15.0544i	−1.01375	−	0.724307i
$433$	19.9403			0.958269			0.479134	−	0.877742i	$-0.340951\pi$
$433$	19.9403			0.958269			0.479134	+	0.877742i	$0.340951\pi$
$434$	3.69372	+	6.39771i	0.177304	+	0.307100i
$435$	−56.9339	+	8.15524i	−2.72977	+	0.391014i
$436$	5.27522	−	9.13695i	0.252637	−	0.437581i
$437$	−7.25572	+	12.5673i	−0.347088	+	0.601174i
$438$	−13.6499	−	17.3761i	−0.652217	−	0.830261i
$439$	−8.17095	−	14.1525i	−0.389978	−	0.675462i	0.602468	−	0.798143i	$-0.294184\pi$
$439$	−8.17095	−	14.1525i	−0.389978	−	0.675462i	−0.992446	+	0.122681i	$0.960851\pi$
$440$	−20.7321			−0.988363
$441$	−5.79838	+	23.7918i	−0.276113	+	1.13294i
$442$	3.15499			0.150068
$443$	−7.23477	−	12.5310i	−0.343734	−	0.595365i	0.641389	−	0.767216i	$-0.278359\pi$
$443$	−7.23477	−	12.5310i	−0.343734	−	0.595365i	−0.985123	+	0.171851i	$0.945025\pi$
$444$	8.53904	−	21.2970i	0.405245	−	1.01071i
$445$	−8.06746	+	13.9733i	−0.382434	+	0.662396i
$446$	−9.46411	+	16.3923i	−0.448139	+	0.776199i
$447$	5.55702	−	13.8596i	0.262838	−	0.655537i
$448$	−0.319637	−	0.553628i	−0.0151014	−	0.0261564i
$449$	8.62001			0.406804			0.203402	−	0.979095i	$-0.434800\pi$
$449$	8.62001			0.406804			0.203402	+	0.979095i	$0.434800\pi$
$450$	−13.1508	+	53.9603i	−0.619936	+	2.54371i
$451$	26.6672			1.25571
$452$	3.99379	+	6.91745i	0.187852	+	0.325370i
$453$	10.2933	+	13.1031i	0.483619	+	0.615639i
$454$	−8.11702	+	14.0591i	−0.380951	+	0.659826i
$455$	12.1687	−	21.0768i	0.570476	−	0.988094i
$456$	−14.6004	+	2.09138i	−0.683728	+	0.0979377i
$457$	13.0856	+	22.6649i	0.612118	+	1.06022i	0.990883	+	0.134727i	$0.0430158\pi$
$457$	13.0856	+	22.6649i	0.612118	+	1.06022i	−0.378764	+	0.925493i	$0.623651\pi$
$458$	17.0988			0.798974
$459$	−5.30975	+	2.41475i	−0.247838	+	0.112711i
$460$	−11.6595			−0.543629
$461$	−4.41717	−	7.65077i	−0.205728	−	0.356332i	0.744636	−	0.667471i	$-0.232623\pi$
$461$	−4.41717	−	7.65077i	−0.205728	−	0.356332i	−0.950365	+	0.311139i	$0.899290\pi$
$462$	40.3491	−	5.77963i	1.87721	−	0.268893i
$463$	8.11654	−	14.0583i	0.377208	−	0.653343i	−0.613447	−	0.789736i	$-0.710218\pi$
$463$	8.11654	−	14.0583i	0.377208	−	0.653343i	0.990655	+	0.136393i	$0.0435510\pi$
$464$	21.0389	−	36.4404i	0.976706	−	1.69170i
$465$	4.51414	+	5.74642i	0.209338	+	0.266484i
$466$	0.457091	+	0.791705i	0.0211743	+	0.0366750i
$467$	22.3414			1.03384			0.516919	−	0.856034i	$-0.327079\pi$
$467$	22.3414			1.03384			0.516919	+	0.856034i	$0.327079\pi$
$468$	−3.88733	−	3.71439i	−0.179692	−	0.171698i
$469$	−3.89394			−0.179805
$470$	4.34879	+	7.53233i	0.200595	+	0.347441i
$471$	−3.18078	+	7.93308i	−0.146562	+	0.365537i
$472$	2.56133	−	4.43635i	0.117895	−	0.204199i
$473$	−11.2576	+	19.4988i	−0.517626	+	0.896555i
$474$	6.29511	−	15.7004i	0.289144	−	0.721145i
$475$	28.8936	+	50.0452i	1.32573	+	2.29623i
$476$	−4.92973			−0.225954
$477$	6.52438	−	1.90827i	0.298731	−	0.0873736i
$478$	−6.55297			−0.299726
$479$	−15.5249	−	26.8899i	−0.709349	−	1.22863i	−0.965099	−	0.261886i	$-0.915655\pi$
$479$	−15.5249	−	26.8899i	−0.709349	−	1.22863i	0.255749	−	0.966743i	$-0.417678\pi$
$480$	−24.1071	−	30.6879i	−1.10033	−	1.40070i
$481$	−9.33352	+	16.1661i	−0.425572	+	0.737112i
$482$	22.0249	−	38.1482i	1.00321	−	1.73760i
$483$	−17.5502	+	2.51390i	−0.798562	+	0.114387i
$484$	−0.382104	−	0.661824i	−0.0173684	−	0.0300829i
$485$	31.4606			1.42855
$486$	26.0289	+	9.08552i	1.18069	+	0.412127i
$487$	−19.2761			−0.873482			−0.436741	−	0.899587i	$-0.643867\pi$
$487$	−19.2761			−0.873482			−0.436741	+	0.899587i	$0.643867\pi$
$488$	11.4204	+	19.7807i	0.516976	+	0.895429i
$489$	−36.8545	+	5.27906i	−1.66662	+	0.238727i
$490$	−28.3884	+	49.1701i	−1.28246	+	2.22128i
$491$	1.18001	−	2.04384i	0.0532532	−	0.0922372i	−0.838170	−	0.545409i	$-0.816374\pi$
$491$	1.18001	−	2.04384i	0.0532532	−	0.0922372i	0.891423	+	0.453172i	$0.149708\pi$
$492$	9.41651	+	11.9871i	0.424529	+	0.540418i
$493$	−4.73900	−	8.20819i	−0.213434	−	0.369678i
$494$	−15.5150			−0.698053
$495$	38.6983	−	11.3186i	1.73936	−	0.508732i
$496$	−5.34610			−0.240047
$497$	−11.3891	−	19.7265i	−0.510871	−	0.884854i
$498$	13.2771	−	33.1141i	0.594962	−	1.48388i
$499$	−19.5594	+	33.8780i	−0.875601	+	1.51659i	−0.0194799	+	0.999810i	$0.506201\pi$
$499$	−19.5594	+	33.8780i	−0.875601	+	1.51659i	−0.856121	+	0.516775i	$0.827132\pi$
$500$	−12.1266	+	21.0038i	−0.542317	+	0.939320i
$501$	2.53290	−	6.31723i	0.113162	−	0.282233i
$502$	7.91843	+	13.7151i	0.353417	+	0.612136i
$503$	13.8861			0.619149			0.309575	−	0.950875i	$-0.399813\pi$
$503$	13.8861			0.619149			0.309575	+	0.950875i	$0.399813\pi$
$504$	−13.0287	−	12.4491i	−0.580344	−	0.554525i
$505$	−59.2173			−2.63513
$506$	7.94343	+	13.7584i	0.353128	+	0.611636i
$507$	−11.2074	−	14.2669i	−0.497740	−	0.633614i
$508$	0.483323	−	0.837140i	0.0214440	−	0.0371421i
$509$	10.6023	−	18.3636i	0.469937	−	0.813954i	−0.529472	−	0.848327i	$-0.677610\pi$
$509$	10.6023	−	18.3636i	0.469937	−	0.813954i	0.999409	+	0.0343729i	$0.0109434\pi$
$510$	−13.3875	+	1.91763i	−0.592808	+	0.0849142i
$511$	−14.0443	−	24.3255i	−0.621284	−	1.07610i
$512$	13.1746			0.582240
$513$	26.1112	−	11.8748i	1.15284	−	0.524284i
$514$	19.1655			0.845355
$515$	14.6508	+	25.3759i	0.645591	+	1.11820i
$516$	−12.7400	+	1.82489i	−0.560849	+	0.0803363i
$517$	2.13654	−	3.70060i	0.0939650	−	0.162752i
$518$	40.4468	−	70.0559i	1.77713	−	3.07808i
$519$	3.70588	+	4.71752i	0.162670	+	0.207076i
$520$	4.82062	+	8.34956i	0.211398	+	0.366152i
$521$	−19.7474			−0.865148			−0.432574	−	0.901598i	$-0.642395\pi$
$521$	−19.7474			−0.865148			−0.432574	+	0.901598i	$0.642395\pi$
$522$	−10.6070	+	43.5224i	−0.464255	+	1.90492i
$523$	−8.45511			−0.369716			−0.184858	−	0.982765i	$-0.559183\pi$
$523$	−8.45511			−0.369716			−0.184858	+	0.982765i	$0.559183\pi$
$524$	6.20421	+	10.7460i	0.271032	+	0.469442i
$525$	−26.2744	+	65.5303i	−1.14671	+	2.85998i
$526$	6.29461	−	10.9026i	0.274458	−	0.475375i
$527$	−0.602104	+	1.04287i	−0.0262281	+	0.0454283i
$528$	−10.9776	+	27.3789i	−0.477739	+	1.19151i
$529$	8.04493	+	13.9342i	0.349780	+	0.605836i
$530$	15.7608			0.684604
$531$	−2.35894	+	9.67918i	−0.102369	+	0.420041i
$532$	24.2425			1.05104
$533$	−6.20064	−	10.7398i	−0.268580	−	0.465194i
$534$	7.76313	+	9.88233i	0.335943	+	0.427650i
$535$	33.2114	−	57.5238i	1.43585	−	2.48697i
$536$	0.771291	−	1.33592i	0.0333147	−	0.0577028i
$537$	13.8371	−	1.98204i	0.597116	−	0.0855313i
$538$	−4.79753	−	8.30957i	−0.206836	−	0.358251i
$539$	27.8941			1.20149
$540$	18.7526	+	13.3984i	0.806984	+	0.576575i
$541$	−15.8000			−0.679295			−0.339647	−	0.940553i	$-0.610308\pi$
$541$	−15.8000			−0.679295			−0.339647	+	0.940553i	$0.610308\pi$
$542$	14.1405	+	24.4920i	0.607385	+	1.05202i
$543$	22.4985	−	3.22270i	0.965503	−	0.138299i
$544$	3.21545	−	5.56932i	0.137861	−	0.238782i
$545$	18.3966	−	31.8638i	0.788023	−	1.36490i
$546$	−11.7096	−	14.9062i	−0.501126	−	0.637925i
$547$	−3.60144	−	6.23788i	−0.153986	−	0.266712i	0.778703	−	0.627393i	$-0.215878\pi$
$547$	−3.60144	−	6.23788i	−0.153986	−	0.266712i	−0.932690	+	0.360680i	$0.882545\pi$
$548$	−19.6972			−0.841421
$549$	−32.1163	−	30.6875i	−1.37069	−	1.30971i
$550$	63.2644			2.69760
$551$	23.3045	+	40.3646i	0.992806	+	1.71959i
$552$	2.61380	−	6.51899i	0.111251	−	0.277467i
$553$	10.7514	−	18.6219i	0.457195	−	0.791885i
$554$	25.4491	−	44.0792i	1.08123	−	1.87274i
$555$	29.7787	−	74.2702i	1.26404	−	3.15259i
$556$	−7.56590	−	13.1045i	−0.320866	−	0.555755i
$557$	11.3119			0.479303			0.239651	−	0.970859i	$-0.422967\pi$
$557$	11.3119			0.479303			0.239651	+	0.970859i	$0.422967\pi$
$558$	5.46263	−	1.59772i	0.231252	−	0.0676371i
$559$	10.4705			0.442854
$560$	−38.1615	−	66.0977i	−1.61262	−	2.79314i
$561$	4.10451	+	5.22497i	0.173292	+	0.220598i
$562$	−9.86884	+	17.0933i	−0.416292	+	0.721039i
$563$	−18.9535	+	32.8284i	−0.798794	+	1.38355i	0.121608	+	0.992578i	$0.461195\pi$
$563$	−18.9535	+	32.8284i	−0.798794	+	1.38355i	−0.920402	+	0.390973i	$0.872138\pi$
$564$	2.41788	−	0.346339i	0.101811	−	0.0145835i
$565$	13.9278	+	24.1236i	0.585947	+	1.01489i
$566$	43.8540			1.84332
$567$	31.1157	+	16.1243i	1.30674	+	0.677159i
$568$	9.02358			0.378621
$569$	4.07477	+	7.05771i	0.170823	+	0.295875i	0.938708	−	0.344714i	$-0.112024\pi$
$569$	4.07477	+	7.05771i	0.170823	+	0.295875i	−0.767885	+	0.640588i	$0.778691\pi$
$570$	65.8343	−	9.43015i	2.75750	−	0.394986i
$571$	−6.66234	+	11.5395i	−0.278810	+	0.482914i	−0.971089	−	0.238716i	$-0.923273\pi$
$571$	−6.66234	+	11.5395i	−0.278810	+	0.482914i	0.692279	+	0.721630i	$0.256607\pi$
$572$	−3.06221	+	5.30391i	−0.128037	+	0.221767i
$573$	−3.92012	−	4.99024i	−0.163765	−	0.208470i
$574$	26.8705	+	46.5411i	1.12155	+	1.94259i
$575$	−27.5174			−1.14756
$576$	−0.472711	+	0.138260i	−0.0196963	+	0.00576082i
$577$	−35.7887			−1.48990			−0.744952	−	0.667118i	$-0.767528\pi$
$577$	−35.7887			−1.48990			−0.744952	+	0.667118i	$0.767528\pi$
$578$	13.9183	+	24.1073i	0.578927	+	1.00273i
$579$	6.35479	−	15.8493i	0.264096	−	0.658674i
$580$	−18.7245	+	32.4318i	−0.777494	+	1.34666i
$581$	22.6759	−	39.2758i	0.940755	−	1.62944i
$582$	9.11900	−	22.7434i	0.377995	−	0.942745i
$583$	−3.87159	−	6.70579i	−0.160345	−	0.277726i
$584$	11.1273			0.460451
$585$	−13.5565	−	12.9534i	−0.560493	−	0.535557i
$586$	45.8703			1.89489
$587$	9.97728	+	17.2811i	0.411806	+	0.713269i	0.995087	−	0.0990010i	$-0.0315647\pi$
$587$	9.97728	+	17.2811i	0.411806	+	0.713269i	−0.583281	+	0.812270i	$0.698231\pi$
$588$	9.84977	+	12.5386i	0.406197	+	0.517082i
$589$	2.96091	−	5.12844i	0.122002	−	0.211314i
$590$	−11.5492	+	20.0038i	−0.475472	+	0.823542i
$591$	−20.0419	+	2.87081i	−0.824412	+	0.118089i
$592$	29.2703	+	50.6977i	1.20300	+	2.08366i
$593$	−33.5917			−1.37945			−0.689723	−	0.724074i	$-0.742268\pi$
$593$	−33.5917			−1.37945			−0.689723	+	0.724074i	$0.742268\pi$
$594$	3.03448	−	31.2564i	0.124506	−	1.28247i
$595$	−17.1917			−0.704793
$596$	−4.86130	−	8.42002i	−0.199127	−	0.344897i
$597$	24.2642	−	3.47562i	0.993068	−	0.142248i
$598$	3.69401	−	6.39821i	0.151059	−	0.261642i
$599$	9.27776	−	16.0695i	0.379079	−	0.656584i	−0.611850	−	0.790974i	$-0.709574\pi$
$599$	9.27776	−	16.0695i	0.379079	−	0.656584i	0.990928	+	0.134390i	$0.0429076\pi$
$600$	−17.2776	−	21.9940i	−0.705354	−	0.897903i
$601$	−8.73903	−	15.1364i	−0.356472	−	0.617428i	0.630896	−	0.775867i	$-0.282687\pi$
$601$	−8.73903	−	15.1364i	−0.356472	−	0.617428i	−0.987369	+	0.158439i	$0.949354\pi$
$602$	−45.3739			−1.84930
$603$	−0.710348	+	2.91469i	−0.0289276	+	0.118695i
$604$	10.8493			0.441454
$605$	−1.33253	−	2.30802i	−0.0541752	−	0.0938342i
$606$	−17.1644	+	42.8092i	−0.697256	+	1.73901i
$607$	−9.50726	+	16.4671i	−0.385888	+	0.668377i	−0.991892	−	0.127084i	$-0.959438\pi$
$607$	−9.50726	+	16.4671i	−0.385888	+	0.668377i	0.606004	+	0.795461i	$0.292771\pi$
$608$	−15.8123	+	27.3877i	−0.641272	+	1.11072i
$609$	−21.1920	+	52.8544i	−0.858743	+	2.14177i
$610$	−51.4952	−	89.1923i	−2.08498	−	3.61129i
$611$	−1.98715			−0.0803916
$612$	−0.899302	+	3.69000i	−0.0363521	+	0.149159i
$613$	−15.0707			−0.608699			−0.304349	−	0.952560i	$-0.598439\pi$
$613$	−15.0707			−0.608699			−0.304349	+	0.952560i	$0.598439\pi$
$614$	8.94006	+	15.4846i	0.360791	+	0.624909i
$615$	32.8388	+	41.8032i	1.32419	+	1.68567i
$616$	−10.2632	+	17.7764i	−0.413518	+	0.716233i
$617$	−3.46795	+	6.00667i	−0.139615	+	0.241820i	−0.927351	−	0.374193i	$-0.877920\pi$
$617$	−3.46795	+	6.00667i	−0.139615	+	0.241820i	0.787736	+	0.616013i	$0.211253\pi$
$618$	22.5913	−	3.23600i	0.908756	−	0.130171i
$619$	−1.15130	−	1.99410i	−0.0462745	−	0.0801498i	0.841960	−	0.539539i	$-0.181402\pi$
$619$	−1.15130	−	1.99410i	−0.0462745	−	0.0801498i	−0.888235	+	0.459389i	$0.848068\pi$
$620$	4.75801			0.191086
$621$	−1.31988	+	13.5953i	−0.0529648	+	0.545560i
$622$	2.10212			0.0842872
$623$	7.98745	+	13.8347i	0.320011	+	0.554274i
$624$	13.5790	−	1.94506i	0.543594	−	0.0778648i
$625$	−16.1197	+	27.9201i	−0.644786	+	1.11680i
$626$	−27.0207	+	46.8012i	−1.07996	+	1.87055i
$627$	−20.1843	−	25.6943i	−0.806084	−	1.02613i
$628$	2.78255	+	4.81952i	0.111036	+	0.192320i
$629$	13.1863			0.525771
$630$	58.7472	+	56.1336i	2.34054	+	2.23642i
$631$	32.7280			1.30288			0.651440	−	0.758700i	$-0.274165\pi$
$631$	32.7280			1.30288			0.651440	+	0.758700i	$0.274165\pi$
$632$	4.25916	+	7.37708i	0.169420	+	0.293444i
$633$	−15.3249	+	38.2213i	−0.609108	+	1.51916i
$634$	14.2724	−	24.7205i	0.566828	−	0.981775i
$635$	1.68552	−	2.91941i	0.0668879	−	0.115853i
$636$	1.64719	−	4.10820i	0.0653153	−	0.162901i
$637$	−6.48594	−	11.2340i	−0.256982	−	0.445106i
$638$	51.0267			2.02017
$639$	−16.8433	+	4.92637i	−0.666311	+	0.194884i
$640$	43.9195			1.73607
$641$	−5.17469	−	8.96282i	−0.204388	−	0.354010i	0.745550	−	0.666450i	$-0.232187\pi$
$641$	−5.17469	−	8.96282i	−0.204388	−	0.354010i	−0.949938	+	0.312440i	$0.898854\pi$
$642$	−31.9585	−	40.6827i	−1.26130	−	1.60562i
$643$	−7.16808	+	12.4155i	−0.282682	+	0.489619i	−0.972044	−	0.234797i	$-0.924557\pi$
$643$	−7.16808	+	12.4155i	−0.282682	+	0.489619i	0.689363	+	0.724416i	$0.257891\pi$
$644$	−5.77195	+	9.99731i	−0.227447	+	0.393949i
$645$	−44.4291	+	6.36405i	−1.74939	+	0.250584i
$646$	5.47985	+	9.49138i	0.215602	+	0.373433i
$647$	6.12773			0.240906			0.120453	−	0.992719i	$-0.461565\pi$
$647$	6.12773			0.240906			0.120453	+	0.992719i	$0.461565\pi$
$648$	−11.6951	+	7.48122i	−0.459427	+	0.293890i
$649$	11.3481			0.445453
$650$	−14.7102	−	25.4788i	−0.576982	−	0.999362i
$651$	7.16187	−	1.02587i	0.280696	−	0.0402071i
$652$	−12.1208	+	20.9938i	−0.474686	+	0.822181i
$653$	−23.2737	+	40.3112i	−0.910770	+	1.57750i	−0.0977899	+	0.995207i	$0.531177\pi$
$653$	−23.2737	+	40.3112i	−0.910770	+	1.57750i	−0.812980	+	0.582292i	$0.802156\pi$
$654$	−17.7026	−	22.5351i	−0.692227	−	0.881193i
$655$	21.6363	+	37.4752i	0.845401	+	1.46428i
$656$	−38.8910			−1.51844
$657$	−20.7701	+	6.07490i	−0.810320	+	0.237004i
$658$	8.61133			0.335705
$659$	−4.17330	−	7.22838i	−0.162569	−	0.281578i	0.773220	−	0.634137i	$-0.218645\pi$
$659$	−4.17330	−	7.22838i	−0.162569	−	0.281578i	−0.935789	+	0.352560i	$0.885311\pi$
$660$	9.77002	−	24.3671i	0.380298	−	0.948489i
$661$	7.23211	−	12.5264i	0.281296	−	0.487220i	−0.690408	−	0.723420i	$-0.742569\pi$
$661$	7.23211	−	12.5264i	0.281296	−	0.487220i	0.971704	+	0.236201i	$0.0759023\pi$
$662$	−19.2439	+	33.3314i	−0.747936	+	1.29546i
$663$	1.14990	−	2.86794i	0.0446586	−	0.111382i
$664$	8.98306	+	15.5591i	0.348610	+	0.603811i
$665$	84.5421			3.27840
$666$	−45.0598	−	43.0551i	−1.74603	−	1.66835i
$667$	−22.1945			−0.859376
$668$	−2.21579	−	3.83786i	−0.0857315	−	0.148491i
$669$	11.4515	+	14.5776i	0.442740	+	0.563601i
$670$	−3.47780	+	6.02373i	−0.134359	+	0.232717i
$671$	−25.2994	+	43.8198i	−0.976671	+	1.69164i
$672$	−38.2469	+	5.47851i	−1.47541	+	0.211338i
$673$	−3.99095	−	6.91252i	−0.153840	−	0.266458i	0.778796	−	0.627277i	$-0.215831\pi$
$673$	−3.99095	−	6.91252i	−0.153840	−	0.266458i	−0.932636	+	0.360819i	$0.882497\pi$
$674$	34.8038			1.34059
$675$	44.2577	+	31.6213i	1.70348	+	1.21710i
$676$	−11.8129			−0.454343
$677$	−0.122685	−	0.212497i	−0.00471517	−	0.00816692i	0.863658	−	0.504078i	$-0.168168\pi$
$677$	−0.122685	−	0.212497i	−0.00471517	−	0.00816692i	−0.868373	+	0.495911i	$0.834834\pi$
$678$	21.4765	−	3.07630i	0.824798	−	0.118145i
$679$	15.5743	−	26.9755i	0.597686	−	1.03522i
$680$	3.40525	−	5.89807i	0.130586	−	0.226181i
$681$	9.82153	+	12.5026i	0.376362	+	0.479102i
$682$	−3.24155	−	5.61452i	−0.124125	−	0.214991i
$683$	16.4767			0.630464			0.315232	−	0.949015i	$-0.397918\pi$
$683$	16.4767			0.630464			0.315232	+	0.949015i	$0.397918\pi$
$684$	4.42241	−	18.1460i	0.169095	−	0.693828i
$685$	−68.6911			−2.62455
$686$	4.00365	+	6.93452i	0.152860	+	0.264761i
$687$	6.23201	−	15.5431i	0.237766	−	0.593006i
$688$	16.4180	−	28.4367i	0.625929	−	1.08414i
$689$	−1.80044	+	3.11846i	−0.0685914	+	0.118804i
$690$	−11.7858	+	29.3946i	−0.448677	+	1.11903i
$691$	−18.0282	−	31.2258i	−0.685826	−	1.18789i	−0.973176	−	0.230060i	$-0.926108\pi$
$691$	−18.0282	−	31.2258i	−0.685826	−	1.18789i	0.287350	−	0.957826i	$-0.407226\pi$
$692$	3.90609			0.148487
$693$	9.45229	−	38.7845i	0.359063	−	1.47330i
$694$	51.5566			1.95706
$695$	−26.3850	−	45.7002i	−1.00084	−	1.73351i
$696$	−13.9355	−	17.7396i	−0.528222	−	0.672418i
$697$	−4.38009	+	7.58655i	−0.165908	+	0.287361i
$698$	7.84303	−	13.5845i	0.296863	−	0.514182i
$699$	0.886269	−	0.126950i	0.0335218	−	0.00480168i
$700$	22.9850	+	39.8111i	0.868750	+	1.50472i
$701$	0.0179290			0.000677169			0.000338584	−	1.00000i	$-0.499892\pi$
$701$	0.0179290			0.000677169			0.000338584		1.00000i	$0.499892\pi$
$702$	−13.2937	+	6.04565i	−0.501737	+	0.228178i
$703$	−64.8448			−2.44567
$704$	0.280508	+	0.485855i	0.0105721	+	0.0183113i
$705$	8.43202	−	1.20781i	0.317568	−	0.0454887i
$706$	19.8421	−	34.3676i	0.746769	−	1.29344i
$707$	−29.3150	+	50.7751i	−1.10250	+	1.90959i
$708$	4.00716	+	5.10105i	0.150598	+	0.191709i
$709$	10.1995	+	17.6661i	0.383052	+	0.663465i	0.991497	−	0.130131i	$-0.0415398\pi$
$709$	10.1995	+	17.6661i	0.383052	+	0.663465i	−0.608445	+	0.793596i	$0.708206\pi$
$710$	−40.6879			−1.52699
$711$	−11.9776	−	11.4447i	−0.449194	−	0.429210i
$712$	−6.32846			−0.237169
$713$	1.40994	+	2.44209i	0.0528027	+	0.0914569i
$714$	−4.98311	+	12.4282i	−0.186488	+	0.465115i
$715$	−10.6790	+	18.4966i	−0.399373	+	0.691734i
$716$	4.55078	−	7.88219i	0.170071	−	0.294571i
$717$	−2.38837	+	5.95675i	−0.0891952	+	0.222459i
$718$	15.2674	+	26.4439i	0.569774	+	0.986877i
$719$	8.27716			0.308686			0.154343	−	0.988017i	$-0.450674\pi$
$719$	8.27716			0.308686			0.154343	+	0.988017i	$0.450674\pi$
$720$	−56.4370	+	16.5068i	−2.10328	+	0.615174i
$721$	29.0110			1.08043
$722$	−10.1465	−	17.5742i	−0.377613	−	0.654044i
$723$	−26.6499	−	33.9249i	−0.991120	−	1.26168i
$724$	7.39936	−	12.8161i	0.274995	−	0.476305i
$725$	−44.1914	+	76.5417i	−1.64123	+	2.84269i
$726$	−2.05475	+	0.294324i	−0.0762589	+	0.0109234i
$727$	6.00049	+	10.3931i	0.222546	+	0.385460i	0.955580	−	0.294731i	$-0.0952300\pi$
$727$	6.00049	+	10.3931i	0.222546	+	0.385460i	−0.733035	+	0.680191i	$0.761897\pi$
$728$	9.54562			0.353784
$729$	17.7456	−	20.3493i	0.657246	−	0.753676i
$730$	−50.1738			−1.85701
$731$	−3.69814	−	6.40537i	−0.136781	−	0.236911i
$732$	−28.6308	+	4.10109i	−1.05822	+	0.151581i
$733$	21.3066	−	36.9042i	0.786979	−	1.36309i	−0.140831	−	0.990034i	$-0.544977\pi$
$733$	21.3066	−	36.9042i	0.786979	−	1.36309i	0.927810	−	0.373054i	$-0.121689\pi$
$734$	5.24917	−	9.09183i	0.193751	−	0.335586i
$735$	34.3497	+	43.7265i	1.26701	+	1.61288i
$736$	−7.52957	−	13.0416i	−0.277544	−	0.480720i
$737$	3.41725			0.125876
$738$	39.7387	−	11.6229i	1.46280	−	0.427844i
$739$	7.81669			0.287542			0.143771	−	0.989611i	$-0.454077\pi$
$739$	7.81669			0.287542			0.143771	+	0.989611i	$0.454077\pi$
$740$	−26.0505	−	45.1208i	−0.957636	−	1.65867i
$741$	−5.65477	+	14.1034i	−0.207733	+	0.518101i
$742$	7.80222	−	13.5138i	0.286429	−	0.496109i
$743$	−19.2261	+	33.3006i	−0.705337	+	1.22168i	0.261233	+	0.965276i	$0.415871\pi$
$743$	−19.2261	+	33.3006i	−0.705337	+	1.22168i	−0.966570	+	0.256404i	$0.917462\pi$
$744$	−1.06664	+	2.66027i	−0.0391048	+	0.0975301i
$745$	−16.9531	−	29.3636i	−0.621114	−	1.07580i
$746$	−3.88432			−0.142215
$747$	−25.2621	−	24.1382i	−0.924292	−	0.883171i
$748$	4.32625			0.158183
$749$	−32.8820	−	56.9533i	−1.20148	−	2.08103i
$750$	40.6944	+	51.8033i	1.48595	+	1.89159i
$751$	−8.47219	+	14.6743i	−0.309154	+	0.535471i	−0.978178	−	0.207770i	$-0.933379\pi$
$751$	−8.47219	+	14.6743i	−0.309154	+	0.535471i	0.669023	+	0.743242i	$0.266713\pi$
$752$	−3.11590	+	5.39690i	−0.113625	+	0.196805i
$753$	15.3533	−	2.19922i	0.559506	−	0.0801440i
$754$	−11.8647	−	20.5503i	−0.432088	−	0.748398i
$755$	37.8356			1.37698
$756$	20.7716	−	9.44642i	0.755455	−	0.343563i
$757$	5.47047			0.198828			0.0994138	−	0.995046i	$-0.468303\pi$
$757$	5.47047			0.198828			0.0994138	+	0.995046i	$0.468303\pi$
$758$	4.95651	+	8.58493i	0.180029	+	0.311819i
$759$	15.4018	−	2.20616i	0.559049	−	0.0800786i
$760$	−16.7457	+	29.0044i	−0.607430	+	1.05210i
$761$	7.47038	−	12.9391i	0.270801	−	0.469041i	−0.698266	−	0.715838i	$-0.746045\pi$
$761$	7.47038	−	12.9391i	0.270801	−	0.469041i	0.969067	+	0.246797i	$0.0793782\pi$
$762$	−1.62194	−	2.06470i	−0.0587566	−	0.0747962i
$763$	−18.2141	−	31.5478i	−0.659396	−	1.14211i
$764$	−4.13190			−0.149487
$765$	−3.13619	+	12.8684i	−0.113389	+	0.465257i
$766$	−30.9178			−1.11711
$767$	−2.63866	−	4.57030i	−0.0952765	−	0.165024i
$768$	12.9419	−	32.2780i	0.467001	−	1.16473i
$769$	4.58624	−	7.94360i	0.165384	−	0.286453i	−0.771408	−	0.636341i	$-0.780447\pi$
$769$	4.58624	−	7.94360i	0.165384	−	0.286453i	0.936792	+	0.349888i	$0.113780\pi$
$770$	46.2776	−	80.1551i	1.66773	−	2.88859i
$771$	6.98528	−	17.4218i	0.251569	−	0.627430i
$772$	−5.55919	−	9.62880i	−0.200080	−	0.346548i
$773$	16.4820			0.592816			0.296408	−	0.955061i	$-0.404211\pi$
$773$	16.4820			0.592816			0.296408	+	0.955061i	$0.404211\pi$
$774$	−8.27729	+	33.9632i	−0.297521	+	1.22078i
$775$	11.2293			0.403368
$776$	6.16975	+	10.6863i	0.221481	+	0.383617i
$777$	−48.9403	−	62.3002i	−1.75572	−	2.23501i
$778$	−4.09478	+	7.09236i	−0.146805	+	0.254273i
$779$	21.5396	−	37.3076i	0.771735	−	1.33668i
$780$	−12.0852	+	1.73110i	−0.432721	+	0.0619833i
$781$	9.99488	+	17.3116i	0.357645	+	0.619459i
$782$	−5.21885			−0.186626
$783$	35.6966	+	25.5046i	1.27569	+	0.911458i
$784$	−40.6804			−1.45287
$785$	9.70376	+	16.8074i	0.346342	+	0.599882i
$786$	33.3629	−	4.77892i	1.19002	−	0.170459i
$787$	10.7951	−	18.6976i	0.384802	−	0.666497i	−0.606940	−	0.794748i	$-0.707603\pi$
$787$	10.7951	−	18.6976i	0.384802	−	0.666497i	0.991742	+	0.128251i	$0.0409363\pi$
$788$	−6.59141	+	11.4167i	−0.234809	+	0.406701i
$789$	−7.61643	−	9.69558i	−0.271152	−	0.345172i
$790$	−19.2048	−	33.2637i	−0.683277	−	1.18347i
$791$	27.5793			0.980608
$792$	11.4338	+	10.9251i	0.406281	+	0.388206i
$793$	23.5304			0.835589
$794$	28.3167	+	49.0460i	1.00492	+	1.74058i
$795$	5.74434	−	14.3268i	0.203731	−	0.508119i
$796$	7.98007	−	13.8219i	0.282846	−	0.489904i
$797$	22.0810	−	38.2453i	0.782148	−	1.35472i	−0.148540	−	0.988906i	$-0.547458\pi$
$797$	22.0810	−	38.2453i	0.782148	−	1.35472i	0.930688	−	0.365813i	$-0.119209\pi$
$798$	24.5049	−	61.1171i	0.867465	−	2.16352i
$799$	0.701856	+	1.21565i	0.0248299	+	0.0430066i
$800$	−59.9683			−2.12020
$801$	11.8126	−	3.45499i	0.417379	−	0.122076i
$802$	−25.0400			−0.884193
$803$	12.3251	+	21.3476i	0.434942	+	0.753342i
$804$	1.20668	+	1.53608i	0.0425562	+	0.0541733i
$805$	−20.1289	+	34.8642i	−0.709449	+	1.22880i
$806$	−1.50745	+	2.61098i	−0.0530976	+	0.0919677i
$807$	−9.30210	+	1.33244i	−0.327449	+	0.0469041i
$808$	−11.6131	−	20.1145i	−0.408549	−	0.707627i
$809$	−49.2574			−1.73180			−0.865900	−	0.500218i	$-0.833253\pi$
$809$	−49.2574			−1.73180			−0.865900	+	0.500218i	$0.833253\pi$
$810$	52.7340	−	33.7333i	1.85288	−	1.18527i
$811$	−2.96236			−0.104022			−0.0520112	−	0.998647i	$-0.516563\pi$
$811$	−2.96236			−0.104022			−0.0520112	+	0.998647i	$0.516563\pi$
$812$	18.5388	+	32.1102i	0.650585	+	1.12685i
$813$	27.4174	−	3.92729i	0.961572	−	0.137736i
$814$	−35.4955	+	61.4800i	−1.24412	+	2.15487i
$815$	−42.2695	+	73.2129i	−1.48064	+	2.56454i
$816$	−5.98595	−	7.62002i	−0.209550	−	0.266754i
$817$	18.1860	+	31.4990i	0.636247	+	1.10201i
$818$	−56.6160			−1.97953
$819$	−17.8178	+	5.21138i	−0.622603	+	0.182100i
$820$	34.6129			1.20873
$821$	18.3715	+	31.8205i	0.641171	+	1.11054i	0.985172	+	0.171572i	$0.0548846\pi$
$821$	18.3715	+	31.8205i	0.641171	+	1.11054i	−0.344000	+	0.938970i	$0.611782\pi$
$822$	−19.9104	+	49.6580i	−0.694456	+	1.73202i
$823$	−26.0434	+	45.1085i	−0.907815	+	1.57238i	−0.0907225	+	0.995876i	$0.528918\pi$
$823$	−26.0434	+	45.1085i	−0.907815	+	1.57238i	−0.817093	+	0.576506i	$0.804416\pi$
$824$	−5.74635	+	9.95297i	−0.200184	+	0.346728i
$825$	23.0580	−	57.5083i	0.802777	−	2.00218i
$826$	11.4346	+	19.8054i	0.397862	+	0.689117i
$827$	23.0042			0.799936			0.399968	−	0.916529i	$-0.369021\pi$
$827$	23.0042			0.799936			0.399968	+	0.916529i	$0.369021\pi$
$828$	6.43024	+	6.14417i	0.223466	+	0.213525i
$829$	−16.7500			−0.581750			−0.290875	−	0.956761i	$-0.593946\pi$
$829$	−16.7500			−0.581750			−0.290875	+	0.956761i	$0.593946\pi$
$830$	−40.5052	−	70.1570i	−1.40596	−	2.43519i
$831$	−30.7932	−	39.1992i	−1.06820	−	1.35981i
$832$	0.130447	−	0.225942i	0.00452245	−	0.00783311i
$833$	−4.58162	+	7.93561i	−0.158744	+	0.274952i
$834$	−40.6853	+	5.82779i	−1.40882	+	0.201800i
$835$	−7.72725	−	13.3840i	−0.267413	−	0.463172i
$836$	−21.2748			−0.735804
$837$	0.538614	−	5.54795i	0.0186172	−	0.191765i
$838$	−41.9762			−1.45004
$839$	−26.4104	−	45.7442i	−0.911790	−	1.57927i	−0.811534	−	0.584305i	$-0.801367\pi$
$839$	−26.4104	−	45.7442i	−0.911790	−	1.57927i	−0.100256	−	0.994962i	$-0.531966\pi$
$840$	−40.5046	+	5.80191i	−1.39754	+	0.200185i
$841$	−21.1431	+	36.6210i	−0.729074	+	1.26279i
$842$	−13.0548	+	22.6115i	−0.449897	+	0.779245i
$843$	11.9412	+	15.2010i	0.411277	+	0.523549i
$844$	13.4062	+	23.2203i	0.461462	+	0.799275i
$845$	−41.1959			−1.41718
$846$	1.57091	−	6.44575i	0.0540092	−	0.221609i
$847$	−2.63864			−0.0906647
$848$	5.64627	+	9.77963i	0.193894	+	0.335834i
$849$	15.9835	−	39.8640i	0.548553	−	1.36813i
$850$	−10.3912	+	17.9981i	−0.356415	+	0.617329i
$851$	15.4391	−	26.7413i	0.529245	−	0.916679i
$852$	−4.25237	+	10.6057i	−0.145684	+	0.363346i
$853$	9.70497	+	16.8095i	0.332292	+	0.575546i	0.982961	−	0.183815i	$-0.0588448\pi$
$853$	9.70497	+	16.8095i	0.332292	+	0.575546i	−0.650669	+	0.759361i	$0.725511\pi$
$854$	−101.969			−3.48931
$855$	15.4225	−	63.2815i	0.527439	−	2.16418i
$856$	26.0524			0.890453
$857$	−17.7352	−	30.7182i	−0.605821	−	1.04931i	−0.991921	−	0.126856i	$-0.959511\pi$
$857$	−17.7352	−	30.7182i	−0.605821	−	1.04931i	0.386100	−	0.922457i	$-0.373822\pi$
$858$	10.2762	+	13.0814i	0.350823	+	0.446592i
$859$	21.6861	−	37.5615i	0.739921	−	1.28158i	−0.212609	−	0.977137i	$-0.568196\pi$
$859$	21.6861	−	37.5615i	0.739921	−	1.28158i	0.952530	−	0.304444i	$-0.0984705\pi$
$860$	−14.6119	+	25.3086i	−0.498263	+	0.863016i
$861$	52.1001	−	7.46285i	1.77557	−	0.254333i
$862$	30.3899	+	52.6368i	1.03508	+	1.79282i
$863$	−49.8761			−1.69780			−0.848901	−	0.528551i	$-0.822735\pi$
$863$	−49.8761			−1.69780			−0.848901	+	0.528551i	$0.822735\pi$
$864$	−2.87638	+	29.6280i	−0.0978566	+	1.00796i
$865$	13.6219			0.463160
$866$	−17.6327	−	30.5407i	−0.599183	−	1.03782i
$867$	26.9867	−	3.86560i	0.916518	−	0.131283i
$868$	2.35541	−	4.07969i	0.0799479	−	0.138474i
$869$	−9.43524	+	16.3423i	−0.320068	+	0.554375i
$870$	62.8359	+	79.9890i	2.13033	+	2.71188i
$871$	−0.794579	−	1.37625i	−0.0269233	−	0.0466325i
$872$	14.4311			0.488698
$873$	−17.3505	−	16.5786i	−0.587227	−	0.561102i
$874$	25.6642			0.868105
$875$	41.8703	+	72.5215i	1.41547	+	2.45167i
$876$	−5.24376	+	13.0783i	−0.177170	+	0.441875i
$877$	−16.0183	+	27.7445i	−0.540899	+	0.936864i	0.457954	+	0.888976i	$0.348582\pi$
$877$	−16.0183	+	27.7445i	−0.540899	+	0.936864i	−0.998853	+	0.0478880i	$0.984751\pi$
$878$	−14.4507	+	25.0294i	−0.487689	+	0.844702i
$879$	16.7184	−	41.6969i	0.563898	−	1.40640i
$880$	33.4899	+	58.0063i	1.12895	+	1.95539i
$881$	−19.6917			−0.663430			−0.331715	−	0.943380i	$-0.607627\pi$
$881$	−19.6917			−0.663430			−0.331715	+	0.943380i	$0.607627\pi$
$882$	41.5671	−	12.1577i	1.39964	−	0.409370i
$883$	−35.0120			−1.17825			−0.589123	−	0.808043i	$-0.700527\pi$
$883$	−35.0120			−1.17825			−0.589123	+	0.808043i	$0.700527\pi$
$884$	−1.00594	−	1.74234i	−0.0338334	−	0.0586012i
$885$	13.9744	+	17.7892i	0.469745	+	0.597977i
$886$	−12.7950	+	22.1617i	−0.429858	+	0.744536i
$887$	15.1681	−	26.2719i	0.509294	−	0.882124i	−0.490648	−	0.871358i	$-0.663240\pi$
$887$	15.1681	−	26.2719i	0.509294	−	0.882124i	0.999942	−	0.0107656i	$-0.00342685\pi$
$888$	31.0675	−	4.45013i	1.04256	−	0.149337i
$889$	−1.66881	−	2.89046i	−0.0559699	−	0.0969428i
$890$	28.5354			0.956510
$891$	−27.3066	−	14.1505i	−0.914807	−	0.474058i
$892$	12.0702			0.404139
$893$	−3.45145	−	5.97808i	−0.115498	−	0.200049i
$894$	−26.1414	+	3.74452i	−0.874301	+	0.125235i
$895$	15.8702	−	27.4880i	0.530483	−	0.918824i
$896$	21.7420	−	37.6582i	0.726348	−	1.25807i
$897$	−4.46972	−	5.68987i	−0.149240	−	0.189979i
$898$	−7.62246	−	13.2025i	−0.254365	−	0.440573i
$899$	9.05713			0.302072
$900$	33.9924	−	9.94219i	1.13308	−	0.331406i
$901$	2.54364			0.0847411
$902$	−23.5811	−	40.8437i	−0.785165	−	1.35995i
$903$	−16.5375	+	41.2456i	−0.550332	+	1.37257i
$904$	−5.46277	+	9.46180i	−0.181689	+	0.314695i
$905$	25.8042	−	44.6942i	0.857761	−	1.48569i
$906$	10.9668	−	27.3520i	0.364348	−	0.908710i
$907$	−5.92394	−	10.2606i	−0.196701	−	0.340697i	0.750756	−	0.660580i	$-0.229690\pi$
$907$	−5.92394	−	10.2606i	−0.196701	−	0.340697i	−0.947457	+	0.319883i	$0.896356\pi$
$908$	10.3521			0.343548
$909$	32.6584	+	31.2055i	1.08321	+	1.03502i
$910$	−43.0418			−1.42682
$911$	6.53200	+	11.3138i	0.216415	+	0.374841i	0.953709	−	0.300730i	$-0.0972303\pi$
$911$	6.53200	+	11.3138i	0.216415	+	0.374841i	−0.737294	+	0.675571i	$0.763897\pi$
$912$	29.4365	+	37.4722i	0.974741	+	1.24083i
$913$	−19.9000	+	34.4678i	−0.658594	+	1.14072i
$914$	23.1425	−	40.0841i	0.765487	−	1.32586i
$915$	−99.8458	+	14.3020i	−3.30080	+	0.472809i
$916$	−5.45178	−	9.44277i	−0.180132	−	0.311998i
$917$	42.8435			1.41482
$918$	8.39374	+	5.99717i	0.277035	+	0.197936i
$919$	21.6116			0.712900			0.356450	−	0.934314i	$-0.383987\pi$
$919$	21.6116			0.712900			0.356450	+	0.934314i	$0.383987\pi$
$920$	−7.97405	−	13.8115i	−0.262897	−	0.455350i
$921$	17.3342	−	2.48296i	0.571180	−	0.0818163i
$922$	−7.81199	+	13.5308i	−0.257274	+	0.445612i
$923$	4.64802	−	8.05060i	0.152991	−	0.264989i
$924$	−16.0567	−	20.4399i	−0.528227	−	0.672424i
$925$	−61.4812	−	106.489i	−2.02149	−	3.50133i
$926$	−28.7090			−0.943437
$927$	5.29231	−	21.7153i	0.173822	−	0.713224i
$928$	−48.3682			−1.58777
$929$	−14.0492	−	24.3340i	−0.460940	−	0.798372i	0.538068	−	0.842902i	$-0.319154\pi$
$929$	−14.0492	−	24.3340i	−0.460940	−	0.798372i	−0.999008	+	0.0445296i	$0.985821\pi$
$930$	4.80953	−	11.9953i	0.157711	−	0.393342i
$931$	22.5306	−	39.0241i	0.738410	−	1.27896i
$932$	0.291478	−	0.504855i	0.00954768	−	0.0165371i
$933$	0.766161	−	1.91086i	0.0250830	−	0.0625587i
$934$	−19.7560	−	34.2184i	−0.646436	−	1.11966i
$935$	15.0872			0.493404
$936$	1.74135	−	7.14509i	0.0569179	−	0.233544i
$937$	3.48892			0.113978			0.0569891	−	0.998375i	$-0.481850\pi$
$937$	3.48892			0.113978			0.0569891	+	0.998375i	$0.481850\pi$
$938$	3.44331	+	5.96399i	0.112428	+	0.194731i
$939$	32.6948	+	41.6200i	1.06696	+	1.35822i
$940$	2.77314	−	4.80322i	0.0904499	−	0.156664i
$941$	11.4261	−	19.7905i	0.372479	−	0.645153i	−0.617467	−	0.786597i	$-0.711841\pi$
$941$	11.4261	−	19.7905i	0.372479	−	0.645153i	0.989946	+	0.141444i	$0.0451745\pi$
$942$	14.9631	−	2.14332i	0.487523	−	0.0698331i
$943$	10.2568	+	17.7653i	0.334008	+	0.578519i
$944$	−16.5499			−0.538654
$945$	72.4380	−	32.9431i	2.35641	−	1.07164i
$946$	39.8194			1.29464
$947$	8.90472	+	15.4234i	0.289364	+	0.501194i	0.973658	−	0.228013i	$-0.0732227\pi$
$947$	8.90472	+	15.4234i	0.289364	+	0.501194i	−0.684294	+	0.729206i	$0.739889\pi$
$948$	−10.6777	+	1.52948i	−0.346795	+	0.0496751i
$949$	5.73164	−	9.92749i	0.186057	−	0.322260i
$950$	51.0998	−	88.5074i	1.65790	−	2.87156i
$951$	−17.2694	−	21.9837i	−0.560000	−	0.712870i
$952$	−3.37148	−	5.83958i	−0.109270	−	0.189262i
$953$	−36.5963			−1.18547			−0.592734	−	0.805398i	$-0.701952\pi$
$953$	−36.5963			−1.18547			−0.592734	+	0.805398i	$0.701952\pi$
$954$	−8.69207	−	8.30537i	−0.281416	−	0.268896i
$955$	−14.4094			−0.466278
$956$	2.08935	+	3.61886i	0.0675744	+	0.117042i
$957$	18.5978	−	46.3841i	0.601180	−	1.49939i
$958$	−27.4565	+	47.5561i	−0.887080	+	1.53647i
$959$	−34.0049	+	58.8983i	−1.09808	+	1.90192i
$960$	−0.416194	+	1.03802i	−0.0134326	+	0.0335019i
$961$	14.9246	+	25.8502i	0.481440	+	0.833878i
$962$	33.0136			1.06440
$963$	−48.6291	+	14.2232i	−1.56705	+	0.458335i
$964$	−28.0897			−0.904707
$965$	−19.3869	−	33.5791i	−0.624086	−	1.08095i
$966$	19.3695	+	24.6571i	0.623204	+	0.793329i
$967$	7.22774	−	12.5188i	0.232428	−	0.402578i	−0.726094	−	0.687596i	$-0.758666\pi$
$967$	7.22774	−	12.5188i	0.232428	−	0.402578i	0.958522	+	0.285018i	$0.0919995\pi$
$968$	0.522648	−	0.905253i	0.0167985	−	0.0290959i
$969$	10.6251	−	1.52194i	0.341326	−	0.0488918i
$970$	−27.8198	−	48.1853i	−0.893240	−	1.54714i
$971$	4.66555			0.149725			0.0748624	−	0.997194i	$-0.476148\pi$
$971$	4.66555			0.149725			0.0748624	+	0.997194i	$0.476148\pi$
$972$	−3.28160	−	17.2712i	−0.105257	−	0.553974i
$973$	−52.2467			−1.67495
$974$	17.0453	+	29.5234i	0.546168	+	0.945991i
$975$	−28.5221	+	4.08553i	−0.913439	+	0.130842i
$976$	36.8962	−	63.9061i	1.18102	−	2.04558i
$977$	14.3557	−	24.8649i	0.459281	−	0.795498i	−0.539642	−	0.841895i	$-0.681440\pi$
$977$	14.3557	−	24.8649i	0.459281	−	0.795498i	0.998923	+	0.0463964i	$0.0147737\pi$
$978$	40.6750	+	51.7785i	1.30064	+	1.65569i
$979$	−7.00966	−	12.1411i	−0.224030	−	0.388031i
$980$	36.2054			1.15654
$981$	−26.9369	+	7.87856i	−0.860028	+	0.251543i
$982$	−4.17382			−0.133192
$983$	8.58705	+	14.8732i	0.273884	+	0.474382i	0.969853	−	0.243691i	$-0.0783581\pi$
$983$	8.58705	+	14.8732i	0.273884	+	0.474382i	−0.695969	+	0.718072i	$0.745025\pi$
$984$	−7.75940	+	19.3525i	−0.247361	+	0.616935i
$985$	−22.9866	+	39.8140i	−0.732414	+	1.26858i
$986$	−8.38116	+	14.5166i	−0.266911	+	0.462303i
$987$	3.13858	−	7.82784i	0.0999021	−	0.249163i
$988$	4.94681	+	8.56812i	0.157379	+	0.272588i
$989$	−17.3198			−0.550738
$990$	−51.5556	−	49.2619i	−1.63854	−	1.56565i
$991$	−5.85901			−0.186117			−0.0930587	−	0.995661i	$-0.529664\pi$
$991$	−5.85901			−0.186117			−0.0930587	+	0.995661i	$0.529664\pi$
$992$	3.07266	+	5.32201i	0.0975571	+	0.168974i
$993$	23.2850	+	29.6414i	0.738926	+	0.940641i
$994$	−20.1422	+	34.8873i	−0.638871	+	1.10656i
$995$	27.8294	−	48.2019i	0.882250	−	1.52810i
$996$	−22.5204	+	3.22584i	−0.713587	+	0.102215i
$997$	−10.5099	−	18.2038i	−0.332853	−	0.576519i	0.650217	−	0.759749i	$-0.274678\pi$
$997$	−10.5099	−	18.2038i	−0.332853	−	0.576519i	−0.983070	+	0.183230i	$0.941345\pi$
$998$	69.1837			2.18997
$999$	−55.5608	+	25.2677i	−1.75787	+	0.799436i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.e.a.202.8	✓	66
9.4	even	3		5427.2.a.p.1.26		33
9.5	odd	6		5427.2.a.o.1.8		33
9.7	even	3	inner	603.2.e.a.403.8	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
603.2.e.a.202.8	✓	66	1.1	even	1	trivial
603.2.e.a.403.8	yes	66	9.7	even	3	inner
5427.2.a.o.1.8		33	9.5	odd	6
5427.2.a.p.1.26		33	9.4	even	3

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.884275 - 1.53161i) q^{2} +(-1.71455 + 0.245593i) q^{3} +(-0.563885 + 0.976678i) q^{4} +(-1.96647 + 3.40603i) q^{5} +(1.89229 + 2.40885i) q^{6} +(1.94697 + 3.37225i) q^{7} -1.54258 q^{8} +(2.87937 - 0.842165i) q^{9} +O(q^{10})\)	\(q+(-0.884275 - 1.53161i) q^{2} +(-1.71455 + 0.245593i) q^{3} +(-0.563885 + 0.976678i) q^{4} +(-1.96647 + 3.40603i) q^{5} +(1.89229 + 2.40885i) q^{6} +(1.94697 + 3.37225i) q^{7} -1.54258 q^{8} +(2.87937 - 0.842165i) q^{9} +6.95560 q^{10} +(-1.70863 - 2.95943i) q^{11} +(0.726944 - 1.81305i) q^{12} +(-0.794579 + 1.37625i) q^{13} +(3.44331 - 5.96399i) q^{14} +(2.53512 - 6.32276i) q^{15} +(2.49184 + 4.31599i) q^{16} +1.12257 q^{17} +(-3.83602 - 3.66536i) q^{18} -5.52036 q^{19} +(-2.21773 - 3.84121i) q^{20} +(-4.16638 - 5.30373i) q^{21} +(-3.02179 + 5.23390i) q^{22} +(1.31436 - 2.27653i) q^{23} +(2.64484 - 0.378848i) q^{24} +(-5.23401 - 9.06557i) q^{25} +2.81051 q^{26} +(-4.72999 + 2.15109i) q^{27} -4.39146 q^{28} +(-4.22156 - 7.31196i) q^{29} +(-11.9257 + 1.70825i) q^{30} +(-0.536361 + 0.929005i) q^{31} +(2.86436 - 4.96121i) q^{32} +(3.65634 + 4.65446i) q^{33} +(-0.992662 - 1.71934i) q^{34} -15.3146 q^{35} +(-0.801109 + 3.28710i) q^{36} +11.7465 q^{37} +(4.88151 + 8.45503i) q^{38} +(1.02435 - 2.55480i) q^{39} +(3.03344 - 5.25408i) q^{40} +(-3.90184 + 6.75819i) q^{41} +(-4.43901 + 11.0712i) q^{42} +(-3.29435 - 5.70598i) q^{43} +3.85388 q^{44} +(-2.79376 + 11.4633i) q^{45} -4.64901 q^{46} +(0.625222 + 1.08292i) q^{47} +(-5.33236 - 6.78800i) q^{48} +(-4.08137 + 7.06913i) q^{49} +(-9.25661 + 16.0329i) q^{50} +(-1.92471 + 0.275696i) q^{51} +(-0.896103 - 1.55210i) q^{52} +2.26591 q^{53} +(7.47724 + 5.34235i) q^{54} +13.4399 q^{55} +(-3.00336 - 5.20197i) q^{56} +(9.46493 - 1.35576i) q^{57} +(-7.46604 + 12.9316i) q^{58} +(-1.66041 + 2.87592i) q^{59} +(4.74578 + 6.04130i) q^{60} +(-7.40341 - 12.8231i) q^{61} +1.89716 q^{62} +(8.44602 + 8.07027i) q^{63} -0.164172 q^{64} +(-3.12503 - 5.41271i) q^{65} +(3.89561 - 9.71592i) q^{66} +(-0.500000 + 0.866025i) q^{67} +(-0.633001 + 1.09639i) q^{68} +(-1.69443 + 4.22603i) q^{69} +(13.5423 + 23.4560i) q^{70} -5.84966 q^{71} +(-4.44166 + 1.29911i) q^{72} -7.21343 q^{73} +(-10.3871 - 17.9910i) q^{74} +(11.2004 + 14.2579i) q^{75} +(3.11285 - 5.39161i) q^{76} +(6.65328 - 11.5238i) q^{77} +(-4.81876 + 0.690242i) q^{78} +(-2.76106 - 4.78229i) q^{79} -19.6005 q^{80} +(7.58152 - 4.84980i) q^{81} +13.8012 q^{82} +(-5.82339 - 10.0864i) q^{83} +(7.52939 - 1.07851i) q^{84} +(-2.20750 + 3.82351i) q^{85} +(-5.82622 + 10.0913i) q^{86} +(9.03385 + 11.4999i) q^{87} +(2.63570 + 4.56516i) q^{88} +4.10251 q^{89} +(20.0277 - 5.85776i) q^{90} -6.18808 q^{91} +(1.48229 + 2.56741i) q^{92} +(0.691461 - 1.72455i) q^{93} +(1.10574 - 1.91519i) q^{94} +(10.8556 - 18.8025i) q^{95} +(-3.69265 + 9.20972i) q^{96} +(-3.99963 - 6.92756i) q^{97} +14.4362 q^{98} +(-7.41209 - 7.08234i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 7 q^{2} - 33 q^{4} - 18 q^{5} - 3 q^{6} + 36 q^{8} + 4 q^{9}+O(q^{10}) \) 66 * q - 7 * q^2 - 33 * q^4 - 18 * q^5 - 3 * q^6 + 36 * q^8 + 4 * q^9	\( 66 q - 7 q^{2} - 33 q^{4} - 18 q^{5} - 3 q^{6} + 36 q^{8} + 4 q^{9} - 8 q^{11} + q^{12} - 7 q^{14} + 3 q^{15} - 33 q^{16} + 66 q^{17} - 11 q^{18} - 29 q^{20} + q^{21} - 17 q^{23} + 47 q^{24} - 33 q^{25} + 60 q^{26} - 21 q^{27} - 54 q^{28} - 39 q^{29} - 34 q^{30} - 53 q^{32} + 8 q^{33} - 6 q^{34} + 62 q^{35} - 35 q^{36} + 24 q^{37} - 30 q^{38} - 5 q^{39} - 6 q^{40} - 38 q^{41} + 65 q^{42} + 22 q^{44} - 9 q^{45} + 12 q^{46} - 58 q^{47} - 59 q^{48} - 33 q^{49} - 31 q^{50} + 26 q^{51} + 9 q^{52} + 128 q^{53} - 22 q^{54} - 36 q^{55} - 32 q^{56} - 34 q^{57} + 3 q^{58} - 39 q^{59} + 127 q^{60} + 138 q^{62} - 35 q^{63} + 132 q^{64} - 28 q^{65} - 94 q^{66} - 33 q^{67} - 62 q^{68} + 60 q^{69} - 6 q^{70} + 42 q^{71} - 34 q^{72} - 25 q^{74} + 55 q^{75} - 6 q^{76} - 91 q^{77} + 125 q^{78} + 116 q^{80} - 90 q^{82} - 61 q^{83} - 26 q^{84} + 15 q^{85} - 47 q^{86} - q^{87} - 12 q^{88} + 110 q^{89} - 91 q^{90} + 36 q^{91} - 41 q^{92} - 11 q^{93} - 21 q^{94} - 6 q^{95} + 80 q^{96} - 12 q^{97} + 80 q^{98} - 38 q^{99}+O(q^{100}) \) 66 * q - 7 * q^2 - 33 * q^4 - 18 * q^5 - 3 * q^6 + 36 * q^8 + 4 * q^9 - 8 * q^11 + q^12 - 7 * q^14 + 3 * q^15 - 33 * q^16 + 66 * q^17 - 11 * q^18 - 29 * q^20 + q^21 - 17 * q^23 + 47 * q^24 - 33 * q^25 + 60 * q^26 - 21 * q^27 - 54 * q^28 - 39 * q^29 - 34 * q^30 - 53 * q^32 + 8 * q^33 - 6 * q^34 + 62 * q^35 - 35 * q^36 + 24 * q^37 - 30 * q^38 - 5 * q^39 - 6 * q^40 - 38 * q^41 + 65 * q^42 + 22 * q^44 - 9 * q^45 + 12 * q^46 - 58 * q^47 - 59 * q^48 - 33 * q^49 - 31 * q^50 + 26 * q^51 + 9 * q^52 + 128 * q^53 - 22 * q^54 - 36 * q^55 - 32 * q^56 - 34 * q^57 + 3 * q^58 - 39 * q^59 + 127 * q^60 + 138 * q^62 - 35 * q^63 + 132 * q^64 - 28 * q^65 - 94 * q^66 - 33 * q^67 - 62 * q^68 + 60 * q^69 - 6 * q^70 + 42 * q^71 - 34 * q^72 - 25 * q^74 + 55 * q^75 - 6 * q^76 - 91 * q^77 + 125 * q^78 + 116 * q^80 - 90 * q^82 - 61 * q^83 - 26 * q^84 + 15 * q^85 - 47 * q^86 - q^87 - 12 * q^88 + 110 * q^89 - 91 * q^90 + 36 * q^91 - 41 * q^92 - 11 * q^93 - 21 * q^94 - 6 * q^95 + 80 * q^96 - 12 * q^97 + 80 * q^98 - 38 * q^99

Introduction

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