LMFDB - Embedded newform 558.2.q.a.185.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [558,2,Mod(185,558)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("558.185"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(558, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 558 = 2 \cdot 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	558.q (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.45565243279$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			185.18
Character	$\chi$	$=$	558.185
Dual form			558.2.q.a.371.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(-1.58459 - 0.699349i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.254546 + 0.146962i) q^{5} +(-1.72197 + 0.186639i) q^{6} +(1.66841 + 2.88977i) q^{7} -1.00000i q^{8} +(2.02182 + 2.21636i) q^{9} +0.293925 q^{10} +(-0.689101 - 1.19356i) q^{11} +(-1.39795 + 1.02262i) q^{12} +(5.42761 + 3.13363i) q^{13} +(2.88977 + 1.66841i) q^{14} +(-0.300572 - 0.410891i) q^{15} +(-0.500000 - 0.866025i) q^{16} -1.42910 q^{17} +(2.85913 + 0.908510i) q^{18} +2.23335 q^{19} +(0.254546 - 0.146962i) q^{20} +(-0.622780 - 5.74589i) q^{21} +(-1.19356 - 0.689101i) q^{22} +(2.37297 - 4.11011i) q^{23} +(-0.699349 + 1.58459i) q^{24} +(-2.45680 - 4.25531i) q^{25} +6.26727 q^{26} +(-1.65374 - 4.92597i) q^{27} +3.33682 q^{28} +(1.98252 + 3.43382i) q^{29} +(-0.465749 - 0.205556i) q^{30} +(4.05593 - 3.81438i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(0.257226 + 2.37322i) q^{33} +(-1.23764 + 0.714549i) q^{34} +0.980774i q^{35} +(2.93033 - 0.642771i) q^{36} +5.87646i q^{37} +(1.93414 - 1.11668i) q^{38} +(-6.40901 - 8.76131i) q^{39} +(0.146962 - 0.254546i) q^{40} +(4.05457 + 2.34091i) q^{41} +(-3.41229 - 4.66470i) q^{42} +(-4.22359 + 2.43849i) q^{43} -1.37820 q^{44} +(0.188926 + 0.861297i) q^{45} -4.74595i q^{46} +(2.19470 - 1.26711i) q^{47} +(0.186639 + 1.72197i) q^{48} +(-2.06718 + 3.58047i) q^{49} +(-4.25531 - 2.45680i) q^{50} +(2.26453 + 0.999439i) q^{51} +(5.42761 - 3.13363i) q^{52} +4.42747 q^{53} +(-3.89517 - 3.43914i) q^{54} -0.405088i q^{55} +(2.88977 - 1.66841i) q^{56} +(-3.53894 - 1.56189i) q^{57} +(3.43382 + 1.98252i) q^{58} +(-10.5590 - 6.09626i) q^{59} +(-0.506128 + 0.0548577i) q^{60} +(2.74322 - 1.58380i) q^{61} +(1.60535 - 5.33131i) q^{62} +(-3.03153 + 9.54039i) q^{63} -1.00000 q^{64} +(0.921052 + 1.59531i) q^{65} +(1.40937 + 1.92665i) q^{66} +(-4.11484 + 7.12712i) q^{67} +(-0.714549 + 1.23764i) q^{68} +(-6.63458 + 4.85329i) q^{69} +(0.490387 + 0.849375i) q^{70} +3.53523i q^{71} +(2.21636 - 2.02182i) q^{72} +6.93097i q^{73} +(2.93823 + 5.08916i) q^{74} +(0.917070 + 8.46107i) q^{75} +(1.11668 - 1.93414i) q^{76} +(2.29941 - 3.98269i) q^{77} +(-9.93102 - 4.38301i) q^{78} +(-0.110368 + 0.0637209i) q^{79} -0.293925i q^{80} +(-0.824472 + 8.96216i) q^{81} +4.68181 q^{82} +(-5.84303 - 10.1204i) q^{83} +(-5.28748 - 2.33360i) q^{84} +(-0.363772 - 0.210024i) q^{85} +(-2.43849 + 4.22359i) q^{86} +(-0.740028 - 6.82765i) q^{87} +(-1.19356 + 0.689101i) q^{88} +0.318924 q^{89} +(0.594263 + 0.651442i) q^{90} +20.9127i q^{91} +(-2.37297 - 4.11011i) q^{92} +(-9.09454 + 3.20770i) q^{93} +(1.26711 - 2.19470i) q^{94} +(0.568491 + 0.328219i) q^{95} +(1.02262 + 1.39795i) q^{96} +(4.33481 + 7.50811i) q^{97} +4.13437i q^{98} +(1.25211 - 3.94046i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} + 12 q^{5} - 4 q^{7} - 4 q^{9} - 32 q^{16} + 8 q^{18} - 8 q^{19} + 12 q^{20} + 44 q^{25} - 8 q^{28} + 8 q^{31} - 36 q^{33} - 8 q^{36} + 36 q^{38} - 8 q^{39} + 24 q^{41} - 8 q^{45} - 48 q^{47}+ \cdots - 16 q^{97}+O(q^{100}) $ 64 * q + 32 * q^4 + 12 * q^5 - 4 * q^7 - 4 * q^9 - 32 * q^16 + 8 * q^18 - 8 * q^19 + 12 * q^20 + 44 * q^25 - 8 * q^28 + 8 * q^31 - 36 * q^33 - 8 * q^36 + 36 * q^38 - 8 * q^39 + 24 * q^41 - 8 * q^45 - 48 * q^47 - 36 * q^49 - 32 * q^51 - 12 * q^59 - 52 * q^63 - 64 * q^64 - 16 * q^66 + 16 * q^67 + 112 * q^69 - 12 * q^70 - 8 * q^72 - 4 * q^76 - 28 * q^78 + 60 * q^81 + 44 * q^87 + 56 * q^90 - 64 * q^93 - 180 * q^95 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/558\mathbb{Z}\right)^\times$.

$n$	$127$	$497$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−1.58459	−	0.699349i	−0.914861	−	0.403769i
$3$	−1.58459	−	0.699349i	−0.914861	−	0.403769i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.254546	+	0.146962i	0.113837	+	0.0657235i	0.555837	−	0.831291i	$-0.312398\pi$
$5$	0.254546	+	0.146962i	0.113837	+	0.0657235i	−0.442001	+	0.897015i	$0.645731\pi$
$6$	−1.72197	+	0.186639i	−0.702990	+	0.0761949i
$7$	1.66841	+	2.88977i	0.630600	+	1.09223i	0.987429	+	0.158061i	$0.0505243\pi$
$7$	1.66841	+	2.88977i	0.630600	+	1.09223i	−0.356830	+	0.934169i	$0.616142\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.02182	+	2.21636i	0.673941	+	0.738785i
$10$	0.293925			0.0929471
$11$	−0.689101	−	1.19356i	−0.207772	−	0.359871i	0.743240	−	0.669024i	$-0.233288\pi$
$11$	−0.689101	−	1.19356i	−0.207772	−	0.359871i	−0.951012	+	0.309153i	$0.899954\pi$
$12$	−1.39795	+	1.02262i	−0.403552	+	0.295204i
$13$	5.42761	+	3.13363i	1.50535	+	0.869114i	0.999981	+	0.00620975i	$0.00197664\pi$
$13$	5.42761	+	3.13363i	1.50535	+	0.869114i	0.505368	+	0.862904i	$0.331357\pi$
$14$	2.88977	+	1.66841i	0.772324	+	0.445901i
$15$	−0.300572	−	0.410891i	−0.0776074	−	0.106092i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.42910			−0.346607			−0.173304	−	0.984868i	$-0.555444\pi$
$17$	−1.42910			−0.346607			−0.173304	+	0.984868i	$0.555444\pi$
$18$	2.85913	+	0.908510i	0.673903	+	0.214138i
$19$	2.23335			0.512366			0.256183	−	0.966628i	$-0.417535\pi$
$19$	2.23335			0.512366			0.256183	+	0.966628i	$0.417535\pi$
$20$	0.254546	−	0.146962i	0.0569183	−	0.0328618i
$21$	−0.622780	−	5.74589i	−0.135902	−	1.25386i
$22$	−1.19356	−	0.689101i	−0.254468	−	0.146917i
$23$	2.37297	−	4.11011i	0.494799	−	0.857018i	−0.505183	−	0.863012i	$-0.668575\pi$
$23$	2.37297	−	4.11011i	0.494799	−	0.857018i	0.999982	+	0.00599485i	$0.00190823\pi$
$24$	−0.699349	+	1.58459i	−0.142754	+	0.323452i
$25$	−2.45680	−	4.25531i	−0.491361	−	0.851062i
$26$	6.26727			1.22911
$27$	−1.65374	−	4.92597i	−0.318263	−	0.948002i
$28$	3.33682			0.630600
$29$	1.98252	+	3.43382i	0.368144	+	0.637644i	0.989275	−	0.146062i	$-0.0466600\pi$
$29$	1.98252	+	3.43382i	0.368144	+	0.637644i	−0.621131	+	0.783706i	$0.713327\pi$
$30$	−0.465749	−	0.205556i	−0.0850337	−	0.0375292i
$31$	4.05593	−	3.81438i	0.728466	−	0.685082i
$31$	4.05593	−	3.81438i	0.728466	−	0.685082i
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	0.257226	+	2.37322i	0.0447773	+	0.413124i
$34$	−1.23764	+	0.714549i	−0.212253	+	0.122544i
$35$			0.980774i			0.165781i
$36$	2.93033	−	0.642771i	0.488389	−	0.107129i
$37$			5.87646i			0.966083i	0.875597	+	0.483042i	$0.160468\pi$
$37$			5.87646i			0.966083i	−0.875597	+	0.483042i	$0.839532\pi$
$38$	1.93414	−	1.11668i	0.313759	−	0.181149i
$39$	−6.40901	−	8.76131i	−1.02626	−	1.40293i
$40$	0.146962	−	0.254546i	0.0232368	−	0.0402473i
$41$	4.05457	+	2.34091i	0.633217	+	0.365588i	0.781997	−	0.623282i	$-0.214201\pi$
$41$	4.05457	+	2.34091i	0.633217	+	0.365588i	−0.148780	+	0.988870i	$0.547535\pi$
$42$	−3.41229	−	4.66470i	−0.526527	−	0.719778i
$43$	−4.22359	+	2.43849i	−0.644091	+	0.371866i	−0.786189	−	0.617987i	$-0.787949\pi$
$43$	−4.22359	+	2.43849i	−0.644091	+	0.371866i	0.142098	+	0.989853i	$0.454615\pi$
$44$	−1.37820			−0.207772
$45$	0.188926	+	0.861297i	0.0281635	+	0.128395i
$46$		−	4.74595i		−	0.699752i
$47$	2.19470	−	1.26711i	0.320130	−	0.184827i	−0.331320	−	0.943518i	$-0.607494\pi$
$47$	2.19470	−	1.26711i	0.320130	−	0.184827i	0.651451	+	0.758691i	$0.274161\pi$
$48$	0.186639	+	1.72197i	0.0269390	+	0.248544i
$49$	−2.06718	+	3.58047i	−0.295312	+	0.511495i
$50$	−4.25531	−	2.45680i	−0.601792	−	0.347445i
$51$	2.26453	+	0.999439i	0.317098	+	0.139949i
$52$	5.42761	−	3.13363i	0.752674	−	0.434557i
$53$	4.42747			0.608159			0.304080	−	0.952647i	$-0.401651\pi$
$53$	4.42747			0.608159			0.304080	+	0.952647i	$0.401651\pi$
$54$	−3.89517	−	3.43914i	−0.530065	−	0.468008i
$55$		−	0.405088i		−	0.0546220i
$56$	2.88977	−	1.66841i	0.386162	−	0.222951i
$57$	−3.53894	−	1.56189i	−0.468744	−	0.206878i
$58$	3.43382	+	1.98252i	0.450882	+	0.260317i
$59$	−10.5590	−	6.09626i	−1.37467	−	0.793666i	−0.383158	−	0.923683i	$-0.625164\pi$
$59$	−10.5590	−	6.09626i	−1.37467	−	0.793666i	−0.991512	+	0.130017i	$0.958497\pi$
$60$	−0.506128	+	0.0548577i	−0.0653409	+	0.00708210i
$61$	2.74322	−	1.58380i	0.351233	−	0.202784i	−0.313995	−	0.949425i	$-0.601668\pi$
$61$	2.74322	−	1.58380i	0.351233	−	0.202784i	0.665228	+	0.746640i	$0.268334\pi$
$62$	1.60535	−	5.33131i	0.203879	−	0.677077i
$63$	−3.03153	+	9.54039i	−0.381937	+	1.20198i
$64$	−1.00000			−0.125000
$65$	0.921052	+	1.59531i	0.114242	+	0.197874i
$66$	1.40937	+	1.92665i	0.173482	+	0.237155i
$67$	−4.11484	+	7.12712i	−0.502708	+	0.870716i	0.497287	+	0.867586i	$0.334330\pi$
$67$	−4.11484	+	7.12712i	−0.502708	+	0.870716i	−0.999995	+	0.00312998i	$0.999004\pi$
$68$	−0.714549	+	1.23764i	−0.0866518	+	0.150085i
$69$	−6.63458	+	4.85329i	−0.798710	+	0.584267i
$70$	0.490387	+	0.849375i	0.0586124	+	0.101520i
$71$			3.53523i			0.419555i	0.977749	+	0.209777i	$0.0672739\pi$
$71$			3.53523i			0.419555i	−0.977749	+	0.209777i	$0.932726\pi$
$72$	2.21636	−	2.02182i	0.261200	−	0.238274i
$73$			6.93097i			0.811208i	0.914049	+	0.405604i	$0.132939\pi$
$73$			6.93097i			0.811208i	−0.914049	+	0.405604i	$0.867061\pi$
$74$	2.93823	+	5.08916i	0.341562	+	0.591603i
$75$	0.917070	+	8.46107i	0.105894	+	0.977000i
$76$	1.11668	−	1.93414i	0.128092	−	0.221861i
$77$	2.29941	−	3.98269i	0.262042	−	0.453870i
$78$	−9.93102	−	4.38301i	−1.12447	−	0.496278i
$79$	−0.110368	+	0.0637209i	−0.0124174	+	0.00716917i	−0.506196	−	0.862419i	$-0.668949\pi$
$79$	−0.110368	+	0.0637209i	−0.0124174	+	0.00716917i	0.493778	+	0.869588i	$0.335615\pi$
$80$		−	0.293925i		−	0.0328618i
$81$	−0.824472	+	8.96216i	−0.0916080	+	0.995795i
$82$	4.68181			0.517020
$83$	−5.84303	−	10.1204i	−0.641356	−	1.11086i	−0.985130	−	0.171808i	$-0.945039\pi$
$83$	−5.84303	−	10.1204i	−0.641356	−	1.11086i	0.343775	−	0.939052i	$-0.388294\pi$
$84$	−5.28748	−	2.33360i	−0.576911	−	0.254617i
$85$	−0.363772	−	0.210024i	−0.0394566	−	0.0227803i
$86$	−2.43849	+	4.22359i	−0.262949	+	0.455441i
$87$	−0.740028	−	6.82765i	−0.0793394	−	0.732001i
$88$	−1.19356	+	0.689101i	−0.127234	+	0.0734584i
$89$	0.318924			0.0338059			0.0169029	−	0.999857i	$-0.494619\pi$
$89$	0.318924			0.0338059			0.0169029	+	0.999857i	$0.494619\pi$
$90$	0.594263	+	0.651442i	0.0626409	+	0.0686680i
$91$			20.9127i			2.19225i
$92$	−2.37297	−	4.11011i	−0.247400	−	0.428509i
$93$	−9.09454	+	3.20770i	−0.943060	+	0.332623i
$94$	1.26711	−	2.19470i	0.130693	−	0.226366i
$95$	0.568491	+	0.328219i	0.0583260	+	0.0336745i
$96$	1.02262	+	1.39795i	0.104370	+	0.142677i
$97$	4.33481	+	7.50811i	0.440133	+	0.762333i	0.997699	−	0.0677995i	$-0.0215978\pi$
$97$	4.33481	+	7.50811i	0.440133	+	0.762333i	−0.557566	+	0.830133i	$0.688264\pi$
$98$			4.13437i			0.417634i
$99$	1.25211	−	3.94046i	0.125842	−	0.396031i
$100$	−4.91361			−0.491361
$101$	−8.71647	+	5.03246i	−0.867321	+	0.500748i	−0.866457	−	0.499251i	$-0.833608\pi$
$101$	−8.71647	+	5.03246i	−0.867321	+	0.500748i	−0.000864119		1.00000i	$0.500275\pi$
$102$	2.46086	−	0.266725i	0.243661	−	0.0264097i
$103$	5.74869	−	9.95702i	0.566435	−	0.981095i	−0.430479	−	0.902600i	$-0.641655\pi$
$103$	5.74869	−	9.95702i	0.566435	−	0.981095i	0.996915	−	0.0784943i	$-0.0250112\pi$
$104$	3.13363	−	5.42761i	0.307278	−	0.532221i
$105$	0.685903	−	1.55412i	0.0669373	−	0.151667i
$106$	3.83430	−	2.21373i	0.372420	−	0.215017i
$107$			14.6419i			1.41549i	0.706468	+	0.707745i	$0.250287\pi$
$107$			14.6419i			1.41549i	−0.706468	+	0.707745i	$0.749713\pi$
$108$	−5.09288	−	1.03080i	−0.490063	−	0.0991887i
$109$	−12.1199			−1.16087			−0.580436	−	0.814306i	$-0.697118\pi$
$109$	−12.1199			−1.16087			−0.580436	+	0.814306i	$0.697118\pi$
$110$	−0.202544	−	0.350816i	−0.0193118	−	0.0334490i
$111$	4.10969	−	9.31175i	0.390075	−	0.883832i
$112$	1.66841	−	2.88977i	0.157650	−	0.273058i
$113$	−7.03255	−	4.06024i	−0.661566	−	0.381956i	0.131307	−	0.991342i	$-0.458083\pi$
$113$	−7.03255	−	4.06024i	−0.661566	−	0.381956i	−0.792874	+	0.609386i	$0.791416\pi$
$114$	−3.84576	+	0.416830i	−0.360188	+	0.0390397i
$115$	1.20806	−	0.697476i	0.112652	−	0.0650399i
$116$	3.96503			0.368144
$117$	4.02842	+	18.3652i	0.372427	+	1.69786i
$118$	−12.1925			−1.12241
$119$	−2.38432	−	4.12977i	−0.218571	−	0.378575i
$120$	−0.410891	+	0.300572i	−0.0375090	+	0.0274384i
$121$	4.55028	−	7.88131i	0.413662	−	0.716483i
$122$	1.58380	−	2.74322i	0.143390	−	0.248359i
$123$	−4.78770	−	6.54492i	−0.431692	−	0.590136i
$124$	−1.27538	−	5.41972i	−0.114533	−	0.486705i
$125$		−	2.91385i		−	0.260623i
$126$	2.14481	+	9.77799i	0.191075	+	0.871093i
$127$			10.4455i			0.926886i	0.886127	+	0.463443i	$0.153386\pi$
$127$			10.4455i			0.926886i	−0.886127	+	0.463443i	$0.846614\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	8.39799	−	0.910233i	0.739402	−	0.0801416i
$130$	1.59531	+	0.921052i	0.139918	+	0.0807816i
$131$	−18.2202	−	10.5194i	−1.59191	−	0.919087i	−0.992980	−	0.118282i	$-0.962261\pi$
$131$	−18.2202	−	10.5194i	−1.59191	−	0.919087i	−0.598925	−	0.800805i	$-0.704405\pi$
$132$	2.18388	+	0.963845i	0.190082	+	0.0838919i
$133$	3.72615	+	6.45388i	0.323098	+	0.559622i
$134$			8.22969i			0.710937i
$135$	0.302977	−	1.49692i	0.0260761	−	0.128835i
$136$			1.42910i			0.122544i
$137$	−10.4848	−	18.1601i	−0.895774	−	1.55153i	−0.832844	−	0.553507i	$-0.813289\pi$
$137$	−10.4848	−	18.1601i	−0.895774	−	1.55153i	−0.0629292	−	0.998018i	$-0.520044\pi$
$138$	−3.31907	+	7.52036i	−0.282538	+	0.640176i
$139$	0.487248	+	0.281313i	0.0413278	+	0.0238606i	0.520522	−	0.853849i	$-0.325738\pi$
$139$	0.487248	+	0.281313i	0.0413278	+	0.0238606i	−0.479194	+	0.877709i	$0.659071\pi$
$140$	0.849375	+	0.490387i	0.0717853	+	0.0414452i
$141$	−4.36385	+	0.472984i	−0.367502	+	0.0398325i
$142$	1.76761	+	3.06160i	0.148335	+	0.256924i
$143$		−	8.63756i		−	0.722309i
$144$	0.908510	−	2.85913i	0.0757092	−	0.238261i
$145$			1.16542i			0.0967829i
$146$	3.46548	+	6.00239i	0.286805	+	0.496762i
$147$	5.77962	−	4.22787i	0.476695	−	0.348709i
$148$	5.08916	+	2.93823i	0.418326	+	0.241521i
$149$	9.64250	+	5.56710i	0.789945	+	0.456075i	0.839943	−	0.542675i	$-0.182588\pi$
$149$	9.64250	+	5.56710i	0.789945	+	0.456075i	−0.0499984	+	0.998749i	$0.515922\pi$
$150$	5.02474	+	6.86896i	0.410268	+	0.560848i
$151$	−7.87062	+	4.54411i	−0.640502	+	0.369794i	−0.784808	−	0.619739i	$-0.787238\pi$
$151$	−7.87062	+	4.54411i	−0.640502	+	0.369794i	0.144306	+	0.989533i	$0.453905\pi$
$152$		−	2.23335i		−	0.181149i
$153$	−2.88938	−	3.16739i	−0.233593	−	0.256069i
$154$		−	4.59881i		−	0.370583i
$155$	1.59299	−	0.374867i	0.127952	−	0.0301100i
$156$	−10.7920	+	1.16971i	−0.864053	+	0.0936521i
$157$	−1.96305	+	3.40011i	−0.156669	+	0.271358i	−0.933665	−	0.358147i	$-0.883409\pi$
$157$	−1.96305	+	3.40011i	−0.156669	+	0.271358i	0.776997	+	0.629505i	$0.216742\pi$
$158$	−0.0637209	+	0.110368i	−0.00506937	+	0.00878040i
$159$	−7.01570	−	3.09635i	−0.556381	−	0.245556i
$160$	−0.146962	−	0.254546i	−0.0116184	−	0.0201236i
$161$	15.8364			1.24808
$162$	3.76706	+	8.17369i	0.295969	+	0.642186i
$163$	−22.8716			−1.79144			−0.895722	−	0.444615i	$-0.853341\pi$
$163$	−22.8716			−1.79144			−0.895722	+	0.444615i	$0.853341\pi$
$164$	4.05457	−	2.34091i	0.316609	−	0.182794i
$165$	−0.283298	+	0.641896i	−0.0220547	+	0.0499715i
$166$	−10.1204	−	5.84303i	−0.785497	−	0.453507i
$167$	10.9960	−	19.0457i	0.850899	−	1.47380i	−0.0294998	−	0.999565i	$-0.509391\pi$
$167$	10.9960	−	19.0457i	0.850899	−	1.47380i	0.880398	−	0.474235i	$-0.157275\pi$
$168$	−5.74589	+	0.622780i	−0.443305	+	0.0480485i
$169$	13.1393	+	22.7580i	1.01072	+	1.75061i
$170$	−0.420047			−0.0322162
$171$	4.51544	+	4.94990i	0.345304	+	0.378529i
$172$			4.87698i			0.371866i
$173$	0.928358	−	0.535988i	0.0705818	−	0.0407504i	−0.464294	−	0.885681i	$-0.653692\pi$
$173$	0.928358	−	0.535988i	0.0705818	−	0.0407504i	0.534876	+	0.844931i	$0.320358\pi$
$174$	−4.05471	−	5.54290i	−0.307387	−	0.420206i
$175$	8.19791	−	14.1992i	0.619704	−	1.07336i
$176$	−0.689101	+	1.19356i	−0.0519430	+	0.0899678i
$177$	12.4683	+	17.0445i	0.937174	+	1.28114i
$178$	0.276196	−	0.159462i	0.0207018	−	0.0119522i
$179$	−13.4794			−1.00750			−0.503748	−	0.863851i	$-0.668046\pi$
$179$	−13.4794			−1.00750			−0.503748	+	0.863851i	$0.668046\pi$
$180$	0.840368	+	0.267033i	0.0626373	+	0.0199035i
$181$		−	8.17517i		−	0.607656i	−0.952727	−	0.303828i	$-0.901735\pi$
$181$		−	8.17517i		−	0.607656i	0.952727	−	0.303828i	$-0.0982647\pi$
$182$	10.4564	+	18.1110i	0.775078	+	1.34247i
$183$	−5.45449	+	0.591195i	−0.403207	+	0.0437024i
$184$	−4.11011	−	2.37297i	−0.303001	−	0.174938i
$185$	−0.863617	+	1.49583i	−0.0634944	+	0.109976i
$186$	−6.27225	+	7.32522i	−0.459904	+	0.537111i
$187$	0.984794	+	1.70571i	0.0720153	+	0.124734i
$188$		−	2.53422i		−	0.184827i
$189$	11.4758	−	12.9975i	0.834741	−	0.945427i
$190$	0.656437			0.0476230
$191$	7.48738	−	4.32284i	0.541767	−	0.312790i	−0.204027	−	0.978965i	$-0.565403\pi$
$191$	7.48738	−	4.32284i	0.541767	−	0.312790i	0.745795	+	0.666176i	$0.232070\pi$
$192$	1.58459	+	0.699349i	0.114358	+	0.0504712i
$193$	5.37331	−	9.30684i	0.386779	−	0.669921i	−0.605235	−	0.796047i	$-0.706921\pi$
$193$	5.37331	−	9.30684i	0.386779	−	0.669921i	0.992014	+	0.126126i	$0.0402542\pi$
$194$	7.50811	+	4.33481i	0.539051	+	0.311221i
$195$	−0.343808	−	3.17204i	−0.0246206	−	0.227155i
$196$	2.06718	+	3.58047i	0.147656	+	0.255748i
$197$	23.8943			1.70240			0.851200	−	0.524841i	$-0.175875\pi$
$197$	23.8943			1.70240			0.851200	+	0.524841i	$0.175875\pi$
$198$	−0.885869	−	4.03859i	−0.0629559	−	0.287010i
$199$		−	22.6790i		−	1.60767i	−0.594849	−	0.803837i	$-0.702788\pi$
$199$		−	22.6790i		−	1.60767i	0.594849	−	0.803837i	$-0.297212\pi$
$200$	−4.25531	+	2.45680i	−0.300896	+	0.173722i
$201$	11.5047	−	8.41582i	0.811477	−	0.593606i
$202$	−5.03246	+	8.71647i	−0.354082	+	0.613289i
$203$	−6.61530	+	11.4580i	−0.464303	+	0.804196i
$204$	1.99780	−	1.46142i	0.139874	−	0.102320i
$205$	0.688050	+	1.19174i	0.0480555	+	0.0832346i
$206$		−	11.4974i		−	0.801061i
$207$	13.9072	−	3.05056i	0.966618	−	0.212028i
$208$		−	6.26727i		−	0.434557i
$209$	−1.53901	−	2.66564i	−0.106455	−	0.184386i
$210$	−0.183050	−	1.68886i	−0.0126317	−	0.116542i
$211$	1.52607	−	2.64323i	0.105059	−	0.181967i	−0.808703	−	0.588217i	$-0.799830\pi$
$211$	1.52607	−	2.64323i	0.105059	−	0.181967i	0.913762	+	0.406249i	$0.133164\pi$
$212$	2.21373	−	3.83430i	0.152040	−	0.263341i
$213$	2.47236	−	5.60187i	0.169403	−	0.383834i
$214$	7.32097	+	12.6803i	0.500451	+	0.866807i
$215$	−1.43346			−0.0977614
$216$	−4.92597	+	1.65374i	−0.335169	+	0.112523i
$217$	17.7896	+	5.35675i	1.20764	+	0.363640i
$218$	−10.4961	+	6.05993i	−0.710886	+	0.410430i
$219$	4.84716	−	10.9827i	0.327541	−	0.742143i
$220$	−0.350816	−	0.202544i	−0.0236520	−	0.0136555i
$221$	−7.75660	−	4.47827i	−0.521765	−	0.301241i
$222$	−1.09677	−	10.1191i	−0.0736107	−	0.679146i
$223$	−6.74823	+	3.89609i	−0.451895	+	0.260901i	−0.708630	−	0.705580i	$-0.750686\pi$
$223$	−6.74823	+	3.89609i	−0.451895	+	0.260901i	0.256735	+	0.966482i	$0.417353\pi$
$224$		−	3.33682i		−	0.222951i
$225$	4.46406	−	14.0486i	0.297604	−	0.936575i
$226$	−8.12049			−0.540167
$227$	22.1452	−	12.7856i	1.46983	−	0.848607i	0.470403	−	0.882452i	$-0.344108\pi$
$227$	22.1452	−	12.7856i	1.46983	−	0.848607i	0.999427	+	0.0338446i	$0.0107751\pi$
$228$	−3.12211	+	2.28386i	−0.206767	+	0.151253i
$229$	−21.7948	−	12.5832i	−1.44024	−	0.831522i	−0.442373	−	0.896831i	$-0.645863\pi$
$229$	−21.7948	−	12.5832i	−1.44024	−	0.831522i	−0.997865	+	0.0653094i	$0.979197\pi$
$230$	0.697476	−	1.20806i	0.0459902	−	0.0796573i
$231$	−6.42890	+	4.70282i	−0.422990	+	0.309423i
$232$	3.43382	−	1.98252i	0.225441	−	0.130159i
$233$			21.6863i			1.42072i	0.703841	+	0.710358i	$0.251467\pi$
$233$			21.6863i			1.42072i	−0.703841	+	0.710358i	$0.748533\pi$
$234$	12.6713	+	13.8905i	0.828349	+	0.908050i
$235$	0.744871			0.0485900
$236$	−10.5590	+	6.09626i	−0.687335	+	0.396833i
$237$	0.219451	−	0.0237856i	0.0142548	−	0.00154504i
$238$	−4.12977	−	2.38432i	−0.267693	−	0.154553i
$239$	−5.72924	+	9.92334i	−0.370594	+	0.641888i	−0.989657	−	0.143454i	$-0.954179\pi$
$239$	−5.72924	+	9.92334i	−0.370594	+	0.641888i	0.619063	+	0.785341i	$0.287513\pi$
$240$	−0.205556	+	0.465749i	−0.0132686	+	0.0300639i
$241$	−10.5193	+	6.07329i	−0.677605	+	0.391215i	−0.798952	−	0.601395i	$-0.794612\pi$
$241$	−10.5193	+	6.07329i	−0.677605	+	0.391215i	0.121347	+	0.992610i	$0.461279\pi$
$242$		−	9.10056i		−	0.585006i
$243$	7.57412	−	13.6247i	0.485880	−	0.874025i
$244$		−	3.16759i		−	0.202784i
$245$	−1.05239	+	0.607596i	−0.0672346	+	0.0388179i
$246$	−7.41873	−	3.27422i	−0.473001	−	0.208757i
$247$	12.1218	+	6.99851i	0.771290	+	0.445304i
$248$	−3.81438	−	4.05593i	−0.242213	−	0.257551i
$249$	2.18107	+	20.1230i	0.138220	+	1.27524i
$250$	−1.45693	−	2.52347i	−0.0921441	−	0.159598i
$251$	−25.4400			−1.60576			−0.802879	−	0.596142i	$-0.796699\pi$
$251$	−25.4400			−1.60576			−0.802879	+	0.596142i	$0.796699\pi$
$252$	6.74646	+	7.39558i	0.424987	+	0.465878i
$253$	−6.54088			−0.411221
$254$	5.22274	+	9.04605i	0.327704	+	0.567600i
$255$	0.429547	+	0.587204i	0.0268993	+	0.0367721i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.10477	+	3.52459i	0.380805	+	0.219858i	0.678169	−	0.734906i	$-0.262774\pi$
$257$	6.10477	+	3.52459i	0.380805	+	0.219858i	−0.297363	+	0.954764i	$0.596107\pi$
$258$	6.81776	−	4.98728i	0.424455	−	0.310494i
$259$	−16.9816	+	9.80434i	−1.05519	+	0.609212i
$260$	1.84210			0.114242
$261$	−3.60227	+	11.3365i	−0.222975	+	0.701714i
$262$	−21.0389			−1.29979
$263$	−1.56915	−	2.71785i	−0.0967579	−	0.167590i	0.813583	−	0.581449i	$-0.197514\pi$
$263$	−1.56915	−	2.71785i	−0.0967579	−	0.167590i	−0.910341	+	0.413859i	$0.864181\pi$
$264$	2.37322	−	0.257226i	0.146061	−	0.0158312i
$265$	1.12700	+	0.650671i	0.0692308	+	0.0399704i
$266$	6.45388	+	3.72615i	0.395712	+	0.228465i
$267$	−0.505363	−	0.223039i	−0.0309277	−	0.0136498i
$268$	4.11484	+	7.12712i	0.251354	+	0.435358i
$269$	−26.2493			−1.60045			−0.800226	−	0.599699i	$-0.795287\pi$
$269$	−26.2493			−1.60045			−0.800226	+	0.599699i	$0.795287\pi$
$270$	−0.486076	−	1.44786i	−0.0295816	−	0.0881141i
$271$			26.4625i			1.60748i	0.594979	+	0.803741i	$0.297160\pi$
$271$			26.4625i			1.60748i	−0.594979	+	0.803741i	$0.702840\pi$
$272$	0.714549	+	1.23764i	0.0433259	+	0.0750427i
$273$	14.6253	−	33.1380i	0.885164	−	2.00560i
$274$	−18.1601	−	10.4848i	−1.09709	−	0.633408i
$275$	−3.38597	+	5.86468i	−0.204182	+	0.353653i
$276$	0.885778	+	8.17236i	0.0533176	+	0.491918i
$277$	3.62066	−	2.09039i	0.217544	−	0.125599i	−0.387268	−	0.921967i	$-0.626581\pi$
$277$	3.62066	−	2.09039i	0.217544	−	0.125599i	0.604813	+	0.796368i	$0.293248\pi$
$278$	0.562626			0.0337440
$279$	16.6544	+	1.27738i	0.997071	+	0.0764750i
$280$	0.980774			0.0586124
$281$	3.26448	−	1.88475i	0.194743	−	0.112435i	−0.399458	−	0.916751i	$-0.630802\pi$
$281$	3.26448	−	1.88475i	0.194743	−	0.112435i	0.594201	+	0.804317i	$0.297468\pi$
$282$	−3.54271	+	2.59154i	−0.210965	+	0.154324i
$283$	12.0387	−	20.8516i	0.715625	−	1.23950i	−0.247093	−	0.968992i	$-0.579475\pi$
$283$	12.0387	−	20.8516i	0.715625	−	1.23950i	0.962718	−	0.270507i	$-0.0871912\pi$
$284$	3.06160	+	1.76761i	0.181672	+	0.104889i
$285$	−0.671284	−	0.917664i	−0.0397634	−	0.0543577i
$286$	−4.31878	−	7.48035i	−0.255375	−	0.442322i
$287$			15.6224i			0.922159i
$288$	−0.642771	−	2.93033i	−0.0378756	−	0.172671i
$289$	−14.9577			−0.879863
$290$	0.582710	+	1.00928i	0.0342179	+	0.0592672i
$291$	−1.61809	−	14.9288i	−0.0948540	−	0.875141i
$292$	6.00239	+	3.46548i	0.351263	+	0.202802i
$293$	−1.74859	−	1.00955i	−0.102154	−	0.0589786i	0.448053	−	0.894007i	$-0.352118\pi$
$293$	−1.74859	−	1.00955i	−0.102154	−	0.0589786i	−0.550207	+	0.835029i	$0.685451\pi$
$294$	2.89137	−	6.55126i	0.168628	−	0.382077i
$295$	−1.79184	−	3.10356i	−0.104325	−	0.180696i
$296$	5.87646			0.341562
$297$	−4.73983	+	5.36833i	−0.275033	+	0.311502i
$298$	11.1342			0.644987
$299$	25.7592	−	14.8721i	1.48969	−	0.860074i
$300$	7.78603	+	3.43633i	0.449527	+	0.198396i
$301$	−14.0933	−	8.13680i	−0.812327	−	0.468997i
$302$	−4.54411	+	7.87062i	−0.261484	+	0.452903i
$303$	17.3314	−	1.87850i	0.995665	−	0.107917i
$304$	−1.11668	−	1.93414i	−0.0640458	−	0.110931i
$305$	0.931033			0.0533108
$306$	−4.08598	−	1.29835i	−0.233580	−	0.0742218i
$307$	3.40720			0.194459			0.0972295	−	0.995262i	$-0.469002\pi$
$307$	3.40720			0.194459			0.0972295	+	0.995262i	$0.469002\pi$
$308$	−2.29941	−	3.98269i	−0.131021	−	0.226935i
$309$	−16.0727	+	11.7574i	−0.914345	+	0.668856i
$310$	1.19214	−	1.12114i	0.0677088	−	0.0636764i
$311$	−0.381978	−	0.220535i	−0.0216600	−	0.0125054i	0.489131	−	0.872210i	$-0.337314\pi$
$311$	−0.381978	−	0.220535i	−0.0216600	−	0.0125054i	−0.510791	+	0.859705i	$0.670647\pi$
$312$	−8.76131	+	6.40901i	−0.496011	+	0.362839i
$313$	11.5561	−	6.67194i	0.653192	−	0.377121i	−0.136486	−	0.990642i	$-0.543581\pi$
$313$	11.5561	−	6.67194i	0.653192	−	0.377121i	0.789678	+	0.613521i	$0.210248\pi$
$314$			3.92610i			0.221563i
$315$	−2.17374	+	1.98295i	−0.122477	+	0.111727i
$316$			0.127442i			0.00716917i
$317$	−2.12441	+	1.22653i	−0.119319	+	0.0688887i	−0.558472	−	0.829524i	$-0.688612\pi$
$317$	−2.12441	+	1.22653i	−0.119319	+	0.0688887i	0.439153	+	0.898412i	$0.355279\pi$
$318$	−7.62395	+	0.826337i	−0.427530	+	0.0463387i
$319$	2.73231	−	4.73250i	0.152980	−	0.264969i
$320$	−0.254546	−	0.146962i	−0.0142296	−	0.00821544i
$321$	10.2398	−	23.2014i	0.571531	−	1.29498i
$322$	13.7147	−	7.91819i	0.764291	−	0.441263i
$323$	−3.19168			−0.177590
$324$	7.34922	+	5.19509i	0.408290	+	0.288616i
$325$		−	30.7949i		−	1.70819i
$326$	−19.8074	+	11.4358i	−1.09703	+	0.633371i
$327$	19.2050	+	8.47601i	1.06204	+	0.468725i
$328$	2.34091	−	4.05457i	0.129255	−	0.223876i
$329$	7.32333	+	4.22813i	0.403748	+	0.233104i
$330$	0.0756051	+	0.697547i	0.00416192	+	0.0383987i
$331$	27.7580	−	16.0261i	1.52572	−	0.880874i	0.526183	−	0.850371i	$-0.323623\pi$
$331$	27.7580	−	16.0261i	1.52572	−	0.880874i	0.999535	−	0.0305023i	$-0.00971069\pi$
$332$	−11.6861			−0.641356
$333$	−13.0243	+	11.8811i	−0.713728	+	0.651083i
$334$		−	21.9921i		−	1.20335i
$335$	−2.09484	+	1.20945i	−0.114453	+	0.0660795i
$336$	−4.66470	+	3.41229i	−0.254480	+	0.186156i
$337$	−7.39401	−	4.26893i	−0.402777	−	0.232544i	0.284904	−	0.958556i	$-0.408038\pi$
$337$	−7.39401	−	4.26893i	−0.402777	−	0.232544i	−0.687682	+	0.726012i	$0.741372\pi$
$338$	22.7580	+	13.1393i	1.23787	+	0.714685i
$339$	8.30415	+	11.3520i	0.451019	+	0.616556i
$340$	−0.363772	+	0.210024i	−0.0197283	+	0.0113901i
$341$	−7.34762	−	2.21249i	−0.397896	−	0.119813i
$342$	6.38544	+	2.02902i	0.345285	+	0.109717i
$343$	9.56210			0.516305
$344$	2.43849	+	4.22359i	0.131475	+	0.227721i
$345$	−2.40206	+	0.260352i	−0.129322	+	0.0140169i
$346$	0.535988	−	0.928358i	0.0288149	−	0.0499089i
$347$	−14.3256	+	24.8126i	−0.769038	+	1.33201i	0.169048	+	0.985608i	$0.445931\pi$
$347$	−14.3256	+	24.8126i	−0.769038	+	1.33201i	−0.938085	+	0.346404i	$0.887403\pi$
$348$	−6.28293	−	2.77294i	−0.336800	−	0.148645i
$349$	7.25810	+	12.5714i	0.388517	+	0.672932i	0.992250	−	0.124255i	$-0.0396540\pi$
$349$	7.25810	+	12.5714i	0.388517	+	0.672932i	−0.603733	+	0.797187i	$0.706321\pi$
$350$		−	16.3958i		−	0.876394i
$351$	6.46029	−	31.9185i	0.344825	−	1.70368i
$352$			1.37820i			0.0734584i
$353$	−7.04069	−	12.1948i	−0.374738	−	0.649066i	0.615550	−	0.788098i	$-0.288934\pi$
$353$	−7.04069	−	12.1948i	−0.374738	−	0.649066i	−0.990288	+	0.139032i	$0.955601\pi$
$354$	19.3201	+	8.52683i	1.02685	+	0.453196i
$355$	−0.519545	+	0.899879i	−0.0275746	+	0.0477606i
$356$	0.159462	−	0.276196i	0.00845147	−	0.0146384i
$357$	0.890014	+	8.21144i	0.0471045	+	0.434596i
$358$	−11.6735	+	6.73969i	−0.616963	+	0.356204i
$359$		−	6.25093i		−	0.329912i	−0.986301	−	0.164956i	$-0.947252\pi$
$359$		−	6.25093i		−	0.329912i	0.986301	−	0.164956i	$-0.0527482\pi$
$360$	0.861297	−	0.188926i	0.0453943	−	0.00995729i
$361$	−14.0121			−0.737481
$362$	−4.08758	−	7.07990i	−0.214839	−	0.372111i
$363$	−12.7221	+	9.30638i	−0.667737	+	0.488458i
$364$	18.1110	+	10.4564i	0.949273	+	0.548063i
$365$	−1.01859	+	1.76425i	−0.0533155	+	0.0923451i
$366$	−4.42812	+	3.23923i	−0.231462	+	0.169317i
$367$	22.2113	−	12.8237i	1.15942	−	0.669391i	0.208255	−	0.978075i	$-0.433222\pi$
$367$	22.2113	−	12.8237i	1.15942	−	0.669391i	0.951165	+	0.308683i	$0.0998883\pi$
$368$	−4.74595			−0.247400
$369$	3.00933	+	13.7193i	0.156660	+	0.714196i
$370$			1.72723i			0.0897947i
$371$	7.38683	+	12.7944i	0.383505	+	0.664250i
$372$	−1.76932	+	9.47995i	−0.0917350	+	0.491513i
$373$	−9.26487	+	16.0472i	−0.479717	+	0.830893i	−0.999729	−	0.0232650i	$-0.992594\pi$
$373$	−9.26487	+	16.0472i	−0.479717	+	0.830893i	0.520013	+	0.854158i	$0.325927\pi$
$374$	1.70571	+	0.984794i	0.0882003	+	0.0509225i
$375$	−2.03780	+	4.61725i	−0.105232	+	0.238434i
$376$	−1.26711	−	2.19470i	−0.0653463	−	0.113183i
$377$			24.8499i			1.27984i
$378$	3.43959	−	16.9940i	0.176913	−	0.874079i
$379$	0.535526			0.0275081			0.0137541	−	0.999905i	$-0.495622\pi$
$379$	0.535526			0.0275081			0.0137541	+	0.999905i	$0.495622\pi$
$380$	0.568491	−	0.328219i	0.0291630	−	0.0168373i
$381$	7.30503	−	16.5518i	0.374248	−	0.847972i
$382$	4.32284	−	7.48738i	0.221176	−	0.383087i
$383$	−11.8298	+	20.4897i	−0.604472	+	1.04698i	0.387662	+	0.921801i	$0.373283\pi$
$383$	−11.8298	+	20.4897i	−0.604472	+	1.04698i	−0.992135	+	0.125175i	$0.960051\pi$
$384$	1.72197	−	0.186639i	0.0878737	−	0.00952437i
$385$	1.17061	−	0.675852i	0.0596598	−	0.0344446i
$386$		−	10.7466i		−	0.546988i
$387$	−13.9439	−	4.43078i	−0.708808	−	0.225229i
$388$	8.66962			0.440133
$389$	5.19506	+	8.99811i	0.263400	+	0.456222i	0.967143	−	0.254232i	$-0.0818227\pi$
$389$	5.19506	+	8.99811i	0.263400	+	0.456222i	−0.703743	+	0.710455i	$0.748489\pi$
$390$	−1.88377	−	2.57516i	−0.0953882	−	0.130398i
$391$	−3.39121	+	5.87376i	−0.171501	+	0.297049i
$392$	3.58047	+	2.06718i	0.180841	+	0.104409i
$393$	21.5147	+	29.4112i	1.08527	+	1.48360i
$394$	20.6931	−	11.9472i	1.04250	−	0.601890i
$395$	−0.0374583			−0.00188473
$396$	−2.78648	−	3.05459i	−0.140026	−	0.153499i
$397$	26.0302			1.30642			0.653208	−	0.757179i	$-0.273423\pi$
$397$	26.0302			1.30642			0.653208	+	0.757179i	$0.273423\pi$
$398$	−11.3395	−	19.6406i	−0.568399	−	0.984496i
$399$	−1.39089	−	12.8326i	−0.0696314	−	0.642433i
$400$	−2.45680	+	4.25531i	−0.122840	+	0.212765i
$401$	9.53749	−	16.5194i	0.476279	−	0.824940i	−0.523351	−	0.852117i	$-0.675318\pi$
$401$	9.53749	−	16.5194i	0.476279	−	0.824940i	0.999631	+	0.0271769i	$0.00865173\pi$
$402$	5.75542	−	13.0406i	0.287054	−	0.650408i
$403$	33.9668	−	7.99318i	1.69201	−	0.398169i
$404$			10.0649i			0.500748i
$405$	−1.52697	+	2.16012i	−0.0758755	+	0.107337i
$406$			13.2306i			0.656623i
$407$	7.01389	−	4.04947i	0.347666	−	0.200725i
$408$	0.999439	−	2.26453i	0.0494796	−	0.112111i
$409$	−19.6873	−	11.3665i	−0.973475	−	0.562036i	−0.0731812	−	0.997319i	$-0.523315\pi$
$409$	−19.6873	−	11.3665i	−0.973475	−	0.562036i	−0.900294	+	0.435283i	$0.856648\pi$
$410$	1.19174	+	0.688050i	0.0588557	+	0.0339804i
$411$	3.91372	+	36.1088i	0.193050	+	1.78112i
$412$	−5.74869	−	9.95702i	−0.283218	−	0.490547i
$413$		−	40.6843i		−	2.00194i
$414$	10.5187	−	9.59546i	0.516967	−	0.471591i
$415$		−	3.43482i		−	0.168609i
$416$	−3.13363	−	5.42761i	−0.153639	−	0.266111i
$417$	−0.575350	−	0.786521i	−0.0281750	−	0.0385161i
$418$	−2.66564	−	1.53901i	−0.130381	−	0.0752752i
$419$	−7.14939	−	4.12770i	−0.349271	−	0.201651i	0.315093	−	0.949061i	$-0.397964\pi$
$419$	−7.14939	−	4.12770i	−0.349271	−	0.201651i	−0.664364	+	0.747409i	$0.731297\pi$
$420$	−1.00296	−	1.37107i	−0.0489392	−	0.0669013i
$421$	−15.4287	−	26.7232i	−0.751947	−	1.30241i	−0.946878	−	0.321593i	$-0.895782\pi$
$421$	−15.4287	−	26.7232i	−0.751947	−	1.30241i	0.194931	−	0.980817i	$-0.437552\pi$
$422$		−	3.05214i		−	0.148576i
$423$	7.24567	+	2.30237i	0.352297	+	0.111945i
$424$		−	4.42747i		−	0.215017i
$425$	3.51102	+	6.08126i	0.170309	+	0.294984i
$426$	−0.659811	−	6.08754i	−0.0319679	−	0.294942i
$427$	9.15362	+	5.28484i	0.442974	+	0.255751i
$428$	12.6803	+	7.32097i	0.612925	+	0.353872i
$429$	−6.04067	+	13.6870i	−0.291646	+	0.660813i
$430$	−1.24142	+	0.716732i	−0.0598664	+	0.0345639i
$431$			5.66394i			0.272822i	0.990652	+	0.136411i	$0.0435568\pi$
$431$			5.66394i			0.272822i	−0.990652	+	0.136411i	$0.956443\pi$
$432$	−3.43914	+	3.89517i	−0.165466	+	0.187406i
$433$		−	29.3320i		−	1.40961i	−0.709402	−	0.704804i	$-0.751035\pi$
$433$		−	29.3320i		−	1.40961i	0.709402	−	0.704804i	$-0.248965\pi$
$434$	18.0846	−	4.25573i	0.868090	−	0.204282i
$435$	0.815036	−	1.84671i	0.0390780	−	0.0885429i
$436$	−6.05993	+	10.4961i	−0.290218	+	0.502672i
$437$	5.29969	−	9.17933i	0.253518	−	0.439107i
$438$	−1.29359	−	11.9349i	−0.0618100	−	0.570271i
$439$	2.68122	+	4.64400i	0.127967	+	0.221646i	0.922889	−	0.385066i	$-0.125821\pi$
$439$	2.68122	+	4.64400i	0.127967	+	0.221646i	−0.794922	+	0.606712i	$0.792488\pi$
$440$	−0.405088			−0.0193118
$441$	−12.1151	+	2.65745i	−0.576908	+	0.126545i
$442$	−8.95654			−0.426019
$443$	−4.39838	+	2.53941i	−0.208973	+	0.120651i	−0.600834	−	0.799374i	$-0.705165\pi$
$443$	−4.39838	+	2.53941i	−0.208973	+	0.120651i	0.391861	+	0.920025i	$0.371831\pi$
$444$	−6.00936	−	8.21497i	−0.285192	−	0.389865i
$445$	0.0811809	+	0.0468698i	0.00384835	+	0.00222184i
$446$	−3.89609	+	6.74823i	−0.184485	+	0.319538i
$447$	−11.3860	−	15.5650i	−0.538540	−	0.736200i
$448$	−1.66841	−	2.88977i	−0.0788250	−	0.136529i
$449$	3.68408			0.173862			0.0869312	−	0.996214i	$-0.472294\pi$
$449$	3.68408			0.173862			0.0869312	+	0.996214i	$0.472294\pi$
$450$	−3.15832	−	14.3985i	−0.148885	−	0.678752i
$451$		−	6.45249i		−	0.303836i
$452$	−7.03255	+	4.06024i	−0.330783	+	0.190978i
$453$	15.6496	−	1.69621i	0.735282	−	0.0796950i
$454$	12.7856	−	22.1452i	0.600056	−	1.03933i
$455$	−3.07339	+	5.32326i	−0.144083	+	0.249558i
$456$	−1.56189	+	3.53894i	−0.0731423	+	0.165726i
$457$	−14.4300	+	8.33114i	−0.675005	+	0.389714i	−0.797971	−	0.602696i	$-0.794093\pi$
$457$	−14.4300	+	8.33114i	−0.675005	+	0.389714i	0.122965	+	0.992411i	$0.460760\pi$
$458$	−25.1664			−1.17595
$459$	2.36336	+	7.03969i	0.110312	+	0.328585i
$460$		−	1.39495i		−	0.0650399i
$461$	13.2402	+	22.9327i	0.616657	+	1.06808i	0.990091	+	0.140425i	$0.0448467\pi$
$461$	13.2402	+	22.9327i	0.616657	+	1.06808i	−0.373434	+	0.927657i	$0.621820\pi$
$462$	−3.21618	+	7.28721i	−0.149630	+	0.339032i
$463$	18.8968	+	10.9100i	0.878207	+	0.507033i	0.870067	−	0.492934i	$-0.164076\pi$
$463$	18.8968	+	10.9100i	0.878207	+	0.507033i	0.00813989	+	0.999967i	$0.497409\pi$
$464$	1.98252	−	3.43382i	0.0920360	−	0.159411i
$465$	−2.78639	−	0.520047i	−0.129216	−	0.0241166i
$466$	10.8431	+	18.7809i	0.502299	+	0.870007i
$467$			30.5580i			1.41405i	0.707186	+	0.707027i	$0.249964\pi$
$467$			30.5580i			1.41405i	−0.707186	+	0.707027i	$0.750036\pi$
$468$	17.9189	+	5.69387i	0.828302	+	0.263199i
$469$	−27.4610			−1.26803
$470$	0.645077	−	0.372436i	0.0297552	−	0.0171792i
$471$	5.48848	−	4.01490i	0.252896	−	0.184997i
$472$	−6.09626	+	10.5590i	−0.280603	+	0.486019i
$473$	5.82096	+	3.36073i	0.267648	+	0.154527i
$474$	0.178157	−	0.130324i	0.00818302	−	0.00598599i
$475$	−5.48691	−	9.50360i	−0.251757	−	0.436055i
$476$	−4.76865			−0.218571
$477$	8.95155	+	9.81285i	0.409863	+	0.449299i
$478$			11.4585i			0.524099i
$479$	−35.9776	+	20.7717i	−1.64386	+	0.949082i	−0.664415	+	0.747364i	$0.731319\pi$
$479$	−35.9776	+	20.7717i	−1.64386	+	0.949082i	−0.979444	+	0.201718i	$0.935347\pi$
$480$	0.0548577	+	0.506128i	0.00250390	+	0.0231015i
$481$	−18.4147	+	31.8951i	−0.839636	+	1.45429i
$482$	−6.07329	+	10.5193i	−0.276631	+	0.479139i
$483$	−25.0941	−	11.0752i	−1.14182	−	0.503937i
$484$	−4.55028	−	7.88131i	−0.206831	−	0.358242i
$485$			2.54822i			0.115709i
$486$	−0.252974	−	15.5864i	−0.0114751	−	0.707014i
$487$		−	3.72421i		−	0.168760i	−0.996434	−	0.0843799i	$-0.973109\pi$
$487$		−	3.72421i		−	0.168760i	0.996434	−	0.0843799i	$-0.0268909\pi$
$488$	−1.58380	−	2.74322i	−0.0716951	−	0.124180i
$489$	36.2420	+	15.9952i	1.63892	+	0.723330i
$490$	−0.607596	+	1.05239i	−0.0274484	+	0.0475420i
$491$	−18.8663	+	32.6774i	−0.851425	+	1.47471i	0.0284970	+	0.999594i	$0.490928\pi$
$491$	−18.8663	+	32.6774i	−0.851425	+	1.47471i	−0.879922	+	0.475118i	$0.842405\pi$
$492$	−8.06192	+	0.873808i	−0.363459	+	0.0393943i
$493$	−2.83321	−	4.90727i	−0.127601	−	0.221012i
$494$	13.9970			0.629755
$495$	0.897819	−	0.819015i	0.0403539	−	0.0368120i
$496$	−5.33131	−	1.60535i	−0.239383	−	0.0720821i
$497$	−10.2160	+	5.89821i	−0.458250	+	0.264571i
$498$	11.9504	+	16.3365i	0.535508	+	0.732055i
$499$	−33.2707	−	19.2088i	−1.48940	−	0.859906i	−0.489474	−	0.872018i	$-0.662811\pi$
$499$	−33.2707	−	19.2088i	−1.48940	−	0.859906i	−0.999927	+	0.0121118i	$0.996145\pi$
$500$	−2.52347	−	1.45693i	−0.112853	−	0.0651558i
$501$	−30.7437	+	22.4895i	−1.37353	+	1.00475i
$502$	−22.0317	+	12.7200i	−0.983322	+	0.567721i
$503$			15.6481i			0.697715i	0.937176	+	0.348857i	$0.113430\pi$
$503$			15.6481i			0.697715i	−0.937176	+	0.348857i	$0.886570\pi$
$504$	9.54039	+	3.03153i	0.424963	+	0.135035i
$505$	−2.95833			−0.131644
$506$	−5.66457	+	3.27044i	−0.251821	+	0.145389i
$507$	−4.90461	−	45.2509i	−0.217821	−	2.00966i
$508$	9.04605	+	5.22274i	0.401354	+	0.231722i
$509$	−0.896398	+	1.55261i	−0.0397321	+	0.0688181i	−0.885208	−	0.465196i	$-0.845984\pi$
$509$	−0.896398	+	1.55261i	−0.0397321	+	0.0688181i	0.845475	+	0.534014i	$0.179317\pi$
$510$	0.665601	+	0.293760i	0.0294733	+	0.0130079i
$511$	−20.0289	+	11.5637i	−0.886027	+	0.511548i
$512$			1.00000i			0.0441942i
$513$	−3.69339	−	11.0014i	−0.163067	−	0.485724i
$514$	7.04918			0.310926
$515$	2.92661	−	1.68968i	0.128962	−	0.0744563i
$516$	3.41071	−	7.72799i	0.150148	−	0.340206i
$517$	−3.02475	−	1.74634i	−0.133028	−	0.0768038i
$518$	−9.80434	+	16.9816i	−0.430778	+	0.746129i
$519$	−1.84591	+	0.200072i	−0.0810263	+	0.00878220i
$520$	1.59531	−	0.921052i	0.0699589	−	0.0403908i
$521$		−	22.3109i		−	0.977460i	−0.872435	−	0.488730i	$-0.837460\pi$
$521$		−	22.3109i		−	0.977460i	0.872435	−	0.488730i	$-0.162540\pi$
$522$	2.54861	+	11.6189i	0.111550	+	0.508544i
$523$		−	18.7594i		−	0.820291i	−0.912020	−	0.410146i	$-0.865478\pi$
$523$		−	18.7594i		−	0.820291i	0.912020	−	0.410146i	$-0.134522\pi$
$524$	−18.2202	+	10.5194i	−0.795953	+	0.459543i
$525$	−22.9205	+	16.7666i	−1.00033	+	0.731756i
$526$	−2.71785	−	1.56915i	−0.118504	−	0.0684182i
$527$	−5.79632	+	5.45112i	−0.252492	+	0.237455i
$528$	1.92665	−	1.40937i	0.0838468	−	0.0613351i
$529$	0.237987	+	0.412206i	0.0103473	+	0.0179220i
$530$	1.30134			0.0565267
$531$	−7.83700	−	35.7282i	−0.340097	−	1.55047i
$532$	7.45229			0.323098
$533$	14.6711	+	25.4111i	0.635475	+	1.10068i
$534$	−0.549177	+	0.0595236i	−0.0237652	+	0.00257584i
$535$	−2.15181	+	3.72705i	−0.0930310	+	0.161134i
$536$	7.12712	+	4.11484i	0.307845	+	0.177734i
$537$	21.3592	+	9.42679i	0.921719	+	0.406796i
$538$	−22.7326	+	13.1247i	−0.980072	+	0.565845i
$539$	5.69800			0.245430
$540$	−1.14489	−	1.01085i	−0.0492680	−	0.0435000i
$541$	−35.2659			−1.51620			−0.758099	−	0.652140i	$-0.773872\pi$
$541$	−35.2659			−1.51620			−0.758099	+	0.652140i	$0.773872\pi$
$542$	13.2312	+	22.9172i	0.568331	+	0.984378i
$543$	−5.71730	+	12.9543i	−0.245353	+	0.555920i
$544$	1.23764	+	0.714549i	0.0530632	+	0.0306361i
$545$	−3.08506	−	1.78116i	−0.132150	−	0.0762966i
$546$	−3.90313	−	36.0110i	−0.167038	−	1.54113i
$547$	−4.55764	−	7.89406i	−0.194870	−	0.337526i	0.751988	−	0.659177i	$-0.229095\pi$
$547$	−4.55764	−	7.89406i	−0.194870	−	0.337526i	−0.946858	+	0.321652i	$0.895762\pi$
$548$	−20.9695			−0.895774
$549$	9.05655	+	2.87779i	0.386524	+	0.122821i
$550$			6.77195i			0.288757i
$551$	4.42765	+	7.66892i	0.188624	+	0.326707i
$552$	4.85329	+	6.63458i	0.206570	+	0.282387i
$553$	−0.368278	−	0.212625i	−0.0156608	−	0.00904175i
$554$	2.09039	−	3.62066i	0.0888121	−	0.153827i
$555$	2.41458	−	1.76630i	0.102493	−	0.0749752i
$556$	0.487248	−	0.281313i	0.0206639	−	0.0119303i
$557$	24.5606			1.04067			0.520333	−	0.853963i	$-0.325808\pi$
$557$	24.5606			1.04067			0.520333	+	0.853963i	$0.325808\pi$
$558$	15.0618	−	7.22094i	0.637617	−	0.305687i
$559$	−30.5653			−1.29278
$560$	0.849375	−	0.490387i	0.0358926	−	0.0207226i
$561$	−0.367601	−	3.39156i	−0.0155201	−	0.143192i
$562$	1.88475	−	3.26448i	0.0795033	−	0.137704i
$563$	16.2161	+	9.36237i	0.683427	+	0.394577i	0.801145	−	0.598470i	$-0.204225\pi$
$563$	16.2161	+	9.36237i	0.683427	+	0.394577i	−0.117718	+	0.993047i	$0.537558\pi$
$564$	−1.77231	+	4.01570i	−0.0746276	+	0.169091i
$565$	−1.19341	−	2.06704i	−0.0502070	−	0.0869610i
$566$		−	24.0773i		−	1.01205i
$567$	−27.2741	+	12.5700i	−1.14541	+	0.527891i
$568$	3.53523			0.148335
$569$	7.54534	+	13.0689i	0.316317	+	0.547877i	0.979717	−	0.200388i	$-0.0642203\pi$
$569$	7.54534	+	13.0689i	0.316317	+	0.547877i	−0.663399	+	0.748265i	$0.730887\pi$
$570$	−1.04018	−	0.459079i	−0.0435684	−	0.0192287i
$571$	27.7815	+	16.0396i	1.16262	+	0.671238i	0.951930	−	0.306315i	$-0.0990961\pi$
$571$	27.7815	+	16.0396i	1.16262	+	0.671238i	0.210688	+	0.977553i	$0.432429\pi$
$572$	−7.48035	−	4.31878i	−0.312769	−	0.180577i
$573$	−14.8876	+	1.61362i	−0.621937	+	0.0674099i
$574$	7.81118	+	13.5294i	0.326032	+	0.564705i
$575$	−23.3197			−0.972500
$576$	−2.02182	−	2.21636i	−0.0842426	−	0.0923482i
$577$	10.2648			0.427330			0.213665	−	0.976907i	$-0.431460\pi$
$577$	10.2648			0.427330			0.213665	+	0.976907i	$0.431460\pi$
$578$	−12.9537	+	7.47884i	−0.538804	+	0.311079i
$579$	−15.0232	+	10.9897i	−0.624343	+	0.456715i
$580$	1.00928	+	0.582710i	0.0419082	+	0.0241957i
$581$	19.4971	−	33.7700i	0.808877	−	1.40102i
$582$	−8.86570	−	12.1197i	−0.367495	−	0.502376i
$583$	−3.05097	−	5.28444i	−0.126358	−	0.218859i
$584$	6.93097			0.286805
$585$	−1.67357	+	5.26681i	−0.0691936	+	0.217756i
$586$	−2.01910			−0.0834084
$587$	−5.28104	−	9.14703i	−0.217972	−	0.377539i	0.736216	−	0.676747i	$-0.236611\pi$
$587$	−5.28104	−	9.14703i	−0.217972	−	0.377539i	−0.954188	+	0.299208i	$0.903277\pi$
$588$	−0.771633	−	7.11924i	−0.0318216	−	0.293592i
$589$	9.05831	−	8.51885i	0.373241	−	0.351013i
$590$	−3.10356	−	1.79184i	−0.127772	−	0.0737690i
$591$	−37.8626	−	16.7105i	−1.55746	−	0.687377i
$592$	5.08916	−	2.93823i	0.209163	−	0.120760i
$593$		−	34.3728i		−	1.41152i	−0.708449	−	0.705762i	$-0.750605\pi$
$593$		−	34.3728i		−	1.41152i	0.708449	−	0.705762i	$-0.249395\pi$
$594$	−1.42065	+	7.01902i	−0.0582900	+	0.287994i
$595$		−	1.40162i		−	0.0574609i
$596$	9.64250	−	5.56710i	0.394972	−	0.228037i
$597$	−15.8606	+	35.9369i	−0.649130	+	1.47080i
$598$	14.8721	−	25.7592i	0.608164	−	1.05337i
$599$	−15.2292	−	8.79256i	−0.622247	−	0.359254i	0.155496	−	0.987836i	$-0.450302\pi$
$599$	−15.2292	−	8.79256i	−0.622247	−	0.359254i	−0.777743	+	0.628582i	$0.783636\pi$
$600$	8.46107	−	0.917070i	0.345422	−	0.0374392i
$601$	−10.3669	+	5.98532i	−0.422874	+	0.244146i	−0.696306	−	0.717745i	$-0.745174\pi$
$601$	−10.3669	+	5.98532i	−0.422874	+	0.244146i	0.273432	+	0.961891i	$0.411841\pi$
$602$	−16.2736			−0.663262
$603$	−24.1157	+	5.28980i	−0.982068	+	0.215418i
$604$			9.08821i			0.369794i
$605$	2.31651	−	1.33744i	0.0941796	−	0.0543746i
$606$	14.0702	−	10.2925i	0.571563	−	0.418106i
$607$	4.78565	−	8.28899i	0.194244	−	0.336440i	−0.752409	−	0.658696i	$-0.771108\pi$
$607$	4.78565	−	8.28899i	0.194244	−	0.336440i	0.946652	+	0.322257i	$0.104441\pi$
$608$	−1.93414	−	1.11668i	−0.0784397	−	0.0452872i
$609$	18.4957	−	13.5298i	0.749482	−	0.548256i
$610$	0.806299	−	0.465517i	0.0326461	−	0.0188482i
$611$	15.8827			0.642544
$612$	−4.18773	+	0.918583i	−0.169279	+	0.0371315i
$613$		−	5.64188i		−	0.227873i	−0.993488	−	0.113937i	$-0.963654\pi$
$613$		−	5.64188i		−	0.227873i	0.993488	−	0.113937i	$-0.0363461\pi$
$614$	2.95072	−	1.70360i	0.119081	−	0.0687517i
$615$	−0.256834	−	2.36960i	−0.0103565	−	0.0955514i
$616$	−3.98269	−	2.29941i	−0.160467	−	0.0926457i
$617$	14.4337	+	8.33328i	0.581077	+	0.335485i	0.761561	−	0.648093i	$-0.224433\pi$
$617$	14.4337	+	8.33328i	0.581077	+	0.335485i	−0.180484	+	0.983578i	$0.557766\pi$
$618$	−8.04068	+	18.2186i	−0.323444	+	0.732859i
$619$	16.8361	−	9.72035i	0.676702	−	0.390694i	−0.121909	−	0.992541i	$-0.538902\pi$
$619$	16.8361	−	9.72035i	0.676702	−	0.390694i	0.798611	+	0.601847i	$0.205568\pi$
$620$	0.471851	−	1.56700i	0.0189500	−	0.0629324i
$621$	−24.1706	−	4.89212i	−0.969931	−	0.196314i
$622$	−0.441070			−0.0176853
$623$	0.532096	+	0.921618i	0.0213180	+	0.0369238i
$624$	−4.38301	+	9.93102i	−0.175461	+	0.397559i
$625$	−11.8558	+	20.5348i	−0.474232	+	0.821394i
$626$	6.67194	−	11.5561i	0.266664	−	0.461876i
$627$	0.574476	+	5.30023i	0.0229424	+	0.211671i
$628$	1.96305	+	3.40011i	0.0783343	+	0.135679i
$629$		−	8.39804i		−	0.334852i
$630$	−0.891043	+	2.80416i	−0.0355000	+	0.111720i
$631$			13.2263i			0.526531i	0.964723	+	0.263266i	$0.0847995\pi$
$631$			13.2263i			0.526531i	−0.964723	+	0.263266i	$0.915200\pi$
$632$	0.0637209	+	0.110368i	0.00253468	+	0.00439020i
$633$	−4.26673	+	3.12117i	−0.169587	+	0.124055i
$634$	−1.22653	+	2.12441i	−0.0487117	+	0.0843711i
$635$	−1.53509	+	2.65886i	−0.0609183	+	0.105514i
$636$	−6.18936	+	4.52760i	−0.245424	+	0.179531i
$637$	−22.4397	+	12.9556i	−0.889095	+	0.513319i
$638$		−	5.46462i		−	0.216346i
$639$	−7.83533	+	7.14760i	−0.309961	+	0.282755i
$640$	−0.293925			−0.0116184
$641$	−12.0787	−	20.9210i	−0.477081	−	0.826328i	0.522574	−	0.852594i	$-0.324972\pi$
$641$	−12.0787	−	20.9210i	−0.477081	−	0.826328i	−0.999655	+	0.0262654i	$0.991638\pi$
$642$	−2.73275	−	25.2129i	−0.107853	−	0.995074i
$643$	25.9743	+	14.9962i	1.02432	+	0.591394i	0.915354	−	0.402651i	$-0.131911\pi$
$643$	25.9743	+	14.9962i	1.02432	+	0.591394i	0.108971	+	0.994045i	$0.465244\pi$
$644$	7.91819	−	13.7147i	0.312020	−	0.540435i
$645$	2.27145	+	1.00249i	0.0894381	+	0.0394731i
$646$	−2.76408	+	1.59584i	−0.108751	+	0.0627875i
$647$	4.16433			0.163717			0.0818584	−	0.996644i	$-0.473914\pi$
$647$	4.16433			0.163717			0.0818584	+	0.996644i	$0.473914\pi$
$648$	8.96216	+	0.824472i	0.352067	+	0.0323883i
$649$			16.8038i			0.659606i
$650$	−15.3974	−	26.6692i	−0.603938	−	1.04605i
$651$	−24.4429	−	20.9294i	−0.957994	−	0.820287i
$652$	−11.4358	+	19.8074i	−0.447861	+	0.775718i
$653$	−33.7669	−	19.4953i	−1.32140	−	0.762911i	−0.337449	−	0.941344i	$-0.609564\pi$
$653$	−33.7669	−	19.4953i	−1.32140	−	0.762911i	−0.983952	+	0.178432i	$0.942897\pi$
$654$	20.8700	−	2.26204i	0.816081	−	0.0884526i
$655$	−3.09192	−	5.35536i	−0.120811	−	0.209251i
$656$		−	4.68181i		−	0.182794i
$657$	−15.3615	+	14.0132i	−0.599309	+	0.546706i
$658$	8.45625			0.329659
$659$	2.97069	−	1.71513i	0.115722	−	0.0668120i	−0.441022	−	0.897496i	$-0.645384\pi$
$659$	2.97069	−	1.71513i	0.115722	−	0.0668120i	0.556744	+	0.830684i	$0.312051\pi$
$660$	0.414249	+	0.566291i	0.0161246	+	0.0220428i
$661$	19.0019	−	32.9122i	0.739086	−	1.28014i	−0.213821	−	0.976873i	$-0.568591\pi$
$661$	19.0019	−	32.9122i	0.739086	−	1.28014i	0.952907	−	0.303262i	$-0.0980758\pi$
$662$	16.0261	−	27.7580i	0.622872	−	1.07885i
$663$	9.15911	+	12.5208i	0.355710	+	0.486266i
$664$	−10.1204	+	5.84303i	−0.392748	+	0.226753i
$665$			2.19041i			0.0849406i
$666$	−5.33882	+	16.8015i	−0.206875	+	0.651046i
$667$	18.8178			0.728629
$668$	−10.9960	−	19.0457i	−0.425449	−	0.736900i
$669$	13.4179	−	1.45432i	0.518765	−	0.0562274i
$670$	−1.20945	+	2.09484i	−0.0467253	+	0.0809306i
$671$	−3.78071	−	2.18279i	−0.145953	−	0.0842657i
$672$	−2.33360	+	5.28748i	−0.0900206	+	0.203969i
$673$	13.6337	−	7.87140i	0.525539	−	0.303420i	−0.213659	−	0.976908i	$-0.568538\pi$
$673$	13.6337	−	7.87140i	0.525539	−	0.303420i	0.739198	+	0.673488i	$0.235205\pi$
$674$	−8.53787			−0.328866
$675$	−16.8986	+	19.1393i	−0.650427	+	0.736673i
$676$	26.2786			1.01072
$677$	15.8422	+	27.4395i	0.608866	+	1.05459i	0.991428	+	0.130656i	$0.0417084\pi$
$677$	15.8422	+	27.4395i	0.608866	+	1.05459i	−0.382562	+	0.923930i	$0.624958\pi$
$678$	12.8676	+	5.67905i	0.494177	+	0.218103i
$679$	−14.4645	+	25.0532i	−0.555096	+	0.961454i
$680$	−0.210024	+	0.363772i	−0.00805404	+	0.0139500i
$681$	−44.0326	+	4.77256i	−1.68733	+	0.182885i
$682$	−7.46948	+	1.75774i	−0.286021	+	0.0673073i
$683$			37.7952i			1.44619i	0.690748	+	0.723096i	$0.257282\pi$
$683$			37.7952i			1.44619i	−0.690748	+	0.723096i	$0.742718\pi$
$684$	6.54446	−	1.43553i	0.250234	−	0.0548890i
$685$		−	6.16346i		−	0.235494i
$686$	8.28102	−	4.78105i	0.316171	−	0.182541i
$687$	25.7356	+	35.1813i	0.981874	+	1.34225i
$688$	4.22359	+	2.43849i	0.161023	+	0.0929665i
$689$	24.0306	+	13.8741i	0.915492	+	0.528560i
$690$	−1.95007	+	1.42650i	−0.0742378	+	0.0543059i
$691$	10.1505	+	17.5812i	0.386143	+	0.668820i	0.991927	−	0.126809i	$-0.0404737\pi$
$691$	10.1505	+	17.5812i	0.386143	+	0.668820i	−0.605784	+	0.795629i	$0.707140\pi$
$692$		−	1.07198i		−	0.0407504i
$693$	13.4761	−	2.95598i	0.511913	−	0.112289i
$694$			28.6512i			1.08758i
$695$	0.0826848	+	0.143214i	0.00313641	+	0.00543242i
$696$	−6.82765	+	0.740028i	−0.258801	+	0.0280507i
$697$	−5.79438	−	3.34539i	−0.219478	−	0.126716i
$698$	12.5714	+	7.25810i	0.475835	+	0.274723i
$699$	15.1663	−	34.3638i	0.573641	−	1.29976i
$700$	−8.19791	−	14.1992i	−0.309852	−	0.536679i
$701$		−	2.14125i		−	0.0808740i	−0.999182	−	0.0404370i	$-0.987125\pi$
$701$		−	2.14125i		−	0.0808740i	0.999182	−	0.0404370i	$-0.0128750\pi$
$702$	−10.3644	−	30.8723i	−0.391181	−	1.16520i
$703$			13.1242i			0.494988i
$704$	0.689101	+	1.19356i	0.0259715	+	0.0449839i
$705$	−1.18031	−	0.520925i	−0.0444531	−	0.0196192i
$706$	−12.1948	−	7.04069i	−0.458959	−	0.264980i
$707$	−29.0853	−	16.7924i	−1.09387	−	0.631543i
$708$	20.9951	−	2.27560i	0.789045	−	0.0855222i
$709$	17.5298	−	10.1208i	0.658346	−	0.380096i	−0.133301	−	0.991076i	$-0.542558\pi$
$709$	17.5298	−	10.1208i	0.658346	−	0.380096i	0.791646	+	0.610980i	$0.209224\pi$
$710$			1.03909i			0.0389964i
$711$	−0.364373	−	0.115782i	−0.0136650	−	0.00434217i
$712$		−	0.318924i		−	0.0119522i
$713$	−6.05291	−	25.7217i	−0.226683	−	0.963286i
$714$	4.87650	+	6.66631i	0.182498	+	0.249480i
$715$	1.26940	−	2.19866i	0.0474727	−	0.0822252i
$716$	−6.73969	+	11.6735i	−0.251874	+	0.436259i
$717$	16.0184	−	11.7176i	0.598216	−	0.437603i
$718$	−3.12547	−	5.41347i	−0.116641	−	0.202029i
$719$	44.8856			1.67395			0.836975	−	0.547241i	$-0.184322\pi$
$719$	44.8856			1.67395			0.836975	+	0.547241i	$0.184322\pi$
$720$	0.651442	−	0.594263i	0.0242778	−	0.0221469i
$721$	38.3647			1.42878
$722$	−12.1349	+	7.00607i	−0.451613	+	0.260739i
$723$	20.9160	−	2.26702i	0.777874	−	0.0843115i
$724$	−7.07990	−	4.08758i	−0.263123	−	0.151914i
$725$	9.74131	−	16.8724i	0.361783	−	0.626627i
$726$	−6.36447	+	14.4206i	−0.236207	+	0.535199i
$727$	15.3725	+	26.6259i	0.570134	+	0.987501i	0.996552	+	0.0829745i	$0.0264420\pi$
$727$	15.3725	+	26.6259i	0.570134	+	0.987501i	−0.426418	+	0.904526i	$0.640225\pi$
$728$	20.9127			0.775078
$729$	−21.5303	+	16.2926i	−0.797417	+	0.603428i
$730$			2.03718i			0.0753995i
$731$	6.03592	−	3.48484i	0.223247	−	0.128892i
$732$	−2.21525	+	5.01932i	−0.0818781	+	0.185519i
$733$	−10.5832	+	18.3306i	−0.390899	+	0.677057i	−0.992568	−	0.121688i	$-0.961169\pi$
$733$	−10.5832	+	18.3306i	−0.390899	+	0.677057i	0.601669	+	0.798745i	$0.294503\pi$
$734$	12.8237	−	22.2113i	0.473331	−	0.819833i
$735$	2.09252	−	0.226802i	0.0771838	−	0.00836572i
$736$	−4.11011	+	2.37297i	−0.151501	+	0.0874690i
$737$	11.3422			0.417794
$738$	9.46579	+	10.3766i	0.348441	+	0.381967i
$739$			35.9785i			1.32349i	0.749728	+	0.661746i	$0.230184\pi$
$739$			35.9785i			1.32349i	−0.749728	+	0.661746i	$0.769816\pi$
$740$	0.863617	+	1.49583i	0.0317472	+	0.0549878i
$741$	−14.3136	−	19.5671i	−0.525823	−	0.718815i
$742$	12.7944	+	7.38683i	0.469696	+	0.271179i
$743$	15.0852	−	26.1284i	0.553424	−	0.958558i	−0.444600	−	0.895729i	$-0.646654\pi$
$743$	15.0852	−	26.1284i	0.553424	−	0.958558i	0.998024	−	0.0628294i	$-0.0200124\pi$
$744$	3.20770	+	9.09454i	0.117600	+	0.333422i
$745$	1.63631	+	2.83417i	0.0599497	+	0.103836i
$746$			18.5297i			0.678422i
$747$	10.6169	−	33.4119i	0.388452	−	1.22248i
$748$	1.96959			0.0720153
$749$	−42.3118	+	24.4288i	−1.54604	+	0.892607i
$750$	0.543838	+	5.01756i	0.0198582	+	0.183215i
$751$	−18.7657	+	32.5031i	−0.684770	+	1.18606i	0.288740	+	0.957408i	$0.406764\pi$
$751$	−18.7657	+	32.5031i	−0.684770	+	1.18606i	−0.973509	+	0.228648i	$0.926570\pi$
$752$	−2.19470	−	1.26711i	−0.0800326	−	0.0462068i
$753$	40.3118	+	17.7914i	1.46904	+	0.648356i
$754$	12.4250	+	21.5207i	0.452490	+	0.783736i
$755$	−2.67125			−0.0972167
$756$	−5.51824	−	16.4371i	−0.200697	−	0.597810i
$757$		−	10.9984i		−	0.399742i	−0.979822	−	0.199871i	$-0.935948\pi$
$757$		−	10.9984i		−	0.399742i	0.979822	−	0.199871i	$-0.0640524\pi$
$758$	0.463779	−	0.267763i	0.0168452	−	0.00972559i
$759$	10.3646	+	4.57436i	0.376210	+	0.166039i
$760$	0.328219	−	0.568491i	0.0119057	−	0.0206213i
$761$	2.04875	−	3.54853i	0.0742670	−	0.128634i	−0.826500	−	0.562936i	$-0.809672\pi$
$761$	2.04875	−	3.54853i	0.0742670	−	0.128634i	0.900767	+	0.434302i	$0.143005\pi$
$762$	−1.94953	−	17.9868i	−0.0706240	−	0.651591i
$763$	−20.2209	−	35.0236i	−0.732046	−	1.26794i
$764$		−	8.64568i		−	0.312790i
$765$	−0.269994	−	1.23088i	−0.00976166	−	0.0445025i
$766$			23.6595i			0.854853i
$767$	−38.2069	−	66.1763i	−1.37957	−	2.38949i
$768$	1.39795	−	1.02262i	0.0504441	−	0.0369005i
$769$	21.8654	−	37.8720i	0.788487	−	1.36570i	−0.138406	−	0.990376i	$-0.544198\pi$
$769$	21.8654	−	37.8720i	0.788487	−	1.36570i	0.926893	−	0.375325i	$-0.122469\pi$
$770$	0.675852	−	1.17061i	0.0243560	−	0.0421859i
$771$	−7.20861	−	9.85438i	−0.259612	−	0.354897i
$772$	−5.37331	−	9.30684i	−0.193390	−	0.334961i
$773$	−9.88211			−0.355435			−0.177717	−	0.984082i	$-0.556871\pi$
$773$	−9.88211			−0.355435			−0.177717	+	0.984082i	$0.556871\pi$
$774$	−14.2912	+	3.13478i	−0.513685	+	0.112677i
$775$	−26.1960	−	7.88804i	−0.940987	−	0.283347i
$776$	7.50811	−	4.33481i	0.269526	−	0.155611i
$777$	33.7655	−	3.65974i	1.21133	−	0.131292i
$778$	8.99811	+	5.19506i	0.322598	+	0.186252i
$779$	9.05528	+	5.22807i	0.324439	+	0.187315i
$780$	−2.91897	−	1.28827i	−0.104516	−	0.0461276i
$781$	4.21950	−	2.43613i	0.150986	−	0.0871716i
$782$			6.78243i			0.242539i
$783$	13.6363	−	15.4445i	0.487321	−	0.551940i
$784$	4.13437			0.147656
$785$	−0.999375	+	0.576989i	−0.0356692	+	0.0205936i
$786$	33.3379	+	14.7135i	1.18912	+	0.524813i
$787$	32.4294	+	18.7231i	1.15598	+	0.667407i	0.950338	−	0.311220i	$-0.100738\pi$
$787$	32.4294	+	18.7231i	1.15598	+	0.667407i	0.205645	+	0.978627i	$0.434071\pi$
$788$	11.9472	−	20.6931i	0.425600	−	0.737161i
$789$	0.585728	+	5.40405i	0.0208525	+	0.192389i
$790$	−0.0324398	+	0.0187292i	−0.00115416	+	0.000666353i
$791$		−	27.0966i		−	0.963444i
$792$	−3.94046	−	1.25211i	−0.140018	−	0.0444918i
$793$	19.8521			0.704970
$794$	22.5428	−	13.0151i	0.800013	−	0.461888i
$795$	−1.33077	−	1.81921i	−0.0471977	−	0.0645206i
$796$	−19.6406	−	11.3395i	−0.696144	−	0.401919i
$797$	1.19124	−	2.06329i	0.0421959	−	0.0730854i	−0.844156	−	0.536097i	$-0.819898\pi$
$797$	1.19124	−	2.06329i	0.0421959	−	0.0730854i	0.886352	+	0.463012i	$0.153231\pi$
$798$	−7.62084	−	10.4179i	−0.269775	−	0.368790i
$799$	−3.13645	+	1.81083i	−0.110960	+	0.0640625i
$800$			4.91361i			0.173722i
$801$	0.644808	+	0.706850i	0.0227832	+	0.0249753i
$802$		−	19.0750i		−	0.673561i
$803$	8.27251	−	4.77614i	0.291931	−	0.168546i
$804$	−1.53598	−	14.1712i	−0.0541698	−	0.499781i
$805$	4.03109	+	2.32735i	0.142077	+	0.0820283i
$806$	25.4196	−	23.9057i	0.895366	−	0.842043i
$807$	41.5943	+	18.3575i	1.46419	+	0.646213i
$808$	5.03246	+	8.71647i	0.177041	+	0.306644i
$809$	45.3221			1.59344			0.796720	−	0.604348i	$-0.206566\pi$
$809$	45.3221			1.59344			0.796720	+	0.604348i	$0.206566\pi$
$810$	−0.242333	+	2.63420i	−0.00851470	+	0.0925563i
$811$	46.5573			1.63485			0.817424	−	0.576036i	$-0.195401\pi$
$811$	46.5573			1.63485			0.817424	+	0.576036i	$0.195401\pi$
$812$	6.61530	+	11.4580i	0.232151	+	0.402098i
$813$	18.5065	−	41.9321i	0.649052	−	1.47062i
$814$	4.04947	−	7.01389i	0.141934	−	0.245837i
$815$	−5.82188	−	3.36127i	−0.203932	−	0.117740i
$816$	−0.266725	−	2.46086i	−0.00933725	−	0.0861473i
$817$	−9.43276	+	5.44600i	−0.330010	+	0.190532i
$818$	−22.7330			−0.794839
$819$	−46.3501	+	42.2818i	−1.61960	+	1.47745i
$820$	1.37610			0.0480555
$821$	17.3795	+	30.1022i	0.606549	+	1.05057i	0.991805	+	0.127764i	$0.0407799\pi$
$821$	17.3795	+	30.1022i	0.606549	+	1.05057i	−0.385256	+	0.922810i	$0.625887\pi$
$822$	21.4438	+	29.3143i	0.747938	+	1.02245i
$823$	4.87079	+	2.81215i	0.169785	+	0.0980255i	0.582485	−	0.812842i	$-0.302081\pi$
$823$	4.87079	+	2.81215i	0.169785	+	0.0980255i	−0.412699	+	0.910867i	$0.635414\pi$
$824$	−9.95702	−	5.74869i	−0.346869	−	0.200265i
$825$	9.46682	−	6.92511i	0.329592	−	0.241101i
$826$	−20.3421	−	35.2336i	−0.707793	−	1.22593i
$827$	16.8515			0.585985			0.292992	−	0.956115i	$-0.405349\pi$
$827$	16.8515			0.585985			0.292992	+	0.956115i	$0.405349\pi$
$828$	4.31174	−	13.5693i	0.149843	−	0.471565i
$829$			11.5377i			0.400722i	0.979722	+	0.200361i	$0.0642115\pi$
$829$			11.5377i			0.400722i	−0.979722	+	0.200361i	$0.935788\pi$
$830$	−1.71741	−	2.97464i	−0.0596122	−	0.103251i
$831$	−7.19916	+	0.780295i	−0.249736	+	0.0270681i
$832$	−5.42761	−	3.13363i	−0.188169	−	0.108639i
$833$	2.95421	−	5.11684i	0.102357	−	0.177288i
$834$	−0.891528	−	0.393472i	−0.0308711	−	0.0136248i
$835$	5.59800	−	3.23201i	0.193727	−	0.111848i
$836$	−3.07801			−0.106455
$837$	−25.4969	−	13.6713i	−0.881303	−	0.472551i
$838$	−8.25540			−0.285178
$839$	11.2407	−	6.48984i	0.388073	−	0.224054i	−0.293252	−	0.956035i	$-0.594737\pi$
$839$	11.2407	−	6.48984i	0.388073	−	0.224054i	0.681325	+	0.731981i	$0.261404\pi$
$840$	−1.55412	−	0.685903i	−0.0536222	−	0.0236659i
$841$	6.63926	−	11.4995i	0.228940	−	0.396536i
$842$	−26.7232	−	15.4287i	−0.920943	−	0.531707i
$843$	−6.49094	+	0.703534i	−0.223560	+	0.0242310i
$844$	−1.52607	−	2.64323i	−0.0525295	−	0.0909837i
$845$			7.72394i			0.265712i
$846$	7.42612	−	1.62893i	0.255315	−	0.0560036i
$847$	30.3669			1.04342
$848$	−2.21373	−	3.83430i	−0.0760199	−	0.131670i
$849$	−33.6588	+	24.6219i	−1.15517	+	0.845021i
$850$	6.08126	+	3.51102i	0.208585	+	0.120427i
$851$	24.1529	+	13.9447i	0.827950	+	0.478017i
$852$	−3.61518	−	4.94206i	−0.123854	−	0.169312i
$853$	−12.6319	−	21.8791i	−0.432507	−	0.749125i	0.564581	−	0.825378i	$-0.309038\pi$
$853$	−12.6319	−	21.8791i	−0.432507	−	0.749125i	−0.997089	+	0.0762528i	$0.975704\pi$
$854$	10.5697			0.361687
$855$	0.421939	+	1.92358i	0.0144300	+	0.0657850i
$856$	14.6419			0.500451
$857$	35.3973	−	20.4366i	1.20915	−	0.698102i	0.246574	−	0.969124i	$-0.420695\pi$
$857$	35.3973	−	20.4366i	1.20915	−	0.698102i	0.962573	+	0.271022i	$0.0873617\pi$
$858$	1.61210	+	14.8736i	0.0550363	+	0.507776i
$859$	−40.3209	−	23.2793i	−1.37573	−	0.794278i	−0.384088	−	0.923296i	$-0.625484\pi$
$859$	−40.3209	−	23.2793i	−1.37573	−	0.794278i	−0.991642	+	0.129018i	$0.958817\pi$
$860$	−0.716732	+	1.24142i	−0.0244404	+	0.0423319i
$861$	10.9255	−	24.7550i	0.372340	−	0.843647i
$862$	2.83197	+	4.90512i	0.0964573	+	0.167069i
$863$	−43.0865			−1.46668			−0.733340	−	0.679862i	$-0.762040\pi$
$863$	−43.0865			−1.46668			−0.733340	+	0.679862i	$0.762040\pi$
$864$	−1.03080	+	5.09288i	−0.0350685	+	0.173263i
$865$	0.315080			0.0107130
$866$	−14.6660	−	25.4023i	−0.498372	−	0.863205i
$867$	23.7017	+	10.4606i	0.804952	+	0.355262i
$868$	13.5339	−	12.7279i	0.459370	−	0.432013i
$869$	0.152109	+	0.0878204i	0.00515996	+	0.00297910i
$870$	−0.217513	−	2.00681i	−0.00737437	−	0.0680374i
$871$	−44.6676	+	25.7888i	−1.51350	+	0.873821i
$872$			12.1199i			0.410430i
$873$	−7.87644	+	24.7876i	−0.266577	+	0.838932i
$874$		−	10.5994i		−	0.358529i
$875$	8.42037	−	4.86150i	0.284660	−	0.164349i
$876$	−7.08772	−	9.68912i	−0.239472	−	0.327365i
$877$	7.61307	−	13.1862i	0.257075	−	0.445267i	−0.708382	−	0.705829i	$-0.750575\pi$
$877$	7.61307	−	13.1862i	0.257075	−	0.445267i	0.965457	+	0.260562i	$0.0839079\pi$
$878$	4.64400	+	2.68122i	0.156728	+	0.0904867i
$879$	2.06477	+	2.82260i	0.0696429	+	0.0952039i
$880$	−0.350816	+	0.202544i	−0.0118260	+	0.00682775i
$881$	20.5454			0.692193			0.346097	−	0.938199i	$-0.387507\pi$
$881$	20.5454			0.692193			0.346097	+	0.938199i	$0.387507\pi$
$882$	−9.16323	+	8.35895i	−0.308542	+	0.281461i
$883$		−	4.50248i		−	0.151520i	−0.997126	−	0.0757602i	$-0.975862\pi$
$883$		−	4.50248i		−	0.151520i	0.997126	−	0.0757602i	$-0.0241384\pi$
$884$	−7.75660	+	4.47827i	−0.260883	+	0.150621i
$885$	0.668854	+	6.17098i	0.0224833	+	0.207435i
$886$	−2.53941	+	4.39838i	−0.0853131	+	0.147767i
$887$	43.5787	+	25.1602i	1.46323	+	0.844796i	0.999159	−	0.0410030i	$-0.0130553\pi$
$887$	43.5787	+	25.1602i	1.46323	+	0.844796i	0.464070	+	0.885799i	$0.346389\pi$
$888$	−9.31175	−	4.10969i	−0.312482	−	0.137912i
$889$	−30.1850	+	17.4273i	−1.01237	+	0.584494i
$890$	0.0937397			0.00314216
$891$	11.2650	−	5.19178i	0.377392	−	0.173931i
$892$			7.79218i			0.260901i
$893$	4.90154	−	2.82991i	0.164024	−	0.0946993i
$894$	−17.6431	−	7.78669i	−0.590073	−	0.260426i
$895$	−3.43113	−	1.98096i	−0.114690	−	0.0662162i
$896$	−2.88977	−	1.66841i	−0.0965405	−	0.0557377i
$897$	−51.2184	+	5.55141i	−1.71013	+	0.185356i
$898$	3.19051	−	1.84204i	0.106469	−	0.0614697i
$899$	21.1388	+	6.36525i	0.705019	+	0.212293i
$900$	−9.93444	−	10.8903i	−0.331148	−	0.363010i
$901$	−6.32729			−0.210793
$902$	−3.22624	−	5.58802i	−0.107422	−	0.186061i
$903$	16.6417	+	22.7496i	0.553800	+	0.757060i
$904$	−4.06024	+	7.03255i	−0.135042	+	0.233899i
$905$	1.20144	−	2.08096i	0.0399373	−	0.0691734i
$906$	12.7048	−	9.29376i	0.422090	−	0.308764i
$907$	14.5490	+	25.1996i	0.483091	+	0.836739i	0.999811	−	0.0194158i	$-0.00618062\pi$
$907$	14.5490	+	25.1996i	0.483091	+	0.836739i	−0.516720	+	0.856154i	$0.672847\pi$
$908$		−	25.5711i		−	0.848607i
$909$	−28.7769	−	9.14407i	−0.954469	−	0.303290i
$910$			6.14677i			0.203763i
$911$	−14.7040	−	25.4682i	−0.487167	−	0.843798i	0.512724	−	0.858553i	$-0.328636\pi$
$911$	−14.7040	−	25.4682i	−0.487167	−	0.843798i	−0.999891	+	0.0147557i	$0.995303\pi$
$912$	0.416830	+	3.84576i	0.0138026	+	0.127346i
$913$	−8.05288	+	13.9480i	−0.266511	+	0.461611i
$914$	−8.33114	+	14.4300i	−0.275570	+	0.477301i
$915$	−1.47530	−	0.651117i	−0.0487720	−	0.0215253i
$916$	−21.7948	+	12.5832i	−0.720119	+	0.415761i
$917$		−	70.2029i		−	2.31830i
$918$	5.56658	+	4.91487i	0.183724	+	0.162215i
$919$	38.0198			1.25416			0.627079	−	0.778956i	$-0.284250\pi$
$919$	38.0198			1.25416			0.627079	+	0.778956i	$0.284250\pi$
$920$	−0.697476	−	1.20806i	−0.0229951	−	0.0398287i
$921$	−5.39900	−	2.38282i	−0.177903	−	0.0785166i
$922$	22.9327	+	13.2402i	0.755247	+	0.436042i
$923$	−11.0781	+	19.1879i	−0.364641	+	0.631576i
$924$	0.858317	+	7.91900i	0.0282365	+	0.260516i
$925$	25.0061	−	14.4373i	0.822197	−	0.474695i
$926$	21.8201			0.717053
$927$	33.6911	−	7.39018i	1.10656	−	0.242725i
$928$		−	3.96503i		−	0.130159i
$929$	23.9557	+	41.4925i	0.785961	+	1.36132i	0.928423	+	0.371524i	$0.121165\pi$
$929$	23.9557	+	41.4925i	0.785961	+	1.36132i	−0.142462	+	0.989800i	$0.545502\pi$
$930$	−2.67311	+	0.942822i	−0.0876547	+	0.0309163i
$931$	−4.61675	+	7.99644i	−0.151308	+	0.262073i
$932$	18.7809	+	10.8431i	0.615188	+	0.355179i
$933$	0.451045	+	0.616592i	0.0147666	+	0.0201863i
$934$	15.2790	+	26.4640i	0.499944	+	0.865928i
$935$			0.578910i			0.0189324i
$936$	18.3652	−	4.02842i	0.600284	−	0.131673i
$937$	28.2514			0.922933			0.461466	−	0.887158i	$-0.347324\pi$
$937$	28.2514			0.922933			0.461466	+	0.887158i	$0.347324\pi$
$938$	−23.7819	+	13.7305i	−0.776507	+	0.448316i
$939$	−22.9777	+	2.49049i	−0.749849	+	0.0812739i
$940$	0.372436	−	0.645077i	0.0121475	−	0.0210401i
$941$	−13.3349	+	23.0967i	−0.434706	+	0.752932i	−0.997272	−	0.0738200i	$-0.976481\pi$
$941$	−13.3349	+	23.0967i	−0.434706	+	0.752932i	0.562566	+	0.826753i	$0.309814\pi$
$942$	2.74572	−	6.22125i	0.0894603	−	0.202699i
$943$	19.2428	−	11.1098i	0.626631	−	0.361786i
$944$			12.1925i			0.396833i
$945$	4.83126	−	1.62195i	0.157161	−	0.0527620i
$946$	6.72146			0.218534
$947$	−2.00845	−	3.47874i	−0.0652660	−	0.113044i	0.831546	−	0.555456i	$-0.187456\pi$
$947$	−2.00845	−	3.47874i	−0.0652660	−	0.113044i	−0.896812	+	0.442412i	$0.854123\pi$
$948$	0.0891263	−	0.201943i	0.00289469	−	0.00655879i
$949$	−21.7191	+	37.6186i	−0.705032	+	1.22115i
$950$	−9.50360	−	5.48691i	−0.308338	−	0.178019i
$951$	4.22408	−	0.457836i	0.136975	−	0.0148463i
$952$	−4.12977	+	2.38432i	−0.133847	+	0.0772763i
$953$	−24.6241			−0.797652			−0.398826	−	0.917027i	$-0.630582\pi$
$953$	−24.6241			−0.797652			−0.398826	+	0.917027i	$0.630582\pi$
$954$	12.6587	+	4.02240i	0.409840	+	0.130230i
$955$	2.54118			0.0822306
$956$	5.72924	+	9.92334i	0.185297	+	0.320944i
$957$	−7.63924	+	5.58821i	−0.246942	+	0.180641i
$958$	−20.7717	+	35.9776i	−0.671102	+	1.16238i
$959$	34.9858	−	60.5971i	1.12975	−	1.95678i
$960$	0.300572	+	0.410891i	0.00970093	+	0.0132614i
$961$	1.90106	−	30.9417i	0.0613244	−	0.998118i
$962$			36.8293i			1.18742i
$963$	−32.4517	+	29.6034i	−1.04574	+	0.953956i
$964$			12.1466i			0.391215i
$965$	2.73551	−	1.57935i	0.0880592	−	0.0508410i
$966$	−27.2697	+	2.95568i	−0.877388	+	0.0950975i
$967$	−42.1430	−	24.3313i	−1.35523	−	0.782441i	−0.366251	−	0.930516i	$-0.619359\pi$
$967$	−42.1430	−	24.3313i	−1.35523	−	0.782441i	−0.988976	+	0.148075i	$0.952692\pi$
$968$	−7.88131	−	4.55028i	−0.253315	−	0.146252i
$969$	5.05749	+	2.23210i	0.162470	+	0.0717053i
$970$	1.27411	+	2.20682i	0.0409091	+	0.0708567i
$971$		−	4.27649i		−	0.137239i	−0.997643	−	0.0686195i	$-0.978141\pi$
$971$		−	4.27649i		−	0.137239i	0.997643	−	0.0686195i	$-0.0218594\pi$
$972$	−8.01228	−	13.3717i	−0.256994	−	0.428899i
$973$			1.87738i			0.0601861i
$974$	−1.86210	−	3.22526i	−0.0596656	−	0.103344i
$975$	−21.5364	+	48.7971i	−0.689716	+	1.56276i
$976$	−2.74322	−	1.58380i	−0.0878082	−	0.0506961i
$977$	−14.9563	−	8.63500i	−0.478493	−	0.276258i	0.241295	−	0.970452i	$-0.422428\pi$
$977$	−14.9563	−	8.63500i	−0.478493	−	0.276258i	−0.719788	+	0.694194i	$0.755761\pi$
$978$	39.3842	−	4.26873i	1.25937	−	0.136499i
$979$	−0.219771	−	0.380655i	−0.00702391	−	0.0121658i
$980$			1.21519i			0.0388179i
$981$	−24.5042	−	26.8619i	−0.782359	−	0.857635i
$982$			37.7326i			1.20410i
$983$	19.2700	+	33.3765i	0.614616	+	1.06455i	0.990452	+	0.137860i	$0.0440224\pi$
$983$	19.2700	+	33.3765i	0.614616	+	1.06455i	−0.375835	+	0.926686i	$0.622644\pi$
$984$	−6.54492	+	4.78770i	−0.208645	+	0.152626i
$985$	6.08221	+	3.51157i	0.193795	+	0.111888i
$986$	−4.90727	−	2.83321i	−0.156279	−	0.0902278i
$987$	−8.64750	−	11.8214i	−0.275253	−	0.376279i
$988$	12.1218	−	6.99851i	0.385645	−	0.222652i
$989$			23.1459i			0.735996i
$990$	0.368026	−	1.15820i	0.0116966	−	0.0368099i
$991$			12.5111i			0.397430i	0.980057	+	0.198715i	$0.0636767\pi$
$991$			12.5111i			0.397430i	−0.980057	+	0.198715i	$0.936323\pi$
$992$	−5.41972	+	1.27538i	−0.172076	+	0.0404935i
$993$	−55.1928	+	5.98218i	−1.75149	+	0.189839i
$994$	−5.89821	+	10.2160i	−0.187080	+	0.324032i
$995$	3.33296	−	5.77286i	0.105662	−	0.183012i
$996$	18.5176	+	8.17263i	0.586751	+	0.258960i
$997$	−4.35689	−	7.54636i	−0.137984	−	0.238996i	0.788749	−	0.614715i	$-0.210729\pi$
$997$	−4.35689	−	7.54636i	−0.137984	−	0.238996i	−0.926733	+	0.375719i	$0.877396\pi$
$998$	−38.4177			−1.21609
$999$	28.9472	−	9.71815i	0.915849	−	0.307469i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	558.2.q.a.185.18	✓	64
3.2	odd	2		1674.2.q.a.557.3		64
9.2	odd	6	inner	558.2.q.a.371.31	yes	64
9.7	even	3		1674.2.q.a.1115.10		64
31.30	odd	2	inner	558.2.q.a.185.31	yes	64
93.92	even	2		1674.2.q.a.557.10		64
279.61	odd	6		1674.2.q.a.1115.3		64
279.92	even	6	inner	558.2.q.a.371.18	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.q.a.185.18	✓	64	1.1	even	1	trivial
558.2.q.a.185.31	yes	64	31.30	odd	2	inner
558.2.q.a.371.18	yes	64	279.92	even	6	inner
558.2.q.a.371.31	yes	64	9.2	odd	6	inner
1674.2.q.a.557.3		64	3.2	odd	2
1674.2.q.a.557.10		64	93.92	even	2
1674.2.q.a.1115.3		64	279.61	odd	6
1674.2.q.a.1115.10		64	9.7	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 558 = 2 \cdot 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	558.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.58459 - 0.699349i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.254546 + 0.146962i) q^{5} +(-1.72197 + 0.186639i) q^{6} +(1.66841 + 2.88977i) q^{7} -1.00000i q^{8} +(2.02182 + 2.21636i) q^{9} +0.293925 q^{10} +(-0.689101 - 1.19356i) q^{11} +(-1.39795 + 1.02262i) q^{12} +(5.42761 + 3.13363i) q^{13} +(2.88977 + 1.66841i) q^{14} +(-0.300572 - 0.410891i) q^{15} +(-0.500000 - 0.866025i) q^{16} -1.42910 q^{17} +(2.85913 + 0.908510i) q^{18} +2.23335 q^{19} +(0.254546 - 0.146962i) q^{20} +(-0.622780 - 5.74589i) q^{21} +(-1.19356 - 0.689101i) q^{22} +(2.37297 - 4.11011i) q^{23} +(-0.699349 + 1.58459i) q^{24} +(-2.45680 - 4.25531i) q^{25} +6.26727 q^{26} +(-1.65374 - 4.92597i) q^{27} +3.33682 q^{28} +(1.98252 + 3.43382i) q^{29} +(-0.465749 - 0.205556i) q^{30} +(4.05593 - 3.81438i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(0.257226 + 2.37322i) q^{33} +(-1.23764 + 0.714549i) q^{34} +0.980774i q^{35} +(2.93033 - 0.642771i) q^{36} +5.87646i q^{37} +(1.93414 - 1.11668i) q^{38} +(-6.40901 - 8.76131i) q^{39} +(0.146962 - 0.254546i) q^{40} +(4.05457 + 2.34091i) q^{41} +(-3.41229 - 4.66470i) q^{42} +(-4.22359 + 2.43849i) q^{43} -1.37820 q^{44} +(0.188926 + 0.861297i) q^{45} -4.74595i q^{46} +(2.19470 - 1.26711i) q^{47} +(0.186639 + 1.72197i) q^{48} +(-2.06718 + 3.58047i) q^{49} +(-4.25531 - 2.45680i) q^{50} +(2.26453 + 0.999439i) q^{51} +(5.42761 - 3.13363i) q^{52} +4.42747 q^{53} +(-3.89517 - 3.43914i) q^{54} -0.405088i q^{55} +(2.88977 - 1.66841i) q^{56} +(-3.53894 - 1.56189i) q^{57} +(3.43382 + 1.98252i) q^{58} +(-10.5590 - 6.09626i) q^{59} +(-0.506128 + 0.0548577i) q^{60} +(2.74322 - 1.58380i) q^{61} +(1.60535 - 5.33131i) q^{62} +(-3.03153 + 9.54039i) q^{63} -1.00000 q^{64} +(0.921052 + 1.59531i) q^{65} +(1.40937 + 1.92665i) q^{66} +(-4.11484 + 7.12712i) q^{67} +(-0.714549 + 1.23764i) q^{68} +(-6.63458 + 4.85329i) q^{69} +(0.490387 + 0.849375i) q^{70} +3.53523i q^{71} +(2.21636 - 2.02182i) q^{72} +6.93097i q^{73} +(2.93823 + 5.08916i) q^{74} +(0.917070 + 8.46107i) q^{75} +(1.11668 - 1.93414i) q^{76} +(2.29941 - 3.98269i) q^{77} +(-9.93102 - 4.38301i) q^{78} +(-0.110368 + 0.0637209i) q^{79} -0.293925i q^{80} +(-0.824472 + 8.96216i) q^{81} +4.68181 q^{82} +(-5.84303 - 10.1204i) q^{83} +(-5.28748 - 2.33360i) q^{84} +(-0.363772 - 0.210024i) q^{85} +(-2.43849 + 4.22359i) q^{86} +(-0.740028 - 6.82765i) q^{87} +(-1.19356 + 0.689101i) q^{88} +0.318924 q^{89} +(0.594263 + 0.651442i) q^{90} +20.9127i q^{91} +(-2.37297 - 4.11011i) q^{92} +(-9.09454 + 3.20770i) q^{93} +(1.26711 - 2.19470i) q^{94} +(0.568491 + 0.328219i) q^{95} +(1.02262 + 1.39795i) q^{96} +(4.33481 + 7.50811i) q^{97} +4.13437i q^{98} +(1.25211 - 3.94046i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} + 12 q^{5} - 4 q^{7} - 4 q^{9} - 32 q^{16} + 8 q^{18} - 8 q^{19} + 12 q^{20} + 44 q^{25} - 8 q^{28} + 8 q^{31} - 36 q^{33} - 8 q^{36} + 36 q^{38} - 8 q^{39} + 24 q^{41} - 8 q^{45} - 48 q^{47}+ \cdots - 16 q^{97}+O(q^{100}) \) 64 * q + 32 * q^4 + 12 * q^5 - 4 * q^7 - 4 * q^9 - 32 * q^16 + 8 * q^18 - 8 * q^19 + 12 * q^20 + 44 * q^25 - 8 * q^28 + 8 * q^31 - 36 * q^33 - 8 * q^36 + 36 * q^38 - 8 * q^39 + 24 * q^41 - 8 * q^45 - 48 * q^47 - 36 * q^49 - 32 * q^51 - 12 * q^59 - 52 * q^63 - 64 * q^64 - 16 * q^66 + 16 * q^67 + 112 * q^69 - 12 * q^70 - 8 * q^72 - 4 * q^76 - 28 * q^78 + 60 * q^81 + 44 * q^87 + 56 * q^90 - 64 * q^93 - 180 * q^95 - 16 * q^97

Introduction

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