LMFDB - Embedded newform 552.2.j.d.323.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(323,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("552.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.j (of order $2$, degree $1$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$42$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.9
Character	$\chi$	$=$	552.323
Dual form			552.2.j.d.323.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07807 - 0.915298i) q^{2} +(1.49079 + 0.881788i) q^{3} +(0.324458 + 1.97351i) q^{4} +1.83050 q^{5} +(-0.800072 - 2.31514i) q^{6} +4.30356i q^{7} +(1.45656 - 2.42455i) q^{8} +(1.44490 + 2.62912i) q^{9} +O(q^{10})$	\(q+(-1.07807 - 0.915298i) q^{2} +(1.49079 + 0.881788i) q^{3} +(0.324458 + 1.97351i) q^{4} +1.83050 q^{5} +(-0.800072 - 2.31514i) q^{6} +4.30356i q^{7} +(1.45656 - 2.42455i) q^{8} +(1.44490 + 2.62912i) q^{9} +(-1.97340 - 1.67545i) q^{10} -5.53536i q^{11} +(-1.25652 + 3.22818i) q^{12} -1.97338i q^{13} +(3.93904 - 4.63953i) q^{14} +(2.72889 + 1.61411i) q^{15} +(-3.78945 + 1.28064i) q^{16} +5.74797i q^{17} +(0.848726 - 4.15688i) q^{18} +5.40233 q^{19} +(0.593920 + 3.61250i) q^{20} +(-3.79483 + 6.41570i) q^{21} +(-5.06651 + 5.96750i) q^{22} +1.00000 q^{23} +(4.30936 - 2.33011i) q^{24} -1.64927 q^{25} +(-1.80623 + 2.12743i) q^{26} +(-0.164281 + 5.19355i) q^{27} +(-8.49310 + 1.39632i) q^{28} -7.03976 q^{29} +(-1.46453 - 4.23787i) q^{30} -3.45204i q^{31} +(5.25745 + 2.08787i) q^{32} +(4.88102 - 8.25206i) q^{33} +(5.26111 - 6.19670i) q^{34} +7.87767i q^{35} +(-4.71977 + 3.70456i) q^{36} +6.42648i q^{37} +(-5.82408 - 4.94474i) q^{38} +(1.74010 - 2.94189i) q^{39} +(2.66623 - 4.43814i) q^{40} +1.85833i q^{41} +(9.96336 - 3.44316i) q^{42} +8.60166 q^{43} +(10.9241 - 1.79599i) q^{44} +(2.64489 + 4.81260i) q^{45} +(-1.07807 - 0.915298i) q^{46} -2.85100 q^{47} +(-6.77853 - 1.43233i) q^{48} -11.5206 q^{49} +(1.77802 + 1.50957i) q^{50} +(-5.06849 + 8.56901i) q^{51} +(3.89447 - 0.640277i) q^{52} -2.24162 q^{53} +(4.93076 - 5.44864i) q^{54} -10.1325i q^{55} +(10.4342 + 6.26839i) q^{56} +(8.05373 + 4.76371i) q^{57} +(7.58934 + 6.44348i) q^{58} +0.271643i q^{59} +(-2.30005 + 5.90919i) q^{60} -14.8704i q^{61} +(-3.15965 + 3.72154i) q^{62} +(-11.3146 + 6.21822i) q^{63} +(-3.75687 - 7.06300i) q^{64} -3.61226i q^{65} +(-12.8152 + 4.42869i) q^{66} -3.34755 q^{67} +(-11.3437 + 1.86497i) q^{68} +(1.49079 + 0.881788i) q^{69} +(7.21042 - 8.49266i) q^{70} +11.8803 q^{71} +(8.47901 + 0.326234i) q^{72} +11.4026 q^{73} +(5.88215 - 6.92818i) q^{74} +(-2.45871 - 1.45431i) q^{75} +(1.75283 + 10.6615i) q^{76} +23.8218 q^{77} +(-4.56865 + 1.57884i) q^{78} -10.4235i q^{79} +(-6.93660 + 2.34421i) q^{80} +(-4.82452 + 7.59763i) q^{81} +(1.70092 - 2.00340i) q^{82} -3.52108i q^{83} +(-13.8927 - 5.40749i) q^{84} +10.5217i q^{85} +(-9.27316 - 7.87308i) q^{86} +(-10.4948 - 6.20758i) q^{87} +(-13.4208 - 8.06259i) q^{88} +0.708930i q^{89} +(1.55359 - 7.60917i) q^{90} +8.49254 q^{91} +(0.324458 + 1.97351i) q^{92} +(3.04397 - 5.14627i) q^{93} +(3.07357 + 2.60952i) q^{94} +9.88897 q^{95} +(5.99670 + 7.74852i) q^{96} -19.4048 q^{97} +(12.4200 + 10.5448i) q^{98} +(14.5531 - 7.99806i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9}+O(q^{10}) $ 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9	$ 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9} - 4 q^{10} - 21 q^{12} - 4 q^{14} - 8 q^{15} - 12 q^{16} - 11 q^{18} + 4 q^{19} - 2 q^{20} + 8 q^{21} + 18 q^{22} + 42 q^{23} + 28 q^{24} + 22 q^{25} + 11 q^{26} - 16 q^{27} + 6 q^{28} + 2 q^{30} - 20 q^{32} + 12 q^{33} + 14 q^{34} - 24 q^{36} - 22 q^{38} + 8 q^{39} + 4 q^{40} - 44 q^{42} + 28 q^{43} + 56 q^{44} - 8 q^{45} + 30 q^{48} - 50 q^{49} + 20 q^{50} + 28 q^{51} - q^{52} + 24 q^{53} + 52 q^{54} - 34 q^{56} - 8 q^{57} - 21 q^{58} - 42 q^{60} - 79 q^{62} - 16 q^{63} + 7 q^{64} - 62 q^{66} - 4 q^{67} + 20 q^{68} + 2 q^{69} - 8 q^{70} + 22 q^{72} + 4 q^{73} + 36 q^{74} - 6 q^{75} + 14 q^{76} + 32 q^{77} + 27 q^{78} - 52 q^{80} + 18 q^{81} + 11 q^{82} - 80 q^{84} - 28 q^{86} - 48 q^{87} - 38 q^{88} - 46 q^{90} - 8 q^{91} + 4 q^{92} - 22 q^{93} + q^{94} - 16 q^{95} + 9 q^{96} + 20 q^{97} + 64 q^{98}+O(q^{100}) $ 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9 - 4 * q^10 - 21 * q^12 - 4 * q^14 - 8 * q^15 - 12 * q^16 - 11 * q^18 + 4 * q^19 - 2 * q^20 + 8 * q^21 + 18 * q^22 + 42 * q^23 + 28 * q^24 + 22 * q^25 + 11 * q^26 - 16 * q^27 + 6 * q^28 + 2 * q^30 - 20 * q^32 + 12 * q^33 + 14 * q^34 - 24 * q^36 - 22 * q^38 + 8 * q^39 + 4 * q^40 - 44 * q^42 + 28 * q^43 + 56 * q^44 - 8 * q^45 + 30 * q^48 - 50 * q^49 + 20 * q^50 + 28 * q^51 - q^52 + 24 * q^53 + 52 * q^54 - 34 * q^56 - 8 * q^57 - 21 * q^58 - 42 * q^60 - 79 * q^62 - 16 * q^63 + 7 * q^64 - 62 * q^66 - 4 * q^67 + 20 * q^68 + 2 * q^69 - 8 * q^70 + 22 * q^72 + 4 * q^73 + 36 * q^74 - 6 * q^75 + 14 * q^76 + 32 * q^77 + 27 * q^78 - 52 * q^80 + 18 * q^81 + 11 * q^82 - 80 * q^84 - 28 * q^86 - 48 * q^87 - 38 * q^88 - 46 * q^90 - 8 * q^91 + 4 * q^92 - 22 * q^93 + q^94 - 16 * q^95 + 9 * q^96 + 20 * q^97 + 64 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.07807	−	0.915298i	−0.762309	−	0.647214i
$2$	−1.07807	−	0.915298i	−0.762309	−	0.647214i
$3$	1.49079	+	0.881788i	0.860707	+	0.509100i
$3$	1.49079	+	0.881788i	0.860707	+	0.509100i
$4$	0.324458	+	1.97351i	0.162229	+	0.986753i
$5$	1.83050			0.818624			0.409312	−	0.912394i	$-0.365769\pi$
$5$	1.83050			0.818624			0.409312	+	0.912394i	$0.365769\pi$
$6$	−0.800072	−	2.31514i	−0.326628	−	0.945153i
$7$			4.30356i			1.62659i	0.581849	+	0.813297i	$0.302329\pi$
$7$			4.30356i			1.62659i	−0.581849	+	0.813297i	$0.697671\pi$
$8$	1.45656	−	2.42455i	0.514972	−	0.857207i
$9$	1.44490	+	2.62912i	0.481634	+	0.876373i
$10$	−1.97340	−	1.67545i	−0.624045	−	0.529825i
$11$		−	5.53536i		−	1.66898i	−0.551027	−	0.834488i	$-0.685764\pi$
$11$		−	5.53536i		−	1.66898i	0.551027	−	0.834488i	$-0.314236\pi$
$12$	−1.25652	+	3.22818i	−0.362725	+	0.931896i
$13$		−	1.97338i		−	0.547316i	−0.961827	−	0.273658i	$-0.911766\pi$
$13$		−	1.97338i		−	0.547316i	0.961827	−	0.273658i	$-0.0882336\pi$
$14$	3.93904	−	4.63953i	1.05275	−	1.23997i
$15$	2.72889	+	1.61411i	0.704596	+	0.416762i
$16$	−3.78945	+	1.28064i	−0.947364	+	0.320160i
$17$			5.74797i			1.39409i	0.717029	+	0.697044i	$0.245502\pi$
$17$			5.74797i			1.39409i	−0.717029	+	0.697044i	$0.754498\pi$
$18$	0.848726	−	4.15688i	0.200047	−	0.979786i
$19$	5.40233			1.23938			0.619690	−	0.784847i	$-0.287258\pi$
$19$	5.40233			1.23938			0.619690	+	0.784847i	$0.287258\pi$
$20$	0.593920	+	3.61250i	0.132805	+	0.807780i
$21$	−3.79483	+	6.41570i	−0.828099	+	1.40002i
$22$	−5.06651	+	5.96750i	−1.08018	+	1.27227i
$23$	1.00000			0.208514
$23$	1.00000			0.208514
$24$	4.30936	−	2.33011i	0.879644	−	0.475632i
$25$	−1.64927			−0.329854
$26$	−1.80623	+	2.12743i	−0.354230	+	0.417224i
$27$	−0.164281	+	5.19355i	−0.0316159	+	0.999500i
$28$	−8.49310	+	1.39632i	−1.60505	+	0.263880i
$29$	−7.03976			−1.30725			−0.653626	−	0.756818i	$-0.726753\pi$
$29$	−7.03976			−1.30725			−0.653626	+	0.756818i	$0.726753\pi$
$30$	−1.46453	−	4.23787i	−0.267386	−	0.773725i
$31$		−	3.45204i		−	0.620005i	−0.950736	−	0.310003i	$-0.899670\pi$
$31$		−	3.45204i		−	0.620005i	0.950736	−	0.310003i	$-0.100330\pi$
$32$	5.25745	+	2.08787i	0.929395	+	0.369086i
$33$	4.88102	−	8.25206i	0.849676	−	1.43650i
$34$	5.26111	−	6.19670i	0.902272	−	1.06272i
$35$			7.87767i			1.33157i
$36$	−4.71977	+	3.70456i	−0.786628	+	0.617427i
$37$			6.42648i			1.05651i	0.849087	+	0.528254i	$0.177153\pi$
$37$			6.42648i			1.05651i	−0.849087	+	0.528254i	$0.822847\pi$
$38$	−5.82408	−	4.94474i	−0.944790	−	0.802143i
$39$	1.74010	−	2.94189i	0.278639	−	0.471079i
$40$	2.66623	−	4.43814i	0.421568	−	0.701731i
$41$			1.85833i			0.290222i	0.989415	+	0.145111i	$0.0463539\pi$
$41$			1.85833i			0.290222i	−0.989415	+	0.145111i	$0.953646\pi$
$42$	9.96336	−	3.44316i	1.53738	−	0.531291i
$43$	8.60166			1.31174			0.655870	−	0.754874i	$-0.272302\pi$
$43$	8.60166			1.31174			0.655870	+	0.754874i	$0.272302\pi$
$44$	10.9241	−	1.79599i	1.64687	−	0.270756i
$45$	2.64489	+	4.81260i	0.394277	+	0.717420i
$46$	−1.07807	−	0.915298i	−0.158952	−	0.134953i
$47$	−2.85100			−0.415861			−0.207931	−	0.978144i	$-0.566673\pi$
$47$	−2.85100			−0.415861			−0.207931	+	0.978144i	$0.566673\pi$
$48$	−6.77853	−	1.43233i	−0.978396	−	0.206739i
$49$	−11.5206			−1.64581
$50$	1.77802	+	1.50957i	0.251451	+	0.213486i
$51$	−5.06849	+	8.56901i	−0.709730	+	1.19990i
$52$	3.89447	−	0.640277i	0.540066	−	0.0887905i
$53$	−2.24162			−0.307910			−0.153955	−	0.988078i	$-0.549201\pi$
$53$	−2.24162			−0.307910			−0.153955	+	0.988078i	$0.549201\pi$
$54$	4.93076	−	5.44864i	0.670991	−	0.741465i
$55$		−	10.1325i		−	1.36626i
$56$	10.4342	+	6.26839i	1.39433	+	0.837649i
$57$	8.05373	+	4.76371i	1.06674	+	0.630969i
$58$	7.58934	+	6.44348i	0.996529	+	0.846071i
$59$			0.271643i			0.0353649i	0.999844	+	0.0176825i	$0.00562880\pi$
$59$			0.271643i			0.0353649i	−0.999844	+	0.0176825i	$0.994371\pi$
$60$	−2.30005	+	5.90919i	−0.296935	+	0.762873i
$61$		−	14.8704i		−	1.90396i	−0.306156	−	0.951981i	$-0.599043\pi$
$61$		−	14.8704i		−	1.90396i	0.306156	−	0.951981i	$-0.400957\pi$
$62$	−3.15965	+	3.72154i	−0.401276	+	0.472635i
$63$	−11.3146	+	6.21822i	−1.42550	+	0.783422i
$64$	−3.75687	−	7.06300i	−0.469609	−	0.882875i
$65$		−	3.61226i		−	0.448046i
$66$	−12.8152	+	4.42869i	−1.57744	+	0.545134i
$67$	−3.34755			−0.408969			−0.204484	−	0.978870i	$-0.565552\pi$
$67$	−3.34755			−0.408969			−0.204484	+	0.978870i	$0.565552\pi$
$68$	−11.3437	+	1.86497i	−1.37562	+	0.226161i
$69$	1.49079	+	0.881788i	0.179470	+	0.106155i
$70$	7.21042	−	8.49266i	0.861810	−	1.01507i
$71$	11.8803			1.40993			0.704966	−	0.709241i	$-0.250962\pi$
$71$	11.8803			1.40993			0.704966	+	0.709241i	$0.250962\pi$
$72$	8.47901	+	0.326234i	0.999261	+	0.0384470i
$73$	11.4026			1.33457			0.667287	−	0.744801i	$-0.267455\pi$
$73$	11.4026			1.33457			0.667287	+	0.744801i	$0.267455\pi$
$74$	5.88215	−	6.92818i	0.683786	−	0.805385i
$75$	−2.45871	−	1.45431i	−0.283908	−	0.167929i
$76$	1.75283	+	10.6615i	0.201063	+	1.22296i
$77$	23.8218			2.71474
$78$	−4.56865	+	1.57884i	−0.517297	+	0.178769i
$79$		−	10.4235i		−	1.17274i	−0.810045	−	0.586368i	$-0.800557\pi$
$79$		−	10.4235i		−	1.17274i	0.810045	−	0.586368i	$-0.199443\pi$
$80$	−6.93660	+	2.34421i	−0.775535	+	0.262091i
$81$	−4.82452	+	7.59763i	−0.536058	+	0.844181i
$82$	1.70092	−	2.00340i	0.187836	−	0.221239i
$83$		−	3.52108i		−	0.386489i	−0.981151	−	0.193245i	$-0.938099\pi$
$83$		−	3.52108i		−	0.386489i	0.981151	−	0.193245i	$-0.0619011\pi$
$84$	−13.8927	−	5.40749i	−1.51582	−	0.590005i
$85$			10.5217i			1.14123i
$86$	−9.27316	−	7.87308i	−0.999951	−	0.848976i
$87$	−10.4948	−	6.20758i	−1.12516	−	0.665522i
$88$	−13.4208	−	8.06259i	−1.43066	−	0.859475i
$89$			0.708930i			0.0751464i	0.999294	+	0.0375732i	$0.0119627\pi$
$89$			0.708930i			0.0751464i	−0.999294	+	0.0375732i	$0.988037\pi$
$90$	1.55359	−	7.60917i	0.163763	−	0.802077i
$91$	8.49254			0.890260
$92$	0.324458	+	1.97351i	0.0338271	+	0.205752i
$93$	3.04397	−	5.14627i	0.315645	−	0.533643i
$94$	3.07357	+	2.60952i	0.317015	+	0.269151i
$95$	9.88897			1.01459
$96$	5.99670	+	7.74852i	0.612035	+	0.790830i
$97$	−19.4048			−1.97026			−0.985128	−	0.171823i	$-0.945034\pi$
$97$	−19.4048			−1.97026			−0.985128	+	0.171823i	$0.945034\pi$
$98$	12.4200	+	10.5448i	1.25461	+	1.06519i
$99$	14.5531	−	7.99806i	1.46264	−	0.803835i
$100$	−0.535119	−	3.25484i	−0.0535119	−	0.325484i
$101$	3.13053			0.311500			0.155750	−	0.987797i	$-0.450221\pi$
$101$	3.13053			0.311500			0.155750	+	0.987797i	$0.450221\pi$
$102$	13.3074	−	4.59879i	1.31763	−	0.455348i
$103$			0.0218782i			0.00215572i	0.999999	+	0.00107786i	$0.000343094\pi$
$103$			0.0218782i			0.00215572i	−0.999999	+	0.00107786i	$0.999657\pi$
$104$	−4.78454	−	2.87434i	−0.469163	−	0.281852i
$105$	−6.94643	+	11.7439i	−0.677902	+	1.14609i
$106$	2.41661	+	2.05175i	0.234722	+	0.199283i
$107$		−	11.8994i		−	1.15035i	−0.818029	−	0.575177i	$-0.804933\pi$
$107$		−	11.8994i		−	1.15035i	0.818029	−	0.575177i	$-0.195067\pi$
$108$	−10.3028	+	1.36088i	−0.991389	+	0.130951i
$109$			3.90774i			0.374294i	0.982332	+	0.187147i	$0.0599240\pi$
$109$			3.90774i			0.374294i	−0.982332	+	0.187147i	$0.940076\pi$
$110$	−9.27425	+	10.9235i	−0.884265	+	1.04151i
$111$	−5.66679	+	9.58053i	−0.537868	+	0.909344i
$112$	−5.51131	−	16.3081i	−0.520770	−	1.54098i
$113$		−	9.65381i		−	0.908154i	−0.890963	−	0.454077i	$-0.849969\pi$
$113$		−	9.65381i		−	0.908154i	0.890963	−	0.454077i	$-0.150031\pi$
$114$	−4.32225	−	12.5072i	−0.404816	−	1.17140i
$115$	1.83050			0.170695
$116$	−2.28411	−	13.8930i	−0.212074	−	1.28993i
$117$	5.18824	−	2.85133i	0.479653	−	0.263606i
$118$	0.248634	−	0.292850i	0.0228887	−	0.0269590i
$119$	−24.7367			−2.26761
$120$	7.88828	−	4.26527i	0.720098	−	0.389364i
$121$	−19.6403			−1.78548
$122$	−13.6109	+	16.0313i	−1.23227	+	1.45141i
$123$	−1.63865	+	2.77037i	−0.147752	+	0.249796i
$124$	6.81263	−	1.12004i	0.611792	−	0.100583i
$125$	−12.1715			−1.08865
$126$	17.8894	+	3.65255i	1.59371	+	0.325395i
$127$		−	16.2450i		−	1.44151i	−0.693188	−	0.720757i	$-0.743794\pi$
$127$		−	16.2450i		−	1.44151i	0.693188	−	0.720757i	$-0.256206\pi$
$128$	−2.41459	+	11.0530i	−0.213422	+	0.976960i
$129$	12.8233	+	7.58483i	1.12902	+	0.667807i
$130$	−3.30630	+	3.89426i	−0.289982	+	0.341550i
$131$		−	3.51628i		−	0.307219i	−0.988132	−	0.153609i	$-0.950910\pi$
$131$		−	3.51628i		−	0.307219i	0.988132	−	0.153609i	$-0.0490897\pi$
$132$	17.8692	+	6.95527i	1.55531	+	0.605379i
$133$			23.2493i			2.01597i
$134$	3.60889	+	3.06401i	0.311760	+	0.264690i
$135$	−0.300716	+	9.50680i	−0.0258815	+	0.818215i
$136$	13.9362	+	8.37226i	1.19502	+	0.717915i
$137$			4.06252i			0.347084i	0.984826	+	0.173542i	$0.0555213\pi$
$137$			4.06252i			0.347084i	−0.984826	+	0.173542i	$0.944479\pi$
$138$	−0.800072	−	2.31514i	−0.0681066	−	0.197078i
$139$	−8.43024			−0.715044			−0.357522	−	0.933905i	$-0.616378\pi$
$139$	−8.43024			−0.715044			−0.357522	+	0.933905i	$0.616378\pi$
$140$	−15.5466	+	2.55597i	−1.31393	+	0.216019i
$141$	−4.25024	−	2.51398i	−0.357935	−	0.211715i
$142$	−12.8078	−	10.8740i	−1.07480	−	0.912527i
$143$	−10.9234			−0.913457
$144$	−8.84234	−	8.11252i	−0.736862	−	0.676044i
$145$	−12.8863			−1.07015
$146$	−12.2928	−	10.4368i	−1.01736	−	0.863754i
$147$	−17.1748	−	10.1588i	−1.41656	−	0.837880i
$148$	−12.6827	+	2.08512i	−1.04251	+	0.171396i
$149$	−8.19313			−0.671208			−0.335604	−	0.942003i	$-0.608940\pi$
$149$	−8.19313			−0.671208			−0.335604	+	0.942003i	$0.608940\pi$
$150$	1.31953	+	3.81830i	0.107740	+	0.311763i
$151$			10.1956i			0.829708i	0.909888	+	0.414854i	$0.136167\pi$
$151$			10.1956i			0.829708i	−0.909888	+	0.414854i	$0.863833\pi$
$152$	7.86882	−	13.0982i	0.638245	−	1.06241i
$153$	−15.1121	+	8.30525i	−1.22174	+	0.671440i
$154$	−25.6815	−	21.8040i	−2.06947	−	1.75702i
$155$		−	6.31897i		−	0.507552i
$156$	6.37042	+	2.47958i	0.510042	+	0.198525i
$157$		−	4.63450i		−	0.369873i	−0.982750	−	0.184937i	$-0.940792\pi$
$157$		−	4.63450i		−	0.369873i	0.982750	−	0.184937i	$-0.0592080\pi$
$158$	−9.54062	+	11.2372i	−0.759011	+	0.893987i
$159$	−3.34178	−	1.97663i	−0.265020	−	0.156757i
$160$	9.62377	+	3.82184i	0.760826	+	0.302143i
$161$			4.30356i			0.339168i
$162$	12.1553	−	3.77488i	0.955007	−	0.296583i
$163$	1.41073			0.110497			0.0552486	−	0.998473i	$-0.482405\pi$
$163$	1.41073			0.110497			0.0552486	+	0.998473i	$0.482405\pi$
$164$	−3.66742	+	0.602949i	−0.286377	+	0.0470824i
$165$	8.93470	−	15.1054i	0.695565	−	1.17595i
$166$	−3.22284	+	3.79596i	−0.250141	+	0.294624i
$167$	−3.74316			−0.289654			−0.144827	−	0.989457i	$-0.546263\pi$
$167$	−3.74316			−0.289654			−0.144827	+	0.989457i	$0.546263\pi$
$168$	10.0278	+	18.5456i	0.773660	+	1.43082i
$169$	9.10579			0.700445
$170$	9.63046	−	11.3431i	0.738622	−	0.869972i
$171$	7.80583	+	14.2034i	0.596927	+	1.08616i
$172$	2.79087	+	16.9754i	0.212802	+	1.29436i
$173$	−0.310249			−0.0235878			−0.0117939	−	0.999930i	$-0.503754\pi$
$173$	−0.310249			−0.0235878			−0.0117939	+	0.999930i	$0.503754\pi$
$174$	5.63231	+	16.2981i	0.426985	+	1.23555i
$175$		−	7.09773i		−	0.536538i
$176$	7.08881	+	20.9760i	0.534339	+	1.58113i
$177$	−0.239532	+	0.404962i	−0.0180043	+	0.0304388i
$178$	0.648882	−	0.764274i	0.0486358	−	0.0572848i
$179$			6.48520i			0.484727i	0.970186	+	0.242363i	$0.0779226\pi$
$179$			6.48520i			0.484727i	−0.970186	+	0.242363i	$0.922077\pi$
$180$	−8.63954	+	6.78120i	−0.643953	+	0.505441i
$181$			4.29128i			0.318968i	0.987201	+	0.159484i	$0.0509831\pi$
$181$			4.29128i			0.318968i	−0.987201	+	0.159484i	$0.949017\pi$
$182$	−9.15553	−	7.77321i	−0.678653	−	0.576189i
$183$	13.1126	−	22.1687i	0.969308	−	1.63875i
$184$	1.45656	−	2.42455i	0.107379	−	0.178740i
$185$			11.7637i			0.864883i
$186$	−7.99197	+	2.76188i	−0.586000	+	0.202511i
$187$	31.8171			2.32670
$188$	−0.925030	−	5.62647i	−0.0674648	−	0.410353i
$189$	−22.3508	−	0.706993i	−1.62578	−	0.0514262i
$190$	−10.6610	−	9.05135i	−0.773428	−	0.656654i
$191$	−4.40995			−0.319093			−0.159547	−	0.987190i	$-0.551003\pi$
$191$	−4.40995			−0.319093			−0.159547	+	0.987190i	$0.551003\pi$
$192$	0.627368	−	13.8422i	0.0452764	−	0.998974i
$193$	13.4247			0.966333			0.483167	−	0.875528i	$-0.339487\pi$
$193$	13.4247			0.966333			0.483167	+	0.875528i	$0.339487\pi$
$194$	20.9196	+	17.7612i	1.50194	+	1.27518i
$195$	3.18525	−	5.38512i	0.228100	−	0.385637i
$196$	−3.73796	−	22.7360i	−0.266997	−	1.62400i
$197$	−0.782509			−0.0557515			−0.0278757	−	0.999611i	$-0.508874\pi$
$197$	−0.782509			−0.0557515			−0.0278757	+	0.999611i	$0.508874\pi$
$198$	−23.0099	−	4.69801i	−1.63524	−	0.333873i
$199$			1.36728i			0.0969240i	0.998825	+	0.0484620i	$0.0154320\pi$
$199$			1.36728i			0.0969240i	−0.998825	+	0.0484620i	$0.984568\pi$
$200$	−2.40226	+	3.99873i	−0.169865	+	0.282753i
$201$	−4.99049	−	2.95183i	−0.352002	−	0.208206i
$202$	−3.37492	−	2.86537i	−0.237459	−	0.201607i
$203$		−	30.2960i		−	2.12637i
$204$	−18.5555	−	7.22241i	−1.29914	−	0.505670i
$205$			3.40167i			0.237583i
$206$	0.0200251	−	0.0235862i	0.00139521	−	0.00164333i
$207$	1.44490	+	2.62912i	0.100428	+	0.182736i
$208$	2.52718	+	7.47802i	0.175229	+	0.518507i
$209$		−	29.9039i		−	2.06849i
$210$	18.2379	−	6.30270i	1.25854	−	0.434928i
$211$	10.0294			0.690451			0.345225	−	0.938520i	$-0.387802\pi$
$211$	10.0294			0.690451			0.345225	+	0.938520i	$0.387802\pi$
$212$	−0.727310	−	4.42384i	−0.0499519	−	0.303831i
$213$	17.7110	+	10.4759i	1.21354	+	0.717797i
$214$	−10.8915	+	12.8283i	−0.744525	+	0.876925i
$215$	15.7453			1.07382
$216$	12.3527	+	7.96303i	0.840497	+	0.541816i
$217$	14.8561			1.00850
$218$	3.57675	−	4.21281i	0.242248	−	0.285327i
$219$	16.9989	+	10.0547i	1.14868	+	0.679432i
$220$	19.9965	−	3.28756i	1.34817	−	0.221648i
$221$	11.3429			0.763006
$222$	14.8782	−	5.14165i	0.998561	−	0.345085i
$223$		−	9.84735i		−	0.659428i	−0.944081	−	0.329714i	$-0.893048\pi$
$223$		−	9.84735i		−	0.659428i	0.944081	−	0.329714i	$-0.106952\pi$
$224$	−8.98526	+	22.6258i	−0.600353	+	1.51175i
$225$	−2.38303	−	4.33612i	−0.158869	−	0.289075i
$226$	−8.83611	+	10.4075i	−0.587770	+	0.692293i
$227$		−	20.7260i		−	1.37563i	−0.725886	−	0.687815i	$-0.758570\pi$
$227$		−	20.7260i		−	1.37563i	0.725886	−	0.687815i	$-0.241430\pi$
$228$	−6.78811	+	17.4397i	−0.449554	+	1.15497i
$229$		−	0.821793i		−	0.0543056i	−0.999631	−	0.0271528i	$-0.991356\pi$
$229$		−	0.821793i		−	0.0543056i	0.999631	−	0.0271528i	$-0.00864407\pi$
$230$	−1.97340	−	1.67545i	−0.130122	−	0.110476i
$231$	35.5132	+	21.0057i	2.33660	+	1.38208i
$232$	−10.2538	+	17.0682i	−0.673197	+	1.12059i
$233$		−	16.3940i		−	1.07401i	−0.843580	−	0.537004i	$-0.819556\pi$
$233$		−	16.3940i		−	1.07401i	0.843580	−	0.537004i	$-0.180444\pi$
$234$	−8.20309	−	1.67486i	−0.536253	−	0.109489i
$235$	−5.21876			−0.340434
$236$	−0.536089	+	0.0881367i	−0.0348964	+	0.00573721i
$237$	9.19132	−	15.5392i	0.597040	−	1.00938i
$238$	26.6679	+	22.6415i	1.72862	+	1.46763i
$239$	−8.35152			−0.540215			−0.270107	−	0.962830i	$-0.587059\pi$
$239$	−8.35152			−0.540215			−0.270107	+	0.962830i	$0.587059\pi$
$240$	−12.4081	−	2.62188i	−0.800939	−	0.169242i
$241$	−17.0601			−1.09894			−0.549468	−	0.835515i	$-0.685170\pi$
$241$	−17.0601			−1.09894			−0.549468	+	0.835515i	$0.685170\pi$
$242$	21.1735	+	17.9767i	1.36109	+	1.15559i
$243$	−13.8918	+	7.07226i	−0.891162	+	0.453686i
$244$	29.3469	−	4.82483i	1.87874	−	0.308878i
$245$	−21.0885			−1.34730
$246$	4.30229	−	1.48679i	0.274304	−	0.0947945i
$247$		−	10.6608i		−	0.678332i
$248$	−8.36965	−	5.02811i	−0.531473	−	0.319285i
$249$	3.10485	−	5.24919i	0.196762	−	0.332654i
$250$	13.1217	+	11.1405i	0.829888	+	0.704590i
$251$		−	5.17403i		−	0.326582i	−0.986578	−	0.163291i	$-0.947789\pi$
$251$		−	5.17403i		−	0.326582i	0.986578	−	0.163291i	$-0.0522110\pi$
$252$	−15.9428	−	20.3118i	−1.00430	−	1.27952i
$253$		−	5.53536i		−	0.348005i
$254$	−14.8691	+	17.5132i	−0.932968	+	1.09888i
$255$	−9.27787	+	15.6856i	−0.581003	+	0.982268i
$256$	12.7199	−	9.70585i	0.794995	−	0.606616i
$257$			16.3114i			1.01748i	0.860920	+	0.508740i	$0.169889\pi$
$257$			16.3114i			1.01748i	−0.860920	+	0.508740i	$0.830111\pi$
$258$	−6.88194	−	19.9141i	−0.428451	−	1.23980i
$259$	−27.6568			−1.71851
$260$	7.12883	−	1.17203i	0.442111	−	0.0726861i
$261$	−10.1718	−	18.5084i	−0.629616	−	1.14564i
$262$	−3.21844	+	3.79079i	−0.198836	+	0.234196i
$263$	13.4611			0.830045			0.415023	−	0.909811i	$-0.363774\pi$
$263$	13.4611			0.830045			0.415023	+	0.909811i	$0.363774\pi$
$264$	−12.8980	−	23.8539i	−0.793819	−	1.46810i
$265$	−4.10328			−0.252062
$266$	21.2800	−	25.0643i	1.30476	−	1.53679i
$267$	−0.625126	+	1.05686i	−0.0382571	+	0.0646791i
$268$	−1.08614	−	6.60642i	−0.0663465	−	0.403551i
$269$	4.22533			0.257623			0.128811	−	0.991669i	$-0.458884\pi$
$269$	4.22533			0.257623			0.128811	+	0.991669i	$0.458884\pi$
$270$	9.02575	−	9.97373i	0.549290	−	0.606982i
$271$		−	15.1174i		−	0.918316i	−0.888355	−	0.459158i	$-0.848151\pi$
$271$		−	15.1174i		−	0.918316i	0.888355	−	0.459158i	$-0.151849\pi$
$272$	−7.36108	−	21.7817i	−0.446331	−	1.32071i
$273$	12.6606	+	7.48862i	0.766254	+	0.453232i
$274$	3.71841	−	4.37967i	0.224638	−	0.264585i
$275$			9.12931i			0.550518i
$276$	−1.25652	+	3.22818i	−0.0756333	+	0.194314i
$277$			23.9099i			1.43661i	0.695730	+	0.718303i	$0.255081\pi$
$277$			23.9099i			1.43661i	−0.695730	+	0.718303i	$0.744919\pi$
$278$	9.08836	+	7.71618i	0.545084	+	0.462786i
$279$	9.07583	−	4.98786i	0.543356	−	0.298616i
$280$	19.0998	+	11.4743i	1.14143	+	0.685720i
$281$		−	3.44801i		−	0.205691i	−0.994697	−	0.102846i	$-0.967205\pi$
$281$		−	3.44801i		−	0.205691i	0.994697	−	0.102846i	$-0.0327947\pi$
$282$	2.28101	+	6.60048i	0.135832	+	0.393053i
$283$	−6.21887			−0.369674			−0.184837	−	0.982769i	$-0.559176\pi$
$283$	−6.21887			−0.369674			−0.184837	+	0.982769i	$0.559176\pi$
$284$	3.85466	+	23.4458i	0.228732	+	1.39126i
$285$	14.7424	+	8.71997i	0.873262	+	0.516526i
$286$	11.7761	+	9.99813i	0.696336	+	0.591202i
$287$	−7.99742			−0.472073
$288$	2.10726	+	16.8392i	0.124171	+	0.992261i
$289$	−16.0391			−0.943479
$290$	13.8923	+	11.7948i	0.815783	+	0.692614i
$291$	−28.9284	−	17.1109i	−1.69581	−	1.00306i
$292$	3.69967	+	22.5031i	0.216507	+	1.31690i
$293$	29.9501			1.74970			0.874851	−	0.484392i	$-0.160959\pi$
$293$	29.9501			1.74970			0.874851	+	0.484392i	$0.160959\pi$
$294$	9.21733	+	26.6719i	0.537566	+	1.55554i
$295$			0.497243i			0.0289506i
$296$	15.5813	+	9.36056i	0.905646	+	0.544071i
$297$	28.7482	+	0.909355i	1.66814	+	0.0527661i
$298$	8.83275	+	7.49916i	0.511667	+	0.434415i
$299$		−	1.97338i		−	0.114123i
$300$	2.07233	−	5.32415i	0.119646	−	0.307390i
$301$			37.0177i			2.13367i
$302$	9.33204	−	10.9916i	0.536999	−	0.632494i
$303$	4.66696	+	2.76046i	0.268110	+	0.158585i
$304$	−20.4719	+	6.91844i	−1.17414	+	0.396800i
$305$		−	27.2203i		−	1.55863i
$306$	23.8936	+	4.87845i	1.36591	+	0.278883i
$307$	−6.54042			−0.373282			−0.186641	−	0.982428i	$-0.559760\pi$
$307$	−6.54042			−0.373282			−0.186641	+	0.982428i	$0.559760\pi$
$308$	7.72916	+	47.0124i	0.440410	+	2.67878i
$309$	−0.0192919	+	0.0326158i	−0.00109748	+	0.00185545i
$310$	−5.78374	+	6.81227i	−0.328494	+	0.386911i
$311$	10.7084			0.607218			0.303609	−	0.952797i	$-0.401808\pi$
$311$	10.7084			0.607218			0.303609	+	0.952797i	$0.401808\pi$
$312$	−4.59819	−	8.50398i	−0.260321	−	0.481443i
$313$	−19.7238			−1.11486			−0.557428	−	0.830225i	$-0.688212\pi$
$313$	−19.7238			−1.11486			−0.557428	+	0.830225i	$0.688212\pi$
$314$	−4.24195	+	4.99630i	−0.239387	+	0.281957i
$315$	−20.7113	+	11.3825i	−1.16695	+	0.641329i
$316$	20.5709	−	3.38199i	1.15720	−	0.190252i
$317$	27.7462			1.55838			0.779191	−	0.626787i	$-0.215630\pi$
$317$	27.7462			1.55838			0.779191	+	0.626787i	$0.215630\pi$
$318$	1.79345	+	5.18966i	0.100572	+	0.291022i
$319$			38.9677i			2.18177i
$320$	−6.87695	−	12.9288i	−0.384433	−	0.722743i
$321$	10.4927	−	17.7394i	0.585646	−	0.990118i
$322$	3.93904	−	4.63953i	0.219514	−	0.258551i
$323$			31.0524i			1.72780i
$324$	−16.5593	−	7.05611i	−0.919963	−	0.392006i
$325$			3.25463i			0.180534i
$326$	−1.52087	−	1.29124i	−0.0842330	−	0.0715154i
$327$	−3.44580	+	5.82561i	−0.190553	+	0.322157i
$328$	4.50560	+	2.70676i	0.248780	+	0.149456i
$329$		−	12.2695i		−	0.676437i
$330$	−23.4581	+	8.10671i	−1.29133	+	0.446260i
$331$	−14.9864			−0.823727			−0.411863	−	0.911246i	$-0.635122\pi$
$331$	−14.9864			−0.823727			−0.411863	+	0.911246i	$0.635122\pi$
$332$	6.94888	−	1.14244i	0.381369	−	0.0626997i
$333$	−16.8960	+	9.28563i	−0.925894	+	0.508850i
$334$	4.03538	+	3.42611i	0.220806	+	0.187468i
$335$	−6.12769			−0.334792
$336$	6.16412	−	29.1718i	0.336281	−	1.59145i
$337$	21.5671			1.17483			0.587417	−	0.809285i	$-0.300145\pi$
$337$	21.5671			1.17483			0.587417	+	0.809285i	$0.300145\pi$
$338$	−9.81665	−	8.33451i	−0.533955	−	0.453338i
$339$	8.51261	−	14.3918i	0.462341	−	0.781654i
$340$	−20.7646	+	3.41383i	−1.12612	+	0.185141i
$341$	−19.1083			−1.03477
$342$	4.58510	−	22.4568i	0.247934	−	1.21433i
$343$		−	19.4548i		−	1.05046i
$344$	12.5288	−	20.8551i	0.675509	−	1.12443i
$345$	2.72889	+	1.61411i	0.146918	+	0.0869009i
$346$	0.334470	+	0.283971i	0.0179812	+	0.0152664i
$347$			10.8450i			0.582189i	0.956694	+	0.291094i	$0.0940194\pi$
$347$			10.8450i			0.582189i	−0.956694	+	0.291094i	$0.905981\pi$
$348$	8.84557	−	22.7256i	0.474172	−	1.21822i
$349$		−	6.59278i		−	0.352904i	−0.984309	−	0.176452i	$-0.943538\pi$
$349$		−	6.59278i		−	0.352904i	0.984309	−	0.176452i	$-0.0564620\pi$
$350$	−6.49654	+	7.65183i	−0.347255	+	0.409008i
$351$	10.2488	+	0.324188i	0.547042	+	0.0173039i
$352$	11.5571	−	29.1019i	0.615995	−	1.55114i
$353$		−	6.47005i		−	0.344366i	−0.985065	−	0.172183i	$-0.944918\pi$
$353$		−	6.47005i		−	0.344366i	0.985065	−	0.172183i	$-0.0550820\pi$
$354$	0.628893	−	0.217334i	0.0334253	−	0.0115512i
$355$	21.7469			1.15420
$356$	−1.39908	+	0.230018i	−0.0741510	+	0.0121909i
$357$	−36.8772	−	21.8125i	−1.95175	−	1.15444i
$358$	5.93590	−	6.99149i	0.313722	−	0.369512i
$359$	−0.701702			−0.0370344			−0.0185172	−	0.999829i	$-0.505895\pi$
$359$	−0.701702			−0.0370344			−0.0185172	+	0.999829i	$0.505895\pi$
$360$	15.5208	+	0.597171i	0.818019	+	0.0314737i
$361$	10.1852			0.536062
$362$	3.92780	−	4.62629i	0.206441	−	0.243152i
$363$	−29.2795	−	17.3185i	−1.53677	−	0.908988i
$364$	2.75547	+	16.7601i	0.144426	+	0.878467i
$365$	20.8725			1.09251
$366$	−34.4272	+	11.8974i	−1.79954	+	0.621887i
$367$			35.7694i			1.86715i	0.358386	+	0.933574i	$0.383327\pi$
$367$			35.7694i			1.86715i	−0.358386	+	0.933574i	$0.616673\pi$
$368$	−3.78945	+	1.28064i	−0.197539	+	0.0667579i
$369$	−4.88576	+	2.68510i	−0.254342	+	0.139781i
$370$	10.7673	−	12.6820i	0.559764	−	0.659308i
$371$		−	9.64693i		−	0.500844i
$372$	11.1438	+	4.33755i	0.577781	+	0.224891i
$373$		−	18.2767i		−	0.946334i	−0.880973	−	0.473167i	$-0.843111\pi$
$373$		−	18.2767i		−	0.946334i	0.880973	−	0.473167i	$-0.156889\pi$
$374$	−34.3010	−	29.1221i	−1.77366	−	1.50587i
$375$	−18.1451	−	10.7327i	−0.937010	−	0.554233i
$376$	−4.15265	+	6.91239i	−0.214157	+	0.356479i
$377$			13.8921i			0.715479i
$378$	23.4485	+	21.2198i	1.20606	+	1.09143i
$379$	−12.1526			−0.624237			−0.312118	−	0.950043i	$-0.601039\pi$
$379$	−12.1526			−0.624237			−0.312118	+	0.950043i	$0.601039\pi$
$380$	3.20855	+	19.5159i	0.164595	+	1.00115i
$381$	14.3247	−	24.2179i	0.733875	−	1.24072i
$382$	4.75423	+	4.03642i	0.243247	+	0.206521i
$383$	−30.4612			−1.55649			−0.778247	−	0.627958i	$-0.783891\pi$
$383$	−30.4612			−1.55649			−0.778247	+	0.627958i	$0.783891\pi$
$384$	−13.3461	+	14.3486i	−0.681065	+	0.732223i
$385$	43.6058			2.22236
$386$	−14.4728	−	12.2876i	−0.736644	−	0.625424i
$387$	12.4285	+	22.6148i	0.631778	+	1.14957i
$388$	−6.29603	−	38.2954i	−0.319632	−	1.94416i
$389$	−33.0744			−1.67694			−0.838468	−	0.544951i	$-0.816548\pi$
$389$	−33.0744			−1.67694			−0.838468	+	0.544951i	$0.816548\pi$
$390$	−8.36291	+	2.89007i	−0.423472	+	0.146344i
$391$			5.74797i			0.290687i
$392$	−16.7805	+	27.9323i	−0.847543	+	1.41080i
$393$	3.10061	−	5.24203i	0.156405	−	0.264425i
$394$	0.843597	+	0.716229i	0.0424998	+	0.0360831i
$395$		−	19.0802i		−	0.960030i
$396$	20.5061	+	26.1257i	1.03047	+	1.31286i
$397$		−	11.4668i		−	0.575502i	−0.957705	−	0.287751i	$-0.907092\pi$
$397$		−	11.4668i		−	0.575502i	0.957705	−	0.287751i	$-0.0929076\pi$
$398$	1.25147	−	1.47402i	0.0627306	−	0.0738860i
$399$	−20.5009	+	34.6597i	−1.02633	+	1.73516i
$400$	6.24983	−	2.11212i	0.312492	−	0.105606i
$401$		−	8.99684i		−	0.449281i	−0.974442	−	0.224640i	$-0.927879\pi$
$401$		−	8.99684i		−	0.449281i	0.974442	−	0.224640i	$-0.0721207\pi$
$402$	2.67828	+	7.75006i	0.133581	+	0.386538i
$403$	−6.81218			−0.339339
$404$	1.01573	+	6.17813i	0.0505343	+	0.307373i
$405$	−8.83128	+	13.9075i	−0.438830	+	0.691067i
$406$	−27.7299	+	32.6612i	−1.37621	+	1.62095i
$407$	35.5729			1.76328
$408$	13.3934	+	24.7701i	0.663073	+	1.22630i
$409$	−7.44058			−0.367913			−0.183956	−	0.982934i	$-0.558891\pi$
$409$	−7.44058			−0.367913			−0.183956	+	0.982934i	$0.558891\pi$
$410$	3.11354	−	3.66722i	0.153767	−	0.181111i
$411$	−3.58228	+	6.05635i	−0.176701	+	0.298738i
$412$	−0.0431768	+	0.00709855i	−0.00212717	+	0.000349721i
$413$	−1.16903			−0.0575243
$414$	0.848726	−	4.15688i	0.0417126	−	0.204300i
$415$		−	6.44534i		−	0.316389i
$416$	4.12014	−	10.3749i	0.202007	−	0.508673i
$417$	−12.5677	−	7.43368i	−0.615443	−	0.364029i
$418$	−27.3710	+	32.2384i	−1.33876	+	1.57683i
$419$			31.5958i			1.54356i	0.635891	+	0.771778i	$0.280633\pi$
$419$			31.5958i			1.54356i	−0.635891	+	0.771778i	$0.719367\pi$
$420$	−25.4306	−	9.89841i	−1.24088	−	0.482993i
$421$		−	35.3022i		−	1.72052i	−0.509854	−	0.860261i	$-0.670301\pi$
$421$		−	35.3022i		−	1.72052i	0.509854	−	0.860261i	$-0.329699\pi$
$422$	−10.8123	−	9.17987i	−0.526336	−	0.446869i
$423$	−4.11942	−	7.49562i	−0.200293	−	0.364450i
$424$	−3.26505	+	5.43491i	−0.158565	+	0.263942i
$425$		−	9.47995i		−	0.459845i
$426$	−9.50509	−	27.5046i	−0.460523	−	1.33260i
$427$	63.9958			3.09697
$428$	23.4835	−	3.86084i	1.13512	−	0.186621i
$429$	−16.2844	−	9.63208i	−0.786219	−	0.465041i
$430$	−16.9745	−	14.4117i	−0.818584	−	0.694993i
$431$	13.1110			0.631535			0.315768	−	0.948837i	$-0.397738\pi$
$431$	13.1110			0.631535			0.315768	+	0.948837i	$0.397738\pi$
$432$	−6.02854	−	19.8911i	−0.290048	−	0.957012i
$433$	−9.46216			−0.454723			−0.227361	−	0.973810i	$-0.573010\pi$
$433$	−9.46216			−0.454723			−0.227361	+	0.973810i	$0.573010\pi$
$434$	−16.0159	−	13.5977i	−0.768786	−	0.652713i
$435$	−19.2107	−	11.3630i	−0.921084	−	0.544813i
$436$	−7.71195	+	1.26790i	−0.369335	+	0.0607212i
$437$	5.40233			0.258429
$438$	−9.12290	−	26.3987i	−0.435909	−	1.26138i
$439$		−	1.25824i		−	0.0600523i	−0.999549	−	0.0300262i	$-0.990441\pi$
$439$		−	1.25824i		−	0.0600523i	0.999549	−	0.0300262i	$-0.00955906\pi$
$440$	−24.5667	−	14.7586i	−1.17117	−	0.703587i
$441$	−16.6462	−	30.2891i	−0.792675	−	1.44234i
$442$	−12.2284	−	10.3821i	−0.581646	−	0.493828i
$443$			27.6996i			1.31605i	0.752997	+	0.658024i	$0.228608\pi$
$443$			27.6996i			1.31605i	−0.752997	+	0.658024i	$0.771392\pi$
$444$	−20.7459	−	8.07497i	−0.984555	−	0.383221i
$445$			1.29770i			0.0615167i
$446$	−9.01327	+	10.6161i	−0.426790	+	0.502687i
$447$	−12.2142	−	7.22460i	−0.577713	−	0.341712i
$448$	30.3960	−	16.1679i	1.43608	−	0.763862i
$449$			39.5862i			1.86819i	0.357029	+	0.934093i	$0.383790\pi$
$449$			39.5862i			1.86819i	−0.357029	+	0.934093i	$0.616210\pi$
$450$	−1.39978	+	6.85582i	−0.0659862	+	0.323186i
$451$	10.2865			0.484373
$452$	19.0518	−	3.13225i	0.896124	−	0.147329i
$453$	−8.99038	+	15.1995i	−0.422405	+	0.714136i
$454$	−18.9704	+	22.3440i	−0.890327	+	1.04866i
$455$	15.5456			0.728789
$456$	23.2806	−	12.5880i	1.09021	−	0.589489i
$457$	−35.5804			−1.66438			−0.832192	−	0.554488i	$-0.812914\pi$
$457$	−35.5804			−1.66438			−0.832192	+	0.554488i	$0.812914\pi$
$458$	−0.752186	+	0.885948i	−0.0351473	+	0.0413976i
$459$	−29.8524	−	0.944281i	−1.39339	−	0.0440753i
$460$	0.593920	+	3.61250i	0.0276917	+	0.168434i
$461$	−11.4883			−0.535063			−0.267531	−	0.963549i	$-0.586208\pi$
$461$	−11.4883			−0.535063			−0.267531	+	0.963549i	$0.586208\pi$
$462$	−19.0591	−	55.1508i	−0.886711	−	2.56585i
$463$			22.9831i			1.06811i	0.845449	+	0.534057i	$0.179333\pi$
$463$			22.9831i			1.06811i	−0.845449	+	0.534057i	$0.820667\pi$
$464$	26.6769	−	9.01540i	1.23844	−	0.418529i
$465$	5.57199	−	9.42024i	0.258395	−	0.436853i
$466$	−15.0054	+	17.6739i	−0.695113	+	0.818726i
$467$			22.8634i			1.05799i	0.848624	+	0.528996i	$0.177431\pi$
$467$			22.8634i			1.05799i	−0.848624	+	0.528996i	$0.822569\pi$
$468$	7.31049	+	9.31388i	0.337927	+	0.430534i
$469$		−	14.4064i		−	0.665225i
$470$	5.62617	+	4.77672i	0.259516	+	0.220334i
$471$	4.08664	−	6.90905i	0.188302	−	0.318352i
$472$	0.658612	+	0.395664i	0.0303151	+	0.0182119i
$473$		−	47.6133i		−	2.18926i
$474$	−24.1319	+	8.33955i	−1.10841	+	0.383048i
$475$	−8.90990			−0.408814
$476$	−8.02603	−	48.8181i	−0.367872	−	2.23757i
$477$	−3.23891	−	5.89347i	−0.148300	−	0.269844i
$478$	9.00350	+	7.64413i	0.411810	+	0.349634i
$479$	9.50578			0.434330			0.217165	−	0.976135i	$-0.430319\pi$
$479$	9.50578			0.434330			0.217165	+	0.976135i	$0.430319\pi$
$480$	10.9770	+	14.1837i	0.501027	+	0.647393i
$481$	12.6819			0.578243
$482$	18.3919	+	15.6151i	0.837729	+	0.711247i
$483$	−3.79483	+	6.41570i	−0.172671	+	0.291924i
$484$	−6.37244	−	38.7602i	−0.289656	−	1.76183i
$485$	−35.5204			−1.61290
$486$	21.4496	+	5.09080i	0.972972	+	0.230924i
$487$		−	10.7081i		−	0.485230i	−0.970123	−	0.242615i	$-0.921995\pi$
$487$		−	10.7081i		−	0.485230i	0.970123	−	0.242615i	$-0.0780051\pi$
$488$	−36.0541	−	21.6597i	−1.63209	−	0.980487i
$489$	2.10311	+	1.24397i	0.0951058	+	0.0562542i
$490$	22.7348	+	19.3023i	1.02706	+	0.871989i
$491$			16.7867i			0.757573i	0.925484	+	0.378787i	$0.123659\pi$
$491$			16.7867i			0.757573i	−0.925484	+	0.378787i	$0.876341\pi$
$492$	−5.99902	−	2.33502i	−0.270457	−	0.105271i
$493$		−	40.4643i		−	1.82242i
$494$	−9.75784	+	11.4931i	−0.439026	+	0.517099i
$495$	26.6395	−	14.6404i	1.19736	−	0.658039i
$496$	4.42082	+	13.0814i	0.198501	+	0.587371i
$497$			51.1276i			2.29339i
$498$	−8.15181	+	2.81712i	−0.365291	+	0.126238i
$499$	15.5035			0.694032			0.347016	−	0.937859i	$-0.387195\pi$
$499$	15.5035			0.694032			0.347016	+	0.937859i	$0.387195\pi$
$500$	−3.94914	−	24.0205i	−0.176611	−	1.07423i
$501$	−5.58026	−	3.30067i	−0.249308	−	0.147463i
$502$	−4.73579	+	5.57796i	−0.211368	+	0.248956i
$503$	15.9310			0.710330			0.355165	−	0.934804i	$-0.384425\pi$
$503$	15.9310			0.710330			0.355165	+	0.934804i	$0.384425\pi$
$504$	−1.40397	+	36.4899i	−0.0625377	+	1.62539i
$505$	5.73044			0.255001
$506$	−5.06651	+	5.96750i	−0.225234	+	0.265288i
$507$	13.5748	+	8.02937i	0.602878	+	0.356597i
$508$	32.0597	−	5.27083i	1.42242	−	0.233855i
$509$	−18.9058			−0.837987			−0.418993	−	0.907989i	$-0.637617\pi$
$509$	−18.9058			−0.837987			−0.418993	+	0.907989i	$0.637617\pi$
$510$	24.3591	−	8.41808i	1.07864	−	0.372759i
$511$			49.0718i			2.17081i
$512$	−22.5967	−	1.17897i	−0.998642	−	0.0521036i
$513$	−0.887500	+	28.0573i	−0.0391841	+	1.23876i
$514$	14.9298	−	17.5848i	0.658527	−	0.775634i
$515$			0.0400480i			0.00176473i
$516$	−10.8081	+	27.7677i	−0.475801	+	1.22241i
$517$			15.7813i			0.694062i
$518$	29.8158	+	25.3142i	1.31003	+	1.11224i
$519$	−0.462516	−	0.273574i	−0.0203022	−	0.0120086i
$520$	−8.75811	−	5.26148i	−0.384068	−	0.230731i
$521$		−	3.77614i		−	0.165436i	−0.996573	−	0.0827179i	$-0.973640\pi$
$521$		−	3.77614i		−	0.165436i	0.996573	−	0.0827179i	$-0.0263601\pi$
$522$	−5.97483	+	29.2635i	−0.261511	+	1.28083i
$523$	−27.6212			−1.20779			−0.603896	−	0.797063i	$-0.706386\pi$
$523$	−27.6212			−1.20779			−0.603896	+	0.797063i	$0.706386\pi$
$524$	6.93940	−	1.14088i	0.303149	−	0.0498398i
$525$	6.25869	−	10.5812i	0.273152	−	0.461802i
$526$	−14.5119	−	12.3209i	−0.632751	−	0.537217i
$527$	19.8422			0.864342
$528$	−7.92848	+	37.5216i	−0.345043	+	1.63292i
$529$	1.00000			0.0434783
$530$	4.42361	+	3.75572i	0.192149	+	0.163138i
$531$	−0.714182	+	0.392497i	−0.0309928	+	0.0170329i
$532$	−45.8826	+	7.54341i	−1.98926	+	0.327048i
$533$	3.66718			0.158843
$534$	1.64127	−	0.567195i	0.0710249	−	0.0245449i
$535$		−	21.7818i		−	0.941708i
$536$	−4.87591	+	8.11630i	−0.210607	+	0.350571i
$537$	−5.71857	+	9.66807i	−0.246775	+	0.417208i
$538$	−4.55519	−	3.86744i	−0.196388	−	0.166737i
$539$			63.7709i			2.74681i
$540$	−18.8593	+	2.49109i	−0.811575	+	0.107200i
$541$			21.3287i			0.916992i	0.888697	+	0.458496i	$0.151612\pi$
$541$			21.3287i			0.916992i	−0.888697	+	0.458496i	$0.848388\pi$
$542$	−13.8369	+	16.2976i	−0.594347	+	0.700040i
$543$	−3.78400	+	6.39739i	−0.162387	+	0.274538i
$544$	−12.0010	+	30.2197i	−0.514538	+	1.29566i
$545$			7.15312i			0.306406i
$546$	−6.79464	−	19.6614i	−0.290784	−	0.841432i
$547$	34.3770			1.46985			0.734927	−	0.678146i	$-0.237216\pi$
$547$	34.3770			1.46985			0.734927	+	0.678146i	$0.237216\pi$
$548$	−8.01740	+	1.31812i	−0.342486	+	0.0563071i
$549$	39.0961	−	21.4863i	1.66858	−	0.917013i
$550$	8.35604	−	9.84201i	0.356303	−	0.419665i
$551$	−38.0311			−1.62018
$552$	4.30936	−	2.33011i	0.183418	−	0.0991762i
$553$	44.8582			1.90756
$554$	21.8847	−	25.7765i	0.929791	−	1.09514i
$555$	−10.3731	+	17.5372i	−0.440312	+	0.744411i
$556$	−2.73526	−	16.6371i	−0.116001	−	0.705571i
$557$	41.7607			1.76946			0.884728	−	0.466107i	$-0.154344\pi$
$557$	41.7607			1.76946			0.884728	+	0.466107i	$0.154344\pi$
$558$	−14.3497	−	2.92984i	−0.607473	−	0.124030i
$559$		−	16.9743i		−	0.717936i
$560$	−10.0885	−	29.8521i	−0.426315	−	1.26148i
$561$	47.4326	+	28.0559i	2.00261	+	1.18452i
$562$	−3.15596	+	3.71719i	−0.133126	+	0.156800i
$563$		−	8.25360i		−	0.347848i	−0.984759	−	0.173924i	$-0.944355\pi$
$563$		−	8.25360i		−	0.347848i	0.984759	−	0.173924i	$-0.0556447\pi$
$564$	3.58233	−	9.20356i	0.150843	−	0.387540i
$565$		−	17.6713i		−	0.743437i
$566$	6.70436	+	5.69212i	0.281805	+	0.239258i
$567$	−32.6969	−	20.7626i	−1.37314	−	0.871948i
$568$	17.3044	−	28.8044i	0.726075	−	1.20860i
$569$			3.81141i			0.159783i	0.996804	+	0.0798914i	$0.0254573\pi$
$569$			3.81141i			0.159783i	−0.996804	+	0.0798914i	$0.974543\pi$
$570$	−7.91188	−	22.8944i	−0.331392	−	0.958939i
$571$	3.83096			0.160321			0.0801603	−	0.996782i	$-0.474457\pi$
$571$	3.83096			0.160321			0.0801603	+	0.996782i	$0.474457\pi$
$572$	−3.54417	−	21.5573i	−0.148189	−	0.901356i
$573$	−6.57431	−	3.88864i	−0.274646	−	0.162450i
$574$	8.62176	+	7.32003i	0.359865	+	0.305532i
$575$	−1.64927			−0.0687793
$576$	13.1411	−	20.0826i	0.547548	−	0.836774i
$577$	−8.00714			−0.333341			−0.166671	−	0.986013i	$-0.553302\pi$
$577$	−8.00714			−0.333341			−0.166671	+	0.986013i	$0.553302\pi$
$578$	17.2913	+	14.6806i	0.719222	+	0.610633i
$579$	20.0134	+	11.8378i	0.831730	+	0.491961i
$580$	−4.18106	−	25.4312i	−0.173609	−	1.05597i
$581$	15.1532			0.628661
$582$	15.5252	+	44.9248i	0.643540	+	1.86219i
$583$			12.4082i			0.513894i
$584$	16.6086	−	27.6462i	0.687268	−	1.14401i
$585$	9.49707	−	5.21937i	0.392655	−	0.215794i
$586$	−32.2882	−	27.4133i	−1.33381	−	1.13243i
$587$		−	28.8211i		−	1.18957i	−0.803883	−	0.594787i	$-0.797236\pi$
$587$		−	28.8211i		−	1.18957i	0.803883	−	0.594787i	$-0.202764\pi$
$588$	14.4759	−	37.1907i	0.596974	−	1.53372i
$589$		−	18.6491i		−	0.768422i
$590$	0.455125	−	0.536061i	0.0187372	−	0.0220693i
$591$	−1.16656	−	0.690007i	−0.0479857	−	0.0283831i
$592$	−8.23001	−	24.3529i	−0.338251	−	1.00090i
$593$			23.5051i			0.965239i	0.875830	+	0.482619i	$0.160315\pi$
$593$			23.5051i			0.965239i	−0.875830	+	0.482619i	$0.839685\pi$
$594$	−30.1602	−	27.2935i	−1.23749	−	1.11987i
$595$	−45.2806			−1.85632
$596$	−2.65833	−	16.1692i	−0.108889	−	0.662316i
$597$	−1.20565	+	2.03833i	−0.0493440	+	0.0834232i
$598$	−1.80623	+	2.12743i	−0.0738621	+	0.0869972i
$599$	43.6686			1.78425			0.892125	−	0.451790i	$-0.149214\pi$
$599$	43.6686			1.78425			0.892125	+	0.451790i	$0.149214\pi$
$600$	−7.10730	+	3.84298i	−0.290154	+	0.156889i
$601$	27.2522			1.11164			0.555819	−	0.831303i	$-0.312405\pi$
$601$	27.2522			1.11164			0.555819	+	0.831303i	$0.312405\pi$
$602$	33.8823	−	39.9076i	1.38094	−	1.62651i
$603$	−4.83688	−	8.80111i	−0.196973	−	0.358409i
$604$	−20.1211	+	3.30805i	−0.818717	+	0.134603i
$605$	−35.9515			−1.46164
$606$	−2.50465	−	7.24763i	−0.101744	−	0.294415i
$607$			13.0652i			0.530299i	0.964207	+	0.265149i	$0.0854213\pi$
$607$			13.0652i			0.530299i	−0.964207	+	0.265149i	$0.914579\pi$
$608$	28.4025	+	11.2793i	1.15187	+	0.457438i
$609$	26.7147	−	45.1650i	1.08253	−	1.83018i
$610$	−24.9147	+	29.3453i	−1.00877	+	1.18816i
$611$			5.62610i			0.227608i
$612$	−21.2937	−	27.1291i	−0.860747	−	1.09663i
$613$			27.2977i			1.10254i	0.834326	+	0.551272i	$0.185857\pi$
$613$			27.2977i			1.10254i	−0.834326	+	0.551272i	$0.814143\pi$
$614$	7.05101	+	5.98644i	0.284556	+	0.241593i
$615$	−2.99955	+	5.07117i	−0.120953	+	0.204489i
$616$	34.6978	−	57.7571i	1.39802	−	2.32710i
$617$			6.29703i			0.253509i	0.991934	+	0.126754i	$0.0404560\pi$
$617$			6.29703i			0.253509i	−0.991934	+	0.126754i	$0.959544\pi$
$618$	0.0506511	−	0.0175041i	0.00203749	−	0.000704119i
$619$	−49.4879			−1.98908			−0.994542	−	0.104334i	$-0.966729\pi$
$619$	−49.4879			−1.98908			−0.994542	+	0.104334i	$0.966729\pi$
$620$	12.4705	−	2.05024i	0.500828	−	0.0823396i
$621$	−0.164281	+	5.19355i	−0.00659236	+	0.208410i
$622$	−11.5444	−	9.80138i	−0.462887	−	0.393000i
$623$	−3.05092			−0.122233
$624$	−2.82653	+	13.3766i	−0.113152	+	0.535492i
$625$	−14.0336			−0.561342
$626$	21.2636	+	18.0532i	0.849865	+	0.721550i
$627$	26.3689	−	44.5804i	1.05307	−	1.78037i
$628$	9.14621	−	1.50370i	0.364973	−	0.0600041i
$629$	−36.9392			−1.47286
$630$	32.7465	+	6.68598i	1.30465	+	0.266376i
$631$			6.23486i			0.248206i	0.992269	+	0.124103i	$0.0396053\pi$
$631$			6.23486i			0.248206i	−0.992269	+	0.124103i	$0.960395\pi$
$632$	−25.2723	−	15.1825i	−1.00528	−	0.603926i
$633$	14.9517	+	8.84378i	0.594276	+	0.351509i
$634$	−29.9123	−	25.3960i	−1.18797	−	1.00861i
$635$		−	29.7365i		−	1.18006i
$636$	2.81663	−	7.23635i	0.111686	−	0.286940i
$637$			22.7345i			0.900775i
$638$	35.6670	−	42.0098i	1.41207	−	1.66318i
$639$	17.1659	+	31.2347i	0.679071	+	1.23563i
$640$	−4.41991	+	20.2326i	−0.174712	+	0.799763i
$641$			20.5361i			0.811128i	0.914067	+	0.405564i	$0.132925\pi$
$641$			20.5361i			0.811128i	−0.914067	+	0.405564i	$0.867075\pi$
$642$	−27.5487	+	9.52034i	−1.08726	+	0.375738i
$643$	38.8627			1.53260			0.766298	−	0.642485i	$-0.222097\pi$
$643$	38.8627			1.53260			0.766298	+	0.642485i	$0.222097\pi$
$644$	−8.49310	+	1.39632i	−0.334675	+	0.0550229i
$645$	23.4730	+	13.8840i	0.924247	+	0.546683i
$646$	28.4222	−	33.4766i	1.11826	−	1.31712i
$647$	−6.42613			−0.252637			−0.126319	−	0.991990i	$-0.540316\pi$
$647$	−6.42613			−0.252637			−0.126319	+	0.991990i	$0.540316\pi$
$648$	11.3936	+	22.7637i	0.447584	+	0.894242i
$649$	1.50364			0.0590232
$650$	2.97896	−	3.50871i	0.116844	−	0.137623i
$651$	22.1473	+	13.0999i	0.868020	+	0.513426i
$652$	0.457724	+	2.78409i	0.0179259	+	0.109034i
$653$	−33.5199			−1.31173			−0.655867	−	0.754876i	$-0.727697\pi$
$653$	−33.5199			−1.31173			−0.655867	+	0.754876i	$0.727697\pi$
$654$	9.04697	−	3.12647i	0.353765	−	0.122255i
$655$		−	6.43655i		−	0.251497i
$656$	−2.37985	−	7.04204i	−0.0929174	−	0.274946i
$657$	16.4756	+	29.9788i	0.642776	+	1.16958i
$658$	−11.2302	+	13.2273i	−0.437799	+	0.515654i
$659$		−	7.84793i		−	0.305712i	−0.988248	−	0.152856i	$-0.951153\pi$
$659$		−	7.84793i		−	0.305712i	0.988248	−	0.152856i	$-0.0488470\pi$
$660$	32.7095	+	12.7316i	1.27322	+	0.495578i
$661$			18.3882i			0.715220i	0.933871	+	0.357610i	$0.116408\pi$
$661$			18.3882i			0.715220i	−0.933871	+	0.357610i	$0.883592\pi$
$662$	16.1563	+	13.7170i	0.627934	+	0.533127i
$663$	16.9099	+	10.0020i	0.656725	+	0.388447i
$664$	−8.53704	−	5.12867i	−0.331301	−	0.199031i
$665$			42.5578i			1.65032i
$666$	26.7141	+	5.45433i	1.03515	+	0.211351i
$667$	−7.03976			−0.272581
$668$	−1.21450	−	7.38715i	−0.0469903	−	0.285817i
$669$	8.68327	−	14.6803i	0.335715	−	0.567574i
$670$	6.60607	+	5.60867i	0.255215	+	0.216682i
$671$	−82.3132			−3.17767
$672$	−33.3462	+	25.8072i	−1.28636	+	0.995533i
$673$	−17.3962			−0.670573			−0.335286	−	0.942116i	$-0.608833\pi$
$673$	−17.3962			−0.670573			−0.335286	+	0.942116i	$0.608833\pi$
$674$	−23.2507	−	19.7403i	−0.895585	−	0.760368i
$675$	0.270944	−	8.56557i	0.0104286	−	0.329689i
$676$	2.95444	+	17.9703i	0.113632	+	0.691167i
$677$	17.5611			0.674929			0.337464	−	0.941338i	$-0.390431\pi$
$677$	17.5611			0.674929			0.337464	+	0.941338i	$0.390431\pi$
$678$	−22.3499	+	7.72374i	−0.858344	+	0.296628i
$679$		−	83.5096i		−	3.20480i
$680$	25.5103	+	15.3254i	0.978274	+	0.587703i
$681$	18.2759	−	30.8980i	0.700334	−	1.18402i
$682$	20.6001	+	17.4898i	0.788817	+	0.669720i
$683$		−	3.44164i		−	0.131691i	−0.997830	−	0.0658454i	$-0.979026\pi$
$683$		−	3.44164i		−	0.131691i	0.997830	−	0.0658454i	$-0.0209744\pi$
$684$	−25.4978	+	20.0133i	−0.974931	+	0.765226i
$685$			7.43644i			0.284132i
$686$	−17.8070	+	20.9736i	−0.679874	+	0.800776i
$687$	0.724647	−	1.22512i	0.0276470	−	0.0467412i
$688$	−32.5956	+	11.0156i	−1.24269	+	0.419967i
$689$			4.42355i			0.168524i
$690$	−1.46453	−	4.23787i	−0.0557537	−	0.161333i
$691$	0.976589			0.0371512			0.0185756	−	0.999827i	$-0.494087\pi$
$691$	0.976589			0.0371512			0.0185756	+	0.999827i	$0.494087\pi$
$692$	−0.100663	−	0.612279i	−0.00382663	−	0.0232754i
$693$	34.4201	+	62.6303i	1.30751	+	2.37913i
$694$	9.92639	−	11.6916i	0.376801	−	0.443808i
$695$	−15.4316			−0.585352
$696$	−30.3369	+	16.4034i	−1.14992	+	0.621771i
$697$	−10.6816			−0.404595
$698$	−6.03436	+	7.10746i	−0.228404	+	0.269021i
$699$	14.4561	−	24.4400i	0.546778	−	0.924407i
$700$	14.0074	−	2.30292i	0.529431	−	0.0870420i
$701$	2.59377			0.0979655			0.0489827	−	0.998800i	$-0.484402\pi$
$701$	2.59377			0.0979655			0.0489827	+	0.998800i	$0.484402\pi$
$702$	−10.7522	−	9.73024i	−0.405816	−	0.367244i
$703$			34.7180i			1.30941i
$704$	−39.0963	+	20.7956i	−1.47350	+	0.783765i
$705$	−7.78007	−	4.60184i	−0.293014	−	0.173315i
$706$	−5.92203	+	6.97515i	−0.222878	+	0.262513i
$707$			13.4724i			0.506683i
$708$	−0.876914	−	0.341324i	−0.0329564	−	0.0128277i
$709$		−	19.4273i		−	0.729609i	−0.931084	−	0.364804i	$-0.881136\pi$
$709$		−	19.4273i		−	0.729609i	0.931084	−	0.364804i	$-0.118864\pi$
$710$	−23.4446	−	19.9049i	−0.879860	−	0.747017i
$711$	27.4046	−	15.0609i	1.02775	−	0.564829i
$712$	1.71883	+	1.03260i	0.0644161	+	0.0386983i
$713$		−	3.45204i		−	0.129280i
$714$	19.7912	+	57.2691i	0.740666	+	2.14324i
$715$	−19.9952			−0.747778
$716$	−12.7986	+	2.10418i	−0.478306	+	0.0786367i
$717$	−12.4503	−	7.36426i	−0.464967	−	0.275023i
$718$	0.756482	+	0.642267i	0.0282317	+	0.0239692i
$719$	−35.3076			−1.31675			−0.658376	−	0.752690i	$-0.728756\pi$
$719$	−35.3076			−1.31675			−0.658376	+	0.752690i	$0.728756\pi$
$720$	−16.1859	−	14.8500i	−0.603213	−	0.553426i
$721$	−0.0941541			−0.00350648
$722$	−10.9803	−	9.32247i	−0.408645	−	0.346947i
$723$	−25.4330	−	15.0434i	−0.945863	−	0.559469i
$724$	−8.46886	+	1.39234i	−0.314743	+	0.0517459i
$725$	11.6105			0.431202
$726$	15.7136	+	45.4700i	0.583187	+	1.68755i
$727$			13.9248i			0.516441i	0.966086	+	0.258221i	$0.0831361\pi$
$727$			13.9248i			0.516441i	−0.966086	+	0.258221i	$0.916864\pi$
$728$	12.3699	−	20.5906i	0.458459	−	0.763138i
$729$	−26.9460	−	1.70640i	−0.998001	−	0.0632001i
$730$	−22.5019	−	19.1045i	−0.832834	−	0.707091i
$731$			49.4420i			1.82868i
$732$	48.0045	+	18.6849i	1.77430	+	0.690614i
$733$			43.5255i			1.60765i	0.594866	+	0.803825i	$0.297205\pi$
$733$			43.5255i			1.60765i	−0.594866	+	0.803825i	$0.702795\pi$
$734$	32.7397	−	38.5618i	1.20844	−	1.42334i
$735$	−31.4385	−	18.5956i	−1.15963	−	0.685909i
$736$	5.25745	+	2.08787i	0.193792	+	0.0769598i
$737$			18.5299i			0.682558i
$738$	7.72484	+	1.57721i	0.284355	+	0.0580579i
$739$	−29.7327			−1.09373			−0.546867	−	0.837220i	$-0.684180\pi$
$739$	−29.7327			−1.09373			−0.546867	+	0.837220i	$0.684180\pi$
$740$	−23.2157	+	3.81682i	−0.853426	+	0.140309i
$741$	9.40059	−	15.8930i	0.345339	−	0.583845i
$742$	−8.82982	+	10.4000i	−0.324153	+	0.381798i
$743$	24.2523			0.889732			0.444866	−	0.895597i	$-0.353251\pi$
$743$	24.2523			0.889732			0.444866	+	0.895597i	$0.353251\pi$
$744$	−8.04365	−	14.8761i	−0.294895	−	0.545384i
$745$	−14.9975			−0.549467
$746$	−16.7287	+	19.7035i	−0.612480	+	0.721398i
$747$	9.25734	−	5.08762i	0.338708	−	0.186146i
$748$	10.3233	+	62.7913i	0.377458	+	2.29588i
$749$	51.2096			1.87116
$750$	9.73806	+	28.1787i	0.355584	+	1.02894i
$751$		−	12.0136i		−	0.438381i	−0.975682	−	0.219190i	$-0.929658\pi$
$751$		−	12.0136i		−	0.438381i	0.975682	−	0.219190i	$-0.0703416\pi$
$752$	10.8037	−	3.65111i	0.393972	−	0.133142i
$753$	4.56240	−	7.71339i	0.166263	−	0.281092i
$754$	12.7154	−	14.9766i	0.463068	−	0.545416i
$755$			18.6631i			0.679219i
$756$	−5.85663	−	44.3388i	−0.213004	−	1.61259i
$757$			3.61536i			0.131402i	0.997839	+	0.0657012i	$0.0209284\pi$
$757$			3.61536i			0.131402i	−0.997839	+	0.0657012i	$0.979072\pi$
$758$	13.1013	+	11.1232i	0.475861	+	0.404015i
$759$	4.88102	−	8.25206i	0.177170	−	0.299531i
$760$	14.4039	−	23.9763i	0.522483	−	0.869711i
$761$			23.9843i			0.869431i	0.900568	+	0.434716i	$0.143151\pi$
$761$			23.9843i			0.869431i	−0.900568	+	0.434716i	$0.856849\pi$
$762$	−37.6096	+	12.9972i	−1.36245	+	0.470839i
$763$	−16.8172			−0.608823
$764$	−1.43084	−	8.70307i	−0.0517661	−	0.314866i
$765$	−27.6627	+	15.2028i	−1.00015	+	0.549657i
$766$	32.8392	+	27.8811i	1.18653	+	1.00738i
$767$	0.536054			0.0193558
$768$	27.5212	−	3.25310i	0.993086	−	0.117386i
$769$	−46.2035			−1.66614			−0.833071	−	0.553166i	$-0.813419\pi$
$769$	−46.2035			−1.66614			−0.833071	+	0.553166i	$0.813419\pi$
$770$	−47.0099	−	39.9123i	−1.69412	−	1.43834i
$771$	−14.3832	+	24.3169i	−0.517999	+	0.875752i
$772$	4.35576	+	26.4938i	0.156767	+	0.953532i
$773$	16.6575			0.599127			0.299564	−	0.954076i	$-0.403159\pi$
$773$	16.6575			0.599127			0.299564	+	0.954076i	$0.403159\pi$
$774$	7.30045	−	35.7561i	0.262409	−	1.28523i
$775$			5.69335i			0.204511i
$776$	−28.2642	+	47.0478i	−1.01463	+	1.68892i
$777$	−41.2304	−	24.3874i	−1.47913	−	0.874893i
$778$	35.6564	+	30.2729i	1.27834	+	1.08534i
$779$			10.0393i			0.359695i
$780$	11.6611	+	4.53887i	0.417533	+	0.162517i
$781$		−	65.7618i		−	2.35314i
$782$	5.26111	−	6.19670i	0.188137	−	0.221593i
$783$	1.15650	−	36.5614i	0.0413299	−	1.30660i
$784$	43.6569	−	14.7538i	1.55918	−	0.526921i
$785$		−	8.48344i		−	0.302787i
$786$	−8.14069	+	2.81328i	−0.290369	+	0.100346i
$787$	21.5944			0.769758			0.384879	−	0.922967i	$-0.374243\pi$
$787$	21.5944			0.769758			0.384879	+	0.922967i	$0.374243\pi$
$788$	−0.253891	−	1.54429i	−0.00904450	−	0.0550129i
$789$	20.0676	+	11.8698i	0.714426	+	0.422576i
$790$	−17.4641	+	20.5698i	−0.621345	+	0.731839i
$791$	41.5457			1.47720
$792$	1.80582	−	46.9344i	0.0641671	−	1.66774i
$793$	−29.3449			−1.04207
$794$	−10.4955	+	12.3620i	−0.372473	+	0.438710i
$795$	−6.11712	−	3.61822i	−0.216952	−	0.128325i
$796$	−2.69834	+	0.443625i	−0.0956401	+	0.0157239i
$797$	−31.2874			−1.10826			−0.554129	−	0.832431i	$-0.686948\pi$
$797$	−31.2874			−1.10826			−0.554129	+	0.832431i	$0.686948\pi$
$798$	53.8253	−	18.6011i	1.90540	−	0.658471i
$799$		−	16.3875i		−	0.579747i
$800$	−8.67096	−	3.44345i	−0.306565	−	0.121744i
$801$	−1.86386	+	1.02433i	−0.0658563	+	0.0361931i
$802$	−8.23479	+	9.69920i	−0.290781	+	0.342490i
$803$		−	63.1176i		−	2.22737i
$804$	4.20625	−	10.8065i	0.148343	−	0.381116i
$805$			7.87767i			0.277651i
$806$	7.34399	+	6.23518i	0.258681	+	0.219625i
$807$	6.29907	+	3.72584i	0.221738	+	0.131156i
$808$	4.55981	−	7.59013i	0.160413	−	0.267020i
$809$		−	9.30604i		−	0.327183i	−0.986528	−	0.163592i	$-0.947692\pi$
$809$		−	9.30604i		−	0.327183i	0.986528	−	0.163592i	$-0.0523079\pi$
$810$	22.2502	−	6.90992i	0.781792	−	0.242790i
$811$	40.9331			1.43735			0.718677	−	0.695344i	$-0.244748\pi$
$811$	40.9331			1.43735			0.718677	+	0.695344i	$0.244748\pi$
$812$	59.7894	−	9.82979i	2.09820	−	0.344958i
$813$	13.3303	−	22.5368i	0.467515	−	0.790401i
$814$	−38.3500	−	32.5598i	−1.34417	−	1.14122i
$815$	2.58235			0.0904558
$816$	8.23299	−	38.9628i	0.288212	−	1.36397i
$817$	46.4690			1.62574
$818$	8.02145	+	6.81035i	0.280463	+	0.238118i
$819$	12.2709	+	22.3279i	0.428779	+	0.780200i
$820$	−6.71321	+	1.10370i	−0.234435	+	0.0385428i
$821$	−7.16025			−0.249894			−0.124947	−	0.992163i	$-0.539876\pi$
$821$	−7.16025			−0.249894			−0.124947	+	0.992163i	$0.539876\pi$
$822$	9.40530	−	3.25030i	0.328048	−	0.113367i
$823$			48.7118i			1.69799i	0.528402	+	0.848994i	$0.322791\pi$
$823$			48.7118i			1.69799i	−0.528402	+	0.848994i	$0.677209\pi$
$824$	0.0530447	+	0.0318669i	0.00184790	+	0.00111014i
$825$	−8.05011	+	13.6099i	−0.280269	+	0.473835i
$826$	1.26030	+	1.07001i	0.0438513	+	0.0372305i
$827$		−	26.9461i		−	0.937007i	−0.883462	−	0.468504i	$-0.844793\pi$
$827$		−	26.9461i		−	0.937007i	0.883462	−	0.468504i	$-0.155207\pi$
$828$	−4.71977	+	3.70456i	−0.164023	+	0.128742i
$829$			34.8055i			1.20884i	0.796665	+	0.604422i	$0.206596\pi$
$829$			34.8055i			1.20884i	−0.796665	+	0.604422i	$0.793404\pi$
$830$	−5.89941	+	6.94851i	−0.204772	+	0.241186i
$831$	−21.0835	+	35.6446i	−0.731377	+	1.23650i
$832$	−13.9379	+	7.41371i	−0.483211	+	0.257024i
$833$		−	66.2203i		−	2.29440i
$834$	6.74480	+	19.5172i	0.233553	+	0.675826i
$835$	−6.85185			−0.237118
$836$	59.0155	−	9.70255i	2.04109	−	0.335570i
$837$	17.9284	+	0.567105i	0.619695	+	0.0196020i
$838$	28.9196	−	34.0624i	0.999011	−	1.17667i
$839$	40.3401			1.39269			0.696347	−	0.717706i	$-0.254808\pi$
$839$	40.3401			1.39269			0.696347	+	0.717706i	$0.254808\pi$
$840$	18.3559	+	33.9477i	0.633337	+	1.17131i
$841$	20.5583			0.708906
$842$	−32.3120	+	38.0581i	−1.11355	+	1.31157i
$843$	3.04041	−	5.14026i	0.104717	−	0.177040i
$844$	3.25411	+	19.7930i	0.112011	+	0.681304i
$845$	16.6681			0.573402
$846$	−2.41972	+	11.8513i	−0.0831917	+	0.407455i
$847$		−	84.5231i		−	2.90425i
$848$	8.49450	−	2.87070i	0.291702	−	0.0985803i
$849$	−9.27102	−	5.48372i	−0.318181	−	0.188201i
$850$	−8.67699	+	10.2200i	−0.297618	+	0.350544i
$851$			6.42648i			0.220297i
$852$	−14.9278	+	38.3518i	−0.511417	+	1.31391i
$853$			5.24107i			0.179451i	0.995967	+	0.0897254i	$0.0285990\pi$
$853$			5.24107i			0.179451i	−0.995967	+	0.0897254i	$0.971401\pi$
$854$	−68.9917	−	58.5752i	−2.36085	−	2.00440i
$855$	14.2886	+	25.9993i	0.488659	+	0.889156i
$856$	−28.8506	−	17.3321i	−0.986092	−	0.592400i
$857$		−	9.70783i		−	0.331613i	−0.986158	−	0.165807i	$-0.946977\pi$
$857$		−	9.70783i		−	0.331613i	0.986158	−	0.165807i	$-0.0530227\pi$
$858$	8.73947	+	25.2891i	0.298360	+	0.863357i
$859$	30.2589			1.03242			0.516210	−	0.856462i	$-0.327342\pi$
$859$	30.2589			1.03242			0.516210	+	0.856462i	$0.327342\pi$
$860$	5.10870	+	31.0735i	0.174205	+	1.05960i
$861$	−11.9225	−	7.05203i	−0.406316	−	0.240332i
$862$	−14.1346	−	12.0005i	−0.481425	−	0.408738i
$863$	−52.2882			−1.77991			−0.889955	−	0.456049i	$-0.849264\pi$
$863$	−52.2882			−1.77991			−0.889955	+	0.456049i	$0.849264\pi$
$864$	−11.7071	+	26.9619i	−0.398285	+	0.917262i
$865$	−0.567911			−0.0193096
$866$	10.2008	+	8.66070i	0.346639	+	0.294303i
$867$	−23.9110	−	14.1431i	−0.812059	−	0.480326i
$868$	4.82017	+	29.3186i	0.163607	+	0.995137i
$869$	−57.6979			−1.95727
$870$	10.3100	+	29.8336i	0.349540	+	1.01145i
$871$			6.60598i			0.223835i
$872$	9.47450	+	5.69186i	0.320847	+	0.192751i
$873$	−28.0380	−	51.0174i	−0.948942	−	1.72668i
$874$	−5.82408	−	4.94474i	−0.197002	−	0.167258i
$875$		−	52.3807i		−	1.77079i
$876$	−14.3275	+	36.8097i	−0.484083	+	1.24368i
$877$			21.9739i			0.742007i	0.928631	+	0.371003i	$0.120986\pi$
$877$			21.9739i			0.742007i	−0.928631	+	0.371003i	$0.879014\pi$
$878$	−1.15166	+	1.35646i	−0.0388667	+	0.0457784i
$879$	44.6492	+	26.4096i	1.50598	+	0.890774i
$880$	12.9761	+	38.3966i	0.437423	+	1.29435i
$881$			1.02628i			0.0345761i	0.999851	+	0.0172881i	$0.00550324\pi$
$881$			1.02628i			0.0345761i	−0.999851	+	0.0172881i	$0.994497\pi$
$882$	−9.77787	+	47.8899i	−0.329238	+	1.61254i
$883$	44.3890			1.49381			0.746905	−	0.664931i	$-0.231539\pi$
$883$	44.3890			1.49381			0.746905	+	0.664931i	$0.231539\pi$
$884$	3.68029	+	22.3853i	0.123782	+	0.752899i
$885$	−0.438462	+	0.741284i	−0.0147388	+	0.0249180i
$886$	25.3534	−	29.8620i	0.851764	−	1.00323i
$887$	−10.8517			−0.364366			−0.182183	−	0.983265i	$-0.558316\pi$
$887$	−10.8517			−0.364366			−0.182183	+	0.983265i	$0.558316\pi$
$888$	14.9744	+	27.6940i	0.502509	+	0.929351i
$889$	69.9115			2.34476
$890$	1.18778	−	1.39900i	0.0398144	−	0.0468947i
$891$	42.0557	+	26.7055i	1.40892	+	0.894667i
$892$	19.4338	−	3.19505i	0.650692	−	0.106978i
$893$	−15.4021			−0.515410
$894$	6.55509	+	18.9683i	0.219235	+	0.634394i
$895$			11.8712i			0.396809i
$896$	−47.5674	−	10.3914i	−1.58912	−	0.347151i
$897$	1.74010	−	2.94189i	0.0581002	−	0.0982267i
$898$	36.2331	−	42.6765i	1.20912	−	1.42413i
$899$			24.3016i			0.810503i
$900$	7.78418	−	6.10982i	0.259473	−	0.203661i
$901$		−	12.8847i		−	0.429253i
$902$	−11.0896	−	9.41523i	−0.369242	−	0.313493i
$903$	−32.6418	+	55.1856i	−1.08625	+	1.83646i
$904$	−23.4061	−	14.0613i	−0.778476	−	0.467673i
$905$			7.85518i			0.261115i
$906$	23.6043	−	8.15723i	0.784201	−	0.271006i
$907$	−0.477448			−0.0158534			−0.00792670	−	0.999969i	$-0.502523\pi$
$907$	−0.477448			−0.0158534			−0.00792670	+	0.999969i	$0.502523\pi$
$908$	40.9028	−	6.72470i	1.35741	−	0.223167i
$909$	4.52331	+	8.23054i	0.150029	+	0.272990i
$910$	−16.7592	−	14.2289i	−0.555562	−	0.471682i
$911$	−3.24981			−0.107671			−0.0538355	−	0.998550i	$-0.517145\pi$
$911$	−3.24981			−0.107671			−0.0538355	+	0.998550i	$0.517145\pi$
$912$	−36.6198	−	7.73793i	−1.21260	−	0.256228i
$913$	−19.4905			−0.645041
$914$	38.3581	+	32.5667i	1.26877	+	1.07721i
$915$	24.0025	−	40.5797i	0.793499	−	1.34152i
$916$	1.62181	−	0.266637i	0.0535862	−	0.00880994i
$917$	15.1325			0.499720
$918$	31.3186	+	28.3418i	1.03367	+	0.935420i
$919$		−	43.8472i		−	1.44639i	−0.690646	−	0.723193i	$-0.742674\pi$
$919$		−	43.8472i		−	1.44639i	0.690646	−	0.723193i	$-0.257326\pi$
$920$	2.66623	−	4.43814i	0.0879031	−	0.146321i
$921$	−9.75038	−	5.76726i	−0.321286	−	0.190038i
$922$	12.3851	+	10.5152i	0.407883	+	0.346300i
$923$		−	23.4443i		−	0.771678i
$924$	−29.9324	+	76.9011i	−0.984705	+	2.52986i
$925$		−	10.5990i		−	0.348493i
$926$	21.0364	−	24.7773i	0.691298	−	0.814232i
$927$	−0.0575203	+	0.0316118i	−0.00188922	+	0.00103827i
$928$	−37.0112	−	14.6981i	−1.21495	−	0.482488i
$929$			22.1729i			0.727471i	0.931502	+	0.363735i	$0.118499\pi$
$929$			22.1729i			0.727471i	−0.931502	+	0.363735i	$0.881501\pi$
$930$	−14.6293	+	5.05563i	−0.479714	+	0.165781i
$931$	−62.2383			−2.03978
$932$	32.3537	−	5.31917i	1.05978	−	0.174235i
$933$	15.9640	+	9.44253i	0.522637	+	0.309135i
$934$	20.9268	−	24.6483i	0.684747	−	0.806516i
$935$	58.2412			1.90469
$936$	0.643782	−	16.7323i	0.0210427	−	0.546911i
$937$	−34.1567			−1.11585			−0.557925	−	0.829891i	$-0.688402\pi$
$937$	−34.1567			−1.11585			−0.557925	+	0.829891i	$0.688402\pi$
$938$	−13.1861	+	15.5311i	−0.430543	+	0.507107i
$939$	−29.4040	−	17.3922i	−0.959565	−	0.567574i
$940$	−1.69327	−	10.2993i	−0.0552283	−	0.335925i
$941$	−47.8273			−1.55913			−0.779563	−	0.626324i	$-0.784559\pi$
$941$	−47.8273			−1.55913			−0.779563	+	0.626324i	$0.784559\pi$
$942$	−10.7295	+	3.70793i	−0.349587	+	0.120811i
$943$			1.85833i			0.0605154i
$944$	−0.347877	−	1.02938i	−0.0113224	−	0.0335034i
$945$	−40.9131	−	1.29415i	−1.33090	−	0.0420987i
$946$	−43.5804	+	51.3303i	−1.41692	+	1.66889i
$947$			12.4792i			0.405520i	0.979228	+	0.202760i	$0.0649911\pi$
$947$			12.4792i			0.405520i	−0.979228	+	0.202760i	$0.935009\pi$
$948$	33.6490	+	13.0973i	1.09287	+	0.425380i
$949$		−	22.5016i		−	0.730434i
$950$	9.60547	+	8.15522i	0.311643	+	0.264590i
$951$	41.3637	+	24.4662i	1.34131	+	0.793372i
$952$	−36.0305	+	59.9754i	−1.16776	+	1.94381i
$953$			30.2700i			0.980540i	0.871571	+	0.490270i	$0.163102\pi$
$953$			30.2700i			0.980540i	−0.871571	+	0.490270i	$0.836898\pi$
$954$	−1.90252	+	9.31813i	−0.0615963	+	0.301686i
$955$	−8.07242			−0.261217
$956$	−2.70972	−	16.4818i	−0.0876385	−	0.533059i
$957$	−34.3612	+	58.0925i	−1.11074	+	1.87787i
$958$	−10.2479	−	8.70062i	−0.331094	−	0.281104i
$959$	−17.4833			−0.564565
$960$	1.14840	−	25.3381i	0.0370643	−	0.817785i
$961$	19.0834			0.615593
$962$	−13.6719	−	11.6077i	−0.440800	−	0.374247i
$963$	31.2848	−	17.1934i	1.00814	−	0.554050i
$964$	−5.53528	−	33.6682i	−0.178279	−	1.08438i
$965$	24.5740			0.791064
$966$	9.96336	−	3.44316i	0.320566	−	0.110782i
$967$			50.0098i			1.60821i	0.594489	+	0.804104i	$0.297354\pi$
$967$			50.0098i			1.60821i	−0.594489	+	0.804104i	$0.702646\pi$
$968$	−28.6072	+	47.6188i	−0.919471	+	1.53053i
$969$	−27.3816	+	46.2926i	−0.879625	+	1.48713i
$970$	38.2934	+	32.5118i	1.22953	+	1.04389i
$971$		−	45.9021i		−	1.47307i	−0.676400	−	0.736535i	$-0.736461\pi$
$971$		−	45.9021i		−	1.47307i	0.676400	−	0.736535i	$-0.263539\pi$
$972$	−18.4645	−	25.1210i	−0.592248	−	0.805756i
$973$		−	36.2800i		−	1.16308i
$974$	−9.80109	+	11.5440i	−0.314047	+	0.369895i
$975$	−2.86989	+	4.85196i	−0.0919101	+	0.155387i
$976$	19.0436	+	56.3508i	0.609572	+	1.80374i
$977$		−	3.50831i		−	0.112241i	−0.998424	−	0.0561204i	$-0.982127\pi$
$977$		−	3.50831i		−	0.112241i	0.998424	−	0.0561204i	$-0.0178731\pi$
$978$	−1.12869	−	3.26605i	−0.0360915	−	0.104437i
$979$	3.92419			0.125418
$980$	−6.84234	−	41.6183i	−0.218570	−	1.32945i
$981$	−10.2739	+	5.64630i	−0.328021	+	0.180272i
$982$	15.3648	−	18.0972i	0.490312	−	0.577504i
$983$	−22.7748			−0.726403			−0.363201	−	0.931711i	$-0.618316\pi$
$983$	−22.7748			−0.726403			−0.363201	+	0.931711i	$0.618316\pi$
$984$	4.33011	+	8.00819i	0.138039	+	0.255292i
$985$	−1.43238			−0.0456395
$986$	−37.0369	+	43.6233i	−1.17950	+	1.38925i
$987$	10.8191	−	18.2912i	0.344374	−	0.582214i
$988$	21.0392	−	3.45899i	0.669347	−	0.110045i
$989$	8.60166			0.273517
$990$	−42.1195	−	8.59971i	−1.33865	−	0.273317i
$991$			39.1893i			1.24489i	0.782664	+	0.622444i	$0.213860\pi$
$991$			39.1893i			1.24489i	−0.782664	+	0.622444i	$0.786140\pi$
$992$	7.20740	−	18.1490i	0.228835	−	0.576230i
$993$	−22.3416	−	13.2148i	−0.708988	−	0.419360i
$994$	46.7970	−	55.1190i	1.48431	−	1.74827i
$995$			2.50281i			0.0793444i
$996$	11.3667	+	4.42429i	0.360168	+	0.140189i
$997$		−	10.7675i		−	0.341011i	−0.985357	−	0.170505i	$-0.945460\pi$
$997$		−	10.7675i		−	0.341011i	0.985357	−	0.170505i	$-0.0545400\pi$
$998$	−16.7138	−	14.1903i	−0.529067	−	0.449187i
$999$	−33.3763	−	1.05575i	−1.05598	−	0.0334024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.j.d.323.9	yes	42
3.2	odd	2		552.2.j.c.323.34	yes	42
4.3	odd	2		2208.2.j.d.47.7		42
8.3	odd	2		552.2.j.c.323.33	✓	42
8.5	even	2		2208.2.j.c.47.7		42
12.11	even	2		2208.2.j.c.47.8		42
24.5	odd	2		2208.2.j.d.47.8		42
24.11	even	2	inner	552.2.j.d.323.10	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.j.c.323.33	✓	42	8.3	odd	2
552.2.j.c.323.34	yes	42	3.2	odd	2
552.2.j.d.323.9	yes	42	1.1	even	1	trivial
552.2.j.d.323.10	yes	42	24.11	even	2	inner
2208.2.j.c.47.7		42	8.5	even	2
2208.2.j.c.47.8		42	12.11	even	2
2208.2.j.d.47.7		42	4.3	odd	2
2208.2.j.d.47.8		42	24.5	odd	2

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07807 - 0.915298i) q^{2} +(1.49079 + 0.881788i) q^{3} +(0.324458 + 1.97351i) q^{4} +1.83050 q^{5} +(-0.800072 - 2.31514i) q^{6} +4.30356i q^{7} +(1.45656 - 2.42455i) q^{8} +(1.44490 + 2.62912i) q^{9} +O(q^{10})\)	\(q+(-1.07807 - 0.915298i) q^{2} +(1.49079 + 0.881788i) q^{3} +(0.324458 + 1.97351i) q^{4} +1.83050 q^{5} +(-0.800072 - 2.31514i) q^{6} +4.30356i q^{7} +(1.45656 - 2.42455i) q^{8} +(1.44490 + 2.62912i) q^{9} +(-1.97340 - 1.67545i) q^{10} -5.53536i q^{11} +(-1.25652 + 3.22818i) q^{12} -1.97338i q^{13} +(3.93904 - 4.63953i) q^{14} +(2.72889 + 1.61411i) q^{15} +(-3.78945 + 1.28064i) q^{16} +5.74797i q^{17} +(0.848726 - 4.15688i) q^{18} +5.40233 q^{19} +(0.593920 + 3.61250i) q^{20} +(-3.79483 + 6.41570i) q^{21} +(-5.06651 + 5.96750i) q^{22} +1.00000 q^{23} +(4.30936 - 2.33011i) q^{24} -1.64927 q^{25} +(-1.80623 + 2.12743i) q^{26} +(-0.164281 + 5.19355i) q^{27} +(-8.49310 + 1.39632i) q^{28} -7.03976 q^{29} +(-1.46453 - 4.23787i) q^{30} -3.45204i q^{31} +(5.25745 + 2.08787i) q^{32} +(4.88102 - 8.25206i) q^{33} +(5.26111 - 6.19670i) q^{34} +7.87767i q^{35} +(-4.71977 + 3.70456i) q^{36} +6.42648i q^{37} +(-5.82408 - 4.94474i) q^{38} +(1.74010 - 2.94189i) q^{39} +(2.66623 - 4.43814i) q^{40} +1.85833i q^{41} +(9.96336 - 3.44316i) q^{42} +8.60166 q^{43} +(10.9241 - 1.79599i) q^{44} +(2.64489 + 4.81260i) q^{45} +(-1.07807 - 0.915298i) q^{46} -2.85100 q^{47} +(-6.77853 - 1.43233i) q^{48} -11.5206 q^{49} +(1.77802 + 1.50957i) q^{50} +(-5.06849 + 8.56901i) q^{51} +(3.89447 - 0.640277i) q^{52} -2.24162 q^{53} +(4.93076 - 5.44864i) q^{54} -10.1325i q^{55} +(10.4342 + 6.26839i) q^{56} +(8.05373 + 4.76371i) q^{57} +(7.58934 + 6.44348i) q^{58} +0.271643i q^{59} +(-2.30005 + 5.90919i) q^{60} -14.8704i q^{61} +(-3.15965 + 3.72154i) q^{62} +(-11.3146 + 6.21822i) q^{63} +(-3.75687 - 7.06300i) q^{64} -3.61226i q^{65} +(-12.8152 + 4.42869i) q^{66} -3.34755 q^{67} +(-11.3437 + 1.86497i) q^{68} +(1.49079 + 0.881788i) q^{69} +(7.21042 - 8.49266i) q^{70} +11.8803 q^{71} +(8.47901 + 0.326234i) q^{72} +11.4026 q^{73} +(5.88215 - 6.92818i) q^{74} +(-2.45871 - 1.45431i) q^{75} +(1.75283 + 10.6615i) q^{76} +23.8218 q^{77} +(-4.56865 + 1.57884i) q^{78} -10.4235i q^{79} +(-6.93660 + 2.34421i) q^{80} +(-4.82452 + 7.59763i) q^{81} +(1.70092 - 2.00340i) q^{82} -3.52108i q^{83} +(-13.8927 - 5.40749i) q^{84} +10.5217i q^{85} +(-9.27316 - 7.87308i) q^{86} +(-10.4948 - 6.20758i) q^{87} +(-13.4208 - 8.06259i) q^{88} +0.708930i q^{89} +(1.55359 - 7.60917i) q^{90} +8.49254 q^{91} +(0.324458 + 1.97351i) q^{92} +(3.04397 - 5.14627i) q^{93} +(3.07357 + 2.60952i) q^{94} +9.88897 q^{95} +(5.99670 + 7.74852i) q^{96} -19.4048 q^{97} +(12.4200 + 10.5448i) q^{98} +(14.5531 - 7.99806i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9}+O(q^{10}) \) 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9	\( 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9} - 4 q^{10} - 21 q^{12} - 4 q^{14} - 8 q^{15} - 12 q^{16} - 11 q^{18} + 4 q^{19} - 2 q^{20} + 8 q^{21} + 18 q^{22} + 42 q^{23} + 28 q^{24} + 22 q^{25} + 11 q^{26} - 16 q^{27} + 6 q^{28} + 2 q^{30} - 20 q^{32} + 12 q^{33} + 14 q^{34} - 24 q^{36} - 22 q^{38} + 8 q^{39} + 4 q^{40} - 44 q^{42} + 28 q^{43} + 56 q^{44} - 8 q^{45} + 30 q^{48} - 50 q^{49} + 20 q^{50} + 28 q^{51} - q^{52} + 24 q^{53} + 52 q^{54} - 34 q^{56} - 8 q^{57} - 21 q^{58} - 42 q^{60} - 79 q^{62} - 16 q^{63} + 7 q^{64} - 62 q^{66} - 4 q^{67} + 20 q^{68} + 2 q^{69} - 8 q^{70} + 22 q^{72} + 4 q^{73} + 36 q^{74} - 6 q^{75} + 14 q^{76} + 32 q^{77} + 27 q^{78} - 52 q^{80} + 18 q^{81} + 11 q^{82} - 80 q^{84} - 28 q^{86} - 48 q^{87} - 38 q^{88} - 46 q^{90} - 8 q^{91} + 4 q^{92} - 22 q^{93} + q^{94} - 16 q^{95} + 9 q^{96} + 20 q^{97} + 64 q^{98}+O(q^{100}) \) 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9 - 4 * q^10 - 21 * q^12 - 4 * q^14 - 8 * q^15 - 12 * q^16 - 11 * q^18 + 4 * q^19 - 2 * q^20 + 8 * q^21 + 18 * q^22 + 42 * q^23 + 28 * q^24 + 22 * q^25 + 11 * q^26 - 16 * q^27 + 6 * q^28 + 2 * q^30 - 20 * q^32 + 12 * q^33 + 14 * q^34 - 24 * q^36 - 22 * q^38 + 8 * q^39 + 4 * q^40 - 44 * q^42 + 28 * q^43 + 56 * q^44 - 8 * q^45 + 30 * q^48 - 50 * q^49 + 20 * q^50 + 28 * q^51 - q^52 + 24 * q^53 + 52 * q^54 - 34 * q^56 - 8 * q^57 - 21 * q^58 - 42 * q^60 - 79 * q^62 - 16 * q^63 + 7 * q^64 - 62 * q^66 - 4 * q^67 + 20 * q^68 + 2 * q^69 - 8 * q^70 + 22 * q^72 + 4 * q^73 + 36 * q^74 - 6 * q^75 + 14 * q^76 + 32 * q^77 + 27 * q^78 - 52 * q^80 + 18 * q^81 + 11 * q^82 - 80 * q^84 - 28 * q^86 - 48 * q^87 - 38 * q^88 - 46 * q^90 - 8 * q^91 + 4 * q^92 - 22 * q^93 + q^94 - 16 * q^95 + 9 * q^96 + 20 * q^97 + 64 * q^98

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