LMFDB - Embedded newform 961.2.d.q.628.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(374,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.374"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,4,6,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			628.1
Root			$1.83925i$ of defining polynomial
Character	$\chi$	$=$	961.628
Dual form			961.2.d.q.531.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.213065 + 0.655747i) q^{2} +(0.278857 + 0.858234i) q^{3} +(1.23343 + 0.896137i) q^{4} +3.70752 q^{5} -0.622199 q^{6} +(-0.617599 - 0.448712i) q^{7} +(-1.96606 + 1.42843i) q^{8} +(1.76825 - 1.28471i) q^{9} +(-0.789942 + 2.43119i) q^{10} +(-3.32961 - 2.41910i) q^{11} +(-0.425146 + 1.30846i) q^{12} +(0.899163 + 2.76734i) q^{13} +(0.425830 - 0.309383i) q^{14} +(1.03387 + 3.18192i) q^{15} +(0.424467 + 1.30637i) q^{16} +(1.05862 - 0.769131i) q^{17} +(0.465690 + 1.43325i) q^{18} +(-1.17412 + 3.61358i) q^{19} +(4.57295 + 3.32244i) q^{20} +(0.212878 - 0.655171i) q^{21} +(2.29574 - 1.66795i) q^{22} +(-2.65597 + 1.92967i) q^{23} +(-1.77418 - 1.28901i) q^{24} +8.74568 q^{25} -2.00625 q^{26} +(3.78584 + 2.75057i) q^{27} +(-0.359656 - 1.10691i) q^{28} +(-1.51283 + 4.65602i) q^{29} -2.30681 q^{30} -5.80746 q^{32} +(1.14767 - 3.53217i) q^{33} +(0.278801 + 0.858060i) q^{34} +(-2.28976 - 1.66361i) q^{35} +3.33228 q^{36} +10.4128 q^{37} +(-2.11943 - 1.53985i) q^{38} +(-2.12429 + 1.54338i) q^{39} +(-7.28921 + 5.29592i) q^{40} +(0.233600 - 0.718947i) q^{41} +(0.384269 + 0.279188i) q^{42} +(2.21160 - 6.80661i) q^{43} +(-1.93898 - 5.96757i) q^{44} +(6.55580 - 4.76307i) q^{45} +(-0.699483 - 2.15279i) q^{46} +(-0.270719 - 0.833189i) q^{47} +(-1.00281 + 0.728584i) q^{48} +(-1.98303 - 6.10315i) q^{49} +(-1.86340 + 5.73495i) q^{50} +(0.955298 + 0.694065i) q^{51} +(-1.37086 + 4.21908i) q^{52} +(2.89281 - 2.10175i) q^{53} +(-2.61031 + 1.89650i) q^{54} +(-12.3446 - 8.96886i) q^{55} +1.85519 q^{56} -3.42871 q^{57} +(-2.73084 - 1.98407i) q^{58} +(0.286542 + 0.881886i) q^{59} +(-1.57623 + 4.85115i) q^{60} -2.31704 q^{61} -1.66853 q^{63} +(0.388433 - 1.19547i) q^{64} +(3.33366 + 10.2599i) q^{65} +(2.07168 + 1.50516i) q^{66} -2.08690 q^{67} +1.99498 q^{68} +(-2.39675 - 1.74134i) q^{69} +(1.57877 - 1.14704i) q^{70} +(6.25862 - 4.54716i) q^{71} +(-1.64137 + 5.05162i) q^{72} +(-4.57700 - 3.32538i) q^{73} +(-2.21860 + 6.82815i) q^{74} +(2.43880 + 7.50584i) q^{75} +(-4.68646 + 3.40491i) q^{76} +(0.970882 + 2.98807i) q^{77} +(-0.559458 - 1.72183i) q^{78} +(-11.4029 + 8.28467i) q^{79} +(1.57372 + 4.84341i) q^{80} +(0.721302 - 2.21994i) q^{81} +(0.421675 + 0.306365i) q^{82} +(4.35952 - 13.4172i) q^{83} +(0.849692 - 0.617338i) q^{84} +(3.92484 - 2.85157i) q^{85} +(3.99219 + 2.90050i) q^{86} -4.41782 q^{87} +10.0017 q^{88} +(-3.58784 - 2.60672i) q^{89} +(1.72655 + 5.31379i) q^{90} +(0.686415 - 2.11257i) q^{91} -5.00520 q^{92} +0.604042 q^{94} +(-4.35308 + 13.3974i) q^{95} +(-1.61945 - 4.98416i) q^{96} +(4.26970 + 3.10212i) q^{97} +4.42463 q^{98} -8.99540 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + 6 q^{3} + 6 q^{4} + 6 q^{5} + 22 q^{6} - 9 q^{7} - 8 q^{8} - 10 q^{9} - 6 q^{10} - 4 q^{11} + 5 q^{12} - 9 q^{13} - 18 q^{14} - 4 q^{15} - 2 q^{16} - 17 q^{17} - 14 q^{18} - 7 q^{19} + 36 q^{20}+ \cdots + 12 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 + 6 * q^5 + 22 * q^6 - 9 * q^7 - 8 * q^8 - 10 * q^9 - 6 * q^10 - 4 * q^11 + 5 * q^12 - 9 * q^13 - 18 * q^14 - 4 * q^15 - 2 * q^16 - 17 * q^17 - 14 * q^18 - 7 * q^19 + 36 * q^20 - 2 * q^21 + 8 * q^22 - 21 * q^23 - 5 * q^24 + 26 * q^25 + 18 * q^26 - 9 * q^27 + 20 * q^28 - 26 * q^29 + 22 * q^30 - 42 * q^32 + 7 * q^33 + 56 * q^34 + 21 * q^35 - 2 * q^36 - 16 * q^37 + 24 * q^38 + 2 * q^39 - 13 * q^40 + 6 * q^41 - 12 * q^42 + 16 * q^43 - 37 * q^44 - 5 * q^45 + 16 * q^46 + 4 * q^47 - 37 * q^48 - 39 * q^49 - 21 * q^50 - 11 * q^51 + 18 * q^52 - 3 * q^53 - 39 * q^54 - 29 * q^55 + 60 * q^56 - 34 * q^57 - 10 * q^58 - 3 * q^59 - 35 * q^60 + 60 * q^61 - 46 * q^63 - 32 * q^64 - 9 * q^65 + 20 * q^66 - 26 * q^67 + 60 * q^68 - 21 * q^69 + 27 * q^70 + 18 * q^71 - 4 * q^72 + 9 * q^73 - 64 * q^74 - 19 * q^75 + 9 * q^76 + 42 * q^77 + 15 * q^78 - 14 * q^79 + 18 * q^80 + 29 * q^81 + 32 * q^82 - 67 * q^83 - 39 * q^84 + 63 * q^85 + 23 * q^86 - 30 * q^87 - 34 * q^88 - 26 * q^89 - 24 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 + 28 * q^95 - 4 * q^96 - 37 * q^97 + 20 * q^98 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.213065	+	0.655747i	−0.150660	+	0.463683i	−0.997695	−	0.0678533i	$-0.978385\pi$
$2$	−0.213065	+	0.655747i	−0.150660	+	0.463683i	0.847036	+	0.531536i	$0.178385\pi$
$3$	0.278857	+	0.858234i	0.160998	+	0.495502i	0.998719	−	0.0505969i	$-0.0161124\pi$
$3$	0.278857	+	0.858234i	0.160998	+	0.495502i	−0.837721	+	0.546099i	$0.816112\pi$
$4$	1.23343	+	0.896137i	0.616714	+	0.448069i
$5$	3.70752			1.65805			0.829026	−	0.559210i	$-0.188896\pi$
$5$	3.70752			1.65805			0.829026	+	0.559210i	$0.188896\pi$
$6$	−0.622199			−0.254012
$7$	−0.617599	−	0.448712i	−0.233430	−	0.169597i	0.464921	−	0.885352i	$-0.346083\pi$
$7$	−0.617599	−	0.448712i	−0.233430	−	0.169597i	−0.698351	+	0.715755i	$0.746083\pi$
$8$	−1.96606	+	1.42843i	−0.695108	+	0.505025i
$9$	1.76825	−	1.28471i	0.589415	−	0.428235i
$10$	−0.789942	+	2.43119i	−0.249802	+	0.768810i
$11$	−3.32961	−	2.41910i	−1.00391	−	0.729387i	−0.0409908	−	0.999160i	$-0.513051\pi$
$11$	−3.32961	−	2.41910i	−1.00391	−	0.729387i	−0.962924	+	0.269773i	$0.913051\pi$
$12$	−0.425146	+	1.30846i	−0.122729	+	0.377721i
$13$	0.899163	+	2.76734i	0.249383	+	0.767521i	0.994885	+	0.101018i	$0.0322099\pi$
$13$	0.899163	+	2.76734i	0.249383	+	0.767521i	−0.745502	+	0.666504i	$0.767790\pi$
$14$	0.425830	−	0.309383i	0.113808	−	0.0826862i
$15$	1.03387	+	3.18192i	0.266943	+	0.821568i
$16$	0.424467	+	1.30637i	0.106117	+	0.326594i
$17$	1.05862	−	0.769131i	0.256753	−	0.186542i	−0.451962	−	0.892037i	$-0.649276\pi$
$17$	1.05862	−	0.769131i	0.256753	−	0.186542i	0.708714	+	0.705496i	$0.249276\pi$
$18$	0.465690	+	1.43325i	0.109764	+	0.337820i
$19$	−1.17412	+	3.61358i	−0.269362	+	0.829012i	0.721294	+	0.692629i	$0.243548\pi$
$19$	−1.17412	+	3.61358i	−0.269362	+	0.829012i	−0.990656	+	0.136383i	$0.956452\pi$
$20$	4.57295	+	3.32244i	1.02254	+	0.742921i
$21$	0.212878	−	0.655171i	0.0464538	−	0.142970i
$22$	2.29574	−	1.66795i	0.489454	−	0.355609i
$23$	−2.65597	+	1.92967i	−0.553808	+	0.402365i	−0.829187	−	0.558971i	$-0.811196\pi$
$23$	−2.65597	+	1.92967i	−0.553808	+	0.402365i	0.275380	+	0.961336i	$0.411196\pi$
$24$	−1.77418	−	1.28901i	−0.362152	−	0.263119i
$25$	8.74568			1.74914
$26$	−2.00625			−0.393458
$27$	3.78584	+	2.75057i	0.728585	+	0.529348i
$28$	−0.359656	−	1.10691i	−0.0679685	−	0.209186i
$29$	−1.51283	+	4.65602i	−0.280926	+	0.864602i	0.706664	+	0.707549i	$0.250199\pi$
$29$	−1.51283	+	4.65602i	−0.280926	+	0.864602i	−0.987590	+	0.157052i	$0.949801\pi$
$30$	−2.30681			−0.421164
$31$		0			0
$31$		0			0
$32$	−5.80746			−1.02662
$33$	1.14767	−	3.53217i	0.199784	−	0.614872i
$34$	0.278801	+	0.858060i	0.0478139	+	0.147156i
$35$	−2.28976	−	1.66361i	−0.387040	−	0.281201i
$36$	3.33228			0.555379
$37$	10.4128			1.71185			0.855925	−	0.517099i	$-0.172988\pi$
$37$	10.4128			1.71185			0.855925	+	0.517099i	$0.172988\pi$
$38$	−2.11943	−	1.53985i	−0.343817	−	0.249797i
$39$	−2.12429	+	1.54338i	−0.340158	+	0.247139i
$40$	−7.28921	+	5.29592i	−1.15252	+	0.837358i
$41$	0.233600	−	0.718947i	0.0364822	−	0.112281i	−0.931157	−	0.364618i	$-0.881199\pi$
$41$	0.233600	−	0.718947i	0.0364822	−	0.112281i	0.967639	+	0.252338i	$0.0811994\pi$
$42$	0.384269	+	0.279188i	0.0592940	+	0.0430796i
$43$	2.21160	−	6.80661i	0.337266	−	1.03800i	−0.628329	−	0.777948i	$-0.716261\pi$
$43$	2.21160	−	6.80661i	0.337266	−	1.03800i	0.965595	−	0.260050i	$-0.0837391\pi$
$44$	−1.93898	−	5.96757i	−0.292313	−	0.899645i
$45$	6.55580	−	4.76307i	0.977281	−	0.710036i
$46$	−0.699483	−	2.15279i	−0.103133	−	0.317411i
$47$	−0.270719	−	0.833189i	−0.0394885	−	0.121533i	0.929369	−	0.369152i	$-0.120352\pi$
$47$	−0.270719	−	0.833189i	−0.0394885	−	0.121533i	−0.968857	+	0.247619i	$0.920352\pi$
$48$	−1.00281	+	0.728584i	−0.144743	+	0.105162i
$49$	−1.98303	−	6.10315i	−0.283290	−	0.871878i
$50$	−1.86340	+	5.73495i	−0.263524	+	0.811044i
$51$	0.955298	+	0.694065i	0.133768	+	0.0971885i
$52$	−1.37086	+	4.21908i	−0.190104	+	0.585081i
$53$	2.89281	−	2.10175i	0.397357	−	0.288697i	−0.371106	−	0.928590i	$-0.621021\pi$
$53$	2.89281	−	2.10175i	0.397357	−	0.288697i	0.768464	+	0.639893i	$0.221021\pi$
$54$	−2.61031	+	1.89650i	−0.355218	+	0.258081i
$55$	−12.3446	−	8.96886i	−1.66454	−	1.20936i
$56$	1.85519			0.247910
$57$	−3.42871			−0.454144
$58$	−2.73084	−	1.98407i	−0.358577	−	0.260521i
$59$	0.286542	+	0.881886i	0.0373046	+	0.114812i	0.967975	−	0.251048i	$-0.0807751\pi$
$59$	0.286542	+	0.881886i	0.0373046	+	0.114812i	−0.930670	+	0.365859i	$0.880775\pi$
$60$	−1.57623	+	4.85115i	−0.203491	+	0.626281i
$61$	−2.31704			−0.296666			−0.148333	−	0.988937i	$-0.547391\pi$
$61$	−2.31704			−0.296666			−0.148333	+	0.988937i	$0.547391\pi$
$62$		0			0
$63$	−1.66853			−0.210215
$64$	0.388433	−	1.19547i	0.0485541	−	0.149434i
$65$	3.33366	+	10.2599i	0.413490	+	1.27259i
$66$	2.07168	+	1.50516i	0.255006	+	0.185273i
$67$	−2.08690			−0.254955			−0.127478	−	0.991841i	$-0.540688\pi$
$67$	−2.08690			−0.254955			−0.127478	+	0.991841i	$0.540688\pi$
$68$	1.99498			0.241926
$69$	−2.39675	−	1.74134i	−0.288535	−	0.209633i
$70$	1.57877	−	1.14704i	0.188699	−	0.137098i
$71$	6.25862	−	4.54716i	0.742762	−	0.539648i	−0.150813	−	0.988562i	$-0.548189\pi$
$71$	6.25862	−	4.54716i	0.742762	−	0.539648i	0.893575	+	0.448914i	$0.148189\pi$
$72$	−1.64137	+	5.05162i	−0.193438	+	0.595340i
$73$	−4.57700	−	3.32538i	−0.535697	−	0.389207i	0.286788	−	0.957994i	$-0.407413\pi$
$73$	−4.57700	−	3.32538i	−0.535697	−	0.389207i	−0.822484	+	0.568788i	$0.807413\pi$
$74$	−2.21860	+	6.82815i	−0.257907	+	0.793756i
$75$	2.43880	+	7.50584i	0.281608	+	0.866700i
$76$	−4.68646	+	3.40491i	−0.537574	+	0.390570i
$77$	0.970882	+	2.98807i	0.110642	+	0.340522i
$78$	−0.559458	−	1.72183i	−0.0633461	−	0.194959i
$79$	−11.4029	+	8.28467i	−1.28292	+	0.932098i	−0.999637	−	0.0269378i	$-0.991424\pi$
$79$	−11.4029	+	8.28467i	−1.28292	+	0.932098i	−0.283286	+	0.959036i	$0.591424\pi$
$80$	1.57372	+	4.84341i	0.175947	+	0.541509i
$81$	0.721302	−	2.21994i	0.0801447	−	0.246660i
$82$	0.421675	+	0.306365i	0.0465662	+	0.0338323i
$83$	4.35952	−	13.4172i	0.478520	−	1.47273i	−0.362631	−	0.931933i	$-0.618122\pi$
$83$	4.35952	−	13.4172i	0.478520	−	1.47273i	0.841151	−	0.540800i	$-0.181878\pi$
$84$	0.849692	−	0.617338i	0.0927090	−	0.0673571i
$85$	3.92484	−	2.85157i	0.425709	−	0.309296i
$86$	3.99219	+	2.90050i	0.430489	+	0.312769i
$87$	−4.41782			−0.473640
$88$	10.0017			1.06619
$89$	−3.58784	−	2.60672i	−0.380310	−	0.276311i	0.381163	−	0.924508i	$-0.375524\pi$
$89$	−3.58784	−	2.60672i	−0.380310	−	0.276311i	−0.761473	+	0.648196i	$0.775524\pi$
$90$	1.72655	+	5.31379i	0.181995	+	0.560122i
$91$	0.686415	−	2.11257i	0.0719559	−	0.221457i
$92$	−5.00520			−0.521828
$93$		0			0
$94$	0.604042			0.0623021
$95$	−4.35308	+	13.3974i	−0.446617	+	1.37454i
$96$	−1.61945	−	4.98416i	−0.165285	−	0.508694i
$97$	4.26970	+	3.10212i	0.433522	+	0.314972i	0.783056	−	0.621951i	$-0.213660\pi$
$97$	4.26970	+	3.10212i	0.433522	+	0.314972i	−0.349533	+	0.936924i	$0.613660\pi$
$98$	4.42463			0.446955
$99$	−8.99540			−0.904072
$100$	10.7872	+	7.83733i	1.07872	+	0.783733i
$101$	−3.08028	+	2.23795i	−0.306499	+	0.222684i	−0.730393	−	0.683027i	$-0.760663\pi$
$101$	−3.08028	+	2.23795i	−0.306499	+	0.222684i	0.423894	+	0.905712i	$0.360663\pi$
$102$	−0.658671	+	0.478553i	−0.0652181	+	0.0473838i
$103$	−1.93003	+	5.94001i	−0.190171	+	0.585286i	−0.999999	−	0.00138104i	$-0.999560\pi$
$103$	−1.93003	+	5.94001i	−0.190171	+	0.585286i	0.809828	+	0.586667i	$0.199560\pi$
$104$	−5.72075	−	4.15637i	−0.560966	−	0.407565i
$105$	0.789248	−	2.42906i	0.0770227	−	0.237052i
$106$	0.761857	+	2.34476i	0.0739981	+	0.227743i
$107$	−1.88289	+	1.36800i	−0.182026	+	0.132250i	−0.675067	−	0.737756i	$-0.735885\pi$
$107$	−1.88289	+	1.36800i	−0.182026	+	0.132250i	0.493041	+	0.870006i	$0.335885\pi$
$108$	2.20467	+	6.78526i	0.212144	+	0.652912i
$109$	0.456365	+	1.40455i	0.0437118	+	0.134531i	0.970531	−	0.240978i	$-0.0774680\pi$
$109$	0.456365	+	1.40455i	0.0437118	+	0.134531i	−0.926819	+	0.375509i	$0.877468\pi$
$110$	8.51150	−	6.18396i	0.811539	−	0.589618i
$111$	2.90368	+	8.93661i	0.275605	+	0.848225i
$112$	0.324035	−	0.997279i	0.0306185	−	0.0942340i
$113$	−5.16197	−	3.75039i	−0.485597	−	0.352807i	0.317891	−	0.948127i	$-0.397025\pi$
$113$	−5.16197	−	3.75039i	−0.485597	−	0.352807i	−0.803489	+	0.595320i	$0.797025\pi$
$114$	0.730538	−	2.24836i	0.0684212	−	0.210579i
$115$	−9.84705	+	7.15430i	−0.918242	+	0.667142i
$116$	−6.03840	+	4.38716i	−0.560652	+	0.407337i
$117$	5.14516	+	3.73818i	0.475670	+	0.345594i
$118$	−0.639346			−0.0588566
$119$	−0.998919			−0.0915708
$120$	−6.57779	−	4.77904i	−0.600467	−	0.436265i
$121$	1.83505	+	5.64771i	0.166823	+	0.513428i
$122$	0.493680	−	1.51939i	0.0446957	−	0.137559i
$123$	0.682166			0.0615089
$124$		0			0
$125$	13.8872			1.24211
$126$	0.355505	−	1.09413i	0.0316709	−	0.0974730i
$127$	0.442517	+	1.36193i	0.0392670	+	0.120851i	0.968768	−	0.247967i	$-0.0797624\pi$
$127$	0.442517	+	1.36193i	0.0392670	+	0.120851i	−0.929501	+	0.368818i	$0.879762\pi$
$128$	−8.69550	−	6.31765i	−0.768581	−	0.558407i
$129$	6.45838			0.568629
$130$	−7.43821			−0.652374
$131$	−5.09106	−	3.69887i	−0.444808	−	0.323172i	0.342734	−	0.939432i	$-0.388647\pi$
$131$	−5.09106	−	3.69887i	−0.444808	−	0.323172i	−0.787543	+	0.616260i	$0.788647\pi$
$132$	4.58088	−	3.32820i	0.398714	−	0.289683i
$133$	2.34659	−	1.70490i	0.203475	−	0.147833i
$134$	0.444645	−	1.36848i	0.0384115	−	0.118218i
$135$	14.0361	+	10.1978i	1.20803	+	0.877687i
$136$	−0.982661	+	3.02432i	−0.0842625	+	0.259333i
$137$	−3.93994	−	12.1259i	−0.336612	−	1.03598i	−0.965923	−	0.258830i	$-0.916663\pi$
$137$	−3.93994	−	12.1259i	−0.336612	−	1.03598i	0.629311	−	0.777153i	$-0.283337\pi$
$138$	1.65254	−	1.20064i	0.140674	−	0.102205i
$139$	−5.78287	−	17.7978i	−0.490496	−	1.50959i	−0.823860	−	0.566794i	$-0.808184\pi$
$139$	−5.78287	−	17.7978i	−0.490496	−	1.50959i	0.333363	−	0.942798i	$-0.391816\pi$
$140$	−1.33343	−	4.10387i	−0.112695	−	0.346841i
$141$	0.639579	−	0.464681i	0.0538623	−	0.0391332i
$142$	1.64829	+	5.07291i	0.138321	+	0.425709i
$143$	3.70061	−	11.3893i	0.309461	−	0.952423i
$144$	2.42887	+	1.76468i	0.202406	+	0.147056i
$145$	−5.60885	+	17.2623i	−0.465790	+	1.43355i
$146$	3.15581	−	2.29283i	0.261176	−	0.189756i
$147$	4.68495	−	3.40381i	0.386408	−	0.280742i
$148$	12.8434	+	9.33128i	1.05572	+	0.767027i
$149$	−20.1353			−1.64955			−0.824774	−	0.565462i	$-0.808698\pi$
$149$	−20.1353			−1.64955			−0.824774	+	0.565462i	$0.808698\pi$
$150$	−5.44155			−0.444301
$151$	12.4366	+	9.03571i	1.01207	+	0.735315i	0.964643	−	0.263559i	$-0.0848964\pi$
$151$	12.4366	+	9.03571i	1.01207	+	0.735315i	0.0474314	+	0.998874i	$0.484896\pi$
$152$	−2.85334	−	8.78167i	−0.231436	−	0.712287i
$153$	0.883790	−	2.72003i	0.0714502	−	0.219901i
$154$	−2.16628			−0.174564
$155$		0			0
$156$	−4.00324			−0.320515
$157$	4.68076	−	14.4059i	0.373566	−	1.14972i	−0.570876	−	0.821037i	$-0.693396\pi$
$157$	4.68076	−	14.4059i	0.373566	−	1.14972i	0.944441	−	0.328680i	$-0.106604\pi$
$158$	−3.00309	−	9.24256i	−0.238913	−	0.735299i
$159$	2.61047	+	1.89662i	0.207024	+	0.150412i
$160$	−21.5313			−1.70220
$161$	2.50619			0.197515
$162$	1.30203	+	0.945983i	0.102297	+	0.0743234i
$163$	0.845317	−	0.614159i	0.0662103	−	0.0481046i	−0.554188	−	0.832392i	$-0.686971\pi$
$163$	0.845317	−	0.614159i	0.0662103	−	0.0481046i	0.620398	+	0.784287i	$0.286971\pi$
$164$	0.932404	−	0.677431i	0.0728085	−	0.0528985i
$165$	4.25501	−	13.0956i	0.331252	−	1.01949i
$166$	7.86944	+	5.71748i	0.610787	+	0.443763i
$167$	3.48862	−	10.7369i	0.269957	−	0.830843i	−0.720552	−	0.693400i	$-0.756112\pi$
$167$	3.48862	−	10.7369i	0.269957	−	0.830843i	0.990510	−	0.137443i	$-0.0438883\pi$
$168$	0.517333	+	1.59219i	0.0399131	+	0.122840i
$169$	3.66756	−	2.66464i	0.282120	−	0.204972i
$170$	1.03366	+	3.18127i	0.0792779	+	0.243992i
$171$	2.56625	+	7.89810i	0.196246	+	0.603983i
$172$	8.82750	−	6.41356i	0.673091	−	0.489029i
$173$	−6.38203	−	19.6419i	−0.485217	−	1.49334i	−0.831667	−	0.555275i	$-0.812613\pi$
$173$	−6.38203	−	19.6419i	−0.485217	−	1.49334i	0.346450	−	0.938068i	$-0.387387\pi$
$174$	0.941283	−	2.89697i	0.0713585	−	0.219619i
$175$	−5.40132	−	3.92429i	−0.408301	−	0.296648i
$176$	1.74695	−	5.37655i	0.131681	−	0.405272i
$177$	−0.676961	+	0.491841i	−0.0508835	+	0.0369690i
$178$	2.47379	−	1.79731i	0.185418	−	0.134714i
$179$	−0.106517	−	0.0773892i	−0.00796146	−	0.00578434i	0.583797	−	0.811899i	$-0.301566\pi$
$179$	−0.106517	−	0.0773892i	−0.00796146	−	0.00578434i	−0.591759	+	0.806115i	$0.701566\pi$
$180$	12.3545			0.920848
$181$	−7.73199			−0.574714			−0.287357	−	0.957824i	$-0.592777\pi$
$181$	−7.73199			−0.574714			−0.287357	+	0.957824i	$0.592777\pi$
$182$	1.23906	+	0.900229i	0.0918451	+	0.0667294i
$183$	−0.646123	−	1.98856i	−0.0477628	−	0.146999i
$184$	2.46540	−	7.58772i	0.181752	−	0.559374i
$185$	38.6056			2.83834
$186$		0			0
$187$	−5.38539			−0.393819
$188$	0.412739	−	1.27028i	0.0301021	−	0.0926447i
$189$	−1.10392	−	3.39750i	−0.0802980	−	0.247132i
$190$	−7.85781	−	5.70903i	−0.570066	−	0.414177i
$191$	−21.1027			−1.52694			−0.763468	−	0.645846i	$-0.776505\pi$
$191$	−21.1027			−1.52694			−0.763468	+	0.645846i	$0.776505\pi$
$192$	1.13431			0.0818620
$193$	−4.58165	−	3.32877i	−0.329795	−	0.239610i	0.410549	−	0.911839i	$-0.365337\pi$
$193$	−4.58165	−	3.32877i	−0.329795	−	0.239610i	−0.740343	+	0.672229i	$0.765337\pi$
$194$	−2.94393	+	2.13889i	−0.211362	+	0.153563i
$195$	−7.87583	+	5.72212i	−0.564000	+	0.409770i
$196$	3.02333	−	9.30486i	0.215952	−	0.664633i
$197$	12.8753	+	9.35448i	0.917330	+	0.666479i	0.942858	−	0.333195i	$-0.108127\pi$
$197$	12.8753	+	9.35448i	0.917330	+	0.666479i	−0.0255278	+	0.999674i	$0.508127\pi$
$198$	1.91661	−	5.89871i	0.136207	−	0.419203i
$199$	1.31686	+	4.05288i	0.0933499	+	0.287301i	0.986820	−	0.161821i	$-0.0517367\pi$
$199$	1.31686	+	4.05288i	0.0933499	+	0.287301i	−0.893470	+	0.449122i	$0.851737\pi$
$200$	−17.1945	+	12.4926i	−1.21584	+	0.883358i
$201$	−0.581946	−	1.79105i	−0.0410473	−	0.126331i
$202$	−0.811230	−	2.49671i	−0.0570779	−	0.175668i
$203$	3.02354	−	2.19673i	0.212211	−	0.154180i
$204$	0.556313	+	1.71216i	0.0389497	+	0.119875i
$205$	0.866076	−	2.66551i	0.0604894	−	0.186167i
$206$	−3.48392	−	2.53122i	−0.242736	−	0.176358i
$207$	−2.21734	+	6.82428i	−0.154116	+	0.474320i
$208$	−3.23352	+	2.34929i	−0.224204	+	0.162894i
$209$	12.6510	−	9.19148i	0.875087	−	0.635788i
$210$	1.42468	+	1.03509i	0.0983126	+	0.0714283i
$211$	−11.5083			−0.792263			−0.396131	−	0.918194i	$-0.629648\pi$
$211$	−11.5083			−0.792263			−0.396131	+	0.918194i	$0.629648\pi$
$212$	5.45152			0.374412
$213$	5.64779	+	4.10336i	0.386980	+	0.281157i
$214$	−0.495884	−	1.52617i	−0.0338979	−	0.104327i
$215$	8.19954	−	25.2356i	0.559204	−	1.72105i
$216$	−11.3722			−0.773780
$217$		0			0
$218$	−1.01826			−0.0689654
$219$	1.57763	−	4.85544i	0.106606	−	0.328100i
$220$	−7.18881	−	22.1249i	−0.484669	−	1.49166i
$221$	3.08032	+	2.23798i	0.207204	+	0.150543i
$222$	−6.47882			−0.434830
$223$	−9.42391			−0.631072			−0.315536	−	0.948914i	$-0.602184\pi$
$223$	−9.42391			−0.631072			−0.315536	+	0.948914i	$0.602184\pi$
$224$	3.58668	+	2.60588i	0.239645	+	0.174112i
$225$	15.4645	−	11.2356i	1.03097	−	0.749042i
$226$	3.55914	−	2.58587i	0.236751	−	0.172009i
$227$	6.72514	−	20.6979i	0.446364	−	1.37377i	−0.434618	−	0.900615i	$-0.643117\pi$
$227$	6.72514	−	20.6979i	0.446364	−	1.37377i	0.880981	−	0.473151i	$-0.156883\pi$
$228$	−4.22906	−	3.07259i	−0.280077	−	0.203488i
$229$	−5.23966	+	16.1260i	−0.346246	+	1.06564i	0.614667	+	0.788787i	$0.289291\pi$
$229$	−5.23966	+	16.1260i	−0.346246	+	1.06564i	−0.960913	+	0.276850i	$0.910709\pi$
$230$	−2.59335	−	7.98150i	−0.171000	−	0.526284i
$231$	−2.29373	+	1.66649i	−0.150916	+	0.109647i
$232$	−3.67647	−	11.3150i	−0.241372	−	0.742866i
$233$	−3.03952	−	9.35469i	−0.199126	−	0.612846i	−0.999904	−	0.0138848i	$-0.995580\pi$
$233$	−3.03952	−	9.35469i	−0.199126	−	0.612846i	0.800778	−	0.598962i	$-0.204420\pi$
$234$	−3.54755	+	2.57744i	−0.231910	+	0.168493i
$235$	−1.00370	−	3.08906i	−0.0654740	−	0.201508i
$236$	−0.436862	+	1.34452i	−0.0284373	+	0.0875210i
$237$	−10.2900	−	7.47609i	−0.668404	−	0.485624i
$238$	0.212835	−	0.655038i	0.0137960	−	0.0424598i
$239$	0.477834	−	0.347167i	0.0309085	−	0.0224563i	−0.572224	−	0.820098i	$-0.693919\pi$
$239$	0.477834	−	0.347167i	0.0309085	−	0.0224563i	0.603132	+	0.797641i	$0.293919\pi$
$240$	−3.71793	+	2.70124i	−0.239992	+	0.174364i
$241$	12.4350	+	9.03452i	0.801006	+	0.581965i	0.911209	−	0.411944i	$-0.135150\pi$
$241$	12.4350	+	9.03452i	0.801006	+	0.581965i	−0.110203	+	0.993909i	$0.535150\pi$
$242$	−4.09445			−0.263201
$243$	16.1450			1.03570
$244$	−2.85790	−	2.07639i	−0.182958	−	0.132927i
$245$	−7.35213	−	22.6275i	−0.469710	−	1.44562i
$246$	−0.145346	+	0.447328i	−0.00926690	+	0.0285206i
$247$	−11.0557			−0.703459
$248$		0			0
$249$	12.7308			0.806783
$250$	−2.95887	+	9.10646i	−0.187135	+	0.575943i
$251$	1.87002	+	5.75532i	0.118034	+	0.363273i	0.992568	−	0.121693i	$-0.0388322\pi$
$251$	1.87002	+	5.75532i	0.118034	+	0.363273i	−0.874533	+	0.484965i	$0.838832\pi$
$252$	−2.05801	−	1.49523i	−0.129642	−	0.0941907i
$253$	13.5114			0.849455
$254$	−0.987363			−0.0619527
$255$	3.54178	+	2.57326i	0.221795	+	0.161144i
$256$	8.02935	−	5.83366i	0.501834	−	0.364604i
$257$	3.66310	−	2.66140i	0.228498	−	0.166013i	−0.467646	−	0.883916i	$-0.654898\pi$
$257$	3.66310	−	2.66140i	0.228498	−	0.166013i	0.696144	+	0.717903i	$0.254898\pi$
$258$	−1.37606	+	4.23506i	−0.0856695	+	0.263663i
$259$	−6.43092	−	4.67234i	−0.399598	−	0.290325i
$260$	−5.08250	+	15.6423i	−0.315203	+	0.970095i
$261$	3.30656	+	10.1765i	0.204671	+	0.629912i
$262$	3.51025	−	2.55035i	0.216864	−	0.157561i
$263$	0.775281	+	2.38607i	0.0478059	+	0.147131i	0.972110	−	0.234525i	$-0.0753536\pi$
$263$	0.775281	+	2.38607i	0.0478059	+	0.147131i	−0.924304	+	0.381657i	$0.875354\pi$
$264$	2.78905	+	8.58383i	0.171654	+	0.528298i
$265$	10.7251	−	7.79226i	0.658839	−	0.478675i
$266$	0.618005	+	1.90202i	0.0378923	+	0.116621i
$267$	1.23668	−	3.80611i	0.0756835	−	0.232930i
$268$	−2.57404	−	1.87015i	−0.157234	−	0.114237i
$269$	−4.12222	+	12.6869i	−0.251336	+	0.773533i	0.743194	+	0.669077i	$0.233310\pi$
$269$	−4.12222	+	12.6869i	−0.251336	+	0.773533i	−0.994530	+	0.104456i	$0.966690\pi$
$270$	−9.67776	+	7.03131i	−0.588970	+	0.427912i
$271$	11.1840	−	8.12564i	0.679379	−	0.493598i	−0.193773	−	0.981046i	$-0.562072\pi$
$271$	11.1840	−	8.12564i	0.679379	−	0.493598i	0.873152	+	0.487449i	$0.162072\pi$
$272$	1.45412	+	1.05648i	0.0881691	+	0.0640586i
$273$	2.00449			0.121317
$274$	8.79097			0.531082
$275$	−29.1197	−	21.1567i	−1.75598	−	1.27580i
$276$	−1.39574	−	4.29563i	−0.0840134	−	0.258567i
$277$	−3.57556	+	11.0044i	−0.214834	+	0.661192i	0.784331	+	0.620343i	$0.213006\pi$
$277$	−3.57556	+	11.0044i	−0.214834	+	0.661192i	−0.999165	+	0.0408496i	$0.986994\pi$
$278$	12.9030			0.773870
$279$		0			0
$280$	6.87814			0.411048
$281$	−4.75866	+	14.6457i	−0.283878	+	0.873686i	0.702855	+	0.711333i	$0.251908\pi$
$281$	−4.75866	+	14.6457i	−0.283878	+	0.873686i	−0.986733	+	0.162353i	$0.948092\pi$
$282$	0.168441	+	0.518409i	0.0100305	+	0.0308708i
$283$	18.3612	+	13.3402i	1.09146	+	0.792993i	0.979645	−	0.200736i	$-0.0643333\pi$
$283$	18.3612	+	13.3402i	1.09146	+	0.792993i	0.111816	+	0.993729i	$0.464333\pi$
$284$	11.7944			0.699871
$285$	−12.7120			−0.752994
$286$	6.68003	+	4.85333i	0.394999	+	0.286983i
$287$	−0.466871	+	0.339202i	−0.0275585	+	0.0200224i
$288$	−10.2690	+	7.46088i	−0.605108	+	0.439637i
$289$	−4.72418	+	14.5395i	−0.277893	+	0.855266i
$290$	−10.1246	−	7.35597i	−0.594539	−	0.431958i
$291$	−1.47171	+	4.52945i	−0.0862730	+	0.265521i
$292$	−2.66539	−	8.20323i	−0.155980	−	0.480058i
$293$	−10.0325	+	7.28904i	−0.586105	+	0.425830i	−0.840920	−	0.541159i	$-0.817986\pi$
$293$	−10.0325	+	7.28904i	−0.586105	+	0.425830i	0.254815	+	0.966990i	$0.417986\pi$
$294$	1.23384	+	3.79737i	0.0719591	+	0.221467i
$295$	1.06236	+	3.26961i	0.0618530	+	0.190364i
$296$	−20.4722	+	14.8739i	−1.18992	+	0.864528i
$297$	−5.95145	−	18.3167i	−0.345338	−	1.06284i
$298$	4.29013	−	13.2037i	0.248521	−	0.764868i
$299$	−7.72821	−	5.61487i	−0.446934	−	0.324716i
$300$	−3.71819	+	11.4434i	−0.214670	+	0.660685i
$301$	−4.42009	+	3.21138i	−0.254769	+	0.185101i
$302$	−8.57493	+	6.23005i	−0.493432	+	0.358499i
$303$	−2.77964	−	2.01953i	−0.159686	−	0.116019i
$304$	−5.21907			−0.299334
$305$	−8.59046			−0.491888
$306$	1.59534	+	1.15908i	0.0911997	+	0.0662605i
$307$	9.49300	+	29.2164i	0.541794	+	1.66747i	0.728493	+	0.685053i	$0.240221\pi$
$307$	9.49300	+	29.2164i	0.541794	+	1.66747i	−0.186699	+	0.982417i	$0.559779\pi$
$308$	−1.48021	+	4.55561i	−0.0843426	+	0.259580i
$309$	−5.63612			−0.320628
$310$		0			0
$311$	2.38141			0.135037			0.0675187	−	0.997718i	$-0.478492\pi$
$311$	2.38141			0.135037			0.0675187	+	0.997718i	$0.478492\pi$
$312$	1.97187	−	6.06878i	0.111635	−	0.343577i
$313$	−3.32057	−	10.2197i	−0.187690	−	0.577650i	0.812295	−	0.583247i	$-0.198218\pi$
$313$	−3.32057	−	10.2197i	−0.187690	−	0.577650i	−0.999984	+	0.00559778i	$0.998218\pi$
$314$	8.44932	+	6.13879i	0.476823	+	0.346432i
$315$	−6.18610			−0.348547
$316$	−21.4888			−1.20884
$317$	−7.07594	−	5.14097i	−0.397425	−	0.288746i	0.371067	−	0.928606i	$-0.378992\pi$
$317$	−7.07594	−	5.14097i	−0.397425	−	0.288746i	−0.768491	+	0.639860i	$0.778992\pi$
$318$	−1.79990	+	1.30770i	−0.100933	+	0.0733324i
$319$	16.3005	−	11.8430i	0.912655	−	0.663083i
$320$	1.44012	−	4.43224i	0.0805052	−	0.247770i
$321$	−1.69913	−	1.23449i	−0.0948359	−	0.0689023i
$322$	−0.533981	+	1.64343i	−0.0297576	+	0.0915845i
$323$	1.53637	+	4.72845i	0.0854858	+	0.263098i
$324$	2.87904	−	2.09175i	0.159947	−	0.116208i
$325$	7.86379	+	24.2022i	0.436204	+	1.34250i
$326$	0.222625	+	0.685170i	0.0123301	+	0.0379480i
$327$	−1.07817	+	0.783335i	−0.0596229	+	0.0433185i
$328$	0.567692	+	1.74718i	0.0313455	+	0.0964716i
$329$	−0.206666	+	0.636051i	−0.0113938	+	0.0350666i
$330$	7.68078	+	5.58042i	0.422813	+	0.307192i
$331$	10.0026	−	30.7848i	0.549793	−	1.69209i	−0.159520	−	0.987195i	$-0.550995\pi$
$331$	10.0026	−	30.7848i	0.549793	−	1.69209i	0.709313	−	0.704893i	$-0.249005\pi$
$332$	17.4008	−	12.6424i	0.954995	−	0.693844i
$333$	18.4124	−	13.3774i	1.00899	−	0.733075i
$334$	6.29736	+	4.57530i	0.344576	+	0.250349i
$335$	−7.73721			−0.422729
$336$	0.946258			0.0516226
$337$	22.4371	+	16.3015i	1.22223	+	0.888000i	0.996283	−	0.0861400i	$-0.0274532\pi$
$337$	22.4371	+	16.3015i	1.22223	+	0.888000i	0.225944	+	0.974140i	$0.427453\pi$
$338$	0.965898	+	2.97273i	0.0525379	+	0.161695i
$339$	1.77926	−	5.47600i	0.0966362	−	0.297416i
$340$	7.39640			0.401126
$341$		0			0
$342$	−5.72593			−0.309623
$343$	−3.16515	+	9.74132i	−0.170902	+	0.525982i
$344$	5.37460	+	16.5413i	0.289779	+	0.891848i
$345$	−8.88598	−	6.45605i	−0.478405	−	0.347582i
$346$	14.2399			0.765540
$347$	25.9161			1.39125			0.695624	−	0.718407i	$-0.255128\pi$
$347$	25.9161			1.39125			0.695624	+	0.718407i	$0.255128\pi$
$348$	−5.44906	−	3.95897i	−0.292100	−	0.212223i
$349$	−4.52559	+	3.28803i	−0.242249	+	0.176004i	−0.702285	−	0.711896i	$-0.747837\pi$
$349$	−4.52559	+	3.28803i	−0.242249	+	0.176004i	0.460036	+	0.887900i	$0.347837\pi$
$350$	3.72417	−	2.70577i	0.199065	−	0.144629i
$351$	−4.20768	+	12.9499i	−0.224589	+	0.691215i
$352$	19.3366	+	14.0488i	1.03064	+	0.748806i
$353$	−3.60591	+	11.0979i	−0.191923	+	0.590679i	0.808075	+	0.589079i	$0.200509\pi$
$353$	−3.60591	+	11.0979i	−0.191923	+	0.590679i	−0.999999	+	0.00160016i	$0.999491\pi$
$354$	−0.178286	−	0.548709i	−0.00947581	−	0.0291635i
$355$	23.2039	−	16.8587i	1.23154	−	0.894765i
$356$	−2.08936	−	6.43039i	−0.110736	−	0.340810i
$357$	−0.278556	−	0.857307i	−0.0147427	−	0.0453735i
$358$	0.0734428	−	0.0533593i	0.00388157	−	0.00282013i
$359$	8.09620	+	24.9175i	0.427301	+	1.31510i	0.900774	+	0.434289i	$0.143000\pi$
$359$	8.09620	+	24.9175i	0.427301	+	1.31510i	−0.473473	+	0.880808i	$0.657000\pi$
$360$	−6.08541	+	18.7290i	−0.320729	+	0.987104i
$361$	3.69193	+	2.68235i	0.194312	+	0.141176i
$362$	1.64742	−	5.07022i	0.0865862	−	0.266485i
$363$	−4.33534	+	3.14981i	−0.227546	+	0.165322i
$364$	2.73979	−	1.99058i	0.143604	−	0.104335i
$365$	−16.9693	−	12.3289i	−0.888213	−	0.645325i
$366$	1.44166			0.0753567
$367$	−27.0146			−1.41015			−0.705076	−	0.709132i	$-0.749087\pi$
$367$	−27.0146			−1.41015			−0.705076	+	0.709132i	$0.749087\pi$
$368$	−3.64825	−	2.65061i	−0.190178	−	0.138173i
$369$	−0.510573	−	1.57138i	−0.0265794	−	0.0818029i
$370$	−8.22549	+	25.3155i	−0.427623	+	1.31609i
$371$	−2.72967			−0.141717
$372$		0			0
$373$	−12.4058			−0.642351			−0.321175	−	0.947020i	$-0.604078\pi$
$373$	−12.4058			−0.642351			−0.321175	+	0.947020i	$0.604078\pi$
$374$	1.14744	−	3.53145i	0.0593326	−	0.182607i
$375$	3.87253	+	11.9184i	0.199977	+	0.615465i
$376$	1.72240	+	1.25140i	0.0888261	+	0.0645359i
$377$	−14.2451			−0.733658
$378$	2.46311			0.126688
$379$	3.75304	+	2.72674i	0.192781	+	0.140063i	0.679989	−	0.733223i	$-0.261985\pi$
$379$	3.75304	+	2.72674i	0.192781	+	0.140063i	−0.487208	+	0.873286i	$0.661985\pi$
$380$	−17.3751	+	12.6238i	−0.891325	+	0.647585i
$381$	−1.04545	+	0.759566i	−0.0535602	+	0.0389137i
$382$	4.49624	−	13.8380i	0.230048	−	0.708014i
$383$	−4.06234	−	2.95147i	−0.207576	−	0.150813i	0.479140	−	0.877738i	$-0.340949\pi$
$383$	−4.06234	−	2.95147i	−0.207576	−	0.150813i	−0.686716	+	0.726926i	$0.740949\pi$
$384$	2.99722	−	9.22450i	0.152951	−	0.470736i
$385$	3.59956	+	11.0783i	0.183451	+	0.564603i
$386$	3.15902	−	2.29516i	0.160790	−	0.116821i
$387$	−4.83383	−	14.8770i	−0.245718	−	0.756241i
$388$	2.48644	+	7.65247i	0.126230	+	0.388496i
$389$	15.0492	−	10.9339i	0.763025	−	0.554370i	−0.136812	−	0.990597i	$-0.543686\pi$
$389$	15.0492	−	10.9339i	0.763025	−	0.554370i	0.899837	+	0.436227i	$0.143686\pi$
$390$	−2.07420	−	6.38373i	−0.105031	−	0.323253i
$391$	−1.32748	+	4.08558i	−0.0671338	+	0.206616i
$392$	12.6167	+	9.16655i	0.637238	+	0.462981i
$393$	1.75482	−	5.40078i	0.0885190	−	0.272433i
$394$	−8.87746	+	6.44985i	−0.447240	+	0.324939i
$395$	−42.2763	+	30.7155i	−2.12715	+	1.54547i
$396$	−11.0952	−	8.06112i	−0.557554	−	0.405086i
$397$	32.5588			1.63408			0.817040	−	0.576581i	$-0.195614\pi$
$397$	32.5588			1.63408			0.817040	+	0.576581i	$0.195614\pi$
$398$	−2.93824			−0.147281
$399$	2.11757	+	1.53850i	0.106011	+	0.0770214i
$400$	3.71225	+	11.4251i	0.185613	+	0.571257i
$401$	3.82880	−	11.7838i	0.191201	−	0.588457i	−0.808799	−	0.588086i	$-0.799882\pi$
$401$	3.82880	−	11.7838i	0.191201	−	0.588457i	1.00000		0.000371451i	$-0.000118236\pi$
$402$	1.29847			0.0647616
$403$		0			0
$404$	−5.80481			−0.288800
$405$	2.67424	−	8.23046i	0.132884	−	0.408975i
$406$	0.796287	+	2.45072i	0.0395190	+	0.121627i
$407$	−34.6705	−	25.1896i	−1.71855	−	1.24860i
$408$	−2.86960			−0.142066
$409$	3.44808			0.170497			0.0852484	−	0.996360i	$-0.472832\pi$
$409$	3.44808			0.170497			0.0852484	+	0.996360i	$0.472832\pi$
$410$	1.56337	+	1.13585i	0.0772092	+	0.0560958i
$411$	9.30817	−	6.76278i	0.459138	−	0.333583i
$412$	−7.70361	+	5.59700i	−0.379530	+	0.275744i
$413$	0.218745	−	0.673226i	0.0107637	−	0.0331273i
$414$	−4.00256	−	2.90803i	−0.196715	−	0.142922i
$415$	16.1630	−	49.7446i	0.793411	−	2.44187i
$416$	−5.22185	−	16.0712i	−0.256022	−	0.787956i
$417$	13.6621	−	9.92611i	0.669037	−	0.486084i
$418$	3.33180	+	10.2542i	0.162964	+	0.501550i
$419$	−12.3752	−	38.0871i	−0.604570	−	1.86068i	−0.499717	−	0.866189i	$-0.666563\pi$
$419$	−12.3752	−	38.0871i	−0.604570	−	1.86068i	−0.104854	−	0.994488i	$-0.533437\pi$
$420$	3.15025	−	2.28879i	0.153716	−	0.111681i
$421$	6.70085	+	20.6231i	0.326580	+	1.00511i	0.970723	+	0.240204i	$0.0772142\pi$
$421$	6.70085	+	20.6231i	0.326580	+	1.00511i	−0.644143	+	0.764905i	$0.722786\pi$
$422$	2.45201	−	7.54652i	0.119362	−	0.367359i
$423$	−1.54910	−	1.12549i	−0.0753199	−	0.0547231i
$424$	−2.68524	+	8.26433i	−0.130407	+	0.401351i
$425$	9.25833	−	6.72657i	0.449095	−	0.326287i
$426$	−3.89411	+	2.82924i	−0.188670	+	0.137077i
$427$	1.43100	+	1.03968i	0.0692510	+	0.0503138i
$428$	−3.54833			−0.171515
$429$	10.8066			0.521750
$430$	14.8011	+	10.7536i	0.713774	+	0.518587i
$431$	−3.59098	−	11.0519i	−0.172972	−	0.532352i	0.826563	−	0.562844i	$-0.190293\pi$
$431$	−3.59098	−	11.0519i	−0.172972	−	0.532352i	−0.999535	+	0.0304917i	$0.990293\pi$
$432$	−1.98632	+	6.11325i	−0.0955667	+	0.294124i
$433$	−24.5964			−1.18203			−0.591015	−	0.806661i	$-0.701272\pi$
$433$	−24.5964			−1.18203			−0.591015	+	0.806661i	$0.701272\pi$
$434$		0			0
$435$	−16.3791			−0.785320
$436$	−0.695773	+	2.14137i	−0.0333215	+	0.102553i
$437$	−3.85460	−	11.8632i	−0.184390	−	0.567495i
$438$	2.84780	+	2.06905i	0.136073	+	0.0988630i
$439$	18.1932			0.868316			0.434158	−	0.900837i	$-0.357046\pi$
$439$	18.1932			0.868316			0.434158	+	0.900837i	$0.357046\pi$
$440$	37.0816			1.76779
$441$	−11.3472	−	8.24425i	−0.540345	−	0.392584i
$442$	−2.12386	+	1.54307i	−0.101021	+	0.0733964i
$443$	−14.3684	+	10.4393i	−0.682664	+	0.495984i	−0.874240	−	0.485493i	$-0.838640\pi$
$443$	−14.3684	+	10.4393i	−0.682664	+	0.495984i	0.191576	+	0.981478i	$0.438640\pi$
$444$	−4.42695	+	13.6247i	−0.210094	+	0.646602i
$445$	−13.3020	−	9.66445i	−0.630574	−	0.458139i
$446$	2.00791	−	6.17970i	0.0950771	−	0.292617i
$447$	−5.61488	−	17.2808i	−0.265575	−	0.817354i
$448$	−0.776318	+	0.564028i	−0.0366776	+	0.0266478i
$449$	2.84252	+	8.74836i	0.134147	+	0.412861i	0.995456	−	0.0952196i	$-0.0303553\pi$
$449$	2.84252	+	8.74836i	0.134147	+	0.412861i	−0.861310	+	0.508080i	$0.830355\pi$
$450$	4.07278	+	12.5347i	0.191993	+	0.590892i
$451$	−2.51700	+	1.82871i	−0.118521	+	0.0861106i
$452$	−3.00605	−	9.25167i	−0.141393	−	0.435162i
$453$	−4.28672	+	13.1932i	−0.201408	+	0.619869i
$454$	12.1397	+	8.81998i	0.569743	+	0.413942i
$455$	2.54490	−	7.83238i	0.119307	−	0.367188i
$456$	6.74106	−	4.89766i	0.315679	−	0.229354i
$457$	−25.2412	+	18.3388i	−1.18074	+	0.857855i	−0.992254	−	0.124222i	$-0.960356\pi$
$457$	−25.2412	+	18.3388i	−1.18074	+	0.857855i	−0.188481	+	0.982077i	$0.560356\pi$
$458$	−9.45819	−	6.87178i	−0.441952	−	0.321097i
$459$	6.12331			0.285812
$460$	−18.5568			−0.865218
$461$	−5.39491	−	3.91963i	−0.251266	−	0.182555i	0.455022	−	0.890480i	$-0.349631\pi$
$461$	−5.39491	−	3.91963i	−0.251266	−	0.182555i	−0.706288	+	0.707925i	$0.749631\pi$
$462$	−0.604082	−	1.85917i	−0.0281044	−	0.0864966i
$463$	−10.9140	+	33.5899i	−0.507217	+	1.56105i	0.289795	+	0.957089i	$0.406413\pi$
$463$	−10.9140	+	33.5899i	−0.507217	+	1.56105i	−0.797011	+	0.603964i	$0.793587\pi$
$464$	−6.72466			−0.312184
$465$		0			0
$466$	6.78192			0.314167
$467$	11.1071	−	34.1842i	0.513977	−	1.58186i	−0.271159	−	0.962535i	$-0.587407\pi$
$467$	11.1071	−	34.1842i	0.513977	−	1.58186i	0.785136	−	0.619324i	$-0.212593\pi$
$468$	2.99626	+	9.22153i	0.138502	+	0.426266i
$469$	1.28886	+	0.936415i	0.0595143	+	0.0432396i
$470$	2.23949			0.103300
$471$	13.6689			0.629830
$472$	−1.82307	−	1.32454i	−0.0839136	−	0.0609668i
$473$	−23.8296	+	17.3132i	−1.09569	+	0.796064i
$474$	7.09485	−	5.15471i	0.325877	−	0.236764i
$475$	−10.2685	+	31.6032i	−0.471151	+	1.45005i
$476$	−1.23209	−	0.895169i	−0.0564729	−	0.0410300i
$477$	2.41507	−	7.43281i	0.110578	−	0.340325i
$478$	0.125844	+	0.387307i	0.00575595	+	0.0177150i
$479$	−26.8953	+	19.5406i	−1.22888	+	0.892832i	−0.996806	−	0.0798671i	$-0.974550\pi$
$479$	−26.8953	+	19.5406i	−1.22888	+	0.892832i	−0.232072	+	0.972699i	$0.574550\pi$
$480$	−6.00415	−	18.4789i	−0.274051	−	0.843441i
$481$	9.36278	+	28.8157i	0.426906	+	1.31388i
$482$	−8.57381	+	6.22924i	−0.390526	+	0.283734i
$483$	0.698869	+	2.15090i	0.0317996	+	0.0978693i
$484$	−2.79772	+	8.61049i	−0.127169	+	0.391386i
$485$	15.8300	+	11.5012i	0.718802	+	0.522241i
$486$	−3.43994	+	10.5871i	−0.156039	+	0.480238i
$487$	23.0694	−	16.7609i	1.04537	−	0.759509i	0.0740472	−	0.997255i	$-0.476408\pi$
$487$	23.0694	−	16.7609i	1.04537	−	0.759509i	0.971327	+	0.237746i	$0.0764084\pi$
$488$	4.55544	−	3.30972i	0.206215	−	0.149824i
$489$	0.762815	+	0.554217i	0.0344957	+	0.0250626i
$490$	16.4044			0.741075
$491$	27.9636			1.26198			0.630991	−	0.775790i	$-0.282649\pi$
$491$	27.9636			1.26198			0.630991	+	0.775790i	$0.282649\pi$
$492$	0.841402	+	0.611315i	0.0379333	+	0.0275602i
$493$	1.97958	+	6.09252i	0.0891557	+	0.274393i
$494$	2.35559	−	7.24975i	0.105983	−	0.326182i
$495$	−33.3506			−1.49900
$496$		0			0
$497$	−5.90568			−0.264906
$498$	−2.71249	+	8.34819i	−0.121550	+	0.374091i
$499$	12.7639	+	39.2834i	0.571392	+	1.75856i	0.648148	+	0.761515i	$0.275544\pi$
$499$	12.7639	+	39.2834i	0.571392	+	1.75856i	−0.0767556	+	0.997050i	$0.524456\pi$
$500$	17.1288	+	12.4448i	0.766023	+	0.556548i
$501$	10.1876			0.455147
$502$	−4.17247			−0.186226
$503$	20.6995	+	15.0391i	0.922947	+	0.670560i	0.944256	−	0.329213i	$-0.106783\pi$
$503$	20.6995	+	15.0391i	0.922947	+	0.670560i	−0.0213090	+	0.999773i	$0.506783\pi$
$504$	3.28043	−	2.38337i	0.146122	−	0.106164i
$505$	−11.4202	+	8.29724i	−0.508191	+	0.369222i
$506$	−2.87881	+	8.86007i	−0.127979	+	0.393878i
$507$	3.30961	+	2.40457i	0.146985	+	0.106791i
$508$	−0.674661	+	2.07639i	−0.0299332	+	0.0921250i
$509$	7.56096	+	23.2702i	0.335134	+	1.03144i	0.966656	+	0.256078i	$0.0824304\pi$
$509$	7.56096	+	23.2702i	0.335134	+	1.03144i	−0.631522	+	0.775358i	$0.717570\pi$
$510$	−2.44203	+	1.77424i	−0.108135	+	0.0785647i
$511$	1.33461	+	4.10750i	0.0590396	+	0.181705i
$512$	−4.52814	−	13.9362i	−0.200118	−	0.615898i
$513$	−14.3845	+	10.4509i	−0.635089	+	0.461419i
$514$	0.964724	+	2.96912i	0.0425522	+	0.130962i
$515$	−7.15560	+	22.0227i	−0.315313	+	0.970435i
$516$	7.96595	+	5.78760i	0.350681	+	0.254785i
$517$	−1.11418	+	3.42909i	−0.0490015	+	0.150811i
$518$	4.43407	−	3.22154i	0.194822	−	0.141546i
$519$	15.0776	−	10.9546i	0.661835	−	0.480851i
$520$	−21.2098	−	15.4098i	−0.930110	−	0.675765i
$521$	14.9656			0.655654			0.327827	−	0.944738i	$-0.393684\pi$
$521$	14.9656			0.655654			0.327827	+	0.944738i	$0.393684\pi$
$522$	−7.37774			−0.322915
$523$	−16.9615	−	12.3233i	−0.741677	−	0.538860i	0.151559	−	0.988448i	$-0.451571\pi$
$523$	−16.9615	−	12.3233i	−0.741677	−	0.538860i	−0.893236	+	0.449589i	$0.851571\pi$
$524$	−2.96476	−	9.12458i	−0.129516	−	0.398609i
$525$	1.86176	−	5.72991i	0.0812539	−	0.250074i
$526$	−1.72984			−0.0754247
$527$		0			0
$528$	5.10148			0.222014
$529$	−3.77686	+	11.6240i	−0.164211	+	0.505391i
$530$	2.82460	+	8.69322i	0.122693	+	0.377609i
$531$	1.63964	+	1.19127i	0.0711544	+	0.0516967i
$532$	4.42217			0.191726
$533$	2.19961			0.0952759
$534$	2.23235	+	1.62190i	0.0966032	+	0.0701863i
$535$	−6.98086	+	5.07189i	−0.301809	+	0.219277i
$536$	4.10297	−	2.98098i	0.177221	−	0.128759i
$537$	0.0367150	−	0.112997i	0.00158437	−	0.00487619i
$538$	−7.44108	−	5.40626i	−0.320808	−	0.233080i
$539$	−8.16142	+	25.1183i	−0.351537	+	1.08192i
$540$	8.17384	+	25.1565i	0.351746	+	1.08256i
$541$	−1.40065	+	1.01763i	−0.0602187	+	0.0437515i	−0.617487	−	0.786581i	$-0.711849\pi$
$541$	−1.40065	+	1.01763i	−0.0602187	+	0.0437515i	0.557269	+	0.830332i	$0.311849\pi$
$542$	2.94545	+	9.06515i	0.126518	+	0.389382i
$543$	−2.15612	−	6.63586i	−0.0925280	−	0.284772i
$544$	−6.14788	+	4.46670i	−0.263588	+	0.191508i
$545$	1.69198	+	5.20738i	0.0724764	+	0.223059i
$546$	−0.427087	+	1.31444i	−0.0182776	+	0.0562527i
$547$	10.6155	+	7.71258i	0.453884	+	0.329766i	0.791127	−	0.611651i	$-0.209494\pi$
$547$	10.6155	+	7.71258i	0.453884	+	0.329766i	−0.337243	+	0.941418i	$0.609494\pi$
$548$	6.00683	−	18.4871i	0.256599	−	0.789730i
$549$	−4.09710	+	2.97671i	−0.174860	+	0.127043i
$550$	20.0778	−	14.5874i	0.856121	−	0.622008i
$551$	−15.0487	−	10.9335i	−0.641094	−	0.465782i
$552$	7.19953			0.306432
$553$	10.7598			0.457554
$554$	−6.45429	−	4.68932i	−0.274217	−	0.199230i
$555$	10.7654	+	33.1326i	0.456967	+	1.40640i
$556$	8.81656	−	27.1346i	0.373905	−	1.15076i
$557$	28.0246			1.18744			0.593721	−	0.804671i	$-0.297658\pi$
$557$	28.0246			1.18744			0.593721	+	0.804671i	$0.297658\pi$
$558$		0			0
$559$	20.8248			0.880794
$560$	1.20137	−	3.69743i	0.0507670	−	0.156245i
$561$	−1.50176	−	4.62193i	−0.0634042	−	0.195138i
$562$	−8.58993	−	6.24095i	−0.362344	−	0.263259i
$563$	22.6519			0.954662			0.477331	−	0.878723i	$-0.341604\pi$
$563$	22.6519			0.954662			0.477331	+	0.878723i	$0.341604\pi$
$564$	1.20529			0.0507520
$565$	−19.1381	−	13.9046i	−0.805145	−	0.584972i
$566$	−12.6599	+	9.19798i	−0.532136	+	0.386620i
$567$	−1.44159	+	1.04738i	−0.0605410	+	0.0439856i
$568$	−5.80956	+	17.8800i	−0.243764	+	0.750227i
$569$	−37.5724	−	27.2979i	−1.57512	−	1.14439i	−0.922039	−	0.387098i	$-0.873478\pi$
$569$	−37.5724	−	27.2979i	−1.57512	−	1.14439i	−0.653078	−	0.757291i	$-0.726522\pi$
$570$	2.70848	−	8.33585i	0.113446	−	0.349150i
$571$	3.86221	+	11.8866i	0.161628	+	0.497441i	0.998772	−	0.0495423i	$-0.0157763\pi$
$571$	3.86221	+	11.8866i	0.161628	+	0.497441i	−0.837144	+	0.546983i	$0.815776\pi$
$572$	14.7708	−	10.7316i	0.617599	−	0.448712i
$573$	−5.88463	−	18.1110i	−0.245834	−	0.756600i
$574$	−0.122956	−	0.378421i	−0.00513210	−	0.0157950i
$575$	−23.2282	+	16.8763i	−0.968685	+	0.703791i
$576$	−0.848987	−	2.61291i	−0.0353745	−	0.108871i
$577$	−9.42017	+	28.9923i	−0.392167	+	1.20696i	0.538980	+	0.842319i	$0.318810\pi$
$577$	−9.42017	+	28.9923i	−0.392167	+	1.20696i	−0.931146	+	0.364646i	$0.881190\pi$
$578$	−8.52769	−	6.19573i	−0.354705	−	0.257708i
$579$	1.57923	−	4.86038i	0.0656307	−	0.201991i
$580$	−22.3875	+	16.2655i	−0.929590	+	0.675386i
$581$	−8.71290	+	6.33030i	−0.361472	+	0.262625i
$582$	−2.65660	−	1.93013i	−0.110120	−	0.0800067i
$583$	−14.7162			−0.609485
$584$	13.7487			0.568926
$585$	19.0758	+	13.8593i	0.788685	+	0.573013i
$586$	−2.64219	−	8.13182i	−0.109148	−	0.335922i
$587$	−10.4009	+	32.0107i	−0.429292	+	1.32123i	0.469532	+	0.882915i	$0.344423\pi$
$587$	−10.4009	+	32.0107i	−0.429292	+	1.32123i	−0.898824	+	0.438310i	$0.855577\pi$
$588$	8.82883			0.364095
$589$		0			0
$590$	−2.37039			−0.0975872
$591$	−4.43796	+	13.6586i	−0.182553	+	0.561841i
$592$	4.41988	+	13.6030i	0.181656	+	0.559080i
$593$	36.3151	+	26.3844i	1.49128	+	1.08348i	0.973697	+	0.227847i	$0.0731687\pi$
$593$	36.3151	+	26.3844i	1.49128	+	1.08348i	0.517585	+	0.855632i	$0.326831\pi$
$594$	13.2791			0.544850
$595$	−3.70351			−0.151829
$596$	−24.8354	−	18.0440i	−1.01730	−	0.739111i
$597$	−3.11111	+	2.26035i	−0.127329	+	0.0925100i
$598$	5.32854	−	3.87141i	0.217900	−	0.158314i
$599$	−6.05198	+	18.6261i	−0.247277	+	0.761041i	0.747976	+	0.663725i	$0.231026\pi$
$599$	−6.05198	+	18.6261i	−0.247277	+	0.761041i	−0.995254	+	0.0973156i	$0.968974\pi$
$600$	−15.5164	−	11.2733i	−0.633453	−	0.460231i
$601$	−9.41249	+	28.9687i	−0.383944	+	1.18166i	0.553300	+	0.832982i	$0.313368\pi$
$601$	−9.41249	+	28.9687i	−0.383944	+	1.18166i	−0.937244	+	0.348675i	$0.886632\pi$
$602$	−1.16409	−	3.58269i	−0.0474446	−	0.146019i
$603$	−3.69015	+	2.68105i	−0.150274	+	0.109181i
$604$	7.24238	+	22.2898i	0.294688	+	0.906958i
$605$	6.80348	+	20.9390i	0.276601	+	0.851290i
$606$	1.91654	−	1.39245i	0.0778543	−	0.0565644i
$607$	−4.13297	−	12.7200i	−0.167752	−	0.516288i	0.831477	−	0.555560i	$-0.187496\pi$
$607$	−4.13297	−	12.7200i	−0.167752	−	0.516288i	−0.999229	+	0.0392723i	$0.987496\pi$
$608$	6.81867	−	20.9857i	0.276534	−	0.851083i
$609$	2.72844	+	1.98233i	0.110562	+	0.0803280i
$610$	1.83033	−	5.63317i	0.0741078	−	0.228080i
$611$	2.06229	−	1.49834i	0.0834315	−	0.0606165i
$612$	3.52761	−	2.56296i	0.142595	−	0.103601i
$613$	−4.20301	−	3.05367i	−0.169758	−	0.123336i	0.499662	−	0.866220i	$-0.333457\pi$
$613$	−4.20301	−	3.05367i	−0.169758	−	0.123336i	−0.669420	+	0.742884i	$0.733457\pi$
$614$	−21.1812			−0.854804
$615$	2.52914			0.101985
$616$	−6.17705	−	4.48789i	−0.248881	−	0.180822i
$617$	−9.27455	−	28.5441i	−0.373379	−	1.14914i	−0.944566	−	0.328323i	$-0.893517\pi$
$617$	−9.27455	−	28.5441i	−0.373379	−	1.14914i	0.571186	−	0.820820i	$-0.306483\pi$
$618$	1.20086	−	3.69587i	0.0483057	−	0.148670i
$619$	−18.3260			−0.736584			−0.368292	−	0.929710i	$-0.620057\pi$
$619$	−18.3260			−0.736584			−0.368292	+	0.929710i	$0.620057\pi$
$620$		0			0
$621$	−15.3628			−0.616487
$622$	−0.507396	+	1.56160i	−0.0203447	+	0.0626146i
$623$	1.04618	+	3.21981i	0.0419143	+	0.128999i
$624$	−2.91793	−	2.12000i	−0.116811	−	0.0848679i
$625$	7.75849			0.310339
$626$	7.40901			0.296123
$627$	11.4163	+	8.29440i	0.455922	+	0.331246i
$628$	18.6831	−	13.5740i	0.745535	−	0.541663i
$629$	11.0232	−	8.00880i	0.439522	−	0.319332i
$630$	1.31804	−	4.05651i	0.0525120	−	0.161615i
$631$	8.36136	+	6.07489i	0.332861	+	0.241837i	0.741643	−	0.670794i	$-0.234047\pi$
$631$	8.36136	+	6.07489i	0.332861	+	0.241837i	−0.408783	+	0.912632i	$0.634047\pi$
$632$	10.5847	−	32.5763i	0.421036	−	1.29582i
$633$	−3.20917	−	9.87680i	−0.127553	−	0.392568i
$634$	4.87881	−	3.54466i	0.193762	−	0.140777i
$635$	1.64064	+	5.04936i	0.0651067	+	0.200378i
$636$	1.52020	+	4.67868i	0.0602797	+	0.185522i
$637$	15.1064	−	10.9754i	0.598537	−	0.434863i
$638$	4.29295	+	13.2124i	0.169960	+	0.523082i
$639$	5.22503	−	16.0810i	0.206699	−	0.636154i
$640$	−32.2387	−	23.4228i	−1.27435	−	0.925868i
$641$	−0.0312886	+	0.0962963i	−0.00123582	+	0.00380348i	−0.951673	−	0.307115i	$-0.900636\pi$
$641$	−0.0312886	+	0.0962963i	−0.00123582	+	0.00380348i	0.950437	+	0.310918i	$0.100636\pi$
$642$	1.17153	−	0.851170i	0.0462368	−	0.0335930i
$643$	−11.0931	+	8.05961i	−0.437469	+	0.317840i	−0.784629	−	0.619966i	$-0.787146\pi$
$643$	−11.0931	+	8.05961i	−0.437469	+	0.317840i	0.347159	+	0.937806i	$0.387146\pi$
$644$	3.09120	+	2.24589i	0.121810	+	0.0885005i
$645$	23.9446			0.942816
$646$	−3.42801			−0.134873
$647$	−8.76519	−	6.36828i	−0.344595	−	0.250363i	0.402003	−	0.915638i	$-0.368314\pi$
$647$	−8.76519	−	6.36828i	−0.344595	−	0.250363i	−0.746598	+	0.665275i	$0.768314\pi$
$648$	1.75290	+	5.39487i	0.0688603	+	0.211930i
$649$	1.17930	−	3.62951i	0.0462916	−	0.142471i
$650$	−17.5460			−0.688212
$651$		0			0
$652$	1.59301			0.0623870
$653$	−7.49434	+	23.0652i	−0.293276	+	0.902611i	0.690519	+	0.723314i	$0.257382\pi$
$653$	−7.49434	+	23.0652i	−0.293276	+	0.902611i	−0.983795	+	0.179297i	$0.942618\pi$
$654$	−0.283950	−	0.873907i	−0.0111033	−	0.0341725i
$655$	−18.8752	−	13.7136i	−0.737515	−	0.535836i
$656$	1.03837			0.0405415
$657$	−12.3654			−0.482420
$658$	−0.373055	−	0.271041i	−0.0145432	−	0.0105663i
$659$	6.90374	−	5.01586i	0.268932	−	0.195390i	−0.445144	−	0.895459i	$-0.646847\pi$
$659$	6.90374	−	5.01586i	0.268932	−	0.195390i	0.714075	+	0.700069i	$0.246847\pi$
$660$	16.9837	−	12.3394i	0.661089	−	0.480309i
$661$	11.7069	−	36.0300i	0.455344	−	1.40141i	−0.415386	−	0.909645i	$-0.636354\pi$
$661$	11.7069	−	36.0300i	0.455344	−	1.40141i	0.870731	−	0.491760i	$-0.163646\pi$
$662$	18.0559	+	13.1183i	0.701761	+	0.509859i
$663$	−1.06174	+	3.26771i	−0.0412347	+	0.126907i
$664$	10.5945	+	32.6064i	0.411144	+	1.26537i
$665$	8.70003	−	6.32094i	0.337373	−	0.245116i
$666$	4.84913	+	14.9241i	0.187900	+	0.578297i
$667$	−4.96657	−	15.2855i	−0.192306	−	0.591858i
$668$	13.9247	−	10.1169i	0.538761	−	0.391433i
$669$	−2.62793	−	8.08792i	−0.101601	−	0.312697i
$670$	1.64853	−	5.07365i	0.0636882	−	0.196012i
$671$	7.71483	+	5.60516i	0.297828	+	0.216385i
$672$	−1.23628	+	3.80488i	−0.0476905	+	0.146776i
$673$	5.76029	−	4.18509i	0.222043	−	0.161323i	−0.471203	−	0.882025i	$-0.656180\pi$
$673$	5.76029	−	4.18509i	0.222043	−	0.161323i	0.693246	+	0.720701i	$0.256180\pi$
$674$	−15.4702	+	11.2398i	−0.595891	+	0.432940i
$675$	33.1097	+	24.0556i	1.27439	+	0.925902i
$676$	6.91154			0.265829
$677$	−48.0610			−1.84713			−0.923567	−	0.383438i	$-0.874740\pi$
$677$	−48.0610			−1.84713			−0.923567	+	0.383438i	$0.874740\pi$
$678$	3.21177	+	2.33349i	0.123347	+	0.0896171i
$679$	−1.24500	−	3.83173i	−0.0477789	−	0.147048i
$680$	−3.64323	+	11.2127i	−0.139712	+	0.429988i
$681$	19.6390			0.752567
$682$		0			0
$683$	32.5731			1.24638			0.623188	−	0.782072i	$-0.285837\pi$
$683$	32.5731			1.24638			0.623188	+	0.782072i	$0.285837\pi$
$684$	−3.91250	+	12.0414i	−0.149598	+	0.460416i
$685$	−14.6074	−	44.9569i	−0.558119	−	1.71771i
$686$	−5.71346	−	4.15107i	−0.218141	−	0.158489i
$687$	−15.3010			−0.583770
$688$	9.83073			0.374793
$689$	8.41734	+	6.11556i	0.320675	+	0.232984i
$690$	6.12682	−	4.45140i	0.233244	−	0.169462i
$691$	−22.0482	+	16.0190i	−0.838753	+	0.609390i	−0.922022	−	0.387137i	$-0.873464\pi$
$691$	−22.0482	+	16.0190i	−0.838753	+	0.609390i	0.0832688	+	0.996527i	$0.473464\pi$
$692$	9.73004	−	29.9460i	0.369881	−	1.13838i
$693$	5.55555	+	4.03634i	0.211038	+	0.153328i
$694$	−5.52180	+	16.9944i	−0.209605	+	0.645097i
$695$	−21.4401	−	65.9857i	−0.813268	−	2.50298i
$696$	8.68571	−	6.31054i	0.329231	−	0.239200i
$697$	−0.305671	−	0.940760i	−0.0115781	−	0.0356338i
$698$	−1.19187	−	3.66820i	−0.0451130	−	0.138844i
$699$	7.18093	−	5.21725i	0.271608	−	0.197334i
$700$	−3.14543	−	9.68065i	−0.118886	−	0.365894i
$701$	2.62329	−	8.07366i	0.0990804	−	0.304938i	−0.889215	−	0.457489i	$-0.848749\pi$
$701$	2.62329	−	8.07366i	0.0990804	−	0.304938i	0.988296	+	0.152551i	$0.0487489\pi$
$702$	−7.59535	−	5.51834i	−0.286668	−	0.208277i
$703$	−12.2259	+	37.6274i	−0.461108	+	1.41914i
$704$	−4.18530	+	3.04080i	−0.157739	+	0.114604i
$705$	2.37125	−	1.72281i	0.0893065	−	0.0648849i
$706$	−6.50909	−	4.72913i	−0.244973	−	0.177983i
$707$	2.90657			0.109313
$708$	−1.27574			−0.0479452
$709$	−18.9198	−	13.7460i	−0.710546	−	0.516242i	0.172804	−	0.984956i	$-0.444717\pi$
$709$	−18.9198	−	13.7460i	−0.710546	−	0.516242i	−0.883350	+	0.468714i	$0.844717\pi$
$710$	6.11106	+	18.8079i	0.229344	+	0.705848i
$711$	−9.51971	+	29.2987i	−0.357017	+	1.09879i
$712$	10.7774			0.403901
$713$		0			0
$714$	0.621526			0.0232600
$715$	13.7201	−	42.2261i	0.513102	−	1.57917i
$716$	−0.0620297	−	0.190908i	−0.00231816	−	0.00713456i
$717$	0.431198	+	0.313283i	0.0161034	+	0.0116998i
$718$	−18.0646			−0.674165
$719$	−12.9769			−0.483956			−0.241978	−	0.970282i	$-0.577796\pi$
$719$	−12.9769			−0.483956			−0.241978	+	0.970282i	$0.577796\pi$
$720$	9.00508	+	6.54257i	0.335599	+	0.243827i
$721$	3.85733	−	2.80252i	0.143655	−	0.104371i
$722$	−2.54556	+	1.84946i	−0.0947360	+	0.0688297i
$723$	−4.28616	+	13.1914i	−0.159404	+	0.490595i
$724$	−9.53684	−	6.92892i	−0.354434	−	0.257511i
$725$	−13.2308	+	40.7201i	−0.491378	+	1.51231i
$726$	−1.14177	−	3.51400i	−0.0423749	−	0.130417i
$727$	10.0504	−	7.30207i	0.372750	−	0.270819i	−0.385600	−	0.922666i	$-0.626006\pi$
$727$	10.0504	−	7.30207i	0.372750	−	0.270819i	0.758350	+	0.651847i	$0.226006\pi$
$728$	1.66812	+	5.13393i	0.0618245	+	0.190276i
$729$	2.33825	+	7.19640i	0.0866020	+	0.266533i
$730$	11.7002	−	8.50069i	0.433044	−	0.314625i
$731$	−2.89393	−	8.90661i	−0.107036	−	0.329423i
$732$	0.985079	−	3.03176i	0.0364096	−	0.112057i
$733$	27.6339	+	20.0772i	1.02068	+	0.741568i	0.966422	−	0.256959i	$-0.0827206\pi$
$733$	27.6339	+	20.0772i	1.02068	+	0.741568i	0.0542580	+	0.998527i	$0.482721\pi$
$734$	5.75587	−	17.7147i	0.212453	−	0.653863i
$735$	17.3695	−	12.6197i	0.640684	−	0.465484i
$736$	15.4244	−	11.2065i	0.568552	−	0.413077i
$737$	6.94855	+	5.04842i	0.255953	+	0.185961i
$738$	1.13921			0.0419351
$739$	12.3749			0.455219			0.227610	−	0.973752i	$-0.426909\pi$
$739$	12.3749			0.455219			0.227610	+	0.973752i	$0.426909\pi$
$740$	47.6171	+	34.5959i	1.75044	+	1.27177i
$741$	−3.08297	−	9.48840i	−0.113256	−	0.348565i
$742$	0.581597	−	1.78997i	0.0213511	−	0.0657119i
$743$	16.2455			0.595990			0.297995	−	0.954567i	$-0.403682\pi$
$743$	16.2455			0.595990			0.297995	+	0.954567i	$0.403682\pi$
$744$		0			0
$745$	−74.6520			−2.73504
$746$	2.64325	−	8.13509i	0.0967763	−	0.297847i
$747$	−9.52849	−	29.3257i	−0.348629	−	1.07297i
$748$	−6.64249	−	4.82605i	−0.242873	−	0.176458i
$749$	1.77671			0.0649196
$750$	−8.64058			−0.315509
$751$	8.72790	+	6.34119i	0.318485	+	0.231393i	0.735529	−	0.677493i	$-0.236934\pi$
$751$	8.72790	+	6.34119i	0.318485	+	0.231393i	−0.417043	+	0.908887i	$0.636934\pi$
$752$	0.973546	−	0.707322i	0.0355016	−	0.0257934i
$753$	−4.41795	+	3.20983i	−0.160999	+	0.116973i
$754$	3.03513	−	9.34115i	0.110533	−	0.340185i
$755$	46.1088	+	33.5000i	1.67807	+	1.21919i
$756$	1.68303	−	5.17983i	0.0612112	−	0.188389i
$757$	−12.7011	−	39.0900i	−0.461630	−	1.42075i	−0.863172	−	0.504910i	$-0.831526\pi$
$757$	−12.7011	−	39.0900i	−0.461630	−	1.42075i	0.401542	−	0.915841i	$-0.368474\pi$
$758$	−2.58769	+	1.88007i	−0.0939893	+	0.0682872i
$759$	3.76776	+	11.5960i	0.136761	+	0.420907i
$760$	−10.5788	−	32.5582i	−0.383733	−	1.18101i
$761$	15.9057	−	11.5562i	0.576581	−	0.418910i	−0.260909	−	0.965363i	$-0.584022\pi$
$761$	15.9057	−	11.5562i	0.576581	−	0.418910i	0.837490	+	0.546453i	$0.184022\pi$
$762$	−0.275333	−	0.847389i	−0.00997428	−	0.0306977i
$763$	0.348386	−	1.07222i	0.0126124	−	0.0388170i
$764$	−26.0286	−	18.9109i	−0.941682	−	0.684172i
$765$	3.27667	−	10.0845i	0.118468	−	0.364607i
$766$	2.80096	−	2.03501i	0.101203	−	0.0735281i
$767$	−2.18283	+	1.58592i	−0.0788174	+	0.0572642i
$768$	7.24569	+	5.26430i	0.261456	+	0.189959i
$769$	3.78834			0.136611			0.0683055	−	0.997664i	$-0.478241\pi$
$769$	3.78834			0.136611			0.0683055	+	0.997664i	$0.478241\pi$
$770$	−8.03151			−0.289435
$771$	3.30558	+	2.40165i	0.119048	+	0.0864932i
$772$	−2.66810	−	8.21158i	−0.0960272	−	0.295541i
$773$	7.83963	−	24.1279i	0.281972	−	0.867820i	−0.705318	−	0.708891i	$-0.749196\pi$
$773$	7.83963	−	24.1279i	0.281972	−	0.867820i	0.987290	−	0.158929i	$-0.0508041\pi$
$774$	10.7855			0.387676
$775$		0			0
$776$	−12.8256			−0.460414
$777$	2.21665	−	6.82215i	0.0795219	−	0.244743i
$778$	3.96340	+	12.1981i	0.142095	+	0.437323i
$779$	2.32370	+	1.68826i	0.0832551	+	0.0604884i
$780$	−14.8421			−0.531431
$781$	−31.8388			−1.13928
$782$	−2.39626	−	1.74099i	−0.0856902	−	0.0622576i
$783$	−18.5341	+	13.4658i	−0.662354	+	0.481228i
$784$	7.13127	−	5.18117i	0.254688	−	0.185042i
$785$	17.3540	−	53.4102i	0.619391	−	1.90629i
$786$	3.16765	+	2.30143i	0.112986	+	0.0820895i
$787$	8.01794	−	24.6767i	0.285809	−	0.879628i	−0.700347	−	0.713803i	$-0.746971\pi$
$787$	8.01794	−	24.6767i	0.285809	−	0.879628i	0.986155	−	0.165825i	$-0.0530288\pi$
$788$	7.49790	+	23.0761i	0.267101	+	0.822054i
$789$	−1.83161	+	1.33075i	−0.0652072	+	0.0473758i
$790$	−11.1340	−	34.2670i	−0.396130	−	1.21916i
$791$	1.50518	+	4.63247i	0.0535181	+	0.164712i
$792$	17.6855	−	12.8493i	0.628428	−	0.456579i
$793$	−2.08340	−	6.41203i	−0.0739835	−	0.227698i
$794$	−6.93714	+	21.3503i	−0.246190	+	0.757695i
$795$	9.67836	+	7.03174i	0.343256	+	0.249390i
$796$	−2.00769	+	6.17903i	−0.0711606	+	0.219010i
$797$	−14.9689	+	10.8756i	−0.530227	+	0.385232i	−0.820443	−	0.571729i	$-0.806273\pi$
$797$	−14.9689	+	10.8756i	−0.530227	+	0.385232i	0.290216	+	0.956961i	$0.406273\pi$
$798$	−1.46005	+	1.06079i	−0.0516851	+	0.0375514i
$799$	−0.927420	−	0.673810i	−0.0328098	−	0.0238377i
$800$	−50.7902			−1.79570
$801$	−9.69305			−0.342487
$802$	6.91143	+	5.02145i	0.244051	+	0.177314i
$803$	7.19517	+	22.1444i	0.253912	+	0.781460i
$804$	0.887235	−	2.73063i	0.0312904	−	0.0963019i
$805$	9.29174			0.327491
$806$		0			0
$807$	−12.0378			−0.423751
$808$	2.85926	−	8.79990i	0.100588	−	0.309579i
$809$	−11.3557	−	34.9493i	−0.399245	−	1.22875i	−0.925606	−	0.378489i	$-0.876444\pi$
$809$	−11.3557	−	34.9493i	−0.399245	−	1.22875i	0.526360	−	0.850262i	$-0.323556\pi$
$810$	4.82731	+	3.50725i	0.169614	+	0.123232i
$811$	−39.4301			−1.38458			−0.692289	−	0.721620i	$-0.743398\pi$
$811$	−39.4301			−1.38458			−0.692289	+	0.721620i	$0.743398\pi$
$812$	5.69788			0.199956
$813$	10.0924	+	7.33259i	0.353957	+	0.257165i
$814$	23.9051	−	17.3680i	0.837872	−	0.608749i
$815$	3.13403	−	2.27700i	0.109780	−	0.0797600i
$816$	−0.501216	+	1.54258i	−0.0175461	+	0.0540013i
$817$	21.9995	+	15.9836i	0.769666	+	0.559195i
$818$	−0.734666	+	2.26107i	−0.0256870	+	0.0790564i
$819$	−1.50028	−	4.61738i	−0.0524240	−	0.161344i
$820$	3.45690	−	2.51159i	0.120720	−	0.0877084i
$821$	−0.457525	−	1.40812i	−0.0159677	−	0.0491436i	0.942755	−	0.333486i	$-0.108225\pi$
$821$	−0.457525	−	1.40812i	−0.0159677	−	0.0491436i	−0.958723	+	0.284342i	$0.908225\pi$
$822$	2.45142	+	7.54471i	0.0855032	+	0.263152i
$823$	−31.4426	+	22.8444i	−1.09602	+	0.796306i	−0.980406	−	0.196988i	$-0.936884\pi$
$823$	−31.4426	+	22.8444i	−1.09602	+	0.796306i	−0.115615	+	0.993294i	$0.536884\pi$
$824$	−4.69032	−	14.4353i	−0.163395	−	0.502878i
$825$	10.0372	−	30.8912i	0.349449	−	1.07549i
$826$	0.394859	+	0.286882i	0.0137389	+	0.00998190i
$827$	−10.4869	+	32.2753i	−0.364665	+	1.12232i	0.585526	+	0.810654i	$0.300888\pi$
$827$	−10.4869	+	32.2753i	−0.364665	+	1.12232i	−0.950191	+	0.311669i	$0.899112\pi$
$828$	−8.85042	+	6.43021i	−0.307573	+	0.223465i
$829$	13.3736	−	9.71650i	0.464485	−	0.337468i	−0.330803	−	0.943700i	$-0.607320\pi$
$829$	13.3736	−	9.71650i	0.464485	−	0.337468i	0.795288	+	0.606232i	$0.207320\pi$
$830$	29.1761	+	21.1977i	1.01272	+	0.735782i
$831$	−10.4415			−0.362210
$832$	3.65754			0.126802
$833$	−6.79340	−	4.93569i	−0.235377	−	0.171012i
$834$	3.59809	+	11.0738i	0.124592	+	0.383454i
$835$	12.9341	−	39.8071i	0.447603	−	1.37758i
$836$	23.8409			0.824555
$837$		0			0
$838$	27.6122			0.953848
$839$	−16.7110	+	51.4313i	−0.576929	+	1.77561i	0.0525843	+	0.998616i	$0.483254\pi$
$839$	−16.7110	+	51.4313i	−0.576929	+	1.77561i	−0.629514	+	0.776989i	$0.716746\pi$
$840$	1.91802	+	5.90306i	0.0661780	+	0.203675i
$841$	4.07162	+	2.95820i	0.140401	+	0.102007i
$842$	−14.9512			−0.515254
$843$	−13.8964			−0.478617
$844$	−14.1946	−	10.3130i	−0.488599	−	0.354988i
$845$	13.5975	−	9.87918i	0.467769	−	0.339854i
$846$	1.06809	−	0.776016i	0.0367218	−	0.0266800i
$847$	1.40087	−	4.31142i	0.0481344	−	0.148142i
$848$	3.97357	+	2.88697i	0.136453	+	0.0991388i
$849$	−6.32886	+	19.4782i	−0.217206	+	0.668491i
$850$	2.43830	+	7.50432i	0.0836330	+	0.257396i
$851$	−27.6560	+	20.0933i	−0.948036	+	0.688789i
$852$	3.28896	+	10.1224i	0.112678	+	0.346787i
$853$	12.2297	+	37.6392i	0.418738	+	1.28874i	0.908865	+	0.417091i	$0.136950\pi$
$853$	12.2297	+	37.6392i	0.418738	+	1.28874i	−0.490127	+	0.871651i	$0.663050\pi$
$854$	−0.986664	+	0.716854i	−0.0337630	+	0.0245302i
$855$	9.51441	+	29.2823i	0.325386	+	1.00143i
$856$	1.74779	−	5.37915i	0.0597383	−	0.183856i
$857$	−10.2948	−	7.47959i	−0.351663	−	0.255498i	0.397903	−	0.917427i	$-0.369738\pi$
$857$	−10.2948	−	7.47959i	−0.351663	−	0.255498i	−0.749566	+	0.661929i	$0.769738\pi$
$858$	−2.30252	+	7.08642i	−0.0786067	+	0.241926i
$859$	−17.1142	+	12.4342i	−0.583930	+	0.424250i	−0.840139	−	0.542372i	$-0.817526\pi$
$859$	−17.1142	+	12.4342i	−0.583930	+	0.424250i	0.256209	+	0.966621i	$0.417526\pi$
$860$	32.7281	−	23.7784i	1.11602	−	0.810835i
$861$	−0.421305	−	0.306096i	−0.0143580	−	0.0104317i
$862$	8.01237			0.272902
$863$	−9.33974			−0.317928			−0.158964	−	0.987284i	$-0.550815\pi$
$863$	−9.33974			−0.317928			−0.158964	+	0.987284i	$0.550815\pi$
$864$	−21.9861	−	15.9739i	−0.747983	−	0.543441i
$865$	−23.6615	−	72.8225i	−0.804514	−	2.47604i
$866$	5.24064	−	16.1290i	0.178084	−	0.548087i
$867$	−13.7957			−0.468526
$868$		0			0
$869$	58.0085			1.96780
$870$	3.48982	−	10.7406i	0.118316	−	0.364139i
$871$	−1.87646	−	5.77515i	−0.0635814	−	0.195683i
$872$	−2.90353	−	2.10954i	−0.0983260	−	0.0714380i
$873$	11.5352			0.390407
$874$	8.60055			0.290918
$875$	−8.57669	−	6.23133i	−0.289945	−	0.210657i
$876$	6.29703	−	4.57506i	0.212757	−	0.154577i
$877$	−18.1505	+	13.1871i	−0.612899	+	0.445297i	−0.850434	−	0.526082i	$-0.823661\pi$
$877$	−18.1505	+	13.1871i	−0.612899	+	0.445297i	0.237535	+	0.971379i	$0.423661\pi$
$878$	−3.87634	+	11.9302i	−0.130820	+	0.402623i
$879$	−9.05334	−	6.57764i	−0.305362	−	0.221858i
$880$	6.47683	−	19.9336i	0.218334	−	0.671963i
$881$	14.3481	+	44.1590i	0.483400	+	1.48775i	0.834284	+	0.551334i	$0.185881\pi$
$881$	14.3481	+	44.1590i	0.483400	+	1.48775i	−0.350884	+	0.936419i	$0.614119\pi$
$882$	7.82384	−	5.68435i	0.263442	−	0.191402i
$883$	−11.2913	−	34.7512i	−0.379984	−	1.16947i	−0.940054	−	0.341026i	$-0.889226\pi$
$883$	−11.2913	−	34.7512i	−0.379984	−	1.16947i	0.560070	−	0.828445i	$-0.310774\pi$
$884$	1.79381	+	5.52077i	0.0603323	+	0.185684i
$885$	−2.50984	+	1.82351i	−0.0843674	+	0.0612965i
$886$	−3.78411	−	11.6463i	−0.127130	−	0.391264i
$887$	8.86417	−	27.2811i	0.297630	−	0.916010i	−0.684696	−	0.728829i	$-0.740065\pi$
$887$	8.86417	−	27.2811i	0.297630	−	0.916010i	0.982325	−	0.187181i	$-0.0599350\pi$
$888$	−18.4741	−	13.4222i	−0.619950	−	0.450420i
$889$	0.337815	−	1.03969i	0.0113299	−	0.0348700i
$890$	9.17161	−	6.66356i	0.307433	−	0.223363i
$891$	−7.77192	+	5.64663i	−0.260369	+	0.189169i
$892$	−11.6237	−	8.44512i	−0.389190	−	0.282763i
$893$	3.32865			0.111389
$894$	12.5282			0.419005
$895$	−0.394914	−	0.286922i	−0.0132005	−	0.00959074i
$896$	2.53553	+	7.80355i	0.0847060	+	0.260698i
$897$	2.66381	−	8.19836i	0.0889420	−	0.273735i
$898$	−6.34235			−0.211647
$899$		0			0
$900$	29.1430			0.971434
$901$	1.44586	−	4.44989i	0.0481685	−	0.148247i
$902$	−0.662885	−	2.04015i	−0.0220717	−	0.0679296i
$903$	−3.98869	−	2.89795i	−0.132735	−	0.0964378i
$904$	15.5059			0.515719
$905$	−28.6665			−0.952906
$906$	−7.73803	−	5.62201i	−0.257079	−	0.186779i
$907$	17.9518	−	13.0427i	0.596079	−	0.433077i	−0.248406	−	0.968656i	$-0.579907\pi$
$907$	17.9518	−	13.0427i	0.596079	−	0.433077i	0.844485	+	0.535579i	$0.179907\pi$
$908$	26.8431	−	19.5027i	0.890820	−	0.647218i
$909$	−2.57158	+	7.91450i	−0.0852938	+	0.262507i
$910$	4.59383	+	3.33761i	0.152284	+	0.110641i
$911$	8.90971	−	27.4213i	0.295192	−	0.908507i	−0.687965	−	0.725744i	$-0.741496\pi$
$911$	8.90971	−	27.4213i	0.295192	−	0.908507i	0.983157	−	0.182763i	$-0.0585042\pi$
$912$	−1.45537	−	4.47918i	−0.0481923	−	0.148320i
$913$	−46.9732	+	34.1280i	−1.55458	+	1.12947i
$914$	−6.64760	−	20.4592i	−0.219883	−	0.676731i
$915$	−2.39551	−	7.37263i	−0.0791932	−	0.243732i
$916$	−20.9139	+	15.1948i	−0.691013	+	0.502051i
$917$	1.48451	+	4.56884i	0.0490227	+	0.150876i
$918$	−1.30466	+	4.01534i	−0.0430603	+	0.132526i
$919$	−38.8832	−	28.2503i	−1.28264	−	0.931893i	−0.283011	−	0.959117i	$-0.591333\pi$
$919$	−38.8832	−	28.2503i	−1.28264	−	0.931893i	−0.999629	+	0.0272242i	$0.991333\pi$
$920$	9.14051	−	28.1316i	0.301354	−	0.927471i
$921$	−22.4274	+	16.2944i	−0.739007	+	0.536920i
$922$	3.71975	−	2.70256i	0.122503	−	0.0890039i
$923$	18.2110	+	13.2311i	0.599424	+	0.435507i
$924$	−4.32255			−0.142201
$925$	91.0668			2.99426
$926$	−19.7010	−	14.3136i	−0.647416	−	0.470376i
$927$	4.21840	+	12.9829i	0.138551	+	0.426415i
$928$	8.78572	−	27.0397i	0.288405	−	0.887621i
$929$	−7.01617			−0.230193			−0.115097	−	0.993354i	$-0.536718\pi$
$929$	−7.01617			−0.230193			−0.115097	+	0.993354i	$0.536718\pi$
$930$		0			0
$931$	24.3825			0.799105
$932$	4.63406	−	14.2622i	0.151794	−	0.467173i
$933$	0.664074	+	2.04381i	0.0217408	+	0.0669113i
$934$	20.0497	+	14.5669i	0.656045	+	0.476644i
$935$	−19.9664			−0.652972
$936$	−15.4554			−0.505176
$937$	10.4207	+	7.57106i	0.340428	+	0.247336i	0.744843	−	0.667240i	$-0.232525\pi$
$937$	10.4207	+	7.57106i	0.340428	+	0.247336i	−0.404414	+	0.914576i	$0.632525\pi$
$938$	−0.888663	+	0.645651i	−0.0290159	+	0.0210813i
$939$	7.84490	−	5.69965i	0.256009	−	0.186001i
$940$	1.53024	−	4.70958i	0.0499108	−	0.153610i
$941$	−40.4826	−	29.4123i	−1.31969	−	0.958815i	−0.999936	−	0.0113156i	$-0.996398\pi$
$941$	−40.4826	−	29.4123i	−1.31969	−	0.958815i	−0.319759	−	0.947499i	$-0.603602\pi$
$942$	−2.91237	+	8.96334i	−0.0948900	+	0.292041i
$943$	0.766899	+	2.36027i	0.0249737	+	0.0768611i
$944$	−1.03045	+	0.748663i	−0.0335382	+	0.0243669i
$945$	−4.09278	−	12.5963i	−0.133138	−	0.409757i
$946$	−6.27584	−	19.3151i	−0.204045	−	0.627987i
$947$	41.9620	−	30.4872i	1.36358	−	0.990701i	0.365375	−	0.930860i	$-0.380941\pi$
$947$	41.9620	−	30.4872i	1.36358	−	0.990701i	0.998208	−	0.0598409i	$-0.0190593\pi$
$948$	−5.99231	−	18.4424i	−0.194621	−	0.598982i
$949$	5.08699	−	15.6562i	0.165131	−	0.508220i
$950$	−18.5358	−	13.4671i	−0.601382	−	0.436929i
$951$	2.43898	−	7.50642i	0.0790894	−	0.243412i
$952$	1.96394	−	1.42688i	0.0636516	−	0.0462456i
$953$	15.1571	−	11.0123i	0.490987	−	0.356723i	−0.314577	−	0.949232i	$-0.601863\pi$
$953$	15.1571	−	11.0123i	0.490987	−	0.356723i	0.805564	+	0.592509i	$0.201863\pi$
$954$	4.35947	+	3.16734i	0.141143	+	0.102547i
$955$	−78.2385			−2.53174
$956$	0.900482			0.0291237
$957$	14.7096	+	10.6872i	0.475494	+	0.345467i
$958$	−7.08322	−	21.7999i	−0.228848	−	0.704323i
$959$	−3.00772	+	9.25682i	−0.0971245	+	0.298918i
$960$	4.20549			0.135731
$961$		0			0
$962$	−20.8907			−0.673542
$963$	−1.57194	+	4.83793i	−0.0506550	+	0.155900i
$964$	7.24144	+	22.2868i	0.233231	+	0.717811i
$965$	−16.9866	−	12.3415i	−0.546817	−	0.397285i
$966$	−1.55935			−0.0501712
$967$	47.7846			1.53665			0.768324	−	0.640061i	$-0.221091\pi$
$967$	47.7846			1.53665			0.768324	+	0.640061i	$0.221091\pi$
$968$	−11.6752	−	8.48250i	−0.375254	−	0.272638i
$969$	−3.62969	+	2.63713i	−0.116603	+	0.0847167i
$970$	−10.9147	+	7.92996i	−0.350449	+	0.254616i
$971$	−9.61063	+	29.5785i	−0.308420	+	0.949219i	0.669959	+	0.742398i	$0.266312\pi$
$971$	−9.61063	+	29.5785i	−0.308420	+	0.949219i	−0.978379	+	0.206821i	$0.933688\pi$
$972$	19.9137	+	14.4682i	0.638733	+	0.464067i
$973$	−4.41460	+	13.5868i	−0.141526	+	0.435571i
$974$	6.07562	+	18.6988i	0.194676	+	0.599150i
$975$	−18.5783	+	13.4979i	−0.594982	+	0.432280i
$976$	−0.983507	−	3.02692i	−0.0314813	−	0.0968894i
$977$	−6.82283	−	20.9985i	−0.218282	−	0.671802i	−0.998904	−	0.0467994i	$-0.985098\pi$
$977$	−6.82283	−	20.9985i	−0.218282	−	0.671802i	0.780623	−	0.625003i	$-0.214902\pi$
$978$	−0.525955	+	0.382129i	−0.0168182	+	0.0122191i
$979$	5.64018	+	17.3587i	0.180261	+	0.554786i
$980$	11.2091	−	34.4979i	0.358060	−	1.10200i
$981$	2.61139	+	1.89729i	0.0833754	+	0.0605758i
$982$	−5.95807	+	18.3371i	−0.190130	+	0.585159i
$983$	−30.4003	+	22.0871i	−0.969620	+	0.704470i	−0.955365	−	0.295428i	$-0.904538\pi$
$983$	−30.4003	+	22.0871i	−0.969620	+	0.704470i	−0.0142549	+	0.999898i	$0.504538\pi$
$984$	−1.34118	+	0.974425i	−0.0427553	+	0.0310635i
$985$	47.7355	+	34.6819i	1.52098	+	1.10506i
$986$	−4.41693			−0.140664
$987$	−0.603511			−0.0192100
$988$	−13.6364	−	9.90744i	−0.433832	−	0.315198i
$989$	7.26059	+	22.3458i	0.230873	+	0.710555i
$990$	7.10585	−	21.8695i	0.225839	−	0.695060i
$991$	6.77397			0.215182			0.107591	−	0.994195i	$-0.465686\pi$
$991$	6.77397			0.215182			0.107591	+	0.994195i	$0.465686\pi$
$992$		0			0
$993$	29.2099			0.926948
$994$	1.25829	−	3.87263i	0.0399106	−	0.122832i
$995$	4.88229	+	15.0261i	0.154779	+	0.476360i
$996$	15.7025	+	11.4086i	0.497554	+	0.361494i
$997$	−29.5733			−0.936595			−0.468298	−	0.883571i	$-0.655132\pi$
$997$	−29.5733			−0.936595			−0.468298	+	0.883571i	$0.655132\pi$
$998$	−28.4795			−0.901502
$999$	39.4211	+	28.6411i	1.24723	+	0.906165i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.q.628.1		16
31.2	even	5		961.2.a.j.1.3		8
31.3	odd	30		961.2.g.k.816.2		16
31.4	even	5	inner	961.2.d.q.531.1		16
31.5	even	3		961.2.g.n.448.1		16
31.6	odd	6		961.2.g.s.846.1		16
31.7	even	15		961.2.g.n.547.1		16
31.8	even	5		961.2.d.n.388.4		16
31.9	even	15		961.2.g.j.338.2		16
31.10	even	15		961.2.c.i.521.3		16
31.11	odd	30		961.2.g.s.844.1		16
31.12	odd	30		961.2.c.j.439.3		16
31.13	odd	30		31.2.g.a.19.2	yes	16
31.14	even	15		961.2.g.l.235.2		16
31.15	odd	10		961.2.d.o.374.4		16
31.16	even	5		961.2.d.n.374.4		16
31.17	odd	30		31.2.g.a.18.2	✓	16
31.18	even	15		961.2.g.l.732.2		16
31.19	even	15		961.2.c.i.439.3		16
31.20	even	15		961.2.g.m.844.1		16
31.21	odd	30		961.2.c.j.521.3		16
31.22	odd	30		961.2.g.k.338.2		16
31.23	odd	10		961.2.d.o.388.4		16
31.24	odd	30		961.2.g.t.547.1		16
31.25	even	3		961.2.g.m.846.1		16
31.26	odd	6		961.2.g.t.448.1		16
31.27	odd	10		961.2.d.p.531.1		16
31.28	even	15		961.2.g.j.816.2		16
31.29	odd	10		961.2.a.i.1.3		8
31.30	odd	2		961.2.d.p.628.1		16
93.2	odd	10		8649.2.a.be.1.6		8
93.17	even	30		279.2.y.c.235.1		16
93.29	even	10		8649.2.a.bf.1.6		8
93.44	even	30		279.2.y.c.19.1		16
124.75	even	30		496.2.bg.c.81.1		16
124.79	even	30		496.2.bg.c.49.1		16
155.13	even	60		775.2.ck.a.174.3		32
155.17	even	60		775.2.ck.a.49.3		32
155.44	odd	30		775.2.bl.a.701.1		16
155.48	even	60		775.2.ck.a.49.2		32
155.79	odd	30		775.2.bl.a.576.1		16
155.137	even	60		775.2.ck.a.174.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.18.2	✓	16	31.17	odd	30
31.2.g.a.19.2	yes	16	31.13	odd	30
279.2.y.c.19.1		16	93.44	even	30
279.2.y.c.235.1		16	93.17	even	30
496.2.bg.c.49.1		16	124.79	even	30
496.2.bg.c.81.1		16	124.75	even	30
775.2.bl.a.576.1		16	155.79	odd	30
775.2.bl.a.701.1		16	155.44	odd	30
775.2.ck.a.49.2		32	155.48	even	60
775.2.ck.a.49.3		32	155.17	even	60
775.2.ck.a.174.2		32	155.137	even	60
775.2.ck.a.174.3		32	155.13	even	60
961.2.a.i.1.3		8	31.29	odd	10
961.2.a.j.1.3		8	31.2	even	5
961.2.c.i.439.3		16	31.19	even	15
961.2.c.i.521.3		16	31.10	even	15
961.2.c.j.439.3		16	31.12	odd	30
961.2.c.j.521.3		16	31.21	odd	30
961.2.d.n.374.4		16	31.16	even	5
961.2.d.n.388.4		16	31.8	even	5
961.2.d.o.374.4		16	31.15	odd	10
961.2.d.o.388.4		16	31.23	odd	10
961.2.d.p.531.1		16	31.27	odd	10
961.2.d.p.628.1		16	31.30	odd	2
961.2.d.q.531.1		16	31.4	even	5	inner
961.2.d.q.628.1		16	1.1	even	1	trivial
961.2.g.j.338.2		16	31.9	even	15
961.2.g.j.816.2		16	31.28	even	15
961.2.g.k.338.2		16	31.22	odd	30
961.2.g.k.816.2		16	31.3	odd	30
961.2.g.l.235.2		16	31.14	even	15
961.2.g.l.732.2		16	31.18	even	15
961.2.g.m.844.1		16	31.20	even	15
961.2.g.m.846.1		16	31.25	even	3
961.2.g.n.448.1		16	31.5	even	3
961.2.g.n.547.1		16	31.7	even	15
961.2.g.s.844.1		16	31.11	odd	30
961.2.g.s.846.1		16	31.6	odd	6
961.2.g.t.448.1		16	31.26	odd	6
961.2.g.t.547.1		16	31.24	odd	30
8649.2.a.be.1.6		8	93.2	odd	10
8649.2.a.bf.1.6		8	93.29	even	10

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.213065 + 0.655747i) q^{2} +(0.278857 + 0.858234i) q^{3} +(1.23343 + 0.896137i) q^{4} +3.70752 q^{5} -0.622199 q^{6} +(-0.617599 - 0.448712i) q^{7} +(-1.96606 + 1.42843i) q^{8} +(1.76825 - 1.28471i) q^{9} +(-0.789942 + 2.43119i) q^{10} +(-3.32961 - 2.41910i) q^{11} +(-0.425146 + 1.30846i) q^{12} +(0.899163 + 2.76734i) q^{13} +(0.425830 - 0.309383i) q^{14} +(1.03387 + 3.18192i) q^{15} +(0.424467 + 1.30637i) q^{16} +(1.05862 - 0.769131i) q^{17} +(0.465690 + 1.43325i) q^{18} +(-1.17412 + 3.61358i) q^{19} +(4.57295 + 3.32244i) q^{20} +(0.212878 - 0.655171i) q^{21} +(2.29574 - 1.66795i) q^{22} +(-2.65597 + 1.92967i) q^{23} +(-1.77418 - 1.28901i) q^{24} +8.74568 q^{25} -2.00625 q^{26} +(3.78584 + 2.75057i) q^{27} +(-0.359656 - 1.10691i) q^{28} +(-1.51283 + 4.65602i) q^{29} -2.30681 q^{30} -5.80746 q^{32} +(1.14767 - 3.53217i) q^{33} +(0.278801 + 0.858060i) q^{34} +(-2.28976 - 1.66361i) q^{35} +3.33228 q^{36} +10.4128 q^{37} +(-2.11943 - 1.53985i) q^{38} +(-2.12429 + 1.54338i) q^{39} +(-7.28921 + 5.29592i) q^{40} +(0.233600 - 0.718947i) q^{41} +(0.384269 + 0.279188i) q^{42} +(2.21160 - 6.80661i) q^{43} +(-1.93898 - 5.96757i) q^{44} +(6.55580 - 4.76307i) q^{45} +(-0.699483 - 2.15279i) q^{46} +(-0.270719 - 0.833189i) q^{47} +(-1.00281 + 0.728584i) q^{48} +(-1.98303 - 6.10315i) q^{49} +(-1.86340 + 5.73495i) q^{50} +(0.955298 + 0.694065i) q^{51} +(-1.37086 + 4.21908i) q^{52} +(2.89281 - 2.10175i) q^{53} +(-2.61031 + 1.89650i) q^{54} +(-12.3446 - 8.96886i) q^{55} +1.85519 q^{56} -3.42871 q^{57} +(-2.73084 - 1.98407i) q^{58} +(0.286542 + 0.881886i) q^{59} +(-1.57623 + 4.85115i) q^{60} -2.31704 q^{61} -1.66853 q^{63} +(0.388433 - 1.19547i) q^{64} +(3.33366 + 10.2599i) q^{65} +(2.07168 + 1.50516i) q^{66} -2.08690 q^{67} +1.99498 q^{68} +(-2.39675 - 1.74134i) q^{69} +(1.57877 - 1.14704i) q^{70} +(6.25862 - 4.54716i) q^{71} +(-1.64137 + 5.05162i) q^{72} +(-4.57700 - 3.32538i) q^{73} +(-2.21860 + 6.82815i) q^{74} +(2.43880 + 7.50584i) q^{75} +(-4.68646 + 3.40491i) q^{76} +(0.970882 + 2.98807i) q^{77} +(-0.559458 - 1.72183i) q^{78} +(-11.4029 + 8.28467i) q^{79} +(1.57372 + 4.84341i) q^{80} +(0.721302 - 2.21994i) q^{81} +(0.421675 + 0.306365i) q^{82} +(4.35952 - 13.4172i) q^{83} +(0.849692 - 0.617338i) q^{84} +(3.92484 - 2.85157i) q^{85} +(3.99219 + 2.90050i) q^{86} -4.41782 q^{87} +10.0017 q^{88} +(-3.58784 - 2.60672i) q^{89} +(1.72655 + 5.31379i) q^{90} +(0.686415 - 2.11257i) q^{91} -5.00520 q^{92} +0.604042 q^{94} +(-4.35308 + 13.3974i) q^{95} +(-1.61945 - 4.98416i) q^{96} +(4.26970 + 3.10212i) q^{97} +4.42463 q^{98} -8.99540 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + 6 q^{3} + 6 q^{4} + 6 q^{5} + 22 q^{6} - 9 q^{7} - 8 q^{8} - 10 q^{9} - 6 q^{10} - 4 q^{11} + 5 q^{12} - 9 q^{13} - 18 q^{14} - 4 q^{15} - 2 q^{16} - 17 q^{17} - 14 q^{18} - 7 q^{19} + 36 q^{20}+ \cdots + 12 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 + 6 * q^5 + 22 * q^6 - 9 * q^7 - 8 * q^8 - 10 * q^9 - 6 * q^10 - 4 * q^11 + 5 * q^12 - 9 * q^13 - 18 * q^14 - 4 * q^15 - 2 * q^16 - 17 * q^17 - 14 * q^18 - 7 * q^19 + 36 * q^20 - 2 * q^21 + 8 * q^22 - 21 * q^23 - 5 * q^24 + 26 * q^25 + 18 * q^26 - 9 * q^27 + 20 * q^28 - 26 * q^29 + 22 * q^30 - 42 * q^32 + 7 * q^33 + 56 * q^34 + 21 * q^35 - 2 * q^36 - 16 * q^37 + 24 * q^38 + 2 * q^39 - 13 * q^40 + 6 * q^41 - 12 * q^42 + 16 * q^43 - 37 * q^44 - 5 * q^45 + 16 * q^46 + 4 * q^47 - 37 * q^48 - 39 * q^49 - 21 * q^50 - 11 * q^51 + 18 * q^52 - 3 * q^53 - 39 * q^54 - 29 * q^55 + 60 * q^56 - 34 * q^57 - 10 * q^58 - 3 * q^59 - 35 * q^60 + 60 * q^61 - 46 * q^63 - 32 * q^64 - 9 * q^65 + 20 * q^66 - 26 * q^67 + 60 * q^68 - 21 * q^69 + 27 * q^70 + 18 * q^71 - 4 * q^72 + 9 * q^73 - 64 * q^74 - 19 * q^75 + 9 * q^76 + 42 * q^77 + 15 * q^78 - 14 * q^79 + 18 * q^80 + 29 * q^81 + 32 * q^82 - 67 * q^83 - 39 * q^84 + 63 * q^85 + 23 * q^86 - 30 * q^87 - 34 * q^88 - 26 * q^89 - 24 * q^90 - 8 * q^91 + 64 * q^92 + 44 * q^94 + 28 * q^95 - 4 * q^96 - 37 * q^97 + 20 * q^98 + 12 * q^99

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