LMFDB - Embedded newform 961.2.d.o.388.1

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,-6,9,-14] 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			388.1
Root			$-1.42343i$ of defining polynomial
Character	$\chi$	$=$	961.388
Dual form			961.2.d.o.374.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.86683 + 1.35633i) q^{2} +(2.05711 + 1.49458i) q^{3} +(1.02738 - 3.16196i) q^{4} -2.49846 q^{5} -5.86740 q^{6} +(0.495008 - 1.52348i) q^{7} +(0.944583 + 2.90713i) q^{8} +(1.07088 + 3.29583i) q^{9} +(4.66419 - 3.38874i) q^{10} +(0.226712 - 0.697749i) q^{11} +(6.83922 - 4.96899i) q^{12} +(1.53388 + 1.11443i) q^{13} +(1.14224 + 3.51546i) q^{14} +(-5.13960 - 3.73414i) q^{15} +(-0.326952 - 0.237545i) q^{16} +(-1.35326 - 4.16490i) q^{17} +(-6.46939 - 4.70029i) q^{18} +(3.75224 - 2.72616i) q^{19} +(-2.56687 + 7.90002i) q^{20} +(3.29524 - 2.39413i) q^{21} +(0.523145 + 1.61007i) q^{22} +(-2.19973 - 6.77006i) q^{23} +(-2.40181 + 7.39202i) q^{24} +1.24230 q^{25} -4.37501 q^{26} +(-0.365721 + 1.12557i) q^{27} +(-4.30861 - 3.13039i) q^{28} +(0.104314 - 0.0757884i) q^{29} +14.6595 q^{30} -5.18091 q^{32} +(1.50921 - 1.09651i) q^{33} +(8.17529 + 5.93970i) q^{34} +(-1.23676 + 3.80635i) q^{35} +11.5215 q^{36} +8.42948 q^{37} +(-3.30721 + 10.1786i) q^{38} +(1.48975 + 4.58499i) q^{39} +(-2.36000 - 7.26334i) q^{40} +(5.96567 - 4.33432i) q^{41} +(-2.90441 + 8.93885i) q^{42} +(-0.186472 + 0.135480i) q^{43} +(-1.97333 - 1.43371i) q^{44} +(-2.67555 - 8.23451i) q^{45} +(13.2889 + 9.65498i) q^{46} +(6.50168 + 4.72375i) q^{47} +(-0.317547 - 0.977310i) q^{48} +(3.58717 + 2.60623i) q^{49} +(-2.31916 + 1.68497i) q^{50} +(3.44097 - 10.5902i) q^{51} +(5.09965 - 3.70511i) q^{52} +(1.77198 + 5.45359i) q^{53} +(-0.843912 - 2.59729i) q^{54} +(-0.566432 + 1.74330i) q^{55} +4.89652 q^{56} +11.7932 q^{57} +(-0.0919419 + 0.282968i) q^{58} +(-7.68867 - 5.58614i) q^{59} +(-17.0875 + 12.4148i) q^{60} -7.84044 q^{61} +5.55122 q^{63} +(10.3258 - 7.50212i) q^{64} +(-3.83233 - 2.78435i) q^{65} +(-1.33021 + 4.09397i) q^{66} +4.82658 q^{67} -14.5596 q^{68} +(5.59330 - 17.2144i) q^{69} +(-2.85385 - 8.78324i) q^{70} +(-1.05221 - 3.23836i) q^{71} +(-8.56987 + 6.22638i) q^{72} +(0.831888 - 2.56029i) q^{73} +(-15.7364 + 11.4332i) q^{74} +(2.55554 + 1.85671i) q^{75} +(-4.76503 - 14.6652i) q^{76} +(-0.950780 - 0.690782i) q^{77} +(-8.99987 - 6.53879i) q^{78} +(1.39921 + 4.30633i) q^{79} +(0.816877 + 0.593496i) q^{80} +(5.97623 - 4.34198i) q^{81} +(-5.25813 + 16.1829i) q^{82} +(-2.16036 + 1.56959i) q^{83} +(-4.18467 - 12.8791i) q^{84} +(3.38106 + 10.4058i) q^{85} +(0.164356 - 0.505834i) q^{86} +0.327856 q^{87} +2.24259 q^{88} +(-0.681255 + 2.09669i) q^{89} +(16.1635 + 11.7435i) q^{90} +(2.45708 - 1.78518i) q^{91} -23.6666 q^{92} -18.5445 q^{94} +(-9.37482 + 6.81121i) q^{95} +(-10.6577 - 7.74327i) q^{96} +(3.79778 - 11.6884i) q^{97} -10.2315 q^{98} +2.54245 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} + 9 q^{3} - 14 q^{4} + 6 q^{5} - 22 q^{6} + 11 q^{7} + 17 q^{8} + 5 q^{9} + 19 q^{10} + 14 q^{11} + 5 q^{12} - q^{13} + 27 q^{14} + 14 q^{15} - 2 q^{16} - 3 q^{17} - 9 q^{18} + 13 q^{19}+ \cdots - 12 q^{99}+O(q^{100}) $ 16 * q - 6 * q^2 + 9 * q^3 - 14 * q^4 + 6 * q^5 - 22 * q^6 + 11 * q^7 + 17 * q^8 + 5 * q^9 + 19 * q^10 + 14 * q^11 + 5 * q^12 - q^13 + 27 * q^14 + 14 * q^15 - 2 * q^16 - 3 * q^17 - 9 * q^18 + 13 * q^19 - 29 * q^20 - 3 * q^21 + 12 * q^22 + q^23 + 25 * q^24 + 26 * q^25 - 18 * q^26 + 9 * q^27 - 15 * q^28 - 14 * q^29 - 22 * q^30 - 42 * q^32 - 13 * q^33 + 49 * q^34 - 9 * q^35 - 2 * q^36 + 16 * q^37 - 31 * q^38 - 3 * q^39 + 2 * q^40 + 16 * q^41 - 18 * q^42 + 14 * q^43 - 33 * q^44 + 5 * q^45 + 34 * q^46 + 14 * q^47 - 38 * q^48 + 41 * q^49 - 6 * q^50 + 9 * q^51 + 17 * q^52 + 3 * q^53 - 46 * q^54 - q^55 + 60 * q^56 + 34 * q^57 - 15 * q^58 + 7 * q^59 - 75 * q^60 - 60 * q^61 - 46 * q^63 + 23 * q^64 - 6 * q^65 - 30 * q^66 - 26 * q^67 - 60 * q^68 - q^69 + 12 * q^70 - 17 * q^71 + q^72 + 11 * q^73 - 56 * q^74 + 4 * q^75 + 24 * q^76 + 18 * q^77 - 15 * q^78 - 6 * q^79 - 42 * q^80 - q^81 - 13 * q^82 - 28 * q^83 - 31 * q^84 + 37 * q^85 + 7 * q^86 - 30 * q^87 + 34 * q^88 + q^89 + 16 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 - 22 * q^95 - 16 * q^96 + 3 * q^97 + 20 * q^98 - 12 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−1.86683	+	1.35633i	−1.32005	+	0.959070i	−0.320115	+	0.947379i	$0.603722\pi$
$2$	−1.86683	+	1.35633i	−1.32005	+	0.959070i	−0.999932	+	0.0116917i	$0.996278\pi$
$3$	2.05711	+	1.49458i	1.18767	+	0.862894i	0.993016	−	0.117978i	$-0.0376413\pi$
$3$	2.05711	+	1.49458i	1.18767	+	0.862894i	0.194655	+	0.980872i	$0.437641\pi$
$4$	1.02738	−	3.16196i	0.513691	−	1.58098i
$5$	−2.49846			−1.11735			−0.558673	−	0.829388i	$-0.688689\pi$
$5$	−2.49846			−1.11735			−0.558673	+	0.829388i	$0.688689\pi$
$6$	−5.86740			−2.39536
$7$	0.495008	−	1.52348i	0.187095	−	0.575820i	−0.812883	−	0.582427i	$-0.802103\pi$
$7$	0.495008	−	1.52348i	0.187095	−	0.575820i	0.999978	+	0.00660707i	$0.00210311\pi$
$8$	0.944583	+	2.90713i	0.333960	+	1.02782i
$9$	1.07088	+	3.29583i	0.356961	+	1.09861i
$10$	4.66419	−	3.38874i	1.47495	−	1.07161i
$11$	0.226712	−	0.697749i	0.0683564	−	0.210379i	−0.911043	−	0.412311i	$-0.864722\pi$
$11$	0.226712	−	0.697749i	0.0683564	−	0.210379i	0.979400	+	0.201931i	$0.0647218\pi$
$12$	6.83922	−	4.96899i	1.97431	−	1.43442i
$13$	1.53388	+	1.11443i	0.425421	+	0.309086i	0.779815	−	0.626010i	$-0.215313\pi$
$13$	1.53388	+	1.11443i	0.425421	+	0.309086i	−0.354394	+	0.935096i	$0.615313\pi$
$14$	1.14224	+	3.51546i	0.305277	+	0.939547i
$15$	−5.13960	−	3.73414i	−1.32704	−	0.964150i
$16$	−0.326952	−	0.237545i	−0.0817381	−	0.0593862i
$17$	−1.35326	−	4.16490i	−0.328214	−	1.01014i	−0.969969	−	0.243228i	$-0.921794\pi$
$17$	−1.35326	−	4.16490i	−0.328214	−	1.01014i	0.641755	−	0.766909i	$-0.278206\pi$
$18$	−6.46939	−	4.70029i	−1.52485	−	1.10787i
$19$	3.75224	−	2.72616i	0.860823	−	0.625425i	−0.0672855	−	0.997734i	$-0.521434\pi$
$19$	3.75224	−	2.72616i	0.860823	−	0.625425i	0.928109	+	0.372309i	$0.121434\pi$
$20$	−2.56687	+	7.90002i	−0.573970	+	1.76650i
$21$	3.29524	−	2.39413i	0.719079	−	0.522442i
$22$	0.523145	+	1.61007i	0.111535	+	0.343269i
$23$	−2.19973	−	6.77006i	−0.458675	−	1.41166i	−0.866766	−	0.498714i	$-0.833806\pi$
$23$	−2.19973	−	6.77006i	−0.458675	−	1.41166i	0.408092	−	0.912941i	$-0.366194\pi$
$24$	−2.40181	+	7.39202i	−0.490268	+	1.50889i
$25$	1.24230			0.248460
$26$	−4.37501			−0.858011
$27$	−0.365721	+	1.12557i	−0.0703831	+	0.216617i
$28$	−4.30861	−	3.13039i	−0.814250	−	0.591588i
$29$	0.104314	−	0.0757884i	0.0193706	−	0.0140736i	−0.578058	−	0.815996i	$-0.696189\pi$
$29$	0.104314	−	0.0757884i	0.0193706	−	0.0140736i	0.597428	+	0.801922i	$0.296189\pi$
$30$	14.6595			2.67644
$31$		0			0
$31$		0			0
$32$	−5.18091			−0.915865
$33$	1.50921	−	1.09651i	0.262720	−	0.190877i
$34$	8.17529	+	5.93970i	1.40205	+	1.01865i
$35$	−1.23676	+	3.80635i	−0.209050	+	0.643390i
$36$	11.5215			1.92025
$37$	8.42948			1.38580			0.692899	−	0.721035i	$-0.256333\pi$
$37$	8.42948			1.38580			0.692899	+	0.721035i	$0.256333\pi$
$38$	−3.30721	+	10.1786i	−0.536501	+	1.65118i
$39$	1.48975	+	4.58499i	0.238551	+	0.734186i
$40$	−2.36000	−	7.26334i	−0.373149	−	1.14843i
$41$	5.96567	−	4.33432i	0.931682	−	0.676907i	−0.0147221	−	0.999892i	$-0.504686\pi$
$41$	5.96567	−	4.33432i	0.931682	−	0.676907i	0.946404	+	0.322985i	$0.104686\pi$
$42$	−2.90441	+	8.93885i	−0.448160	+	1.37930i
$43$	−0.186472	+	0.135480i	−0.0284367	+	0.0206605i	−0.601913	−	0.798562i	$-0.705595\pi$
$43$	−0.186472	+	0.135480i	−0.0284367	+	0.0206605i	0.573476	+	0.819222i	$0.305595\pi$
$44$	−1.97333	−	1.43371i	−0.297491	−	0.216140i
$45$	−2.67555	−	8.23451i	−0.398848	−	1.22753i
$46$	13.2889	+	9.65498i	1.95935	+	1.42355i
$47$	6.50168	+	4.72375i	0.948368	+	0.689030i	0.950420	−	0.310968i	$-0.100653\pi$
$47$	6.50168	+	4.72375i	0.948368	+	0.689030i	−0.00205222	+	0.999998i	$0.500653\pi$
$48$	−0.317547	−	0.977310i	−0.0458340	−	0.141063i
$49$	3.58717	+	2.60623i	0.512453	+	0.372319i
$50$	−2.31916	+	1.68497i	−0.327979	+	0.238290i
$51$	3.44097	−	10.5902i	0.481832	−	1.48293i
$52$	5.09965	−	3.70511i	0.707194	−	0.513806i
$53$	1.77198	+	5.45359i	0.243400	+	0.749108i	0.995896	+	0.0905104i	$0.0288498\pi$
$53$	1.77198	+	5.45359i	0.243400	+	0.749108i	−0.752496	+	0.658597i	$0.771150\pi$
$54$	−0.843912	−	2.59729i	−0.114842	−	0.353447i
$55$	−0.566432	+	1.74330i	−0.0763776	+	0.235066i
$56$	4.89652			0.654324
$57$	11.7932			1.56205
$58$	−0.0919419	+	0.282968i	−0.0120726	+	0.0371555i
$59$	−7.68867	−	5.58614i	−1.00098	−	0.727254i	−0.0386815	−	0.999252i	$-0.512316\pi$
$59$	−7.68867	−	5.58614i	−1.00098	−	0.727254i	−0.962298	+	0.271997i	$0.912316\pi$
$60$	−17.0875	+	12.4148i	−2.20599	+	1.60274i
$61$	−7.84044			−1.00387			−0.501933	−	0.864907i	$-0.667377\pi$
$61$	−7.84044			−1.00387			−0.501933	+	0.864907i	$0.667377\pi$
$62$		0			0
$63$	5.55122			0.699388
$64$	10.3258	−	7.50212i	1.29072	−	0.937765i
$65$	−3.83233	−	2.78435i	−0.475342	−	0.345356i
$66$	−1.33021	+	4.09397i	−0.163738	+	0.503933i
$67$	4.82658			0.589660			0.294830	−	0.955550i	$-0.404737\pi$
$67$	4.82658			0.589660			0.294830	+	0.955550i	$0.404737\pi$
$68$	−14.5596			−1.76561
$69$	5.59330	−	17.2144i	0.673354	−	2.07237i
$70$	−2.85385	−	8.78324i	−0.341100	−	1.04980i
$71$	−1.05221	−	3.23836i	−0.124874	−	0.384323i	0.869004	−	0.494805i	$-0.164761\pi$
$71$	−1.05221	−	3.23836i	−0.124874	−	0.384323i	−0.993878	+	0.110482i	$0.964761\pi$
$72$	−8.56987	+	6.22638i	−1.00997	+	0.733785i
$73$	0.831888	−	2.56029i	0.0973651	−	0.299659i	−0.890498	−	0.454988i	$-0.849644\pi$
$73$	0.831888	−	2.56029i	0.0973651	−	0.299659i	0.987863	+	0.155329i	$0.0496437\pi$
$74$	−15.7364	+	11.4332i	−1.82932	+	1.32908i
$75$	2.55554	+	1.85671i	0.295089	+	0.214394i
$76$	−4.76503	−	14.6652i	−0.546586	−	1.68222i
$77$	−0.950780	−	0.690782i	−0.108351	−	0.0787219i
$78$	−8.99987	−	6.53879i	−1.01903	−	0.740372i
$79$	1.39921	+	4.30633i	0.157424	+	0.484500i	0.998398	−	0.0565742i	$-0.0180178\pi$
$79$	1.39921	+	4.30633i	0.157424	+	0.484500i	−0.840975	+	0.541074i	$0.818018\pi$
$80$	0.816877	+	0.593496i	0.0913296	+	0.0663549i
$81$	5.97623	−	4.34198i	0.664025	−	0.482443i
$82$	−5.25813	+	16.1829i	−0.580663	+	1.78710i
$83$	−2.16036	+	1.56959i	−0.237130	+	0.172285i	−0.700004	−	0.714139i	$-0.746818\pi$
$83$	−2.16036	+	1.56959i	−0.237130	+	0.172285i	0.462874	+	0.886424i	$0.346818\pi$
$84$	−4.18467	−	12.8791i	−0.456585	−	1.40522i
$85$	3.38106	+	10.4058i	0.366728	+	1.12867i
$86$	0.164356	−	0.505834i	0.0177229	−	0.0545455i
$87$	0.327856			0.0351499
$88$	2.24259			0.239061
$89$	−0.681255	+	2.09669i	−0.0722129	+	0.222248i	−0.980649	−	0.195776i	$-0.937277\pi$
$89$	−0.681255	+	2.09669i	−0.0722129	+	0.222248i	0.908436	+	0.418025i	$0.137277\pi$
$90$	16.1635	+	11.7435i	1.70378	+	1.23787i
$91$	2.45708	−	1.78518i	0.257572	−	0.187137i
$92$	−23.6666			−2.46741
$93$		0			0
$94$	−18.5445			−1.91272
$95$	−9.37482	+	6.81121i	−0.961837	+	0.698815i
$96$	−10.6577	−	7.74327i	−1.08775	−	0.790294i
$97$	3.79778	−	11.6884i	0.385606	−	1.18677i	−0.550434	−	0.834879i	$-0.685538\pi$
$97$	3.79778	−	11.6884i	0.385606	−	1.18677i	0.936040	−	0.351894i	$-0.114462\pi$
$98$	−10.2315			−1.03354
$99$	2.54245			0.255526
$100$	1.27632	−	3.92810i	0.127632	−	0.392810i
$101$	2.26952	+	6.98486i	0.225826	+	0.695020i	0.998207	+	0.0598605i	$0.0190656\pi$
$101$	2.26952	+	6.98486i	0.225826	+	0.695020i	−0.772381	+	0.635159i	$0.780934\pi$
$102$	7.94012	+	24.4372i	0.786189	+	2.41964i
$103$	−4.52140	+	3.28499i	−0.445506	+	0.323679i	−0.787819	−	0.615907i	$-0.788790\pi$
$103$	−4.52140	+	3.28499i	−0.445506	+	0.323679i	0.342313	+	0.939586i	$0.388790\pi$
$104$	−1.79091	+	5.51184i	−0.175613	+	0.540480i
$105$	−8.23301	+	5.98163i	−0.803460	+	0.583748i
$106$	−10.7048	−	7.77752i	−1.03975	−	0.755420i
$107$	0.563696	+	1.73488i	0.0544946	+	0.167717i	0.974600	−	0.223955i	$-0.0718968\pi$
$107$	0.563696	+	1.73488i	0.0544946	+	0.167717i	−0.920105	+	0.391672i	$0.871897\pi$
$108$	3.18328	+	2.31279i	0.306312	+	0.222548i
$109$	−9.51832	−	6.91546i	−0.911689	−	0.662381i	0.0297521	−	0.999557i	$-0.490528\pi$
$109$	−9.51832	−	6.91546i	−0.911689	−	0.662381i	−0.941442	+	0.337176i	$0.890528\pi$
$110$	−1.30706	−	4.02271i	−0.124623	−	0.383550i
$111$	17.3403	+	12.5985i	1.64587	+	1.19580i
$112$	−0.523738	+	0.380518i	−0.0494886	+	0.0359556i
$113$	3.41604	−	10.5135i	0.321354	−	0.989026i	−0.651706	−	0.758472i	$-0.725946\pi$
$113$	3.41604	−	10.5135i	0.321354	−	0.989026i	0.973060	−	0.230554i	$-0.0740537\pi$
$114$	−22.0159	+	15.9955i	−2.06198	+	1.49812i
$115$	5.49593	+	16.9147i	0.512498	+	1.57731i
$116$	−0.132470	−	0.407700i	−0.0122995	−	0.0378540i
$117$	−2.03037	+	6.24882i	−0.187707	+	0.577704i
$118$	21.9301			2.01883
$119$	−7.01501			−0.643065
$120$	6.00083	−	18.4687i	0.547799	−	1.68595i
$121$	8.46373	+	6.14926i	0.769430	+	0.559024i
$122$	14.6368	−	10.6342i	1.32515	−	0.962777i
$123$	18.7500			1.69063
$124$		0			0
$125$	9.38846			0.839730
$126$	−10.3632	+	7.52929i	−0.923225	+	0.670762i
$127$	1.04123	+	0.756499i	0.0923943	+	0.0671284i	0.633023	−	0.774133i	$-0.281814\pi$
$127$	1.04123	+	0.756499i	0.0923943	+	0.0671284i	−0.540629	+	0.841261i	$0.681814\pi$
$128$	−5.89913	+	18.1557i	−0.521414	+	1.60475i
$129$	−0.586077			−0.0516012
$130$	10.9308			0.958694
$131$	−2.47843	+	7.62781i	−0.216541	+	0.666445i	0.782500	+	0.622651i	$0.213944\pi$
$131$	−2.47843	+	7.62781i	−0.216541	+	0.666445i	−0.999041	+	0.0437937i	$0.986056\pi$
$132$	−1.91657	−	5.89859i	−0.166816	−	0.513406i
$133$	−2.29586	−	7.06593i	−0.199076	−	0.612693i
$134$	−9.01039	+	6.54643i	−0.778379	+	0.565526i
$135$	0.913740	−	2.81220i	0.0786422	−	0.242036i
$136$	10.8296	−	7.86819i	0.928634	−	0.674692i
$137$	13.3300	+	9.68479i	1.13886	+	0.827428i	0.986960	−	0.160969i	$-0.0514618\pi$
$137$	13.3300	+	9.68479i	1.13886	+	0.827428i	0.151897	+	0.988396i	$0.451462\pi$
$138$	12.9067	+	39.7227i	1.09869	+	3.38142i
$139$	−5.93804	−	4.31424i	−0.503658	−	0.365929i	0.306755	−	0.951789i	$-0.400757\pi$
$139$	−5.93804	−	4.31424i	−0.503658	−	0.365929i	−0.810412	+	0.585860i	$0.800757\pi$
$140$	10.7649	+	7.82114i	0.909799	+	0.661007i
$141$	6.31466	+	19.4345i	0.531790	+	1.63668i
$142$	6.35658	+	4.61833i	0.533433	+	0.387561i
$143$	1.12534	−	0.817606i	0.0941056	−	0.0683717i
$144$	0.432781	−	1.33196i	0.0360651	−	0.110997i
$145$	−0.260624	+	0.189354i	−0.0216436	+	0.0157250i
$146$	1.91960	+	5.90793i	0.158868	+	0.488944i
$147$	3.48398	+	10.7226i	0.287354	+	0.884385i
$148$	8.66030	−	26.6537i	0.711872	−	2.19092i
$149$	−6.36193			−0.521189			−0.260595	−	0.965448i	$-0.583919\pi$
$149$	−6.36193			−0.521189			−0.260595	+	0.965448i	$0.583919\pi$
$150$	−7.28907			−0.595150
$151$	−1.70724	+	5.25433i	−0.138933	+	0.427592i	−0.996181	−	0.0873120i	$-0.972172\pi$
$151$	−1.70724	+	5.25433i	−0.138933	+	0.427592i	0.857248	+	0.514904i	$0.172172\pi$
$152$	11.4696	+	8.33316i	0.930308	+	0.675908i
$153$	12.2777	−	8.92024i	0.992590	−	0.721159i
$154$	2.71187			0.218529
$155$		0			0
$156$	16.0281			1.28327
$157$	−6.46767	+	4.69903i	−0.516176	+	0.375024i	−0.815161	−	0.579234i	$-0.803352\pi$
$157$	−6.46767	+	4.69903i	−0.516176	+	0.375024i	0.298985	+	0.954258i	$0.403352\pi$
$158$	−8.45290	−	6.14139i	−0.672476	−	0.488583i
$159$	−4.50565	+	13.8670i	−0.357321	+	1.09972i
$160$	12.9443			1.02334
$161$	−11.4029			−0.898675
$162$	−5.26743	+	16.2115i	−0.413848	+	1.27369i
$163$	−5.27350	−	16.2302i	−0.413052	−	1.27124i	−0.913981	−	0.405756i	$-0.867008\pi$
$163$	−5.27350	−	16.2302i	−0.413052	−	1.27124i	0.500929	−	0.865488i	$-0.332992\pi$
$164$	−7.57590	−	23.3162i	−0.591578	−	1.82069i
$165$	−3.77070	+	2.73957i	−0.293549	+	0.213276i
$166$	1.90413	−	5.86032i	0.147789	−	0.454849i
$167$	19.7175	−	14.3256i	1.52579	−	1.10855i	0.567265	−	0.823535i	$-0.308001\pi$
$167$	19.7175	−	14.3256i	1.52579	−	1.10855i	0.958523	−	0.285015i	$-0.0919986\pi$
$168$	10.0727	+	7.31821i	0.777122	+	0.564612i
$169$	−2.90639	−	8.94495i	−0.223568	−	0.688073i
$170$	−20.4256	−	14.8401i	−1.56657	−	1.13818i
$171$	13.0032	+	9.44737i	0.994379	+	0.722458i
$172$	0.236803	+	0.728805i	0.0180561	+	0.0555709i
$173$	−7.25980	−	5.27455i	−0.551952	−	0.401017i	0.276553	−	0.960999i	$-0.410808\pi$
$173$	−7.25980	−	5.27455i	−0.551952	−	0.401017i	−0.828505	+	0.559982i	$0.810808\pi$
$174$	−0.612051	+	0.444681i	−0.0463995	+	0.0337112i
$175$	0.614948	−	1.89261i	0.0464857	−	0.143068i
$176$	−0.239871	+	0.174276i	−0.0180809	+	0.0131366i
$177$	−7.46750	−	22.9826i	−0.561292	−	1.72748i
$178$	−1.57201	−	4.83816i	−0.117827	−	0.362635i
$179$	−3.48896	+	10.7379i	−0.260777	+	0.802590i	0.731859	+	0.681456i	$0.238653\pi$
$179$	−3.48896	+	10.7379i	−0.260777	+	0.802590i	−0.992636	+	0.121134i	$0.961347\pi$
$180$	−28.7860			−2.14558
$181$	−14.9410			−1.11056			−0.555279	−	0.831664i	$-0.687389\pi$
$181$	−14.9410			−1.11056			−0.555279	+	0.831664i	$0.687389\pi$
$182$	−2.16567	+	6.66523i	−0.160530	+	0.494060i
$183$	−16.1286	−	11.7181i	−1.19226	−	0.866229i
$184$	17.6036	−	12.7898i	1.29775	−	0.942874i
$185$	−21.0607			−1.54841
$186$		0			0
$187$	−3.21286			−0.234947
$188$	21.6160	−	15.7050i	1.57651	−	1.14540i
$189$	1.53375	+	1.11434i	0.111564	+	0.0810560i
$190$	8.26294	−	25.4307i	0.599457	−	1.84494i
$191$	2.26093			0.163595			0.0817975	−	0.996649i	$-0.473934\pi$
$191$	2.26093			0.163595			0.0817975	+	0.996649i	$0.473934\pi$
$192$	32.4537			2.34215
$193$	7.93069	−	24.4082i	0.570864	−	1.75694i	−0.0789873	−	0.996876i	$-0.525169\pi$
$193$	7.93069	−	24.4082i	0.570864	−	1.75694i	0.649851	−	0.760062i	$-0.274831\pi$
$194$	8.76347	+	26.9712i	0.629181	+	1.93642i
$195$	−3.72209	−	11.4554i	−0.266544	−	0.820339i
$196$	11.9262	−	8.66488i	0.851871	−	0.618920i
$197$	−1.91458	+	5.89247i	−0.136408	+	0.419821i	−0.995806	−	0.0914857i	$-0.970838\pi$
$197$	−1.91458	+	5.89247i	−0.136408	+	0.419821i	0.859398	+	0.511307i	$0.170838\pi$
$198$	−4.74631	+	3.44840i	−0.337306	+	0.245067i
$199$	3.69667	+	2.68579i	0.262050	+	0.190390i	0.711050	−	0.703141i	$-0.248220\pi$
$199$	3.69667	+	2.68579i	0.262050	+	0.190390i	−0.449000	+	0.893532i	$0.648220\pi$
$200$	1.17345	+	3.61152i	0.0829758	+	0.255373i
$201$	9.92879	+	7.21369i	0.700323	+	0.508814i
$202$	−13.7106	−	9.96132i	−0.964673	−	0.700876i
$203$	−0.0638258	−	0.196436i	−0.00447969	−	0.0137871i
$204$	−29.9506	−	21.7604i	−2.09696	−	1.52353i
$205$	−14.9050	+	10.8291i	−1.04101	+	0.756338i
$206$	3.98514	−	12.2650i	0.277658	−	0.854544i
$207$	19.9574	−	14.4999i	1.38713	−	1.00781i
$208$	−0.236778	−	0.728729i	−0.0164176	−	0.0505282i
$209$	−1.05150	−	3.23618i	−0.0727336	−	0.223851i
$210$	7.25655	−	22.3334i	0.500749	−	1.54115i
$211$	−18.6168			−1.28163			−0.640816	−	0.767695i	$-0.721404\pi$
$211$	−18.6168			−1.28163			−0.640816	+	0.767695i	$0.721404\pi$
$212$	19.0645			1.30936
$213$	2.67547	−	8.23426i	0.183321	−	0.564203i
$214$	−3.40539	−	2.47416i	−0.232788	−	0.169130i
$215$	0.465892	−	0.338490i	0.0317736	−	0.0230849i
$216$	−3.61764			−0.246149
$217$		0			0
$218$	27.1487			1.83874
$219$	5.53783	−	4.02347i	0.374212	−	0.271881i
$220$	4.93029	+	3.58207i	0.332400	+	0.241503i
$221$	2.56575	−	7.89656i	0.172591	−	0.531180i
$222$	−49.4591			−3.31948
$223$	6.21495			0.416184			0.208092	−	0.978109i	$-0.433275\pi$
$223$	6.21495			0.416184			0.208092	+	0.978109i	$0.433275\pi$
$224$	−2.56459	+	7.89300i	−0.171354	+	0.527373i
$225$	1.33036	+	4.09441i	0.0886904	+	0.272961i
$226$	7.88260	+	24.2602i	0.524343	+	1.61376i
$227$	10.5559	−	7.66930i	0.700619	−	0.509030i	−0.179515	−	0.983755i	$-0.557453\pi$
$227$	10.5559	−	7.66930i	0.700619	−	0.509030i	0.880134	+	0.474726i	$0.157453\pi$
$228$	12.1161	−	37.2897i	0.802412	−	2.46957i
$229$	−12.3601	+	8.98014i	−0.816779	+	0.593425i	−0.915788	−	0.401662i	$-0.868433\pi$
$229$	−12.3601	+	8.98014i	−0.816779	+	0.593425i	0.0990091	+	0.995087i	$0.468433\pi$
$230$	−33.2019	−	24.1226i	−2.18927	−	1.59060i
$231$	−0.923430	−	2.84203i	−0.0607572	−	0.186992i
$232$	0.318860	+	0.231665i	0.0209342	+	0.0152096i
$233$	−10.5668	−	7.67721i	−0.692253	−	0.502951i	0.185147	−	0.982711i	$-0.440724\pi$
$233$	−10.5668	−	7.67721i	−0.692253	−	0.502951i	−0.877400	+	0.479760i	$0.840724\pi$
$234$	−4.68512	−	14.4193i	−0.306276	−	0.942621i
$235$	−16.2442	−	11.8021i	−1.05965	−	0.769884i
$236$	−25.5624	+	18.5721i	−1.66397	+	1.20894i
$237$	−3.55781	+	10.9498i	−0.231105	+	0.711267i
$238$	13.0958	−	9.51467i	0.848876	−	0.616744i
$239$	−7.24405	−	22.2949i	−0.468578	−	1.44214i	−0.854426	−	0.519573i	$-0.826091\pi$
$239$	−7.24405	−	22.2949i	−0.468578	−	1.44214i	0.385848	−	0.922563i	$-0.373909\pi$
$240$	0.793379	+	2.44177i	0.0512124	+	0.157616i
$241$	7.63645	−	23.5026i	0.491907	−	1.51393i	−0.329814	−	0.944046i	$-0.606986\pi$
$241$	7.63645	−	23.5026i	0.491907	−	1.51393i	0.821722	−	0.569889i	$-0.193014\pi$
$242$	−24.1408			−1.55183
$243$	22.3337			1.43271
$244$	−8.05513	+	24.7911i	−0.515677	+	1.58709i
$245$	−8.96240	−	6.51156i	−0.572587	−	0.416009i
$246$	−35.0030	+	25.4312i	−2.23171	+	1.62143i
$247$	8.79358			0.559522
$248$		0			0
$249$	−6.78996			−0.430296
$250$	−17.5266	+	12.7339i	−1.10848	+	0.805360i
$251$	18.7645	+	13.6332i	1.18440	+	0.860518i	0.992661	−	0.120927i	$-0.0385868\pi$
$251$	18.7645	+	13.6332i	1.18440	+	0.860518i	0.191741	+	0.981446i	$0.438587\pi$
$252$	5.70323	−	17.5527i	0.359270	−	1.10572i
$253$	−5.22251			−0.328336
$254$	−2.96986			−0.186346
$255$	−8.59711	+	26.4592i	−0.538372	+	1.65694i
$256$	−5.72420	−	17.6173i	−0.357763	−	1.10108i
$257$	4.74221	+	14.5950i	0.295811	+	0.910412i	0.982948	+	0.183884i	$0.0588672\pi$
$257$	4.74221	+	14.5950i	0.295811	+	0.910412i	−0.687137	+	0.726528i	$0.741133\pi$
$258$	1.09410	−	0.794914i	0.0681160	−	0.0494892i
$259$	4.17266	−	12.8421i	0.259276	−	0.797970i
$260$	−12.7413	+	9.25707i	−0.790180	+	0.574099i
$261$	0.361494	+	0.262641i	0.0223759	+	0.0162571i
$262$	−5.71903	−	17.6014i	−0.353323	−	1.08742i
$263$	5.50607	+	4.00039i	0.339519	+	0.246675i	0.744459	−	0.667668i	$-0.232708\pi$
$263$	5.50607	+	4.00039i	0.339519	+	0.246675i	−0.404940	+	0.914343i	$0.632708\pi$
$264$	4.61325	+	3.35173i	0.283926	+	0.206284i
$265$	−4.42721	−	13.6256i	−0.271962	−	0.837012i
$266$	13.8697	+	10.0769i	0.850406	+	0.617856i
$267$	−4.53507	+	3.29492i	−0.277542	+	0.201646i
$268$	4.95874	−	15.2614i	0.302903	−	0.932241i
$269$	−8.51057	+	6.18329i	−0.518899	+	0.377002i	−0.816189	−	0.577785i	$-0.803917\pi$
$269$	−8.51057	+	6.18329i	−0.518899	+	0.377002i	0.297290	+	0.954787i	$0.403917\pi$
$270$	2.10848	+	6.48923i	0.128318	+	0.394922i
$271$	−0.487363	−	1.49995i	−0.0296052	−	0.0911154i	0.935162	−	0.354220i	$-0.115254\pi$
$271$	−0.487363	−	1.49995i	−0.0296052	−	0.0911154i	−0.964767	+	0.263105i	$0.915254\pi$
$272$	−0.546900	+	1.68319i	−0.0331607	+	0.102058i
$273$	7.72256			0.467391
$274$	−38.0206			−2.29691
$275$	0.281645	−	0.866813i	0.0169838	−	0.0522708i
$276$	−48.6847	−	35.3715i	−2.93048	−	2.12912i
$277$	−9.79020	+	7.11300i	−0.588236	+	0.427379i	−0.841684	−	0.539970i	$-0.818435\pi$
$277$	−9.79020	+	7.11300i	−0.588236	+	0.427379i	0.253448	+	0.967349i	$0.418435\pi$
$278$	16.9368			1.01580
$279$		0			0
$280$	−12.2337			−0.731106
$281$	17.3718	−	12.6214i	1.03632	−	0.752927i	0.0667525	−	0.997770i	$-0.478736\pi$
$281$	17.3718	−	12.6214i	1.03632	−	0.752927i	0.969563	+	0.244842i	$0.0787362\pi$
$282$	−38.1480	−	27.7161i	−2.27168	−	1.65047i
$283$	−0.212853	+	0.655094i	−0.0126528	+	0.0389413i	−0.957184	−	0.289482i	$-0.906517\pi$
$283$	−0.212853	+	0.655094i	−0.0126528	+	0.0389413i	0.944531	+	0.328423i	$0.106517\pi$
$284$	−11.3206			−0.671753
$285$	−29.4649			−1.74535
$286$	−0.991870	+	3.05266i	−0.0586505	+	0.180508i
$287$	−3.65018	−	11.2341i	−0.215463	−	0.663127i
$288$	−5.54815	−	17.0754i	−0.326928	−	1.00618i
$289$	−1.76183	+	1.28004i	−0.103637	+	0.0752967i
$290$	0.229713	−	0.706984i	0.0134892	−	0.0415155i
$291$	25.2816	−	18.3681i	1.48203	−	1.07676i
$292$	−7.24086	−	5.26079i	−0.423739	−	0.307864i
$293$	2.78482	+	8.57081i	0.162691	+	0.500712i	0.998859	−	0.0477622i	$-0.0152090\pi$
$293$	2.78482	+	8.57081i	0.162691	+	0.500712i	−0.836168	+	0.548474i	$0.815209\pi$
$294$	−21.0474	−	15.2918i	−1.22751	−	0.891837i
$295$	19.2098	+	13.9568i	1.11844	+	0.812594i
$296$	7.96234	+	24.5056i	0.462801	+	1.42436i
$297$	0.702455	+	0.510363i	0.0407606	+	0.0296143i
$298$	11.8766	−	8.62887i	0.687994	−	0.499857i
$299$	4.17063	−	12.8359i	0.241194	−	0.742317i
$300$	8.49636	−	6.17297i	0.490538	−	0.356396i
$301$	0.114095	+	0.351149i	0.00657634	+	0.0202399i
$302$	−3.93949	−	12.1245i	−0.226692	−	0.697688i
$303$	−5.77076	+	17.7606i	−0.331522	+	1.02032i
$304$	−1.87439			−0.107504
$305$	19.5890			1.12166
$306$	−10.8215	+	33.3051i	−0.618623	+	1.90393i
$307$	25.3486	+	18.4169i	1.44672	+	1.05111i	0.986583	+	0.163260i	$0.0522010\pi$
$307$	25.3486	+	18.4169i	1.44672	+	1.05111i	0.460141	+	0.887846i	$0.347799\pi$
$308$	−3.16104	+	2.29663i	−0.180117	+	0.130863i
$309$	−14.2107			−0.808416
$310$		0			0
$311$	−17.7139			−1.00447			−0.502233	−	0.864732i	$-0.667488\pi$
$311$	−17.7139			−1.00447			−0.502233	+	0.864732i	$0.667488\pi$
$312$	−11.9219	+	8.66180i	−0.674947	+	0.490378i
$313$	17.5303	+	12.7365i	0.990874	+	0.719912i	0.960112	−	0.279615i	$-0.0902067\pi$
$313$	17.5303	+	12.7365i	0.990874	+	0.719912i	0.0307616	+	0.999527i	$0.490207\pi$
$314$	5.70058	−	17.5446i	0.321702	−	0.990098i
$315$	−13.8695			−0.781458
$316$	15.0540			0.846852
$317$	0.313976	−	0.966318i	0.0176346	−	0.0542738i	−0.941852	−	0.336028i	$-0.890916\pi$
$317$	0.313976	−	0.966318i	0.0176346	−	0.0542738i	0.959487	+	0.281754i	$0.0909163\pi$
$318$	−10.3969	−	31.9984i	−0.583030	−	1.79438i
$319$	−0.0292321	−	0.0899671i	−0.00163668	−	0.00503719i
$320$	−25.7985	+	18.7437i	−1.44218	+	1.04781i
$321$	−1.43332	+	4.41132i	−0.0800004	+	0.246216i
$322$	21.2873	−	15.4661i	1.18629	−	0.861893i
$323$	−16.4320	−	11.9385i	−0.914299	−	0.664277i
$324$	−7.58930	−	23.3575i	−0.421628	−	1.29764i
$325$	1.90553	+	1.38445i	0.105700	+	0.0767955i
$326$	31.8582	+	23.1463i	1.76446	+	1.28196i
$327$	−9.24451	−	28.4517i	−0.511223	−	1.57338i
$328$	18.2355	+	13.2489i	1.00689	+	0.731545i
$329$	10.4149	−	7.56687i	0.574192	−	0.417175i
$330$	3.32348	−	10.2286i	0.182952	−	0.563068i
$331$	−21.5922	+	15.6877i	−1.18682	+	0.862272i	−0.992924	−	0.118751i	$-0.962111\pi$
$331$	−21.5922	+	15.6877i	−1.18682	+	0.862272i	−0.193891	+	0.981023i	$0.562111\pi$
$332$	2.74347	+	8.44353i	0.150568	+	0.463399i
$333$	9.02697	+	27.7822i	0.494675	+	1.52245i
$334$	−17.3790	+	53.4870i	−0.950935	+	2.92668i
$335$	−12.0590			−0.658854
$336$	−1.64610			−0.0898020
$337$	9.87048	−	30.3782i	0.537679	−	1.65481i	−0.200108	−	0.979774i	$-0.564129\pi$
$337$	9.87048	−	30.3782i	0.537679	−	1.65481i	0.737788	−	0.675033i	$-0.235871\pi$
$338$	17.5580	+	12.7567i	0.955031	+	0.693871i
$339$	22.7404	−	16.5218i	1.23509	−	0.897343i
$340$	36.3765			1.97279
$341$		0			0
$342$	−37.0885			−2.00552
$343$	14.8178	−	10.7658i	0.800088	−	0.581298i
$344$	−0.569994	−	0.414125i	−0.0307320	−	0.0223281i
$345$	−13.9746	+	43.0095i	−0.752368	+	2.31555i
$346$	20.7068			1.11321
$347$	3.12131			0.167561			0.0837804	−	0.996484i	$-0.473301\pi$
$347$	3.12131			0.167561			0.0837804	+	0.996484i	$0.473301\pi$
$348$	0.336834	−	1.03667i	0.0180562	−	0.0555712i
$349$	−6.80655	−	20.9484i	−0.364346	−	1.12134i	−0.950389	−	0.311063i	$-0.899315\pi$
$349$	−6.80655	−	20.9484i	−0.364346	−	1.12134i	0.586043	−	0.810280i	$-0.300685\pi$
$350$	1.41901	+	4.36726i	0.0758492	+	0.233440i
$351$	−1.81534	+	1.31892i	−0.0968958	+	0.0703989i
$352$	−1.17458	+	3.61498i	−0.0626052	+	0.192679i
$353$	−3.99039	+	2.89919i	−0.212387	+	0.154308i	−0.688893	−	0.724863i	$-0.741903\pi$
$353$	−3.99039	+	2.89919i	−0.212387	+	0.154308i	0.476506	+	0.879171i	$0.341903\pi$
$354$	45.1125	+	32.7762i	2.39770	+	1.74203i
$355$	2.62890	+	8.09092i	0.139527	+	0.429421i
$356$	5.92973	+	4.30820i	0.314275	+	0.228334i
$357$	−14.4306	−	10.4845i	−0.763750	−	0.554897i
$358$	−8.05087	−	24.7780i	−0.425502	−	1.30956i
$359$	0.291942	+	0.212108i	0.0154081	+	0.0111946i	0.595463	−	0.803383i	$-0.296969\pi$
$359$	0.291942	+	0.212108i	0.0154081	+	0.0111946i	−0.580055	+	0.814578i	$0.696969\pi$
$360$	21.4115	−	15.5563i	1.12848	−	0.819892i
$361$	0.776030	−	2.38838i	0.0408437	−	0.125704i
$362$	27.8924	−	20.2650i	1.46599	−	1.06510i
$363$	8.22027	+	25.2994i	0.431452	+	1.32787i
$364$	−3.12029	−	9.60325i	−0.163547	−	0.503347i
$365$	−2.07844	+	6.39677i	−0.108790	+	0.334822i
$366$	46.0030			2.40462
$367$	−29.3869			−1.53398			−0.766992	−	0.641657i	$-0.778247\pi$
$367$	−29.3869			−1.53398			−0.766992	+	0.641657i	$0.778247\pi$
$368$	−0.888987	+	2.73602i	−0.0463416	+	0.142625i
$369$	20.6737	+	15.0203i	1.07623	+	0.781928i
$370$	39.3167	−	28.5653i	2.04398	−	1.48504i
$371$	9.18555			0.476890
$372$		0			0
$373$	17.7284			0.917941			0.458971	−	0.888451i	$-0.348218\pi$
$373$	17.7284			0.917941			0.458971	+	0.888451i	$0.348218\pi$
$374$	5.99786	−	4.35770i	0.310142	−	0.225331i
$375$	19.3131	+	14.0318i	0.997323	+	0.724597i
$376$	−7.59116	+	23.3632i	−0.391484	+	1.20486i
$377$	0.244465			0.0125906
$378$	−4.37466			−0.225008
$379$	−0.760312	+	2.34000i	−0.0390546	+	0.120198i	−0.968683	−	0.248301i	$-0.920128\pi$
$379$	−0.760312	+	2.34000i	−0.0390546	+	0.120198i	0.929628	+	0.368498i	$0.120128\pi$
$380$	11.9052	+	36.6405i	0.610725	+	1.87962i
$381$	1.01128	+	3.11240i	0.0518094	+	0.159453i
$382$	−4.22077	+	3.06657i	−0.215953	+	0.156899i
$383$	−5.90776	+	18.1822i	−0.301872	+	0.929068i	0.678953	+	0.734181i	$0.262434\pi$
$383$	−5.90776	+	18.1822i	−0.301872	+	0.929068i	−0.980826	+	0.194886i	$0.937566\pi$
$384$	−39.2701	+	28.5314i	−2.00400	+	1.45599i
$385$	2.37549	+	1.72589i	0.121066	+	0.0879596i
$386$	18.3003	+	56.3225i	0.931460	+	2.86674i
$387$	−0.646208	−	0.469497i	−0.0328486	−	0.0238659i
$388$	−33.0563	−	24.0168i	−1.67818	−	1.21927i
$389$	1.62885	+	5.01308i	0.0825858	+	0.254173i	0.983820	−	0.179159i	$-0.0573377\pi$
$389$	1.62885	+	5.01308i	0.0825858	+	0.254173i	−0.901234	+	0.433332i	$0.857338\pi$
$390$	22.4858	+	16.3369i	1.13861	+	0.827251i
$391$	−25.2199	+	18.3233i	−1.27542	+	0.926649i
$392$	−4.18827	+	12.8902i	−0.211539	+	0.651051i
$393$	−16.4987	+	11.9870i	−0.832251	+	0.604665i
$394$	−4.41794	−	13.5970i	−0.222573	−	0.685009i
$395$	−3.49587	−	10.7592i	−0.175897	−	0.541354i
$396$	2.61207	−	8.03911i	0.131261	−	0.403981i
$397$	16.9255			0.849467			0.424733	−	0.905319i	$-0.360368\pi$
$397$	16.9255			0.849467			0.424733	+	0.905319i	$0.360368\pi$
$398$	−10.5439			−0.528516
$399$	5.83773	−	17.9667i	0.292252	−	0.899460i
$400$	−0.406173	−	0.295102i	−0.0203086	−	0.0147551i
$401$	−30.7747	+	22.3591i	−1.53682	+	1.11656i	−0.584524	+	0.811377i	$0.698719\pi$
$401$	−30.7747	+	22.3591i	−1.53682	+	1.11656i	−0.952293	+	0.305186i	$0.901281\pi$
$402$	−28.3195			−1.41245
$403$		0			0
$404$	24.4175			1.21482
$405$	−14.9314	+	10.8483i	−0.741945	+	0.539055i
$406$	0.385583	+	0.280143i	0.0191362	+	0.0139032i
$407$	1.91107	−	5.88166i	0.0947281	−	0.291543i
$408$	34.0373			1.68510
$409$	0.498684			0.0246583			0.0123292	−	0.999924i	$-0.496075\pi$
$409$	0.498684			0.0246583			0.0123292	+	0.999924i	$0.496075\pi$
$410$	13.1372	−	40.4322i	0.648801	−	1.99680i
$411$	12.9465	+	39.8453i	0.638605	+	1.96542i
$412$	5.74179	+	17.6714i	0.282877	+	0.870607i
$413$	−12.3163	+	8.94832i	−0.606046	+	0.440318i
$414$	−17.5903	+	54.1375i	−0.864518	+	2.66071i
$415$	5.39757	−	3.92156i	0.264956	−	0.192502i
$416$	−7.94688	−	5.77375i	−0.389628	−	0.283081i
$417$	−5.76723	−	17.7497i	−0.282422	−	0.869206i
$418$	6.35229	+	4.61521i	0.310701	+	0.225737i
$419$	−10.9298	−	7.94098i	−0.533957	−	0.387942i	0.287879	−	0.957667i	$-0.407050\pi$
$419$	−10.9298	−	7.94098i	−0.533957	−	0.387942i	−0.821836	+	0.569725i	$0.807050\pi$
$420$	10.4552	+	32.1779i	0.510163	+	1.57012i
$421$	25.0109	+	18.1714i	1.21895	+	0.885622i	0.996013	−	0.0892097i	$-0.0284341\pi$
$421$	25.0109	+	18.1714i	1.21895	+	0.885622i	0.222941	+	0.974832i	$0.428434\pi$
$422$	34.7543	−	25.2505i	1.69181	−	1.22917i
$423$	−8.60616	+	26.4871i	−0.418446	+	1.28784i
$424$	−14.1805	+	10.3027i	−0.688665	+	0.500345i
$425$	−1.68115	−	5.17406i	−0.0815479	−	0.250979i
$426$	6.17373	+	19.0008i	0.299118	+	0.920591i
$427$	−3.88108	+	11.9447i	−0.187818	+	0.578046i
$428$	6.06475			0.293151
$429$	3.53692			0.170764
$430$	−0.410636	+	1.26381i	−0.0198026	+	0.0609462i
$431$	9.75253	+	7.08563i	0.469763	+	0.341303i	0.797349	−	0.603519i	$-0.206235\pi$
$431$	9.75253	+	7.08563i	0.469763	+	0.341303i	−0.327586	+	0.944821i	$0.606235\pi$
$432$	0.386948	−	0.281134i	0.0186170	−	0.0135261i
$433$	−32.3919			−1.55665			−0.778327	−	0.627860i	$-0.783931\pi$
$433$	−32.3919			−1.55665			−0.778327	+	0.627860i	$0.783931\pi$
$434$		0			0
$435$	−0.819136			−0.0392745
$436$	−31.6454	+	22.9917i	−1.51554	+	1.10110i
$437$	−26.7102	−	19.4061i	−1.27772	−	0.928319i
$438$	−4.88102	+	15.0222i	−0.233224	+	0.717790i
$439$	12.3682			0.590300			0.295150	−	0.955451i	$-0.404630\pi$
$439$	12.3682			0.590300			0.295150	+	0.955451i	$0.404630\pi$
$440$	−5.60303			−0.267114
$441$	−4.74827	+	14.6137i	−0.226108	+	0.695890i
$442$	5.92053	+	18.2215i	0.281611	+	0.866709i
$443$	−1.45961	−	4.49223i	−0.0693483	−	0.213432i	0.910376	−	0.413782i	$-0.135792\pi$
$443$	−1.45961	−	4.49223i	−0.0693483	−	0.213432i	−0.979725	+	0.200349i	$0.935792\pi$
$444$	57.6511	−	41.8859i	2.73600	−	1.98782i
$445$	1.70209	−	5.23849i	0.0806867	−	0.248328i
$446$	−11.6023	+	8.42953i	−0.549383	+	0.399150i
$447$	−13.0872	−	9.50838i	−0.619002	−	0.449731i
$448$	−6.31796	−	19.4447i	−0.298496	−	0.918676i
$449$	12.9315	+	9.39528i	0.610275	+	0.443390i	0.849511	−	0.527571i	$-0.176897\pi$
$449$	12.9315	+	9.39528i	0.610275	+	0.443390i	−0.239236	+	0.970961i	$0.576897\pi$
$450$	−8.03692	−	5.83917i	−0.378864	−	0.275261i
$451$	−1.67177	−	5.14519i	−0.0787207	−	0.242277i
$452$	−29.7336	−	21.6027i	−1.39855	−	1.01611i
$453$	−11.3650	+	8.25713i	−0.533973	+	0.387954i
$454$	−9.30393	+	28.6345i	−0.436655	+	1.34389i
$455$	−6.13892	+	4.46019i	−0.287797	+	0.209097i
$456$	11.1397	+	34.2844i	0.521663	+	1.60551i
$457$	1.40842	+	4.33468i	0.0658832	+	0.202768i	0.978579	−	0.205872i	$-0.0660032\pi$
$457$	1.40842	+	4.33468i	0.0658832	+	0.202768i	−0.912696	+	0.408640i	$0.866003\pi$
$458$	10.8942	−	33.5288i	0.509051	−	1.56670i
$459$	5.18283			0.241914
$460$	59.1301			2.75695
$461$	−5.25050	+	16.1594i	−0.244540	+	0.752618i	0.751171	+	0.660107i	$0.229489\pi$
$461$	−5.25050	+	16.1594i	−0.244540	+	0.752618i	−0.995712	+	0.0925105i	$0.970511\pi$
$462$	5.57861	+	4.05310i	0.259540	+	0.188567i
$463$	−22.1896	+	16.1217i	−1.03124	+	0.749239i	−0.968556	−	0.248795i	$-0.919965\pi$
$463$	−22.1896	+	16.1217i	−1.03124	+	0.749239i	−0.0626822	+	0.998034i	$0.519965\pi$
$464$	−0.0521088			−0.00241909
$465$		0			0
$466$	30.1392			1.39617
$467$	18.5350	−	13.4665i	0.857697	−	0.623153i	−0.0695608	−	0.997578i	$-0.522160\pi$
$467$	18.5350	−	13.4665i	0.857697	−	0.623153i	0.927257	+	0.374425i	$0.122160\pi$
$468$	17.6726	+	12.8399i	0.816914	+	0.593523i
$469$	2.38919	−	7.35318i	0.110323	−	0.339538i
$470$	46.3327			2.13717
$471$	−20.3277			−0.936653
$472$	8.97705	−	27.6285i	0.413202	−	1.27171i
$473$	0.0522553	+	0.160825i	0.00240270	+	0.00739476i
$474$	−8.20974	−	25.2670i	−0.377086	−	1.16055i
$475$	4.66141	−	3.38671i	0.213880	−	0.155393i
$476$	−7.20710	+	22.1812i	−0.330337	+	1.01667i
$477$	−16.0765	+	11.6803i	−0.736094	+	0.534804i
$478$	43.7626	+	31.7954i	2.00166	+	1.45429i
$479$	2.79569	+	8.60426i	0.127738	+	0.393139i	0.994390	−	0.105775i	$-0.0337324\pi$
$479$	2.79569	+	8.60426i	0.127738	+	0.393139i	−0.866652	+	0.498914i	$0.833732\pi$
$480$	26.6278	+	19.3462i	1.21539	+	0.883031i
$481$	12.9298	+	9.39403i	0.589547	+	0.428331i
$482$	17.6213	+	54.2329i	0.802629	+	2.47024i
$483$	−23.4570	−	17.0425i	−1.06733	−	0.775461i
$484$	28.1392	−	20.4443i	1.27905	−	0.929287i
$485$	−9.48859	+	29.2029i	−0.430855	+	1.32603i
$486$	−41.6931	+	30.2918i	−1.89124	+	1.37406i
$487$	−7.29980	−	22.4665i	−0.330786	−	1.01805i	−0.968761	−	0.247997i	$-0.920228\pi$
$487$	−7.29980	−	22.4665i	−0.330786	−	1.01805i	0.637975	−	0.770057i	$-0.279772\pi$
$488$	−7.40594	−	22.7931i	−0.335251	−	1.03180i
$489$	13.4091	−	41.2688i	0.606378	−	1.86624i
$490$	25.5631			1.15482
$491$	9.22692			0.416405			0.208202	−	0.978086i	$-0.433239\pi$
$491$	9.22692			0.416405			0.208202	+	0.978086i	$0.433239\pi$
$492$	19.2634	−	59.2867i	0.868462	−	2.67285i
$493$	−0.456815	−	0.331896i	−0.0205739	−	0.0149478i
$494$	−16.4161	+	11.9270i	−0.738596	+	0.536621i
$495$	−6.35220			−0.285510
$496$		0			0
$497$	−5.45442			−0.244664
$498$	12.6757	−	9.20943i	0.568011	−	0.412684i
$499$	−22.9874	−	16.7013i	−1.02906	−	0.747653i	−0.0609364	−	0.998142i	$-0.519409\pi$
$499$	−22.9874	−	16.7013i	−1.02906	−	0.747653i	−0.968119	+	0.250489i	$0.919409\pi$
$500$	9.64554	−	29.6859i	0.431362	−	1.32759i
$501$	61.9718			2.76870
$502$	−53.5211			−2.38876
$503$	5.64823	−	17.3835i	0.251842	−	0.775091i	−0.742593	−	0.669743i	$-0.766404\pi$
$503$	5.64823	−	17.3835i	0.251842	−	0.775091i	0.994435	−	0.105348i	$-0.0335957\pi$
$504$	5.24359	+	16.1381i	0.233568	+	0.718848i
$505$	−5.67030	−	17.4514i	−0.252325	−	0.776577i
$506$	9.74952	−	7.08344i	0.433419	−	0.314898i
$507$	7.39015	−	22.7445i	0.328208	−	1.01012i
$508$	3.46176	−	2.51512i	0.153591	−	0.111590i
$509$	−8.40274	−	6.10495i	−0.372445	−	0.270597i	0.385779	−	0.922591i	$-0.373933\pi$
$509$	−8.40274	−	6.10495i	−0.372445	−	0.270597i	−0.758224	+	0.651994i	$0.773933\pi$
$510$	−19.8381	−	61.0553i	−0.878444	−	2.70357i
$511$	−3.48875	−	2.53472i	−0.154333	−	0.112130i
$512$	3.69272	+	2.68292i	0.163197	+	0.118569i
$513$	1.69623	+	5.22044i	0.0748902	+	0.230488i
$514$	−28.6486	−	20.8144i	−1.26363	−	0.918083i
$515$	11.2965	−	8.20740i	0.497784	−	0.361661i
$516$	−0.602125	+	1.85315i	−0.0265071	+	0.0815804i
$517$	4.77000	−	3.46561i	0.209785	−	0.152417i
$518$	9.62851	+	29.6335i	0.423053	+	1.30202i
$519$	−7.05096	−	21.7006i	−0.309503	−	0.952552i
$520$	4.47451	−	13.7711i	0.196220	−	0.603903i
$521$	9.25044			0.405269			0.202635	−	0.979254i	$-0.435050\pi$
$521$	9.25044			0.405269			0.202635	+	0.979254i	$0.435050\pi$
$522$	−1.03107			−0.0451289
$523$	−2.03184	+	6.25335i	−0.0888461	+	0.273440i	−0.985601	−	0.169087i	$-0.945918\pi$
$523$	−2.03184	+	6.25335i	−0.0888461	+	0.273440i	0.896755	+	0.442527i	$0.145918\pi$
$524$	21.5725	+	15.6734i	0.942400	+	0.684694i
$525$	4.09367	−	2.97422i	0.178662	−	0.129806i
$526$	−15.7047			−0.684759
$527$		0			0
$528$	−0.753909			−0.0328097
$529$	−22.3875	+	16.2655i	−0.973371	+	0.707195i
$530$	26.7456	+	19.4318i	1.16176	+	0.844064i
$531$	10.1774	−	31.3227i	0.441660	−	1.35929i
$532$	−24.7009			−1.07092
$533$	13.9809			0.605579
$534$	3.99720	−	12.3021i	0.172976	−	0.532364i
$535$	−1.40837	−	4.33453i	−0.0608893	−	0.187398i
$536$	4.55910	+	14.0315i	0.196923	+	0.606067i
$537$	−23.2258	+	16.8745i	−1.00227	+	0.728190i
$538$	7.50119	−	23.0863i	0.323399	−	0.995321i
$539$	2.63175	−	1.91208i	0.113358	−	0.0823591i
$540$	−7.95331	−	5.77842i	−0.342256	−	0.248663i
$541$	−0.680850	−	2.09544i	−0.0292720	−	0.0900900i	0.935353	−	0.353715i	$-0.115082\pi$
$541$	−0.680850	−	2.09544i	−0.0292720	−	0.0900900i	−0.964625	+	0.263625i	$0.915082\pi$
$542$	2.94425	+	2.13912i	0.126466	+	0.0918831i
$543$	−30.7353	−	22.3305i	−1.31898	−	0.958294i
$544$	7.01112	+	21.5780i	0.300599	+	0.925150i
$545$	23.7811	+	17.2780i	1.01867	+	0.740108i
$546$	−14.4167	+	10.4743i	−0.616978	+	0.448261i
$547$	−1.50289	+	4.62541i	−0.0642588	+	0.197768i	−0.978031	−	0.208458i	$-0.933156\pi$
$547$	−1.50289	+	4.62541i	−0.0642588	+	0.197768i	0.913773	+	0.406226i	$0.133156\pi$
$548$	44.3179	−	32.1988i	1.89317	−	1.37547i
$549$	−8.39618	−	25.8408i	−0.358340	−	1.10286i
$550$	0.649903	+	2.00019i	0.0277119	+	0.0852886i
$551$	0.184799	−	0.568753i	0.00787271	−	0.0242297i
$552$	55.3277			2.35491
$553$	7.25322			0.308438
$554$	8.62905	−	26.5575i	0.366613	−	1.12832i
$555$	−43.3241	−	31.4768i	−1.83901	−	1.33612i
$556$	−19.7421	+	14.3435i	−0.837251	+	0.608298i
$557$	11.0363			0.467623			0.233811	−	0.972282i	$-0.424880\pi$
$557$	11.0363			0.467623			0.233811	+	0.972282i	$0.424880\pi$
$558$		0			0
$559$	−0.437007			−0.0184834
$560$	1.30854	−	0.950708i	0.0552958	−	0.0401748i
$561$	−6.60919	−	4.80186i	−0.279040	−	0.202735i
$562$	−15.3115	+	47.1238i	−0.645875	+	1.98780i
$563$	−11.1924			−0.471704			−0.235852	−	0.971789i	$-0.575788\pi$
$563$	−11.1924			−0.471704			−0.235852	+	0.971789i	$0.575788\pi$
$564$	67.9387			2.86074
$565$	−8.53483	+	26.2675i	−0.359063	+	1.10508i
$566$	−0.491164	−	1.51165i	−0.0206452	−	0.0635393i
$567$	−3.65663	−	11.2540i	−0.153564	−	0.472622i
$568$	8.42043	−	6.11780i	0.353314	−	0.256697i
$569$	−14.4997	+	44.6255i	−0.607859	+	1.87080i	−0.132061	+	0.991242i	$0.542160\pi$
$569$	−14.4997	+	44.6255i	−0.607859	+	1.87080i	−0.475797	+	0.879555i	$0.657840\pi$
$570$	55.0059	−	39.9641i	2.30394	−	1.67391i
$571$	16.5522	+	12.0259i	0.692689	+	0.503268i	0.877543	−	0.479498i	$-0.159181\pi$
$571$	16.5522	+	12.0259i	0.692689	+	0.503268i	−0.184854	+	0.982766i	$0.559181\pi$
$572$	−1.42908	−	4.39827i	−0.0597530	−	0.183901i
$573$	4.65097	+	3.37913i	0.194297	+	0.141165i
$574$	22.0514	+	16.0213i	0.920407	+	0.668715i
$575$	−2.73272	−	8.41044i	−0.113962	−	0.350740i
$576$	35.7834	+	25.9982i	1.49098	+	1.08326i
$577$	−2.95157	+	2.14444i	−0.122876	+	0.0892744i	−0.647526	−	0.762044i	$-0.724196\pi$
$577$	−2.95157	+	2.14444i	−0.122876	+	0.0892744i	0.524650	+	0.851318i	$0.324196\pi$
$578$	1.55287	−	4.77925i	0.0645909	−	0.198790i
$579$	52.7941	−	38.3572i	2.19405	−	1.59407i
$580$	0.330970	+	1.01862i	0.0137428	+	0.0422959i
$581$	1.32184	+	4.06822i	0.0548393	+	0.168778i
$582$	−22.2831	+	68.5803i	−0.923664	+	2.84275i
$583$	4.20696			0.174235
$584$	8.22887			0.340513
$585$	5.07279	−	15.6124i	0.209734	−	0.645494i
$586$	−16.8236	−	12.2231i	−0.694978	−	0.504931i
$587$	18.5043	−	13.4442i	0.763755	−	0.554901i	−0.136305	−	0.990667i	$-0.543523\pi$
$587$	18.5043	−	13.4442i	0.763755	−	0.554901i	0.900060	+	0.435766i	$0.143523\pi$
$588$	37.4838			1.54580
$589$		0			0
$590$	−54.7914			−2.25573
$591$	−12.7452	+	9.25996i	−0.524269	+	0.380904i
$592$	−2.75604	−	2.00238i	−0.113272	−	0.0822972i
$593$	−6.01340	+	18.5073i	−0.246941	+	0.760005i	0.748371	+	0.663281i	$0.230837\pi$
$593$	−6.01340	+	18.5073i	−0.246941	+	0.760005i	−0.995311	+	0.0967243i	$0.969163\pi$
$594$	−2.00358			−0.0822081
$595$	17.5267			0.718525
$596$	−6.53613	+	20.1161i	−0.267730	+	0.823990i
$597$	3.59033	+	11.0499i	0.146942	+	0.452242i
$598$	9.62383	+	29.6191i	0.393548	+	1.21122i
$599$	−28.4546	+	20.6735i	−1.16262	+	0.844696i	−0.990108	−	0.140311i	$-0.955190\pi$
$599$	−28.4546	+	20.6735i	−1.16262	+	0.844696i	−0.172517	+	0.985007i	$0.555190\pi$
$600$	−2.98377	+	9.18310i	−0.121812	+	0.374899i
$601$	−4.76354	+	3.46091i	−0.194309	+	0.141174i	−0.680686	−	0.732575i	$-0.738318\pi$
$601$	−4.76354	+	3.46091i	−0.194309	+	0.141174i	0.486377	+	0.873749i	$0.338318\pi$
$602$	−0.689270	−	0.500784i	−0.0280925	−	0.0204104i
$603$	5.16869	+	15.9076i	0.210485	+	0.647808i
$604$	14.8600	+	10.7964i	0.604645	+	0.439300i
$605$	−21.1463	−	15.3637i	−0.859719	−	0.624622i
$606$	−13.3162	−	40.9830i	−0.540933	−	1.66482i
$607$	−31.4585	−	22.8559i	−1.27686	−	0.927694i	−0.277408	−	0.960752i	$-0.589475\pi$
$607$	−31.4585	−	22.8559i	−1.27686	−	0.927694i	−0.999453	+	0.0330586i	$0.989475\pi$
$608$	−19.4400	+	14.1240i	−0.788398	+	0.572805i
$609$	0.162291	−	0.499481i	0.00657638	−	0.0202400i
$610$	−36.5693	+	26.5692i	−1.48065	+	1.07575i
$611$	4.70851	+	14.4913i	0.190486	+	0.586255i
$612$	−15.5916	−	47.9859i	−0.630252	−	1.93972i
$613$	−14.0919	+	43.3704i	−0.569167	+	1.75172i	0.0860667	+	0.996289i	$0.472570\pi$
$613$	−14.0919	+	43.3704i	−0.569167	+	1.75172i	−0.655234	+	0.755426i	$0.727430\pi$
$614$	−72.3009			−2.91783
$615$	−46.8461			−1.88902
$616$	1.11010	−	3.41654i	0.0447272	−	0.137656i
$617$	5.36093	+	3.89495i	0.215823	+	0.156805i	0.690444	−	0.723385i	$-0.257415\pi$
$617$	5.36093	+	3.89495i	0.215823	+	0.156805i	−0.474621	+	0.880190i	$0.657415\pi$
$618$	26.5288	−	19.2743i	1.06715	−	0.775328i
$619$	41.5360			1.66947			0.834736	−	0.550650i	$-0.185620\pi$
$619$	41.5360			1.66947			0.834736	+	0.550650i	$0.185620\pi$
$620$		0			0
$621$	8.42469			0.338071
$622$	33.0689	−	24.0260i	1.32594	−	0.963353i
$623$	2.85703	+	2.07575i	0.114464	+	0.0831632i
$624$	0.602062	−	1.85296i	0.0241018	−	0.0741776i
$625$	−29.6682			−1.18673
$626$	−50.0011			−1.99845
$627$	2.67367	−	8.22871i	0.106776	−	0.328623i
$628$	8.21338	+	25.2782i	0.327750	+	1.00871i
$629$	−11.4073	−	35.1080i	−0.454838	−	1.39985i
$630$	25.8920	−	18.8116i	1.03156	−	0.749473i
$631$	3.44391	−	10.5993i	0.137100	−	0.421950i	−0.858811	−	0.512293i	$-0.828796\pi$
$631$	3.44391	−	10.5993i	0.137100	−	0.421950i	0.995911	+	0.0903431i	$0.0287964\pi$
$632$	−11.1974	+	8.13537i	−0.445408	+	0.323608i
$633$	−38.2967	−	27.8242i	−1.52216	−	1.10591i
$634$	0.724507	+	2.22980i	0.0287739	+	0.0885568i
$635$	−2.60147	−	1.89008i	−0.103236	−	0.0750056i
$636$	39.2177	+	28.4934i	1.55508	+	1.12983i
$637$	2.59782	+	7.99527i	0.102929	+	0.316784i
$638$	0.176596	+	0.128305i	0.00699151	+	0.00507963i
$639$	9.54632	−	6.93581i	0.377647	−	0.274376i
$640$	14.7387	−	45.3612i	0.582600	−	1.79306i
$641$	−14.2009	+	10.3176i	−0.560903	+	0.407520i	−0.831789	−	0.555092i	$-0.812683\pi$
$641$	−14.2009	+	10.3176i	−0.560903	+	0.407520i	0.270887	+	0.962611i	$0.412683\pi$
$642$	−3.30743	−	10.1792i	−0.130534	−	0.401742i
$643$	−0.678617	−	2.08857i	−0.0267621	−	0.0823651i	0.936783	−	0.349910i	$-0.113788\pi$
$643$	−0.678617	−	2.08857i	−0.0267621	−	0.0823651i	−0.963545	+	0.267545i	$0.913788\pi$
$644$	−11.7152	+	36.0555i	−0.461642	+	1.42079i
$645$	1.46429			0.0576563
$646$	46.8682			1.84401
$647$	−10.0259	+	30.8566i	−0.394160	+	1.21310i	0.535454	+	0.844564i	$0.320140\pi$
$647$	−10.0259	+	30.8566i	−0.394160	+	1.21310i	−0.929614	+	0.368535i	$0.879860\pi$
$648$	18.2677	+	13.2723i	0.717625	+	0.521385i
$649$	−5.64084	+	4.09831i	−0.221422	+	0.160873i
$650$	−5.43508			−0.213181
$651$		0			0
$652$	−56.7370			−2.22199
$653$	−13.3407	+	9.69256i	−0.522061	+	0.379299i	−0.817380	−	0.576099i	$-0.804574\pi$
$653$	−13.3407	+	9.69256i	−0.522061	+	0.379299i	0.295319	+	0.955399i	$0.404574\pi$
$654$	55.8478	+	40.5758i	2.18382	+	1.58664i
$655$	6.19225	−	19.0578i	0.241951	−	0.744649i
$656$	−2.98009			−0.116353
$657$	9.32914			0.363964
$658$	−9.17967	+	28.2521i	−0.357861	+	1.10138i
$659$	−6.10043	−	18.7752i	−0.237639	−	0.731377i	−0.996760	−	0.0804282i	$-0.974371\pi$
$659$	−6.10043	−	18.7752i	−0.237639	−	0.731377i	0.759122	−	0.650949i	$-0.225629\pi$
$660$	4.78847	+	14.7374i	0.186391	+	0.573652i
$661$	−9.53088	+	6.92459i	−0.370708	+	0.269335i	−0.757505	−	0.652830i	$-0.773582\pi$
$661$	−9.53088	+	6.92459i	−0.370708	+	0.269335i	0.386796	+	0.922165i	$0.373582\pi$
$662$	19.0313	−	58.5723i	0.739673	−	2.27648i
$663$	17.0800	−	12.4094i	0.663333	−	0.481940i
$664$	−6.60364	−	4.79783i	−0.256271	−	0.186192i
$665$	5.73611	+	17.6539i	0.222437	+	0.684590i
$666$	−54.5336	−	39.6210i	−2.11313	−	1.53528i
$667$	−0.742554	−	0.539497i	−0.0287518	−	0.0208894i
$668$	−25.0396	−	77.0639i	−0.968810	−	2.98169i
$669$	12.7848	+	9.28872i	0.494290	+	0.359123i
$670$	22.5121	−	16.3560i	0.869718	−	0.631887i
$671$	−1.77752	+	5.47066i	−0.0686206	+	0.211192i
$672$	−17.0723	+	12.4038i	−0.658579	+	0.478486i
$673$	15.5689	+	47.9162i	0.600138	+	1.84704i	0.527277	+	0.849693i	$0.323213\pi$
$673$	15.5689	+	47.9162i	0.600138	+	1.84704i	0.0728608	+	0.997342i	$0.476787\pi$
$674$	22.7764	+	70.0985i	0.877314	+	2.70009i
$675$	−0.454335	+	1.39830i	−0.0174874	+	0.0538206i
$676$	−31.2695			−1.20267
$677$	−3.97995			−0.152962			−0.0764810	−	0.997071i	$-0.524368\pi$
$677$	−3.97995			−0.152962			−0.0764810	+	0.997071i	$0.524368\pi$
$678$	−20.0433	+	61.6869i	−0.769758	+	2.36907i
$679$	−15.9270	−	11.5717i	−0.611223	−	0.444079i
$680$	−27.0574	+	19.6584i	−1.03760	+	0.753864i
$681$	33.1770			1.27134
$682$		0			0
$683$	5.23244			0.200214			0.100107	−	0.994977i	$-0.468082\pi$
$683$	5.23244			0.200214			0.100107	+	0.994977i	$0.468082\pi$
$684$	43.2314	−	31.4095i	1.65300	−	1.20097i
$685$	−33.3044	−	24.1971i	−1.27250	−	0.924522i
$686$	−13.0604	+	40.1958i	−0.498648	+	1.53468i
$687$	−38.8476			−1.48213
$688$	0.0931499			0.00355130
$689$	−3.35963	+	10.3399i	−0.127992	+	0.393918i
$690$	−32.2468	−	99.2455i	−1.22762	−	3.77821i
$691$	2.84158	+	8.74547i	0.108099	+	0.332693i	0.990445	−	0.137907i	$-0.0440374\pi$
$691$	2.84158	+	8.74547i	0.108099	+	0.332693i	−0.882347	+	0.470600i	$0.844037\pi$
$692$	−24.1365	+	17.5362i	−0.917532	+	0.666626i
$693$	1.25853	−	3.87336i	0.0478076	−	0.147137i
$694$	−5.82695	+	4.23353i	−0.221188	+	0.160703i
$695$	14.8359	+	10.7789i	0.562760	+	0.408869i
$696$	0.309687	+	0.953120i	0.0117387	+	0.0361279i
$697$	−26.1251	−	18.9810i	−0.989560	−	0.718957i
$698$	41.1196	+	29.8751i	1.55640	+	1.13079i
$699$	−10.2628	−	31.5857i	−0.388175	−	1.19468i
$700$	−5.35258	−	3.88888i	−0.202309	−	0.146986i
$701$	32.8091	−	23.8372i	1.23918	−	0.900319i	0.241640	−	0.970366i	$-0.422315\pi$
$701$	32.8091	−	23.8372i	1.23918	−	0.900319i	0.997544	+	0.0700465i	$0.0223148\pi$
$702$	1.60004	−	4.92441i	0.0603895	−	0.185860i
$703$	31.6294	−	22.9801i	1.19293	−	0.866712i
$704$	−2.89361	−	8.90563i	−0.109057	−	0.335643i
$705$	−15.7769	−	48.5564i	−0.594193	−	1.82874i
$706$	3.51712	−	10.8246i	0.132368	−	0.407388i
$707$	11.7647			0.442457
$708$	−80.3420			−3.01944
$709$	−11.5220	+	35.4612i	−0.432719	+	1.33177i	0.462687	+	0.886521i	$0.346885\pi$
$709$	−11.5220	+	35.4612i	−0.432719	+	1.33177i	−0.895406	+	0.445250i	$0.853115\pi$
$710$	−15.8817	−	11.5387i	−0.596028	−	0.433040i
$711$	−12.6946	+	9.22314i	−0.476083	+	0.345895i
$712$	−6.73883			−0.252548
$713$		0			0
$714$	41.1599			1.54037
$715$	−2.81161	+	2.04276i	−0.105148	+	0.0763948i
$716$	30.3684	+	22.0639i	1.13492	+	0.824567i
$717$	18.4196	−	56.6897i	0.687893	−	2.11712i
$718$	−0.832694			−0.0310759
$719$	−18.5799			−0.692912			−0.346456	−	0.938066i	$-0.612615\pi$
$719$	−18.5799			−0.692912			−0.346456	+	0.938066i	$0.612615\pi$
$720$	−1.08129	+	3.32786i	−0.0402971	+	0.124022i
$721$	2.76647	+	8.51433i	0.103029	+	0.317090i
$722$	1.79071	+	5.51124i	0.0666434	+	0.205107i
$723$	50.8354	−	36.9341i	1.89059	−	1.37359i
$724$	−15.3502	+	47.2430i	−0.570484	+	1.75577i
$725$	0.129589	−	0.0941519i	0.00481282	−	0.00349671i
$726$	−49.6601	−	36.0802i	−1.84306	−	1.33906i
$727$	5.06083	+	15.5756i	0.187696	+	0.577668i	0.999984	−	0.00558775i	$-0.00177865\pi$
$727$	5.06083	+	15.5756i	0.187696	+	0.577668i	−0.812289	+	0.583255i	$0.801779\pi$
$728$	7.51065	+	5.45681i	0.278363	+	0.202243i
$729$	28.0140	+	20.3534i	1.03756	+	0.753829i
$730$	−4.79605	−	14.7607i	−0.177510	−	0.546319i
$731$	0.816604	+	0.593298i	0.0302032	+	0.0219439i
$732$	−53.6225	+	38.9590i	−1.98194	+	1.43997i
$733$	−0.355783	+	1.09499i	−0.0131411	+	0.0404443i	−0.957412	−	0.288725i	$-0.906769\pi$
$733$	−0.355783	+	1.09499i	−0.0131411	+	0.0404443i	0.944271	+	0.329169i	$0.106769\pi$
$734$	54.8603	−	39.8583i	2.02493	−	1.47120i
$735$	−8.70459	−	26.7900i	−0.321074	−	0.988163i
$736$	11.3966	+	35.0751i	0.420084	+	1.29289i
$737$	1.09425	−	3.36774i	0.0403070	−	0.124052i
$738$	−58.9668			−2.17060
$739$	−20.7158			−0.762043			−0.381022	−	0.924566i	$-0.624428\pi$
$739$	−20.7158			−0.762043			−0.381022	+	0.924566i	$0.624428\pi$
$740$	−21.6374	+	66.5931i	−0.795407	+	2.44801i
$741$	18.0893	+	13.1427i	0.664529	+	0.482808i
$742$	−17.1479	+	12.4586i	−0.629517	+	0.457371i
$743$	−35.2367			−1.29271			−0.646354	−	0.763038i	$-0.723707\pi$
$743$	−35.2367			−1.29271			−0.646354	+	0.763038i	$0.723707\pi$
$744$		0			0
$745$	15.8950			0.582348
$746$	−33.0959	+	24.0456i	−1.21173	+	0.880370i
$747$	−7.48660	−	5.43934i	−0.273921	−	0.199015i
$748$	−3.30083	+	10.1589i	−0.120690	+	0.371447i
$749$	2.92208			0.106771
$750$	−55.0859			−2.01145
$751$	−13.3328	+	41.0342i	−0.486521	+	1.49736i	0.343245	+	0.939246i	$0.388474\pi$
$751$	−13.3328	+	41.0342i	−0.486521	+	1.49736i	−0.829766	+	0.558112i	$0.811526\pi$
$752$	−1.00364	−	3.08888i	−0.0365989	−	0.112640i
$753$	18.2247	+	56.0898i	0.664144	+	2.04403i
$754$	−0.456375	+	0.331576i	−0.0166202	+	0.0120753i
$755$	4.26546	−	13.1277i	0.155236	−	0.477767i
$756$	5.09923	−	3.70481i	0.185457	−	0.134743i
$757$	22.1174	+	16.0692i	0.803870	+	0.584045i	0.912047	−	0.410086i	$-0.134501\pi$
$757$	22.1174	+	16.0692i	0.803870	+	0.584045i	−0.108177	+	0.994132i	$0.534501\pi$
$758$	−1.75444	−	5.39961i	−0.0637241	−	0.196123i
$759$	−10.7433	−	7.80543i	−0.389955	−	0.283319i
$760$	−28.6563	−	20.8201i	−1.03947	−	0.755223i
$761$	5.31261	+	16.3505i	0.192582	+	0.592706i	0.999996	+	0.00272136i	$0.000866238\pi$
$761$	5.31261	+	16.3505i	0.192582	+	0.592706i	−0.807414	+	0.589985i	$0.799134\pi$
$762$	−6.10932	−	4.43868i	−0.221317	−	0.160797i
$763$	−15.2472	+	11.0777i	−0.551985	+	0.401041i
$764$	2.32284	−	7.14896i	0.0840373	−	0.258640i
$765$	−30.6752	+	22.2869i	−1.10907	+	0.805783i
$766$	−13.6323	−	41.9560i	−0.492556	−	1.51593i
$767$	−5.56812	−	17.1369i	−0.201053	−	0.618778i
$768$	14.5551	−	44.7959i	0.525211	−	1.61643i
$769$	14.0567			0.506899			0.253450	−	0.967349i	$-0.418435\pi$
$769$	14.0567			0.506899			0.253450	+	0.967349i	$0.418435\pi$
$770$	−6.77550			−0.244172
$771$	−12.0581	+	37.1111i	−0.434263	+	1.33652i
$772$	−69.0297	−	50.1530i	−2.48443	−	1.80505i
$773$	17.9900	−	13.0705i	0.647054	−	0.470112i	−0.215212	−	0.976567i	$-0.569044\pi$
$773$	17.9900	−	13.0705i	0.647054	−	0.470112i	0.862266	+	0.506455i	$0.169044\pi$
$774$	1.84315			0.0662507
$775$		0			0
$776$	37.5668			1.34857
$777$	27.7771	−	20.1813i	0.996498	−	0.723998i
$778$	−9.84016	−	7.14930i	−0.352787	−	0.256315i
$779$	10.5686	−	32.5268i	0.378659	−	1.16539i
$780$	−40.0455			−1.43386
$781$	−2.49811			−0.0893895
$782$	22.2287	−	68.4129i	0.794897	−	2.44644i
$783$	0.0471557	+	0.145130i	0.00168521	+	0.00518654i
$784$	−0.553737	−	1.70423i	−0.0197763	−	0.0608653i
$785$	16.1592	−	11.7403i	0.576747	−	0.419031i
$786$	14.5419	−	44.7554i	0.518693	−	1.59637i
$787$	−25.9159	+	18.8290i	−0.923802	+	0.671182i	−0.944467	−	0.328605i	$-0.893422\pi$
$787$	−25.9159	+	18.8290i	−0.923802	+	0.671182i	0.0206654	+	0.999786i	$0.493422\pi$
$788$	16.6647	+	12.1076i	0.593657	+	0.431317i
$789$	5.34768	+	16.4585i	0.190383	+	0.585937i
$790$	21.1192	+	15.3440i	0.751388	+	0.545915i
$791$	−14.3261	−	10.4085i	−0.509377	−	0.370084i
$792$	2.40155	+	7.39122i	0.0853354	+	0.262635i
$793$	−12.0263	−	8.73759i	−0.427065	−	0.310281i
$794$	−31.5970	+	22.9566i	−1.12134	+	0.814698i
$795$	11.2572	−	34.6460i	0.399251	−	1.22877i
$796$	12.2902	−	8.92938i	0.435616	−	0.316493i
$797$	8.04966	+	24.7743i	0.285134	+	0.877551i	0.986359	+	0.164611i	$0.0526369\pi$
$797$	8.04966	+	24.7743i	0.285134	+	0.877551i	−0.701225	+	0.712940i	$0.747363\pi$
$798$	13.4707	+	41.4586i	0.476859	+	1.46762i
$799$	10.8755	−	33.4714i	0.384748	−	1.18413i
$800$	−6.43625			−0.227556
$801$	−7.63987			−0.269942
$802$	27.1247	−	83.4814i	0.957808	−	2.94783i
$803$	−1.59784	−	1.16090i	−0.0563865	−	0.0409672i
$804$	33.0100	−	23.9832i	1.16417	−	0.845822i
$805$	28.4897			1.00413
$806$		0			0
$807$	−26.7486			−0.941594
$808$	−18.1621	+	13.1956i	−0.638942	+	0.464218i
$809$	7.06224	+	5.13102i	0.248295	+	0.180397i	0.704971	−	0.709236i	$-0.250960\pi$
$809$	7.06224	+	5.13102i	0.248295	+	0.180397i	−0.456676	+	0.889633i	$0.650960\pi$
$810$	13.1605	−	40.5037i	0.462411	−	1.42316i
$811$	−50.0784			−1.75849			−0.879245	−	0.476369i	$-0.841953\pi$
$811$	−50.0784			−1.75849			−0.879245	+	0.476369i	$0.841953\pi$
$812$	−0.686695			−0.0240983
$813$	1.23923	−	3.81396i	0.0434617	−	0.133761i
$814$	4.40984	+	13.5721i	0.154565	+	0.475701i
$815$	13.1756	+	40.5504i	0.461522	+	1.42042i
$816$	−3.64068	+	2.64511i	−0.127449	+	0.0925973i
$817$	−0.330347	+	1.01670i	−0.0115574	+	0.0355700i
$818$	−0.930957	+	0.676380i	−0.0325501	+	0.0236491i
$819$	8.51489	+	6.18643i	0.297534	+	0.216171i
$820$	18.9281	+	58.2546i	0.660997	+	2.03434i
$821$	41.0844	+	29.8495i	1.43385	+	1.04176i	0.989283	+	0.146013i	$0.0466441\pi$
$821$	41.0844	+	29.8495i	1.43385	+	1.04176i	0.444572	+	0.895743i	$0.353356\pi$
$822$	−78.2123	−	56.8246i	−2.72797	−	1.98199i
$823$	−1.95583	−	6.01943i	−0.0681760	−	0.209824i	0.911164	−	0.412043i	$-0.135185\pi$
$823$	−1.95583	−	6.01943i	−0.0681760	−	0.209824i	−0.979340	+	0.202219i	$0.935185\pi$
$824$	−13.8207	−	10.0413i	−0.481467	−	0.349806i
$825$	1.87489	−	1.36219i	0.0652753	−	0.0474253i
$826$	10.8556	−	33.4100i	0.377713	−	1.16248i
$827$	−2.99130	+	2.17331i	−0.104018	+	0.0755733i	−0.638578	−	0.769557i	$-0.720477\pi$
$827$	−2.99130	+	2.17331i	−0.104018	+	0.0755733i	0.534561	+	0.845130i	$0.320477\pi$
$828$	−25.3441	−	78.0012i	−0.880769	−	2.71073i
$829$	8.04729	+	24.7670i	0.279494	+	0.860193i	0.987995	+	0.154484i	$0.0493715\pi$
$829$	8.04729	+	24.7670i	0.279494	+	0.860193i	−0.708501	+	0.705709i	$0.750628\pi$
$830$	−4.75740	+	14.6418i	−0.165132	+	0.508223i
$831$	−30.7704			−1.06741
$832$	24.1990			0.838951
$833$	6.00033	−	18.4671i	0.207899	−	0.639848i
$834$	34.8409	+	25.3134i	1.20644	+	0.876530i
$835$	−49.2635	+	35.7920i	−1.70483	+	1.23863i
$836$	−11.3130			−0.391267
$837$		0			0
$838$	31.1747			1.07691
$839$	−6.06196	+	4.40427i	−0.209282	+	0.152052i	−0.687489	−	0.726195i	$-0.741287\pi$
$839$	−6.06196	+	4.40427i	−0.209282	+	0.152052i	0.478207	+	0.878247i	$0.341287\pi$
$840$	−25.1661	−	18.2843i	−0.868314	−	0.630867i
$841$	−8.95636	+	27.5648i	−0.308840	+	0.950511i
$842$	−71.3374			−2.45845
$843$	54.5992			1.88050
$844$	−19.1265	+	58.8655i	−0.658363	+	2.02623i
$845$	7.26150	+	22.3486i	0.249803	+	0.768815i
$846$	−19.8590	−	61.1196i	−0.682765	−	2.10133i
$847$	13.5579	−	9.85037i	0.465854	−	0.338463i
$848$	0.716119	−	2.20399i	0.0245916	−	0.0756852i
$849$	−1.41695	+	1.02947i	−0.0486296	+	0.0353314i
$850$	10.1562	+	7.37888i	0.348353	+	0.253093i
$851$	−18.5425	−	57.0681i	−0.635630	−	1.95627i
$852$	−23.2877	−	16.9195i	−0.797822	−	0.579652i
$853$	35.2626	+	25.6198i	1.20737	+	0.877204i	0.994989	−	0.0999836i	$-0.0318790\pi$
$853$	35.2626	+	25.6198i	1.20737	+	0.877204i	0.212378	+	0.977187i	$0.431879\pi$
$854$	−8.95569	−	27.5628i	−0.306457	−	0.943179i
$855$	−32.4879	−	23.6039i	−1.11106	−	0.807235i
$856$	−4.51106	+	3.27747i	−0.154185	+	0.112022i
$857$	12.1205	−	37.3031i	0.414029	−	1.27425i	−0.499088	−	0.866551i	$-0.666332\pi$
$857$	12.1205	−	37.3031i	0.414029	−	1.27425i	0.913117	−	0.407698i	$-0.133668\pi$
$858$	−6.60282	+	4.79723i	−0.225416	+	0.163775i
$859$	−5.62451	−	17.3105i	−0.191906	−	0.590625i	−0.999999	−	0.00157032i	$-0.999500\pi$
$859$	−5.62451	−	17.3105i	−0.191906	−	0.590625i	0.808093	−	0.589055i	$-0.200500\pi$
$860$	−0.591643	−	1.82089i	−0.0201749	−	0.0620918i
$861$	9.28139	−	28.5652i	0.316309	−	0.973499i
$862$	−27.8168			−0.947443
$863$	44.9477			1.53004			0.765018	−	0.644009i	$-0.222730\pi$
$863$	44.9477			1.53004			0.765018	+	0.644009i	$0.222730\pi$
$864$	1.89477	−	5.83151i	0.0644614	−	0.198392i
$865$	18.1383	+	13.1783i	0.616721	+	0.448074i
$866$	60.4700	−	43.9340i	2.05486	−	1.49294i
$867$	−5.53740			−0.188060
$868$		0			0
$869$	3.32196			0.112690
$870$	1.52919	−	1.11102i	0.0518442	−	0.0376670i
$871$	7.40338	+	5.37887i	0.250854	+	0.182256i
$872$	11.1133	−	34.2032i	0.376343	−	1.15827i
$873$	42.5899			1.44145
$874$	76.1844			2.57698
$875$	4.64736	−	14.3031i	0.157109	−	0.483533i
$876$	−7.03257	−	21.6440i	−0.237608	−	0.731283i
$877$	−13.1799	−	40.5636i	−0.445054	−	1.36973i	−0.882425	−	0.470453i	$-0.844090\pi$
$877$	−13.1799	−	40.5636i	−0.445054	−	1.36973i	0.437371	−	0.899281i	$-0.355910\pi$
$878$	−23.0892	+	16.7753i	−0.779224	+	0.566139i
$879$	−7.08104	+	21.7932i	−0.238837	+	0.735066i
$880$	0.599307	−	0.435422i	0.0202026	−	0.0146781i
$881$	7.21362	+	5.24100i	0.243033	+	0.176574i	0.702633	−	0.711552i	$-0.252007\pi$
$881$	7.21362	+	5.24100i	0.243033	+	0.176574i	−0.459600	+	0.888126i	$0.652007\pi$
$882$	−10.9568	−	33.7215i	−0.368934	−	1.13546i
$883$	−38.0791	−	27.6661i	−1.28146	−	0.931038i	−0.281867	−	0.959453i	$-0.590954\pi$
$883$	−38.0791	−	27.6661i	−1.28146	−	0.931038i	−0.999596	+	0.0284158i	$0.990954\pi$
$884$	−22.3326	−	16.2256i	−0.751126	−	0.545725i
$885$	18.6572	+	57.4211i	0.627156	+	1.93019i
$886$	8.81779	+	6.40650i	0.296239	+	0.215231i
$887$	−2.55372	+	1.85538i	−0.0857454	+	0.0622977i	−0.629832	−	0.776731i	$-0.716876\pi$
$887$	−2.55372	+	1.85538i	−0.0857454	+	0.0622977i	0.544087	+	0.839029i	$0.316876\pi$
$888$	−20.2460	+	62.3109i	−0.679412	+	2.09102i
$889$	1.66793	−	1.21182i	0.0559404	−	0.0406431i
$890$	3.92761	+	12.0879i	0.131654	+	0.405189i
$891$	−1.67473	−	5.15429i	−0.0561056	−	0.172675i
$892$	6.38513	−	19.6514i	0.213790	−	0.657978i
$893$	37.2736			1.24731
$894$	37.3280			1.24843
$895$	8.71703	−	26.8283i	0.291378	−	0.896770i
$896$	24.7396	+	17.9744i	0.826492	+	0.600482i
$897$	27.7636	−	20.1714i	0.927000	−	0.673505i
$898$	−36.8840			−1.23083
$899$		0			0
$900$	14.3131			0.477105
$901$	20.3157	−	14.7602i	0.676815	−	0.491735i
$902$	10.0995	+	7.33771i	0.336276	+	0.244319i
$903$	−0.290113	+	0.892875i	−0.00965434	+	0.0297130i
$904$	33.7908			1.12386
$905$	37.3296			1.24088
$906$	10.0170	−	30.8293i	0.332794	−	1.02423i
$907$	8.33208	+	25.6435i	0.276662	+	0.851478i	0.988775	+	0.149413i	$0.0477384\pi$
$907$	8.33208	+	25.6435i	0.276662	+	0.851478i	−0.712113	+	0.702065i	$0.752262\pi$
$908$	−13.4051	−	41.2566i	−0.444863	−	1.36915i
$909$	−20.5906	+	14.9599i	−0.682946	+	0.496189i
$910$	5.41083	−	16.6528i	0.179367	−	0.552035i
$911$	−4.10820	+	2.98479i	−0.136111	+	0.0988903i	−0.653757	−	0.756704i	$-0.726808\pi$
$911$	−4.10820	+	2.98479i	−0.136111	+	0.0988903i	0.517646	+	0.855595i	$0.326808\pi$
$912$	−3.85582	−	2.80142i	−0.127679	−	0.0927642i
$913$	0.605401	+	1.86323i	0.0200359	+	0.0616640i
$914$	−8.50854	−	6.18181i	−0.281437	−	0.204476i
$915$	40.2967	+	29.2773i	1.33217	+	0.967876i
$916$	15.6963	+	48.3082i	0.518620	+	1.59615i
$917$	10.3940	+	7.55165i	0.343239	+	0.249377i
$918$	−9.67545	+	7.02962i	−0.319337	+	0.232012i
$919$	−15.2274	+	46.8652i	−0.502306	+	1.54594i	0.302946	+	0.953008i	$0.402030\pi$
$919$	−15.2274	+	46.8652i	−0.502306	+	1.54594i	−0.805253	+	0.592932i	$0.797970\pi$
$920$	−43.9819	+	31.9547i	−1.45004	+	1.05352i
$921$	24.6195	+	75.7709i	0.811239	+	2.49674i
$922$	−12.1157	−	37.2882i	−0.399009	−	1.22802i
$923$	1.99496	−	6.13986i	0.0656649	−	0.202096i
$924$	−9.93508			−0.326840
$925$	10.4719			0.344315
$926$	19.5578	−	60.1929i	0.642711	−	1.97806i
$927$	−15.6686	−	11.3839i	−0.514626	−	0.373898i
$928$	−0.540441	+	0.392653i	−0.0177408	+	0.0128895i
$929$	−39.9606			−1.31107			−0.655533	−	0.755167i	$-0.727556\pi$
$929$	−39.9606			−1.31107			−0.655533	+	0.755167i	$0.727556\pi$
$930$		0			0
$931$	20.5649			0.673989
$932$	−35.1311	+	25.5243i	−1.15076	+	0.836075i
$933$	−36.4395	−	26.4748i	−1.19297	−	0.866747i
$934$	−16.3367	+	50.2791i	−0.534552	+	1.64518i
$935$	8.02720			0.262517
$936$	−20.0840			−0.656465
$937$	13.9334	−	42.8825i	0.455183	−	1.40091i	−0.415737	−	0.909485i	$-0.636476\pi$
$937$	13.9334	−	42.8825i	0.455183	−	1.40091i	0.870920	−	0.491424i	$-0.163524\pi$
$938$	5.51313	+	16.9677i	0.180010	+	0.554014i
$939$	17.0261	+	52.4009i	0.555625	+	1.71004i
$940$	−54.0067	+	39.2382i	−1.76151	+	1.27981i
$941$	15.5103	−	47.7357i	0.505621	−	1.55614i	−0.294104	−	0.955773i	$-0.595021\pi$
$941$	15.5103	−	47.7357i	0.505621	−	1.55614i	0.799725	−	0.600367i	$-0.204979\pi$
$942$	37.9484	−	27.5711i	1.23643	−	0.898316i
$943$	−42.4664	−	30.8537i	−1.38290	−	1.00473i
$944$	1.18687	+	3.65281i	0.0386293	+	0.118889i
$945$	−3.83202	−	2.78412i	−0.124656	−	0.0905675i
$946$	−0.315684	−	0.229358i	−0.0102638	−	0.00745707i
$947$	9.37123	+	28.8417i	0.304524	+	0.937229i	0.979854	+	0.199713i	$0.0640011\pi$
$947$	9.37123	+	28.8417i	0.304524	+	0.937229i	−0.675330	+	0.737516i	$0.735999\pi$
$948$	30.9676	+	22.4993i	1.00578	+	0.730743i
$949$	4.12927	−	3.00009i	0.134042	−	0.0973869i
$950$	−4.10855	+	12.6448i	−0.133299	+	0.410252i
$951$	2.09012	−	1.51856i	0.0677767	−	0.0492426i
$952$	−6.62626	−	20.3935i	−0.214758	−	0.660958i
$953$	−10.9631	−	33.7411i	−0.355131	−	1.09298i	−0.955934	−	0.293583i	$-0.905152\pi$
$953$	−10.9631	−	33.7411i	−0.355131	−	1.09298i	0.600803	−	0.799397i	$-0.294848\pi$
$954$	14.1698	−	43.6102i	0.458764	−	1.41193i
$955$	−5.64884			−0.182792
$956$	−77.9379			−2.52069
$957$	0.0743291	−	0.228761i	0.00240272	−	0.00739481i
$958$	−16.8893	−	12.2708i	−0.545668	−	0.396451i
$959$	21.3530	−	15.5139i	0.689524	−	0.500969i
$960$	−81.0843			−2.61698
$961$		0			0
$962$	−36.8791			−1.18903
$963$	−5.11422	+	3.71570i	−0.164804	+	0.119737i
$964$	−66.4686	−	48.2923i	−2.14081	−	1.55539i
$965$	−19.8145	+	60.9828i	−0.637852	+	1.96311i
$966$	66.9055			2.15265
$967$	−35.4443			−1.13981			−0.569906	−	0.821710i	$-0.693021\pi$
$967$	−35.4443			−1.13981			−0.569906	+	0.821710i	$0.693021\pi$
$968$	−9.88199	+	30.4136i	−0.317619	+	0.977531i
$969$	−15.9593	−	49.1176i	−0.512686	−	1.57789i
$970$	−21.8952	−	67.3864i	−0.703012	−	2.16365i
$971$	32.4393	−	23.5686i	1.04103	−	0.756351i	0.0705422	−	0.997509i	$-0.477527\pi$
$971$	32.4393	−	23.5686i	1.04103	−	0.756351i	0.970486	+	0.241158i	$0.0775271\pi$
$972$	22.9452	−	70.6181i	0.735968	−	2.26508i
$973$	−9.51202	+	6.91088i	−0.304941	+	0.221553i
$974$	44.0995	+	32.0401i	1.41304	+	1.02663i
$975$	1.85072	+	5.69593i	0.0592705	+	0.182416i
$976$	2.56345	+	1.86246i	0.0820540	+	0.0596157i
$977$	31.2854	+	22.7302i	1.00091	+	0.727202i	0.962283	−	0.272052i	$-0.0877022\pi$
$977$	31.2854	+	22.7302i	1.00091	+	0.727202i	0.0386252	+	0.999254i	$0.487702\pi$
$978$	30.9417	+	95.2289i	0.989408	+	3.04508i
$979$	1.30851	+	0.950690i	0.0418202	+	0.0303842i
$980$	−29.7971	+	21.6489i	−0.951834	+	0.691548i
$981$	12.5992	−	38.7764i	0.402262	−	1.23804i
$982$	−17.2251	+	12.5147i	−0.549674	+	0.399362i
$983$	−6.66846	−	20.5234i	−0.212691	−	0.654595i	−0.999309	−	0.0371560i	$-0.988170\pi$
$983$	−6.66846	−	20.5234i	−0.212691	−	0.654595i	0.786619	−	0.617439i	$-0.211830\pi$
$984$	17.7109	+	54.5086i	0.564604	+	1.73767i
$985$	4.78350	−	14.7221i	0.152415	−	0.469085i
$986$	1.30296			0.0414946
$987$	32.7338			1.04193
$988$	9.03438	−	27.8049i	0.287422	−	0.884593i
$989$	1.32739	+	0.964407i	0.0422086	+	0.0306663i
$990$	11.8585	−	8.61568i	0.376887	−	0.273824i
$991$	46.8764			1.48908			0.744538	−	0.667580i	$-0.232670\pi$
$991$	46.8764			1.48908			0.744538	+	0.667580i	$0.232670\pi$
$992$		0			0
$993$	−67.8639			−2.15360
$994$	10.1825	−	7.39800i	0.322968	−	0.234650i
$995$	−9.23597	−	6.71033i	−0.292800	−	0.212732i
$996$	−6.97589	+	21.4696i	−0.221039	+	0.680290i
$997$	44.5389			1.41056			0.705281	−	0.708928i	$-0.250821\pi$
$997$	44.5389			1.41056			0.705281	+	0.708928i	$0.250821\pi$
$998$	65.5659			2.07545
$999$	−3.08284	+	9.48801i	−0.0975367	+	0.300187i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.o.388.1		16
31.2	even	5	inner	961.2.d.o.374.1		16
31.3	odd	30		961.2.g.n.547.2		16
31.4	even	5		961.2.d.p.628.4		16
31.5	even	3		961.2.g.k.338.1		16
31.6	odd	6		961.2.g.l.235.1		16
31.7	even	15		961.2.g.s.846.2		16
31.8	even	5		961.2.a.i.1.8		8
31.9	even	15		961.2.c.j.521.8		16
31.10	even	15		31.2.g.a.19.1	yes	16
31.11	odd	30		961.2.g.n.448.2		16
31.12	odd	30		961.2.g.j.816.1		16
31.13	odd	30		961.2.g.m.844.2		16
31.14	even	15		961.2.c.j.439.8		16
31.15	odd	10		961.2.d.q.531.4		16
31.16	even	5		961.2.d.p.531.4		16
31.17	odd	30		961.2.c.i.439.8		16
31.18	even	15		961.2.g.s.844.2		16
31.19	even	15		961.2.g.k.816.1		16
31.20	even	15		961.2.g.t.448.2		16
31.21	odd	30		961.2.g.l.732.1		16
31.22	odd	30		961.2.c.i.521.8		16
31.23	odd	10		961.2.a.j.1.8		8
31.24	odd	30		961.2.g.m.846.2		16
31.25	even	3		31.2.g.a.18.1	✓	16
31.26	odd	6		961.2.g.j.338.1		16
31.27	odd	10		961.2.d.q.628.4		16
31.28	even	15		961.2.g.t.547.2		16
31.29	odd	10		961.2.d.n.374.1		16
31.30	odd	2		961.2.d.n.388.1		16
93.8	odd	10		8649.2.a.bf.1.1		8
93.23	even	10		8649.2.a.be.1.1		8
93.41	odd	30		279.2.y.c.19.2		16
93.56	odd	6		279.2.y.c.235.2		16
124.87	odd	6		496.2.bg.c.49.2		16
124.103	odd	30		496.2.bg.c.81.2		16
155.72	odd	60		775.2.ck.a.174.4		32
155.87	odd	12		775.2.ck.a.49.1		32
155.103	odd	60		775.2.ck.a.174.1		32
155.118	odd	12		775.2.ck.a.49.4		32
155.134	even	30		775.2.bl.a.701.2		16
155.149	even	6		775.2.bl.a.576.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.18.1	✓	16	31.25	even	3
31.2.g.a.19.1	yes	16	31.10	even	15
279.2.y.c.19.2		16	93.41	odd	30
279.2.y.c.235.2		16	93.56	odd	6
496.2.bg.c.49.2		16	124.87	odd	6
496.2.bg.c.81.2		16	124.103	odd	30
775.2.bl.a.576.2		16	155.149	even	6
775.2.bl.a.701.2		16	155.134	even	30
775.2.ck.a.49.1		32	155.87	odd	12
775.2.ck.a.49.4		32	155.118	odd	12
775.2.ck.a.174.1		32	155.103	odd	60
775.2.ck.a.174.4		32	155.72	odd	60
961.2.a.i.1.8		8	31.8	even	5
961.2.a.j.1.8		8	31.23	odd	10
961.2.c.i.439.8		16	31.17	odd	30
961.2.c.i.521.8		16	31.22	odd	30
961.2.c.j.439.8		16	31.14	even	15
961.2.c.j.521.8		16	31.9	even	15
961.2.d.n.374.1		16	31.29	odd	10
961.2.d.n.388.1		16	31.30	odd	2
961.2.d.o.374.1		16	31.2	even	5	inner
961.2.d.o.388.1		16	1.1	even	1	trivial
961.2.d.p.531.4		16	31.16	even	5
961.2.d.p.628.4		16	31.4	even	5
961.2.d.q.531.4		16	31.15	odd	10
961.2.d.q.628.4		16	31.27	odd	10
961.2.g.j.338.1		16	31.26	odd	6
961.2.g.j.816.1		16	31.12	odd	30
961.2.g.k.338.1		16	31.5	even	3
961.2.g.k.816.1		16	31.19	even	15
961.2.g.l.235.1		16	31.6	odd	6
961.2.g.l.732.1		16	31.21	odd	30
961.2.g.m.844.2		16	31.13	odd	30
961.2.g.m.846.2		16	31.24	odd	30
961.2.g.n.448.2		16	31.11	odd	30
961.2.g.n.547.2		16	31.3	odd	30
961.2.g.s.844.2		16	31.18	even	15
961.2.g.s.846.2		16	31.7	even	15
961.2.g.t.448.2		16	31.20	even	15
961.2.g.t.547.2		16	31.28	even	15
8649.2.a.be.1.1		8	93.23	even	10
8649.2.a.bf.1.1		8	93.8	odd	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+(-1.86683 + 1.35633i) q^{2} +(2.05711 + 1.49458i) q^{3} +(1.02738 - 3.16196i) q^{4} -2.49846 q^{5} -5.86740 q^{6} +(0.495008 - 1.52348i) q^{7} +(0.944583 + 2.90713i) q^{8} +(1.07088 + 3.29583i) q^{9} +(4.66419 - 3.38874i) q^{10} +(0.226712 - 0.697749i) q^{11} +(6.83922 - 4.96899i) q^{12} +(1.53388 + 1.11443i) q^{13} +(1.14224 + 3.51546i) q^{14} +(-5.13960 - 3.73414i) q^{15} +(-0.326952 - 0.237545i) q^{16} +(-1.35326 - 4.16490i) q^{17} +(-6.46939 - 4.70029i) q^{18} +(3.75224 - 2.72616i) q^{19} +(-2.56687 + 7.90002i) q^{20} +(3.29524 - 2.39413i) q^{21} +(0.523145 + 1.61007i) q^{22} +(-2.19973 - 6.77006i) q^{23} +(-2.40181 + 7.39202i) q^{24} +1.24230 q^{25} -4.37501 q^{26} +(-0.365721 + 1.12557i) q^{27} +(-4.30861 - 3.13039i) q^{28} +(0.104314 - 0.0757884i) q^{29} +14.6595 q^{30} -5.18091 q^{32} +(1.50921 - 1.09651i) q^{33} +(8.17529 + 5.93970i) q^{34} +(-1.23676 + 3.80635i) q^{35} +11.5215 q^{36} +8.42948 q^{37} +(-3.30721 + 10.1786i) q^{38} +(1.48975 + 4.58499i) q^{39} +(-2.36000 - 7.26334i) q^{40} +(5.96567 - 4.33432i) q^{41} +(-2.90441 + 8.93885i) q^{42} +(-0.186472 + 0.135480i) q^{43} +(-1.97333 - 1.43371i) q^{44} +(-2.67555 - 8.23451i) q^{45} +(13.2889 + 9.65498i) q^{46} +(6.50168 + 4.72375i) q^{47} +(-0.317547 - 0.977310i) q^{48} +(3.58717 + 2.60623i) q^{49} +(-2.31916 + 1.68497i) q^{50} +(3.44097 - 10.5902i) q^{51} +(5.09965 - 3.70511i) q^{52} +(1.77198 + 5.45359i) q^{53} +(-0.843912 - 2.59729i) q^{54} +(-0.566432 + 1.74330i) q^{55} +4.89652 q^{56} +11.7932 q^{57} +(-0.0919419 + 0.282968i) q^{58} +(-7.68867 - 5.58614i) q^{59} +(-17.0875 + 12.4148i) q^{60} -7.84044 q^{61} +5.55122 q^{63} +(10.3258 - 7.50212i) q^{64} +(-3.83233 - 2.78435i) q^{65} +(-1.33021 + 4.09397i) q^{66} +4.82658 q^{67} -14.5596 q^{68} +(5.59330 - 17.2144i) q^{69} +(-2.85385 - 8.78324i) q^{70} +(-1.05221 - 3.23836i) q^{71} +(-8.56987 + 6.22638i) q^{72} +(0.831888 - 2.56029i) q^{73} +(-15.7364 + 11.4332i) q^{74} +(2.55554 + 1.85671i) q^{75} +(-4.76503 - 14.6652i) q^{76} +(-0.950780 - 0.690782i) q^{77} +(-8.99987 - 6.53879i) q^{78} +(1.39921 + 4.30633i) q^{79} +(0.816877 + 0.593496i) q^{80} +(5.97623 - 4.34198i) q^{81} +(-5.25813 + 16.1829i) q^{82} +(-2.16036 + 1.56959i) q^{83} +(-4.18467 - 12.8791i) q^{84} +(3.38106 + 10.4058i) q^{85} +(0.164356 - 0.505834i) q^{86} +0.327856 q^{87} +2.24259 q^{88} +(-0.681255 + 2.09669i) q^{89} +(16.1635 + 11.7435i) q^{90} +(2.45708 - 1.78518i) q^{91} -23.6666 q^{92} -18.5445 q^{94} +(-9.37482 + 6.81121i) q^{95} +(-10.6577 - 7.74327i) q^{96} +(3.79778 - 11.6884i) q^{97} -10.2315 q^{98} +2.54245 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} + 9 q^{3} - 14 q^{4} + 6 q^{5} - 22 q^{6} + 11 q^{7} + 17 q^{8} + 5 q^{9} + 19 q^{10} + 14 q^{11} + 5 q^{12} - q^{13} + 27 q^{14} + 14 q^{15} - 2 q^{16} - 3 q^{17} - 9 q^{18} + 13 q^{19}+ \cdots - 12 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 + 9 * q^3 - 14 * q^4 + 6 * q^5 - 22 * q^6 + 11 * q^7 + 17 * q^8 + 5 * q^9 + 19 * q^10 + 14 * q^11 + 5 * q^12 - q^13 + 27 * q^14 + 14 * q^15 - 2 * q^16 - 3 * q^17 - 9 * q^18 + 13 * q^19 - 29 * q^20 - 3 * q^21 + 12 * q^22 + q^23 + 25 * q^24 + 26 * q^25 - 18 * q^26 + 9 * q^27 - 15 * q^28 - 14 * q^29 - 22 * q^30 - 42 * q^32 - 13 * q^33 + 49 * q^34 - 9 * q^35 - 2 * q^36 + 16 * q^37 - 31 * q^38 - 3 * q^39 + 2 * q^40 + 16 * q^41 - 18 * q^42 + 14 * q^43 - 33 * q^44 + 5 * q^45 + 34 * q^46 + 14 * q^47 - 38 * q^48 + 41 * q^49 - 6 * q^50 + 9 * q^51 + 17 * q^52 + 3 * q^53 - 46 * q^54 - q^55 + 60 * q^56 + 34 * q^57 - 15 * q^58 + 7 * q^59 - 75 * q^60 - 60 * q^61 - 46 * q^63 + 23 * q^64 - 6 * q^65 - 30 * q^66 - 26 * q^67 - 60 * q^68 - q^69 + 12 * q^70 - 17 * q^71 + q^72 + 11 * q^73 - 56 * q^74 + 4 * q^75 + 24 * q^76 + 18 * q^77 - 15 * q^78 - 6 * q^79 - 42 * q^80 - q^81 - 13 * q^82 - 28 * q^83 - 31 * q^84 + 37 * q^85 + 7 * q^86 - 30 * q^87 + 34 * q^88 + q^89 + 16 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 - 22 * q^95 - 16 * q^96 + 3 * q^97 + 20 * q^98 - 12 * q^99

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