LMFDB - Embedded newform 961.2.d.n.388.4

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			388.4
Root			$1.83925i$ of defining polynomial
Character	$\chi$	$=$	961.388
Dual form			961.2.d.n.374.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.557811 - 0.405274i) q^{2} +(-0.730058 - 0.530418i) q^{3} +(-0.471127 + 1.44998i) q^{4} +3.70752 q^{5} -0.622199 q^{6} +(0.235902 - 0.726031i) q^{7} +(0.750969 + 2.31124i) q^{8} +(-0.675410 - 2.07870i) q^{9} +(2.06809 - 1.50256i) q^{10} +(1.27180 - 3.91419i) q^{11} +(1.11305 - 0.808675i) q^{12} +(-2.35404 - 1.71031i) q^{13} +(-0.162653 - 0.500593i) q^{14} +(-2.70670 - 1.96653i) q^{15} +(-1.11127 - 0.807384i) q^{16} +(-0.404356 - 1.24448i) q^{17} +(-1.21919 - 0.885796i) q^{18} +(3.07389 - 2.23331i) q^{19} +(-1.74671 + 5.37583i) q^{20} +(-0.557322 + 0.404918i) q^{21} +(-0.876895 - 2.69881i) q^{22} +(1.01449 + 3.12228i) q^{23} +(0.677675 - 2.08567i) q^{24} +8.74568 q^{25} -2.00625 q^{26} +(-1.44606 + 4.45052i) q^{27} +(0.941591 + 0.684106i) q^{28} +(3.96065 - 2.87758i) q^{29} -2.30681 q^{30} -5.80746 q^{32} +(-3.00464 + 2.18300i) q^{33} +(-0.729910 - 0.530310i) q^{34} +(0.874609 - 2.69177i) q^{35} +3.33228 q^{36} +10.4128 q^{37} +(0.809549 - 2.49154i) q^{38} +(0.811405 + 2.49725i) q^{39} +(2.78423 + 8.56898i) q^{40} +(-0.611573 + 0.444334i) q^{41} +(-0.146778 + 0.451736i) q^{42} +(-5.79005 + 4.20671i) q^{43} +(5.07632 + 3.68816i) q^{44} +(-2.50409 - 7.70681i) q^{45} +(1.83127 + 1.33050i) q^{46} +(0.708753 + 0.514939i) q^{47} +(0.383039 + 1.17887i) q^{48} +(5.19165 + 3.77195i) q^{49} +(4.87844 - 3.54439i) q^{50} +(-0.364891 + 1.12302i) q^{51} +(3.58897 - 2.60754i) q^{52} +(-1.10495 - 3.40070i) q^{53} +(0.997049 + 3.06860i) q^{54} +(4.71521 - 14.5119i) q^{55} +1.85519 q^{56} -3.42871 q^{57} +(1.04309 - 3.21029i) q^{58} +(-0.750177 - 0.545036i) q^{59} +(4.12664 - 2.99818i) q^{60} -2.31704 q^{61} -1.66853 q^{63} +(-1.01693 + 0.738843i) q^{64} +(-8.72763 - 6.34100i) q^{65} +(-0.791311 + 2.43540i) q^{66} -2.08690 q^{67} +1.99498 q^{68} +(0.915477 - 2.81755i) q^{69} +(-0.603037 - 1.85596i) q^{70} +(-2.39058 - 7.35745i) q^{71} +(4.29717 - 3.12207i) q^{72} +(1.74826 - 5.38058i) q^{73} +(5.80837 - 4.22003i) q^{74} +(-6.38485 - 4.63886i) q^{75} +(1.79007 + 5.50926i) q^{76} +(-2.54180 - 1.84673i) q^{77} +(1.46468 + 1.06415i) q^{78} +(4.35551 + 13.4049i) q^{79} +(-4.12005 - 2.99339i) q^{80} +(-1.88839 + 1.37200i) q^{81} +(-0.161066 + 0.495709i) q^{82} +(-11.4134 + 8.29231i) q^{83} +(-0.324554 - 0.998873i) q^{84} +(-1.49916 - 4.61393i) q^{85} +(-1.52488 + 4.69311i) q^{86} -4.41782 q^{87} +10.0017 q^{88} +(1.37043 - 4.21776i) q^{89} +(-4.52018 - 3.28410i) q^{90} +(-1.79706 + 1.30564i) q^{91} -5.00520 q^{92} +0.604042 q^{94} +(11.3965 - 8.28005i) q^{95} +(4.23978 + 3.08038i) q^{96} +(-1.63088 + 5.01933i) q^{97} +4.42463 q^{98} -8.99540 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 $

$2$	0.557811	−	0.405274i	0.394432	−	0.286572i	−0.372837	−	0.927897i	$-0.621615\pi$
$2$	0.557811	−	0.405274i	0.394432	−	0.286572i	0.767269	+	0.641325i	$0.221615\pi$
$3$	−0.730058	−	0.530418i	−0.421499	−	0.306237i	0.356742	−	0.934203i	$-0.383888\pi$
$3$	−0.730058	−	0.530418i	−0.421499	−	0.306237i	−0.778241	+	0.627966i	$0.783888\pi$
$4$	−0.471127	+	1.44998i	−0.235564	+	0.724990i
$5$	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
$7$	0.235902	−	0.726031i	0.0891625	−	0.274414i	−0.896526	−	0.442991i	$-0.853917\pi$
$7$	0.235902	−	0.726031i	0.0891625	−	0.274414i	0.985688	+	0.168577i	$0.0539173\pi$
$8$	0.750969	+	2.31124i	0.265508	+	0.817148i
$9$	−0.675410	−	2.07870i	−0.225137	−	0.692899i
$10$	2.06809	−	1.50256i	0.653989	−	0.475151i
$11$	1.27180	−	3.91419i	0.383461	−	1.18017i	−0.554129	−	0.832431i	$-0.686949\pi$
$11$	1.27180	−	3.91419i	0.383461	−	1.18017i	0.937590	−	0.347742i	$-0.113051\pi$
$12$	1.11305	−	0.808675i	0.321309	−	0.233444i
$13$	−2.35404	−	1.71031i	−0.652893	−	0.474354i	0.211363	−	0.977408i	$-0.432210\pi$
$13$	−2.35404	−	1.71031i	−0.652893	−	0.474354i	−0.864255	+	0.503053i	$0.832210\pi$
$14$	−0.162653	−	0.500593i	−0.0434707	−	0.133789i
$15$	−2.70670	−	1.96653i	−0.698867	−	0.507757i
$16$	−1.11127	−	0.807384i	−0.277817	−	0.201846i
$17$	−0.404356	−	1.24448i	−0.0980708	−	0.301831i	0.889971	−	0.456017i	$-0.150724\pi$
$17$	−0.404356	−	1.24448i	−0.0980708	−	0.301831i	−0.988042	+	0.154186i	$0.950724\pi$
$18$	−1.21919	−	0.885796i	−0.287367	−	0.208784i
$19$	3.07389	−	2.23331i	0.705200	−	0.512358i	−0.176422	−	0.984315i	$-0.556452\pi$
$19$	3.07389	−	2.23331i	0.705200	−	0.512358i	0.881621	+	0.471957i	$0.156452\pi$
$20$	−1.74671	+	5.37583i	−0.390577	+	1.20207i
$21$	−0.557322	+	0.404918i	−0.121618	+	0.0883603i
$22$	−0.876895	−	2.69881i	−0.186955	−	0.575387i
$23$	1.01449	+	3.12228i	0.211536	+	0.651040i	0.999381	+	0.0351674i	$0.0111964\pi$
$23$	1.01449	+	3.12228i	0.211536	+	0.651040i	−0.787846	+	0.615873i	$0.788804\pi$
$24$	0.677675	−	2.08567i	0.138330	−	0.425735i
$25$	8.74568			1.74914
$26$	−2.00625			−0.393458
$27$	−1.44606	+	4.45052i	−0.278295	+	0.856503i
$28$	0.941591	+	0.684106i	0.177944	+	0.129284i
$29$	3.96065	−	2.87758i	0.735474	−	0.534353i	−0.155816	−	0.987786i	$-0.549801\pi$
$29$	3.96065	−	2.87758i	0.735474	−	0.534353i	0.891290	+	0.453433i	$0.149801\pi$
$30$	−2.30681			−0.421164
$31$		0			0
$31$		0			0
$32$	−5.80746			−1.02662
$33$	−3.00464	+	2.18300i	−0.523041	+	0.380012i
$34$	−0.729910	−	0.530310i	−0.125178	−	0.0909475i
$35$	0.874609	−	2.69177i	0.147836	−	0.454992i
$36$	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	$0.172988\pi$
$38$	0.809549	−	2.49154i	0.131326	−	0.404181i
$39$	0.811405	+	2.49725i	0.129929	+	0.399880i
$40$	2.78423	+	8.56898i	0.440225	+	1.35487i
$41$	−0.611573	+	0.444334i	−0.0955117	+	0.0693933i	−0.634516	−	0.772910i	$-0.718801\pi$
$41$	−0.611573	+	0.444334i	−0.0955117	+	0.0693933i	0.539004	+	0.842303i	$0.318801\pi$
$42$	−0.146778	+	0.451736i	−0.0226483	+	0.0697043i
$43$	−5.79005	+	4.20671i	−0.882974	+	0.641518i	−0.934037	−	0.357178i	$-0.883739\pi$
$43$	−5.79005	+	4.20671i	−0.882974	+	0.641518i	0.0510629	+	0.998695i	$0.483739\pi$
$44$	5.07632	+	3.68816i	0.765284	+	0.556011i
$45$	−2.50409	−	7.70681i	−0.373288	−	1.14886i
$46$	1.83127	+	1.33050i	0.270006	+	0.196171i
$47$	0.708753	+	0.514939i	0.103382	+	0.0751116i	0.638275	−	0.769808i	$-0.279648\pi$
$47$	0.708753	+	0.514939i	0.103382	+	0.0751116i	−0.534893	+	0.844920i	$0.679648\pi$
$48$	0.383039	+	1.17887i	0.0552870	+	0.170156i
$49$	5.19165	+	3.77195i	0.741664	+	0.538850i
$50$	4.87844	−	3.54439i	0.689915	−	0.501253i
$51$	−0.364891	+	1.12302i	−0.0510950	+	0.157254i
$52$	3.58897	−	2.60754i	0.497700	−	0.361600i
$53$	−1.10495	−	3.40070i	−0.151777	−	0.467122i	0.846043	−	0.533115i	$-0.178979\pi$
$53$	−1.10495	−	3.40070i	−0.151777	−	0.467122i	−0.997820	+	0.0659929i	$0.978979\pi$
$54$	0.997049	+	3.06860i	0.135681	+	0.417584i
$55$	4.71521	−	14.5119i	0.635799	−	1.95679i
$56$	1.85519			0.247910
$57$	−3.42871			−0.454144
$58$	1.04309	−	3.21029i	0.136964	−	0.421532i
$59$	−0.750177	−	0.545036i	−0.0976647	−	0.0709576i	0.537881	−	0.843021i	$-0.319225\pi$
$59$	−0.750177	−	0.545036i	−0.0976647	−	0.0709576i	−0.635546	+	0.772063i	$0.719225\pi$
$60$	4.12664	−	2.99818i	0.532746	−	0.387063i
$61$	−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
$64$	−1.01693	+	0.738843i	−0.127116	+	0.0923554i
$65$	−8.72763	−	6.34100i	−1.08253	−	0.786504i
$66$	−0.791311	+	2.43540i	−0.0974036	+	0.299778i
$67$	−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
$69$	0.915477	−	2.81755i	0.110210	−	0.339193i
$70$	−0.603037	−	1.85596i	−0.0720767	−	0.221829i
$71$	−2.39058	−	7.35745i	−0.283710	−	0.873169i	−0.986782	−	0.162051i	$-0.948189\pi$
$71$	−2.39058	−	7.35745i	−0.283710	−	0.873169i	0.703073	−	0.711118i	$-0.251811\pi$
$72$	4.29717	−	3.12207i	0.506426	−	0.367940i
$73$	1.74826	−	5.38058i	0.204618	−	0.629749i	−0.795111	−	0.606464i	$-0.792587\pi$
$73$	1.74826	−	5.38058i	0.204618	−	0.629749i	0.999729	−	0.0232853i	$-0.00741261\pi$
$74$	5.80837	−	4.22003i	0.675209	−	0.490568i
$75$	−6.38485	−	4.63886i	−0.737259	−	0.535650i
$76$	1.79007	+	5.50926i	0.205335	+	0.631956i
$77$	−2.54180	−	1.84673i	−0.289665	−	0.210454i
$78$	1.46468	+	1.06415i	0.165842	+	0.120492i
$79$	4.35551	+	13.4049i	0.490033	+	1.50817i	0.824557	+	0.565779i	$0.191424\pi$
$79$	4.35551	+	13.4049i	0.490033	+	1.50817i	−0.334524	+	0.942387i	$0.608576\pi$
$80$	−4.12005	−	2.99339i	−0.460635	−	0.334671i
$81$	−1.88839	+	1.37200i	−0.209822	+	0.152444i
$82$	−0.161066	+	0.495709i	−0.0177867	+	0.0547419i
$83$	−11.4134	+	8.29231i	−1.25278	+	0.910199i	−0.998380	−	0.0568999i	$-0.981878\pi$
$83$	−11.4134	+	8.29231i	−1.25278	+	0.910199i	−0.254401	+	0.967099i	$0.581878\pi$
$84$	−0.324554	−	0.998873i	−0.0354117	−	0.108986i
$85$	−1.49916	−	4.61393i	−0.162606	−	0.500451i
$86$	−1.52488	+	4.69311i	−0.164432	+	0.506071i
$87$	−4.41782			−0.473640
$88$	10.0017			1.06619
$89$	1.37043	−	4.21776i	0.145266	−	0.447081i	−0.851780	−	0.523900i	$-0.824476\pi$
$89$	1.37043	−	4.21776i	0.145266	−	0.447081i	0.997045	+	0.0768191i	$0.0244764\pi$
$90$	−4.52018	−	3.28410i	−0.476469	−	0.346175i
$91$	−1.79706	+	1.30564i	−0.188383	+	0.136868i
$92$	−5.00520			−0.521828
$93$		0			0
$94$	0.604042			0.0623021
$95$	11.3965	−	8.28005i	1.16926	−	0.849515i
$96$	4.23978	+	3.08038i	0.432721	+	0.314390i
$97$	−1.63088	+	5.01933i	−0.165591	+	0.509636i	−0.999079	−	0.0429007i	$-0.986340\pi$
$97$	−1.63088	+	5.01933i	−0.165591	+	0.509636i	0.833489	+	0.552537i	$0.186340\pi$
$98$	4.42463			0.446955
$99$	−8.99540			−0.904072
$100$	−4.12033	+	12.6811i	−0.412033	+	1.26811i
$101$	1.17656	+	3.62108i	0.117072	+	0.360311i	0.992374	−	0.123267i	$-0.0393371\pi$
$101$	1.17656	+	3.62108i	0.117072	+	0.360311i	−0.875301	+	0.483578i	$0.839337\pi$
$102$	0.251590	+	0.774314i	0.0249111	+	0.0766685i
$103$	5.05287	−	3.67113i	0.497874	−	0.361727i	−0.310330	−	0.950629i	$-0.600440\pi$
$103$	5.05287	−	3.67113i	0.497874	−	0.361727i	0.808204	+	0.588902i	$0.200440\pi$
$104$	2.18513	−	6.72515i	0.214270	−	0.659455i
$105$	−2.06628	+	1.50124i	−0.201648	+	0.146506i
$106$	−1.99457	−	1.44914i	−0.193730	−	0.140753i
$107$	0.719201	+	2.21347i	0.0695278	+	0.213985i	0.979783	−	0.200063i	$-0.0641147\pi$
$107$	0.719201	+	2.21347i	0.0695278	+	0.213985i	−0.910255	+	0.414048i	$0.864115\pi$
$108$	−5.77189	−	4.19352i	−0.555400	−	0.403522i
$109$	−1.19478	−	0.868057i	−0.114439	−	0.0831448i	0.529094	−	0.848563i	$-0.322532\pi$
$109$	−1.19478	−	0.868057i	−0.114439	−	0.0831448i	−0.643533	+	0.765419i	$0.722532\pi$
$110$	−3.25110	−	10.0059i	−0.309980	−	0.954022i
$111$	−7.60193	−	5.52313i	−0.721543	−	0.524232i
$112$	−0.848336	+	0.616352i	−0.0801602	+	0.0582398i
$113$	1.97170	−	6.06826i	0.185482	−	0.570854i	−0.814475	−	0.580199i	$-0.802975\pi$
$113$	1.97170	−	6.06826i	0.185482	−	0.570854i	0.999956	+	0.00934524i	$0.00297473\pi$
$114$	−1.91257	+	1.38957i	−0.179129	+	0.130145i
$115$	3.76124	+	11.5759i	0.350737	+	1.07946i
$116$	2.30647	+	7.09857i	0.214150	+	0.659086i
$117$	−1.96527	+	6.04849i	−0.181690	+	0.559183i
$118$	−0.639346			−0.0588566
$119$	−0.998919			−0.0915708
$120$	2.51249	−	7.73265i	0.229358	−	0.705891i
$121$	−4.80423	−	3.49047i	−0.436748	−	0.317316i
$122$	−1.29247	+	0.939035i	−0.117015	+	0.0850162i
$123$	0.682166			0.0615089
$124$		0			0
$125$	13.8872			1.24211
$126$	−0.930724	+	0.676211i	−0.0829155	+	0.0602417i
$127$	−1.15852	−	0.841717i	−0.102802	−	0.0746903i	0.535197	−	0.844728i	$-0.320238\pi$
$127$	−1.15852	−	0.841717i	−0.102802	−	0.0746903i	−0.637999	+	0.770037i	$0.720238\pi$
$128$	3.32139	−	10.2222i	0.293572	−	0.903521i
$129$	6.45838			0.568629
$130$	−7.43821			−0.652374
$131$	1.94461	−	5.98490i	0.169902	−	0.522903i	−0.829462	−	0.558563i	$-0.811353\pi$
$131$	1.94461	−	5.98490i	0.169902	−	0.522903i	0.999364	+	0.0356592i	$0.0113531\pi$
$132$	−1.74974	−	5.38514i	−0.152295	−	0.468717i
$133$	−0.896318	−	2.75858i	−0.0777207	−	0.239200i
$134$	−1.16410	+	0.845765i	−0.100562	+	0.0730629i
$135$	−5.36130	+	16.5004i	−0.461427	+	1.42013i
$136$	2.57264	−	1.86913i	0.220602	−	0.160277i
$137$	10.3149	+	7.49421i	0.881261	+	0.640273i	0.933585	−	0.358357i	$-0.116663\pi$
$137$	10.3149	+	7.49421i	0.881261	+	0.640273i	−0.0523242	+	0.998630i	$0.516663\pi$
$138$	−0.631214	−	1.94268i	−0.0537325	−	0.165372i
$139$	15.1397	+	10.9997i	1.28414	+	0.932979i	0.999670	−	0.0257067i	$-0.00818361\pi$
$139$	15.1397	+	10.9997i	1.28414	+	0.932979i	0.284466	+	0.958686i	$0.408184\pi$
$140$	3.49096	+	2.53633i	0.295040	+	0.214359i
$141$	−0.244298	−	0.751870i	−0.0205736	−	0.0633189i
$142$	−4.31528	−	3.13523i	−0.362130	−	0.263103i
$143$	−9.68833	+	7.03899i	−0.810179	+	0.588630i
$144$	−0.927746	+	2.85531i	−0.0773122	+	0.237942i
$145$	14.6842	−	10.6687i	1.21945	−	0.885985i
$146$	−1.20541	−	3.70987i	−0.0997605	−	0.307031i
$147$	−1.78949	−	5.50749i	−0.147595	−	0.454250i
$148$	−4.90575	+	15.0983i	−0.403250	+	1.24108i
$149$	−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
$151$	−4.75035	+	14.6201i	−0.386578	+	1.18977i	0.548751	+	0.835986i	$0.315104\pi$
$151$	−4.75035	+	14.6201i	−0.386578	+	1.18977i	−0.935329	+	0.353779i	$0.884896\pi$
$152$	7.47013	+	5.42737i	0.605908	+	0.440218i
$153$	−2.31379	+	1.68107i	−0.187059	+	0.135906i
$154$	−2.16628			−0.174564
$155$		0			0
$156$	−4.00324			−0.320515
$157$	−12.2544	+	8.90334i	−0.978008	+	0.710564i	−0.957262	−	0.289221i	$-0.906604\pi$
$157$	−12.2544	+	8.90334i	−0.978008	+	0.710564i	−0.0207452	+	0.999785i	$0.506604\pi$
$158$	7.86219	+	5.71222i	0.625483	+	0.454440i
$159$	−0.997111	+	3.06879i	−0.0790760	+	0.243371i
$160$	−21.5313			−1.70220
$161$	2.50619			0.197515
$162$	−0.497333	+	1.53063i	−0.0390741	+	0.120258i
$163$	−0.322882	−	0.993730i	−0.0252901	−	0.0778349i	0.937615	−	0.347676i	$-0.113029\pi$
$163$	−0.322882	−	0.993730i	−0.0252901	−	0.0778349i	−0.962905	+	0.269841i	$0.913029\pi$
$164$	−0.356147	−	1.09611i	−0.0278104	−	0.0855916i
$165$	−11.1398	+	8.09351i	−0.867229	+	0.630079i
$166$	−3.00586	+	9.25108i	−0.233300	+	0.718023i
$167$	−9.13332	+	6.63574i	−0.706757	+	0.513489i	−0.882126	−	0.471014i	$-0.843888\pi$
$167$	−9.13332	+	6.63574i	−0.706757	+	0.513489i	0.175369	+	0.984503i	$0.443888\pi$
$168$	−1.35440	−	0.984026i	−0.104494	−	0.0759192i
$169$	−1.40088	−	4.31147i	−0.107760	−	0.331652i
$170$	−2.70615	−	1.96613i	−0.207552	−	0.150796i
$171$	−6.71853	−	4.88129i	−0.513778	−	0.373282i
$172$	−3.37181	−	10.3774i	−0.257098	−	0.791266i
$173$	16.7084	+	12.1393i	1.27031	+	0.922937i	0.999215	−	0.0396145i	$-0.0126130\pi$
$173$	16.7084	+	12.1393i	1.27031	+	0.922937i	0.271099	+	0.962552i	$0.412613\pi$
$174$	−2.46431	+	1.79043i	−0.186819	+	0.135732i
$175$	2.06312	−	6.34963i	0.155957	−	0.479987i
$176$	−4.57356	+	3.32289i	−0.344745	+	0.250472i
$177$	0.258576	+	0.795815i	0.0194358	+	0.0598171i
$178$	−0.944903	−	2.90811i	−0.0708235	−	0.217972i
$179$	0.0406859	−	0.125218i	0.00304101	−	0.00935926i	−0.949524	−	0.313693i	$-0.898434\pi$
$179$	0.0406859	−	0.125218i	0.00304101	−	0.00935926i	0.952566	+	0.304334i	$0.0984338\pi$
$180$	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	$0.592777\pi$
$182$	−0.473278	+	1.45660i	−0.0350817	+	0.107970i
$183$	1.69157	+	1.22900i	0.125045	+	0.0908502i
$184$	−6.45450	+	4.68947i	−0.475832	+	0.345712i
$185$	38.6056			2.83834
$186$		0			0
$187$	−5.38539			−0.393819
$188$	−1.08056	+	0.785076i	−0.0788083	+	0.0572576i
$189$	2.89009	+	2.09977i	0.210223	+	0.152736i
$190$	3.00142	−	9.23741i	0.217746	−	0.670152i
$191$	−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
$193$	1.75004	−	5.38606i	0.125970	−	0.387697i	−0.868106	−	0.496378i	$-0.834663\pi$
$193$	1.75004	−	5.38606i	0.125970	−	0.387697i	0.994077	+	0.108682i	$0.0346629\pi$
$194$	1.12448	+	3.46079i	0.0807330	+	0.248471i
$195$	3.00830	+	9.25859i	0.215429	+	0.663021i
$196$	−7.91519	+	5.75072i	−0.565370	+	0.410766i
$197$	−4.91794	+	15.1359i	−0.350389	+	1.07839i	0.608246	+	0.793748i	$0.291873\pi$
$197$	−4.91794	+	15.1359i	−0.350389	+	1.07839i	−0.958635	+	0.284638i	$0.908127\pi$
$198$	−5.01774	+	3.64560i	−0.356595	+	0.259082i
$199$	−3.44759	−	2.50482i	−0.244393	−	0.177562i	0.458845	−	0.888516i	$-0.348263\pi$
$199$	−3.44759	−	2.50482i	−0.244393	−	0.177562i	−0.703238	+	0.710954i	$0.748263\pi$
$200$	6.56773	+	20.2134i	0.464409	+	1.42930i
$201$	1.52356	+	1.10693i	0.107463	+	0.0780767i
$202$	2.12383	+	1.54305i	0.149432	+	0.108569i
$203$	−1.15489	−	3.55438i	−0.0810572	−	0.249468i
$204$	−1.45645	−	1.05817i	−0.101972	−	0.0740868i
$205$	−2.26742	+	1.64737i	−0.158363	+	0.115058i
$206$	1.33074	−	4.09559i	0.0927170	−	0.285353i
$207$	5.80508	−	4.21764i	0.403481	−	0.293146i
$208$	1.23509	+	3.80123i	0.0856383	+	0.263568i
$209$	−4.83225	−	14.8721i	−0.334254	−	1.02873i
$210$	−0.544181	+	1.67482i	−0.0375521	+	0.115573i
$211$	−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
$213$	−2.15726	+	6.63937i	−0.147813	+	0.454922i
$214$	1.29824	+	0.943228i	0.0887460	+	0.0644777i
$215$	−21.4667	+	15.5965i	−1.46402	+	1.06367i
$216$	−11.3722			−0.773780
$217$		0			0
$218$	−1.01826			−0.0689654
$219$	−4.13028	+	3.00083i	−0.279099	+	0.202777i
$220$	18.8205	+	13.6739i	1.26888	+	0.921896i
$221$	−1.17658	+	3.62113i	−0.0791450	+	0.243583i
$222$	−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	$0.602184\pi$
$224$	−1.36999	+	4.21640i	−0.0915363	+	0.281720i
$225$	−5.90692	−	18.1796i	−0.393795	−	1.21197i
$226$	−1.35947	−	4.18402i	−0.0904307	−	0.278317i
$227$	−17.6067	+	12.7920i	−1.16859	+	0.849034i	−0.990840	−	0.135041i	$-0.956883\pi$
$227$	−17.6067	+	12.7920i	−1.16859	+	0.849034i	−0.177755	+	0.984075i	$0.556883\pi$
$228$	1.61536	−	4.97156i	0.106980	−	0.329250i
$229$	13.7176	−	9.96642i	0.906485	−	0.658600i	−0.0336385	−	0.999434i	$-0.510709\pi$
$229$	13.7176	−	9.96642i	0.906485	−	0.658600i	0.940123	+	0.340834i	$0.110709\pi$
$230$	6.78947	+	4.93284i	0.447684	+	0.325262i
$231$	0.876125	+	2.69644i	0.0576448	+	0.177412i
$232$	9.62511	+	6.99305i	0.631920	+	0.459117i
$233$	7.95758	+	5.78152i	0.521318	+	0.378760i	0.817100	−	0.576496i	$-0.195580\pi$
$233$	7.95758	+	5.78152i	0.521318	+	0.378760i	−0.295782	+	0.955255i	$0.595580\pi$
$234$	1.35504	+	4.17039i	0.0885819	+	0.272627i
$235$	2.62771	+	1.90915i	0.171413	+	0.124539i
$236$	1.14372	−	0.830961i	0.0744498	−	0.0540910i
$237$	3.93041	−	12.0966i	0.255308	−	0.785757i
$238$	−0.557208	+	0.404836i	−0.0361185	+	0.0262416i
$239$	−0.182516	−	0.561727i	−0.0118060	−	0.0363351i	0.944980	−	0.327128i	$-0.106081\pi$
$239$	−0.182516	−	0.561727i	−0.0118060	−	0.0363351i	−0.956786	+	0.290793i	$0.906081\pi$
$240$	1.42012	+	4.37069i	0.0916687	+	0.282127i
$241$	−4.74973	+	14.6182i	−0.305957	+	0.941639i	0.673361	+	0.739313i	$0.264850\pi$
$241$	−4.74973	+	14.6182i	−0.305957	+	0.941639i	−0.979318	+	0.202325i	$0.935150\pi$
$242$	−4.09445			−0.263201
$243$	16.1450			1.03570
$244$	1.09162	−	3.35966i	0.0698838	−	0.215080i
$245$	19.2481	+	13.9846i	1.22972	+	0.893442i
$246$	0.380520	−	0.276464i	0.0242611	−	0.0176267i
$247$	−11.0557			−0.703459
$248$		0			0
$249$	12.7308			0.806783
$250$	7.74642	−	5.62810i	0.489926	−	0.355952i
$251$	−4.89577	−	3.55698i	−0.309018	−	0.224515i	0.422457	−	0.906383i	$-0.361168\pi$
$251$	−4.89577	−	3.55698i	−0.309018	−	0.224515i	−0.731475	+	0.681868i	$0.761168\pi$
$252$	0.786090	−	2.41933i	0.0495190	−	0.152404i
$253$	13.5114			0.849455
$254$	−0.987363			−0.0619527
$255$	−1.35284	+	4.16362i	−0.0847182	+	0.260736i
$256$	−3.06694	−	9.43906i	−0.191684	−	0.589942i
$257$	−1.39918	−	4.30623i	−0.0872784	−	0.268615i	0.897886	−	0.440228i	$-0.145102\pi$
$257$	−1.39918	−	4.30623i	−0.0872784	−	0.268615i	−0.985165	+	0.171612i	$0.945102\pi$
$258$	3.60256	−	2.61741i	0.224286	−	0.162953i
$259$	2.45639	−	7.56000i	0.152633	−	0.469756i
$260$	13.3061	−	9.66748i	0.825212	−	0.599552i
$261$	−8.65668	−	6.28945i	−0.535835	−	0.389307i
$262$	−1.34080	−	4.12655i	−0.0828347	−	0.254939i
$263$	−2.02971	−	1.47467i	−0.125157	−	0.0909322i	0.523445	−	0.852059i	$-0.324646\pi$
$263$	−2.02971	−	1.47467i	−0.125157	−	0.0909322i	−0.648603	+	0.761127i	$0.724646\pi$
$264$	−7.30184	−	5.30510i	−0.449397	−	0.326506i
$265$	−4.09663	−	12.6081i	−0.251654	−	0.774512i
$266$	−1.61796	−	1.17552i	−0.0992034	−	0.0720755i
$267$	−3.23767	+	2.35230i	−0.198142	+	0.143959i
$268$	0.983194	−	3.02596i	0.0600581	−	0.184840i
$269$	10.7921	−	7.84092i	0.658006	−	0.478069i	−0.207983	−	0.978132i	$-0.566690\pi$
$269$	10.7921	−	7.84092i	0.658006	−	0.478069i	0.865989	+	0.500063i	$0.166690\pi$
$270$	3.69658	+	11.3769i	0.224967	+	0.692376i
$271$	−4.27190	−	13.1476i	−0.259500	−	0.798658i	−0.992910	−	0.118871i	$-0.962072\pi$
$271$	−4.27190	−	13.1476i	−0.259500	−	0.798658i	0.733410	−	0.679787i	$-0.237928\pi$
$272$	−0.555425	+	1.70942i	−0.0336776	+	0.103649i
$273$	2.00449			0.121317
$274$	8.79097			0.531082
$275$	11.1227	−	34.2322i	0.670726	−	2.06428i
$276$	3.65408	+	2.65485i	0.219950	+	0.159803i
$277$	9.36093	−	6.80111i	0.562444	−	0.408639i	−0.269909	−	0.962886i	$-0.586994\pi$
$277$	9.36093	−	6.80111i	0.562444	−	0.408639i	0.832353	+	0.554247i	$0.186994\pi$
$278$	12.9030			0.773870
$279$		0			0
$280$	6.87814			0.411048
$281$	12.4583	−	9.05151i	0.743202	−	0.539968i	−0.150510	−	0.988608i	$-0.548092\pi$
$281$	12.4583	−	9.05151i	0.743202	−	0.539968i	0.893712	+	0.448641i	$0.148092\pi$
$282$	−0.440985	−	0.320395i	−0.0262603	−	0.0190792i
$283$	−7.01336	+	21.5849i	−0.416901	+	1.28309i	0.493638	+	0.869667i	$0.335667\pi$
$283$	−7.01336	+	21.5849i	−0.416901	+	1.28309i	−0.910539	+	0.413422i	$0.864333\pi$
$284$	11.7944			0.699871
$285$	−12.7120			−0.752994
$286$	−2.55155	+	7.85285i	−0.150876	+	0.464349i
$287$	0.178329	+	0.548840i	0.0105264	+	0.0323970i
$288$	3.92242	+	12.0720i	0.231131	+	0.711347i
$289$	12.3681	−	8.98592i	0.727533	−	0.528584i
$290$	3.86726	−	11.9022i	0.227094	−	0.698922i
$291$	3.85298	−	2.79935i	0.225866	−	0.164101i
$292$	6.97809	+	5.06988i	0.408362	+	0.296692i
$293$	3.83208	+	11.7939i	0.223872	+	0.689008i	0.998404	+	0.0564732i	$0.0179855\pi$
$293$	3.83208	+	11.7939i	0.223872	+	0.689008i	−0.774532	+	0.632535i	$0.782014\pi$
$294$	−3.23024	−	2.34690i	−0.188391	−	0.136874i
$295$	−2.78129	−	2.02073i	−0.161933	−	0.117651i
$296$	7.81967	+	24.0665i	0.454509	+	1.39884i
$297$	15.5811	+	11.3203i	0.904106	+	0.656872i
$298$	−11.2317	+	8.16031i	−0.650635	+	0.472714i
$299$	2.95191	−	9.08505i	0.170714	−	0.525402i
$300$	9.73434	−	7.07241i	0.562012	−	0.408326i
$301$	1.68832	+	5.19612i	0.0973133	+	0.299499i
$302$	3.27533	+	10.0804i	0.188474	+	0.580064i
$303$	1.06173	−	3.26767i	0.0609947	−	0.187723i
$304$	−5.21907			−0.299334
$305$	−8.59046			−0.491888
$306$	−0.609367	+	1.87544i	−0.0348352	+	0.107212i
$307$	−24.8530	−	18.0568i	−1.41844	−	1.03055i	−0.992027	−	0.126023i	$-0.959779\pi$
$307$	−24.8530	−	18.0568i	−1.41844	−	1.03055i	−0.426408	−	0.904531i	$-0.640221\pi$
$308$	3.87523	−	2.81552i	0.220812	−	0.160429i
$309$	−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	$0.478492\pi$
$312$	−5.16241	+	3.75071i	−0.292264	+	0.212342i
$313$	8.69337	+	6.31610i	0.491378	+	0.357007i	0.805714	−	0.592305i	$-0.201782\pi$
$313$	8.69337	+	6.31610i	0.491378	+	0.357007i	−0.314336	+	0.949312i	$0.601782\pi$
$314$	−3.22735	+	9.93277i	−0.182130	+	0.560539i
$315$	−6.18610			−0.348547
$316$	−21.4888			−1.20884
$317$	2.70277	−	8.31827i	0.151803	−	0.467201i	−0.846020	−	0.533151i	$-0.821008\pi$
$317$	2.70277	−	8.31827i	0.151803	−	0.467201i	0.997823	+	0.0659501i	$0.0210078\pi$
$318$	0.687501	+	2.11591i	0.0385531	+	0.118654i
$319$	−6.22625	−	19.1624i	−0.348603	−	1.07289i
$320$	−3.77029	+	2.73927i	−0.210765	+	0.153130i
$321$	0.649008	−	1.99744i	0.0362241	−	0.111486i
$322$	1.39798	−	1.01569i	0.0779065	−	0.0566024i
$323$	−4.02226	−	2.92235i	−0.223805	−	0.162604i
$324$	−1.09970	−	3.38452i	−0.0610943	−	0.188029i
$325$	−20.5877	−	14.9578i	−1.14200	−	0.829710i
$326$	−0.582840	−	0.423458i	−0.0322805	−	0.0234532i
$327$	0.411824	+	1.26746i	0.0227739	+	0.0700909i
$328$	−1.48624	−	1.07981i	−0.0820637	−	0.0596227i
$329$	0.541058	−	0.393101i	0.0298295	−	0.0216724i
$330$	−2.93380	+	9.02930i	−0.161500	+	0.497047i
$331$	−26.1872	+	19.0261i	−1.43938	+	1.04577i	−0.451204	+	0.892421i	$0.649005\pi$
$331$	−26.1872	+	19.0261i	−1.43938	+	1.04577i	−0.988172	+	0.153347i	$0.950995\pi$
$332$	−6.64653	−	20.4559i	−0.364776	−	1.12266i
$333$	−7.03290	−	21.6450i	−0.385400	−	1.18614i
$334$	−2.40538	+	7.40299i	−0.131616	+	0.405073i
$335$	−7.73721			−0.422729
$336$	0.946258			0.0516226
$337$	−8.57021	+	26.3764i	−0.466849	+	1.43681i	0.389792	+	0.920903i	$0.372547\pi$
$337$	−8.57021	+	26.3764i	−0.466849	+	1.43681i	−0.856642	+	0.515912i	$0.827453\pi$
$338$	−2.52875	−	1.83725i	−0.137546	−	0.0999331i
$339$	−4.65817	+	3.38436i	−0.252997	+	0.183813i
$340$	7.39640			0.401126
$341$		0			0
$342$	−5.72593			−0.309623
$343$	8.28646	−	6.02047i	0.447427	−	0.325075i
$344$	−14.0709	−	10.2231i	−0.758651	−	0.551192i
$345$	3.39414	−	10.4461i	0.182735	−	0.562399i
$346$	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	$0.255128\pi$
$348$	2.08136	−	6.40576i	0.111572	−	0.343385i
$349$	1.72862	+	5.32015i	0.0925309	+	0.284781i	0.986602	−	0.163144i	$-0.0521634\pi$
$349$	1.72862	+	5.32015i	0.0925309	+	0.284781i	−0.894071	+	0.447924i	$0.852163\pi$
$350$	−1.42251	−	4.37802i	−0.0760362	−	0.234015i
$351$	11.0159	−	8.00348i	0.587983	−	0.427194i
$352$	−7.38591	+	22.7315i	−0.393671	+	1.21159i
$353$	9.44040	−	6.85885i	0.502462	−	0.365060i	−0.307495	−	0.951550i	$-0.599491\pi$
$353$	9.44040	−	6.85885i	0.502462	−	0.365060i	0.809957	+	0.586490i	$0.199491\pi$
$354$	0.466759	+	0.339121i	0.0248080	+	0.0180241i
$355$	−8.86312	−	27.2779i	−0.470406	−	1.44776i
$356$	5.47002	+	3.97420i	0.289910	+	0.210632i
$357$	0.729269	+	0.529845i	0.0385970	+	0.0280424i
$358$	−0.0280526	−	0.0863372i	−0.00148263	−	0.00456306i
$359$	−21.1961	−	15.3999i	−1.11869	−	0.812775i	−0.134679	−	0.990889i	$-0.543000\pi$
$359$	−21.1961	−	15.3999i	−1.11869	−	0.812775i	−0.984010	+	0.178115i	$0.943000\pi$
$360$	15.9318	−	11.5751i	0.839681	−	0.610064i
$361$	−1.41019	+	4.34013i	−0.0742207	+	0.228428i
$362$	−4.31299	+	3.13357i	−0.226686	+	0.164697i
$363$	1.65595	+	5.09650i	0.0869149	+	0.267497i
$364$	−1.04651	−	3.22082i	−0.0548519	−	0.168817i
$365$	6.48169	−	19.9486i	0.339267	−	1.04416i
$366$	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	$0.749087\pi$
$368$	1.39351	−	4.28877i	0.0726416	−	0.223568i
$369$	1.33670	+	0.971168i	0.0695857	+	0.0505570i
$370$	21.5346	−	15.6458i	1.11953	−	0.813387i
$371$	−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	$0.604078\pi$
$374$	−3.00403	+	2.18256i	−0.155335	+	0.112857i
$375$	−10.1384	−	7.36600i	−0.523546	−	0.380379i
$376$	−0.657899	+	2.02480i	−0.0339285	+	0.104421i
$377$	−14.2451			−0.733658
$378$	2.46311			0.126688
$379$	−1.43353	+	4.41196i	−0.0736357	+	0.226627i	−0.981100	−	0.193502i	$-0.938015\pi$
$379$	−1.43353	+	4.41196i	−0.0736357	+	0.226627i	0.907464	+	0.420129i	$0.138015\pi$
$380$	6.63670	+	20.4257i	0.340456	+	1.04782i
$381$	0.399327	+	1.22900i	0.0204582	+	0.0629638i
$382$	−11.7713	+	8.55236i	−0.602273	+	0.437577i
$383$	1.55168	−	4.77557i	0.0792870	−	0.244020i	−0.903554	−	0.428474i	$-0.859051\pi$
$383$	1.55168	−	4.77557i	0.0792870	−	0.244020i	0.982841	+	0.184453i	$0.0590515\pi$
$384$	−7.84683	+	5.70106i	−0.400432	+	0.290931i
$385$	−9.42378	−	6.84677i	−0.480280	−	0.348944i
$386$	−1.20664	−	3.71365i	−0.0614162	−	0.189020i
$387$	12.6551	+	9.19450i	0.643297	+	0.467383i
$388$	−6.50958	−	4.72949i	−0.330474	−	0.240103i
$389$	−5.74828	−	17.6914i	−0.291450	−	0.896989i	−0.984391	−	0.175996i	$-0.943686\pi$
$389$	−5.74828	−	17.6914i	−0.291450	−	0.896989i	0.692941	−	0.720994i	$-0.256314\pi$
$390$	5.43032	+	3.94536i	0.274975	+	0.199781i
$391$	3.47540	−	2.52503i	0.175758	−	0.127696i
$392$	−4.81914	+	14.8318i	−0.243403	+	0.749118i
$393$	−4.59418	+	3.33787i	−0.231746	+	0.168373i
$394$	3.39089	+	10.4361i	0.170830	+	0.525762i
$395$	16.1481	+	49.6988i	0.812500	+	2.50062i
$396$	4.23798	−	13.0432i	0.212966	−	0.655443i
$397$	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
$399$	−0.808838	+	2.48935i	−0.0404926	+	0.124623i
$400$	−9.71880	−	7.06112i	−0.485940	−	0.353056i
$401$	−10.0239	+	7.28282i	−0.500572	+	0.363687i	−0.809235	−	0.587485i	$-0.800118\pi$
$401$	−10.0239	+	7.28282i	−0.500572	+	0.363687i	0.308664	+	0.951171i	$0.400118\pi$
$402$	1.29847			0.0647616
$403$		0			0
$404$	−5.80481			−0.288800
$405$	−7.00125	+	5.08671i	−0.347895	+	0.252760i
$406$	−2.08471	−	1.51463i	−0.103462	−	0.0751697i
$407$	13.2429	−	40.7576i	0.656429	−	2.02028i
$408$	−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	$0.472832\pi$
$410$	−0.597153	+	1.83785i	−0.0294913	+	0.0907649i
$411$	−3.55540	−	10.9424i	−0.175375	−	0.539749i
$412$	2.94252	+	9.05613i	0.144967	+	0.446164i
$413$	−0.572681	+	0.416077i	−0.0281798	+	0.0204738i
$414$	1.52884	−	4.70529i	0.0751385	−	0.231252i
$415$	−42.3153	+	30.7439i	−2.07718	+	1.50916i
$416$	13.6710	+	9.93255i	0.670275	+	0.486983i
$417$	−5.21846	−	16.0608i	−0.255549	−	0.786500i
$418$	−8.72276	−	6.33746i	−0.426644	−	0.309975i
$419$	32.3988	+	23.5391i	1.58279	+	1.14996i	0.913412	+	0.407035i	$0.133437\pi$
$419$	32.3988	+	23.5391i	1.58279	+	1.14996i	0.669374	+	0.742926i	$0.266563\pi$
$420$	−1.20329	−	3.70334i	−0.0587144	−	0.180704i
$421$	−17.5431	−	12.7458i	−0.854997	−	0.621191i	0.0715226	−	0.997439i	$-0.477214\pi$
$421$	−17.5431	−	12.7458i	−0.854997	−	0.621191i	−0.926519	+	0.376248i	$0.877214\pi$
$422$	−6.41945	+	4.66400i	−0.312494	+	0.227040i
$423$	0.591704	−	1.82108i	0.0287696	−	0.0885439i
$424$	7.03006	−	5.10763i	0.341410	−	0.248049i
$425$	−3.53637	−	10.8838i	−0.171539	−	0.527943i
$426$	1.48742	+	4.57780i	0.0720656	+	0.221795i
$427$	−0.546594	+	1.68224i	−0.0264515	+	0.0814094i
$428$	−3.54833			−0.171515
$429$	10.8066			0.521750
$430$	−5.65353	+	17.3998i	−0.272637	+	0.839091i
$431$	9.40132	+	6.83046i	0.452846	+	0.329012i	0.790718	−	0.612180i	$-0.209707\pi$
$431$	9.40132	+	6.83046i	0.452846	+	0.329012i	−0.337873	+	0.941192i	$0.609707\pi$
$432$	5.20024	−	3.77820i	0.250197	−	0.181779i
$433$	−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
$436$	1.82156	−	1.32344i	0.0872368	−	0.0633813i
$437$	10.0915	+	7.33188i	0.482740	+	0.350731i
$438$	−1.08776	+	3.34779i	−0.0519753	+	0.159964i
$439$	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
$441$	4.33426	−	13.3395i	0.206393	−	0.635214i
$442$	0.811240	+	2.49674i	0.0385868	+	0.118758i
$443$	5.48825	+	16.8911i	0.260754	+	0.802520i	0.992641	+	0.121093i	$0.0386400\pi$
$443$	5.48825	+	16.8911i	0.260754	+	0.802520i	−0.731887	+	0.681426i	$0.761360\pi$
$444$	11.5899	−	8.42056i	0.550032	−	0.399622i
$445$	5.08090	−	15.6374i	0.240858	−	0.741284i
$446$	−5.25676	+	3.81926i	−0.248915	+	0.180847i
$447$	14.6999	+	10.6801i	0.695283	+	0.505153i
$448$	0.296527	+	0.912617i	0.0140096	+	0.0431171i
$449$	−7.44180	−	5.40679i	−0.351200	−	0.255162i	0.398172	−	0.917311i	$-0.369645\pi$
$449$	−7.44180	−	5.40679i	−0.351200	−	0.255162i	−0.749372	+	0.662149i	$0.769645\pi$
$450$	−10.6627	−	7.74688i	−0.502643	−	0.365192i
$451$	0.961410	+	2.95892i	0.0452710	+	0.139330i
$452$	7.86994	+	5.71785i	0.370171	+	0.268945i
$453$	11.2228	−	8.15383i	0.527292	−	0.383100i
$454$	−4.63694	+	14.2710i	−0.217622	+	0.669773i
$455$	−6.66262	+	4.84068i	−0.312349	+	0.226935i
$456$	−2.57485	−	7.92459i	−0.120579	−	0.371103i
$457$	9.64130	+	29.6729i	0.451001	+	1.38804i	0.875767	+	0.482735i	$0.160356\pi$
$457$	9.64130	+	29.6729i	0.451001	+	1.38804i	−0.424766	+	0.905303i	$0.639644\pi$
$458$	3.61271	−	11.1188i	0.168811	−	0.519546i
$459$	6.12331			0.285812
$460$	−18.5568			−0.865218
$461$	2.06067	−	6.34209i	0.0959750	−	0.295381i	−0.891532	−	0.452959i	$-0.850369\pi$
$461$	2.06067	−	6.34209i	0.0959750	−	0.295381i	0.987507	+	0.157578i	$0.0503685\pi$
$462$	1.58151	+	1.14903i	0.0735784	+	0.0534578i
$463$	28.5732	−	20.7597i	1.32791	−	0.964784i	0.328114	−	0.944638i	$-0.393587\pi$
$463$	28.5732	−	20.7597i	1.32791	−	0.964784i	0.999797	−	0.0201457i	$-0.00641301\pi$
$464$	−6.72466			−0.312184
$465$		0			0
$466$	6.78192			0.314167
$467$	−29.0789	+	21.1270i	−1.34561	+	0.977642i	−0.346391	+	0.938090i	$0.612593\pi$
$467$	−29.0789	+	21.1270i	−1.34561	+	0.977642i	−0.999218	+	0.0395520i	$0.987407\pi$
$468$	−7.84430	−	5.69922i	−0.362603	−	0.263447i
$469$	−0.492303	+	1.51515i	−0.0227324	+	0.0699632i
$470$	2.23949			0.103300
$471$	13.6689			0.629830
$472$	0.696351	−	2.14315i	0.0320521	−	0.0986463i
$473$	9.10211	+	28.0134i	0.418516	+	1.28806i
$474$	−2.70999	−	8.34050i	−0.124474	−	0.383092i
$475$	26.8833	−	19.5318i	1.23349	−	0.896183i
$476$	0.470618	−	1.44841i	0.0215707	−	0.0663879i
$477$	−6.32273	+	4.59373i	−0.289498	+	0.210332i
$478$	−0.329463	−	0.239369i	−0.0150693	−	0.0109485i
$479$	10.2731	+	31.6173i	0.469389	+	1.44463i	0.853377	+	0.521294i	$0.174550\pi$
$479$	10.2731	+	31.6173i	0.469389	+	1.44463i	−0.383988	+	0.923338i	$0.625450\pi$
$480$	15.7191	+	11.4206i	0.717474	+	0.521275i
$481$	−24.5121	−	17.8091i	−1.11765	−	0.812024i
$482$	3.27490	+	10.0791i	0.149168	+	0.459091i
$483$	−1.82966	−	1.32933i	−0.0832526	−	0.0604865i
$484$	7.32452	−	5.32158i	0.332933	−	0.241890i
$485$	−6.04652	+	18.6093i	−0.274558	+	0.845003i
$486$	9.00588	−	6.54316i	0.408515	−	0.296804i
$487$	−8.81173	−	27.1197i	−0.399298	−	1.22891i	−0.925564	−	0.378592i	$-0.876408\pi$
$487$	−8.81173	−	27.1197i	−0.399298	−	1.22891i	0.526266	−	0.850320i	$-0.323592\pi$
$488$	−1.74002	−	5.35524i	−0.0787672	−	0.242420i
$489$	−0.291369	+	0.896743i	−0.0131762	+	0.0405521i
$490$	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	$0.282649\pi$
$492$	−0.321387	+	0.989128i	−0.0144892	+	0.0445933i
$493$	−5.18260	−	3.76538i	−0.233413	−	0.169584i
$494$	−6.16701	+	4.48059i	−0.277467	+	0.201591i
$495$	−33.3506			−1.49900
$496$		0			0
$497$	−5.90568			−0.264906
$498$	7.10139	−	5.15946i	0.318221	−	0.231201i
$499$	−33.4164	−	24.2784i	−1.49592	−	1.08685i	−0.971970	−	0.235106i	$-0.924456\pi$
$499$	−33.4164	−	24.2784i	−1.49592	−	1.08685i	−0.523955	−	0.851746i	$-0.675544\pi$
$500$	−6.54262	+	20.1361i	−0.292595	+	0.900514i
$501$	10.1876			0.455147
$502$	−4.17247			−0.186226
$503$	−7.90652	+	24.3338i	−0.352534	+	1.08499i	0.604891	+	0.796308i	$0.293217\pi$
$503$	−7.90652	+	24.3338i	−0.352534	+	1.08499i	−0.957425	+	0.288681i	$0.906783\pi$
$504$	−1.25301	−	3.85638i	−0.0558136	−	0.171777i
$505$	4.36212	+	13.4252i	0.194112	+	0.597414i
$506$	7.53682	−	5.47582i	0.335053	−	0.243430i
$507$	−1.26416	+	3.89068i	−0.0561432	+	0.172791i
$508$	1.76629	−	1.28328i	0.0783662	−	0.0569364i
$509$	−19.7949	−	14.3818i	−0.877392	−	0.637462i	0.0551686	−	0.998477i	$-0.482430\pi$
$509$	−19.7949	−	14.3818i	−0.877392	−	0.637462i	−0.932560	+	0.361015i	$0.882430\pi$
$510$	0.932774	+	2.87078i	0.0413039	+	0.127120i
$511$	−3.49405	−	2.53858i	−0.154568	−	0.112300i
$512$	11.8548	+	8.61304i	0.523915	+	0.380646i
$513$	5.49437	+	16.9099i	0.242583	+	0.746592i
$514$	−2.52568	−	1.83501i	−0.111403	−	0.0809390i
$515$	18.7336	−	13.6108i	0.825501	−	0.599762i
$516$	−3.04272	+	9.36453i	−0.133948	+	0.412250i
$517$	2.91696	−	2.11929i	0.128288	−	0.0932065i
$518$	−1.69367	−	5.21257i	−0.0744154	−	0.229027i
$519$	−5.75915	−	17.7248i	−0.252799	−	0.778034i
$520$	8.10141	−	24.9336i	0.355270	−	1.09341i
$521$	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
$523$	6.47873	−	19.9395i	0.283295	−	0.871893i	−0.703609	−	0.710587i	$-0.748429\pi$
$523$	6.47873	−	19.9395i	0.283295	−	0.871893i	0.986904	−	0.161306i	$-0.0515706\pi$
$524$	7.76183	+	5.63930i	0.339077	+	0.246354i
$525$	−4.87415	+	3.54128i	−0.212726	+	0.154554i
$526$	−1.72984			−0.0754247
$527$		0			0
$528$	5.10148			0.222014
$529$	9.88796	−	7.18402i	0.429911	−	0.312349i
$530$	−7.39489	−	5.37271i	−0.321214	−	0.233375i
$531$	−0.626287	+	1.92751i	−0.0271786	+	0.0836470i
$532$	4.42217			0.191726
$533$	2.19961			0.0952759
$534$	−0.852681	+	2.62428i	−0.0368991	+	0.113564i
$535$	2.66645	+	8.20649i	0.115281	+	0.354798i
$536$	−1.56719	−	4.82333i	−0.0676925	−	0.208336i
$537$	−0.0961211	+	0.0698361i	−0.00414793	+	0.00301365i
$538$	2.84224	−	8.74751i	0.122538	−	0.377132i
$539$	21.3669	−	15.5239i	0.920336	−	0.668663i
$540$	−21.3994	−	15.5476i	−0.920883	−	0.669060i
$541$	0.535002	+	1.64657i	0.0230015	+	0.0707914i	0.961898	−	0.273407i	$-0.0881507\pi$
$541$	0.535002	+	1.64657i	0.0230015	+	0.0707914i	−0.938897	+	0.344199i	$0.888151\pi$
$542$	−7.71128	−	5.60257i	−0.331228	−	0.240651i
$543$	5.64480	+	4.10118i	0.242241	+	0.175999i
$544$	2.34828	+	7.22727i	0.100682	+	0.309867i
$545$	−4.42966	−	3.21834i	−0.189746	−	0.137858i
$546$	1.11813	−	0.812367i	0.0478514	−	0.0347661i
$547$	−4.05474	+	12.4792i	−0.173368	+	0.533573i	−0.999555	−	0.0298233i	$-0.990506\pi$
$547$	−4.05474	+	12.4792i	−0.173368	+	0.533573i	0.826187	+	0.563396i	$0.190506\pi$
$548$	−15.7261	+	11.4257i	−0.671785	+	0.488080i
$549$	1.56495	+	4.81643i	0.0667905	+	0.205560i
$550$	−7.66904	−	23.6029i	−0.327009	−	1.00643i
$551$	5.74807	−	17.6908i	0.244876	−	0.753651i
$552$	7.19953			0.306432
$553$	10.7598			0.457554
$554$	2.46532	−	7.58748i	0.104741	−	0.322361i
$555$	−28.1843	−	20.4771i	−1.19636	−	0.869204i
$556$	−23.0820	+	16.7701i	−0.978897	+	0.711210i
$557$	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
$560$	−3.14522	+	2.28514i	−0.132910	+	0.0965646i
$561$	3.93165	+	2.85651i	0.165994	+	0.120602i
$562$	3.28106	−	10.0981i	0.138403	−	0.425961i
$563$	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
$565$	7.31010	−	22.4982i	0.307538	−	0.946505i
$566$	4.83566	+	14.8826i	0.203258	+	0.625564i
$567$	0.550638	+	1.69469i	0.0231246	+	0.0711702i
$568$	15.2096	−	11.0504i	0.638181	−	0.463666i
$569$	14.3514	−	44.1690i	0.601641	−	1.85166i	0.0832264	−	0.996531i	$-0.473478\pi$
$569$	14.3514	−	44.1690i	0.601641	−	1.85166i	0.518414	−	0.855130i	$-0.326522\pi$
$570$	−7.09090	+	5.15184i	−0.297005	+	0.215787i
$571$	−10.1114	−	7.34635i	−0.423148	−	0.307435i	0.355755	−	0.934579i	$-0.384224\pi$
$571$	−10.1114	−	7.34635i	−0.423148	−	0.307435i	−0.778903	+	0.627144i	$0.784224\pi$
$572$	−5.64195	−	17.3642i	−0.235902	−	0.726032i
$573$	15.4062	+	11.1932i	0.643602	+	0.467604i
$574$	0.321904	+	0.233877i	0.0134360	+	0.00976184i
$575$	8.87240	+	27.3064i	0.370005	+	1.13876i
$576$	2.22268	+	1.61487i	0.0926115	+	0.0672862i
$577$	24.6623	−	17.9182i	1.02671	−	0.745945i	0.0590589	−	0.998255i	$-0.481190\pi$
$577$	24.6623	−	17.9182i	1.02671	−	0.745945i	0.967647	+	0.252309i	$0.0811900\pi$
$578$	3.25729	−	10.0249i	0.135485	−	0.416981i
$579$	−4.13449	+	3.00388i	−0.171823	+	0.124837i
$580$	8.55126	+	26.3181i	0.355072	+	1.09280i
$581$	3.32803	+	10.2426i	0.138070	+	0.424936i
$582$	1.01473	−	3.12302i	0.0420620	−	0.129453i
$583$	−14.7162			−0.609485
$584$	13.7487			0.568926
$585$	−7.28629	+	22.4249i	−0.301251	+	0.927155i
$586$	6.91734	+	5.02574i	0.285753	+	0.207612i
$587$	27.2300	−	19.7837i	1.12390	−	0.816562i	0.139105	−	0.990278i	$-0.455577\pi$
$587$	27.2300	−	19.7837i	1.12390	−	0.816562i	0.984796	+	0.173716i	$0.0555774\pi$
$588$	8.82883			0.364095
$589$		0			0
$590$	−2.37039			−0.0975872
$591$	11.6187	−	8.44150i	0.477930	−	0.347237i
$592$	−11.5714	−	8.40712i	−0.475582	−	0.345530i
$593$	−13.8711	+	42.6909i	−0.569619	+	1.75311i	0.0841933	+	0.996449i	$0.473169\pi$
$593$	−13.8711	+	42.6909i	−0.569619	+	1.75311i	−0.653812	+	0.756657i	$0.726831\pi$
$594$	13.2791			0.544850
$595$	−3.70351			−0.151829
$596$	9.48629	−	29.1958i	0.388574	−	1.19591i
$597$	1.18834	+	3.65733i	0.0486354	+	0.149684i
$598$	−2.03532	−	6.26408i	−0.0832305	−	0.256157i
$599$	15.8443	−	11.5115i	0.647380	−	0.470349i	−0.214998	−	0.976615i	$-0.568974\pi$
$599$	15.8443	−	11.5115i	0.647380	−	0.470349i	0.862378	+	0.506265i	$0.168974\pi$
$600$	5.92673	−	18.2406i	0.241958	−	0.744669i
$601$	24.6422	−	17.9036i	1.00518	−	0.730304i	0.0419852	−	0.999118i	$-0.486632\pi$
$601$	24.6422	−	17.9036i	1.00518	−	0.730304i	0.963192	+	0.268814i	$0.0866318\pi$
$602$	3.04762	+	2.21422i	0.124212	+	0.0902450i
$603$	1.40951	+	4.33803i	0.0573997	+	0.176658i
$604$	−18.9608	−	13.7758i	−0.771504	−	0.560531i
$605$	−17.8117	−	12.9410i	−0.724150	−	0.526126i
$606$	−0.732055	−	2.25303i	−0.0297377	−	0.0915232i
$607$	10.8203	+	7.86137i	0.439180	+	0.319083i	0.785309	−	0.619104i	$-0.212504\pi$
$607$	10.8203	+	7.86137i	0.439180	+	0.319083i	−0.346129	+	0.938187i	$0.612504\pi$
$608$	−17.8515	+	12.9699i	−0.723975	+	0.525998i
$609$	−1.04217	+	3.20747i	−0.0422309	+	0.129973i
$610$	−4.79186	+	3.48149i	−0.194017	+	0.140961i
$611$	−0.787726	−	2.42437i	−0.0318680	−	0.0980796i
$612$	−1.34743	−	4.14695i	−0.0544665	−	0.167631i
$613$	1.60541	−	4.94093i	0.0648418	−	0.199562i	−0.913387	−	0.407093i	$-0.866543\pi$
$613$	1.60541	−	4.94093i	0.0648418	−	0.199562i	0.978229	+	0.207530i	$0.0665426\pi$
$614$	−21.1812			−0.854804
$615$	2.52914			0.101985
$616$	2.35942	−	7.26156i	0.0950639	−	0.292577i
$617$	24.2811	+	17.6412i	0.977520	+	0.710210i	0.957153	−	0.289583i	$-0.0935166\pi$
$617$	24.2811	+	17.6412i	0.977520	+	0.710210i	0.0203666	+	0.999793i	$0.493517\pi$
$618$	−3.14389	+	2.28417i	−0.126466	+	0.0918828i
$619$	−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
$622$	1.32838	−	0.965124i	0.0532631	−	0.0386979i
$623$	−2.73893	−	1.98995i	−0.109733	−	0.0797257i
$624$	1.11455	−	3.43023i	0.0446177	−	0.137319i
$625$	7.75849			0.310339
$626$	7.40901			0.296123
$627$	−4.36062	+	13.4206i	−0.174147	+	0.535968i
$628$	−7.13629	−	21.9632i	−0.284769	−	0.876429i
$629$	−4.21047	−	12.9585i	−0.167883	−	0.516689i
$630$	−3.45068	+	2.50706i	−0.137478	+	0.0998838i
$631$	−3.19376	+	9.82937i	−0.127141	+	0.391301i	−0.994285	−	0.106757i	$-0.965953\pi$
$631$	−3.19376	+	9.82937i	−0.127141	+	0.391301i	0.867144	+	0.498058i	$0.165953\pi$
$632$	−27.7111	+	20.1333i	−1.10229	+	0.800859i
$633$	8.40171	+	6.10420i	0.333938	+	0.242620i
$634$	−1.86354	−	5.73539i	−0.0740106	−	0.227781i
$635$	−4.29525	−	3.12068i	−0.170452	−	0.123840i
$636$	−3.97992	−	2.89158i	−0.157814	−	0.114659i
$637$	−5.77013	−	17.7586i	−0.228621	−	0.703623i
$638$	−11.2391	−	8.16569i	−0.444960	−	0.323283i
$639$	−13.6793	+	9.93860i	−0.541145	+	0.393165i
$640$	12.3141	−	37.8989i	0.486757	−	1.49809i
$641$	0.0819146	−	0.0595144i	0.00323543	−	0.00235068i	−0.586166	−	0.810191i	$-0.699364\pi$
$641$	0.0819146	−	0.0595144i	0.00323543	−	0.00235068i	0.589402	+	0.807840i	$0.299364\pi$
$642$	−0.447486	−	1.37722i	−0.0176609	−	0.0543546i
$643$	4.23719	+	13.0407i	0.167098	+	0.514276i	0.999185	−	0.0403701i	$-0.0128537\pi$
$643$	4.23719	+	13.0407i	0.167098	+	0.514276i	−0.832086	+	0.554646i	$0.812854\pi$
$644$	−1.18073	+	3.63393i	−0.0465275	+	0.143197i
$645$	23.9446			0.942816
$646$	−3.42801			−0.134873
$647$	3.34800	−	10.3041i	0.131624	−	0.405096i	−0.863426	−	0.504476i	$-0.831686\pi$
$647$	3.34800	−	10.3041i	0.131624	−	0.405096i	0.995050	+	0.0993798i	$0.0316859\pi$
$648$	−4.58915	−	3.33421i	−0.180279	−	0.130980i
$649$	−3.08745	+	2.24316i	−0.121193	+	0.0880518i
$650$	−17.5460			−0.688212
$651$		0			0
$652$	1.59301			0.0623870
$653$	19.6204	−	14.2551i	0.767807	−	0.557844i	−0.133488	−	0.991050i	$-0.542618\pi$
$653$	19.6204	−	14.2551i	0.767807	−	0.557844i	0.901295	+	0.433206i	$0.142618\pi$
$654$	0.743389	+	0.540104i	0.0290688	+	0.0211197i
$655$	7.20968	−	22.1891i	0.281706	−	0.867001i
$656$	1.03837			0.0405415
$657$	−12.3654			−0.482420
$658$	0.142494	−	0.438553i	0.00555501	−	0.0170966i
$659$	−2.63699	−	8.11583i	−0.102723	−	0.316148i	0.886467	−	0.462793i	$-0.153153\pi$
$659$	−2.63699	−	8.11583i	−0.102723	−	0.316148i	−0.989189	+	0.146645i	$0.953153\pi$
$660$	−6.48719	−	19.9655i	−0.252513	−	0.777156i
$661$	−30.6490	+	22.2678i	−1.19211	+	0.866116i	−0.993485	−	0.113960i	$-0.963646\pi$
$661$	−30.6490	+	22.2678i	−1.19211	+	0.866116i	−0.198621	+	0.980076i	$0.563646\pi$
$662$	−6.89672	+	21.2259i	−0.268049	+	0.824969i
$663$	2.77968	−	2.01956i	0.107954	−	0.0784330i
$664$	−27.7366	−	20.1518i	−1.07639	−	0.782043i
$665$	−3.32311	−	10.2275i	−0.128865	−	0.396605i
$666$	−12.6952	−	9.22360i	−0.491929	−	0.357407i
$667$	13.0026	+	9.44697i	0.503464	+	0.365788i
$668$	−5.31875	−	16.3694i	−0.205788	−	0.633352i
$669$	6.88000	+	4.99861i	0.265996	+	0.193257i
$670$	−4.31590	+	3.13569i	−0.166738	+	0.121142i
$671$	−2.94680	+	9.06933i	−0.113760	+	0.350118i
$672$	3.23662	−	2.35154i	0.124855	−	0.0907128i
$673$	−2.20023	−	6.77162i	−0.0848128	−	0.261027i	0.899652	−	0.436607i	$-0.143820\pi$
$673$	−2.20023	−	6.77162i	−0.0848128	−	0.261027i	−0.984465	+	0.175580i	$0.943820\pi$
$674$	5.90910	+	18.1863i	0.227610	+	0.700512i
$675$	−12.6468	+	38.9228i	−0.486775	+	1.49814i
$676$	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	$0.874740\pi$
$678$	−1.22679	+	3.77566i	−0.0471145	+	0.145004i
$679$	3.25946	+	2.36814i	0.125087	+	0.0908808i
$680$	9.53810	−	6.92984i	0.365769	−	0.265747i
$681$	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	$0.285837\pi$
$684$	10.2431	−	7.44202i	0.391653	−	0.284553i
$685$	38.2426	+	27.7849i	1.46118	+	1.06161i
$686$	2.18235	−	6.71657i	0.0833224	−	0.256440i
$687$	−15.3010			−0.583770
$688$	9.83073			0.374793
$689$	−3.21514	+	9.89518i	−0.122487	+	0.376976i
$690$	−2.34024	−	7.20251i	−0.0890913	−	0.274195i
$691$	8.42167	+	25.9192i	0.320375	+	0.986014i	0.973485	+	0.228750i	$0.0734640\pi$
$691$	8.42167	+	25.9192i	0.320375	+	0.986014i	−0.653110	+	0.757263i	$0.726536\pi$
$692$	−25.4736	+	18.5076i	−0.968360	+	0.703555i
$693$	−2.12203	+	6.53094i	−0.0806093	+	0.248090i
$694$	14.4563	−	10.5031i	0.548753	−	0.398692i
$695$	56.1308	+	40.7814i	2.12916	+	1.54693i
$696$	−3.31765	−	10.2107i	−0.125755	−	0.387034i
$697$	0.800258	+	0.581421i	0.0303119	+	0.0220229i
$698$	3.12036	+	2.26707i	0.118107	+	0.0858100i
$699$	−2.74287	−	8.44168i	−0.103745	−	0.319294i
$700$	8.23485	+	5.98297i	0.311248	+	0.226135i
$701$	−6.86787	+	4.98980i	−0.259396	+	0.188462i	−0.709881	−	0.704322i	$-0.751251\pi$
$701$	−6.86787	+	4.98980i	−0.259396	+	0.188462i	0.450485	+	0.892784i	$0.351251\pi$
$702$	2.90117	−	8.92887i	0.109497	−	0.336998i
$703$	32.0078	−	23.2550i	1.20720	−	0.877080i
$704$	1.59864	+	4.92012i	0.0602511	+	0.185434i
$705$	−0.905737	−	2.78757i	−0.0341120	−	0.104986i
$706$	2.48625	−	7.65189i	0.0935712	−	0.287983i
$707$	2.90657			0.109313
$708$	−1.27574			−0.0479452
$709$	7.22670	−	22.2415i	0.271404	−	0.835297i	−0.718744	−	0.695275i	$-0.755283\pi$
$709$	7.22670	−	22.2415i	0.271404	−	0.835297i	0.990148	−	0.140022i	$-0.0447174\pi$
$710$	−15.9990	−	11.6239i	−0.600430	−	0.436238i
$711$	24.9229	−	18.1076i	0.934683	−	0.679087i
$712$	10.7774			0.403901
$713$		0			0
$714$	0.621526			0.0232600
$715$	−35.9197	+	26.0972i	−1.34332	+	0.975978i
$716$	0.162396	+	0.117988i	0.00606902	+	0.00440940i
$717$	−0.164703	+	0.506903i	−0.00615094	+	0.0189306i
$718$	−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	$0.577796\pi$
$720$	−3.43963	+	10.5861i	−0.128188	+	0.394521i
$721$	−1.47337	−	4.53457i	−0.0548712	−	0.168876i
$722$	0.972318	+	2.99249i	0.0361859	+	0.111369i
$723$	11.2213	−	8.15276i	0.417325	−	0.303204i
$724$	3.64275	−	11.2112i	0.135382	−	0.416662i
$725$	34.6386	−	25.1664i	1.28644	−	0.934656i
$726$	2.98918	+	2.17177i	0.110939	+	0.0806019i
$727$	−3.83892	−	11.8150i	−0.142378	−	0.438194i	0.854287	−	0.519802i	$-0.173994\pi$
$727$	−3.83892	−	11.8150i	−0.142378	−	0.438194i	−0.996664	+	0.0816083i	$0.973994\pi$
$728$	−4.36719	−	3.17295i	−0.161859	−	0.117597i
$729$	−6.12163	−	4.44762i	−0.226727	−	0.164727i
$730$	−4.46908	−	13.7544i	−0.165408	−	0.509074i
$731$	7.57641	+	5.50459i	0.280224	+	0.203594i
$732$	−2.57897	+	1.87373i	−0.0953215	+	0.0692551i
$733$	−10.5552	+	32.4856i	−0.389865	+	1.19988i	0.543024	+	0.839717i	$0.317279\pi$
$733$	−10.5552	+	32.4856i	−0.389865	+	1.19988i	−0.932889	+	0.360164i	$0.882721\pi$
$734$	−15.0691	+	10.9483i	−0.556209	+	0.404110i
$735$	−6.63457	−	20.4191i	−0.244720	−	0.753170i
$736$	−5.89161	−	18.1325i	−0.217168	−	0.668373i
$737$	−2.65411	+	8.16851i	−0.0977654	+	0.300891i
$738$	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	$0.426909\pi$
$740$	−18.1881	+	55.9773i	−0.668609	+	2.05777i
$741$	8.07131	+	5.86415i	0.296507	+	0.215425i
$742$	−1.52264	+	1.10626i	−0.0558979	+	0.0406122i
$743$	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
$746$	−6.92012	+	5.02776i	−0.253364	+	0.184080i
$747$	24.9459	+	18.1243i	0.912723	+	0.663132i
$748$	2.53720	−	7.80871i	0.0927694	−	0.285515i
$749$	1.77671			0.0649196
$750$	−8.64058			−0.315509
$751$	−3.33376	+	10.2603i	−0.121651	+	0.374402i	−0.993276	−	0.115771i	$-0.963066\pi$
$751$	−3.33376	+	10.2603i	−0.121651	+	0.374402i	0.871625	+	0.490173i	$0.163066\pi$
$752$	−0.371861	−	1.14447i	−0.0135604	−	0.0417346i
$753$	1.68750	+	5.19361i	0.0614961	+	0.189266i
$754$	−7.94606	+	5.77315i	−0.289378	+	0.210246i
$755$	−17.6120	+	54.2042i	−0.640966	+	1.97269i
$756$	−4.40623	+	3.20131i	−0.160253	+	0.116431i
$757$	33.2519	+	24.1590i	1.20856	+	0.878072i	0.995099	−	0.0988790i	$-0.0315257\pi$
$757$	33.2519	+	24.1590i	1.20856	+	0.878072i	0.213463	+	0.976951i	$0.431526\pi$
$758$	0.988411	+	3.04202i	0.0359007	+	0.110491i
$759$	−9.86411	−	7.16670i	−0.358045	−	0.260135i
$760$	27.6956	+	20.1221i	1.00463	+	0.729904i
$761$	−6.07543	−	18.6983i	−0.220234	−	0.677811i	−0.998740	−	0.0501745i	$-0.984022\pi$
$761$	−6.07543	−	18.6983i	−0.220234	−	0.677811i	0.778506	−	0.627637i	$-0.215978\pi$
$762$	0.720832	+	0.523715i	0.0261130	+	0.0189722i
$763$	−0.912086	+	0.662669i	−0.0330197	+	0.0239902i
$764$	9.94205	−	30.5985i	0.359691	−	1.10701i
$765$	−8.57842	+	6.23259i	−0.310154	+	0.225340i
$766$	−1.06987	−	3.29272i	−0.0386560	−	0.118971i
$767$	0.833766	+	2.56607i	0.0301056	+	0.0926554i
$768$	−2.76761	+	8.51782i	−0.0998674	+	0.307360i
$769$	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
$771$	−1.26262	+	3.88595i	−0.0454722	+	0.139949i
$772$	6.98519	+	5.07504i	0.251402	+	0.182655i
$773$	−20.5244	+	14.9119i	−0.738212	+	0.536342i	−0.892151	−	0.451738i	$-0.850804\pi$
$773$	−20.5244	+	14.9119i	−0.738212	+	0.536342i	0.153939	+	0.988080i	$0.450804\pi$
$774$	10.7855			0.387676
$775$		0			0
$776$	−12.8256			−0.460414
$777$	−5.80327	+	4.21632i	−0.208191	+	0.151260i
$778$	−10.3763	−	7.53883i	−0.372009	−	0.270280i
$779$	−0.887573	+	2.73167i	−0.0318006	+	0.0978722i
$780$	−14.8421			−0.531431
$781$	−31.8388			−1.13928
$782$	0.915291	−	2.81698i	0.0327307	−	0.100735i
$783$	7.07939	+	21.7881i	0.252997	+	0.778644i
$784$	−2.72390	−	8.38331i	−0.0972822	−	0.299404i
$785$	−45.4334	+	33.0093i	−1.62159	+	1.17815i
$786$	−1.20994	+	3.72380i	−0.0431570	+	0.132824i
$787$	−20.9912	+	15.2510i	−0.748257	+	0.543640i	−0.895286	−	0.445492i	$-0.853029\pi$
$787$	−20.9912	+	15.2510i	−0.748257	+	0.543640i	0.147029	+	0.989132i	$0.453029\pi$
$788$	−19.6297	−	14.2618i	−0.699281	−	0.508057i
$789$	0.699615	+	2.15319i	0.0249069	+	0.0766557i
$790$	29.1492	+	21.1781i	1.03708	+	0.753484i
$791$	−3.94062	−	2.86303i	−0.140112	−	0.101797i
$792$	−6.75527	−	20.7906i	−0.240038	−	0.738761i
$793$	5.45440	+	3.96285i	0.193691	+	0.140725i
$794$	18.1617	−	13.1952i	0.644534	−	0.468281i
$795$	−3.69680	+	11.3776i	−0.131112	+	0.403522i
$796$	5.25619	−	3.81885i	0.186301	−	0.135355i
$797$	5.71762	+	17.5970i	0.202529	+	0.623319i	0.999806	+	0.0197056i	$0.00627291\pi$
$797$	5.71762	+	17.5970i	0.202529	+	0.623319i	−0.797277	+	0.603613i	$0.793727\pi$
$798$	0.557688	+	1.71639i	0.0197419	+	0.0607595i
$799$	0.354243	−	1.09025i	0.0125322	−	0.0385702i
$800$	−50.7902			−1.79570
$801$	−9.69305			−0.342487
$802$	−2.63993	+	8.12488i	−0.0932192	+	0.286899i
$803$	−18.8372	−	13.6860i	−0.664750	−	0.482969i
$804$	−2.32281	+	1.68762i	−0.0819193	+	0.0595178i
$805$	9.29174			0.327491
$806$		0			0
$807$	−12.0378			−0.423751
$808$	−7.48564	+	5.43864i	−0.263344	+	0.191331i
$809$	29.7296	+	21.5998i	1.04524	+	0.759410i	0.971301	−	0.237853i	$-0.0764437\pi$
$809$	29.7296	+	21.5998i	1.04524	+	0.759410i	0.0739368	+	0.997263i	$0.476444\pi$
$810$	−1.84387	+	5.67484i	−0.0647869	+	0.199394i
$811$	−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
$813$	−3.85497	+	11.8644i	−0.135200	+	0.416102i
$814$	−9.13092	−	28.1021i	−0.320039	−	0.984977i
$815$	−1.19709	−	3.68427i	−0.0419323	−	0.129054i
$816$	1.31220	−	0.953370i	0.0459362	−	0.0333746i
$817$	−8.40307	+	25.8620i	−0.293986	+	0.904796i
$818$	1.92338	−	1.39742i	0.0672494	−	0.0488595i
$819$	3.92778	+	2.85370i	0.137248	+	0.0997163i
$820$	−1.32042	−	4.06383i	−0.0461111	−	0.141915i
$821$	1.19782	+	0.870264i	0.0418041	+	0.0303724i	0.608491	−	0.793561i	$-0.291775\pi$
$821$	1.19782	+	0.870264i	0.0418041	+	0.0303724i	−0.566687	+	0.823933i	$0.691775\pi$
$822$	−6.41791	−	4.66289i	−0.223850	−	0.162637i
$823$	12.0100	+	36.9630i	0.418643	+	1.28845i	0.908952	+	0.416901i	$0.136884\pi$
$823$	12.0100	+	36.9630i	0.418643	+	1.28845i	−0.490309	+	0.871549i	$0.663116\pi$
$824$	12.2794	+	8.92152i	0.427774	+	0.310796i
$825$	−26.2776	+	19.0918i	−0.914870	+	0.664692i
$826$	−0.150823	+	0.464185i	−0.00524780	+	0.0161511i
$827$	27.4550	−	19.9472i	0.954705	−	0.693634i	0.00279002	−	0.999996i	$-0.499112\pi$
$827$	27.4550	−	19.9472i	0.954705	−	0.693634i	0.951915	+	0.306362i	$0.0991119\pi$
$828$	3.38056	+	10.4043i	0.117483	+	0.361574i
$829$	−5.10827	−	15.7216i	−0.177417	−	0.546035i	0.822318	−	0.569028i	$-0.192680\pi$
$829$	−5.10827	−	15.7216i	−0.177417	−	0.546035i	−0.999736	+	0.0229933i	$0.992680\pi$
$830$	−11.1443	+	34.2985i	−0.386823	+	1.19052i
$831$	−10.4415			−0.362210
$832$	3.65754			0.126802
$833$	2.59485	−	7.98612i	0.0899061	−	0.276703i
$834$	−9.41993	−	6.84398i	−0.326185	−	0.236988i
$835$	−33.8619	+	24.6021i	−1.17184	+	0.851392i
$836$	23.8409			0.824555
$837$		0			0
$838$	27.6122			0.953848
$839$	43.7501	−	31.7863i	1.51042	−	1.09738i	0.544430	−	0.838806i	$-0.316746\pi$
$839$	43.7501	−	31.7863i	1.51042	−	1.09738i	0.965990	−	0.258579i	$-0.0832542\pi$
$840$	−5.02144	−	3.64829i	−0.173256	−	0.125878i
$841$	−1.55522	+	4.78647i	−0.0536282	+	0.165051i
$842$	−14.9512			−0.515254
$843$	−13.8964			−0.478617
$844$	5.42187	−	16.6868i	0.186628	−	0.574383i
$845$	−5.19379	−	15.9848i	−0.178672	−	0.549896i
$846$	−0.407976	−	1.25562i	−0.0140265	−	0.0431691i
$847$	−3.66752	+	2.66461i	−0.126017	+	0.0915570i
$848$	−1.51777	+	4.67121i	−0.0521204	+	0.160410i
$849$	16.5692	−	12.0382i	0.568653	−	0.413150i
$850$	−6.38355	−	4.63792i	−0.218954	−	0.159079i
$851$	10.5637	+	32.5116i	0.362118	+	1.11448i
$852$	−8.61062	−	6.25598i	−0.294995	−	0.214326i
$853$	−32.0178	−	23.2623i	−1.09627	−	0.796487i	−0.115823	−	0.993270i	$-0.536950\pi$
$853$	−32.0178	−	23.2623i	−1.09627	−	0.796487i	−0.980447	+	0.196783i	$0.936950\pi$
$854$	0.376872	+	1.15989i	0.0128963	+	0.0396907i
$855$	−24.9090	−	18.0975i	−0.851871	−	0.618921i
$856$	−4.57578	+	3.32450i	−0.156397	+	0.113629i
$857$	3.93225	−	12.1022i	0.134323	−	0.413404i	−0.861161	−	0.508333i	$-0.830262\pi$
$857$	3.93225	−	12.1022i	0.134323	−	0.413404i	0.995484	+	0.0949280i	$0.0302621\pi$
$858$	6.02807	−	4.37965i	0.205795	−	0.149519i
$859$	6.53705	+	20.1190i	0.223041	+	0.686451i	0.998485	+	0.0550332i	$0.0175265\pi$
$859$	6.53705	+	20.1190i	0.223041	+	0.686451i	−0.775443	+	0.631417i	$0.782474\pi$
$860$	−12.5010	−	38.4742i	−0.426281	−	1.31196i
$861$	0.160924	−	0.495274i	0.00548428	−	0.0168789i
$862$	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	$0.550815\pi$
$864$	8.39795	−	25.8462i	0.285704	−	0.879307i
$865$	61.9466	+	45.0068i	2.10625	+	1.53028i
$866$	−13.7202	+	9.96829i	−0.466230	+	0.338736i
$867$	−13.7957			−0.468526
$868$		0			0
$869$	58.0085			1.96780
$870$	−9.13647	+	6.63804i	−0.309755	+	0.225051i
$871$	4.91264	+	3.56924i	0.166458	+	0.120939i
$872$	1.10905	−	3.41331i	0.0375572	−	0.115589i
$873$	11.5352			0.390407
$874$	8.60055			0.290918
$875$	3.27600	−	10.0825i	0.110749	−	0.340851i
$876$	−2.40525	−	7.40260i	−0.0812659	−	0.250111i
$877$	6.93287	+	21.3372i	0.234107	+	0.720506i	0.997239	+	0.0742633i	$0.0236605\pi$
$877$	6.93287	+	21.3372i	0.234107	+	0.720506i	−0.763132	+	0.646242i	$0.776339\pi$
$878$	10.1484	−	7.37324i	0.342492	−	0.248835i
$879$	3.45807	−	10.6428i	0.116638	−	0.358974i
$880$	−16.9566	+	12.3197i	−0.571606	+	0.415296i
$881$	−37.5639	−	27.2917i	−1.26556	−	0.919482i	−0.266542	−	0.963823i	$-0.585881\pi$
$881$	−37.5639	−	27.2917i	−1.26556	−	0.919482i	−0.999016	+	0.0443414i	$0.985881\pi$
$882$	−2.98844	−	9.19748i	−0.100626	−	0.309695i
$883$	29.5611	+	21.4774i	0.994811	+	0.722773i	0.960969	−	0.276654i	$-0.0892257\pi$
$883$	29.5611	+	21.4774i	0.994811	+	0.722773i	0.0338419	+	0.999427i	$0.489226\pi$
$884$	−4.69625	−	3.41202i	−0.157952	−	0.114759i
$885$	0.958674	+	2.95050i	0.0322255	+	0.0991799i
$886$	9.90692	+	7.19780i	0.332829	+	0.241815i
$887$	−23.2067	+	16.8606i	−0.779204	+	0.566125i	−0.904740	−	0.425964i	$-0.859935\pi$
$887$	−23.2067	+	16.8606i	−0.779204	+	0.566125i	0.125536	+	0.992089i	$0.459935\pi$
$888$	7.05648	−	21.7176i	0.236800	−	0.728796i
$889$	−0.884410	+	0.642561i	−0.0296622	+	0.0215508i
$890$	−3.50324	−	10.7819i	−0.117429	−	0.361409i
$891$	2.96861	+	9.13643i	0.0994521	+	0.306082i
$892$	4.43986	−	13.6645i	0.148658	−	0.457521i
$893$	3.32865			0.111389
$894$	12.5282			0.419005
$895$	0.150844	−	0.464249i	0.00504215	−	0.0155181i
$896$	−6.63810	−	4.82286i	−0.221763	−	0.161120i
$897$	−6.97394	+	5.06687i	−0.232853	+	0.169178i
$898$	−6.34235			−0.211647
$899$		0			0
$900$	29.1430			0.971434
$901$	−3.78531	+	2.75019i	−0.126107	+	0.0916220i
$902$	1.73546	+	1.26088i	0.0577844	+	0.0419828i
$903$	1.52354	−	4.68898i	0.0507004	−	0.156040i
$904$	15.5059			0.515719
$905$	−28.6665			−0.952906
$906$	2.95566	−	9.09660i	0.0981953	−	0.302214i
$907$	−6.85697	−	21.1036i	−0.227682	−	0.700733i	−0.998008	−	0.0630831i	$-0.979907\pi$
$907$	−6.85697	−	21.1036i	−0.227682	−	0.700733i	0.770326	−	0.637650i	$-0.220093\pi$
$908$	−10.2532	−	31.5560i	−0.340263	−	1.04722i
$909$	6.73247	−	4.89143i	0.223302	−	0.162238i
$910$	−1.75469	+	5.40037i	−0.0581673	+	0.179021i
$911$	−23.3259	+	16.9473i	−0.772822	+	0.561488i	−0.902816	−	0.430026i	$-0.858504\pi$
$911$	−23.3259	+	16.9473i	−0.772822	+	0.561488i	0.129994	+	0.991515i	$0.458504\pi$
$912$	3.81022	+	2.76829i	0.126169	+	0.0916671i
$913$	17.9422	+	55.2203i	0.593799	+	1.82752i
$914$	17.4037	+	12.6445i	0.575662	+	0.418243i
$915$	6.27153	+	4.55653i	0.207330	+	0.150634i
$916$	7.98838	+	24.5857i	0.263944	+	0.812335i
$917$	−3.88649	−	2.82370i	−0.128343	−	0.0932467i
$918$	3.41565	−	2.48162i	0.112733	−	0.0819056i
$919$	14.8521	−	45.7100i	0.489925	−	1.50783i	−0.334794	−	0.942291i	$-0.608667\pi$
$919$	14.8521	−	45.7100i	0.489925	−	1.50783i	0.824719	−	0.565543i	$-0.191333\pi$
$920$	−23.9302	+	17.3863i	−0.788954	+	0.573209i
$921$	8.56649	+	26.3649i	0.282275	+	0.868755i
$922$	−1.42082	−	4.37283i	−0.0467921	−	0.144011i
$923$	−6.95600	+	21.4084i	−0.228959	+	0.704665i
$924$	−4.32255			−0.142201
$925$	91.0668			2.99426
$926$	7.52513	−	23.1600i	0.247291	−	0.761084i
$927$	−11.0439	−	8.02388i	−0.362730	−	0.263539i
$928$	−23.0013	+	16.7114i	−0.755055	+	0.548580i
$929$	−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
$932$	−12.1321	+	8.81450i	−0.397401	+	0.288729i
$933$	−1.73857	−	1.26314i	−0.0569182	−	0.0413535i
$934$	−7.65829	+	23.5698i	−0.250587	+	0.771227i
$935$	−19.9664			−0.652972
$936$	−15.4554			−0.505176
$937$	−3.98034	+	12.2502i	−0.130032	+	0.400197i	−0.994784	−	0.102001i	$-0.967475\pi$
$937$	−3.98034	+	12.2502i	−0.130032	+	0.400197i	0.864752	+	0.502199i	$0.167475\pi$
$938$	0.339439	+	1.04469i	0.0110831	+	0.0341102i
$939$	−2.99649	−	9.22223i	−0.0977866	−	0.300956i
$940$	−4.00621	+	2.91068i	−0.130668	+	0.0949360i
$941$	15.4630	−	47.5901i	0.504079	−	1.55139i	−0.298235	−	0.954492i	$-0.596398\pi$
$941$	15.4630	−	47.5901i	0.504079	−	1.55139i	0.802314	−	0.596902i	$-0.203602\pi$
$942$	7.62467	−	5.53965i	0.248425	−	0.180492i
$943$	−2.00777	−	1.45873i	−0.0653819	−	0.0475028i
$944$	0.393595	+	1.21136i	0.0128104	+	0.0394265i
$945$	10.7150	+	7.78494i	0.348560	+	0.253244i
$946$	16.4304	+	11.9374i	0.534197	+	0.388117i
$947$	−16.0281	−	49.3293i	−0.520842	−	1.60299i	−0.772394	−	0.635144i	$-0.780941\pi$
$947$	−16.0281	−	49.3293i	−0.520842	−	1.60299i	0.251551	−	0.967844i	$-0.419059\pi$
$948$	15.6881	+	11.3980i	0.509525	+	0.370191i
$949$	−13.3179	+	9.67603i	−0.432318	+	0.314097i
$950$	7.08006	−	21.7902i	0.229707	−	0.706967i
$951$	−6.38534	+	4.63922i	−0.207059	+	0.150437i
$952$	−0.750157	−	2.30875i	−0.0243127	−	0.0748269i
$953$	−5.78950	−	17.8183i	−0.187540	−	0.577190i	0.812443	−	0.583041i	$-0.198137\pi$
$953$	−5.78950	−	17.8183i	−0.187540	−	0.577190i	−0.999983	+	0.00585146i	$0.998137\pi$
$954$	−1.66517	+	5.12487i	−0.0539119	+	0.165924i
$955$	−78.2385			−2.53174
$956$	0.900482			0.0291237
$957$	−5.61857	+	17.2922i	−0.181623	+	0.558977i
$958$	18.5441	+	13.4731i	0.599133	+	0.435296i
$959$	7.87432	−	5.72103i	0.254275	−	0.184742i
$960$	4.20549			0.135731
$961$		0			0
$962$	−20.8907			−0.673542
$963$	4.11539	−	2.99001i	0.132617	−	0.0963516i
$964$	−18.9583	−	13.7740i	−0.610606	−	0.443632i
$965$	6.48829	−	19.9689i	0.208865	−	0.642821i
$966$	−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	$0.221091\pi$
$968$	4.45952	−	13.7250i	0.143334	−	0.441137i
$969$	1.38642	+	4.26696i	0.0445382	+	0.137075i
$970$	4.16903	+	12.8309i	0.133859	+	0.411977i
$971$	25.1610	−	18.2805i	0.807454	−	0.586649i	−0.105638	−	0.994405i	$-0.533688\pi$
$971$	25.1610	−	18.2805i	0.807454	−	0.586649i	0.913091	+	0.407755i	$0.133688\pi$
$972$	−7.60637	+	23.4100i	−0.243974	+	0.750876i
$973$	11.5576	−	8.39708i	0.370519	−	0.269198i
$974$	−15.9062	−	11.5565i	−0.509667	−	0.370295i
$975$	7.09629	+	21.8401i	0.227263	+	0.699444i
$976$	2.57485	+	1.87074i	0.0824191	+	0.0598810i
$977$	17.8624	+	12.9778i	0.571469	+	0.415197i	0.835639	−	0.549280i	$-0.185098\pi$
$977$	17.8624	+	12.9778i	0.571469	+	0.415197i	−0.264170	+	0.964476i	$0.585098\pi$
$978$	0.200897	+	0.618298i	0.00642398	+	0.0197710i
$979$	−14.7662	−	10.7283i	−0.471929	−	0.342877i
$980$	−29.3457	+	21.3209i	−0.937413	+	0.681071i
$981$	−0.997464	+	3.06988i	−0.0318466	+	0.0980136i
$982$	15.5984	−	11.3329i	0.497766	−	0.361648i
$983$	11.6119	+	35.7377i	0.370362	+	1.13986i	0.946555	+	0.322543i	$0.104538\pi$
$983$	11.6119	+	35.7377i	0.370362	+	1.13986i	−0.576193	+	0.817314i	$0.695462\pi$
$984$	0.512285	+	1.57665i	0.0163311	+	0.0502618i
$985$	−18.2334	+	56.1165i	−0.580963	+	1.78802i
$986$	−4.41693			−0.140664
$987$	−0.603511			−0.0192100
$988$	5.20865	−	16.0306i	0.165709	−	0.510001i
$989$	−19.0085	−	13.8105i	−0.604434	−	0.439147i
$990$	−18.6033	+	13.5161i	−0.591253	+	0.429571i
$991$	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
$994$	−3.29426	+	2.39342i	−0.104487	+	0.0759146i
$995$	−12.7820	−	9.28666i	−0.405216	−	0.294407i
$996$	−5.99783	+	18.4594i	−0.190049	+	0.584909i
$997$	−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
$999$	−15.0575	+	46.3423i	−0.476399	+	1.46621i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.n.388.4		16
31.2	even	5	inner	961.2.d.n.374.4		16
31.3	odd	30		961.2.g.t.547.1		16
31.4	even	5		961.2.d.q.628.1		16
31.5	even	3		961.2.g.j.338.2		16
31.6	odd	6		31.2.g.a.18.2	✓	16
31.7	even	15		961.2.g.m.846.1		16
31.8	even	5		961.2.a.j.1.3		8
31.9	even	15		961.2.c.i.521.3		16
31.10	even	15		961.2.g.l.732.2		16
31.11	odd	30		961.2.g.t.448.1		16
31.12	odd	30		961.2.g.k.816.2		16
31.13	odd	30		961.2.g.s.844.1		16
31.14	even	15		961.2.c.i.439.3		16
31.15	odd	10		961.2.d.p.531.1		16
31.16	even	5		961.2.d.q.531.1		16
31.17	odd	30		961.2.c.j.439.3		16
31.18	even	15		961.2.g.m.844.1		16
31.19	even	15		961.2.g.j.816.2		16
31.20	even	15		961.2.g.n.448.1		16
31.21	odd	30		31.2.g.a.19.2	yes	16
31.22	odd	30		961.2.c.j.521.3		16
31.23	odd	10		961.2.a.i.1.3		8
31.24	odd	30		961.2.g.s.846.1		16
31.25	even	3		961.2.g.l.235.2		16
31.26	odd	6		961.2.g.k.338.2		16
31.27	odd	10		961.2.d.p.628.1		16
31.28	even	15		961.2.g.n.547.1		16
31.29	odd	10		961.2.d.o.374.4		16
31.30	odd	2		961.2.d.o.388.4		16
93.8	odd	10		8649.2.a.be.1.6		8
93.23	even	10		8649.2.a.bf.1.6		8
93.68	even	6		279.2.y.c.235.1		16
93.83	even	30		279.2.y.c.19.1		16
124.83	even	30		496.2.bg.c.81.1		16
124.99	even	6		496.2.bg.c.49.1		16
155.37	even	12		775.2.ck.a.49.3		32
155.52	even	60		775.2.ck.a.174.2		32
155.68	even	12		775.2.ck.a.49.2		32
155.83	even	60		775.2.ck.a.174.3		32
155.99	odd	6		775.2.bl.a.576.1		16
155.114	odd	30		775.2.bl.a.701.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.18.2	✓	16	31.6	odd	6
31.2.g.a.19.2	yes	16	31.21	odd	30
279.2.y.c.19.1		16	93.83	even	30
279.2.y.c.235.1		16	93.68	even	6
496.2.bg.c.49.1		16	124.99	even	6
496.2.bg.c.81.1		16	124.83	even	30
775.2.bl.a.576.1		16	155.99	odd	6
775.2.bl.a.701.1		16	155.114	odd	30
775.2.ck.a.49.2		32	155.68	even	12
775.2.ck.a.49.3		32	155.37	even	12
775.2.ck.a.174.2		32	155.52	even	60
775.2.ck.a.174.3		32	155.83	even	60
961.2.a.i.1.3		8	31.23	odd	10
961.2.a.j.1.3		8	31.8	even	5
961.2.c.i.439.3		16	31.14	even	15
961.2.c.i.521.3		16	31.9	even	15
961.2.c.j.439.3		16	31.17	odd	30
961.2.c.j.521.3		16	31.22	odd	30
961.2.d.n.374.4		16	31.2	even	5	inner
961.2.d.n.388.4		16	1.1	even	1	trivial
961.2.d.o.374.4		16	31.29	odd	10
961.2.d.o.388.4		16	31.30	odd	2
961.2.d.p.531.1		16	31.15	odd	10
961.2.d.p.628.1		16	31.27	odd	10
961.2.d.q.531.1		16	31.16	even	5
961.2.d.q.628.1		16	31.4	even	5
961.2.g.j.338.2		16	31.5	even	3
961.2.g.j.816.2		16	31.19	even	15
961.2.g.k.338.2		16	31.26	odd	6
961.2.g.k.816.2		16	31.12	odd	30
961.2.g.l.235.2		16	31.25	even	3
961.2.g.l.732.2		16	31.10	even	15
961.2.g.m.844.1		16	31.18	even	15
961.2.g.m.846.1		16	31.7	even	15
961.2.g.n.448.1		16	31.20	even	15
961.2.g.n.547.1		16	31.28	even	15
961.2.g.s.844.1		16	31.13	odd	30
961.2.g.s.846.1		16	31.24	odd	30
961.2.g.t.448.1		16	31.11	odd	30
961.2.g.t.547.1		16	31.3	odd	30
8649.2.a.be.1.6		8	93.8	odd	10
8649.2.a.bf.1.6		8	93.23	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+(0.557811 - 0.405274i) q^{2} +(-0.730058 - 0.530418i) q^{3} +(-0.471127 + 1.44998i) q^{4} +3.70752 q^{5} -0.622199 q^{6} +(0.235902 - 0.726031i) q^{7} +(0.750969 + 2.31124i) q^{8} +(-0.675410 - 2.07870i) q^{9} +(2.06809 - 1.50256i) q^{10} +(1.27180 - 3.91419i) q^{11} +(1.11305 - 0.808675i) q^{12} +(-2.35404 - 1.71031i) q^{13} +(-0.162653 - 0.500593i) q^{14} +(-2.70670 - 1.96653i) q^{15} +(-1.11127 - 0.807384i) q^{16} +(-0.404356 - 1.24448i) q^{17} +(-1.21919 - 0.885796i) q^{18} +(3.07389 - 2.23331i) q^{19} +(-1.74671 + 5.37583i) q^{20} +(-0.557322 + 0.404918i) q^{21} +(-0.876895 - 2.69881i) q^{22} +(1.01449 + 3.12228i) q^{23} +(0.677675 - 2.08567i) q^{24} +8.74568 q^{25} -2.00625 q^{26} +(-1.44606 + 4.45052i) q^{27} +(0.941591 + 0.684106i) q^{28} +(3.96065 - 2.87758i) q^{29} -2.30681 q^{30} -5.80746 q^{32} +(-3.00464 + 2.18300i) q^{33} +(-0.729910 - 0.530310i) q^{34} +(0.874609 - 2.69177i) q^{35} +3.33228 q^{36} +10.4128 q^{37} +(0.809549 - 2.49154i) q^{38} +(0.811405 + 2.49725i) q^{39} +(2.78423 + 8.56898i) q^{40} +(-0.611573 + 0.444334i) q^{41} +(-0.146778 + 0.451736i) q^{42} +(-5.79005 + 4.20671i) q^{43} +(5.07632 + 3.68816i) q^{44} +(-2.50409 - 7.70681i) q^{45} +(1.83127 + 1.33050i) q^{46} +(0.708753 + 0.514939i) q^{47} +(0.383039 + 1.17887i) q^{48} +(5.19165 + 3.77195i) q^{49} +(4.87844 - 3.54439i) q^{50} +(-0.364891 + 1.12302i) q^{51} +(3.58897 - 2.60754i) q^{52} +(-1.10495 - 3.40070i) q^{53} +(0.997049 + 3.06860i) q^{54} +(4.71521 - 14.5119i) q^{55} +1.85519 q^{56} -3.42871 q^{57} +(1.04309 - 3.21029i) q^{58} +(-0.750177 - 0.545036i) q^{59} +(4.12664 - 2.99818i) q^{60} -2.31704 q^{61} -1.66853 q^{63} +(-1.01693 + 0.738843i) q^{64} +(-8.72763 - 6.34100i) q^{65} +(-0.791311 + 2.43540i) q^{66} -2.08690 q^{67} +1.99498 q^{68} +(0.915477 - 2.81755i) q^{69} +(-0.603037 - 1.85596i) q^{70} +(-2.39058 - 7.35745i) q^{71} +(4.29717 - 3.12207i) q^{72} +(1.74826 - 5.38058i) q^{73} +(5.80837 - 4.22003i) q^{74} +(-6.38485 - 4.63886i) q^{75} +(1.79007 + 5.50926i) q^{76} +(-2.54180 - 1.84673i) q^{77} +(1.46468 + 1.06415i) q^{78} +(4.35551 + 13.4049i) q^{79} +(-4.12005 - 2.99339i) q^{80} +(-1.88839 + 1.37200i) q^{81} +(-0.161066 + 0.495709i) q^{82} +(-11.4134 + 8.29231i) q^{83} +(-0.324554 - 0.998873i) q^{84} +(-1.49916 - 4.61393i) q^{85} +(-1.52488 + 4.69311i) q^{86} -4.41782 q^{87} +10.0017 q^{88} +(1.37043 - 4.21776i) q^{89} +(-4.52018 - 3.28410i) q^{90} +(-1.79706 + 1.30564i) q^{91} -5.00520 q^{92} +0.604042 q^{94} +(11.3965 - 8.28005i) q^{95} +(4.23978 + 3.08038i) q^{96} +(-1.63088 + 5.01933i) q^{97} +4.42463 q^{98} -8.99540 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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