LMFDB - Embedded newform 1000.2.t.b.701.41

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1000,2,Mod(101,1000)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1000.101"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1000, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.t (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [224] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$56$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			701.41
Character	$\chi$	$=$	1000.701
Dual form			1000.2.t.b.301.41

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.961518 - 1.03706i) q^{2} +(-0.232961 + 0.0756938i) q^{3} +(-0.150967 - 1.99429i) q^{4} +(-0.145498 + 0.314375i) q^{6} -1.59435 q^{7} +(-2.21335 - 1.76099i) q^{8} +(-2.37851 + 1.72809i) q^{9} +(-2.84212 + 3.91185i) q^{11} +(0.186125 + 0.453166i) q^{12} +(-1.09172 - 1.50262i) q^{13} +(-1.53300 + 1.65343i) q^{14} +(-3.95442 + 0.602144i) q^{16} +(-1.35781 + 4.17890i) q^{17} +(-0.494857 + 4.12823i) q^{18} +(2.84592 + 0.924695i) q^{19} +(0.371422 - 0.120682i) q^{21} +(1.32405 + 6.70875i) q^{22} +(4.65342 + 3.38091i) q^{23} +(0.648921 + 0.242706i) q^{24} +(-2.60801 - 0.312625i) q^{26} +(0.855230 - 1.17712i) q^{27} +(0.240694 + 3.17961i) q^{28} +(-3.24693 + 1.05499i) q^{29} +(-0.378200 + 1.16398i) q^{31} +(-3.17779 + 4.67992i) q^{32} +(0.366003 - 1.12644i) q^{33} +(3.02820 + 5.42621i) q^{34} +(3.80539 + 4.48256i) q^{36} +(-4.64888 - 6.39864i) q^{37} +(3.69536 - 2.06226i) q^{38} +(0.368067 + 0.267416i) q^{39} +(-6.95275 + 5.05147i) q^{41} +(0.231975 - 0.501224i) q^{42} -10.9570i q^{43} +(8.23044 + 5.07747i) q^{44} +(7.98053 - 1.57505i) q^{46} +(-0.289478 - 0.890923i) q^{47} +(0.875648 - 0.439601i) q^{48} -4.45804 q^{49} -1.07630i q^{51} +(-2.83185 + 2.40405i) q^{52} +(5.12271 - 1.66447i) q^{53} +(-0.398422 - 2.01874i) q^{54} +(3.52886 + 2.80763i) q^{56} -0.732983 q^{57} +(-2.02790 + 4.38164i) q^{58} +(-5.45825 - 7.51263i) q^{59} +(-3.06376 + 4.21690i) q^{61} +(0.843466 + 1.51140i) q^{62} +(3.79218 - 2.75518i) q^{63} +(1.79784 + 7.79537i) q^{64} +(-0.816262 - 1.46266i) q^{66} +(-2.33135 - 0.757501i) q^{67} +(8.53894 + 2.07699i) q^{68} +(-1.33998 - 0.435386i) q^{69} +(4.47330 + 13.7674i) q^{71} +(8.30762 + 0.363664i) q^{72} +(-2.60150 - 1.89010i) q^{73} +(-11.1057 - 1.33126i) q^{74} +(1.41448 - 5.81520i) q^{76} +(4.53134 - 6.23686i) q^{77} +(0.631228 - 0.124580i) q^{78} +(3.26966 + 10.0630i) q^{79} +(2.61539 - 8.04936i) q^{81} +(-1.44654 + 12.0675i) q^{82} +(1.66114 + 0.539736i) q^{83} +(-0.296749 - 0.722506i) q^{84} +(-11.3630 - 10.5353i) q^{86} +(0.676554 - 0.491545i) q^{87} +(13.1793 - 3.65334i) q^{88} +(-9.19471 - 6.68035i) q^{89} +(1.74058 + 2.39570i) q^{91} +(6.04001 - 9.79069i) q^{92} -0.299790i q^{93} +(-1.20227 - 0.556433i) q^{94} +(0.386061 - 1.33078i) q^{96} +(4.42235 + 13.6106i) q^{97} +(-4.28649 + 4.62324i) q^{98} -14.2158i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9} + 6 q^{14} - 30 q^{16} + 32 q^{24} - 28 q^{26} - 36 q^{31} - 18 q^{34} + 82 q^{36} + 20 q^{39} - 20 q^{41} + 64 q^{44} + 26 q^{46} + 160 q^{49} - 86 q^{54} + 72 q^{56}+ \cdots + 92 q^{96}+O(q^{100}) $ 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9 + 6 * q^14 - 30 * q^16 + 32 * q^24 - 28 * q^26 - 36 * q^31 - 18 * q^34 + 82 * q^36 + 20 * q^39 - 20 * q^41 + 64 * q^44 + 26 * q^46 + 160 * q^49 - 86 * q^54 + 72 * q^56 + 72 * q^64 + 80 * q^66 + 44 * q^71 - 8 * q^74 - 72 * q^76 - 28 * q^79 - 12 * q^81 - 156 * q^84 - 118 * q^86 - 48 * q^89 - 90 * q^94 + 92 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.961518	−	1.03706i	0.679896	−	0.733309i
$2$	0.961518	−	1.03706i	0.679896	−	0.733309i
$3$	−0.232961	+	0.0756938i	−0.134500	+	0.0437018i	−0.375494	−	0.926825i	$-0.622527\pi$
$3$	−0.232961	+	0.0756938i	−0.134500	+	0.0437018i	0.240993	+	0.970527i	$0.422527\pi$
$4$	−0.150967	−	1.99429i	−0.0754833	−	0.997147i
$5$		0			0
$5$		0			0
$6$	−0.145498	+	0.314375i	−0.0593993	+	0.128343i
$7$	−1.59435			−0.602608			−0.301304	−	0.953528i	$-0.597422\pi$
$7$	−1.59435			−0.602608			−0.301304	+	0.953528i	$0.597422\pi$
$8$	−2.21335	−	1.76099i	−0.782537	−	0.622604i
$9$	−2.37851	+	1.72809i	−0.792836	+	0.576029i
$10$		0			0
$11$	−2.84212	+	3.91185i	−0.856932	+	1.17947i	0.125360	+	0.992111i	$0.459991\pi$
$11$	−2.84212	+	3.91185i	−0.856932	+	1.17947i	−0.982292	+	0.187355i	$0.940009\pi$
$12$	0.186125	+	0.453166i	0.0537297	+	0.130818i
$13$	−1.09172	−	1.50262i	−0.302788	−	0.416752i	0.630327	−	0.776330i	$-0.282921\pi$
$13$	−1.09172	−	1.50262i	−0.302788	−	0.416752i	−0.933115	+	0.359578i	$0.882921\pi$
$14$	−1.53300	+	1.65343i	−0.409711	+	0.441898i
$15$		0			0
$16$	−3.95442	+	0.602144i	−0.988605	+	0.150536i
$17$	−1.35781	+	4.17890i	−0.329317	+	1.01353i	0.640138	+	0.768260i	$0.278877\pi$
$17$	−1.35781	+	4.17890i	−0.329317	+	1.01353i	−0.969454	+	0.245272i	$0.921123\pi$
$18$	−0.494857	+	4.12823i	−0.116639	+	0.973034i
$19$	2.84592	+	0.924695i	0.652899	+	0.212140i	0.616692	−	0.787205i	$-0.288472\pi$
$19$	2.84592	+	0.924695i	0.652899	+	0.212140i	0.0362069	+	0.999344i	$0.488472\pi$
$20$		0			0
$21$	0.371422	−	0.120682i	0.0810510	−	0.0263351i
$22$	1.32405	+	6.70875i	0.282288	+	1.43031i
$23$	4.65342	+	3.38091i	0.970305	+	0.704968i	0.955521	−	0.294923i	$-0.0952940\pi$
$23$	4.65342	+	3.38091i	0.970305	+	0.704968i	0.0147838	+	0.999891i	$0.495294\pi$
$24$	0.648921	+	0.242706i	0.132460	+	0.0495421i
$25$		0			0
$26$	−2.60801	−	0.312625i	−0.511472	−	0.0613108i
$27$	0.855230	−	1.17712i	0.164589	−	0.226537i
$28$	0.240694	+	3.17961i	0.0454869	+	0.600889i
$29$	−3.24693	+	1.05499i	−0.602941	+	0.195907i	−0.594551	−	0.804058i	$-0.702670\pi$
$29$	−3.24693	+	1.05499i	−0.602941	+	0.195907i	−0.00838909	+	0.999965i	$0.502670\pi$
$30$		0			0
$31$	−0.378200	+	1.16398i	−0.0679268	+	0.209057i	−0.979258	−	0.202616i	$-0.935056\pi$
$31$	−0.378200	+	1.16398i	−0.0679268	+	0.209057i	0.911331	+	0.411673i	$0.135056\pi$
$32$	−3.17779	+	4.67992i	−0.561759	+	0.827301i
$33$	0.366003	−	1.12644i	0.0637129	−	0.196088i
$34$	3.02820	+	5.42621i	0.519331	+	0.930587i
$35$		0			0
$36$	3.80539	+	4.48256i	0.634232	+	0.747094i
$37$	−4.64888	−	6.39864i	−0.764271	−	1.05193i	−0.996847	−	0.0793510i	$-0.974715\pi$
$37$	−4.64888	−	6.39864i	−0.764271	−	1.05193i	0.232575	−	0.972578i	$-0.425285\pi$
$38$	3.69536	−	2.06226i	0.599467	−	0.334543i
$39$	0.368067	+	0.267416i	0.0589379	+	0.0428209i
$40$		0			0
$41$	−6.95275	+	5.05147i	−1.08584	+	0.788907i	−0.978691	−	0.205336i	$-0.934171\pi$
$41$	−6.95275	+	5.05147i	−1.08584	+	0.788907i	−0.107146	+	0.994243i	$0.534171\pi$
$42$	0.231975	−	0.501224i	0.0357945	−	0.0773405i
$43$		−	10.9570i		−	1.67092i	−0.549549	−	0.835461i	$-0.685201\pi$
$43$		−	10.9570i		−	1.67092i	0.549549	−	0.835461i	$-0.314799\pi$
$44$	8.23044	+	5.07747i	1.24078	+	0.765457i
$45$		0			0
$46$	7.98053	−	1.57505i	1.17667	−	0.232228i
$47$	−0.289478	−	0.890923i	−0.0422248	−	0.129954i	0.927722	−	0.373272i	$-0.121764\pi$
$47$	−0.289478	−	0.890923i	−0.0422248	−	0.129954i	−0.969947	+	0.243318i	$0.921764\pi$
$48$	0.875648	−	0.439601i	0.126389	−	0.0634509i
$49$	−4.45804			−0.636864
$50$		0			0
$51$		−	1.07630i		−	0.150712i
$52$	−2.83185	+	2.40405i	−0.392707	+	0.333382i
$53$	5.12271	−	1.66447i	0.703659	−	0.228633i	0.0647347	−	0.997903i	$-0.479380\pi$
$53$	5.12271	−	1.66447i	0.703659	−	0.228633i	0.638924	+	0.769270i	$0.279380\pi$
$54$	−0.398422	−	2.01874i	−0.0542184	−	0.274716i
$55$		0			0
$56$	3.52886	+	2.80763i	0.471563	+	0.375186i
$57$	−0.732983			−0.0970860
$58$	−2.02790	+	4.38164i	−0.266276	+	0.575338i
$59$	−5.45825	−	7.51263i	−0.710603	−	0.978061i	−0.999784	−	0.0207867i	$-0.993383\pi$
$59$	−5.45825	−	7.51263i	−0.710603	−	0.978061i	0.289181	−	0.957274i	$-0.406617\pi$
$60$		0			0
$61$	−3.06376	+	4.21690i	−0.392274	+	0.539919i	−0.958784	−	0.284136i	$-0.908293\pi$
$61$	−3.06376	+	4.21690i	−0.392274	+	0.539919i	0.566510	+	0.824055i	$0.308293\pi$
$62$	0.843466	+	1.51140i	0.107120	+	0.191948i
$63$	3.79218	−	2.75518i	0.477770	−	0.347120i
$64$	1.79784	+	7.79537i	0.224730	+	0.974421i
$65$		0			0
$66$	−0.816262	−	1.46266i	−0.100475	−	0.180041i
$67$	−2.33135	−	0.757501i	−0.284819	−	0.0925434i	0.163123	−	0.986606i	$-0.447843\pi$
$67$	−2.33135	−	0.757501i	−0.284819	−	0.0925434i	−0.447943	+	0.894062i	$0.647843\pi$
$68$	8.53894	+	2.07699i	1.03550	+	0.251872i
$69$	−1.33998	−	0.435386i	−0.161315	−	0.0524143i
$70$		0			0
$71$	4.47330	+	13.7674i	0.530883	+	1.63389i	0.752381	+	0.658728i	$0.228905\pi$
$71$	4.47330	+	13.7674i	0.530883	+	1.63389i	−0.221499	+	0.975161i	$0.571095\pi$
$72$	8.30762	+	0.363664i	0.979062	+	0.0428582i
$73$	−2.60150	−	1.89010i	−0.304482	−	0.221219i	0.425043	−	0.905173i	$-0.360259\pi$
$73$	−2.60150	−	1.89010i	−0.304482	−	0.221219i	−0.729525	+	0.683954i	$0.760259\pi$
$74$	−11.1057	−	1.33126i	−1.29101	−	0.154756i
$75$		0			0
$76$	1.41448	−	5.81520i	0.162251	−	0.667049i
$77$	4.53134	−	6.23686i	0.516394	−	0.710756i
$78$	0.631228	−	0.124580i	0.0714725	−	0.0141059i
$79$	3.26966	+	10.0630i	0.367865	+	1.13217i	0.948167	+	0.317772i	$0.102935\pi$
$79$	3.26966	+	10.0630i	0.367865	+	1.13217i	−0.580302	+	0.814402i	$0.697065\pi$
$80$		0			0
$81$	2.61539	−	8.04936i	0.290599	−	0.894373i
$82$	−1.44654	+	12.0675i	−0.159744	+	1.33263i
$83$	1.66114	+	0.539736i	0.182333	+	0.0592437i	0.398761	−	0.917055i	$-0.369440\pi$
$83$	1.66114	+	0.539736i	0.182333	+	0.0592437i	−0.216427	+	0.976299i	$0.569440\pi$
$84$	−0.296749	−	0.722506i	−0.0323779	−	0.0788319i
$85$		0			0
$86$	−11.3630	−	10.5353i	−1.22530	−	1.13605i
$87$	0.676554	−	0.491545i	0.0725342	−	0.0526992i
$88$	13.1793	−	3.65334i	1.40492	−	0.389447i
$89$	−9.19471	−	6.68035i	−0.974637	−	0.708116i	−0.0181337	−	0.999836i	$-0.505772\pi$
$89$	−9.19471	−	6.68035i	−0.974637	−	0.708116i	−0.956504	+	0.291720i	$0.905772\pi$
$90$		0			0
$91$	1.74058	+	2.39570i	0.182462	+	0.251138i
$92$	6.04001	−	9.79069i	0.629715	−	1.02075i
$93$		−	0.299790i		−	0.0310868i
$94$	−1.20227	−	0.556433i	−0.124005	−	0.0573917i
$95$		0			0
$96$	0.386061	−	1.33078i	0.0394022	−	0.135822i
$97$	4.42235	+	13.6106i	0.449022	+	1.38195i	0.878012	+	0.478638i	$0.158869\pi$
$97$	4.42235	+	13.6106i	0.449022	+	1.38195i	−0.428990	+	0.903309i	$0.641131\pi$
$98$	−4.28649	+	4.62324i	−0.433001	+	0.467018i
$99$		−	14.2158i		−	1.42874i
$100$		0			0
$101$			9.35559i			0.930916i	0.885070	+	0.465458i	$0.154110\pi$
$101$			9.35559i			0.930916i	−0.885070	+	0.465458i	$0.845890\pi$
$102$	−1.11618	−	1.03488i	−0.110519	−	0.102469i
$103$	−2.77679	−	8.54607i	−0.273605	−	0.842069i	−0.989585	−	0.143949i	$-0.954020\pi$
$103$	−2.77679	−	8.54607i	−0.273605	−	0.842069i	0.715980	−	0.698121i	$-0.245980\pi$
$104$	−0.229744	+	5.24833i	−0.0225283	+	0.514641i
$105$		0			0
$106$	3.19943	−	6.91295i	0.310756	−	0.671445i
$107$		−	1.58107i		−	0.152847i	−0.997075	−	0.0764237i	$-0.975650\pi$
$107$		−	1.58107i		−	0.152847i	0.997075	−	0.0764237i	$-0.0243502\pi$
$108$	−2.47664	−	1.52787i	−0.238315	−	0.147020i
$109$	−2.12791	−	2.92882i	−0.203817	−	0.280530i	0.694856	−	0.719149i	$-0.255468\pi$
$109$	−2.12791	−	2.92882i	−0.203817	−	0.280530i	−0.898673	+	0.438618i	$0.855468\pi$
$110$		0			0
$111$	1.56735	+	1.13874i	0.148766	+	0.108085i
$112$	6.30473	−	0.960029i	0.595741	−	0.0907142i
$113$	−16.3390	+	11.8710i	−1.53705	+	1.11673i	−0.584892	+	0.811111i	$0.698863\pi$
$113$	−16.3390	+	11.8710i	−1.53705	+	1.11673i	−0.952154	+	0.305618i	$0.901137\pi$
$114$	−0.704777	+	0.760144i	−0.0660084	+	0.0711940i
$115$		0			0
$116$	2.59415	+	6.31607i	0.240860	+	0.586433i
$117$	5.19332	+	1.68741i	0.480123	+	0.156001i
$118$	−13.0392	−	1.56303i	−1.20036	−	0.143888i
$119$	2.16482	−	6.66264i	0.198449	−	0.610763i
$120$		0			0
$121$	−3.82569	−	11.7743i	−0.347790	−	1.07039i
$122$	1.42730	+	7.23192i	0.129222	+	0.654747i
$123$	1.23736	−	1.70308i	0.111569	−	0.153561i
$124$	2.37842	+	0.578520i	0.213588	+	0.0519527i
$125$		0			0
$126$	0.788975	−	6.58185i	0.0702875	−	0.586358i
$127$	−8.20214	−	5.95921i	−0.727822	−	0.528794i	0.161051	−	0.986946i	$-0.448512\pi$
$127$	−8.20214	−	5.95921i	−0.727822	−	0.528794i	−0.888874	+	0.458152i	$0.848512\pi$
$128$	9.81288	+	5.63093i	0.867344	+	0.497709i
$129$	0.829374	+	2.55255i	0.0730223	+	0.224740i
$130$		0			0
$131$	5.82215	+	1.89173i	0.508683	+	0.165281i	0.552103	−	0.833776i	$-0.313825\pi$
$131$	5.82215	+	1.89173i	0.508683	+	0.165281i	−0.0434199	+	0.999057i	$0.513825\pi$
$132$	−2.30171	−	0.559862i	−0.200338	−	0.0487297i
$133$	−4.53740	−	1.47429i	−0.393442	−	0.127837i
$134$	−3.02720	+	1.68939i	−0.261510	+	0.145941i
$135$		0			0
$136$	10.3643	−	6.85829i	0.888732	−	0.588093i
$137$	1.90752	−	1.38590i	0.162971	−	0.118405i	−0.503311	−	0.864105i	$-0.667885\pi$
$137$	1.90752	−	1.38590i	0.162971	−	0.118405i	0.666282	+	0.745700i	$0.267885\pi$
$138$	−1.73993	+	0.971002i	−0.148113	+	0.0826572i
$139$	−11.6027	+	15.9697i	−0.984127	+	1.35453i	−0.0495502	+	0.998772i	$0.515779\pi$
$139$	−11.6027	+	15.9697i	−0.984127	+	1.35453i	−0.934576	+	0.355762i	$0.884221\pi$
$140$		0			0
$141$	0.134875	+	0.185639i	0.0113585	+	0.0156336i
$142$	18.5787	+	8.59854i	1.55909	+	0.721573i
$143$	8.98081			0.751013
$144$	8.36506	−	8.26579i	0.697089	−	0.688816i
$145$		0			0
$146$	−4.46153	+	0.880533i	−0.369238	+	0.0728735i
$147$	1.03855	−	0.337446i	0.0856584	−	0.0278321i
$148$	−12.0589	+	10.2372i	−0.991239	+	0.841494i
$149$		−	12.5490i		−	1.02806i	−0.857774	−	0.514028i	$-0.828153\pi$
$149$		−	12.5490i		−	1.02806i	0.857774	−	0.514028i	$-0.171847\pi$
$150$		0			0
$151$	10.1466			0.825718			0.412859	−	0.910795i	$-0.364530\pi$
$151$	10.1466			0.825718			0.412859	+	0.910795i	$0.364530\pi$
$152$	−4.67064	−	7.05831i	−0.378839	−	0.572504i
$153$	−3.99195	−	12.2860i	−0.322730	−	0.993262i
$154$	−2.11100	−	10.6961i	−0.170109	−	0.861916i
$155$		0			0
$156$	0.477741	−	0.774405i	0.0382499	−	0.0620020i
$157$			7.71018i			0.615340i	0.951493	+	0.307670i	$0.0995492\pi$
$157$			7.71018i			0.615340i	−0.951493	+	0.307670i	$0.900451\pi$
$158$	13.5797	+	6.28492i	1.08034	+	0.500001i
$159$	−1.06740	+	0.775515i	−0.0846507	+	0.0615023i
$160$		0			0
$161$	−7.41918	−	5.39035i	−0.584714	−	0.424819i
$162$	−5.83288	−	10.4519i	−0.458274	−	0.821180i
$163$	5.55848	+	7.65059i	0.435374	+	0.599240i	0.969176	−	0.246369i	$-0.0792374\pi$
$163$	5.55848	+	7.65059i	0.435374	+	0.599240i	−0.533803	+	0.845609i	$0.679237\pi$
$164$	11.1237	+	13.1032i	0.868619	+	1.02319i
$165$		0			0
$166$	2.15695	−	1.20372i	0.167412	−	0.0934270i
$167$	6.56132	−	20.1937i	0.507730	−	1.56263i	−0.288402	−	0.957509i	$-0.593124\pi$
$167$	6.56132	−	20.1937i	0.507730	−	1.56263i	0.796132	−	0.605123i	$-0.206876\pi$
$168$	−1.03461	−	0.386958i	−0.0798217	−	0.0298545i
$169$	2.95120	−	9.08286i	0.227015	−	0.698682i
$170$		0			0
$171$	−8.36700	+	2.71860i	−0.639841	+	0.207897i
$172$	−21.8514	+	1.65414i	−1.66616	+	0.126127i
$173$	10.6052	−	14.5968i	0.806296	−	1.10977i	−0.185588	−	0.982628i	$-0.559419\pi$
$173$	10.6052	−	14.5968i	0.806296	−	1.10977i	0.991884	−	0.127144i	$-0.0405809\pi$
$174$	0.140759	−	1.17425i	0.0106709	−	0.0890199i
$175$		0			0
$176$	8.88345	−	17.1804i	0.669615	−	1.29502i
$177$	1.84022	+	1.33700i	0.138319	+	0.100495i
$178$	−15.7688	+	3.11215i	−1.18192	+	0.233265i
$179$	4.37062	−	1.42010i	0.326675	−	0.106143i	−0.141088	−	0.989997i	$-0.545060\pi$
$179$	4.37062	−	1.42010i	0.326675	−	0.106143i	0.467763	+	0.883854i	$0.345060\pi$
$180$		0			0
$181$	−20.8534	−	6.77570i	−1.55002	−	0.503633i	−0.595904	−	0.803056i	$-0.703206\pi$
$181$	−20.8534	−	6.77570i	−1.55002	−	0.503633i	−0.954121	+	0.299422i	$0.903206\pi$
$182$	4.15808	+	0.498434i	0.308217	+	0.0369464i
$183$	0.394545	−	1.21428i	0.0291656	−	0.0897624i
$184$	−4.34591	−	15.6777i	−0.320384	−	1.15578i
$185$		0			0
$186$	−0.310899	−	0.288253i	−0.0227962	−	0.0211358i
$187$	−12.4882	−	17.1885i	−0.913225	−	1.25695i
$188$	−1.73306	+	0.711804i	−0.126396	+	0.0519137i
$189$	−1.36354	+	1.87675i	−0.0991827	+	0.136513i
$190$		0			0
$191$	5.50448	−	3.99924i	0.398290	−	0.289375i	−0.370554	−	0.928811i	$-0.620832\pi$
$191$	5.50448	−	3.99924i	0.398290	−	0.289375i	0.768844	+	0.639436i	$0.220832\pi$
$192$	−1.00889	−	1.67994i	−0.0728102	−	0.121239i
$193$	−5.92258			−0.426317			−0.213158	−	0.977018i	$-0.568375\pi$
$193$	−5.92258			−0.426317			−0.213158	+	0.977018i	$0.568375\pi$
$194$	18.3671	+	8.50061i	1.31868	+	0.610308i
$195$		0			0
$196$	0.673016	+	8.89065i	0.0480726	+	0.635047i
$197$	−8.87830	+	2.88473i	−0.632552	+	0.205529i	−0.607705	−	0.794163i	$-0.707910\pi$
$197$	−8.87830	+	2.88473i	−0.632552	+	0.205529i	−0.0248470	+	0.999691i	$0.507910\pi$
$198$	−14.7426	−	13.6687i	−1.04771	−	0.971395i
$199$	21.5328			1.52642			0.763211	−	0.646149i	$-0.223622\pi$
$199$	21.5328			1.52642			0.763211	+	0.646149i	$0.223622\pi$
$200$		0			0
$201$	0.600452			0.0423526
$202$	9.70226	+	8.99557i	0.682649	+	0.632926i
$203$	5.17675	−	1.68203i	0.363337	−	0.118055i
$204$	−2.14646	+	0.162485i	−0.150282	+	0.0113763i
$205$		0			0
$206$	−11.5327	−	5.33752i	−0.803520	−	0.371883i
$207$	−16.9107			−1.17538
$208$	5.22190	+	5.28462i	0.362074	+	0.366422i
$209$	−11.7057	+	8.50470i	−0.809701	+	0.588283i
$210$		0			0
$211$	0.604508	−	0.832033i	0.0416160	−	0.0572795i	−0.787702	−	0.616057i	$-0.788729\pi$
$211$	0.604508	−	0.832033i	0.0416160	−	0.0572795i	0.829318	+	0.558777i	$0.188729\pi$
$212$	−4.09280	−	9.96491i	−0.281095	−	0.684393i
$213$	−2.08421	−	2.86867i	−0.142808	−	0.196558i
$214$	−1.63965	−	1.52022i	−0.112084	−	0.103920i
$215$		0			0
$216$	−3.96582	+	1.09933i	−0.269840	+	0.0748003i
$217$	0.602984	−	1.85579i	0.0409332	−	0.125980i
$218$	−5.08338	−	0.609351i	−0.344290	−	0.0412704i
$219$	0.749118	+	0.243403i	0.0506207	+	0.0164477i
$220$		0			0
$221$	7.76164	−	2.52191i	0.522105	−	0.169642i
$222$	2.68797	−	0.530502i	0.180405	−	0.0356050i
$223$	16.4740	+	11.9690i	1.10318	+	0.801506i	0.981576	−	0.191073i	$-0.0611968\pi$
$223$	16.4740	+	11.9690i	1.10318	+	0.801506i	0.121602	+	0.992579i	$0.461197\pi$
$224$	5.06651	−	7.46144i	0.338520	−	0.498538i
$225$		0			0
$226$	−3.39939	+	28.3586i	−0.226124	+	1.88639i
$227$	0.720114	−	0.991152i	0.0477956	−	0.0657850i	−0.784450	−	0.620192i	$-0.787055\pi$
$227$	0.720114	−	0.991152i	0.0477956	−	0.0657850i	0.832246	+	0.554407i	$0.187055\pi$
$228$	0.110656	+	1.46178i	0.00732837	+	0.0968090i
$229$	−0.927598	+	0.301395i	−0.0612974	+	0.0199167i	−0.339505	−	0.940604i	$-0.610260\pi$
$229$	−0.927598	+	0.301395i	−0.0612974	+	0.0199167i	0.278208	+	0.960521i	$0.410260\pi$
$230$		0			0
$231$	−0.583537	+	1.79594i	−0.0383939	+	0.118164i
$232$	9.04443	+	3.38275i	0.593796	+	0.222088i
$233$	−0.781559	+	2.40539i	−0.0512017	+	0.157583i	−0.973388	−	0.229163i	$-0.926401\pi$
$233$	−0.781559	+	2.40539i	−0.0512017	+	0.157583i	0.922186	+	0.386746i	$0.126401\pi$
$234$	6.74341	−	3.76328i	0.440830	−	0.246013i
$235$		0			0
$236$	−14.1584	+	12.0195i	−0.921632	+	0.782403i
$237$	−1.52341	−	2.09679i	−0.0989560	−	0.136201i
$238$	−4.82801	−	8.65128i	−0.312953	−	0.560779i
$239$	15.9729	+	11.6050i	1.03320	+	0.750665i	0.968947	−	0.247269i	$-0.0795331\pi$
$239$	15.9729	+	11.6050i	1.03320	+	0.750665i	0.0642544	+	0.997934i	$0.479533\pi$
$240$		0			0
$241$	12.9006	−	9.37282i	0.830999	−	0.603756i	−0.0888425	−	0.996046i	$-0.528317\pi$
$241$	12.9006	−	9.37282i	0.830999	−	0.603756i	0.919842	+	0.392289i	$0.128317\pi$
$242$	−15.8890	−	7.35371i	−1.02139	−	0.472715i
$243$			6.43817i			0.413009i
$244$	8.87227	+	5.47343i	0.567989	+	0.350400i
$245$		0			0
$246$	−0.576443	−	2.92075i	−0.0367527	−	0.186220i
$247$	−1.71747	−	5.28584i	−0.109280	−	0.336330i
$248$	2.88685	−	1.91029i	0.183315	−	0.121304i
$249$	−0.427835			−0.0271129
$250$		0			0
$251$		−	15.4738i		−	0.976698i	−0.872648	−	0.488349i	$-0.837599\pi$
$251$		−	15.4738i		−	0.976698i	0.872648	−	0.488349i	$-0.162401\pi$
$252$	−6.06713	−	7.14678i	−0.382193	−	0.450205i
$253$	−26.4512	+	8.59451i	−1.66297	+	0.540332i
$254$	−14.0665	+	2.77619i	−0.882613	+	0.174194i
$255$		0			0
$256$	15.2748	−	4.76226i	0.954678	−	0.297641i
$257$	6.14189			0.383120			0.191560	−	0.981481i	$-0.438645\pi$
$257$	6.14189			0.383120			0.191560	+	0.981481i	$0.438645\pi$
$258$	3.44460	+	1.59422i	0.214451	+	0.0992516i
$259$	7.41195	+	10.2017i	0.460556	+	0.633901i
$260$		0			0
$261$	5.89974	−	8.12030i	0.365185	−	0.502634i
$262$	7.55993	−	4.21896i	0.467054	−	0.260648i
$263$	−18.2699	+	13.2738i	−1.12657	+	0.818500i	−0.985192	−	0.171456i	$-0.945153\pi$
$263$	−18.2699	+	13.2738i	−1.12657	+	0.818500i	−0.141377	+	0.989956i	$0.545153\pi$
$264$	−2.79374	+	1.84868i	−0.171943	+	0.113778i
$265$		0			0
$266$	−5.89171	+	3.28797i	−0.361244	+	0.201599i
$267$	2.64767	+	0.860281i	0.162035	+	0.0526484i
$268$	−1.15872	+	4.76375i	−0.0707803	+	0.290992i
$269$	20.0823	+	6.52512i	1.22444	+	0.397844i	0.848696	−	0.528881i	$-0.177388\pi$
$269$	20.0823	+	6.52512i	1.22444	+	0.397844i	0.375741	+	0.926725i	$0.377388\pi$
$270$		0			0
$271$	−1.68049	−	5.17201i	−0.102082	−	0.314177i	0.886952	−	0.461861i	$-0.152818\pi$
$271$	−1.68049	−	5.17201i	−0.102082	−	0.314177i	−0.989035	+	0.147684i	$0.952818\pi$
$272$	2.85304	−	17.3427i	0.172991	−	1.05156i
$273$	−0.586828	−	0.426355i	−0.0355164	−	0.0258042i
$274$	0.396866	−	3.31077i	0.0239756	−	0.200011i
$275$		0			0
$276$	−0.665996	+	2.73804i	−0.0400882	+	0.164811i
$277$	1.58397	−	2.18015i	0.0951714	−	0.130992i	−0.758776	−	0.651352i	$-0.774202\pi$
$277$	1.58397	−	2.18015i	0.0951714	−	0.130992i	0.853947	+	0.520360i	$0.174202\pi$
$278$	5.40529	+	27.3878i	0.324188	+	1.64261i
$279$	−1.11191	−	3.42210i	−0.0665682	−	0.204876i
$280$		0			0
$281$	−2.50433	+	7.70752i	−0.149396	+	0.459792i	−0.997550	−	0.0699568i	$-0.977714\pi$
$281$	−2.50433	+	7.70752i	−0.149396	+	0.459792i	0.848154	+	0.529749i	$0.177714\pi$
$282$	0.322202	+	0.0386228i	0.0191869	+	0.00229995i
$283$	−20.0273	−	6.50726i	−1.19050	−	0.386816i	−0.354241	−	0.935154i	$-0.615261\pi$
$283$	−20.0273	−	6.50726i	−1.19050	−	0.386816i	−0.836257	+	0.548338i	$0.815261\pi$
$284$	26.7809	−	10.9995i	1.58915	−	0.652699i
$285$		0			0
$286$	8.63521	−	9.31359i	0.510611	−	0.550724i
$287$	11.0851	−	8.05382i	0.654334	−	0.475402i
$288$	−0.528920	−	16.6227i	−0.0311669	−	0.979504i
$289$	−1.86629	−	1.35594i	−0.109782	−	0.0797610i
$290$		0			0
$291$	−2.06047	−	2.83600i	−0.120787	−	0.166249i
$292$	−3.37668	+	5.47350i	−0.197605	+	0.320312i
$293$			26.3688i			1.54048i	0.637751	+	0.770242i	$0.279865\pi$
$293$			26.3688i			1.54048i	−0.637751	+	0.770242i	$0.720135\pi$
$294$	0.648637	−	1.40150i	0.0378292	−	0.0817369i
$295$		0			0
$296$	−0.978325	+	22.3491i	−0.0568640	+	1.29901i
$297$	2.17405	+	6.69105i	0.126151	+	0.388254i
$298$	−13.0140	−	12.0661i	−0.753882	−	0.698970i
$299$		−	10.6833i		−	0.617832i
$300$		0			0
$301$			17.4693i			1.00691i
$302$	9.75613	−	10.5226i	0.561402	−	0.605506i
$303$	−0.708160	−	2.17949i	−0.0406827	−	0.125209i
$304$	−11.8108	−	1.94298i	−0.677393	−	0.111438i
$305$		0			0
$306$	−16.5796	−	7.67330i	−0.947790	−	0.438654i
$307$			18.9501i			1.08154i	0.841171	+	0.540770i	$0.181867\pi$
$307$			18.9501i			1.08154i	−0.841171	+	0.540770i	$0.818133\pi$
$308$	−13.1222	−	8.09527i	−0.747707	−	0.461271i
$309$	1.29377	+	1.78072i	0.0735999	+	0.101302i
$310$		0			0
$311$	10.7210	+	7.78926i	0.607932	+	0.441689i	0.848686	−	0.528898i	$-0.177395\pi$
$311$	10.7210	+	7.78926i	0.607932	+	0.441689i	−0.240753	+	0.970586i	$0.577395\pi$
$312$	−0.343744	−	1.24005i	−0.0194607	−	0.0702039i
$313$	−13.9133	+	10.1086i	−0.786426	+	0.571372i	−0.906901	−	0.421345i	$-0.861558\pi$
$313$	−13.9133	+	10.1086i	−0.786426	+	0.571372i	0.120475	+	0.992716i	$0.461558\pi$
$314$	7.99589	+	7.41348i	0.451234	+	0.418367i
$315$		0			0
$316$	19.5749	−	8.03984i	1.10118	−	0.452276i
$317$	2.20790	+	0.717389i	0.124008	+	0.0402926i	0.370364	−	0.928887i	$-0.379233\pi$
$317$	2.20790	+	0.717389i	0.124008	+	0.0402926i	−0.246356	+	0.969180i	$0.579233\pi$
$318$	−0.222077	+	1.85263i	−0.0124535	+	0.103890i
$319$	5.10121	−	15.6999i	0.285613	−	0.879027i
$320$		0			0
$321$	0.119677	+	0.368327i	0.00667971	+	0.0205580i
$322$	−12.7238	+	2.51118i	−0.709068	+	0.139943i
$323$	−7.72842	+	10.6373i	−0.430021	+	0.591873i
$324$	−16.4476	−	4.00068i	−0.913757	−	0.222260i
$325$		0			0
$326$	13.2787	+	1.59173i	0.735437	+	0.0881578i
$327$	0.717415	+	0.521233i	0.0396731	+	0.0288242i
$328$	24.2845	+	1.06305i	1.34088	+	0.0586969i
$329$	0.461530	+	1.42044i	0.0254450	+	0.0783116i
$330$		0			0
$331$	10.8707	+	3.53209i	0.597505	+	0.194141i	0.592127	−	0.805844i	$-0.298288\pi$
$331$	10.8707	+	3.53209i	0.597505	+	0.194141i	0.00537779	+	0.999986i	$0.498288\pi$
$332$	0.825615	−	3.39427i	0.0453115	−	0.186285i
$333$	22.1148	+	7.18554i	1.21188	+	0.393765i
$334$	−14.6331	−	26.2210i	−0.800688	−	1.43475i
$335$		0			0
$336$	−1.39609	+	0.700878i	−0.0761630	+	0.0382361i
$337$	−11.2300	+	8.15904i	−0.611735	+	0.444451i	−0.850025	−	0.526743i	$-0.823413\pi$
$337$	−11.2300	+	8.15904i	−0.611735	+	0.444451i	0.238290	+	0.971194i	$0.423413\pi$
$338$	−6.58180	−	11.7939i	−0.358003	−	0.641503i
$339$	2.90780	−	4.00225i	0.157930	−	0.217372i
$340$		0			0
$341$	−3.47842	−	4.78764i	−0.188367	−	0.259265i
$342$	−5.22568	+	11.2910i	−0.282572	+	0.610549i
$343$	18.2681			0.986387
$344$	−19.2951	+	24.2516i	−1.04032	+	1.30756i
$345$		0			0
$346$	−4.94059	−	25.0332i	−0.265608	−	1.34579i
$347$	−15.4461	+	5.01875i	−0.829191	+	0.269421i	−0.692705	−	0.721221i	$-0.743581\pi$
$347$	−15.4461	+	5.01875i	−0.829191	+	0.269421i	−0.136486	+	0.990642i	$0.543581\pi$
$348$	−1.08242	−	1.27504i	−0.0580240	−	0.0683494i
$349$			10.1963i			0.545797i	0.962043	+	0.272899i	$0.0879824\pi$
$349$			10.1963i			0.545797i	−0.962043	+	0.272899i	$0.912018\pi$
$350$		0			0
$351$	−2.70244			−0.144245
$352$	−9.27547	−	25.7319i	−0.494384	−	1.37152i
$353$	−4.14740	−	12.7644i	−0.220744	−	0.679379i	−0.998696	−	0.0510557i	$-0.983741\pi$
$353$	−4.14740	−	12.7644i	−0.220744	−	0.679379i	0.777952	−	0.628324i	$-0.216259\pi$
$354$	3.15595	−	0.622862i	0.167737	−	0.0331047i
$355$		0			0
$356$	−11.9345	+	19.3455i	−0.632526	+	1.02531i
$357$			1.71600i			0.0908204i
$358$	2.72970	−	5.89802i	0.144269	−	0.311720i
$359$	−6.13662	+	4.45851i	−0.323878	+	0.235311i	−0.737829	−	0.674988i	$-0.764149\pi$
$359$	−6.13662	+	4.45851i	−0.323878	+	0.235311i	0.413950	+	0.910299i	$0.364149\pi$
$360$		0			0
$361$	−8.12712	−	5.90470i	−0.427743	−	0.310774i
$362$	−27.0777	+	15.1112i	−1.42317	+	0.794228i
$363$	1.78248	+	2.45337i	0.0935558	+	0.128768i
$364$	4.51497	−	3.83290i	0.236649	−	0.200899i
$365$		0			0
$366$	−0.879917	−	1.57672i	−0.0459940	−	0.0824165i
$367$	−2.70498	+	8.32507i	−0.141199	+	0.434565i	−0.996503	−	0.0835618i	$-0.973370\pi$
$367$	−2.70498	+	8.32507i	−0.141199	+	0.434565i	0.855304	+	0.518127i	$0.173370\pi$
$368$	−20.4374	−	10.5675i	−1.06537	−	0.550869i
$369$	7.80780	−	24.0299i	0.406458	−	1.25095i
$370$		0			0
$371$	−8.16740	+	2.65375i	−0.424030	+	0.137776i
$372$	−0.597870	+	0.0452583i	−0.0309981	+	0.00234653i
$373$	−3.48778	+	4.80051i	−0.180590	+	0.248561i	−0.889709	−	0.456528i	$-0.849093\pi$
$373$	−3.48778	+	4.80051i	−0.180590	+	0.248561i	0.709119	+	0.705089i	$0.249093\pi$
$374$	−29.8330	−	3.57612i	−1.54263	−	0.184917i
$375$		0			0
$376$	−0.928188	+	2.48169i	−0.0478676	+	0.127983i
$377$	5.12999	+	3.72715i	0.264208	+	0.191958i
$378$	0.635225	+	3.21859i	0.0326725	+	0.165546i
$379$	−5.13756	+	1.66929i	−0.263899	+	0.0857458i	−0.437978	−	0.898986i	$-0.644305\pi$
$379$	−5.13756	+	1.66929i	−0.263899	+	0.0857458i	0.174079	+	0.984732i	$0.444305\pi$
$380$		0			0
$381$	2.36186	+	0.767414i	0.121002	+	0.0393158i
$382$	1.14522	−	9.55378i	0.0585948	−	0.488814i
$383$	8.42878	−	25.9411i	0.430690	−	1.32553i	−0.466749	−	0.884390i	$-0.654575\pi$
$383$	8.42878	−	25.9411i	0.430690	−	1.32553i	0.897439	−	0.441139i	$-0.145425\pi$
$384$	−2.71225	−	0.569016i	−0.138409	−	0.0290375i
$385$		0			0
$386$	−5.69467	+	6.14205i	−0.289851	+	0.312622i
$387$	18.9346	+	26.0613i	0.962501	+	1.32477i
$388$	26.4759	−	10.8742i	1.34411	−	0.552055i
$389$	−17.0621	+	23.4839i	−0.865081	+	1.19068i	0.115253	+	0.993336i	$0.463232\pi$
$389$	−17.0621	+	23.4839i	−0.865081	+	1.19068i	−0.980334	+	0.197346i	$0.936768\pi$
$390$		0			0
$391$	−20.4469	+	14.8556i	−1.03405	+	0.751278i
$392$	9.86721	+	7.85057i	0.498370	+	0.396513i
$393$	−1.49953			−0.0756412
$394$	−5.54501	+	11.9810i	−0.279354	+	0.603594i
$395$		0			0
$396$	−28.3505	+	2.14611i	−1.42467	+	0.107846i
$397$	10.3426	−	3.36051i	0.519080	−	0.168659i	−0.0377479	−	0.999287i	$-0.512018\pi$
$397$	10.3426	−	3.36051i	0.519080	−	0.168659i	0.556828	+	0.830628i	$0.312018\pi$
$398$	20.7042	−	22.3307i	1.03781	−	1.11934i
$399$	1.16863			0.0585048
$400$		0			0
$401$	−27.9140			−1.39396			−0.696980	−	0.717090i	$-0.745474\pi$
$401$	−27.9140			−1.39396			−0.696980	+	0.717090i	$0.745474\pi$
$402$	0.577345	−	0.622702i	0.0287954	−	0.0310576i
$403$	2.16191	−	0.702447i	0.107692	−	0.0349914i
$404$	18.6578	−	1.41238i	0.928260	−	0.0702686i
$405$		0			0
$406$	3.23318	−	6.98588i	0.160460	−	0.346703i
$407$	38.2432			1.89564
$408$	−1.89535	+	2.38223i	−0.0938340	+	0.117938i
$409$	−8.51534	+	6.18676i	−0.421057	+	0.305916i	−0.778063	−	0.628186i	$-0.783797\pi$
$409$	−8.51534	+	6.18676i	−0.421057	+	0.305916i	0.357006	+	0.934102i	$0.383797\pi$
$410$		0			0
$411$	−0.339476	+	0.467248i	−0.0167451	+	0.0230476i
$412$	−16.6242	+	6.82790i	−0.819014	+	0.336387i
$413$	8.70236	+	11.9778i	0.428215	+	0.589388i
$414$	−16.2599	+	17.5373i	−0.799133	+	0.861913i
$415$		0			0
$416$	10.5014	−	0.334144i	0.514873	−	0.0163828i
$417$	1.49417	−	4.59858i	0.0731698	−	0.225193i
$418$	−2.43541	+	20.3169i	−0.119120	+	0.993732i
$419$	22.7262	+	7.38420i	1.11025	+	0.360742i	0.806039	−	0.591863i	$-0.201607\pi$
$419$	22.7262	+	7.38420i	1.11025	+	0.360742i	0.304211	+	0.952605i	$0.401607\pi$
$420$		0			0
$421$	30.5748	−	9.93434i	1.49012	−	0.484170i	0.553003	−	0.833179i	$-0.313482\pi$
$421$	30.5748	−	9.93434i	1.49012	−	0.484170i	0.937119	+	0.349009i	$0.113482\pi$
$422$	−0.281620	−	1.42692i	−0.0137090	−	0.0694615i
$423$	2.22812	+	1.61882i	0.108335	+	0.0787099i
$424$	−14.2695	−	5.33698i	−0.692987	−	0.259187i
$425$		0			0
$426$	−4.97898	−	0.596836i	−0.241232	−	0.0289168i
$427$	4.88471	−	6.72323i	0.236388	−	0.325360i
$428$	−3.15311	+	0.238688i	−0.152411	+	0.0115374i
$429$	−2.09218	+	0.679791i	−0.101012	+	0.0328206i
$430$		0			0
$431$	1.14163	−	3.51358i	0.0549904	−	0.169243i	−0.919789	−	0.392413i	$-0.871640\pi$
$431$	1.14163	−	3.51358i	0.0549904	−	0.169243i	0.974780	+	0.223170i	$0.0716404\pi$
$432$	−2.67314	+	5.16981i	−0.128611	+	0.248732i
$433$	3.09474	−	9.52464i	0.148724	−	0.457725i	−0.848747	−	0.528799i	$-0.822643\pi$
$433$	3.09474	−	9.52464i	0.148724	−	0.457725i	0.997471	+	0.0710739i	$0.0226426\pi$
$434$	−1.34478	−	2.40971i	−0.0645515	−	0.115670i
$435$		0			0
$436$	−5.51969	+	4.68584i	−0.264345	+	0.224411i
$437$	10.1169	+	13.9248i	0.483959	+	0.666113i
$438$	0.972713	−	0.542840i	0.0464780	−	0.0259379i
$439$	−23.2982	−	16.9271i	−1.11196	−	0.807887i	−0.128989	−	0.991646i	$-0.541173\pi$
$439$	−23.2982	−	16.9271i	−1.11196	−	0.807887i	−0.982971	+	0.183759i	$0.941173\pi$
$440$		0			0
$441$	10.6035	−	7.70389i	0.504929	−	0.366852i
$442$	4.84760	−	10.4741i	0.230577	−	0.498203i
$443$		−	21.7711i		−	1.03438i	−0.855872	−	0.517188i	$-0.826979\pi$
$443$		−	21.7711i		−	1.03438i	0.855872	−	0.517188i	$-0.173021\pi$
$444$	2.03437	−	3.29766i	0.0965471	−	0.156500i
$445$		0			0
$446$	28.2525	−	5.57596i	1.33780	−	0.264030i
$447$	0.949882	+	2.92344i	0.0449279	+	0.138274i
$448$	−2.86638	−	12.4286i	−0.135424	−	0.587194i
$449$	2.36468			0.111596			0.0557981	−	0.998442i	$-0.482230\pi$
$449$	2.36468			0.111596			0.0557981	+	0.998442i	$0.482230\pi$
$450$		0			0
$451$		−	41.5550i		−	1.95675i
$452$	26.1409	+	30.7927i	1.22956	+	1.44837i
$453$	−2.36376	+	0.768034i	−0.111059	+	0.0360854i
$454$	−0.335477	−	1.69981i	−0.0157447	−	0.0797759i
$455$		0			0
$456$	1.62235	+	1.29078i	0.0759734	+	0.0604461i
$457$	11.3909			0.532843			0.266422	−	0.963857i	$-0.414159\pi$
$457$	11.3909			0.532843			0.266422	+	0.963857i	$0.414159\pi$
$458$	−0.579339	+	1.25177i	−0.0270707	+	0.0584912i
$459$	3.75784	+	5.17223i	0.175401	+	0.241419i
$460$		0			0
$461$	21.5814	−	29.7043i	1.00515	−	1.38347i	0.0830335	−	0.996547i	$-0.473539\pi$
$461$	21.5814	−	29.7043i	1.00515	−	1.38347i	0.922114	−	0.386919i	$-0.126461\pi$
$462$	1.30141	+	2.33199i	0.0605470	+	0.108494i
$463$	−12.3951	+	9.00559i	−0.576051	+	0.418525i	−0.837298	−	0.546747i	$-0.815866\pi$
$463$	−12.3951	+	9.00559i	−0.576051	+	0.418525i	0.261247	+	0.965272i	$0.415866\pi$
$464$	12.2045	−	6.12700i	0.566579	−	0.284439i
$465$		0			0
$466$	1.74304	+	3.12335i	0.0807448	+	0.144686i
$467$	28.7275	+	9.33412i	1.32935	+	0.431931i	0.885695	−	0.464267i	$-0.153682\pi$
$467$	28.7275	+	9.33412i	1.32935	+	0.431931i	0.443653	+	0.896199i	$0.353682\pi$
$468$	2.58118	−	10.6117i	0.119315	−	0.490528i
$469$	3.71699	+	1.20772i	0.171634	+	0.0557674i
$470$		0			0
$471$	−0.583613	−	1.79618i	−0.0268915	−	0.0827634i
$472$	−1.14865	+	26.2400i	−0.0528709	+	1.20779i
$473$	42.8620	+	31.1411i	1.97080	+	1.43187i
$474$	−3.63927	−	0.436245i	−0.167157	−	0.0200374i
$475$		0			0
$476$	−13.6141	−	3.31146i	−0.624000	−	0.151780i
$477$	−9.30807	+	12.8115i	−0.426187	+	0.586596i
$478$	27.3933	−	5.40637i	1.25294	−	0.247282i
$479$	10.3930	+	31.9863i	0.474868	+	1.46149i	0.846136	+	0.532967i	$0.178923\pi$
$479$	10.3930	+	31.9863i	0.474868	+	1.46149i	−0.371268	+	0.928526i	$0.621077\pi$
$480$		0			0
$481$	−4.53945	+	13.9710i	−0.206981	+	0.637023i
$482$	2.68401	−	22.3907i	0.122253	−	1.01987i
$483$	2.13640	+	0.694158i	0.0972095	+	0.0315853i
$484$	−22.9038	+	9.40707i	−1.04108	+	0.427594i
$485$		0			0
$486$	6.67674	+	6.19042i	0.302863	+	0.280803i
$487$	−28.8574	+	20.9661i	−1.30765	+	0.950065i	−0.999999	−	0.00143291i	$-0.999544\pi$
$487$	−28.8574	+	20.9661i	−1.30765	+	0.950065i	−0.307654	+	0.951498i	$0.599544\pi$
$488$	14.2071	−	3.93824i	0.643125	−	0.178276i
$489$	−1.87401	−	1.36155i	−0.0847458	−	0.0615714i
$490$		0			0
$491$	19.3917	+	26.6904i	0.875135	+	1.20452i	0.977745	+	0.209798i	$0.0672808\pi$
$491$	19.3917	+	26.6904i	0.875135	+	1.20452i	−0.102610	+	0.994722i	$0.532719\pi$
$492$	−3.58324	−	2.21055i	−0.161545	−	0.0996592i
$493$		−	15.0011i		−	0.675615i
$494$	−7.13309	−	3.30132i	−0.320933	−	0.148533i
$495$		0			0
$496$	0.794678	−	4.83060i	0.0356821	−	0.216900i
$497$	−7.13200	−	21.9501i	−0.319914	−	0.984594i
$498$	−0.411371	+	0.443689i	−0.0184340	+	0.0198822i
$499$			34.7937i			1.55758i	0.627285	+	0.778790i	$0.284166\pi$
$499$			34.7937i			1.55758i	−0.627285	+	0.778790i	$0.715834\pi$
$500$		0			0
$501$			5.20100i			0.232363i
$502$	−16.0472	−	14.8783i	−0.716221	−	0.664053i
$503$	−5.30944	−	16.3408i	−0.236736	−	0.728600i	−0.996886	−	0.0788520i	$-0.974875\pi$
$503$	−5.30944	−	16.3408i	−0.236736	−	0.728600i	0.760150	−	0.649748i	$-0.225125\pi$
$504$	−13.2453	−	0.579808i	−0.589991	−	0.0258267i
$505$		0			0
$506$	−16.5203	+	35.6951i	−0.734417	+	1.58684i
$507$			2.33934i			0.103894i
$508$	−10.6462	+	17.2571i	−0.472347	+	0.765661i
$509$	−3.41389	−	4.69882i	−0.151318	−	0.208271i	0.726628	−	0.687031i	$-0.241086\pi$
$509$	−3.41389	−	4.69882i	−0.151318	−	0.208271i	−0.877946	+	0.478760i	$0.841086\pi$
$510$		0			0
$511$	4.14770	+	3.01348i	0.183484	+	0.133309i
$512$	9.74831	−	20.4199i	0.430819	−	0.902438i
$513$	3.52240	−	2.55917i	0.155518	−	0.112990i
$514$	5.90553	−	6.36947i	0.260482	−	0.280945i
$515$		0			0
$516$	4.96533	−	2.03937i	0.218587	−	0.0897781i
$517$	4.30788	+	1.39972i	0.189461	+	0.0615595i
$518$	17.7064	+	2.12249i	0.777975	+	0.0932569i
$519$	−1.36571	+	4.20323i	−0.0599481	+	0.184501i
$520$		0			0
$521$	1.56244	+	4.80869i	0.0684517	+	0.210673i	0.979431	−	0.201779i	$-0.0646724\pi$
$521$	1.56244	+	4.80869i	0.0684517	+	0.210673i	−0.910979	+	0.412452i	$0.864672\pi$
$522$	−2.74849	−	13.9262i	−0.120298	−	0.609532i
$523$	−11.5984	+	15.9638i	−0.507161	+	0.698047i	−0.983437	−	0.181249i	$-0.941986\pi$
$523$	−11.5984	+	15.9638i	−0.507161	+	0.698047i	0.476277	+	0.879296i	$0.341986\pi$
$524$	2.89372	−	11.8967i	0.126413	−	0.519708i
$525$		0			0
$526$	−3.80111	+	31.7099i	−0.165736	+	1.38262i
$527$	−4.35064	−	3.16092i	−0.189517	−	0.137692i
$528$	−0.769048	+	4.67480i	−0.0334685	+	0.203445i
$529$	3.11638	+	9.59125i	0.135495	+	0.417011i
$530$		0			0
$531$	25.9650	+	8.43653i	1.12678	+	0.366114i
$532$	−2.25517	+	9.27147i	−0.0977741	+	0.401969i
$533$	15.1809	+	4.93257i	0.657557	+	0.213653i
$534$	3.43794	−	1.91861i	0.148774	−	0.0830263i
$535$		0			0
$536$	3.82614	+	5.78209i	0.165264	+	0.249748i
$537$	−0.910692	+	0.661657i	−0.0392993	+	0.0285526i
$538$	26.0764	−	14.5524i	1.12423	−	0.627398i
$539$	12.6703	−	17.4392i	0.545749	−	0.751159i
$540$		0			0
$541$	−12.7304	−	17.5219i	−0.547322	−	0.753324i	0.442324	−	0.896855i	$-0.354154\pi$
$541$	−12.7304	−	17.5219i	−0.547322	−	0.753324i	−0.989646	+	0.143532i	$0.954154\pi$
$542$	−6.97948	−	3.23022i	−0.299794	−	0.138750i
$543$	5.37093			0.230489
$544$	−15.2421	−	19.6341i	−0.653500	−	0.841805i
$545$		0			0
$546$	−1.00640	+	0.198625i	−0.0430699	+	0.00850034i
$547$	−1.61054	+	0.523296i	−0.0688618	+	0.0223745i	−0.343245	−	0.939246i	$-0.611526\pi$
$547$	−1.61054	+	0.523296i	−0.0688618	+	0.0223745i	0.274384	+	0.961620i	$0.411526\pi$
$548$	−3.05186	−	3.59494i	−0.130369	−	0.153568i
$549$		−	15.3244i		−	0.654029i
$550$		0			0
$551$	−10.2161			−0.435219
$552$	2.19914	+	3.32335i	0.0936014	+	0.141451i
$553$	−5.21298	−	16.0439i	−0.221679	−	0.682257i
$554$	−0.737917	−	3.73891i	−0.0313511	−	0.158851i
$555$		0			0
$556$	33.5999	+	20.7283i	1.42495	+	0.879074i
$557$			1.82388i			0.0772805i	0.999253	+	0.0386402i	$0.0123026\pi$
$557$			1.82388i			0.0772805i	−0.999253	+	0.0386402i	$0.987697\pi$
$558$	−4.61803	−	2.13730i	−0.195497	−	0.0904792i
$559$	−16.4642	+	11.9619i	−0.696360	+	0.505935i
$560$		0			0
$561$	4.21032	+	3.05898i	0.177760	+	0.129150i
$562$	5.58517	+	10.0080i	0.235596	+	0.422164i
$563$	24.8339	+	34.1809i	1.04662	+	1.44055i	0.891700	+	0.452627i	$0.149513\pi$
$563$	24.8339	+	34.1809i	1.04662	+	1.44055i	0.154924	+	0.987926i	$0.450487\pi$
$564$	0.349857	−	0.297005i	0.0147316	−	0.0125062i
$565$		0			0
$566$	−26.0050	+	14.5126i	−1.09307	+	0.610008i
$567$	−4.16986	+	12.8335i	−0.175118	+	0.538956i
$568$	14.3432	−	38.3495i	0.601829	−	1.60911i
$569$	−8.58452	+	26.4204i	−0.359882	+	1.10760i	0.593243	+	0.805024i	$0.297847\pi$
$569$	−8.58452	+	26.4204i	−0.359882	+	1.10760i	−0.953125	+	0.302578i	$0.902153\pi$
$570$		0			0
$571$	−26.0253	+	8.45612i	−1.08912	+	0.353878i	−0.797908	−	0.602780i	$-0.794060\pi$
$571$	−26.0253	+	8.45612i	−1.08912	+	0.353878i	−0.291216	+	0.956657i	$0.594060\pi$
$572$	−1.35580	−	17.9104i	−0.0566890	−	0.748870i
$573$	−0.979614	+	1.34832i	−0.0409239	+	0.0563270i
$574$	2.30630	−	19.2398i	0.0962630	−	0.803053i
$575$		0			0
$576$	−17.7473	−	15.4345i	−0.739469	−	0.643106i
$577$	−7.00015	−	5.08591i	−0.291420	−	0.211729i	0.432463	−	0.901652i	$-0.357645\pi$
$577$	−7.00015	−	5.08591i	−0.291420	−	0.211729i	−0.723883	+	0.689923i	$0.757645\pi$
$578$	−3.20065	+	0.631685i	−0.133130	+	0.0262746i
$579$	1.37973	−	0.448303i	0.0573398	−	0.0186308i
$580$		0			0
$581$	−2.64843	−	0.860528i	−0.109875	−	0.0357007i
$582$	−4.92227	−	0.590039i	−0.204035	−	0.0244579i
$583$	−8.04822	+	24.7699i	−0.333323	+	1.02586i
$584$	2.42958	+	8.76466i	0.100537	+	0.362684i
$585$		0			0
$586$	27.3459	+	25.3541i	1.12965	+	1.04737i
$587$	1.23640	+	1.70175i	0.0510315	+	0.0702388i	0.833770	−	0.552112i	$-0.186178\pi$
$587$	1.23640	+	1.70175i	0.0510315	+	0.0702388i	−0.782739	+	0.622351i	$0.786178\pi$
$588$	−0.829754	−	2.02024i	−0.0342185	−	0.0833131i
$589$	−2.15266	+	2.96288i	−0.0886986	+	0.122083i
$590$		0			0
$591$	1.84994	−	1.34406i	0.0760965	−	0.0552874i
$592$	22.2365	+	22.5036i	0.913915	+	0.924892i
$593$	39.8777			1.63758			0.818791	−	0.574091i	$-0.194645\pi$
$593$	39.8777			1.63758			0.818791	+	0.574091i	$0.194645\pi$
$594$	9.02938	+	4.17895i	0.370480	+	0.171464i
$595$		0			0
$596$	−25.0264	+	1.89448i	−1.02512	+	0.0776010i
$597$	−5.01632	+	1.62990i	−0.205304	+	0.0667074i
$598$	−11.0792	−	10.2722i	−0.453061	−	0.420061i
$599$	−13.7239			−0.560745			−0.280373	−	0.959891i	$-0.590458\pi$
$599$	−13.7239			−0.560745			−0.280373	+	0.959891i	$0.590458\pi$
$600$		0			0
$601$	25.6448			1.04607			0.523036	−	0.852310i	$-0.324799\pi$
$601$	25.6448			1.04607			0.523036	+	0.852310i	$0.324799\pi$
$602$	18.1166	+	16.7970i	0.738377	+	0.684595i
$603$	6.85416	−	2.22705i	0.279123	−	0.0906926i
$604$	−1.53180	−	20.2353i	−0.0623279	−	0.823362i
$605$		0			0
$606$	−2.94116	−	1.36122i	−0.119477	−	0.0552958i
$607$	−9.08062			−0.368571			−0.184286	−	0.982873i	$-0.558997\pi$
$607$	−9.08062			−0.368571			−0.184286	+	0.982873i	$0.558997\pi$
$608$	−13.3712	+	10.3802i	−0.542275	+	0.420973i
$609$	−1.07866	+	0.783696i	−0.0437097	+	0.0317570i
$610$		0			0
$611$	−1.02269	+	1.40761i	−0.0413736	+	0.0569459i
$612$	−23.8992	+	9.81590i	−0.966067	+	0.396784i
$613$	−24.1729	−	33.2712i	−0.976335	−	1.34381i	−0.938780	−	0.344516i	$-0.888043\pi$
$613$	−24.1729	−	33.2712i	−0.976335	−	1.34381i	−0.0375550	−	0.999295i	$-0.511957\pi$
$614$	19.6523	+	18.2209i	0.793102	+	0.735334i
$615$		0			0
$616$	−21.0125	+	5.82470i	−0.846617	+	0.234684i
$617$	−11.6227	+	35.7710i	−0.467912	+	1.44009i	0.387370	+	0.921924i	$0.373384\pi$
$617$	−11.6227	+	35.7710i	−0.467912	+	1.44009i	−0.855283	+	0.518162i	$0.826616\pi$
$618$	3.09069	+	0.370484i	0.124326	+	0.0149031i
$619$	−23.5409	−	7.64891i	−0.946190	−	0.307436i	−0.205024	−	0.978757i	$-0.565727\pi$
$619$	−23.5409	−	7.64891i	−0.946190	−	0.307436i	−0.741167	+	0.671321i	$0.765727\pi$
$620$		0			0
$621$	7.95948	−	2.58619i	0.319403	−	0.103780i
$622$	18.3863	−	3.62875i	0.737225	−	0.145500i
$623$	14.6596	+	10.6508i	0.587324	+	0.426716i
$624$	−1.61651	−	0.835847i	−0.0647123	−	0.0334606i
$625$		0			0
$626$	−2.89471	+	24.1485i	−0.115696	+	0.965166i
$627$	2.08323	−	2.86732i	0.0831961	−	0.114510i
$628$	15.3764	−	1.16398i	0.613584	−	0.0464479i
$629$	33.0516	−	10.7391i	1.31785	−	0.428196i
$630$		0			0
$631$	2.94258	−	9.05633i	0.117142	−	0.360527i	−0.875246	−	0.483679i	$-0.839300\pi$
$631$	2.94258	−	9.05633i	0.117142	−	0.360527i	0.992388	+	0.123152i	$0.0393003\pi$
$632$	10.4839	−	28.0307i	0.417027	−	1.11500i
$633$	−0.0778472	+	0.239589i	−0.00309415	+	0.00952281i
$634$	2.86691	−	1.59993i	0.113859	−	0.0635413i
$635$		0			0
$636$	1.70775	+	2.01164i	0.0677166	+	0.0797668i
$637$	4.86692	+	6.69875i	0.192835	+	0.265414i
$638$	−11.3768	−	20.3860i	−0.450411	−	0.807089i
$639$	−34.4310	−	25.0156i	−1.36207	−	0.989602i
$640$		0			0
$641$	−16.5944	+	12.0565i	−0.655440	+	0.476205i	−0.865120	−	0.501565i	$-0.832758\pi$
$641$	−16.5944	+	12.0565i	−0.655440	+	0.476205i	0.209680	+	0.977770i	$0.432758\pi$
$642$	0.497047	+	0.230042i	0.0196169	+	0.00907903i
$643$		−	3.19936i		−	0.126170i	−0.998008	−	0.0630852i	$-0.979906\pi$
$643$		−	3.19936i		−	0.126170i	0.998008	−	0.0630852i	$-0.0200940\pi$
$644$	−9.62990	+	15.6098i	−0.379471	+	0.615112i
$645$		0			0
$646$	3.60041	+	18.2427i	0.141656	+	0.717750i
$647$	−2.25397	−	6.93701i	−0.0886128	−	0.272722i	0.896924	−	0.442185i	$-0.145797\pi$
$647$	−2.25397	−	6.93701i	−0.0886128	−	0.272722i	−0.985537	+	0.169463i	$0.945797\pi$
$648$	−19.9636	+	13.2104i	−0.784245	+	0.518952i
$649$	44.9013			1.76253
$650$		0			0
$651$			0.477971i			0.0187331i
$652$	14.4184	−	12.2402i	0.564667	−	0.479364i
$653$	−34.9692	+	11.3622i	−1.36845	+	0.444637i	−0.898856	−	0.438244i	$-0.855601\pi$
$653$	−34.9692	+	11.3622i	−1.36845	+	0.444637i	−0.469596	+	0.882881i	$0.655601\pi$
$654$	1.23035	−	0.242825i	0.0481107	−	0.00949519i
$655$		0			0
$656$	24.4524	−	24.1622i	0.954705	−	0.943375i
$657$	9.45395			0.368834
$658$	1.91685	+	0.887150i	0.0747265	+	0.0345847i
$659$	6.86949	+	9.45505i	0.267598	+	0.368316i	0.921577	−	0.388196i	$-0.126902\pi$
$659$	6.86949	+	9.45505i	0.267598	+	0.368316i	−0.653979	+	0.756512i	$0.726902\pi$
$660$		0			0
$661$	−11.7497	+	16.1721i	−0.457012	+	0.629023i	−0.973886	−	0.227039i	$-0.927096\pi$
$661$	−11.7497	+	16.1721i	−0.457012	+	0.629023i	0.516874	+	0.856062i	$0.327096\pi$
$662$	14.1153	−	7.87730i	0.548607	−	0.306160i
$663$	−1.61727	+	1.17502i	−0.0628096	+	0.0456338i
$664$	−2.72621	−	4.11986i	−0.105797	−	0.159882i
$665$		0			0
$666$	28.7156	−	16.0253i	1.11271	−	0.620966i
$667$	−18.6762	−	6.06826i	−0.723144	−	0.234964i
$668$	−41.2626	−	10.0366i	−1.59650	−	0.388329i
$669$	−4.74378	−	1.54135i	−0.183405	−	0.0595919i
$670$		0			0
$671$	−7.78830	−	23.9699i	−0.300664	−	0.925348i
$672$	−0.615517	+	2.12173i	−0.0237441	+	0.0818475i
$673$	5.02552	+	3.65125i	0.193720	+	0.140746i	0.680417	−	0.732825i	$-0.261799\pi$
$673$	5.02552	+	3.65125i	0.193720	+	0.140746i	−0.486698	+	0.873571i	$0.661799\pi$
$674$	−2.33643	+	19.4911i	−0.0899959	+	0.750771i
$675$		0			0
$676$	−18.5594	−	4.51435i	−0.713824	−	0.173629i
$677$	−4.52233	+	6.22446i	−0.173807	+	0.239225i	−0.887030	−	0.461713i	$-0.847235\pi$
$677$	−4.52233	+	6.22446i	−0.173807	+	0.239225i	0.713222	+	0.700938i	$0.247235\pi$
$678$	−1.35465	−	6.86378i	−0.0520249	−	0.263602i
$679$	−7.05078	−	21.7001i	−0.270584	−	0.832772i
$680$		0			0
$681$	−0.0927347	+	0.285408i	−0.00355360	+	0.0109369i
$682$	−8.30961	−	0.996083i	−0.318191	−	0.0381420i
$683$	−25.3851	−	8.24813i	−0.971336	−	0.315606i	−0.219981	−	0.975504i	$-0.570599\pi$
$683$	−25.3851	−	8.24813i	−0.971336	−	0.315606i	−0.751355	+	0.659898i	$0.770599\pi$
$684$	6.68483	+	16.2758i	0.255601	+	0.622323i
$685$		0			0
$686$	17.5651	−	18.9451i	0.670641	−	0.723326i
$687$	0.193281	−	0.140427i	0.00737413	−	0.00535762i
$688$	6.59767	+	43.3284i	0.251534	+	1.65188i
$689$	−8.09362	−	5.88036i	−0.308342	−	0.224024i
$690$		0			0
$691$	−29.7127	−	40.8960i	−1.13033	−	1.55576i	−0.787451	−	0.616378i	$-0.788600\pi$
$691$	−29.7127	−	40.8960i	−1.13033	−	1.55576i	−0.342874	−	0.939381i	$-0.611400\pi$
$692$	−30.7113	−	18.9462i	−1.16747	−	0.720226i
$693$			22.6650i			0.860971i
$694$	−9.64700	+	20.8441i	−0.366195	+	0.791231i
$695$		0			0
$696$	−2.36306	−	0.103442i	−0.0895714	−	0.00392097i
$697$	−11.6691	−	35.9138i	−0.441999	−	1.36033i
$698$	10.5742	+	9.80396i	0.400238	+	0.371085i
$699$		−	0.619523i		−	0.0234325i
$700$		0			0
$701$			45.0199i			1.70038i	0.526477	+	0.850190i	$0.323513\pi$
$701$			45.0199i			1.70038i	−0.526477	+	0.850190i	$0.676487\pi$
$702$	−2.59844	+	2.80258i	−0.0980718	+	0.105776i
$703$	−7.31355	−	22.5088i	−0.275836	−	0.848936i
$704$	−35.6040	−	15.1225i	−1.34187	−	0.569952i
$705$		0			0
$706$	−17.2252	−	7.97210i	−0.648278	−	0.300034i
$707$		−	14.9161i		−	0.560978i
$708$	2.38856	−	3.87178i	0.0897674	−	0.145510i
$709$	23.2922	+	32.0589i	0.874756	+	1.20400i	0.977846	+	0.209326i	$0.0671271\pi$
$709$	23.2922	+	32.0589i	0.874756	+	1.20400i	−0.103090	+	0.994672i	$0.532873\pi$
$710$		0			0
$711$	−25.1666	−	18.2846i	−0.943822	−	0.685727i
$712$	8.58710	+	30.9777i	0.321815	+	1.16094i
$713$	−5.69523	+	4.13783i	−0.213288	+	0.154963i
$714$	1.77959	+	1.64997i	0.0665994	+	0.0617484i
$715$		0			0
$716$	−3.49191	−	8.50191i	−0.130499	−	0.317731i
$717$	−4.59950	−	1.49447i	−0.171771	−	0.0558119i
$718$	−1.27674	+	10.6509i	−0.0476476	+	0.397490i
$719$	6.66328	−	20.5075i	0.248499	−	0.764800i	−0.746543	−	0.665337i	$-0.768288\pi$
$719$	6.66328	−	20.5075i	0.248499	−	0.764800i	0.995041	−	0.0994625i	$-0.0317123\pi$
$720$		0			0
$721$	4.42717	+	13.6254i	0.164877	+	0.507438i
$722$	−13.9379	+	2.75080i	−0.518714	+	0.102374i
$723$	−2.29587	+	3.16000i	−0.0853845	+	0.117522i
$724$	−10.3646	+	42.6108i	−0.385196	+	1.58362i
$725$		0			0
$726$	4.25816	+	0.510431i	0.158035	+	0.0189439i
$727$	32.8992	+	23.9026i	1.22016	+	0.886500i	0.996114	−	0.0880780i	$-0.0280725\pi$
$727$	32.8992	+	23.9026i	1.22016	+	0.886500i	0.224049	+	0.974578i	$0.428072\pi$
$728$	0.366293	−	8.36767i	0.0135757	−	0.310127i
$729$	7.35885	+	22.6482i	0.272550	+	0.838823i
$730$		0			0
$731$	45.7881	+	14.8775i	1.69353	+	0.550263i
$732$	−2.48120	−	0.603522i	−0.0917079	−	0.0223068i
$733$	−1.01139	−	0.328621i	−0.0373566	−	0.0121379i	0.290279	−	0.956942i	$-0.406252\pi$
$733$	−1.01139	−	0.328621i	−0.0373566	−	0.0121379i	−0.327636	+	0.944804i	$0.606252\pi$
$734$	6.03267	+	10.8099i	0.222670	+	0.399001i
$735$		0			0
$736$	−30.6100	+	11.0338i	−1.12830	+	0.406712i
$737$	9.58920	−	6.96696i	0.353223	−	0.256631i
$738$	−17.4130	−	31.2023i	−0.640982	−	1.14857i
$739$	−4.06593	+	5.59628i	−0.149568	+	0.205862i	−0.877226	−	0.480077i	$-0.840609\pi$
$739$	−4.06593	+	5.59628i	−0.149568	+	0.205862i	0.727658	+	0.685940i	$0.240609\pi$
$740$		0			0
$741$	0.800210	+	1.10140i	0.0293965	+	0.0404608i
$742$	−5.10102	+	11.0217i	−0.187264	+	0.404618i
$743$	−31.5085			−1.15594			−0.577968	−	0.816059i	$-0.696154\pi$
$743$	−31.5085			−1.15594			−0.577968	+	0.816059i	$0.696154\pi$
$744$	−0.527927	+	0.663540i	−0.0193547	+	0.0243266i
$745$		0			0
$746$	1.62484	+	8.23280i	0.0594895	+	0.301424i
$747$	−4.88374	+	1.58682i	−0.178687	+	0.0580588i
$748$	−32.3936	+	27.5000i	−1.18443	+	1.00550i
$749$			2.52077i			0.0921071i
$750$		0			0
$751$	−31.8120			−1.16084			−0.580418	−	0.814319i	$-0.697111\pi$
$751$	−31.8120			−1.16084			−0.580418	+	0.814319i	$0.697111\pi$
$752$	1.68118	+	3.34877i	0.0613064	+	0.122117i
$753$	1.17127	+	3.60480i	0.0426835	+	0.131366i
$754$	8.79784	−	1.73635i	0.320398	−	0.0632343i
$755$		0			0
$756$	3.94863	+	2.43597i	0.143610	+	0.0885952i
$757$		−	32.4034i		−	1.17772i	−0.808235	−	0.588860i	$-0.799577\pi$
$757$		−	32.4034i		−	1.17772i	0.808235	−	0.588860i	$-0.200423\pi$
$758$	−3.20870	+	6.93298i	−0.116545	+	0.251817i
$759$	5.51155	−	4.00438i	0.200057	−	0.145350i
$760$		0			0
$761$	32.4295	+	23.5614i	1.17557	+	0.854099i	0.991665	−	0.128845i	$-0.0411271\pi$
$761$	32.4295	+	23.5614i	1.17557	+	0.854099i	0.183902	+	0.982945i	$0.441127\pi$
$762$	3.06682	−	1.71149i	0.111099	−	0.0620009i
$763$	3.39264	+	4.66957i	0.122822	+	0.169050i
$764$	−8.80665	−	10.3738i	−0.318613	−	0.375311i
$765$		0			0
$766$	−18.7979	−	33.6839i	−0.679197	−	1.21705i
$767$	−5.32977	+	16.4033i	−0.192447	+	0.592290i
$768$	−3.19798	+	2.26563i	−0.115397	+	0.0817540i
$769$	7.33782	−	22.5835i	0.264609	−	0.814382i	−0.727175	−	0.686453i	$-0.759167\pi$
$769$	7.33782	−	22.5835i	0.264609	−	0.814382i	0.991783	−	0.127929i	$-0.0408331\pi$
$770$		0			0
$771$	−1.43082	+	0.464902i	−0.0515298	+	0.0167430i
$772$	0.894113	+	11.8114i	0.0321798	+	0.425101i
$773$	24.9098	−	34.2854i	0.895943	−	1.23316i	−0.0758016	−	0.997123i	$-0.524152\pi$
$773$	24.9098	−	34.2854i	0.895943	−	1.23316i	0.971744	−	0.236036i	$-0.0758484\pi$
$774$	45.2329	+	5.42213i	1.62586	+	0.194894i
$775$		0			0
$776$	14.1799	−	37.9127i	0.509029	−	1.36099i
$777$	−2.49890	−	1.81556i	−0.0896476	−	0.0651328i
$778$	7.94864	+	40.2745i	0.284972	+	1.44391i
$779$	−24.4580	+	7.94690i	−0.876300	+	0.284727i
$780$		0			0
$781$	−66.5696	−	21.6298i	−2.38205	−	0.773974i
$782$	−4.25405	+	35.4885i	−0.152124	+	1.26907i
$783$	−1.53502	+	4.72430i	−0.0548571	+	0.168833i
$784$	17.6290	−	2.68438i	0.629606	−	0.0958709i
$785$		0			0
$786$	−1.44182	+	1.55509i	−0.0514281	+	0.0554683i
$787$	−17.2985	−	23.8094i	−0.616627	−	0.848714i	0.380475	−	0.924791i	$-0.375760\pi$
$787$	−17.2985	−	23.8094i	−0.616627	−	0.848714i	−0.997102	+	0.0760773i	$0.975760\pi$
$788$	7.09333	+	17.2704i	0.252690	+	0.615234i
$789$	3.25143	−	4.47521i	0.115754	−	0.159322i
$790$		0			0
$791$	26.0501	−	18.9265i	0.926236	−	0.672950i
$792$	−25.0339	+	31.4645i	−0.889540	+	1.11804i
$793$	9.68116			0.343788
$794$	6.45955	−	13.9570i	0.229241	−	0.495316i
$795$		0			0
$796$	−3.25074	−	42.9428i	−0.115219	−	1.52207i
$797$	−9.01881	+	2.93039i	−0.319462	+	0.103800i	−0.464359	−	0.885647i	$-0.653715\pi$
$797$	−9.01881	+	2.93039i	−0.319462	+	0.103800i	0.144896	+	0.989447i	$0.453715\pi$
$798$	1.12366	−	1.21194i	0.0397772	−	0.0429021i
$799$	4.11613			0.145618
$800$		0			0
$801$	33.4139			1.18062
$802$	−26.8398	+	28.9484i	−0.947748	+	1.02220i
$803$	14.7876	−	4.80477i	0.521842	−	0.169557i
$804$	−0.0906482	−	1.19748i	−0.00319692	−	0.0422318i
$805$		0			0
$806$	1.35024	−	2.91743i	0.0475601	−	0.102762i
$807$	−5.17230			−0.182074
$808$	16.4751	−	20.7072i	0.579592	−	0.728477i
$809$	18.6979	−	13.5848i	0.657383	−	0.477617i	−0.208395	−	0.978045i	$-0.566824\pi$
$809$	18.6979	−	13.5848i	0.657383	−	0.477617i	0.865778	+	0.500428i	$0.166824\pi$
$810$		0			0
$811$	−22.3488	+	30.7604i	−0.784771	+	1.08014i	0.209968	+	0.977708i	$0.432664\pi$
$811$	−22.3488	+	30.7604i	−0.784771	+	1.08014i	−0.994740	+	0.102437i	$0.967336\pi$
$812$	−4.13598	−	10.0700i	−0.145144	−	0.353389i
$813$	0.782978	+	1.07768i	0.0274602	+	0.0377958i
$814$	36.7715	−	39.6603i	1.28884	−	1.39009i
$815$		0			0
$816$	0.648088	+	4.25614i	0.0226876	+	0.148995i
$817$	10.1319	−	31.1827i	0.354469	−	1.09094i
$818$	−1.77164	+	14.7796i	−0.0619441	+	0.516755i
$819$	−8.27997	−	2.69033i	−0.289326	−	0.0940076i
$820$		0			0
$821$	7.25976	−	2.35884i	0.253367	−	0.0823240i	−0.179580	−	0.983743i	$-0.557474\pi$
$821$	7.25976	−	2.35884i	0.253367	−	0.0823240i	0.432947	+	0.901419i	$0.357474\pi$
$822$	0.158150	+	0.801322i	0.00551612	+	0.0279493i
$823$	−18.1266	−	13.1698i	−0.631855	−	0.459069i	0.225188	−	0.974315i	$-0.427700\pi$
$823$	−18.1266	−	13.1698i	−0.631855	−	0.459069i	−0.857042	+	0.515246i	$0.827700\pi$
$824$	−8.90353	+	23.8053i	−0.310169	+	0.829298i
$825$		0			0
$826$	20.7891	+	2.49201i	0.723345	+	0.0867083i
$827$	−18.6693	+	25.6961i	−0.649196	+	0.893542i	−0.999064	−	0.0432571i	$-0.986227\pi$
$827$	−18.6693	+	25.6961i	−0.649196	+	0.893542i	0.349868	+	0.936799i	$0.386227\pi$
$828$	2.55295	+	33.7249i	0.0887212	+	1.17202i
$829$	−1.36860	+	0.444686i	−0.0475335	+	0.0154446i	−0.332687	−	0.943037i	$-0.607955\pi$
$829$	−1.36860	+	0.444686i	−0.0475335	+	0.0154446i	0.285154	+	0.958482i	$0.407955\pi$
$830$		0			0
$831$	−0.203980	+	0.627786i	−0.00707599	+	0.0217777i
$832$	9.75075	−	11.2118i	0.338046	−	0.388699i
$833$	6.05317	−	18.6297i	0.209730	−	0.645482i
$834$	−3.33231	−	5.97115i	−0.115388	−	0.206764i
$835$		0			0
$836$	18.7280	+	22.0607i	0.647723	+	0.762986i
$837$	1.04670	+	1.44066i	0.0361793	+	0.0497965i
$838$	29.5095	−	16.4683i	1.01939	−	0.568888i
$839$	24.7233	+	17.9626i	0.853544	+	0.620136i	0.926121	−	0.377227i	$-0.123122\pi$
$839$	24.7233	+	17.9626i	0.853544	+	0.620136i	−0.0725766	+	0.997363i	$0.523122\pi$
$840$		0			0
$841$	−14.0319	+	10.1948i	−0.483859	+	0.351544i
$842$	19.0957	−	41.2598i	0.658082	−	1.42191i
$843$		−	1.98512i		−	0.0683711i
$844$	−1.75058	−	1.07996i	−0.0602574	−	0.0371736i
$845$		0			0
$846$	3.82119	−	0.754155i	0.131375	−	0.0259284i
$847$	6.09949	+	18.7723i	0.209581	+	0.645024i
$848$	−19.2551	+	9.66662i	−0.661223	+	0.331953i
$849$	5.15814			0.177027
$850$		0			0
$851$		−	45.4930i		−	1.55948i
$852$	−5.40633	+	4.58960i	−0.185218	+	0.157237i
$853$	12.0902	−	3.92833i	0.413960	−	0.134504i	−0.0946304	−	0.995512i	$-0.530167\pi$
$853$	12.0902	−	3.92833i	0.413960	−	0.134504i	0.508590	+	0.861009i	$0.330167\pi$
$854$	−2.27562	−	11.5302i	−0.0778701	−	0.394556i
$855$		0			0
$856$	−2.78424	+	3.49945i	−0.0951633	+	0.119609i
$857$	−36.9869			−1.26345			−0.631724	−	0.775194i	$-0.717652\pi$
$857$	−36.9869			−1.26345			−0.631724	+	0.775194i	$0.717652\pi$
$858$	−1.30669	+	2.82334i	−0.0446097	+	0.0963872i
$859$	−16.1605	−	22.2430i	−0.551388	−	0.758921i	0.438811	−	0.898579i	$-0.355400\pi$
$859$	−16.1605	−	22.2430i	−0.551388	−	0.758921i	−0.990200	+	0.139658i	$0.955400\pi$
$860$		0			0
$861$	−1.97278	+	2.71530i	−0.0672323	+	0.0925373i
$862$	−2.54608	−	4.56230i	−0.0867197	−	0.155393i
$863$	−37.1971	+	27.0253i	−1.26620	+	0.919951i	−0.999045	−	0.0437013i	$-0.986085\pi$
$863$	−37.1971	+	27.0253i	−1.26620	+	0.919951i	−0.267159	+	0.963652i	$0.586085\pi$
$864$	2.79110	+	7.74305i	0.0949553	+	0.263424i
$865$		0			0
$866$	−6.90192	−	12.3675i	−0.234537	−	0.420266i
$867$	0.537409	+	0.174615i	0.0182514	+	0.00593023i
$868$	−3.79203	−	0.922365i	−0.128710	−	0.0313071i
$869$	−48.6576	−	15.8098i	−1.65060	−	0.536311i
$870$		0			0
$871$	1.40694	+	4.33011i	0.0476722	+	0.146720i
$872$	−0.447804	+	10.2297i	−0.0151646	+	0.346423i
$873$	−34.0389	−	24.7307i	−1.15204	−	0.837008i
$874$	24.1684	+	2.89710i	0.817508	+	0.0979958i
$875$		0			0
$876$	0.372326	−	1.53071i	0.0125797	−	0.0517178i
$877$	10.4421	−	14.3723i	0.352604	−	0.485317i	−0.595466	−	0.803381i	$-0.703032\pi$
$877$	10.4421	−	14.3723i	0.352604	−	0.485317i	0.948069	+	0.318063i	$0.103032\pi$
$878$	−39.9559	+	7.88576i	−1.34845	+	0.266132i
$879$	−1.99596	−	6.14292i	−0.0673220	−	0.207196i
$880$		0			0
$881$	−1.85556	+	5.71084i	−0.0625155	+	0.192403i	−0.977436	−	0.211231i	$-0.932253\pi$
$881$	−1.85556	+	5.71084i	−0.0625155	+	0.192403i	0.914921	+	0.403634i	$0.132253\pi$
$882$	2.20609	−	18.4038i	0.0742830	−	0.619690i
$883$	−23.6121	−	7.67204i	−0.794611	−	0.258185i	−0.116545	−	0.993185i	$-0.537182\pi$
$883$	−23.6121	−	7.67204i	−0.794611	−	0.258185i	−0.678066	+	0.735001i	$0.737182\pi$
$884$	−6.20118	−	15.0983i	−0.208568	−	0.507810i
$885$		0			0
$886$	−22.5778	−	20.9333i	−0.758517	−	0.703268i
$887$	6.32030	−	4.59197i	0.212215	−	0.154183i	−0.476600	−	0.879120i	$-0.658131\pi$
$887$	6.32030	−	4.59197i	0.212215	−	0.154183i	0.688815	+	0.724937i	$0.258131\pi$
$888$	−1.46377	−	5.28052i	−0.0491210	−	0.177203i
$889$	13.0771	+	9.50107i	0.438592	+	0.318655i
$890$		0			0
$891$	24.0546	+	33.1083i	0.805858	+	1.10917i
$892$	21.3827	−	34.6608i	0.715947	−	1.16053i
$893$		−	2.80317i		−	0.0938046i
$894$	3.94509	+	1.82586i	0.131944	+	0.0610658i
$895$		0			0
$896$	−15.6452	−	8.97768i	−0.522669	−	0.299923i
$897$	0.808660	+	2.48880i	0.0270004	+	0.0830986i
$898$	2.27368	−	2.45230i	0.0758737	−	0.0818344i
$899$		−	4.17837i		−	0.139356i
$900$		0			0
$901$			23.6673i			0.788473i
$902$	−43.0948	−	39.9559i	−1.43490	−	1.33038i
$903$	−1.32231	−	4.06966i	−0.0440039	−	0.135430i
$904$	57.0687	+	2.49817i	1.89808	+	0.0830878i
$905$		0			0
$906$	−1.47631	+	3.18983i	−0.0490471	+	0.105975i
$907$		−	33.1767i		−	1.10162i	−0.834632	−	0.550808i	$-0.814320\pi$
$907$		−	33.1767i		−	1.10162i	0.834632	−	0.550808i	$-0.185680\pi$
$908$	−2.08536	−	1.28649i	−0.0692051	−	0.0426936i
$909$	−16.1673	−	22.2524i	−0.536235	−	0.738064i
$910$		0			0
$911$	3.00382	+	2.18240i	0.0995209	+	0.0723062i	0.636433	−	0.771332i	$-0.280409\pi$
$911$	3.00382	+	2.18240i	0.0995209	+	0.0723062i	−0.536912	+	0.843638i	$0.680409\pi$
$912$	2.89852	−	0.441361i	0.0959797	−	0.0146149i
$913$	−6.83251	+	4.96411i	−0.226123	+	0.164288i
$914$	10.9525	−	11.8130i	0.362278	−	0.390739i
$915$		0			0
$916$	0.741107	+	1.80440i	0.0244869	+	0.0596192i
$917$	−9.28255	−	3.01608i	−0.306537	−	0.0995998i
$918$	8.97712	+	1.07610i	0.296289	+	0.0355165i
$919$	−10.6715	+	32.8435i	−0.352020	+	1.08341i	0.605697	+	0.795695i	$0.292894\pi$
$919$	−10.6715	+	32.8435i	−0.352020	+	1.08341i	−0.957717	+	0.287711i	$0.907106\pi$
$920$		0			0
$921$	−1.43440	−	4.41464i	−0.0472652	−	0.145467i
$922$	−10.0541	−	50.9423i	−0.331113	−	1.67770i
$923$	15.8036	−	21.7518i	0.520181	−	0.715968i
$924$	3.66973	+	0.892616i	0.120725	+	0.0293649i
$925$		0			0
$926$	−2.57885	+	21.5135i	−0.0847462	+	0.706977i
$927$	21.3730	+	15.5284i	0.701981	+	0.510019i
$928$	5.38078	−	18.5479i	0.176633	−	0.608866i
$929$	−0.229893	−	0.707539i	−0.00754256	−	0.0232136i	0.947214	−	0.320601i	$-0.103885\pi$
$929$	−0.229893	−	0.707539i	−0.00754256	−	0.0232136i	−0.954757	+	0.297387i	$0.903885\pi$
$930$		0			0
$931$	−12.6872	−	4.12233i	−0.415807	−	0.135104i
$932$	4.91505	+	1.19553i	0.160998	+	0.0391607i
$933$	−3.08718	−	1.00309i	−0.101070	−	0.0328395i
$934$	37.3020	−	20.8170i	1.22056	−	0.681154i
$935$		0			0
$936$	−8.52312	−	12.8802i	−0.278587	−	0.421003i
$937$	19.8502	−	14.4220i	0.648479	−	0.471148i	−0.214274	−	0.976774i	$-0.568738\pi$
$937$	19.8502	−	14.4220i	0.648479	−	0.471148i	0.862753	+	0.505626i	$0.168738\pi$
$938$	4.82642	−	2.69347i	0.157588	−	0.0879450i
$939$	2.47610	−	3.40806i	0.0808046	−	0.111218i
$940$		0			0
$941$	6.85654	+	9.43722i	0.223517	+	0.307645i	0.906017	−	0.423241i	$-0.139108\pi$
$941$	6.85654	+	9.43722i	0.223517	+	0.307645i	−0.682500	+	0.730885i	$0.739108\pi$
$942$	−2.42389	−	1.12182i	−0.0789745	−	0.0365508i
$943$	−49.4326			−1.60975
$944$	26.1079	+	26.4214i	0.849739	+	0.859944i
$945$		0			0
$946$	73.5075	−	14.5076i	2.38994	−	0.471681i
$947$	47.0221	−	15.2784i	1.52801	−	0.496481i	0.579973	−	0.814635i	$-0.303063\pi$
$947$	47.0221	−	15.2784i	1.52801	−	0.496481i	0.948039	+	0.318154i	$0.103063\pi$
$948$	−3.95164	+	3.35467i	−0.128343	+	0.108955i
$949$			5.97252i			0.193876i
$950$		0			0
$951$	−0.568657			−0.0184400
$952$	−16.5243	+	10.9345i	−0.535557	+	0.354390i
$953$	11.6368	+	35.8144i	0.376953	+	1.16014i	0.942151	+	0.335187i	$0.108800\pi$
$953$	11.6368	+	35.8144i	0.376953	+	1.16014i	−0.565198	+	0.824955i	$0.691200\pi$
$954$	4.33631	+	21.9714i	0.140393	+	0.711351i
$955$		0			0
$956$	20.7324	−	33.6066i	0.670534	−	1.08692i
$957$			4.04361i			0.130711i
$958$	43.1646	+	19.9773i	1.39459	+	0.645438i
$959$	−3.04126	+	2.20961i	−0.0982075	+	0.0713519i
$960$		0			0
$961$	23.8677	+	17.3409i	0.769926	+	0.559384i
$962$	10.1239	+	18.1410i	0.326409	+	0.584890i
$963$	2.73222	+	3.76058i	0.0880446	+	0.121183i
$964$	−20.6397	−	24.3126i	−0.664761	−	0.783055i
$965$		0			0
$966$	2.77407	−	1.54812i	0.0892541	−	0.0498099i
$967$	−1.17113	+	3.60438i	−0.0376611	+	0.115909i	−0.968120	−	0.250488i	$-0.919409\pi$
$967$	−1.17113	+	3.60438i	−0.0376611	+	0.115909i	0.930459	+	0.366397i	$0.119409\pi$
$968$	−12.2668	+	32.7976i	−0.394268	+	1.05415i
$969$	0.995250	−	3.06306i	0.0319720	−	0.0983998i
$970$		0			0
$971$	−50.3226	+	16.3508i	−1.61493	+	0.524722i	−0.970738	−	0.240143i	$-0.922806\pi$
$971$	−50.3226	+	16.3508i	−1.61493	+	0.524722i	−0.644191	+	0.764865i	$0.722806\pi$
$972$	12.8396	−	0.971949i	0.411831	−	0.0311753i
$973$	18.4987	−	25.4613i	0.593043	−	0.816253i
$974$	−6.00387	+	50.0860i	−0.192376	+	1.60486i
$975$		0			0
$976$	9.57621	−	18.5202i	0.306527	−	0.592818i
$977$	−32.5072	−	23.6179i	−1.04000	−	0.755603i	−0.0697129	−	0.997567i	$-0.522208\pi$
$977$	−32.5072	−	23.6179i	−1.04000	−	0.755603i	−0.970285	+	0.241964i	$0.922208\pi$
$978$	−3.21390	+	0.634300i	−0.102769	+	0.0202827i
$979$	52.2650	−	16.9819i	1.67040	−	0.542745i
$980$		0			0
$981$	10.1225	+	3.28901i	0.323187	+	0.105010i
$982$	46.3249	+	5.55302i	1.47829	+	0.177204i
$983$	−2.61133	+	8.03684i	−0.0832885	+	0.256336i	−0.984025	−	0.178030i	$-0.943027\pi$
$983$	−2.61133	+	8.03684i	−0.0832885	+	0.256336i	0.900737	+	0.434366i	$0.143027\pi$
$984$	−5.73781	+	1.59053i	−0.182915	+	0.0507043i
$985$		0			0
$986$	−15.5570	−	14.4238i	−0.495435	−	0.459348i
$987$	−0.215037	−	0.295974i	−0.00684472	−	0.00942094i
$988$	−10.2822	+	4.22313i	−0.327122	+	0.134356i
$989$	37.0445	−	50.9874i	1.17795	−	1.62130i
$990$		0			0
$991$	19.3979	−	14.0934i	0.616193	−	0.447691i	−0.235397	−	0.971899i	$-0.575639\pi$
$991$	19.3979	−	14.0934i	0.616193	−	0.447691i	0.851590	+	0.524209i	$0.175639\pi$
$992$	−4.24550	−	5.46883i	−0.134795	−	0.173636i
$993$	−2.79980			−0.0888490
$994$	−29.6210	−	13.7091i	−0.939520	−	0.434826i
$995$		0			0
$996$	0.0645888	+	0.853229i	0.00204658	+	0.0270356i
$997$	8.67368	−	2.81825i	0.274698	−	0.0892548i	−0.168428	−	0.985714i	$-0.553869\pi$
$997$	8.67368	−	2.81825i	0.274698	−	0.0892548i	0.443127	+	0.896459i	$0.353869\pi$
$998$	36.0830	+	33.4548i	1.14219	+	1.05899i
$999$	−11.5078			−0.364092

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.t.b.701.41		224
5.2	odd	4		200.2.o.a.109.22	yes	112
5.3	odd	4		1000.2.o.a.549.7		112
5.4	even	2	inner	1000.2.t.b.701.16		224
8.5	even	2	inner	1000.2.t.b.701.20		224
20.7	even	4		800.2.be.a.209.14		112
25.2	odd	20		1000.2.o.a.949.24		112
25.11	even	5	inner	1000.2.t.b.301.20		224
25.14	even	10	inner	1000.2.t.b.301.37		224
25.23	odd	20		200.2.o.a.189.5	yes	112
40.13	odd	4		1000.2.o.a.549.24		112
40.27	even	4		800.2.be.a.209.15		112
40.29	even	2	inner	1000.2.t.b.701.37		224
40.37	odd	4		200.2.o.a.109.5	✓	112
100.23	even	20		800.2.be.a.689.15		112
200.61	even	10	inner	1000.2.t.b.301.41		224
200.77	odd	20		1000.2.o.a.949.7		112
200.123	even	20		800.2.be.a.689.14		112
200.173	odd	20		200.2.o.a.189.22	yes	112
200.189	even	10	inner	1000.2.t.b.301.16		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.109.5	✓	112	40.37	odd	4
200.2.o.a.109.22	yes	112	5.2	odd	4
200.2.o.a.189.5	yes	112	25.23	odd	20
200.2.o.a.189.22	yes	112	200.173	odd	20
800.2.be.a.209.14		112	20.7	even	4
800.2.be.a.209.15		112	40.27	even	4
800.2.be.a.689.14		112	200.123	even	20
800.2.be.a.689.15		112	100.23	even	20
1000.2.o.a.549.7		112	5.3	odd	4
1000.2.o.a.549.24		112	40.13	odd	4
1000.2.o.a.949.7		112	200.77	odd	20
1000.2.o.a.949.24		112	25.2	odd	20
1000.2.t.b.301.16		224	200.189	even	10	inner
1000.2.t.b.301.20		224	25.11	even	5	inner
1000.2.t.b.301.37		224	25.14	even	10	inner
1000.2.t.b.301.41		224	200.61	even	10	inner
1000.2.t.b.701.16		224	5.4	even	2	inner
1000.2.t.b.701.20		224	8.5	even	2	inner
1000.2.t.b.701.37		224	40.29	even	2	inner
1000.2.t.b.701.41		224	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.t (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.961518 - 1.03706i) q^{2} +(-0.232961 + 0.0756938i) q^{3} +(-0.150967 - 1.99429i) q^{4} +(-0.145498 + 0.314375i) q^{6} -1.59435 q^{7} +(-2.21335 - 1.76099i) q^{8} +(-2.37851 + 1.72809i) q^{9} +(-2.84212 + 3.91185i) q^{11} +(0.186125 + 0.453166i) q^{12} +(-1.09172 - 1.50262i) q^{13} +(-1.53300 + 1.65343i) q^{14} +(-3.95442 + 0.602144i) q^{16} +(-1.35781 + 4.17890i) q^{17} +(-0.494857 + 4.12823i) q^{18} +(2.84592 + 0.924695i) q^{19} +(0.371422 - 0.120682i) q^{21} +(1.32405 + 6.70875i) q^{22} +(4.65342 + 3.38091i) q^{23} +(0.648921 + 0.242706i) q^{24} +(-2.60801 - 0.312625i) q^{26} +(0.855230 - 1.17712i) q^{27} +(0.240694 + 3.17961i) q^{28} +(-3.24693 + 1.05499i) q^{29} +(-0.378200 + 1.16398i) q^{31} +(-3.17779 + 4.67992i) q^{32} +(0.366003 - 1.12644i) q^{33} +(3.02820 + 5.42621i) q^{34} +(3.80539 + 4.48256i) q^{36} +(-4.64888 - 6.39864i) q^{37} +(3.69536 - 2.06226i) q^{38} +(0.368067 + 0.267416i) q^{39} +(-6.95275 + 5.05147i) q^{41} +(0.231975 - 0.501224i) q^{42} -10.9570i q^{43} +(8.23044 + 5.07747i) q^{44} +(7.98053 - 1.57505i) q^{46} +(-0.289478 - 0.890923i) q^{47} +(0.875648 - 0.439601i) q^{48} -4.45804 q^{49} -1.07630i q^{51} +(-2.83185 + 2.40405i) q^{52} +(5.12271 - 1.66447i) q^{53} +(-0.398422 - 2.01874i) q^{54} +(3.52886 + 2.80763i) q^{56} -0.732983 q^{57} +(-2.02790 + 4.38164i) q^{58} +(-5.45825 - 7.51263i) q^{59} +(-3.06376 + 4.21690i) q^{61} +(0.843466 + 1.51140i) q^{62} +(3.79218 - 2.75518i) q^{63} +(1.79784 + 7.79537i) q^{64} +(-0.816262 - 1.46266i) q^{66} +(-2.33135 - 0.757501i) q^{67} +(8.53894 + 2.07699i) q^{68} +(-1.33998 - 0.435386i) q^{69} +(4.47330 + 13.7674i) q^{71} +(8.30762 + 0.363664i) q^{72} +(-2.60150 - 1.89010i) q^{73} +(-11.1057 - 1.33126i) q^{74} +(1.41448 - 5.81520i) q^{76} +(4.53134 - 6.23686i) q^{77} +(0.631228 - 0.124580i) q^{78} +(3.26966 + 10.0630i) q^{79} +(2.61539 - 8.04936i) q^{81} +(-1.44654 + 12.0675i) q^{82} +(1.66114 + 0.539736i) q^{83} +(-0.296749 - 0.722506i) q^{84} +(-11.3630 - 10.5353i) q^{86} +(0.676554 - 0.491545i) q^{87} +(13.1793 - 3.65334i) q^{88} +(-9.19471 - 6.68035i) q^{89} +(1.74058 + 2.39570i) q^{91} +(6.04001 - 9.79069i) q^{92} -0.299790i q^{93} +(-1.20227 - 0.556433i) q^{94} +(0.386061 - 1.33078i) q^{96} +(4.42235 + 13.6106i) q^{97} +(-4.28649 + 4.62324i) q^{98} -14.2158i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9} + 6 q^{14} - 30 q^{16} + 32 q^{24} - 28 q^{26} - 36 q^{31} - 18 q^{34} + 82 q^{36} + 20 q^{39} - 20 q^{41} + 64 q^{44} + 26 q^{46} + 160 q^{49} - 86 q^{54} + 72 q^{56}+ \cdots + 92 q^{96}+O(q^{100}) \) 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9 + 6 * q^14 - 30 * q^16 + 32 * q^24 - 28 * q^26 - 36 * q^31 - 18 * q^34 + 82 * q^36 + 20 * q^39 - 20 * q^41 + 64 * q^44 + 26 * q^46 + 160 * q^49 - 86 * q^54 + 72 * q^56 + 72 * q^64 + 80 * q^66 + 44 * q^71 - 8 * q^74 - 72 * q^76 - 28 * q^79 - 12 * q^81 - 156 * q^84 - 118 * q^86 - 48 * q^89 - 90 * q^94 + 92 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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