LMFDB - Embedded newform 847.2.i.b.241.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [847,2,Mod(241,847)] 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("847.241"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(847, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.i (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48] 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			241.18
Character	$\chi$	$=$	847.241
Dual form			847.2.i.b.362.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.21617 - 0.702153i) q^{2} +(0.177127 + 0.102264i) q^{3} +(-0.0139610 + 0.0241811i) q^{4} +(-1.31641 + 0.760032i) q^{5} +0.287221 q^{6} +(-1.53513 - 2.15485i) q^{7} +2.84782i q^{8} +(-1.47908 - 2.56185i) q^{9} +(-1.06732 + 1.84865i) q^{10} +(-0.00494574 + 0.00285542i) q^{12} -6.30332 q^{13} +(-3.38001 - 1.54275i) q^{14} -0.310897 q^{15} +(1.97169 + 3.41506i) q^{16} +(1.37058 - 2.37392i) q^{17} +(-3.59762 - 2.07709i) q^{18} +(-3.29895 - 5.71394i) q^{19} -0.0424432i q^{20} +(-0.0515495 - 0.538671i) q^{21} +(0.513095 + 0.888707i) q^{23} +(-0.291231 + 0.504427i) q^{24} +(-1.34470 + 2.32909i) q^{25} +(-7.66588 + 4.42590i) q^{26} -1.21862i q^{27} +(0.0735386 - 0.00703745i) q^{28} -3.58201i q^{29} +(-0.378102 + 0.218297i) q^{30} +(-0.481097 - 0.277762i) q^{31} +(-0.136779 - 0.0789694i) q^{32} -3.84944i q^{34} +(3.65862 + 1.66992i) q^{35} +0.0825978 q^{36} +(-2.17557 - 3.76821i) q^{37} +(-8.02413 - 4.63273i) q^{38} +(-1.11649 - 0.644605i) q^{39} +(-2.16444 - 3.74892i) q^{40} +7.29166 q^{41} +(-0.440923 - 0.618918i) q^{42} +9.51832i q^{43} +(3.89418 + 2.24830i) q^{45} +(1.24802 + 0.720543i) q^{46} +(-6.35725 + 3.67036i) q^{47} +0.806534i q^{48} +(-2.28674 + 6.61595i) q^{49} +3.77675i q^{50} +(0.485535 - 0.280324i) q^{51} +(0.0880005 - 0.152421i) q^{52} +(-1.50207 + 2.60165i) q^{53} +(-0.855656 - 1.48204i) q^{54} +(6.13663 - 4.37179i) q^{56} -1.34946i q^{57} +(-2.51512 - 4.35631i) q^{58} +(-0.625169 - 0.360942i) q^{59} +(0.00434043 - 0.00751784i) q^{60} +(-3.93250 - 6.81128i) q^{61} -0.780125 q^{62} +(-3.24980 + 7.11998i) q^{63} -8.10855 q^{64} +(8.29778 - 4.79073i) q^{65} +(-2.16696 + 3.75328i) q^{67} +(0.0382693 + 0.0662845i) q^{68} +0.209886i q^{69} +(5.62204 - 0.538014i) q^{70} +4.78880 q^{71} +(7.29570 - 4.21217i) q^{72} +(4.87390 - 8.44184i) q^{73} +(-5.29172 - 3.05517i) q^{74} +(-0.476366 + 0.275030i) q^{75} +0.184226 q^{76} -1.81045 q^{78} +(2.38913 - 1.37937i) q^{79} +(-5.19112 - 2.99709i) q^{80} +(-4.31263 + 7.46970i) q^{81} +(8.86787 - 5.11987i) q^{82} -7.23743 q^{83} +(0.0137454 + 0.00627385i) q^{84} +4.16675i q^{85} +(6.68332 + 11.5758i) q^{86} +(0.366312 - 0.634471i) q^{87} +(0.985593 - 0.569032i) q^{89} +6.31462 q^{90} +(9.67643 + 13.5827i) q^{91} -0.0286532 q^{92} +(-0.0568103 - 0.0983983i) q^{93} +(-5.15431 + 8.92753i) q^{94} +(8.68556 + 5.01461i) q^{95} +(-0.0161515 - 0.0279752i) q^{96} +8.02487i q^{97} +(1.86437 + 9.65173i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{3} + 16 q^{4} + 14 q^{9} - 12 q^{12} + 32 q^{14} + 20 q^{15} + 8 q^{16} + 10 q^{23} - 24 q^{25} - 78 q^{26} - 6 q^{31} + 72 q^{36} - 36 q^{37} - 102 q^{38} + 44 q^{42} - 84 q^{45} - 12 q^{47}+ \cdots + 68 q^{93}+O(q^{100}) $ 48 * q + 6 * q^3 + 16 * q^4 + 14 * q^9 - 12 * q^12 + 32 * q^14 + 20 * q^15 + 8 * q^16 + 10 * q^23 - 24 * q^25 - 78 * q^26 - 6 * q^31 + 72 * q^36 - 36 * q^37 - 102 * q^38 + 44 * q^42 - 84 * q^45 - 12 * q^47 - 46 * q^49 + 12 * q^53 - 8 * q^56 - 74 * q^58 + 132 * q^59 + 20 * q^60 + 12 * q^64 + 44 * q^67 + 38 * q^70 - 100 * q^71 - 42 * q^75 + 92 * q^78 + 90 * q^80 - 4 * q^81 + 66 * q^82 - 22 * q^86 + 6 * q^89 + 58 * q^91 + 80 * q^92 + 68 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.21617	−	0.702153i	0.859959	−	0.496497i	−0.00403964	−	0.999992i	$-0.501286\pi$
$2$	1.21617	−	0.702153i	0.859959	−	0.496497i	0.863999	+	0.503494i	$0.167953\pi$
$3$	0.177127	+	0.102264i	0.102264	+	0.0590424i	0.550260	−	0.834993i	$-0.314529\pi$
$3$	0.177127	+	0.102264i	0.102264	+	0.0590424i	−0.447996	+	0.894036i	$0.647862\pi$
$4$	−0.0139610	+	0.0241811i	−0.00698049	+	0.0120906i
$5$	−1.31641	+	0.760032i	−0.588719	+	0.339897i	−0.764591	−	0.644516i	$-0.777059\pi$
$5$	−1.31641	+	0.760032i	−0.588719	+	0.339897i	0.175872	+	0.984413i	$0.443725\pi$
$6$	0.287221			0.117258
$7$	−1.53513	−	2.15485i	−0.580226	−	0.814456i
$7$	−1.53513	−	2.15485i	−0.580226	−	0.814456i
$8$			2.84782i			1.00686i
$9$	−1.47908	−	2.56185i	−0.493028	−	0.853950i
$10$	−1.06732	+	1.84865i	−0.337516	+	0.584595i
$11$		0			0
$11$		0			0
$12$	−0.00494574	+	0.00285542i	−0.00142771	+	0.000824289i
$13$	−6.30332			−1.74823			−0.874113	−	0.485722i	$-0.838557\pi$
$13$	−6.30332			−1.74823			−0.874113	+	0.485722i	$0.838557\pi$
$14$	−3.38001	−	1.54275i	−0.903345	−	0.412318i
$15$	−0.310897			−0.0802733
$16$	1.97169	+	3.41506i	0.492922	+	0.853766i
$17$	1.37058	−	2.37392i	0.332415	−	0.575760i	−0.650570	−	0.759447i	$-0.725470\pi$
$17$	1.37058	−	2.37392i	0.332415	−	0.575760i	0.982985	+	0.183687i	$0.0588032\pi$
$18$	−3.59762	−	2.07709i	−0.847968	−	0.489574i
$19$	−3.29895	−	5.71394i	−0.756830	−	1.31087i	−0.944459	−	0.328628i	$-0.893414\pi$
$19$	−3.29895	−	5.71394i	−0.756830	−	1.31087i	0.187629	−	0.982240i	$-0.439920\pi$
$20$		−	0.0424432i		−	0.00949058i
$21$	−0.0515495	−	0.538671i	−0.0112490	−	0.117548i
$22$		0			0
$23$	0.513095	+	0.888707i	0.106988	+	0.185308i	0.914549	−	0.404476i	$-0.132546\pi$
$23$	0.513095	+	0.888707i	0.106988	+	0.185308i	−0.807561	+	0.589784i	$0.799213\pi$
$24$	−0.291231	+	0.504427i	−0.0594473	+	0.102966i
$25$	−1.34470	+	2.32909i	−0.268940	+	0.465818i
$26$	−7.66588	+	4.42590i	−1.50340	+	0.867990i
$27$		−	1.21862i		−	0.234523i
$28$	0.0735386	−	0.00703745i	0.0138975	−	0.00132995i
$29$		−	3.58201i		−	0.665162i	−0.943075	−	0.332581i	$-0.892081\pi$
$29$		−	3.58201i		−	0.665162i	0.943075	−	0.332581i	$-0.107919\pi$
$30$	−0.378102	+	0.218297i	−0.0690317	+	0.0398555i
$31$	−0.481097	−	0.277762i	−0.0864076	−	0.0498875i	0.456174	−	0.889891i	$-0.349220\pi$
$31$	−0.481097	−	0.277762i	−0.0864076	−	0.0498875i	−0.542581	+	0.840003i	$0.682553\pi$
$32$	−0.136779	−	0.0789694i	−0.0241793	−	0.0139599i
$33$		0			0
$34$		−	3.84944i		−	0.660173i
$35$	3.65862	+	1.66992i	0.618420	+	0.282268i
$36$	0.0825978			0.0137663
$37$	−2.17557	−	3.76821i	−0.357662	−	0.619489i	0.629908	−	0.776670i	$-0.283093\pi$
$37$	−2.17557	−	3.76821i	−0.357662	−	0.619489i	−0.987570	+	0.157181i	$0.949759\pi$
$38$	−8.02413	−	4.63273i	−1.30169	−	0.751528i
$39$	−1.11649	−	0.644605i	−0.178781	−	0.103219i
$40$	−2.16444	−	3.74892i	−0.342228	−	0.592756i
$41$	7.29166			1.13877			0.569383	−	0.822072i	$-0.307182\pi$
$41$	7.29166			1.13877			0.569383	+	0.822072i	$0.307182\pi$
$42$	−0.440923	−	0.618918i	−0.0680358	−	0.0955011i
$43$			9.51832i			1.45153i	0.687943	+	0.725765i	$0.258514\pi$
$43$			9.51832i			1.45153i	−0.687943	+	0.725765i	$0.741486\pi$
$44$		0			0
$45$	3.89418	+	2.24830i	0.580509	+	0.335157i
$46$	1.24802	+	0.720543i	0.184010	+	0.106238i
$47$	−6.35725	+	3.67036i	−0.927301	+	0.535377i	−0.885957	−	0.463768i	$-0.846497\pi$
$47$	−6.35725	+	3.67036i	−0.927301	+	0.535377i	−0.0413437	+	0.999145i	$0.513164\pi$
$48$			0.806534i			0.116413i
$49$	−2.28674	+	6.61595i	−0.326676	+	0.945136i
$50$			3.77675i			0.534113i
$51$	0.485535	−	0.280324i	0.0679885	−	0.0392532i
$52$	0.0880005	−	0.152421i	0.0122035	−	0.0211370i
$53$	−1.50207	+	2.60165i	−0.206325	+	0.357365i	−0.950554	−	0.310559i	$-0.899484\pi$
$53$	−1.50207	+	2.60165i	−0.206325	+	0.357365i	0.744229	+	0.667924i	$0.232817\pi$
$54$	−0.855656	−	1.48204i	−0.116440	−	0.201680i
$55$		0			0
$56$	6.13663	−	4.37179i	0.820041	−	0.584205i
$57$		−	1.34946i		−	0.178740i
$58$	−2.51512	−	4.35631i	−0.330251	−	0.572012i
$59$	−0.625169	−	0.360942i	−0.0813901	−	0.0469906i	0.458753	−	0.888564i	$-0.348296\pi$
$59$	−0.625169	−	0.360942i	−0.0813901	−	0.0469906i	−0.540143	+	0.841573i	$0.681630\pi$
$60$	0.00434043	−	0.00751784i	0.000560347	−	0.000970549i
$61$	−3.93250	−	6.81128i	−0.503505	−	0.872096i	−0.999992	−	0.00405149i	$-0.998710\pi$
$61$	−3.93250	−	6.81128i	−0.503505	−	0.872096i	0.496487	−	0.868044i	$-0.334623\pi$
$62$	−0.780125			−0.0990760
$63$	−3.24980	+	7.11998i	−0.409437	+	0.897033i
$64$	−8.10855			−1.01357
$65$	8.29778	−	4.79073i	1.02921	−	0.594217i
$66$		0			0
$67$	−2.16696	+	3.75328i	−0.264736	+	0.458536i	−0.967494	−	0.252892i	$-0.918618\pi$
$67$	−2.16696	+	3.75328i	−0.264736	+	0.458536i	0.702758	+	0.711429i	$0.251952\pi$
$68$	0.0382693	+	0.0662845i	0.00464084	+	0.00803817i
$69$			0.209886i			0.0252673i
$70$	5.62204	−	0.538014i	0.671962	−	0.0643050i
$71$	4.78880			0.568326			0.284163	−	0.958776i	$-0.408284\pi$
$71$	4.78880			0.568326			0.284163	+	0.958776i	$0.408284\pi$
$72$	7.29570	−	4.21217i	0.859806	−	0.496409i
$73$	4.87390	−	8.44184i	0.570447	−	0.988043i	−0.426073	−	0.904689i	$-0.640103\pi$
$73$	4.87390	−	8.44184i	0.570447	−	0.988043i	0.996520	−	0.0833540i	$-0.0265632\pi$
$74$	−5.29172	−	3.05517i	−0.615150	−	0.355157i
$75$	−0.476366	+	0.275030i	−0.0550060	+	0.0317578i
$76$	0.184226			0.0211322
$77$		0			0
$78$	−1.81045			−0.204993
$79$	2.38913	−	1.37937i	0.268799	−	0.155191i	−0.359543	−	0.933129i	$-0.617067\pi$
$79$	2.38913	−	1.37937i	0.268799	−	0.155191i	0.628342	+	0.777938i	$0.283734\pi$
$80$	−5.19112	−	2.99709i	−0.580385	−	0.335085i
$81$	−4.31263	+	7.46970i	−0.479181	+	0.829966i
$82$	8.86787	−	5.11987i	0.979292	−	0.565395i
$83$	−7.23743			−0.794411			−0.397206	−	0.917730i	$-0.630020\pi$
$83$	−7.23743			−0.794411			−0.397206	+	0.917730i	$0.630020\pi$
$84$	0.0137454	+	0.00627385i	0.00149974	+	0.000684534i
$85$			4.16675i			0.451947i
$86$	6.68332	+	11.5758i	0.720681	+	1.24826i
$87$	0.366312	−	0.634471i	0.0392727	−	0.0680224i
$88$		0			0
$89$	0.985593	−	0.569032i	0.104473	−	0.0603173i	−0.446853	−	0.894607i	$-0.647455\pi$
$89$	0.985593	−	0.569032i	0.104473	−	0.0603173i	0.551326	+	0.834290i	$0.314122\pi$
$90$	6.31462			0.665619
$91$	9.67643	+	13.5827i	1.01437	+	1.42385i
$92$	−0.0286532			−0.00298731
$93$	−0.0568103	−	0.0983983i	−0.00589095	−	0.0102034i
$94$	−5.15431	+	8.92753i	−0.531627	+	0.920805i
$95$	8.68556	+	5.01461i	0.891120	+	0.514488i
$96$	−0.0161515	−	0.0279752i	−0.00164846	−	0.00285521i
$97$			8.02487i			0.814802i	0.913249	+	0.407401i	$0.133565\pi$
$97$			8.02487i			0.814802i	−0.913249	+	0.407401i	$0.866435\pi$
$98$	1.86437	+	9.65173i	0.188329	+	0.974972i
$99$		0			0
$100$	−0.0375467	−	0.0650328i	−0.00375467	−	0.00650328i
$101$	−3.45164	+	5.97841i	−0.343451	+	0.594874i	−0.985071	−	0.172148i	$-0.944929\pi$
$101$	−3.45164	+	5.97841i	−0.343451	+	0.594874i	0.641620	+	0.767022i	$0.278263\pi$
$102$	0.393660	−	0.681840i	0.0389782	−	0.0675122i
$103$	1.92511	−	1.11146i	0.189686	−	0.109516i	−0.402149	−	0.915574i	$-0.631737\pi$
$103$	1.92511	−	1.11146i	0.189686	−	0.109516i	0.591836	+	0.806059i	$0.298403\pi$
$104$		−	17.9508i		−	1.76022i
$105$	0.477268	+	0.669936i	0.0465766	+	0.0653790i
$106$			4.21872i			0.409759i
$107$	14.0770	−	8.12736i	1.36087	−	0.785701i	0.371134	−	0.928579i	$-0.378969\pi$
$107$	14.0770	−	8.12736i	1.36087	−	0.785701i	0.989740	+	0.142878i	$0.0456355\pi$
$108$	0.0294675	+	0.0170131i	0.00283551	+	0.00163708i
$109$	−1.53706	−	0.887424i	−0.147224	−	0.0849998i	0.424579	−	0.905391i	$-0.360422\pi$
$109$	−1.53706	−	0.887424i	−0.147224	−	0.0849998i	−0.571802	+	0.820391i	$0.693756\pi$
$110$		0			0
$111$		−	0.889935i		−	0.0844689i
$112$	4.33214	−	9.49126i	0.409349	−	0.896840i
$113$	11.1709			1.05087			0.525433	−	0.850835i	$-0.323903\pi$
$113$	11.1709			1.05087			0.525433	+	0.850835i	$0.323903\pi$
$114$	−0.947527	−	1.64117i	−0.0887441	−	0.153709i
$115$	−1.35089	−	0.779938i	−0.125971	−	0.0727296i
$116$	0.0866169	+	0.0500083i	0.00804218	+	0.00464315i
$117$	9.32314	+	16.1482i	0.861925	+	1.49290i
$118$	−1.01375			−0.0933229
$119$	−7.21946	+	0.690884i	−0.661807	+	0.0633332i
$120$		−	0.885380i		−	0.0808238i
$121$		0			0
$122$	−9.56513	−	5.52243i	−0.865986	−	0.499978i
$123$	1.29155	+	0.745678i	0.116455	+	0.0672355i
$124$	0.0134332	−	0.00775565i	0.00120633	−	0.000696478i
$125$		−	11.6884i		−	1.04544i
$126$	1.04702	+	10.9409i	0.0932759	+	0.974696i
$127$		−	3.89250i		−	0.345404i	−0.984974	−	0.172702i	$-0.944750\pi$
$127$		−	3.89250i		−	0.345404i	0.984974	−	0.172702i	$-0.0552497\pi$
$128$	−9.58778	+	5.53551i	−0.847448	+	0.489274i
$129$	−0.973385	+	1.68595i	−0.0857018	+	0.148440i
$130$	6.72765	−	11.6526i	0.590054	−	1.02200i
$131$	−7.02508	−	12.1678i	−0.613784	−	1.06311i	−0.990596	−	0.136816i	$-0.956313\pi$
$131$	−7.02508	−	12.1678i	−0.613784	−	1.06311i	0.376812	−	0.926290i	$-0.377020\pi$
$132$		0			0
$133$	−7.24835	+	15.8804i	−0.628512	+	1.37700i
$134$			6.08615i			0.525763i
$135$	0.926188	+	1.60421i	0.0797136	+	0.138068i
$136$	6.76051	+	3.90318i	0.579709	+	0.334695i
$137$	−5.20849	+	9.02138i	−0.444992	+	0.770748i	−0.998052	−	0.0623933i	$-0.980127\pi$
$137$	−5.20849	+	9.02138i	−0.444992	+	0.770748i	0.553060	+	0.833141i	$0.313460\pi$
$138$	0.147372	+	0.255256i	0.0125451	+	0.0217288i
$139$	2.12376			0.180135			0.0900676	−	0.995936i	$-0.471292\pi$
$139$	2.12376			0.180135			0.0900676	+	0.995936i	$0.471292\pi$
$140$	−0.0914586	+	0.0651559i	−0.00772966	+	0.00550668i
$141$	−1.50139			−0.126440
$142$	5.82397	−	3.36247i	0.488737	−	0.282172i
$143$		0			0
$144$	5.83258	−	10.1023i	0.486049	−	0.841861i
$145$	2.72244	+	4.71541i	0.226086	+	0.391593i
$146$		−	13.6889i		−	1.13290i
$147$	−1.08162	+	0.938013i	−0.0892105	+	0.0773660i
$148$	0.121493			0.00998663
$149$	4.32561	−	2.49739i	0.354368	−	0.204594i	−0.312239	−	0.950003i	$-0.601079\pi$
$149$	4.32561	−	2.49739i	0.354368	−	0.204594i	0.666607	+	0.745409i	$0.267746\pi$
$150$	−0.386227	+	0.668965i	−0.0315353	+	0.0546207i
$151$	−1.94081	−	1.12053i	−0.157941	−	0.0911872i	0.418946	−	0.908011i	$-0.362399\pi$
$151$	−1.94081	−	1.12053i	−0.157941	−	0.0911872i	−0.576887	+	0.816824i	$0.695733\pi$
$152$	16.2723	−	9.39482i	1.31986	−	0.762020i
$153$	−8.10883			−0.655560
$154$		0			0
$155$	0.844431			0.0678264
$156$	0.0311746	−	0.0179986i	0.00249596	−	0.00144104i
$157$	−4.14623	−	2.39383i	−0.330905	−	0.191048i	0.325338	−	0.945598i	$-0.394522\pi$
$157$	−4.14623	−	2.39383i	−0.330905	−	0.191048i	−0.656243	+	0.754550i	$0.727855\pi$
$158$	1.93705	−	3.35508i	0.154104	−	0.266916i
$159$	−0.532113	+	0.307216i	−0.0421993	+	0.0243638i
$160$	0.240077			0.0189798
$161$	1.12736	−	2.46993i	0.0888483	−	0.194657i
$162$			12.1125i			0.951649i
$163$	−0.320992	−	0.555974i	−0.0251420	−	0.0435472i	0.853181	−	0.521616i	$-0.174670\pi$
$163$	−0.320992	−	0.555974i	−0.0251420	−	0.0435472i	−0.878323	+	0.478068i	$0.841337\pi$
$164$	−0.101799	+	0.176321i	−0.00794914	+	0.0137683i
$165$		0			0
$166$	−8.80191	+	5.08179i	−0.683161	+	0.394423i
$167$	−14.2545			−1.10305			−0.551525	−	0.834159i	$-0.685954\pi$
$167$	−14.2545			−1.10305			−0.551525	+	0.834159i	$0.685954\pi$
$168$	1.53404	−	0.146804i	0.118354	−	0.0113262i
$169$	26.7319			2.05630
$170$	2.92570	+	5.06746i	0.224391	+	0.388656i
$171$	−9.75883	+	16.9028i	−0.746277	+	1.29259i
$172$	−0.230164	−	0.132885i	−0.0175498	−	0.0101324i
$173$	−7.70880	−	13.3520i	−0.586089	−	1.01514i	−0.994739	−	0.102445i	$-0.967334\pi$
$173$	−7.70880	−	13.3520i	−0.586089	−	1.01514i	0.408650	−	0.912691i	$-0.366000\pi$
$174$		−	1.02883i		−	0.0779953i
$175$	7.08313	−	0.677838i	0.535434	−	0.0512397i
$176$		0			0
$177$	−0.0738230	−	0.127865i	−0.00554887	−	0.00961093i
$178$	0.799096	−	1.38407i	0.0598948	−	0.103741i
$179$	2.24931	−	3.89592i	0.168122	−	0.291195i	−0.769638	−	0.638481i	$-0.779563\pi$
$179$	2.24931	−	3.89592i	0.168122	−	0.291195i	0.937759	+	0.347286i	$0.112897\pi$
$180$	−0.108733	+	0.0627770i	−0.00810448	+	0.00467912i
$181$		−	6.22085i		−	0.462392i	−0.972907	−	0.231196i	$-0.925736\pi$
$181$		−	6.22085i		−	0.462392i	0.972907	−	0.231196i	$-0.0742639\pi$
$182$	21.3053	+	9.72446i	1.57925	+	0.720825i
$183$		−	1.60862i		−	0.118912i
$184$	−2.53088	+	1.46121i	−0.186579	+	0.107722i
$185$	5.72792	+	3.30701i	0.421125	+	0.243136i
$186$	−0.138181	−	0.0797791i	−0.0101319	−	0.00584968i
$187$		0			0
$188$		−	0.204967i		−	0.0149488i
$189$	−2.62593	+	1.87074i	−0.191009	+	0.136076i
$190$	14.0841			1.02177
$191$	−4.68141	−	8.10844i	−0.338735	−	0.586706i	0.645460	−	0.763794i	$-0.276666\pi$
$191$	−4.68141	−	8.10844i	−0.338735	−	0.586706i	−0.984195	+	0.177088i	$0.943332\pi$
$192$	−1.43624	−	0.829216i	−0.103652	−	0.0598435i
$193$	0.944070	+	0.545059i	0.0679556	+	0.0392342i	0.533593	−	0.845741i	$-0.320841\pi$
$193$	0.944070	+	0.545059i	0.0679556	+	0.0392342i	−0.465637	+	0.884976i	$0.654175\pi$
$194$	5.63469	+	9.75957i	0.404547	+	0.700696i
$195$	1.95968			0.140336
$196$	−0.128056	−	0.147661i	−0.00914686	−	0.0105472i
$197$		−	10.2948i		−	0.733475i	−0.930325	−	0.366737i	$-0.880475\pi$
$197$		−	10.2948i		−	0.733475i	0.930325	−	0.366737i	$-0.119525\pi$
$198$		0			0
$199$	−2.09410	−	1.20903i	−0.148447	−	0.0857058i	0.423937	−	0.905692i	$-0.360648\pi$
$199$	−2.09410	−	1.20903i	−0.148447	−	0.0857058i	−0.572384	+	0.819986i	$0.693981\pi$
$200$	−6.63285	−	3.82947i	−0.469013	−	0.270785i
$201$	−0.767654	+	0.443205i	−0.0541462	+	0.0312613i
$202$			9.69432i			0.682090i
$203$	−7.71868	+	5.49886i	−0.541745	+	0.385944i
$204$			0.0156544i			0.00109602i
$205$	−9.59885	+	5.54190i	−0.670413	+	0.387063i
$206$	1.56083	−	2.70344i	0.108748	−	0.188358i
$207$	1.51782	−	2.62895i	0.105496	−	0.182724i
$208$	−12.4282	−	21.5262i	−0.861740	−	1.49258i
$209$		0			0
$210$	1.05083	+	0.479637i	0.0725145	+	0.0330981i
$211$		−	26.5210i		−	1.82578i	−0.408207	−	0.912889i	$-0.633846\pi$
$211$		−	26.5210i		−	1.82578i	0.408207	−	0.912889i	$-0.366154\pi$
$212$	−0.0419406	−	0.0726433i	−0.00288049	−	0.00498916i
$213$	0.848226	+	0.489724i	0.0581195	+	0.0335553i
$214$	11.4133	−	19.7684i	0.780198	−	1.35134i
$215$	−7.23423	−	12.5301i	−0.493370	−	0.854542i
$216$	3.47041			0.236131
$217$	0.140014	+	1.46309i	0.00950478	+	0.0993212i
$218$	−2.49243			−0.168809
$219$	1.72660	−	0.996853i	0.116673	−	0.0673611i
$220$		0			0
$221$	−8.63922	+	14.9636i	−0.581137	+	1.00656i
$222$	−0.624871	−	1.08231i	−0.0419386	−	0.0726398i
$223$		−	11.4522i		−	0.766898i	−0.923562	−	0.383449i	$-0.874736\pi$
$223$		−	11.4522i		−	0.766898i	0.923562	−	0.383449i	$-0.125264\pi$
$224$	0.0398069	+	0.415966i	0.00265971	+	0.0277929i
$225$	7.95571			0.530380
$226$	13.5856	−	7.84366i	0.903702	−	0.521753i
$227$	−9.63853	+	16.6944i	−0.639732	+	1.10805i	0.345760	+	0.938323i	$0.387621\pi$
$227$	−9.63853	+	16.6944i	−0.639732	+	1.10805i	−0.985492	+	0.169725i	$0.945712\pi$
$228$	0.0326314	+	0.0188398i	0.00216107	+	0.00124769i
$229$	19.9137	−	11.4972i	1.31593	−	0.759754i	0.332860	−	0.942976i	$-0.391986\pi$
$229$	19.9137	−	11.4972i	1.31593	−	0.759754i	0.983071	+	0.183223i	$0.0586529\pi$
$230$	−2.19054			−0.144440
$231$		0			0
$232$	10.2009			0.669724
$233$	−7.62052	+	4.39971i	−0.499237	+	0.288234i	−0.728398	−	0.685154i	$-0.759735\pi$
$233$	−7.62052	+	4.39971i	−0.499237	+	0.288234i	0.229162	+	0.973388i	$0.426402\pi$
$234$	22.6770	+	13.0926i	1.48244	+	0.855887i
$235$	5.57919	−	9.66343i	0.363946	−	0.630373i
$236$	0.0174559	−	0.0100782i	0.00113629	−	0.000656035i
$237$	0.564241			0.0366514
$238$	−8.29495	+	5.90940i	−0.537682	+	0.383049i
$239$			9.67008i			0.625505i	0.949835	+	0.312753i	$0.101251\pi$
$239$			9.67008i			0.625505i	−0.949835	+	0.312753i	$0.898749\pi$
$240$	−0.612992	−	1.06173i	−0.0395685	−	0.0685346i
$241$	−12.5688	+	21.7698i	−0.809628	+	1.40232i	0.103494	+	0.994630i	$0.466998\pi$
$241$	−12.5688	+	21.7698i	−0.809628	+	1.40232i	−0.913122	+	0.407687i	$0.866335\pi$
$242$		0			0
$243$	−4.69383	+	2.70998i	−0.301109	+	0.173845i
$244$	0.219606			0.0140588
$245$	−2.01805	−	10.4473i	−0.128928	−	0.667455i
$246$	2.09432			0.133529
$247$	20.7943	+	36.0168i	1.32311	+	2.29169i
$248$	0.791017	−	1.37008i	0.0502296	−	0.0870002i
$249$	−1.28195	−	0.740132i	−0.0812400	−	0.0469039i
$250$	−8.20704	−	14.2150i	−0.519059	−	0.899037i
$251$		−	21.6529i		−	1.36672i	−0.730082	−	0.683360i	$-0.760518\pi$
$251$		−	21.6529i		−	1.36672i	0.730082	−	0.683360i	$-0.239482\pi$
$252$	−0.126799	−	0.177986i	−0.00798756	−	0.0112120i
$253$		0			0
$254$	−2.73313	−	4.73392i	−0.171492	−	0.297033i
$255$	−0.426110	+	0.738044i	−0.0266841	+	0.0462181i
$256$	0.334998	−	0.580233i	0.0209374	−	0.0362646i
$257$	−13.6421	+	7.87627i	−0.850971	+	0.491308i	−0.860978	−	0.508642i	$-0.830148\pi$
$257$	−13.6421	+	7.87627i	−0.850971	+	0.491308i	0.0100075	+	0.999950i	$0.496814\pi$
$258$			2.73386i			0.170203i
$259$	−4.78011	+	10.4727i	−0.297022	+	0.650744i
$260$			0.267533i			0.0165917i
$261$	−9.17656	+	5.29809i	−0.568015	+	0.327943i
$262$	−17.0873	−	9.86537i	−1.05566	−	0.609485i
$263$	−17.0102	−	9.82083i	−1.04889	−	0.605579i	−0.126554	−	0.991960i	$-0.540392\pi$
$263$	−17.0102	−	9.82083i	−1.04889	−	0.605579i	−0.922339	+	0.386381i	$0.873725\pi$
$264$		0			0
$265$		−	4.56648i		−	0.280516i
$266$	2.33527	+	24.4026i	0.143185	+	1.49622i
$267$	0.232767			0.0142451
$268$	−0.0605057	−	0.104799i	−0.00369597	−	0.00640161i
$269$	−24.8369	−	14.3396i	−1.51433	−	0.874300i	−0.999859	−	0.0167943i	$-0.994654\pi$
$269$	−24.8369	−	14.3396i	−1.51433	−	0.874300i	−0.514474	−	0.857506i	$-0.672013\pi$
$270$	2.25280	+	1.30065i	0.137101	+	0.0791552i
$271$	−2.70791	−	4.69023i	−0.164494	−	0.284911i	0.771982	−	0.635645i	$-0.219266\pi$
$271$	−2.70791	−	4.69023i	−0.164494	−	0.284911i	−0.936475	+	0.350733i	$0.885932\pi$
$272$	10.8094			0.655419
$273$	0.324933	+	3.39542i	0.0196658	+	0.205500i
$274$			14.6286i			0.883749i
$275$		0			0
$276$	−0.00507527	−	0.00293021i	−0.000305495	−	0.000176378i
$277$	2.20310	+	1.27196i	0.132371	+	0.0764245i	0.564723	−	0.825280i	$-0.308983\pi$
$277$	2.20310	+	1.27196i	0.132371	+	0.0764245i	−0.432352	+	0.901705i	$0.642316\pi$
$278$	2.58285	−	1.49121i	0.154909	−	0.0894367i
$279$			1.64333i			0.0983837i
$280$	−4.75565	+	10.4191i	−0.284204	+	0.622662i
$281$			21.0813i			1.25760i	0.777566	+	0.628801i	$0.216454\pi$
$281$			21.0813i			1.25760i	−0.777566	+	0.628801i	$0.783546\pi$
$282$	−1.82594	+	1.05421i	−0.108733	+	0.0627770i
$283$	−3.56518	+	6.17507i	−0.211928	+	0.367070i	−0.952318	−	0.305108i	$-0.901308\pi$
$283$	−3.56518	+	6.17507i	−0.211928	+	0.367070i	0.740390	+	0.672178i	$0.234641\pi$
$284$	−0.0668563	+	0.115798i	−0.00396719	+	0.00687138i
$285$	1.02563	+	1.77645i	0.0607532	+	0.105228i
$286$		0			0
$287$	−11.1937	−	15.7124i	−0.660741	−	0.927475i
$288$			0.467210i			0.0275306i
$289$	4.74301	+	8.21513i	0.279000	+	0.483243i
$290$	6.62188	+	3.82314i	0.388850	+	0.224503i
$291$	−0.820658	+	1.42142i	−0.0481078	+	0.0833252i
$292$	0.136089	+	0.235713i	0.00796399	+	0.0137940i
$293$	6.35473			0.371247			0.185624	−	0.982621i	$-0.440569\pi$
$293$	6.35473			0.371247			0.185624	+	0.982621i	$0.440569\pi$
$294$	−0.656799	+	1.90024i	−0.0383053	+	0.110824i
$295$	1.09731			0.0638878
$296$	10.7312	−	6.19565i	0.623738	−	0.360115i
$297$		0			0
$298$	3.50711	−	6.07449i	0.203161	−	0.351886i
$299$	−3.23420	−	5.60181i	−0.187039	−	0.323961i
$300$		−	0.0153588i		−	0.000886738i
$301$	20.5105	−	14.6119i	1.18221	−	0.842215i
$302$	−3.14713			−0.181097
$303$	−1.22276	+	0.705959i	−0.0702456	+	0.0405563i
$304$	13.0090	−	22.5322i	0.746116	−	1.29231i
$305$	10.3536	+	5.97765i	0.592845	+	0.342279i
$306$	−9.86168	+	5.69364i	−0.563755	+	0.325484i
$307$	20.5417			1.17238			0.586189	−	0.810174i	$-0.300628\pi$
$307$	20.5417			1.17238			0.586189	+	0.810174i	$0.300628\pi$
$308$		0			0
$309$	0.454652			0.0258642
$310$	1.02697	−	0.592921i	0.0583279	−	0.0336756i
$311$	−14.0250	−	8.09736i	−0.795287	−	0.459159i	0.0465335	−	0.998917i	$-0.485183\pi$
$311$	−14.0250	−	8.09736i	−0.795287	−	0.459159i	−0.841821	+	0.539758i	$0.818516\pi$
$312$	1.83572	−	3.17957i	0.103927	−	0.180007i
$313$	23.7929	−	13.7368i	1.34485	−	0.776452i	0.357339	−	0.933975i	$-0.383684\pi$
$313$	23.7929	−	13.7368i	1.34485	−	0.776452i	0.987515	+	0.157523i	$0.0503508\pi$
$314$	−6.72334			−0.379420
$315$	−1.13333	−	11.8428i	−0.0638557	−	0.667266i
$316$			0.0770292i			0.00433323i
$317$	10.1067	+	17.5053i	0.567648	+	0.983195i	0.996798	+	0.0799617i	$0.0254798\pi$
$317$	10.1067	+	17.5053i	0.567648	+	0.983195i	−0.429150	+	0.903233i	$0.641187\pi$
$318$	−0.431425	+	0.747250i	−0.0241931	+	0.0419037i
$319$		0			0
$320$	10.6742	−	6.16276i	0.596707	−	0.344509i
$321$	3.32456			0.185559
$322$	−0.363212	−	3.79542i	−0.0202410	−	0.211510i
$323$	−18.0859			−1.00633
$324$	−0.120417	−	0.208568i	−0.00668984	−	0.0115871i
$325$	8.47609	−	14.6810i	0.470169	−	0.814356i
$326$	−0.780758	−	0.450771i	−0.0432422	−	0.0249659i
$327$	−0.181504	−	0.314374i	−0.0100372	−	0.0173849i
$328$			20.7654i			1.14658i
$329$	17.6683	+	8.06442i	0.974085	+	0.444606i
$330$		0			0
$331$	−0.0955258	−	0.165455i	−0.00525057	−	0.00909426i	0.863388	−	0.504540i	$-0.168338\pi$
$331$	−0.0955258	−	0.165455i	−0.00525057	−	0.00909426i	−0.868639	+	0.495446i	$0.835005\pi$
$332$	0.101042	−	0.175009i	0.00554538	−	0.00960488i
$333$	−6.43571	+	11.1470i	−0.352675	+	0.610851i
$334$	−17.3359	+	10.0089i	−0.948577	+	0.547661i
$335$		−	6.58783i		−	0.359932i
$336$	1.73796	−	1.23814i	0.0948134	−	0.0675459i
$337$		−	4.52569i		−	0.246530i	−0.992374	−	0.123265i	$-0.960663\pi$
$337$		−	4.52569i		−	0.246530i	0.992374	−	0.123265i	$-0.0393365\pi$
$338$	32.5104	−	18.7699i	1.76833	−	1.02095i
$339$	1.97866	+	1.14238i	0.107466	+	0.0620457i
$340$	−0.100757	−	0.0581719i	−0.00546430	−	0.00315481i
$341$		0			0
$342$			27.4088i			1.48210i
$343$	17.7668	−	5.22880i	0.959318	−	0.282329i
$344$	−27.1065			−1.46148
$345$	−0.159520	−	0.276296i	−0.00858826	−	0.0148753i
$346$	−18.7504	−	10.8255i	−1.00803	−	0.581984i
$347$	−13.8786	−	8.01280i	−0.745041	−	0.430150i	0.0788584	−	0.996886i	$-0.474872\pi$
$347$	−13.8786	−	8.01280i	−0.745041	−	0.430150i	−0.823899	+	0.566736i	$0.808206\pi$
$348$	0.0102281	+	0.0177157i	0.000548286	+	0.000949659i
$349$	−28.5380			−1.52760			−0.763802	−	0.645451i	$-0.776669\pi$
$349$	−28.5380			−1.52760			−0.763802	+	0.645451i	$0.776669\pi$
$350$	8.13832	−	5.79781i	0.435011	−	0.309906i
$351$			7.68133i			0.409999i
$352$		0			0
$353$	18.1201	+	10.4617i	0.964438	+	0.556818i	0.897536	−	0.440941i	$-0.145355\pi$
$353$	18.1201	+	10.4617i	0.964438	+	0.556818i	0.0669018	+	0.997760i	$0.478689\pi$
$354$	−0.179562	−	0.103670i	−0.00954361	−	0.00551000i
$355$	−6.30404	+	3.63964i	−0.334584	+	0.193172i
$356$			0.0317770i			0.00168418i
$357$	−1.34942	−	0.615920i	−0.0714186	−	0.0325979i
$358$		−	6.31745i		−	0.333888i
$359$	4.10800	−	2.37175i	0.216812	−	0.125176i	−0.387661	−	0.921802i	$-0.626717\pi$
$359$	4.10800	−	2.37175i	0.216812	−	0.125176i	0.604473	+	0.796626i	$0.293384\pi$
$360$	−6.40277	+	11.0899i	−0.337456	+	0.584491i
$361$	−12.2661	+	21.2455i	−0.645583	+	1.11818i
$362$	−4.36799	−	7.56558i	−0.229577	−	0.397638i
$363$		0			0
$364$	−0.463537	+	0.0443593i	−0.0242960	+	0.00232506i
$365$			14.8173i			0.775572i
$366$	−1.12950	−	1.95635i	−0.0590397	−	0.102260i
$367$	0.634469	+	0.366311i	0.0331190	+	0.0191213i	0.516468	−	0.856306i	$-0.327246\pi$
$367$	0.634469	+	0.366311i	0.0331190	+	0.0191213i	−0.483349	+	0.875428i	$0.660580\pi$
$368$	−2.02333	+	3.50451i	−0.105473	+	0.182685i
$369$	−10.7850	−	18.6801i	−0.561444	−	0.972449i
$370$	9.28813			0.482867
$371$	7.91204	−	0.757162i	0.410773	−	0.0393099i
$372$	0.00317251			0.000164487
$373$	4.67716	−	2.70036i	0.242174	−	0.139819i	−0.374001	−	0.927428i	$-0.622014\pi$
$373$	4.67716	−	2.70036i	0.242174	−	0.139819i	0.616176	+	0.787609i	$0.288681\pi$
$374$		0			0
$375$	1.19531	−	2.07033i	0.0617254	−	0.106911i
$376$	−10.4525	−	18.1043i	−0.539049	−	0.933660i
$377$			22.5785i			1.16285i
$378$	−1.88002	+	4.11894i	−0.0966980	+	0.211855i
$379$	−25.6805			−1.31912			−0.659559	−	0.751653i	$-0.729257\pi$
$379$	−25.6805			−1.31912			−0.659559	+	0.751653i	$0.729257\pi$
$380$	−0.242518	+	0.140018i	−0.0124409	+	0.00718276i
$381$	0.398064	−	0.689467i	0.0203934	−	0.0353225i
$382$	−11.3867	−	6.57413i	−0.582596	−	0.336362i
$383$	−32.6057	+	18.8249i	−1.66607	+	0.961908i	−0.696350	+	0.717703i	$0.745194\pi$
$383$	−32.6057	+	18.8249i	−1.66607	+	0.961908i	−0.969724	+	0.244205i	$0.921473\pi$
$384$	−2.26434			−0.115552
$385$		0			0
$386$	1.53086			0.0779187
$387$	24.3845	−	14.0784i	1.23953	−	0.715645i
$388$	−0.194050	−	0.112035i	−0.00985141	−	0.00568771i
$389$	−11.8336	+	20.4964i	−0.599988	+	1.03921i	0.392835	+	0.919609i	$0.371494\pi$
$389$	−11.8336	+	20.4964i	−0.599988	+	1.03921i	−0.992822	+	0.119600i	$0.961839\pi$
$390$	2.38330	−	1.37600i	0.120683	−	0.0696764i
$391$	2.81296			0.142257
$392$	−18.8411	−	6.51222i	−0.951618	−	0.328917i
$393$		−	2.87366i		−	0.144957i
$394$	−7.22853	−	12.5202i	−0.364168	−	0.630758i
$395$	−2.09673	+	3.63164i	−0.105498	+	0.182728i
$396$		0			0
$397$	16.2965	−	9.40879i	0.817898	−	0.472214i	−0.0317930	−	0.999494i	$-0.510122\pi$
$397$	16.2965	−	9.40879i	0.817898	−	0.472214i	0.849691	+	0.527281i	$0.176788\pi$
$398$	−3.39570			−0.170211
$399$	−2.90788	+	2.07160i	−0.145576	+	0.103710i
$400$	−10.6053			−0.530266
$401$	−7.74102	−	13.4078i	−0.386568	−	0.669555i	0.605417	−	0.795908i	$-0.293006\pi$
$401$	−7.74102	−	13.4078i	−0.386568	−	0.669555i	−0.991985	+	0.126353i	$0.959673\pi$
$402$	−0.622396	+	1.07802i	−0.0310423	+	0.0537669i
$403$	3.03251	+	1.75082i	0.151060	+	0.0872146i
$404$	−0.0963764	−	0.166929i	−0.00479491	−	0.00830502i
$405$		−	13.1110i		−	0.651489i
$406$	−5.52615	+	12.1072i	−0.274258	+	0.600871i
$407$		0			0
$408$	0.798313	+	1.38272i	0.0395224	+	0.0684548i
$409$	−10.2602	+	17.7712i	−0.507334	+	0.878729i	0.492630	+	0.870239i	$0.336036\pi$
$409$	−10.2602	+	17.7712i	−0.507334	+	0.878729i	−0.999964	+	0.00848977i	$0.997298\pi$
$410$	−7.78253	+	13.4797i	−0.384352	+	0.665717i
$411$	−1.84513	+	1.06529i	−0.0910136	+	0.0525467i
$412$			0.0620683i			0.00305789i
$413$	0.181944	+	1.90124i	0.00895286	+	0.0935538i
$414$		−	4.26298i		−	0.209514i
$415$	9.52746	−	5.50068i	0.467685	−	0.270018i
$416$	0.862162	+	0.497769i	0.0422710	+	0.0244052i
$417$	0.376176	+	0.217185i	0.0184214	+	0.0106356i
$418$		0			0
$419$		−	11.3707i		−	0.555494i	−0.960654	−	0.277747i	$-0.910412\pi$
$419$		−	11.3707i		−	0.555494i	0.960654	−	0.277747i	$-0.0895877\pi$
$420$	−0.0228629	+	0.00218792i	−0.00111560	+	0.000106760i
$421$	−14.7298			−0.717888			−0.358944	−	0.933359i	$-0.616863\pi$
$421$	−14.7298			−0.717888			−0.358944	+	0.933359i	$0.616863\pi$
$422$	−18.6218	−	32.2539i	−0.906495	−	1.57009i
$423$	18.8058	+	10.8575i	0.914370	+	0.527912i
$424$	−7.40906	−	4.27762i	−0.359816	−	0.207740i
$425$	3.68605	+	6.38443i	0.178800	+	0.309690i
$426$	1.37544			0.0666405
$427$	−8.64037	+	18.9302i	−0.418137	+	0.916094i
$428$			0.453863i			0.0219383i
$429$		0			0
$430$	−17.5960	−	10.1591i	−0.848556	−	0.489914i
$431$	10.3056	+	5.94992i	0.496402	+	0.286598i	0.727226	−	0.686398i	$-0.240809\pi$
$431$	10.3056	+	5.94992i	0.496402	+	0.286598i	−0.230825	+	0.972995i	$0.574142\pi$
$432$	4.16166	−	2.40273i	0.200228	−	0.115602i
$433$			31.3716i			1.50762i	0.657091	+	0.753811i	$0.271787\pi$
$433$			31.3716i			1.50762i	−0.657091	+	0.753811i	$0.728213\pi$
$434$	1.19760	+	1.68105i	0.0574864	+	0.0806930i
$435$			1.11364i			0.0533947i
$436$	0.0429178	−	0.0247786i	0.00205539	−	0.00118668i
$437$	3.38535	−	5.86359i	0.161943	−	0.280494i
$438$	1.39989	−	2.42468i	0.0668892	−	0.115855i
$439$	12.3534	+	21.3966i	0.589593	+	1.02121i	0.994286	+	0.106753i	$0.0340453\pi$
$439$	12.3534	+	21.3966i	0.589593	+	1.02121i	−0.404692	+	0.914453i	$0.632621\pi$
$440$		0			0
$441$	20.3313	−	3.92728i	0.968159	−	0.187013i
$442$			24.2642i			1.15413i
$443$	−16.6832	−	28.8962i	−0.792645	−	1.37290i	−0.924324	−	0.381609i	$-0.875370\pi$
$443$	−16.6832	−	28.8962i	−0.792645	−	1.37290i	0.131679	−	0.991292i	$-0.457963\pi$
$444$	0.0215196	+	0.0124244i	0.00102128	+	0.000589634i
$445$	−0.864966	+	1.49816i	−0.0410033	+	0.0710198i
$446$	−8.04122	−	13.9278i	−0.380763	−	0.659501i
$447$	1.02158			0.0483190
$448$	12.4477	+	17.4727i	0.588098	+	0.825507i
$449$	23.4430			1.10635			0.553173	−	0.833066i	$-0.313417\pi$
$449$	23.4430			1.10635			0.553173	+	0.833066i	$0.313417\pi$
$450$	9.67546	−	5.58613i	0.456105	−	0.263333i
$451$		0			0
$452$	−0.155956	+	0.270124i	−0.00733556	+	0.0127056i
$453$	−0.229180	−	0.396951i	−0.0107678	−	0.0186504i
$454$			27.0709i			1.27050i
$455$	−23.0615	−	10.5261i	−1.08114	−	0.493469i
$456$	3.84302			0.179966
$457$	1.30596	−	0.753999i	0.0610905	−	0.0352706i	−0.469144	−	0.883122i	$-0.655437\pi$
$457$	1.30596	−	0.753999i	0.0610905	−	0.0352706i	0.530234	+	0.847851i	$0.322104\pi$
$458$	16.1455	−	27.9649i	0.754431	−	1.30671i
$459$	−2.89290	−	1.67022i	−0.135029	−	0.0779590i
$460$	0.0377195	−	0.0217774i	0.00175868	−	0.00101538i
$461$	−15.7812			−0.735004			−0.367502	−	0.930023i	$-0.619787\pi$
$461$	−15.7812			−0.735004			−0.367502	+	0.930023i	$0.619787\pi$
$462$		0			0
$463$	−8.99614			−0.418086			−0.209043	−	0.977906i	$-0.567035\pi$
$463$	−8.99614			−0.418086			−0.209043	+	0.977906i	$0.567035\pi$
$464$	12.2328	−	7.06260i	0.567893	−	0.327873i
$465$	0.149572	+	0.0863553i	0.00693622	+	0.00400463i
$466$	−6.17854	+	10.7015i	−0.286215	+	0.495739i
$467$	28.6175	−	16.5223i	1.32426	−	0.764561i	0.339853	−	0.940478i	$-0.389623\pi$
$467$	28.6175	−	16.5223i	1.32426	−	0.764561i	0.984405	+	0.175918i	$0.0562892\pi$
$468$	−0.520641			−0.0240666
$469$	11.4143	−	1.09232i	0.527064	−	0.0504387i
$470$		−	15.6698i		−	0.722793i
$471$	−0.489607	−	0.848024i	−0.0225599	−	0.0390749i
$472$	1.02790	−	1.78037i	0.0473129	−	0.0819483i
$473$		0			0
$474$	0.686210	−	0.396183i	0.0315187	−	0.0181973i
$475$	17.7444			0.814168
$476$	0.0840844	−	0.184220i	0.00385400	−	0.00844371i
$477$	8.88673			0.406895
$478$	6.78988	+	11.7604i	0.310562	+	0.537909i
$479$	−14.0093	+	24.2649i	−0.640103	+	1.10869i	0.345306	+	0.938490i	$0.387775\pi$
$479$	−14.0093	+	24.2649i	−0.640103	+	1.10869i	−0.985409	+	0.170201i	$0.945558\pi$
$480$	0.0425242	+	0.0245514i	0.00194095	+	0.00112061i
$481$	13.7133	+	23.7522i	0.625275	+	1.08301i
$482$			35.3009i			1.60791i
$483$	0.452271	−	0.322202i	0.0205791	−	0.0146607i
$484$		0			0
$485$	−6.09916	−	10.5641i	−0.276949	−	0.479689i
$486$	−3.80565	+	6.59157i	−0.172628	+	0.299000i
$487$	8.56693	−	14.8384i	0.388204	−	0.672390i	−0.604004	−	0.796982i	$-0.706429\pi$
$487$	8.56693	−	14.8384i	0.388204	−	0.672390i	0.992208	+	0.124592i	$0.0397621\pi$
$488$	19.3973	−	11.1991i	0.878076	−	0.506958i
$489$		−	0.131304i		−	0.00593777i
$490$	−9.78991	−	11.2887i	−0.442263	−	0.509972i
$491$		−	27.9452i		−	1.26115i	−0.776129	−	0.630574i	$-0.782820\pi$
$491$		−	27.9452i		−	1.26115i	0.776129	−	0.630574i	$-0.217180\pi$
$492$	−0.0360626	+	0.0208208i	−0.00162583	+	0.000938673i
$493$	−8.50339	−	4.90944i	−0.382974	−	0.221110i
$494$	50.5787	+	29.2016i	2.27564	+	1.31384i
$495$		0			0
$496$		−	2.19064i		−	0.0983625i
$497$	−7.35144	−	10.3191i	−0.329757	−	0.462876i
$498$	−2.07874			−0.0931507
$499$	−6.68193	−	11.5734i	−0.299124	−	0.518099i	0.676811	−	0.736156i	$-0.263361\pi$
$499$	−6.68193	−	11.5734i	−0.299124	−	0.518099i	−0.975936	+	0.218058i	$0.930028\pi$
$500$	0.282638	+	0.163181i	0.0126400	+	0.00729769i
$501$	−2.52487	−	1.45773i	−0.112803	−	0.0651267i
$502$	−15.2037	−	26.3335i	−0.678573	−	1.17532i
$503$	−10.3449			−0.461255			−0.230627	−	0.973042i	$-0.574078\pi$
$503$	−10.3449			−0.461255			−0.230627	+	0.973042i	$0.574078\pi$
$504$	−20.2765	−	9.25487i	−0.903185	−	0.412245i
$505$		−	10.4934i		−	0.466951i
$506$		0			0
$507$	4.73494	+	2.73372i	0.210286	+	0.121409i
$508$	0.0941250	+	0.0543431i	0.00417612	+	0.00241109i
$509$	−2.56125	+	1.47874i	−0.113525	+	0.0655439i	−0.555688	−	0.831391i	$-0.687545\pi$
$509$	−2.56125	+	1.47874i	−0.113525	+	0.0655439i	0.442162	+	0.896935i	$0.354212\pi$
$510$			1.19678i			0.0529943i
$511$	−25.6730	+	2.45684i	−1.13570	+	0.108684i
$512$		−	23.0829i		−	1.02013i
$513$	−6.96311	+	4.02015i	−0.307429	+	0.177494i
$514$	−11.0607	+	19.1577i	−0.487867	+	0.845010i
$515$	−1.68949	+	2.92629i	−0.0744480	+	0.128948i
$516$	−0.0271788	−	0.0470751i	−0.00119648	−	0.00207236i
$517$		0			0
$518$	1.54005	+	16.0929i	0.0676660	+	0.707083i
$519$		−	3.15334i		−	0.138416i
$520$	13.6432	+	23.6306i	0.598292	+	1.03627i
$521$	16.0894	+	9.28923i	0.704890	+	0.406968i	0.809166	−	0.587580i	$-0.199919\pi$
$521$	16.0894	+	9.28923i	0.704890	+	0.406968i	−0.104276	+	0.994548i	$0.533253\pi$
$522$	−7.44014	+	12.8867i	−0.325646	+	0.564036i
$523$	15.8973	+	27.5349i	0.695140	+	1.20402i	0.970133	+	0.242572i	$0.0779910\pi$
$523$	15.8973	+	27.5349i	0.695140	+	1.20402i	−0.274993	+	0.961446i	$0.588676\pi$
$524$	0.392308			0.0171381
$525$	1.32393	+	0.604289i	0.0577812	+	0.0263733i
$526$	−27.5829			−1.20267
$527$	−1.31877	+	0.761391i	−0.0574464	+	0.0331667i
$528$		0			0
$529$	10.9735	−	19.0066i	0.477107	−	0.826374i
$530$	−3.20637	−	5.55359i	−0.139276	−	0.241233i
$531$			2.13545i			0.0926707i
$532$	−0.282811	−	0.396979i	−0.0122614	−	0.0172112i
$533$	−45.9617			−1.99082
$534$	0.283083	−	0.163438i	0.0122502	−	0.00707266i
$535$	−12.3541	+	21.3979i	−0.534115	+	0.925114i
$536$	−10.6887	−	6.17112i	−0.461681	−	0.266552i
$537$	0.796829	−	0.460049i	0.0343857	−	0.0198526i
$538$	−40.2744			−1.73635
$539$		0			0
$540$	−0.0517220			−0.00222576
$541$	−18.3856	+	10.6149i	−0.790458	+	0.456371i	−0.840124	−	0.542395i	$-0.817518\pi$
$541$	−18.3856	+	10.6149i	−0.790458	+	0.456371i	0.0496656	+	0.998766i	$0.484184\pi$
$542$	−6.58652	−	3.80273i	−0.282915	−	0.163341i
$543$	0.636171	−	1.10188i	0.0273007	−	0.0472862i
$544$	−0.374934	+	0.216468i	−0.0160752	+	0.00928100i
$545$	2.69788			0.115565
$546$	2.77928	+	3.90124i	0.118942	+	0.166958i
$547$		−	23.5878i		−	1.00854i	−0.863545	−	0.504271i	$-0.831761\pi$
$547$		−	23.5878i		−	1.00854i	0.863545	−	0.504271i	$-0.168239\pi$
$548$	−0.145431	−	0.251894i	−0.00621252	−	0.0107604i
$549$	−11.6330	+	20.1489i	−0.496484	+	0.859935i
$550$		0			0
$551$	−20.4674	+	11.8168i	−0.871939	+	0.503414i
$552$	−0.597717			−0.0254405
$553$	−6.63996	−	3.03071i	−0.282360	−	0.128879i
$554$	3.57244			0.151778
$555$	0.676380	+	1.17152i	0.0287107	+	0.0497284i
$556$	−0.0296498	+	0.0513550i	−0.00125743	+	0.00217794i
$557$	−21.7682	−	12.5679i	−0.922347	−	0.532517i	−0.0379638	−	0.999279i	$-0.512087\pi$
$557$	−21.7682	−	12.5679i	−0.922347	−	0.532517i	−0.884383	+	0.466762i	$0.845420\pi$
$558$	1.15387	+	1.99856i	0.0488473	+	0.0846059i
$559$		−	59.9970i		−	2.53760i
$560$	1.51078	+	15.7870i	0.0638419	+	0.667123i
$561$		0			0
$562$	14.8023	+	25.6383i	0.624397	+	1.08149i
$563$	8.15057	−	14.1172i	0.343506	−	0.594969i	−0.641575	−	0.767060i	$-0.721719\pi$
$563$	8.15057	−	14.1172i	0.343506	−	0.594969i	0.985081	+	0.172091i	$0.0550522\pi$
$564$	0.0209609	−	0.0363053i	0.000882611	−	0.00152873i
$565$	−14.7055	+	8.49022i	−0.618665	+	0.357186i
$566$			10.0132i			0.420887i
$567$	22.7165	−	2.17391i	0.954004	−	0.0912957i
$568$			13.6377i			0.572223i
$569$	−29.7448	+	17.1731i	−1.24696	+	0.719936i	−0.970503	−	0.241089i	$-0.922495\pi$
$569$	−29.7448	+	17.1731i	−1.24696	+	0.719936i	−0.276462	+	0.961025i	$0.589162\pi$
$570$	2.49468	+	1.44030i	0.104491	+	0.0603276i
$571$	−18.1029	−	10.4517i	−0.757584	−	0.437392i	0.0708434	−	0.997487i	$-0.477431\pi$
$571$	−18.1029	−	10.4517i	−0.757584	−	0.437392i	−0.828428	+	0.560096i	$0.810764\pi$
$572$		0			0
$573$		−	1.91497i		−	0.0799988i
$574$	−24.6459	−	11.2492i	−1.02870	−	0.469534i
$575$	−2.75984			−0.115093
$576$	11.9932	+	20.7729i	0.499718	+	0.865536i
$577$	18.3285	+	10.5820i	0.763027	+	0.440534i	0.830382	−	0.557195i	$-0.188122\pi$
$577$	18.3285	+	10.5820i	0.763027	+	0.440534i	−0.0673542	+	0.997729i	$0.521456\pi$
$578$	11.5366	+	6.66064i	0.479858	+	0.277046i
$579$	0.111480	+	0.193090i	0.00463296	+	0.00802453i
$580$	−0.152032			−0.00631277
$581$	11.1104	+	15.5956i	0.460938	+	0.647013i
$582$			2.30491i			0.0955417i
$583$		0			0
$584$	24.0409	+	13.8800i	0.994819	+	0.574359i
$585$	−24.5462	−	14.1718i	−1.01486	−	0.585931i
$586$	7.72841	−	4.46200i	0.319257	−	0.184323i
$587$		−	15.5245i		−	0.640763i	−0.947289	−	0.320381i	$-0.896189\pi$
$587$		−	15.5245i		−	0.640763i	0.947289	−	0.320381i	$-0.103811\pi$
$588$	−0.00758175	−	0.0392503i	−0.000312666	−	0.00161866i
$589$			3.66528i			0.151025i
$590$	1.33451	−	0.770480i	0.0549409	−	0.0317201i
$591$	1.05279	−	1.82349i	0.0433061	−	0.0750083i
$592$	8.57911	−	14.8595i	0.352599	−	0.610720i
$593$	−3.79829	−	6.57883i	−0.155977	−	0.270160i	0.777437	−	0.628960i	$-0.216519\pi$
$593$	−3.79829	−	6.57883i	−0.155977	−	0.270160i	−0.933414	+	0.358800i	$0.883186\pi$
$594$		0			0
$595$	8.97871	−	6.39651i	0.368091	−	0.262231i
$596$			0.139464i			0.00571268i
$597$	−0.247281	−	0.428304i	−0.0101206	−	0.0175293i
$598$	−7.86666	−	4.54182i	−0.321691	−	0.185729i
$599$	15.3707	−	26.6228i	0.628028	−	1.08778i	−0.359919	−	0.932984i	$-0.617196\pi$
$599$	15.3707	−	26.6228i	0.628028	−	1.08778i	0.987947	−	0.154793i	$-0.0494710\pi$
$600$	−0.783238	−	1.35661i	−0.0319756	−	0.0553833i
$601$	−45.5703			−1.85885			−0.929425	−	0.369010i	$-0.879697\pi$
$601$	−45.5703			−1.85885			−0.929425	+	0.369010i	$0.879697\pi$
$602$	14.6844	−	32.1720i	0.598492	−	1.31123i
$603$	12.8205			0.522089
$604$	0.0541912	−	0.0312873i	0.00220501	−	0.00127306i
$605$		0			0
$606$	−0.991383	+	1.71713i	−0.0402722	+	0.0697535i
$607$	8.63427	+	14.9550i	0.350454	+	0.607004i	0.986329	−	0.164788i	$-0.0526940\pi$
$607$	8.63427	+	14.9550i	0.350454	+	0.607004i	−0.635875	+	0.771792i	$0.719361\pi$
$608$			1.04206i			0.0422612i
$609$	−1.92952	+	0.184651i	−0.0781883	+	0.00748242i
$610$	16.7889			0.679763
$611$	40.0718	−	23.1355i	1.62113	−	0.935961i
$612$	0.113207	−	0.196081i	0.00457613	−	0.00792609i
$613$	35.2218	+	20.3353i	1.42259	+	0.821335i	0.996520	−	0.0833532i	$-0.0265630\pi$
$613$	35.2218	+	20.3353i	1.42259	+	0.821335i	0.426074	+	0.904688i	$0.359896\pi$
$614$	24.9821	−	14.4234i	1.00820	−	0.582083i
$615$	−2.26696			−0.0914125
$616$		0			0
$617$	−9.08065			−0.365573			−0.182787	−	0.983153i	$-0.558512\pi$
$617$	−9.08065			−0.365573			−0.182787	+	0.983153i	$0.558512\pi$
$618$	0.552932	−	0.319235i	0.0222422	−	0.0128415i
$619$	−0.427433	−	0.246779i	−0.0171800	−	0.00991888i	0.491385	−	0.870942i	$-0.336491\pi$
$619$	−0.427433	−	0.246779i	−0.0171800	−	0.00991888i	−0.508565	+	0.861023i	$0.669824\pi$
$620$	−0.0117891	+	0.0204193i	−0.000473461	+	0.000820059i
$621$	1.08299	−	0.625267i	0.0434590	−	0.0250911i
$622$	−22.7424			−0.911885
$623$	−2.73919	−	1.25026i	−0.109743	−	0.0500907i
$624$		−	5.08384i		−	0.203517i
$625$	2.16005	+	3.74131i	0.0864019	+	0.149652i
$626$	19.2907	−	33.4125i	0.771013	−	1.33543i
$627$		0			0
$628$	0.115771	−	0.0668403i	0.00461976	−	0.00266722i
$629$	−11.9272			−0.475569
$630$	−9.69377	−	13.6070i	−0.386209	−	0.542117i
$631$	−41.6754			−1.65907			−0.829537	−	0.558452i	$-0.811395\pi$
$631$	−41.6754			−1.65907			−0.829537	+	0.558452i	$0.811395\pi$
$632$	3.92820	+	6.80383i	0.156255	+	0.270642i
$633$	2.71215	−	4.69758i	0.107798	−	0.186712i
$634$	24.5828	+	14.1929i	0.976308	+	0.563671i
$635$	2.95843	+	5.12414i	0.117402	+	0.203345i
$636$		−	0.0171561i		−	0.000680285i
$637$	14.4140	−	41.7025i	0.571105	−	1.65231i
$638$		0			0
$639$	−7.08303	−	12.2682i	−0.280200	−	0.485321i
$640$	8.41433	−	14.5740i	0.332605	−	0.576090i
$641$	15.9661	−	27.6542i	0.630625	−	1.09227i	−0.356799	−	0.934181i	$-0.616132\pi$
$641$	15.9661	−	27.6542i	0.630625	−	1.09227i	0.987424	−	0.158093i	$-0.0505346\pi$
$642$	4.04321	−	2.33435i	0.159573	−	0.0921294i
$643$			21.1371i			0.833568i	0.909006	+	0.416784i	$0.136843\pi$
$643$			21.1371i			0.833568i	−0.909006	+	0.416784i	$0.863157\pi$
$644$	0.0439865	+	0.0617434i	0.00173331	+	0.00243303i
$645$		−	2.95922i		−	0.116519i
$646$	−21.9955	+	12.6991i	−0.865400	+	0.499639i
$647$	−13.7966	−	7.96549i	−0.542401	−	0.313156i	0.203650	−	0.979044i	$-0.434719\pi$
$647$	−13.7966	−	7.96549i	−0.542401	−	0.313156i	−0.746052	+	0.665888i	$0.768053\pi$
$648$	−21.2724	−	12.2816i	−0.835658	−	0.482468i
$649$		0			0
$650$		−	23.8061i		−	0.933750i
$651$	−0.124822	+	0.273472i	−0.00489216	+	0.0107182i
$652$	0.0179254			0.000702014
$653$	23.2536	+	40.2764i	0.909984	+	1.57614i	0.814084	+	0.580747i	$0.197239\pi$
$653$	23.2536	+	40.2764i	0.909984	+	1.57614i	0.0958992	+	0.995391i	$0.469427\pi$
$654$	−0.441477	−	0.254887i	−0.0172631	−	0.00996687i
$655$	18.4958	+	10.6786i	0.722692	+	0.417247i
$656$	14.3769	+	24.9015i	0.561323	+	0.972240i
$657$	−28.8356			−1.12498
$658$	27.1500	−	2.59819i	1.05842	−	0.101288i
$659$		−	15.0416i		−	0.585939i	−0.956122	−	0.292970i	$-0.905357\pi$
$659$		−	15.0416i		−	0.585939i	0.956122	−	0.292970i	$-0.0946435\pi$
$660$		0			0
$661$	−2.85554	−	1.64864i	−0.111067	−	0.0641248i	0.443437	−	0.896305i	$-0.353759\pi$
$661$	−2.85554	−	1.64864i	−0.111067	−	0.0641248i	−0.554505	+	0.832181i	$0.687092\pi$
$662$	−0.232350	−	0.134147i	−0.00903055	−	0.00521379i
$663$	−3.06048	+	1.76697i	−0.118859	+	0.0686234i
$664$		−	20.6109i		−	0.799859i
$665$	−2.52777	−	26.4142i	−0.0980226	−	1.02430i
$666$			18.0754i			0.700409i
$667$	3.18335	−	1.83791i	0.123260	−	0.0711642i
$668$	0.199007	−	0.344691i	0.00769982	−	0.0133365i
$669$	1.17116	−	2.02850i	0.0452795	−	0.0784264i
$670$	−4.62567	−	8.01190i	−0.178705	−	0.309527i
$671$		0			0
$672$	−0.0354877	+	0.0777498i	−0.00136897	+	0.00299926i
$673$			17.4494i			0.672624i	0.941751	+	0.336312i	$0.109180\pi$
$673$			17.4494i			0.672624i	−0.941751	+	0.336312i	$0.890820\pi$
$674$	−3.17773	−	5.50399i	−0.122401	−	0.212006i
$675$	2.83827	+	1.63868i	0.109245	+	0.0630727i
$676$	−0.373203	+	0.646406i	−0.0143540	+	0.0248618i
$677$	−7.19304	−	12.4587i	−0.276451	−	0.478827i	0.694049	−	0.719927i	$-0.255825\pi$
$677$	−7.19304	−	12.4587i	−0.276451	−	0.478827i	−0.970500	+	0.241101i	$0.922492\pi$
$678$	3.20851			0.123222
$679$	17.2924	−	12.3192i	0.663620	−	0.472769i
$680$	−11.8662			−0.455047
$681$	−3.41449	+	1.97136i	−0.130844	+	0.0755426i
$682$		0			0
$683$	−7.01481	+	12.1500i	−0.268414	+	0.464907i	−0.968453	−	0.249198i	$-0.919833\pi$
$683$	−7.01481	+	12.1500i	−0.268414	+	0.464907i	0.700038	+	0.714105i	$0.253166\pi$
$684$	−0.272486	−	0.471959i	−0.0104188	−	0.0180458i
$685$		−	15.8345i		−	0.605005i
$686$	17.9360	−	18.8341i	0.684798	−	0.719090i
$687$	4.70300			0.179431
$688$	−32.5057	+	18.7672i	−1.23927	+	0.715491i
$689$	9.46800	−	16.3991i	0.360702	−	0.624755i
$690$	−0.388005	−	0.224015i	−0.0147711	−	0.00852810i
$691$	15.4202	−	8.90288i	0.586613	−	0.338681i	−0.177144	−	0.984185i	$-0.556686\pi$
$691$	15.4202	−	8.90288i	0.586613	−	0.338681i	0.763757	+	0.645504i	$0.223352\pi$
$692$	0.430489			0.0163648
$693$		0			0
$694$	−22.5049			−0.854273
$695$	−2.79575	+	1.61413i	−0.106049	+	0.0612274i
$696$	1.80686	+	1.04319i	0.0684889	+	0.0395421i
$697$	9.99383	−	17.3098i	0.378543	−	0.655656i
$698$	−34.7069	+	20.0380i	−1.31368	+	0.758451i
$699$	−1.79973			−0.0680722
$700$	−0.0824966	+	0.180741i	−0.00311808	+	0.00683138i
$701$		−	45.2040i		−	1.70733i	−0.520822	−	0.853666i	$-0.674374\pi$
$701$		−	45.2040i		−	1.70733i	0.520822	−	0.853666i	$-0.325626\pi$
$702$	5.39348	+	9.34177i	0.203564	+	0.352583i
$703$	−14.3542	+	24.8622i	−0.541379	+	0.937696i
$704$		0			0
$705$	1.97645	−	1.14110i	0.0744374	−	0.0429765i
$706$	29.3828			1.10584
$707$	18.1813	−	1.73990i	0.683778	−	0.0654358i
$708$	0.00412256			0.000154935
$709$	−2.87180	−	4.97411i	−0.107853	−	0.186807i	0.807047	−	0.590487i	$-0.201064\pi$
$709$	−2.87180	−	4.97411i	−0.107853	−	0.186807i	−0.914900	+	0.403680i	$0.867731\pi$
$710$	−5.11117	+	8.85281i	−0.191819	+	0.332240i
$711$	−7.06746	−	4.08040i	−0.265050	−	0.153027i
$712$	1.62050	+	2.80680i	0.0607310	+	0.105189i
$713$		−	0.570073i		−	0.0213494i
$714$	−2.07358	+	0.198436i	−0.0776019	+	0.00742630i
$715$		0			0
$716$	0.0628052	+	0.108782i	0.00234714	+	0.00406537i
$717$	−0.988905	+	1.71283i	−0.0369313	+	0.0639669i
$718$	3.33067	−	5.76889i	0.124299	−	0.215293i
$719$	39.2414	−	22.6560i	1.46346	−	0.844928i	0.464288	−	0.885684i	$-0.346310\pi$
$719$	39.2414	−	22.6560i	1.46346	−	0.844928i	0.999169	+	0.0407566i	$0.0129768\pi$
$720$			17.7318i			0.660826i
$721$	−5.35032	−	2.44207i	−0.199256	−	0.0909475i
$722$			34.4507i			1.28212i
$723$	−4.45255	+	2.57068i	−0.165592	+	0.0956047i
$724$	0.150427	+	0.0868491i	0.00559058	+	0.00322772i
$725$	8.34282	+	4.81673i	0.309845	+	0.178889i
$726$		0			0
$727$			11.2267i			0.416374i	0.978089	+	0.208187i	$0.0667562\pi$
$727$			11.2267i			0.416374i	−0.978089	+	0.208187i	$0.933244\pi$
$728$	−38.6811	+	27.5568i	−1.43362	+	1.02132i
$729$	24.7672			0.917305
$730$	10.4040	+	18.0203i	0.385070	+	0.666960i
$731$	22.5957	+	13.0456i	0.835733	+	0.482511i
$732$	0.0388982	+	0.0224579i	0.00143772	+	0.000830067i
$733$	6.53663	+	11.3218i	0.241436	+	0.418179i	0.961124	−	0.276119i	$-0.0890483\pi$
$733$	6.53663	+	11.3218i	0.241436	+	0.418179i	−0.719688	+	0.694298i	$0.755715\pi$
$734$	1.02883			0.0379746
$735$	0.710939	−	2.05688i	0.0262234	−	0.0758692i
$736$		−	0.162075i		−	0.00597418i
$737$		0			0
$738$	−26.2326	−	15.1454i	−0.965637	−	0.557511i
$739$	0.772740	+	0.446142i	0.0284257	+	0.0164116i	0.514146	−	0.857703i	$-0.328109\pi$
$739$	0.772740	+	0.446142i	0.0284257	+	0.0164116i	−0.485720	+	0.874115i	$0.661442\pi$
$740$	−0.159935	+	0.0923383i	−0.00587931	+	0.00339442i
$741$			8.50607i			0.312478i
$742$	9.09071	−	6.47630i	0.333730	−	0.237752i
$743$			7.83971i			0.287611i	0.989606	+	0.143806i	$0.0459340\pi$
$743$			7.83971i			0.287611i	−0.989606	+	0.143806i	$0.954066\pi$
$744$	0.280221	−	0.161786i	0.0102734	−	0.00593135i
$745$	−3.79620	+	6.57521i	−0.139082	+	0.240897i
$746$	3.79214	−	6.56817i	0.138840	−	0.240478i
$747$	10.7048	+	18.5412i	0.391667	+	0.678387i
$748$		0			0
$749$	−39.1233	−	17.8572i	−1.42953	−	0.652488i
$750$		−	3.35715i		−	0.122586i
$751$	12.3981	+	21.4741i	0.452412	+	0.783601i	0.998535	−	0.0541038i	$-0.0172302\pi$
$751$	12.3981	+	21.4741i	0.452412	+	0.783601i	−0.546123	+	0.837705i	$0.683897\pi$
$752$	−25.0690	−	14.4736i	−0.914174	−	0.527798i
$753$	2.21432	−	3.83532i	0.0806944	−	0.139767i
$754$	15.8536	+	27.4592i	0.577354	+	1.00001i
$755$	3.40655			0.123977
$756$	−0.00857596	−	0.0896153i	−0.000311905	−	0.00325928i
$757$	35.0126			1.27255			0.636277	−	0.771460i	$-0.280473\pi$
$757$	35.0126			1.27255			0.636277	+	0.771460i	$0.280473\pi$
$758$	−31.2317	+	18.0316i	−1.13439	+	0.654938i
$759$		0			0
$760$	−14.2807	+	24.7350i	−0.518017	+	0.897231i
$761$	−1.11935	−	1.93877i	−0.0405763	−	0.0702802i	0.845024	−	0.534728i	$-0.179586\pi$
$761$	−1.11935	−	1.93877i	−0.0405763	−	0.0702802i	−0.885600	+	0.464448i	$0.846253\pi$
$762$		−	1.11801i		−	0.0405012i
$763$	0.447333	+	4.67445i	0.0161945	+	0.169226i
$764$	0.261428			0.00945813
$765$	10.6746	−	6.16297i	0.385940	−	0.222823i
$766$	−26.4360	+	45.7884i	−0.955170	+	1.65440i
$767$	3.94064	+	2.27513i	0.142288	+	0.0821502i
$768$	0.118674	−	0.0685167i	0.00428229	−	0.00247238i
$769$	16.6808			0.601525			0.300762	−	0.953699i	$-0.402759\pi$
$769$	16.6808			0.601525			0.300762	+	0.953699i	$0.402759\pi$
$770$		0			0
$771$	−3.22185			−0.116032
$772$	−0.0263603	+	0.0152191i	−0.000948727	+	0.000547748i
$773$	32.4062	+	18.7097i	1.16557	+	0.672942i	0.952633	−	0.304123i	$-0.0983635\pi$
$773$	32.4062	+	18.7097i	1.16557	+	0.672942i	0.212938	+	0.977066i	$0.431697\pi$
$774$	19.7704	−	34.2433i	0.710632	−	1.23085i
$775$	1.29386	−	0.747013i	0.0464770	−	0.0268335i
$776$	−22.8534			−0.820390
$777$	−1.91767	+	1.36617i	−0.0687962	+	0.0490110i
$778$			33.2360i			1.19157i
$779$	−24.0548	−	41.6641i	−0.861853	−	1.49277i
$780$	−0.0273591	+	0.0473873i	−0.000979613	+	0.00169674i
$781$		0			0
$782$	3.42102	−	1.97513i	0.122336	−	0.0706305i
$783$	−4.36509			−0.155996
$784$	−27.1026	+	5.23525i	−0.967951	+	0.186973i
$785$	7.27755			0.259747
$786$	−2.01775	−	3.49485i	−0.0719709	−	0.124657i
$787$	14.0551	−	24.3442i	0.501011	−	0.867776i	−0.498989	−	0.866609i	$-0.666295\pi$
$787$	14.0551	−	24.3442i	0.501011	−	0.867776i	0.999999	−	0.00116744i	$-0.000371609\pi$
$788$	0.248940	+	0.143726i	0.00886812	+	0.00512001i
$789$	−2.00864	−	3.47907i	−0.0715096	−	0.123858i
$790$			5.88890i			0.209518i
$791$	−17.1488	−	24.0715i	−0.609740	−	0.855884i
$792$		0			0
$793$	24.7878	+	42.9337i	0.880240	+	1.52462i
$794$	13.2128	−	22.8853i	0.468906	−	0.812169i
$795$	0.466988	−	0.808847i	0.0165624	−	0.0286868i
$796$	0.0584714	−	0.0337585i	0.00207246	−	0.00119654i
$797$			25.1696i			0.891552i	0.895144	+	0.445776i	$0.147072\pi$
$797$			25.1696i			0.891552i	−0.895144	+	0.445776i	$0.852928\pi$
$798$	−2.08188	+	4.56118i	−0.0736978	+	0.161464i
$799$			20.1221i			0.711870i
$800$	0.367854	−	0.212381i	0.0130056	−	0.00750879i
$801$	−2.91555	−	1.68329i	−0.103016	−	0.0594762i
$802$	−18.8287	−	10.8708i	−0.664865	−	0.383860i
$803$		0			0
$804$		−	0.0247503i		−	0.000872876i
$805$	0.393151	+	4.10828i	0.0138568	+	0.144798i
$806$	4.91738			0.173207
$807$	−2.93286	−	5.07986i	−0.103242	−	0.178820i
$808$	−17.0255	−	9.82966i	−0.598954	−	0.345806i
$809$	27.9468	+	16.1351i	0.982558	+	0.567280i	0.903041	−	0.429553i	$-0.141329\pi$
$809$	27.9468	+	16.1351i	0.982558	+	0.567280i	0.0795165	+	0.996834i	$0.474662\pi$
$810$	−9.20590	−	15.9451i	−0.323462	−	0.560253i
$811$	−0.408049			−0.0143285			−0.00716427	−	0.999974i	$-0.502280\pi$
$811$	−0.408049			−0.0143285			−0.00716427	+	0.999974i	$0.502280\pi$
$812$	−0.0252082	−	0.263416i	−0.000884634	−	0.00924408i
$813$		−	1.10769i		−	0.0388484i
$814$		0			0
$815$	0.845116	+	0.487928i	0.0296031	+	0.0170914i
$816$	1.91465	+	1.10542i	0.0670260	+	0.0386975i
$817$	54.3871	−	31.4004i	1.90276	−	1.09856i
$818$			28.8169i			1.00756i
$819$	20.4846	−	44.8795i	0.715788	−	1.56822i
$820$		−	0.309481i		−	0.0108076i
$821$	−6.26316	+	3.61604i	−0.218586	+	0.126201i	−0.605295	−	0.796001i	$-0.706945\pi$
$821$	−6.26316	+	3.61604i	−0.218586	+	0.126201i	0.386709	+	0.922202i	$0.373612\pi$
$822$	−1.49599	+	2.59113i	−0.0521786	+	0.0903761i
$823$	−15.0145	+	26.0059i	−0.523372	+	0.906507i	0.476258	+	0.879306i	$0.341993\pi$
$823$	−15.0145	+	26.0059i	−0.523372	+	0.906507i	−0.999630	+	0.0272015i	$0.991340\pi$
$824$	3.16525	+	5.48237i	0.110267	+	0.190987i
$825$		0			0
$826$	1.55623	+	2.18447i	0.0541483	+	0.0760074i
$827$		−	13.9107i		−	0.483721i	−0.970311	−	0.241861i	$-0.922242\pi$
$827$		−	13.9107i		−	0.483721i	0.970311	−	0.241861i	$-0.0777577\pi$
$828$	0.0423806	+	0.0734053i	0.00147283	+	0.00255101i
$829$	23.9715	+	13.8399i	0.832564	+	0.480681i	0.854730	−	0.519073i	$-0.173723\pi$
$829$	23.9715	+	13.8399i	0.832564	+	0.480681i	−0.0221660	+	0.999754i	$0.507056\pi$
$830$	7.72465	−	13.3795i	0.268126	−	0.464408i
$831$	0.260152	+	0.450596i	0.00902457	+	0.0156310i
$832$	51.1108			1.77195
$833$	12.5716	+	14.4962i	0.435579	+	0.502265i
$834$	0.609990			0.0211222
$835$	18.7649	−	10.8339i	0.649386	−	0.374923i
$836$		0			0
$837$	−0.338485	+	0.586273i	−0.0116998	+	0.0202646i
$838$	−7.98396	−	13.8286i	−0.275801	−	0.477702i
$839$			12.1213i			0.418475i	0.977865	+	0.209238i	$0.0670982\pi$
$839$			12.1213i			0.418475i	−0.977865	+	0.209238i	$0.932902\pi$
$840$	−1.90786	+	1.35918i	−0.0658274	+	0.0468960i
$841$	16.1692			0.557560
$842$	−17.9139	+	10.3426i	−0.617354	+	0.356429i
$843$	−2.15586	+	3.73406i	−0.0742519	+	0.128608i
$844$	0.641307	+	0.370259i	0.0220747	+	0.0127448i
$845$	−35.1902	+	20.3171i	−1.21058	+	0.698929i
$846$	30.4947			1.04843
$847$		0			0
$848$	−11.8464			−0.406808
$849$	−1.26298	+	0.729182i	−0.0433454	+	0.0250255i
$850$	8.96569	+	5.17635i	0.307521	+	0.177547i
$851$	2.23255	−	3.86690i	0.0765310	−	0.132556i
$852$	−0.0236841	+	0.0136740i	−0.000811405	+	0.000468465i
$853$	56.4171			1.93168			0.965842	−	0.259131i	$-0.0834360\pi$
$853$	56.4171			1.93168			0.965842	+	0.259131i	$0.0834360\pi$
$854$	2.78375	+	29.0891i	0.0952579	+	0.995407i
$855$		−	29.6681i		−	1.01463i
$856$	23.1453	+	40.0888i	0.791090	+	1.37021i
$857$	10.8680	−	18.8240i	0.371244	−	0.643014i	−0.618513	−	0.785775i	$-0.712265\pi$
$857$	10.8680	−	18.8240i	0.371244	−	0.643014i	0.989757	+	0.142760i	$0.0455978\pi$
$858$		0			0
$859$	47.8041	−	27.5997i	1.63105	−	0.941689i	0.647285	−	0.762248i	$-0.275905\pi$
$859$	47.8041	−	27.5997i	1.63105	−	0.941689i	0.983769	−	0.179441i	$-0.0574288\pi$
$860$	0.403988			0.0137759
$861$	−0.375881	−	3.92781i	−0.0128100	−	0.133859i
$862$	16.7110			0.569180
$863$	−15.3439	−	26.5764i	−0.522313	−	0.904672i	−0.999663	−	0.0259588i	$-0.991736\pi$
$863$	−15.3439	−	26.5764i	−0.522313	−	0.904672i	0.477350	−	0.878713i	$-0.341597\pi$
$864$	−0.0962335	+	0.166681i	−0.00327393	+	0.00567061i
$865$	20.2960	+	11.7179i	0.690083	+	0.398420i
$866$	22.0277	+	38.1530i	0.748530	+	1.29649i
$867$			1.94016i			0.0658914i
$868$	−0.0373339	−	0.0170405i	−0.00126720	−	0.000578392i
$869$		0			0
$870$	0.781943	+	1.35436i	0.0265103	+	0.0459173i
$871$	13.6590	−	23.6581i	0.462819	−	0.801626i
$872$	2.52723	−	4.37729i	0.0855827	−	0.148234i
$873$	20.5585	−	11.8695i	0.695800	−	0.401720i
$874$		−	9.50813i		−	0.321617i
$875$	−25.1867	+	17.9432i	−0.851466	+	0.606592i
$876$			0.0556681i			0.00188085i
$877$	1.47798	−	0.853314i	0.0499079	−	0.0288144i	−0.474838	−	0.880073i	$-0.657493\pi$
$877$	1.47798	−	0.853314i	0.0499079	−	0.0288144i	0.524746	+	0.851259i	$0.324160\pi$
$878$	30.0474	+	17.3479i	1.01405	+	0.585463i
$879$	1.12560	+	0.649863i	0.0379654	+	0.0219193i
$880$		0			0
$881$			5.50028i			0.185309i	0.995698	+	0.0926546i	$0.0295352\pi$
$881$			5.50028i			0.185309i	−0.995698	+	0.0926546i	$0.970465\pi$
$882$	21.9687	−	19.0519i	0.739725	−	0.641512i
$883$	−20.3004			−0.683162			−0.341581	−	0.939852i	$-0.610962\pi$
$883$	−20.3004			−0.683162			−0.341581	+	0.939852i	$0.610962\pi$
$884$	−0.241224	−	0.417812i	−0.00811324	−	0.0140525i
$885$	0.194363	+	0.112216i	0.00653345	+	0.00377209i
$886$	−40.5792	−	23.4284i	−1.36328	−	0.787092i
$887$	8.24337	+	14.2779i	0.276785	+	0.479406i	0.970584	−	0.240763i	$-0.0773976\pi$
$887$	8.24337	+	14.2779i	0.276785	+	0.479406i	−0.693799	+	0.720169i	$0.744064\pi$
$888$	2.53438			0.0850482
$889$	−8.38774	+	5.97550i	−0.281316	+	0.200412i
$890$			2.42935i			0.0814322i
$891$		0			0
$892$	0.276928	+	0.159884i	0.00927222	+	0.00535332i
$893$	41.9445	+	24.2166i	1.40362	+	0.810379i
$894$	1.24241	−	0.717304i	0.0415523	−	0.0239902i
$895$			6.83820i			0.228576i
$896$	26.6467	+	12.1625i	0.890203	+	0.406319i
$897$		−	1.32298i		−	0.0441729i
$898$	28.5106	−	16.4606i	0.951412	−	0.549298i
$899$	−0.994944	+	1.72329i	−0.0331832	+	0.0574751i
$900$	−0.111069	+	0.192378i	−0.00370231	+	0.00641260i
$901$	4.11741	+	7.13157i	0.137171	+	0.237587i
$902$		0			0
$903$	5.12725	−	0.490664i	0.170624	−	0.0163283i
$904$			31.8127i			1.05807i
$905$	4.72805	+	8.18922i	0.157166	+	0.272219i
$906$	−0.557442	−	0.321839i	−0.0185198	−	0.0106924i
$907$	−6.09383	+	10.5548i	−0.202342	+	0.350467i	−0.949283	−	0.314424i	$-0.898189\pi$
$907$	−6.09383	+	10.5548i	−0.202342	+	0.350467i	0.746940	+	0.664891i	$0.231522\pi$
$908$	−0.269127	−	0.466141i	−0.00893128	−	0.0154694i
$909$	20.4210			0.677323
$910$	−35.4375	+	3.39128i	−1.17474	+	0.112420i
$911$	30.6021			1.01389			0.506947	−	0.861977i	$-0.330774\pi$
$911$	30.6021			1.01389			0.506947	+	0.861977i	$0.330774\pi$
$912$	4.60849	−	2.66071i	0.152602	−	0.0881050i
$913$		0			0
$914$	1.05885	−	1.83398i	0.0350235	−	0.0606625i
$915$	1.22260	+	2.11761i	0.0404180	+	0.0700060i
$916$			0.642046i			0.0212138i
$917$	−15.4353	+	33.8172i	−0.509719	+	1.11674i
$918$	−4.69099			−0.154826
$919$	−44.0360	+	25.4242i	−1.45262	+	0.838668i	−0.998629	−	0.0523411i	$-0.983332\pi$
$919$	−44.0360	+	25.4242i	−1.45262	+	0.838668i	−0.453986	+	0.891009i	$0.649998\pi$
$920$	2.22113	−	3.84711i	0.0732284	−	0.126835i
$921$	3.63850	+	2.10069i	0.119893	+	0.0692200i
$922$	−19.1926	+	11.0808i	−0.632073	+	0.364928i
$923$	−30.1853			−0.993562
$924$		0			0
$925$	11.7020			0.384759
$926$	−10.9408	+	6.31667i	−0.359537	+	0.207579i
$927$	−5.69479	−	3.28789i	−0.187041	−	0.107988i
$928$	−0.282869	+	0.489943i	−0.00928563	+	0.0160832i
$929$	14.9439	−	8.62787i	0.490294	−	0.283071i	−0.234403	−	0.972140i	$-0.575313\pi$
$929$	14.9439	−	8.62787i	0.490294	−	0.283071i	0.724696	+	0.689068i	$0.241980\pi$
$930$	0.242539			0.00795316
$931$	45.3470	−	8.75940i	1.48619	−	0.287078i
$932$		−	0.245697i		−	0.00804807i
$933$	−1.65614	−	2.86852i	−0.0542197	−	0.0939113i
$934$	23.2024	−	40.1877i	0.759205	−	1.31498i
$935$		0			0
$936$	−45.9871	+	26.5507i	−1.50314	+	0.867836i
$937$	0.555443			0.0181455			0.00907277	−	0.999959i	$-0.497112\pi$
$937$	0.555443			0.0181455			0.00907277	+	0.999959i	$0.497112\pi$
$938$	13.1147	−	9.34305i	0.428211	−	0.305061i
$939$	5.61916			0.183374
$940$	0.155782	+	0.269822i	0.00508104	+	0.00880062i
$941$	15.6720	−	27.1448i	0.510894	−	0.884894i	−0.489026	−	0.872269i	$-0.662648\pi$
$941$	15.6720	−	27.1448i	0.510894	−	0.884894i	0.999920	−	0.0126252i	$-0.00401883\pi$
$942$	−1.19089	−	0.687558i	−0.0388011	−	0.0224019i
$943$	3.74132	+	6.48015i	0.121834	+	0.211023i
$944$		−	2.84666i		−	0.0926508i
$945$	2.03500	−	4.45846i	0.0661984	−	0.145034i
$946$		0			0
$947$	−28.5500	−	49.4500i	−0.927749	−	1.60691i	−0.787079	−	0.616853i	$-0.788407\pi$
$947$	−28.5500	−	49.4500i	−0.927749	−	1.60691i	−0.140671	−	0.990056i	$-0.544926\pi$
$948$	−0.00787735	+	0.0136440i	−0.000255844	+	0.000443135i
$949$	−30.7217	+	53.2116i	−0.997270	+	1.72732i
$950$	21.5801	−	12.4593i	0.700151	−	0.404233i
$951$			4.13422i			0.134061i
$952$	−1.96752	−	20.5598i	−0.0637676	−	0.666346i
$953$		−	0.0596816i		−	0.00193328i	−1.00000		0.000966639i	$-0.999692\pi$
$953$		−	0.0596816i		−	0.00193328i	1.00000		0.000966639i	$-0.000307691\pi$
$954$	10.8077	−	6.23985i	0.349913	−	0.202022i
$955$	12.3253	+	7.11604i	0.398839	+	0.230270i
$956$	−0.233833	−	0.135004i	−0.00756271	−	0.00436633i
$957$		0			0
$958$			39.3468i			1.27124i
$959$	27.4354	−	2.62550i	0.885936	−	0.0847818i
$960$	2.52092			0.0813624
$961$	−15.3457	−	26.5795i	−0.495022	−	0.857404i
$962$	33.3554	+	19.2577i	1.07542	+	0.620895i
$963$	−41.6421	−	24.0421i	−1.34190	−	0.774746i
$964$	−0.350946	−	0.607856i	−0.0113032	−	0.0195777i
$965$	−1.65705			−0.0533423
$966$	0.323801	−	0.709415i	0.0104181	−	0.0228251i
$967$		−	27.4643i		−	0.883194i	−0.897214	−	0.441597i	$-0.854412\pi$
$967$		−	27.4643i		−	0.883194i	0.897214	−	0.441597i	$-0.145588\pi$
$968$		0			0
$969$	−3.20351	−	1.84955i	−0.102911	−	0.0594159i
$970$	−14.8352	−	8.56509i	−0.476329	−	0.275008i
$971$	−5.97105	+	3.44739i	−0.191620	+	0.110632i	−0.592741	−	0.805393i	$-0.701954\pi$
$971$	−5.97105	+	3.44739i	−0.191620	+	0.110632i	0.401121	+	0.916025i	$0.368621\pi$
$972$		−	0.151336i		−	0.00485410i
$973$	−3.26026	−	4.57639i	−0.104519	−	0.146712i
$974$		−	24.0612i		−	0.770970i
$975$	3.00269	−	1.73360i	0.0961630	−	0.0555198i
$976$	15.5073	−	26.8595i	0.496377	−	0.859750i
$977$	7.05508	−	12.2198i	0.225712	−	0.390945i	−0.730821	−	0.682569i	$-0.760862\pi$
$977$	7.05508	−	12.2198i	0.225712	−	0.390945i	0.956533	+	0.291625i	$0.0941958\pi$
$978$	−0.0921956	−	0.159687i	−0.00294809	−	0.00510624i
$979$		0			0
$980$	0.280802	+	0.0970563i	0.00896989	+	0.00310035i
$981$			5.25030i			0.167629i
$982$	−19.6218	−	33.9860i	−0.626157	−	1.08454i
$983$	−18.6919	−	10.7918i	−0.596178	−	0.344204i	0.171359	−	0.985209i	$-0.445184\pi$
$983$	−18.6919	−	10.7918i	−0.596178	−	0.344204i	−0.767537	+	0.641005i	$0.778518\pi$
$984$	−2.12356	+	3.67811i	−0.0676966	+	0.117254i
$985$	7.82439	+	13.5522i	0.249306	+	0.431810i
$986$	−13.7887			−0.439122
$987$	2.30483	+	3.23526i	0.0733636	+	0.102980i
$988$	−1.16124			−0.0369438
$989$	−8.45900	+	4.88380i	−0.268980	+	0.155296i
$990$		0			0
$991$	16.2034	−	28.0651i	0.514717	−	0.891516i	−0.485137	−	0.874438i	$-0.661230\pi$
$991$	16.2034	−	28.0651i	0.514717	−	0.891516i	0.999854	−	0.0170778i	$-0.00543631\pi$
$992$	0.0438693	+	0.0759839i	0.00139285	+	0.00241249i
$993$		−	0.0390755i		−	0.00124002i
$994$	−16.1862	−	7.38793i	−0.513394	−	0.234331i
$995$	3.67561			0.116525
$996$	0.0357944	−	0.0206659i	0.00113419	−	0.000654825i
$997$	−14.7705	+	25.5832i	−0.467786	+	0.810228i	−0.999322	−	0.0368069i	$-0.988281\pi$
$997$	−14.7705	+	25.5832i	−0.467786	+	0.810228i	0.531537	+	0.847035i	$0.321615\pi$
$998$	−16.2527	−	9.38349i	−0.514469	−	0.297029i
$999$	−4.59200	+	2.65119i	−0.145284	+	0.0838800i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.i.b.241.18		48
7.5	odd	6	inner	847.2.i.b.362.7		48
11.2	odd	10		77.2.n.a.73.5	yes	48
11.3	even	5		847.2.r.a.717.2		48
11.4	even	5		847.2.r.d.94.5		48
11.5	even	5		77.2.n.a.52.2	yes	48
11.6	odd	10		847.2.r.c.360.5		48
11.7	odd	10		847.2.r.a.94.2		48
11.8	odd	10		847.2.r.d.717.5		48
11.9	even	5		847.2.r.c.766.2		48
11.10	odd	2	inner	847.2.i.b.241.7		48
33.2	even	10		693.2.cg.a.73.2		48
33.5	odd	10		693.2.cg.a.514.5		48
77.2	odd	30		539.2.s.d.117.2		48
77.5	odd	30		77.2.n.a.19.5	✓	48
77.13	even	10		539.2.s.d.227.5		48
77.16	even	15		539.2.s.d.19.5		48
77.19	even	30		847.2.r.d.838.5		48
77.24	even	30		539.2.m.a.293.4		48
77.26	odd	30		847.2.r.d.215.5		48
77.27	odd	10		539.2.s.d.129.2		48
77.38	odd	30		539.2.m.a.195.3		48
77.40	even	30		847.2.r.a.215.2		48
77.46	odd	30		539.2.m.a.293.3		48
77.47	odd	30		847.2.r.a.838.2		48
77.54	even	6	inner	847.2.i.b.362.18		48
77.60	even	15		539.2.m.a.195.4		48
77.61	even	30		847.2.r.c.481.2		48
77.68	even	30		77.2.n.a.40.2	yes	48
77.75	odd	30		847.2.r.c.40.5		48
231.5	even	30		693.2.cg.a.19.2		48
231.68	odd	30		693.2.cg.a.271.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.n.a.19.5	✓	48	77.5	odd	30
77.2.n.a.40.2	yes	48	77.68	even	30
77.2.n.a.52.2	yes	48	11.5	even	5
77.2.n.a.73.5	yes	48	11.2	odd	10
539.2.m.a.195.3		48	77.38	odd	30
539.2.m.a.195.4		48	77.60	even	15
539.2.m.a.293.3		48	77.46	odd	30
539.2.m.a.293.4		48	77.24	even	30
539.2.s.d.19.5		48	77.16	even	15
539.2.s.d.117.2		48	77.2	odd	30
539.2.s.d.129.2		48	77.27	odd	10
539.2.s.d.227.5		48	77.13	even	10
693.2.cg.a.19.2		48	231.5	even	30
693.2.cg.a.73.2		48	33.2	even	10
693.2.cg.a.271.5		48	231.68	odd	30
693.2.cg.a.514.5		48	33.5	odd	10
847.2.i.b.241.7		48	11.10	odd	2	inner
847.2.i.b.241.18		48	1.1	even	1	trivial
847.2.i.b.362.7		48	7.5	odd	6	inner
847.2.i.b.362.18		48	77.54	even	6	inner
847.2.r.a.94.2		48	11.7	odd	10
847.2.r.a.215.2		48	77.40	even	30
847.2.r.a.717.2		48	11.3	even	5
847.2.r.a.838.2		48	77.47	odd	30
847.2.r.c.40.5		48	77.75	odd	30
847.2.r.c.360.5		48	11.6	odd	10
847.2.r.c.481.2		48	77.61	even	30
847.2.r.c.766.2		48	11.9	even	5
847.2.r.d.94.5		48	11.4	even	5
847.2.r.d.215.5		48	77.26	odd	30
847.2.r.d.717.5		48	11.8	odd	10
847.2.r.d.838.5		48	77.19	even	30

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.21617 - 0.702153i) q^{2} +(0.177127 + 0.102264i) q^{3} +(-0.0139610 + 0.0241811i) q^{4} +(-1.31641 + 0.760032i) q^{5} +0.287221 q^{6} +(-1.53513 - 2.15485i) q^{7} +2.84782i q^{8} +(-1.47908 - 2.56185i) q^{9} +(-1.06732 + 1.84865i) q^{10} +(-0.00494574 + 0.00285542i) q^{12} -6.30332 q^{13} +(-3.38001 - 1.54275i) q^{14} -0.310897 q^{15} +(1.97169 + 3.41506i) q^{16} +(1.37058 - 2.37392i) q^{17} +(-3.59762 - 2.07709i) q^{18} +(-3.29895 - 5.71394i) q^{19} -0.0424432i q^{20} +(-0.0515495 - 0.538671i) q^{21} +(0.513095 + 0.888707i) q^{23} +(-0.291231 + 0.504427i) q^{24} +(-1.34470 + 2.32909i) q^{25} +(-7.66588 + 4.42590i) q^{26} -1.21862i q^{27} +(0.0735386 - 0.00703745i) q^{28} -3.58201i q^{29} +(-0.378102 + 0.218297i) q^{30} +(-0.481097 - 0.277762i) q^{31} +(-0.136779 - 0.0789694i) q^{32} -3.84944i q^{34} +(3.65862 + 1.66992i) q^{35} +0.0825978 q^{36} +(-2.17557 - 3.76821i) q^{37} +(-8.02413 - 4.63273i) q^{38} +(-1.11649 - 0.644605i) q^{39} +(-2.16444 - 3.74892i) q^{40} +7.29166 q^{41} +(-0.440923 - 0.618918i) q^{42} +9.51832i q^{43} +(3.89418 + 2.24830i) q^{45} +(1.24802 + 0.720543i) q^{46} +(-6.35725 + 3.67036i) q^{47} +0.806534i q^{48} +(-2.28674 + 6.61595i) q^{49} +3.77675i q^{50} +(0.485535 - 0.280324i) q^{51} +(0.0880005 - 0.152421i) q^{52} +(-1.50207 + 2.60165i) q^{53} +(-0.855656 - 1.48204i) q^{54} +(6.13663 - 4.37179i) q^{56} -1.34946i q^{57} +(-2.51512 - 4.35631i) q^{58} +(-0.625169 - 0.360942i) q^{59} +(0.00434043 - 0.00751784i) q^{60} +(-3.93250 - 6.81128i) q^{61} -0.780125 q^{62} +(-3.24980 + 7.11998i) q^{63} -8.10855 q^{64} +(8.29778 - 4.79073i) q^{65} +(-2.16696 + 3.75328i) q^{67} +(0.0382693 + 0.0662845i) q^{68} +0.209886i q^{69} +(5.62204 - 0.538014i) q^{70} +4.78880 q^{71} +(7.29570 - 4.21217i) q^{72} +(4.87390 - 8.44184i) q^{73} +(-5.29172 - 3.05517i) q^{74} +(-0.476366 + 0.275030i) q^{75} +0.184226 q^{76} -1.81045 q^{78} +(2.38913 - 1.37937i) q^{79} +(-5.19112 - 2.99709i) q^{80} +(-4.31263 + 7.46970i) q^{81} +(8.86787 - 5.11987i) q^{82} -7.23743 q^{83} +(0.0137454 + 0.00627385i) q^{84} +4.16675i q^{85} +(6.68332 + 11.5758i) q^{86} +(0.366312 - 0.634471i) q^{87} +(0.985593 - 0.569032i) q^{89} +6.31462 q^{90} +(9.67643 + 13.5827i) q^{91} -0.0286532 q^{92} +(-0.0568103 - 0.0983983i) q^{93} +(-5.15431 + 8.92753i) q^{94} +(8.68556 + 5.01461i) q^{95} +(-0.0161515 - 0.0279752i) q^{96} +8.02487i q^{97} +(1.86437 + 9.65173i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{3} + 16 q^{4} + 14 q^{9} - 12 q^{12} + 32 q^{14} + 20 q^{15} + 8 q^{16} + 10 q^{23} - 24 q^{25} - 78 q^{26} - 6 q^{31} + 72 q^{36} - 36 q^{37} - 102 q^{38} + 44 q^{42} - 84 q^{45} - 12 q^{47}+ \cdots + 68 q^{93}+O(q^{100}) \) 48 * q + 6 * q^3 + 16 * q^4 + 14 * q^9 - 12 * q^12 + 32 * q^14 + 20 * q^15 + 8 * q^16 + 10 * q^23 - 24 * q^25 - 78 * q^26 - 6 * q^31 + 72 * q^36 - 36 * q^37 - 102 * q^38 + 44 * q^42 - 84 * q^45 - 12 * q^47 - 46 * q^49 + 12 * q^53 - 8 * q^56 - 74 * q^58 + 132 * q^59 + 20 * q^60 + 12 * q^64 + 44 * q^67 + 38 * q^70 - 100 * q^71 - 42 * q^75 + 92 * q^78 + 90 * q^80 - 4 * q^81 + 66 * q^82 - 22 * q^86 + 6 * q^89 + 58 * q^91 + 80 * q^92 + 68 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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