LMFDB - Embedded newform 961.2.d.s.374.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

sage:traces = [64,8,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			374.10
Character	$\chi$	$=$	961.374
Dual form			961.2.d.s.388.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.06472 + 0.773568i) q^{2} +(0.998704 - 0.725601i) q^{3} +(-0.0828021 - 0.254839i) q^{4} +0.00727825 q^{5} +1.62465 q^{6} +(-0.245643 - 0.756011i) q^{7} +(0.922351 - 2.83870i) q^{8} +(-0.456138 + 1.40385i) q^{9} +(0.00774933 + 0.00563022i) q^{10} +(1.22916 + 3.78297i) q^{11} +(-0.267606 - 0.194427i) q^{12} +(5.10468 - 3.70877i) q^{13} +(0.323284 - 0.994966i) q^{14} +(0.00726882 - 0.00528110i) q^{15} +(2.74442 - 1.99394i) q^{16} +(1.94089 - 5.97344i) q^{17} +(-1.57163 + 1.14186i) q^{18} +(-3.02135 - 2.19514i) q^{19} +(-0.000602654 - 0.00185478i) q^{20} +(-0.793887 - 0.576793i) q^{21} +(-1.61767 + 4.97867i) q^{22} +(0.149463 - 0.460000i) q^{23} +(-1.13861 - 3.50428i) q^{24} -4.99995 q^{25} +8.30406 q^{26} +(1.70750 + 5.25514i) q^{27} +(-0.172321 + 0.125199i) q^{28} +(1.31103 + 0.952516i) q^{29} +0.0118246 q^{30} -1.50508 q^{32} +(3.97250 + 2.88619i) q^{33} +(6.68738 - 4.85866i) q^{34} +(-0.00178785 - 0.00550244i) q^{35} +0.395524 q^{36} +7.49037 q^{37} +(-1.51882 - 4.67444i) q^{38} +(2.40698 - 7.40792i) q^{39} +(0.00671310 - 0.0206608i) q^{40} +(3.25942 + 2.36811i) q^{41} +(-0.399083 - 1.22825i) q^{42} +(-0.567529 - 0.412334i) q^{43} +(0.862271 - 0.626476i) q^{44} +(-0.00331989 + 0.0102176i) q^{45} +(0.514978 - 0.374153i) q^{46} +(-3.48307 + 2.53060i) q^{47} +(1.29406 - 3.98271i) q^{48} +(5.15191 - 3.74308i) q^{49} +(-5.32357 - 3.86780i) q^{50} +(-2.39596 - 7.37401i) q^{51} +(-1.36782 - 0.993776i) q^{52} +(-1.26069 + 3.88001i) q^{53} +(-2.24719 + 6.91615i) q^{54} +(0.00894615 + 0.0275334i) q^{55} -2.37266 q^{56} -4.61023 q^{57} +(0.659046 + 2.02833i) q^{58} +(11.0864 - 8.05477i) q^{59} +(-0.00194770 - 0.00141509i) q^{60} -5.02369 q^{61} +1.17337 q^{63} +(-7.09134 - 5.15216i) q^{64} +(0.0371531 - 0.0269933i) q^{65} +(1.99695 + 6.14599i) q^{66} -14.5255 q^{67} -1.68297 q^{68} +(-0.184507 - 0.567854i) q^{69} +(0.00235294 - 0.00724161i) q^{70} +(-2.90885 + 8.95253i) q^{71} +(3.56439 + 2.58968i) q^{72} +(1.36684 + 4.20670i) q^{73} +(7.97519 + 5.79431i) q^{74} +(-4.99347 + 3.62797i) q^{75} +(-0.309233 + 0.951720i) q^{76} +(2.55804 - 1.85852i) q^{77} +(8.29330 - 6.02544i) q^{78} +(-3.23196 + 9.94696i) q^{79} +(0.0199746 - 0.0145124i) q^{80} +(1.93587 + 1.40649i) q^{81} +(1.63849 + 5.04276i) q^{82} +(1.62460 + 1.18034i) q^{83} +(-0.0812536 + 0.250073i) q^{84} +(0.0141263 - 0.0434762i) q^{85} +(-0.285294 - 0.878044i) q^{86} +2.00047 q^{87} +11.8725 q^{88} +(-0.346834 - 1.06744i) q^{89} +(-0.0114387 + 0.00831074i) q^{90} +(-4.05780 - 2.94816i) q^{91} -0.129602 q^{92} -5.66611 q^{94} +(-0.0219902 - 0.0159768i) q^{95} +(-1.50313 + 1.09208i) q^{96} +(2.24819 + 6.91921i) q^{97} +8.38089 q^{98} -5.87139 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 8 q^{2} - 8 q^{4} - 64 q^{5} + 16 q^{7} - 8 q^{10} + 8 q^{14} + 8 q^{16} + 24 q^{18} + 32 q^{19} + 24 q^{20} + 8 q^{28} - 32 q^{32} + 32 q^{33} + 16 q^{35} - 160 q^{36} + 24 q^{38} + 32 q^{39} + 32 q^{41}+ \cdots + 64 q^{98}+O(q^{100}) $ 64 * q + 8 * q^2 - 8 * q^4 - 64 * q^5 + 16 * q^7 - 8 * q^10 + 8 * q^14 + 8 * q^16 + 24 * q^18 + 32 * q^19 + 24 * q^20 + 8 * q^28 - 32 * q^32 + 32 * q^33 + 16 * q^35 - 160 * q^36 + 24 * q^38 + 32 * q^39 + 32 * q^41 + 16 * q^45 + 32 * q^47 + 16 * q^49 + 32 * q^50 + 32 * q^51 - 192 * q^56 + 64 * q^59 - 64 * q^63 + 16 * q^64 + 64 * q^67 + 32 * q^69 - 88 * q^70 + 48 * q^71 - 48 * q^72 - 40 * q^76 - 32 * q^78 + 40 * q^80 + 16 * q^81 - 88 * q^82 - 128 * q^87 - 40 * q^90 - 128 * q^94 + 48 * q^95 + 64 * q^98

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	1.06472	+	0.773568i	0.752874	+	0.546995i	0.896716	−	0.442605i	$-0.145946\pi$
$2$	1.06472	+	0.773568i	0.752874	+	0.546995i	−0.143842	+	0.989601i	$0.545946\pi$
$3$	0.998704	−	0.725601i	0.576602	−	0.418926i	−0.260896	−	0.965367i	$-0.584018\pi$
$3$	0.998704	−	0.725601i	0.576602	−	0.418926i	0.837497	+	0.546441i	$0.184018\pi$
$4$	−0.0828021	−	0.254839i	−0.0414011	−	0.127419i
$5$	0.00727825			0.00325493			0.00162747	−	0.999999i	$-0.499482\pi$
$5$	0.00727825			0.00325493			0.00162747	+	0.999999i	$0.499482\pi$
$6$	1.62465			0.663259
$7$	−0.245643	−	0.756011i	−0.0928443	−	0.285745i	0.893842	−	0.448383i	$-0.148000\pi$
$7$	−0.245643	−	0.756011i	−0.0928443	−	0.285745i	−0.986686	+	0.162637i	$0.948000\pi$
$8$	0.922351	−	2.83870i	0.326100	−	1.00363i
$9$	−0.456138	+	1.40385i	−0.152046	+	0.467950i
$10$	0.00774933	+	0.00563022i	0.00245055	+	0.00178043i
$11$	1.22916	+	3.78297i	0.370606	+	1.14061i	0.946395	+	0.323011i	$0.104695\pi$
$11$	1.22916	+	3.78297i	0.370606	+	1.14061i	−0.575789	+	0.817598i	$0.695305\pi$
$12$	−0.267606	−	0.194427i	−0.0772512	−	0.0561263i
$13$	5.10468	−	3.70877i	1.41578	−	1.02863i	0.423334	−	0.905974i	$-0.360860\pi$
$13$	5.10468	−	3.70877i	1.41578	−	1.02863i	0.992450	−	0.122653i	$-0.0391403\pi$
$14$	0.323284	−	0.994966i	0.0864013	−	0.265916i
$15$	0.00726882	−	0.00528110i	0.00187680	−	0.00136358i
$16$	2.74442	−	1.99394i	0.686106	−	0.498485i
$17$	1.94089	−	5.97344i	0.470735	−	1.44877i	−0.380890	−	0.924621i	$-0.624382\pi$
$17$	1.94089	−	5.97344i	0.470735	−	1.44877i	0.851624	−	0.524152i	$-0.175618\pi$
$18$	−1.57163	+	1.14186i	−0.370438	+	0.269139i
$19$	−3.02135	−	2.19514i	−0.693146	−	0.503600i	0.184547	−	0.982824i	$-0.440918\pi$
$19$	−3.02135	−	2.19514i	−0.693146	−	0.503600i	−0.877693	+	0.479224i	$0.840918\pi$
$20$	−0.000602654	−	0.00185478i	−0.000134758	−	0.000414741i
$21$	−0.793887	−	0.576793i	−0.173240	−	0.125866i
$22$	−1.61767	+	4.97867i	−0.344888	+	1.06146i
$23$	0.149463	−	0.460000i	0.0311652	−	0.0959165i	−0.934264	−	0.356582i	$-0.883942\pi$
$23$	0.149463	−	0.460000i	0.0311652	−	0.0959165i	0.965429	+	0.260666i	$0.0839420\pi$
$24$	−1.13861	−	3.50428i	−0.232418	−	0.715309i
$25$	−4.99995			−0.999989
$26$	8.30406			1.62856
$27$	1.70750	+	5.25514i	0.328608	+	1.01135i
$28$	−0.172321	+	0.125199i	−0.0325656	+	0.0236603i
$29$	1.31103	+	0.952516i	0.243451	+	0.176878i	0.702820	−	0.711368i	$-0.251924\pi$
$29$	1.31103	+	0.952516i	0.243451	+	0.176878i	−0.459368	+	0.888246i	$0.651924\pi$
$30$	0.0118246			0.00215886
$31$		0			0
$31$		0			0
$32$	−1.50508			−0.266062
$33$	3.97250	+	2.88619i	0.691523	+	0.502421i
$34$	6.68738	−	4.85866i	1.14688	−	0.833254i
$35$	−0.00178785	−	0.00550244i	−0.000302202	−	0.000930082i
$36$	0.395524			0.0659207
$37$	7.49037			1.23141			0.615705	−	0.787977i	$-0.288871\pi$
$37$	7.49037			1.23141			0.615705	+	0.787977i	$0.288871\pi$
$38$	−1.51882	−	4.67444i	−0.246385	−	0.758295i
$39$	2.40698	−	7.40792i	0.385425	−	1.18622i
$40$	0.00671310	−	0.0206608i	0.00106143	−	0.00326676i
$41$	3.25942	+	2.36811i	0.509035	+	0.369836i	0.812458	−	0.583020i	$-0.198129\pi$
$41$	3.25942	+	2.36811i	0.509035	+	0.369836i	−0.303422	+	0.952856i	$0.598129\pi$
$42$	−0.399083	−	1.22825i	−0.0615798	−	0.189523i
$43$	−0.567529	−	0.412334i	−0.0865473	−	0.0628803i	0.543670	−	0.839299i	$-0.317034\pi$
$43$	−0.567529	−	0.412334i	−0.0865473	−	0.0628803i	−0.630217	+	0.776419i	$0.717034\pi$
$44$	0.862271	−	0.626476i	0.129992	−	0.0944449i
$45$	−0.00331989	+	0.0102176i	−0.000494900	+	0.00152314i
$46$	0.514978	−	0.374153i	0.0759293	−	0.0551659i
$47$	−3.48307	+	2.53060i	−0.508059	+	0.369126i	−0.812087	−	0.583537i	$-0.801668\pi$
$47$	−3.48307	+	2.53060i	−0.508059	+	0.369126i	0.304028	+	0.952663i	$0.401668\pi$
$48$	1.29406	−	3.98271i	0.186782	−	0.574855i
$49$	5.15191	−	3.74308i	0.735987	−	0.534726i
$50$	−5.32357	−	3.86780i	−0.752866	−	0.546989i
$51$	−2.39596	−	7.37401i	−0.335502	−	1.03257i
$52$	−1.36782	−	0.993776i	−0.189682	−	0.137812i
$53$	−1.26069	+	3.88001i	−0.173169	+	0.532961i	−0.999545	−	0.0301584i	$-0.990399\pi$
$53$	−1.26069	+	3.88001i	−0.173169	+	0.532961i	0.826376	+	0.563119i	$0.190399\pi$
$54$	−2.24719	+	6.91615i	−0.305804	+	0.941169i
$55$	0.00894615	+	0.0275334i	0.00120630	+	0.00371261i
$56$	−2.37266			−0.317060
$57$	−4.61023			−0.610640
$58$	0.659046	+	2.02833i	0.0865370	+	0.266333i
$59$	11.0864	−	8.05477i	1.44333	−	1.04864i	0.455999	−	0.889980i	$-0.349282\pi$
$59$	11.0864	−	8.05477i	1.44333	−	1.04864i	0.987333	−	0.158662i	$-0.0507181\pi$
$60$	−0.00194770	−	0.00141509i	−0.000251447	−	0.000182687i
$61$	−5.02369			−0.643218			−0.321609	−	0.946873i	$-0.604224\pi$
$61$	−5.02369			−0.643218			−0.321609	+	0.946873i	$0.604224\pi$
$62$		0			0
$63$	1.17337			0.147831
$64$	−7.09134	−	5.15216i	−0.886418	−	0.644020i
$65$	0.0371531	−	0.0269933i	0.00460828	−	0.00334811i
$66$	1.99695	+	6.14599i	0.245808	+	0.756519i
$67$	−14.5255			−1.77457			−0.887287	−	0.461217i	$-0.847413\pi$
$67$	−14.5255			−1.77457			−0.887287	+	0.461217i	$0.847413\pi$
$68$	−1.68297			−0.204091
$69$	−0.184507	−	0.567854i	−0.0222120	−	0.0683616i
$70$	0.00235294	−	0.00724161i	0.000281230	−	0.000865538i
$71$	−2.90885	+	8.95253i	−0.345217	+	1.06247i	0.616250	+	0.787551i	$0.288651\pi$
$71$	−2.90885	+	8.95253i	−0.345217	+	1.06247i	−0.961467	+	0.274919i	$0.911349\pi$
$72$	3.56439	+	2.58968i	0.420068	+	0.305197i
$73$	1.36684	+	4.20670i	0.159976	+	0.492357i	0.998631	−	0.0523068i	$-0.0166574\pi$
$73$	1.36684	+	4.20670i	0.159976	+	0.492357i	−0.838655	+	0.544664i	$0.816657\pi$
$74$	7.97519	+	5.79431i	0.927097	+	0.673575i
$75$	−4.99347	+	3.62797i	−0.576596	+	0.418921i
$76$	−0.309233	+	0.951720i	−0.0354714	+	0.109170i
$77$	2.55804	−	1.85852i	0.291515	−	0.211798i
$78$	8.29330	−	6.02544i	0.939031	−	0.682246i
$79$	−3.23196	+	9.94696i	−0.363624	+	1.11912i	0.587214	+	0.809432i	$0.300225\pi$
$79$	−3.23196	+	9.94696i	−0.363624	+	1.11912i	−0.950838	+	0.309688i	$0.899775\pi$
$80$	0.0199746	−	0.0145124i	0.00223323	−	0.00162254i
$81$	1.93587	+	1.40649i	0.215096	+	0.156277i
$82$	1.63849	+	5.04276i	0.180941	+	0.556880i
$83$	1.62460	+	1.18034i	0.178323	+	0.129559i	0.673366	−	0.739309i	$-0.264848\pi$
$83$	1.62460	+	1.18034i	0.178323	+	0.129559i	−0.495043	+	0.868868i	$0.664848\pi$
$84$	−0.0812536	+	0.250073i	−0.00886549	+	0.0272852i
$85$	0.0141263	−	0.0434762i	0.00153221	−	0.00471566i
$86$	−0.285294	−	0.878044i	−0.0307640	−	0.0946819i
$87$	2.00047			0.214473
$88$	11.8725			1.26561
$89$	−0.346834	−	1.06744i	−0.0367643	−	0.113149i	0.930990	−	0.365044i	$-0.118946\pi$
$89$	−0.346834	−	1.06744i	−0.0367643	−	0.113149i	−0.967754	+	0.251895i	$0.918946\pi$
$90$	−0.0114387	+	0.00831074i	−0.00120575	+	0.000876028i
$91$	−4.05780	−	2.94816i	−0.425373	−	0.309052i
$92$	−0.129602			−0.0135119
$93$		0			0
$94$	−5.66611			−0.584414
$95$	−0.0219902	−	0.0159768i	−0.00225614	−	0.00163918i
$96$	−1.50313	+	1.09208i	−0.153412	+	0.111460i
$97$	2.24819	+	6.91921i	0.228269	+	0.702540i	0.997943	+	0.0641030i	$0.0204186\pi$
$97$	2.24819	+	6.91921i	0.228269	+	0.702540i	−0.769674	+	0.638437i	$0.779581\pi$
$98$	8.38089			0.846598
$99$	−5.87139			−0.590097
$100$	0.414006	+	1.27418i	0.0414006	+	0.127418i
$101$	−1.98773	+	6.11760i	−0.197786	+	0.608724i	0.802146	+	0.597127i	$0.203691\pi$
$101$	−1.98773	+	6.11760i	−0.197786	+	0.608724i	−0.999933	+	0.0115963i	$0.996309\pi$
$102$	3.15326	−	9.70473i	0.312219	−	0.960912i
$103$	6.90531	+	5.01700i	0.680400	+	0.494340i	0.873490	−	0.486841i	$-0.161851\pi$
$103$	6.90531	+	5.01700i	0.680400	+	0.494340i	−0.193090	+	0.981181i	$0.561851\pi$
$104$	−5.81979	−	17.9115i	−0.570677	−	1.75636i
$105$	−0.00577811	−	0.00419804i	−0.000563886	−	0.000409687i
$106$	−4.34375	+	3.15592i	−0.421902	+	0.306530i
$107$	−4.17628	+	12.8533i	−0.403737	+	1.24257i	0.518209	+	0.855254i	$0.326599\pi$
$107$	−4.17628	+	12.8533i	−0.403737	+	1.24257i	−0.921946	+	0.387319i	$0.873401\pi$
$108$	1.19783	−	0.870274i	0.115261	−	0.0837422i
$109$	−8.27699	+	6.01358i	−0.792792	+	0.575997i	−0.908791	−	0.417253i	$-0.862993\pi$
$109$	−8.27699	+	6.01358i	−0.792792	+	0.575997i	0.115999	+	0.993249i	$0.462993\pi$
$110$	−0.0117738	+	0.0362360i	−0.00112259	+	0.00345496i
$111$	7.48066	−	5.43502i	0.710033	−	0.515869i
$112$	−2.18159	−	1.58502i	−0.206141	−	0.149770i
$113$	−2.57237	−	7.91695i	−0.241988	−	0.744764i	−0.996117	−	0.0880373i	$-0.971941\pi$
$113$	−2.57237	−	7.91695i	−0.241988	−	0.744764i	0.754129	−	0.656727i	$-0.228059\pi$
$114$	−4.90863	−	3.56633i	−0.459735	−	0.334017i
$115$	0.00108783	−	0.00334799i	0.000101441	−	0.000312202i
$116$	0.134182	−	0.412970i	0.0124585	−	0.0383433i
$117$	2.87811	+	8.85791i	0.266081	+	0.818914i
$118$	18.0349			1.66025
$119$	−4.99276			−0.457685
$120$	−0.00828709	−	0.0255051i	−0.000756505	−	0.00232828i
$121$	−3.90086	+	2.83414i	−0.354623	+	0.257649i
$122$	−5.34885	−	3.88617i	−0.484262	−	0.351837i
$123$	4.97349			0.448445
$124$		0			0
$125$	−0.0727821			−0.00650983
$126$	1.24932	+	0.907684i	0.111298	+	0.0808629i
$127$	−9.09849	+	6.61044i	−0.807361	+	0.586582i	−0.913064	−	0.407816i	$-0.866291\pi$
$127$	−9.09849	+	6.61044i	−0.807361	+	0.586582i	0.105704	+	0.994398i	$0.466291\pi$
$128$	−2.63459	−	8.10844i	−0.232867	−	0.716692i
$129$	−0.865983			−0.0762455
$130$	0.0604390			0.00530086
$131$	0.199494	+	0.613981i	0.0174299	+	0.0536437i	0.959393	−	0.282072i	$-0.0910218\pi$
$131$	0.199494	+	0.613981i	0.0174299	+	0.0536437i	−0.941963	+	0.335716i	$0.891022\pi$
$132$	0.406581	−	1.25133i	0.0353884	−	0.108914i
$133$	−0.917378	+	2.82340i	−0.0795468	+	0.244820i
$134$	−15.4657	−	11.2365i	−1.33603	−	0.970684i
$135$	0.0124276	+	0.0382482i	0.00106960	+	0.00329189i
$136$	−15.1667	−	11.0192i	−1.30053	−	0.944891i
$137$	−2.33317	+	1.69515i	−0.199336	+	0.144826i	−0.682976	−	0.730441i	$-0.739315\pi$
$137$	−2.33317	+	1.69515i	−0.199336	+	0.144826i	0.483640	+	0.875267i	$0.339315\pi$
$138$	0.242824	−	0.747337i	0.0206706	−	0.0636175i
$139$	−2.73354	+	1.98603i	−0.231855	+	0.168453i	−0.697647	−	0.716442i	$-0.745770\pi$
$139$	−2.73354	+	1.98603i	−0.231855	+	0.168453i	0.465792	+	0.884894i	$0.345770\pi$
$140$	−0.00125420		0.000911227i	−0.000105999		7.70128e-5i
$141$	−1.64235	+	5.05464i	−0.138311	+	0.425678i
$142$	−10.0225	+	7.28179i	−0.841071	+	0.611074i
$143$	20.3046	+	14.7522i	1.69796	+	1.23364i
$144$	1.54735	+	4.76227i	0.128946	+	0.396856i
$145$	0.00954197	+	0.00693265i	0.000792418	+	0.000575725i
$146$	−1.79886	+	5.53632i	−0.148875	+	0.458189i
$147$	2.42925	−	7.47645i	0.200361	−	0.616648i
$148$	−0.620219	−	1.90884i	−0.0509817	−	0.156905i
$149$	−11.7699			−0.964230			−0.482115	−	0.876108i	$-0.660131\pi$
$149$	−11.7699			−0.964230			−0.482115	+	0.876108i	$0.660131\pi$
$150$	−8.12315			−0.663252
$151$	−5.52168	−	16.9940i	−0.449348	−	1.38295i	−0.877644	−	0.479313i	$-0.840886\pi$
$151$	−5.52168	−	16.9940i	−0.449348	−	1.38295i	0.428296	−	0.903639i	$-0.359114\pi$
$152$	−9.01811	+	6.55204i	−0.731465	+	0.531441i
$153$	7.50050	+	5.44943i	0.606379	+	0.440560i
$154$	4.16130			0.335327
$155$		0			0
$156$	−2.08713			−0.167104
$157$	−2.15276	−	1.56407i	−0.171809	−	0.124826i	0.498558	−	0.866856i	$-0.333863\pi$
$157$	−2.15276	−	1.56407i	−0.171809	−	0.124826i	−0.670367	+	0.742030i	$0.733863\pi$
$158$	−11.1358	+	8.09063i	−0.885917	+	0.643656i
$159$	1.55628	+	4.78974i	0.123421	+	0.379851i
$160$	−0.0109543			−0.000866015
$161$	−0.384479			−0.0303012
$162$	0.973151	+	2.99505i	0.0764579	+	0.235313i
$163$	−5.22391	+	16.0775i	−0.409168	+	1.25929i	0.508196	+	0.861241i	$0.330312\pi$
$163$	−5.22391	+	16.0775i	−0.409168	+	1.25929i	−0.917364	+	0.398049i	$0.869688\pi$
$164$	0.333598	−	1.02671i	0.0260496	−	0.0801726i
$165$	0.0289128	+	0.0210064i	0.00225086	+	0.00163535i
$166$	0.816680	+	2.51348i	0.0633866	+	0.195084i
$167$	12.5257	+	9.10042i	0.969265	+	0.704212i	0.955284	−	0.295690i	$-0.0955496\pi$
$167$	12.5257	+	9.10042i	0.969265	+	0.704212i	0.0139808	+	0.999902i	$0.495550\pi$
$168$	−2.36959	+	1.72161i	−0.182818	+	0.132825i
$169$	8.28558	−	25.5004i	0.637353	−	1.96157i
$170$	0.0486724	−	0.0353626i	0.00373300	−	0.00271219i
$171$	4.45980	−	3.24024i	0.341050	−	0.247787i
$172$	−0.0580860	+	0.178770i	−0.00442902	+	0.0136311i
$173$	−5.59083	+	4.06197i	−0.425063	+	0.308826i	−0.779672	−	0.626189i	$-0.784614\pi$
$173$	−5.59083	+	4.06197i	−0.425063	+	0.308826i	0.354609	+	0.935015i	$0.384614\pi$
$174$	2.12995	+	1.54750i	0.161471	+	0.117316i
$175$	1.22820	+	3.78002i	0.0928433	+	0.285742i
$176$	10.9164	+	7.93120i	0.822852	+	0.597837i
$177$	5.22752	−	16.0887i	0.392925	−	1.20930i
$178$	0.456458	−	1.40483i	0.0342130	−	0.105297i
$179$	4.47490	+	13.7723i	0.334470	+	1.02939i	0.966983	+	0.254842i	$0.0820236\pi$
$179$	4.47490	+	13.7723i	0.334470	+	1.02939i	−0.632513	+	0.774550i	$0.717976\pi$
$180$	0.00287872			0.000214567
$181$	−17.3533			−1.28986			−0.644932	−	0.764240i	$-0.723114\pi$
$181$	−17.3533			−1.28986			−0.644932	+	0.764240i	$0.723114\pi$
$182$	−2.03984	−	6.27797i	−0.151203	−	0.465354i
$183$	−5.01718	+	3.64520i	−0.370881	+	0.269461i
$184$	−1.16795	−	0.848562i	−0.0861021	−	0.0625568i
$185$	0.0545168			0.00400815
$186$		0			0
$187$	24.9830			1.82694
$188$	0.933301	+	0.678083i	0.0680680	+	0.0494543i
$189$	3.55351	−	2.58178i	0.258480	−	0.187797i
$190$	−0.0110543	−	0.0340218i	−0.000801966	−	0.00246820i
$191$	14.9051			1.07850			0.539248	−	0.842147i	$-0.318709\pi$
$191$	14.9051			1.07850			0.539248	+	0.842147i	$0.318709\pi$
$192$	−10.8206			−0.780907
$193$	3.17531	+	9.77259i	0.228564	+	0.703446i	0.997910	+	0.0646149i	$0.0205819\pi$
$193$	3.17531	+	9.77259i	0.228564	+	0.703446i	−0.769347	+	0.638832i	$0.779418\pi$
$194$	−2.95878	+	9.10619i	−0.212428	+	0.653786i
$195$	0.0175186	−	0.0539167i	0.00125453	−	0.00386105i
$196$	−1.38047	−	1.00297i	−0.0986050	−	0.0716407i
$197$	4.51326	+	13.8904i	0.321556	+	0.989648i	0.972971	+	0.230927i	$0.0741757\pi$
$197$	4.51326	+	13.8904i	0.321556	+	0.989648i	−0.651415	+	0.758722i	$0.725824\pi$
$198$	−6.25142	−	4.54192i	−0.444269	−	0.322780i
$199$	8.56892	−	6.22569i	0.607435	−	0.441327i	−0.241075	−	0.970506i	$-0.577500\pi$
$199$	8.56892	−	6.22569i	0.607435	−	0.441327i	0.848510	+	0.529179i	$0.177500\pi$
$200$	−4.61171	+	14.1934i	−0.326097	+	1.00362i
$201$	−14.5067	+	10.5397i	−1.02322	+	0.743415i
$202$	−6.84876	+	4.97592i	−0.481877	+	0.350104i
$203$	0.398069	−	1.22513i	0.0279389	−	0.0859872i
$204$	−1.68079	+	1.22117i	−0.117679	+	0.0854988i
$205$	0.0237229	+	0.0172357i	0.00165688	+	0.00120379i
$206$	3.47126	+	10.6834i	0.241854	+	0.744351i
$207$	0.577594	+	0.419647i	0.0401456	+	0.0291675i
$208$	6.61434	−	20.3569i	0.458622	−	1.41149i
$209$	4.59043	−	14.1279i	0.317527	−	0.977246i
$210$	−0.00290463	−	0.00893952i	−0.000200438	−	0.000616885i
$211$	16.5603			1.14006			0.570030	−	0.821624i	$-0.306931\pi$
$211$	16.5603			1.14006			0.570030	+	0.821624i	$0.306931\pi$
$212$	1.09317			0.0750789
$213$	3.59088	+	11.0516i	0.246043	+	0.757243i
$214$	−14.3895	+	10.4546i	−0.983644	+	0.714660i
$215$	−0.00413062	−	0.00300107i	−0.000281706	−	0.000204671i
$216$	16.4927			1.12219
$217$		0			0
$218$	−13.4646			−0.911940
$219$	4.41745	+	3.20947i	0.298504	+	0.216876i
$220$	0.00627582	−	0.00455965i	0.000423116	−	0.000307412i
$221$	−12.2465	−	37.6908i	−0.823788	−	2.53536i
$222$	12.1692			0.816744
$223$	−0.805193			−0.0539197			−0.0269599	−	0.999637i	$-0.508583\pi$
$223$	−0.805193			−0.0539197			−0.0269599	+	0.999637i	$0.508583\pi$
$224$	0.369711	+	1.13785i	0.0247024	+	0.0760261i
$225$	2.28067	−	7.01917i	0.152044	−	0.467945i
$226$	3.38543	−	10.4193i	0.225195	−	0.693080i
$227$	−10.9012	−	7.92017i	−0.723537	−	0.525680i	0.163975	−	0.986464i	$-0.447568\pi$
$227$	−10.9012	−	7.92017i	−0.723537	−	0.525680i	−0.887512	+	0.460784i	$0.847568\pi$
$228$	0.381737	+	1.17487i	0.0252812	+	0.0778074i
$229$	−10.4764	−	7.61153i	−0.692298	−	0.502984i	0.185116	−	0.982717i	$-0.440734\pi$
$229$	−10.4764	−	7.61153i	−0.692298	−	0.502984i	−0.877415	+	0.479732i	$0.840734\pi$
$230$	0.00374814	−	0.00272318i	0.000247145	−	0.000179561i
$231$	1.20618	−	3.71223i	0.0793605	−	0.244246i
$232$	3.91314	−	2.84306i	0.256910	−	0.186656i
$233$	−9.99617	+	7.26264i	−0.654871	+	0.475791i	−0.864927	−	0.501898i	$-0.832635\pi$
$233$	−9.99617	+	7.26264i	−0.654871	+	0.475791i	0.210056	+	0.977689i	$0.432635\pi$
$234$	−3.78780	+	11.6577i	−0.247616	+	0.762084i
$235$	−0.0253507	+	0.0184183i	−0.00165370	+	0.00120148i
$236$	−2.97065	−	2.15830i	−0.193373	−	0.140494i
$237$	3.98975	+	12.2792i	0.259162	+	0.797618i
$238$	−5.31591	−	3.86224i	−0.344580	−	0.250352i
$239$	4.92361	−	15.1533i	0.318482	−	0.980186i	−0.655816	−	0.754921i	$-0.727675\pi$
$239$	4.92361	−	15.1533i	0.318482	−	0.980186i	0.974298	−	0.225265i	$-0.0723248\pi$
$240$	0.00941850	−	0.0289872i	0.000607962	−	0.00187111i
$241$	−6.34157	−	19.5173i	−0.408496	−	1.25722i	−0.917940	−	0.396718i	$-0.870149\pi$
$241$	−6.34157	−	19.5173i	−0.408496	−	1.25722i	0.509444	−	0.860504i	$-0.329851\pi$
$242$	−6.34574			−0.407919
$243$	−13.6228			−0.873906
$244$	0.415972	+	1.28023i	0.0266299	+	0.0819584i
$245$	0.0374969	−	0.0272431i	0.00239559	−	0.00174050i
$246$	5.29540	+	3.84733i	0.337622	+	0.245297i
$247$	−23.5643			−1.49936
$248$		0			0
$249$	2.47896			0.157097
$250$	−0.0774929	−	0.0563019i	−0.00490108	−	0.00356085i
$251$	3.42169	−	2.48600i	0.215975	−	0.156915i	−0.474538	−	0.880235i	$-0.657385\pi$
$251$	3.42169	−	2.48600i	0.215975	−	0.156915i	0.690513	+	0.723320i	$0.257385\pi$
$252$	−0.0971578	−	0.299021i	−0.00612036	−	0.0188365i
$253$	1.92388			0.120953
$254$	−14.8010			−0.928698
$255$	−0.0174384	−	0.0536699i	−0.00109204	−	0.00336094i
$256$	−1.94999	+	6.00144i	−0.121874	+	0.375090i
$257$	5.73155	−	17.6399i	0.357524	−	1.10035i	−0.597007	−	0.802236i	$-0.703644\pi$
$257$	5.73155	−	17.6399i	0.357524	−	1.10035i	0.954531	−	0.298110i	$-0.0963563\pi$
$258$	−0.922034	−	0.669897i	−0.0574033	−	0.0417059i
$259$	−1.83996	−	5.66281i	−0.114329	−	0.351870i
$260$	−0.00995530	−	0.00723295i	−0.000617402	−	0.000448569i
$261$	−1.93520	+	1.40600i	−0.119786	+	0.0870294i
$262$	−0.262549	+	0.808043i	−0.0162203	+	0.0499211i
$263$	11.7199	−	8.51497i	0.722677	−	0.525056i	−0.164561	−	0.986367i	$-0.552621\pi$
$263$	11.7199	−	8.51497i	0.722677	−	0.525056i	0.887238	+	0.461311i	$0.152621\pi$
$264$	11.8571	−	8.61467i	0.729752	−	0.530196i
$265$	−0.00917564	+	0.0282397i	−0.000563655	+	0.00173475i
$266$	−3.16085	+	2.29649i	−0.193804	+	0.140807i
$267$	−1.12092	−	0.814398i	−0.0685993	−	0.0498403i
$268$	1.20274	+	3.70166i	0.0734693	+	0.226115i
$269$	12.1686	+	8.84099i	0.741931	+	0.539045i	0.893315	−	0.449430i	$-0.148373\pi$
$269$	12.1686	+	8.84099i	0.741931	+	0.539045i	−0.151384	+	0.988475i	$0.548373\pi$
$270$	−0.0163556	+	0.0503375i	−0.000995372	+	0.00306344i
$271$	−7.08115	+	21.7935i	−0.430149	+	1.32386i	0.467828	+	0.883820i	$0.345037\pi$
$271$	−7.08115	+	21.7935i	−0.430149	+	1.32386i	−0.897977	+	0.440043i	$0.854963\pi$
$272$	−6.58407	−	20.2637i	−0.399218	−	1.22867i
$273$	−6.19173			−0.374741
$274$	−3.79549			−0.229294
$275$	−6.14575	−	18.9147i	−0.370602	−	1.14060i
$276$	−0.129434	+	0.0940390i	−0.00779099	+	0.00566048i
$277$	11.6908	+	8.49387i	0.702433	+	0.510347i	0.880724	−	0.473630i	$-0.157057\pi$
$277$	11.6908	+	8.49387i	0.702433	+	0.510347i	−0.178291	+	0.983978i	$0.557057\pi$
$278$	−4.44679			−0.266701
$279$		0			0
$280$	−0.0172688			−0.00103201
$281$	4.70657	+	3.41952i	0.280771	+	0.203992i	0.719253	−	0.694748i	$-0.244484\pi$
$281$	4.70657	+	3.41952i	0.280771	+	0.203992i	−0.438483	+	0.898740i	$0.644484\pi$
$282$	−5.65876	+	4.11133i	−0.336974	+	0.244826i
$283$	0.798195	+	2.45659i	0.0474478	+	0.146029i	0.971974	−	0.235090i	$-0.0755386\pi$
$283$	0.798195	+	2.45659i	0.0474478	+	0.146029i	−0.924526	+	0.381120i	$0.875539\pi$
$284$	2.52231			0.149672
$285$	−0.0335544			−0.00198759
$286$	10.2070	+	31.4140i	0.603555	+	1.85755i
$287$	0.989662	−	3.04587i	0.0584179	−	0.179792i
$288$	0.686523	−	2.11290i	0.0404537	−	0.124504i
$289$	−18.1617	−	13.1952i	−1.06833	−	0.776191i
$290$	0.00479670	+	0.0147627i	0.000281672	+	0.000866897i
$291$	7.26586	+	5.27896i	0.425932	+	0.309458i
$292$	0.958852	−	0.696647i	0.0561126	−	0.0407682i
$293$	5.70146	−	17.5473i	0.333083	−	1.02512i	−0.634576	−	0.772861i	$-0.718825\pi$
$293$	5.70146	−	17.5473i	0.333083	−	1.02512i	0.967659	−	0.252263i	$-0.0811750\pi$
$294$	8.37003	−	6.08118i	0.488150	−	0.354662i
$295$	0.0806899	−	0.0586247i	0.00469795	−	0.00341326i
$296$	6.90875	−	21.2630i	0.401563	−	1.23588i
$297$	−17.7813	+	12.9188i	−1.03177	+	0.749628i
$298$	−12.5317	−	9.10484i	−0.725944	−	0.527429i
$299$	−0.943071	−	2.90247i	−0.0545392	−	0.167854i
$300$	1.33802	+	0.972125i	0.0772504	+	0.0561257i
$301$	−0.172320	+	0.530345i	−0.00993234	+	0.0305686i
$302$	7.26693	−	22.3653i	0.418165	−	1.28698i
$303$	2.45378	+	7.55196i	0.140966	+	0.433849i
$304$	−12.6689			−0.726609
$305$	−0.0365637			−0.00209363
$306$	3.77046	+	11.6043i	0.215543	+	0.663373i
$307$	−1.33143	+	0.967344i	−0.0759890	+	0.0552092i	−0.625131	−	0.780520i	$-0.714955\pi$
$307$	−1.33143	+	0.967344i	−0.0759890	+	0.0552092i	0.549142	+	0.835729i	$0.314955\pi$
$308$	−0.685434	−	0.497997i	−0.0390562	−	0.0283760i
$309$	10.5367			0.599412
$310$		0			0
$311$	−19.2427			−1.09115			−0.545576	−	0.838061i	$-0.683689\pi$
$311$	−19.2427			−1.09115			−0.545576	+	0.838061i	$0.683689\pi$
$312$	−18.8088	−	13.6654i	−1.06484	−	0.773651i
$313$	12.4613	−	9.05366i	0.704354	−	0.511743i	−0.176993	−	0.984212i	$-0.556637\pi$
$313$	12.4613	−	9.05366i	0.704354	−	0.511743i	0.881347	+	0.472469i	$0.156637\pi$
$314$	−1.08218	−	3.33061i	−0.0610710	−	0.187957i
$315$	0.00854010			0.000481180
$316$	2.80248			0.157652
$317$	−8.93858	−	27.5101i	−0.502041	−	1.54512i	−0.805689	−	0.592338i	$-0.798205\pi$
$317$	−8.93858	−	27.5101i	−0.502041	−	1.54512i	0.303649	−	0.952784i	$-0.401795\pi$
$318$	−2.04818	+	6.30365i	−0.114856	+	0.353491i
$319$	−1.99188	+	6.13037i	−0.111524	+	0.343235i
$320$	−0.0516125	−	0.0374987i	−0.00288523	−	0.00209624i
$321$	5.15548	+	15.8669i	0.287751	+	0.885606i
$322$	−0.409365	−	0.297421i	−0.0228130	−	0.0165746i
$323$	−18.9767	+	13.7874i	−1.05589	+	0.767149i
$324$	0.198134	−	0.609794i	0.0110075	−	0.0338775i
$325$	−25.5231	+	18.5436i	−1.41577	+	1.02862i
$326$	−17.9991	+	13.0771i	−0.996878	+	0.724274i
$327$	−3.90280	+	12.0116i	−0.215825	+	0.664242i
$328$	9.72868	−	7.06830i	0.537176	−	0.390282i
$329$	2.76876	+	2.01162i	0.152646	+	0.110904i
$330$	0.0145343	+	0.0447321i	0.000800089	+	0.00246242i
$331$	−1.49434	−	1.08570i	−0.0821364	−	0.0596756i	0.545959	−	0.837812i	$-0.316165\pi$
$331$	−1.49434	−	1.08570i	−0.0821364	−	0.0596756i	−0.628096	+	0.778136i	$0.716165\pi$
$332$	0.166277	−	0.511747i	0.00912561	−	0.0280857i
$333$	−3.41664	+	10.5154i	−0.187231	+	0.576238i
$334$	6.29659	+	19.3789i	0.344534	+	1.06037i
$335$	−0.105720			−0.00577612
$336$	−3.32885			−0.181604
$337$	5.70863	+	17.5694i	0.310969	+	0.957064i	0.977382	+	0.211481i	$0.0678287\pi$
$337$	5.70863	+	17.5694i	0.310969	+	0.957064i	−0.666413	+	0.745583i	$0.732171\pi$
$338$	28.5482	−	20.7415i	1.55282	−	1.12819i
$339$	−8.31358	−	6.04017i	−0.451532	−	0.328057i
$340$	−0.0122491			−0.000664301
$341$		0			0
$342$	7.25501			0.392306
$343$	−8.59705	−	6.24612i	−0.464197	−	0.337259i
$344$	−1.69395	+	1.23073i	−0.0913319	+	0.0663565i
$345$	−0.00134289	−	0.00413298i	−7.22986e−5	−	0.000222512i
$346$	−9.09490			−0.488945
$347$	12.1294			0.651142			0.325571	−	0.945518i	$-0.394444\pi$
$347$	12.1294			0.651142			0.325571	+	0.945518i	$0.394444\pi$
$348$	−0.165643	−	0.509798i	−0.00887942	−	0.0273280i
$349$	0.333970	−	1.02785i	0.0178770	−	0.0550197i	−0.941720	−	0.336398i	$-0.890791\pi$
$349$	0.333970	−	1.02785i	0.0178770	−	0.0550197i	0.959597	+	0.281378i	$0.0907914\pi$
$350$	−1.61640	+	4.97478i	−0.0864004	+	0.265913i
$351$	28.2063	+	20.4931i	1.50554	+	1.09384i
$352$	−1.84998	−	5.69366i	−0.0986044	−	0.303473i
$353$	14.8645	+	10.7997i	0.791159	+	0.574810i	0.908307	−	0.418304i	$-0.137375\pi$
$353$	14.8645	+	10.7997i	0.791159	+	0.574810i	−0.117149	+	0.993114i	$0.537375\pi$
$354$	18.0116	−	13.0862i	0.957303	−	0.695522i
$355$	−0.0211714	+	0.0651588i	−0.00112366	+	0.00345827i
$356$	−0.243308	+	0.176773i	−0.0128953	+	0.00936897i
$357$	−4.98629	+	3.62275i	−0.263902	+	0.191736i
$358$	−5.88930	+	18.1254i	−0.311259	+	0.957957i
$359$	22.4047	−	16.2780i	1.18247	−	0.859118i	0.190026	−	0.981779i	$-0.439143\pi$
$359$	22.4047	−	16.2780i	1.18247	−	0.859118i	0.992449	+	0.122661i	$0.0391427\pi$
$360$	0.0259425	+	0.0188484i	0.00136729	+	0.000993396i
$361$	−1.56139	−	4.80547i	−0.0821786	−	0.252920i
$362$	−18.4765	−	13.4240i	−0.971105	−	0.705549i
$363$	−1.83935	+	5.66093i	−0.0965407	+	0.297122i
$364$	−0.415312	+	1.27820i	−0.0217683	+	0.0669958i
$365$	0.00994820	+	0.0306174i	0.000520712	+	0.00160259i
$366$	−8.16173			−0.426620
$367$	5.52561			0.288434			0.144217	−	0.989546i	$-0.453934\pi$
$367$	5.52561			0.288434			0.144217	+	0.989546i	$0.453934\pi$
$368$	−0.507022	−	1.56045i	−0.0264304	−	0.0813443i
$369$	−4.81121	+	3.49555i	−0.250461	+	0.181971i
$370$	0.0580454	+	0.0421725i	0.00301764	+	0.00219244i
$371$	3.24301			0.168369
$372$		0			0
$373$	5.64476			0.292274			0.146137	−	0.989264i	$-0.453316\pi$
$373$	5.64476			0.292274			0.146137	+	0.989264i	$0.453316\pi$
$374$	26.6001	+	19.3261i	1.37546	+	0.999328i
$375$	−0.0726878	+	0.0528108i	−0.00375358	+	0.00272714i
$376$	3.97101	+	12.2215i	0.204789	+	0.630277i
$377$	10.2250			0.526616
$378$	5.78070			0.297327
$379$	−3.45250	−	10.6257i	−0.177343	−	0.545806i	0.822390	−	0.568925i	$-0.192640\pi$
$379$	−3.45250	−	10.6257i	−0.177343	−	0.545806i	−0.999733	+	0.0231185i	$0.992640\pi$
$380$	−0.00225067	+	0.00692686i	−0.000115457	+	0.000355340i
$381$	−4.29016	+	13.2037i	−0.219791	+	0.676448i
$382$	15.8698	+	11.5301i	0.811972	+	0.589932i
$383$	−5.72315	−	17.6141i	−0.292439	−	0.900036i	−0.984070	−	0.177784i	$-0.943107\pi$
$383$	−5.72315	−	17.6141i	−0.292439	−	0.900036i	0.691630	−	0.722252i	$-0.256893\pi$
$384$	−8.51467	−	6.18627i	−0.434512	−	0.315692i
$385$	0.0186180	−	0.0135268i	0.000948862	−	0.000689389i
$386$	−4.17893	+	12.8614i	−0.212702	+	0.654630i
$387$	0.837726	−	0.608644i	0.0425840	−	0.0309391i
$388$	1.57713	−	1.14585i	0.0800666	−	0.0581718i
$389$	7.28844	−	22.4315i	0.369539	−	1.13732i	−0.577551	−	0.816354i	$-0.695992\pi$
$389$	7.28844	−	22.4315i	0.369539	−	1.13732i	0.947090	−	0.320968i	$-0.104008\pi$
$390$	0.0603607	−	0.0438546i	0.00305648	−	0.00222067i
$391$	−2.45769	−	1.78562i	−0.124291	−	0.0903025i
$392$	−5.87363	−	18.0772i	−0.296663	−	0.913035i
$393$	0.644741	+	0.468432i	0.0325229	+	0.0236292i
$394$	−5.93977	+	18.2807i	−0.299241	+	0.920970i
$395$	−0.0235230	+	0.0723964i	−0.00118357	+	0.00364266i
$396$	0.486164	+	1.49626i	0.0244306	+	0.0751898i
$397$	10.9091			0.547514			0.273757	−	0.961799i	$-0.411734\pi$
$397$	10.9091			0.547514			0.273757	+	0.961799i	$0.411734\pi$
$398$	13.9395			0.698726
$399$	1.13247	+	3.48539i	0.0566945	+	0.174488i
$400$	−13.7220	+	9.96960i	−0.686099	+	0.498480i
$401$	−8.63294	−	6.27220i	−0.431109	−	0.313219i	0.350983	−	0.936382i	$-0.385847\pi$
$401$	−8.63294	−	6.27220i	−0.431109	−	0.313219i	−0.782092	+	0.623163i	$0.785847\pi$
$402$	−23.5988			−1.17700
$403$		0			0
$404$	1.72359			0.0857517
$405$	0.0140897	+	0.0102368i	0.000700124	+	0.000508670i
$406$	1.37155	−	0.996492i	0.0680691	−	0.0494551i
$407$	9.20688	+	28.3359i	0.456368	+	1.40456i
$408$	−23.1426			−1.14573
$409$	9.42592			0.466082			0.233041	−	0.972467i	$-0.425132\pi$
$409$	9.42592			0.466082			0.233041	+	0.972467i	$0.425132\pi$
$410$	0.0119254	+	0.0367025i	0.000588951	+	0.00181261i
$411$	−1.10014	+	3.38590i	−0.0542661	+	0.167014i
$412$	0.706752	−	2.17516i	0.0348192	−	0.107162i
$413$	−8.81281	−	6.40288i	−0.433650	−	0.315065i
$414$	0.290354	+	0.893617i	0.0142701	+	0.0439189i
$415$	0.0118243	+	0.00859083i	0.000580430	+	0.000421707i
$416$	−7.68293	+	5.58198i	−0.376687	+	0.273679i
$417$	−1.28893	+	3.96691i	−0.0631191	+	0.194260i
$418$	15.8164	−	11.4913i	0.773606	−	0.562058i
$419$	23.6286	−	17.1672i	1.15433	−	0.838671i	0.165281	−	0.986247i	$-0.447147\pi$
$419$	23.6286	−	17.1672i	1.15433	−	0.838671i	0.989051	+	0.147575i	$0.0471469\pi$
$420$	−0.000591384		0.00182009i	−2.88566e−5		8.88114e-5i
$421$	−0.482705	+	0.350705i	−0.0235256	+	0.0170923i	−0.599486	−	0.800385i	$-0.704628\pi$
$421$	−0.482705	+	0.350705i	−0.0235256	+	0.0170923i	0.575960	+	0.817478i	$0.304628\pi$
$422$	17.6322	+	12.8105i	0.858322	+	0.623608i
$423$	−1.96382	−	6.04401i	−0.0954842	−	0.293870i
$424$	9.85141	+	7.15747i	0.478427	+	0.347597i
$425$	−9.70435	+	29.8669i	−0.470730	+	1.44876i
$426$	−4.72586	+	14.5447i	−0.228969	+	0.704693i
$427$	1.23404	+	3.79797i	0.0597191	+	0.183797i
$428$	3.62132			0.175043
$429$	30.9825			1.49585
$430$	−0.00207644	−	0.00639063i	−0.000100135	−	0.000308183i
$431$	19.4200	−	14.1095i	0.935429	−	0.679629i	−0.0118874	−	0.999929i	$-0.503784\pi$
$431$	19.4200	−	14.1095i	0.935429	−	0.679629i	0.947316	+	0.320301i	$0.103784\pi$
$432$	15.1645	+	11.0177i	0.729605	+	0.530089i
$433$	12.5443			0.602840			0.301420	−	0.953492i	$-0.402539\pi$
$433$	12.5443			0.602840			0.301420	+	0.953492i	$0.402539\pi$
$434$		0			0
$435$	0.0145599			0.000698096
$436$	2.21785	+	1.61136i	0.106216	+	0.0771701i
$437$	−1.46134	+	1.06173i	−0.0699056	+	0.0507894i
$438$	2.22063	+	6.83440i	0.106106	+	0.326560i
$439$	−39.1172			−1.86696			−0.933482	−	0.358625i	$-0.883246\pi$
$439$	−39.1172			−1.86696			−0.933482	+	0.358625i	$0.883246\pi$
$440$	0.0864107			0.00411947
$441$	2.90474	+	8.93986i	0.138321	+	0.425708i
$442$	16.1173	−	49.6039i	0.766620	−	2.35941i
$443$	−2.31518	+	7.12538i	−0.109997	+	0.338537i	−0.990871	−	0.134815i	$-0.956956\pi$
$443$	−2.31518	+	7.12538i	−0.109997	+	0.338537i	0.880873	+	0.473352i	$0.156956\pi$
$444$	−2.00447	−	1.45633i	−0.0951279	−	0.0691144i
$445$	−0.00252434	−	0.00776913i	−0.000119665	−	0.000368292i
$446$	−0.857309	−	0.622872i	−0.0405948	−	0.0294938i
$447$	−11.7547	+	8.54027i	−0.555977	+	0.403941i
$448$	−2.15315	+	6.62673i	−0.101727	+	0.313083i
$449$	14.1692	−	10.2945i	0.668686	−	0.485829i	−0.200899	−	0.979612i	$-0.564386\pi$
$449$	14.1692	−	10.2945i	0.668686	−	0.485829i	0.869585	+	0.493783i	$0.164386\pi$
$450$	7.85809	−	5.70924i	0.370434	−	0.269136i
$451$	−4.95212	+	15.2411i	−0.233186	+	0.717674i
$452$	−1.80455	+	1.31108i	−0.0848788	+	0.0616680i
$453$	−17.8454	−	12.9654i	−0.838449	−	0.609169i
$454$	−5.47997	−	16.8656i	−0.257188	−	0.791543i
$455$	−0.0295337	−	0.0214575i	−0.00138456	−	0.00100594i
$456$	−4.25225	+	13.0871i	−0.199130	+	0.612859i
$457$	1.51235	−	4.65453i	0.0707446	−	0.217730i	−0.909433	−	0.415851i	$-0.863484\pi$
$457$	1.51235	−	4.65453i	0.0707446	−	0.217730i	0.980178	+	0.198121i	$0.0634839\pi$
$458$	−5.26642	−	16.2084i	−0.246084	−	0.757368i
$459$	34.7054			1.61991
$460$	−0.000943272	0		−4.39803e−5	0
$461$	−6.26602	−	19.2848i	−0.291837	−	0.898183i	−0.984265	−	0.176696i	$-0.943459\pi$
$461$	−6.26602	−	19.2848i	−0.291837	−	0.898183i	0.692428	−	0.721487i	$-0.256541\pi$
$462$	4.15590	−	3.01944i	0.193350	−	0.140477i
$463$	−18.5716	−	13.4931i	−0.863097	−	0.627077i	0.0656286	−	0.997844i	$-0.479095\pi$
$463$	−18.5716	−	13.4931i	−0.863097	−	0.627077i	−0.928726	+	0.370767i	$0.879095\pi$
$464$	5.49727			0.255204
$465$		0			0
$466$	−16.2613			−0.753291
$467$	−22.0760	−	16.0391i	−1.02155	−	0.742203i	−0.0549533	−	0.998489i	$-0.517501\pi$
$467$	−22.0760	−	16.0391i	−1.02155	−	0.742203i	−0.966601	+	0.256286i	$0.917501\pi$
$468$	2.01902	−	1.46691i	0.0933295	−	0.0678078i
$469$	3.56809	+	10.9815i	0.164759	+	0.507077i
$470$	−0.0412394			−0.00190223
$471$	−3.28486			−0.151358
$472$	−12.6395	−	38.9005i	−0.581782	−	1.79054i
$473$	0.862263	−	2.65377i	0.0396469	−	0.122021i
$474$	−5.25080	+	16.1603i	−0.241177	+	0.742267i
$475$	15.1066	+	10.9756i	0.693139	+	0.503595i
$476$	0.413411	+	1.27235i	0.0189487	+	0.0583180i
$477$	−4.87190	−	3.53964i	−0.223069	−	0.162069i
$478$	16.9644	−	12.3254i	0.775934	−	0.563749i
$479$	−10.6278	+	32.7089i	−0.485594	+	1.49451i	0.345524	+	0.938410i	$0.387701\pi$
$479$	−10.6278	+	32.7089i	−0.485594	+	1.49451i	−0.831118	+	0.556096i	$0.812299\pi$
$480$	−0.0109401	+	0.00794846i	−0.000499346	+	0.000362796i
$481$	38.2360	−	27.7800i	1.74341	−	1.26666i
$482$	8.34596	−	25.6862i	0.380148	−	1.16998i
$483$	−0.383981	+	0.278979i	−0.0174717	+	0.0126940i
$484$	1.04525	+	0.759416i	0.0475112	+	0.0345189i
$485$	0.0163629	+	0.0503598i	0.000743000	+	0.00228672i
$486$	−14.5046	−	10.5382i	−0.657941	−	0.478022i
$487$	−8.43857	+	25.9713i	−0.382388	+	1.17687i	0.555969	+	0.831203i	$0.312347\pi$
$487$	−8.43857	+	25.9713i	−0.382388	+	1.17687i	−0.938357	+	0.345667i	$0.887653\pi$
$488$	−4.63361	+	14.2608i	−0.209754	+	0.645555i
$489$	6.44874	+	19.8472i	0.291622	+	0.897520i
$490$	0.0609982			0.00275562
$491$	35.5025			1.60221			0.801103	−	0.598526i	$-0.204247\pi$
$491$	35.5025			1.60221			0.801103	+	0.598526i	$0.204247\pi$
$492$	−0.411816	−	1.26744i	−0.0185661	−	0.0571405i
$493$	8.23436	−	5.98261i	0.370857	−	0.269443i
$494$	−25.0895	−	18.2286i	−1.12883	−	0.820143i
$495$	−0.0427334			−0.00192073
$496$		0			0
$497$	7.48275			0.335647
$498$	2.63941	+	1.91764i	0.118275	+	0.0859315i
$499$	−9.06727	+	6.58776i	−0.405907	+	0.294908i	−0.771943	−	0.635692i	$-0.780715\pi$
$499$	−9.06727	+	6.58776i	−0.405907	+	0.294908i	0.366036	+	0.930601i	$0.380715\pi$
$500$	0.00602651	+	0.0185477i	0.000269514	+	0.000829478i
$501$	19.1127			0.853892
$502$	5.56625			0.248434
$503$	−0.525127	−	1.61617i	−0.0234142	−	0.0720616i	0.938667	−	0.344826i	$-0.112062\pi$
$503$	−0.525127	−	1.61617i	−0.0234142	−	0.0720616i	−0.962081	+	0.272764i	$0.912062\pi$
$504$	1.08226	−	3.33086i	0.0482078	−	0.148368i
$505$	−0.0144672	+	0.0445254i	−0.000643781	+	0.00198135i
$506$	2.04840	+	1.48825i	0.0910626	+	0.0661609i
$507$	−10.2283	−	31.4794i	−0.454253	−	1.39805i
$508$	2.43797	+	1.77129i	0.108167	+	0.0785883i
$509$	33.5807	−	24.3978i	1.48844	−	1.08141i	0.513724	−	0.857956i	$-0.328266\pi$
$509$	33.5807	−	24.3978i	1.48844	−	1.08141i	0.974714	−	0.223458i	$-0.0717344\pi$
$510$	0.0229502	−	0.0706335i	0.00101625	−	0.00312770i
$511$	2.84456	−	2.06669i	0.125836	−	0.0914251i
$512$	−20.5136	+	14.9040i	−0.906583	+	0.658671i
$513$	6.37683	−	19.6259i	0.281544	−	0.866503i
$514$	19.7482	−	14.3479i	0.871055	−	0.632858i
$515$	0.0502585	+	0.0365150i	0.00221466	+	0.00160904i
$516$	0.0717052	+	0.220686i	0.00315665	+	0.00971516i
$517$	−13.8545	−	10.0659i	−0.609318	−	0.442696i
$518$	2.42152	−	7.45266i	0.106395	−	0.327451i
$519$	−2.63621	+	8.11341i	−0.115717	+	0.356139i
$520$	−0.0423579	−	0.130364i	−0.00185752	−	0.00571684i
$521$	−32.5673			−1.42680			−0.713399	−	0.700758i	$-0.752845\pi$
$521$	−32.5673			−1.42680			−0.713399	+	0.700758i	$0.752845\pi$
$522$	−3.14809			−0.137788
$523$	4.49129	+	13.8228i	0.196390	+	0.604428i	0.999958	+	0.00921351i	$0.00293279\pi$
$523$	4.49129	+	13.8228i	0.196390	+	0.604428i	−0.803567	+	0.595214i	$0.797067\pi$
$524$	0.139947	−	0.101678i	0.00611363	−	0.00444182i
$525$	3.96939	+	2.88393i	0.173239	+	0.125865i
$526$	19.0653			0.831288
$527$		0			0
$528$	16.6571			0.724907
$529$	18.4181	+	13.3816i	0.800788	+	0.581807i
$530$	−0.0316149	+	0.0229695i	−0.00137326	+	0.000997733i
$531$	6.25074	+	19.2378i	0.271259	+	0.834849i
$532$	0.795472			0.0344881
$533$	25.4210			1.10111
$534$	−0.563482	−	1.73422i	−0.0243843	−	0.0750470i
$535$	−0.0303960	+	0.0935494i	−0.00131414	+	0.00404449i
$536$	−13.3976	+	41.2337i	−0.578689	+	1.78102i
$537$	14.4623	+	10.5075i	0.624095	+	0.453432i
$538$	6.11708	+	18.8264i	0.263726	+	0.811666i
$539$	20.4925	+	14.8887i	0.882674	+	0.641300i
$540$	0.00871810	−	0.00633407i	0.000375167	−	0.000272575i
$541$	−2.59517	+	7.98712i	−0.111575	+	0.343393i	−0.991217	−	0.132243i	$-0.957782\pi$
$541$	−2.59517	+	7.98712i	−0.111575	+	0.343393i	0.879642	+	0.475636i	$0.157782\pi$
$542$	−24.3983	+	17.7264i	−1.04799	+	0.761413i
$543$	−17.3309	+	12.5916i	−0.743738	+	0.540357i
$544$	−2.92119	+	8.99049i	−0.125245	+	0.385464i
$545$	−0.0602420	+	0.0437684i	−0.00258048	+	0.00187483i
$546$	−6.59249	−	4.78972i	−0.282132	−	0.204981i
$547$	3.86046	+	11.8813i	0.165062	+	0.508007i	0.999041	−	0.0437886i	$-0.0139428\pi$
$547$	3.86046	+	11.8813i	0.165062	+	0.508007i	−0.833979	+	0.551796i	$0.813943\pi$
$548$	0.625180	+	0.454220i	0.0267064	+	0.0194033i
$549$	2.29150	−	7.05251i	0.0977988	−	0.300994i
$550$	8.08825	−	24.8931i	0.344884	−	1.06144i
$551$	−1.87016	−	5.75577i	−0.0796717	−	0.245204i
$552$	−1.78215			−0.0758533
$553$	8.31392			0.353544
$554$	5.87691	+	18.0873i	0.249686	+	0.768455i
$555$	0.0544461	−	0.0395574i	0.00231111	−	0.00167912i
$556$	0.732460	+	0.532163i	0.0310632	+	0.0225687i
$557$	−16.8308			−0.713144			−0.356572	−	0.934268i	$-0.616054\pi$
$557$	−16.8308			−0.713144			−0.356572	+	0.934268i	$0.616054\pi$
$558$		0			0
$559$	−4.42630			−0.187213
$560$	−0.0158782	−	0.0115362i	−0.000670975	−	0.000487492i
$561$	24.9507	−	18.1277i	1.05342	−	0.765353i
$562$	2.36597	+	7.28171i	0.0998024	+	0.307160i
$563$	−16.7349			−0.705291			−0.352645	−	0.935757i	$-0.614718\pi$
$563$	−16.7349			−0.705291			−0.352645	+	0.935757i	$0.614718\pi$
$564$	1.42411			0.0599658
$565$	−0.0187224	−	0.0576215i	−0.000787656	−	0.00242416i
$566$	−1.05048	+	3.23305i	−0.0441551	+	0.135895i
$567$	0.587790	−	1.80903i	0.0246849	−	0.0759722i
$568$	22.7306	+	16.5148i	0.953755	+	0.692944i
$569$	1.64962	+	5.07700i	0.0691556	+	0.212839i	0.979662	−	0.200657i	$-0.0643076\pi$
$569$	1.64962	+	5.07700i	0.0691556	+	0.212839i	−0.910506	+	0.413496i	$0.864308\pi$
$570$	−0.0357262	−	0.0259566i	−0.00149641	−	0.00108720i
$571$	−29.1251	+	21.1606i	−1.21885	+	0.885545i	−0.996004	−	0.0893088i	$-0.971534\pi$
$571$	−29.1251	+	21.1606i	−1.21885	+	0.885545i	−0.222844	+	0.974854i	$0.571534\pi$
$572$	2.07816	−	6.39592i	0.0868923	−	0.267427i
$573$	14.8858	−	10.8152i	0.621863	−	0.451810i
$574$	3.40990	−	2.47744i	0.142327	−	0.103406i
$575$	−0.747307	+	2.29997i	−0.0311648	+	0.0959155i
$576$	10.4675	−	7.60507i	0.436145	−	0.316878i
$577$	−1.85205	−	1.34559i	−0.0771017	−	0.0560176i	0.548567	−	0.836107i	$-0.315174\pi$
$577$	−1.85205	−	1.34559i	−0.0771017	−	0.0560176i	−0.625668	+	0.780089i	$0.715174\pi$
$578$	−9.12979	−	28.0986i	−0.379749	−	1.16875i
$579$	10.2622	+	7.45592i	0.426482	+	0.309857i
$580$	0.000976612	−	0.00300570i	4.05516e−5	−	0.000124805i
$581$	0.493281	−	1.51816i	0.0204647	−	0.0629840i
$582$	3.65251	+	11.2413i	0.151402	+	0.465966i
$583$	−16.2276			−0.672078
$584$	13.2023			0.546314
$585$	0.0209476	+	0.0644701i	0.000866077	+	0.00266551i
$586$	19.6445	−	14.2726i	0.811508	−	0.589595i
$587$	−1.69705	−	1.23298i	−0.0700446	−	0.0508904i	0.552212	−	0.833704i	$-0.313784\pi$
$587$	−1.69705	−	1.23298i	−0.0700446	−	0.0508904i	−0.622257	+	0.782813i	$0.713784\pi$
$588$	−2.10644			−0.0868680
$589$		0			0
$590$	0.131263			0.00540400
$591$	14.5863	+	10.5975i	0.599999	+	0.435925i
$592$	20.5568	−	14.9354i	0.844877	−	0.613839i
$593$	−2.05214	−	6.31583i	−0.0842711	−	0.259360i	0.900038	−	0.435811i	$-0.143538\pi$
$593$	−2.05214	−	6.31583i	−0.0842711	−	0.259360i	−0.984309	+	0.176451i	$0.943538\pi$
$594$	−28.9258			−1.18684
$595$	−0.0363385			−0.00148973
$596$	0.974575	+	2.99943i	0.0399201	+	0.122862i
$597$	4.04045	−	12.4352i	0.165365	−	0.508940i
$598$	1.24115	−	3.81987i	0.0507544	−	0.156206i
$599$	−24.8553	−	18.0584i	−1.01556	−	0.737847i	−0.0501917	−	0.998740i	$-0.515983\pi$
$599$	−24.8553	−	18.0584i	−1.01556	−	0.737847i	−0.965368	+	0.260892i	$0.915983\pi$
$600$	5.69299	+	17.5212i	0.232416	+	0.715301i
$601$	−13.7212	−	9.96901i	−0.559698	−	0.406645i	0.271650	−	0.962396i	$-0.412431\pi$
$601$	−13.7212	−	9.96901i	−0.559698	−	0.406645i	−0.831348	+	0.555751i	$0.812431\pi$
$602$	−0.593731	+	0.431371i	−0.0241987	+	0.0175814i
$603$	6.62564	−	20.3916i	0.269817	−	0.830412i
$604$	−3.87352	+	2.81428i	−0.157611	+	0.114511i
$605$	−0.0283914	+	0.0206276i	−0.00115427	+	0.000838630i
$606$	−3.22935	+	9.93893i	−0.131184	+	0.403742i
$607$	−14.4948	+	10.5311i	−0.588327	+	0.427445i	−0.841717	−	0.539920i	$-0.818455\pi$
$607$	−14.4948	+	10.5311i	−0.588327	+	0.427445i	0.253389	+	0.967364i	$0.418455\pi$
$608$	4.54737	+	3.30386i	0.184420	+	0.133989i
$609$	−0.491402	−	1.51238i	−0.0199126	−	0.0612847i
$610$	−0.0389303	−	0.0282845i	−0.00157624	−	0.00114521i
$611$	−8.39457	+	25.8358i	−0.339608	+	1.04521i
$612$	0.767669	−	2.36264i	0.0310312	−	0.0955041i
$613$	−5.45553	−	16.7904i	−0.220347	−	0.678158i	−0.998731	−	0.0503690i	$-0.983960\pi$
$613$	−5.45553	−	16.7904i	−0.220347	−	0.678158i	0.778384	−	0.627789i	$-0.216040\pi$
$614$	−2.16592			−0.0874093
$615$	0.0361983			0.00145966
$616$	−2.91639	−	8.97572i	−0.117505	−	0.361642i
$617$	−16.4572	+	11.9569i	−0.662544	+	0.481366i	−0.867521	−	0.497401i	$-0.834288\pi$
$617$	−16.4572	+	11.9569i	−0.662544	+	0.481366i	0.204977	+	0.978767i	$0.434288\pi$
$618$	11.2187	+	8.15085i	0.451282	+	0.327875i
$619$	16.4294			0.660354			0.330177	−	0.943919i	$-0.392892\pi$
$619$	16.4294			0.660354			0.330177	+	0.943919i	$0.392892\pi$
$620$		0			0
$621$	2.67257			0.107247
$622$	−20.4882	−	14.8855i	−0.821500	−	0.596855i
$623$	−0.721803	+	0.524420i	−0.0289184	+	0.0210105i
$624$	−8.16518	−	25.1298i	−0.326869	−	1.00600i
$625$	24.9992			0.999968
$626$	20.2715			0.810211
$627$	−5.66673	−	17.4404i	−0.226307	−	0.696502i
$628$	−0.220333	+	0.678114i	−0.00879223	+	0.0270597i
$629$	14.5380	−	44.7433i	0.579667	−	1.78403i
$630$	0.00909286	+	0.00660635i	0.000362268	+	0.000263203i
$631$	3.21869	+	9.90612i	0.128134	+	0.394357i	0.994459	−	0.105124i	$-0.0335241\pi$
$631$	3.21869	+	9.90612i	0.128134	+	0.394357i	−0.866325	+	0.499481i	$0.833524\pi$
$632$	25.2555	+	18.3492i	1.00461	+	0.729891i
$633$	16.5389	−	12.0162i	0.657361	−	0.477601i
$634$	11.7638	−	36.2053i	0.467201	−	1.43790i
$635$	−0.0662211	+	0.0481124i	−0.00262790	+	0.00190928i
$636$	1.09175	−	0.793202i	0.0432907	−	0.0314525i
$637$	12.4166	−	38.2144i	0.491965	−	1.51411i
$638$	−6.86306	+	4.98631i	−0.271711	+	0.197410i
$639$	−11.2412	−	8.16718i	−0.444693	−	0.323089i
$640$	−0.0191752	−	0.0590153i	−0.000757967	−	0.00233278i
$641$	18.4567	+	13.4095i	0.728994	+	0.529645i	0.889245	−	0.457431i	$-0.151230\pi$
$641$	18.4567	+	13.4095i	0.728994	+	0.529645i	−0.160251	+	0.987076i	$0.551230\pi$
$642$	−6.78498	+	20.8820i	−0.267782	+	0.824148i
$643$	−7.41261	+	22.8137i	−0.292325	+	0.899683i	0.691782	+	0.722106i	$0.256826\pi$
$643$	−7.41261	+	22.8137i	−0.292325	+	0.899683i	−0.984107	+	0.177577i	$0.943174\pi$
$644$	0.0318357	+	0.0979803i	0.00125450	+	0.00386096i
$645$	−0.00630284			−0.000248174
$646$	−30.8704			−1.21458
$647$	6.08563	+	18.7296i	0.239251	+	0.736338i	0.996529	+	0.0832458i	$0.0265287\pi$
$647$	6.08563	+	18.7296i	0.239251	+	0.736338i	−0.757278	+	0.653092i	$0.773471\pi$
$648$	5.77816	−	4.19808i	0.226988	−	0.164916i
$649$	44.0980	+	32.0391i	1.73100	+	1.25764i
$650$	−41.5199			−1.62854
$651$		0			0
$652$	4.52973			0.177398
$653$	4.01925	+	2.92015i	0.157285	+	0.114274i	0.663644	−	0.748048i	$-0.269009\pi$
$653$	4.01925	+	2.92015i	0.157285	+	0.114274i	−0.506359	+	0.862323i	$0.669009\pi$
$654$	−13.4472	+	9.76995i	−0.525826	+	0.382035i
$655$	0.00145197	+	0.00446870i	5.67332e−5	+	0.000174607i
$656$	13.6671			0.533610
$657$	−6.52904			−0.254722
$658$	1.39184	+	4.28364i	0.0542596	+	0.166994i
$659$	0.477032	−	1.46815i	0.0185825	−	0.0571911i	−0.941335	−	0.337473i	$-0.890428\pi$
$659$	0.477032	−	1.46815i	0.0185825	−	0.0571911i	0.959918	+	0.280282i	$0.0904279\pi$
$660$	0.00295920	−	0.00910748i	0.000115187	−	0.000354508i
$661$	−12.9739	−	9.42612i	−0.504628	−	0.366634i	0.306154	−	0.951982i	$-0.400958\pi$
$661$	−12.9739	−	9.42612i	−0.504628	−	0.366634i	−0.810782	+	0.585348i	$0.800958\pi$
$662$	−0.751198	−	2.31195i	−0.0291961	−	0.0898565i
$663$	−39.5791	−	28.7559i	−1.53713	−	1.11679i
$664$	4.84910	−	3.52308i	0.188182	−	0.136722i
$665$	−0.00667691	+	0.0205494i	−0.000258919	+	0.000796872i
$666$	−11.7721	+	8.55295i	−0.456161	+	0.331420i
$667$	0.634107	−	0.460705i	0.0245527	−	0.0178386i
$668$	1.28199	−	3.94556i	0.0496017	−	0.152658i
$669$	−0.804150	+	0.584249i	−0.0310902	+	0.0225884i
$670$	−0.112563	−	0.0817819i	−0.00434869	−	0.00315951i
$671$	−6.17493	−	19.0045i	−0.238381	−	0.733660i
$672$	1.19486	+	0.868117i	0.0460928	+	0.0334883i
$673$	12.3833	−	38.1117i	0.477339	−	1.46910i	−0.365438	−	0.930836i	$-0.619081\pi$
$673$	12.3833	−	38.1117i	0.477339	−	1.46910i	0.842777	−	0.538263i	$-0.180919\pi$
$674$	−7.51297	+	23.1225i	−0.289389	+	0.890647i
$675$	−8.53741	−	26.2754i	−0.328605	−	1.01134i
$676$	−7.18455			−0.276329
$677$	−36.5467			−1.40461			−0.702303	−	0.711879i	$-0.747845\pi$
$677$	−36.5467			−1.40461			−0.702303	+	0.711879i	$0.747845\pi$
$678$	−4.17920	−	12.8622i	−0.160501	−	0.493971i
$679$	4.67875	−	3.39931i	0.179554	−	0.130454i
$680$	−0.110387	−	0.0802007i	−0.00423314	−	0.00307556i
$681$	−16.6339			−0.637414
$682$		0			0
$683$	−37.5447			−1.43661			−0.718303	−	0.695730i	$-0.755081\pi$
$683$	−37.5447			−1.43661			−0.718303	+	0.695730i	$0.755081\pi$
$684$	−1.19502	−	0.868232i	−0.0456927	−	0.0331977i
$685$	−0.0169814	+	0.0123377i	−0.000648825	+	0.000471399i
$686$	−4.32169	−	13.3008i	−0.165003	−	0.507827i
$687$	−15.9857			−0.609894
$688$	−2.37971			−0.0907255
$689$	7.95463	+	24.4818i	0.303047	+	0.932684i
$690$	0.00176734	−	0.00543930i	6.72814e−5	−	0.000207071i
$691$	0.574543	−	1.76826i	0.0218566	−	0.0672678i	−0.939533	−	0.342458i	$-0.888741\pi$
$691$	0.574543	−	1.76826i	0.0218566	−	0.0672678i	0.961390	+	0.275190i	$0.0887407\pi$
$692$	1.49808	+	1.08842i	0.0569485	+	0.0413755i
$693$	1.44227	+	4.43884i	0.0547871	+	0.168618i
$694$	12.9145	+	9.38294i	0.490228	+	0.356171i
$695$	−0.0198954	+	0.0144548i	−0.000754674	+	0.000548303i
$696$	1.84514	−	5.67875i	0.0699398	−	0.215252i
$697$	20.4719	−	14.8737i	0.775429	−	0.563382i
$698$	1.15070	−	0.836033i	0.0435547	−	0.0316443i
$699$	−4.71343	+	14.5065i	−0.178278	+	0.548685i
$700$	0.861597	−	0.625987i	0.0325653	−	0.0236601i
$701$	−34.9431	−	25.3876i	−1.31978	−	0.958878i	−0.999935	−	0.0114087i	$-0.996368\pi$
$701$	−34.9431	−	25.3876i	−1.31978	−	0.958878i	−0.319847	−	0.947469i	$-0.603632\pi$
$702$	14.1792	+	43.6390i	0.535159	+	1.64705i
$703$	−22.6311	−	16.4424i	−0.853547	−	0.620138i
$704$	10.7741	−	33.1592i	0.406063	−	1.24973i
$705$	−0.0119535	+	0.0367890i	−0.000450193	+	0.00138555i
$706$	7.47232	+	22.9974i	0.281224	+	0.865520i
$707$	5.11324			0.192303
$708$	−4.53287			−0.170356
$709$	14.9906	+	46.1365i	0.562986	+	1.73269i	0.673862	+	0.738857i	$0.264634\pi$
$709$	14.9906	+	46.1365i	0.562986	+	1.73269i	−0.110876	+	0.993834i	$0.535366\pi$
$710$	−0.0729464	+	0.0529987i	−0.00273763	+	0.00198900i
$711$	−12.4898	−	9.07437i	−0.468404	−	0.340316i
$712$	−3.35006			−0.125549
$713$		0			0
$714$	−8.11147			−0.303564
$715$	0.147782	+	0.107370i	0.00552674	+	0.00401541i
$716$	3.13919	−	2.28076i	0.117317	−	0.0852359i
$717$	−6.07802	−	18.7062i	−0.226988	−	0.698597i
$718$	36.4470			1.36019
$719$	−26.6658			−0.994466			−0.497233	−	0.867617i	$-0.665651\pi$
$719$	−26.6658			−0.994466			−0.497233	+	0.867617i	$0.665651\pi$
$720$	0.0112620	+	0.0346610i	0.000419711	+	0.00129174i
$721$	2.09667	−	6.45288i	0.0780840	−	0.240318i
$722$	2.05491	−	6.32435i	0.0764757	−	0.235368i
$723$	−20.4951	−	14.8906i	−0.762222	−	0.553787i
$724$	1.43689	+	4.42230i	0.0534017	+	0.164354i
$725$	−6.55506	−	4.76253i	−0.243449	−	0.176876i
$726$	−6.33751	+	4.60447i	−0.235207	+	0.170888i
$727$	−11.3616	+	34.9675i	−0.421380	+	1.29687i	0.485038	+	0.874493i	$0.338806\pi$
$727$	−11.3616	+	34.9675i	−0.421380	+	1.29687i	−0.906418	+	0.422381i	$0.861194\pi$
$728$	−12.1117	+	8.79965i	−0.448889	+	0.326137i
$729$	−19.4128	+	14.1042i	−0.718992	+	0.522378i
$730$	−0.0130925	+	0.0402947i	−0.000484577	+	0.00149137i
$731$	−3.56456	+	2.58981i	−0.131840	+	0.0957875i
$732$	1.34437	+	0.976742i	0.0496894	+	0.0361014i
$733$	15.3238	+	47.1618i	0.565997	+	1.74196i	0.664969	+	0.746871i	$0.268445\pi$
$733$	15.3238	+	47.1618i	0.565997	+	1.74196i	−0.0989720	+	0.995090i	$0.531555\pi$
$734$	5.88325	+	4.27443i	0.217155	+	0.157772i
$735$	0.0176807	−	0.0544155i	0.000652161	−	0.00200715i
$736$	−0.224953	+	0.692335i	−0.00829188	+	0.0255198i
$737$	−17.8542	−	54.9496i	−0.657669	−	2.02410i
$738$	−7.82666			−0.288103
$739$	30.9679			1.13917			0.569587	−	0.821931i	$-0.307103\pi$
$739$	30.9679			1.13917			0.569587	+	0.821931i	$0.307103\pi$
$740$	−0.00451411	−	0.0138930i	−0.000165942	−	0.000510717i
$741$	−23.5338	+	17.0983i	−0.864535	+	0.628121i
$742$	3.45292	+	2.50869i	0.126761	+	0.0920970i
$743$	45.6267			1.67388			0.836940	−	0.547294i	$-0.184342\pi$
$743$	45.6267			1.67388			0.836940	+	0.547294i	$0.184342\pi$
$744$		0			0
$745$	−0.0856644			−0.00313850
$746$	6.01011	+	4.36660i	0.220046	+	0.159873i
$747$	−2.39807	+	1.74230i	−0.0877407	+	0.0637473i
$748$	−2.06865	−	6.36665i	−0.0756373	−	0.232788i
$749$	10.7431			0.392544
$750$	−0.118245			−0.00431770
$751$	8.83461	+	27.1901i	0.322380	+	0.992183i	0.972610	+	0.232445i	$0.0746726\pi$
$751$	8.83461	+	27.1901i	0.322380	+	0.992183i	−0.650230	+	0.759738i	$0.725327\pi$
$752$	−4.51316	+	13.8901i	−0.164578	+	0.506519i
$753$	1.61341	−	4.96556i	0.0587958	−	0.180955i
$754$	10.8868	+	7.90975i	0.396475	+	0.288056i
$755$	−0.0401882	−	0.123687i	−0.00146260	−	0.00450141i
$756$	−0.952176	−	0.691796i	−0.0346303	−	0.0251604i
$757$	6.40269	−	4.65183i	0.232710	−	0.169074i	−0.465319	−	0.885143i	$-0.654061\pi$
$757$	6.40269	−	4.65183i	0.232710	−	0.169074i	0.698029	+	0.716069i	$0.254061\pi$
$758$	4.54375	−	13.9842i	0.165036	−	0.507929i
$759$	1.92139	−	1.39597i	0.0697419	−	0.0506705i
$760$	−0.0656360	+	0.0476874i	−0.00238087	+	0.00172980i
$761$	−7.06738	+	21.7512i	−0.256192	+	0.788479i	0.737400	+	0.675456i	$0.236053\pi$
$761$	−7.06738	+	21.7512i	−0.256192	+	0.788479i	−0.993592	+	0.113023i	$0.963947\pi$
$762$	−14.7818	+	10.7396i	−0.535489	+	0.389056i
$763$	6.57952	+	4.78030i	0.238195	+	0.173059i
$764$	−1.23417	−	3.79840i	−0.0446509	−	0.137421i
$765$	0.0545905	+	0.0396623i	0.00197372	+	0.00143399i
$766$	7.53208	−	23.1814i	0.272145	−	0.837577i
$767$	26.7195	−	82.2341i	0.964784	−	2.96930i
$768$	2.40719	+	7.40858i	0.0868621	+	0.267334i
$769$	−23.2138			−0.837110			−0.418555	−	0.908191i	$-0.637463\pi$
$769$	−23.2138			−0.837110			−0.418555	+	0.908191i	$0.637463\pi$
$770$	0.0302870			0.00109147
$771$	−7.07540	−	21.7758i	−0.254814	−	0.784238i
$772$	2.22751	−	1.61838i	0.0801699	−	0.0582469i
$773$	−18.0972	−	13.1484i	−0.650912	−	0.472915i	0.212670	−	0.977124i	$-0.431784\pi$
$773$	−18.0972	−	13.1484i	−0.650912	−	0.472915i	−0.863582	+	0.504209i	$0.831784\pi$
$774$	1.36277			0.0489839
$775$		0			0
$776$	21.7152			0.779531
$777$	−5.94651	−	4.32039i	−0.213330	−	0.154993i
$778$	25.1125	−	18.2453i	0.900326	−	0.654125i
$779$	−4.64953	−	14.3098i	−0.166587	−	0.512701i
$780$	−0.0151906			−0.000543912
$781$	−37.4426			−1.33980
$782$	−1.23547	−	3.80238i	−0.0441803	−	0.135973i
$783$	−2.76703	+	8.51605i	−0.0988856	+	0.304339i
$784$	6.67554	−	20.5452i	0.238412	−	0.733757i
$785$	−0.0156683	−	0.0113837i	−0.000559226	−	0.000406301i
$786$	0.324108	+	0.997502i	0.0115605	+	0.0355797i
$787$	9.27391	+	6.73789i	0.330579	+	0.240180i	0.740676	−	0.671862i	$-0.234505\pi$
$787$	9.27391	+	6.73789i	0.330579	+	0.240180i	−0.410097	+	0.912042i	$0.634505\pi$
$788$	3.16610	−	2.30030i	0.112788	−	0.0819450i
$789$	5.52619	−	17.0079i	0.196738	−	0.605496i
$790$	−0.0810491	+	0.0588856i	−0.00288360	+	0.00209506i
$791$	−5.35342	+	3.88949i	−0.190346	+	0.138294i
$792$	−5.41548	+	16.6671i	−0.192431	+	0.592241i
$793$	−25.6443	+	18.6317i	−0.910657	+	0.661631i
$794$	11.6152	+	8.43896i	0.412209	+	0.299487i
$795$	0.0113270	+	0.0348610i	0.000401728	+	0.00123639i
$796$	−2.29607	−	1.66819i	−0.0813821	−	0.0591275i
$797$	10.9362	−	33.6582i	0.387380	−	1.19223i	−0.547359	−	0.836898i	$-0.684367\pi$
$797$	10.9362	−	33.6582i	0.387380	−	1.19223i	0.934739	−	0.355335i	$-0.115633\pi$
$798$	−1.49041	+	4.58703i	−0.0527601	+	0.162379i
$799$	8.35614	+	25.7176i	0.295619	+	0.909822i
$800$	7.52530			0.266060
$801$	1.65673			0.0585378
$802$	−4.33974	−	13.3563i	−0.153241	−	0.471629i
$803$	−14.2338	+	10.3414i	−0.502298	+	0.364941i
$804$	3.88712	+	2.82415i	0.137088	+	0.0996003i
$805$	−0.00279834			−9.86284e−5
$806$		0			0
$807$	18.5678			0.653619
$808$	15.5327	+	11.2851i	0.546437	+	0.397010i
$809$	8.78598	−	6.38339i	0.308899	−	0.224428i	−0.422525	−	0.906351i	$-0.638856\pi$
$809$	8.78598	−	6.38339i	0.308899	−	0.224428i	0.731424	+	0.681923i	$0.238856\pi$
$810$	0.00708283	+	0.0217987i	0.000248865	+	0.000765929i
$811$	41.2607			1.44886			0.724429	−	0.689349i	$-0.242103\pi$
$811$	41.2607			1.44886			0.724429	+	0.689349i	$0.242103\pi$
$812$	−0.345171			−0.0121131
$813$	8.74143	+	26.9034i	0.306575	+	0.943542i
$814$	−12.1169	+	37.2921i	−0.424698	+	1.30709i
$815$	−0.0380209	+	0.117016i	−0.00133181	+	0.00409890i
$816$	−21.2789	−	15.4600i	−0.744910	−	0.541209i
$817$	0.809574	+	2.49161i	0.0283234	+	0.0871705i
$818$	10.0360	+	7.29159i	0.350901	+	0.254944i
$819$	5.98969	−	4.35177i	0.209297	−	0.152063i
$820$	0.00242801	−	0.00747265i	8.47898e−5	−	0.000260956i
$821$	−4.78145	+	3.47393i	−0.166874	+	0.121241i	−0.668088	−	0.744083i	$-0.732887\pi$
$821$	−4.78145	+	3.47393i	−0.166874	+	0.121241i	0.501214	+	0.865323i	$0.332887\pi$
$822$	−3.79057	+	2.75401i	−0.132211	+	0.0960572i
$823$	3.43254	−	10.5643i	0.119651	−	0.368247i	−0.873238	−	0.487294i	$-0.837984\pi$
$823$	3.43254	−	10.5643i	0.119651	−	0.368247i	0.992889	+	0.119047i	$0.0379839\pi$
$824$	20.6109	−	14.9747i	0.718015	−	0.521668i
$825$	−19.8623	−	14.4308i	−0.691516	−	0.502416i
$826$	−4.43015	−	13.6346i	−0.154145	−	0.474409i
$827$	4.43731	+	3.22389i	0.154300	+	0.112106i	0.662257	−	0.749277i	$-0.269599\pi$
$827$	4.43731	+	3.22389i	0.154300	+	0.112106i	−0.507956	+	0.861383i	$0.669599\pi$
$828$	0.0591162	−	0.181941i	0.00205443	−	0.00632289i
$829$	−11.4773	+	35.3234i	−0.398622	+	1.22683i	0.527483	+	0.849565i	$0.323136\pi$
$829$	−11.4773	+	35.3234i	−0.398622	+	1.22683i	−0.926105	+	0.377266i	$0.876864\pi$
$830$	0.00594400	+	0.0182937i	0.000206319	+	0.000634985i
$831$	17.8388			0.618822
$832$	−55.3072			−1.91743
$833$	−12.3598	−	38.0395i	−0.428241	−	1.31799i
$834$	−4.44103	+	3.22660i	−0.153780	+	0.111728i
$835$	0.0911649	+	0.0662352i	0.00315489	+	0.00229216i
$836$	−3.98043			−0.137666
$837$		0			0
$838$	38.4379			1.32782
$839$	−29.2866	−	21.2780i	−1.01109	−	0.734597i	−0.0466496	−	0.998911i	$-0.514854\pi$
$839$	−29.2866	−	21.2780i	−1.01109	−	0.734597i	−0.964437	+	0.264314i	$0.914854\pi$
$840$	−0.0172464	+	0.0125303i	−0.000595059	+	0.000432336i
$841$	−8.14999	−	25.0831i	−0.281034	−	0.864934i
$842$	−0.785242			−0.0270612
$843$	7.18168			0.247350
$844$	−1.37123	−	4.22022i	−0.0471997	−	0.145266i
$845$	0.0603045	−	0.185598i	0.00207454	−	0.00638478i
$846$	2.58453	−	7.95436i	0.0888579	−	0.273477i
$847$	3.10086	+	2.25291i	0.106547	+	0.0774107i
$848$	4.27664	+	13.1621i	0.146860	+	0.451990i
$849$	2.57967	+	1.87424i	0.0885339	+	0.0643237i
$850$	−33.4365	+	24.2931i	−1.14686	+	0.833245i
$851$	1.11953	−	3.44557i	0.0383771	−	0.118113i
$852$	2.51904	−	1.83019i	0.0863009	−	0.0627013i
$853$	9.04001	−	6.56795i	0.309524	−	0.224882i	−0.422168	−	0.906517i	$-0.638731\pi$
$853$	9.04001	−	6.56795i	0.309524	−	0.224882i	0.731692	+	0.681635i	$0.238731\pi$
$854$	−1.62408	+	4.99840i	−0.0555749	+	0.171042i
$855$	0.0324596	−	0.0235832i	0.00111009	−	0.000806530i
$856$	32.6347	+	23.7105i	1.11543	+	0.810407i
$857$	16.9546	+	52.1808i	0.579157	+	1.78246i	0.621568	+	0.783360i	$0.286496\pi$
$857$	16.9546	+	52.1808i	0.579157	+	1.78246i	−0.0424114	+	0.999100i	$0.513504\pi$
$858$	32.9879	+	23.9671i	1.12619	+	0.818223i
$859$	6.15280	−	18.9364i	0.209931	−	0.646101i	−0.789544	−	0.613694i	$-0.789683\pi$
$859$	6.15280	−	18.9364i	0.209931	−	0.646101i	0.999475	−	0.0324067i	$-0.0103172\pi$
$860$	−0.000422765		0.00130114i	−1.44162e−5		4.43684e-5i
$861$	−1.22170	−	3.76002i	−0.0416355	−	0.128141i
$862$	31.5916			1.07601
$863$	−11.1772			−0.380477			−0.190238	−	0.981738i	$-0.560926\pi$
$863$	−11.1772			−0.380477			−0.190238	+	0.981738i	$0.560926\pi$
$864$	−2.56992	−	7.90939i	−0.0874304	−	0.269083i
$865$	−0.0406914	+	0.0295640i	−0.00138355	+	0.00100521i
$866$	13.3562	+	9.70385i	0.453862	+	0.329750i
$867$	−27.7126			−0.941170
$868$		0			0
$869$	−41.6017			−1.41124
$870$	0.0155023	+	0.0112631i	0.000525578	+	0.000381855i
$871$	−74.1481	+	53.8718i	−2.51241	+	1.82538i
$872$	9.43650	+	29.0426i	0.319560	+	0.983505i
$873$	−10.7390			−0.363461
$874$	−2.37725			−0.0804117
$875$	0.0178784	+	0.0550241i	0.000604401	+	0.00186015i
$876$	0.452122	−	1.39149i	0.0152758	−	0.0470140i
$877$	−8.51296	+	26.2002i	−0.287462	+	0.884718i	0.698187	+	0.715915i	$0.253990\pi$
$877$	−8.51296	+	26.2002i	−0.287462	+	0.884718i	−0.985650	+	0.168803i	$0.946010\pi$
$878$	−41.6491	−	30.2598i	−1.40559	−	1.02122i
$879$	−7.03826	−	21.6615i	−0.237395	−	0.730626i
$880$	0.0794520	+	0.0577253i	0.00267833	+	0.00194592i
$881$	11.5386	−	8.38325i	0.388744	−	0.282439i	−0.376197	−	0.926540i	$-0.622768\pi$
$881$	11.5386	−	8.38325i	0.388744	−	0.282439i	0.764941	+	0.644101i	$0.222768\pi$
$882$	−3.82284	+	11.7655i	−0.128722	+	0.396165i
$883$	−15.1083	+	10.9768i	−0.508434	+	0.369399i	−0.812229	−	0.583338i	$-0.801746\pi$
$883$	−15.1083	+	10.9768i	−0.508434	+	0.369399i	0.303795	+	0.952737i	$0.401746\pi$
$884$	−8.59105	+	6.24176i	−0.288948	+	0.209933i
$885$	0.0380472	−	0.117097i	0.00127894	−	0.00393618i
$886$	−7.97699	+	5.79563i	−0.267992	+	0.194708i
$887$	28.1040	+	20.4188i	0.943641	+	0.685595i	0.949294	−	0.314389i	$-0.101800\pi$
$887$	28.1040	+	20.4188i	0.943641	+	0.685595i	−0.00565356	+	0.999984i	$0.501800\pi$
$888$	−8.52862	−	26.2484i	−0.286202	−	0.880838i
$889$	7.23255	+	5.25475i	0.242572	+	0.176239i
$890$	0.00332222	−	0.0102247i	0.000111361	−	0.000342734i
$891$	−2.94122	+	9.05214i	−0.0985345	+	0.303258i
$892$	0.0666717	+	0.205194i	0.00223233	+	0.00687042i
$893$	16.0786			0.538051
$894$	−19.1220			−0.639534
$895$	0.0325695	+	0.100238i	0.00108868	+	0.00335060i
$896$	−5.48291	+	3.98356i	−0.183171	+	0.133082i
$897$	−3.04789	−	2.21442i	−0.101766	−	0.0739373i
$898$	23.0498			0.769183
$899$		0			0
$900$	−1.97760			−0.0659200
$901$	20.7302	+	15.0614i	0.690622	+	0.501767i
$902$	−17.0627	+	12.3967i	−0.568124	+	0.412767i
$903$	0.212723	+	0.654693i	0.00707897	+	0.0217868i
$904$	−24.8465			−0.826383
$905$	−0.126302			−0.00419842
$906$	−8.97078	−	27.6092i	−0.298034	−	0.917255i
$907$	−1.96839	+	6.05808i	−0.0653593	+	0.201155i	−0.978403	−	0.206706i	$-0.933725\pi$
$907$	−1.96839	+	6.05808i	−0.0653593	+	0.201155i	0.913044	+	0.407862i	$0.133725\pi$
$908$	−1.11573	+	3.43385i	−0.0370267	+	0.113956i
$909$	−7.68150	−	5.58094i	−0.254779	−	0.185108i
$910$	−0.0148464	−	0.0456926i	−0.000492154	−	0.00151470i
$911$	−43.9635	−	31.9414i	−1.45658	−	1.05827i	−0.984238	−	0.176848i	$-0.943410\pi$
$911$	−43.9635	−	31.9414i	−1.45658	−	1.05827i	−0.472339	−	0.881417i	$-0.656590\pi$
$912$	−12.6524	+	9.19253i	−0.418964	+	0.304395i
$913$	−2.46831	+	7.59666i	−0.0816890	+	0.251413i
$914$	5.21083	−	3.78589i	0.172359	−	0.125226i
$915$	−0.0365163	+	0.0265306i	−0.00120719	+	0.000877076i
$916$	−1.07225	+	3.30004i	−0.0354280	+	0.109036i
$917$	0.415172	−	0.301640i	0.0137102	−	0.00996103i
$918$	36.9517	+	26.8470i	1.21959	+	0.886082i
$919$	−13.8120	−	42.5091i	−0.455617	−	1.40225i	−0.870409	−	0.492329i	$-0.836146\pi$
$919$	−13.8120	−	42.5091i	−0.455617	−	1.40225i	0.414792	−	0.909916i	$-0.363854\pi$
$920$	−0.00850060	−	0.00617605i	−0.000280257	−	0.000203618i
$921$	−0.627803	+	1.93218i	−0.0206868	+	0.0636675i
$922$	8.24653	−	25.3802i	0.271585	−	0.835853i
$923$	18.3541	+	56.4881i	0.604132	+	1.85933i
$924$	−1.04589			−0.0344073
$925$	−37.4515			−1.23140
$926$	−9.33587	−	28.7328i	−0.306796	−	0.944220i
$927$	−10.1929	+	7.40556i	−0.334778	+	0.243231i
$928$	−1.97319	−	1.43361i	−0.0647732	−	0.0470605i
$929$	15.4573			0.507139			0.253569	−	0.967317i	$-0.418395\pi$
$929$	15.4573			0.507139			0.253569	+	0.967317i	$0.418395\pi$
$930$		0			0
$931$	−23.7823			−0.779434
$932$	2.67851	+	1.94605i	0.0877374	+	0.0637449i
$933$	−19.2177	+	13.9625i	−0.629160	+	0.457112i
$934$	−11.0975	−	34.1545i	−0.363121	−	1.11757i
$935$	0.181833			0.00594657
$936$	27.7996			0.908659
$937$	−1.64333	−	5.05765i	−0.0536852	−	0.165226i	0.920619	−	0.390462i	$-0.127685\pi$
$937$	−1.64333	−	5.05765i	−0.0536852	−	0.165226i	−0.974304	+	0.225236i	$0.927685\pi$
$938$	−4.69587	+	14.4524i	−0.153326	+	0.471887i
$939$	5.87580	−	18.0839i	0.191750	−	0.590144i
$940$	0.00679280	+	0.00493526i	0.000221557	+	0.000160970i
$941$	4.13429	+	12.7240i	0.134774	+	0.414791i	0.995555	−	0.0941844i	$-0.0300243\pi$
$941$	4.13429	+	12.7240i	0.134774	+	0.414791i	−0.860781	+	0.508976i	$0.830024\pi$
$942$	−3.49747	−	2.54106i	−0.113954	−	0.0827922i
$943$	1.57649	−	1.14539i	0.0513376	−	0.0372989i
$944$	14.3652	−	44.2114i	0.467546	−	1.43896i
$945$	0.0258634	−	0.0187908i	0.000841335	−	0.000611266i
$946$	2.97094	−	2.15852i	0.0965938	−	0.0701795i
$947$	−2.07588	+	6.38890i	−0.0674570	+	0.207611i	−0.979103	−	0.203365i	$-0.934812\pi$
$947$	−2.07588	+	6.38890i	−0.0674570	+	0.207611i	0.911646	+	0.410976i	$0.134812\pi$
$948$	2.79885	−	2.03348i	0.0909025	−	0.0660445i
$949$	22.5789	+	16.4046i	0.732943	+	0.532515i
$950$	7.59402	+	23.3720i	0.246382	+	0.758287i
$951$	−28.8884	−	20.9886i	−0.936769	−	0.680603i
$952$	−4.60508	+	14.1730i	−0.149251	+	0.459348i
$953$	6.36940	−	19.6030i	0.206325	−	0.635003i	−0.793331	−	0.608790i	$-0.791655\pi$
$953$	6.36940	−	19.6030i	0.206325	−	0.635003i	0.999656	−	0.0262129i	$-0.00834479\pi$
$954$	−2.44908	−	7.53750i	−0.0792919	−	0.244035i
$955$	0.108483			0.00351043
$956$	−4.26933			−0.138080
$957$	2.45891	+	7.56773i	0.0794851	+	0.244630i
$958$	−36.6182	+	26.6047i	−1.18308	+	0.859557i
$959$	1.85468	+	1.34750i	0.0598906	+	0.0435131i
$960$	−0.0787547			−0.00254180
$961$		0			0
$962$	62.2005			2.00543
$963$	−16.1391	−	11.7257i	−0.520075	−	0.377857i
$964$	−4.44868	+	3.23215i	−0.143282	+	0.104101i
$965$	0.0231107	+	0.0711273i	0.000743959	+	0.00228967i
$966$	−0.624643			−0.0200976
$967$	−59.1290			−1.90146			−0.950731	−	0.310018i	$-0.899665\pi$
$967$	−59.1290			−1.90146			−0.950731	+	0.310018i	$0.899665\pi$
$968$	4.44732	+	13.6874i	0.142942	+	0.439931i
$969$	−8.94796	+	27.5390i	−0.287450	+	0.884679i
$970$	−0.0215347	+	0.0662771i	−0.000691439	+	0.00212803i
$971$	37.0382	+	26.9098i	1.18861	+	0.863577i	0.993117	−	0.117128i	$-0.0373688\pi$
$971$	37.0382	+	26.9098i	1.18861	+	0.863577i	0.195494	+	0.980705i	$0.437369\pi$
$972$	1.12800	+	3.47163i	0.0361806	+	0.111353i
$973$	2.17294	+	1.57873i	0.0696611	+	0.0506118i
$974$	−29.0753	+	21.1244i	−0.931633	+	0.676871i
$975$	−12.0348	+	37.0392i	−0.385421	+	1.18620i
$976$	−13.7871	+	10.0169i	−0.441316	+	0.320635i
$977$	−6.01653	+	4.37127i	−0.192486	+	0.139849i	−0.679854	−	0.733347i	$-0.737957\pi$
$977$	−6.01653	+	4.37127i	−0.192486	+	0.139849i	0.487368	+	0.873197i	$0.337957\pi$
$978$	−8.48701	+	26.1203i	−0.271385	+	0.835236i
$979$	3.61180	−	2.62412i	0.115434	−	0.0838674i
$980$	−0.0100474	−	0.00729987i	−0.000320953	−	0.000233186i
$981$	−4.66671	−	14.3627i	−0.148997	−	0.458565i
$982$	37.8004	+	27.4636i	1.20626	+	0.876399i
$983$	−8.40838	+	25.8783i	−0.268186	+	0.825391i	0.722757	+	0.691103i	$0.242875\pi$
$983$	−8.40838	+	25.8783i	−0.268186	+	0.825391i	−0.990942	+	0.134288i	$0.957125\pi$
$984$	4.58731	−	14.1183i	0.146238	−	0.450074i
$985$	0.0328486	+	0.101098i	0.00104664	+	0.00322124i
$986$	13.3953			0.426593
$987$	4.22480			0.134477
$988$	1.95118	+	6.00510i	0.0620751	+	0.191048i
$989$	−0.274498	+	0.199434i	−0.00872853	+	0.00634165i
$990$	−0.0454994	−	0.0330572i	−0.00144606	−	0.00105063i
$991$	17.2059			0.546563			0.273282	−	0.961934i	$-0.411891\pi$
$991$	17.2059			0.546563			0.273282	+	0.961934i	$0.411891\pi$
$992$		0			0
$993$	−2.28019			−0.0723597
$994$	7.96708	+	5.78842i	0.252700	+	0.183598i
$995$	0.0623668	−	0.0453121i	0.00197716	−	0.00143649i
$996$	−0.205263	−	0.631734i	−0.00650400	−	0.0200173i
$997$	29.5057			0.934454			0.467227	−	0.884137i	$-0.345253\pi$
$997$	29.5057			0.934454			0.467227	+	0.884137i	$0.345253\pi$
$998$	−14.7502			−0.466910
$999$	12.7898	+	39.3630i	0.404652	+	1.24539i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.s.374.10		64
31.2	even	5	inner	961.2.d.s.628.7		64
31.3	odd	30		961.2.g.w.235.10		128
31.4	even	5		961.2.a.l.1.7	✓	16
31.5	even	3		961.2.g.w.732.9		128
31.6	odd	6		961.2.g.w.816.9		128
31.7	even	15		961.2.c.l.439.8		32
31.8	even	5	inner	961.2.d.s.531.7		64
31.9	even	15		961.2.g.w.844.8		128
31.10	even	15		961.2.g.w.448.7		128
31.11	odd	30		961.2.c.l.521.7		32
31.12	odd	30		961.2.g.w.846.7		128
31.13	odd	30		961.2.g.w.338.9		128
31.14	even	15		961.2.g.w.547.7		128
31.15	odd	10	inner	961.2.d.s.388.9		64
31.16	even	5	inner	961.2.d.s.388.10		64
31.17	odd	30		961.2.g.w.547.8		128
31.18	even	15		961.2.g.w.338.10		128
31.19	even	15		961.2.g.w.846.8		128
31.20	even	15		961.2.c.l.521.8		32
31.21	odd	30		961.2.g.w.448.8		128
31.22	odd	30		961.2.g.w.844.7		128
31.23	odd	10	inner	961.2.d.s.531.8		64
31.24	odd	30		961.2.c.l.439.7		32
31.25	even	3		961.2.g.w.816.10		128
31.26	odd	6		961.2.g.w.732.10		128
31.27	odd	10		961.2.a.l.1.8	yes	16
31.28	even	15		961.2.g.w.235.9		128
31.29	odd	10	inner	961.2.d.s.628.8		64
31.30	odd	2	inner	961.2.d.s.374.9		64
93.35	odd	10		8649.2.a.bs.1.9		16
93.89	even	10		8649.2.a.bs.1.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.l.1.7	✓	16	31.4	even	5
961.2.a.l.1.8	yes	16	31.27	odd	10
961.2.c.l.439.7		32	31.24	odd	30
961.2.c.l.439.8		32	31.7	even	15
961.2.c.l.521.7		32	31.11	odd	30
961.2.c.l.521.8		32	31.20	even	15
961.2.d.s.374.9		64	31.30	odd	2	inner
961.2.d.s.374.10		64	1.1	even	1	trivial
961.2.d.s.388.9		64	31.15	odd	10	inner
961.2.d.s.388.10		64	31.16	even	5	inner
961.2.d.s.531.7		64	31.8	even	5	inner
961.2.d.s.531.8		64	31.23	odd	10	inner
961.2.d.s.628.7		64	31.2	even	5	inner
961.2.d.s.628.8		64	31.29	odd	10	inner
961.2.g.w.235.9		128	31.28	even	15
961.2.g.w.235.10		128	31.3	odd	30
961.2.g.w.338.9		128	31.13	odd	30
961.2.g.w.338.10		128	31.18	even	15
961.2.g.w.448.7		128	31.10	even	15
961.2.g.w.448.8		128	31.21	odd	30
961.2.g.w.547.7		128	31.14	even	15
961.2.g.w.547.8		128	31.17	odd	30
961.2.g.w.732.9		128	31.5	even	3
961.2.g.w.732.10		128	31.26	odd	6
961.2.g.w.816.9		128	31.6	odd	6
961.2.g.w.816.10		128	31.25	even	3
961.2.g.w.844.7		128	31.22	odd	30
961.2.g.w.844.8		128	31.9	even	15
961.2.g.w.846.7		128	31.12	odd	30
961.2.g.w.846.8		128	31.19	even	15
8649.2.a.bs.1.9		16	93.35	odd	10
8649.2.a.bs.1.10		16	93.89	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(1.06472 + 0.773568i) q^{2} +(0.998704 - 0.725601i) q^{3} +(-0.0828021 - 0.254839i) q^{4} +0.00727825 q^{5} +1.62465 q^{6} +(-0.245643 - 0.756011i) q^{7} +(0.922351 - 2.83870i) q^{8} +(-0.456138 + 1.40385i) q^{9} +(0.00774933 + 0.00563022i) q^{10} +(1.22916 + 3.78297i) q^{11} +(-0.267606 - 0.194427i) q^{12} +(5.10468 - 3.70877i) q^{13} +(0.323284 - 0.994966i) q^{14} +(0.00726882 - 0.00528110i) q^{15} +(2.74442 - 1.99394i) q^{16} +(1.94089 - 5.97344i) q^{17} +(-1.57163 + 1.14186i) q^{18} +(-3.02135 - 2.19514i) q^{19} +(-0.000602654 - 0.00185478i) q^{20} +(-0.793887 - 0.576793i) q^{21} +(-1.61767 + 4.97867i) q^{22} +(0.149463 - 0.460000i) q^{23} +(-1.13861 - 3.50428i) q^{24} -4.99995 q^{25} +8.30406 q^{26} +(1.70750 + 5.25514i) q^{27} +(-0.172321 + 0.125199i) q^{28} +(1.31103 + 0.952516i) q^{29} +0.0118246 q^{30} -1.50508 q^{32} +(3.97250 + 2.88619i) q^{33} +(6.68738 - 4.85866i) q^{34} +(-0.00178785 - 0.00550244i) q^{35} +0.395524 q^{36} +7.49037 q^{37} +(-1.51882 - 4.67444i) q^{38} +(2.40698 - 7.40792i) q^{39} +(0.00671310 - 0.0206608i) q^{40} +(3.25942 + 2.36811i) q^{41} +(-0.399083 - 1.22825i) q^{42} +(-0.567529 - 0.412334i) q^{43} +(0.862271 - 0.626476i) q^{44} +(-0.00331989 + 0.0102176i) q^{45} +(0.514978 - 0.374153i) q^{46} +(-3.48307 + 2.53060i) q^{47} +(1.29406 - 3.98271i) q^{48} +(5.15191 - 3.74308i) q^{49} +(-5.32357 - 3.86780i) q^{50} +(-2.39596 - 7.37401i) q^{51} +(-1.36782 - 0.993776i) q^{52} +(-1.26069 + 3.88001i) q^{53} +(-2.24719 + 6.91615i) q^{54} +(0.00894615 + 0.0275334i) q^{55} -2.37266 q^{56} -4.61023 q^{57} +(0.659046 + 2.02833i) q^{58} +(11.0864 - 8.05477i) q^{59} +(-0.00194770 - 0.00141509i) q^{60} -5.02369 q^{61} +1.17337 q^{63} +(-7.09134 - 5.15216i) q^{64} +(0.0371531 - 0.0269933i) q^{65} +(1.99695 + 6.14599i) q^{66} -14.5255 q^{67} -1.68297 q^{68} +(-0.184507 - 0.567854i) q^{69} +(0.00235294 - 0.00724161i) q^{70} +(-2.90885 + 8.95253i) q^{71} +(3.56439 + 2.58968i) q^{72} +(1.36684 + 4.20670i) q^{73} +(7.97519 + 5.79431i) q^{74} +(-4.99347 + 3.62797i) q^{75} +(-0.309233 + 0.951720i) q^{76} +(2.55804 - 1.85852i) q^{77} +(8.29330 - 6.02544i) q^{78} +(-3.23196 + 9.94696i) q^{79} +(0.0199746 - 0.0145124i) q^{80} +(1.93587 + 1.40649i) q^{81} +(1.63849 + 5.04276i) q^{82} +(1.62460 + 1.18034i) q^{83} +(-0.0812536 + 0.250073i) q^{84} +(0.0141263 - 0.0434762i) q^{85} +(-0.285294 - 0.878044i) q^{86} +2.00047 q^{87} +11.8725 q^{88} +(-0.346834 - 1.06744i) q^{89} +(-0.0114387 + 0.00831074i) q^{90} +(-4.05780 - 2.94816i) q^{91} -0.129602 q^{92} -5.66611 q^{94} +(-0.0219902 - 0.0159768i) q^{95} +(-1.50313 + 1.09208i) q^{96} +(2.24819 + 6.91921i) q^{97} +8.38089 q^{98} -5.87139 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{2} - 8 q^{4} - 64 q^{5} + 16 q^{7} - 8 q^{10} + 8 q^{14} + 8 q^{16} + 24 q^{18} + 32 q^{19} + 24 q^{20} + 8 q^{28} - 32 q^{32} + 32 q^{33} + 16 q^{35} - 160 q^{36} + 24 q^{38} + 32 q^{39} + 32 q^{41}+ \cdots + 64 q^{98}+O(q^{100}) \) 64 * q + 8 * q^2 - 8 * q^4 - 64 * q^5 + 16 * q^7 - 8 * q^10 + 8 * q^14 + 8 * q^16 + 24 * q^18 + 32 * q^19 + 24 * q^20 + 8 * q^28 - 32 * q^32 + 32 * q^33 + 16 * q^35 - 160 * q^36 + 24 * q^38 + 32 * q^39 + 32 * q^41 + 16 * q^45 + 32 * q^47 + 16 * q^49 + 32 * q^50 + 32 * q^51 - 192 * q^56 + 64 * q^59 - 64 * q^63 + 16 * q^64 + 64 * q^67 + 32 * q^69 - 88 * q^70 + 48 * q^71 - 48 * q^72 - 40 * q^76 - 32 * q^78 + 40 * q^80 + 16 * q^81 - 88 * q^82 - 128 * q^87 - 40 * q^90 - 128 * q^94 + 48 * q^95 + 64 * q^98

Introduction

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