LMFDB - Embedded newform 820.2.k.c.247.38

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(83,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.83"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [108] 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:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			247.38
Character	$\chi$	$=$	820.247
Dual form			820.2.k.c.83.38

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.850658 - 1.12977i) q^{2} +(-1.73461 - 1.73461i) q^{3} +(-0.552763 - 1.92210i) q^{4} +(2.10007 - 0.767920i) q^{5} +(-3.43527 + 0.484152i) q^{6} +(1.19221 - 1.19221i) q^{7} +(-2.64174 - 1.01055i) q^{8} +3.01775i q^{9} +(0.918869 - 3.02584i) q^{10} -4.02815i q^{11} +(-2.37526 + 4.29292i) q^{12} +(-0.809077 + 0.809077i) q^{13} +(-0.332763 - 2.36109i) q^{14} +(-4.97485 - 2.31076i) q^{15} +(-3.38891 + 2.12493i) q^{16} +(-0.339384 - 0.339384i) q^{17} +(3.40936 + 2.56707i) q^{18} +4.20643 q^{19} +(-2.63686 - 3.61206i) q^{20} -4.13605 q^{21} +(-4.55088 - 3.42657i) q^{22} +(-1.29540 - 1.29540i) q^{23} +(2.82948 + 6.33530i) q^{24} +(3.82060 - 3.22537i) q^{25} +(0.225824 + 1.60232i) q^{26} +(0.0307830 - 0.0307830i) q^{27} +(-2.95056 - 1.63254i) q^{28} +4.18189i q^{29} +(-6.84252 + 3.65477i) q^{30} -5.69498i q^{31} +(-0.482116 + 5.63627i) q^{32} +(-6.98726 + 6.98726i) q^{33} +(-0.672126 + 0.0947266i) q^{34} +(1.58821 - 3.41926i) q^{35} +(5.80040 - 1.66810i) q^{36} +(4.60427 + 4.60427i) q^{37} +(3.57824 - 4.75231i) q^{38} +2.80687 q^{39} +(-6.32386 - 0.0935821i) q^{40} +1.00000 q^{41} +(-3.51836 + 4.67279i) q^{42} +(0.412275 + 0.412275i) q^{43} +(-7.74248 + 2.22661i) q^{44} +(2.31739 + 6.33748i) q^{45} +(-2.56545 + 0.361563i) q^{46} +(-8.15524 + 8.15524i) q^{47} +(9.56435 + 2.19251i) q^{48} +4.15725i q^{49} +(-0.393909 - 7.06009i) q^{50} +1.17740i q^{51} +(2.00235 + 1.10790i) q^{52} +(0.269408 - 0.269408i) q^{53} +(-0.00859193 - 0.0609635i) q^{54} +(-3.09329 - 8.45939i) q^{55} +(-4.35431 + 1.94473i) q^{56} +(-7.29652 - 7.29652i) q^{57} +(4.72458 + 3.55736i) q^{58} +5.44652 q^{59} +(-1.69160 + 10.8394i) q^{60} +0.729813 q^{61} +(-6.43402 - 4.84448i) q^{62} +(3.59780 + 3.59780i) q^{63} +(5.95758 + 5.33922i) q^{64} +(-1.07781 + 2.32042i) q^{65} +(1.95024 + 13.8378i) q^{66} +(-9.31927 + 9.31927i) q^{67} +(-0.464730 + 0.839928i) q^{68} +4.49403i q^{69} +(-2.51196 - 4.70293i) q^{70} -1.57249i q^{71} +(3.04958 - 7.97210i) q^{72} +(5.88887 - 5.88887i) q^{73} +(9.11843 - 1.28511i) q^{74} +(-12.2220 - 1.03249i) q^{75} +(-2.32516 - 8.08517i) q^{76} +(-4.80241 - 4.80241i) q^{77} +(2.38768 - 3.17112i) q^{78} +13.9425 q^{79} +(-5.48517 + 7.06491i) q^{80} +8.94645 q^{81} +(0.850658 - 1.12977i) q^{82} +(3.59692 + 3.59692i) q^{83} +(2.28626 + 7.94989i) q^{84} +(-0.973351 - 0.452111i) q^{85} +(0.816481 - 0.115071i) q^{86} +(7.25395 - 7.25395i) q^{87} +(-4.07064 + 10.6413i) q^{88} -6.99649i q^{89} +(9.13120 + 2.77291i) q^{90} +1.92919i q^{91} +(-1.77383 + 3.20593i) q^{92} +(-9.87857 + 9.87857i) q^{93} +(2.27623 + 16.1509i) q^{94} +(8.83381 - 3.23020i) q^{95} +(10.6130 - 8.94045i) q^{96} +(-9.75595 - 9.75595i) q^{97} +(4.69674 + 3.53640i) q^{98} +12.1559 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + 12 q^{2} - 4 q^{6} - 24 q^{8} + 4 q^{10} - 16 q^{13} + 52 q^{16} - 8 q^{17} + 18 q^{18} + 38 q^{20} + 72 q^{21} + 10 q^{22} - 12 q^{25} + 24 q^{26} - 58 q^{28} - 70 q^{30} - 38 q^{32} + 8 q^{33}+ \cdots + 122 q^{98}+O(q^{100}) $ 108 * q + 12 * q^2 - 4 * q^6 - 24 * q^8 + 4 * q^10 - 16 * q^13 + 52 * q^16 - 8 * q^17 + 18 * q^18 + 38 * q^20 + 72 * q^21 + 10 * q^22 - 12 * q^25 + 24 * q^26 - 58 * q^28 - 70 * q^30 - 38 * q^32 + 8 * q^33 + 72 * q^36 - 44 * q^37 + 56 * q^38 + 50 * q^40 + 108 * q^41 - 72 * q^42 - 4 * q^45 - 4 * q^46 - 94 * q^48 - 56 * q^50 - 50 * q^52 - 16 * q^53 - 32 * q^56 - 112 * q^57 + 68 * q^58 + 136 * q^60 + 8 * q^61 + 2 * q^62 - 48 * q^65 + 16 * q^66 - 16 * q^68 - 48 * q^70 - 42 * q^72 - 20 * q^73 - 12 * q^76 + 72 * q^77 + 100 * q^78 + 72 * q^80 - 52 * q^81 + 12 * q^82 - 32 * q^85 - 20 * q^86 - 38 * q^88 - 50 * q^90 + 8 * q^92 + 24 * q^93 + 44 * q^96 - 56 * q^97 + 122 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.850658	−	1.12977i	0.601506	−	0.798868i
$2$	0.850658	−	1.12977i	0.601506	−	0.798868i
$3$	−1.73461	−	1.73461i	−1.00148	−	1.00148i	−0.999999	−	0.00147886i	$-0.999529\pi$
$3$	−1.73461	−	1.73461i	−1.00148	−	1.00148i	−0.00147886	−	0.999999i	$-0.500471\pi$
$4$	−0.552763	−	1.92210i	−0.276382	−	0.961048i
$5$	2.10007	−	0.767920i	0.939180	−	0.343424i
$5$	2.10007	−	0.767920i	0.939180	−	0.343424i
$6$	−3.43527	+	0.484152i	−1.40244	+	0.197654i
$7$	1.19221	−	1.19221i	0.450614	−	0.450614i	−0.444944	−	0.895558i	$-0.646776\pi$
$7$	1.19221	−	1.19221i	0.450614	−	0.450614i	0.895558	+	0.444944i	$0.146776\pi$
$8$	−2.64174	−	1.01055i	−0.933996	−	0.357283i
$9$			3.01775i			1.00592i
$10$	0.918869	−	3.02584i	0.290572	−	0.956853i
$11$		−	4.02815i		−	1.21453i	−0.794499	−	0.607266i	$-0.792266\pi$
$11$		−	4.02815i		−	1.21453i	0.794499	−	0.607266i	$-0.207734\pi$
$12$	−2.37526	+	4.29292i	−0.685678	+	1.23926i
$13$	−0.809077	+	0.809077i	−0.224398	+	0.224398i	−0.810347	−	0.585950i	$-0.800722\pi$
$13$	−0.809077	+	0.809077i	−0.224398	+	0.224398i	0.585950	+	0.810347i	$0.300722\pi$
$14$	−0.332763	−	2.36109i	−0.0889345	−	0.631029i
$15$	−4.97485	−	2.31076i	−1.28450	−	0.596637i
$16$	−3.38891	+	2.12493i	−0.847226	+	0.531232i
$17$	−0.339384	−	0.339384i	−0.0823127	−	0.0823127i	0.664752	−	0.747064i	$-0.268537\pi$
$17$	−0.339384	−	0.339384i	−0.0823127	−	0.0823127i	−0.747064	+	0.664752i	$0.768537\pi$
$18$	3.40936	+	2.56707i	0.803594	+	0.605064i
$19$	4.20643			0.965022			0.482511	−	0.875890i	$-0.339725\pi$
$19$	4.20643			0.965022			0.482511	+	0.875890i	$0.339725\pi$
$20$	−2.63686	−	3.61206i	−0.589619	−	0.807681i
$21$	−4.13605			−0.902561
$22$	−4.55088	−	3.42657i	−0.970251	−	0.730548i
$23$	−1.29540	−	1.29540i	−0.270109	−	0.270109i	0.559035	−	0.829144i	$-0.311172\pi$
$23$	−1.29540	−	1.29540i	−0.270109	−	0.270109i	−0.829144	+	0.559035i	$0.811172\pi$
$24$	2.82948	+	6.33530i	0.577565	+	1.29319i
$25$	3.82060	−	3.22537i	0.764120	−	0.645074i
$26$	0.225824	+	1.60232i	0.0442877	+	0.314241i
$27$	0.0307830	−	0.0307830i	0.00592418	−	0.00592418i
$28$	−2.95056	−	1.63254i	−0.557604	−	0.308521i
$29$			4.18189i			0.776558i	0.921542	+	0.388279i	$0.126930\pi$
$29$			4.18189i			0.776558i	−0.921542	+	0.388279i	$0.873070\pi$
$30$	−6.84252	+	3.65477i	−1.24927	+	0.667266i
$31$		−	5.69498i		−	1.02285i	−0.859328	−	0.511424i	$-0.829118\pi$
$31$		−	5.69498i		−	1.02285i	0.859328	−	0.511424i	$-0.170882\pi$
$32$	−0.482116	+	5.63627i	−0.0852268	+	0.996362i
$33$	−6.98726	+	6.98726i	−1.21633	+	1.21633i
$34$	−0.672126	+	0.0947266i	−0.115269	+	0.0162455i
$35$	1.58821	−	3.41926i	0.268456	−	0.577960i
$36$	5.80040	−	1.66810i	0.966733	−	0.278017i
$37$	4.60427	+	4.60427i	0.756937	+	0.756937i	0.975764	−	0.218826i	$-0.0702229\pi$
$37$	4.60427	+	4.60427i	0.756937	+	0.756937i	−0.218826	+	0.975764i	$0.570223\pi$
$38$	3.57824	−	4.75231i	0.580466	−	0.770926i
$39$	2.80687			0.449458
$40$	−6.32386	−	0.0935821i	−0.999891	−	0.0147966i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	−3.51836	+	4.67279i	−0.542895	+	0.721027i
$43$	0.412275	+	0.412275i	0.0628714	+	0.0628714i	0.737843	−	0.674972i	$-0.235844\pi$
$43$	0.412275	+	0.412275i	0.0628714	+	0.0628714i	−0.674972	+	0.737843i	$0.735844\pi$
$44$	−7.74248	+	2.22661i	−1.16722	+	0.335674i
$45$	2.31739	+	6.33748i	0.345456	+	0.944736i
$46$	−2.56545	+	0.361563i	−0.378254	+	0.0533095i
$47$	−8.15524	+	8.15524i	−1.18956	+	1.18956i	−0.212376	+	0.977188i	$0.568120\pi$
$47$	−8.15524	+	8.15524i	−1.18956	+	1.18956i	−0.977188	+	0.212376i	$0.931880\pi$
$48$	9.56435	+	2.19251i	1.38050	+	0.316461i
$49$			4.15725i			0.593893i
$50$	−0.393909	−	7.06009i	−0.0557071	−	0.998447i
$51$			1.17740i			0.164869i
$52$	2.00235	+	1.10790i	0.277676	+	0.153637i
$53$	0.269408	−	0.269408i	0.0370060	−	0.0370060i	−0.688362	−	0.725368i	$-0.741670\pi$
$53$	0.269408	−	0.269408i	0.0370060	−	0.0370060i	0.725368	+	0.688362i	$0.241670\pi$
$54$	−0.00859193	−	0.0609635i	−0.00116921	−	0.00829608i
$55$	−3.09329	−	8.45939i	−0.417099	−	1.14066i
$56$	−4.35431	+	1.94473i	−0.581869	+	0.259875i
$57$	−7.29652	−	7.29652i	−0.966448	−	0.966448i
$58$	4.72458	+	3.55736i	0.620367	+	0.467104i
$59$	5.44652			0.709076			0.354538	−	0.935042i	$-0.384638\pi$
$59$	5.44652			0.709076			0.354538	+	0.935042i	$0.384638\pi$
$60$	−1.69160	+	10.8394i	−0.218384	+	1.39937i
$61$	0.729813			0.0934429			0.0467215	−	0.998908i	$-0.485123\pi$
$61$	0.729813			0.0934429			0.0467215	+	0.998908i	$0.485123\pi$
$62$	−6.43402	−	4.84448i	−0.817121	−	0.615249i
$63$	3.59780	+	3.59780i	0.453280	+	0.453280i
$64$	5.95758	+	5.33922i	0.744697	+	0.667402i
$65$	−1.07781	+	2.32042i	−0.133686	+	0.287813i
$66$	1.95024	+	13.8378i	0.240058	+	1.70331i
$67$	−9.31927	+	9.31927i	−1.13853	+	1.13853i	−0.149816	+	0.988714i	$0.547868\pi$
$67$	−9.31927	+	9.31927i	−1.13853	+	1.13853i	−0.988714	+	0.149816i	$0.952132\pi$
$68$	−0.464730	+	0.839928i	−0.0563568	+	0.101856i
$69$			4.49403i			0.541017i
$70$	−2.51196	−	4.70293i	−0.300236	−	0.562108i
$71$		−	1.57249i		−	0.186620i	−0.995637	−	0.0933101i	$-0.970255\pi$
$71$		−	1.57249i		−	0.186620i	0.995637	−	0.0933101i	$-0.0297448\pi$
$72$	3.04958	−	7.97210i	0.359397	−	0.939521i
$73$	5.88887	−	5.88887i	0.689240	−	0.689240i	−0.272824	−	0.962064i	$-0.587958\pi$
$73$	5.88887	−	5.88887i	0.689240	−	0.689240i	0.962064	+	0.272824i	$0.0879577\pi$
$74$	9.11843	−	1.28511i	1.06000	−	0.149391i
$75$	−12.2220	−	1.03249i	−1.41128	−	0.119221i
$76$	−2.32516	−	8.08517i	−0.266715	−	0.927433i
$77$	−4.80241	−	4.80241i	−0.547286	−	0.547286i
$78$	2.38768	−	3.17112i	0.270352	−	0.359058i
$79$	13.9425			1.56866			0.784329	−	0.620345i	$-0.213008\pi$
$79$	13.9425			1.56866			0.784329	+	0.620345i	$0.213008\pi$
$80$	−5.48517	+	7.06491i	−0.613260	+	0.789881i
$81$	8.94645			0.994050
$82$	0.850658	−	1.12977i	0.0939394	−	0.124762i
$83$	3.59692	+	3.59692i	0.394813	+	0.394813i	0.876399	−	0.481586i	$-0.159939\pi$
$83$	3.59692	+	3.59692i	0.394813	+	0.394813i	−0.481586	+	0.876399i	$0.659939\pi$
$84$	2.28626	+	7.94989i	0.249451	+	0.867404i
$85$	−0.973351	−	0.452111i	−0.105575	−	0.0490383i
$86$	0.816481	−	0.115071i	0.0880434	−	0.0124085i
$87$	7.25395	−	7.25395i	0.777705	−	0.777705i
$88$	−4.07064	+	10.6413i	−0.433932	+	1.13437i
$89$		−	6.99649i		−	0.741627i	−0.928707	−	0.370813i	$-0.879079\pi$
$89$		−	6.99649i		−	0.741627i	0.928707	−	0.370813i	$-0.120921\pi$
$90$	9.13120	+	2.77291i	0.962513	+	0.292291i
$91$			1.92919i			0.202234i
$92$	−1.77383	+	3.20593i	−0.184935	+	0.334241i
$93$	−9.87857	+	9.87857i	−1.02436	+	1.02436i
$94$	2.27623	+	16.1509i	0.234776	+	1.66584i
$95$	8.83381	−	3.23020i	0.906330	−	0.331412i
$96$	10.6130	−	8.94045i	1.08319	−	0.912481i
$97$	−9.75595	−	9.75595i	−0.990566	−	0.990566i	0.00938975	−	0.999956i	$-0.497011\pi$
$97$	−9.75595	−	9.75595i	−0.990566	−	0.990566i	−0.999956	+	0.00938975i	$0.997011\pi$
$98$	4.69674	+	3.53640i	0.474443	+	0.357230i
$99$	12.1559			1.22172
$100$	−8.31136	−	5.56069i	−0.831136	−	0.556069i
$101$	−0.471180			−0.0468842			−0.0234421	−	0.999725i	$-0.507463\pi$
$101$	−0.471180			−0.0468842			−0.0234421	+	0.999725i	$0.507463\pi$
$102$	1.33019	+	1.00156i	0.131708	+	0.0991695i
$103$	−13.6131	−	13.6131i	−1.34134	−	1.34134i	−0.894725	−	0.446618i	$-0.852628\pi$
$103$	−13.6131	−	13.6131i	−1.34134	−	1.34134i	−0.446618	−	0.894725i	$-0.647372\pi$
$104$	2.95498	−	1.31976i	0.289760	−	0.129413i
$105$	−8.68601	+	3.17616i	−0.847667	+	0.309961i
$106$	−0.0751952	−	0.533542i	−0.00730360	−	0.0518222i
$107$	3.09088	−	3.09088i	0.298806	−	0.298806i	−0.541740	−	0.840546i	$-0.682234\pi$
$107$	3.09088	−	3.09088i	0.298806	−	0.298806i	0.840546	+	0.541740i	$0.182234\pi$
$108$	−0.0761835	−	0.0421521i	−0.00733076	−	0.00405609i
$109$		−	14.2850i		−	1.36826i	−0.729362	−	0.684128i	$-0.760183\pi$
$109$		−	14.2850i		−	1.36826i	0.729362	−	0.684128i	$-0.239817\pi$
$110$	−12.1885	−	3.70134i	−1.16213	−	0.352909i
$111$		−	15.9732i		−	1.51611i
$112$	−1.50693	+	6.57367i	−0.142392	+	0.621153i
$113$	2.75749	−	2.75749i	0.259403	−	0.259403i	−0.565408	−	0.824811i	$-0.691281\pi$
$113$	2.75749	−	2.75749i	0.259403	−	0.259403i	0.824811	+	0.565408i	$0.191281\pi$
$114$	−14.4502	+	2.03656i	−1.35339	+	0.190741i
$115$	−3.71519	−	1.72567i	−0.346444	−	0.160919i
$116$	8.03799	−	2.31160i	0.746309	−	0.214626i
$117$	−2.44159	−	2.44159i	−0.225725	−	0.225725i
$118$	4.63312	−	6.15331i	0.426513	−	0.566458i
$119$	−0.809237			−0.0741826
$120$	10.8071	+	11.1318i	0.986550	+	1.01619i
$121$	−5.22596			−0.475087
$122$	0.620821	−	0.824521i	0.0562065	−	0.0746486i
$123$	−1.73461	−	1.73461i	−0.156405	−	0.156405i
$124$	−10.9463	+	3.14798i	−0.983006	+	0.282697i
$125$	5.54670	−	9.70742i	0.496112	−	0.868258i
$126$	7.12518	−	1.00419i	0.634762	−	0.0894606i
$127$	9.54013	−	9.54013i	0.846550	−	0.846550i	−0.143151	−	0.989701i	$-0.545724\pi$
$127$	9.54013	−	9.54013i	0.846550	−	0.846550i	0.989701	+	0.143151i	$0.0457235\pi$
$128$	11.1000	−	2.18885i	0.981106	−	0.193469i
$129$		−	1.43027i		−	0.125929i
$130$	1.70470	+	3.19157i	0.149512	+	0.279919i
$131$			19.9501i			1.74305i	0.490353	+	0.871524i	$0.336868\pi$
$131$			19.9501i			1.74305i	−0.490353	+	0.871524i	$0.663132\pi$
$132$	17.2925	+	9.56789i	1.50512	+	0.832778i
$133$	5.01497	−	5.01497i	0.434853	−	0.434853i
$134$	2.60113	+	18.4561i	0.224703	+	1.59437i
$135$	0.0410076	−	0.0882853i	0.00352937	−	0.00759839i
$136$	0.553600	+	1.23953i	0.0474708	+	0.106289i
$137$	−9.99072	−	9.99072i	−0.853565	−	0.853565i	0.137005	−	0.990570i	$-0.456252\pi$
$137$	−9.99072	−	9.99072i	−0.853565	−	0.853565i	−0.990570	+	0.137005i	$0.956252\pi$
$138$	5.07722	+	3.82288i	0.432202	+	0.325425i
$139$	−4.82361			−0.409133			−0.204567	−	0.978853i	$-0.565579\pi$
$139$	−4.82361			−0.409133			−0.204567	+	0.978853i	$0.565579\pi$
$140$	−7.45005	−	1.16265i	−0.629644	−	0.0982619i
$141$	28.2923			2.38264
$142$	−1.77655	−	1.33765i	−0.149085	−	0.112253i
$143$	3.25908	+	3.25908i	0.272538	+	0.272538i
$144$	−6.41250	−	10.2269i	−0.534375	−	0.852238i
$145$	3.21136	+	8.78227i	0.266689	+	0.729328i
$146$	−1.64366	−	11.6625i	−0.136030	−	0.965194i
$147$	7.21121	−	7.21121i	0.594771	−	0.594771i
$148$	6.30478	−	11.3949i	0.518249	−	0.936657i
$149$		−	16.3870i		−	1.34248i	−0.741241	−	0.671239i	$-0.765762\pi$
$149$		−	16.3870i		−	1.34248i	0.741241	−	0.671239i	$-0.234238\pi$
$150$	−11.5632	+	12.9298i	−0.944133	+	1.05571i
$151$		−	13.0755i		−	1.06407i	−0.846723	−	0.532034i	$-0.821428\pi$
$151$		−	13.0755i		−	1.06407i	0.846723	−	0.532034i	$-0.178572\pi$
$152$	−11.1123	−	4.25081i	−0.901327	−	0.344786i
$153$	1.02418	−	1.02418i	0.0827997	−	0.0827997i
$154$	−9.51083	+	1.34042i	−0.766405	+	0.108014i
$155$	−4.37329	−	11.9599i	−0.351271	−	0.960639i
$156$	−1.55153	−	5.39507i	−0.124222	−	0.431951i
$157$	11.6419	+	11.6419i	0.929126	+	0.929126i	0.997649	−	0.0685237i	$-0.0218289\pi$
$157$	11.6419	+	11.6419i	0.929126	+	0.929126i	−0.0685237	+	0.997649i	$0.521829\pi$
$158$	11.8603	−	15.7519i	0.943557	−	1.25315i
$159$	−0.934635			−0.0741213
$160$	3.31573	+	12.2068i	0.262131	+	0.965032i
$161$	−3.08879			−0.243430
$162$	7.61036	−	10.1074i	0.597927	−	0.794115i
$163$	−3.14829	−	3.14829i	−0.246593	−	0.246593i	0.572978	−	0.819571i	$-0.305788\pi$
$163$	−3.14829	−	3.14829i	−0.246593	−	0.246593i	−0.819571	+	0.572978i	$0.805788\pi$
$164$	−0.552763	−	1.92210i	−0.0431636	−	0.150090i
$165$	−9.30810	+	20.0394i	−0.724634	+	1.56007i
$166$	7.12343	−	1.00395i	0.552886	−	0.0779214i
$167$	1.04606	−	1.04606i	0.0809462	−	0.0809462i	−0.665474	−	0.746421i	$-0.731771\pi$
$167$	1.04606	−	1.04606i	0.0809462	−	0.0809462i	0.746421	+	0.665474i	$0.231771\pi$
$168$	10.9264	+	4.17969i	0.842988	+	0.322470i
$169$			11.6908i			0.899291i
$170$	−1.33877	+	0.715071i	−0.102679	+	0.0548435i
$171$			12.6940i			0.970731i
$172$	0.564542	−	1.02032i	0.0430459	−	0.0777989i
$173$	8.62879	−	8.62879i	0.656034	−	0.656034i	−0.298405	−	0.954439i	$-0.596455\pi$
$173$	8.62879	−	8.62879i	0.656034	−	0.656034i	0.954439	+	0.298405i	$0.0964546\pi$
$174$	−2.02467	−	14.3659i	−0.153490	−	1.08908i
$175$	0.709638	−	8.40030i	0.0536436	−	0.635003i
$176$	8.55952	+	13.6510i	0.645198	+	1.02898i
$177$	−9.44758	−	9.44758i	−0.710124	−	0.710124i
$178$	−7.90443	−	5.95162i	−0.592462	−	0.446093i
$179$	7.62133			0.569645			0.284822	−	0.958580i	$-0.408065\pi$
$179$	7.62133			0.569645			0.284822	+	0.958580i	$0.408065\pi$
$180$	10.9003	−	7.95737i	0.812459	−	0.593107i
$181$	0.848933			0.0631007			0.0315503	−	0.999502i	$-0.489956\pi$
$181$	0.848933			0.0631007			0.0315503	+	0.999502i	$0.489956\pi$
$182$	2.17954	+	1.64108i	0.161558	+	0.121645i
$183$	−1.26594	−	1.26594i	−0.0935810	−	0.0935810i
$184$	2.11304	+	4.73117i	0.155776	+	0.348787i
$185$	13.2050	+	6.13359i	0.970851	+	0.450950i
$186$	2.75724	+	19.5638i	0.202170	+	1.43449i
$187$	−1.36709	+	1.36709i	−0.0999715	+	0.0999715i
$188$	20.1831	+	11.1672i	1.47200	+	0.814454i
$189$		−	0.0733998i		−	0.00533905i
$190$	3.86516	−	12.7280i	0.280408	−	0.923385i
$191$			4.93773i			0.357281i	0.983914	+	0.178641i	$0.0571699\pi$
$191$			4.93773i			0.357281i	−0.983914	+	0.178641i	$0.942830\pi$
$192$	−1.07262	−	19.5955i	−0.0774095	−	1.41419i
$193$	6.49046	−	6.49046i	0.467194	−	0.467194i	−0.433810	−	0.901004i	$-0.642831\pi$
$193$	6.49046	−	6.49046i	0.467194	−	0.467194i	0.901004	+	0.433810i	$0.142831\pi$
$194$	−19.3209	+	2.72301i	−1.38716	+	0.195501i
$195$	5.89462	−	2.15545i	0.422122	−	0.154355i
$196$	7.99064	−	2.29798i	0.570760	−	0.164141i
$197$	−8.24214	−	8.24214i	−0.587228	−	0.587228i	0.349652	−	0.936880i	$-0.386300\pi$
$197$	−8.24214	−	8.24214i	−0.587228	−	0.587228i	−0.936880	+	0.349652i	$0.886300\pi$
$198$	10.3405	−	13.7334i	0.734869	−	0.975991i
$199$	3.15529			0.223673			0.111836	−	0.993727i	$-0.464327\pi$
$199$	3.15529			0.223673			0.111836	+	0.993727i	$0.464327\pi$
$200$	−13.3524	+	4.65969i	−0.944159	+	0.329490i
$201$	32.3306			2.28043
$202$	−0.400813	+	0.532325i	−0.0282011	+	0.0374543i
$203$	4.98571	+	4.98571i	0.349928	+	0.349928i
$204$	2.26307	−	0.650823i	0.158447	−	0.0455667i
$205$	2.10007	−	0.767920i	0.146675	−	0.0536338i
$206$	−26.9599	+	3.79961i	−1.87838	+	0.264731i
$207$	3.90919	−	3.90919i	0.271707	−	0.271707i
$208$	1.02265	−	4.46112i	0.0709083	−	0.309323i
$209$		−	16.9441i		−	1.17205i
$210$	−3.80049	+	12.5150i	−0.262259	+	0.863618i
$211$			12.2107i			0.840618i	0.907381	+	0.420309i	$0.138078\pi$
$211$			12.2107i			0.840618i	−0.907381	+	0.420309i	$0.861922\pi$
$212$	−0.666746	−	0.368909i	−0.0457923	−	0.0253367i
$213$	−2.72766	+	2.72766i	−0.186896	+	0.186896i
$214$	−0.862705	−	6.12126i	−0.0589733	−	0.418441i
$215$	1.18240	+	0.549213i	0.0806391	+	0.0374560i
$216$	−0.112428	+	0.0502129i	−0.00764978	+	0.00341655i
$217$	−6.78963	−	6.78963i	−0.460910	−	0.460910i
$218$	−16.1388	−	12.1516i	−1.09306	−	0.823013i
$219$	−20.4298			−1.38052
$220$	−14.5499	+	10.6216i	−0.980955	+	0.716111i
$221$	0.549176			0.0369416
$222$	−18.0461	−	13.5877i	−1.21117	−	0.911950i
$223$	10.1856	+	10.1856i	0.682080	+	0.682080i	0.960468	−	0.278389i	$-0.0898004\pi$
$223$	10.1856	+	10.1856i	0.682080	+	0.682080i	−0.278389	+	0.960468i	$0.589800\pi$
$224$	6.14486	+	7.29443i	0.410571	+	0.487379i
$225$	9.73335	+	11.5296i	0.648890	+	0.768640i
$226$	−0.769652	−	5.46101i	−0.0511965	−	0.363261i
$227$	−18.8653	+	18.8653i	−1.25213	+	1.25213i	−0.297372	+	0.954762i	$0.596110\pi$
$227$	−18.8653	+	18.8653i	−1.25213	+	1.25213i	−0.954762	+	0.297372i	$0.903890\pi$
$228$	−9.99137	+	18.0579i	−0.661695	+	1.19591i
$229$			14.5362i			0.960580i	0.877110	+	0.480290i	$0.159469\pi$
$229$			14.5362i			0.960580i	−0.877110	+	0.480290i	$0.840531\pi$
$230$	−5.10997	+	2.72936i	−0.336941	+	0.179969i
$231$			16.6606i			1.09619i
$232$	4.22601	−	11.0475i	0.277451	−	0.725302i
$233$	−21.0073	+	21.0073i	−1.37624	+	1.37624i	−0.525349	+	0.850887i	$0.676065\pi$
$233$	−21.0073	+	21.0073i	−1.37624	+	1.37624i	−0.850887	+	0.525349i	$0.823935\pi$
$234$	−4.83539	+	0.681479i	−0.316099	+	0.0445497i
$235$	−10.8640	+	23.3892i	−0.708690	+	1.52574i
$236$	−3.01063	−	10.4687i	−0.195976	−	0.681456i
$237$	−24.1849	−	24.1849i	−1.57098	−	1.57098i
$238$	−0.688384	+	0.914252i	−0.0446213	+	0.0592622i
$239$	−17.3400			−1.12163			−0.560816	−	0.827941i	$-0.689512\pi$
$239$	−17.3400			−1.12163			−0.560816	+	0.827941i	$0.689512\pi$
$240$	21.7695	−	2.74023i	1.40521	−	0.176881i
$241$	26.8759			1.73123			0.865615	−	0.500711i	$-0.166928\pi$
$241$	26.8759			1.73123			0.865615	+	0.500711i	$0.166928\pi$
$242$	−4.44550	+	5.90414i	−0.285768	+	0.379532i
$243$	−15.6109	−	15.6109i	−1.00144	−	1.00144i
$244$	−0.403414	−	1.40277i	−0.0258259	−	0.0898032i
$245$	3.19244	+	8.73053i	0.203957	+	0.557773i
$246$	−3.43527	+	0.484152i	−0.219025	+	0.0308684i
$247$	−3.40333	+	3.40333i	−0.216549	+	0.216549i
$248$	−5.75506	+	15.0447i	−0.365446	+	0.955336i
$249$		−	12.4785i		−	0.790793i
$250$	−6.24882	−	14.5242i	−0.395210	−	0.918591i
$251$			18.2984i			1.15499i	0.816396	+	0.577493i	$0.195969\pi$
$251$			18.2984i			1.15499i	−0.816396	+	0.577493i	$0.804031\pi$
$252$	4.92658	−	8.90405i	0.310346	−	0.560902i
$253$	−5.21806	+	5.21806i	−0.328056	+	0.328056i
$254$	−2.66278	−	18.8935i	−0.167077	−	1.18549i
$255$	0.904147	+	2.47262i	0.0566199	+	0.154842i
$256$	6.96936	−	14.4024i	0.435585	−	0.900148i
$257$	6.60489	+	6.60489i	0.412002	+	0.412002i	0.882435	−	0.470434i	$-0.155903\pi$
$257$	6.60489	+	6.60489i	0.412002	+	0.412002i	−0.470434	+	0.882435i	$0.655903\pi$
$258$	−1.61588	−	1.21667i	−0.100600	−	0.0757467i
$259$	10.9785			0.682174
$260$	5.05586	+	0.789014i	0.313551	+	0.0489326i
$261$	−12.6199			−0.781151
$262$	22.5390	+	16.9707i	1.39247	+	1.04845i
$263$	−8.98275	−	8.98275i	−0.553900	−	0.553900i	0.373664	−	0.927564i	$-0.378101\pi$
$263$	−8.98275	−	8.98275i	−0.553900	−	0.553900i	−0.927564	+	0.373664i	$0.878101\pi$
$264$	25.5195	−	11.3976i	1.57062	−	0.701471i
$265$	0.358892	−	0.772659i	0.0220466	−	0.0474640i
$266$	−1.39974	−	9.93179i	−0.0858238	−	0.608957i
$267$	−12.1362	+	12.1362i	−0.742723	+	0.742723i
$268$	23.0639	+	12.7612i	1.40885	+	0.779513i
$269$		−	0.807155i		−	0.0492131i	−0.999697	−	0.0246066i	$-0.992167\pi$
$269$		−	0.807155i		−	0.0492131i	0.999697	−	0.0246066i	$-0.00783330\pi$
$270$	−0.0648587	−	0.121430i	−0.00394717	−	0.00738998i
$271$			3.29795i			0.200336i	0.994971	+	0.100168i	$0.0319380\pi$
$271$			3.29795i			0.200336i	−0.994971	+	0.100168i	$0.968062\pi$
$272$	1.87131	+	0.428974i	0.113465	+	0.0260103i
$273$	3.34638	−	3.34638i	0.202532	−	0.202532i
$274$	−19.7859	+	2.78854i	−1.19531	+	0.168462i
$275$	−12.9923	−	15.3899i	−0.783463	−	0.928048i
$276$	8.63795	−	2.48413i	0.519943	−	0.149527i
$277$	20.4138	+	20.4138i	1.22655	+	1.22655i	0.965262	+	0.261283i	$0.0841455\pi$
$277$	20.4138	+	20.4138i	1.22655	+	1.22655i	0.261283	+	0.965262i	$0.415854\pi$
$278$	−4.10324	+	5.44957i	−0.246096	+	0.326844i
$279$	17.1860			1.02890
$280$	−7.65097	+	7.42783i	−0.457233	+	0.443898i
$281$	4.55009			0.271436			0.135718	−	0.990748i	$-0.456666\pi$
$281$	4.55009			0.271436			0.135718	+	0.990748i	$0.456666\pi$
$282$	24.0671	−	31.9638i	1.43317	−	1.90342i
$283$	1.82990	+	1.82990i	0.108776	+	0.108776i	0.759400	−	0.650624i	$-0.225493\pi$
$283$	1.82990	+	1.82990i	0.108776	+	0.108776i	−0.650624	+	0.759400i	$0.725493\pi$
$284$	−3.02247	+	0.869215i	−0.179351	+	0.0515784i
$285$	−20.9264	−	9.72008i	−1.23957	−	0.575768i
$286$	6.45437	−	0.909652i	0.381655	−	0.0537888i
$287$	1.19221	−	1.19221i	0.0703742	−	0.0703742i
$288$	−17.0088	−	1.45490i	−1.00226	−	0.0857310i
$289$		−	16.7696i		−	0.986449i
$290$	12.6537	+	3.84261i	0.743052	+	0.225646i
$291$			33.8455i			1.98406i
$292$	−14.5741	−	8.06382i	−0.852886	−	0.471899i
$293$	−2.47914	+	2.47914i	−0.144833	+	0.144833i	−0.775805	−	0.630972i	$-0.782656\pi$
$293$	−2.47914	+	2.47914i	−0.144833	+	0.144833i	0.630972	+	0.775805i	$0.282656\pi$
$294$	−2.01274	−	14.2813i	−0.117386	−	0.832902i
$295$	11.4381	−	4.18249i	0.665950	−	0.243514i
$296$	−7.51044	−	16.8161i	−0.436536	−	0.977417i
$297$	−0.123998	−	0.123998i	−0.00719511	−	0.00719511i
$298$	−18.5136	−	13.9398i	−1.07246	−	0.807508i
$299$	2.09616			0.121224
$300$	4.77134	+	24.0626i	0.275474	+	1.38926i
$301$	0.983040			0.0566615
$302$	−14.7723	−	11.1228i	−0.850051	−	0.640044i
$303$	0.817314	+	0.817314i	0.0469534	+	0.0469534i
$304$	−14.2552	+	8.93837i	−0.817592	+	0.512651i
$305$	1.53266	−	0.560437i	0.0877598	−	0.0320906i
$306$	−0.285861	−	2.02831i	−0.0163416	−	0.115951i
$307$	4.45472	−	4.45472i	0.254244	−	0.254244i	−0.568464	−	0.822708i	$-0.692462\pi$
$307$	4.45472	−	4.45472i	0.254244	−	0.254244i	0.822708	+	0.568464i	$0.192462\pi$
$308$	−6.57610	+	11.8853i	−0.374708	+	0.677227i
$309$			47.2270i			2.68665i
$310$	−17.2321	−	5.23294i	−0.978716	−	0.297211i
$311$		−	4.78019i		−	0.271060i	−0.990773	−	0.135530i	$-0.956726\pi$
$311$		−	4.78019i		−	0.271060i	0.990773	−	0.135530i	$-0.0432737\pi$
$312$	−7.41501	−	2.83648i	−0.419792	−	0.160584i
$313$	−3.52240	+	3.52240i	−0.199098	+	0.199098i	−0.799613	−	0.600515i	$-0.794962\pi$
$313$	−3.52240	+	3.52240i	−0.199098	+	0.199098i	0.600515	+	0.799613i	$0.294962\pi$
$314$	23.0560	−	3.24941i	1.30112	−	0.183375i
$315$	10.3185	+	4.79281i	0.581379	+	0.270044i
$316$	−7.70692	−	26.7989i	−0.433548	−	1.50756i
$317$	−20.1919	−	20.1919i	−1.13409	−	1.13409i	−0.989491	−	0.144597i	$-0.953811\pi$
$317$	−20.1919	−	20.1919i	−1.13409	−	1.13409i	−0.144597	−	0.989491i	$-0.546189\pi$
$318$	−0.795054	+	1.05592i	−0.0445844	+	0.0592132i
$319$	16.8453			0.943154
$320$	16.6114	+	6.63780i	0.928607	+	0.371064i
$321$	−10.7229			−0.598496
$322$	−2.62750	+	3.48962i	−0.146425	+	0.194469i
$323$	−1.42760	−	1.42760i	−0.0794336	−	0.0794336i
$324$	−4.94527	−	17.1959i	−0.274737	−	0.955329i
$325$	−0.481585	+	5.70073i	−0.0267135	+	0.316220i
$326$	−6.23496	+	0.878728i	−0.345322	+	0.0486682i
$327$	−24.7789	+	24.7789i	−1.37028	+	1.37028i
$328$	−2.64174	−	1.01055i	−0.145866	−	0.0557983i
$329$			19.4456i			1.07207i
$330$	14.7219	+	27.5627i	0.810416	+	1.51728i
$331$		−	17.6160i		−	0.968260i	−0.874996	−	0.484130i	$-0.839136\pi$
$331$		−	17.6160i		−	0.968260i	0.874996	−	0.484130i	$-0.160864\pi$
$332$	4.92537	−	8.90186i	0.270315	−	0.488553i
$333$	−13.8945	+	13.8945i	−0.761415	+	0.761415i
$334$	−0.291968	−	2.07164i	−0.0159758	−	0.113355i
$335$	−12.4147	+	26.7276i	−0.678287	+	1.46028i
$336$	14.0167	−	8.78882i	0.764673	−	0.479469i
$337$	22.2233	+	22.2233i	1.21058	+	1.21058i	0.970837	+	0.239742i	$0.0770627\pi$
$337$	22.2233	+	22.2233i	1.21058	+	1.21058i	0.239742	+	0.970837i	$0.422937\pi$
$338$	13.2079	+	9.94486i	0.718416	+	0.540929i
$339$	−9.56635			−0.519573
$340$	−0.330968	+	2.12078i	−0.0179493	+	0.115016i
$341$	−22.9402			−1.24228
$342$	14.3413	+	10.7982i	0.775486	+	0.583900i
$343$	13.3018	+	13.3018i	0.718231	+	0.718231i
$344$	−0.672499	−	1.50575i	−0.0362587	−	0.0811845i
$345$	3.45105	+	9.43778i	0.185798	+	0.508113i
$346$	−2.40841	−	17.0887i	−0.129477	−	0.918694i
$347$	23.3249	−	23.3249i	1.25215	−	1.25215i	0.297392	−	0.954755i	$-0.403883\pi$
$347$	23.3249	−	23.3249i	1.25215	−	1.25215i	0.954755	−	0.297392i	$-0.0961168\pi$
$348$	−17.9525	−	9.93307i	−0.962355	−	0.532468i
$349$			7.83755i			0.419535i	0.977751	+	0.209767i	$0.0672706\pi$
$349$			7.83755i			0.419535i	−0.977751	+	0.209767i	$0.932729\pi$
$350$	−8.88676	−	7.94751i	−0.475017	−	0.424812i
$351$			0.0498116i			0.00265874i
$352$	22.7037	+	1.94203i	1.21011	+	0.103511i
$353$	21.1022	−	21.1022i	1.12316	−	1.12316i	0.131892	−	0.991264i	$-0.457895\pi$
$353$	21.1022	−	21.1022i	1.12316	−	1.12316i	0.991264	−	0.131892i	$-0.0421052\pi$
$354$	−18.7103	+	2.63694i	−0.994439	+	0.140152i
$355$	−1.20755	−	3.30234i	−0.0640898	−	0.175270i
$356$	−13.4479	+	3.86740i	−0.712739	+	0.204972i
$357$	1.40371	+	1.40371i	0.0742923	+	0.0742923i
$358$	6.48314	−	8.61035i	0.342645	−	0.455071i
$359$	−10.1203			−0.534130			−0.267065	−	0.963679i	$-0.586054\pi$
$359$	−10.1203			−0.534130			−0.267065	+	0.963679i	$0.586054\pi$
$360$	0.282407	−	19.0838i	0.0148842	−	1.00581i
$361$	−1.30591			−0.0687321
$362$	0.722151	−	0.959099i	0.0379554	−	0.0504091i
$363$	9.06501	+	9.06501i	0.475790	+	0.475790i
$364$	3.70808	−	1.06638i	0.194356	−	0.0558937i
$365$	7.84487	−	16.8892i	0.410619	−	0.884022i
$366$	−2.50710	+	0.353341i	−0.131048	+	0.0184694i
$367$	−22.8049	+	22.8049i	−1.19040	+	1.19040i	−0.213451	+	0.976954i	$0.568470\pi$
$367$	−22.8049	+	22.8049i	−1.19040	+	1.19040i	−0.976954	+	0.213451i	$0.931530\pi$
$368$	7.14262	+	1.63735i	0.372335	+	0.0853530i
$369$			3.01775i			0.157098i
$370$	18.1625	−	9.70104i	0.944222	−	0.504333i
$371$		−	0.642383i		−	0.0333509i
$372$	24.4481	+	13.5270i	1.26757	+	0.701345i
$373$	6.89178	−	6.89178i	0.356843	−	0.356843i	−0.505805	−	0.862648i	$-0.668804\pi$
$373$	6.89178	−	6.89178i	0.356843	−	0.356843i	0.862648	+	0.505805i	$0.168804\pi$
$374$	0.381572	+	2.70742i	0.0197306	+	0.139997i
$375$	−26.4600	+	7.21723i	−1.36639	+	0.372696i
$376$	29.7853	−	13.3028i	1.53606	−	0.686037i
$377$	−3.38347	−	3.38347i	−0.174258	−	0.174258i
$378$	−0.0829249	−	0.0624381i	−0.00426520	−	0.00321147i
$379$	28.6069			1.46944			0.734718	−	0.678373i	$-0.237314\pi$
$379$	28.6069			1.46944			0.734718	+	0.678373i	$0.237314\pi$
$380$	−11.0918	−	15.1939i	−0.568996	−	0.779430i
$381$	−33.0968			−1.69560
$382$	5.57850	+	4.20031i	0.285421	+	0.214907i
$383$	5.18753	+	5.18753i	0.265070	+	0.265070i	0.827110	−	0.562040i	$-0.189983\pi$
$383$	5.18753	+	5.18753i	0.265070	+	0.265070i	−0.562040	+	0.827110i	$0.689983\pi$
$384$	−23.0509	−	15.4573i	−1.17631	−	0.788801i
$385$	−13.7733	−	6.39754i	−0.701951	−	0.326049i
$386$	−1.81157	−	12.8539i	−0.0922067	−	0.654246i
$387$	−1.24414	+	1.24414i	−0.0632433	+	0.0632433i
$388$	−13.3591	+	24.1446i	−0.678207	+	1.22576i
$389$			11.9556i			0.606171i	0.952963	+	0.303086i	$0.0980168\pi$
$389$			11.9556i			0.606171i	−0.952963	+	0.303086i	$0.901983\pi$
$390$	2.57914	−	8.49312i	0.130600	−	0.430066i
$391$			0.879276i			0.0444669i
$392$	4.20111	−	10.9824i	0.212188	−	0.554694i
$393$	34.6056	−	34.6056i	1.74562	−	1.74562i
$394$	−16.3230	+	2.30049i	−0.822339	+	0.115897i
$395$	29.2803	−	10.7067i	1.47325	−	0.538715i
$396$	−6.71935	−	23.3649i	−0.337660	−	1.17413i
$397$	13.9851	+	13.9851i	0.701891	+	0.701891i	0.964816	−	0.262925i	$-0.0846873\pi$
$397$	13.9851	+	13.9851i	0.701891	+	0.701891i	−0.262925	+	0.964816i	$0.584687\pi$
$398$	2.68407	−	3.56475i	0.134540	−	0.178685i
$399$	−17.3980			−0.870991
$400$	−6.09396	+	19.0490i	−0.304698	+	0.952449i
$401$	12.9974			0.649060			0.324530	−	0.945875i	$-0.394794\pi$
$401$	12.9974			0.649060			0.324530	+	0.945875i	$0.394794\pi$
$402$	27.5023	−	36.5262i	1.37169	−	1.82176i
$403$	4.60768	+	4.60768i	0.229525	+	0.229525i
$404$	0.260451	+	0.905653i	0.0129579	+	0.0450579i
$405$	18.7882	−	6.87015i	0.933592	−	0.341381i
$406$	9.87384	−	1.39158i	0.490030	−	0.0690628i
$407$	18.5467	−	18.5467i	0.919324	−	0.919324i
$408$	1.18982	−	3.11038i	0.0589048	−	0.153987i
$409$			4.96260i			0.245385i	0.992445	+	0.122692i	$0.0391529\pi$
$409$			4.96260i			0.245385i	−0.992445	+	0.122692i	$0.960847\pi$
$410$	0.918869	−	3.02584i	0.0453797	−	0.149435i
$411$			34.6600i			1.70965i
$412$	−18.6409	+	33.6906i	−0.918372	+	1.65982i
$413$	6.49341	−	6.49341i	0.319520	−	0.319520i
$414$	−1.09111	−	7.74186i	−0.0536249	−	0.380492i
$415$	10.3159	+	4.79164i	0.506389	+	0.235212i
$416$	−4.17011	−	4.95025i	−0.204456	−	0.242706i
$417$	8.36708	+	8.36708i	0.409738	+	0.409738i
$418$	−19.1430	−	14.4137i	−0.936314	−	0.704995i
$419$	19.4749			0.951409			0.475705	−	0.879605i	$-0.342193\pi$
$419$	19.4749			0.951409			0.475705	+	0.879605i	$0.342193\pi$
$420$	10.9062	+	14.9397i	0.532167	+	0.728981i
$421$	−35.8743			−1.74841			−0.874204	−	0.485558i	$-0.838616\pi$
$421$	−35.8743			−1.74841			−0.874204	+	0.485558i	$0.838616\pi$
$422$	13.7953	+	10.3871i	0.671543	+	0.505637i
$423$	−24.6104	−	24.6104i	−1.19660	−	1.19660i
$424$	−0.983955	+	0.439455i	−0.0477851	+	0.0213418i
$425$	−2.39129	−	0.202011i	−0.115995	−	0.00979896i
$426$	0.761325	+	5.40193i	0.0368863	+	0.261724i
$427$	0.870093	−	0.870093i	0.0421067	−	0.0421067i
$428$	−7.64949	−	4.23244i	−0.369752	−	0.204583i
$429$		−	11.3065i		−	0.545881i
$430$	1.62630	−	0.868650i	0.0784273	−	0.0418900i
$431$		−	20.1367i		−	0.969951i	−0.874528	−	0.484975i	$-0.838829\pi$
$431$		−	20.1367i		−	0.969951i	0.874528	−	0.484975i	$-0.161171\pi$
$432$	−0.0389089	+	0.169732i	−0.00187201	+	0.00816624i
$433$	2.73734	−	2.73734i	0.131548	−	0.131548i	−0.638267	−	0.769815i	$-0.720348\pi$
$433$	2.73734	−	2.73734i	0.131548	−	0.131548i	0.769815	+	0.638267i	$0.220348\pi$
$434$	−13.4464	+	1.89508i	−0.645447	+	0.0909665i
$435$	9.66336	−	20.8043i	0.463323	−	0.997488i
$436$	−27.4572	+	7.89623i	−1.31496	+	0.378161i
$437$	−5.44901	−	5.44901i	−0.260662	−	0.260662i
$438$	−17.3788	+	23.0810i	−0.830389	+	1.10285i
$439$	22.0544			1.05260			0.526300	−	0.850299i	$-0.323579\pi$
$439$	22.0544			1.05260			0.526300	+	0.850299i	$0.323579\pi$
$440$	−0.376962	+	25.4734i	−0.0179710	+	1.21440i
$441$	−12.5455			−0.597406
$442$	0.467160	−	0.620443i	0.0222206	−	0.0295114i
$443$	−19.2001	−	19.2001i	−0.912225	−	0.912225i	0.0842223	−	0.996447i	$-0.473159\pi$
$443$	−19.2001	−	19.2001i	−0.912225	−	0.912225i	−0.996447	+	0.0842223i	$0.973159\pi$
$444$	−30.7021	+	8.82942i	−1.45706	+	0.419026i
$445$	−5.37274	−	14.6931i	−0.254692	−	0.696521i
$446$	20.1719	−	2.84294i	0.955167	−	0.134617i
$447$	−28.4251	+	28.4251i	−1.34446	+	1.34446i
$448$	13.4682	−	0.737220i	0.636313	−	0.0348304i
$449$		−	21.6592i		−	1.02216i	−0.859533	−	0.511080i	$-0.829246\pi$
$449$		−	21.6592i		−	1.02216i	0.859533	−	0.511080i	$-0.170754\pi$
$450$	21.3056	−	1.18872i	1.00435	−	0.0560367i
$451$		−	4.02815i		−	0.189678i
$452$	−6.82440	−	3.77592i	−0.320993	−	0.177604i
$453$	−22.6809	+	22.6809i	−1.06564	+	1.06564i
$454$	5.26555	+	37.3614i	0.247125	+	1.75346i
$455$	1.48146	+	4.05143i	0.0694519	+	0.189934i
$456$	11.9020	+	26.6490i	0.557363	+	1.24795i
$457$	9.64959	+	9.64959i	0.451389	+	0.451389i	0.895815	−	0.444427i	$-0.146593\pi$
$457$	9.64959	+	9.64959i	0.451389	+	0.451389i	−0.444427	+	0.895815i	$0.646593\pi$
$458$	16.4226	+	12.3653i	0.767377	+	0.577794i
$459$	−0.0208945			−0.000975272
$460$	−1.26328	+	8.09484i	−0.0589006	+	0.377424i
$461$	−20.5463			−0.956935			−0.478468	−	0.878105i	$-0.658808\pi$
$461$	−20.5463			−0.956935			−0.478468	+	0.878105i	$0.658808\pi$
$462$	18.8227	+	14.1725i	0.875711	+	0.659364i
$463$	24.8325	+	24.8325i	1.15406	+	1.15406i	0.985730	+	0.168334i	$0.0538388\pi$
$463$	24.8325	+	24.8325i	1.15406	+	1.15406i	0.168334	+	0.985730i	$0.446161\pi$
$464$	−8.88622	−	14.1720i	−0.412532	−	0.657920i
$465$	−13.1598	+	28.3316i	−0.610269	+	1.31385i
$466$	5.86342	+	41.6035i	0.271618	+	1.92725i
$467$	−15.2663	+	15.2663i	−0.706440	+	0.706440i	−0.965785	−	0.259345i	$-0.916493\pi$
$467$	−15.2663	+	15.2663i	−0.706440	+	0.706440i	0.259345	+	0.965785i	$0.416493\pi$
$468$	−3.34335	+	6.04259i	−0.154546	+	0.279319i
$469$			22.2211i			1.02608i
$470$	17.1828	+	32.1700i	0.792585	+	1.48389i
$471$		−	40.3884i		−	1.86100i
$472$	−14.3883	−	5.50397i	−0.662274	−	0.253341i
$473$	1.66070	−	1.66070i	0.0763593	−	0.0763593i
$474$	−47.8964	+	6.75031i	−2.19995	+	0.310052i
$475$	16.0711	−	13.5673i	0.737393	−	0.622511i
$476$	0.447317	+	1.55543i	0.0205027	+	0.0712931i
$477$	0.813004	+	0.813004i	0.0372249	+	0.0372249i
$478$	−14.7504	+	19.5902i	−0.674668	+	0.896036i
$479$	4.80890			0.219724			0.109862	−	0.993947i	$-0.464959\pi$
$479$	4.80890			0.219724			0.109862	+	0.993947i	$0.464959\pi$
$480$	15.4225	−	26.9255i	0.703940	−	1.22898i
$481$	−7.45042			−0.339710
$482$	22.8622	−	30.3636i	1.04134	−	1.38302i
$483$	5.35784	+	5.35784i	0.243790	+	0.243790i
$484$	2.88872	+	10.0448i	0.131306	+	0.456582i
$485$	−27.9800	−	12.9964i	−1.27050	−	0.590136i
$486$	−30.9164	+	4.35722i	−1.40239	+	0.197648i
$487$	4.14169	−	4.14169i	0.187678	−	0.187678i	−0.607014	−	0.794691i	$-0.707633\pi$
$487$	4.14169	−	4.14169i	0.187678	−	0.187678i	0.794691	+	0.607014i	$0.207633\pi$
$488$	−1.92798	−	0.737512i	−0.0872753	−	0.0333856i
$489$			10.9221i			0.493914i
$490$	12.5792	+	3.81997i	0.568269	+	0.172569i
$491$			36.1178i			1.62997i	0.579480	+	0.814987i	$0.303256\pi$
$491$			36.1178i			1.62997i	−0.579480	+	0.814987i	$0.696744\pi$
$492$	−2.37526	+	4.29292i	−0.107085	+	0.193540i
$493$	1.41927	−	1.41927i	0.0639206	−	0.0639206i
$494$	0.949914	+	6.74005i	0.0427386	+	0.303249i
$495$	25.5283	−	9.33477i	1.14741	−	0.419567i
$496$	12.1014	+	19.2997i	0.543370	+	0.866584i
$497$	−1.87474	−	1.87474i	−0.0840937	−	0.0840937i
$498$	−14.0978	−	10.6149i	−0.631739	−	0.475666i
$499$	−19.6148			−0.878078			−0.439039	−	0.898468i	$-0.644681\pi$
$499$	−19.6148			−0.878078			−0.439039	+	0.898468i	$0.644681\pi$
$500$	−21.7246	−	5.29539i	−0.971554	−	0.236817i
$501$	−3.62900			−0.162132
$502$	20.6730	+	15.5657i	0.922682	+	0.694731i
$503$	−17.4984	−	17.4984i	−0.780214	−	0.780214i	0.199653	−	0.979867i	$-0.436018\pi$
$503$	−17.4984	−	17.4984i	−0.780214	−	0.780214i	−0.979867	+	0.199653i	$0.936018\pi$
$504$	−5.86870	−	13.1402i	−0.261412	−	0.585311i
$505$	−0.989511	+	0.361828i	−0.0440327	+	0.0161011i
$506$	1.45643	+	10.3340i	0.0647461	+	0.459402i
$507$	20.2790	−	20.2790i	0.900620	−	0.900620i
$508$	−23.6105	−	13.0636i	−1.04755	−	0.579604i
$509$			35.9686i			1.59428i	0.603795	+	0.797140i	$0.293655\pi$
$509$			35.9686i			1.59428i	−0.603795	+	0.797140i	$0.706345\pi$
$510$	3.56261	+	1.08187i	0.157755	+	0.0479062i
$511$		−	14.0416i		−	0.621163i
$512$	−10.3428	−	20.1253i	−0.457093	−	0.889419i
$513$	0.129487	−	0.129487i	0.00571697	−	0.00571697i
$514$	13.0805	−	1.84351i	0.576957	−	0.0813138i
$515$	−39.0424	−	18.1348i	−1.72041	−	0.799114i
$516$	−2.74912	+	0.790603i	−0.121023	+	0.0348043i
$517$	32.8505	+	32.8505i	1.44476	+	1.44476i
$518$	9.33899	−	12.4032i	0.410331	−	0.544967i
$519$	−29.9352			−1.31401
$520$	5.19221	−	5.04078i	0.227693	−	0.221053i
$521$	7.17372			0.314286			0.157143	−	0.987576i	$-0.449772\pi$
$521$	7.17372			0.314286			0.157143	+	0.987576i	$0.449772\pi$
$522$	−10.7352	+	14.2576i	−0.469867	+	0.624037i
$523$	24.2846	+	24.2846i	1.06189	+	1.06189i	0.997954	+	0.0639394i	$0.0203664\pi$
$523$	24.2846	+	24.2846i	1.06189	+	1.06189i	0.0639394	+	0.997954i	$0.479634\pi$
$524$	38.3460	−	11.0277i	1.67515	−	0.481746i
$525$	−15.8022	+	13.3403i	−0.689665	+	0.582219i
$526$	−17.7897	+	2.50720i	−0.775667	+	0.109319i
$527$	−1.93279	+	1.93279i	−0.0841935	+	0.0841935i
$528$	8.83174	−	38.5266i	0.384352	−	1.67666i
$529$		−	19.6439i		−	0.854082i
$530$	−0.567633	−	1.06273i	−0.0246564	−	0.0461622i
$531$			16.4362i			0.713270i
$532$	−12.4113	−	6.86716i	−0.538100	−	0.297729i
$533$	−0.809077	+	0.809077i	−0.0350450	+	0.0350450i
$534$	3.38737	+	24.0348i	0.146586	+	1.04009i
$535$	4.11752	−	8.86461i	0.178016	−	0.383251i
$536$	34.0367	−	15.2015i	1.47016	−	0.656605i
$537$	−13.2200	−	13.2200i	−0.570487	−	0.570487i
$538$	−0.911900	−	0.686613i	−0.0393148	−	0.0296020i
$539$	16.7460			0.721302
$540$	−0.192360	−	0.0300196i	−0.00827787	−	0.00129184i
$541$	−43.7163			−1.87951			−0.939754	−	0.341850i	$-0.888946\pi$
$541$	−43.7163			−1.87951			−0.939754	+	0.341850i	$0.888946\pi$
$542$	3.72592	+	2.80542i	0.160042	+	0.120503i
$543$	−1.47257	−	1.47257i	−0.0631939	−	0.0631939i
$544$	2.07648	−	1.74924i	0.0890285	−	0.0749980i
$545$	−10.9697	−	29.9995i	−0.469892	−	1.28504i
$546$	−0.934020	−	6.62727i	−0.0399724	−	0.283621i
$547$	−4.05775	+	4.05775i	−0.173497	+	0.173497i	−0.788514	−	0.615017i	$-0.789149\pi$
$547$	−4.05775	+	4.05775i	−0.173497	+	0.173497i	0.615017	+	0.788514i	$0.289149\pi$
$548$	−13.6806	+	24.7256i	−0.584407	+	1.05623i
$549$			2.20239i			0.0939957i
$550$	−28.4391	+	1.58672i	−1.21265	+	0.0676581i
$551$			17.5908i			0.749395i
$552$	4.54144	−	11.8720i	0.193296	−	0.505308i
$553$	16.6225	−	16.6225i	0.706860	−	0.706860i
$554$	40.4280	−	5.69775i	1.71762	−	0.242074i
$555$	−12.2662	−	33.5449i	−0.520669	−	1.42390i
$556$	2.66632	+	9.27144i	0.113077	+	0.393197i
$557$	−20.3398	−	20.3398i	−0.861826	−	0.861826i	0.129724	−	0.991550i	$-0.458591\pi$
$557$	−20.3398	−	20.3398i	−0.861826	−	0.861826i	−0.991550	+	0.129724i	$0.958591\pi$
$558$	14.6194	−	19.4162i	0.618889	−	0.821955i
$559$	−0.667124			−0.0282164
$560$	1.88339	+	14.9624i	0.0795877	+	0.632276i
$561$	4.74273			0.200238
$562$	3.87057	−	5.14056i	0.163270	−	0.216841i
$563$	−8.97565	−	8.97565i	−0.378279	−	0.378279i	0.492202	−	0.870481i	$-0.336192\pi$
$563$	−8.97565	−	8.97565i	−0.378279	−	0.378279i	−0.870481	+	0.492202i	$0.836192\pi$
$564$	−15.6390	−	54.3806i	−0.658519	−	2.28984i
$565$	3.67340	−	7.90846i	0.154541	−	0.332711i
$566$	3.62399	−	0.510750i	0.152328	−	0.0214684i
$567$	10.6661	−	10.6661i	0.447933	−	0.447933i
$568$	−1.58908	+	4.15411i	−0.0666762	+	0.174302i
$569$		−	0.150643i		−	0.00631527i	−0.999995	−	0.00315763i	$-0.998995\pi$
$569$		−	0.150643i		−	0.00631527i	0.999995	−	0.00315763i	$-0.00100511\pi$
$570$	−28.7826	+	15.3735i	−1.20557	+	0.643927i
$571$			4.12312i			0.172547i	0.996271	+	0.0862736i	$0.0274959\pi$
$571$			4.12312i			0.172547i	−0.996271	+	0.0862736i	$0.972504\pi$
$572$	4.46276	−	8.06576i	0.186598	−	0.337247i
$573$	8.56503	−	8.56503i	0.357809	−	0.357809i
$574$	−0.332763	−	2.36109i	−0.0138892	−	0.0985502i
$575$	−9.12735	−	0.771057i	−0.380637	−	0.0321553i
$576$	−16.1124	+	17.9785i	−0.671350	+	0.749103i
$577$	−25.1465	−	25.1465i	−1.04686	−	1.04686i	−0.998847	−	0.0480152i	$-0.984710\pi$
$577$	−25.1465	−	25.1465i	−1.04686	−	1.04686i	−0.0480152	−	0.998847i	$-0.515290\pi$
$578$	−18.9458	−	14.2652i	−0.788043	−	0.593355i
$579$	−22.5169			−0.935768
$580$	15.1052	−	11.0271i	0.627211	−	0.457873i
$581$	8.57659			0.355817
$582$	38.2377	+	28.7910i	1.58500	+	1.19342i
$583$	−1.08521	−	1.08521i	−0.0449449	−	0.0449449i
$584$	−21.5079	+	9.60587i	−0.890001	+	0.397494i
$585$	−7.00245	−	3.25257i	−0.289516	−	0.134477i
$586$	0.691960	+	4.90975i	0.0285846	+	0.202820i
$587$	−22.4571	+	22.4571i	−0.926902	+	0.926902i	−0.997505	−	0.0706023i	$-0.977508\pi$
$587$	−22.4571	+	22.4571i	−0.926902	+	0.926902i	0.0706023	+	0.997505i	$0.477508\pi$
$588$	−17.8467	−	9.87455i	−0.735987	−	0.407219i
$589$		−	23.9556i		−	0.987071i
$590$	5.00463	−	16.4803i	0.206037	−	0.678482i
$591$			28.5938i			1.17619i
$592$	−25.3872	−	5.81969i	−1.04341	−	0.239188i
$593$	−31.1826	+	31.1826i	−1.28051	+	1.28051i	−0.340140	+	0.940375i	$0.610475\pi$
$593$	−31.1826	+	31.1826i	−1.28051	+	1.28051i	−0.940375	+	0.340140i	$0.889525\pi$
$594$	−0.245570	+	0.0346095i	−0.0100758	+	0.00142005i
$595$	−1.69946	+	0.621429i	−0.0696709	+	0.0254761i
$596$	−31.4974	+	9.05815i	−1.29019	+	0.371036i
$597$	−5.47320	−	5.47320i	−0.224003	−	0.224003i
$598$	1.78311	−	2.36817i	0.0729168	−	0.0968419i
$599$	−36.9215			−1.50857			−0.754286	−	0.656546i	$-0.772017\pi$
$599$	−36.9215			−1.50857			−0.754286	+	0.656546i	$0.772017\pi$
$600$	31.2440	+	15.0785i	1.27553	+	0.615578i
$601$	−19.1488			−0.781098			−0.390549	−	0.920582i	$-0.627715\pi$
$601$	−19.1488			−0.781098			−0.390549	+	0.920582i	$0.627715\pi$
$602$	0.836231	−	1.11061i	0.0340822	−	0.0452651i
$603$	−28.1232	−	28.1232i	−1.14527	−	1.14527i
$604$	−25.1324	+	7.22766i	−1.02262	+	0.294089i
$605$	−10.9749	+	4.01312i	−0.446193	+	0.163156i
$606$	1.61863	−	0.228123i	0.0657524	−	0.00926686i
$607$	7.79352	−	7.79352i	0.316329	−	0.316329i	−0.531026	−	0.847355i	$-0.678193\pi$
$607$	7.79352	−	7.79352i	0.316329	−	0.316329i	0.847355	+	0.531026i	$0.178193\pi$
$608$	−2.02799	+	23.7086i	−0.0822458	+	0.961511i
$609$		−	17.2965i		−	0.700890i
$610$	0.670602	−	2.20829i	0.0271519	−	0.0894112i
$611$		−	13.1964i		−	0.533871i
$612$	−2.53469	−	1.40244i	−0.102459	−	0.0566901i
$613$	14.3260	−	14.3260i	0.578621	−	0.578621i	−0.355902	−	0.934523i	$-0.615826\pi$
$613$	14.3260	−	14.3260i	0.578621	−	0.578621i	0.934523	+	0.355902i	$0.115826\pi$
$614$	−1.24337	−	8.82224i	−0.0501783	−	0.356037i
$615$	−4.97485	−	2.31076i	−0.200605	−	0.0931790i
$616$	7.83365	+	17.5398i	0.315627	+	0.706699i
$617$	16.0568	+	16.0568i	0.646423	+	0.646423i	0.952127	−	0.305703i	$-0.0988916\pi$
$617$	16.0568	+	16.0568i	0.646423	+	0.646423i	−0.305703	+	0.952127i	$0.598892\pi$
$618$	53.3557	+	40.1740i	2.14628	+	1.61604i
$619$	13.0984			0.526468			0.263234	−	0.964732i	$-0.415211\pi$
$619$	13.0984			0.526468			0.263234	+	0.964732i	$0.415211\pi$
$620$	−20.5706	+	15.0168i	−0.826135	+	0.603091i
$621$	−0.0797525			−0.00320036
$622$	−5.40052	−	4.06630i	−0.216541	−	0.163044i
$623$	−8.34131	−	8.34131i	−0.334188	−	0.334188i
$624$	−9.51220	+	5.96439i	−0.380793	+	0.238767i
$625$	4.19395	−	24.6457i	0.167758	−	0.985828i
$626$	0.983148	+	6.97586i	0.0392945	+	0.278811i
$627$	−29.3915	+	29.3915i	−1.17378	+	1.17378i
$628$	15.9416	−	28.8121i	0.636141	−	1.14973i
$629$		−	3.12523i		−	0.124611i
$630$	14.1923	−	7.58044i	0.565433	−	0.302012i
$631$			28.9292i			1.15165i	0.817572	+	0.575826i	$0.195320\pi$
$631$			28.9292i			1.15165i	−0.817572	+	0.575826i	$0.804680\pi$
$632$	−36.8326	−	14.0896i	−1.46512	−	0.560455i
$633$	21.1808	−	21.1808i	0.841861	−	0.841861i
$634$	−39.9885	+	5.63581i	−1.58815	+	0.223827i
$635$	12.7089	−	27.3610i	0.504337	−	1.08579i
$636$	0.516632	+	1.79646i	0.0204858	+	0.0712342i
$637$	−3.36354	−	3.36354i	−0.133268	−	0.133268i
$638$	14.3296	−	19.0313i	0.567312	−	0.753456i
$639$	4.74537			0.187724
$640$	21.6298	−	13.1206i	0.854994	−	0.518638i
$641$	−6.06791			−0.239668			−0.119834	−	0.992794i	$-0.538236\pi$
$641$	−6.06791			−0.239668			−0.119834	+	0.992794i	$0.538236\pi$
$642$	−9.12155	+	12.1145i	−0.359999	+	0.478120i
$643$	27.8619	+	27.8619i	1.09877	+	1.09877i	0.994555	+	0.104210i	$0.0332316\pi$
$643$	27.8619	+	27.8619i	1.09877	+	1.09877i	0.104210	+	0.994555i	$0.466768\pi$
$644$	1.70737	+	5.93694i	0.0672797	+	0.233948i
$645$	−1.09833	−	3.00368i	−0.0432469	−	0.118270i
$646$	−2.82725	+	0.398461i	−0.111237	+	0.0156772i
$647$	2.65043	−	2.65043i	0.104199	−	0.104199i	−0.653085	−	0.757284i	$-0.726526\pi$
$647$	2.65043	−	2.65043i	0.104199	−	0.104199i	0.757284	+	0.653085i	$0.226526\pi$
$648$	−23.6342	−	9.04083i	−0.928438	−	0.355157i
$649$		−	21.9394i		−	0.861195i
$650$	6.03086	+	5.39345i	0.236550	+	0.211549i
$651$			23.5547i			0.923183i
$652$	−4.31105	+	7.79157i	−0.168834	+	0.305141i
$653$	20.0573	−	20.0573i	0.784903	−	0.784903i	−0.195751	−	0.980654i	$-0.562714\pi$
$653$	20.0573	−	20.0573i	0.784903	−	0.784903i	0.980654	+	0.195751i	$0.0627144\pi$
$654$	6.91612	+	49.0729i	0.270442	+	1.91890i
$655$	15.3201	+	41.8966i	0.598604	+	1.63704i
$656$	−3.38891	+	2.12493i	−0.132315	+	0.0829645i
$657$	17.7711	+	17.7711i	0.693317	+	0.693317i
$658$	21.9690	+	16.5415i	0.856443	+	0.644856i
$659$	12.2990			0.479101			0.239550	−	0.970884i	$-0.423000\pi$
$659$	12.2990			0.479101			0.239550	+	0.970884i	$0.423000\pi$
$660$	43.6628	+	6.81400i	1.69957	+	0.265235i
$661$	4.67919			0.181999			0.0909997	−	0.995851i	$-0.470994\pi$
$661$	4.67919			0.181999			0.0909997	+	0.995851i	$0.470994\pi$
$662$	−19.9020	−	14.9851i	−0.773513	−	0.582414i
$663$	−0.952606	−	0.952606i	−0.0369961	−	0.0369961i
$664$	−5.86726	−	13.1370i	−0.227694	−	0.509814i
$665$	6.68070	−	14.3829i	0.259066	−	0.557744i
$666$	3.87814	+	27.5171i	0.150275	+	1.06627i
$667$	5.41722	−	5.41722i	0.209756	−	0.209756i
$668$	−2.58884	−	1.43240i	−0.100165	−	0.0554211i
$669$		−	35.3362i		−	1.36617i
$670$	19.6354	+	36.7618i	0.758582	+	1.42023i
$671$		−	2.93979i		−	0.113489i
$672$	1.99406	−	23.3119i	0.0769224	−	0.899277i
$673$	0.936252	−	0.936252i	0.0360899	−	0.0360899i	−0.688832	−	0.724921i	$-0.741876\pi$
$673$	0.936252	−	0.936252i	0.0360899	−	0.0360899i	0.724921	+	0.688832i	$0.241876\pi$
$674$	44.0116	−	6.20280i	1.69526	−	0.238923i
$675$	0.0183229	−	0.216896i	0.000705247	−	0.00834833i
$676$	22.4708	−	6.46224i	0.864262	−	0.248548i
$677$	23.9486	+	23.9486i	0.920421	+	0.920421i	0.997059	−	0.0766377i	$-0.0244185\pi$
$677$	23.9486	+	23.9486i	0.920421	+	0.920421i	−0.0766377	+	0.997059i	$0.524418\pi$
$678$	−8.13768	+	10.8078i	−0.312526	+	0.415070i
$679$	−23.2623			−0.892727
$680$	2.11446	+	2.17798i	0.0810858	+	0.0835217i
$681$	65.4479			2.50797
$682$	−19.5143	+	25.9172i	−0.747240	+	0.992420i
$683$	7.26579	+	7.26579i	0.278018	+	0.278018i	0.832317	−	0.554300i	$-0.187014\pi$
$683$	7.26579	+	7.26579i	0.278018	+	0.278018i	−0.554300	+	0.832317i	$0.687014\pi$
$684$	24.3990	−	7.01675i	0.932919	−	0.268292i
$685$	−28.6533	−	13.3092i	−1.09479	−	0.508517i
$686$	26.3433	−	3.71272i	1.00579	−	0.141752i
$687$	25.2147	−	25.2147i	0.961999	−	0.961999i
$688$	−2.27322	−	0.521106i	−0.0866656	−	0.0198670i
$689$			0.435943i			0.0166081i
$690$	13.5982	+	4.12942i	0.517674	+	0.157204i
$691$		−	26.3604i		−	1.00280i	−0.865217	−	0.501398i	$-0.832819\pi$
$691$		−	26.3604i		−	1.00280i	0.865217	−	0.501398i	$-0.167181\pi$
$692$	−21.3550	−	11.8157i	−0.811796	−	0.449165i
$693$	14.4925	−	14.4925i	0.550523	−	0.550523i
$694$	−6.51029	−	46.1933i	−0.247127	−	1.75347i
$695$	−10.1299	+	3.70414i	−0.384250	+	0.140506i
$696$	−26.4935	+	11.8326i	−1.00423	+	0.448513i
$697$	−0.339384	−	0.339384i	−0.0128551	−	0.0128551i
$698$	8.85464	+	6.66707i	0.335153	+	0.252352i
$699$	72.8791			2.75654
$700$	−16.5385	+	3.27939i	−0.625095	+	0.123949i
$701$	15.9649			0.602986			0.301493	−	0.953468i	$-0.402515\pi$
$701$	15.9649			0.602986			0.301493	+	0.953468i	$0.402515\pi$
$702$	0.0562757	+	0.0423726i	0.00212399	+	0.00159925i
$703$	19.3676	+	19.3676i	0.730461	+	0.730461i
$704$	21.5071	−	23.9980i	0.810581	−	0.904459i
$705$	59.4159	−	21.7262i	2.23773	−	0.818257i
$706$	−5.88990	−	41.7914i	−0.221669	−	1.57284i
$707$	−0.561747	+	0.561747i	−0.0211267	+	0.0211267i
$708$	−12.9369	+	23.3814i	−0.486198	+	0.878728i
$709$			35.8367i			1.34587i	0.739700	+	0.672937i	$0.234967\pi$
$709$			35.8367i			1.34587i	−0.739700	+	0.672937i	$0.765033\pi$
$710$	−4.75809	−	1.44491i	−0.178568	−	0.0542265i
$711$			42.0750i			1.57794i
$712$	−7.07030	+	18.4829i	−0.264971	+	0.692676i
$713$	−7.37727	+	7.37727i	−0.276281	+	0.276281i
$714$	2.77995	−	0.391794i	0.104037	−	0.0146625i
$715$	9.34701	+	4.34159i	0.349558	+	0.162366i
$716$	−4.21279	−	14.6489i	−0.157439	−	0.547456i
$717$	30.0781	+	30.0781i	1.12329	+	1.12329i
$718$	−8.60892	+	11.4336i	−0.321282	+	0.426699i
$719$	38.4310			1.43324			0.716618	−	0.697466i	$-0.245689\pi$
$719$	38.4310			1.43324			0.716618	+	0.697466i	$0.245689\pi$
$720$	−21.3201	−	16.5528i	−0.794553	−	0.616888i
$721$	−32.4596			−1.20886
$722$	−1.11088	+	1.47538i	−0.0413427	+	0.0549079i
$723$	−46.6192	−	46.6192i	−1.73379	−	1.73379i
$724$	−0.469259	−	1.63173i	−0.0174399	−	0.0606428i
$725$	13.4882	+	15.9773i	0.500937	+	0.593383i
$726$	17.9526	−	2.53016i	0.666283	−	0.0939031i
$727$	−6.57510	+	6.57510i	−0.243857	+	0.243857i	−0.818444	−	0.574587i	$-0.805163\pi$
$727$	−6.57510	+	6.57510i	−0.243857	+	0.243857i	0.574587	+	0.818444i	$0.305163\pi$
$728$	1.94954	−	5.09641i	0.0722547	−	0.188885i
$729$			27.3185i			1.01180i
$730$	−12.4077	−	23.2298i	−0.459228	−	0.859775i
$731$		−	0.279839i		−	0.0103502i
$732$	−1.73349	+	3.13303i	−0.0640718	+	0.115800i
$733$	−22.4799	+	22.4799i	−0.830315	+	0.830315i	−0.987560	−	0.157245i	$-0.949739\pi$
$733$	−22.4799	+	22.4799i	−0.830315	+	0.830315i	0.157245	+	0.987560i	$0.449739\pi$
$734$	6.36514	+	45.1634i	0.234942	+	1.66701i
$735$	9.60643	−	20.6817i	0.354338	−	0.762856i
$736$	7.92575	−	6.67669i	0.292147	−	0.246106i
$737$	37.5394	+	37.5394i	1.38278	+	1.38278i
$738$	3.40936	+	2.56707i	0.125500	+	0.0944951i
$739$	27.7449			1.02061			0.510307	−	0.859992i	$-0.329532\pi$
$739$	27.7449			1.02061			0.510307	+	0.859992i	$0.329532\pi$
$740$	4.49010	−	28.7717i	0.165059	−	1.05767i
$741$	11.8069			0.433737
$742$	−0.725745	−	0.546448i	−0.0266430	−	0.0200607i
$743$	−9.61246	−	9.61246i	−0.352647	−	0.352647i	0.508447	−	0.861094i	$-0.330220\pi$
$743$	−9.61246	−	9.61246i	−0.352647	−	0.352647i	−0.861094	+	0.508447i	$0.830220\pi$
$744$	36.0794	−	16.1138i	1.32273	−	0.590762i
$745$	−12.5839	−	34.4139i	−0.461039	−	1.26083i
$746$	−1.92359	−	13.6487i	−0.0704275	−	0.499714i
$747$	−10.8546	+	10.8546i	−0.397148	+	0.397148i
$748$	3.38335	+	1.87200i	0.123708	+	0.0684471i
$749$		−	7.36998i		−	0.269293i
$750$	−14.3546	+	36.0331i	−0.524154	+	1.31574i
$751$		−	33.9677i		−	1.23950i	−0.784799	−	0.619750i	$-0.787234\pi$
$751$		−	33.9677i		−	1.23950i	0.784799	−	0.619750i	$-0.212766\pi$
$752$	10.3080	−	44.9666i	0.375895	−	1.63976i
$753$	31.7406	−	31.7406i	1.15669	−	1.15669i
$754$	−6.70072	+	0.944371i	−0.244026	+	0.0343920i
$755$	−10.0409	−	27.4595i	−0.365427	−	0.999353i
$756$	−0.141081	+	0.0405727i	−0.00513108	+	0.00147562i
$757$	13.2933	+	13.2933i	0.483154	+	0.483154i	0.906138	−	0.422983i	$-0.139017\pi$
$757$	13.2933	+	13.2933i	0.483154	+	0.483154i	−0.422983	+	0.906138i	$0.639017\pi$
$758$	24.3347	−	32.3192i	0.883874	−	1.17389i
$759$	18.1026			0.657083
$760$	−26.6009	−	0.393647i	−0.964917	−	0.0142791i
$761$	36.5509			1.32497			0.662485	−	0.749075i	$-0.269502\pi$
$761$	36.5509			1.32497			0.662485	+	0.749075i	$0.269502\pi$
$762$	−28.1541	+	37.3918i	−1.01991	+	1.35456i
$763$	−17.0308	−	17.0308i	−0.616556	−	0.616556i
$764$	9.49078	−	2.72939i	0.343364	−	0.0987460i
$765$	1.36436	−	2.93733i	0.0493284	−	0.106199i
$766$	10.2735	−	1.44791i	0.371198	−	0.0523150i
$767$	−4.40665	+	4.40665i	−0.159115	+	0.159115i
$768$	−37.0716	+	12.8934i	−1.33771	+	0.465250i
$769$			30.4508i			1.09808i	0.835794	+	0.549042i	$0.185007\pi$
$769$			30.4508i			1.09808i	−0.835794	+	0.549042i	$0.814993\pi$
$770$	−18.9441	+	10.1185i	−0.682698	+	0.364646i
$771$		−	22.9138i		−	0.825221i
$772$	−16.0630	−	8.88760i	−0.578120	−	0.319872i
$773$	−25.5875	+	25.5875i	−0.920320	+	0.920320i	−0.997052	−	0.0767318i	$-0.975551\pi$
$773$	−25.5875	+	25.5875i	−0.920320	+	0.920320i	0.0767318	+	0.997052i	$0.475551\pi$
$774$	0.347256	+	2.46393i	0.0124819	+	0.0885643i
$775$	−18.3684	−	21.7582i	−0.659813	−	0.781579i
$776$	15.9138	+	35.6315i	0.571272	+	1.27910i
$777$	−19.0435	−	19.0435i	−0.683182	−	0.683182i
$778$	13.5070	+	10.1701i	0.484251	+	0.364615i
$779$	4.20643			0.150711
$780$	−7.40131	−	10.1386i	−0.265009	−	0.363019i
$781$	−6.33422			−0.226656
$782$	0.993380	+	0.747963i	0.0355232	+	0.0267471i
$783$	0.128731	+	0.128731i	0.00460047	+	0.00460047i
$784$	−8.83386	−	14.0885i	−0.315495	−	0.503162i
$785$	33.3889	+	15.5088i	1.19170	+	0.553533i
$786$	−9.65889	−	68.5340i	−0.344521	−	2.44453i
$787$	−20.4444	+	20.4444i	−0.728764	+	0.728764i	−0.970374	−	0.241609i	$-0.922325\pi$
$787$	−20.4444	+	20.4444i	−0.728764	+	0.728764i	0.241609	+	0.970374i	$0.422325\pi$
$788$	−11.2862	+	20.3981i	−0.402055	+	0.726653i
$789$			31.1631i			1.10944i
$790$	12.8114	−	42.1878i	0.455808	−	1.50098i
$791$		−	6.57504i		−	0.233781i
$792$	−32.1128	−	12.2842i	−1.14108	−	0.436499i
$793$	−0.590475	+	0.590475i	−0.0209684	+	0.0209684i
$794$	27.6964	−	3.90342i	0.982910	−	0.138527i
$795$	−1.96280	+	0.717724i	−0.0696133	+	0.0254551i
$796$	−1.74413	−	6.06477i	−0.0618190	−	0.214960i
$797$	7.81866	+	7.81866i	0.276951	+	0.276951i	0.831891	−	0.554940i	$-0.187259\pi$
$797$	7.81866	+	7.81866i	0.276951	+	0.276951i	−0.554940	+	0.831891i	$0.687259\pi$
$798$	−14.7998	+	19.6558i	−0.523906	+	0.695807i
$799$	5.53552			0.195833
$800$	16.3371	+	23.0889i	0.577604	+	0.816317i
$801$	21.1136			0.746014
$802$	11.0564	−	14.6841i	0.390413	−	0.518514i
$803$	−23.7212	−	23.7212i	−0.837104	−	0.837104i
$804$	−17.8712	−	62.1425i	−0.630268	−	2.19160i
$805$	−6.48667	+	2.37194i	−0.228625	+	0.0835999i
$806$	9.12517	−	1.28606i	0.321420	−	0.0452996i
$807$	−1.40010	+	1.40010i	−0.0492858	+	0.0492858i
$808$	1.24473	+	0.476151i	0.0437896	+	0.0167509i
$809$		−	15.2368i		−	0.535698i	−0.963461	−	0.267849i	$-0.913687\pi$
$809$		−	15.2368i		−	0.535698i	0.963461	−	0.267849i	$-0.0863129\pi$
$810$	8.22061	−	27.0705i	0.288843	−	0.951160i
$811$		−	13.6670i		−	0.479912i	−0.970784	−	0.239956i	$-0.922867\pi$
$811$		−	13.6670i		−	0.479912i	0.970784	−	0.239956i	$-0.0771330\pi$
$812$	6.82709	−	12.3389i	0.239584	−	0.433011i
$813$	5.72065	−	5.72065i	0.200632	−	0.200632i
$814$	−5.17662	−	36.7304i	−0.181440	−	1.28740i
$815$	−9.02926	−	4.19400i	−0.316281	−	0.146909i
$816$	−2.50189	−	3.99009i	−0.0875836	−	0.139681i
$817$	1.73421	+	1.73421i	0.0606723	+	0.0606723i
$818$	5.60660	+	4.22148i	0.196030	+	0.147600i
$819$	−5.82179			−0.203430
$820$	−2.63686	−	3.61206i	−0.0920831	−	0.126139i
$821$	−28.7443			−1.00318			−0.501591	−	0.865105i	$-0.667252\pi$
$821$	−28.7443			−1.00318			−0.501591	+	0.865105i	$0.667252\pi$
$822$	39.1579	+	29.4838i	1.36579	+	1.02837i
$823$	7.37471	+	7.37471i	0.257066	+	0.257066i	0.823860	−	0.566794i	$-0.191816\pi$
$823$	7.37471	+	7.37471i	0.257066	+	0.257066i	−0.566794	+	0.823860i	$0.691816\pi$
$824$	22.2056	+	49.7191i	0.773570	+	1.73205i
$825$	−4.15901	+	49.2321i	−0.144798	+	1.71404i
$826$	−1.81240	−	12.8597i	−0.0630613	−	0.447447i
$827$	−16.1240	+	16.1240i	−0.560686	+	0.560686i	−0.929502	−	0.368817i	$-0.879763\pi$
$827$	−16.1240	+	16.1240i	−0.560686	+	0.560686i	0.368817	+	0.929502i	$0.379763\pi$
$828$	−9.67469	−	5.35298i	−0.336219	−	0.186029i
$829$			49.1497i			1.70704i	0.521060	+	0.853520i	$0.325537\pi$
$829$			49.1497i			1.70704i	−0.521060	+	0.853520i	$0.674463\pi$
$830$	14.1888	−	7.57858i	0.492499	−	0.263057i
$831$		−	70.8199i		−	2.45672i
$832$	−9.13998	+	0.500303i	−0.316872	+	0.0173449i
$833$	1.41091	−	1.41091i	0.0488850	−	0.0488850i
$834$	16.5704	−	2.33536i	0.573786	−	0.0808670i
$835$	1.39350	−	3.00008i	0.0482242	−	0.103822i
$836$	−32.5682	+	9.36610i	−1.12640	+	0.323933i
$837$	−0.175308	−	0.175308i	−0.00605954	−	0.00605954i
$838$	16.5664	−	22.0021i	0.572278	−	0.760051i
$839$	17.6328			0.608751			0.304376	−	0.952552i	$-0.401552\pi$
$839$	17.6328			0.608751			0.304376	+	0.952552i	$0.401552\pi$
$840$	26.1558	+	0.387061i	0.902462	+	0.0133549i
$841$	11.5118			0.396958
$842$	−30.5168	+	40.5298i	−1.05168	+	1.39675i
$843$	−7.89263	−	7.89263i	−0.271837	−	0.271837i
$844$	23.4701	−	6.74962i	0.807874	−	0.232332i
$845$	8.97759	+	24.5515i	0.308838	+	0.844597i
$846$	−48.7392	+	6.86910i	−1.67569	+	0.236164i
$847$	−6.23046	+	6.23046i	−0.214081	+	0.214081i
$848$	−0.340525	+	1.48547i	−0.0116937	+	0.0510112i
$849$		−	6.34833i		−	0.217874i
$850$	−2.26240	+	2.52977i	−0.0775995	+	0.0867703i
$851$		−	11.9287i		−	0.408912i
$852$	6.75057	+	3.73507i	0.231271	+	0.127961i
$853$	−21.5659	+	21.5659i	−0.738403	+	0.738403i	−0.972269	−	0.233866i	$-0.924862\pi$
$853$	−21.5659	+	21.5659i	−0.738403	+	0.738403i	0.233866	+	0.972269i	$0.424862\pi$
$854$	−0.242854	−	1.72316i	−0.00831030	−	0.0589652i
$855$	9.74793	+	26.6582i	0.333372	+	0.911691i
$856$	−11.2888	+	5.04181i	−0.385843	+	0.172326i
$857$	−29.2248	−	29.2248i	−0.998302	−	0.998302i	0.00169682	−	0.999999i	$-0.499460\pi$
$857$	−29.2248	−	29.2248i	−0.998302	−	0.998302i	−0.999999	+	0.00169682i	$0.999460\pi$
$858$	−12.7737	−	9.61793i	−0.436087	−	0.328351i
$859$	21.4596			0.732191			0.366095	−	0.930577i	$-0.380694\pi$
$859$	21.4596			0.732191			0.366095	+	0.930577i	$0.380694\pi$
$860$	0.402052	−	2.57627i	0.0137099	−	0.0878502i
$861$	−4.13605			−0.140956
$862$	−22.7498	−	17.1294i	−0.774863	−	0.583431i
$863$	−15.8786	−	15.8786i	−0.540514	−	0.540514i	0.383166	−	0.923680i	$-0.374834\pi$
$863$	−15.8786	−	15.8786i	−0.540514	−	0.540514i	−0.923680	+	0.383166i	$0.874834\pi$
$864$	0.158660	+	0.188342i	0.00539773	+	0.00640753i
$865$	11.4949	−	24.7473i	0.390837	−	0.841433i
$866$	−0.764029	−	5.42111i	−0.0259628	−	0.184217i
$867$	−29.0888	+	29.0888i	−0.987907	+	0.987907i
$868$	−9.29726	+	16.8034i	−0.315570	+	0.570344i
$869$		−	56.1626i		−	1.90518i
$870$	−15.2838	−	28.6147i	−0.518171	−	0.970129i
$871$		−	15.0800i		−	0.510967i
$872$	−14.4357	+	37.7373i	−0.488855	+	1.27795i
$873$	29.4410	−	29.4410i	0.996426	−	0.996426i
$874$	−10.7914	+	1.52089i	−0.365024	+	0.0514449i
$875$	−4.96047	−	18.1862i	−0.167694	−	0.614805i
$876$	11.2928	+	39.2680i	0.381550	+	1.32674i
$877$	17.9936	+	17.9936i	0.607601	+	0.607601i	0.942319	−	0.334717i	$-0.108641\pi$
$877$	17.9936	+	17.9936i	0.607601	+	0.607601i	−0.334717	+	0.942319i	$0.608641\pi$
$878$	18.7607	−	24.9164i	0.633145	−	0.840888i
$879$	8.60067			0.290094
$880$	28.4585	+	22.0951i	0.959335	+	0.744824i
$881$	−5.90202			−0.198844			−0.0994221	−	0.995045i	$-0.531699\pi$
$881$	−5.90202			−0.198844			−0.0994221	+	0.995045i	$0.531699\pi$
$882$	−10.6720	+	14.1736i	−0.359343	+	0.477249i
$883$	17.8376	+	17.8376i	0.600283	+	0.600283i	0.940387	−	0.340105i	$-0.110463\pi$
$883$	17.8376	+	17.8376i	0.600283	+	0.600283i	−0.340105	+	0.940387i	$0.610463\pi$
$884$	−0.303564	−	1.05557i	−0.0102100	−	0.0355026i
$885$	−27.0956	−	12.5856i	−0.910808	−	0.423061i
$886$	−38.0244	+	5.35900i	−1.27746	+	0.180039i
$887$	−3.93049	+	3.93049i	−0.131973	+	0.131973i	−0.770008	−	0.638035i	$-0.779748\pi$
$887$	−3.93049	+	3.93049i	−0.131973	+	0.131973i	0.638035	+	0.770008i	$0.279748\pi$
$888$	−16.1417	+	42.1971i	−0.541681	+	1.41604i
$889$		−	22.7477i		−	0.762935i
$890$	−21.1702	−	6.42886i	−0.709628	−	0.215496i
$891$		−	36.0376i		−	1.20730i
$892$	13.9475	−	25.2080i	0.466997	−	0.844025i
$893$	−34.3045	+	34.3045i	−1.14796	+	1.14796i
$894$	7.93382	+	56.2939i	0.265347	+	1.88275i
$895$	16.0053	−	5.85257i	0.534999	−	0.195630i
$896$	10.6239	−	15.8431i	0.354921	−	0.529281i
$897$	−3.63601	−	3.63601i	−0.121403	−	0.121403i
$898$	−24.4699	−	18.4245i	−0.816571	−	0.614835i
$899$	23.8158			0.794301
$900$	16.7808	−	25.0816i	0.559358	−	0.836053i
$901$	−0.182865			−0.00609213
$902$	−4.55088	−	3.42657i	−0.151528	−	0.114092i
$903$	−1.70519	−	1.70519i	−0.0567452	−	0.0567452i
$904$	−10.0712	+	4.49799i	−0.334962	+	0.149601i
$905$	1.78282	−	0.651912i	0.0592629	−	0.0216703i
$906$	6.33054	+	44.9179i	0.210318	+	1.49230i
$907$	40.0074	−	40.0074i	1.32842	−	1.32842i	0.421678	−	0.906745i	$-0.361441\pi$
$907$	40.0074	−	40.0074i	1.32842	−	1.32842i	0.906745	−	0.421678i	$-0.138559\pi$
$908$	46.6890	+	25.8329i	1.54943	+	0.857294i
$909$		−	1.42190i		−	0.0471615i
$910$	5.83740	+	1.77267i	0.193508	+	0.0587634i
$911$			38.8693i			1.28780i	0.765110	+	0.643899i	$0.222684\pi$
$911$			38.8693i			1.28780i	−0.765110	+	0.643899i	$0.777316\pi$
$912$	40.2318	+	9.22263i	1.33221	+	0.305392i
$913$	14.4889	−	14.4889i	0.479513	−	0.479513i
$914$	19.1103	−	2.69333i	0.632113	−	0.0890873i
$915$	−3.63071	−	1.68643i	−0.120027	−	0.0557515i
$916$	27.9400	−	8.03509i	0.923163	−	0.265487i
$917$	23.7848	+	23.7848i	0.785442	+	0.785442i
$918$	−0.0177741	+	0.0236060i	−0.000586632	+	0.000779114i
$919$	−39.1154			−1.29030			−0.645149	−	0.764057i	$-0.723205\pi$
$919$	−39.1154			−1.29030			−0.645149	+	0.764057i	$0.723205\pi$
$920$	8.07070	+	8.31315i	0.266083	+	0.274077i
$921$	−15.4544			−0.509240
$922$	−17.4778	+	23.2126i	−0.575602	+	0.764465i
$923$	1.27226	+	1.27226i	0.0418771	+	0.0418771i
$924$	32.0233	−	9.20939i	1.05349	−	0.302967i
$925$	32.4416	+	2.74059i	1.06667	+	0.0901100i
$926$	49.1790	−	6.93108i	1.61612	−	0.227769i
$927$	41.0810	−	41.0810i	1.34928	−	1.34928i
$928$	−23.5703	−	2.01615i	−0.773732	−	0.0661835i
$929$			47.6946i			1.56481i	0.622771	+	0.782404i	$0.286007\pi$
$929$			47.6946i			1.56481i	−0.622771	+	0.782404i	$0.713993\pi$
$930$	20.8138	+	38.9680i	0.682512	+	1.27781i
$931$			17.4872i			0.573120i
$932$	51.9902	+	28.7660i	1.70300	+	0.942262i
$933$	−8.29177	+	8.29177i	−0.271460	+	0.271460i
$934$	4.26102	+	30.2338i	0.139425	+	0.989280i
$935$	−1.82117	+	3.92080i	−0.0595586	+	0.128224i
$936$	3.98270	+	8.91739i	0.130178	+	0.291474i
$937$	26.6067	+	26.6067i	0.869204	+	0.869204i	0.992384	−	0.123180i	$-0.0393094\pi$
$937$	26.6067	+	26.6067i	0.869204	+	0.869204i	−0.123180	+	0.992384i	$0.539309\pi$
$938$	25.1048	+	18.9026i	0.819700	+	0.617191i
$939$	12.2200			0.398784
$940$	50.9614	+	7.95301i	1.66218	+	0.259399i
$941$	−41.7503			−1.36102			−0.680511	−	0.732738i	$-0.738242\pi$
$941$	−41.7503			−1.36102			−0.680511	+	0.732738i	$0.738242\pi$
$942$	−45.6296	−	34.3567i	−1.48669	−	1.11940i
$943$	−1.29540	−	1.29540i	−0.0421840	−	0.0421840i
$944$	−18.4577	+	11.5735i	−0.600748	+	0.376684i
$945$	−0.0563651	−	0.154145i	−0.00183356	−	0.00501433i
$946$	−0.463524	−	3.28891i	−0.0150705	−	0.106932i
$947$	18.8783	−	18.8783i	0.613463	−	0.613463i	−0.330384	−	0.943847i	$-0.607178\pi$
$947$	18.8783	−	18.8783i	0.613463	−	0.613463i	0.943847	+	0.330384i	$0.107178\pi$
$948$	−33.1171	+	59.8541i	−1.07559	+	1.94397i
$949$			9.52910i			0.309328i
$950$	−1.65695	−	29.6978i	−0.0537586	−	0.963524i
$951$			70.0500i			2.27153i
$952$	2.13779	+	0.817774i	0.0692863	+	0.0265042i
$953$	8.80988	−	8.80988i	0.285380	−	0.285380i	−0.549870	−	0.835250i	$-0.685323\pi$
$953$	8.80988	−	8.80988i	0.285380	−	0.285380i	0.835250	+	0.549870i	$0.185323\pi$
$954$	1.61010	−	0.226920i	0.0521288	−	0.00734681i
$955$	3.79178	+	10.3696i	0.122699	+	0.335552i
$956$	9.58492	+	33.3291i	0.309998	+	1.07794i
$957$	−29.2200	−	29.2200i	−0.944548	−	0.944548i
$958$	4.09072	−	5.43295i	0.132165	−	0.175531i
$959$	−23.8222			−0.769258
$960$	−17.3004	−	40.3284i	−0.558367	−	1.30159i
$961$	−1.43278			−0.0462187
$962$	−6.33775	+	8.41726i	−0.204337	+	0.271383i
$963$	9.32749	+	9.32749i	0.300574	+	0.300574i
$964$	−14.8560	−	51.6581i	−0.478480	−	1.66379i
$965$	8.64628	−	18.6146i	0.278334	−	0.599225i
$966$	10.6108	−	1.49544i	0.341397	−	0.0481151i
$967$	9.32272	−	9.32272i	0.299799	−	0.299799i	−0.541136	−	0.840935i	$-0.682006\pi$
$967$	9.32272	−	9.32272i	0.299799	−	0.299799i	0.840935	+	0.541136i	$0.182006\pi$
$968$	13.8056	+	5.28109i	0.443730	+	0.169741i
$969$			4.95265i			0.159102i
$970$	−38.4843	+	20.5555i	−1.23566	+	0.659996i
$971$		−	41.5696i		−	1.33403i	−0.745043	−	0.667016i	$-0.767571\pi$
$971$		−	41.5696i		−	1.33403i	0.745043	−	0.667016i	$-0.232429\pi$
$972$	−21.3766	+	38.6349i	−0.685654	+	1.23921i
$973$	−5.75077	+	5.75077i	−0.184361	+	0.184361i
$974$	−1.15600	−	8.20232i	−0.0370406	−	0.262819i
$975$	10.7239	−	9.05319i	0.343440	−	0.289934i
$976$	−2.47327	+	1.55080i	−0.0791673	+	0.0496399i
$977$	−16.1348	−	16.1348i	−0.516197	−	0.516197i	0.400222	−	0.916418i	$-0.368933\pi$
$977$	−16.1348	−	16.1348i	−0.516197	−	0.516197i	−0.916418	+	0.400222i	$0.868933\pi$
$978$	12.3395	+	9.29097i	0.394573	+	0.297092i
$979$	−28.1829			−0.900729
$980$	15.0162	−	10.9621i	0.479676	−	0.350171i
$981$	43.1085			1.37635
$982$	40.8048	+	30.7239i	1.30213	+	0.980438i
$983$	−1.26930	−	1.26930i	−0.0404842	−	0.0404842i	0.686575	−	0.727059i	$-0.259113\pi$
$983$	−1.26930	−	1.26930i	−0.0404842	−	0.0404842i	−0.727059	+	0.686575i	$0.759113\pi$
$984$	2.82948	+	6.33530i	0.0902005	+	0.201962i
$985$	−23.6384	−	10.9798i	−0.753181	−	0.349845i
$986$	−0.396136	−	2.81076i	−0.0126155	−	0.0895127i
$987$	33.7305	−	33.7305i	1.07365	−	1.07365i
$988$	8.42276	+	4.66029i	0.267964	+	0.148264i
$989$		−	1.06812i		−	0.0339643i
$990$	11.1697	−	36.7818i	0.354996	−	1.16900i
$991$		−	42.1399i		−	1.33862i	−0.742985	−	0.669308i	$-0.766590\pi$
$991$		−	42.1399i		−	1.33862i	0.742985	−	0.669308i	$-0.233410\pi$
$992$	32.0984	+	2.74564i	1.01913	+	0.0871741i
$993$	−30.5568	+	30.5568i	−0.969691	+	0.969691i
$994$	−3.71279	+	0.523265i	−0.117763	+	0.0165970i
$995$	6.62633	−	2.42301i	0.210069	−	0.0768145i
$996$	−23.9849	+	6.89766i	−0.759990	+	0.218561i
$997$	31.3866	+	31.3866i	0.994023	+	0.994023i	0.999982	−	0.00595958i	$-0.00189701\pi$
$997$	31.3866	+	31.3866i	0.994023	+	0.994023i	−0.00595958	+	0.999982i	$0.501897\pi$
$998$	−16.6855	+	22.1602i	−0.528169	+	0.701469i
$999$	0.283466			0.00896847

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.k.c.247.38	yes	108
4.3	odd	2	inner	820.2.k.c.247.11	yes	108
5.3	odd	4	inner	820.2.k.c.83.11	✓	108
20.3	even	4	inner	820.2.k.c.83.38	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.k.c.83.11	✓	108	5.3	odd	4	inner
820.2.k.c.83.38	yes	108	20.3	even	4	inner
820.2.k.c.247.11	yes	108	4.3	odd	2	inner
820.2.k.c.247.38	yes	108	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.850658 - 1.12977i) q^{2} +(-1.73461 - 1.73461i) q^{3} +(-0.552763 - 1.92210i) q^{4} +(2.10007 - 0.767920i) q^{5} +(-3.43527 + 0.484152i) q^{6} +(1.19221 - 1.19221i) q^{7} +(-2.64174 - 1.01055i) q^{8} +3.01775i q^{9} +(0.918869 - 3.02584i) q^{10} -4.02815i q^{11} +(-2.37526 + 4.29292i) q^{12} +(-0.809077 + 0.809077i) q^{13} +(-0.332763 - 2.36109i) q^{14} +(-4.97485 - 2.31076i) q^{15} +(-3.38891 + 2.12493i) q^{16} +(-0.339384 - 0.339384i) q^{17} +(3.40936 + 2.56707i) q^{18} +4.20643 q^{19} +(-2.63686 - 3.61206i) q^{20} -4.13605 q^{21} +(-4.55088 - 3.42657i) q^{22} +(-1.29540 - 1.29540i) q^{23} +(2.82948 + 6.33530i) q^{24} +(3.82060 - 3.22537i) q^{25} +(0.225824 + 1.60232i) q^{26} +(0.0307830 - 0.0307830i) q^{27} +(-2.95056 - 1.63254i) q^{28} +4.18189i q^{29} +(-6.84252 + 3.65477i) q^{30} -5.69498i q^{31} +(-0.482116 + 5.63627i) q^{32} +(-6.98726 + 6.98726i) q^{33} +(-0.672126 + 0.0947266i) q^{34} +(1.58821 - 3.41926i) q^{35} +(5.80040 - 1.66810i) q^{36} +(4.60427 + 4.60427i) q^{37} +(3.57824 - 4.75231i) q^{38} +2.80687 q^{39} +(-6.32386 - 0.0935821i) q^{40} +1.00000 q^{41} +(-3.51836 + 4.67279i) q^{42} +(0.412275 + 0.412275i) q^{43} +(-7.74248 + 2.22661i) q^{44} +(2.31739 + 6.33748i) q^{45} +(-2.56545 + 0.361563i) q^{46} +(-8.15524 + 8.15524i) q^{47} +(9.56435 + 2.19251i) q^{48} +4.15725i q^{49} +(-0.393909 - 7.06009i) q^{50} +1.17740i q^{51} +(2.00235 + 1.10790i) q^{52} +(0.269408 - 0.269408i) q^{53} +(-0.00859193 - 0.0609635i) q^{54} +(-3.09329 - 8.45939i) q^{55} +(-4.35431 + 1.94473i) q^{56} +(-7.29652 - 7.29652i) q^{57} +(4.72458 + 3.55736i) q^{58} +5.44652 q^{59} +(-1.69160 + 10.8394i) q^{60} +0.729813 q^{61} +(-6.43402 - 4.84448i) q^{62} +(3.59780 + 3.59780i) q^{63} +(5.95758 + 5.33922i) q^{64} +(-1.07781 + 2.32042i) q^{65} +(1.95024 + 13.8378i) q^{66} +(-9.31927 + 9.31927i) q^{67} +(-0.464730 + 0.839928i) q^{68} +4.49403i q^{69} +(-2.51196 - 4.70293i) q^{70} -1.57249i q^{71} +(3.04958 - 7.97210i) q^{72} +(5.88887 - 5.88887i) q^{73} +(9.11843 - 1.28511i) q^{74} +(-12.2220 - 1.03249i) q^{75} +(-2.32516 - 8.08517i) q^{76} +(-4.80241 - 4.80241i) q^{77} +(2.38768 - 3.17112i) q^{78} +13.9425 q^{79} +(-5.48517 + 7.06491i) q^{80} +8.94645 q^{81} +(0.850658 - 1.12977i) q^{82} +(3.59692 + 3.59692i) q^{83} +(2.28626 + 7.94989i) q^{84} +(-0.973351 - 0.452111i) q^{85} +(0.816481 - 0.115071i) q^{86} +(7.25395 - 7.25395i) q^{87} +(-4.07064 + 10.6413i) q^{88} -6.99649i q^{89} +(9.13120 + 2.77291i) q^{90} +1.92919i q^{91} +(-1.77383 + 3.20593i) q^{92} +(-9.87857 + 9.87857i) q^{93} +(2.27623 + 16.1509i) q^{94} +(8.83381 - 3.23020i) q^{95} +(10.6130 - 8.94045i) q^{96} +(-9.75595 - 9.75595i) q^{97} +(4.69674 + 3.53640i) q^{98} +12.1559 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 12 q^{2} - 4 q^{6} - 24 q^{8} + 4 q^{10} - 16 q^{13} + 52 q^{16} - 8 q^{17} + 18 q^{18} + 38 q^{20} + 72 q^{21} + 10 q^{22} - 12 q^{25} + 24 q^{26} - 58 q^{28} - 70 q^{30} - 38 q^{32} + 8 q^{33}+ \cdots + 122 q^{98}+O(q^{100}) \) 108 * q + 12 * q^2 - 4 * q^6 - 24 * q^8 + 4 * q^10 - 16 * q^13 + 52 * q^16 - 8 * q^17 + 18 * q^18 + 38 * q^20 + 72 * q^21 + 10 * q^22 - 12 * q^25 + 24 * q^26 - 58 * q^28 - 70 * q^30 - 38 * q^32 + 8 * q^33 + 72 * q^36 - 44 * q^37 + 56 * q^38 + 50 * q^40 + 108 * q^41 - 72 * q^42 - 4 * q^45 - 4 * q^46 - 94 * q^48 - 56 * q^50 - 50 * q^52 - 16 * q^53 - 32 * q^56 - 112 * q^57 + 68 * q^58 + 136 * q^60 + 8 * q^61 + 2 * q^62 - 48 * q^65 + 16 * q^66 - 16 * q^68 - 48 * q^70 - 42 * q^72 - 20 * q^73 - 12 * q^76 + 72 * q^77 + 100 * q^78 + 72 * q^80 - 52 * q^81 + 12 * q^82 - 32 * q^85 - 20 * q^86 - 38 * q^88 - 50 * q^90 + 8 * q^92 + 24 * q^93 + 44 * q^96 - 56 * q^97 + 122 * q^98

Introduction

L-functions

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