LMFDB - Embedded newform 820.2.k.c.83.11

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			83.11
Character	$\chi$	$=$	820.83
Dual form			820.2.k.c.247.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.12977 - 0.850658i) 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} +(1.01055 - 2.64174i) q^{8} -3.01775i q^{9} +(-1.71936 - 2.65401i) q^{10} -4.02815i q^{11} +(4.29292 + 2.37526i) 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} +(-2.56707 + 3.40936i) q^{18} -4.20643 q^{19} +(-0.315172 + 4.46102i) q^{20} -4.13605 q^{21} +(-3.42657 + 4.55088i) 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} +(1.63254 - 2.95056i) q^{28} -4.18189i q^{29} +(-7.58610 - 1.62126i) q^{30} -5.69498i q^{31} +(5.63627 + 0.482116i) 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} +(4.75231 + 3.57824i) q^{38} -2.80687 q^{39} +(4.15087 - 4.77182i) q^{40} +1.00000 q^{41} +(4.67279 + 3.51836i) 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} +(-2.19251 + 9.56435i) q^{48} -4.15725i q^{49} +(-1.57271 - 6.89395i) q^{50} +1.17740i q^{51} +(1.10790 - 2.00235i) 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} +(-3.55736 + 4.72458i) q^{58} -5.44652 q^{59} +(7.19142 + 8.28483i) q^{60} +0.729813 q^{61} +(-4.84448 + 6.43402i) 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} +(-0.839928 - 0.464730i) q^{68} -4.49403i q^{69} +(-1.11431 + 5.21400i) q^{70} -1.57249i q^{71} +(-7.97210 - 3.04958i) 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} +(3.17112 + 2.38768i) q^{78} -13.9425 q^{79} +(-8.74872 + 1.86010i) q^{80} +8.94645 q^{81} +(-1.12977 - 0.850658i) 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} +(-10.6413 - 4.07064i) q^{88} +6.99649i q^{89} +(-8.00914 + 5.18860i) q^{90} +1.92919i q^{91} +(3.20593 + 1.77383i) 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} +(-3.53640 + 4.69674i) 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 $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.12977	−	0.850658i	−0.798868	−	0.601506i
$2$	−1.12977	−	0.850658i	−0.798868	−	0.601506i
$3$	1.73461	−	1.73461i	1.00148	−	1.00148i	0.00147886	−	0.999999i	$-0.499529\pi$
$3$	1.73461	−	1.73461i	1.00148	−	1.00148i	0.999999	−	0.00147886i	$-0.000470737\pi$
$4$	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	$-0.353224\pi$
$7$	−1.19221	−	1.19221i	−0.450614	−	0.450614i	−0.895558	+	0.444944i	$0.853224\pi$
$8$	1.01055	−	2.64174i	0.357283	−	0.933996i
$9$		−	3.01775i		−	1.00592i
$10$	−1.71936	−	2.65401i	−0.543710	−	0.839273i
$11$		−	4.02815i		−	1.21453i	−0.794499	−	0.607266i	$-0.792266\pi$
$11$		−	4.02815i		−	1.21453i	0.794499	−	0.607266i	$-0.207734\pi$
$12$	4.29292	+	2.37526i	1.23926	+	0.685678i
$13$	−0.809077	−	0.809077i	−0.224398	−	0.224398i	0.585950	−	0.810347i	$-0.300722\pi$
$13$	−0.809077	−	0.809077i	−0.224398	−	0.224398i	−0.810347	+	0.585950i	$0.800722\pi$
$14$	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	−0.747064	−	0.664752i	$-0.768537\pi$
$17$	−0.339384	+	0.339384i	−0.0823127	+	0.0823127i	0.664752	+	0.747064i	$0.268537\pi$
$18$	−2.56707	+	3.40936i	−0.605064	+	0.803594i
$19$	−4.20643			−0.965022			−0.482511	−	0.875890i	$-0.660275\pi$
$19$	−4.20643			−0.965022			−0.482511	+	0.875890i	$0.660275\pi$
$20$	−0.315172	+	4.46102i	−0.0704747	+	0.997514i
$21$	−4.13605			−0.902561
$22$	−3.42657	+	4.55088i	−0.730548	+	0.970251i
$23$	1.29540	−	1.29540i	0.270109	−	0.270109i	−0.559035	−	0.829144i	$-0.688828\pi$
$23$	1.29540	−	1.29540i	0.270109	−	0.270109i	0.829144	+	0.559035i	$0.188828\pi$
$24$	−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
$28$	1.63254	−	2.95056i	0.308521	−	0.557604i
$29$		−	4.18189i		−	0.776558i	−0.921542	−	0.388279i	$-0.873070\pi$
$29$		−	4.18189i		−	0.776558i	0.921542	−	0.388279i	$-0.126930\pi$
$30$	−7.58610	−	1.62126i	−1.38503	−	0.296000i
$31$		−	5.69498i		−	1.02285i	−0.859328	−	0.511424i	$-0.829118\pi$
$31$		−	5.69498i		−	1.02285i	0.859328	−	0.511424i	$-0.170882\pi$
$32$	5.63627	+	0.482116i	0.996362	+	0.0852268i
$33$	−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	−0.218826	−	0.975764i	$-0.570223\pi$
$37$	4.60427	−	4.60427i	0.756937	−	0.756937i	0.975764	+	0.218826i	$0.0702229\pi$
$38$	4.75231	+	3.57824i	0.770926	+	0.580466i
$39$	−2.80687			−0.449458
$40$	4.15087	−	4.77182i	0.656310	−	0.754491i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	4.67279	+	3.51836i	0.721027	+	0.542895i
$43$	−0.412275	+	0.412275i	−0.0628714	+	0.0628714i	−0.737843	−	0.674972i	$-0.764156\pi$
$43$	−0.412275	+	0.412275i	−0.0628714	+	0.0628714i	0.674972	+	0.737843i	$0.264156\pi$
$44$	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	0.977188	+	0.212376i	$0.0681202\pi$
$47$	8.15524	+	8.15524i	1.18956	+	1.18956i	0.212376	+	0.977188i	$0.431880\pi$
$48$	−2.19251	+	9.56435i	−0.316461	+	1.38050i
$49$		−	4.15725i		−	0.593893i
$50$	−1.57271	−	6.89395i	−0.222415	−	0.974952i
$51$			1.17740i			0.164869i
$52$	1.10790	−	2.00235i	0.153637	−	0.277676i
$53$	0.269408	+	0.269408i	0.0370060	+	0.0370060i	0.725368	−	0.688362i	$-0.241670\pi$
$53$	0.269408	+	0.269408i	0.0370060	+	0.0370060i	−0.688362	+	0.725368i	$0.741670\pi$
$54$	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
$58$	−3.55736	+	4.72458i	−0.467104	+	0.620367i
$59$	−5.44652			−0.709076			−0.354538	−	0.935042i	$-0.615362\pi$
$59$	−5.44652			−0.709076			−0.354538	+	0.935042i	$0.615362\pi$
$60$	7.19142	+	8.28483i	0.928409	+	1.06957i
$61$	0.729813			0.0934429			0.0467215	−	0.998908i	$-0.485123\pi$
$61$	0.729813			0.0934429			0.0467215	+	0.998908i	$0.485123\pi$
$62$	−4.84448	+	6.43402i	−0.615249	+	0.817121i
$63$	−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	0.988714	+	0.149816i	$0.0478683\pi$
$67$	9.31927	+	9.31927i	1.13853	+	1.13853i	0.149816	+	0.988714i	$0.452132\pi$
$68$	−0.839928	−	0.464730i	−0.101856	−	0.0563568i
$69$		−	4.49403i		−	0.541017i
$70$	−1.11431	+	5.21400i	−0.133185	+	0.623192i
$71$		−	1.57249i		−	0.186620i	−0.995637	−	0.0933101i	$-0.970255\pi$
$71$		−	1.57249i		−	0.186620i	0.995637	−	0.0933101i	$-0.0297448\pi$
$72$	−7.97210	−	3.04958i	−0.939521	−	0.359397i
$73$	5.88887	+	5.88887i	0.689240	+	0.689240i	0.962064	−	0.272824i	$-0.0879577\pi$
$73$	5.88887	+	5.88887i	0.689240	+	0.689240i	−0.272824	+	0.962064i	$0.587958\pi$
$74$	−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
$78$	3.17112	+	2.38768i	0.359058	+	0.270352i
$79$	−13.9425			−1.56866			−0.784329	−	0.620345i	$-0.786992\pi$
$79$	−13.9425			−1.56866			−0.784329	+	0.620345i	$0.786992\pi$
$80$	−8.74872	+	1.86010i	−0.978136	+	0.207965i
$81$	8.94645			0.994050
$82$	−1.12977	−	0.850658i	−0.124762	−	0.0939394i
$83$	−3.59692	+	3.59692i	−0.394813	+	0.394813i	−0.876399	−	0.481586i	$-0.840061\pi$
$83$	−3.59692	+	3.59692i	−0.394813	+	0.394813i	0.481586	+	0.876399i	$0.340061\pi$
$84$	−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
$88$	−10.6413	−	4.07064i	−1.13437	−	0.433932i
$89$			6.99649i			0.741627i	0.928707	+	0.370813i	$0.120921\pi$
$89$			6.99649i			0.741627i	−0.928707	+	0.370813i	$0.879079\pi$
$90$	−8.00914	+	5.18860i	−0.844238	+	0.546926i
$91$			1.92919i			0.202234i
$92$	3.20593	+	1.77383i	0.334241	+	0.184935i
$93$	−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	−0.999956	−	0.00938975i	$-0.997011\pi$
$97$	−9.75595	+	9.75595i	−0.990566	+	0.990566i	0.00938975	+	0.999956i	$0.497011\pi$
$98$	−3.53640	+	4.69674i	−0.357230	+	0.474443i
$99$	−12.1559			−1.22172
$100$	−4.08759	+	9.12643i	−0.408759	+	0.912643i
$101$	−0.471180			−0.0468842			−0.0234421	−	0.999725i	$-0.507463\pi$
$101$	−0.471180			−0.0468842			−0.0234421	+	0.999725i	$0.507463\pi$
$102$	1.00156	−	1.33019i	0.0991695	−	0.131708i
$103$	13.6131	−	13.6131i	1.34134	−	1.34134i	0.446618	−	0.894725i	$-0.352628\pi$
$103$	13.6131	−	13.6131i	1.34134	−	1.34134i	0.894725	−	0.446618i	$-0.147372\pi$
$104$	−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	$-0.317766\pi$
$107$	−3.09088	−	3.09088i	−0.298806	−	0.298806i	−0.840546	+	0.541740i	$0.817766\pi$
$108$	0.0421521	−	0.0761835i	0.00405609	−	0.00733076i
$109$			14.2850i			1.36826i	0.729362	+	0.684128i	$0.239817\pi$
$109$			14.2850i			1.36826i	−0.729362	+	0.684128i	$0.760183\pi$
$110$	−10.6908	+	6.92584i	−1.01932	+	0.660353i
$111$		−	15.9732i		−	1.51611i
$112$	6.57367	+	1.50693i	0.621153	+	0.142392i
$113$	2.75749	+	2.75749i	0.259403	+	0.259403i	0.824811	−	0.565408i	$-0.191281\pi$
$113$	2.75749	+	2.75749i	0.259403	+	0.259403i	−0.565408	+	0.824811i	$0.691281\pi$
$114$	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
$118$	6.15331	+	4.63312i	0.566458	+	0.426513i
$119$	0.809237			0.0741826
$120$	−1.07711	−	15.4774i	−0.0983262	−	1.41289i
$121$	−5.22596			−0.475087
$122$	−0.824521	−	0.620821i	−0.0746486	−	0.0562065i
$123$	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	$-0.454276\pi$
$127$	−9.54013	−	9.54013i	−0.846550	−	0.846550i	−0.989701	+	0.143151i	$0.954276\pi$
$128$	2.18885	+	11.1000i	0.193469	+	0.981106i
$129$			1.43027i			0.125929i
$130$	−0.756205	+	3.53840i	−0.0663236	+	0.310338i
$131$			19.9501i			1.74305i	0.490353	+	0.871524i	$0.336868\pi$
$131$			19.9501i			1.74305i	−0.490353	+	0.871524i	$0.663132\pi$
$132$	9.56789	−	17.2925i	0.832778	−	1.50512i
$133$	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	−0.990570	−	0.137005i	$-0.956252\pi$
$137$	−9.99072	+	9.99072i	−0.853565	+	0.853565i	0.137005	+	0.990570i	$0.456252\pi$
$138$	−3.82288	+	5.07722i	−0.325425	+	0.432202i
$139$	4.82361			0.409133			0.204567	−	0.978853i	$-0.434421\pi$
$139$	4.82361			0.409133			0.204567	+	0.978853i	$0.434421\pi$
$140$	5.69424	−	4.94273i	0.481251	−	0.417737i
$141$	28.2923			2.38264
$142$	−1.33765	+	1.77655i	−0.112253	+	0.149085i
$143$	−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
$148$	11.3949	+	6.30478i	0.936657	+	0.518249i
$149$			16.3870i			1.34248i	0.741241	+	0.671239i	$0.234238\pi$
$149$			16.3870i			1.34248i	−0.741241	+	0.671239i	$0.765762\pi$
$150$	−14.6864	−	9.23027i	−1.19914	−	0.753649i
$151$		−	13.0755i		−	1.06407i	−0.846723	−	0.532034i	$-0.821428\pi$
$151$		−	13.0755i		−	1.06407i	0.846723	−	0.532034i	$-0.178572\pi$
$152$	−4.25081	+	11.1123i	−0.344786	+	0.901327i
$153$	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	−0.0685237	−	0.997649i	$-0.521829\pi$
$157$	11.6419	−	11.6419i	0.929126	−	0.929126i	0.997649	+	0.0685237i	$0.0218289\pi$
$158$	15.7519	+	11.8603i	1.25315	+	0.943557i
$159$	0.934635			0.0741213
$160$	11.4663	+	5.34068i	0.906494	+	0.422218i
$161$	−3.08879			−0.243430
$162$	−10.1074	−	7.61036i	−0.794115	−	0.597927i
$163$	3.14829	−	3.14829i	0.246593	−	0.246593i	−0.572978	−	0.819571i	$-0.694212\pi$
$163$	3.14829	−	3.14829i	0.246593	−	0.246593i	0.819571	+	0.572978i	$0.194212\pi$
$164$	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	$-0.268229\pi$
$167$	−1.04606	−	1.04606i	−0.0809462	−	0.0809462i	−0.746421	+	0.665474i	$0.768229\pi$
$168$	−4.17969	+	10.9264i	−0.322470	+	0.842988i
$169$		−	11.6908i		−	0.899291i
$170$	1.48425	+	0.317206i	0.113837	+	0.0243286i
$171$			12.6940i			0.970731i
$172$	−1.02032	−	0.564542i	−0.0777989	−	0.0430459i
$173$	8.62879	+	8.62879i	0.656034	+	0.656034i	0.954439	−	0.298405i	$-0.0964546\pi$
$173$	8.62879	+	8.62879i	0.656034	+	0.656034i	−0.298405	+	0.954439i	$0.596455\pi$
$174$	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
$178$	5.95162	−	7.90443i	0.446093	−	0.592462i
$179$	−7.62133			−0.569645			−0.284822	−	0.958580i	$-0.591935\pi$
$179$	−7.62133			−0.569645			−0.284822	+	0.958580i	$0.591935\pi$
$180$	13.4622	+	0.951110i	1.00341	+	0.0708916i
$181$	0.848933			0.0631007			0.0315503	−	0.999502i	$-0.489956\pi$
$181$	0.848933			0.0631007			0.0315503	+	0.999502i	$0.489956\pi$
$182$	1.64108	−	2.17954i	0.121645	−	0.161558i
$183$	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
$188$	−11.1672	+	20.1831i	−0.814454	+	1.47200i
$189$			0.0733998i			0.00533905i
$190$	7.23239	+	11.1639i	0.524692	+	0.809917i
$191$			4.93773i			0.357281i	0.983914	+	0.178641i	$0.0571699\pi$
$191$			4.93773i			0.357281i	−0.983914	+	0.178641i	$0.942830\pi$
$192$	−19.5955	+	1.07262i	−1.41419	+	0.0774095i
$193$	6.49046	+	6.49046i	0.467194	+	0.467194i	0.901004	−	0.433810i	$-0.142831\pi$
$193$	6.49046	+	6.49046i	0.467194	+	0.467194i	−0.433810	+	0.901004i	$0.642831\pi$
$194$	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	−0.936880	−	0.349652i	$-0.886300\pi$
$197$	−8.24214	+	8.24214i	−0.587228	+	0.587228i	0.349652	+	0.936880i	$0.386300\pi$
$198$	13.7334	+	10.3405i	0.975991	+	0.734869i
$199$	−3.15529			−0.223673			−0.111836	−	0.993727i	$-0.535673\pi$
$199$	−3.15529			−0.223673			−0.111836	+	0.993727i	$0.535673\pi$
$200$	12.3815	−	6.83363i	0.875504	−	0.483211i
$201$	32.3306			2.28043
$202$	0.532325	+	0.400813i	0.0374543	+	0.0282011i
$203$	−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
$208$	4.46112	+	1.02265i	0.309323	+	0.0709083i
$209$			16.9441i			1.17205i
$210$	7.11137	+	10.9771i	0.490731	+	0.757495i
$211$			12.2107i			0.840618i	0.907381	+	0.420309i	$0.138078\pi$
$211$			12.2107i			0.840618i	−0.907381	+	0.420309i	$0.861922\pi$
$212$	−0.368909	+	0.666746i	−0.0253367	+	0.0457923i
$213$	−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
$218$	12.1516	−	16.1388i	0.823013	−	1.09306i
$219$	20.4298			1.38052
$220$	17.9696	+	1.26956i	1.21151	+	0.0855937i
$221$	0.549176			0.0369416
$222$	−13.5877	+	18.0461i	−0.911950	+	1.21117i
$223$	−10.1856	+	10.1856i	−0.682080	+	0.682080i	−0.960468	−	0.278389i	$-0.910200\pi$
$223$	−10.1856	+	10.1856i	−0.682080	+	0.682080i	0.278389	+	0.960468i	$0.410200\pi$
$224$	−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	0.954762	+	0.297372i	$0.0961102\pi$
$227$	18.8653	+	18.8653i	1.25213	+	1.25213i	0.297372	+	0.954762i	$0.403890\pi$
$228$	−18.0579	−	9.99137i	−1.19591	−	0.661695i
$229$		−	14.5362i		−	0.960580i	−0.877110	−	0.480290i	$-0.840531\pi$
$229$		−	14.5362i		−	0.960580i	0.877110	−	0.480290i	$-0.159469\pi$
$230$	−5.66527	−	1.21075i	−0.373557	−	0.0798343i
$231$			16.6606i			1.09619i
$232$	−11.0475	−	4.22601i	−0.725302	−	0.277451i
$233$	−21.0073	−	21.0073i	−1.37624	−	1.37624i	−0.850887	−	0.525349i	$-0.823935\pi$
$233$	−21.0073	−	21.0073i	−1.37624	−	1.37624i	−0.525349	−	0.850887i	$-0.676065\pi$
$234$	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
$238$	−0.914252	−	0.688384i	−0.0592622	−	0.0446213i
$239$	17.3400			1.12163			0.560816	−	0.827941i	$-0.310488\pi$
$239$	17.3400			1.12163			0.560816	+	0.827941i	$0.310488\pi$
$240$	−11.9491	+	18.4022i	−0.771309	+	1.18785i
$241$	26.8759			1.73123			0.865615	−	0.500711i	$-0.166928\pi$
$241$	26.8759			1.73123			0.865615	+	0.500711i	$0.166928\pi$
$242$	5.90414	+	4.44550i	0.379532	+	0.285768i
$243$	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
$248$	−15.0447	−	5.75506i	−0.955336	−	0.365446i
$249$			12.4785i			0.790793i
$250$	1.99119	−	15.6855i	0.125934	−	0.992039i
$251$			18.2984i			1.15499i	0.816396	+	0.577493i	$0.195969\pi$
$251$			18.2984i			1.15499i	−0.816396	+	0.577493i	$0.804031\pi$
$252$	−8.90405	−	4.92658i	−0.560902	−	0.310346i
$253$	−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	−0.470434	−	0.882435i	$-0.655903\pi$
$257$	6.60489	−	6.60489i	0.412002	−	0.412002i	0.882435	+	0.470434i	$0.155903\pi$
$258$	1.21667	−	1.61588i	0.0757467	−	0.100600i
$259$	−10.9785			−0.682174
$260$	3.86430	−	3.35431i	0.239654	−	0.208025i
$261$	−12.6199			−0.781151
$262$	16.9707	−	22.5390i	1.04845	−	1.39247i
$263$	8.98275	−	8.98275i	0.553900	−	0.553900i	−0.373664	−	0.927564i	$-0.621899\pi$
$263$	8.98275	−	8.98275i	0.553900	−	0.553900i	0.927564	+	0.373664i	$0.121899\pi$
$264$	−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
$268$	−12.7612	+	23.0639i	−0.779513	+	1.40885i
$269$			0.807155i			0.0492131i	0.999697	+	0.0246066i	$0.00783330\pi$
$269$			0.807155i			0.0492131i	−0.999697	+	0.0246066i	$0.992167\pi$
$270$	−0.0287714	+	0.134626i	−0.00175097	+	0.00819305i
$271$			3.29795i			0.200336i	0.994971	+	0.100168i	$0.0319380\pi$
$271$			3.29795i			0.200336i	−0.994971	+	0.100168i	$0.968062\pi$
$272$	0.428974	−	1.87131i	0.0260103	−	0.113465i
$273$	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	0.261283	−	0.965262i	$-0.415854\pi$
$277$	20.4138	−	20.4138i	1.22655	−	1.22655i	0.965262	−	0.261283i	$-0.0841455\pi$
$278$	−5.44957	−	4.10324i	−0.326844	−	0.246096i
$279$	−17.1860			−1.02890
$280$	−10.6378	+	0.740308i	−0.635728	+	0.0442418i
$281$	4.55009			0.271436			0.135718	−	0.990748i	$-0.456666\pi$
$281$	4.55009			0.271436			0.135718	+	0.990748i	$0.456666\pi$
$282$	−31.9638	−	24.0671i	−1.90342	−	1.43317i
$283$	−1.82990	+	1.82990i	−0.108776	+	0.108776i	−0.759400	−	0.650624i	$-0.774507\pi$
$283$	−1.82990	+	1.82990i	−0.108776	+	0.108776i	0.650624	+	0.759400i	$0.274507\pi$
$284$	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
$288$	1.45490	−	17.0088i	0.0857310	−	1.00226i
$289$			16.7696i			0.986449i
$290$	−11.0988	+	7.19019i	−0.651744	+	0.422222i
$291$			33.8455i			1.98406i
$292$	−8.06382	+	14.5741i	−0.471899	+	0.852886i
$293$	−2.47914	−	2.47914i	−0.144833	−	0.144833i	0.630972	−	0.775805i	$-0.282656\pi$
$293$	−2.47914	−	2.47914i	−0.144833	−	0.144833i	−0.775805	+	0.630972i	$0.782656\pi$
$294$	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
$298$	13.9398	−	18.5136i	0.807508	−	1.07246i
$299$	−2.09616			−0.121224
$300$	8.74042	+	22.9212i	0.504629	+	1.32335i
$301$	0.983040			0.0566615
$302$	−11.1228	+	14.7723i	−0.640044	+	0.850051i
$303$	−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	$-0.307538\pi$
$307$	−4.45472	−	4.45472i	−0.254244	−	0.254244i	−0.822708	+	0.568464i	$0.807538\pi$
$308$	−11.8853	−	6.57610i	−0.677227	−	0.374708i
$309$		−	47.2270i		−	2.68665i
$310$	−15.1146	+	9.79173i	−0.858449	+	0.556133i
$311$		−	4.78019i		−	0.271060i	−0.990773	−	0.135530i	$-0.956726\pi$
$311$		−	4.78019i		−	0.271060i	0.990773	−	0.135530i	$-0.0432737\pi$
$312$	−2.83648	+	7.41501i	−0.160584	+	0.419792i
$313$	−3.52240	−	3.52240i	−0.199098	−	0.199098i	0.600515	−	0.799613i	$-0.294962\pi$
$313$	−3.52240	−	3.52240i	−0.199098	−	0.199098i	−0.799613	+	0.600515i	$0.794962\pi$
$314$	−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	−0.144597	+	0.989491i	$0.546189\pi$
$317$	−20.1919	+	20.1919i	−1.13409	+	1.13409i	−0.989491	+	0.144597i	$0.953811\pi$
$318$	−1.05592	−	0.795054i	−0.0592132	−	0.0445844i
$319$	−16.8453			−0.943154
$320$	−8.41125	−	15.7877i	−0.470203	−	0.882558i
$321$	−10.7229			−0.598496
$322$	3.48962	+	2.62750i	0.194469	+	0.146425i
$323$	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
$328$	1.01055	−	2.64174i	0.0557983	−	0.145866i
$329$		−	19.4456i		−	1.07207i
$330$	−6.53066	+	30.5579i	−0.359501	+	1.68216i
$331$		−	17.6160i		−	0.968260i	−0.874996	−	0.484130i	$-0.839136\pi$
$331$		−	17.6160i		−	0.968260i	0.874996	−	0.484130i	$-0.160864\pi$
$332$	−8.90186	−	4.92537i	−0.488553	−	0.270315i
$333$	−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	0.239742	−	0.970837i	$-0.422937\pi$
$337$	22.2233	−	22.2233i	1.21058	−	1.21058i	0.970837	−	0.239742i	$-0.0770627\pi$
$338$	−9.94486	+	13.2079i	−0.540929	+	0.718416i
$339$	9.56635			0.519573
$340$	−1.40703	−	1.62096i	−0.0763071	−	0.0879090i
$341$	−22.9402			−1.24228
$342$	10.7982	−	14.3413i	0.583900	−	0.775486i
$343$	−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	−0.954755	−	0.297392i	$-0.903883\pi$
$347$	−23.3249	−	23.3249i	−1.25215	−	1.25215i	−0.297392	−	0.954755i	$-0.596117\pi$
$348$	9.93307	−	17.9525i	0.532468	−	0.962355i
$349$		−	7.83755i		−	0.419535i	−0.977751	−	0.209767i	$-0.932729\pi$
$349$		−	7.83755i		−	0.419535i	0.977751	−	0.209767i	$-0.0672706\pi$
$350$	−6.34405	+	10.0941i	−0.339104	+	0.539551i
$351$			0.0498116i			0.00265874i
$352$	1.94203	−	22.7037i	0.103511	−	1.21011i
$353$	21.1022	+	21.1022i	1.12316	+	1.12316i	0.991264	+	0.131892i	$0.0421052\pi$
$353$	21.1022	+	21.1022i	1.12316	+	1.12316i	0.131892	+	0.991264i	$0.457895\pi$
$354$	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
$358$	8.61035	+	6.48314i	0.455071	+	0.342645i
$359$	10.1203			0.534130			0.267065	−	0.963679i	$-0.413946\pi$
$359$	10.1203			0.534130			0.267065	+	0.963679i	$0.413946\pi$
$360$	−14.4001	−	12.5263i	−0.758954	−	0.660192i
$361$	−1.30591			−0.0687321
$362$	−0.959099	−	0.722151i	−0.0504091	−	0.0379554i
$363$	−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	0.976954	+	0.213451i	$0.0684704\pi$
$367$	22.8049	+	22.8049i	1.19040	+	1.19040i	0.213451	+	0.976954i	$0.431530\pi$
$368$	−1.63735	+	7.14262i	−0.0853530	+	0.372335i
$369$		−	3.01775i		−	0.157098i
$370$	−20.1362	−	4.30339i	−1.04683	−	0.223723i
$371$		−	0.642383i		−	0.0333509i
$372$	13.5270	−	24.4481i	0.701345	−	1.26757i
$373$	6.89178	+	6.89178i	0.356843	+	0.356843i	0.862648	−	0.505805i	$-0.168804\pi$
$373$	6.89178	+	6.89178i	0.356843	+	0.356843i	−0.505805	+	0.862648i	$0.668804\pi$
$374$	−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
$378$	0.0624381	−	0.0829249i	0.00321147	−	0.00426520i
$379$	−28.6069			−1.46944			−0.734718	−	0.678373i	$-0.762686\pi$
$379$	−28.6069			−1.46944			−0.734718	+	0.678373i	$0.762686\pi$
$380$	1.32575	−	18.7650i	0.0680096	−	0.962623i
$381$	−33.0968			−1.69560
$382$	4.20031	−	5.57850i	0.214907	−	0.285421i
$383$	−5.18753	+	5.18753i	−0.265070	+	0.265070i	−0.827110	−	0.562040i	$-0.810017\pi$
$383$	−5.18753	+	5.18753i	−0.265070	+	0.265070i	0.562040	+	0.827110i	$0.310017\pi$
$384$	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
$388$	−24.1446	−	13.3591i	−1.22576	−	0.678207i
$389$		−	11.9556i		−	0.606171i	−0.952963	−	0.303086i	$-0.901983\pi$
$389$		−	11.9556i		−	0.606171i	0.952963	−	0.303086i	$-0.0980168\pi$
$390$	4.82602	+	7.44946i	0.244375	+	0.377218i
$391$			0.879276i			0.0444669i
$392$	−10.9824	−	4.20111i	−0.554694	−	0.212188i
$393$	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	−0.262925	−	0.964816i	$-0.584687\pi$
$397$	13.9851	−	13.9851i	0.701891	−	0.701891i	0.964816	+	0.262925i	$0.0846873\pi$
$398$	3.56475	+	2.68407i	0.178685	+	0.134540i
$399$	17.3980			0.870991
$400$	−19.8013	−	2.81198i	−0.990067	−	0.140599i
$401$	12.9974			0.649060			0.324530	−	0.945875i	$-0.394794\pi$
$401$	12.9974			0.649060			0.324530	+	0.945875i	$0.394794\pi$
$402$	−36.5262	−	27.5023i	−1.82176	−	1.37169i
$403$	−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
$408$	3.11038	+	1.18982i	0.153987	+	0.0589048i
$409$		−	4.96260i		−	0.245385i	−0.992445	−	0.122692i	$-0.960847\pi$
$409$		−	4.96260i		−	0.245385i	0.992445	−	0.122692i	$-0.0391529\pi$
$410$	−1.71936	−	2.65401i	−0.0849133	−	0.131072i
$411$			34.6600i			1.70965i
$412$	33.6906	+	18.6409i	1.65982	+	0.918372i
$413$	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
$418$	14.4137	−	19.1430i	0.704995	−	0.936314i
$419$	−19.4749			−0.951409			−0.475705	−	0.879605i	$-0.657807\pi$
$419$	−19.4749			−0.951409			−0.475705	+	0.879605i	$0.657807\pi$
$420$	1.30357	−	18.4510i	0.0636077	−	0.900317i
$421$	−35.8743			−1.74841			−0.874204	−	0.485558i	$-0.838616\pi$
$421$	−35.8743			−1.74841			−0.874204	+	0.485558i	$0.838616\pi$
$422$	10.3871	−	13.7953i	0.505637	−	0.671543i
$423$	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
$428$	4.23244	−	7.64949i	0.204583	−	0.369752i
$429$			11.3065i			0.545881i
$430$	1.80303	+	0.385334i	0.0869500	+	0.0185824i
$431$		−	20.1367i		−	0.969951i	−0.874528	−	0.484975i	$-0.838829\pi$
$431$		−	20.1367i		−	0.969951i	0.874528	−	0.484975i	$-0.161171\pi$
$432$	0.169732	+	0.0389089i	0.00816624	+	0.00187201i
$433$	2.73734	+	2.73734i	0.131548	+	0.131548i	0.769815	−	0.638267i	$-0.220348\pi$
$433$	2.73734	+	2.73734i	0.131548	+	0.131548i	−0.638267	+	0.769815i	$0.720348\pi$
$434$	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
$438$	−23.0810	−	17.3788i	−1.10285	−	0.830389i
$439$	−22.0544			−1.05260			−0.526300	−	0.850299i	$-0.676421\pi$
$439$	−22.0544			−1.05260			−0.526300	+	0.850299i	$0.676421\pi$
$440$	−19.2216	−	16.7203i	−0.916354	−	0.797110i
$441$	−12.5455			−0.597406
$442$	−0.620443	−	0.467160i	−0.0295114	−	0.0222206i
$443$	19.2001	−	19.2001i	0.912225	−	0.912225i	−0.0842223	−	0.996447i	$-0.526841\pi$
$443$	19.2001	−	19.2001i	0.912225	−	0.912225i	0.996447	+	0.0842223i	$0.0268406\pi$
$444$	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
$448$	0.737220	+	13.4682i	0.0348304	+	0.636313i
$449$			21.6592i			1.02216i	0.859533	+	0.511080i	$0.170754\pi$
$449$			21.6592i			1.02216i	−0.859533	+	0.511080i	$0.829246\pi$
$450$	−20.8042	+	4.74605i	−0.980719	+	0.223731i
$451$		−	4.02815i		−	0.189678i
$452$	−3.77592	+	6.82440i	−0.177604	+	0.320993i
$453$	−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	−0.444427	−	0.895815i	$-0.646593\pi$
$457$	9.64959	−	9.64959i	0.451389	−	0.451389i	0.895815	+	0.444427i	$0.146593\pi$
$458$	−12.3653	+	16.4226i	−0.577794	+	0.767377i
$459$	0.0208945			0.000975272
$460$	5.37052	+	6.18707i	0.250402	+	0.288474i
$461$	−20.5463			−0.956935			−0.478468	−	0.878105i	$-0.658808\pi$
$461$	−20.5463			−0.956935			−0.478468	+	0.878105i	$0.658808\pi$
$462$	14.1725	−	18.8227i	0.659364	−	0.875711i
$463$	−24.8325	+	24.8325i	−1.15406	+	1.15406i	−0.168334	+	0.985730i	$0.553839\pi$
$463$	−24.8325	+	24.8325i	−1.15406	+	1.15406i	−0.985730	+	0.168334i	$0.946161\pi$
$464$	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	$-0.0835067\pi$
$467$	15.2663	+	15.2663i	0.706440	+	0.706440i	−0.259345	+	0.965785i	$0.583507\pi$
$468$	−6.04259	−	3.34335i	−0.279319	−	0.154546i
$469$		−	22.2211i		−	1.02608i
$470$	7.62231	−	35.6659i	0.351591	−	1.64515i
$471$		−	40.3884i		−	1.86100i
$472$	−5.50397	+	14.3883i	−0.253341	+	0.662274i
$473$	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
$478$	−19.5902	−	14.7504i	−0.896036	−	0.674668i
$479$	−4.80890			−0.219724			−0.109862	−	0.993947i	$-0.535041\pi$
$479$	−4.80890			−0.219724			−0.109862	+	0.993947i	$0.535041\pi$
$480$	29.1536	−	10.6256i	1.33068	−	0.484992i
$481$	−7.45042			−0.339710
$482$	−30.3636	−	22.8622i	−1.38302	−	1.04134i
$483$	−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	$-0.292367\pi$
$487$	−4.14169	−	4.14169i	−0.187678	−	0.187678i	−0.794691	+	0.607014i	$0.792367\pi$
$488$	0.737512	−	1.92798i	0.0333856	−	0.0872753i
$489$		−	10.9221i		−	0.493914i
$490$	−11.0334	+	7.14782i	−0.498439	+	0.322906i
$491$			36.1178i			1.62997i	0.579480	+	0.814987i	$0.303256\pi$
$491$			36.1178i			1.62997i	−0.579480	+	0.814987i	$0.696744\pi$
$492$	4.29292	+	2.37526i	0.193540	+	0.107085i
$493$	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
$498$	10.6149	−	14.0978i	0.475666	−	0.631739i
$499$	19.6148			0.878078			0.439039	−	0.898468i	$-0.355319\pi$
$499$	19.6148			0.878078			0.439039	+	0.898468i	$0.355319\pi$
$500$	−15.5926	+	16.0272i	−0.697322	+	0.716758i
$501$	−3.62900			−0.162132
$502$	15.5657	−	20.6730i	0.694731	−	0.922682i
$503$	17.4984	−	17.4984i	0.780214	−	0.780214i	−0.199653	−	0.979867i	$-0.563982\pi$
$503$	17.4984	−	17.4984i	0.780214	−	0.780214i	0.979867	+	0.199653i	$0.0639815\pi$
$504$	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
$508$	13.0636	−	23.6105i	0.579604	−	1.04755i
$509$		−	35.9686i		−	1.59428i	−0.603795	−	0.797140i	$-0.706345\pi$
$509$		−	35.9686i		−	1.59428i	0.603795	−	0.797140i	$-0.293655\pi$
$510$	3.12483	−	2.02437i	0.138370	−	0.0896408i
$511$		−	14.0416i		−	0.621163i
$512$	−20.1253	+	10.3428i	−0.889419	+	0.457093i
$513$	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
$518$	12.4032	+	9.33899i	0.544967	+	0.410331i
$519$	29.9352			1.31401
$520$	−7.21914	+	0.502398i	−0.316580	+	0.0220316i
$521$	7.17372			0.314286			0.157143	−	0.987576i	$-0.449772\pi$
$521$	7.17372			0.314286			0.157143	+	0.987576i	$0.449772\pi$
$522$	14.2576	+	10.7352i	0.624037	+	0.469867i
$523$	−24.2846	+	24.2846i	−1.06189	+	1.06189i	−0.0639394	+	0.997954i	$0.520366\pi$
$523$	−24.2846	+	24.2846i	−1.06189	+	1.06189i	−0.997954	+	0.0639394i	$0.979634\pi$
$524$	−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
$528$	38.5266	+	8.83174i	1.67666	+	0.384352i
$529$			19.6439i			0.854082i
$530$	0.251802	−	1.17822i	0.0109376	−	0.0511787i
$531$			16.4362i			0.713270i
$532$	−6.86716	+	12.4113i	−0.297729	+	0.538100i
$533$	−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
$538$	0.686613	−	0.911900i	0.0296020	−	0.0393148i
$539$	−16.7460			−0.721302
$540$	0.147025	−	0.127621i	0.00632696	−	0.00549195i
$541$	−43.7163			−1.87951			−0.939754	−	0.341850i	$-0.888946\pi$
$541$	−43.7163			−1.87951			−0.939754	+	0.341850i	$0.888946\pi$
$542$	2.80542	−	3.72592i	0.120503	−	0.160042i
$543$	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	$-0.210851\pi$
$547$	4.05775	+	4.05775i	0.173497	+	0.173497i	−0.615017	+	0.788514i	$0.710851\pi$
$548$	−24.7256	−	13.6806i	−1.05623	−	0.584407i
$549$		−	2.20239i		−	0.0939957i
$550$	−27.7698	+	6.33512i	−1.18411	+	0.270131i
$551$			17.5908i			0.749395i
$552$	−11.8720	−	4.54144i	−0.505308	−	0.193296i
$553$	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	−0.991550	−	0.129724i	$-0.958591\pi$
$557$	−20.3398	+	20.3398i	−0.861826	+	0.861826i	0.129724	+	0.991550i	$0.458591\pi$
$558$	19.4162	+	14.6194i	0.821955	+	0.618889i
$559$	0.667124			0.0282164
$560$	12.6480	+	8.21271i	0.534474	+	0.347050i
$561$	4.74273			0.200238
$562$	−5.14056	−	3.87057i	−0.216841	−	0.163270i
$563$	8.97565	−	8.97565i	0.378279	−	0.378279i	−0.492202	−	0.870481i	$-0.663808\pi$
$563$	8.97565	−	8.97565i	0.378279	−	0.378279i	0.870481	+	0.492202i	$0.163808\pi$
$564$	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
$568$	−4.15411	−	1.58908i	−0.174302	−	0.0666762i
$569$			0.150643i			0.00631527i	0.999995	+	0.00315763i	$0.00100511\pi$
$569$			0.150643i			0.00631527i	−0.999995	+	0.00315763i	$0.998995\pi$
$570$	31.9105	+	6.81971i	1.33658	+	0.285646i
$571$			4.12312i			0.172547i	0.996271	+	0.0862736i	$0.0274959\pi$
$571$			4.12312i			0.172547i	−0.996271	+	0.0862736i	$0.972504\pi$
$572$	−8.06576	−	4.46276i	−0.337247	−	0.186598i
$573$	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	−0.0480152	+	0.998847i	$0.515290\pi$
$577$	−25.1465	+	25.1465i	−1.04686	+	1.04686i	−0.998847	+	0.0480152i	$0.984710\pi$
$578$	14.2652	−	18.9458i	0.593355	−	0.788043i
$579$	22.5169			0.935768
$580$	18.6555	+	1.31802i	0.774627	+	0.0547276i
$581$	8.57659			0.355817
$582$	28.7910	−	38.2377i	1.19342	−	1.58500i
$583$	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	$-0.0224921\pi$
$587$	22.4571	+	22.4571i	0.926902	+	0.926902i	−0.0706023	+	0.997505i	$0.522492\pi$
$588$	9.87455	−	17.8467i	0.407219	−	0.735987i
$589$			23.9556i			0.987071i
$590$	9.36453	+	14.4551i	0.385532	+	0.595108i
$591$			28.5938i			1.17619i
$592$	−5.81969	+	25.3872i	−0.239188	+	1.04341i
$593$	−31.1826	−	31.1826i	−1.28051	−	1.28051i	−0.940375	−	0.340140i	$-0.889525\pi$
$593$	−31.1826	−	31.1826i	−1.28051	−	1.28051i	−0.340140	−	0.940375i	$-0.610475\pi$
$594$	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
$598$	2.36817	+	1.78311i	0.0968419	+	0.0729168i
$599$	36.9215			1.50857			0.754286	−	0.656546i	$-0.227983\pi$
$599$	36.9215			1.50857			0.754286	+	0.656546i	$0.227983\pi$
$600$	9.62339	−	33.3308i	0.392873	−	1.36072i
$601$	−19.1488			−0.781098			−0.390549	−	0.920582i	$-0.627715\pi$
$601$	−19.1488			−0.781098			−0.390549	+	0.920582i	$0.627715\pi$
$602$	−1.11061	−	0.836231i	−0.0452651	−	0.0340822i
$603$	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	$-0.321807\pi$
$607$	−7.79352	−	7.79352i	−0.316329	−	0.316329i	−0.847355	+	0.531026i	$0.821807\pi$
$608$	−23.7086	−	2.02799i	−0.961511	−	0.0822458i
$609$			17.2965i			0.700890i
$610$	−1.25481	−	1.93693i	−0.0508059	−	0.0784241i
$611$		−	13.1964i		−	0.533871i
$612$	−1.40244	+	2.53469i	−0.0566901	+	0.102459i
$613$	14.3260	+	14.3260i	0.578621	+	0.578621i	0.934523	−	0.355902i	$-0.115826\pi$
$613$	14.3260	+	14.3260i	0.578621	+	0.578621i	−0.355902	+	0.934523i	$0.615826\pi$
$614$	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	−0.305703	−	0.952127i	$-0.598892\pi$
$617$	16.0568	−	16.0568i	0.646423	−	0.646423i	0.952127	+	0.305703i	$0.0988916\pi$
$618$	−40.1740	+	53.3557i	−1.61604	+	2.14628i
$619$	−13.0984			−0.526468			−0.263234	−	0.964732i	$-0.584789\pi$
$619$	−13.0984			−0.526468			−0.263234	+	0.964732i	$0.584789\pi$
$620$	25.4054	+	1.79490i	1.02031	+	0.0720849i
$621$	−0.0797525			−0.00320036
$622$	−4.06630	+	5.40052i	−0.163044	+	0.216541i
$623$	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
$628$	28.8121	+	15.9416i	1.14973	+	0.636141i
$629$			3.12523i			0.124611i
$630$	15.7345	+	3.36269i	0.626879	+	0.133973i
$631$			28.9292i			1.15165i	0.817572	+	0.575826i	$0.195320\pi$
$631$			28.9292i			1.15165i	−0.817572	+	0.575826i	$0.804680\pi$
$632$	−14.0896	+	36.8326i	−0.560455	+	1.46512i
$633$	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
$638$	19.0313	+	14.3296i	0.753456	+	0.567312i
$639$	−4.74537			−0.187724
$640$	−3.92712	+	24.9916i	−0.155233	+	0.987878i
$641$	−6.06791			−0.239668			−0.119834	−	0.992794i	$-0.538236\pi$
$641$	−6.06791			−0.239668			−0.119834	+	0.992794i	$0.538236\pi$
$642$	12.1145	+	9.12155i	0.478120	+	0.359999i
$643$	−27.8619	+	27.8619i	−1.09877	+	1.09877i	−0.104210	+	0.994555i	$0.533232\pi$
$643$	−27.8619	+	27.8619i	−1.09877	+	1.09877i	−0.994555	+	0.104210i	$0.966768\pi$
$644$	−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	$-0.273474\pi$
$647$	−2.65043	−	2.65043i	−0.104199	−	0.104199i	−0.757284	+	0.653085i	$0.773474\pi$
$648$	9.04083	−	23.6342i	0.355157	−	0.928438i
$649$			21.9394i			0.861195i
$650$	−4.30529	+	6.85018i	−0.168867	+	0.268686i
$651$			23.5547i			0.923183i
$652$	7.79157	+	4.31105i	0.305141	+	0.168834i
$653$	20.0573	+	20.0573i	0.784903	+	0.784903i	0.980654	−	0.195751i	$-0.0627144\pi$
$653$	20.0573	+	20.0573i	0.784903	+	0.784903i	−0.195751	+	0.980654i	$0.562714\pi$
$654$	−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
$658$	−16.5415	+	21.9690i	−0.644856	+	0.856443i
$659$	−12.2990			−0.479101			−0.239550	−	0.970884i	$-0.577000\pi$
$659$	−12.2990			−0.479101			−0.239550	+	0.970884i	$0.577000\pi$
$660$	33.3725	−	28.9681i	1.29902	−	1.12758i
$661$	4.67919			0.181999			0.0909997	−	0.995851i	$-0.470994\pi$
$661$	4.67919			0.181999			0.0909997	+	0.995851i	$0.470994\pi$
$662$	−14.9851	+	19.9020i	−0.582414	+	0.773513i
$663$	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
$668$	1.43240	−	2.58884i	0.0554211	−	0.100165i
$669$			35.3362i			1.36617i
$670$	8.71028	−	40.7567i	0.336507	−	1.57457i
$671$		−	2.93979i		−	0.113489i
$672$	−23.3119	−	1.99406i	−0.899277	−	0.0769224i
$673$	0.936252	+	0.936252i	0.0360899	+	0.0360899i	0.724921	−	0.688832i	$-0.241876\pi$
$673$	0.936252	+	0.936252i	0.0360899	+	0.0360899i	−0.688832	+	0.724921i	$0.741876\pi$
$674$	−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	−0.0766377	−	0.997059i	$-0.524418\pi$
$677$	23.9486	−	23.9486i	0.920421	−	0.920421i	0.997059	+	0.0766377i	$0.0244185\pi$
$678$	−10.8078	−	8.13768i	−0.415070	−	0.312526i
$679$	23.2623			0.892727
$680$	0.210741	+	3.02822i	0.00808156	+	0.116127i
$681$	65.4479			2.50797
$682$	25.9172	+	19.5143i	0.992420	+	0.747240i
$683$	−7.26579	+	7.26579i	−0.278018	+	0.278018i	−0.832317	−	0.554300i	$-0.812986\pi$
$683$	−7.26579	+	7.26579i	−0.278018	+	0.278018i	0.554300	+	0.832317i	$0.312986\pi$
$684$	−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
$688$	0.521106	−	2.27322i	0.0198670	−	0.0866656i
$689$		−	0.435943i		−	0.0166081i
$690$	−11.9272	+	7.72686i	−0.454061	+	0.294157i
$691$		−	26.3604i		−	1.00280i	−0.865217	−	0.501398i	$-0.832819\pi$
$691$		−	26.3604i		−	1.00280i	0.865217	−	0.501398i	$-0.167181\pi$
$692$	−11.8157	+	21.3550i	−0.449165	+	0.811796i
$693$	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
$698$	−6.66707	+	8.85464i	−0.252352	+	0.335153i
$699$	−72.8791			−2.75654
$700$	15.7539	−	6.00737i	0.595443	−	0.227057i
$701$	15.9649			0.602986			0.301493	−	0.953468i	$-0.402515\pi$
$701$	15.9649			0.602986			0.301493	+	0.953468i	$0.402515\pi$
$702$	0.0423726	−	0.0562757i	0.00159925	−	0.00212399i
$703$	−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
$708$	−23.3814	−	12.9369i	−0.878728	−	0.486198i
$709$		−	35.8367i		−	1.34587i	−0.739700	−	0.672937i	$-0.765033\pi$
$709$		−	35.8367i		−	1.34587i	0.739700	−	0.672937i	$-0.234967\pi$
$710$	−4.17341	+	2.70368i	−0.156625	+	0.101467i
$711$			42.0750i			1.57794i
$712$	18.4829	+	7.07030i	0.692676	+	0.264971i
$713$	−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
$718$	−11.4336	−	8.60892i	−0.426699	−	0.321282i
$719$	−38.4310			−1.43324			−0.716618	−	0.697466i	$-0.754311\pi$
$719$	−38.4310			−1.43324			−0.716618	+	0.697466i	$0.754311\pi$
$720$	5.61330	+	26.4014i	0.209195	+	0.983922i
$721$	−32.4596			−1.20886
$722$	1.47538	+	1.11088i	0.0549079	+	0.0413427i
$723$	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	$-0.194837\pi$
$727$	6.57510	+	6.57510i	0.243857	+	0.243857i	−0.574587	+	0.818444i	$0.694837\pi$
$728$	5.09641	+	1.94954i	0.188885	+	0.0722547i
$729$		−	27.3185i		−	1.01180i
$730$	5.50404	−	25.7542i	0.203714	−	0.953207i
$731$		−	0.279839i		−	0.0103502i
$732$	3.13303	+	1.73349i	0.115800	+	0.0640718i
$733$	−22.4799	−	22.4799i	−0.830315	−	0.830315i	0.157245	−	0.987560i	$-0.449739\pi$
$733$	−22.4799	−	22.4799i	−0.830315	−	0.830315i	−0.987560	+	0.157245i	$0.949739\pi$
$734$	−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
$738$	−2.56707	+	3.40936i	−0.0944951	+	0.125500i
$739$	−27.7449			−1.02061			−0.510307	−	0.859992i	$-0.670468\pi$
$739$	−27.7449			−1.02061			−0.510307	+	0.859992i	$0.670468\pi$
$740$	19.0886	+	21.9909i	0.701710	+	0.808400i
$741$	11.8069			0.433737
$742$	−0.546448	+	0.725745i	−0.0200607	+	0.0266430i
$743$	9.61246	−	9.61246i	0.352647	−	0.352647i	−0.508447	−	0.861094i	$-0.669780\pi$
$743$	9.61246	−	9.61246i	0.352647	−	0.352647i	0.861094	+	0.508447i	$0.169780\pi$
$744$	−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
$748$	−1.87200	+	3.38335i	−0.0684471	+	0.123708i
$749$			7.36998i			0.269293i
$750$	−23.7543	−	30.6622i	−0.867385	−	1.11962i
$751$		−	33.9677i		−	1.23950i	−0.784799	−	0.619750i	$-0.787234\pi$
$751$		−	33.9677i		−	1.23950i	0.784799	−	0.619750i	$-0.212766\pi$
$752$	−44.9666	−	10.3080i	−1.63976	−	0.375895i
$753$	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	−0.422983	−	0.906138i	$-0.639017\pi$
$757$	13.2933	−	13.2933i	0.483154	−	0.483154i	0.906138	+	0.422983i	$0.139017\pi$
$758$	32.3192	+	24.3347i	1.17389	+	0.883874i
$759$	−18.1026			−0.657083
$760$	−17.4604	+	20.0724i	−0.633354	+	0.728101i
$761$	36.5509			1.32497			0.662485	−	0.749075i	$-0.269502\pi$
$761$	36.5509			1.32497			0.662485	+	0.749075i	$0.269502\pi$
$762$	37.3918	+	28.1541i	1.35456	+	1.01991i
$763$	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
$768$	−12.8934	−	37.0716i	−0.465250	−	1.33771i
$769$		−	30.4508i		−	1.09808i	−0.835794	−	0.549042i	$-0.814993\pi$
$769$		−	30.4508i		−	1.09808i	0.835794	−	0.549042i	$-0.185007\pi$
$770$	21.0028	+	4.48858i	0.756887	+	0.161757i
$771$		−	22.9138i		−	0.825221i
$772$	−8.88760	+	16.0630i	−0.319872	+	0.578120i
$773$	−25.5875	−	25.5875i	−0.920320	−	0.920320i	0.0767318	−	0.997052i	$-0.475551\pi$
$773$	−25.5875	−	25.5875i	−0.920320	−	0.920320i	−0.997052	+	0.0767318i	$0.975551\pi$
$774$	−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
$778$	−10.1701	+	13.5070i	−0.364615	+	0.484251i
$779$	−4.20643			−0.150711
$780$	0.884647	−	12.5215i	0.0316754	−	0.448341i
$781$	−6.33422			−0.226656
$782$	0.747963	−	0.993380i	0.0267471	−	0.0355232i
$783$	−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	$-0.0776753\pi$
$787$	20.4444	+	20.4444i	0.728764	+	0.728764i	−0.241609	+	0.970374i	$0.577675\pi$
$788$	−20.3981	−	11.2862i	−0.726653	−	0.402055i
$789$		−	31.1631i		−	1.10944i
$790$	23.9723	+	37.0037i	0.852895	+	1.31653i
$791$		−	6.57504i		−	0.233781i
$792$	−12.2842	+	32.1128i	−0.436499	+	1.14108i
$793$	−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	−0.554940	−	0.831891i	$-0.687259\pi$
$797$	7.81866	−	7.81866i	0.276951	−	0.276951i	0.831891	+	0.554940i	$0.187259\pi$
$798$	−19.6558	−	14.7998i	−0.695807	−	0.523906i
$799$	−5.53552			−0.195833
$800$	19.9789	+	20.0210i	0.706362	+	0.707851i
$801$	21.1136			0.746014
$802$	−14.6841	−	11.0564i	−0.518514	−	0.390413i
$803$	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
$808$	−0.476151	+	1.24473i	−0.0167509	+	0.0437896i
$809$			15.2368i			0.535698i	0.963461	+	0.267849i	$0.0863129\pi$
$809$			15.2368i			0.535698i	−0.963461	+	0.267849i	$0.913687\pi$
$810$	−15.3822	−	23.7440i	−0.540475	−	0.834279i
$811$		−	13.6670i		−	0.479912i	−0.970784	−	0.239956i	$-0.922867\pi$
$811$		−	13.6670i		−	0.479912i	0.970784	−	0.239956i	$-0.0771330\pi$
$812$	−12.3389	−	6.82709i	−0.433011	−	0.239584i
$813$	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
$818$	−4.22148	+	5.60660i	−0.147600	+	0.196030i
$819$	5.82179			0.203430
$820$	−0.315172	+	4.46102i	−0.0110063	+	0.155785i
$821$	−28.7443			−1.00318			−0.501591	−	0.865105i	$-0.667252\pi$
$821$	−28.7443			−1.00318			−0.501591	+	0.865105i	$0.667252\pi$
$822$	29.4838	−	39.1579i	1.02837	−	1.36579i
$823$	−7.37471	+	7.37471i	−0.257066	+	0.257066i	−0.823860	−	0.566794i	$-0.808184\pi$
$823$	−7.37471	+	7.37471i	−0.257066	+	0.257066i	0.566794	+	0.823860i	$0.308184\pi$
$824$	−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	$-0.120237\pi$
$827$	16.1240	+	16.1240i	0.560686	+	0.560686i	−0.368817	+	0.929502i	$0.620237\pi$
$828$	5.35298	−	9.67469i	0.186029	−	0.336219i
$829$		−	49.1497i		−	1.70704i	−0.521060	−	0.853520i	$-0.674463\pi$
$829$		−	49.1497i		−	1.70704i	0.521060	−	0.853520i	$-0.325537\pi$
$830$	15.7307	+	3.36187i	0.546020	+	0.116692i
$831$		−	70.8199i		−	2.45672i
$832$	0.500303	+	9.13998i	0.0173449	+	0.316872i
$833$	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
$838$	22.0021	+	16.5664i	0.760051	+	0.572278i
$839$	−17.6328			−0.608751			−0.304376	−	0.952552i	$-0.598448\pi$
$839$	−17.6328			−0.608751			−0.304376	+	0.952552i	$0.598448\pi$
$840$	−17.1682	+	19.7365i	−0.592360	+	0.680974i
$841$	11.5118			0.396958
$842$	40.5298	+	30.5168i	1.39675	+	1.05168i
$843$	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
$848$	−1.48547	−	0.340525i	−0.0510112	−	0.0116937i
$849$			6.34833i			0.217874i
$850$	2.87345	+	1.80594i	0.0985586	+	0.0619434i
$851$		−	11.9287i		−	0.408912i
$852$	3.73507	−	6.75057i	0.127961	−	0.231271i
$853$	−21.5659	−	21.5659i	−0.738403	−	0.738403i	0.233866	−	0.972269i	$-0.424862\pi$
$853$	−21.5659	−	21.5659i	−0.738403	−	0.738403i	−0.972269	+	0.233866i	$0.924862\pi$
$854$	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	−0.999999	−	0.00169682i	$-0.999460\pi$
$857$	−29.2248	+	29.2248i	−0.998302	+	0.998302i	0.00169682	+	0.999999i	$0.499460\pi$
$858$	9.61793	−	12.7737i	0.328351	−	0.436087i
$859$	−21.4596			−0.732191			−0.366095	−	0.930577i	$-0.619306\pi$
$859$	−21.4596			−0.732191			−0.366095	+	0.930577i	$0.619306\pi$
$860$	−1.70923	−	1.96910i	−0.0582842	−	0.0671459i
$861$	−4.13605			−0.140956
$862$	−17.1294	+	22.7498i	−0.583431	+	0.774863i
$863$	15.8786	−	15.8786i	0.540514	−	0.540514i	−0.383166	−	0.923680i	$-0.625166\pi$
$863$	15.8786	−	15.8786i	0.540514	−	0.540514i	0.923680	+	0.383166i	$0.125166\pi$
$864$	−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
$868$	−16.8034	−	9.29726i	−0.570344	−	0.315570i
$869$			56.1626i			1.90518i
$870$	−6.77992	+	31.7243i	−0.229861	+	1.07555i
$871$		−	15.0800i		−	0.510967i
$872$	37.7373	+	14.4357i	1.27795	+	0.488855i
$873$	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	−0.334717	−	0.942319i	$-0.608641\pi$
$877$	17.9936	−	17.9936i	0.607601	−	0.607601i	0.942319	+	0.334717i	$0.108641\pi$
$878$	24.9164	+	18.7607i	0.840888	+	0.633145i
$879$	−8.60067			−0.290094
$880$	7.49274	+	35.2411i	0.252580	+	1.18798i
$881$	−5.90202			−0.198844			−0.0994221	−	0.995045i	$-0.531699\pi$
$881$	−5.90202			−0.198844			−0.0994221	+	0.995045i	$0.531699\pi$
$882$	14.1736	+	10.6720i	0.477249	+	0.359343i
$883$	−17.8376	+	17.8376i	−0.600283	+	0.600283i	−0.940387	−	0.340105i	$-0.889537\pi$
$883$	−17.8376	+	17.8376i	−0.600283	+	0.600283i	0.340105	+	0.940387i	$0.389537\pi$
$884$	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	$-0.220252\pi$
$887$	3.93049	+	3.93049i	0.131973	+	0.131973i	−0.638035	+	0.770008i	$0.720252\pi$
$888$	−42.1971	−	16.1417i	−1.41604	−	0.541681i
$889$			22.7477i			0.762935i
$890$	18.5688	−	12.0295i	0.622427	−	0.403230i
$891$		−	36.0376i		−	1.20730i
$892$	−25.2080	−	13.9475i	−0.844025	−	0.466997i
$893$	−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
$898$	18.4245	−	24.4699i	0.614835	−	0.816571i
$899$	−23.8158			−0.794301
$900$	27.5412	+	12.3353i	0.918041	+	0.411177i
$901$	−0.182865			−0.00609213
$902$	−3.42657	+	4.55088i	−0.114092	+	0.151528i
$903$	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	−0.906745	−	0.421678i	$-0.861441\pi$
$907$	−40.0074	−	40.0074i	−1.32842	−	1.32842i	−0.421678	−	0.906745i	$-0.638559\pi$
$908$	−25.8329	+	46.6890i	−0.857294	+	1.54943i
$909$			1.42190i			0.0471615i
$910$	5.12009	−	3.31697i	0.169729	−	0.109956i
$911$			38.8693i			1.28780i	0.765110	+	0.643899i	$0.222684\pi$
$911$			38.8693i			1.28780i	−0.765110	+	0.643899i	$0.777316\pi$
$912$	9.22263	−	40.2318i	0.305392	−	1.33221i
$913$	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
$918$	−0.0236060	−	0.0177741i	−0.000779114	−	0.000586632i
$919$	39.1154			1.29030			0.645149	−	0.764057i	$-0.276795\pi$
$919$	39.1154			1.29030			0.645149	+	0.764057i	$0.276795\pi$
$920$	−0.804381	−	11.5584i	−0.0265196	−	0.381071i
$921$	−15.4544			−0.509240
$922$	23.2126	+	17.4778i	0.764465	+	0.575602i
$923$	−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
$928$	2.01615	−	23.5703i	0.0661835	−	0.773732i
$929$		−	47.6946i		−	1.56481i	−0.622771	−	0.782404i	$-0.713993\pi$
$929$		−	47.6946i		−	1.56481i	0.622771	−	0.782404i	$-0.286007\pi$
$930$	−9.23303	+	43.2027i	−0.302763	+	1.41667i
$931$			17.4872i			0.573120i
$932$	28.7660	−	51.9902i	0.942262	−	1.70300i
$933$	−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	−0.123180	−	0.992384i	$-0.539309\pi$
$937$	26.6067	−	26.6067i	0.869204	−	0.869204i	0.992384	+	0.123180i	$0.0393094\pi$
$938$	−18.9026	+	25.1048i	−0.617191	+	0.819700i
$939$	−12.2200			−0.398784
$940$	−38.9510	+	33.8104i	−1.27044	+	1.10277i
$941$	−41.7503			−1.36102			−0.680511	−	0.732738i	$-0.738242\pi$
$941$	−41.7503			−1.36102			−0.680511	+	0.732738i	$0.738242\pi$
$942$	−34.3567	+	45.6296i	−1.11940	+	1.48669i
$943$	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	$-0.392822\pi$
$947$	−18.8783	−	18.8783i	−0.613463	−	0.613463i	−0.943847	+	0.330384i	$0.892822\pi$
$948$	−59.8541	−	33.1171i	−1.94397	−	1.07559i
$949$		−	9.52910i		−	0.309328i
$950$	6.61552	+	28.9990i	0.214636	+	0.940850i
$951$			70.0500i			2.27153i
$952$	0.817774	−	2.13779i	0.0265042	−	0.0692863i
$953$	8.80988	+	8.80988i	0.285380	+	0.285380i	0.835250	−	0.549870i	$-0.185323\pi$
$953$	8.80988	+	8.80988i	0.285380	+	0.285380i	−0.549870	+	0.835250i	$0.685323\pi$
$954$	−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
$958$	5.43295	+	4.09072i	0.175531	+	0.132165i
$959$	23.8222			0.769258
$960$	−41.9757	−	12.7952i	−1.35476	−	0.412964i
$961$	−1.43278			−0.0462187
$962$	8.41726	+	6.33775i	0.271383	+	0.204337i
$963$	−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	$-0.317994\pi$
$967$	−9.32272	−	9.32272i	−0.299799	−	0.299799i	−0.840935	+	0.541136i	$0.817994\pi$
$968$	−5.28109	+	13.8056i	−0.169741	+	0.443730i
$969$		−	4.95265i		−	0.159102i
$970$	42.6664	+	9.11842i	1.36994	+	0.292775i
$971$		−	41.5696i		−	1.33403i	−0.745043	−	0.667016i	$-0.767571\pi$
$971$		−	41.5696i		−	1.33403i	0.745043	−	0.667016i	$-0.232429\pi$
$972$	38.6349	+	21.3766i	1.23921	+	0.685654i
$973$	−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	−0.916418	−	0.400222i	$-0.868933\pi$
$977$	−16.1348	+	16.1348i	−0.516197	+	0.516197i	0.400222	+	0.916418i	$0.368933\pi$
$978$	−9.29097	+	12.3395i	−0.297092	+	0.394573i
$979$	28.1829			0.900729
$980$	18.5456	+	1.31025i	0.592416	+	0.0418544i
$981$	43.1085			1.37635
$982$	30.7239	−	40.8048i	0.980438	−	1.30213i
$983$	1.26930	−	1.26930i	0.0404842	−	0.0404842i	−0.686575	−	0.727059i	$-0.740887\pi$
$983$	1.26930	−	1.26930i	0.0404842	−	0.0404842i	0.727059	+	0.686575i	$0.240887\pi$
$984$	−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
$988$	−4.66029	+	8.42276i	−0.148264	+	0.267964i
$989$			1.06812i			0.0339643i
$990$	20.9004	+	32.2620i	0.664260	+	1.02535i
$991$		−	42.1399i		−	1.33862i	−0.742985	−	0.669308i	$-0.766590\pi$
$991$		−	42.1399i		−	1.33862i	0.742985	−	0.669308i	$-0.233410\pi$
$992$	2.74564	−	32.0984i	0.0871741	−	1.01913i
$993$	−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	−0.00595958	−	0.999982i	$-0.501897\pi$
$997$	31.3866	−	31.3866i	0.994023	−	0.994023i	0.999982	+	0.00595958i	$0.00189701\pi$
$998$	−22.1602	−	16.6855i	−0.701469	−	0.528169i
$999$	−0.283466			−0.00896847

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.k.c.83.11	✓	108	1.1	even	1	trivial
820.2.k.c.83.38	yes	108	4.3	odd	2	inner
820.2.k.c.247.11	yes	108	20.7	even	4	inner
820.2.k.c.247.38	yes	108	5.2	odd	4	inner

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+(-1.12977 - 0.850658i) 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} +(1.01055 - 2.64174i) q^{8} -3.01775i q^{9} +(-1.71936 - 2.65401i) q^{10} -4.02815i q^{11} +(4.29292 + 2.37526i) 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} +(-2.56707 + 3.40936i) q^{18} -4.20643 q^{19} +(-0.315172 + 4.46102i) q^{20} -4.13605 q^{21} +(-3.42657 + 4.55088i) 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} +(1.63254 - 2.95056i) q^{28} -4.18189i q^{29} +(-7.58610 - 1.62126i) q^{30} -5.69498i q^{31} +(5.63627 + 0.482116i) 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} +(4.75231 + 3.57824i) q^{38} -2.80687 q^{39} +(4.15087 - 4.77182i) q^{40} +1.00000 q^{41} +(4.67279 + 3.51836i) 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} +(-2.19251 + 9.56435i) q^{48} -4.15725i q^{49} +(-1.57271 - 6.89395i) q^{50} +1.17740i q^{51} +(1.10790 - 2.00235i) 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} +(-3.55736 + 4.72458i) q^{58} -5.44652 q^{59} +(7.19142 + 8.28483i) q^{60} +0.729813 q^{61} +(-4.84448 + 6.43402i) 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} +(-0.839928 - 0.464730i) q^{68} -4.49403i q^{69} +(-1.11431 + 5.21400i) q^{70} -1.57249i q^{71} +(-7.97210 - 3.04958i) 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} +(3.17112 + 2.38768i) q^{78} -13.9425 q^{79} +(-8.74872 + 1.86010i) q^{80} +8.94645 q^{81} +(-1.12977 - 0.850658i) 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} +(-10.6413 - 4.07064i) q^{88} +6.99649i q^{89} +(-8.00914 + 5.18860i) q^{90} +1.92919i q^{91} +(3.20593 + 1.77383i) 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} +(-3.53640 + 4.69674i) 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

Modular forms

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Database

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