LMFDB - Embedded newform 840.2.u.e.629.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(629,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.629"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.u (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [160,0,0,-24,0,0,0,0,-32,0,0,0,0,0,-48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(15)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$160$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			629.12
Character	$\chi$	$=$	840.629
Dual form			840.2.u.e.629.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.29842 - 0.560458i) q^{2} +(0.135991 + 1.72670i) q^{3} +(1.37177 + 1.45542i) q^{4} +(1.93600 + 1.11889i) q^{5} +(0.791172 - 2.31820i) q^{6} +(2.16054 + 1.52711i) q^{7} +(-0.965432 - 2.65856i) q^{8} +(-2.96301 + 0.469633i) q^{9} +(-1.88664 - 2.53783i) q^{10} -4.91211 q^{11} +(-2.32653 + 2.56657i) q^{12} +3.98673i q^{13} +(-1.94940 - 3.19372i) q^{14} +(-1.66871 + 3.49505i) q^{15} +(-0.236479 + 3.99300i) q^{16} +0.676832i q^{17} +(4.11044 + 1.05087i) q^{18} -5.93148 q^{19} +(1.02729 + 4.35255i) q^{20} +(-2.34306 + 3.93828i) q^{21} +(6.37797 + 2.75303i) q^{22} +1.13099 q^{23} +(4.45926 - 2.02856i) q^{24} +(2.49617 + 4.33234i) q^{25} +(2.23440 - 5.17643i) q^{26} +(-1.21386 - 5.05238i) q^{27} +(0.741180 + 5.23934i) q^{28} +2.19038 q^{29} +(4.12552 - 3.60279i) q^{30} -4.17468i q^{31} +(2.54496 - 5.05205i) q^{32} +(-0.668004 - 8.48176i) q^{33} +(0.379336 - 0.878810i) q^{34} +(2.47412 + 5.37389i) q^{35} +(-4.74809 - 3.66819i) q^{36} -7.89938 q^{37} +(7.70154 + 3.32435i) q^{38} +(-6.88390 + 0.542160i) q^{39} +(1.10556 - 6.22718i) q^{40} -1.89178 q^{41} +(5.24951 - 3.80035i) q^{42} +9.82318 q^{43} +(-6.73830 - 7.14917i) q^{44} +(-6.26185 - 2.40608i) q^{45} +(-1.46850 - 0.633873i) q^{46} -10.1570i q^{47} +(-6.92689 + 0.134684i) q^{48} +(2.33585 + 6.59877i) q^{49} +(-0.812970 - 7.02418i) q^{50} +(-1.16869 + 0.0920432i) q^{51} +(-5.80235 + 5.46888i) q^{52} +13.0881i q^{53} +(-1.25555 + 7.24041i) q^{54} +(-9.50983 - 5.49611i) q^{55} +(1.97407 - 7.21824i) q^{56} +(-0.806630 - 10.2419i) q^{57} +(-2.84403 - 1.22762i) q^{58} +5.42133i q^{59} +(-7.37586 + 2.36574i) q^{60} +10.1704 q^{61} +(-2.33974 + 5.42048i) q^{62} +(-7.11888 - 3.51020i) q^{63} +(-6.13588 + 5.13332i) q^{64} +(-4.46071 + 7.71829i) q^{65} +(-3.88632 + 11.3872i) q^{66} +4.83299 q^{67} +(-0.985073 + 0.928459i) q^{68} +(0.153805 + 1.95289i) q^{69} +(-0.200597 - 8.36420i) q^{70} +1.84999i q^{71} +(4.10914 + 7.42395i) q^{72} +9.95203 q^{73} +(10.2567 + 4.42727i) q^{74} +(-7.14121 + 4.89930i) q^{75} +(-8.13665 - 8.63278i) q^{76} +(-10.6128 - 7.50135i) q^{77} +(9.24203 + 3.15419i) q^{78} -9.58477 q^{79} +(-4.92556 + 7.46585i) q^{80} +(8.55889 - 2.78306i) q^{81} +(2.45632 + 1.06027i) q^{82} -10.5193 q^{83} +(-8.94599 + 1.99230i) q^{84} +(-0.757301 + 1.31034i) q^{85} +(-12.7546 - 5.50548i) q^{86} +(0.297873 + 3.78214i) q^{87} +(4.74231 + 13.0591i) q^{88} -5.53129 q^{89} +(6.78199 + 6.63360i) q^{90} +(-6.08819 + 8.61348i) q^{91} +(1.55146 + 1.64606i) q^{92} +(7.20844 - 0.567720i) q^{93} +(-5.69255 + 13.1880i) q^{94} +(-11.4833 - 6.63668i) q^{95} +(9.06948 + 3.70736i) q^{96} +7.68488 q^{97} +(0.665433 - 9.87710i) q^{98} +(14.5546 - 2.30689i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 24 q^{4} - 32 q^{9} - 48 q^{15} - 104 q^{16} - 16 q^{25} - 32 q^{30} + 48 q^{36} - 64 q^{39} - 64 q^{46} + 144 q^{49} + 16 q^{60} - 72 q^{64} + 8 q^{70} - 96 q^{79} + 16 q^{81} - 72 q^{84}+O(q^{100}) $ 160 * q - 24 * q^4 - 32 * q^9 - 48 * q^15 - 104 * q^16 - 16 * q^25 - 32 * q^30 + 48 * q^36 - 64 * q^39 - 64 * q^46 + 144 * q^49 + 16 * q^60 - 72 * q^64 + 8 * q^70 - 96 * q^79 + 16 * q^81 - 72 * q^84

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.29842	−	0.560458i	−0.918119	−	0.396304i
$2$	−1.29842	−	0.560458i	−0.918119	−	0.396304i
$3$	0.135991	+	1.72670i	0.0785146	+	0.996913i
$3$	0.135991	+	1.72670i	0.0785146	+	0.996913i
$4$	1.37177	+	1.45542i	0.685886	+	0.727709i
$5$	1.93600	+	1.11889i	0.865804	+	0.500383i
$5$	1.93600	+	1.11889i	0.865804	+	0.500383i
$6$	0.791172	−	2.31820i	0.322995	−	0.946401i
$7$	2.16054	+	1.52711i	0.816607	+	0.577195i
$7$	2.16054	+	1.52711i	0.816607	+	0.577195i
$8$	−0.965432	−	2.65856i	−0.341332	−	0.939943i
$9$	−2.96301	+	0.469633i	−0.987671	+	0.156544i
$10$	−1.88664	−	2.53783i	−0.596608	−	0.802533i
$11$	−4.91211			−1.48106			−0.740528	−	0.672025i	$-0.765425\pi$
$11$	−4.91211			−1.48106			−0.740528	+	0.672025i	$0.765425\pi$
$12$	−2.32653	+	2.56657i	−0.671610	+	0.740905i
$13$			3.98673i			1.10572i	0.833274	+	0.552860i	$0.186463\pi$
$13$			3.98673i			1.10572i	−0.833274	+	0.552860i	$0.813537\pi$
$14$	−1.94940	−	3.19372i	−0.520998	−	0.853558i
$15$	−1.66871	+	3.49505i	−0.430860	+	0.902419i
$16$	−0.236479	+	3.99300i	−0.0591197	+	0.998251i
$17$			0.676832i			0.164156i	0.996626	+	0.0820779i	$0.0261556\pi$
$17$			0.676832i			0.164156i	−0.996626	+	0.0820779i	$0.973844\pi$
$18$	4.11044	+	1.05087i	0.968839	+	0.247691i
$19$	−5.93148			−1.36078			−0.680388	−	0.732852i	$-0.738189\pi$
$19$	−5.93148			−1.36078			−0.680388	+	0.732852i	$0.738189\pi$
$20$	1.02729	+	4.35255i	0.229710	+	0.973259i
$21$	−2.34306	+	3.93828i	−0.511297	+	0.859404i
$22$	6.37797	+	2.75303i	1.35979	+	0.586949i
$23$	1.13099			0.235828			0.117914	−	0.993024i	$-0.462379\pi$
$23$	1.13099			0.235828			0.117914	+	0.993024i	$0.462379\pi$
$24$	4.45926	−	2.02856i	0.910242	−	0.414077i
$25$	2.49617	+	4.33234i	0.499233	+	0.866468i
$26$	2.23440	−	5.17643i	0.438201	−	1.01518i
$27$	−1.21386	−	5.05238i	−0.233608	−	0.972331i
$28$	0.741180	+	5.23934i	0.140070	+	0.990142i
$29$	2.19038			0.406743			0.203372	−	0.979102i	$-0.434810\pi$
$29$	2.19038			0.406743			0.203372	+	0.979102i	$0.434810\pi$
$30$	4.12552	−	3.60279i	0.753213	−	0.657776i
$31$		−	4.17468i		−	0.749795i	−0.927066	−	0.374897i	$-0.877678\pi$
$31$		−	4.17468i		−	0.749795i	0.927066	−	0.374897i	$-0.122322\pi$
$32$	2.54496	−	5.05205i	0.449890	−	0.893084i
$33$	−0.668004	−	8.48176i	−0.116285	−	1.47648i
$34$	0.379336	−	0.878810i	0.0650556	−	0.150715i
$35$	2.47412	+	5.37389i	0.418203	+	0.908354i
$36$	−4.74809	−	3.66819i	−0.791349	−	0.611365i
$37$	−7.89938			−1.29865			−0.649325	−	0.760511i	$-0.724948\pi$
$37$	−7.89938			−1.29865			−0.649325	+	0.760511i	$0.724948\pi$
$38$	7.70154	+	3.32435i	1.24935	+	0.539281i
$39$	−6.88390	+	0.542160i	−1.10231	+	0.0868151i
$40$	1.10556	−	6.22718i	0.174805	−	0.984603i
$41$	−1.89178			−0.295447			−0.147723	−	0.989029i	$-0.547195\pi$
$41$	−1.89178			−0.295447			−0.147723	+	0.989029i	$0.547195\pi$
$42$	5.24951	−	3.80035i	0.810017	−	0.586406i
$43$	9.82318			1.49802			0.749010	−	0.662558i	$-0.230529\pi$
$43$	9.82318			1.49802			0.749010	+	0.662558i	$0.230529\pi$
$44$	−6.73830	−	7.14917i	−1.01584	−	1.07778i
$45$	−6.26185	−	2.40608i	−0.933462	−	0.358677i
$46$	−1.46850	−	0.633873i	−0.216518	−	0.0934595i
$47$		−	10.1570i		−	1.48154i	−0.671756	−	0.740772i	$-0.734460\pi$
$47$		−	10.1570i		−	1.48154i	0.671756	−	0.740772i	$-0.265540\pi$
$48$	−6.92689	+	0.134684i	−0.999811	+	0.0194400i
$49$	2.33585	+	6.59877i	0.333693	+	0.942682i
$50$	−0.812970	−	7.02418i	−0.114971	−	0.993369i
$51$	−1.16869	+	0.0920432i	−0.163649	+	0.0128886i
$52$	−5.80235	+	5.46888i	−0.804642	+	0.758398i
$53$			13.0881i			1.79779i	0.438160	+	0.898897i	$0.355630\pi$
$53$			13.0881i			1.79779i	−0.438160	+	0.898897i	$0.644370\pi$
$54$	−1.25555	+	7.24041i	−0.170859	+	0.985296i
$55$	−9.50983	−	5.49611i	−1.28230	−	0.741096i
$56$	1.97407	−	7.21824i	0.263796	−	0.964578i
$57$	−0.806630	−	10.2419i	−0.106841	−	1.35657i
$58$	−2.84403	−	1.22762i	−0.373439	−	0.161194i
$59$			5.42133i			0.705797i	0.935662	+	0.352898i	$0.114804\pi$
$59$			5.42133i			0.705797i	−0.935662	+	0.352898i	$0.885196\pi$
$60$	−7.37586	+	2.36574i	−0.952219	+	0.305416i
$61$	10.1704			1.30218			0.651091	−	0.759000i	$-0.274312\pi$
$61$	10.1704			1.30218			0.651091	+	0.759000i	$0.274312\pi$
$62$	−2.33974	+	5.42048i	−0.297147	+	0.688401i
$63$	−7.11888	−	3.51020i	−0.896895	−	0.442243i
$64$	−6.13588	+	5.13332i	−0.766985	+	0.641665i
$65$	−4.46071	+	7.71829i	−0.553283	+	0.957336i
$66$	−3.88632	+	11.3872i	−0.478374	+	1.40167i
$67$	4.83299			0.590444			0.295222	−	0.955429i	$-0.404606\pi$
$67$	4.83299			0.590444			0.295222	+	0.955429i	$0.404606\pi$
$68$	−0.985073	+	0.928459i	−0.119458	+	0.112592i
$69$	0.153805	+	1.95289i	0.0185159	+	0.235100i
$70$	−0.200597	−	8.36420i	−0.0239760	−	0.999713i
$71$			1.84999i			0.219553i	0.993956	+	0.109777i	$0.0350136\pi$
$71$			1.84999i			0.219553i	−0.993956	+	0.109777i	$0.964986\pi$
$72$	4.10914	+	7.42395i	0.484266	+	0.874921i
$73$	9.95203			1.16480			0.582399	−	0.812903i	$-0.302114\pi$
$73$	9.95203			1.16480			0.582399	+	0.812903i	$0.302114\pi$
$74$	10.2567	+	4.42727i	1.19232	+	0.514660i
$75$	−7.14121	+	4.89930i	−0.824596	+	0.565723i
$76$	−8.13665	−	8.63278i	−0.933337	−	0.990248i
$77$	−10.6128	−	7.50135i	−1.20944	−	0.854858i
$78$	9.24203	+	3.15419i	1.04645	+	0.357142i
$79$	−9.58477			−1.07837			−0.539185	−	0.842187i	$-0.681268\pi$
$79$	−9.58477			−1.07837			−0.539185	+	0.842187i	$0.681268\pi$
$80$	−4.92556	+	7.46585i	−0.550694	+	0.834707i
$81$	8.55889	−	2.78306i	0.950988	−	0.309229i
$82$	2.45632	+	1.06027i	0.271255	+	0.117087i
$83$	−10.5193			−1.15464			−0.577321	−	0.816517i	$-0.695902\pi$
$83$	−10.5193			−1.15464			−0.577321	+	0.816517i	$0.695902\pi$
$84$	−8.94599	+	1.99230i	−0.976088	+	0.217378i
$85$	−0.757301	+	1.31034i	−0.0821408	+	0.142127i
$86$	−12.7546	−	5.50548i	−1.37536	−	0.593671i
$87$	0.297873	+	3.78214i	0.0319353	+	0.405488i
$88$	4.74231	+	13.0591i	0.505532	+	1.39211i
$89$	−5.53129			−0.586315			−0.293158	−	0.956064i	$-0.594706\pi$
$89$	−5.53129			−0.586315			−0.293158	+	0.956064i	$0.594706\pi$
$90$	6.78199	+	6.63360i	0.714884	+	0.699243i
$91$	−6.08819	+	8.61348i	−0.638215	+	0.902938i
$92$	1.55146	+	1.64606i	0.161751	+	0.171614i
$93$	7.20844	−	0.567720i	0.747480	−	0.0588698i
$94$	−5.69255	+	13.1880i	−0.587142	+	1.36023i
$95$	−11.4833	−	6.63668i	−1.17816	−	0.680909i
$96$	9.06948	+	3.70736i	0.925650	+	0.378381i
$97$	7.68488			0.780281			0.390141	−	0.920755i	$-0.372426\pi$
$97$	7.68488			0.780281			0.390141	+	0.920755i	$0.372426\pi$
$98$	0.665433	−	9.87710i	0.0672188	−	0.997738i
$99$	14.5546	−	2.30689i	1.46280	−	0.231851i
$100$	−2.88119	+	9.57595i	−0.288119	+	0.957595i
$101$			4.26763i			0.424645i	0.977200	+	0.212323i	$0.0681028\pi$
$101$			4.26763i			0.424645i	−0.977200	+	0.212323i	$0.931897\pi$
$102$	1.56903	+	0.535491i	0.155357	+	0.0530215i
$103$	−4.47336			−0.440774			−0.220387	−	0.975413i	$-0.570732\pi$
$103$	−4.47336			−0.440774			−0.220387	+	0.975413i	$0.570732\pi$
$104$	10.5990	−	3.84891i	1.03931	−	0.377417i
$105$	−8.94266	+	5.00288i	−0.872715	+	0.488231i
$106$	7.33536	−	16.9939i	0.712473	−	1.65059i
$107$			15.7177i			1.51948i	0.650225	+	0.759742i	$0.274675\pi$
$107$			15.7177i			1.51948i	−0.650225	+	0.759742i	$0.725325\pi$
$108$	5.68818	−	8.69739i	0.547345	−	0.836907i
$109$		−	2.41416i		−	0.231235i	−0.993294	−	0.115617i	$-0.963115\pi$
$109$		−	2.41416i		−	0.231235i	0.993294	−	0.115617i	$-0.0368846\pi$
$110$	9.26738	+	12.4661i	0.883610	+	1.18860i
$111$	−1.07425	−	13.6399i	−0.101963	−	1.29464i
$112$	−6.60869	+	8.26591i	−0.624463	+	0.781055i
$113$	9.95759			0.936731			0.468365	−	0.883535i	$-0.344843\pi$
$113$	9.95759			0.936731			0.468365	+	0.883535i	$0.344843\pi$
$114$	−4.69283	+	13.7504i	−0.439523	+	1.28784i
$115$	2.18959	+	1.26545i	0.204181	+	0.118004i
$116$	3.00470	+	3.18792i	0.278980	+	0.295991i
$117$	−1.87230	−	11.8127i	−0.173094	−	1.09209i
$118$	3.03843	−	7.03915i	0.279710	−	0.648006i
$119$	−1.03360	+	1.46232i	−0.0947499	+	0.134051i
$120$	10.9028	+	1.06214i	0.995288	+	0.0969598i
$121$	13.1288			1.19353
$122$	−13.2054	−	5.70007i	−1.19556	−	0.516060i
$123$	−0.257266	−	3.26655i	−0.0231969	−	0.294535i
$124$	6.07590	−	5.72671i	0.545632	−	0.514274i
$125$	−0.0148422	+	11.1803i	−0.00132752	+	0.999999i
$126$	7.27596	+	8.54754i	0.648194	+	0.761475i
$127$			9.83591i			0.872796i	0.899754	+	0.436398i	$0.143746\pi$
$127$			9.83591i			0.872796i	−0.899754	+	0.436398i	$0.856254\pi$
$128$	10.8439	−	3.22628i	0.958478	−	0.285166i
$129$	1.33587	+	16.9617i	0.117616	+	1.49340i
$130$	10.1176	−	7.52152i	0.887376	−	0.659681i
$131$		−	10.5440i		−	0.921233i	−0.887599	−	0.460616i	$-0.847628\pi$
$131$		−	10.5440i		−	0.921233i	0.887599	−	0.460616i	$-0.152372\pi$
$132$	11.4281	−	12.6073i	0.994693	−	1.09732i
$133$	−12.8152	−	9.05805i	−1.11122	−	0.785432i
$134$	−6.27523	−	2.70869i	−0.542098	−	0.233995i
$135$	3.30303	−	11.1396i	0.284279	−	0.958741i
$136$	1.79940	−	0.653435i	0.154297	−	0.0560316i
$137$	−8.93986			−0.763784			−0.381892	−	0.924207i	$-0.624727\pi$
$137$	−8.93986			−0.763784			−0.381892	+	0.924207i	$0.624727\pi$
$138$	0.894808	−	2.62186i	0.0761712	−	0.223188i
$139$	6.80452			0.577152			0.288576	−	0.957457i	$-0.406818\pi$
$139$	6.80452			0.577152			0.288576	+	0.957457i	$0.406818\pi$
$140$	−4.42732	+	10.9726i	−0.374177	+	0.927357i
$141$	17.5381	−	1.38126i	1.47697	−	0.116323i
$142$	1.03684	−	2.40206i	0.0870099	−	0.201576i
$143$		−	19.5832i		−	1.63763i
$144$	−1.17456	−	11.9424i	−0.0978798	−	0.995198i
$145$	4.24057	+	2.45080i	0.352160	+	0.203528i
$146$	−12.9219	−	5.57770i	−1.06942	−	0.461614i
$147$	−11.0765	+	4.93069i	−0.913572	+	0.406677i
$148$	−10.8362	−	11.4969i	−0.890726	−	0.945039i
$149$	−11.4973			−0.941898			−0.470949	−	0.882160i	$-0.656088\pi$
$149$	−11.4973			−0.941898			−0.470949	+	0.882160i	$0.656088\pi$
$150$	12.0181	−	2.35899i	0.981275	−	0.192610i
$151$	7.58956			0.617630			0.308815	−	0.951122i	$-0.400068\pi$
$151$	7.58956			0.617630			0.308815	+	0.951122i	$0.400068\pi$
$152$	5.72644	+	15.7692i	0.464476	+	1.27905i
$153$	−0.317863	−	2.00546i	−0.0256977	−	0.162132i
$154$	9.57564	+	15.6879i	0.771627	+	1.26417i
$155$	4.67101	−	8.08217i	0.375185	−	0.649175i
$156$	−10.2322	−	9.27522i	−0.819233	−	0.742612i
$157$			7.08186i			0.565194i	0.959239	+	0.282597i	$0.0911960\pi$
$157$			7.08186i			0.565194i	−0.959239	+	0.282597i	$0.908804\pi$
$158$	12.4450	+	5.37186i	0.990073	+	0.427362i
$159$	−22.5993	+	1.77987i	−1.79224	+	0.141153i
$160$	10.5797	−	6.93321i	0.836401	−	0.548119i
$161$	2.44355	+	1.72715i	0.192579	+	0.136119i
$162$	−12.6728	−	1.18333i	−0.995669	−	0.0929712i
$163$	−15.9698			−1.25085			−0.625426	−	0.780284i	$-0.715075\pi$
$163$	−15.9698			−1.25085			−0.625426	+	0.780284i	$0.715075\pi$
$164$	−2.59510	−	2.75333i	−0.202643	−	0.214999i
$165$	8.19691	−	17.1681i	0.638128	−	1.33653i
$166$	13.6584	+	5.89563i	1.06010	+	0.457589i
$167$			14.7327i			1.14005i	0.821626	+	0.570027i	$0.193067\pi$
$167$			14.7327i			1.14005i	−0.821626	+	0.570027i	$0.806933\pi$
$168$	12.7322	+	2.42702i	0.982313	+	0.187248i
$169$	−2.89400			−0.222615
$170$	1.71769	−	1.27694i	0.131740	−	0.0979366i
$171$	17.5751	−	2.78562i	1.34400	−	0.213022i
$172$	13.4752	+	14.2968i	1.02747	+	1.09012i
$173$	10.8693			0.826375			0.413187	−	0.910646i	$-0.364415\pi$
$173$	10.8693			0.826375			0.413187	+	0.910646i	$0.364415\pi$
$174$	1.73297	−	5.07774i	0.131376	−	0.384942i
$175$	−1.22291	+	13.1721i	−0.0924432	+	0.995718i
$176$	1.16161	−	19.6141i	0.0875597	−	1.47847i
$177$	−9.36103	+	0.737253i	−0.703618	+	0.0554154i
$178$	7.18192	+	3.10006i	0.538307	+	0.232359i
$179$	−10.2327			−0.764825			−0.382413	−	0.923992i	$-0.624907\pi$
$179$	−10.2327			−0.764825			−0.382413	+	0.923992i	$0.624907\pi$
$180$	−5.08799	−	12.4142i	−0.379236	−	0.925300i
$181$	4.82355			0.358532			0.179266	−	0.983801i	$-0.442628\pi$
$181$	4.82355			0.358532			0.179266	+	0.983801i	$0.442628\pi$
$182$	12.7325	−	7.77171i	0.943796	−	0.576077i
$183$	1.38308	+	17.5612i	0.102240	+	1.29816i
$184$	−1.09189	−	3.00681i	−0.0804955	−	0.221665i
$185$	−15.2932	−	8.83854i	−1.12438	−	0.649822i
$186$	−9.67774	−	3.30289i	−0.709606	−	0.242180i
$187$		−	3.32467i		−	0.243124i
$188$	14.7826	−	13.9330i	1.07813	−	1.01617i
$189$	5.09296	−	12.7696i	0.370459	−	0.928849i
$190$	11.1906	+	15.0531i	0.811849	+	1.09207i
$191$			13.3579i			0.966546i	0.875470	+	0.483273i	$0.160552\pi$
$191$			13.3579i			0.966546i	−0.875470	+	0.483273i	$0.839448\pi$
$192$	−9.69815	−	9.89676i	−0.699903	−	0.714237i
$193$			3.40976i			0.245440i	0.992441	+	0.122720i	$0.0391617\pi$
$193$			3.40976i			0.245440i	−0.992441	+	0.122720i	$0.960838\pi$
$194$	−9.97818	−	4.30706i	−0.716392	−	0.309229i
$195$	−13.9338	−	6.65271i	−0.997822	−	0.476410i
$196$	−6.39972	+	12.4517i	−0.457123	+	0.889404i
$197$		−	16.3303i		−	1.16349i	−0.813373	−	0.581743i	$-0.802371\pi$
$197$		−	16.3303i		−	1.16349i	0.813373	−	0.581743i	$-0.197629\pi$
$198$	−20.1909	−	5.16197i	−1.43491	−	0.366845i
$199$		−	21.5780i		−	1.52962i	−0.644253	−	0.764812i	$-0.722832\pi$
$199$		−	21.5780i		−	1.52962i	0.644253	−	0.764812i	$-0.277168\pi$
$200$	9.10790	−	10.8188i	0.644026	−	0.765004i
$201$	0.657244	+	8.34514i	0.0463584	+	0.588621i
$202$	2.39183	−	5.54117i	0.168289	−	0.389875i
$203$	4.73240	+	3.34496i	0.332149	+	0.234770i
$204$	−1.73714	−	1.57467i	−0.121624	−	0.110249i
$205$	−3.66248	−	2.11670i	−0.255799	−	0.147837i
$206$	5.80829	+	2.50713i	0.404683	+	0.174680i
$207$	−3.35114	+	0.531151i	−0.232920	+	0.0369175i
$208$	−15.9190	−	0.942777i	−1.10379	−	0.0653698i
$209$	29.1361			2.01539
$210$	14.4152	−	1.48383i	0.994744	−	0.102394i
$211$		−	1.99213i		−	0.137144i	−0.997646	−	0.0685720i	$-0.978156\pi$
$211$		−	1.99213i		−	0.137144i	0.997646	−	0.0685720i	$-0.0218443\pi$
$212$	−19.0487	+	17.9540i	−1.30827	+	1.23308i
$213$	−3.19438	+	0.251582i	−0.218876	+	0.0172381i
$214$	8.80910	−	20.4081i	0.602177	−	1.39507i
$215$	19.0176	+	10.9911i	1.29699	+	0.749584i
$216$	−12.2602	+	8.10485i	−0.834198	+	0.551465i
$217$	6.37521	−	9.01956i	0.432778	−	0.612287i
$218$	−1.35304	+	3.13459i	−0.0916392	+	0.212301i
$219$	1.35339	+	17.1842i	0.0914536	+	1.16120i
$220$	−5.04618	−	21.3802i	−0.340214	−	1.44145i
$221$	−2.69834			−0.181510
$222$	−6.24977	+	18.3123i	−0.419457	+	1.22904i
$223$	7.19212			0.481620			0.240810	−	0.970572i	$-0.422587\pi$
$223$	7.19212			0.481620			0.240810	+	0.970572i	$0.422587\pi$
$224$	13.2135	−	7.02869i	0.882866	−	0.469624i
$225$	−9.43078	−	11.6645i	−0.628719	−	0.777633i
$226$	−12.9291	−	5.58081i	−0.860031	−	0.371230i
$227$	28.3622			1.88246			0.941232	−	0.337760i	$-0.109669\pi$
$227$	28.3622			1.88246			0.941232	+	0.337760i	$0.109669\pi$
$228$	13.7997	−	15.2236i	0.913911	−	1.00821i
$229$	6.18020			0.408399			0.204200	−	0.978929i	$-0.434541\pi$
$229$	6.18020			0.408399			0.204200	+	0.978929i	$0.434541\pi$
$230$	−2.13377	−	2.87026i	−0.140697	−	0.189260i
$231$	11.5094	−	19.3453i	0.757260	−	1.27283i
$232$	−2.11466	−	5.82326i	−0.138834	−	0.382315i
$233$	22.3929			1.46701			0.733505	−	0.679684i	$-0.237883\pi$
$233$	22.3929			1.46701			0.733505	+	0.679684i	$0.237883\pi$
$234$	−4.18951	+	16.3872i	−0.273877	+	1.07126i
$235$	11.3645	−	19.6638i	0.741340	−	1.28273i
$236$	−7.89030	+	7.43683i	−0.513615	+	0.484096i
$237$	−1.30344	−	16.5501i	−0.0846678	−	1.07504i
$238$	2.16161	−	1.31941i	0.140117	−	0.0855248i
$239$			16.3438i			1.05719i	0.848874	+	0.528595i	$0.177281\pi$
$239$			16.3438i			1.05719i	−0.848874	+	0.528595i	$0.822719\pi$
$240$	−13.5611	−	7.48969i	−0.875368	−	0.483457i
$241$		−	5.55547i		−	0.357860i	−0.983862	−	0.178930i	$-0.942737\pi$
$241$		−	5.55547i		−	0.357860i	0.983862	−	0.178930i	$-0.0572635\pi$
$242$	−17.0467	−	7.35815i	−1.09580	−	0.473000i
$243$	5.96945	+	14.4002i	0.382941	+	0.923773i
$244$	13.9514	+	14.8021i	0.893149	+	0.947609i
$245$	−2.86111	+	15.3888i	−0.182790	+	0.983152i
$246$	−1.49673	+	4.38553i	−0.0954278	+	0.279611i
$247$		−	23.6472i		−	1.50464i
$248$	−11.0986	+	4.03037i	−0.704764	+	0.255929i
$249$	−1.43053	−	18.1637i	−0.0906563	−	1.15108i
$250$	6.28538	−	14.5084i	0.397522	−	0.917592i
$251$			9.85902i			0.622296i	0.950361	+	0.311148i	$0.100713\pi$
$251$			9.85902i			0.622296i	−0.950361	+	0.311148i	$0.899287\pi$
$252$	−4.65669	−	15.1761i	−0.293344	−	0.956007i
$253$	−5.55555			−0.349274
$254$	5.51262	−	12.7711i	0.345893	−	0.801331i
$255$	−2.36556	−	1.12944i	−0.148137	−	0.0707282i
$256$	−15.8882	−	1.88852i	−0.993010	−	0.118033i
$257$			2.41358i			0.150555i	0.997163	+	0.0752775i	$0.0239843\pi$
$257$			2.41358i			0.150555i	−0.997163	+	0.0752775i	$0.976016\pi$
$258$	7.77183	−	22.7721i	0.483853	−	1.41773i
$259$	−17.0669	−	12.0632i	−1.06049	−	0.749574i
$260$	−17.3524	+	4.09554i	−1.07615	+	0.253995i
$261$	−6.49012	+	1.02868i	−0.401729	+	0.0636734i
$262$	−5.90947	+	13.6905i	−0.365088	+	0.845802i
$263$	25.4442			1.56896			0.784478	−	0.620157i	$-0.212931\pi$
$263$	25.4442			1.56896			0.784478	+	0.620157i	$0.212931\pi$
$264$	−21.9043	+	9.96449i	−1.34812	+	0.613272i
$265$	−14.6442	+	25.3386i	−0.899586	+	1.55654i
$266$	11.5628	+	18.9435i	0.708961	+	1.16150i
$267$	−0.752207	−	9.55090i	−0.0460343	−	0.584505i
$268$	6.62976	+	7.03402i	0.404977	+	0.429671i
$269$		−	24.0971i		−	1.46923i	−0.678485	−	0.734614i	$-0.737363\pi$
$269$		−	24.0971i		−	1.46923i	0.678485	−	0.734614i	$-0.262637\pi$
$270$	−10.5320	+	12.6126i	−0.640956	+	0.767578i
$271$		−	13.8976i		−	0.844219i	−0.906545	−	0.422109i	$-0.861290\pi$
$271$		−	13.8976i		−	0.844219i	0.906545	−	0.422109i	$-0.138710\pi$
$272$	−2.70259	−	0.160056i	−0.163869	−	0.00970485i
$273$	−15.7009	−	9.34114i	−0.950260	−	0.565351i
$274$	11.6077	+	5.01042i	0.701244	+	0.302690i
$275$	−12.2614	−	21.2809i	−0.739393	−	1.28329i
$276$	−2.63128	+	2.90277i	−0.158384	+	0.174726i
$277$	17.0980			1.02732			0.513658	−	0.857995i	$-0.328290\pi$
$277$	17.0980			1.02732			0.513658	+	0.857995i	$0.328290\pi$
$278$	−8.83510	−	3.81365i	−0.529894	−	0.228727i
$279$	1.96057	+	12.3696i	0.117376	+	0.740551i
$280$	11.8982	−	11.7657i	0.711055	−	0.703137i
$281$			30.4295i			1.81527i	0.419759	+	0.907636i	$0.362115\pi$
$281$			30.4295i			1.81527i	−0.419759	+	0.907636i	$0.637885\pi$
$282$	−23.5459	−	8.03591i	−1.40214	−	0.478531i
$283$		−	22.3052i		−	1.32591i	−0.748660	−	0.662954i	$-0.769302\pi$
$283$		−	22.3052i		−	1.32591i	0.748660	−	0.662954i	$-0.230698\pi$
$284$	−2.69251	+	2.53777i	−0.159771	+	0.150589i
$285$	9.89795	−	20.7308i	0.586304	−	1.22799i
$286$	−10.9756	+	25.4272i	−0.649000	+	1.50354i
$287$	−4.08727	−	2.88897i	−0.241264	−	0.170530i
$288$	−5.16814	+	16.1645i	−0.304536	+	0.952501i
$289$	16.5419			0.973053
$290$	−4.13246	−	5.55882i	−0.242666	−	0.326425i
$291$	1.04508	+	13.2695i	0.0612635	+	0.777873i
$292$	13.6519	+	14.4844i	0.798918	+	0.847633i
$293$	17.5340			1.02434			0.512172	−	0.858883i	$-0.328841\pi$
$293$	17.5340			1.02434			0.512172	+	0.858883i	$0.328841\pi$
$294$	17.1453	−	0.194195i	0.999936	−	0.0113257i
$295$	−6.06588	+	10.4957i	−0.353169	+	0.611082i
$296$	7.62631	+	21.0010i	0.443270	+	1.22066i
$297$	5.96262	+	24.8178i	0.345986	+	1.44008i
$298$	14.9283	+	6.44377i	0.864775	+	0.373278i
$299$			4.50895i			0.260759i
$300$	−16.9266	−	3.67271i	−0.977260	−	0.212044i
$301$	21.2233	+	15.0011i	1.22329	+	0.864649i
$302$	−9.85441	−	4.25363i	−0.567058	−	0.244769i
$303$	−7.36894	+	0.580361i	−0.423334	+	0.0333409i
$304$	1.40267	−	23.6844i	0.0804487	−	1.35840i
$305$	19.6898	+	11.3795i	1.12743	+	0.651590i
$306$	−0.711259	+	2.78207i	−0.0406600	+	0.159041i
$307$			7.61316i			0.434506i	0.976115	+	0.217253i	$0.0697096\pi$
$307$			7.61316i			0.434506i	−0.976115	+	0.217253i	$0.930290\pi$
$308$	−3.64076	−	25.7362i	−0.207451	−	1.46646i
$309$	−0.608339	−	7.72418i	−0.0346072	−	0.439413i
$310$	−10.5946	+	7.87612i	−0.601735	+	0.447333i
$311$	8.35008			0.473489			0.236745	−	0.971572i	$-0.423919\pi$
$311$	8.35008			0.473489			0.236745	+	0.971572i	$0.423919\pi$
$312$	8.08730	+	17.7778i	0.457853	+	1.00647i
$313$	−4.70357			−0.265862			−0.132931	−	0.991125i	$-0.542439\pi$
$313$	−4.70357			−0.265862			−0.132931	+	0.991125i	$0.542439\pi$
$314$	3.96909	−	9.19521i	0.223989	−	0.518916i
$315$	−9.85461	−	14.7610i	−0.555244	−	0.831687i
$316$	−13.1481	−	13.9498i	−0.739640	−	0.784739i
$317$		−	0.884992i		−	0.0497061i	−0.999691	−	0.0248531i	$-0.992088\pi$
$317$		−	0.884992i		−	0.0497061i	0.999691	−	0.0248531i	$-0.00791179\pi$
$318$	30.3409	+	10.3550i	1.70143	+	0.580678i
$319$	−10.7594			−0.602410
$320$	−17.6227	+	3.07271i	−0.985137	+	0.171769i
$321$	−27.1398	+	2.13747i	−1.51479	+	0.119302i
$322$	−2.20475	−	3.61207i	−0.122866	−	0.201293i
$323$		−	4.01462i		−	0.223379i
$324$	15.7914	+	8.63903i	0.877298	+	0.479946i
$325$	−17.2719	+	9.95154i	−0.958070	+	0.552012i
$326$	20.7355	+	8.95041i	1.14843	+	0.495717i
$327$	4.16854	−	0.328305i	0.230521	−	0.0181553i
$328$	1.82639	+	5.02942i	0.100845	+	0.277703i
$329$	15.5108	−	21.9445i	0.855140	−	1.20984i
$330$	−20.2650	+	17.6973i	−1.11555	+	0.974204i
$331$			25.5215i			1.40279i	0.712774	+	0.701394i	$0.247438\pi$
$331$			25.5215i			1.40279i	−0.712774	+	0.701394i	$0.752562\pi$
$332$	−14.4301	−	15.3100i	−0.791954	−	0.840244i
$333$	23.4060	−	3.70981i	1.28264	−	0.203296i
$334$	8.25709	−	19.1292i	0.451808	−	1.04671i
$335$	9.35665	+	5.40759i	0.511208	+	0.295448i
$336$	−15.1715	−	10.2872i	−0.827673	−	0.561211i
$337$			4.29542i			0.233987i	0.993133	+	0.116993i	$0.0373256\pi$
$337$			4.29542i			0.233987i	−0.993133	+	0.116993i	$0.962674\pi$
$338$	3.75762	+	1.62197i	0.204387	+	0.0882233i
$339$	1.35414	+	17.1938i	0.0735470	+	0.933839i
$340$	−2.94594	+	0.695306i	−0.159766	+	0.0377082i
$341$			20.5065i			1.11049i
$342$	−24.3810	−	6.23319i	−1.31837	−	0.337052i
$343$	−5.03039	+	17.8240i	−0.271615	+	0.962406i
$344$	−9.48361	−	26.1155i	−0.511322	−	1.40805i
$345$	−1.88730	+	3.95287i	−0.101609	+	0.212815i
$346$	−14.1128	−	6.09177i	−0.758711	−	0.327496i
$347$			24.1689i			1.29745i	0.761022	+	0.648726i	$0.224698\pi$
$347$			24.1689i			1.29745i	−0.761022	+	0.648726i	$0.775302\pi$
$348$	−5.09597	+	5.62176i	−0.273173	+	0.301358i
$349$	−23.2278			−1.24336			−0.621678	−	0.783273i	$-0.713549\pi$
$349$	−23.2278			−1.24336			−0.621678	+	0.783273i	$0.713549\pi$
$350$	8.97026	−	16.4175i	0.479481	−	0.877552i
$351$	20.1425	−	4.83934i	1.07513	−	0.258305i
$352$	−12.5011	+	24.8162i	−0.666312	+	1.32271i
$353$		−	8.59750i		−	0.457599i	−0.973474	−	0.228799i	$-0.926520\pi$
$353$		−	8.59750i		−	0.457599i	0.973474	−	0.228799i	$-0.0734800\pi$
$354$	12.5677	+	4.28921i	0.667967	+	0.227969i
$355$	−2.06994	+	3.58157i	−0.109861	+	0.190090i
$356$	−7.58767	−	8.05033i	−0.402146	−	0.426667i
$357$	−2.66556	−	1.58586i	−0.141076	−	0.0839324i
$358$	13.2863	+	5.73498i	0.702201	+	0.303103i
$359$			6.47793i			0.341892i	0.985280	+	0.170946i	$0.0546824\pi$
$359$			6.47793i			0.341892i	−0.985280	+	0.170946i	$0.945318\pi$
$360$	−0.351313	+	18.9704i	−0.0185158	+	0.999829i
$361$	16.1825			0.851710
$362$	−6.26298	−	2.70340i	−0.329175	−	0.142088i
$363$	1.78540	+	22.6696i	0.0937094	+	1.18984i
$364$	−20.8878	+	2.95488i	−1.09482	+	0.154878i
$365$	19.2671	+	11.1352i	1.00849	+	0.582845i
$366$	8.04652	−	23.5769i	0.420598	−	1.23239i
$367$	−23.8897			−1.24703			−0.623517	−	0.781810i	$-0.714297\pi$
$367$	−23.8897			−1.24703			−0.623517	+	0.781810i	$0.714297\pi$
$368$	−0.267455	+	4.51605i	−0.0139421	+	0.235415i
$369$	5.60538	−	0.888444i	0.291804	−	0.0462505i
$370$	14.9033	+	20.0473i	0.774784	+	1.04221i
$371$	−19.9871	+	28.2774i	−1.03768	+	1.46809i
$372$	10.7146	+	9.71250i	0.555527	+	0.503570i
$373$	−7.72660			−0.400068			−0.200034	−	0.979789i	$-0.564105\pi$
$373$	−7.72660			−0.400068			−0.200034	+	0.979789i	$0.564105\pi$
$374$	−1.86334	+	4.31681i	−0.0963510	+	0.223217i
$375$	−19.3071	+	1.49480i	−0.997016	+	0.0771911i
$376$	−27.0029	+	9.80585i	−1.39257	+	0.505698i
$377$			8.73245i			0.449744i
$378$	−13.7696	+	13.7258i	−0.708232	+	0.705980i
$379$			1.00894i			0.0518258i	0.999664	+	0.0259129i	$0.00824925\pi$
$379$			1.00894i			0.0518258i	−0.999664	+	0.0259129i	$0.991751\pi$
$380$	−6.09338	−	25.8171i	−0.312584	−	1.32439i
$381$	−16.9837	+	1.33760i	−0.870102	+	0.0685272i
$382$	7.48657	−	17.3442i	0.383046	−	0.887405i
$383$			0.850409i			0.0434539i	0.999764	+	0.0217269i	$0.00691644\pi$
$383$			0.850409i			0.0434539i	−0.999764	+	0.0217269i	$0.993084\pi$
$384$	7.04551	+	18.2855i	0.359540	+	0.933130i
$385$	−12.1532	−	26.3971i	−0.619382	−	1.34532i
$386$	1.91103	−	4.42729i	0.0972687	−	0.225343i
$387$	−29.1062	+	4.61329i	−1.47955	+	0.234507i
$388$	10.5419	+	11.1847i	0.535184	+	0.567818i
$389$	−19.6638			−0.996993			−0.498496	−	0.866892i	$-0.666114\pi$
$389$	−19.6638			−0.996993			−0.498496	+	0.866892i	$0.666114\pi$
$390$	14.3633	+	16.4473i	0.727316	+	0.832842i
$391$			0.765490i			0.0387125i
$392$	15.2881	−	12.5807i	0.772167	−	0.635419i
$393$	18.2064	−	1.43389i	0.918389	−	0.0723302i
$394$	−9.15246	+	21.2035i	−0.461094	+	1.06822i
$395$	−18.5561	−	10.7243i	−0.933657	−	0.539598i
$396$	23.3231	+	18.0185i	1.17203	+	0.905466i
$397$		−	4.56276i		−	0.228998i	−0.993423	−	0.114499i	$-0.963474\pi$
$397$		−	4.56276i		−	0.228998i	0.993423	−	0.114499i	$-0.0365263\pi$
$398$	−12.0936	+	28.0173i	−0.606196	+	1.40438i
$399$	13.8978	−	23.3599i	0.695761	−	1.16946i
$400$	−17.8893	+	8.94270i	−0.894467	+	0.447135i
$401$		−	30.8889i		−	1.54252i	−0.636522	−	0.771258i	$-0.719628\pi$
$401$		−	30.8889i		−	1.54252i	0.636522	−	0.771258i	$-0.280372\pi$
$402$	3.82373	−	11.2038i	0.190710	−	0.558796i
$403$	16.6433			0.829063
$404$	−6.21119	+	5.85422i	−0.309018	+	0.291258i
$405$	19.6839	+	4.18847i	0.978102	+	0.208127i
$406$	−4.26992	−	6.99546i	−0.211912	−	0.347179i
$407$	38.8026			1.92337
$408$	1.37299	+	3.01817i	0.0679732	+	0.149421i
$409$			9.93988i			0.491495i	0.969334	+	0.245748i	$0.0790335\pi$
$409$			9.93988i			0.491495i	−0.969334	+	0.245748i	$0.920967\pi$
$410$	3.56911	+	4.80103i	0.176266	+	0.237106i
$411$	−1.21574	−	15.4365i	−0.0599682	−	0.761426i
$412$	−6.13644	−	6.51061i	−0.302321	−	0.320755i
$413$	−8.27898	+	11.7130i	−0.407382	+	0.576358i
$414$	4.64886	+	1.18852i	0.228479	+	0.0584125i
$415$	−20.3653	−	11.7699i	−0.999694	−	0.577764i
$416$	20.1411	+	10.1461i	0.987500	+	0.497452i
$417$	0.925355	+	11.7494i	0.0453148	+	0.575370i
$418$	−37.8308	−	16.3296i	−1.85036	−	0.798705i
$419$		−	17.0569i		−	0.833282i	−0.909071	−	0.416641i	$-0.863207\pi$
$419$		−	17.0569i		−	0.833282i	0.909071	−	0.416641i	$-0.136793\pi$
$420$	−19.5486	−	6.15250i	−0.953873	−	0.300211i
$421$			11.8697i			0.578493i	0.957255	+	0.289246i	$0.0934047\pi$
$421$			11.8697i			0.578493i	−0.957255	+	0.289246i	$0.906595\pi$
$422$	−1.11651	+	2.58662i	−0.0543507	+	0.125915i
$423$	4.77005	+	30.0952i	0.231928	+	1.46328i
$424$	34.7956	−	12.6357i	1.68982	−	0.613644i
$425$	−2.93226	+	1.68949i	−0.142236	+	0.0819521i
$426$	4.28864	+	1.46366i	0.207786	+	0.0709146i
$427$	21.9735	+	15.5313i	1.06337	+	0.751613i
$428$	−22.8758	+	21.5611i	−1.10574	+	1.04219i
$429$	33.8145	−	2.66315i	1.63258	−	0.128578i
$430$	−18.5328	−	24.9296i	−0.893731	−	1.20221i
$431$		−	11.0477i		−	0.532147i	−0.963953	−	0.266074i	$-0.914274\pi$
$431$		−	11.0477i		−	0.532147i	0.963953	−	0.266074i	$-0.0857264\pi$
$432$	20.4612	−	3.65217i	0.984441	−	0.175715i
$433$	27.0777			1.30127			0.650636	−	0.759390i	$-0.274503\pi$
$433$	27.0777			1.30127			0.650636	+	0.759390i	$0.274503\pi$
$434$	−13.3328	+	8.13810i	−0.639993	+	0.390642i
$435$	−3.65512	+	7.65549i	−0.175250	+	0.367053i
$436$	3.51361	−	3.31168i	0.168271	−	0.158601i
$437$	−6.70845			−0.320909
$438$	7.87377	−	23.0708i	0.376223	−	1.10236i
$439$			9.69545i			0.462739i	0.972866	+	0.231369i	$0.0743206\pi$
$439$			9.69545i			0.462739i	−0.972866	+	0.231369i	$0.925679\pi$
$440$	−5.43066	+	30.5886i	−0.258896	+	1.45825i
$441$	−10.0202	−	18.4553i	−0.477150	−	0.878822i
$442$	3.50358	+	1.51231i	0.166648	+	0.0719332i
$443$		−	15.4033i		−	0.731831i	−0.930648	−	0.365916i	$-0.880756\pi$
$443$		−	15.4033i		−	0.731831i	0.930648	−	0.365916i	$-0.119244\pi$
$444$	18.3781	−	20.2743i	0.872186	−	0.962176i
$445$	−10.7086	−	6.18891i	−0.507634	−	0.293382i
$446$	−9.33836	−	4.03088i	−0.442184	−	0.190868i
$447$	−1.56354	−	19.8525i	−0.0739527	−	0.938990i
$448$	−21.0960	+	1.72054i	−0.996691	+	0.0812879i
$449$			4.67550i			0.220650i	0.993896	+	0.110325i	$0.0351892\pi$
$449$			4.67550i			0.220650i	−0.993896	+	0.110325i	$0.964811\pi$
$450$	5.70763	+	20.4309i	0.269060	+	0.963123i
$451$	9.29264			0.437573
$452$	13.6595	+	14.4924i	0.642491	+	0.681667i
$453$	1.03211	+	13.1049i	0.0484929	+	0.615723i
$454$	−36.8259	−	15.8958i	−1.72833	−	0.746028i
$455$	−21.4242	+	9.86365i	−1.00438	+	0.462415i
$456$	−26.4500	+	12.0323i	−1.23863	+	0.563466i
$457$			30.1183i			1.40887i	0.709767	+	0.704437i	$0.248800\pi$
$457$			30.1183i			1.40887i	−0.709767	+	0.704437i	$0.751200\pi$
$458$	−8.02448	−	3.46375i	−0.374959	−	0.161850i
$459$	3.41961	−	0.821580i	0.159614	−	0.0383481i
$460$	1.16186	+	4.92269i	0.0541720	+	0.229522i
$461$		−	20.9199i		−	0.974336i	−0.873308	−	0.487168i	$-0.838030\pi$
$461$		−	20.9199i		−	0.974336i	0.873308	−	0.487168i	$-0.161970\pi$
$462$	−25.7862	+	18.6677i	−1.19968	+	0.868501i
$463$		−	13.4430i		−	0.624750i	−0.949959	−	0.312375i	$-0.898876\pi$
$463$		−	13.4430i		−	0.624750i	0.949959	−	0.312375i	$-0.101124\pi$
$464$	−0.517979	+	8.74619i	−0.0240466	+	0.406032i
$465$	14.5907	+	6.96635i	0.676629	+	0.323057i
$466$	−29.0754	−	12.5503i	−1.34689	−	0.581382i
$467$	0.520283			0.0240758			0.0120379	−	0.999928i	$-0.496168\pi$
$467$	0.520283			0.0240758			0.0120379	+	0.999928i	$0.496168\pi$
$468$	14.6241	−	18.9294i	0.675998	−	0.875010i
$469$	10.4419	+	7.38052i	0.482160	+	0.340801i
$470$	−25.7767	+	19.1625i	−1.18899	+	0.883901i
$471$	−12.2283	+	0.963072i	−0.563450	+	0.0443760i
$472$	14.4129	−	5.23392i	0.663409	−	0.240911i
$473$	−48.2525			−2.21865
$474$	−7.58320	+	22.2194i	−0.348308	+	1.02057i
$475$	−14.8060	−	25.6972i	−0.679345	−	1.17907i
$476$	−3.54615	+	0.501654i	−0.162538	+	0.0229933i
$477$	−6.14663	−	38.7803i	−0.281435	−	1.77563i
$478$	9.16000	−	21.2210i	0.418969	−	0.970627i
$479$	−11.6263			−0.531221			−0.265611	−	0.964080i	$-0.585574\pi$
$479$	−11.6263			−0.531221			−0.265611	+	0.964080i	$0.585574\pi$
$480$	13.4104	+	17.3252i	0.612096	+	0.790783i
$481$		−	31.4927i		−	1.43594i
$482$	−3.11361	+	7.21332i	−0.141821	+	0.328558i
$483$	−2.64998	+	4.45416i	−0.120578	+	0.202671i
$484$	18.0097	+	19.1079i	0.818625	+	0.868541i
$485$	14.8779	+	8.59854i	0.675571	+	0.390440i
$486$	0.319872	−	22.0431i	0.0145097	−	0.999895i
$487$			2.49358i			0.112995i	0.998403	+	0.0564975i	$0.0179933\pi$
$487$			2.49358i			0.112995i	−0.998403	+	0.0564975i	$0.982007\pi$
$488$	−9.81880	−	27.0385i	−0.444476	−	1.22398i
$489$	−2.17175	−	27.5751i	−0.0982101	−	1.24699i
$490$	12.3397	−	18.3775i	0.557450	−	0.830211i
$491$	25.3505			1.14405			0.572027	−	0.820235i	$-0.306157\pi$
$491$	25.3505			1.14405			0.572027	+	0.820235i	$0.306157\pi$
$492$	4.40128	−	4.85539i	0.198425	−	0.218898i
$493$			1.48252i			0.0667693i
$494$	−13.2533	+	30.7039i	−0.596293	+	1.38144i
$495$	30.7589	+	11.8189i	1.38251	+	0.531221i
$496$	16.6695	+	0.987224i	0.748483	+	0.0443277i
$497$	−2.82514	+	3.99697i	−0.126725	+	0.179289i
$498$	−8.32258	+	24.3858i	−0.372944	+	1.09275i
$499$		−	37.9208i		−	1.69757i	−0.528738	−	0.848785i	$-0.677335\pi$
$499$		−	37.9208i		−	1.69757i	0.528738	−	0.848785i	$-0.322665\pi$
$500$	−16.2924	+	15.3153i	−0.728619	+	0.684920i
$501$	−25.4391	+	2.00353i	−1.13653	+	0.0895109i
$502$	5.52557	−	12.8011i	0.246618	−	0.571342i
$503$			14.1570i			0.631231i	0.948887	+	0.315616i	$0.102211\pi$
$503$			14.1570i			0.631231i	−0.948887	+	0.315616i	$0.897789\pi$
$504$	−2.45927	+	22.3148i	−0.109544	+	0.993982i
$505$	−4.77501	+	8.26212i	−0.212485	+	0.367660i
$506$	7.21342	+	3.11365i	0.320676	+	0.138419i
$507$	−0.393558	−	4.99708i	−0.0174785	−	0.221928i
$508$	−14.3154	+	13.4926i	−0.635141	+	0.598639i
$509$		−	2.91476i		−	0.129195i	−0.997911	−	0.0645973i	$-0.979424\pi$
$509$		−	2.91476i		−	0.129195i	0.997911	−	0.0645973i	$-0.0205763\pi$
$510$	2.43848	+	2.79228i	0.107978	+	0.123644i
$511$	21.5017	+	15.1979i	0.951181	+	0.672315i
$512$	19.5710	+	11.3567i	0.864925	+	0.501902i
$513$	7.20000	+	29.9681i	0.317888	+	1.32312i
$514$	1.35271	−	3.13383i	0.0596656	−	0.138227i
$515$	−8.66042	−	5.00521i	−0.381624	−	0.220556i
$516$	−22.8539	+	25.2119i	−1.00609	+	1.10989i
$517$			49.8921i			2.19425i
$518$	15.3990	+	25.2284i	0.676594	+	1.10847i
$519$	1.47813	+	18.7680i	0.0648825	+	0.823824i
$520$	24.8261	+	4.40759i	1.08869	+	0.193285i
$521$	28.0030			1.22683			0.613416	−	0.789760i	$-0.289795\pi$
$521$	28.0030			1.22683			0.613416	+	0.789760i	$0.289795\pi$
$522$	9.00342	+	2.30179i	0.394069	+	0.100747i
$523$		−	6.62390i		−	0.289643i	−0.989458	−	0.144821i	$-0.953739\pi$
$523$		−	6.62390i		−	0.289643i	0.989458	−	0.144821i	$-0.0462608\pi$
$524$	15.3459	−	14.4640i	0.670389	−	0.631861i
$525$	−22.9106	−	0.320309i	−0.999902	−	0.0139794i
$526$	−33.0372	−	14.2604i	−1.44049	−	0.621783i
$527$	2.82556			0.123083
$528$	34.0257	−	0.661585i	1.48078	−	0.0287918i
$529$	−21.7209			−0.944385
$530$	33.2155	−	24.6926i	1.44279	−	1.07258i
$531$	−2.54604	−	16.0635i	−0.110489	−	0.697095i
$532$	−4.39630	−	31.0770i	−0.190604	−	1.34736i
$533$		−	7.54202i		−	0.326681i
$534$	−4.37620	+	12.8226i	−0.189377	+	0.554889i
$535$	−17.5863	+	30.4293i	−0.760324	+	1.31558i
$536$	−4.66592	−	12.8488i	−0.201537	−	0.554983i
$537$	−1.39155	−	17.6688i	−0.0600500	−	0.762464i
$538$	−13.5054	+	31.2881i	−0.582261	+	1.34893i
$539$	−11.4739	−	32.4139i	−0.494218	−	1.39617i
$540$	20.7437	−	10.4737i	0.892668	−	0.450715i
$541$			24.1789i			1.03953i	0.854309	+	0.519766i	$0.173981\pi$
$541$			24.1789i			1.03953i	−0.854309	+	0.519766i	$0.826019\pi$
$542$	−7.78902	+	18.0449i	−0.334567	+	0.775094i
$543$	0.655961	+	8.32885i	0.0281500	+	0.357425i
$544$	3.41939	+	1.72251i	0.146605	+	0.0738520i
$545$	2.70118	−	4.67381i	0.115706	−	0.200204i
$546$	15.1509	+	20.9284i	0.648401	+	0.895652i
$547$	32.1623			1.37516			0.687581	−	0.726108i	$-0.258673\pi$
$547$	32.1623			1.37516			0.687581	+	0.726108i	$0.258673\pi$
$548$	−12.2635	−	13.0112i	−0.523869	−	0.555812i
$549$	−30.1349	+	4.77634i	−1.28613	+	0.203849i
$550$	3.99340	+	34.5035i	0.170279	+	1.47124i
$551$	−12.9922			−0.553486
$552$	5.04338	−	2.29428i	0.214660	−	0.0976510i
$553$	−20.7083	−	14.6370i	−0.880604	−	0.622430i
$554$	−22.2003	−	9.58269i	−0.943199	−	0.407130i
$555$	13.1818	−	27.6087i	0.559536	−	1.17193i
$556$	9.33425	+	9.90341i	0.395860	+	0.419998i
$557$		−	28.9539i		−	1.22682i	−0.789766	−	0.613408i	$-0.789798\pi$
$557$		−	28.9539i		−	1.22682i	0.789766	−	0.613408i	$-0.210202\pi$
$558$	4.38703	−	17.1598i	0.185718	−	0.726431i
$559$			39.1623i			1.65639i
$560$	−22.0431	+	8.60836i	−0.931489	+	0.363770i
$561$	5.74072	−	0.452126i	0.242374	−	0.0190888i
$562$	17.0545	−	39.5102i	0.719399	−	1.66664i
$563$	18.3114			0.771733			0.385867	−	0.922555i	$-0.373903\pi$
$563$	18.3114			0.771733			0.385867	+	0.922555i	$0.373903\pi$
$564$	26.0685	+	23.6304i	1.09768	+	0.995020i
$565$	19.2779	+	11.1415i	0.811025	+	0.468724i
$566$	−12.5012	+	28.9615i	−0.525463	+	1.21734i
$567$	22.7419	+	7.05749i	0.955068	+	0.296387i
$568$	4.91831	−	1.78604i	0.206368	−	0.0749406i
$569$			15.5054i			0.650022i	0.945710	+	0.325011i	$0.105368\pi$
$569$			15.5054i			0.650022i	−0.945710	+	0.325011i	$0.894632\pi$
$570$	−24.4704	+	21.3699i	−1.02495	+	0.895086i
$571$		−	22.9342i		−	0.959766i	−0.877333	−	0.479883i	$-0.840679\pi$
$571$		−	22.9342i		−	0.959766i	0.877333	−	0.479883i	$-0.159321\pi$
$572$	28.5018	−	26.8638i	1.19172	−	1.12323i
$573$	−23.0652	+	1.81656i	−0.963563	+	0.0758880i
$574$	3.68783	+	6.04183i	0.153927	+	0.252181i
$575$	2.82314	+	4.89983i	0.117733	+	0.204337i
$576$	15.7699	−	18.0917i	0.657080	−	0.753821i
$577$	−34.2228			−1.42472			−0.712358	−	0.701817i	$-0.752373\pi$
$577$	−34.2228			−1.42472			−0.712358	+	0.701817i	$0.752373\pi$
$578$	−21.4783	−	9.27105i	−0.893379	−	0.385625i
$579$	−5.88764	+	0.463697i	−0.244682	+	0.0192706i
$580$	2.25017	+	9.53373i	0.0934330	+	0.395867i
$581$	−22.7273	−	16.0642i	−0.942889	−	0.666454i
$582$	6.08007	−	17.8151i	0.252027	−	0.738459i
$583$		−	64.2904i		−	2.66263i
$584$	−9.60801	−	26.4581i	−0.397582	−	1.09484i
$585$	9.59238	−	24.9643i	0.396596	−	1.03215i
$586$	−22.7664	−	9.82705i	−0.940471	−	0.405952i
$587$	28.3254			1.16911			0.584557	−	0.811352i	$-0.301268\pi$
$587$	28.3254			1.16911			0.584557	+	0.811352i	$0.301268\pi$
$588$	−22.3706	−	9.35710i	−0.922549	−	0.385880i
$589$			24.7621i			1.02030i
$590$	13.7584	−	10.2281i	0.566425	−	0.421084i
$591$	28.1976	−	2.22078i	1.15989	−	0.0913506i
$592$	1.86804	−	31.5422i	0.0767758	−	1.29638i
$593$			22.4706i			0.922757i	0.887203	+	0.461378i	$0.152645\pi$
$593$			22.4706i			0.922757i	−0.887203	+	0.461378i	$0.847355\pi$
$594$	6.16740	−	35.5657i	0.253051	−	1.45928i
$595$	−3.63722	+	1.67456i	−0.149112	+	0.0686504i
$596$	−15.7717	−	16.7334i	−0.646035	−	0.685427i
$597$	37.2588	−	2.93442i	1.52490	−	0.120098i
$598$	2.52708	−	5.85450i	0.103340	−	0.239408i
$599$		−	39.6684i		−	1.62081i	−0.585872	−	0.810403i	$-0.699248\pi$
$599$		−	39.6684i		−	1.62081i	0.585872	−	0.810403i	$-0.300752\pi$
$600$	19.9194	+	14.2554i	0.813208	+	0.581974i
$601$			4.47305i			0.182460i	0.995830	+	0.0912298i	$0.0290798\pi$
$601$			4.47305i			0.182460i	−0.995830	+	0.0912298i	$0.970920\pi$
$602$	−19.1493	−	31.3725i	−0.780465	−	1.27865i
$603$	−14.3202	+	2.26973i	−0.583164	+	0.0924307i
$604$	10.4112	+	11.0460i	0.423624	+	0.449454i
$605$	25.4173	+	14.6897i	1.03336	+	0.597222i
$606$	9.89322	+	3.37643i	0.401885	+	0.137158i
$607$	−23.3900			−0.949371			−0.474685	−	0.880156i	$-0.657438\pi$
$607$	−23.3900			−0.949371			−0.474685	+	0.880156i	$0.657438\pi$
$608$	−15.0954	+	29.9661i	−0.612199	+	1.21529i
$609$	−5.13219	+	8.62634i	−0.207967	+	0.349557i
$610$	−19.1878	−	25.8107i	−0.776892	−	1.04504i
$611$	40.4930			1.63817
$612$	2.48275	−	3.21366i	0.100359	−	0.129905i
$613$	−25.9593			−1.04849			−0.524243	−	0.851569i	$-0.675652\pi$
$613$	−25.9593			−1.04849			−0.524243	+	0.851569i	$0.675652\pi$
$614$	4.26686	−	9.88505i	0.172196	−	0.398928i
$615$	3.15684	−	6.61188i	0.127296	−	0.266617i
$616$	−9.69685	+	35.4568i	−0.390697	+	1.42860i
$617$	0.716676			0.0288523			0.0144262	−	0.999896i	$-0.495408\pi$
$617$	0.716676			0.0288523			0.0144262	+	0.999896i	$0.495408\pi$
$618$	−3.53920	+	10.3701i	−0.142368	+	0.417149i
$619$	−0.161608			−0.00649556			−0.00324778	−	0.999995i	$-0.501034\pi$
$619$	−0.161608			−0.00649556			−0.00324778	+	0.999995i	$0.501034\pi$
$620$	18.1705	−	4.28863i	0.729745	−	0.172235i
$621$	−1.37287	−	5.71419i	−0.0550912	−	0.229303i
$622$	−10.8419	−	4.67987i	−0.434720	−	0.187646i
$623$	−11.9506	−	8.44690i	−0.478789	−	0.338418i
$624$	−0.536950	−	27.6156i	−0.0214952	−	1.10551i
$625$	−12.5383	+	21.6285i	−0.501532	+	0.865139i
$626$	6.10720	+	2.63616i	0.244093	+	0.105362i
$627$	3.96225	+	50.3094i	0.158237	+	2.00916i
$628$	−10.3071	+	9.71471i	−0.411297	+	0.387659i
$629$		−	5.34655i		−	0.213181i
$630$	4.52248	+	24.6890i	0.180180	+	0.983634i
$631$	12.7413			0.507221			0.253611	−	0.967306i	$-0.418382\pi$
$631$	12.7413			0.507221			0.253611	+	0.967306i	$0.418382\pi$
$632$	9.25344	+	25.4817i	0.368082	+	1.01361i
$633$	3.43982	−	0.270913i	0.136721	−	0.0107678i
$634$	−0.496001	+	1.14909i	−0.0196987	+	0.0456362i
$635$	−11.0053	+	19.0423i	−0.436733	+	0.755670i
$636$	−33.5916	−	30.4499i	−1.33199	−	1.20742i
$637$	−26.3075	+	9.31239i	−1.04234	+	0.368970i
$638$	13.9702	+	6.03019i	0.553084	+	0.238737i
$639$	−0.868817	−	5.48154i	−0.0343699	−	0.216847i
$640$	24.6037	+	5.88712i	0.972546	+	0.232709i
$641$		−	14.5460i		−	0.574531i	−0.957851	−	0.287266i	$-0.907254\pi$
$641$		−	14.5460i		−	0.574531i	0.957851	−	0.287266i	$-0.0927462\pi$
$642$	36.4367	+	12.4354i	1.43804	+	0.490785i
$643$		−	42.8475i		−	1.68974i	−0.534970	−	0.844871i	$-0.679677\pi$
$643$		−	42.8475i		−	1.68974i	0.534970	−	0.844871i	$-0.320323\pi$
$644$	0.838267	+	5.92564i	0.0330324	+	0.233503i
$645$	−16.3921	+	34.3325i	−0.645437	+	1.35184i
$646$	−2.25003	+	5.21265i	−0.0885261	+	0.205089i
$647$		−	19.8509i		−	0.780419i	−0.920726	−	0.390210i	$-0.872403\pi$
$647$		−	19.8509i		−	0.780419i	0.920726	−	0.390210i	$-0.127597\pi$
$648$	−15.6620	−	20.0675i	−0.615260	−	0.788324i
$649$		−	26.6302i		−	1.04533i
$650$	28.0035	−	3.24109i	1.09839	−	0.127126i
$651$	16.4411	+	9.78152i	0.644377	+	0.383368i
$652$	−21.9069	−	23.2427i	−0.857942	−	0.910256i
$653$		−	21.7949i		−	0.852902i	−0.904511	−	0.426451i	$-0.859764\pi$
$653$		−	21.7949i		−	0.852902i	0.904511	−	0.426451i	$-0.140236\pi$
$654$	−5.59650	−	1.91002i	−0.218841	−	0.0746875i
$655$	11.7976	−	20.4131i	0.460969	−	0.797607i
$656$	0.447367	−	7.55389i	0.0174667	−	0.294930i
$657$	−29.4880	+	4.67381i	−1.15044	+	0.182343i
$658$	−32.4385	+	19.7999i	−1.26458	+	0.771882i
$659$	0.262720			0.0102341			0.00511706	−	0.999987i	$-0.498371\pi$
$659$	0.262720			0.0102341			0.00511706	+	0.999987i	$0.498371\pi$
$660$	36.2310	−	11.6208i	1.41029	−	0.452338i
$661$	−3.96725			−0.154308			−0.0771541	−	0.997019i	$-0.524583\pi$
$661$	−3.96725			−0.154308			−0.0771541	+	0.997019i	$0.524583\pi$
$662$	14.3037	−	33.1375i	0.555930	−	1.28793i
$663$	−0.366951	−	4.65924i	−0.0142512	−	0.180950i
$664$	10.1557	+	27.9662i	0.394116	+	1.08530i
$665$	−14.6752	−	31.8752i	−0.569080	−	1.23607i
$666$	−32.4699	−	8.30118i	−1.25818	−	0.321664i
$667$	2.47730			0.0959214
$668$	−21.4423	+	20.2100i	−0.829627	+	0.781948i
$669$	0.978065	+	12.4187i	0.0378142	+	0.480133i
$670$	−9.11811	−	12.2653i	−0.352263	−	0.473850i
$671$	−49.9580			−1.92861
$672$	13.9334	+	21.8600i	0.537493	+	0.843268i
$673$		−	33.8854i		−	1.30619i	−0.757277	−	0.653094i	$-0.773471\pi$
$673$		−	33.8854i		−	1.30619i	0.757277	−	0.653094i	$-0.226529\pi$
$674$	2.40741	−	5.57725i	0.0927298	−	0.214828i
$675$	18.8586	−	17.8704i	0.725868	−	0.687834i
$676$	−3.96991	−	4.21197i	−0.152689	−	0.161999i
$677$	−37.4703			−1.44010			−0.720051	−	0.693921i	$-0.755882\pi$
$677$	−37.4703			−1.44010			−0.720051	+	0.693921i	$0.755882\pi$
$678$	7.87817	−	23.0837i	0.302559	−	0.886523i
$679$	16.6035	+	11.7357i	0.637183	+	0.450374i
$680$	4.21475	+	0.748281i	0.161628	+	0.0286953i
$681$	3.85701	+	48.9731i	0.147801	+	1.87665i
$682$	11.4930	−	26.6260i	0.440091	−	1.01956i
$683$		−	16.6108i		−	0.635596i	−0.948158	−	0.317798i	$-0.897057\pi$
$683$		−	16.6108i		−	0.635596i	0.948158	−	0.317798i	$-0.102943\pi$
$684$	28.1632	+	21.7578i	1.07685	+	0.831930i
$685$	−17.3075	−	10.0027i	−0.661287	−	0.382184i
$686$	16.5212	−	20.3237i	0.630781	−	0.775961i
$687$	0.840454	+	10.6714i	0.0320653	+	0.407139i
$688$	−2.32297	+	39.2240i	−0.0885626	+	1.49540i
$689$	−52.1788			−1.98786
$690$	4.66592	−	4.07472i	0.177629	−	0.155122i
$691$	5.46652			0.207956			0.103978	−	0.994580i	$-0.466843\pi$
$691$	5.46652			0.207956			0.103978	+	0.994580i	$0.466843\pi$
$692$	14.9102	+	15.8193i	0.566799	+	0.601360i
$693$	34.9687	+	17.2425i	1.32835	+	0.654987i
$694$	13.5456	−	31.3813i	0.514186	−	1.19122i
$695$	13.1735	+	7.61351i	0.499700	+	0.288797i
$696$	9.76746	−	4.44331i	0.370235	−	0.168423i
$697$		−	1.28042i		−	0.0484993i
$698$	30.1594	+	13.0182i	1.14155	+	0.492747i
$699$	3.04524	+	38.6660i	0.115182	+	1.46248i
$700$	−20.8485	+	16.2893i	−0.787998	+	0.615678i
$701$	−6.39939			−0.241702			−0.120851	−	0.992671i	$-0.538562\pi$
$701$	−6.39939			−0.241702			−0.120851	+	0.992671i	$0.538562\pi$
$702$	−28.8656	−	5.00554i	−1.08946	−	0.188922i
$703$	46.8550			1.76717
$704$	30.1401	−	25.2154i	1.13595	−	0.950342i
$705$	35.4991	+	16.9491i	1.33697	+	0.638339i
$706$	−4.81854	+	11.1631i	−0.181348	+	0.420130i
$707$	−6.51716	+	9.22038i	−0.245103	+	0.346768i
$708$	−13.9142	−	12.6129i	−0.522928	−	0.474020i
$709$		−	46.4979i		−	1.74626i	−0.487483	−	0.873132i	$-0.662085\pi$
$709$		−	46.4979i		−	1.74626i	0.487483	−	0.873132i	$-0.337915\pi$
$710$	4.69496	−	3.49026i	0.176199	−	0.130987i
$711$	28.3998	−	4.50133i	1.06508	−	0.168813i
$712$	5.34008	+	14.7053i	0.200128	+	0.551103i
$713$		−	4.72153i		−	0.176823i
$714$	2.57220	+	3.55304i	0.0962620	+	0.132969i
$715$	21.9115	−	37.9131i	0.819444	−	1.41787i
$716$	−14.0369	−	14.8928i	−0.524583	−	0.556570i
$717$	−28.2208	+	2.22261i	−1.05393	+	0.0830049i
$718$	3.63061	−	8.41106i	0.135493	−	0.313898i
$719$	23.4319			0.873861			0.436931	−	0.899495i	$-0.356065\pi$
$719$	23.4319			0.873861			0.436931	+	0.899495i	$0.356065\pi$
$720$	11.0883	−	24.4346i	0.413236	−	0.910624i
$721$	−9.66487	−	6.83134i	−0.359939	−	0.254412i
$722$	−21.0116	−	9.06961i	−0.781971	−	0.337536i
$723$	9.59266	−	0.755496i	0.356755	−	0.0280972i
$724$	6.61682	+	7.02028i	0.245912	+	0.260907i
$725$	5.46755	+	9.48947i	0.203060	+	0.352430i
$726$	10.3872	−	30.4352i	0.385503	−	1.12956i
$727$	21.8578			0.810662			0.405331	−	0.914170i	$-0.367156\pi$
$727$	21.8578			0.810662			0.405331	+	0.914170i	$0.367156\pi$
$728$	28.7772	+	7.87008i	1.06655	+	0.291685i
$729$	−24.0531	+	12.2658i	−0.890855	+	0.454288i
$730$	−18.7759	−	25.2566i	−0.694927	−	0.934788i
$731$			6.64864i			0.245909i
$732$	−23.6616	+	26.1030i	−0.874559	+	0.964793i
$733$		−	11.0759i		−	0.409098i	−0.978856	−	0.204549i	$-0.934427\pi$
$733$		−	11.0759i		−	0.409098i	0.978856	−	0.204549i	$-0.0655728\pi$
$734$	31.0188	+	13.3892i	1.14493	+	0.494205i
$735$	−26.9609	−	2.84755i	−0.994469	−	0.105034i
$736$	2.87833	−	5.71382i	0.106097	−	0.210614i
$737$	−23.7402			−0.874480
$738$	−7.77605	−	1.98801i	−0.286240	−	0.0731796i
$739$			33.3063i			1.22519i	0.790396	+	0.612597i	$0.209875\pi$
$739$			33.3063i			1.22519i	−0.790396	+	0.612597i	$0.790125\pi$
$740$	−8.11499	−	34.3824i	−0.298313	−	1.26392i
$741$	40.8317	−	3.21581i	1.49999	−	0.118136i
$742$	41.7999	−	25.5140i	1.53452	−	0.936647i
$743$	−40.7456			−1.49481			−0.747406	−	0.664367i	$-0.768701\pi$
$743$	−40.7456			−1.49481			−0.747406	+	0.664367i	$0.768701\pi$
$744$	−8.46858	−	18.6160i	−0.310473	−	0.682495i
$745$	−22.2588	−	12.8643i	−0.815499	−	0.471310i
$746$	10.0323	+	4.33044i	0.367310	+	0.158549i
$747$	31.1688	−	4.94021i	1.14041	−	0.180753i
$748$	4.83878	−	4.56069i	0.176923	−	0.166755i
$749$	−24.0027	+	33.9586i	−0.877038	+	1.24082i
$750$	25.9065	+	8.87998i	0.945971	+	0.324251i
$751$	−12.0799			−0.440800			−0.220400	−	0.975410i	$-0.570736\pi$
$751$	−12.0799			−0.440800			−0.220400	+	0.975410i	$0.570736\pi$
$752$	40.5568	+	2.40191i	1.47895	+	0.0875885i
$753$	−17.0236	+	1.34074i	−0.620375	+	0.0488593i
$754$	4.89417	−	11.3384i	0.178235	−	0.412919i
$755$	14.6934	+	8.49189i	0.534746	+	0.309051i
$756$	25.5714	−	10.1046i	0.930024	−	0.367499i
$757$	3.29010			0.119581			0.0597903	−	0.998211i	$-0.480957\pi$
$757$	3.29010			0.119581			0.0597903	+	0.998211i	$0.480957\pi$
$758$	0.565469	−	1.31003i	0.0205388	−	0.0475823i
$759$	−0.755506	−	9.59279i	−0.0274231	−	0.348196i
$760$	−6.55764	+	36.9364i	−0.237871	+	1.33982i
$761$	25.6191			0.928690			0.464345	−	0.885654i	$-0.346290\pi$
$761$	25.6191			0.928690			0.464345	+	0.885654i	$0.346290\pi$
$762$	22.8016	+	7.78190i	0.826015	+	0.281909i
$763$	3.68670	−	5.21588i	0.133467	−	0.188828i
$764$	−19.4414	+	18.3241i	−0.703364	+	0.662941i
$765$	1.62851	−	4.23822i	0.0588789	−	0.153233i
$766$	0.476619	−	1.10419i	0.0172209	−	0.0398958i
$767$	−21.6134			−0.780413
$768$	1.10027	−	27.6910i	0.0397025	−	0.999212i
$769$		−	17.4725i		−	0.630074i	−0.949079	−	0.315037i	$-0.897983\pi$
$769$		−	17.4725i		−	0.630074i	0.949079	−	0.315037i	$-0.102017\pi$
$770$	0.985356	+	41.0858i	0.0355098	+	1.48063i
$771$	−4.16754	+	0.328226i	−0.150090	+	0.0118208i
$772$	−4.96262	+	4.67741i	−0.178609	+	0.168344i
$773$	11.6083			0.417522			0.208761	−	0.977967i	$-0.433057\pi$
$773$	11.6083			0.417522			0.208761	+	0.977967i	$0.433057\pi$
$774$	40.3775	+	10.3228i	1.45134	+	0.371047i
$775$	18.0861	−	10.4207i	0.649673	−	0.374323i
$776$	−7.41923	−	20.4307i	−0.266335	−	0.733420i
$777$	18.5087	−	31.1100i	0.663996	−	1.11606i
$778$	25.5318	+	11.0207i	0.915358	+	0.395112i
$779$	11.2211			0.402037
$780$	−9.43157	−	29.4055i	−0.337704	−	1.05289i
$781$		−	9.08735i		−	0.325171i
$782$	0.429026	−	0.993926i	0.0153419	−	0.0355427i
$783$	−2.65882	−	11.0666i	−0.0950184	−	0.395489i
$784$	−26.9013	+	7.76658i	−0.960761	+	0.277378i
$785$	−7.92383	+	13.7105i	−0.282814	+	0.489348i
$786$	−24.4431	−	8.34211i	−0.871855	−	0.297553i
$787$		−	16.9012i		−	0.602461i	−0.953551	−	0.301231i	$-0.902603\pi$
$787$		−	16.9012i		−	0.602461i	0.953551	−	0.301231i	$-0.0973974\pi$
$788$	23.7674	−	22.4015i	0.846679	−	0.798019i
$789$	3.46019	+	43.9346i	0.123186	+	1.56411i
$790$	18.0830	+	24.3245i	0.643364	+	0.865428i
$791$	21.5137	+	15.2064i	0.764941	+	0.540676i
$792$	−20.1845	−	36.4672i	−0.717226	−	1.29581i
$793$			40.5465i			1.43985i
$794$	−2.55724	+	5.92436i	−0.0907529	+	0.210248i
$795$	−45.7437	−	21.8404i	−1.62236	−	0.774598i
$796$	31.4050	−	29.6001i	1.11312	−	1.04915i
$797$	−33.9621			−1.20300			−0.601501	−	0.798872i	$-0.705430\pi$
$797$	−33.9621			−1.20300			−0.601501	+	0.798872i	$0.705430\pi$
$798$	−31.1374	+	22.5417i	−1.10225	+	0.797967i
$799$	6.87455			0.243204
$800$	28.2398	−	1.58512i	0.998428	−	0.0560425i
$801$	16.3893	−	2.59768i	0.579087	−	0.0917844i
$802$	−17.3119	+	40.1066i	−0.611305	+	1.41621i
$803$	−48.8855			−1.72513
$804$	−11.2441	+	12.4042i	−0.396548	+	0.437462i
$805$	2.79821	+	6.07782i	0.0986239	+	0.214215i
$806$	−21.6100	−	9.32789i	−0.761179	−	0.328561i
$807$	41.6086	−	3.27700i	1.46469	−	0.115356i
$808$	11.3458	−	4.12011i	0.399142	−	0.144945i
$809$			2.91273i			0.102406i	0.998688	+	0.0512031i	$0.0163056\pi$
$809$			2.91273i			0.102406i	−0.998688	+	0.0512031i	$0.983694\pi$
$810$	−23.2105	−	16.4704i	−0.815533	−	0.578711i
$811$	28.8933			1.01458			0.507291	−	0.861775i	$-0.330647\pi$
$811$	28.8933			1.01458			0.507291	+	0.861775i	$0.330647\pi$
$812$	1.62347	+	11.4761i	0.0569725	+	0.402733i
$813$	23.9970	−	1.88995i	0.841613	−	0.0662835i
$814$	−50.3820	−	21.7472i	−1.76589	−	0.762240i
$815$	−30.9175	−	17.8685i	−1.08299	−	0.625905i
$816$	−0.0911587	−	4.68834i	−0.00319119	−	0.164125i
$817$	−58.2660			−2.03847
$818$	5.57089	−	12.9061i	0.194782	−	0.451251i
$819$	13.9942	−	28.3811i	0.488997	−	0.991714i
$820$	−1.94342	−	8.23407i	−0.0678671	−	0.287546i
$821$	25.8420			0.901893			0.450947	−	0.892551i	$-0.351086\pi$
$821$	25.8420			0.901893			0.450947	+	0.892551i	$0.351086\pi$
$822$	−7.07297	+	20.7244i	−0.246698	+	0.722845i
$823$		−	17.0702i		−	0.595030i	−0.954717	−	0.297515i	$-0.903842\pi$
$823$		−	17.0702i		−	0.595030i	0.954717	−	0.297515i	$-0.0961579\pi$
$824$	4.31873	+	11.8927i	0.150450	+	0.414302i
$825$	35.0784	−	24.0659i	1.22127	−	0.837867i
$826$	17.3142	−	10.5683i	0.602439	−	0.367719i
$827$			22.5646i			0.784647i	0.919827	+	0.392323i	$0.128329\pi$
$827$			22.5646i			0.784647i	−0.919827	+	0.392323i	$0.871671\pi$
$828$	−5.37005	−	4.14869i	−0.186622	−	0.144177i
$829$	36.6005			1.27119			0.635593	−	0.772024i	$-0.280756\pi$
$829$	36.6005			1.27119			0.635593	+	0.772024i	$0.280756\pi$
$830$	19.8461	+	26.6962i	0.688869	+	0.926639i
$831$	2.32517	+	29.5231i	0.0806593	+	1.02414i
$832$	−20.4651	−	24.4621i	−0.709501	−	0.848070i
$833$	−4.46626	+	1.58098i	−0.154747	+	0.0547776i
$834$	5.38354	−	15.7742i	0.186417	−	0.546217i
$835$	−16.4843	+	28.5226i	−0.570464	+	0.987064i
$836$	39.9681	+	42.4052i	1.38233	+	1.46661i
$837$	−21.0921	+	5.06749i	−0.729049	+	0.175158i
$838$	−9.55966	+	22.1469i	−0.330233	+	0.765052i
$839$	31.5392			1.08885			0.544427	−	0.838808i	$-0.316747\pi$
$839$	31.5392			1.08885			0.544427	+	0.838808i	$0.316747\pi$
$840$	21.9340	+	18.9447i	0.756794	+	0.653653i
$841$	−24.2022			−0.834560
$842$	6.65246	−	15.4118i	0.229259	−	0.531126i
$843$	−52.5427	+	4.13814i	−1.80967	+	0.142525i
$844$	2.89938	−	2.73275i	0.0998009	−	0.0940652i
$845$	−5.60277	−	3.23807i	−0.192741	−	0.111393i
$846$	10.6736	−	41.7495i	0.366966	−	1.43538i
$847$	28.3653	+	20.0492i	0.974643	+	0.688898i
$848$	−52.2610	−	3.09507i	−1.79465	−	0.106285i
$849$	38.5145	−	3.03332i	1.32181	−	0.104103i
$850$	4.75419	−	0.550244i	0.163067	−	0.0188732i
$851$	−8.93412			−0.306258
$852$	−4.74813	−	4.30405i	−0.162668	−	0.147454i
$853$		−	14.2692i		−	0.488568i	−0.969704	−	0.244284i	$-0.921447\pi$
$853$		−	14.2692i		−	0.488568i	0.969704	−	0.244284i	$-0.0785529\pi$
$854$	−19.8261	−	32.4813i	−0.678434	−	1.11149i
$855$	37.1421	+	14.2716i	1.27023	+	0.488079i
$856$	41.7864	−	15.1743i	1.42823	−	0.518648i
$857$		−	44.9590i		−	1.53577i	−0.640587	−	0.767886i	$-0.721309\pi$
$857$		−	44.9590i		−	1.53577i	0.640587	−	0.767886i	$-0.278691\pi$
$858$	−45.3978	−	15.4937i	−1.54986	−	0.528947i
$859$	8.35557			0.285088			0.142544	−	0.989788i	$-0.454472\pi$
$859$	8.35557			0.285088			0.142544	+	0.989788i	$0.454472\pi$
$860$	10.0913	+	42.7558i	0.344110	+	1.45796i
$861$	4.43256	−	7.45038i	0.151061	−	0.253908i
$862$	−6.19175	+	14.3445i	−0.210892	+	0.488575i
$863$	−33.6919			−1.14689			−0.573444	−	0.819245i	$-0.694393\pi$
$863$	−33.6919			−1.14689			−0.573444	+	0.819245i	$0.694393\pi$
$864$	−28.6141	−	6.72562i	−0.973471	−	0.228810i
$865$	21.0429	+	12.1615i	0.715479	+	0.413504i
$866$	−35.1581	−	15.1759i	−1.19472	−	0.515699i
$867$	2.24955	+	28.5630i	0.0763989	+	0.970049i
$868$	21.8726	−	3.09419i	0.742403	−	0.105024i
$869$	47.0814			1.59713
$870$	9.03645	−	7.89148i	0.306364	−	0.267546i
$871$			19.2678i			0.652865i
$872$	−6.41819	+	2.33071i	−0.217347	+	0.0789277i
$873$	−22.7704	+	3.60908i	−0.770661	+	0.122149i
$874$	8.71037	+	3.75981i	0.294633	+	0.127177i
$875$	−17.1057	+	24.1329i	−0.578278	+	0.815840i
$876$	−23.1537	+	25.5426i	−0.782289	+	0.863004i
$877$	7.24055			0.244496			0.122248	−	0.992500i	$-0.460990\pi$
$877$	7.24055			0.244496			0.122248	+	0.992500i	$0.460990\pi$
$878$	5.43390	−	12.5887i	0.183385	−	0.424849i
$879$	2.38446	+	30.2759i	0.0804260	+	1.02118i
$880$	24.1949	−	36.6731i	0.815609	−	1.23625i
$881$	−41.5264			−1.39906			−0.699531	−	0.714603i	$-0.746608\pi$
$881$	−41.5264			−1.39906			−0.699531	+	0.714603i	$0.746608\pi$
$882$	2.66693	+	29.5785i	0.0898003	+	0.995960i
$883$	−10.8468			−0.365023			−0.182512	−	0.983204i	$-0.558423\pi$
$883$	−10.8468			−0.365023			−0.182512	+	0.983204i	$0.558423\pi$
$884$	−3.70151	−	3.92722i	−0.124495	−	0.132087i
$885$	−18.9478	−	9.04665i	−0.636924	−	0.304100i
$886$	−8.63289	+	19.9999i	−0.290028	+	0.671909i
$887$			37.6663i			1.26471i	0.774678	+	0.632355i	$0.217912\pi$
$887$			37.6663i			1.26471i	−0.774678	+	0.632355i	$0.782088\pi$
$888$	−35.2253	+	16.0243i	−1.18209	+	0.537741i
$889$	−15.0206	+	21.2509i	−0.503773	+	0.712731i
$890$	10.4355	+	14.0375i	0.349800	+	0.470537i
$891$	−42.0422	+	13.6707i	−1.40847	+	0.457985i
$892$	9.86595	+	10.4675i	0.330336	+	0.350479i
$893$			60.2458i			2.01605i
$894$	−9.09637	+	26.6531i	−0.304228	+	0.891413i
$895$	−19.8104	−	11.4492i	−0.662189	−	0.382706i
$896$	28.3556	+	9.58943i	0.947296	+	0.320360i
$897$	−7.78562	+	0.613178i	−0.259954	+	0.0204734i
$898$	2.62042	−	6.07075i	0.0874446	−	0.202583i
$899$		−	9.14414i		−	0.304974i
$900$	4.03981	−	29.7268i	0.134660	−	0.990892i
$901$	−8.85847			−0.295118
$902$	−12.0657	−	5.20814i	−0.401745	−	0.173412i
$903$	−23.0163	+	38.6865i	−0.765934	+	1.28740i
$904$	−9.61337	−	26.4728i	−0.319736	−	0.880473i
$905$	9.33838	+	5.39703i	0.310418	+	0.179403i
$906$	6.00465	−	17.5941i	0.199491	−	0.584525i
$907$	−47.3931			−1.57366			−0.786831	−	0.617168i	$-0.788280\pi$
$907$	−47.3931			−1.57366			−0.786831	+	0.617168i	$0.788280\pi$
$908$	38.9065	+	41.2788i	1.29116	+	1.36989i
$909$	−2.00422	−	12.6451i	−0.0664759	−	0.419410i
$910$	33.3458	−	0.799727i	1.10540	−	0.0265107i
$911$			53.2694i			1.76489i	0.470413	+	0.882446i	$0.344105\pi$
$911$			53.2694i			1.76489i	−0.470413	+	0.882446i	$0.655895\pi$
$912$	41.0868	−	0.798879i	1.36052	−	0.0264535i
$913$	51.6719			1.71009
$914$	16.8800	−	39.1061i	0.558342	−	1.29351i
$915$	−16.9714	+	35.5460i	−0.561059	+	1.17511i
$916$	8.47784	+	8.99478i	0.280116	+	0.297196i
$917$	16.1019	−	22.7807i	0.531731	−	0.752285i
$918$	−4.90054	−	0.849796i	−0.161742	−	0.0280475i
$919$	19.2426			0.634754			0.317377	−	0.948299i	$-0.397198\pi$
$919$	19.2426			0.634754			0.317377	+	0.948299i	$0.397198\pi$
$920$	1.25038	−	7.04288i	0.0412239	−	0.232197i
$921$	−13.1457	+	1.03532i	−0.433164	+	0.0341150i
$922$	−11.7247	+	27.1627i	−0.386133	+	0.894557i
$923$	−7.37541			−0.242764
$924$	43.9437	−	9.78640i	1.44564	−	0.321949i
$925$	−19.7182	−	34.2228i	−0.648329	−	1.12524i
$926$	−7.53425	+	17.4546i	−0.247591	+	0.573595i
$927$	13.2546	−	2.10084i	0.435339	−	0.0690007i
$928$	5.57443	−	11.0659i	0.182990	−	0.363256i
$929$	14.6916			0.482015			0.241007	−	0.970523i	$-0.422522\pi$
$929$	14.6916			0.482015			0.241007	+	0.970523i	$0.422522\pi$
$930$	−15.0405	−	17.2227i	−0.493197	−	0.564755i
$931$	−13.8550	−	39.1405i	−0.454081	−	1.28278i
$932$	30.7180	+	32.5911i	1.00620	+	1.06756i
$933$	1.13554	+	14.4181i	0.0371758	+	0.472028i
$934$	−0.675544	−	0.291597i	−0.0221045	−	0.00954135i
$935$	3.71994	−	6.43655i	0.121655	−	0.210498i
$936$	−29.5973	+	16.3820i	−0.967417	+	0.535463i
$937$	39.8368			1.30141			0.650706	−	0.759330i	$-0.274473\pi$
$937$	39.8368			1.30141			0.650706	+	0.759330i	$0.274473\pi$
$938$	−9.42141	−	15.4352i	−0.307620	−	0.503978i
$939$	−0.639645	−	8.12167i	−0.0208740	−	0.265041i
$940$	44.2086	−	10.4342i	1.44193	−	0.340326i
$941$			23.1444i			0.754486i	0.926114	+	0.377243i	$0.123128\pi$
$941$			23.1444i			0.754486i	−0.926114	+	0.377243i	$0.876872\pi$
$942$	16.4172	+	5.60297i	0.534900	+	0.182555i
$943$	−2.13959			−0.0696746
$944$	−21.6474	−	1.28203i	−0.704562	−	0.0417265i
$945$	24.1477	−	19.0234i	0.785525	−	0.618830i
$946$	62.6519	+	27.0435i	2.03699	+	0.879261i
$947$			43.7023i			1.42013i	0.704134	+	0.710067i	$0.251335\pi$
$947$			43.7023i			1.42013i	−0.704134	+	0.710067i	$0.748665\pi$
$948$	22.2992	−	24.6000i	0.724244	−	0.798970i
$949$			39.6760i			1.28794i
$950$	4.82212	+	41.6638i	0.156450	+	1.35175i
$951$	1.52812	−	0.120351i	0.0495527	−	0.00390266i
$952$	4.88554	+	1.33611i	0.158341	+	0.0433037i
$953$	36.5317			1.18338			0.591689	−	0.806166i	$-0.298461\pi$
$953$	36.5317			1.18338			0.591689	+	0.806166i	$0.298461\pi$
$954$	−13.7539	+	53.7980i	−0.445298	+	1.74177i
$955$	−14.9461	+	25.8609i	−0.483644	+	0.836840i
$956$	−23.7870	+	22.4199i	−0.769327	+	0.725113i
$957$	−1.46318	−	18.5783i	−0.0472980	−	0.600550i
$958$	15.0958	+	6.51608i	0.487725	+	0.210525i
$959$	−19.3149	−	13.6522i	−0.623711	−	0.440852i
$960$	−7.70218	−	30.0113i	−0.248587	−	0.968610i
$961$	13.5720			0.437808
$962$	−17.6503	+	40.8906i	−0.569069	+	1.31837i
$963$	−7.38154	−	46.5716i	−0.237867	−	1.50075i
$964$	8.08553	−	7.62085i	0.260418	−	0.245451i
$965$	−3.81515	+	6.60128i	−0.122814	+	0.212503i
$966$	5.93715	−	4.29816i	0.191025	−	0.138291i
$967$			36.3751i			1.16974i	0.811126	+	0.584872i	$0.198855\pi$
$967$			36.3751i			1.16974i	−0.811126	+	0.584872i	$0.801145\pi$
$968$	−12.6750	−	34.9037i	−0.407389	−	1.12185i
$969$	6.93205	−	0.545953i	0.222690	−	0.0175385i
$970$	−14.4986	−	19.5029i	−0.465522	−	0.626202i
$971$			2.78507i			0.0893771i	0.999001	+	0.0446885i	$0.0142295\pi$
$971$			2.78507i			0.0893771i	−0.999001	+	0.0446885i	$0.985770\pi$
$972$	−12.7696	+	28.4418i	−0.409584	+	0.912272i
$973$	14.7014	+	10.3913i	0.471306	+	0.333129i
$974$	1.39755	−	3.23771i	0.0447804	−	0.103743i
$975$	−19.5322	−	28.4701i	−0.625530	−	0.911771i
$976$	−2.40508	+	40.6103i	−0.0769847	+	1.29990i
$977$	7.27766			0.232833			0.116417	−	0.993200i	$-0.462859\pi$
$977$	7.27766			0.232833			0.116417	+	0.993200i	$0.462859\pi$
$978$	−12.6349	+	37.0212i	−0.404019	+	1.18381i
$979$	27.1703			0.868366
$980$	−26.3219	+	16.9458i	−0.840821	+	0.541313i
$981$	1.13377	+	7.15319i	0.0361985	+	0.228384i
$982$	−32.9156	−	14.2079i	−1.05038	−	0.453393i
$983$			19.1824i			0.611822i	0.952060	+	0.305911i	$0.0989610\pi$
$983$			19.1824i			0.611822i	−0.952060	+	0.305911i	$0.901039\pi$
$984$	−8.43594	+	3.83759i	−0.268928	+	0.122338i
$985$	18.2718	−	31.6154i	0.582189	−	1.00735i
$986$	0.830890	−	1.92493i	0.0264609	−	0.0613022i
$987$	40.0010	+	23.7983i	1.27325	+	0.757510i
$988$	34.4166	−	32.4386i	1.09494	−	1.03201i
$989$	11.1099			0.353275
$990$	−33.3139	−	32.5850i	−1.05878	−	1.03562i
$991$	−8.81398			−0.279985			−0.139993	−	0.990153i	$-0.544708\pi$
$991$	−8.81398			−0.279985			−0.139993	+	0.990153i	$0.544708\pi$
$992$	−21.0907	−	10.6244i	−0.669630	−	0.337325i
$993$	−44.0680	+	3.47070i	−1.39846	+	0.110139i
$994$	5.90835	−	3.60636i	0.187402	−	0.114387i
$995$	24.1434	−	41.7750i	0.765398	−	1.32436i
$996$	24.4734	−	26.9985i	0.775470	−	0.855480i
$997$		−	27.5716i		−	0.873202i	−0.899655	−	0.436601i	$-0.856182\pi$
$997$		−	27.5716i		−	0.873202i	0.899655	−	0.436601i	$-0.143818\pi$
$998$	−21.2531	+	49.2371i	−0.672754	+	1.55857i
$999$	9.58875	+	39.9107i	0.303375	+	1.26272i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.u.e.629.12	yes	160
3.2	odd	2	inner	840.2.u.e.629.150	yes	160
5.4	even	2	inner	840.2.u.e.629.149	yes	160
7.6	odd	2	inner	840.2.u.e.629.9	✓	160
8.5	even	2	inner	840.2.u.e.629.13	yes	160
15.14	odd	2	inner	840.2.u.e.629.11	yes	160
21.20	even	2	inner	840.2.u.e.629.151	yes	160
24.5	odd	2	inner	840.2.u.e.629.147	yes	160
35.34	odd	2	inner	840.2.u.e.629.152	yes	160
40.29	even	2	inner	840.2.u.e.629.148	yes	160
56.13	odd	2	inner	840.2.u.e.629.16	yes	160
105.104	even	2	inner	840.2.u.e.629.10	yes	160
120.29	odd	2	inner	840.2.u.e.629.14	yes	160
168.125	even	2	inner	840.2.u.e.629.146	yes	160
280.69	odd	2	inner	840.2.u.e.629.145	yes	160
840.629	even	2	inner	840.2.u.e.629.15	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.u.e.629.9	✓	160	7.6	odd	2	inner
840.2.u.e.629.10	yes	160	105.104	even	2	inner
840.2.u.e.629.11	yes	160	15.14	odd	2	inner
840.2.u.e.629.12	yes	160	1.1	even	1	trivial
840.2.u.e.629.13	yes	160	8.5	even	2	inner
840.2.u.e.629.14	yes	160	120.29	odd	2	inner
840.2.u.e.629.15	yes	160	840.629	even	2	inner
840.2.u.e.629.16	yes	160	56.13	odd	2	inner
840.2.u.e.629.145	yes	160	280.69	odd	2	inner
840.2.u.e.629.146	yes	160	168.125	even	2	inner
840.2.u.e.629.147	yes	160	24.5	odd	2	inner
840.2.u.e.629.148	yes	160	40.29	even	2	inner
840.2.u.e.629.149	yes	160	5.4	even	2	inner
840.2.u.e.629.150	yes	160	3.2	odd	2	inner
840.2.u.e.629.151	yes	160	21.20	even	2	inner
840.2.u.e.629.152	yes	160	35.34	odd	2	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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.u (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29842 - 0.560458i) q^{2} +(0.135991 + 1.72670i) q^{3} +(1.37177 + 1.45542i) q^{4} +(1.93600 + 1.11889i) q^{5} +(0.791172 - 2.31820i) q^{6} +(2.16054 + 1.52711i) q^{7} +(-0.965432 - 2.65856i) q^{8} +(-2.96301 + 0.469633i) q^{9} +(-1.88664 - 2.53783i) q^{10} -4.91211 q^{11} +(-2.32653 + 2.56657i) q^{12} +3.98673i q^{13} +(-1.94940 - 3.19372i) q^{14} +(-1.66871 + 3.49505i) q^{15} +(-0.236479 + 3.99300i) q^{16} +0.676832i q^{17} +(4.11044 + 1.05087i) q^{18} -5.93148 q^{19} +(1.02729 + 4.35255i) q^{20} +(-2.34306 + 3.93828i) q^{21} +(6.37797 + 2.75303i) q^{22} +1.13099 q^{23} +(4.45926 - 2.02856i) q^{24} +(2.49617 + 4.33234i) q^{25} +(2.23440 - 5.17643i) q^{26} +(-1.21386 - 5.05238i) q^{27} +(0.741180 + 5.23934i) q^{28} +2.19038 q^{29} +(4.12552 - 3.60279i) q^{30} -4.17468i q^{31} +(2.54496 - 5.05205i) q^{32} +(-0.668004 - 8.48176i) q^{33} +(0.379336 - 0.878810i) q^{34} +(2.47412 + 5.37389i) q^{35} +(-4.74809 - 3.66819i) q^{36} -7.89938 q^{37} +(7.70154 + 3.32435i) q^{38} +(-6.88390 + 0.542160i) q^{39} +(1.10556 - 6.22718i) q^{40} -1.89178 q^{41} +(5.24951 - 3.80035i) q^{42} +9.82318 q^{43} +(-6.73830 - 7.14917i) q^{44} +(-6.26185 - 2.40608i) q^{45} +(-1.46850 - 0.633873i) q^{46} -10.1570i q^{47} +(-6.92689 + 0.134684i) q^{48} +(2.33585 + 6.59877i) q^{49} +(-0.812970 - 7.02418i) q^{50} +(-1.16869 + 0.0920432i) q^{51} +(-5.80235 + 5.46888i) q^{52} +13.0881i q^{53} +(-1.25555 + 7.24041i) q^{54} +(-9.50983 - 5.49611i) q^{55} +(1.97407 - 7.21824i) q^{56} +(-0.806630 - 10.2419i) q^{57} +(-2.84403 - 1.22762i) q^{58} +5.42133i q^{59} +(-7.37586 + 2.36574i) q^{60} +10.1704 q^{61} +(-2.33974 + 5.42048i) q^{62} +(-7.11888 - 3.51020i) q^{63} +(-6.13588 + 5.13332i) q^{64} +(-4.46071 + 7.71829i) q^{65} +(-3.88632 + 11.3872i) q^{66} +4.83299 q^{67} +(-0.985073 + 0.928459i) q^{68} +(0.153805 + 1.95289i) q^{69} +(-0.200597 - 8.36420i) q^{70} +1.84999i q^{71} +(4.10914 + 7.42395i) q^{72} +9.95203 q^{73} +(10.2567 + 4.42727i) q^{74} +(-7.14121 + 4.89930i) q^{75} +(-8.13665 - 8.63278i) q^{76} +(-10.6128 - 7.50135i) q^{77} +(9.24203 + 3.15419i) q^{78} -9.58477 q^{79} +(-4.92556 + 7.46585i) q^{80} +(8.55889 - 2.78306i) q^{81} +(2.45632 + 1.06027i) q^{82} -10.5193 q^{83} +(-8.94599 + 1.99230i) q^{84} +(-0.757301 + 1.31034i) q^{85} +(-12.7546 - 5.50548i) q^{86} +(0.297873 + 3.78214i) q^{87} +(4.74231 + 13.0591i) q^{88} -5.53129 q^{89} +(6.78199 + 6.63360i) q^{90} +(-6.08819 + 8.61348i) q^{91} +(1.55146 + 1.64606i) q^{92} +(7.20844 - 0.567720i) q^{93} +(-5.69255 + 13.1880i) q^{94} +(-11.4833 - 6.63668i) q^{95} +(9.06948 + 3.70736i) q^{96} +7.68488 q^{97} +(0.665433 - 9.87710i) q^{98} +(14.5546 - 2.30689i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 24 q^{4} - 32 q^{9} - 48 q^{15} - 104 q^{16} - 16 q^{25} - 32 q^{30} + 48 q^{36} - 64 q^{39} - 64 q^{46} + 144 q^{49} + 16 q^{60} - 72 q^{64} + 8 q^{70} - 96 q^{79} + 16 q^{81} - 72 q^{84}+O(q^{100}) \) 160 * q - 24 * q^4 - 32 * q^9 - 48 * q^15 - 104 * q^16 - 16 * q^25 - 32 * q^30 + 48 * q^36 - 64 * q^39 - 64 * q^46 + 144 * q^49 + 16 * q^60 - 72 * q^64 + 8 * q^70 - 96 * q^79 + 16 * q^81 - 72 * q^84

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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