LMFDB - Embedded newform 840.2.u.e.629.151

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)

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")

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);

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			629.151
Character	$\chi$	$=$	840.629
Dual form			840.2.u.e.629.148

$q$-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} +(1.14432 - 2.16576i) 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} +(2.69962 - 2.17072i) q^{12} -3.98673i q^{13} +(-3.66116 + 0.771938i) q^{14} +(2.19527 - 3.19073i) q^{15} +(-0.236479 + 3.99300i) q^{16} +0.676832i q^{17} +(-3.58402 - 2.27043i) 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} +(4.72184 - 1.30547i) q^{24} +(2.49617 + 4.33234i) q^{25} +(2.23440 - 5.17643i) q^{26} +(-1.21386 + 5.05238i) q^{27} +(-5.18635 - 1.04963i) q^{28} -2.19038 q^{29} +(4.63865 - 2.91254i) q^{30} +4.17468i q^{31} +(-2.54496 + 5.05205i) q^{32} +(0.668004 - 8.48176i) q^{33} +(-0.379336 + 0.878810i) q^{34} +(-5.89147 + 0.539081i) q^{35} +(-3.38107 - 4.95665i) 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} +(0.835023 + 6.42672i) q^{42} +9.82318 q^{43} +(6.73830 + 7.14917i) q^{44} +(-5.21091 - 4.22450i) q^{45} +(-1.46850 - 0.633873i) q^{46} -10.1570i q^{47} +(6.86258 + 0.951343i) 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} +(-4.40775 + 5.87978i) q^{54} +(9.50983 + 5.49611i) q^{55} +(-6.14578 - 4.26960i) q^{56} +(0.806630 - 10.2419i) q^{57} +(-2.84403 - 1.22762i) q^{58} +5.42133i q^{59} +(7.65526 - 1.18193i) 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} +(5.62102 - 10.6385i) q^{66} +4.83299 q^{67} +(-0.985073 + 0.928459i) q^{68} +(-0.153805 + 1.95289i) q^{69} +(-7.95171 - 2.60197i) q^{70} -1.84999i q^{71} +(-1.61204 - 8.33075i) q^{72} -9.95203 q^{73} +(-10.2567 - 4.42727i) q^{74} +(7.82012 - 3.72098i) q^{75} +(8.13665 + 8.63278i) q^{76} +(-10.6128 + 7.50135i) q^{77} +(-8.63431 - 4.56209i) 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} +(-2.51770 + 8.81256i) 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} +(-4.39829 - 8.40566i) 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} +(8.37730 + 5.08143i) q^{96} -7.68488 q^{97} +(6.73124 - 7.25881i) 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
$6$	1.14432	−	2.16576i	0.467166	−	0.884169i
$7$	−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	$-0.234575\pi$
$11$	4.91211			1.48106			0.740528	+	0.672025i	$0.234575\pi$
$12$	2.69962	−	2.17072i	0.779314	−	0.626633i
$13$		−	3.98673i		−	1.10572i	−0.833274	−	0.552860i	$-0.813537\pi$
$13$		−	3.98673i		−	1.10572i	0.833274	−	0.552860i	$-0.186463\pi$
$14$	−3.66116	+	0.771938i	−0.978487	+	0.206309i
$15$	2.19527	−	3.19073i	0.566817	−	0.823844i
$16$	−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	$0.973844\pi$
$18$	−3.58402	−	2.27043i	−0.844761	−	0.535144i
$19$	5.93148			1.36078			0.680388	−	0.732852i	$-0.261811\pi$
$19$	5.93148			1.36078			0.680388	+	0.732852i	$0.261811\pi$
$20$	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	$-0.537621\pi$
$23$	−1.13099			−0.235828			−0.117914	+	0.993024i	$0.537621\pi$
$24$	4.72184	−	1.30547i	0.963841	−	0.266479i
$25$	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
$28$	−5.18635	−	1.04963i	−0.980129	−	0.198362i
$29$	−2.19038			−0.406743			−0.203372	−	0.979102i	$-0.565190\pi$
$29$	−2.19038			−0.406743			−0.203372	+	0.979102i	$0.565190\pi$
$30$	4.63865	−	2.91254i	0.846898	−	0.531755i
$31$			4.17468i			0.749795i	0.927066	+	0.374897i	$0.122322\pi$
$31$			4.17468i			0.749795i	−0.927066	+	0.374897i	$0.877678\pi$
$32$	−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
$35$	−5.89147	+	0.539081i	−0.995840	+	0.0911213i
$36$	−3.38107	−	4.95665i	−0.563511	−	0.826108i
$37$	−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	$0.547195\pi$
$42$	0.835023	+	6.42672i	0.128847	+	0.991665i
$43$	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
$45$	−5.21091	−	4.22450i	−0.776797	−	0.629751i
$46$	−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	$-0.265540\pi$
$48$	6.86258	+	0.951343i	0.990527	+	0.137315i
$49$	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	$-0.644370\pi$
$53$		−	13.0881i		−	1.79779i	0.438160	−	0.898897i	$-0.355630\pi$
$54$	−4.40775	+	5.87978i	−0.599818	+	0.800136i
$55$	9.50983	+	5.49611i	1.28230	+	0.741096i
$56$	−6.14578	−	4.26960i	−0.821264	−	0.570549i
$57$	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	$0.885196\pi$
$60$	7.65526	−	1.18193i	0.988290	−	0.152586i
$61$	−10.1704			−1.30218			−0.651091	−	0.759000i	$-0.725688\pi$
$61$	−10.1704			−1.30218			−0.651091	+	0.759000i	$0.725688\pi$
$62$	−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
$66$	5.62102	−	10.6385i	0.691900	−	1.30950i
$67$	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
$70$	−7.95171	−	2.60197i	−0.950412	−	0.310995i
$71$		−	1.84999i		−	0.219553i	−0.993956	−	0.109777i	$-0.964986\pi$
$71$		−	1.84999i		−	0.219553i	0.993956	−	0.109777i	$-0.0350136\pi$
$72$	−1.61204	−	8.33075i	−0.189981	−	0.981788i
$73$	−9.95203			−1.16480			−0.582399	−	0.812903i	$-0.697886\pi$
$73$	−9.95203			−1.16480			−0.582399	+	0.812903i	$0.697886\pi$
$74$	−10.2567	−	4.42727i	−1.19232	−	0.514660i
$75$	7.82012	−	3.72098i	0.902990	−	0.429662i
$76$	8.13665	+	8.63278i	0.933337	+	0.990248i
$77$	−10.6128	+	7.50135i	−1.20944	+	0.854858i
$78$	−8.63431	−	4.56209i	−0.977643	−	0.516555i
$79$	−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	$0.695902\pi$
$84$	−2.51770	+	8.81256i	−0.274704	+	0.961529i
$85$	−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	$0.594706\pi$
$90$	−4.39829	−	8.40566i	−0.463620	−	0.886034i
$91$	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
$96$	8.37730	+	5.08143i	0.855004	+	0.518621i
$97$	−7.68488			−0.780281			−0.390141	−	0.920755i	$-0.627574\pi$
$97$	−7.68488			−0.780281			−0.390141	+	0.920755i	$0.627574\pi$
$98$	6.73124	−	7.25881i	0.679958	−	0.733251i
$99$	−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	$0.931897\pi$
$102$	1.46586	+	0.774512i	0.145142	+	0.0766881i
$103$	4.47336			0.440774			0.220387	−	0.975413i	$-0.429268\pi$
$103$	4.47336			0.440774			0.220387	+	0.975413i	$0.429268\pi$
$104$	10.5990	−	3.84891i	1.03931	−	0.377417i
$105$	0.129645	+	10.2461i	0.0126520	+	0.999920i
$106$	7.33536	−	16.9939i	0.712473	−	1.65059i
$107$		−	15.7177i		−	1.51948i	−0.650225	−	0.759742i	$-0.725325\pi$
$107$		−	15.7177i		−	1.51948i	0.650225	−	0.759742i	$-0.274675\pi$
$108$	−9.01846	+	5.16404i	−0.867802	+	0.496910i
$109$		−	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
$112$	−5.58685	−	8.98817i	−0.527908	−	0.849302i
$113$	−9.95759			−0.936731			−0.468365	−	0.883535i	$-0.655157\pi$
$113$	−9.95759			−0.936731			−0.468365	+	0.883535i	$0.655157\pi$
$114$	6.78751	−	12.8462i	0.635708	−	1.20316i
$115$	−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
$120$	10.6021	+	2.75582i	0.967839	+	0.251571i
$121$	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
$126$	11.2106	−	0.567859i	0.998720	−	0.0505889i
$127$			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	$-0.152372\pi$
$132$	13.2608	−	10.6628i	1.15421	−	0.928079i
$133$	−12.8152	+	9.05805i	−1.11122	+	0.785432i
$134$	6.27523	+	2.70869i	0.542098	+	0.233995i
$135$	−8.00309	+	8.42321i	−0.688797	+	0.724955i
$136$	−1.79940	+	0.653435i	−0.154297	+	0.0560316i
$137$	8.93986			0.763784			0.381892	−	0.924207i	$-0.375273\pi$
$137$	8.93986			0.763784			0.381892	+	0.924207i	$0.375273\pi$
$138$	−1.29421	+	2.44946i	−0.110171	+	0.208512i
$139$	−6.80452			−0.577152			−0.288576	−	0.957457i	$-0.593182\pi$
$139$	−6.80452			−0.577152			−0.288576	+	0.957457i	$0.593182\pi$
$140$	−8.86634	−	7.83505i	−0.749343	−	0.662182i
$141$	−17.5381	−	1.38126i	−1.47697	−	0.116323i
$142$	1.03684	−	2.40206i	0.0870099	−	0.201576i
$143$		−	19.5832i		−	1.63763i
$144$	2.57594	−	11.7203i	0.214661	−	0.976689i
$145$	−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	$-0.343912\pi$
$149$	11.4973			0.941898			0.470949	+	0.882160i	$0.343912\pi$
$150$	12.2392	−	0.448531i	0.999329	−	0.0366224i
$151$	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
$154$	−17.9840	+	3.79184i	−1.44919	+	0.305556i
$155$	−4.67101	+	8.08217i	−0.375185	+	0.649175i
$156$	−8.65407	−	10.7627i	−0.692881	−	0.861703i
$157$		−	7.08186i		−	0.565194i	−0.959239	−	0.282597i	$-0.908804\pi$
$157$		−	7.08186i		−	0.565194i	0.959239	−	0.282597i	$-0.0911960\pi$
$158$	−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
$162$	9.55322	+	8.41047i	0.750572	+	0.660789i
$163$	−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
$165$	10.7834	−	15.6732i	0.839488	−	1.22016i
$166$	−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	$0.806933\pi$
$168$	−8.20810	+	10.0313i	−0.633269	+	0.773932i
$169$	−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	$0.364415\pi$
$174$	−2.50649	+	4.74385i	−0.190017	+	0.359630i
$175$	−12.0090	−	5.54825i	−0.907798	−	0.419408i
$176$	−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	$-0.375093\pi$
$179$	10.2327			0.764825			0.382413	+	0.923992i	$0.375093\pi$
$180$	−0.999786	−	13.3791i	−0.0745196	−	0.997220i
$181$	−4.82355			−0.358532			−0.179266	−	0.983801i	$-0.557372\pi$
$181$	−4.82355			−0.358532			−0.179266	+	0.983801i	$0.557372\pi$
$182$	3.07751	+	14.5961i	0.228120	+	1.08193i
$183$	−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
$186$	9.04137	+	4.77717i	0.662946	+	0.350279i
$187$			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	$-0.839448\pi$
$191$		−	13.3579i		−	0.966546i	0.875470	−	0.483273i	$-0.160552\pi$
$192$	8.02929	+	11.2929i	0.579464	+	0.814998i
$193$			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
$195$	−12.7206	−	8.75195i	−0.910940	−	0.626740i
$196$	12.8082	−	5.65238i	0.914873	−	0.403742i
$197$			16.3303i			1.16349i	0.813373	+	0.581743i	$0.197629\pi$
$197$			16.3303i			1.16349i	−0.813373	+	0.581743i	$0.802371\pi$
$198$	−17.6051	−	11.1526i	−1.25114	−	0.792579i
$199$			21.5780i			1.52962i	0.644253	+	0.764812i	$0.277168\pi$
$199$			21.5780i			1.52962i	−0.644253	+	0.764812i	$0.722832\pi$
$200$	−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
$204$	1.46921	+	1.82719i	0.102865	+	0.127929i
$205$	−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
$210$	−5.57420	+	13.3764i	−0.384656	+	0.923060i
$211$		−	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
$216$	−14.6040	+	1.65061i	−0.993673	+	0.112309i
$217$	−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
$222$	−9.03941	+	17.1082i	−0.606685	+	1.14823i
$223$	−7.19212			−0.481620			−0.240810	−	0.970572i	$-0.577413\pi$
$223$	−7.19212			−0.481620			−0.240810	+	0.970572i	$0.577413\pi$
$224$	−2.21656	−	14.8016i	−0.148100	−	0.988972i
$225$	−5.36156	−	14.0091i	−0.357438	−	0.933937i
$226$	−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	$0.109669\pi$
$228$	16.0128	−	12.8756i	1.06047	−	0.852707i
$229$	−6.18020			−0.408399			−0.204200	−	0.978929i	$-0.565459\pi$
$229$	−6.18020			−0.408399			−0.204200	+	0.978929i	$0.565459\pi$
$230$	−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	$-0.762117\pi$
$233$	−22.3929			−1.46701			−0.733505	+	0.679684i	$0.762117\pi$
$234$	−9.05157	+	14.2885i	−0.591719	+	0.934068i
$235$	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
$238$	−0.522472	−	2.47799i	−0.0338669	−	0.160624i
$239$		−	16.3438i		−	1.05719i	−0.848874	−	0.528595i	$-0.822719\pi$
$239$		−	16.3438i		−	1.05719i	0.848874	−	0.528595i	$-0.177281\pi$
$240$	12.2215	+	9.52027i	0.788893	+	0.614531i
$241$			5.55547i			0.357860i	0.983862	+	0.178930i	$0.0572635\pi$
$241$			5.55547i			0.357860i	−0.983862	+	0.178930i	$0.942737\pi$
$242$	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
$245$	11.9055	−	10.1616i	0.760615	−	0.649204i
$246$	−2.16480	+	4.09715i	−0.138023	+	0.261225i
$247$		−	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	$0.899287\pi$
$252$	14.8743	+	5.54576i	0.936992	+	0.349350i
$253$	−5.55555			−0.349274
$254$	−5.51262	+	12.7711i	−0.345893	+	0.801331i
$255$	2.15959	+	1.48583i	0.135239	+	0.0930463i
$256$	−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	$0.976016\pi$
$258$	11.2408	−	21.2747i	0.699825	−	1.32450i
$259$	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	$-0.787069\pi$
$263$	−25.4442			−1.56896			−0.784478	+	0.620157i	$0.787069\pi$
$264$	23.1942	−	6.41263i	1.42750	−	0.394670i
$265$	14.6442	−	25.3386i	0.899586	−	1.55654i
$266$	−21.7161	+	4.57874i	−1.33150	+	0.280740i
$267$	−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	$-0.262637\pi$
$270$	−15.1122	+	6.45144i	−0.919700	+	0.392622i
$271$			13.8976i			0.844219i	0.906545	+	0.422109i	$0.138710\pi$
$271$			13.8976i			0.844219i	−0.906545	+	0.422109i	$0.861290\pi$
$272$	−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
$276$	−3.05325	+	2.45507i	−0.183784	+	0.147778i
$277$	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
$280$	−7.12099	−	15.1424i	−0.425561	−	0.904930i
$281$		−	30.4295i		−	1.81527i	−0.419759	−	0.907636i	$-0.637885\pi$
$281$		−	30.4295i		−	1.81527i	0.419759	−	0.907636i	$-0.362115\pi$
$282$	−21.9976	−	11.6228i	−1.30994	−	0.692128i
$283$			22.3052i			1.32591i	0.748660	+	0.662954i	$0.230698\pi$
$283$			22.3052i			1.32591i	−0.748660	+	0.662954i	$0.769302\pi$
$284$	2.69251	−	2.53777i	0.159771	−	0.150589i
$285$	13.0212	−	18.9258i	0.771310	−	1.12107i
$286$	10.9756	−	25.4272i	0.649000	−	1.50354i
$287$	4.08727	−	2.88897i	0.241264	−	0.170530i
$288$	9.91336	−	13.7741i	0.584150	−	0.811645i
$289$	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	$0.328841\pi$
$294$	−11.6184	−	12.6100i	−0.677601	−	0.735430i
$295$	−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
$300$	16.1430	+	6.27720i	0.932017	+	0.362414i
$301$	−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
$306$	1.53670	−	2.42578i	0.0878471	−	0.138672i
$307$		−	7.61316i		−	0.434506i	−0.976115	−	0.217253i	$-0.930290\pi$
$307$		−	7.61316i		−	0.434506i	0.976115	−	0.217253i	$-0.0697096\pi$
$308$	−25.4759	−	5.15590i	−1.45163	−	0.293785i
$309$	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	$0.423919\pi$
$312$	−5.20457	−	18.8247i	−0.294651	−	1.06574i
$313$	4.70357			0.265862			0.132931	−	0.991125i	$-0.457561\pi$
$313$	4.70357			0.265862			0.132931	+	0.991125i	$0.457561\pi$
$314$	3.96909	−	9.19521i	0.223989	−	0.518916i
$315$	17.7097	+	1.16953i	0.997827	+	0.0658954i
$316$	−13.1481	−	13.9498i	−0.739640	−	0.784739i
$317$			0.884992i			0.0497061i	0.999691	+	0.0248531i	$0.00791179\pi$
$317$			0.884992i			0.0497061i	−0.999691	+	0.0248531i	$0.992088\pi$
$318$	−28.3458	−	14.9770i	−1.58955	−	0.839869i
$319$	−10.7594			−0.602410
$320$	−17.6227	+	3.07271i	−0.985137	+	0.171769i
$321$	−27.1398	−	2.13747i	−1.51479	−	0.119302i
$322$	4.14074	−	0.873055i	0.230754	−	0.0486534i
$323$			4.01462i			0.223379i
$324$	7.69034	+	16.2745i	0.427241	+	0.904138i
$325$	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
$330$	22.7856	−	14.3067i	1.25430	−	0.787560i
$331$			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
$336$	−16.2797	+	8.42452i	−0.888128	+	0.459595i
$337$			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
$342$	−21.2585	−	13.4670i	−1.14953	−	0.728211i
$343$	5.03039	+	17.8240i	0.271615	+	0.962406i
$344$	9.48361	+	26.1155i	0.511322	+	1.40805i
$345$	−2.48283	+	3.60869i	−0.133671	+	0.194285i
$346$	14.1128	+	6.09177i	0.758711	+	0.327496i
$347$		−	24.1689i		−	1.29745i	−0.761022	−	0.648726i	$-0.775302\pi$
$347$		−	24.1689i		−	1.29745i	0.761022	−	0.648726i	$-0.224698\pi$
$348$	−5.91320	+	4.75470i	−0.316981	+	0.254879i
$349$	23.2278			1.24336			0.621678	−	0.783273i	$-0.286451\pi$
$349$	23.2278			1.24336			0.621678	+	0.783273i	$0.286451\pi$
$350$	−12.4832	−	13.9345i	−0.667253	−	0.744831i
$351$	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	$-0.0734800\pi$
$354$	11.7413	+	6.20373i	0.624044	+	0.329725i
$355$	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	$-0.945318\pi$
$359$		−	6.47793i		−	0.341892i	0.985280	−	0.170946i	$-0.0546824\pi$
$360$	6.20029	−	17.9320i	0.326784	−	0.945099i
$361$	16.1825			0.851710
$362$	−6.26298	−	2.70340i	−0.329175	−	0.142088i
$363$	1.78540	−	22.6696i	0.0937094	−	1.18984i
$364$	−4.18460	+	20.6766i	−0.219332	+	1.08375i
$365$	−19.2671	−	11.1352i	−1.00849	−	0.582845i
$366$	−11.6381	+	22.0266i	−0.608336	+	1.15135i
$367$	23.8897			1.24703			0.623517	−	0.781810i	$-0.285703\pi$
$367$	23.8897			1.24703			0.623517	+	0.781810i	$0.285703\pi$
$368$	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
$372$	9.06207	+	11.2701i	0.469846	+	0.584326i
$373$	−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
$375$	19.3031	+	1.54606i	0.996808	+	0.0798380i
$376$	27.0029	−	9.80585i	1.39257	−	0.505698i
$377$			8.73245i			0.449744i
$378$	0.544019	−	19.4346i	0.0279813	−	0.999608i
$379$			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	$0.993084\pi$
$384$	4.09615	+	19.1630i	0.209031	+	0.977909i
$385$	−28.9395	+	2.64802i	−1.47490	+	0.134956i
$386$	−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	$-0.333886\pi$
$389$	19.6638			0.996993			0.498496	+	0.866892i	$0.333886\pi$
$390$	−11.6115	−	18.4930i	−0.587972	−	0.936431i
$391$		−	0.765490i		−	0.0387125i
$392$	19.7983	−	0.160674i	0.999967	−	0.00811524i
$393$	−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
$396$	−16.6082	−	24.3476i	−0.834592	−	1.22351i
$397$			4.56276i			0.228998i	0.993423	+	0.114499i	$0.0365263\pi$
$397$			4.56276i			0.228998i	−0.993423	+	0.114499i	$0.963474\pi$
$398$	−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	$0.280372\pi$
$401$			30.8889i			1.54252i	−0.636522	+	0.771258i	$0.719628\pi$
$402$	5.53048	−	10.4671i	0.275835	−	0.522052i
$403$	16.6433			0.829063
$404$	−6.21119	+	5.85422i	−0.309018	+	0.291258i
$405$	13.4560	+	14.9645i	0.668636	+	0.743590i
$406$	8.01934	−	1.69084i	0.397993	−	0.0839149i
$407$	−38.8026			−1.92337
$408$	0.883587	+	3.19589i	0.0437441	+	0.158220i
$409$		−	9.93988i		−	0.491495i	−0.969334	−	0.245748i	$-0.920967\pi$
$409$		−	9.93988i		−	0.491495i	0.969334	−	0.245748i	$-0.0790335\pi$
$410$	−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
$414$	4.05349	+	2.56783i	0.199218	+	0.126202i
$415$	−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	$-0.136793\pi$
$420$	−14.7346	+	14.2440i	−0.718973	+	0.695038i
$421$			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
$426$	−4.00664	−	2.11698i	−0.194122	−	0.102568i
$427$	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	$0.0857264\pi$
$431$			11.0477i			0.532147i	−0.963953	+	0.266074i	$0.914274\pi$
$432$	−19.8871	−	6.04174i	−0.956819	−	0.290683i
$433$	−27.0777			−1.30127			−0.650636	−	0.759390i	$-0.725497\pi$
$433$	−27.0777			−1.30127			−0.650636	+	0.759390i	$0.725497\pi$
$434$	−3.22260	−	15.2842i	−0.154690	−	0.733664i
$435$	−4.80848	+	6.98892i	−0.230549	+	0.335093i
$436$	3.51361	−	3.31168i	0.168271	−	0.158601i
$437$	−6.70845			−0.320909
$438$	−11.3883	+	21.5537i	−0.544154	+	1.02988i
$439$		−	9.69545i		−	0.462739i	−0.972866	−	0.231369i	$-0.925679\pi$
$439$		−	9.69545i		−	0.462739i	0.972866	−	0.231369i	$-0.0743206\pi$
$440$	−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	$0.119244\pi$
$443$			15.4033i			0.731831i	−0.930648	+	0.365916i	$0.880756\pi$
$444$	−21.3253	+	17.1473i	−1.01206	+	0.813777i
$445$	−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
$448$	5.41765	−	20.4609i	0.255960	−	0.966687i
$449$		−	4.67550i		−	0.220650i	−0.993896	−	0.110325i	$-0.964811\pi$
$449$		−	4.67550i		−	0.220650i	0.993896	−	0.110325i	$-0.0351892\pi$
$450$	0.889948	−	21.1945i	0.0419525	−	0.999120i
$451$	−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
$455$	2.14917	+	23.4877i	0.100755	+	1.10112i
$456$	28.0075	−	7.74340i	1.31157	−	0.362618i
$457$			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	$-0.161970\pi$
$462$	4.10172	+	31.5688i	0.190829	+	1.46871i
$463$		−	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
$465$	13.3203	+	9.16456i	0.617714	+	0.424996i
$466$	−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	$0.496168\pi$
$468$	−19.7608	+	13.4794i	−0.913444	+	0.623085i
$469$	−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
$474$	−10.9680	+	20.7583i	−0.503778	+	0.953462i
$475$	14.8060	+	25.6972i	0.679345	+	1.17907i
$476$	0.710424	−	3.51029i	0.0325622	−	0.160894i
$477$	−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	$0.585574\pi$
$480$	10.5329	+	19.2109i	0.480757	+	0.876854i
$481$			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
$486$	15.8215	−	15.3518i	0.717680	−	0.696373i
$487$			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
$490$	21.1535	−	6.52151i	0.955617	−	0.294612i
$491$	−25.3505			−1.14405			−0.572027	−	0.820235i	$-0.693843\pi$
$491$	−25.3505			−1.14405			−0.572027	+	0.820235i	$0.693843\pi$
$492$	−5.10710	+	4.10653i	−0.230246	+	0.185137i
$493$		−	1.48252i		−	0.0667693i
$494$	13.2533	−	30.7039i	0.596293	−	1.38144i
$495$	−25.5966	−	20.7512i	−1.15048	−	0.932696i
$496$	−16.6695	−	0.987224i	−0.748483	−	0.0443277i
$497$	2.82514	+	3.99697i	0.126725	+	0.179289i
$498$	−12.0374	+	22.7823i	−0.539410	+	1.02090i
$499$		−	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	$0.897789\pi$
$504$	16.2049	+	15.5371i	0.721822	+	0.692079i
$505$	−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	$-0.0205763\pi$
$510$	1.97130	+	3.13959i	0.0872907	+	0.139023i
$511$	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
$516$	26.5189	−	21.3234i	1.16743	−	0.938709i
$517$		−	49.8921i		−	2.19425i
$518$	28.9209	−	6.09783i	1.27071	−	0.267923i
$519$	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	$0.289795\pi$
$522$	7.85036	+	4.97309i	0.343601	+	0.217666i
$523$			6.62390i			0.289643i	0.989458	+	0.144821i	$0.0462608\pi$
$523$			6.62390i			0.289643i	−0.989458	+	0.144821i	$0.953739\pi$
$524$	15.3459	−	14.4640i	0.670389	−	0.631861i
$525$	−11.2133	+	19.9815i	−0.489389	+	0.872066i
$526$	−33.0372	−	14.2604i	−1.44049	−	0.621783i
$527$	−2.82556			−0.123083
$528$	33.7097	+	4.67310i	1.46703	+	0.203371i
$529$	−21.7209			−0.944385
$530$	33.2155	−	24.6926i	1.44279	−	1.07258i
$531$	2.54604	−	16.0635i	0.110489	−	0.697095i
$532$	−30.7628	−	6.22587i	−1.33374	−	0.269926i
$533$			7.54202i			0.326681i
$534$	−6.32956	+	11.9795i	−0.273907	+	0.518402i
$535$	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
$540$	−23.2377	−	0.0931073i	−0.999992	−	0.00400670i
$541$			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
$546$	25.6216	−	3.32901i	1.09650	−	0.142468i
$547$	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
$552$	−5.34035	+	1.47648i	−0.227300	+	0.0628431i
$553$	20.7083	−	14.6370i	0.880604	−	0.622430i
$554$	22.2003	+	9.58269i	0.943199	+	0.407130i
$555$	−17.3413	+	25.2048i	−0.736096	+	1.06988i
$556$	−9.33425	−	9.90341i	−0.395860	−	0.419998i
$557$			28.9539i			1.22682i	0.789766	+	0.613408i	$0.210202\pi$
$557$			28.9539i			1.22682i	−0.789766	+	0.613408i	$0.789798\pi$
$558$	9.47830	−	14.9621i	0.401249	−	0.633397i
$559$		−	39.1623i		−	1.65639i
$560$	−0.759343	−	23.6521i	−0.0320881	−	0.999485i
$561$	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	$0.373903\pi$
$564$	−22.0479	−	27.4200i	−0.928385	−	1.15459i
$565$	−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	$-0.894632\pi$
$569$		−	15.5054i		−	0.650022i	0.945710	−	0.325011i	$-0.105368\pi$
$570$	27.5141	−	17.2757i	1.15244	−	0.723600i
$571$		−	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
$574$	6.92612	−	1.46034i	0.289091	−	0.0609534i
$575$	−2.82314	−	4.89983i	−0.117733	−	0.204337i
$576$	20.5915	−	12.3285i	0.857978	−	0.513686i
$577$	34.2228			1.42472			0.712358	−	0.701817i	$-0.247627\pi$
$577$	34.2228			1.42472			0.712358	+	0.701817i	$0.247627\pi$
$578$	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
$582$	−8.79396	+	16.6436i	−0.364521	+	0.689901i
$583$		−	64.2904i		−	2.66263i
$584$	−9.60801	−	26.4581i	−0.397582	−	1.09484i
$585$	−16.8419	+	20.7745i	−0.696328	+	0.858920i
$586$	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	$0.301268\pi$
$588$	−8.01819	−	22.8847i	−0.330664	−	0.943748i
$589$			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	$0.847355\pi$
$594$	−21.6513	+	28.8821i	−0.888365	+	1.18505i
$595$	−0.364867	−	3.98753i	−0.0149581	−	0.163473i
$596$	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	$0.300752\pi$
$599$			39.6684i			1.62081i	−0.585872	+	0.810403i	$0.699248\pi$
$600$	17.4422	+	17.1979i	0.712077	+	0.702102i
$601$		−	4.47305i		−	0.182460i	−0.995830	−	0.0912298i	$-0.970920\pi$
$601$		−	4.47305i		−	0.182460i	0.995830	−	0.0912298i	$-0.0290798\pi$
$602$	−35.9642	+	7.58289i	−1.46579	+	0.309055i
$603$	−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
$606$	9.24269	+	4.88353i	0.375458	+	0.198380i
$607$	23.3900			0.949371			0.474685	−	0.880156i	$-0.342562\pi$
$607$	23.3900			0.949371			0.474685	+	0.880156i	$0.342562\pi$
$608$	−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
$612$	3.35482	−	2.28841i	0.135610	−	0.0925037i
$613$	−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
$615$	−4.15298	+	6.03617i	−0.167464	+	0.243402i
$616$	−30.1887	−	20.9727i	−1.21634	−	0.845015i
$617$	−0.716676			−0.0288523			−0.0144262	−	0.999896i	$-0.504592\pi$
$617$	−0.716676			−0.0288523			−0.0144262	+	0.999896i	$0.504592\pi$
$618$	5.11896	−	9.68825i	0.205915	−	0.389719i
$619$	0.161608			0.00649556			0.00324778	−	0.999995i	$-0.498966\pi$
$619$	0.161608			0.00649556			0.00324778	+	0.999995i	$0.498966\pi$
$620$	−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
$624$	3.79274	−	27.3592i	0.151831	−	1.09525i
$625$	−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
$630$	22.3391	+	11.4441i	0.890009	+	0.455942i
$631$	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
$636$	−28.4107	−	35.3331i	−1.12656	−	1.40105i
$637$	−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	$0.0927462\pi$
$641$			14.5460i			0.574531i	−0.957851	+	0.287266i	$0.907254\pi$
$642$	−34.0408	−	17.9860i	−1.34348	−	0.709852i
$643$			42.8475i			1.68974i	0.534970	+	0.844871i	$0.320323\pi$
$643$			42.8475i			1.68974i	−0.534970	+	0.844871i	$0.679677\pi$
$644$	5.86572	+	1.18712i	0.231142	+	0.0467792i
$645$	21.5645	−	31.3431i	0.849103	−	1.23414i
$646$	−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	$-0.127597\pi$
$648$	0.864097	+	25.4412i	0.0339449	+	0.999424i
$649$			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	$0.140236\pi$
$653$			21.7949i			0.852902i	−0.904511	+	0.426451i	$0.859764\pi$
$654$	−5.22850	−	2.76257i	−0.204451	−	0.108025i
$655$	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
$658$	7.84055	+	37.1863i	0.305656	+	1.44967i
$659$	−0.262720			−0.0102341			−0.00511706	−	0.999987i	$-0.501629\pi$
$659$	−0.262720			−0.0102341			−0.00511706	+	0.999987i	$0.501629\pi$
$660$	37.6035	−	5.80575i	1.46371	−	0.225988i
$661$	3.96725			0.154308			0.0771541	−	0.997019i	$-0.475417\pi$
$661$	3.96725			0.154308			0.0771541	+	0.997019i	$0.475417\pi$
$662$	−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
$665$	−34.9451	+	3.19755i	−1.35511	+	0.123996i
$666$	28.3115	+	17.9349i	1.09705	+	0.694965i
$667$	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
$672$	−25.8594	+	1.81446i	−0.997547	+	0.0699945i
$673$		−	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
$675$	−24.9186	+	7.35272i	−0.959118	+	0.283006i
$676$	−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	$0.755882\pi$
$678$	−11.3947	+	21.5658i	−0.437609	+	0.828229i
$679$	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	$0.102943\pi$
$683$			16.6108i			0.635596i	−0.948158	+	0.317798i	$0.897057\pi$
$684$	−20.0547	−	29.4003i	−0.766812	−	1.12415i
$685$	17.3075	+	10.0027i	0.661287	+	0.382184i
$686$	−3.45808	+	25.9623i	−0.132030	+	0.991246i
$687$	−0.840454	+	10.6714i	−0.0320653	+	0.407139i
$688$	−2.32297	+	39.2240i	−0.0885626	+	1.49540i
$689$	−52.1788			−1.98786
$690$	−5.24627	+	3.29406i	−0.199722	+	0.125403i
$691$	−5.46652			−0.207956			−0.103978	−	0.994580i	$-0.533157\pi$
$691$	−5.46652			−0.207956			−0.103978	+	0.994580i	$0.533157\pi$
$692$	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
$696$	−10.3426	+	2.85948i	−0.392036	+	0.108388i
$697$		−	1.28042i		−	0.0484993i
$698$	30.1594	+	13.0182i	1.14155	+	0.492747i
$699$	−3.04524	+	38.6660i	−0.115182	+	1.46248i
$700$	−8.39865	−	25.0891i	−0.317439	−	0.948279i
$701$	6.39939			0.241702			0.120851	−	0.992671i	$-0.461438\pi$
$701$	6.39939			0.241702			0.120851	+	0.992671i	$0.461438\pi$
$702$	23.4411	+	17.5725i	0.884726	+	0.663231i
$703$	−46.8550			−1.76717
$704$	−30.1401	+	25.2154i	−1.13595	+	0.950342i
$705$	−32.4082	−	22.2973i	−1.22056	−	0.839764i
$706$	4.81854	−	11.1631i	0.181348	−	0.420130i
$707$	−6.51716	−	9.22038i	−0.245103	−	0.346768i
$708$	11.7682	+	14.6355i	0.442276	+	0.550038i
$709$		−	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
$714$	−4.34981	+	0.565170i	−0.162788	+	0.0211510i
$715$	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	$0.356065\pi$
$720$	18.1007	−	19.8082i	0.674573	−	0.738208i
$721$	−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
$726$	15.0236	−	28.4339i	0.557576	−	1.05528i
$727$	−21.8578			−0.810662			−0.405331	−	0.914170i	$-0.632844\pi$
$727$	−21.8578			−0.810662			−0.405331	+	0.914170i	$0.632844\pi$
$728$	−17.0217	+	24.5015i	−0.630867	+	0.908087i
$729$	−24.0531	−	12.2658i	−0.890855	−	0.454288i
$730$	−18.7759	−	25.2566i	−0.694927	−	0.934788i
$731$			6.64864i			0.245909i
$732$	−27.4562	+	22.0770i	−1.01481	+	0.815991i
$733$			11.0759i			0.409098i	0.978856	+	0.204549i	$0.0655728\pi$
$733$			11.0759i			0.409098i	−0.978856	+	0.204549i	$0.934427\pi$
$734$	31.0188	+	13.3892i	1.14493	+	0.494205i
$735$	−15.9271	−	21.9392i	−0.587480	−	0.809239i
$736$	2.87833	−	5.71382i	0.106097	−	0.210614i
$737$	23.7402			0.874480
$738$	6.78018	+	4.29515i	0.249582	+	0.158107i
$739$			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
$742$	10.1032	+	47.9178i	0.370901	+	1.75912i
$743$	40.7456			1.49481			0.747406	−	0.664367i	$-0.231299\pi$
$743$	40.7456			1.49481			0.747406	+	0.664367i	$0.231299\pi$
$744$	5.44994	+	19.7122i	0.199804	+	0.722683i
$745$	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
$750$	24.1970	+	12.8260i	0.883549	+	0.468340i
$751$	−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
$756$	11.5987	−	24.9293i	0.421839	−	0.906671i
$757$	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	$0.346290\pi$
$762$	21.3023	+	11.2554i	0.771700	+	0.407741i
$763$	3.68670	+	5.21588i	0.133467	+	0.188828i
$764$	19.4414	−	18.3241i	0.703364	−	0.662941i
$765$	2.85927	−	3.52691i	0.103377	−	0.127516i
$766$	−0.476619	+	1.10419i	−0.0172209	+	0.0398958i
$767$	21.6134			0.780413
$768$	−5.42157	+	27.1773i	−0.195634	+	0.980677i
$769$			17.4725i			0.630074i	0.949079	+	0.315037i	$0.102017\pi$
$769$			17.4725i			0.630074i	−0.949079	+	0.315037i	$0.897983\pi$
$770$	−39.0597	−	12.7812i	−1.40761	−	0.460601i
$771$	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	$0.433057\pi$
$774$	−35.2064	−	22.3028i	−1.26547	−	0.801657i
$775$	−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
$780$	−4.71201	−	30.5194i	−0.168717	−	1.09277i
$781$		−	9.08735i		−	0.325171i
$782$	0.429026	−	0.993926i	0.0153419	−	0.0355427i
$783$	2.65882	−	11.0666i	0.0950184	−	0.395489i
$784$	25.7965	+	10.8875i	0.921305	+	0.388840i
$785$	7.92383	−	13.7105i	0.282814	−	0.489348i
$786$	−22.8358	−	12.0657i	−0.814526	−	0.430369i
$787$			16.9012i			0.602461i	0.953551	+	0.301231i	$0.0973974\pi$
$787$			16.9012i			0.602461i	−0.953551	+	0.301231i	$0.902603\pi$
$788$	−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
$792$	−7.91851	−	40.9215i	−0.281372	−	1.45408i
$793$			40.5465i			1.43985i
$794$	−2.55724	+	5.92436i	−0.0907529	+	0.210248i
$795$	−41.7608	−	28.7320i	−1.48110	−	1.01902i
$796$	−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	$0.705430\pi$
$798$	4.95292	+	38.1200i	0.175332	+	1.34943i
$799$	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
$804$	13.0473	−	10.4911i	0.460141	−	0.369992i
$805$	6.66319	−	0.609695i	0.234847	−	0.0214889i
$806$	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	$-0.983694\pi$
$809$		−	2.91273i		−	0.102406i	0.998688	−	0.0512031i	$-0.0163056\pi$
$810$	9.08460	+	26.9717i	0.319200	+	0.947687i
$811$	−28.8933			−1.01458			−0.507291	−	0.861775i	$-0.669353\pi$
$811$	−28.8933			−1.01458			−0.507291	+	0.861775i	$0.669353\pi$
$812$	11.3601	+	2.29909i	0.398661	+	0.0806823i
$813$	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
$816$	−0.643899	+	4.64481i	−0.0225410	+	0.162601i
$817$	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	$-0.648914\pi$
$821$	−25.8420			−0.901893			−0.450947	+	0.892551i	$0.648914\pi$
$822$	10.2300	−	19.3616i	0.356814	−	0.675314i
$823$		−	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
$825$	38.4133	−	18.2779i	1.33738	−	0.636354i
$826$	−4.18493	−	19.8484i	−0.145612	−	0.690613i
$827$		−	22.5646i		−	0.784647i	−0.919827	−	0.392323i	$-0.871671\pi$
$827$		−	22.5646i		−	0.784647i	0.919827	−	0.392323i	$-0.128329\pi$
$828$	3.82396	+	5.60592i	0.132892	+	0.194819i
$829$	−36.6005			−1.27119			−0.635593	−	0.772024i	$-0.719244\pi$
$829$	−36.6005			−1.27119			−0.635593	+	0.772024i	$0.719244\pi$
$830$	−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
$834$	−7.78654	+	14.7370i	−0.269626	+	0.510300i
$835$	−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	$0.316747\pi$
$840$	−27.1148	+	10.2366i	−0.935549	+	0.353197i
$841$	−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
$846$	−23.0606	+	36.4027i	−0.792840	+	1.25155i
$847$	−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
$852$	−4.01581	−	4.99428i	−0.137579	−	0.171101i
$853$			14.2692i			0.488568i	0.969704	+	0.244284i	$0.0785529\pi$
$853$			14.2692i			0.488568i	−0.969704	+	0.244284i	$0.921447\pi$
$854$	37.2354	−	7.85090i	1.27417	−	0.268652i
$855$	−30.9085	−	25.0575i	−1.05705	−	0.856949i
$856$	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	$-0.278691\pi$
$858$	−42.4127	−	22.4095i	−1.44794	−	0.765047i
$859$	−8.35557			−0.285088			−0.142544	−	0.989788i	$-0.545528\pi$
$859$	−8.35557			−0.285088			−0.142544	+	0.989788i	$0.545528\pi$
$860$	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	$-0.305607\pi$
$863$	33.6919			1.14689			0.573444	+	0.819245i	$0.305607\pi$
$864$	−22.4356	−	18.9906i	−0.763276	−	0.646073i
$865$	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
$868$	4.38188	−	21.6514i	0.148731	−	0.734896i
$869$	−47.0814			−1.59713
$870$	−10.1604	+	6.37958i	−0.344470	+	0.216288i
$871$		−	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
$875$	−17.0416	−	24.1782i	−0.576110	−	0.817372i
$876$	−26.8667	+	21.6031i	−0.907743	+	0.729901i
$877$	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	$0.746608\pi$
$882$	−23.3537	+	18.3467i	−0.786361	+	0.617767i
$883$	−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
$885$	17.2980	+	11.9013i	0.581466	+	0.400058i
$886$	−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	$0.782088\pi$
$888$	−37.2996	+	10.3124i	−1.25169	+	0.346063i
$889$	−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
$894$	13.1566	−	24.9005i	0.440023	−	0.832797i
$895$	19.8104	+	11.4492i	0.662189	+	0.382706i
$896$	18.5019	−	23.5304i	0.618104	−	0.786097i
$897$	7.78562	+	0.613178i	0.259954	+	0.0204734i
$898$	2.62042	−	6.07075i	0.0874446	−	0.202583i
$899$		−	9.14414i		−	0.304974i
$900$	13.0342	−	27.0206i	0.434472	−	0.900685i
$901$	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
$906$	8.68488	−	16.4372i	0.288536	−	0.546089i
$907$	−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
$910$	−10.3734	+	31.7013i	−0.343873	+	1.05089i
$911$		−	53.2694i		−	1.76489i	−0.470413	−	0.882446i	$-0.655895\pi$
$911$		−	53.2694i		−	1.76489i	0.470413	−	0.882446i	$-0.344105\pi$
$912$	40.7053	+	5.64287i	1.34789	+	0.186854i
$913$	−51.6719			−1.71009
$914$	−16.8800	+	39.1061i	−0.558342	+	1.29351i
$915$	−22.3267	+	32.4509i	−0.738099	+	1.07280i
$916$	−8.47784	−	8.99478i	−0.280116	−	0.297196i
$917$	16.1019	+	22.7807i	0.531731	+	0.752285i
$918$	−3.97962	−	2.98330i	−0.131347	−	0.0984637i
$919$	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
$924$	−12.3672	+	43.2882i	−0.406852	+	1.42408i
$925$	−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	$0.422522\pi$
$930$	12.1589	+	19.3649i	0.398707	+	0.635000i
$931$	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
$936$	−33.2124	+	6.42676i	−1.08558	+	0.210065i
$937$	−39.8368			−1.30141			−0.650706	−	0.759330i	$-0.725527\pi$
$937$	−39.8368			−1.30141			−0.650706	+	0.759330i	$0.725527\pi$
$938$	−17.6944	+	3.73077i	−0.577741	+	0.121814i
$939$	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	$0.876872\pi$
$942$	−15.3376	−	8.10391i	−0.499728	−	0.264040i
$943$	2.13959			0.0696746
$944$	−21.6474	−	1.28203i	−0.704562	−	0.0417265i
$945$	4.42779	−	30.4203i	0.144036	−	0.989572i
$946$	62.6519	+	27.0435i	2.03699	+	0.879261i
$947$		−	43.7023i		−	1.42013i	−0.704134	−	0.710067i	$-0.748665\pi$
$947$		−	43.7023i		−	1.42013i	0.704134	−	0.710067i	$-0.251335\pi$
$948$	−25.8753	+	20.8059i	−0.840389	+	0.675743i
$949$			39.6760i			1.28794i
$950$	4.82212	+	41.6638i	0.156450	+	1.35175i
$951$	1.52812	+	0.120351i	0.0495527	+	0.00390266i
$952$	2.88980	−	4.15966i	0.0936589	−	0.134815i
$953$	−36.5317			−1.18338			−0.591689	−	0.806166i	$-0.701539\pi$
$953$	−36.5317			−1.18338			−0.591689	+	0.806166i	$0.701539\pi$
$954$	−29.7156	+	46.9081i	−0.962079	+	1.51871i
$955$	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
$960$	2.90912	+	30.8470i	0.0938915	+	0.995582i
$961$	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
$966$	−0.944403	−	7.26856i	−0.0303857	−	0.233862i
$967$			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	$0.985770\pi$
$972$	29.1470	−	11.0658i	0.934891	−	0.354934i
$973$	14.7014	−	10.3913i	0.471306	−	0.333129i
$974$	−1.39755	+	3.23771i	−0.0447804	+	0.103743i
$975$	−14.8345	−	31.1767i	−0.475085	−	0.998453i
$976$	2.40508	−	40.6103i	0.0769847	−	1.29990i
$977$	−7.27766			−0.232833			−0.116417	−	0.993200i	$-0.537141\pi$
$977$	−7.27766			−0.232833			−0.116417	+	0.993200i	$0.537141\pi$
$978$	−18.2746	+	34.5868i	−0.584356	+	1.10596i
$979$	−27.1703			−0.868366
$980$	31.1211	+	3.38801i	0.994126	+	0.108226i
$981$	−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	$0.901039\pi$
$984$	−8.93269	+	2.46967i	−0.284764	+	0.0787303i
$985$	−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
$990$	−21.6049	−	41.2895i	−0.686647	−	1.31227i
$991$	−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
$994$	1.42808	+	6.77311i	0.0452959	+	0.214830i
$995$	−24.1434	+	41.7750i	−0.765398	+	1.32436i
$996$	−28.3981	+	22.8345i	−0.899830	+	0.723538i
$997$			27.5716i			0.873202i	0.899655	+	0.436601i	$0.143818\pi$
$997$			27.5716i			0.873202i	−0.899655	+	0.436601i	$0.856182\pi$
$998$	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.629.151	yes	160
3.2	odd	2	inner	840.2.u.e.629.9	✓	160
5.4	even	2	inner	840.2.u.e.629.10	yes	160
7.6	odd	2	inner	840.2.u.e.629.150	yes	160
8.5	even	2	inner	840.2.u.e.629.146	yes	160
15.14	odd	2	inner	840.2.u.e.629.152	yes	160
21.20	even	2	inner	840.2.u.e.629.12	yes	160
24.5	odd	2	inner	840.2.u.e.629.16	yes	160
35.34	odd	2	inner	840.2.u.e.629.11	yes	160
40.29	even	2	inner	840.2.u.e.629.15	yes	160
56.13	odd	2	inner	840.2.u.e.629.147	yes	160
105.104	even	2	inner	840.2.u.e.629.149	yes	160
120.29	odd	2	inner	840.2.u.e.629.145	yes	160
168.125	even	2	inner	840.2.u.e.629.13	yes	160
280.69	odd	2	inner	840.2.u.e.629.14	yes	160
840.629	even	2	inner	840.2.u.e.629.148	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.u.e.629.9	✓	160	3.2	odd	2	inner
840.2.u.e.629.10	yes	160	5.4	even	2	inner
840.2.u.e.629.11	yes	160	35.34	odd	2	inner
840.2.u.e.629.12	yes	160	21.20	even	2	inner
840.2.u.e.629.13	yes	160	168.125	even	2	inner
840.2.u.e.629.14	yes	160	280.69	odd	2	inner
840.2.u.e.629.15	yes	160	40.29	even	2	inner
840.2.u.e.629.16	yes	160	24.5	odd	2	inner
840.2.u.e.629.145	yes	160	120.29	odd	2	inner
840.2.u.e.629.146	yes	160	8.5	even	2	inner
840.2.u.e.629.147	yes	160	56.13	odd	2	inner
840.2.u.e.629.148	yes	160	840.629	even	2	inner
840.2.u.e.629.149	yes	160	105.104	even	2	inner
840.2.u.e.629.150	yes	160	7.6	odd	2	inner
840.2.u.e.629.151	yes	160	1.1	even	1	trivial
840.2.u.e.629.152	yes	160	15.14	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} +(1.14432 - 2.16576i) 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} +(2.69962 - 2.17072i) q^{12} -3.98673i q^{13} +(-3.66116 + 0.771938i) q^{14} +(2.19527 - 3.19073i) q^{15} +(-0.236479 + 3.99300i) q^{16} +0.676832i q^{17} +(-3.58402 - 2.27043i) 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} +(4.72184 - 1.30547i) q^{24} +(2.49617 + 4.33234i) q^{25} +(2.23440 - 5.17643i) q^{26} +(-1.21386 + 5.05238i) q^{27} +(-5.18635 - 1.04963i) q^{28} -2.19038 q^{29} +(4.63865 - 2.91254i) q^{30} +4.17468i q^{31} +(-2.54496 + 5.05205i) q^{32} +(0.668004 - 8.48176i) q^{33} +(-0.379336 + 0.878810i) q^{34} +(-5.89147 + 0.539081i) q^{35} +(-3.38107 - 4.95665i) 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} +(0.835023 + 6.42672i) q^{42} +9.82318 q^{43} +(6.73830 + 7.14917i) q^{44} +(-5.21091 - 4.22450i) q^{45} +(-1.46850 - 0.633873i) q^{46} -10.1570i q^{47} +(6.86258 + 0.951343i) 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} +(-4.40775 + 5.87978i) q^{54} +(9.50983 + 5.49611i) q^{55} +(-6.14578 - 4.26960i) q^{56} +(0.806630 - 10.2419i) q^{57} +(-2.84403 - 1.22762i) q^{58} +5.42133i q^{59} +(7.65526 - 1.18193i) 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} +(5.62102 - 10.6385i) q^{66} +4.83299 q^{67} +(-0.985073 + 0.928459i) q^{68} +(-0.153805 + 1.95289i) q^{69} +(-7.95171 - 2.60197i) q^{70} -1.84999i q^{71} +(-1.61204 - 8.33075i) q^{72} -9.95203 q^{73} +(-10.2567 - 4.42727i) q^{74} +(7.82012 - 3.72098i) q^{75} +(8.13665 + 8.63278i) q^{76} +(-10.6128 + 7.50135i) q^{77} +(-8.63431 - 4.56209i) 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} +(-2.51770 + 8.81256i) 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} +(-4.39829 - 8.40566i) 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} +(8.37730 + 5.08143i) q^{96} -7.68488 q^{97} +(6.73124 - 7.25881i) 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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