LMFDB - Embedded newform 840.2.u.e.629.16

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			629.16
Character	$\chi$	$=$	840.629
Dual form			840.2.u.e.629.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.29842 + 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} +(-3.14082 - 0.367741i) q^{10} +4.91211 q^{11} +(2.69962 + 2.17072i) 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} +(3.58402 - 2.27043i) q^{18} -5.93148 q^{19} +(4.28420 - 1.28282i) q^{20} +(-2.93069 - 3.52294i) 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} +(-0.741180 + 5.23934i) q^{28} -2.19038 q^{29} +(0.207855 - 5.47328i) 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} +(-4.84371 + 4.06675i) q^{40} +1.89178 q^{41} +(5.77971 + 2.93171i) 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} +(6.86258 - 0.951343i) q^{48} +(2.33585 - 6.59877i) q^{49} +(-5.66916 - 4.22618i) 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} +(-1.97407 - 7.21824i) q^{56} +(-0.806630 - 10.2419i) q^{57} +(2.84403 - 1.22762i) q^{58} +5.42133i q^{59} +(2.79766 + 7.22309i) q^{60} +10.1704 q^{61} +(-2.33974 - 5.42048i) q^{62} +(5.68452 - 5.53952i) 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} +(7.34745 - 4.00187i) q^{70} +1.84999i q^{71} +(1.61204 - 8.33075i) 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} +(8.63431 - 4.56209i) q^{78} -9.58477 q^{79} +(4.00991 - 7.99504i) q^{80} +(8.55889 - 2.78306i) q^{81} +(-2.45632 + 1.06027i) q^{82} -10.5193 q^{83} +(-9.14758 - 0.567294i) 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} +(9.47900 - 0.385414i) 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} +(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
$6$	−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
$10$	−3.14082	−	0.367741i	−0.993215	−	0.116290i
$11$	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	$0.186463\pi$
$13$			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	$-0.973844\pi$
$17$		−	0.676832i		−	0.164156i	0.996626	−	0.0820779i	$-0.0261556\pi$
$18$	3.58402	−	2.27043i	0.844761	−	0.535144i
$19$	−5.93148			−1.36078			−0.680388	−	0.732852i	$-0.738189\pi$
$19$	−5.93148			−1.36078			−0.680388	+	0.732852i	$0.738189\pi$
$20$	4.28420	−	1.28282i	0.957976	−	0.286847i
$21$	−2.93069	−	3.52294i	−0.639528	−	0.768767i
$22$	−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	$0.462379\pi$
$24$	−4.72184	−	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
$28$	−0.741180	+	5.23934i	−0.140070	+	0.990142i
$29$	−2.19038			−0.406743			−0.203372	−	0.979102i	$-0.565190\pi$
$29$	−2.19038			−0.406743			−0.203372	+	0.979102i	$0.565190\pi$
$30$	0.207855	−	5.47328i	0.0379490	−	0.999280i
$31$			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	$-0.275052\pi$
$37$	7.89938			1.29865			0.649325	+	0.760511i	$0.275052\pi$
$38$	7.70154	−	3.32435i	1.24935	−	0.539281i
$39$	−6.88390	+	0.542160i	−1.10231	+	0.0868151i
$40$	−4.84371	+	4.06675i	−0.765858	+	0.643010i
$41$	1.89178			0.295447			0.147723	−	0.989029i	$-0.452805\pi$
$41$	1.89178			0.295447			0.147723	+	0.989029i	$0.452805\pi$
$42$	5.77971	+	2.93171i	0.891829	+	0.452373i
$43$	−9.82318			−1.49802			−0.749010	−	0.662558i	$-0.769471\pi$
$43$	−9.82318			−1.49802			−0.749010	+	0.662558i	$0.769471\pi$
$44$	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	$0.265540\pi$
$47$			10.1570i			1.48154i	−0.671756	+	0.740772i	$0.734460\pi$
$48$	6.86258	−	0.951343i	0.990527	−	0.137315i
$49$	2.33585	−	6.59877i	0.333693	−	0.942682i
$50$	−5.66916	−	4.22618i	−0.801740	−	0.597673i
$51$	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
$56$	−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	$0.885196\pi$
$60$	2.79766	+	7.22309i	0.361177	+	0.932497i
$61$	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
$63$	5.68452	−	5.53952i	0.716182	−	0.697914i
$64$	−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	$-0.595394\pi$
$67$	−4.83299			−0.590444			−0.295222	+	0.955429i	$0.595394\pi$
$68$	−0.985073	−	0.928459i	−0.119458	−	0.112592i
$69$	0.153805	+	1.95289i	0.0185159	+	0.235100i
$70$	7.34745	−	4.00187i	0.878188	−	0.478315i
$71$			1.84999i			0.219553i	0.993956	+	0.109777i	$0.0350136\pi$
$71$			1.84999i			0.219553i	−0.993956	+	0.109777i	$0.964986\pi$
$72$	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
$75$	−7.14121	+	4.89930i	−0.824596	+	0.565723i
$76$	−8.13665	+	8.63278i	−0.933337	+	0.990248i
$77$	−10.6128	+	7.50135i	−1.20944	+	0.854858i
$78$	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	$0.681268\pi$
$80$	4.00991	−	7.99504i	0.448322	−	0.893872i
$81$	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	$0.695902\pi$
$84$	−9.14758	−	0.567294i	−0.998083	−	0.0618968i
$85$	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	$-0.405294\pi$
$89$	5.53129			0.586315			0.293158	+	0.956064i	$0.405294\pi$
$90$	9.47900	−	0.385414i	0.999174	−	0.0406262i
$91$	−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	$0.627574\pi$
$98$	0.665433	+	9.87710i	0.0672188	+	0.997738i
$99$	−14.5546	+	2.30689i	−1.46280	+	0.231851i
$100$	9.72953	+	2.31002i	0.972953	+	0.231002i
$101$			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
$105$	−1.73202	−	10.0995i	−0.169028	−	0.985611i
$106$	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	$0.0368846\pi$
$109$			2.41416i			0.231235i	−0.993294	+	0.115617i	$0.963115\pi$
$110$	−15.4281	−	1.80638i	−1.47101	−	0.172232i
$111$	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	$0.344843\pi$
$114$	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
$120$	−7.68078	−	7.81061i	−0.701156	−	0.713008i
$121$	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
$126$	−4.27621	+	10.3785i	−0.380955	+	0.924594i
$127$			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
$130$	1.46608	−	12.5216i	0.128584	−	1.09822i
$131$		−	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
$135$	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	$0.624727\pi$
$138$	−1.29421	−	2.44946i	−0.110171	−	0.208512i
$139$	6.80452			0.577152			0.288576	−	0.957457i	$-0.406818\pi$
$139$	6.80452			0.577152			0.288576	+	0.957457i	$0.406818\pi$
$140$	−7.29717	+	9.31404i	−0.616723	+	0.787180i
$141$	−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
$147$	11.7118	+	3.13594i	0.965972	+	0.258648i
$148$	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	$0.343912\pi$
$150$	6.52641	−	10.3637i	0.532879	−	0.846191i
$151$	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
$156$	−8.65407	+	10.7627i	−0.692881	+	0.861703i
$157$			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
$160$	−0.725653	+	12.6283i	−0.0573679	+	0.998353i
$161$	−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	$-0.284925\pi$
$163$	15.9698			1.25085			0.625426	+	0.780284i	$0.284925\pi$
$164$	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	$-0.806933\pi$
$167$		−	14.7327i		−	1.14005i	0.821626	−	0.570027i	$-0.193067\pi$
$168$	12.1953	−	4.39025i	0.940889	−	0.338715i
$169$	−2.89400			−0.222615
$170$	−0.248899	+	2.12581i	−0.0190897	+	0.163042i
$171$	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	$0.375093\pi$
$180$	−12.0917	+	5.81301i	−0.901261	+	0.433276i
$181$	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
$186$	9.04137	−	4.77717i	0.662946	−	0.350279i
$187$		−	3.32467i		−	0.243124i
$188$	14.7826	+	13.9330i	1.07813	+	1.01617i
$189$	10.3382	+	9.06215i	0.751990	+	0.659175i
$190$	18.6297	+	2.18125i	1.35154	+	0.158244i
$191$			13.3579i			0.966546i	0.875470	+	0.483273i	$0.160552\pi$
$191$			13.3579i			0.966546i	−0.875470	+	0.483273i	$0.839448\pi$
$192$	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
$195$	−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	$0.197629\pi$
$197$			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	$0.722832\pi$
$200$	−13.9277	+	2.45363i	−0.984834	+	0.173498i
$201$	−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
$210$	7.90924	+	12.1426i	0.545789	+	0.837922i
$211$			1.99213i			0.137144i	0.997646	+	0.0685720i	$0.0218443\pi$
$211$			1.99213i			0.137144i	−0.997646	+	0.0685720i	$0.978156\pi$
$212$	−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
$220$	21.0445	−	6.30135i	1.41882	−	0.424837i
$221$	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	$0.577413\pi$
$224$	−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	$0.109669\pi$
$228$	−16.0128	−	12.8756i	−1.06047	−	0.852707i
$229$	6.18020			0.408399			0.204200	−	0.978929i	$-0.434541\pi$
$229$	6.18020			0.408399			0.204200	+	0.978929i	$0.434541\pi$
$230$	−3.55224	−	0.415912i	−0.234228	−	0.0274244i
$231$	−14.3959	−	17.3050i	−0.947178	−	1.13859i
$232$	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	$0.237883\pi$
$234$	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
$238$	−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	$0.822719\pi$
$240$	14.3504	+	5.83668i	0.926313	+	0.376756i
$241$			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
$250$	−6.24684	−	14.5250i	−0.395085	−	0.918645i
$251$			9.85902i			0.622296i	0.950361	+	0.311148i	$0.100713\pi$
$251$			9.85902i			0.622296i	−0.950361	+	0.311148i	$0.899287\pi$
$252$	−0.264442	−	15.8723i	−0.0166583	−	0.999861i
$253$	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	$-0.976016\pi$
$257$		−	2.41358i		−	0.150555i	0.997163	−	0.0752775i	$-0.0239843\pi$
$258$	11.2408	+	21.2747i	0.699825	+	1.32450i
$259$	−17.0669	+	12.0632i	−1.06049	+	0.749574i
$260$	5.11425	+	17.0799i	0.317172	+	1.05925i
$261$	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	$0.212931\pi$
$264$	−23.1942	−	6.41263i	−1.42750	−	0.394670i
$265$	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	$-0.262637\pi$
$270$	1.95456	+	16.3150i	0.118951	+	0.992900i
$271$			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
$273$	14.0450	−	11.6839i	0.850041	−	0.707139i
$274$	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	$-0.671710\pi$
$277$	−17.0980			−1.02732			−0.513658	+	0.857995i	$0.671710\pi$
$278$	−8.83510	+	3.81365i	−0.529894	+	0.228727i
$279$	−1.96057	−	12.3696i	−0.117376	−	0.740551i
$280$	4.25463	−	16.1833i	0.254263	−	0.967135i
$281$			30.4295i			1.81527i	0.419759	+	0.907636i	$0.362115\pi$
$281$			30.4295i			1.81527i	−0.419759	+	0.907636i	$0.637885\pi$
$282$	21.9976	−	11.6228i	1.30994	−	0.692128i
$283$		−	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
$288$	−9.91336	−	13.7741i	−0.584150	−	0.811645i
$289$	16.5419			0.973053
$290$	6.87959	+	0.805493i	0.403984	+	0.0473002i
$291$	−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	$0.328841\pi$
$294$	−16.9643	+	2.49221i	−0.989381	+	0.145348i
$295$	−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
$300$	−2.66559	+	17.1142i	−0.153898	+	0.988087i
$301$	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	$0.0697096\pi$
$307$			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
$310$	1.53520	−	13.1119i	0.0871936	−	0.744708i
$311$	−8.35008			−0.473489			−0.236745	−	0.971572i	$-0.576081\pi$
$311$	−8.35008			−0.473489			−0.236745	+	0.971572i	$0.576081\pi$
$312$	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
$315$	17.2033	−	4.36413i	0.969297	−	0.245891i
$316$	−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
$320$	−6.13543	−	16.8035i	−0.342981	−	0.939342i
$321$	27.1398	−	2.13747i	1.51479	−	0.119302i
$322$	2.20475	−	3.61207i	0.122866	−	0.201293i
$323$			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
$330$	1.02101	−	26.8853i	0.0562047	−	1.47999i
$331$		−	25.5215i		−	1.40279i	−0.712774	−	0.701394i	$-0.752562\pi$
$331$		−	25.5215i		−	1.40279i	0.712774	−	0.701394i	$-0.247438\pi$
$332$	−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
$336$	−13.3740	+	12.5353i	−0.729614	+	0.683859i
$337$			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
$340$	−0.868253	−	2.89968i	−0.0470876	−	0.157257i
$341$			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
$345$	−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	$-0.775302\pi$
$347$		−	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	$-0.713549\pi$
$349$	−23.2278			−1.24336			−0.621678	+	0.783273i	$0.713549\pi$
$350$	18.7023	+	0.473378i	0.999680	+	0.0253031i
$351$	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	$0.0734800\pi$
$353$			8.59750i			0.457599i	−0.973474	+	0.228799i	$0.926520\pi$
$354$	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
$357$	−2.38443	+	1.98358i	−0.126198	+	0.104982i
$358$	−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	$0.945318\pi$
$360$	12.4421	−	14.3246i	0.655756	−	0.754973i
$361$	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
$366$	−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
$370$	−24.8105	−	2.90493i	−1.28984	−	0.151020i
$371$	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	$-0.435895\pi$
$373$	7.72660			0.400068			0.200034	+	0.979789i	$0.435895\pi$
$374$	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
$378$	−18.5022	−	5.97235i	−0.951650	−	0.307185i
$379$		−	1.00894i		−	0.0518258i	−0.999664	−	0.0259129i	$-0.991751\pi$
$379$		−	1.00894i		−	0.0518258i	0.999664	−	0.0259129i	$-0.00824925\pi$
$380$	−25.4117	+	7.60902i	−1.30359	+	0.390335i
$381$	−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	$-0.993084\pi$
$383$		−	0.850409i		−	0.0434539i	0.999764	−	0.0217269i	$-0.00691644\pi$
$384$	−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	$0.333886\pi$
$390$	21.8205	+	0.828663i	1.10492	+	0.0419610i
$391$		−	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
$396$	−16.6082	+	24.3476i	−0.834592	+	1.22351i
$397$		−	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
$399$	17.3833	+	20.8962i	0.870255	+	1.04612i
$400$	16.7087	−	10.9917i	0.835437	−	0.549585i
$401$		−	30.8889i		−	1.54252i	−0.636522	−	0.771258i	$-0.719628\pi$
$401$		−	30.8889i		−	1.54252i	0.636522	−	0.771258i	$-0.280372\pi$
$402$	5.53048	+	10.4671i	0.275835	+	0.522052i
$403$	−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
$408$	−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	$-0.0790335\pi$
$410$	−5.94175	−	0.695686i	−0.293442	−	0.0343575i
$411$	−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	$-0.136793\pi$
$420$	−17.0749	−	11.3334i	−0.833172	−	0.553014i
$421$		−	11.8697i		−	0.578493i	−0.957255	−	0.289246i	$-0.906595\pi$
$421$		−	11.8697i		−	0.578493i	0.957255	−	0.289246i	$-0.0934047\pi$
$422$	−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
$430$	30.8529	+	3.61239i	1.48786	+	0.174205i
$431$		−	11.0477i		−	0.532147i	−0.963953	−	0.266074i	$-0.914274\pi$
$431$		−	11.0477i		−	0.532147i	0.963953	−	0.266074i	$-0.0857264\pi$
$432$	−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	$0.725497\pi$
$434$	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
$438$	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	$-0.0743206\pi$
$440$	−23.7928	+	19.9763i	−1.13428	+	0.952334i
$441$	−3.82215	+	20.6492i	−0.182007	+	0.983297i
$442$	−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
$448$	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	$0.964811\pi$
$450$	18.7826	+	9.85981i	0.885418	+	0.464796i
$451$	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
$460$	4.84539	−	1.45086i	0.225917	−	0.0676465i
$461$		−	20.9199i		−	0.974336i	−0.873308	−	0.487168i	$-0.838030\pi$
$461$		−	20.9199i		−	0.974336i	0.873308	−	0.487168i	$-0.161970\pi$
$462$	28.3906	+	14.4009i	1.32085	+	0.669990i
$463$		−	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	$0.496168\pi$
$468$	−19.7608	−	13.4794i	−0.913444	−	0.623085i
$469$	10.4419	−	7.38052i	0.482160	−	0.340801i
$470$	3.73513	−	31.9012i	0.172289	−	1.47149i
$471$	−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
$476$	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	$-0.414426\pi$
$479$	11.6263			0.531221			0.265611	+	0.964080i	$0.414426\pi$
$480$	−21.9040	+	0.464348i	−0.999775	+	0.0211945i
$481$			31.4927i			1.43594i
$482$	−3.11361	−	7.21332i	−0.141821	−	0.328558i
$483$	−3.31458	−	3.98441i	−0.150819	−	0.181297i
$484$	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
$490$	−9.76313	+	19.8666i	−0.441053	+	0.897481i
$491$	−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
$495$	−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
$498$	12.0374	+	22.7823i	0.539410	+	1.02090i
$499$			37.9208i			1.69757i	0.528738	+	0.848785i	$0.322665\pi$
$499$			37.9208i			1.69757i	−0.528738	+	0.848785i	$0.677335\pi$
$500$	16.2517	+	15.3585i	0.726797	+	0.686852i
$501$	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	$-0.897789\pi$
$503$		−	14.1570i		−	0.631231i	0.948887	−	0.315616i	$-0.102211\pi$
$504$	9.23912	+	20.4607i	0.411543	+	0.911390i
$505$	−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	$-0.0205763\pi$
$510$	−3.70449	−	0.140683i	−0.164038	−	0.00622956i
$511$	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
$518$	15.3990	−	25.2284i	0.676594	−	1.10847i
$519$	1.47813	+	18.7680i	0.0648825	+	0.823824i
$520$	−16.2130	−	19.3106i	−0.710988	−	0.846824i
$521$	−28.0030			−1.22683			−0.613416	−	0.789760i	$-0.710205\pi$
$521$	−28.0030			−1.22683			−0.613416	+	0.789760i	$0.710205\pi$
$522$	−7.85036	+	4.97309i	−0.343601	+	0.217666i
$523$		−	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
$525$	7.94706	−	21.4906i	0.346838	−	0.937925i
$526$	−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
$530$	−4.81305	+	41.1075i	−0.209065	+	1.78560i
$531$	−2.54604	−	16.0635i	−0.110489	−	0.697095i
$532$	4.39630	−	31.0770i	0.190604	−	1.34736i
$533$			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
$540$	−11.6817	−	20.0882i	−0.502701	−	0.864460i
$541$		−	24.1789i		−	1.03953i	−0.854309	−	0.519766i	$-0.826019\pi$
$541$		−	24.1789i		−	1.03953i	0.854309	−	0.519766i	$-0.173981\pi$
$542$	−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
$546$	−11.6879	+	23.0421i	−0.500197	+	0.986113i
$547$	−32.1623			−1.37516			−0.687581	−	0.726108i	$-0.741327\pi$
$547$	−32.1623			−1.37516			−0.687581	+	0.726108i	$0.741327\pi$
$548$	−12.2635	+	13.0112i	−0.523869	+	0.555812i
$549$	−30.1349	+	4.77634i	−1.28613	+	0.203849i
$550$	−27.8475	−	20.7595i	−1.18742	−	0.885187i
$551$	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
$555$	−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	$0.210202\pi$
$557$			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
$560$	3.54576	+	23.3972i	0.149836	+	0.988711i
$561$	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
$567$	−14.2418	+	19.0833i	−0.598098	+	0.801423i
$568$	−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	$0.894632\pi$
$570$	−1.23289	+	32.4647i	−0.0516401	+	1.35980i
$571$			22.9342i			0.959766i	0.877333	+	0.479883i	$0.159321\pi$
$571$			22.9342i			0.959766i	−0.877333	+	0.479883i	$0.840679\pi$
$572$	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
$576$	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
$580$	−9.38403	+	2.80986i	−0.389650	+	0.116673i
$581$	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
$585$	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	$0.301268\pi$
$588$	20.6300	−	12.7437i	0.850767	−	0.525543i
$589$		−	24.7621i		−	1.02030i
$590$	1.99365	−	17.0274i	0.0820771	−	0.701008i
$591$	−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	$-0.847355\pi$
$593$		−	22.4706i		−	0.922757i	0.887203	−	0.461378i	$-0.152645\pi$
$594$	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	$-0.699248\pi$
$599$		−	39.6684i		−	1.62081i	0.585872	−	0.810403i	$-0.300752\pi$
$600$	−6.13073	−	23.7153i	−0.250286	−	0.968172i
$601$		−	4.47305i		−	0.182460i	−0.995830	−	0.0912298i	$-0.970920\pi$
$601$		−	4.47305i		−	0.182460i	0.995830	−	0.0912298i	$-0.0290798\pi$
$602$	−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
$606$	9.24269	−	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
$609$	6.41932	+	7.71657i	0.260124	+	0.312691i
$610$	−31.9433	−	3.74006i	−1.29335	−	0.151431i
$611$	−40.4930			−1.63817
$612$	3.35482	+	2.28841i	0.135610	+	0.0925037i
$613$	25.9593			1.04849			0.524243	−	0.851569i	$-0.324348\pi$
$613$	25.9593			1.04849			0.524243	+	0.851569i	$0.324348\pi$
$614$	−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	$0.495408\pi$
$618$	−5.11896	−	9.68825i	−0.205915	−	0.389719i
$619$	−0.161608			−0.00649556			−0.00324778	−	0.999995i	$-0.501034\pi$
$619$	−0.161608			−0.00649556			−0.00324778	+	0.999995i	$0.501034\pi$
$620$	5.35536	+	17.8852i	0.215076	+	0.718286i
$621$	−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
$630$	−19.8912	+	15.3082i	−0.792483	+	0.609894i
$631$	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
$640$	17.3840	+	18.3793i	0.687162	+	0.726504i
$641$		−	14.5460i		−	0.574531i	−0.957851	−	0.287266i	$-0.907254\pi$
$641$		−	14.5460i		−	0.574531i	0.957851	−	0.287266i	$-0.0927462\pi$
$642$	−34.0408	+	17.9860i	−1.34348	+	0.709852i
$643$		−	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	$0.127597\pi$
$647$			19.8509i			0.780419i	−0.920726	+	0.390210i	$0.872403\pi$
$648$	−0.864097	+	25.4412i	−0.0339449	+	0.999424i
$649$			26.6302i			1.04533i
$650$	16.8486	−	22.6014i	0.660858	−	0.886500i
$651$	14.7071	−	12.2347i	0.576418	−	0.479515i
$652$	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
$658$	32.4385	+	19.7999i	1.26458	+	0.771882i
$659$	−0.262720			−0.0102341			−0.00511706	−	0.999987i	$-0.501629\pi$
$659$	−0.262720			−0.0102341			−0.00511706	+	0.999987i	$0.501629\pi$
$660$	13.7424	+	35.4806i	0.534923	+	1.38108i
$661$	−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
$665$	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
$670$	15.1796	+	1.77729i	0.586438	+	0.0686626i
$671$	49.9580			1.92861
$672$	10.3395	−	23.7717i	0.398857	−	0.917013i
$673$		−	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	$0.755882\pi$
$678$	−11.3947	−	21.5658i	−0.437609	−	0.828229i
$679$	16.6035	−	11.7357i	0.637183	−	0.450374i
$680$	2.75251	+	3.27838i	0.105554	+	0.125720i
$681$	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
$686$	−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
$690$	0.235083	−	6.19023i	0.00894944	−	0.235658i
$691$	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
$693$	27.9230	−	27.2107i	1.06071	−	1.03365i
$694$	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
$700$	−24.5487	+	9.86722i	−0.927853	+	0.372946i
$701$	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
$705$	−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
$708$	−11.7682	+	14.6355i	−0.442276	+	0.550038i
$709$			46.4979i			1.74626i	0.487483	+	0.873132i	$0.337915\pi$
$709$			46.4979i			1.74626i	−0.487483	+	0.873132i	$0.662085\pi$
$710$	0.680317	−	5.81049i	0.0255318	−	0.218064i
$711$	28.3998	−	4.50133i	1.06508	−	0.168813i
$712$	−5.34008	+	14.7053i	−0.200128	+	0.551103i
$713$			4.72153i			0.176823i
$714$	1.98427	−	3.91189i	0.0742596	−	0.146399i
$715$	−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	$-0.643935\pi$
$719$	−23.4319			−0.873861			−0.436931	+	0.899495i	$0.643935\pi$
$720$	−8.12669	+	25.5726i	−0.302864	+	0.953034i
$721$	−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	$0.632844\pi$
$728$	28.7772	−	7.87008i	1.06655	−	0.291685i
$729$	−24.0531	+	12.2658i	−0.890855	+	0.454288i
$730$	31.2576	+	3.65977i	1.15689	+	0.135454i
$731$			6.64864i			0.245909i
$732$	27.4562	+	22.0770i	1.01481	+	0.815991i
$733$		−	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
$735$	19.1652	+	19.1754i	0.706919	+	0.707295i
$736$	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	$-0.790125\pi$
$739$		−	33.3063i		−	1.22519i	0.790396	−	0.612597i	$-0.209875\pi$
$740$	33.8425	−	10.1335i	1.24408	−	0.372514i
$741$	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	$0.768701\pi$
$744$	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
$750$	24.2309	−	12.7617i	0.884789	−	0.465992i
$751$	−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
$756$	27.3708	−	2.61511i	0.995467	−	0.0951106i
$757$	−3.29010			−0.119581			−0.0597903	−	0.998211i	$-0.519043\pi$
$757$	−3.29010			−0.119581			−0.0597903	+	0.998211i	$0.519043\pi$
$758$	0.565469	+	1.31003i	0.0205388	+	0.0475823i
$759$	0.755506	+	9.59279i	0.0274231	+	0.348196i
$760$	28.7304	−	24.1219i	1.04216	−	0.874992i
$761$	−25.6191			−0.928690			−0.464345	−	0.885654i	$-0.653710\pi$
$761$	−25.6191			−0.928690			−0.464345	+	0.885654i	$0.653710\pi$
$762$	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
$765$	−1.62851	+	4.23822i	−0.0588789	+	0.153233i
$766$	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	$0.897983\pi$
$770$	36.0915	−	19.6576i	1.30065	−	0.708412i
$771$	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
$777$	−23.1506	−	27.8290i	−0.830523	−	0.998360i
$778$	−25.5318	+	11.0207i	−0.915358	+	0.395112i
$779$	−11.2211			−0.402037
$780$	−28.7965	+	11.1535i	−1.03108	+	0.399360i
$781$			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
$786$	−22.8358	+	12.0657i	−0.814526	+	0.430369i
$787$		−	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
$790$	30.1040	+	3.52471i	1.07105	+	0.125404i
$791$	−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
$795$	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	$0.705430\pi$
$798$	−34.2823	−	17.3894i	−1.21358	−	0.615578i
$799$	6.87455			0.243204
$800$	−15.5345	+	23.6364i	−0.549228	+	0.835672i
$801$	−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	$0.0163056\pi$
$809$			2.91273i			0.102406i	−0.998688	+	0.0512031i	$0.983694\pi$
$810$	−27.9054	+	5.59364i	−0.980496	+	0.196540i
$811$	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
$816$	−0.643899	−	4.64481i	−0.0225410	−	0.162601i
$817$	58.2660			2.03847
$818$	5.57089	+	12.9061i	0.194782	+	0.451251i
$819$	22.0845	+	22.6626i	0.771697	+	0.791896i
$820$	8.10478	−	2.42681i	0.283031	−	0.0847480i
$821$	−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
$825$	−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	$-0.871671\pi$
$827$		−	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	$-0.280756\pi$
$829$	36.6005			1.27119			0.635593	+	0.772024i	$0.280756\pi$
$830$	33.0392	+	3.86838i	1.14681	+	0.134273i
$831$	−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	$-0.683253\pi$
$839$	−31.5392			−1.08885			−0.544427	+	0.838808i	$0.683253\pi$
$840$	28.5223	+	5.14571i	0.984113	+	0.177544i
$841$	−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
$850$	−2.86041	+	3.83707i	−0.0981114	+	0.131610i
$851$	8.93412			0.306258
$852$	−4.01581	+	4.99428i	−0.137579	+	0.171101i
$853$		−	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	$0.278691\pi$
$857$			44.9590i			1.53577i	−0.640587	+	0.767886i	$0.721309\pi$
$858$	42.4127	−	22.4095i	1.44794	−	0.765047i
$859$	8.35557			0.285088			0.142544	−	0.989788i	$-0.454472\pi$
$859$	8.35557			0.285088			0.142544	+	0.989788i	$0.454472\pi$
$860$	−42.0845	+	12.6014i	−1.43507	+	0.429703i
$861$	−5.54422	−	6.66463i	−0.188947	−	0.227130i
$862$	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	$0.694393\pi$
$864$	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
$868$	−21.8726	−	3.09419i	−0.742403	−	0.105024i
$869$	−47.0814			−1.59713
$870$	−0.455282	+	11.9886i	−0.0154355	+	0.406450i
$871$		−	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	$-0.539010\pi$
$877$	−7.24055			−0.244496			−0.122248	+	0.992500i	$0.539010\pi$
$878$	5.43390	+	12.5887i	0.183385	+	0.424849i
$879$	2.38446	+	30.2759i	0.0804260	+	1.02118i
$880$	19.6971	−	39.2725i	0.663990	−	1.32388i
$881$	41.5264			1.39906			0.699531	−	0.714603i	$-0.253392\pi$
$881$	41.5264			1.39906			0.699531	+	0.714603i	$0.253392\pi$
$882$	−6.61030	−	28.9535i	−0.222580	−	0.974914i
$883$	10.8468			0.365023			0.182512	−	0.983204i	$-0.441577\pi$
$883$	10.8468			0.365023			0.182512	+	0.983204i	$0.441577\pi$
$884$	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	$-0.782088\pi$
$887$		−	37.6663i		−	1.26471i	0.774678	−	0.632355i	$-0.217912\pi$
$888$	−37.2996	−	10.3124i	−1.25169	−	0.346063i
$889$	−15.0206	−	21.2509i	−0.503773	−	0.712731i
$890$	−17.3728	−	2.03408i	−0.582337	−	0.0681826i
$891$	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
$896$	−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
$900$	−29.9136	−	2.27530i	−0.997120	−	0.0758434i
$901$	−8.85847			−0.295118
$902$	−12.0657	+	5.20814i	−0.401745	+	0.173412i
$903$	28.7887	+	34.6064i	0.958027	+	1.15163i
$904$	−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	$-0.211720\pi$
$907$	47.3931			1.57366			0.786831	+	0.617168i	$0.211720\pi$
$908$	38.9065	−	41.2788i	1.29116	−	1.36989i
$909$	−2.00422	−	12.6451i	−0.0664759	−	0.419410i
$910$	15.9544	+	29.2923i	0.528883	+	0.971030i
$911$			53.2694i			1.76489i	0.470413	+	0.882446i	$0.344105\pi$
$911$			53.2694i			1.76489i	−0.470413	+	0.882446i	$0.655895\pi$
$912$	−40.7053	+	5.64287i	−1.34789	+	0.186854i
$913$	−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
$918$	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	$0.397198\pi$
$920$	−5.47819	+	4.59946i	−0.180611	+	0.151640i
$921$	−13.1457	+	1.03532i	−0.433164	+	0.0341150i
$922$	11.7247	+	27.1627i	0.386133	+	0.894557i
$923$	−7.37541			−0.242764
$924$	−44.9339	−	2.78661i	−1.47822	−	0.0916727i
$925$	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	$-0.577478\pi$
$929$	−14.6916			−0.482015			−0.241007	+	0.970523i	$0.577478\pi$
$930$	22.8492	+	0.867730i	0.749255	+	0.0284540i
$931$	−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	$0.725527\pi$
$938$	−9.42141	+	15.4352i	−0.307620	+	0.503978i
$939$	0.639645	+	8.12167i	0.0208740	+	0.265041i
$940$	13.0295	+	43.5144i	0.424977	+	1.41928i
$941$			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
$945$	9.87507	+	29.1116i	0.321236	+	0.946999i
$946$	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
$950$	33.6265	+	25.0675i	1.09099	+	0.813298i
$951$	−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	$0.298461\pi$
$954$	−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
$960$	28.1803	−	12.8792i	0.909514	−	0.415674i
$961$	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
$966$	6.53680	+	3.31574i	0.210318	+	0.106682i
$967$			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
$970$	24.1368	+	2.82605i	0.774987	+	0.0907389i
$971$			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
$975$	−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	$0.462859\pi$
$978$	−18.2746	−	34.5868i	−0.584356	−	1.10596i
$979$	27.1703			0.868366
$980$	1.54221	−	31.2669i	0.0492641	−	0.998786i
$981$	−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	$-0.901039\pi$
$983$		−	19.1824i		−	0.611822i	0.952060	−	0.305911i	$-0.0989610\pi$
$984$	−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
$987$	35.7823	−	29.7669i	1.13896	−	0.947490i
$988$	−34.4166	−	32.4386i	−1.09494	−	1.03201i
$989$	−11.1099			−0.353275
$990$	46.5619	−	1.89319i	1.47983	−	0.0601696i
$991$	−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
$996$	−28.3981	−	22.8345i	−0.899830	−	0.723538i
$997$		−	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.629.16	yes	160
3.2	odd	2	inner	840.2.u.e.629.146	yes	160
5.4	even	2	inner	840.2.u.e.629.145	yes	160
7.6	odd	2	inner	840.2.u.e.629.13	yes	160
8.5	even	2	inner	840.2.u.e.629.9	✓	160
15.14	odd	2	inner	840.2.u.e.629.15	yes	160
21.20	even	2	inner	840.2.u.e.629.147	yes	160
24.5	odd	2	inner	840.2.u.e.629.151	yes	160
35.34	odd	2	inner	840.2.u.e.629.148	yes	160
40.29	even	2	inner	840.2.u.e.629.152	yes	160
56.13	odd	2	inner	840.2.u.e.629.12	yes	160
105.104	even	2	inner	840.2.u.e.629.14	yes	160
120.29	odd	2	inner	840.2.u.e.629.10	yes	160
168.125	even	2	inner	840.2.u.e.629.150	yes	160
280.69	odd	2	inner	840.2.u.e.629.149	yes	160
840.629	even	2	inner	840.2.u.e.629.11	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.u.e.629.9	✓	160	8.5	even	2	inner
840.2.u.e.629.10	yes	160	120.29	odd	2	inner
840.2.u.e.629.11	yes	160	840.629	even	2	inner
840.2.u.e.629.12	yes	160	56.13	odd	2	inner
840.2.u.e.629.13	yes	160	7.6	odd	2	inner
840.2.u.e.629.14	yes	160	105.104	even	2	inner
840.2.u.e.629.15	yes	160	15.14	odd	2	inner
840.2.u.e.629.16	yes	160	1.1	even	1	trivial
840.2.u.e.629.145	yes	160	5.4	even	2	inner
840.2.u.e.629.146	yes	160	3.2	odd	2	inner
840.2.u.e.629.147	yes	160	21.20	even	2	inner
840.2.u.e.629.148	yes	160	35.34	odd	2	inner
840.2.u.e.629.149	yes	160	280.69	odd	2	inner
840.2.u.e.629.150	yes	160	168.125	even	2	inner
840.2.u.e.629.151	yes	160	24.5	odd	2	inner
840.2.u.e.629.152	yes	160	40.29	even	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} +(-3.14082 - 0.367741i) q^{10} +4.91211 q^{11} +(2.69962 + 2.17072i) 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} +(3.58402 - 2.27043i) q^{18} -5.93148 q^{19} +(4.28420 - 1.28282i) q^{20} +(-2.93069 - 3.52294i) 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} +(-0.741180 + 5.23934i) q^{28} -2.19038 q^{29} +(0.207855 - 5.47328i) 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} +(-4.84371 + 4.06675i) q^{40} +1.89178 q^{41} +(5.77971 + 2.93171i) 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} +(6.86258 - 0.951343i) q^{48} +(2.33585 - 6.59877i) q^{49} +(-5.66916 - 4.22618i) 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} +(-1.97407 - 7.21824i) q^{56} +(-0.806630 - 10.2419i) q^{57} +(2.84403 - 1.22762i) q^{58} +5.42133i q^{59} +(2.79766 + 7.22309i) q^{60} +10.1704 q^{61} +(-2.33974 - 5.42048i) q^{62} +(5.68452 - 5.53952i) 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} +(7.34745 - 4.00187i) q^{70} +1.84999i q^{71} +(1.61204 - 8.33075i) 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} +(8.63431 - 4.56209i) q^{78} -9.58477 q^{79} +(4.00991 - 7.99504i) q^{80} +(8.55889 - 2.78306i) q^{81} +(-2.45632 + 1.06027i) q^{82} -10.5193 q^{83} +(-9.14758 - 0.567294i) 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} +(9.47900 - 0.385414i) 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} +(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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