LMFDB - Embedded newform 640.2.bm.a.101.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [640,2,Mod(21,640)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("640.21"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(640, base_ring=CyclotomicField(32)) chi = DirichletCharacter(H, H._module([0, 13, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (of order $32$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			101.11
Character	$\chi$	$=$	640.101
Dual form			640.2.bm.a.621.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.24207 - 0.676215i) q^{2} +(-1.91317 + 1.02261i) q^{3} +(1.08547 + 1.67981i) q^{4} +(0.634393 + 0.773010i) q^{5} +(3.06779 + 0.0235610i) q^{6} +(1.30433 - 0.871523i) q^{7} +(-0.212313 - 2.82045i) q^{8} +(0.947771 - 1.41844i) q^{9} +(-0.265239 - 1.38912i) q^{10} +(4.30776 - 1.30674i) q^{11} +(-3.79447 - 2.10375i) q^{12} +(-1.78842 - 1.46772i) q^{13} +(-2.20940 + 0.200487i) q^{14} +(-2.00419 - 0.830162i) q^{15} +(-1.64352 + 3.64676i) q^{16} +(-3.37125 + 1.39642i) q^{17} +(-2.13637 + 1.12090i) q^{18} +(-0.478702 - 4.86035i) q^{19} +(-0.609897 + 1.90474i) q^{20} +(-1.60417 + 3.00119i) q^{21} +(-6.23417 - 1.28990i) q^{22} +(1.75216 - 0.348527i) q^{23} +(3.29041 + 5.17888i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(1.22885 + 3.03236i) q^{26} +(0.275156 - 2.79370i) q^{27} +(2.87980 + 1.24501i) q^{28} +(1.43505 - 4.73072i) q^{29} +(1.92797 + 2.38638i) q^{30} +(6.30899 + 6.30899i) q^{31} +(4.50735 - 3.41815i) q^{32} +(-6.90518 + 6.90518i) q^{33} +(5.13160 + 0.545242i) q^{34} +(1.50115 + 0.455369i) q^{35} +(3.41148 + 0.0524044i) q^{36} +(2.80856 + 0.276619i) q^{37} +(-2.69206 + 6.36059i) q^{38} +(4.92245 + 0.979135i) q^{39} +(2.04555 - 1.95339i) q^{40} +(0.0310011 + 0.155853i) q^{41} +(4.02193 - 2.64292i) q^{42} +(10.1425 + 5.42129i) q^{43} +(6.87101 + 5.81778i) q^{44} +(1.69773 - 0.167212i) q^{45} +(-2.41199 - 0.751944i) q^{46} +(-3.52943 - 8.52080i) q^{47} +(-0.584880 - 8.65754i) q^{48} +(-1.73707 + 4.19366i) q^{49} +(0.905537 - 1.08628i) q^{50} +(5.02178 - 6.11905i) q^{51} +(0.524214 - 4.59736i) q^{52} +(-1.37955 - 4.54778i) q^{53} +(-2.23091 + 3.28391i) q^{54} +(3.74294 + 2.50095i) q^{55} +(-2.73501 - 3.49375i) q^{56} +(5.88608 + 8.80914i) q^{57} +(-4.98141 + 4.90548i) q^{58} +(11.2003 - 9.19187i) q^{59} +(-0.780968 - 4.26777i) q^{60} +(3.91997 + 7.33375i) q^{61} +(-3.56996 - 12.1024i) q^{62} -2.67611i q^{63} +(-7.90985 + 1.19764i) q^{64} -2.31358i q^{65} +(13.2461 - 3.90732i) q^{66} +(0.890432 + 1.66588i) q^{67} +(-6.00510 - 4.14729i) q^{68} +(-2.99578 + 2.45857i) q^{69} +(-1.55661 - 1.58070i) q^{70} +(1.82930 + 2.73774i) q^{71} +(-4.20186 - 2.37198i) q^{72} +(6.55322 + 4.37872i) q^{73} +(-3.30137 - 2.24277i) q^{74} +(-0.629720 - 2.07591i) q^{75} +(7.64484 - 6.07988i) q^{76} +(4.47986 - 5.45873i) q^{77} +(-5.45191 - 4.54478i) q^{78} +(1.68330 - 4.06385i) q^{79} +(-3.86162 + 1.04302i) q^{80} +(4.28896 + 10.3545i) q^{81} +(0.0668846 - 0.214543i) q^{82} +(4.08896 - 0.402727i) q^{83} +(-6.78269 + 0.562995i) q^{84} +(-3.21814 - 1.72013i) q^{85} +(-8.93174 - 13.5921i) q^{86} +(2.09219 + 10.5182i) q^{87} +(-4.60020 - 11.8724i) q^{88} +(5.08280 + 1.01103i) q^{89} +(-2.22177 - 0.940340i) q^{90} +(-3.61183 - 0.355734i) q^{91} +(2.48738 + 2.56499i) q^{92} +(-18.5218 - 5.61852i) q^{93} +(-1.37810 + 12.9701i) q^{94} +(3.45341 - 3.45341i) q^{95} +(-5.12789 + 11.1488i) q^{96} +(1.41030 + 1.41030i) q^{97} +(4.99337 - 4.03418i) q^{98} +(2.22923 - 7.34879i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

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 $

$2$	−1.24207	−	0.676215i	−0.878275	−	0.478156i
$2$	−1.24207	−	0.676215i	−0.878275	−	0.478156i
$3$	−1.91317	+	1.02261i	−1.10457	+	0.590404i	−0.919804	−	0.392379i	$-0.871652\pi$
$3$	−1.91317	+	1.02261i	−1.10457	+	0.590404i	−0.184764	+	0.982783i	$0.559152\pi$
$4$	1.08547	+	1.67981i	0.542734	+	0.839905i
$5$	0.634393	+	0.773010i	0.283709	+	0.345701i
$5$	0.634393	+	0.773010i	0.283709	+	0.345701i
$6$	3.06779	+	0.0235610i	1.25242	+	0.00961875i
$7$	1.30433	−	0.871523i	0.492989	−	0.329405i	−0.284101	−	0.958794i	$-0.591695\pi$
$7$	1.30433	−	0.871523i	0.492989	−	0.329405i	0.777090	+	0.629390i	$0.216695\pi$
$8$	−0.212313	−	2.82045i	−0.0750641	−	0.997179i
$9$	0.947771	−	1.41844i	0.315924	−	0.472813i
$10$	−0.265239	−	1.38912i	−0.0838759	−	0.439278i
$11$	4.30776	−	1.30674i	1.29884	−	0.393998i	0.436214	−	0.899843i	$-0.356319\pi$
$11$	4.30776	−	1.30674i	1.29884	−	0.393998i	0.862624	+	0.505845i	$0.168819\pi$
$12$	−3.79447	−	2.10375i	−1.09537	−	0.607300i
$13$	−1.78842	−	1.46772i	−0.496018	−	0.407071i	0.352847	−	0.935681i	$-0.385214\pi$
$13$	−1.78842	−	1.46772i	−0.496018	−	0.407071i	−0.848865	+	0.528610i	$0.822714\pi$
$14$	−2.20940	+	0.200487i	−0.590487	+	0.0535823i
$15$	−2.00419	−	0.830162i	−0.517479	−	0.214347i
$16$	−1.64352	+	3.64676i	−0.410880	+	0.911689i
$17$	−3.37125	+	1.39642i	−0.817648	+	0.338681i	−0.752001	−	0.659162i	$-0.770911\pi$
$17$	−3.37125	+	1.39642i	−0.817648	+	0.338681i	−0.0656470	+	0.997843i	$0.520911\pi$
$18$	−2.13637	+	1.12090i	−0.503546	+	0.264199i
$19$	−0.478702	−	4.86035i	−0.109822	−	1.11504i	−0.879268	−	0.476328i	$-0.841967\pi$
$19$	−0.478702	−	4.86035i	−0.109822	−	1.11504i	0.769446	−	0.638712i	$-0.220533\pi$
$20$	−0.609897	+	1.90474i	−0.136377	+	0.425912i
$21$	−1.60417	+	3.00119i	−0.350058	+	0.654913i
$22$	−6.23417	−	1.28990i	−1.32913	−	0.275008i
$23$	1.75216	−	0.348527i	0.365351	−	0.0726729i	−0.00900085	−	0.999959i	$-0.502865\pi$
$23$	1.75216	−	0.348527i	0.365351	−	0.0726729i	0.374352	+	0.927287i	$0.377865\pi$
$24$	3.29041	+	5.17888i	0.671652	+	1.05713i
$25$	−0.195090	+	0.980785i	−0.0390181	+	0.196157i
$26$	1.22885	+	3.03236i	0.240997	+	0.594694i
$27$	0.275156	−	2.79370i	0.0529538	−	0.537649i
$28$	2.87980	+	1.24501i	0.544230	+	0.235285i
$29$	1.43505	−	4.73072i	0.266482	−	0.878474i	−0.716939	−	0.697136i	$-0.754457\pi$
$29$	1.43505	−	4.73072i	0.266482	−	0.878474i	0.983421	−	0.181338i	$-0.0580426\pi$
$30$	1.92797	+	2.38638i	0.351998	+	0.435691i
$31$	6.30899	+	6.30899i	1.13313	+	1.13313i	0.989654	+	0.143474i	$0.0458272\pi$
$31$	6.30899	+	6.30899i	1.13313	+	1.13313i	0.143474	+	0.989654i	$0.454173\pi$
$32$	4.50735	−	3.41815i	0.796795	−	0.604249i
$33$	−6.90518	+	6.90518i	−1.20204	+	1.20204i
$34$	5.13160	+	0.545242i	0.880062	+	0.0935083i
$35$	1.50115	+	0.455369i	0.253741	+	0.0769715i
$36$	3.41148	+	0.0524044i	0.568580	+	0.00873407i
$37$	2.80856	+	0.276619i	0.461725	+	0.0454759i	0.326206	−	0.945299i	$-0.394230\pi$
$37$	2.80856	+	0.276619i	0.461725	+	0.0454759i	0.135519	+	0.990775i	$0.456730\pi$
$38$	−2.69206	+	6.36059i	−0.436709	+	1.03182i
$39$	4.92245	+	0.979135i	0.788222	+	0.156787i
$40$	2.04555	−	1.95339i	0.323429	−	0.308859i
$41$	0.0310011	+	0.155853i	0.00484156	+	0.0243401i	0.983131	−	0.182905i	$-0.0585502\pi$
$41$	0.0310011	+	0.155853i	0.00484156	+	0.0243401i	−0.978289	+	0.207245i	$0.933550\pi$
$42$	4.02193	−	2.64292i	0.620598	−	0.407811i
$43$	10.1425	+	5.42129i	1.54672	+	0.826739i	0.999944	−	0.0105410i	$-0.00335538\pi$
$43$	10.1425	+	5.42129i	1.54672	+	0.826739i	0.546775	+	0.837280i	$0.315855\pi$
$44$	6.87101	+	5.81778i	1.03584	+	0.877064i
$45$	1.69773	−	0.167212i	0.253082	−	0.0249264i
$46$	−2.41199	−	0.751944i	−0.355628	−	0.110868i
$47$	−3.52943	−	8.52080i	−0.514821	−	1.24289i	−0.941049	−	0.338271i	$-0.890158\pi$
$47$	−3.52943	−	8.52080i	−0.514821	−	1.24289i	0.426228	−	0.904616i	$-0.359842\pi$
$48$	−0.584880	−	8.65754i	−0.0844202	−	1.24961i
$49$	−1.73707	+	4.19366i	−0.248153	+	0.599094i
$50$	0.905537	−	1.08628i	0.128062	−	0.153623i
$51$	5.02178	−	6.11905i	0.703189	−	0.856839i
$52$	0.524214	−	4.59736i	0.0726955	−	0.637539i
$53$	−1.37955	−	4.54778i	−0.189496	−	0.624685i	−0.999279	−	0.0379562i	$-0.987915\pi$
$53$	−1.37955	−	4.54778i	−0.189496	−	0.624685i	0.809783	−	0.586729i	$-0.199585\pi$
$54$	−2.23091	+	3.28391i	−0.303588	+	0.446883i
$55$	3.74294	+	2.50095i	0.504698	+	0.337228i
$56$	−2.73501	−	3.49375i	−0.365481	−	0.466872i
$57$	5.88608	+	8.80914i	0.779630	+	1.16680i
$58$	−4.98141	+	4.90548i	−0.654092	+	0.644121i
$59$	11.2003	−	9.19187i	1.45816	−	1.19668i	0.518261	−	0.855223i	$-0.326580\pi$
$59$	11.2003	−	9.19187i	1.45816	−	1.19668i	0.939897	−	0.341457i	$-0.110920\pi$
$60$	−0.780968	−	4.26777i	−0.100823	−	0.550967i
$61$	3.91997	+	7.33375i	0.501901	+	0.938991i	0.997515	+	0.0704482i	$0.0224429\pi$
$61$	3.91997	+	7.33375i	0.501901	+	0.938991i	−0.495614	+	0.868543i	$0.665057\pi$
$62$	−3.56996	−	12.1024i	−0.453386	−	1.53701i
$63$		−	2.67611i		−	0.337158i
$64$	−7.90985	+	1.19764i	−0.988731	+	0.149705i
$65$		−	2.31358i		−	0.286964i
$66$	13.2461	−	3.90732i	1.63048	−	0.480958i
$67$	0.890432	+	1.66588i	0.108784	+	0.203520i	0.930423	−	0.366488i	$-0.119440\pi$
$67$	0.890432	+	1.66588i	0.108784	+	0.203520i	−0.821639	+	0.570008i	$0.806940\pi$
$68$	−6.00510	−	4.14729i	−0.728225	−	0.502933i
$69$	−2.99578	+	2.45857i	−0.360649	+	0.295977i
$70$	−1.55661	−	1.58070i	−0.186050	−	0.188930i
$71$	1.82930	+	2.73774i	0.217098	+	0.324910i	0.923994	−	0.382408i	$-0.124905\pi$
$71$	1.82930	+	2.73774i	0.217098	+	0.324910i	−0.706896	+	0.707318i	$0.749905\pi$
$72$	−4.20186	−	2.37198i	−0.495194	−	0.279541i
$73$	6.55322	+	4.37872i	0.766997	+	0.512491i	0.876445	−	0.481502i	$-0.159908\pi$
$73$	6.55322	+	4.37872i	0.766997	+	0.512491i	−0.109448	+	0.993992i	$0.534908\pi$
$74$	−3.30137	−	2.24277i	−0.383777	−	0.260717i
$75$	−0.629720	−	2.07591i	−0.0727138	−	0.239705i
$76$	7.64484	−	6.07988i	0.876923	−	0.697410i
$77$	4.47986	−	5.45873i	0.510528	−	0.622080i
$78$	−5.45191	−	4.54478i	−0.617307	−	0.514595i
$79$	1.68330	−	4.06385i	0.189386	−	0.457219i	−0.800455	−	0.599392i	$-0.795409\pi$
$79$	1.68330	−	4.06385i	0.189386	−	0.457219i	0.989842	+	0.142173i	$0.0454090\pi$
$80$	−3.86162	+	1.04302i	−0.431742	+	0.116613i
$81$	4.28896	+	10.3545i	0.476551	+	1.15050i
$82$	0.0668846	−	0.214543i	0.00738617	−	0.0236924i
$83$	4.08896	−	0.402727i	0.448821	−	0.0442051i	0.128918	−	0.991655i	$-0.458850\pi$
$83$	4.08896	−	0.402727i	0.448821	−	0.0442051i	0.319903	+	0.947450i	$0.396350\pi$
$84$	−6.78269	+	0.562995i	−0.740052	+	0.0614278i
$85$	−3.21814	−	1.72013i	−0.349057	−	0.186575i
$86$	−8.93174	−	13.5921i	−0.963135	−	1.46568i
$87$	2.09219	+	10.5182i	0.224307	+	1.12767i
$88$	−4.60020	−	11.8724i	−0.490383	−	1.26560i
$89$	5.08280	+	1.01103i	0.538775	+	0.107169i	0.456975	−	0.889480i	$-0.348933\pi$
$89$	5.08280	+	1.01103i	0.538775	+	0.107169i	0.0818006	+	0.996649i	$0.473933\pi$
$90$	−2.22177	−	0.940340i	−0.234195	−	0.0991206i
$91$	−3.61183	−	0.355734i	−0.378623	−	0.0372911i
$92$	2.48738	+	2.56499i	0.259327	+	0.267418i
$93$	−18.5218	−	5.61852i	−1.92062	−	0.582614i
$94$	−1.37810	+	12.9701i	−0.142140	+	1.33776i
$95$	3.45341	−	3.45341i	0.354313	−	0.354313i
$96$	−5.12789	+	11.1488i	−0.523363	+	1.13787i
$97$	1.41030	+	1.41030i	0.143194	+	0.143194i	0.775070	−	0.631876i	$-0.217715\pi$
$97$	1.41030	+	1.41030i	0.143194	+	0.143194i	−0.631876	+	0.775070i	$0.717715\pi$
$98$	4.99337	−	4.03418i	0.504407	−	0.407513i
$99$	2.22923	−	7.34879i	0.224046	−	0.738581i
$100$	−1.85930	+	0.736896i	−0.185930	+	0.0736896i
$101$	−0.265529	+	2.69596i	−0.0264211	+	0.268258i	0.972894	+	0.231252i	$0.0742822\pi$
$101$	−0.265529	+	2.69596i	−0.0264211	+	0.268258i	−0.999315	+	0.0370063i	$0.988218\pi$
$102$	−10.3752	+	4.20448i	−1.02730	+	0.416306i
$103$	−3.45047	+	17.3467i	−0.339985	+	1.70922i	0.311236	+	0.950333i	$0.399257\pi$
$103$	−3.45047	+	17.3467i	−0.339985	+	1.70922i	−0.651221	+	0.758888i	$0.725743\pi$
$104$	−3.75991	+	5.35575i	−0.368690	+	0.525175i
$105$	−3.33762	+	0.663894i	−0.325718	+	0.0647894i
$106$	−1.36177	+	6.58153i	−0.132267	+	0.639254i
$107$	3.71824	−	6.95634i	0.359456	−	0.672495i	−0.635577	−	0.772037i	$-0.719238\pi$
$107$	3.71824	−	6.95634i	0.359456	−	0.672495i	0.995033	+	0.0995423i	$0.0317379\pi$
$108$	4.99156	−	2.57027i	0.480314	−	0.247324i
$109$	−1.01789	−	10.3348i	−0.0974957	−	0.989891i	−0.912126	−	0.409910i	$-0.865560\pi$
$109$	−1.01789	−	10.3348i	−0.0974957	−	0.989891i	0.814630	−	0.579981i	$-0.196940\pi$
$110$	−2.95781	−	5.63738i	−0.282016	−	0.537503i
$111$	−5.65612	+	2.34284i	−0.536855	+	0.222373i
$112$	1.03455	+	6.18893i	0.0977555	+	0.584799i
$113$	−1.98093	−	0.820526i	−0.186350	−	0.0771886i	0.287557	−	0.957763i	$-0.407157\pi$
$113$	−1.98093	−	0.820526i	−0.186350	−	0.0771886i	−0.473907	+	0.880575i	$0.657157\pi$
$114$	−1.35404	−	14.9218i	−0.126818	−	1.39755i
$115$	1.38098	+	1.13334i	0.128777	+	0.105684i
$116$	9.50442	−	2.72444i	0.882463	−	0.252958i
$117$	−3.77688	+	1.14570i	−0.349172	+	0.105920i
$118$	−20.1272	+	3.84311i	−1.85286	+	0.353787i
$119$	−3.18020	+	4.75950i	−0.291528	+	0.436303i
$120$	−1.91591	+	5.82896i	−0.174898	+	0.532109i
$121$	7.70303	−	5.14700i	0.700276	−	0.467909i
$122$	0.0903166	−	11.7598i	0.00817688	−	1.06468i
$123$	−0.218687	−	0.266471i	−0.0197183	−	0.0240269i
$124$	−3.74970	+	17.4461i	−0.336733	+	1.56671i
$125$	−0.881921	+	0.471397i	−0.0788814	+	0.0421630i
$126$	−1.80963	+	3.32391i	−0.161214	+	0.296118i
$127$	1.29775			0.115157			0.0575784	−	0.998341i	$-0.481662\pi$
$127$	1.29775			0.115157			0.0575784	+	0.998341i	$0.481662\pi$
$128$	10.6344	+	3.86121i	0.939960	+	0.341286i
$129$	−24.9482			−2.19657
$130$	−1.56447	+	2.87362i	−0.137213	+	0.252033i
$131$	−18.6523	+	9.96986i	−1.62966	+	0.871070i	−0.634485	+	0.772935i	$0.718788\pi$
$131$	−18.6523	+	9.96986i	−1.62966	+	0.871070i	−0.995173	+	0.0981354i	$0.968712\pi$
$132$	−19.0947	−	4.10403i	−1.66198	−	0.357210i
$133$	−4.86029	−	5.92228i	−0.421440	−	0.513527i
$134$	0.0205157	−	2.67126i	0.00177228	−	0.230762i
$135$	2.33412	−	1.55961i	0.200889	−	0.134230i
$136$	4.65428	+	9.21195i	0.399101	+	0.789918i
$137$	−5.42039	+	8.11218i	−0.463095	+	0.693070i	−0.987362	−	0.158484i	$-0.949339\pi$
$137$	−5.42039	+	8.11218i	−0.463095	+	0.693070i	0.524267	+	0.851554i	$0.324339\pi$
$138$	5.38348	−	1.02792i	0.458272	−	0.0875028i
$139$	−16.9413	+	5.13909i	−1.43694	+	0.435892i	−0.910213	−	0.414140i	$-0.864082\pi$
$139$	−16.9413	+	5.13909i	−1.43694	+	0.435892i	−0.526731	+	0.850032i	$0.676582\pi$
$140$	0.864518	+	3.01594i	0.0730651	+	0.254893i
$141$	15.4659	+	12.6925i	1.30246	+	1.06890i
$142$	−0.420816	−	4.63746i	−0.0353141	−	0.389167i
$143$	−9.62200	−	3.98556i	−0.804632	−	0.333290i
$144$	3.61503	+	5.78752i	0.301252	+	0.482294i
$145$	4.56729	−	1.89183i	0.379292	−	0.157108i
$146$	−5.17860	−	9.87006i	−0.428584	−	0.816852i
$147$	−0.965168	−	9.79951i	−0.0796057	−	0.808250i
$148$	2.58393	+	5.01811i	0.212398	+	0.412486i
$149$	−0.965242	+	1.80584i	−0.0790757	+	0.147940i	−0.918352	−	0.395766i	$-0.870479\pi$
$149$	−0.965242	+	1.80584i	−0.0790757	+	0.147940i	0.839276	+	0.543706i	$0.182979\pi$
$150$	−0.621604	+	3.00425i	−0.0507538	+	0.245296i
$151$	23.6467	−	4.70362i	1.92434	−	0.382775i	0.924340	−	0.381570i	$-0.124617\pi$
$151$	23.6467	−	4.70362i	1.92434	−	0.382775i	0.999999	−	0.00120459i	$-0.000383433\pi$
$152$	−13.6067	+	2.38207i	−1.10365	+	0.193212i
$153$	−1.21444	+	6.10540i	−0.0981816	+	0.493592i
$154$	−9.25557	+	3.75077i	−0.745835	+	0.302245i
$155$	−0.874534	+	8.87929i	−0.0702443	+	0.713202i
$156$	3.69839	+	9.33159i	0.296109	+	0.747125i
$157$	1.32253	−	4.35979i	0.105549	−	0.347949i	−0.888218	−	0.459422i	$-0.848057\pi$
$157$	1.32253	−	4.35979i	0.105549	−	0.347949i	0.993768	+	0.111472i	$0.0355567\pi$
$158$	−4.83881	+	3.90931i	−0.384955	+	0.311008i
$159$	7.28992	+	7.28992i	0.578128	+	0.578128i
$160$	5.50170	+	1.31578i	0.434948	+	0.104022i
$161$	1.98164	−	1.98164i	0.156175	−	0.156175i
$162$	1.67466	−	15.7612i	0.131574	−	1.23832i
$163$	0.797149	+	0.241812i	0.0624375	+	0.0189402i	0.321349	−	0.946961i	$-0.395864\pi$
$163$	0.797149	+	0.241812i	0.0624375	+	0.0189402i	−0.258911	+	0.965901i	$0.583364\pi$
$164$	−0.228153	+	0.221249i	−0.0178157	+	0.0172767i
$165$	−9.71837	−	0.957176i	−0.756574	−	0.0745160i
$166$	−5.35110	−	2.26480i	−0.415326	−	0.175782i
$167$	−1.96479	−	0.390822i	−0.152040	−	0.0302427i	0.118483	−	0.992956i	$-0.462197\pi$
$167$	−1.96479	−	0.390822i	−0.152040	−	0.0302427i	−0.270524	+	0.962713i	$0.587197\pi$
$168$	8.80527	+	3.88728i	0.679342	+	0.299910i
$169$	−1.49193	−	7.50043i	−0.114764	−	0.576956i
$170$	2.83397	+	4.31268i	0.217356	+	0.330767i
$171$	−7.34781	−	3.92749i	−0.561901	−	0.300342i
$172$	1.90264	+	22.9221i	0.145075	+	1.74780i
$173$	23.5170	−	2.31622i	1.78797	−	0.176099i	0.850917	−	0.525299i	$-0.176047\pi$
$173$	23.5170	−	2.31622i	1.78797	−	0.176099i	0.937048	+	0.349200i	$0.113547\pi$
$174$	4.51389	−	14.4791i	0.342197	−	1.09765i
$175$	0.600315	+	1.44929i	0.0453796	+	0.109556i
$176$	−2.31451	+	17.8570i	−0.174462	+	1.34602i
$177$	−12.0284	+	29.0392i	−0.904111	+	2.18272i
$178$	−5.62951	−	4.69283i	−0.421949	−	0.351743i
$179$	9.43723	−	11.4993i	0.705372	−	0.859498i	−0.289857	−	0.957070i	$-0.593608\pi$
$179$	9.43723	−	11.4993i	0.705372	−	0.859498i	0.995228	+	0.0975723i	$0.0311077\pi$
$180$	2.12371	+	2.67036i	0.158292	+	0.199037i
$181$	−2.40635	−	7.93268i	−0.178863	−	0.589632i	−0.999826	−	0.0186506i	$-0.994063\pi$
$181$	−2.40635	−	7.93268i	−0.178863	−	0.589632i	0.820963	−	0.570981i	$-0.193437\pi$
$182$	4.24559	+	2.88422i	0.314704	+	0.213792i
$183$	−14.9991	−	10.0221i	−1.10877	−	0.740855i
$184$	−1.35501	−	4.86789i	−0.0998927	−	0.358865i
$185$	1.56790	+	2.34653i	0.115274	+	0.172520i
$186$	19.2060	+	19.5033i	1.40825	+	1.43005i
$187$	−12.6978	+	10.4208i	−0.928553	+	0.762043i
$188$	10.4822	−	15.1778i	0.764496	−	1.10696i
$189$	−2.07588	−	3.88371i	−0.150998	−	0.282498i
$190$	−6.62462	+	1.95413i	−0.480601	+	0.141767i
$191$		−	13.0219i		−	0.942234i	−0.882071	−	0.471117i	$-0.843851\pi$
$191$		−	13.0219i		−	0.942234i	0.882071	−	0.471117i	$-0.156149\pi$
$192$	13.9081	−	10.3800i	1.00373	−	0.749110i
$193$			4.50730i			0.324442i	0.986754	+	0.162221i	$0.0518658\pi$
$193$			4.50730i			0.324442i	−0.986754	+	0.162221i	$0.948134\pi$
$194$	−0.798022	−	2.70535i	−0.0572947	−	0.194233i
$195$	2.36588	+	4.42626i	0.169425	+	0.316971i
$196$	−8.93008	+	1.63413i	−0.637863	+	0.116724i
$197$	3.78646	−	3.10746i	0.269774	−	0.221398i	−0.489774	−	0.871850i	$-0.662921\pi$
$197$	3.78646	−	3.10746i	0.269774	−	0.221398i	0.759547	+	0.650452i	$0.225421\pi$
$198$	−7.73821	+	7.62026i	−0.549931	+	0.541548i
$199$	−10.9821	−	16.4359i	−0.778499	−	1.16511i	−0.982523	−	0.186141i	$-0.940402\pi$
$199$	−10.9821	−	16.4359i	−0.778499	−	1.16511i	0.204024	−	0.978966i	$-0.434598\pi$
$200$	2.80767	+	0.342008i	0.198532	+	0.0241836i
$201$	−3.40709	−	2.27655i	−0.240318	−	0.160575i
$202$	2.15285	−	3.16902i	0.151474	−	0.222971i
$203$	−2.25116	−	7.42109i	−0.158001	−	0.520858i
$204$	15.7298	+	1.79359i	1.10131	+	0.125577i
$205$	−0.100809	+	0.122836i	−0.00704081	+	0.00857926i
$206$	16.0158	−	19.2125i	1.11587	−	1.33860i
$207$	1.16629	−	2.81566i	0.0810624	−	0.195702i
$208$	8.29171	−	4.10971i	0.574926	−	0.284957i
$209$	−8.41336	−	20.3117i	−0.581965	−	1.40499i
$210$	4.59449	+	1.43235i	0.317050	+	0.0988413i
$211$	−15.2620	+	1.50318i	−1.05068	+	0.103483i	−0.608589	−	0.793486i	$-0.708264\pi$
$211$	−15.2620	+	1.50318i	−1.05068	+	0.103483i	−0.442094	+	0.896969i	$0.645764\pi$
$212$	6.14194	−	7.25385i	0.421830	−	0.498197i
$213$	−6.29940	−	3.36710i	−0.431628	−	0.230710i
$214$	−9.32229	+	6.12592i	−0.637259	+	0.418759i
$215$	2.24363	+	11.2795i	0.153014	+	0.769256i
$216$	−7.93792	−	0.182922i	−0.540107	−	0.0124462i
$217$	13.7274	+	2.73055i	0.931877	+	0.185362i
$218$	−5.72423	+	13.5248i	−0.387694	+	0.916014i
$219$	−17.0151	−	1.67585i	−1.14978	−	0.113243i
$220$	−0.138283	+	9.00213i	−0.00932306	+	0.606923i
$221$	8.07875	+	2.45066i	0.543435	+	0.164849i
$222$	8.60955	+	0.914782i	0.577835	+	0.0613961i
$223$	14.8932	−	14.8932i	0.997323	−	0.997323i	−0.00267373	−	0.999996i	$-0.500851\pi$
$223$	14.8932	−	14.8932i	0.997323	−	0.997323i	0.999996	+	0.00267373i	$0.000851077\pi$
$224$	2.90006	−	8.38665i	0.193769	−	0.560356i
$225$	1.20628	+	1.20628i	0.0804189	+	0.0804189i
$226$	1.90559	+	2.35868i	0.126758	+	0.156897i
$227$	−6.06370	+	19.9893i	−0.402462	+	1.32674i	0.488461	+	0.872586i	$0.337558\pi$
$227$	−6.06370	+	19.9893i	−0.402462	+	1.32674i	−0.890923	+	0.454154i	$0.849942\pi$
$228$	−8.40852	+	19.4495i	−0.556868	+	1.28808i
$229$	−1.42996	+	14.5186i	−0.0944943	+	0.959417i	0.824689	+	0.565586i	$0.191350\pi$
$229$	−1.42996	+	14.5186i	−0.0944943	+	0.959417i	−0.919183	+	0.393830i	$0.871150\pi$
$230$	−0.948887	−	2.34152i	−0.0625678	−	0.154395i
$231$	−2.98858	+	15.0246i	−0.196634	+	0.988547i
$232$	−13.6474	−	3.04309i	−0.895998	−	0.199788i
$233$	−9.79508	+	1.94836i	−0.641697	+	0.127641i	−0.505205	−	0.863000i	$-0.668583\pi$
$233$	−9.79508	+	1.94836i	−0.641697	+	0.127641i	−0.136492	+	0.990641i	$0.543583\pi$
$234$	5.46588	+	1.13094i	0.357316	+	0.0739317i
$235$	4.34762	−	8.13383i	0.283608	−	0.530592i
$236$	27.5982	+	8.83694i	1.79649	+	0.575235i
$237$	0.935293	+	9.49619i	0.0607538	+	0.616844i
$238$	7.16847	−	3.76113i	0.464663	−	0.243798i
$239$	5.48316	−	2.27120i	0.354676	−	0.146912i	−0.198229	−	0.980156i	$-0.563519\pi$
$239$	5.48316	−	2.27120i	0.354676	−	0.146912i	0.552906	+	0.833244i	$0.313519\pi$
$240$	6.32132	−	5.94440i	0.408040	−	0.383710i
$241$	−0.104422	−	0.0432531i	−0.00672643	−	0.00278618i	0.379318	−	0.925266i	$-0.376159\pi$
$241$	−0.104422	−	0.0432531i	−0.00672643	−	0.00278618i	−0.386044	+	0.922480i	$0.626159\pi$
$242$	−13.0482	+	1.18403i	−0.838768	+	0.0761120i
$243$	−12.2840	−	10.0812i	−0.788021	−	0.646712i
$244$	−8.06430	+	14.5454i	−0.516264	+	0.931171i
$245$	−4.34373	+	1.31765i	−0.277510	+	0.0841819i
$246$	0.0914327	+	0.478854i	0.00582954	+	0.0305306i
$247$	−6.27749	+	9.39493i	−0.399427	+	0.597785i
$248$	16.4547	−	19.1337i	1.04487	−	1.21499i
$249$	−7.41103	+	4.95189i	−0.469655	+	0.313813i
$250$	1.41417	+	0.0108610i	0.0894401	+	0.000686912i
$251$	−19.4234	−	23.6675i	−1.22600	−	1.49388i	−0.812060	−	0.583574i	$-0.801654\pi$
$251$	−19.4234	−	23.6675i	−1.22600	−	1.49388i	−0.413935	−	0.910306i	$-0.635846\pi$
$252$	4.49536	−	2.90483i	0.283181	−	0.182987i
$253$	7.09246	−	3.79100i	0.445899	−	0.238338i
$254$	−1.61190	−	0.877558i	−0.101139	−	0.0550629i
$255$	7.91587			0.495711
$256$	−10.5977	−	11.9870i	−0.662355	−	0.749190i
$257$	−16.5671			−1.03342			−0.516712	−	0.856159i	$-0.672844\pi$
$257$	−16.5671			−1.03342			−0.516712	+	0.856159i	$0.672844\pi$
$258$	30.9874	+	16.8703i	1.92919	+	1.05030i
$259$	3.90436	−	2.08692i	0.242605	−	0.129675i
$260$	3.88637	−	2.51131i	0.241022	−	0.155745i
$261$	−5.35015	−	6.51917i	−0.331166	−	0.403527i
$262$	29.9092	+	0.229707i	1.84780	+	0.0141913i
$263$	13.7000	−	9.15402i	0.844776	−	0.564461i	−0.0561559	−	0.998422i	$-0.517884\pi$
$263$	13.7000	−	9.15402i	0.844776	−	0.564461i	0.900932	+	0.433961i	$0.142884\pi$
$264$	20.9417	+	18.0096i	1.28888	+	1.10842i
$265$	2.64030	−	3.95149i	0.162192	−	0.242738i
$266$	2.03208	+	10.6425i	0.124595	+	0.652532i
$267$	−10.7581	+	3.26344i	−0.658387	+	0.199720i
$268$	−1.83183	+	3.30402i	−0.111897	+	0.201825i
$269$	−23.8095	−	19.5399i	−1.45169	−	1.19137i	−0.944051	−	0.329800i	$-0.893019\pi$
$269$	−23.8095	−	19.5399i	−1.45169	−	1.19137i	−0.507638	−	0.861571i	$-0.669481\pi$
$270$	−3.95377	+	0.358775i	−0.240619	+	0.0218344i
$271$	−2.83441	−	1.17405i	−0.172178	−	0.0713186i	0.294929	−	0.955519i	$-0.404704\pi$
$271$	−2.83441	−	1.17405i	−0.172178	−	0.0713186i	−0.467108	+	0.884201i	$0.654704\pi$
$272$	0.448319	−	14.5892i	0.0271834	−	0.884598i
$273$	7.27381	−	3.01291i	0.440231	−	0.182350i
$274$	12.2181	−	6.41054i	0.738120	−	0.387275i
$275$	0.441233	+	4.47992i	0.0266074	+	0.270149i
$276$	−7.38175	−	2.36364i	−0.444329	−	0.142274i
$277$	9.10087	−	17.0265i	0.546818	−	1.02303i	−0.445020	−	0.895521i	$-0.646803\pi$
$277$	9.10087	−	17.0265i	0.546818	−	1.02303i	0.991838	−	0.127504i	$-0.0406967\pi$
$278$	24.5174	+	5.07286i	1.47046	+	0.304250i
$279$	14.9284	−	2.96944i	0.893740	−	0.177776i
$280$	0.965631	−	4.33060i	0.0577075	−	0.258803i
$281$	2.20749	−	11.0978i	0.131688	−	0.662039i	−0.857393	−	0.514663i	$-0.827917\pi$
$281$	2.20749	−	11.0978i	0.131688	−	0.662039i	0.989081	−	0.147376i	$-0.0470828\pi$
$282$	−10.6268	−	26.2232i	−0.632816	−	1.56157i
$283$	−0.853690	+	8.66766i	−0.0507466	+	0.515239i	0.935889	+	0.352296i	$0.114599\pi$
$283$	−0.853690	+	8.66766i	−0.0507466	+	0.515239i	−0.986635	+	0.162944i	$0.947901\pi$
$284$	−2.61324	+	6.04461i	−0.155067	+	0.358682i
$285$	−3.07547	+	10.1385i	−0.182175	+	0.600550i
$286$	9.25609	+	11.4569i	0.547324	+	0.677459i
$287$	0.176265	+	0.176265i	0.0104046	+	0.0104046i
$288$	−0.576500	−	9.63303i	−0.0339706	−	0.567632i
$289$	−2.60548	+	2.60548i	−0.153263	+	0.153263i
$290$	−6.95217	−	0.738681i	−0.408245	−	0.0433768i
$291$	−4.14032	−	1.25595i	−0.242710	−	0.0736253i
$292$	−0.242110	+	15.7611i	−0.0141684	+	0.922350i
$293$	11.5404	+	1.13663i	0.674199	+	0.0664028i	0.429322	−	0.903151i	$-0.358753\pi$
$293$	11.5404	+	1.13663i	0.674199	+	0.0664028i	0.244877	+	0.969554i	$0.421253\pi$
$294$	−5.42777	+	12.8243i	−0.316554	+	0.747930i
$295$	14.2108	+	2.82671i	0.827386	+	0.164577i
$296$	0.183894	−	7.98013i	0.0106886	−	0.463835i
$297$	−2.46535	−	12.3942i	−0.143054	−	0.719182i
$298$	2.42003	−	1.59027i	0.140189	−	0.0921217i
$299$	−3.64514	−	1.94837i	−0.210804	−	0.112677i
$300$	2.80359	−	3.31114i	0.161865	−	0.191169i
$301$	17.9539	−	1.76831i	1.03485	−	0.101924i
$302$	−32.5514	−	10.1480i	−1.87312	−	0.583953i
$303$	−2.24892	−	5.42936i	−0.129197	−	0.311909i
$304$	18.5113	+	6.24237i	1.06169	+	0.358024i
$305$	−3.18226	+	7.68266i	−0.182216	+	0.439908i
$306$	5.63697	−	6.76210i	0.322244	−	0.386563i
$307$	4.40752	−	5.37058i	0.251550	−	0.306515i	−0.631891	−	0.775058i	$-0.717721\pi$
$307$	4.40752	−	5.37058i	0.251550	−	0.306515i	0.883441	+	0.468543i	$0.155221\pi$
$308$	14.0324	+	1.60004i	0.799569	+	0.0911709i
$309$	−11.1376	−	36.7156i	−0.633594	−	2.08868i
$310$	7.09054	−	10.4373i	0.402716	−	0.592800i
$311$	2.84754	+	1.90267i	0.161469	+	0.107890i	0.633680	−	0.773596i	$-0.281544\pi$
$311$	2.84754	+	1.90267i	0.161469	+	0.107890i	−0.472210	+	0.881486i	$0.656544\pi$
$312$	1.71650	−	14.0914i	0.0971776	−	0.797767i
$313$	−0.0679200	−	0.101649i	−0.00383907	−	0.00574557i	0.829545	−	0.558440i	$-0.188600\pi$
$313$	−0.0679200	−	0.101649i	−0.00383907	−	0.00574557i	−0.833384	+	0.552694i	$0.813600\pi$
$314$	−4.59083	+	4.52085i	−0.259075	+	0.255126i
$315$	2.06866	−	1.69771i	0.116556	−	0.0956550i
$316$	8.65367	−	1.58355i	0.486807	−	0.0890818i
$317$	12.3075	+	23.0257i	0.691259	+	1.29325i	0.945345	+	0.326072i	$0.105725\pi$
$317$	12.3075	+	23.0257i	0.691259	+	1.29325i	−0.254086	+	0.967182i	$0.581775\pi$
$318$	−4.12503	−	13.9841i	−0.231320	−	0.784191i
$319$		−	22.2541i		−	1.24599i
$320$	−5.94374	−	5.35462i	−0.332265	−	0.299332i
$321$			17.1110i			0.955041i
$322$	−3.80135	+	1.12132i	−0.211841	+	0.0624888i
$323$	8.40090	+	15.7170i	0.467438	+	0.874516i
$324$	−12.7380	+	18.4441i	−0.707666	+	1.02467i
$325$	1.78842	−	1.46772i	0.0992036	−	0.0814143i
$326$	−0.826596	−	0.839391i	−0.0457809	−	0.0464896i
$327$	12.5158	+	18.7312i	0.692126	+	1.03584i
$328$	0.432993	−	0.120527i	0.0239080	−	0.00665497i
$329$	−12.0296	−	8.03793i	−0.663214	−	0.443145i
$330$	11.4236	+	7.76058i	0.628850	+	0.427206i
$331$	−7.76282	−	25.5906i	−0.426683	−	1.40659i	−0.862274	−	0.506441i	$-0.830961\pi$
$331$	−7.76282	−	25.5906i	−0.426683	−	1.40659i	0.435591	−	0.900145i	$-0.356539\pi$
$332$	5.11494	+	6.43152i	0.280719	+	0.352976i
$333$	3.05424	−	3.72160i	0.167371	−	0.203943i
$334$	2.17613	+	1.81405i	0.119073	+	0.0992604i
$335$	−0.722859	+	1.74514i	−0.0394940	+	0.0953470i
$336$	−8.30812	−	10.7825i	−0.453245	−	0.588235i
$337$	7.93187	+	19.1492i	0.432077	+	1.04313i	0.978617	+	0.205692i	$0.0659446\pi$
$337$	7.93187	+	19.1492i	0.432077	+	1.04313i	−0.546540	+	0.837433i	$0.684055\pi$
$338$	−3.21882	+	10.3249i	−0.175081	+	0.561601i
$339$	4.62892	−	0.455909i	0.251409	−	0.0247616i
$340$	−0.603694	−	7.27302i	−0.0327399	−	0.394435i
$341$	35.4218	+	18.9334i	1.91820	+	1.02530i
$342$	6.47066	+	9.84690i	0.349893	+	0.532459i
$343$	3.53143	+	17.7537i	0.190679	+	0.958609i
$344$	13.1371	−	29.7574i	0.708303	−	1.60441i
$345$	−3.80100	−	0.756066i	−0.204639	−	0.0407052i
$346$	−30.7760	−	13.0256i	−1.65453	−	0.700263i
$347$	2.61693	+	0.257746i	0.140484	+	0.0138365i	0.168015	−	0.985784i	$-0.446264\pi$
$347$	2.61693	+	0.257746i	0.140484	+	0.0138365i	−0.0275305	+	0.999621i	$0.508764\pi$
$348$	−15.3975	+	14.9316i	−0.825393	+	0.800419i
$349$	−2.62035	−	0.794875i	−0.140264	−	0.0425487i	0.219372	−	0.975641i	$-0.429599\pi$
$349$	−2.62035	−	0.794875i	−0.140264	−	0.0425487i	−0.359636	+	0.933093i	$0.617099\pi$
$350$	0.234398	−	2.20606i	0.0125291	−	0.117919i
$351$	−4.59246	+	4.59246i	−0.245127	+	0.245127i
$352$	14.9499	−	20.6145i	0.796835	−	1.09876i
$353$	−15.2778	−	15.2778i	−0.813155	−	0.813155i	0.171951	−	0.985106i	$-0.444993\pi$
$353$	−15.2778	−	15.2778i	−0.813155	−	0.813155i	−0.985106	+	0.171951i	$0.944993\pi$
$354$	34.5768	−	27.9348i	1.83774	−	1.48472i
$355$	−0.955808	+	3.15088i	−0.0507290	+	0.167231i
$356$	3.81887	+	9.63557i	0.202400	+	0.510684i
$357$	1.21714	−	12.3578i	0.0644179	−	0.654046i
$358$	−19.4977	+	7.90132i	−1.03048	+	0.417598i
$359$	−0.966246	+	4.85764i	−0.0509965	+	0.256377i	−0.997870	−	0.0652285i	$-0.979222\pi$
$359$	−0.966246	+	4.85764i	−0.0509965	+	0.256377i	0.946874	+	0.321605i	$0.104222\pi$
$360$	−0.832062	−	4.75285i	−0.0438535	−	0.250497i
$361$	−4.75890	+	0.946604i	−0.250469	+	0.0498213i
$362$	−2.37534	+	11.4801i	−0.124845	+	0.603383i
$363$	−9.47382	+	17.7243i	−0.497247	+	0.930283i
$364$	−3.32296	−	6.45332i	−0.174170	−	0.338246i
$365$	0.772522	+	7.84354i	0.0404356	+	0.410550i
$366$	11.8529	+	22.5908i	0.619559	+	1.18084i
$367$	−20.2364	+	8.38219i	−1.05633	+	0.437547i	−0.842148	−	0.539247i	$-0.818709\pi$
$367$	−20.2364	+	8.38219i	−1.05633	+	0.437547i	−0.214183	+	0.976793i	$0.568709\pi$
$368$	−1.60872	+	6.96253i	−0.0838604	+	0.362947i
$369$	0.250450	+	0.103740i	0.0130379	+	0.00540048i
$370$	−0.360683	−	3.97479i	−0.0187510	−	0.206640i
$371$	−5.76288	−	4.72947i	−0.299194	−	0.245542i
$372$	−10.6668	−	37.2118i	−0.553045	−	1.92934i
$373$	4.59353	−	1.39343i	0.237844	−	0.0721492i	−0.169112	−	0.985597i	$-0.554090\pi$
$373$	4.59353	−	1.39343i	0.237844	−	0.0721492i	0.406956	+	0.913448i	$0.366590\pi$
$374$	22.8182	−	4.35692i	1.17990	−	0.225291i
$375$	1.20521	−	1.80372i	0.0622367	−	0.0931438i
$376$	−23.2831	+	11.7637i	−1.20074	+	0.606664i
$377$	−9.50983	+	6.35427i	−0.489781	+	0.327261i
$378$	−0.0478286	+	6.22757i	−0.00246004	+	0.320312i
$379$	9.65892	+	11.7694i	0.496145	+	0.604555i	0.959531	−	0.281602i	$-0.0908657\pi$
$379$	9.65892	+	11.7694i	0.496145	+	0.604555i	−0.463386	+	0.886157i	$0.653366\pi$
$380$	9.54965	+	2.05251i	0.489887	+	0.105291i
$381$	−2.48282	+	1.32709i	−0.127198	+	0.0679890i
$382$	−8.80562	+	16.1741i	−0.450535	+	0.827541i
$383$	−16.9772			−0.867492			−0.433746	−	0.901035i	$-0.642809\pi$
$383$	−16.9772			−0.867492			−0.433746	+	0.901035i	$0.642809\pi$
$384$	−24.2940	+	3.48774i	−1.23975	+	0.177983i
$385$	7.06165			0.359895
$386$	3.04790	−	5.59837i	0.155134	−	0.284950i
$387$	17.3026	−	9.24841i	0.879538	−	0.470123i
$388$	−0.838199	+	3.89986i	−0.0425531	+	0.197986i
$389$	11.6247	+	14.1647i	0.589394	+	0.718179i	0.979241	−	0.202701i	$-0.0649720\pi$
$389$	11.6247	+	14.1647i	0.589394	+	0.718179i	−0.389847	+	0.920880i	$0.627472\pi$
$390$	0.0545102	−	7.09756i	0.00276023	−	0.359399i
$391$	−5.42029	+	3.62172i	−0.274116	+	0.183158i
$392$	12.1968	+	4.00894i	0.616031	+	0.202482i
$393$	25.4897	−	38.1480i	1.28579	−	1.92431i
$394$	−6.80435	+	1.29923i	−0.342798	+	0.0654541i
$395$	4.20928	−	1.27687i	0.211792	−	0.0642463i
$396$	14.7643	−	4.23219i	0.741935	−	0.212676i
$397$	0.116147	+	0.0953197i	0.00582927	+	0.00478396i	0.637303	−	0.770613i	$-0.280050\pi$
$397$	0.116147	+	0.0953197i	0.00582927	+	0.00478396i	−0.631474	+	0.775397i	$0.717550\pi$
$398$	2.52634	+	27.8407i	0.126634	+	1.39553i
$399$	15.3547	+	6.36014i	0.768698	+	0.318405i
$400$	−3.25605	−	2.32339i	−0.162803	−	0.116169i
$401$	−28.5452	+	11.8238i	−1.42548	+	0.590453i	−0.956231	−	0.292613i	$-0.905475\pi$
$401$	−28.5452	+	11.8238i	−1.42548	+	0.590453i	−0.469249	+	0.883066i	$0.655475\pi$
$402$	2.69241	+	5.13155i	0.134285	+	0.255939i
$403$	−2.02330	−	20.5429i	−0.100788	−	1.02332i
$404$	−4.81693	+	2.48034i	−0.239651	+	0.123402i
$405$	−5.28322	+	9.88421i	−0.262525	+	0.491150i
$406$	−2.22215	+	10.7398i	−0.110283	+	0.533006i
$407$	12.4601	−	2.47846i	0.617623	−	0.122853i
$408$	−18.3247	−	12.8645i	−0.907206	−	0.636888i
$409$	−4.63893	+	23.3215i	−0.229380	+	1.15317i	0.678713	+	0.734404i	$0.262538\pi$
$409$	−4.63893	+	23.3215i	−0.229380	+	1.15317i	−0.908093	+	0.418768i	$0.862462\pi$
$410$	0.208275	−	0.0844024i	0.0102860	−	0.00416834i
$411$	2.07452	−	21.0629i	0.102328	−	1.03896i
$412$	−32.8845	+	13.0331i	−1.62010	+	0.642097i
$413$	6.59795	−	21.7505i	0.324664	−	1.07027i
$414$	−3.35260	+	2.70859i	−0.164771	+	0.133120i
$415$	2.90532	+	2.90532i	0.142617	+	0.142617i
$416$	−13.0779	−	0.502438i	−0.641197	−	0.0246340i
$417$	27.1563	−	27.1563i	1.32985	−	1.32985i
$418$	−3.28507	+	30.9177i	−0.160678	+	1.51223i
$419$	10.1242	+	3.07115i	0.494601	+	0.150035i	0.527724	−	0.849416i	$-0.323045\pi$
$419$	10.1242	+	3.07115i	0.494601	+	0.150035i	−0.0331236	+	0.999451i	$0.510545\pi$
$420$	−4.73810	−	4.88593i	−0.231195	−	0.238409i
$421$	−36.7104	−	3.61566i	−1.78916	−	0.176216i	−0.851632	−	0.524139i	$-0.824387\pi$
$421$	−36.7104	−	3.61566i	−1.78916	−	0.176216i	−0.937523	+	0.347923i	$0.886887\pi$
$422$	19.9730	+	8.45337i	0.972270	+	0.411503i
$423$	−15.4313	−	3.06948i	−0.750297	−	0.149243i
$424$	−12.5339	+	4.85651i	−0.608699	+	0.235853i
$425$	−0.711887	−	3.57890i	−0.0345316	−	0.173602i
$426$	5.54741	+	8.44192i	0.268773	+	0.409012i
$427$	11.5045	+	6.14926i	0.556740	+	0.297584i
$428$	15.7214	−	1.30495i	0.759921	−	0.0630769i
$429$	22.4842	−	2.21450i	1.08555	−	0.106917i
$430$	4.84062	−	15.5271i	0.233435	−	0.748783i
$431$	6.87646	+	16.6012i	0.331227	+	0.799654i	0.998495	+	0.0548360i	$0.0174636\pi$
$431$	6.87646	+	16.6012i	0.331227	+	0.799654i	−0.667268	+	0.744818i	$0.732536\pi$
$432$	9.73574	+	5.59494i	0.468411	+	0.269186i
$433$	6.74007	−	16.2720i	0.323907	−	0.781981i	−0.675113	−	0.737715i	$-0.735905\pi$
$433$	6.74007	−	16.2720i	0.323907	−	0.781981i	0.999020	−	0.0442661i	$-0.0140949\pi$
$434$	−15.2039	−	12.6742i	−0.729812	−	0.608381i
$435$	−6.80338	+	8.28994i	−0.326197	+	0.397472i
$436$	16.2556	−	12.9279i	0.778500	−	0.619134i
$437$	−2.53273	−	8.34928i	−0.121157	−	0.399400i
$438$	20.0007	+	13.5874i	0.955672	+	0.649231i
$439$	24.5070	+	16.3751i	1.16966	+	0.781539i	0.979742	−	0.200262i	$-0.0641793\pi$
$439$	24.5070	+	16.3751i	1.16966	+	0.781539i	0.189913	+	0.981801i	$0.439179\pi$
$440$	6.25913	−	11.0877i	0.298392	−	0.528588i
$441$	4.30210	+	6.43855i	0.204862	+	0.306598i
$442$	−8.37718	−	8.50685i	−0.398462	−	0.404630i
$443$	−19.8243	+	16.2694i	−0.941883	+	0.772983i	−0.974011	−	0.226500i	$-0.927272\pi$
$443$	−19.8243	+	16.2694i	−0.941883	+	0.772983i	0.0321281	+	0.999484i	$0.489772\pi$
$444$	−10.0751	−	6.95813i	−0.478142	−	0.330218i
$445$	2.44295	+	4.57045i	0.115807	+	0.216660i
$446$	−28.5694	+	8.42738i	−1.35280	+	0.399048i
$447$		−	4.44194i		−	0.210097i
$448$	−9.27325	+	8.45572i	−0.438120	+	0.399495i
$449$			29.7939i			1.40606i	0.711159	+	0.703031i	$0.248170\pi$
$449$			29.7939i			1.40606i	−0.711159	+	0.703031i	$0.751830\pi$
$450$	−0.682580	−	2.31399i	−0.0321771	−	0.109083i
$451$	0.337205	+	0.630866i	0.0158784	+	0.0297063i
$452$	−0.771903	−	4.21823i	−0.0363073	−	0.198409i
$453$	−40.4301	+	33.1801i	−1.89957	+	1.55894i
$454$	21.0486	−	20.7278i	0.987861	−	0.972803i
$455$	−2.01633	−	3.01766i	−0.0945272	−	0.141470i
$456$	23.5960	−	18.4717i	1.10498	−	0.865015i
$457$	−10.9367	−	7.30769i	−0.511598	−	0.341839i	0.272826	−	0.962063i	$-0.412042\pi$
$457$	−10.9367	−	7.30769i	−0.511598	−	0.341839i	−0.784425	+	0.620224i	$0.787042\pi$
$458$	11.5938	−	17.0661i	0.541743	−	0.797449i
$459$	2.97356	+	9.80251i	0.138794	+	0.457542i
$460$	−0.404787	+	3.54998i	−0.0188733	+	0.165519i
$461$	4.25517	−	5.18495i	0.198183	−	0.241487i	−0.664431	−	0.747350i	$-0.731326\pi$
$461$	4.25517	−	5.18495i	0.198183	−	0.241487i	0.862614	+	0.505863i	$0.168826\pi$
$462$	13.8719	−	16.6407i	0.645379	−	0.774195i
$463$	6.42029	−	15.4999i	0.298376	−	0.720343i	−0.701594	−	0.712577i	$-0.747528\pi$
$463$	6.42029	−	15.4999i	0.298376	−	0.720343i	0.999970	−	0.00776626i	$-0.00247210\pi$
$464$	14.8933	+	13.0083i	0.691403	+	0.603896i
$465$	−7.40692	−	17.8819i	−0.343488	−	0.829253i
$466$	13.4837	+	4.20358i	0.624619	+	0.194727i
$467$	−0.242730	+	0.0239069i	−0.0112322	+	0.00110628i	−0.103632	−	0.994616i	$-0.533046\pi$
$467$	−0.242730	+	0.0239069i	−0.0112322	+	0.00110628i	0.0923995	+	0.995722i	$0.470546\pi$
$468$	−6.02424	−	5.10081i	−0.278471	−	0.235785i
$469$	2.61327	+	1.39682i	0.120669	+	0.0644992i
$470$	−10.9003	+	7.16285i	−0.502791	+	0.330397i
$471$	1.92815	+	9.69345i	0.0888443	+	0.446651i
$472$	−28.3032	−	29.6384i	−1.30276	−	1.36422i
$473$	50.7757	+	10.0999i	2.33467	+	0.464395i
$474$	5.25977	−	12.4274i	0.241589	−	0.570809i
$475$	4.86035	+	0.478702i	0.223008	+	0.0219644i
$476$	−11.4471	−	0.175840i	−0.524675	−	0.00805963i
$477$	−7.75825	−	2.35344i	−0.355226	−	0.107757i
$478$	−8.34628	−	0.886809i	−0.381750	−	0.0405617i
$479$	11.6793	−	11.6793i	0.533643	−	0.533643i	−0.388012	−	0.921655i	$-0.626838\pi$
$479$	11.6793	−	11.6793i	0.533643	−	0.533643i	0.921655	+	0.388012i	$0.126838\pi$
$480$	−11.8712	+	3.10878i	−0.541844	+	0.141896i
$481$	−4.61688	−	4.61688i	−0.210512	−	0.210512i
$482$	0.100451	+	0.124335i	0.00457543	+	0.00566331i
$483$	−1.76477	+	5.81767i	−0.0802998	+	0.264713i
$484$	17.0074	+	7.35272i	0.773063	+	0.334215i
$485$	−0.195492	+	1.98486i	−0.00887681	+	0.0901278i
$486$	8.44052	+	20.8282i	0.382870	+	0.944788i
$487$	−0.691953	+	3.47868i	−0.0313554	+	0.157634i	−0.993291	−	0.115642i	$-0.963107\pi$
$487$	−0.691953	+	3.47868i	−0.0313554	+	0.157634i	0.961936	+	0.273276i	$0.0881074\pi$
$488$	19.8522	−	12.6131i	0.898667	−	0.570970i
$489$	−1.77236	+	0.352544i	−0.0801489	+	0.0159426i
$490$	6.28622	+	1.30067i	0.283983	+	0.0587584i
$491$	−5.03702	+	9.42361i	−0.227318	+	0.425281i	−0.969561	−	0.244849i	$-0.921262\pi$
$491$	−5.03702	+	9.42361i	−0.227318	+	0.425281i	0.742244	+	0.670130i	$0.233762\pi$
$492$	0.210243	−	0.656598i	0.00947847	−	0.0296017i
$493$	1.76815	+	17.9524i	0.0796337	+	0.808534i
$494$	14.1501	−	7.42422i	0.636642	−	0.334031i
$495$	7.09490	−	2.93880i	0.318892	−	0.132089i
$496$	−33.3763	+	12.6384i	−1.49864	+	0.567481i
$497$	4.77201	+	1.97663i	0.214054	+	0.0886641i
$498$	12.5535	−	1.13914i	0.562538	−	0.0510462i
$499$	33.1671	+	27.2196i	1.48476	+	1.21851i	0.919188	+	0.393818i	$0.128846\pi$
$499$	33.1671	+	27.2196i	1.48476	+	1.21851i	0.565576	+	0.824696i	$0.308654\pi$
$500$	−1.74915	−	0.969774i	−0.0782245	−	0.0433696i
$501$	4.15864	−	1.26151i	0.185794	−	0.0563601i
$502$	8.12090	+	42.5311i	0.362454	+	1.89825i
$503$	18.1599	−	27.1783i	0.809711	−	1.21182i	−0.164544	−	0.986370i	$-0.552615\pi$
$503$	18.1599	−	27.1783i	0.809711	−	1.21182i	0.974255	−	0.225449i	$-0.0723849\pi$
$504$	−7.54783	+	0.568175i	−0.336207	+	0.0253085i
$505$	−2.25246	+	1.50504i	−0.100233	+	0.0669736i
$506$	−11.3729	−	0.0873450i	−0.505585	−	0.00388296i
$507$	10.5243	+	12.8239i	0.467401	+	0.569530i
$508$	1.40867	+	2.17997i	0.0624995	+	0.0967207i
$509$	−38.1214	+	20.3763i	−1.68970	+	0.903165i	−0.709618	+	0.704587i	$0.751132\pi$
$509$	−38.1214	+	20.3763i	−1.68970	+	0.903165i	−0.980085	+	0.198578i	$0.936368\pi$
$510$	−9.83205	−	5.35283i	−0.435371	−	0.237027i
$511$	12.3637			0.546938
$512$	5.05724	+	22.0550i	0.223501	+	0.974704i
$513$	−13.7101			−0.605315
$514$	20.5774	+	11.2029i	0.907631	+	0.494138i
$515$	−15.5981	+	8.33738i	−0.687336	+	0.367389i
$516$	−27.0805	−	41.9082i	−1.19215	−	1.84491i
$517$	−26.3385	−	32.0935i	−1.15836	−	1.41147i
$518$	−6.26069	−	0.0480829i	−0.275079	−	0.00211264i
$519$	−42.6234	+	28.4801i	−1.87096	+	1.25014i
$520$	−6.52532	+	0.491203i	−0.286154	+	0.0215407i
$521$	15.0670	−	22.5494i	0.660098	−	0.987906i	−0.338795	−	0.940860i	$-0.610019\pi$
$521$	15.0670	−	22.5494i	0.660098	−	0.987906i	0.998893	−	0.0470460i	$-0.0149807\pi$
$522$	2.23689	+	11.7151i	0.0979060	+	0.512756i
$523$	−30.8923	+	9.37108i	−1.35083	+	0.409769i	−0.881053	−	0.473018i	$-0.843165\pi$
$523$	−30.8923	+	9.37108i	−1.35083	+	0.409769i	−0.469774	+	0.882787i	$0.655665\pi$
$524$	−36.9939	−	20.5103i	−1.61609	−	0.895998i
$525$	−2.63056	−	2.15885i	−0.114807	−	0.0942198i
$526$	−23.2064	+	2.10581i	−1.01185	+	0.0918176i
$527$	−30.0791	−	12.4592i	−1.31027	−	0.542731i
$528$	−13.8327	−	36.5303i	−0.601992	−	1.58978i
$529$	−18.3006	+	7.58037i	−0.795679	+	0.329581i
$530$	−5.95149	+	3.12261i	−0.258516	+	0.135638i
$531$	−2.42277	−	24.5988i	−0.105139	−	1.06750i
$532$	4.67261	−	14.5928i	0.202583	−	0.632678i
$533$	0.173305	−	0.324231i	0.00750668	−	0.0140440i
$534$	15.5691	+	3.22139i	0.673742	+	0.139403i
$535$	7.73615	−	1.53882i	0.334463	−	0.0665288i
$536$	4.50948	−	2.86511i	0.194780	−	0.123754i
$537$	−6.29571	+	31.6507i	−0.271680	+	1.36583i
$538$	16.3598	+	40.3702i	0.705321	+	1.74048i
$539$	−2.00284	+	20.3352i	−0.0862684	+	0.875897i
$540$	5.15346	+	2.22797i	0.221770	+	0.0958766i
$541$	4.82830	−	15.9168i	0.207585	−	0.684315i	−0.789887	−	0.613252i	$-0.789861\pi$
$541$	4.82830	−	15.9168i	0.207585	−	0.684315i	0.997472	−	0.0710627i	$-0.0226390\pi$
$542$	2.72662	+	3.37492i	0.117118	+	0.144965i
$543$	12.7158	+	12.7158i	0.545687	+	0.545687i
$544$	−10.4223	+	17.8176i	−0.446850	+	0.763923i
$545$	7.34314	−	7.34314i	0.314546	−	0.314546i
$546$	−11.0719	−	1.17642i	−0.473836	−	0.0503459i
$547$	19.8773	+	6.02970i	0.849890	+	0.257811i	0.685038	−	0.728507i	$-0.259785\pi$
$547$	19.8773	+	6.02970i	0.849890	+	0.257811i	0.164852	+	0.986318i	$0.447285\pi$
$548$	−19.5106	−	0.299705i	−0.833450	−	0.0128028i
$549$	14.1177	+	1.39047i	0.602530	+	0.0593440i
$550$	2.48134	−	5.86273i	0.105805	−	0.249988i
$551$	−23.6799	−	4.71023i	−1.00880	−	0.200663i
$552$	7.57031	+	7.92744i	0.322214	+	0.337414i
$553$	−1.34616	−	6.76763i	−0.0572447	−	0.287789i
$554$	−22.8175	+	14.9940i	−0.969423	+	0.637033i
$555$	−5.39925	−	2.88596i	−0.229185	−	0.122502i
$556$	−27.0220	−	22.8799i	−1.14599	−	0.970323i
$557$	37.9781	−	3.74052i	1.60919	−	0.158491i	0.746908	−	0.664927i	$-0.231537\pi$
$557$	37.9781	−	3.74052i	1.60919	−	0.158491i	0.862277	+	0.506436i	$0.169037\pi$
$558$	−20.5501	−	6.40655i	−0.869954	−	0.271211i
$559$	−10.1821	−	24.5819i	−0.430659	−	1.03970i
$560$	−4.12780	+	4.72593i	−0.174431	+	0.199707i
$561$	13.6366	−	32.9216i	0.575736	−	1.38995i
$562$	−10.2463	+	12.2915i	−0.432216	+	0.518485i
$563$	13.6285	−	16.6063i	0.574372	−	0.699874i	−0.402081	−	0.915604i	$-0.631713\pi$
$563$	13.6285	−	16.6063i	0.574372	−	0.699874i	0.976453	+	0.215730i	$0.0692131\pi$
$564$	−4.53329	+	39.7570i	−0.190886	+	1.67407i
$565$	−0.622411	−	2.05181i	−0.0261850	−	0.0863204i
$566$	6.92154	−	10.1886i	0.290934	−	0.428257i
$567$	14.6183	+	9.76767i	0.613913	+	0.410204i
$568$	7.33328	−	5.74071i	0.307697	−	0.240875i
$569$	1.79954	+	2.69320i	0.0754406	+	0.112905i	0.867271	−	0.497836i	$-0.165872\pi$
$569$	1.79954	+	2.69320i	0.0754406	+	0.112905i	−0.791831	+	0.610741i	$0.790872\pi$
$570$	10.6757	−	10.5130i	0.447156	−	0.440340i
$571$	−9.55911	+	7.84496i	−0.400036	+	0.328301i	−0.812806	−	0.582534i	$-0.802061\pi$
$571$	−9.55911	+	7.84496i	−0.400036	+	0.328301i	0.412770	+	0.910835i	$0.364561\pi$
$572$	−3.74938	−	20.4893i	−0.156770	−	0.856702i
$573$	13.3164	+	24.9132i	0.556299	+	1.04076i
$574$	−0.0997402	−	0.338126i	−0.00416308	−	0.0141131i
$575$			1.78649i			0.0745018i
$576$	−5.79795	+	12.3547i	−0.241581	+	0.514780i
$577$			2.67042i			0.111171i	0.998454	+	0.0555855i	$0.0177025\pi$
$577$			2.67042i			0.111171i	−0.998454	+	0.0555855i	$0.982297\pi$
$578$	4.99804	−	1.47432i	0.207891	−	0.0613236i
$579$	−4.60921	−	8.62322i	−0.191552	−	0.358369i
$580$	8.13556	+	5.61865i	0.337811	+	0.233302i
$581$	4.98235	−	4.08891i	0.206703	−	0.169636i
$582$	4.29327	+	4.35972i	0.177962	+	0.180716i
$583$	−11.8856	−	17.7880i	−0.492250	−	0.736704i
$584$	10.9586	−	19.4127i	0.453471	−	0.803303i
$585$	−3.28167	−	2.19274i	−0.135680	−	0.0906586i
$586$	−13.5654	−	9.21558i	−0.560381	−	0.380692i
$587$	−9.55023	−	31.4829i	−0.394180	−	1.29944i	−0.899657	−	0.436598i	$-0.856183\pi$
$587$	−9.55023	−	31.4829i	−0.394180	−	1.29944i	0.505477	−	0.862840i	$-0.331317\pi$
$588$	15.4137	−	12.2584i	0.635649	−	0.505526i
$589$	27.6437	−	33.6840i	1.13904	−	1.38793i
$590$	−15.7394	−	13.1205i	−0.647979	−	0.540164i
$591$	−4.06640	+	9.81717i	−0.167269	+	0.403824i
$592$	−5.62469	+	9.78751i	−0.231173	+	0.402264i
$593$	15.0539	+	36.3434i	0.618190	+	1.49244i	0.853803	+	0.520596i	$0.174290\pi$
$593$	15.0539	+	36.3434i	0.618190	+	1.49244i	−0.235613	+	0.971847i	$0.575710\pi$
$594$	−5.31898	+	17.0615i	−0.218240	+	0.700042i
$595$	−5.69664	+	0.561070i	−0.233540	+	0.0230016i
$596$	−4.08121	+	0.338759i	−0.167173	+	0.0138761i
$597$	37.8180	+	20.2142i	1.54779	+	0.827311i
$598$	3.21000	+	4.88490i	0.131267	+	0.199759i
$599$	2.33516	+	11.7396i	0.0954121	+	0.479669i	0.998716	+	0.0506669i	$0.0161347\pi$
$599$	2.33516	+	11.7396i	0.0954121	+	0.479669i	−0.903304	+	0.429002i	$0.858865\pi$
$600$	−5.72129	+	2.21684i	−0.233571	+	0.0905019i
$601$	−45.1082	−	8.97258i	−1.84000	−	0.365999i	−0.852389	−	0.522908i	$-0.824847\pi$
$601$	−45.1082	−	8.97258i	−1.84000	−	0.365999i	−0.987613	+	0.156908i	$0.949847\pi$
$602$	−23.4958	−	9.94435i	−0.957616	−	0.405301i
$603$	3.20688	+	0.315850i	0.130594	+	0.0128624i
$604$	33.5689	+	34.6163i	1.36590	+	1.40852i
$605$	8.86544	+	2.68930i	0.360431	+	0.109336i
$606$	−0.878107	+	8.26439i	−0.0356707	+	0.335718i
$607$	−20.5866	+	20.5866i	−0.835584	+	0.835584i	−0.988274	−	0.152690i	$-0.951206\pi$
$607$	−20.5866	+	20.5866i	−0.835584	+	0.835584i	0.152690	+	0.988274i	$0.451206\pi$
$608$	−18.7711	−	20.2710i	−0.761268	−	0.822099i
$609$	11.8957	+	11.8957i	0.482039	+	0.482039i
$610$	9.14772	−	7.39050i	0.370380	−	0.299233i
$611$	−6.19403	+	20.4190i	−0.250583	+	0.826063i
$612$	−11.5741	+	4.58718i	−0.467857	+	0.185426i
$613$	2.15627	−	21.8930i	0.0870911	−	0.884250i	−0.848036	−	0.529938i	$-0.822215\pi$
$613$	2.15627	−	21.8930i	0.0870911	−	0.884250i	0.935127	−	0.354312i	$-0.115285\pi$
$614$	−9.10610	+	3.69019i	−0.367492	+	0.148924i
$615$	0.0672512	−	0.338095i	0.00271183	−	0.0136333i
$616$	−16.3472	−	11.4763i	−0.658647	−	0.462392i
$617$	−46.9112	+	9.33122i	−1.88857	+	0.375661i	−0.997013	−	0.0772388i	$-0.975390\pi$
$617$	−46.9112	+	9.33122i	−1.88857	+	0.375661i	−0.891562	+	0.452900i	$0.850390\pi$
$618$	−10.9940	+	53.1347i	−0.442245	+	2.13739i
$619$	−19.8231	+	37.0863i	−0.796756	+	1.49063i	0.0731022	+	0.997324i	$0.476710\pi$
$619$	−19.8231	+	37.0863i	−0.796756	+	1.49063i	−0.869858	+	0.493301i	$0.835790\pi$
$620$	−15.8648	+	8.16914i	−0.637146	+	0.328080i
$621$	−0.491563	−	4.99093i	−0.0197258	−	0.200279i
$622$	−2.25023	−	4.28879i	−0.0902260	−	0.171965i
$623$	7.51076	−	3.11106i	0.300912	−	0.124642i
$624$	−11.6608	+	16.3417i	−0.466806	+	0.654193i
$625$	−0.923880	−	0.382683i	−0.0369552	−	0.0153073i
$626$	0.0156244	+	0.172184i	0.000624478	+	0.00688186i
$627$	36.8671	+	30.2560i	1.47233	+	1.20831i
$628$	8.75919	−	2.51082i	0.349530	−	0.100193i
$629$	−9.85463	+	2.98937i	−0.392930	+	0.119194i
$630$	−3.71743	+	0.709809i	−0.148106	+	0.0282795i
$631$	−2.19484	+	3.28481i	−0.0873751	+	0.130766i	−0.872582	−	0.488467i	$-0.837556\pi$
$631$	−2.19484	+	3.28481i	−0.0873751	+	0.130766i	0.785207	+	0.619233i	$0.212556\pi$
$632$	−11.8193	−	3.88486i	−0.470145	−	0.154531i
$633$	27.6617	−	18.4830i	1.09945	−	0.734632i
$634$	0.283566	−	36.9220i	0.0112619	−	1.46636i
$635$	0.823284	+	1.00317i	0.0326710	+	0.0398098i
$636$	−4.33270	+	20.1587i	−0.171803	+	0.799343i
$637$	9.26171	−	4.95048i	0.366962	−	0.196145i
$638$	−15.0485	+	27.6411i	−0.595777	+	1.09432i
$639$	5.61708			0.222208
$640$	3.76166	+	10.6700i	0.148693	+	0.421771i
$641$	−23.9947			−0.947734			−0.473867	−	0.880596i	$-0.657142\pi$
$641$	−23.9947			−0.947734			−0.473867	+	0.880596i	$0.657142\pi$
$642$	11.5707	−	21.2530i	0.456658	−	0.838788i
$643$	−44.6314	+	23.8560i	−1.76009	+	0.940789i	−0.849324	+	0.527873i	$0.822990\pi$
$643$	−44.6314	+	23.8560i	−1.76009	+	0.940789i	−0.910769	+	0.412916i	$0.864510\pi$
$644$	5.47979	+	1.17777i	0.215934	+	0.0464108i
$645$	−15.8270	−	19.2852i	−0.623186	−	0.759355i
$646$	0.193558	−	25.2024i	0.00761542	−	0.991574i
$647$	−18.7526	+	12.5301i	−0.737240	+	0.492608i	−0.866609	−	0.498989i	$-0.833705\pi$
$647$	−18.7526	+	12.5301i	−0.737240	+	0.492608i	0.129369	+	0.991597i	$0.458705\pi$
$648$	28.2936	−	14.2952i	1.11148	−	0.561567i
$649$	36.2369	−	54.2323i	1.42242	−	2.12880i
$650$	−3.21383	+	0.613650i	−0.126057	+	0.0240693i
$651$	−29.0551	+	8.81377i	−1.13876	+	0.345439i
$652$	0.459080	+	1.60154i	0.0179790	+	0.0627211i
$653$	−8.75331	−	7.18366i	−0.342544	−	0.281118i	0.447354	−	0.894357i	$-0.352366\pi$
$653$	−8.75331	−	7.18366i	−0.342544	−	0.281118i	−0.789898	+	0.613239i	$0.789866\pi$
$654$	−2.87916	−	31.7289i	−0.112584	−	1.24070i
$655$	−19.5397	−	8.09361i	−0.763479	−	0.316243i
$656$	−0.619309	−	0.143094i	−0.0241800	−	0.00558688i
$657$	12.4219	−	5.14532i	0.484625	−	0.200738i
$658$	9.50623	+	18.1182i	0.370591	+	0.706323i
$659$	−4.19620	−	42.6047i	−0.163461	−	1.65964i	−0.631083	−	0.775715i	$-0.717389\pi$
$659$	−4.19620	−	42.6047i	−0.163461	−	1.65964i	0.467623	−	0.883928i	$-0.345111\pi$
$660$	−8.94110	−	17.3640i	−0.348032	−	0.675893i
$661$	2.27088	−	4.24851i	0.0883269	−	0.165248i	−0.833879	−	0.551947i	$-0.813885\pi$
$661$	2.27088	−	4.24851i	0.0883269	−	0.165248i	0.922206	+	0.386699i	$0.126385\pi$
$662$	−7.66278	+	37.0346i	−0.297822	+	1.43939i
$663$	−17.9621	+	3.57288i	−0.697589	+	0.138759i
$664$	−2.00401	−	11.4472i	−0.0777707	−	0.444237i
$665$	1.49465	−	7.51411i	0.0579600	−	0.291385i
$666$	−6.31018	+	2.55716i	−0.244514	+	0.0990880i
$667$	0.865656	−	8.78916i	0.0335184	−	0.340318i
$668$	−1.47621	−	3.72471i	−0.0571165	−	0.144113i
$669$	−13.2633	+	43.7231i	−0.512788	+	1.69043i
$670$	2.07793	−	1.67877i	0.0802774	−	0.0648566i
$671$	26.4696	+	26.4696i	1.02185	+	1.02185i
$672$	3.02795	+	19.0107i	0.116806	+	0.733354i
$673$	12.4980	−	12.4980i	0.481764	−	0.481764i	−0.423931	−	0.905695i	$-0.639350\pi$
$673$	12.4980	−	12.4980i	0.481764	−	0.481764i	0.905695	+	0.423931i	$0.139350\pi$
$674$	3.09706	−	29.1483i	0.119294	−	1.12275i
$675$	2.68634	+	0.814894i	0.103397	+	0.0313653i
$676$	10.9798	−	10.6476i	0.422302	−	0.409524i
$677$	−3.63658	−	0.358171i	−0.139765	−	0.0137656i	0.0278927	−	0.999611i	$-0.491120\pi$
$677$	−3.63658	−	0.358171i	−0.139765	−	0.0137656i	−0.167658	+	0.985845i	$0.553620\pi$
$678$	−6.05773	−	2.56387i	−0.232646	−	0.0984650i
$679$	3.06860	+	0.610382i	0.117762	+	0.0234243i
$680$	−4.16829	+	9.44181i	−0.159847	+	0.362077i
$681$	−8.84042	−	44.4438i	−0.338766	−	1.70309i
$682$	−31.1933	−	47.4693i	−1.19445	−	1.81769i
$683$	−7.70784	−	4.11993i	−0.294932	−	0.157645i	0.317294	−	0.948327i	$-0.397226\pi$
$683$	−7.70784	−	4.11993i	−0.294932	−	0.157645i	−0.612226	+	0.790683i	$0.709726\pi$
$684$	−1.37838	−	16.6061i	−0.0527037	−	0.634949i
$685$	−9.70946	+	0.956298i	−0.370979	+	0.0365383i
$686$	7.61903	−	24.4393i	0.290896	−	0.933097i
$687$	−12.1111	−	29.2388i	−0.462068	−	1.11553i
$688$	−36.4396	+	28.0773i	−1.38924	+	1.07044i
$689$	−4.20763	+	10.1581i	−0.160298	+	0.386994i
$690$	4.20984	+	3.50938i	0.160266	+	0.133600i
$691$	11.3716	−	13.8563i	0.432594	−	0.527118i	−0.510395	−	0.859940i	$-0.670501\pi$
$691$	11.3716	−	13.8563i	0.432594	−	0.527118i	0.942990	+	0.332822i	$0.108001\pi$
$692$	29.4178	+	36.9899i	1.11830	+	1.40615i
$693$	−3.49699	−	11.5280i	−0.132840	−	0.437914i
$694$	−3.07612	−	2.08975i	−0.116768	−	0.0793257i
$695$	−14.7200	−	9.83561i	−0.558363	−	0.373086i
$696$	29.2217	−	8.13407i	1.10765	−	0.308321i
$697$	−0.322148	−	0.482129i	−0.0122022	−	0.0182619i
$698$	2.71715	+	2.75921i	0.102846	+	0.104438i
$699$	16.7472	−	13.7441i	0.633438	−	0.519849i
$700$	−1.78291	+	2.58157i	−0.0673876	+	0.0975743i
$701$	12.1504	+	22.7318i	0.458915	+	0.858569i	0.999847	+	0.0175028i	$0.00557160\pi$
$701$	12.1504	+	22.7318i	0.458915	+	0.858569i	−0.540932	+	0.841066i	$0.681928\pi$
$702$	8.80964	−	2.59866i	0.332498	−	0.0980802i
$703$		−	13.7830i		−	0.519836i
$704$	−32.5087	+	15.4953i	−1.22522	+	0.584000i
$705$			20.0073i			0.753519i
$706$	8.64500	+	29.3071i	0.325359	+	1.10299i
$707$	2.00326	+	3.74783i	0.0753402	+	0.140952i
$708$	−61.8367	+	11.3156i	−2.32397	+	0.425267i
$709$	14.4291	−	11.8416i	0.541895	−	0.444722i	−0.323200	−	0.946331i	$-0.604758\pi$
$709$	14.4291	−	11.8416i	0.541895	−	0.444722i	0.865094	+	0.501609i	$0.167258\pi$
$710$	3.31785	−	3.26727i	0.124517	−	0.122619i
$711$	−4.16894	−	6.23926i	−0.156348	−	0.233991i
$712$	1.77241	−	14.5504i	0.0664240	−	0.545300i
$713$	13.2532	+	8.85553i	0.496337	+	0.331642i
$714$	−9.86832	+	14.5262i	−0.369313	+	0.543630i
$715$	−3.02325	−	9.96632i	−0.113063	−	0.372719i
$716$	29.5604	+	3.37063i	1.10473	+	0.125966i
$717$	−8.16766	+	9.95233i	−0.305027	+	0.371676i
$718$	4.48495	−	5.38014i	0.167377	−	0.200785i
$719$	−10.8405	+	26.1713i	−0.404283	+	0.976026i	0.582331	+	0.812952i	$0.302141\pi$
$719$	−10.8405	+	26.1713i	−0.404283	+	0.976026i	−0.986614	+	0.163074i	$0.947859\pi$
$720$	−2.18047	+	6.46602i	−0.0812613	+	0.240974i
$721$	10.6175	+	25.6329i	0.395416	+	0.954619i
$722$	6.55099	+	2.04229i	0.243803	+	0.0760062i
$723$	0.244008	−	0.0240327i	0.00907477	−	0.000893787i
$724$	10.7134	−	12.6529i	0.398159	−	0.470241i
$725$	4.35986	+	2.33039i	0.161921	+	0.0865487i
$726$	23.7525	−	15.6084i	0.881540	−	0.579283i
$727$	−0.783207	−	3.93745i	−0.0290475	−	0.146032i	0.963540	−	0.267565i	$-0.0862190\pi$
$727$	−0.783207	−	3.93745i	−0.0290475	−	0.146032i	−0.992587	+	0.121533i	$0.961219\pi$
$728$	−0.236489	+	10.2625i	−0.00876488	+	0.380354i
$729$	0.833887	+	0.165870i	0.0308847	+	0.00614335i
$730$	4.34439	−	10.2646i	0.160793	−	0.379910i
$731$	−41.7633	−	4.11333i	−1.54467	−	0.152137i
$732$	0.554145	−	36.0744i	0.0204818	−	1.33335i
$733$	−4.39880	−	1.33436i	−0.162473	−	0.0492858i	0.208000	−	0.978129i	$-0.433305\pi$
$733$	−4.39880	−	1.33436i	−0.162473	−	0.0492858i	−0.370474	+	0.928843i	$0.620805\pi$
$734$	30.8031	+	3.27289i	1.13696	+	0.120805i
$735$	6.96283	−	6.96283i	0.256828	−	0.256828i
$736$	6.70631	−	7.56009i	0.247198	−	0.278669i
$737$	6.01265	+	6.01265i	0.221479	+	0.221479i
$738$	−0.240926	−	0.298210i	−0.00886859	−	0.0109773i
$739$	5.56228	−	18.3364i	0.204612	−	0.674515i	−0.793234	−	0.608917i	$-0.791604\pi$
$739$	5.56228	−	18.3364i	0.204612	−	0.674515i	0.997846	−	0.0655984i	$-0.0208956\pi$
$740$	−2.23982	+	5.18086i	−0.0823374	+	0.190452i
$741$	2.40255	−	24.3935i	0.0882599	−	0.896118i
$742$	3.95975	+	9.77127i	0.145367	+	0.358715i
$743$	0.266223	−	1.33839i	0.00976678	−	0.0491009i	−0.975595	−	0.219580i	$-0.929531\pi$
$743$	0.266223	−	1.33839i	0.00976678	−	0.0491009i	0.985361	+	0.170479i	$0.0545314\pi$
$744$	−11.9143	+	53.4326i	−0.436800	+	1.95893i
$745$	−2.00828	+	0.399471i	−0.0735776	+	0.0146355i
$746$	−6.64774	−	1.37548i	−0.243391	−	0.0503597i
$747$	3.30415	−	6.18163i	0.120893	−	0.226174i
$748$	−31.2879	−	10.0184i	−1.14400	−	0.366309i
$749$	−1.21281	−	12.3139i	−0.0443151	−	0.449939i
$750$	−2.71666	+	1.42537i	−0.0991982	+	0.0520470i
$751$	27.5125	−	11.3960i	1.00394	−	0.415847i	0.180702	−	0.983538i	$-0.442163\pi$
$751$	27.5125	−	11.3960i	1.00394	−	0.415847i	0.823242	+	0.567690i	$0.192163\pi$
$752$	36.8740	+	1.13312i	1.34466	+	0.0413208i
$753$	61.3629	+	25.4173i	2.23619	+	0.926260i
$754$	16.1087	−	1.46175i	0.586645	−	0.0532337i
$755$	18.6372	+	15.2952i	0.678278	+	0.556649i
$756$	4.27058	−	7.70273i	0.155320	−	0.280146i
$757$	48.5112	−	14.7157i	1.76317	−	0.534851i	0.768674	−	0.639641i	$-0.220917\pi$
$757$	48.5112	−	14.7157i	1.76317	−	0.534851i	0.994494	+	0.104789i	$0.0334168\pi$
$758$	−4.03838	−	21.1499i	−0.146681	−	0.768200i
$759$	−9.69236	+	14.5056i	−0.351810	+	0.526521i
$760$	−10.4734	−	9.00697i	−0.379909	−	0.326717i
$761$	32.7887	−	21.9087i	1.18859	−	0.794190i	0.205741	−	0.978606i	$-0.434040\pi$
$761$	32.7887	−	21.9087i	1.18859	−	0.794190i	0.982848	+	0.184416i	$0.0590395\pi$
$762$	3.98123	+	0.0305764i	0.144225	+	0.00110766i
$763$	−10.3346	−	12.5928i	−0.374139	−	0.455890i
$764$	21.8744	−	14.1349i	0.791387	−	0.511382i
$765$	−5.48997	+	2.93445i	−0.198490	+	0.106095i
$766$	21.0868	+	11.4802i	0.761897	+	0.414797i
$767$	−33.5219			−1.21041
$768$	32.5332	+	12.0959i	1.17394	+	0.436474i
$769$	−10.7135			−0.386338			−0.193169	−	0.981166i	$-0.561877\pi$
$769$	−10.7135			−0.386338			−0.193169	+	0.981166i	$0.561877\pi$
$770$	−8.77105	−	4.77519i	−0.316087	−	0.172086i
$771$	31.6956	−	16.9416i	1.14149	−	0.610138i
$772$	−7.57140	+	4.89253i	−0.272501	+	0.176086i
$773$	10.7848	+	13.1413i	0.387903	+	0.472661i	0.929949	−	0.367688i	$-0.119850\pi$
$773$	10.7848	+	13.1413i	0.387903	+	0.472661i	−0.542047	+	0.840348i	$0.682350\pi$
$774$	−27.7449	−	0.213084i	−0.997268	−	0.00765916i
$775$	−7.41858	+	4.95694i	−0.266483	+	0.178059i
$776$	3.67825	−	4.27710i	0.132041	−	0.153539i
$777$	−5.33559	+	7.98527i	−0.191413	+	0.286470i
$778$	−4.86026	−	25.4543i	−0.174249	−	0.912581i
$779$	0.742659	−	0.225283i	0.0266085	−	0.00807161i
$780$	−4.86718	+	8.77880i	−0.174273	+	0.314331i
$781$	11.4577	+	9.40311i	0.409989	+	0.336470i
$782$	9.18143	−	0.833147i	0.328327	−	0.0297933i
$783$	−12.8214	−	5.31079i	−0.458199	−	0.189792i
$784$	−12.4383	−	13.2270i	−0.444227	−	0.472394i
$785$	4.20917	−	1.74350i	0.150232	−	0.0622280i
$786$	−57.4562	+	30.1460i	−2.04939	+	1.07527i
$787$	−1.38293	−	14.0412i	−0.0492962	−	0.500513i	−0.987853	−	0.155389i	$-0.950337\pi$
$787$	−1.38293	−	14.0412i	−0.0492962	−	0.500513i	0.938557	−	0.345124i	$-0.112163\pi$
$788$	9.33002	+	2.98747i	0.332368	+	0.106424i
$789$	−16.8493	+	31.5229i	−0.599852	+	1.12224i
$790$	−6.09165	−	1.26041i	−0.216731	−	0.0448435i
$791$	−3.29888	+	0.656188i	−0.117295	+	0.0233314i
$792$	−21.2002	−	4.72718i	−0.753315	−	0.167973i
$793$	3.75332	−	18.8692i	0.133284	−	0.670066i
$794$	−0.0798064	−	0.196934i	−0.00283222	−	0.00698893i
$795$	−1.01051	+	10.2599i	−0.0358390	+	0.363880i
$796$	15.6884	−	36.2884i	0.556061	−	1.28621i
$797$	−13.0514	+	43.0246i	−0.462303	+	1.52401i	0.347713	+	0.937601i	$0.386958\pi$
$797$	−13.0514	+	43.0246i	−0.462303	+	1.52401i	−0.810016	+	0.586408i	$0.800542\pi$
$798$	−14.7708	−	18.2828i	−0.522881	−	0.647205i
$799$	23.7972	+	23.7972i	0.841884	+	0.841884i
$800$	2.47313	+	5.08760i	0.0874384	+	0.179874i
$801$	6.25141	−	6.25141i	0.220883	−	0.220883i
$802$	43.4505	+	4.61670i	1.53429	+	0.163021i
$803$	33.9516	+	10.2991i	1.19813	+	0.363447i
$804$	0.125875	−	8.19438i	0.00443928	−	0.288994i
$805$	2.78897	+	0.274690i	0.0982984	+	0.00968154i
$806$	−11.3783	+	26.8839i	−0.400785	+	0.946945i
$807$	65.5332	+	13.0354i	2.30688	+	0.458867i
$808$	7.66020	+	0.176522i	0.269485	+	0.00621002i
$809$	5.32460	+	26.7686i	0.187203	+	0.941133i	0.954129	+	0.299397i	$0.0967855\pi$
$809$	5.32460	+	26.7686i	0.187203	+	0.941133i	−0.766926	+	0.641736i	$0.778214\pi$
$810$	13.2460	−	8.70427i	0.465416	−	0.305837i
$811$	47.1650	+	25.2102i	1.65619	+	0.885250i	0.990260	+	0.139233i	$0.0444638\pi$
$811$	47.1650	+	25.2102i	1.65619	+	0.885250i	0.665927	+	0.746017i	$0.268036\pi$
$812$	10.0224	−	11.8369i	0.351719	−	0.415393i
$813$	6.62330	−	0.652338i	0.232289	−	0.0228785i
$814$	−17.1522	−	5.34726i	−0.601185	−	0.187421i
$815$	0.318782	+	0.769608i	0.0111665	+	0.0269582i
$816$	14.0613	+	28.3700i	0.492244	+	0.993148i
$817$	21.4941	−	51.8913i	0.751983	−	1.81545i
$818$	21.5322	−	25.8299i	0.752855	−	0.903123i
$819$	−3.92777	+	4.78601i	−0.137248	+	0.167237i
$820$	−0.315767	−	0.0360053i	−0.0110270	−	0.00125736i
$821$	−0.590156	−	1.94548i	−0.0205966	−	0.0678978i	0.946040	−	0.324051i	$-0.105045\pi$
$821$	−0.590156	−	1.94548i	−0.0205966	−	0.0678978i	−0.966636	+	0.256153i	$0.917545\pi$
$822$	−16.8197	+	24.7588i	−0.586656	+	0.863561i
$823$	−26.6352	−	17.7971i	−0.928445	−	0.620367i	−0.00330545	−	0.999995i	$-0.501052\pi$
$823$	−26.6352	−	17.7971i	−0.928445	−	0.620367i	−0.925139	+	0.379628i	$0.876052\pi$
$824$	49.6580	+	6.04894i	1.72992	+	0.210725i
$825$	−5.42536	−	8.11963i	−0.188887	−	0.282689i
$826$	−22.9031	+	22.5540i	−0.796902	+	0.784755i
$827$	2.89554	−	2.37631i	0.100688	−	0.0826324i	−0.582702	−	0.812686i	$-0.698005\pi$
$827$	2.89554	−	2.37631i	0.100688	−	0.0826324i	0.683390	+	0.730053i	$0.260505\pi$
$828$	5.99574	−	1.09717i	0.208366	−	0.0381294i
$829$	−12.3847	−	23.1701i	−0.430137	−	0.804730i	0.569716	−	0.821841i	$-0.307053\pi$
$829$	−12.3847	−	23.1701i	−0.430137	−	0.804730i	−0.999854	+	0.0171112i	$0.994553\pi$
$830$	−1.64399	−	5.57323i	−0.0570636	−	0.193449i
$831$			41.8813i			1.45284i
$832$	15.9039	+	9.46754i	0.551369	+	0.328228i
$833$		−	16.5635i		−	0.573892i
$834$	−52.0935	+	15.3665i	−1.80385	+	0.532098i
$835$	−0.944343	−	1.76674i	−0.0326803	−	0.0611406i
$836$	24.9873	−	36.1805i	0.864203	−	1.25133i
$837$	19.3614	−	15.8895i	0.669228	−	0.549221i
$838$	−10.4982	−	10.6607i	−0.362655	−	0.368269i
$839$	−27.6391	−	41.3648i	−0.954207	−	1.42807i	−0.903125	−	0.429377i	$-0.858733\pi$
$839$	−27.6391	−	41.3648i	−0.954207	−	1.42807i	−0.0510812	−	0.998695i	$-0.516267\pi$
$840$	2.58110	+	9.27263i	0.0890564	+	0.319936i
$841$	3.79223	+	2.53389i	0.130767	+	0.0873754i
$842$	43.1519	+	29.3150i	1.48711	+	1.01026i
$843$	7.12541	+	23.4893i	0.245412	+	0.809016i
$844$	−19.0915	−	24.0057i	−0.657157	−	0.826310i
$845$	4.85144	−	5.91150i	0.166895	−	0.203362i
$846$	17.0911	+	14.2474i	0.587606	+	0.489836i
$847$	5.56154	−	13.4267i	0.191097	−	0.461348i
$848$	18.8520	+	2.44347i	0.647379	+	0.0839090i
$849$	−7.23038	−	17.4557i	−0.248146	−	0.599078i
$850$	−1.53589	+	4.92663i	−0.0526806	+	0.168982i
$851$	5.01747	−	0.494177i	0.171997	−	0.0169402i
$852$	−1.18171	−	14.2367i	−0.0404847	−	0.487741i
$853$	9.77785	+	5.22637i	0.334787	+	0.178948i	0.630221	−	0.776416i	$-0.282964\pi$
$853$	9.77785	+	5.22637i	0.334787	+	0.178948i	−0.295434	+	0.955363i	$0.595464\pi$
$854$	−10.1311	−	15.4173i	−0.346679	−	0.527569i
$855$	−1.62541	−	8.17150i	−0.0555880	−	0.279460i
$856$	−20.4094	−	9.01018i	−0.697580	−	0.307962i
$857$	−17.5710	−	3.49509i	−0.600213	−	0.119390i	−0.114374	−	0.993438i	$-0.536486\pi$
$857$	−17.5710	−	3.49509i	−0.600213	−	0.119390i	−0.485840	+	0.874048i	$0.661486\pi$
$858$	−29.4244	−	12.4536i	−1.00453	−	0.425158i
$859$	32.5414	+	3.20505i	1.11030	+	0.109355i	0.636499	−	0.771278i	$-0.280382\pi$
$859$	32.5414	+	3.20505i	1.11030	+	0.109355i	0.473800	+	0.880633i	$0.342882\pi$
$860$	−16.5120	+	16.0124i	−0.563055	+	0.546019i
$861$	−0.517475	−	0.156974i	−0.0176355	−	0.00534967i
$862$	2.68497	−	25.2698i	0.0914504	−	0.860694i
$863$	−4.89248	+	4.89248i	−0.166542	+	0.166542i	−0.785458	−	0.618916i	$-0.787572\pi$
$863$	−4.89248	+	4.89248i	−0.166542	+	0.166542i	0.618916	+	0.785458i	$0.287572\pi$
$864$	−8.30908	−	13.5327i	−0.282681	−	0.460393i
$865$	16.7095	+	16.7095i	0.568140	+	0.568140i
$866$	−19.3750	+	15.6532i	−0.658388	+	0.531916i
$867$	2.32033	−	7.64910i	0.0788025	−	0.259777i
$868$	10.3138	+	26.0233i	0.350075	+	0.883290i
$869$	1.94085	−	19.7057i	0.0658387	−	0.668471i
$870$	14.0560	−	5.69613i	0.476544	−	0.193117i
$871$	0.852577	−	4.28619i	0.0288885	−	0.145232i
$872$	−28.9325	+	5.06510i	−0.979780	+	0.171526i
$873$	3.33706	−	0.663783i	0.112942	−	0.0224656i
$874$	−2.50009	+	12.0830i	−0.0845667	+	0.408715i
$875$	−0.739480	+	1.38347i	−0.0249990	+	0.0467698i
$876$	−15.6543	−	30.4013i	−0.528909	−	1.02716i
$877$	−1.44868	−	14.7087i	−0.0489184	−	0.496677i	−0.988161	−	0.153422i	$-0.950971\pi$
$877$	−1.44868	−	14.7087i	−0.0489184	−	0.496677i	0.939242	−	0.343255i	$-0.111529\pi$
$878$	−19.3663	−	36.9109i	−0.653582	−	1.24568i
$879$	−23.2411	+	9.62678i	−0.783903	+	0.324703i
$880$	−15.2720	+	9.53923i	−0.514818	+	0.321567i
$881$	26.8835	+	11.1355i	0.905729	+	0.375165i	0.786420	−	0.617692i	$-0.211932\pi$
$881$	26.8835	+	11.1355i	0.905729	+	0.375165i	0.119309	+	0.992857i	$0.461932\pi$
$882$	−0.989664	−	10.9063i	−0.0333237	−	0.367233i
$883$	21.7500	+	17.8498i	0.731947	+	0.600693i	0.924764	−	0.380542i	$-0.124262\pi$
$883$	21.7500	+	17.8498i	0.731947	+	0.600693i	−0.192817	+	0.981235i	$0.561762\pi$
$884$	4.65257	+	16.2309i	0.156483	+	0.545903i
$885$	−30.0783	+	9.12416i	−1.01107	+	0.306705i
$886$	35.6248	−	6.80222i	1.19684	−	0.228525i
$887$	−1.65772	+	2.48096i	−0.0556609	+	0.0833025i	−0.858256	−	0.513221i	$-0.828452\pi$
$887$	−1.65772	+	2.48096i	−0.0556609	+	0.0833025i	0.802595	+	0.596524i	$0.203452\pi$
$888$	7.80873	+	15.4554i	0.262044	+	0.518649i
$889$	1.69269	−	1.13102i	0.0567710	−	0.0379332i
$890$	0.0562859	−	7.32877i	0.00188671	−	0.245661i
$891$	32.0064	+	38.9999i	1.07226	+	1.30655i
$892$	41.1838	+	8.85165i	1.37894	+	0.296375i
$893$	−39.7245	+	21.2332i	−1.32933	+	0.710542i
$894$	−3.00371	+	5.51720i	−0.100459	+	0.184523i
$895$	14.8760			0.497249
$896$	17.2359	−	4.23188i	0.575811	−	0.141377i
$897$	8.96618			0.299372
$898$	20.1471	−	37.0061i	0.672317	−	1.23491i
$899$	38.8998	−	20.7924i	1.29738	−	0.693465i
$900$	−0.716945	+	3.33571i	−0.0238982	+	0.111190i
$901$	11.0014	+	13.4053i	0.366510	+	0.446594i
$902$	0.00776924	−	1.01160i	0.000258688	−	0.0336827i
$903$	−32.5406	+	21.7429i	−1.08288	+	0.723559i
$904$	−1.89367	+	5.76131i	−0.0629827	+	0.191618i
$905$	4.60547	−	6.89258i	0.153091	−	0.229117i
$906$	72.6538	−	13.8726i	2.41376	−	0.460885i
$907$	−53.1575	+	16.1251i	−1.76507	+	0.535427i	−0.994759	−	0.102247i	$-0.967397\pi$
$907$	−53.1575	+	16.1251i	−1.76507	+	0.535427i	−0.770307	+	0.637674i	$0.779897\pi$
$908$	−40.1603	+	11.5119i	−1.33276	+	0.382037i
$909$	3.57240	+	2.93179i	0.118489	+	0.0972414i
$910$	0.463841	+	5.11161i	0.0153762	+	0.169448i
$911$	14.7884	+	6.12557i	0.489963	+	0.202949i	0.613966	−	0.789333i	$-0.289573\pi$
$911$	14.7884	+	6.12557i	0.489963	+	0.202949i	−0.124003	+	0.992282i	$0.539573\pi$
$912$	−41.7987	+	6.98711i	−1.38409	+	0.231366i
$913$	17.0880	−	7.07807i	0.565530	−	0.234250i
$914$	8.64260	+	16.4722i	0.285872	+	0.544853i
$915$	−1.76816	−	17.9524i	−0.0584536	−	0.593489i
$916$	−25.9407	+	13.3574i	−0.857104	+	0.441342i
$917$	−15.6397	+	29.2598i	−0.516469	+	0.966245i
$918$	2.93524	−	14.1861i	0.0968772	−	0.468213i
$919$	41.6588	−	8.28646i	1.37420	−	0.273345i	0.547884	−	0.836554i	$-0.315434\pi$
$919$	41.6588	−	8.28646i	1.37420	−	0.273345i	0.826314	+	0.563209i	$0.190434\pi$
$920$	2.90332	−	4.13559i	0.0957196	−	0.136346i
$921$	−2.94032	+	14.7820i	−0.0968868	+	0.487083i
$922$	−8.79135	+	3.56265i	−0.289528	+	0.117329i
$923$	0.746676	−	7.58113i	0.0245771	−	0.249536i
$924$	−28.4825	+	11.2885i	−0.937006	+	0.371364i
$925$	−0.819227	+	2.70063i	−0.0269360	+	0.0887961i
$926$	−18.4557	+	14.9105i	−0.606493	+	0.489989i
$927$	21.3350	+	21.3350i	0.700733	+	0.700733i
$928$	−9.70205	−	26.2283i	−0.318485	−	0.860985i
$929$	−32.5623	+	32.5623i	−1.06834	+	1.06834i	−0.0708486	+	0.997487i	$0.522571\pi$
$929$	−32.5623	+	32.5623i	−1.06834	+	1.06834i	−0.997487	+	0.0708486i	$0.977429\pi$
$930$	−2.89209	+	27.2192i	−0.0948354	+	0.892553i
$931$	21.2142	+	6.43525i	0.695266	+	0.210907i
$932$	−13.9051	−	14.3390i	−0.455477	−	0.469689i
$933$	−7.39351	−	0.728197i	−0.242053	−	0.0238401i
$934$	0.317654	+	0.134444i	0.0103940	+	0.00439914i
$935$	−16.1108	−	3.20463i	−0.526878	−	0.104803i
$936$	4.03328	+	10.4092i	0.131832	+	0.340237i
$937$	8.19970	+	41.2227i	0.267872	+	1.34669i	0.847063	+	0.531493i	$0.178369\pi$
$937$	8.19970	+	41.2227i	0.267872	+	1.34669i	−0.579190	+	0.815192i	$0.696631\pi$
$938$	−2.30131	−	3.50208i	−0.0751403	−	0.114347i
$939$	0.233890	+	0.125017i	0.00763272	+	0.00407977i
$940$	18.3825	−	1.52583i	0.599571	−	0.0497671i
$941$	−34.8307	+	3.43052i	−1.13545	+	0.111832i	−0.648227	−	0.761447i	$-0.724489\pi$
$941$	−34.8307	+	3.43052i	−1.13545	+	0.111832i	−0.487220	+	0.873279i	$0.661989\pi$
$942$	4.15996	−	13.3438i	0.135539	−	0.434763i
$943$	0.108638	+	0.262275i	0.00353774	+	0.00854086i
$944$	15.1126	+	55.9519i	0.491872	+	1.82108i
$945$	1.68522	−	4.06848i	0.0548202	−	0.132348i
$946$	−56.2372	−	46.8801i	−1.82843	−	1.52420i
$947$	−4.91133	+	5.98447i	−0.159597	+	0.194469i	−0.846669	−	0.532120i	$-0.821396\pi$
$947$	−4.91133	+	5.98447i	−0.159597	+	0.194469i	0.687072	+	0.726589i	$0.258896\pi$
$948$	−14.9366	+	11.8789i	−0.485117	+	0.385810i
$949$	−5.29318	−	17.4493i	−0.171824	−	0.566427i
$950$	−5.71318	−	3.88122i	−0.185360	−	0.125923i
$951$	−47.0927	−	31.4663i	−1.52708	−	1.02037i
$952$	14.0991	+	7.95908i	0.456955	+	0.257955i
$953$	11.1435	+	16.6775i	0.360974	+	0.540236i	0.966857	−	0.255318i	$-0.0821801\pi$
$953$	11.1435	+	16.6775i	0.360974	+	0.540236i	−0.605883	+	0.795554i	$0.707180\pi$
$954$	8.04485	+	8.16937i	0.260462	+	0.264493i
$955$	10.0661	−	8.26103i	0.325731	−	0.267321i
$956$	9.76698	+	6.74536i	0.315887	+	0.218160i
$957$	22.7572	+	42.5758i	0.735636	+	1.37628i
$958$	−22.4043	+	6.60880i	−0.723850	+	0.213521i
$959$			15.3049i			0.494222i
$960$	16.8471	+	4.16616i	0.543737	+	0.134462i
$961$			48.6067i			1.56796i
$962$	2.61248	+	8.85649i	0.0842297	+	0.285545i
$963$	−6.34311	−	11.8671i	−0.204404	−	0.382413i
$964$	−0.0406900	−	0.222359i	−0.00131054	−	0.00716171i
$965$	−3.48419	+	2.85940i	−0.112160	+	0.0920473i
$966$	6.12595	−	6.03258i	0.197099	−	0.194095i
$967$	25.9122	+	38.7803i	0.833279	+	1.24709i	0.966670	+	0.256027i	$0.0824135\pi$
$967$	25.9122	+	38.7803i	0.833279	+	1.24709i	−0.133391	+	0.991064i	$0.542586\pi$
$968$	−16.1523	−	20.6332i	−0.519155	−	0.663177i
$969$	−32.1447	−	21.4784i	−1.03264	−	0.689985i
$970$	1.58500	−	2.33314i	0.0508914	−	0.0749125i
$971$	−9.04256	−	29.8093i	−0.290189	−	0.956626i	−0.973920	−	0.226892i	$-0.927144\pi$
$971$	−9.04256	−	29.8093i	−0.290189	−	0.956626i	0.683731	−	0.729735i	$-0.260356\pi$
$972$	3.60065	−	31.5777i	0.115491	−	1.01286i
$973$	−17.6182	+	21.4678i	−0.564813	+	0.688226i
$974$	3.21179	−	3.85285i	0.102912	−	0.123453i
$975$	−1.92064	+	4.63684i	−0.0615098	+	0.148498i
$976$	−33.1870	+	2.24202i	−1.06229	+	0.0717654i
$977$	−2.17753	−	5.25703i	−0.0696655	−	0.168187i	0.885212	−	0.465189i	$-0.154013\pi$
$977$	−2.17753	−	5.25703i	−0.0696655	−	0.168187i	−0.954877	+	0.297001i	$0.904013\pi$
$978$	2.43979	+	0.760611i	0.0780158	+	0.0243217i
$979$	23.2166	−	2.28664i	0.742006	−	0.0730812i
$980$	−6.92838	−	5.86636i	−0.221319	−	0.187394i
$981$	−15.6240	−	8.35118i	−0.498835	−	0.266633i
$982$	12.6287	−	8.29865i	0.402998	−	0.264821i
$983$	−10.9158	−	54.8773i	−0.348159	−	1.75031i	−0.616845	−	0.787085i	$-0.711589\pi$
$983$	−10.9158	−	54.8773i	−0.348159	−	1.75031i	0.268686	−	0.963228i	$-0.413411\pi$
$984$	−0.705137	+	0.673371i	−0.0224789	+	0.0214663i
$985$	4.80420	+	0.955615i	0.153075	+	0.0304484i
$986$	9.94349	−	23.4937i	0.316665	−	0.748193i
$987$	31.2343	+	3.07631i	0.994199	+	0.0979201i
$988$	−22.5957	−	0.347097i	−0.718865	−	0.0110426i
$989$	19.6608	+	5.96404i	0.625178	+	0.189646i
$990$	−10.7996	−	1.14748i	−0.343234	−	0.0364693i
$991$	−1.44063	+	1.44063i	−0.0457632	+	0.0457632i	−0.729618	−	0.683855i	$-0.760302\pi$
$991$	−1.44063	+	1.44063i	−0.0457632	+	0.0457632i	0.683855	+	0.729618i	$0.260302\pi$
$992$	50.0019	+	6.87178i	1.58756	+	0.218179i
$993$	41.0208	+	41.0208i	1.30175	+	1.30175i
$994$	−4.59054	−	5.68202i	−0.145603	−	0.180223i
$995$	5.73812	−	18.9161i	0.181911	−	0.599679i
$996$	−16.3627	−	7.07400i	−0.518471	−	0.224148i
$997$	2.76073	−	28.0301i	0.0874331	−	0.887723i	−0.847002	−	0.531590i	$-0.821595\pi$
$997$	2.76073	−	28.0301i	0.0874331	−	0.887723i	0.934435	−	0.356134i	$-0.115905\pi$
$998$	−22.7896	−	56.2366i	−0.721391	−	1.78014i
$999$	1.54558	−	7.77018i	0.0489001	−	0.245837i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.101.11	✓	1024
128.109	even	32	inner	640.2.bm.a.621.11	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.101.11	✓	1024	1.1	even	1	trivial
640.2.bm.a.621.11	yes	1024	128.109	even	32	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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.24207 - 0.676215i) q^{2} +(-1.91317 + 1.02261i) q^{3} +(1.08547 + 1.67981i) q^{4} +(0.634393 + 0.773010i) q^{5} +(3.06779 + 0.0235610i) q^{6} +(1.30433 - 0.871523i) q^{7} +(-0.212313 - 2.82045i) q^{8} +(0.947771 - 1.41844i) q^{9} +(-0.265239 - 1.38912i) q^{10} +(4.30776 - 1.30674i) q^{11} +(-3.79447 - 2.10375i) q^{12} +(-1.78842 - 1.46772i) q^{13} +(-2.20940 + 0.200487i) q^{14} +(-2.00419 - 0.830162i) q^{15} +(-1.64352 + 3.64676i) q^{16} +(-3.37125 + 1.39642i) q^{17} +(-2.13637 + 1.12090i) q^{18} +(-0.478702 - 4.86035i) q^{19} +(-0.609897 + 1.90474i) q^{20} +(-1.60417 + 3.00119i) q^{21} +(-6.23417 - 1.28990i) q^{22} +(1.75216 - 0.348527i) q^{23} +(3.29041 + 5.17888i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(1.22885 + 3.03236i) q^{26} +(0.275156 - 2.79370i) q^{27} +(2.87980 + 1.24501i) q^{28} +(1.43505 - 4.73072i) q^{29} +(1.92797 + 2.38638i) q^{30} +(6.30899 + 6.30899i) q^{31} +(4.50735 - 3.41815i) q^{32} +(-6.90518 + 6.90518i) q^{33} +(5.13160 + 0.545242i) q^{34} +(1.50115 + 0.455369i) q^{35} +(3.41148 + 0.0524044i) q^{36} +(2.80856 + 0.276619i) q^{37} +(-2.69206 + 6.36059i) q^{38} +(4.92245 + 0.979135i) q^{39} +(2.04555 - 1.95339i) q^{40} +(0.0310011 + 0.155853i) q^{41} +(4.02193 - 2.64292i) q^{42} +(10.1425 + 5.42129i) q^{43} +(6.87101 + 5.81778i) q^{44} +(1.69773 - 0.167212i) q^{45} +(-2.41199 - 0.751944i) q^{46} +(-3.52943 - 8.52080i) q^{47} +(-0.584880 - 8.65754i) q^{48} +(-1.73707 + 4.19366i) q^{49} +(0.905537 - 1.08628i) q^{50} +(5.02178 - 6.11905i) q^{51} +(0.524214 - 4.59736i) q^{52} +(-1.37955 - 4.54778i) q^{53} +(-2.23091 + 3.28391i) q^{54} +(3.74294 + 2.50095i) q^{55} +(-2.73501 - 3.49375i) q^{56} +(5.88608 + 8.80914i) q^{57} +(-4.98141 + 4.90548i) q^{58} +(11.2003 - 9.19187i) q^{59} +(-0.780968 - 4.26777i) q^{60} +(3.91997 + 7.33375i) q^{61} +(-3.56996 - 12.1024i) q^{62} -2.67611i q^{63} +(-7.90985 + 1.19764i) q^{64} -2.31358i q^{65} +(13.2461 - 3.90732i) q^{66} +(0.890432 + 1.66588i) q^{67} +(-6.00510 - 4.14729i) q^{68} +(-2.99578 + 2.45857i) q^{69} +(-1.55661 - 1.58070i) q^{70} +(1.82930 + 2.73774i) q^{71} +(-4.20186 - 2.37198i) q^{72} +(6.55322 + 4.37872i) q^{73} +(-3.30137 - 2.24277i) q^{74} +(-0.629720 - 2.07591i) q^{75} +(7.64484 - 6.07988i) q^{76} +(4.47986 - 5.45873i) q^{77} +(-5.45191 - 4.54478i) q^{78} +(1.68330 - 4.06385i) q^{79} +(-3.86162 + 1.04302i) q^{80} +(4.28896 + 10.3545i) q^{81} +(0.0668846 - 0.214543i) q^{82} +(4.08896 - 0.402727i) q^{83} +(-6.78269 + 0.562995i) q^{84} +(-3.21814 - 1.72013i) q^{85} +(-8.93174 - 13.5921i) q^{86} +(2.09219 + 10.5182i) q^{87} +(-4.60020 - 11.8724i) q^{88} +(5.08280 + 1.01103i) q^{89} +(-2.22177 - 0.940340i) q^{90} +(-3.61183 - 0.355734i) q^{91} +(2.48738 + 2.56499i) q^{92} +(-18.5218 - 5.61852i) q^{93} +(-1.37810 + 12.9701i) q^{94} +(3.45341 - 3.45341i) q^{95} +(-5.12789 + 11.1488i) q^{96} +(1.41030 + 1.41030i) q^{97} +(4.99337 - 4.03418i) q^{98} +(2.22923 - 7.34879i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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