LMFDB - Embedded newform 780.2.g.d.131.26

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [780,2,Mod(131,780)] 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("780.131"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(780, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	780.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$6.22833135766$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.26
Character	$\chi$	$=$	780.131
Dual form			780.2.g.d.131.25

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.995955 + 1.00403i) q^{2} +(1.28760 + 1.15849i) q^{3} +(-0.0161485 + 1.99993i) q^{4} +1.00000i q^{5} +(0.119236 + 2.44659i) q^{6} +0.208113i q^{7} +(-2.02408 + 1.97563i) q^{8} +(0.315820 + 2.98333i) q^{9} +(-1.00403 + 0.995955i) q^{10} +2.52509 q^{11} +(-2.33769 + 2.55641i) q^{12} +1.00000 q^{13} +(-0.208952 + 0.207272i) q^{14} +(-1.15849 + 1.28760i) q^{15} +(-3.99948 - 0.0645918i) q^{16} -5.47450i q^{17} +(-2.68081 + 3.28835i) q^{18} +0.298607i q^{19} +(-1.99993 - 0.0161485i) q^{20} +(-0.241097 + 0.267967i) q^{21} +(2.51487 + 2.53526i) q^{22} +0.0118097 q^{23} +(-4.89494 + 0.198956i) q^{24} -1.00000 q^{25} +(0.995955 + 1.00403i) q^{26} +(-3.04950 + 4.20720i) q^{27} +(-0.416213 - 0.00336072i) q^{28} +3.31988i q^{29} +(-2.44659 + 0.119236i) q^{30} -11.0515i q^{31} +(-3.91845 - 4.07992i) q^{32} +(3.25130 + 2.92528i) q^{33} +(5.49655 - 5.45235i) q^{34} -0.208113 q^{35} +(-5.97157 + 0.583443i) q^{36} -8.22687 q^{37} +(-0.299810 + 0.297399i) q^{38} +(1.28760 + 1.15849i) q^{39} +(-1.97563 - 2.02408i) q^{40} +10.1864i q^{41} +(-0.509168 + 0.0248147i) q^{42} -1.40862i q^{43} +(-0.0407763 + 5.05001i) q^{44} +(-2.98333 + 0.315820i) q^{45} +(0.0117620 + 0.0118573i) q^{46} +12.6976 q^{47} +(-5.07489 - 4.71651i) q^{48} +6.95669 q^{49} +(-0.995955 - 1.00403i) q^{50} +(6.34213 - 7.04895i) q^{51} +(-0.0161485 + 1.99993i) q^{52} +3.88887i q^{53} +(-7.26132 + 1.12840i) q^{54} +2.52509i q^{55} +(-0.411155 - 0.421237i) q^{56} +(-0.345932 + 0.384486i) q^{57} +(-3.33326 + 3.30645i) q^{58} -0.0815526 q^{59} +(-2.55641 - 2.33769i) q^{60} -5.26046 q^{61} +(11.0961 - 11.0068i) q^{62} +(-0.620871 + 0.0657264i) q^{63} +(0.193765 - 7.99765i) q^{64} +1.00000i q^{65} +(0.301082 + 6.17784i) q^{66} -12.3370i q^{67} +(10.9486 + 0.0884047i) q^{68} +(0.0152062 + 0.0136814i) q^{69} +(-0.207272 - 0.208952i) q^{70} +1.76869 q^{71} +(-6.53320 - 5.41454i) q^{72} +6.47719 q^{73} +(-8.19359 - 8.26002i) q^{74} +(-1.28760 - 1.15849i) q^{75} +(-0.597195 - 0.00482205i) q^{76} +0.525504i q^{77} +(0.119236 + 2.44659i) q^{78} -7.40605i q^{79} +(0.0645918 - 3.99948i) q^{80} +(-8.80052 + 1.88439i) q^{81} +(-10.2274 + 10.1452i) q^{82} +7.21026 q^{83} +(-0.532022 - 0.486505i) q^{84} +5.47450 q^{85} +(1.41430 - 1.40292i) q^{86} +(-3.84604 + 4.27468i) q^{87} +(-5.11096 + 4.98864i) q^{88} +12.7672i q^{89} +(-3.28835 - 2.68081i) q^{90} +0.208113i q^{91} +(-0.000190709 + 0.0236187i) q^{92} +(12.8030 - 14.2299i) q^{93} +(12.6462 + 12.7487i) q^{94} -0.298607 q^{95} +(-0.318853 - 9.79277i) q^{96} +8.78578 q^{97} +(6.92855 + 6.98472i) q^{98} +(0.797472 + 7.53316i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 6 q^{4} + 10 q^{6} + 12 q^{9} + 6 q^{10} - 20 q^{12} + 32 q^{13} - 6 q^{16} + 4 q^{18} + 20 q^{21} + 16 q^{22} + 10 q^{24} - 32 q^{25} + 16 q^{28} + 16 q^{33} + 28 q^{34} + 30 q^{36} - 24 q^{37}+ \cdots + 112 q^{97}+O(q^{100}) $ 32 * q + 6 * q^4 + 10 * q^6 + 12 * q^9 + 6 * q^10 - 20 * q^12 + 32 * q^13 - 6 * q^16 + 4 * q^18 + 20 * q^21 + 16 * q^22 + 10 * q^24 - 32 * q^25 + 16 * q^28 + 16 * q^33 + 28 * q^34 + 30 * q^36 - 24 * q^37 + 6 * q^40 + 20 * q^45 - 80 * q^46 - 16 * q^48 + 16 * q^49 + 6 * q^52 + 2 * q^54 - 64 * q^57 - 100 * q^58 + 14 * q^60 + 16 * q^61 + 126 * q^64 + 60 * q^66 - 4 * q^69 - 16 * q^70 - 16 * q^72 - 104 * q^73 + 20 * q^76 + 10 * q^78 - 72 * q^81 - 116 * q^82 + 20 * q^84 + 24 * q^85 - 14 * q^90 + 16 * q^93 + 28 * q^94 - 74 * q^96 + 112 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/780\mathbb{Z}\right)^\times$.

$n$	$157$	$301$	$391$	$521$
$\chi(n)$	$1$	$1$	$-1$	$-1$

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 $

$2$	0.995955	+	1.00403i	0.704246	+	0.709956i
$2$	0.995955	+	1.00403i	0.704246	+	0.709956i
$3$	1.28760	+	1.15849i	0.743395	+	0.668852i
$3$	1.28760	+	1.15849i	0.743395	+	0.668852i
$4$	−0.0161485	+	1.99993i	−0.00807424	+	0.999967i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	0.119236	+	2.44659i	0.0486780	+	0.998815i
$7$			0.208113i			0.0786595i	0.999226	+	0.0393298i	$0.0125223\pi$
$7$			0.208113i			0.0786595i	−0.999226	+	0.0393298i	$0.987478\pi$
$8$	−2.02408	+	1.97563i	−0.715619	+	0.698491i
$9$	0.315820	+	2.98333i	0.105273	+	0.994443i
$10$	−1.00403	+	0.995955i	−0.317502	+	0.314949i
$11$	2.52509			0.761342			0.380671	−	0.924711i	$-0.375693\pi$
$11$	2.52509			0.761342			0.380671	+	0.924711i	$0.375693\pi$
$12$	−2.33769	+	2.55641i	−0.674833	+	0.737971i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	−0.208952	+	0.207272i	−0.0558448	+	0.0553957i
$15$	−1.15849	+	1.28760i	−0.299120	+	0.332457i
$16$	−3.99948	−	0.0645918i	−0.999870	−	0.0161479i
$17$		−	5.47450i		−	1.32776i	−0.747839	−	0.663880i	$-0.768909\pi$
$17$		−	5.47450i		−	1.32776i	0.747839	−	0.663880i	$-0.231091\pi$
$18$	−2.68081	+	3.28835i	−0.631872	+	0.775072i
$19$			0.298607i			0.0685052i	0.999413	+	0.0342526i	$0.0109051\pi$
$19$			0.298607i			0.0685052i	−0.999413	+	0.0342526i	$0.989095\pi$
$20$	−1.99993	−	0.0161485i	−0.447199	−	0.00361091i
$21$	−0.241097	+	0.267967i	−0.0526116	+	0.0584751i
$22$	2.51487	+	2.53526i	0.536172	+	0.540519i
$23$	0.0118097			0.00246250			0.00123125	−	0.999999i	$-0.499608\pi$
$23$	0.0118097			0.00246250			0.00123125	+	0.999999i	$0.499608\pi$
$24$	−4.89494	+	0.198956i	−0.999175	+	0.0406117i
$25$	−1.00000			−0.200000
$26$	0.995955	+	1.00403i	0.195323	+	0.196906i
$27$	−3.04950	+	4.20720i	−0.586876	+	0.809677i
$28$	−0.416213	−	0.00336072i	−0.0786569	−	0.000635116i
$29$			3.31988i			0.616487i	0.951308	+	0.308243i	$0.0997411\pi$
$29$			3.31988i			0.616487i	−0.951308	+	0.308243i	$0.900259\pi$
$30$	−2.44659	+	0.119236i	−0.446683	+	0.0217694i
$31$		−	11.0515i		−	1.98491i	−0.122598	−	0.992456i	$-0.539123\pi$
$31$		−	11.0515i		−	1.98491i	0.122598	−	0.992456i	$-0.460877\pi$
$32$	−3.91845	−	4.07992i	−0.692690	−	0.721235i
$33$	3.25130	+	2.92528i	0.565978	+	0.509225i
$34$	5.49655	−	5.45235i	0.942651	−	0.935070i
$35$	−0.208113			−0.0351776
$36$	−5.97157	+	0.583443i	−0.995261	+	0.0972405i
$37$	−8.22687			−1.35249			−0.676245	−	0.736677i	$-0.736394\pi$
$37$	−8.22687			−1.35249			−0.676245	+	0.736677i	$0.736394\pi$
$38$	−0.299810	+	0.297399i	−0.0486357	+	0.0482445i
$39$	1.28760	+	1.15849i	0.206181	+	0.185506i
$40$	−1.97563	−	2.02408i	−0.312375	−	0.320034i
$41$			10.1864i			1.59085i	0.606054	+	0.795423i	$0.292751\pi$
$41$			10.1864i			1.59085i	−0.606054	+	0.795423i	$0.707249\pi$
$42$	−0.509168	+	0.0248147i	−0.0785663	+	0.00382898i
$43$		−	1.40862i		−	0.214813i	−0.994215	−	0.107406i	$-0.965745\pi$
$43$		−	1.40862i		−	0.214813i	0.994215	−	0.107406i	$-0.0342546\pi$
$44$	−0.0407763	+	5.05001i	−0.00614726	+	0.761317i
$45$	−2.98333	+	0.315820i	−0.444729	+	0.0470797i
$46$	0.0117620	+	0.0118573i	0.00173421	+	0.00174827i
$47$	12.6976			1.85213			0.926065	−	0.377364i	$-0.123169\pi$
$47$	12.6976			1.85213			0.926065	+	0.377364i	$0.123169\pi$
$48$	−5.07489	−	4.71651i	−0.732498	−	0.680769i
$49$	6.95669			0.993813
$50$	−0.995955	−	1.00403i	−0.140849	−	0.141991i
$51$	6.34213	−	7.04895i	0.888075	−	0.987051i
$52$	−0.0161485	+	1.99993i	−0.00223939	+	0.277341i
$53$			3.88887i			0.534177i	0.963672	+	0.267088i	$0.0860616\pi$
$53$			3.88887i			0.534177i	−0.963672	+	0.267088i	$0.913938\pi$
$54$	−7.26132	+	1.12840i	−0.988140	+	0.153556i
$55$			2.52509i			0.340482i
$56$	−0.411155	−	0.421237i	−0.0549430	−	0.0562902i
$57$	−0.345932	+	0.384486i	−0.0458199	+	0.0509265i
$58$	−3.33326	+	3.30645i	−0.437678	+	0.434158i
$59$	−0.0815526			−0.0106172			−0.00530862	−	0.999986i	$-0.501690\pi$
$59$	−0.0815526			−0.0106172			−0.00530862	+	0.999986i	$0.501690\pi$
$60$	−2.55641	−	2.33769i	−0.330031	−	0.301794i
$61$	−5.26046			−0.673532			−0.336766	−	0.941588i	$-0.609333\pi$
$61$	−5.26046			−0.673532			−0.336766	+	0.941588i	$0.609333\pi$
$62$	11.0961	−	11.0068i	1.40920	−	1.39787i
$63$	−0.620871	+	0.0657264i	−0.0782224	+	0.00828075i
$64$	0.193765	−	7.99765i	0.0242206	−	0.999707i
$65$			1.00000i			0.124035i
$66$	0.301082	+	6.17784i	0.0370606	+	0.760439i
$67$		−	12.3370i		−	1.50721i	−0.657328	−	0.753604i	$-0.728313\pi$
$67$		−	12.3370i		−	1.50721i	0.657328	−	0.753604i	$-0.271687\pi$
$68$	10.9486	+	0.0884047i	1.32772	+	0.0107207i
$69$	0.0152062	+	0.0136814i	0.00183061	+	0.00164705i
$70$	−0.207272	−	0.208952i	−0.0247737	−	0.0249745i
$71$	1.76869			0.209905			0.104953	−	0.994477i	$-0.466531\pi$
$71$	1.76869			0.209905			0.104953	+	0.994477i	$0.466531\pi$
$72$	−6.53320	−	5.41454i	−0.769945	−	0.638110i
$73$	6.47719			0.758098			0.379049	−	0.925377i	$-0.376251\pi$
$73$	6.47719			0.758098			0.379049	+	0.925377i	$0.376251\pi$
$74$	−8.19359	−	8.26002i	−0.952486	−	0.960208i
$75$	−1.28760	−	1.15849i	−0.148679	−	0.133770i
$76$	−0.597195	−	0.00482205i	−0.0685030	−	0.000553127i
$77$			0.525504i			0.0598868i
$78$	0.119236	+	2.44659i	0.0135008	+	0.277021i
$79$		−	7.40605i		−	0.833245i	−0.909080	−	0.416623i	$-0.863214\pi$
$79$		−	7.40605i		−	0.833245i	0.909080	−	0.416623i	$-0.136786\pi$
$80$	0.0645918	−	3.99948i	0.00722158	−	0.447155i
$81$	−8.80052	+	1.88439i	−0.977835	+	0.209377i
$82$	−10.2274	+	10.1452i	−1.12943	+	1.12035i
$83$	7.21026			0.791429			0.395714	−	0.918374i	$-0.370497\pi$
$83$	7.21026			0.791429			0.395714	+	0.918374i	$0.370497\pi$
$84$	−0.532022	−	0.486505i	−0.0580484	−	0.0530820i
$85$	5.47450			0.593792
$86$	1.41430	−	1.40292i	0.152508	−	0.151281i
$87$	−3.84604	+	4.27468i	−0.412338	+	0.458293i
$88$	−5.11096	+	4.98864i	−0.544831	+	0.531791i
$89$			12.7672i			1.35332i	0.736296	+	0.676660i	$0.236573\pi$
$89$			12.7672i			1.35332i	−0.736296	+	0.676660i	$0.763427\pi$
$90$	−3.28835	−	2.68081i	−0.346623	−	0.282582i
$91$			0.208113i			0.0218162i
$92$	−0.000190709		0.0236187i	−1.98828e−5		0.00246242i
$93$	12.8030	−	14.2299i	1.32761	−	1.47557i
$94$	12.6462	+	12.7487i	1.30436	+	1.31493i
$95$	−0.298607			−0.0306365
$96$	−0.318853	−	9.79277i	−0.0325428	−	0.999470i
$97$	8.78578			0.892060			0.446030	−	0.895018i	$-0.352837\pi$
$97$	8.78578			0.892060			0.446030	+	0.895018i	$0.352837\pi$
$98$	6.92855	+	6.98472i	0.699889	+	0.705563i
$99$	0.797472	+	7.53316i	0.0801490	+	0.757111i
$100$	0.0161485	−	1.99993i	0.00161485	−	0.199993i
$101$		−	9.80391i		−	0.975525i	−0.872976	−	0.487763i	$-0.837813\pi$
$101$		−	9.80391i		−	0.975525i	0.872976	−	0.487763i	$-0.162187\pi$
$102$	13.3938	−	0.652758i	1.32619	−	0.0646327i
$103$			3.34007i			0.329107i	0.986368	+	0.164554i	$0.0526184\pi$
$103$			3.34007i			0.329107i	−0.986368	+	0.164554i	$0.947382\pi$
$104$	−2.02408	+	1.97563i	−0.198477	+	0.193727i
$105$	−0.267967	−	0.241097i	−0.0261509	−	0.0235286i
$106$	−3.90453	+	3.87313i	−0.379242	+	0.376192i
$107$	7.32200			0.707845			0.353922	−	0.935275i	$-0.384848\pi$
$107$	7.32200			0.707845			0.353922	+	0.935275i	$0.384848\pi$
$108$	−8.36489	−	6.16674i	−0.804912	−	0.593394i
$109$	−9.87309			−0.945670			−0.472835	−	0.881151i	$-0.656769\pi$
$109$	−9.87309			−0.945670			−0.472835	+	0.881151i	$0.656769\pi$
$110$	−2.53526	+	2.51487i	−0.241727	+	0.239784i
$111$	−10.5929	−	9.53072i	−1.00543	−	0.904616i
$112$	0.0134424	−	0.832345i	0.00127019	−	0.0786493i
$113$			11.6443i			1.09540i	0.836674	+	0.547701i	$0.184497\pi$
$113$			11.6443i			1.09540i	−0.836674	+	0.547701i	$0.815503\pi$
$114$	−0.730568	+	0.0356048i	−0.0684240	+	0.00333469i
$115$			0.0118097i			0.00110126i
$116$	−6.63955	−	0.0536110i	−0.616467	−	0.00497766i
$117$	0.315820	+	2.98333i	0.0291976	+	0.275809i
$118$	−0.0812227	−	0.0818811i	−0.00747715	−	0.00753777i
$119$	1.13932			0.104441
$120$	−0.198956	−	4.89494i	−0.0181621	−	0.446845i
$121$	−4.62394			−0.420358
$122$	−5.23917	−	5.28165i	−0.474333	−	0.478178i
$123$	−11.8008	+	13.1160i	−1.06404	+	1.18263i
$124$	22.1023	+	0.178465i	1.98485	+	0.0160267i
$125$		−	1.00000i		−	0.0894427i
$126$	−0.684351	−	0.557912i	−0.0609668	−	0.0497028i
$127$		−	6.82558i		−	0.605672i	−0.953043	−	0.302836i	$-0.902067\pi$
$127$		−	6.82558i		−	0.605672i	0.953043	−	0.302836i	$-0.0979335\pi$
$128$	8.22286	−	7.77075i	0.726805	−	0.686844i
$129$	1.63187	−	1.81374i	0.143678	−	0.159691i
$130$	−1.00403	+	0.995955i	−0.0880592	+	0.0873510i
$131$	−1.73842			−0.151886			−0.0759432	−	0.997112i	$-0.524197\pi$
$131$	−1.73842			−0.151886			−0.0759432	+	0.997112i	$0.524197\pi$
$132$	−5.90287	+	6.45514i	−0.513779	+	0.561848i
$133$	−0.0621442			−0.00538859
$134$	12.3867	−	12.2871i	1.07005	−	1.06145i
$135$	−4.20720	−	3.04950i	−0.362098	−	0.262459i
$136$	10.8156	+	11.0808i	0.927429	+	0.950170i
$137$		−	19.8462i		−	1.69558i	−0.530335	−	0.847788i	$-0.677934\pi$
$137$		−	19.8462i		−	1.69558i	0.530335	−	0.847788i	$-0.322066\pi$
$138$	0.00140815	+	0.0288935i	0.000119869	+	0.00245958i
$139$			5.56298i			0.471846i	0.971772	+	0.235923i	$0.0758113\pi$
$139$			5.56298i			0.471846i	−0.971772	+	0.235923i	$0.924189\pi$
$140$	0.00336072	−	0.416213i	0.000284032	−	0.0351765i
$141$	16.3494	+	14.7100i	1.37686	+	1.23880i
$142$	1.76154	+	1.77582i	0.147825	+	0.149023i
$143$	2.52509			0.211158
$144$	−1.07042	−	11.9522i	−0.0892014	−	0.996014i
$145$	−3.31988			−0.275701
$146$	6.45099	+	6.50329i	0.533888	+	0.538216i
$147$	8.95742	+	8.05923i	0.738796	+	0.664714i
$148$	0.132851	−	16.4532i	0.0109203	−	1.35245i
$149$			9.64297i			0.789983i	0.918685	+	0.394991i	$0.129252\pi$
$149$			9.64297i			0.789983i	−0.918685	+	0.394991i	$0.870748\pi$
$150$	−0.119236	−	2.44659i	−0.00973559	−	0.199763i
$151$		−	0.566350i		−	0.0460889i	−0.999734	−	0.0230445i	$-0.992664\pi$
$151$		−	0.566350i		−	0.0460889i	0.999734	−	0.0230445i	$-0.00733593\pi$
$152$	−0.589938	−	0.604404i	−0.0478503	−	0.0490236i
$153$	16.3322	−	1.72895i	1.32038	−	0.139778i
$154$	−0.527622	+	0.523379i	−0.0425170	+	0.0421750i
$155$	11.0515			0.887680
$156$	−2.33769	+	2.55641i	−0.187165	+	0.204676i
$157$	−6.81815			−0.544147			−0.272074	−	0.962276i	$-0.587709\pi$
$157$	−6.81815			−0.544147			−0.272074	+	0.962276i	$0.587709\pi$
$158$	7.43589	−	7.37609i	0.591567	−	0.586810i
$159$	−4.50520	+	5.00730i	−0.357285	+	0.397105i
$160$	4.07992	−	3.91845i	0.322546	−	0.309780i
$161$			0.00245776i			0.000193699i
$162$	−10.6569	−	6.95921i	−0.837285	−	0.546767i
$163$		−	9.97769i		−	0.781513i	−0.920494	−	0.390756i	$-0.872213\pi$
$163$		−	9.97769i		−	0.781513i	0.920494	−	0.390756i	$-0.127787\pi$
$164$	−20.3721	−	0.164495i	−1.59079	−	0.0128449i
$165$	−2.92528	+	3.25130i	−0.227732	+	0.253113i
$166$	7.18109	+	7.23931i	0.557361	+	0.561880i
$167$	−14.2261			−1.10085			−0.550426	−	0.834884i	$-0.685535\pi$
$167$	−14.2261			−1.10085			−0.550426	+	0.834884i	$0.685535\pi$
$168$	−0.0414054	−	1.01870i	−0.00319450	−	0.0785946i
$169$	1.00000			0.0769231
$170$	5.45235	+	5.49655i	0.418176	+	0.421566i
$171$	−0.890844	+	0.0943061i	−0.0681245	+	0.00721177i
$172$	2.81715	+	0.0227471i	0.214806	+	0.00173445i
$173$			2.62887i			0.199869i	0.994994	+	0.0999346i	$0.0318633\pi$
$173$			2.62887i			0.199869i	−0.994994	+	0.0999346i	$0.968137\pi$
$174$	−8.12238	+	0.395850i	−0.615756	+	0.0300093i
$175$		−	0.208113i		−	0.0157319i
$176$	−10.0990	−	0.163100i	−0.761243	−	0.0122941i
$177$	−0.105007	−	0.0944775i	−0.00789281	−	0.00710136i
$178$	−12.8186	+	12.7155i	−0.960797	+	0.953071i
$179$	12.9002			0.964210			0.482105	−	0.876113i	$-0.339872\pi$
$179$	12.9002			0.964210			0.482105	+	0.876113i	$0.339872\pi$
$180$	−0.583443	−	5.97157i	−0.0434873	−	0.445094i
$181$	−12.7040			−0.944278			−0.472139	−	0.881524i	$-0.656518\pi$
$181$	−12.7040			−0.944278			−0.472139	+	0.881524i	$0.656518\pi$
$182$	−0.208952	+	0.207272i	−0.0154886	+	0.0153640i
$183$	−6.77335	−	6.09416i	−0.500701	−	0.450494i
$184$	−0.0239038	+	0.0233317i	−0.00176221	+	0.00172003i
$185$		−	8.22687i		−	0.604852i
$186$	27.0385	−	1.31774i	1.98256	−	0.0966215i
$187$		−	13.8236i		−	1.01088i
$188$	−0.205046	+	25.3943i	−0.0149545	+	1.85207i
$189$	−0.875576	−	0.634641i	−0.0636888	−	0.0461634i
$190$	−0.297399	−	0.299810i	−0.0215756	−	0.0217505i
$191$	−25.1309			−1.81841			−0.909204	−	0.416351i	$-0.863309\pi$
$191$	−25.1309			−1.81841			−0.909204	+	0.416351i	$0.863309\pi$
$192$	9.51466	−	10.0733i	0.686662	−	0.726977i
$193$	19.6770			1.41638			0.708190	−	0.706021i	$-0.249512\pi$
$193$	19.6770			1.41638			0.708190	+	0.706021i	$0.249512\pi$
$194$	8.75023	+	8.82117i	0.628230	+	0.633323i
$195$	−1.15849	+	1.28760i	−0.0829609	+	0.0922068i
$196$	−0.112340	+	13.9129i	−0.00802428	+	0.993780i
$197$		−	11.7538i		−	0.837425i	−0.908119	−	0.418712i	$-0.862482\pi$
$197$		−	11.7538i		−	0.837425i	0.908119	−	0.418712i	$-0.137518\pi$
$198$	−6.76927	+	8.30338i	−0.481071	+	0.590095i
$199$			9.07048i			0.642989i	0.946911	+	0.321495i	$0.104185\pi$
$199$			9.07048i			0.642989i	−0.946911	+	0.321495i	$0.895815\pi$
$200$	2.02408	−	1.97563i	0.143124	−	0.139698i
$201$	14.2923	−	15.8851i	1.00810	−	1.12045i
$202$	9.84341	−	9.76425i	0.692580	−	0.687010i
$203$	−0.690912			−0.0484925
$204$	13.9950	+	12.7977i	0.979848	+	0.896016i
$205$	−10.1864			−0.711448
$206$	−3.35353	+	3.32656i	−0.233652	+	0.231773i
$207$	0.00372975	+	0.0352323i	0.000259235	+	0.00244882i
$208$	−3.99948	−	0.0645918i	−0.277314	−	0.00447863i
$209$			0.754009i			0.0521559i
$210$	−0.0248147	−	0.509168i	−0.00171237	−	0.0351359i
$211$			19.4794i			1.34102i	0.741902	+	0.670508i	$0.233924\pi$
$211$			19.4794i			1.34102i	−0.741902	+	0.670508i	$0.766076\pi$
$212$	−7.77748	−	0.0627992i	−0.534159	−	0.00431307i
$213$	2.27736	+	2.04900i	0.156042	+	0.140395i
$214$	7.29238	+	7.35150i	0.498497	+	0.502538i
$215$	1.40862			0.0960672
$216$	−2.13947	−	14.5404i	−0.145573	−	0.989348i
$217$	2.29997			0.156132
$218$	−9.83315	−	9.91287i	−0.665985	−	0.671384i
$219$	8.34003	+	7.50374i	0.563567	+	0.507056i
$220$	−5.05001	−	0.0407763i	−0.340471	−	0.00274914i
$221$		−	5.47450i		−	0.368254i
$222$	−0.980941	−	20.1278i	−0.0658364	−	1.35089i
$223$		−	6.68238i		−	0.447485i	−0.974648	−	0.223742i	$-0.928173\pi$
$223$		−	6.68238i		−	0.447485i	0.974648	−	0.223742i	$-0.0718275\pi$
$224$	0.849087	−	0.815482i	0.0567320	−	0.0544867i
$225$	−0.315820	−	2.98333i	−0.0210547	−	0.198889i
$226$	−11.6912	+	11.5972i	−0.777687	+	0.771433i
$227$	−6.87009			−0.455984			−0.227992	−	0.973663i	$-0.573216\pi$
$227$	−6.87009			−0.455984			−0.227992	+	0.973663i	$0.573216\pi$
$228$	−0.763361	−	0.698051i	−0.0505548	−	0.0462296i
$229$	10.3393			0.683238			0.341619	−	0.939838i	$-0.389025\pi$
$229$	10.3393			0.683238			0.341619	+	0.939838i	$0.389025\pi$
$230$	−0.0118573	+	0.0117620i	−0.000781848	+	0.000775560i
$231$	−0.608790	+	0.676639i	−0.0400554	+	0.0445196i
$232$	−6.55886	−	6.71969i	−0.430610	−	0.441169i
$233$		−	12.0890i		−	0.791974i	−0.918256	−	0.395987i	$-0.870403\pi$
$233$		−	12.0890i		−	0.791974i	0.918256	−	0.395987i	$-0.129597\pi$
$234$	−2.68081	+	3.28835i	−0.175250	+	0.214966i
$235$			12.6976i			0.828298i
$236$	0.00131695	−	0.163100i	8.57261e−5	−	0.0106169i
$237$	8.57980	−	9.53601i	0.557318	−	0.619431i
$238$	1.13471	+	1.14391i	0.0735522	+	0.0741485i
$239$	27.2110			1.76013			0.880066	−	0.474851i	$-0.157498\pi$
$239$	27.2110			1.76013			0.880066	+	0.474851i	$0.157498\pi$
$240$	4.71651	−	5.07489i	0.304449	−	0.327583i
$241$	2.36214			0.152159			0.0760795	−	0.997102i	$-0.475760\pi$
$241$	2.36214			0.152159			0.0760795	+	0.997102i	$0.475760\pi$
$242$	−4.60524	−	4.64257i	−0.296036	−	0.298436i
$243$	−13.5146	−	7.76894i	−0.866960	−	0.498378i
$244$	0.0849483	−	10.5206i	0.00543826	−	0.673510i
$245$			6.95669i			0.444447i
$246$	−24.9219	+	1.21459i	−1.58896	+	0.0774392i
$247$			0.298607i			0.0189999i
$248$	21.8337	+	22.3691i	1.38644	+	1.42044i
$249$	9.28392	+	8.35299i	0.588345	+	0.529349i
$250$	1.00403	−	0.995955i	0.0635004	−	0.0629897i
$251$	−6.53665			−0.412590			−0.206295	−	0.978490i	$-0.566141\pi$
$251$	−6.53665			−0.412590			−0.206295	+	0.978490i	$0.566141\pi$
$252$	−0.121422	−	1.24276i	−0.00764889	−	0.0782867i
$253$	0.0298206			0.00187480
$254$	6.85308	−	6.79797i	0.430001	−	0.426543i
$255$	7.04895	+	6.34213i	0.441423	+	0.397159i
$256$	15.9917	+	0.516667i	0.999478	+	0.0322917i
$257$		−	7.67420i		−	0.478704i	−0.970933	−	0.239352i	$-0.923065\pi$
$257$		−	7.67420i		−	0.478704i	0.970933	−	0.239352i	$-0.0769349\pi$
$258$	3.44631	−	0.167959i	0.214558	−	0.0104566i
$259$		−	1.71212i		−	0.106386i
$260$	−1.99993	−	0.0161485i	−0.124031	−	0.00100149i
$261$	−9.90430	+	1.04848i	−0.613061	+	0.0648996i
$262$	−1.73139	−	1.74542i	−0.106965	−	0.107833i
$263$	−15.8615			−0.978062			−0.489031	−	0.872266i	$-0.662650\pi$
$263$	−15.8615			−0.978062			−0.489031	+	0.872266i	$0.662650\pi$
$264$	−12.3601	+	0.502381i	−0.760714	+	0.0309194i
$265$	−3.88887			−0.238891
$266$	−0.0618928	−	0.0623946i	−0.00379489	−	0.00382566i
$267$	−14.7906	+	16.4390i	−0.905171	+	1.00605i
$268$	24.6733	+	0.199224i	1.50716	+	0.0121696i
$269$			19.0683i			1.16262i	0.813683	+	0.581308i	$0.197459\pi$
$269$			19.0683i			1.16262i	−0.813683	+	0.581308i	$0.802541\pi$
$270$	−1.12840	−	7.26132i	−0.0686723	−	0.441910i
$271$		−	29.7746i		−	1.80868i	−0.426817	−	0.904338i	$-0.640365\pi$
$271$		−	29.7746i		−	1.80868i	0.426817	−	0.904338i	$-0.359635\pi$
$272$	−0.353607	+	21.8951i	−0.0214406	+	1.32759i
$273$	−0.241097	+	0.267967i	−0.0145918	+	0.0162181i
$274$	19.9262	−	19.7659i	1.20378	−	1.19410i
$275$	−2.52509			−0.152268
$276$	−0.0276075	+	0.0301905i	−0.00166178	+	0.00181725i
$277$	−30.3793			−1.82532			−0.912658	−	0.408724i	$-0.865974\pi$
$277$	−30.3793			−1.82532			−0.912658	+	0.408724i	$0.865974\pi$
$278$	−5.58539	+	5.54048i	−0.334990	+	0.332296i
$279$	32.9704	−	3.49029i	1.97388	−	0.208958i
$280$	0.421237	−	0.411155i	0.0251738	−	0.0245712i
$281$		−	31.1314i		−	1.85714i	−0.371154	−	0.928571i	$-0.621038\pi$
$281$		−	31.1314i		−	1.85714i	0.371154	−	0.928571i	$-0.378962\pi$
$282$	1.51401	+	31.0657i	0.0901579	+	1.84993i
$283$		−	6.05544i		−	0.359958i	−0.983670	−	0.179979i	$-0.942397\pi$
$283$		−	6.05544i		−	0.359958i	0.983670	−	0.179979i	$-0.0576030\pi$
$284$	−0.0285617	+	3.53727i	−0.00169482	+	0.209898i
$285$	−0.384486	−	0.345932i	−0.0227750	−	0.0204913i
$286$	2.51487	+	2.53526i	0.148707	+	0.149913i
$287$	−2.11992			−0.125135
$288$	10.9342	−	12.9785i	0.644306	−	0.764768i
$289$	−12.9701			−0.762947
$290$	−3.30645	−	3.33326i	−0.194162	−	0.195736i
$291$	11.3126	+	10.1782i	0.663153	+	0.596657i
$292$	−0.104597	+	12.9540i	−0.00612106	+	0.758074i
$293$		−	12.4677i		−	0.728371i	−0.931326	−	0.364185i	$-0.881347\pi$
$293$		−	12.4677i		−	0.728371i	0.931326	−	0.364185i	$-0.118653\pi$
$294$	0.829489	+	17.0201i	0.0483768	+	0.992635i
$295$		−	0.0815526i		−	0.00474817i
$296$	16.6518	−	16.2533i	0.967867	−	0.944702i
$297$	−7.70024	+	10.6236i	−0.446813	+	0.616441i
$298$	−9.68182	+	9.60396i	−0.560853	+	0.556343i
$299$	0.0118097			0.000682974
$300$	2.33769	−	2.55641i	0.134967	−	0.147594i
$301$	0.293153			0.0168971
$302$	0.568632	−	0.564059i	0.0327211	−	0.0324579i
$303$	11.3577	−	12.6235i	0.652482	−	0.725201i
$304$	0.0192876	−	1.19427i	0.00110622	−	0.0684963i
$305$		−	5.26046i		−	0.301213i
$306$	18.0021	+	14.6761i	1.02911	+	0.838975i
$307$			13.1547i			0.750776i	0.926868	+	0.375388i	$0.122490\pi$
$307$			13.1547i			0.750776i	−0.926868	+	0.375388i	$0.877510\pi$
$308$	−1.05097	−	0.00848609i	−0.0598848	−	0.000483540i
$309$	−3.86943	+	4.30067i	−0.220124	+	0.244657i
$310$	11.0068	+	11.0961i	0.625145	+	0.630213i
$311$	−10.0408			−0.569362			−0.284681	−	0.958622i	$-0.591888\pi$
$311$	−10.0408			−0.569362			−0.284681	+	0.958622i	$0.591888\pi$
$312$	−4.89494	+	0.198956i	−0.277121	+	0.0112637i
$313$	−22.8593			−1.29208			−0.646042	−	0.763302i	$-0.723577\pi$
$313$	−22.8593			−1.29208			−0.646042	+	0.763302i	$0.723577\pi$
$314$	−6.79056	−	6.84562i	−0.383214	−	0.386320i
$315$	−0.0657264	−	0.620871i	−0.00370326	−	0.0349821i
$316$	14.8116	+	0.119596i	0.833218	+	0.00672782i
$317$		−	5.23245i		−	0.293884i	−0.989145	−	0.146942i	$-0.953057\pi$
$317$		−	5.23245i		−	0.293884i	0.989145	−	0.146942i	$-0.0469431\pi$
$318$	−9.51444	+	0.463693i	−0.533544	+	0.0260026i
$319$			8.38299i			0.469357i
$320$	7.99765	+	0.193765i	0.447082	+	0.0108318i
$321$	9.42780	+	8.48244i	0.526208	+	0.473444i
$322$	−0.00246767	+	0.00244782i	−0.000137518	+	0.000136412i
$323$	1.63472			0.0909585
$324$	−3.62654	−	17.6309i	−0.201475	−	0.979494i
$325$	−1.00000			−0.0554700
$326$	10.0179	−	9.93733i	0.554840	−	0.550378i
$327$	−12.7126	−	11.4378i	−0.703007	−	0.632514i
$328$	−20.1245	−	20.6180i	−1.11119	−	1.13844i
$329$			2.64253i			0.145688i
$330$	−6.17784	+	0.301082i	−0.340079	+	0.0165740i
$331$			28.7723i			1.58147i	0.612159	+	0.790735i	$0.290301\pi$
$331$			28.7723i			1.58147i	−0.612159	+	0.790735i	$0.709699\pi$
$332$	−0.116435	+	14.4201i	−0.00639018	+	0.791403i
$333$	−2.59821	−	24.5435i	−0.142381	−	1.34497i
$334$	−14.1686	−	14.2835i	−0.775271	−	0.781556i
$335$	12.3370			0.674044
$336$	0.981569	−	1.05615i	0.0535490	−	0.0576179i
$337$	−28.0835			−1.52981			−0.764903	−	0.644145i	$-0.777213\pi$
$337$	−28.0835			−1.52981			−0.764903	+	0.644145i	$0.777213\pi$
$338$	0.995955	+	1.00403i	0.0541728	+	0.0546120i
$339$	−13.4897	+	14.9932i	−0.732662	+	0.814317i
$340$	−0.0884047	+	10.9486i	−0.00479442	+	0.593773i
$341$		−	27.9061i		−	1.51120i
$342$	−0.981926	−	0.800509i	−0.0530965	−	0.0432865i
$343$			2.90458i			0.156832i
$344$	2.78292	+	2.85116i	0.150045	+	0.153724i
$345$	−0.0136814	+	0.0152062i	−0.000736582	+	0.000818674i
$346$	−2.63946	+	2.61823i	−0.141898	+	0.140757i
$347$	22.4514			1.20526			0.602628	−	0.798023i	$-0.294120\pi$
$347$	22.4514			1.20526			0.602628	+	0.798023i	$0.294120\pi$
$348$	−8.48696	−	7.76085i	−0.454949	−	0.416025i
$349$	−21.8617			−1.17023			−0.585114	−	0.810951i	$-0.698950\pi$
$349$	−21.8617			−1.17023			−0.585114	+	0.810951i	$0.698950\pi$
$350$	0.208952	−	0.207272i	0.0111690	−	0.0110791i
$351$	−3.04950	+	4.20720i	−0.162770	+	0.224564i
$352$	−9.89442	−	10.3022i	−0.527374	−	0.549107i
$353$			7.20477i			0.383471i	0.981447	+	0.191736i	$0.0614116\pi$
$353$			7.20477i			0.383471i	−0.981447	+	0.191736i	$0.938588\pi$
$354$	−0.00972401	−	0.199525i	−0.000516826	−	0.0106047i
$355$			1.76869i			0.0938724i
$356$	−25.5336	−	0.206171i	−1.35328	−	0.0109270i
$357$	1.46698	+	1.31988i	0.0776409	+	0.0698556i
$358$	12.8481	+	12.9522i	0.679041	+	0.684546i
$359$	−21.8194			−1.15159			−0.575793	−	0.817596i	$-0.695306\pi$
$359$	−21.8194			−1.15159			−0.575793	+	0.817596i	$0.695306\pi$
$360$	5.41454	−	6.53320i	0.285371	−	0.344330i
$361$	18.9108			0.995307
$362$	−12.6526	−	12.7551i	−0.665004	−	0.670395i
$363$	−5.95378	−	5.35677i	−0.312492	−	0.281158i
$364$	−0.416213	−	0.00336072i	−0.0218155	−	0.000176149i
$365$			6.47719i			0.339032i
$366$	−0.627236	−	12.8702i	−0.0327862	−	0.672734i
$367$			0.193078i			0.0100786i	0.999987	+	0.00503930i	$0.00160406\pi$
$367$			0.193078i			0.0100786i	−0.999987	+	0.00503930i	$0.998396\pi$
$368$	−0.0472328		0.000762812i	−0.00246218		3.97643e-5i
$369$	−30.3894	+	3.21706i	−1.58201	+	0.167474i
$370$	8.26002	−	8.19359i	0.429418	−	0.425965i
$371$	−0.809325			−0.0420181
$372$	28.2522	+	25.8350i	1.46481	+	1.33948i
$373$	7.40910			0.383629			0.191814	−	0.981431i	$-0.438563\pi$
$373$	7.40910			0.383629			0.191814	+	0.981431i	$0.438563\pi$
$374$	13.8793	−	13.7676i	0.717680	−	0.711908i
$375$	1.15849	−	1.28760i	0.0598240	−	0.0664913i
$376$	−25.7008	+	25.0857i	−1.32542	+	1.29370i
$377$			3.31988i			0.170983i
$378$	−0.234836	−	1.51118i	−0.0120786	−	0.0777266i
$379$			25.8698i			1.32884i	0.747359	+	0.664420i	$0.231321\pi$
$379$			25.8698i			1.32884i	−0.747359	+	0.664420i	$0.768679\pi$
$380$	0.00482205	−	0.597195i	0.000247366	−	0.0306355i
$381$	7.90734	−	8.78861i	0.405105	−	0.450254i
$382$	−25.0292	−	25.2322i	−1.28061	−	1.29099i
$383$	−11.2119			−0.572904			−0.286452	−	0.958095i	$-0.592476\pi$
$383$	−11.2119			−0.572904			−0.286452	+	0.958095i	$0.592476\pi$
$384$	19.5900	−	0.479547i	0.999701	−	0.0244718i
$385$	−0.525504			−0.0267822
$386$	19.5974	+	19.7563i	0.997481	+	1.00557i
$387$	4.20238	−	0.444871i	0.213619	−	0.0226141i
$388$	−0.141877	+	17.5710i	−0.00720271	+	0.892031i
$389$			20.2983i			1.02916i	0.857441	+	0.514582i	$0.172053\pi$
$389$			20.2983i			1.02916i	−0.857441	+	0.514582i	$0.827947\pi$
$390$	−2.44659	+	0.119236i	−0.123888	+	0.00603776i
$391$		−	0.0646523i		−	0.00326961i
$392$	−14.0809	+	13.7438i	−0.711191	+	0.694169i
$393$	−2.23839	−	2.01393i	−0.112912	−	0.101590i
$394$	11.8012	−	11.7063i	0.594535	−	0.589753i
$395$	7.40605			0.372639
$396$	−15.0787	+	1.47324i	−0.757734	+	0.0740333i
$397$	−5.53330			−0.277708			−0.138854	−	0.990313i	$-0.544342\pi$
$397$	−5.53330			−0.277708			−0.138854	+	0.990313i	$0.544342\pi$
$398$	−9.10703	+	9.03379i	−0.456494	+	0.452823i
$399$	−0.0800168	−	0.0719932i	−0.00400585	−	0.00360417i
$400$	3.99948	+	0.0645918i	0.199974	+	0.00322959i
$401$			23.4222i			1.16965i	0.811161	+	0.584823i	$0.198836\pi$
$401$			23.4222i			1.16965i	−0.811161	+	0.584823i	$0.801164\pi$
$402$	30.1836	−	1.47102i	1.50542	−	0.0733679i
$403$		−	11.0515i		−	0.550516i
$404$	19.6072	+	0.158318i	0.975494	+	0.00787662i
$405$	−1.88439	−	8.80052i	−0.0936361	−	0.437301i
$406$	−0.688117	−	0.693696i	−0.0341507	−	0.0344276i
$407$	−20.7736			−1.02971
$408$	1.08918	+	26.7973i	0.0539226	+	1.32666i
$409$	−15.3701			−0.760004			−0.380002	−	0.924986i	$-0.624077\pi$
$409$	−15.3701			−0.760004			−0.380002	+	0.924986i	$0.624077\pi$
$410$	−10.1452	−	10.2274i	−0.501035	−	0.505097i
$411$	22.9916	−	25.5540i	1.13409	−	1.26048i
$412$	−6.67993	−	0.0539371i	−0.329097	−	0.00265729i
$413$		−	0.0169722i		−	0.000835147i
$414$	−0.0316596	+	0.0388346i	−0.00155599	+	0.00190862i
$415$			7.21026i			0.353938i
$416$	−3.91845	−	4.07992i	−0.192118	−	0.200035i
$417$	−6.44464	+	7.16289i	−0.315595	+	0.350768i
$418$	−0.757047	+	0.750959i	−0.0370284	+	0.0367306i
$419$	−27.3974			−1.33845			−0.669226	−	0.743059i	$-0.733374\pi$
$419$	−27.3974			−1.33845			−0.669226	+	0.743059i	$0.733374\pi$
$420$	0.486505	−	0.532022i	0.0237390	−	0.0259600i
$421$	−7.39446			−0.360384			−0.180192	−	0.983631i	$-0.557672\pi$
$421$	−7.39446			−0.360384			−0.180192	+	0.983631i	$0.557672\pi$
$422$	−19.5579	+	19.4006i	−0.952062	+	0.944406i
$423$	4.01014	+	37.8810i	0.194980	+	1.84184i
$424$	−7.68296	−	7.87136i	−0.373118	−	0.382267i
$425$			5.47450i			0.265552i
$426$	0.210892	+	4.32725i	0.0102177	+	0.209656i
$427$		−	1.09477i		−	0.0529797i
$428$	−0.118239	+	14.6435i	−0.00571531	+	0.707822i
$429$	3.25130	+	2.92528i	0.156974	+	0.141234i
$430$	1.40292	+	1.41430i	0.0676550	+	0.0682035i
$431$	23.1528			1.11523			0.557615	−	0.830100i	$-0.311716\pi$
$431$	23.1528			1.11523			0.557615	+	0.830100i	$0.311716\pi$
$432$	12.4681	−	16.6297i	0.599874	−	0.800094i
$433$	−22.9010			−1.10055			−0.550276	−	0.834983i	$-0.685477\pi$
$433$	−22.9010			−1.10055			−0.550276	+	0.834983i	$0.685477\pi$
$434$	2.29067	+	2.30924i	0.109956	+	0.110847i
$435$	−4.27468	−	3.84604i	−0.204955	−	0.184403i
$436$	0.159435	−	19.7455i	0.00763557	−	0.945640i
$437$			0.00352647i			0.000168694i
$438$	0.772316	+	15.8470i	0.0369027	+	0.757200i
$439$		−	29.2978i		−	1.39831i	−0.714972	−	0.699153i	$-0.753561\pi$
$439$		−	29.2978i		−	1.39831i	0.714972	−	0.699153i	$-0.246439\pi$
$440$	−4.98864	−	5.11096i	−0.237824	−	0.243656i
$441$	2.19706	+	20.7541i	0.104622	+	0.988290i
$442$	5.49655	−	5.45235i	0.261444	−	0.259342i
$443$	−33.4752			−1.59046			−0.795228	−	0.606310i	$-0.792649\pi$
$443$	−33.4752			−1.59046			−0.795228	+	0.606310i	$0.792649\pi$
$444$	19.2319	−	21.0312i	0.912704	−	0.998098i
$445$	−12.7672			−0.605223
$446$	6.70930	−	6.65534i	0.317695	−	0.315140i
$447$	−11.1712	+	12.4163i	−0.528382	+	0.587270i
$448$	1.66442	+	0.0403251i	0.0786364	+	0.00190518i
$449$		−	29.8314i		−	1.40783i	−0.710284	−	0.703916i	$-0.751433\pi$
$449$		−	29.8314i		−	1.40783i	0.710284	−	0.703916i	$-0.248567\pi$
$450$	2.68081	−	3.28835i	0.126374	−	0.155014i
$451$			25.7215i			1.21118i
$452$	−23.2878	−	0.188038i	−1.09537	−	0.00884454i
$453$	0.656109	−	0.729231i	0.0308267	−	0.0342623i
$454$	−6.84230	−	6.89777i	−0.321125	−	0.323729i
$455$	−0.208113			−0.00975651
$456$	−0.0594097	−	1.46166i	−0.00278211	−	0.0684487i
$457$	15.0930			0.706022			0.353011	−	0.935619i	$-0.385158\pi$
$457$	15.0930			0.706022			0.353011	+	0.935619i	$0.385158\pi$
$458$	10.2974	+	10.3809i	0.481168	+	0.485069i
$459$	23.0323	+	16.6945i	1.07506	+	0.779231i
$460$	−0.0236187		0.000190709i	−0.00110123		8.89186e-6i
$461$			12.6833i			0.590719i	0.955386	+	0.295360i	$0.0954394\pi$
$461$			12.6833i			0.590719i	−0.955386	+	0.295360i	$0.904561\pi$
$462$	−1.28569	+	0.0626591i	−0.0598158	+	0.00291517i
$463$		−	40.0604i		−	1.86176i	−0.365322	−	0.930881i	$-0.619041\pi$
$463$		−	40.0604i		−	1.86176i	0.365322	−	0.930881i	$-0.380959\pi$
$464$	0.214437	−	13.2778i	0.00995499	−	0.616406i
$465$	14.2299	+	12.8030i	0.659897	+	0.593727i
$466$	12.1377	−	12.0401i	0.562266	−	0.557745i
$467$	22.6244			1.04693			0.523467	−	0.852046i	$-0.324638\pi$
$467$	22.6244			1.04693			0.523467	+	0.852046i	$0.324638\pi$
$468$	−5.97157	+	0.583443i	−0.276036	+	0.0269697i
$469$	2.56750			0.118556
$470$	−12.7487	+	12.6462i	−0.588055	+	0.583326i
$471$	−8.77903	−	7.89873i	−0.404517	−	0.363954i
$472$	0.165069	−	0.161118i	0.00759790	−	0.00741605i
$473$		−	3.55689i		−	0.163546i
$474$	18.1195	−	0.883069i	0.832258	−	0.0405607i
$475$		−	0.298607i		−	0.0137010i
$476$	−0.0183982	+	2.27856i	−0.000843281	+	0.104438i
$477$	−11.6018	+	1.22818i	−0.531209	+	0.0562346i
$478$	27.1009	+	27.3206i	1.23957	+	1.24962i
$479$	−34.2532			−1.56507			−0.782533	−	0.622609i	$-0.786073\pi$
$479$	−34.2532			−1.56507			−0.782533	+	0.622609i	$0.786073\pi$
$480$	9.79277	−	0.318853i	0.446977	−	0.0145536i
$481$	−8.22687			−0.375113
$482$	2.35259	+	2.37166i	0.107157	+	0.108026i
$483$	−0.00284729	+	0.00316461i	−0.000129556	+	0.000143995i
$484$	0.0746696	−	9.24758i	0.00339407	−	0.420345i
$485$			8.78578i			0.398942i
$486$	−5.65966	−	21.3065i	−0.256727	−	0.966484i
$487$		−	10.2210i		−	0.463156i	−0.972816	−	0.231578i	$-0.925611\pi$
$487$		−	10.2210i		−	0.463156i	0.972816	−	0.231578i	$-0.0743888\pi$
$488$	10.6476	−	10.3927i	0.481992	−	0.470456i
$489$	11.5590	−	12.8473i	0.522717	−	0.580973i
$490$	−6.98472	+	6.92855i	−0.315537	+	0.313000i
$491$	−12.1968			−0.550432			−0.275216	−	0.961382i	$-0.588749\pi$
$491$	−12.1968			−0.550432			−0.275216	+	0.961382i	$0.588749\pi$
$492$	−26.0405	−	23.8126i	−1.17400	−	1.07356i
$493$	18.1747			0.818546
$494$	−0.299810	+	0.297399i	−0.0134891	+	0.0133806i
$495$	−7.53316	+	0.797472i	−0.338591	+	0.0358437i
$496$	−0.713838	+	44.2003i	−0.0320523	+	1.98465i
$497$			0.368088i			0.0165110i
$498$	0.859724	+	17.6405i	0.0385251	+	0.790491i
$499$		−	12.7371i		−	0.570192i	−0.958499	−	0.285096i	$-0.907974\pi$
$499$		−	12.7371i		−	0.570192i	0.958499	−	0.285096i	$-0.0920255\pi$
$500$	1.99993	+	0.0161485i	0.0894398	+	0.000722182i
$501$	−18.3176	−	16.4808i	−0.818368	−	0.736307i
$502$	−6.51021	−	6.56298i	−0.290565	−	0.292920i
$503$	−3.38096			−0.150750			−0.0753748	−	0.997155i	$-0.524015\pi$
$503$	−3.38096			−0.150750			−0.0753748	+	0.997155i	$0.524015\pi$
$504$	1.12684	−	1.35965i	0.0501934	−	0.0605635i
$505$	9.80391			0.436268
$506$	0.0296999	+	0.0299407i	0.00132032	+	0.00133103i
$507$	1.28760	+	1.15849i	0.0571843	+	0.0514502i
$508$	13.6507	+	0.110223i	0.605653	+	0.00489034i
$509$			26.5081i			1.17495i	0.809242	+	0.587476i	$0.199878\pi$
$509$			26.5081i			1.17495i	−0.809242	+	0.587476i	$0.800122\pi$
$510$	0.652758	+	13.3938i	0.0289046	+	0.593088i
$511$			1.34799i			0.0596316i
$512$	15.4082	+	16.5707i	0.680953	+	0.732327i
$513$	−1.25630	−	0.910602i	−0.0554671	−	0.0402041i
$514$	7.70512	−	7.64316i	0.339858	−	0.337125i
$515$	−3.34007			−0.147181
$516$	3.60101	+	3.29292i	0.158526	+	0.144963i
$517$	32.0624			1.41010
$518$	1.71902	−	1.70520i	0.0755295	−	0.0749221i
$519$	−3.04551	+	3.38493i	−0.133683	+	0.148582i
$520$	−1.97563	−	2.02408i	−0.0866371	−	0.0887616i
$521$			35.9519i			1.57508i	0.616262	+	0.787541i	$0.288646\pi$
$521$			35.9519i			1.57508i	−0.616262	+	0.787541i	$0.711354\pi$
$522$	−10.9169	−	8.89997i	−0.477822	−	0.389541i
$523$		−	2.02905i		−	0.0887243i	−0.999016	−	0.0443622i	$-0.985874\pi$
$523$		−	2.02905i		−	0.0887243i	0.999016	−	0.0443622i	$-0.0141256\pi$
$524$	0.0280728	−	3.47672i	0.00122637	−	0.151881i
$525$	0.241097	−	0.267967i	0.0105223	−	0.0116950i
$526$	−15.7973	−	15.9254i	−0.688797	−	0.694381i
$527$	−60.5015			−2.63549
$528$	−12.8145	−	11.9096i	−0.557681	−	0.518298i
$529$	−22.9999			−0.999994
$530$	−3.87313	−	3.90453i	−0.168238	−	0.169602i
$531$	−0.0257559	−	0.243298i	−0.00111771	−	0.0105582i
$532$	0.00100353	−	0.124284i	4.35087e−5	−	0.00538841i
$533$			10.1864i			0.441221i
$534$	−31.2360	+	1.52231i	−1.35172	+	0.0658769i
$535$			7.32200i			0.316558i
$536$	24.3734	+	24.9711i	1.05277	+	1.07859i
$537$	16.6103	+	14.9448i	0.716789	+	0.644914i
$538$	−19.1452	+	18.9912i	−0.825406	+	0.818768i
$539$	17.5662			0.756631
$540$	6.16674	−	8.36489i	0.265374	−	0.359968i
$541$	36.2826			1.55991			0.779954	−	0.625836i	$-0.215242\pi$
$541$	36.2826			1.55991			0.779954	+	0.625836i	$0.215242\pi$
$542$	29.8945	−	29.6541i	1.28408	−	1.27375i
$543$	−16.3576	−	14.7174i	−0.701972	−	0.631582i
$544$	−22.3355	+	21.4515i	−0.957628	+	0.919726i
$545$		−	9.87309i		−	0.422917i
$546$	−0.509168	+	0.0248147i	−0.0217904	+	0.00106197i
$547$		−	23.2624i		−	0.994627i	−0.867571	−	0.497313i	$-0.834320\pi$
$547$		−	23.2624i		−	0.994627i	0.867571	−	0.497313i	$-0.165680\pi$
$548$	39.6911	+	0.320486i	1.69552	+	0.0136905i
$549$	−1.66136	−	15.6937i	−0.0709050	−	0.669790i
$550$	−2.51487	−	2.53526i	−0.107234	−	0.108104i
$551$	−0.991341			−0.0422325
$552$	−0.0578079	+	0.00234962i	−0.00246047	+	0.000100006i
$553$	1.54130			0.0655427
$554$	−30.2564	−	30.5017i	−1.28547	−	1.29589i
$555$	9.53072	−	10.5929i	0.404557	−	0.449644i
$556$	−11.1256	−	0.0898337i	−0.471831	−	0.00380980i
$557$			1.98101i			0.0839380i	0.999119	+	0.0419690i	$0.0133631\pi$
$557$			1.98101i			0.0839380i	−0.999119	+	0.0419690i	$0.986637\pi$
$558$	36.3413	+	29.6270i	1.53845	+	1.25421i
$559$		−	1.40862i		−	0.0595784i
$560$	0.832345	+	0.0134424i	0.0351730	+	0.000568046i
$561$	16.0144	−	17.7992i	0.676129	−	0.751483i
$562$	31.2568	−	31.0054i	1.31849	−	1.30789i
$563$	−28.8589			−1.21626			−0.608129	−	0.793838i	$-0.708080\pi$
$563$	−28.8589			−1.21626			−0.608129	+	0.793838i	$0.708080\pi$
$564$	−29.6830	+	32.4601i	−1.24988	+	1.36682i
$565$	−11.6443			−0.489879
$566$	6.07984	−	6.03094i	0.255555	−	0.253499i
$567$	−0.392167	−	1.83151i	−0.0164695	−	0.0769160i
$568$	−3.57996	+	3.49428i	−0.150212	+	0.146617i
$569$		−	8.04926i		−	0.337443i	−0.985664	−	0.168721i	$-0.946036\pi$
$569$		−	8.04926i		−	0.337443i	0.985664	−	0.168721i	$-0.0539638\pi$
$570$	−0.0356048	−	0.730568i	−0.00149132	−	0.0306001i
$571$			6.64396i			0.278041i	0.990290	+	0.139020i	$0.0443954\pi$
$571$			6.64396i			0.278041i	−0.990290	+	0.139020i	$0.955605\pi$
$572$	−0.0407763	+	5.05001i	−0.00170494	+	0.211151i
$573$	−32.3585	−	29.1138i	−1.35180	−	1.21625i
$574$	−2.11135	−	2.12847i	−0.0881260	−	0.0888405i
$575$	−0.0118097			−0.000492500
$576$	23.9208	−	1.94775i	0.996701	−	0.0811564i
$577$	12.1203			0.504575			0.252288	−	0.967652i	$-0.418817\pi$
$577$	12.1203			0.504575			0.252288	+	0.967652i	$0.418817\pi$
$578$	−12.9176	−	13.0224i	−0.537303	−	0.541659i
$579$	25.3361	+	22.7955i	1.05293	+	0.947350i
$580$	0.0536110	−	6.63955i	0.00222608	−	0.275692i
$581$			1.50055i			0.0622534i
$582$	1.04758	+	21.4952i	0.0434237	+	0.891003i
$583$			9.81972i			0.406691i
$584$	−13.1103	+	12.7965i	−0.542509	+	0.529525i
$585$	−2.98333	+	0.315820i	−0.123346	+	0.0130575i
$586$	12.5179	−	12.4173i	0.517111	−	0.512953i
$587$	22.0128			0.908565			0.454282	−	0.890858i	$-0.349896\pi$
$587$	22.0128			0.908565			0.454282	+	0.890858i	$0.349896\pi$
$588$	−16.2626	+	17.7841i	−0.670657	+	0.733405i
$589$	3.30007			0.135977
$590$	0.0818811	−	0.0812227i	0.00337099	−	0.00334388i
$591$	13.6166	−	15.1342i	0.560114	−	0.622538i
$592$	32.9032	+	0.531389i	1.35231	+	0.0218399i
$593$			3.11888i			0.128077i	0.997947	+	0.0640386i	$0.0203981\pi$
$593$			3.11888i			0.128077i	−0.997947	+	0.0640386i	$0.979602\pi$
$594$	−18.3354	+	2.84931i	−0.752312	+	0.116909i
$595$			1.13932i			0.0467074i
$596$	−19.2853	−	0.155719i	−0.789957	−	0.00637851i
$597$	−10.5080	+	11.6791i	−0.430065	+	0.477995i
$598$	0.0117620	+	0.0118573i	0.000480982	+	0.000484882i
$599$	10.2086			0.417113			0.208556	−	0.978010i	$-0.433124\pi$
$599$	10.2086			0.417113			0.208556	+	0.978010i	$0.433124\pi$
$600$	4.89494	−	0.198956i	0.199835	−	0.00812234i
$601$	19.8334			0.809023			0.404511	−	0.914533i	$-0.367442\pi$
$601$	19.8334			0.809023			0.404511	+	0.914533i	$0.367442\pi$
$602$	0.291967	+	0.294334i	0.0118997	+	0.0119962i
$603$	36.8054	−	3.89628i	1.49883	−	0.158669i
$604$	1.13266	+	0.00914569i	0.0460874	+	0.000372133i
$605$		−	4.62394i		−	0.187990i
$606$	23.9861	−	1.16898i	0.974369	−	0.0474866i
$607$		−	16.0637i		−	0.652007i	−0.945369	−	0.326004i	$-0.894298\pi$
$607$		−	16.0637i		−	0.652007i	0.945369	−	0.326004i	$-0.105702\pi$
$608$	1.21829	−	1.17008i	0.0494084	−	0.0474529i
$609$	−0.889618	−	0.800412i	−0.0360491	−	0.0324343i
$610$	5.28165	−	5.23917i	0.213848	−	0.212128i
$611$	12.6976			0.513688
$612$	3.19406	+	32.6913i	0.129112	+	1.32147i
$613$	−20.5282			−0.829126			−0.414563	−	0.910021i	$-0.636066\pi$
$613$	−20.5282			−0.829126			−0.414563	+	0.910021i	$0.636066\pi$
$614$	−13.2077	+	13.1014i	−0.533018	+	0.528731i
$615$	−13.1160	−	11.8008i	−0.528887	−	0.475854i
$616$	−1.03820	−	1.06366i	−0.0418304	−	0.0428561i
$617$			9.34473i			0.376205i	0.982149	+	0.188102i	$0.0602337\pi$
$617$			9.34473i			0.376205i	−0.982149	+	0.188102i	$0.939766\pi$
$618$	−8.17178	+	0.398258i	−0.328717	+	0.0160203i
$619$			25.9117i			1.04148i	0.853716	+	0.520739i	$0.174343\pi$
$619$			25.9117i			1.04148i	−0.853716	+	0.520739i	$0.825657\pi$
$620$	−0.178465	+	22.1023i	−0.00716734	+	0.887651i
$621$	−0.0360137	+	0.0496859i	−0.00144518	+	0.00199383i
$622$	−10.0002	−	10.0813i	−0.400971	−	0.404222i
$623$	−2.65703			−0.106451
$624$	−5.07489	−	4.71651i	−0.203158	−	0.188811i
$625$	1.00000			0.0400000
$626$	−22.7668	−	22.9514i	−0.909945	−	0.917322i
$627$	−0.873509	+	0.970861i	−0.0348846	+	0.0387724i
$628$	0.110103	−	13.6358i	0.00439357	−	0.544129i
$629$			45.0380i			1.79578i
$630$	0.557912	−	0.684351i	0.0222278	−	0.0272652i
$631$			37.3810i			1.48811i	0.668117	+	0.744056i	$0.267101\pi$
$631$			37.3810i			1.48811i	−0.668117	+	0.744056i	$0.732899\pi$
$632$	14.6316	+	14.9904i	0.582014	+	0.596286i
$633$	−22.5666	+	25.0816i	−0.896942	+	0.996905i
$634$	5.25354	−	5.21129i	0.208645	−	0.206967i
$635$	6.82558			0.270865
$636$	−9.94152	−	9.09096i	−0.394207	−	0.360480i
$637$	6.95669			0.275634
$638$	−8.41676	+	8.34908i	−0.333223	+	0.330543i
$639$	0.558588	+	5.27659i	0.0220974	+	0.208739i
$640$	7.77075	+	8.22286i	0.307166	+	0.325037i
$641$		−	28.4005i		−	1.12175i	−0.827899	−	0.560877i	$-0.810464\pi$
$641$		−	28.4005i		−	1.12175i	0.827899	−	0.560877i	$-0.189536\pi$
$642$	0.873047	+	17.9139i	0.0344564	+	0.707006i
$643$		−	3.09069i		−	0.121885i	−0.998141	−	0.0609425i	$-0.980589\pi$
$643$		−	3.09069i		−	0.121885i	0.998141	−	0.0609425i	$-0.0194106\pi$
$644$	−0.00491537		3.96891e-5i	−0.000193693		1.56397e-6i
$645$	1.81374	+	1.63187i	0.0714159	+	0.0642548i
$646$	1.62811	+	1.64131i	0.0640572	+	0.0645765i
$647$	25.0811			0.986041			0.493021	−	0.870018i	$-0.335893\pi$
$647$	25.0811			0.986041			0.493021	+	0.870018i	$0.335893\pi$
$648$	14.0901	−	21.2007i	0.553509	−	0.832843i
$649$	−0.205927			−0.00808335
$650$	−0.995955	−	1.00403i	−0.0390646	−	0.0393813i
$651$	2.96144	+	2.66449i	0.116068	+	0.104429i
$652$	19.9547	+	0.161124i	0.781487	+	0.00631012i
$653$			4.64808i			0.181893i	0.995856	+	0.0909467i	$0.0289893\pi$
$653$			4.64808i			0.181893i	−0.995856	+	0.0909467i	$0.971011\pi$
$654$	−1.17723	−	24.1554i	−0.0460333	−	0.944549i
$655$		−	1.73842i		−	0.0679256i
$656$	0.657957	−	40.7402i	0.0256889	−	1.59064i
$657$	2.04563	+	19.3236i	0.0798075	+	0.753886i
$658$	−2.65318	+	2.63184i	−0.103432	+	0.102600i
$659$	−16.9122			−0.658808			−0.329404	−	0.944189i	$-0.606848\pi$
$659$	−16.9122			−0.658808			−0.329404	+	0.944189i	$0.606848\pi$
$660$	−6.45514	−	5.90287i	−0.251266	−	0.229769i
$661$	48.0774			1.86999			0.934997	−	0.354655i	$-0.115402\pi$
$661$	48.0774			1.86999			0.934997	+	0.354655i	$0.115402\pi$
$662$	−28.8882	+	28.6559i	−1.12277	+	1.11374i
$663$	6.34213	−	7.04895i	0.246308	−	0.273759i
$664$	−14.5941	+	14.2448i	−0.566361	+	0.552806i
$665$		−	0.0621442i		−	0.00240985i
$666$	22.0547	−	27.0529i	0.854601	−	1.04828i
$667$			0.0392069i			0.00151810i
$668$	0.229730	−	28.4513i	0.00888854	−	1.10082i
$669$	7.74144	−	8.60422i	0.299301	−	0.332658i
$670$	12.2871	+	12.3867i	0.474693	+	0.478542i
$671$	−13.2831			−0.512788
$672$	2.03801	−	0.0663576i	0.0786178	−	0.00255980i
$673$	34.1142			1.31501			0.657503	−	0.753452i	$-0.271613\pi$
$673$	34.1142			1.31501			0.657503	+	0.753452i	$0.271613\pi$
$674$	−27.9699	−	28.1967i	−1.07736	−	1.08609i
$675$	3.04950	−	4.20720i	0.117375	−	0.161935i
$676$	−0.0161485	+	1.99993i	−0.000621095	+	0.0769206i
$677$			1.62392i			0.0624122i	0.999513	+	0.0312061i	$0.00993482\pi$
$677$			1.62392i			0.0624122i	−0.999513	+	0.0312061i	$0.990065\pi$
$678$	−28.4888	+	1.38842i	−1.09410	+	0.0533220i
$679$			1.82844i			0.0701690i
$680$	−11.0808	+	10.8156i	−0.424929	+	0.414759i
$681$	−8.84592	−	7.95891i	−0.338976	−	0.304986i
$682$	28.0185	−	27.7932i	1.07288	−	1.06426i
$683$	39.4425			1.50922			0.754612	−	0.656171i	$-0.227825\pi$
$683$	39.4425			1.50922			0.754612	+	0.656171i	$0.227825\pi$
$684$	−0.174220	−	1.78315i	−0.00666148	−	0.0681806i
$685$	19.8462			0.758285
$686$	−2.91628	+	2.89283i	−0.111344	+	0.110449i
$687$	13.3128	+	11.9779i	0.507916	+	0.456986i
$688$	−0.0909854	+	5.63375i	−0.00346879	+	0.214785i
$689$			3.88887i			0.148154i
$690$	−0.0288935	+	0.00140815i	−0.00109996	+	5.36072e-5i
$691$		−	14.1104i		−	0.536784i	−0.963310	−	0.268392i	$-0.913508\pi$
$691$		−	14.1104i		−	0.536784i	0.963310	−	0.268392i	$-0.0864923\pi$
$692$	−5.25756	−	0.0424522i	−0.199863	−	0.00161379i
$693$	−1.56775	+	0.165965i	−0.0595540	+	0.00630448i
$694$	22.3606	+	22.5419i	0.848797	+	0.855678i
$695$	−5.56298			−0.211016
$696$	−0.660510	−	16.2506i	−0.0250366	−	0.615978i
$697$	55.7653			2.11226
$698$	−21.7732	−	21.9498i	−0.824129	−	0.830810i
$699$	14.0049	−	15.5657i	0.529714	−	0.588750i
$700$	0.416213	+	0.00336072i	0.0157314	+	0.000127023i
$701$		−	21.9599i		−	0.829414i	−0.909955	−	0.414707i	$-0.863884\pi$
$701$		−	21.9599i		−	0.829414i	0.909955	−	0.414707i	$-0.136116\pi$
$702$	−7.26132	+	1.12840i	−0.274061	+	0.0425888i
$703$		−	2.45660i		−	0.0926526i
$704$	0.489273	−	20.1948i	0.0184402	−	0.761119i
$705$	−14.7100	+	16.3494i	−0.554009	+	0.615753i
$706$	−7.23380	+	7.17562i	−0.272248	+	0.270058i
$707$	2.04033			0.0767344
$708$	0.190645	−	0.208481i	0.00716486	−	0.00783521i
$709$	−27.5190			−1.03350			−0.516748	−	0.856137i	$-0.672858\pi$
$709$	−27.5190			−1.03350			−0.516748	+	0.856137i	$0.672858\pi$
$710$	−1.77582	+	1.76154i	−0.0666452	+	0.0661093i
$711$	22.0947	−	2.33898i	0.828615	−	0.0877185i
$712$	−25.2233	−	25.8418i	−0.945282	−	0.968461i
$713$		−	0.130516i		−	0.00488785i
$714$	0.135848	+	2.78744i	0.00508397	+	0.104317i
$715$			2.52509i			0.0944329i
$716$	−0.208319	+	25.7997i	−0.00778526	+	0.964178i
$717$	35.0368	+	31.5236i	1.30847	+	1.17727i
$718$	−21.7312	−	21.9073i	−0.811000	−	0.817575i
$719$	−7.97499			−0.297417			−0.148708	−	0.988881i	$-0.547512\pi$
$719$	−7.97499			−0.297417			−0.148708	+	0.988881i	$0.547512\pi$
$720$	11.9522	−	1.07042i	0.445431	−	0.0398921i
$721$	−0.695114			−0.0258874
$722$	18.8343	+	18.9870i	0.700941	+	0.706624i
$723$	3.04149	+	2.73651i	0.113114	+	0.101772i
$724$	0.205150	−	25.4071i	0.00762432	−	0.944247i
$725$		−	3.31988i		−	0.123297i
$726$	−0.551341	−	11.3129i	−0.0204622	−	0.419860i
$727$			9.11116i			0.337914i	0.985623	+	0.168957i	$0.0540399\pi$
$727$			9.11116i			0.337914i	−0.985623	+	0.168957i	$0.945960\pi$
$728$	−0.411155	−	0.421237i	−0.0152384	−	0.0156121i
$729$	−8.40114	−	25.6597i	−0.311153	−	0.950360i
$730$	−6.50329	+	6.45099i	−0.240698	+	0.238762i
$731$	−7.71149			−0.285220
$732$	12.2973	−	13.4479i	0.454522	−	0.497047i
$733$	48.7640			1.80114			0.900569	−	0.434713i	$-0.143150\pi$
$733$	48.7640			1.80114			0.900569	+	0.434713i	$0.143150\pi$
$734$	−0.193856	+	0.192297i	−0.00715535	+	0.00709781i
$735$	−8.05923	+	8.95742i	−0.297269	+	0.330399i
$736$	−0.0462758	−	0.0481828i	−0.00170575	−	0.00177604i
$737$		−	31.1521i		−	1.14750i
$738$	−33.4964	−	27.3077i	−1.23302	−	1.00521i
$739$		−	18.2206i		−	0.670254i	−0.942173	−	0.335127i	$-0.891221\pi$
$739$		−	18.2206i		−	0.670254i	0.942173	−	0.335127i	$-0.108779\pi$
$740$	16.4532	+	0.132851i	0.604832	+	0.00488372i
$741$	−0.345932	+	0.384486i	−0.0127081	+	0.0141245i
$742$	−0.806051	−	0.812586i	−0.0295911	−	0.0298310i
$743$	42.6780			1.56570			0.782852	−	0.622208i	$-0.213764\pi$
$743$	42.6780			1.56570			0.782852	+	0.622208i	$0.213764\pi$
$744$	2.19877	+	54.0965i	0.0806107	+	1.98328i
$745$	−9.64297			−0.353291
$746$	7.37913	+	7.43896i	0.270169	+	0.272360i
$747$	2.27714	+	21.5106i	0.0833163	+	0.787031i
$748$	27.6462	+	0.223230i	1.01085	+	0.00816208i
$749$			1.52381i			0.0556787i
$750$	2.44659	−	0.119236i	0.0893367	−	0.00435389i
$751$			31.6319i			1.15427i	0.816650	+	0.577133i	$0.195828\pi$
$751$			31.6319i			1.15427i	−0.816650	+	0.577133i	$0.804172\pi$
$752$	−50.7836	−	0.820158i	−1.85189	−	0.0299081i
$753$	−8.41658	−	7.57262i	−0.306717	−	0.275961i
$754$	−3.33326	+	3.30645i	−0.121390	+	0.120414i
$755$	0.566350			0.0206116
$756$	1.28338	−	1.74085i	0.0466761	−	0.0633140i
$757$	−23.8095			−0.865369			−0.432685	−	0.901545i	$-0.642434\pi$
$757$	−23.8095			−0.865369			−0.432685	+	0.901545i	$0.642434\pi$
$758$	−25.9740	+	25.7651i	−0.943418	+	0.935831i
$759$	0.0383969	+	0.0345467i	0.00139372	+	0.00125397i
$760$	0.604404	−	0.589938i	0.0219240	−	0.0213993i
$761$		−	19.3812i		−	0.702569i	−0.936269	−	0.351284i	$-0.885745\pi$
$761$		−	19.3812i		−	0.702569i	0.936269	−	0.351284i	$-0.114255\pi$
$762$	16.6994	−	0.813856i	0.604954	−	0.0294829i
$763$		−	2.05472i		−	0.0743860i
$764$	0.405826	−	50.2602i	0.0146823	−	1.81835i
$765$	1.72895	+	16.3322i	0.0625105	+	0.590493i
$766$	−11.1666	−	11.2571i	−0.403465	−	0.406736i
$767$	−0.0815526			−0.00294469
$768$	19.9923	+	19.1914i	0.721409	+	0.692509i
$769$	−10.8729			−0.392087			−0.196043	−	0.980595i	$-0.562809\pi$
$769$	−10.8729			−0.392087			−0.196043	+	0.980595i	$0.562809\pi$
$770$	−0.523379	−	0.527622i	−0.0188613	−	0.0190142i
$771$	8.89046	−	9.88129i	0.320182	−	0.355866i
$772$	−0.317753	+	39.3527i	−0.0114362	+	1.41633i
$773$		−	13.4249i		−	0.482859i	−0.970418	−	0.241429i	$-0.922384\pi$
$773$		−	13.4249i		−	0.482859i	0.970418	−	0.241429i	$-0.0776162\pi$
$774$	4.63205	+	3.77624i	0.166495	+	0.135734i
$775$			11.0515i			0.396983i
$776$	−17.7831	+	17.3574i	−0.638375	+	0.623096i
$777$	1.98347	−	2.20453i	0.0711566	−	0.0790870i
$778$	−20.3801	+	20.2162i	−0.730660	+	0.724785i
$779$	−3.04173			−0.108981
$780$	−2.55641	−	2.33769i	−0.0915340	−	0.0837027i
$781$	4.46610			0.159809
$782$	0.0649128	−	0.0643908i	0.00232128	−	0.00230261i
$783$	−13.9674	−	10.1240i	−0.499155	−	0.361801i
$784$	−27.8231	−	0.449345i	−0.993683	−	0.0160480i
$785$		−	6.81815i		−	0.243350i
$786$	−0.207282	−	4.25319i	−0.00739352	−	0.151706i
$787$		−	14.3212i		−	0.510495i	−0.966876	−	0.255248i	$-0.917843\pi$
$787$		−	14.3212i		−	0.510495i	0.966876	−	0.255248i	$-0.0821570\pi$
$788$	23.5069	+	0.189806i	0.837398	+	0.00676157i
$789$	−20.4232	−	18.3753i	−0.727087	−	0.654179i
$790$	7.37609	+	7.43589i	0.262429	+	0.264557i
$791$	−2.42333			−0.0861638
$792$	−16.4969	−	13.6722i	−0.586192	−	0.485820i
$793$	−5.26046			−0.186804
$794$	−5.51092	−	5.55559i	−0.195575	−	0.197161i
$795$	−5.00730	−	4.50520i	−0.177591	−	0.159783i
$796$	−18.1404	−	0.146474i	−0.642968	−	0.00519165i
$797$		−	29.3102i		−	1.03822i	−0.854707	−	0.519110i	$-0.826263\pi$
$797$		−	29.3102i		−	1.03822i	0.854707	−	0.519110i	$-0.173737\pi$
$798$	−0.00740984	−	0.152041i	−0.000262305	−	0.00538220i
$799$		−	69.5128i		−	2.45918i
$800$	3.91845	+	4.07992i	0.138538	+	0.144247i
$801$	−38.0888	+	4.03213i	−1.34580	+	0.142468i
$802$	−23.5165	+	23.3274i	−0.830398	+	0.823720i
$803$	16.3555			0.577172
$804$	31.5385	+	28.8402i	1.11228	+	1.01711i
$805$	−0.00245776			−8.66248e−5
$806$	11.0961	−	11.0068i	0.390842	−	0.387699i
$807$	−22.0904	+	24.5524i	−0.777619	+	0.864284i
$808$	19.3689	+	19.8439i	0.681396	+	0.698104i
$809$		−	22.8065i		−	0.801834i	−0.916114	−	0.400917i	$-0.868692\pi$
$809$		−	22.8065i		−	0.801834i	0.916114	−	0.400917i	$-0.131308\pi$
$810$	6.95921	−	10.6569i	0.244522	−	0.374445i
$811$		−	6.56401i		−	0.230493i	−0.993337	−	0.115247i	$-0.963234\pi$
$811$		−	6.56401i		−	0.230493i	0.993337	−	0.115247i	$-0.0367659\pi$
$812$	0.0111572	−	1.38178i	0.000391540	−	0.0484910i
$813$	34.4934	−	38.3377i	1.20974	−	1.34456i
$814$	−20.6895	−	20.8573i	−0.725168	−	0.731047i
$815$	9.97769			0.349503
$816$	−25.8205	+	27.7825i	−0.903898	+	0.972581i
$817$	0.420625			0.0147158
$818$	−15.3080	−	15.4321i	−0.535230	−	0.539569i
$819$	−0.620871	+	0.0657264i	−0.0216950	+	0.00229667i
$820$	0.164495	−	20.3721i	0.00574440	−	0.711425i
$821$			3.07048i			0.107161i	0.998564	+	0.0535803i	$0.0170633\pi$
$821$			3.07048i			0.107161i	−0.998564	+	0.0535803i	$0.982937\pi$
$822$	48.5555	−	2.36639i	1.69357	−	0.0825372i
$823$		−	47.6806i		−	1.66204i	−0.556242	−	0.831020i	$-0.687757\pi$
$823$		−	47.6806i		−	1.66204i	0.556242	−	0.831020i	$-0.312243\pi$
$824$	−6.59875	−	6.76056i	−0.229878	−	0.235515i
$825$	−3.25130	−	2.92528i	−0.113196	−	0.101845i
$826$	0.0170406	−	0.0169035i	0.000592917	−	0.000588149i
$827$	50.9861			1.77296			0.886480	−	0.462766i	$-0.153143\pi$
$827$	50.9861			1.77296			0.886480	+	0.462766i	$0.153143\pi$
$828$	−0.0705226	+	0.00689030i	−0.00245083	+	0.000239455i
$829$	31.4647			1.09282			0.546408	−	0.837519i	$-0.315995\pi$
$829$	31.4647			1.09282			0.546408	+	0.837519i	$0.315995\pi$
$830$	−7.23931	+	7.18109i	−0.251280	+	0.249259i
$831$	−39.1164	−	35.1940i	−1.35693	−	1.22087i
$832$	0.193765	−	7.99765i	0.00671759	−	0.277269i
$833$		−	38.0844i		−	1.31954i
$834$	−13.6103	+	0.663309i	−0.471287	+	0.0229685i
$835$		−	14.2261i		−	0.492316i
$836$	−1.50797	−	0.0121761i	−0.0521542	−	0.000421119i
$837$	46.4960	+	33.7016i	1.60714	+	1.16490i
$838$	−27.2866	−	27.5078i	−0.942599	−	0.950241i
$839$	−7.13796			−0.246430			−0.123215	−	0.992380i	$-0.539320\pi$
$839$	−7.13796			−0.246430			−0.123215	+	0.992380i	$0.539320\pi$
$840$	1.01870	−	0.0414054i	0.0351486	−	0.00142862i
$841$	17.9784			0.619944
$842$	−7.36454	−	7.42425i	−0.253799	−	0.255856i
$843$	36.0653	−	40.0847i	1.24215	−	1.38059i
$844$	−38.9575	−	0.314562i	−1.34097	−	0.0108277i
$845$			1.00000i			0.0344010i
$846$	−34.0397	+	41.7541i	−1.17031	+	1.43553i
$847$		−	0.962305i		−	0.0330652i
$848$	0.251189	−	15.5534i	0.00862586	−	0.534107i
$849$	7.01514	−	7.79697i	0.240759	−	0.267591i
$850$	−5.49655	+	5.45235i	−0.188530	+	0.187014i
$851$	−0.0971572			−0.00333050
$852$	−4.13465	+	4.52149i	−0.141651	+	0.154904i
$853$	−30.0514			−1.02894			−0.514471	−	0.857508i	$-0.672012\pi$
$853$	−30.0514			−1.02894			−0.514471	+	0.857508i	$0.672012\pi$
$854$	1.09918	−	1.09034i	0.0376133	−	0.0373108i
$855$	−0.0943061	−	0.890844i	−0.00322520	−	0.0304662i
$856$	−14.8203	+	14.4656i	−0.506547	+	0.494423i
$857$			29.7412i			1.01594i	0.861375	+	0.507970i	$0.169604\pi$
$857$			29.7412i			1.01594i	−0.861375	+	0.507970i	$0.830396\pi$
$858$	0.301082	+	6.17784i	0.0102788	+	0.210908i
$859$			40.6794i			1.38796i	0.719993	+	0.693981i	$0.244145\pi$
$859$			40.6794i			1.38796i	−0.719993	+	0.693981i	$0.755855\pi$
$860$	−0.0227471	+	2.81715i	−0.000775669	+	0.0960641i
$861$	−2.72961	−	2.45590i	−0.0930249	−	0.0836970i
$862$	23.0591	+	23.2461i	0.785397	+	0.791764i
$863$	−28.9035			−0.983888			−0.491944	−	0.870627i	$-0.663714\pi$
$863$	−28.9035			−0.983888			−0.491944	+	0.870627i	$0.663714\pi$
$864$	29.1144	−	4.04400i	0.990491	−	0.137580i
$865$	−2.62887			−0.0893842
$866$	−22.8084	−	22.9933i	−0.775059	−	0.781343i
$867$	−16.7003	−	15.0257i	−0.567171	−	0.510299i
$868$	−0.0371410	+	4.59979i	−0.00126065	+	0.156127i
$869$		−	18.7009i		−	0.634385i
$870$	−0.395850	−	8.12238i	−0.0134206	−	0.275374i
$871$		−	12.3370i		−	0.418025i
$872$	19.9839	−	19.5056i	0.676740	−	0.660542i
$873$	2.77472	+	26.2109i	0.0939101	+	0.887103i
$874$	−0.00354068	+	0.00351221i	−0.000119765	+	0.000118802i
$875$	0.208113			0.00703552
$876$	−15.1417	+	16.5583i	−0.511590	+	0.559454i
$877$	46.9152			1.58421			0.792107	−	0.610382i	$-0.208984\pi$
$877$	46.9152			1.58421			0.792107	+	0.610382i	$0.208984\pi$
$878$	29.4158	−	29.1792i	0.992735	−	0.984752i
$879$	14.4437	−	16.0534i	0.487173	−	0.541468i
$880$	0.163100	−	10.0990i	0.00549809	−	0.340438i
$881$			33.9403i			1.14348i	0.820436	+	0.571738i	$0.193731\pi$
$881$			33.9403i			1.14348i	−0.820436	+	0.571738i	$0.806269\pi$
$882$	−18.6495	+	22.8761i	−0.627963	+	0.770277i
$883$			55.2438i			1.85910i	0.368695	+	0.929550i	$0.379805\pi$
$883$			55.2438i			1.85910i	−0.368695	+	0.929550i	$0.620195\pi$
$884$	10.9486	+	0.0884047i	0.368242	+	0.00297337i
$885$	0.0944775	−	0.105007i	0.00317583	−	0.00352977i
$886$	−33.3398	−	33.6101i	−1.12007	−	1.12915i
$887$	39.4863			1.32582			0.662909	−	0.748700i	$-0.269321\pi$
$887$	39.4863			1.32582			0.662909	+	0.748700i	$0.269321\pi$
$888$	40.2700	−	1.63679i	1.35137	−	0.0549269i
$889$	1.42050			0.0476419
$890$	−12.7155	−	12.8186i	−0.426226	−	0.429682i
$891$	−22.2221	+	4.75825i	−0.744467	+	0.159407i
$892$	13.3643	+	0.107910i	0.447470	+	0.00361310i
$893$			3.79158i			0.126881i
$894$	−23.5924	+	1.14979i	−0.789046	+	0.0384548i
$895$			12.9002i			0.431208i
$896$	1.61720	+	1.71129i	0.0540268	+	0.0571701i
$897$	0.0152062	+	0.0136814i	0.000507720	+	0.000456809i
$898$	29.9516	−	29.7107i	0.999498	−	0.991460i
$899$	36.6898			1.22367
$900$	5.97157	−	0.583443i	0.199052	−	0.0194481i
$901$	21.2896			0.709259
$902$	−25.8251	+	25.6175i	−0.859883	+	0.852968i
$903$	0.377464	+	0.339614i	0.0125612	+	0.0113016i
$904$	−23.0048	−	23.5689i	−0.765129	−	0.783891i
$905$		−	12.7040i		−	0.422294i
$906$	1.38562	−	0.0675294i	0.0460343	−	0.00224351i
$907$			4.88820i			0.162310i	0.996701	+	0.0811551i	$0.0258609\pi$
$907$			4.88820i			0.162310i	−0.996701	+	0.0811551i	$0.974139\pi$
$908$	0.110942	−	13.7397i	0.00368172	−	0.455969i
$909$	29.2483	−	3.09627i	0.970105	−	0.102697i
$910$	−0.207272	−	0.208952i	−0.00687099	−	0.00692669i
$911$	−3.88505			−0.128718			−0.0643588	−	0.997927i	$-0.520500\pi$
$911$	−3.88505			−0.128718			−0.0643588	+	0.997927i	$0.520500\pi$
$912$	1.40838	−	1.51540i	0.0466362	−	0.0501799i
$913$	18.2065			0.602548
$914$	15.0320	+	15.1538i	0.497213	+	0.501244i
$915$	6.09416	−	6.77335i	0.201467	−	0.223920i
$916$	−0.166963	+	20.6779i	−0.00551663	+	0.683216i
$917$		−	0.361788i		−	0.0119473i
$918$	6.17743	+	39.7520i	0.203886	+	1.31201i
$919$			17.3023i			0.570751i	0.958416	+	0.285376i	$0.0921183\pi$
$919$			17.3023i			0.570751i	−0.958416	+	0.285376i	$0.907882\pi$
$920$	−0.0233317	−	0.0239038i	−0.000769222	−	0.000788085i
$921$	−15.2395	+	16.9379i	−0.502158	+	0.558123i
$922$	−12.7344	+	12.6320i	−0.419384	+	0.416012i
$923$	1.76869			0.0582172
$924$	−1.34340	−	1.22847i	−0.0441947	−	0.0404136i
$925$	8.22687			0.270498
$926$	40.2218	−	39.8983i	1.32177	−	1.31114i
$927$	−9.96454	+	1.05486i	−0.327279	+	0.0346462i
$928$	13.5449	−	13.0088i	0.444632	−	0.427034i
$929$		−	9.17907i		−	0.301155i	−0.988598	−	0.150578i	$-0.951887\pi$
$929$		−	9.17907i		−	0.301155i	0.988598	−	0.150578i	$-0.0481134\pi$
$930$	1.31774	+	27.0385i	0.0432105	+	0.886628i
$931$			2.07732i			0.0680813i
$932$	24.1771	+	0.195218i	0.791948	+	0.00639458i
$933$	−12.9285	−	11.6321i	−0.423261	−	0.380819i
$934$	22.5329	+	22.7156i	0.737300	+	0.743277i
$935$	13.8236			0.452079
$936$	−6.53320	−	5.41454i	−0.213544	−	0.176980i
$937$	−31.1561			−1.01783			−0.508913	−	0.860818i	$-0.669952\pi$
$937$	−31.1561			−1.01783			−0.508913	+	0.860818i	$0.669952\pi$
$938$	2.55712	+	2.57785i	0.0834928	+	0.0841697i
$939$	−29.4336	−	26.4822i	−0.960529	−	0.864213i
$940$	−25.3943	−	0.205046i	−0.828271	−	0.00668787i
$941$			43.3144i			1.41201i	0.708208	+	0.706004i	$0.249504\pi$
$941$			43.3144i			1.41201i	−0.708208	+	0.706004i	$0.750496\pi$
$942$	−0.812969	−	16.6812i	−0.0264880	−	0.543502i
$943$			0.120298i			0.00391746i
$944$	0.326168	+	0.00526763i	0.0106159	+	0.000171447i
$945$	0.634641	−	0.875576i	0.0206449	−	0.0284825i
$946$	3.57122	−	3.54250i	0.116110	−	0.115177i
$947$	52.7472			1.71405			0.857027	−	0.515271i	$-0.172309\pi$
$947$	52.7472			1.71405			0.857027	+	0.515271i	$0.172309\pi$
$948$	18.9329	+	17.3130i	0.614911	+	0.562301i
$949$	6.47719			0.210259
$950$	0.299810	−	0.297399i	0.00972713	−	0.00964891i
$951$	6.06173	−	6.73730i	0.196565	−	0.218472i
$952$	−2.30606	+	2.25087i	−0.0747399	+	0.0729511i
$953$			36.8574i			1.19393i	0.802268	+	0.596964i	$0.203627\pi$
$953$			36.8574i			1.19393i	−0.802268	+	0.596964i	$0.796373\pi$
$954$	−12.7880	−	10.4253i	−0.414026	−	0.337532i
$955$		−	25.1309i		−	0.813217i
$956$	−0.439416	+	54.4202i	−0.0142117	+	1.76008i
$957$	−9.71157	+	10.7939i	−0.313931	+	0.348918i
$958$	−34.1146	−	34.3912i	−1.10219	−	1.11113i
$959$	4.13027			0.133373
$960$	10.0733	+	9.51466i	0.325114	+	0.307084i
$961$	−91.1362			−2.93988
$962$	−8.19359	−	8.26002i	−0.264172	−	0.266314i
$963$	2.31243	+	21.8439i	0.0745172	+	0.703911i
$964$	−0.0381450	+	4.72413i	−0.00122857	+	0.152154i
$965$			19.6770i			0.633425i
$966$	−0.00601313		0.000293054i	−0.000193469		9.42887e-6i
$967$		−	7.75515i		−	0.249389i	−0.992195	−	0.124694i	$-0.960205\pi$
$967$		−	7.75515i		−	0.249389i	0.992195	−	0.124694i	$-0.0397951\pi$
$968$	9.35921	−	9.13520i	0.300816	−	0.293617i
$969$	2.10487	+	1.89381i	0.0676181	+	0.0608378i
$970$	−8.82117	+	8.75023i	−0.283231	+	0.280953i
$971$	33.9405			1.08920			0.544602	−	0.838695i	$-0.316681\pi$
$971$	33.9405			1.08920			0.544602	+	0.838695i	$0.316681\pi$
$972$	15.7556	−	26.9028i	0.505361	−	0.862908i
$973$	−1.15773			−0.0371152
$974$	10.2621	−	10.1796i	0.328820	−	0.326176i
$975$	−1.28760	−	1.15849i	−0.0412362	−	0.0371012i
$976$	21.0391	+	0.339782i	0.673444	+	0.0108762i
$977$		−	33.6692i		−	1.07717i	−0.842570	−	0.538587i	$-0.818958\pi$
$977$		−	33.6692i		−	1.07717i	0.842570	−	0.538587i	$-0.181042\pi$
$978$	24.4113	−	1.18970i	0.780586	−	0.0380425i
$979$			32.2383i			1.03034i
$980$	−13.9129	−	0.112340i	−0.444432	−	0.00358857i
$981$	−3.11812	−	29.4547i	−0.0995539	−	0.940416i
$982$	−12.1474	−	12.2459i	−0.387640	−	0.390783i
$983$	−19.8583			−0.633380			−0.316690	−	0.948529i	$-0.602572\pi$
$983$	−19.8583			−0.633380			−0.316690	+	0.948529i	$0.602572\pi$
$984$	−2.02664	−	49.8617i	−0.0646070	−	1.58953i
$985$	11.7538			0.374508
$986$	18.1012	+	18.2479i	0.576458	+	0.581132i
$987$	−3.06134	+	3.40252i	−0.0974435	+	0.108304i
$988$	−0.597195	−	0.00482205i	−0.0189993	−	0.000153410i
$989$		−	0.0166354i		−	0.000528976i
$990$	−8.30338	−	6.76927i	−0.263899	−	0.215141i
$991$			45.4986i			1.44531i	0.691208	+	0.722656i	$0.257079\pi$
$991$			45.4986i			1.44531i	−0.691208	+	0.722656i	$0.742921\pi$
$992$	−45.0894	+	43.3048i	−1.43159	+	1.37493i
$993$	−33.3323	+	37.0472i	−1.05777	+	1.17566i
$994$	−0.369572	+	0.366599i	−0.0117221	+	0.0116278i
$995$	−9.07048			−0.287554
$996$	−16.8554	+	18.4323i	−0.534082	+	0.584051i
$997$	29.7314			0.941604			0.470802	−	0.882239i	$-0.343965\pi$
$997$	29.7314			0.941604			0.470802	+	0.882239i	$0.343965\pi$
$998$	12.7884	−	12.6856i	0.404811	−	0.401556i
$999$	25.0878	−	34.6121i	0.793744	−	1.09508i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	780.2.g.d.131.26	yes	32
3.2	odd	2	inner	780.2.g.d.131.7	✓	32
4.3	odd	2	inner	780.2.g.d.131.8	yes	32
12.11	even	2	inner	780.2.g.d.131.25	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
780.2.g.d.131.7	✓	32	3.2	odd	2	inner
780.2.g.d.131.8	yes	32	4.3	odd	2	inner
780.2.g.d.131.25	yes	32	12.11	even	2	inner
780.2.g.d.131.26	yes	32	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	780.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.995955 + 1.00403i) q^{2} +(1.28760 + 1.15849i) q^{3} +(-0.0161485 + 1.99993i) q^{4} +1.00000i q^{5} +(0.119236 + 2.44659i) q^{6} +0.208113i q^{7} +(-2.02408 + 1.97563i) q^{8} +(0.315820 + 2.98333i) q^{9} +(-1.00403 + 0.995955i) q^{10} +2.52509 q^{11} +(-2.33769 + 2.55641i) q^{12} +1.00000 q^{13} +(-0.208952 + 0.207272i) q^{14} +(-1.15849 + 1.28760i) q^{15} +(-3.99948 - 0.0645918i) q^{16} -5.47450i q^{17} +(-2.68081 + 3.28835i) q^{18} +0.298607i q^{19} +(-1.99993 - 0.0161485i) q^{20} +(-0.241097 + 0.267967i) q^{21} +(2.51487 + 2.53526i) q^{22} +0.0118097 q^{23} +(-4.89494 + 0.198956i) q^{24} -1.00000 q^{25} +(0.995955 + 1.00403i) q^{26} +(-3.04950 + 4.20720i) q^{27} +(-0.416213 - 0.00336072i) q^{28} +3.31988i q^{29} +(-2.44659 + 0.119236i) q^{30} -11.0515i q^{31} +(-3.91845 - 4.07992i) q^{32} +(3.25130 + 2.92528i) q^{33} +(5.49655 - 5.45235i) q^{34} -0.208113 q^{35} +(-5.97157 + 0.583443i) q^{36} -8.22687 q^{37} +(-0.299810 + 0.297399i) q^{38} +(1.28760 + 1.15849i) q^{39} +(-1.97563 - 2.02408i) q^{40} +10.1864i q^{41} +(-0.509168 + 0.0248147i) q^{42} -1.40862i q^{43} +(-0.0407763 + 5.05001i) q^{44} +(-2.98333 + 0.315820i) q^{45} +(0.0117620 + 0.0118573i) q^{46} +12.6976 q^{47} +(-5.07489 - 4.71651i) q^{48} +6.95669 q^{49} +(-0.995955 - 1.00403i) q^{50} +(6.34213 - 7.04895i) q^{51} +(-0.0161485 + 1.99993i) q^{52} +3.88887i q^{53} +(-7.26132 + 1.12840i) q^{54} +2.52509i q^{55} +(-0.411155 - 0.421237i) q^{56} +(-0.345932 + 0.384486i) q^{57} +(-3.33326 + 3.30645i) q^{58} -0.0815526 q^{59} +(-2.55641 - 2.33769i) q^{60} -5.26046 q^{61} +(11.0961 - 11.0068i) q^{62} +(-0.620871 + 0.0657264i) q^{63} +(0.193765 - 7.99765i) q^{64} +1.00000i q^{65} +(0.301082 + 6.17784i) q^{66} -12.3370i q^{67} +(10.9486 + 0.0884047i) q^{68} +(0.0152062 + 0.0136814i) q^{69} +(-0.207272 - 0.208952i) q^{70} +1.76869 q^{71} +(-6.53320 - 5.41454i) q^{72} +6.47719 q^{73} +(-8.19359 - 8.26002i) q^{74} +(-1.28760 - 1.15849i) q^{75} +(-0.597195 - 0.00482205i) q^{76} +0.525504i q^{77} +(0.119236 + 2.44659i) q^{78} -7.40605i q^{79} +(0.0645918 - 3.99948i) q^{80} +(-8.80052 + 1.88439i) q^{81} +(-10.2274 + 10.1452i) q^{82} +7.21026 q^{83} +(-0.532022 - 0.486505i) q^{84} +5.47450 q^{85} +(1.41430 - 1.40292i) q^{86} +(-3.84604 + 4.27468i) q^{87} +(-5.11096 + 4.98864i) q^{88} +12.7672i q^{89} +(-3.28835 - 2.68081i) q^{90} +0.208113i q^{91} +(-0.000190709 + 0.0236187i) q^{92} +(12.8030 - 14.2299i) q^{93} +(12.6462 + 12.7487i) q^{94} -0.298607 q^{95} +(-0.318853 - 9.79277i) q^{96} +8.78578 q^{97} +(6.92855 + 6.98472i) q^{98} +(0.797472 + 7.53316i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 6 q^{4} + 10 q^{6} + 12 q^{9} + 6 q^{10} - 20 q^{12} + 32 q^{13} - 6 q^{16} + 4 q^{18} + 20 q^{21} + 16 q^{22} + 10 q^{24} - 32 q^{25} + 16 q^{28} + 16 q^{33} + 28 q^{34} + 30 q^{36} - 24 q^{37}+ \cdots + 112 q^{97}+O(q^{100}) \) 32 * q + 6 * q^4 + 10 * q^6 + 12 * q^9 + 6 * q^10 - 20 * q^12 + 32 * q^13 - 6 * q^16 + 4 * q^18 + 20 * q^21 + 16 * q^22 + 10 * q^24 - 32 * q^25 + 16 * q^28 + 16 * q^33 + 28 * q^34 + 30 * q^36 - 24 * q^37 + 6 * q^40 + 20 * q^45 - 80 * q^46 - 16 * q^48 + 16 * q^49 + 6 * q^52 + 2 * q^54 - 64 * q^57 - 100 * q^58 + 14 * q^60 + 16 * q^61 + 126 * q^64 + 60 * q^66 - 4 * q^69 - 16 * q^70 - 16 * q^72 - 104 * q^73 + 20 * q^76 + 10 * q^78 - 72 * q^81 - 116 * q^82 + 20 * q^84 + 24 * q^85 - 14 * q^90 + 16 * q^93 + 28 * q^94 - 74 * q^96 + 112 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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