LMFDB - Embedded newform 99.2.m.b.31.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [99,2,Mod(4,99)] 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("99.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(99, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([10, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.m (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			31.7
Character	$\chi$	$=$	99.31
Dual form			99.2.m.b.16.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.45109 - 0.308439i) q^{2} +(0.266086 - 1.71149i) q^{3} +(0.183441 - 0.0816732i) q^{4} +(0.0707467 + 0.0150377i) q^{5} +(-0.141775 - 2.56560i) q^{6} +(-0.203853 + 1.93954i) q^{7} +(-2.15937 + 1.56887i) q^{8} +(-2.85840 - 0.910807i) q^{9} +0.107298 q^{10} +(3.25999 - 0.610280i) q^{11} +(-0.0909718 - 0.335689i) q^{12} +(0.742450 + 0.824574i) q^{13} +(0.302419 + 2.87732i) q^{14} +(0.0445615 - 0.117081i) q^{15} +(-2.91827 + 3.24106i) q^{16} +(-0.0576906 - 0.177553i) q^{17} +(-4.42872 - 0.440023i) q^{18} +(-4.20255 + 3.05333i) q^{19} +(0.0142060 - 0.00301958i) q^{20} +(3.26525 + 0.864976i) q^{21} +(4.54231 - 1.89108i) q^{22} +(3.42420 - 5.93089i) q^{23} +(2.11054 + 4.11320i) q^{24} +(-4.56295 - 2.03156i) q^{25} +(1.33169 + 0.967532i) q^{26} +(-2.31942 + 4.64976i) q^{27} +(0.121013 + 0.372440i) q^{28} +(0.337596 - 3.21201i) q^{29} +(0.0285505 - 0.183640i) q^{30} +(1.10232 + 1.22425i) q^{31} +(-0.565872 + 0.980120i) q^{32} +(-0.177051 - 5.74183i) q^{33} +(-0.138479 - 0.239852i) q^{34} +(-0.0435881 + 0.134150i) q^{35} +(-0.598735 + 0.0663750i) q^{36} +(-7.75416 - 5.63373i) q^{37} +(-5.15652 + 5.72690i) q^{38} +(1.60881 - 1.05129i) q^{39} +(-0.176361 + 0.0785208i) q^{40} +(-0.529271 - 5.03568i) q^{41} +(5.00497 + 0.248028i) q^{42} +(4.06266 + 7.03673i) q^{43} +(0.548173 - 0.378204i) q^{44} +(-0.188526 - 0.107420i) q^{45} +(3.13951 - 9.66242i) q^{46} +(7.93189 + 3.53150i) q^{47} +(4.77054 + 5.85699i) q^{48} +(3.12679 + 0.664620i) q^{49} +(-7.24787 - 1.54058i) q^{50} +(-0.319231 + 0.0514924i) q^{51} +(0.203541 + 0.0906224i) q^{52} +(0.467571 - 1.43904i) q^{53} +(-1.93152 + 7.46263i) q^{54} +(0.239811 + 0.00584740i) q^{55} +(-2.60269 - 4.50800i) q^{56} +(4.10751 + 8.00508i) q^{57} +(-0.500827 - 4.76505i) q^{58} +(-4.84750 + 2.15825i) q^{59} +(-0.00138796 - 0.0251169i) q^{60} +(4.73508 - 5.25884i) q^{61} +(1.97717 + 1.43649i) q^{62} +(2.34924 - 5.35829i) q^{63} +(2.17659 - 6.69887i) q^{64} +(0.0401262 + 0.0695006i) q^{65} +(-2.02792 - 8.27732i) q^{66} +(-0.447660 + 0.775370i) q^{67} +(-0.0250842 - 0.0278588i) q^{68} +(-9.23953 - 7.43861i) q^{69} +(-0.0218731 + 0.208109i) q^{70} +(-0.476791 - 1.46741i) q^{71} +(7.60128 - 2.51770i) q^{72} +(9.31301 + 6.76630i) q^{73} +(-12.9897 - 5.78337i) q^{74} +(-4.69112 + 7.26887i) q^{75} +(-0.521545 + 0.903343i) q^{76} +(0.519100 + 6.44728i) q^{77} +(2.01027 - 2.02173i) q^{78} +(12.9790 - 2.75878i) q^{79} +(-0.255196 + 0.185411i) q^{80} +(7.34086 + 5.20689i) q^{81} +(-2.32122 - 7.14398i) q^{82} +(-12.0223 + 13.3521i) q^{83} +(0.669627 - 0.108012i) q^{84} +(-0.00141143 - 0.0134288i) q^{85} +(8.06569 + 8.95785i) q^{86} +(-5.40749 - 1.43246i) q^{87} +(-6.08208 + 6.43234i) q^{88} -12.3990 q^{89} +(-0.306701 - 0.0977279i) q^{90} +(-1.75064 + 1.27192i) q^{91} +(0.143744 - 1.36763i) q^{92} +(2.38859 - 1.56085i) q^{93} +(12.5992 + 2.67803i) q^{94} +(-0.343232 + 0.152817i) q^{95} +(1.52689 + 1.22928i) q^{96} +(-10.2251 + 2.17341i) q^{97} +4.74225 q^{98} +(-9.87420 - 1.22480i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - q^{2} - 12 q^{3} + 11 q^{4} - 8 q^{5} - 7 q^{6} - 2 q^{7} + 6 q^{8} - 22 q^{9} - 8 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 10 q^{14} - 20 q^{15} - 9 q^{16} - 20 q^{17} - 21 q^{18} + 8 q^{19}+ \cdots - 182 q^{99}+O(q^{100}) $ 72 * q - q^2 - 12 * q^3 + 11 * q^4 - 8 * q^5 - 7 * q^6 - 2 * q^7 + 6 * q^8 - 22 * q^9 - 8 * q^10 - 2 * q^11 - 16 * q^12 - 11 * q^13 - 10 * q^14 - 20 * q^15 - 9 * q^16 - 20 * q^17 - 21 * q^18 + 8 * q^19 - 45 * q^20 - 16 * q^21 - 16 * q^22 + 20 * q^23 + 36 * q^24 + 11 * q^25 - 12 * q^26 + 27 * q^27 - 54 * q^28 - 23 * q^29 - 6 * q^30 + 3 * q^31 + 18 * q^32 + 28 * q^33 + 8 * q^34 + 18 * q^35 + 75 * q^36 - 42 * q^37 - q^38 - 11 * q^39 - 25 * q^40 + 10 * q^41 + 61 * q^42 - 8 * q^43 + 38 * q^44 + 40 * q^45 - 18 * q^46 - 34 * q^47 - 50 * q^48 + q^49 + 42 * q^51 - 27 * q^52 + 4 * q^53 + 34 * q^54 + 18 * q^55 + 114 * q^56 - 21 * q^57 + q^58 - 16 * q^59 - 63 * q^60 - 3 * q^61 + 184 * q^62 - 10 * q^63 + 26 * q^64 + 84 * q^65 + 93 * q^66 + 10 * q^67 - 23 * q^68 + 42 * q^69 - 46 * q^70 - 48 * q^71 + 2 * q^72 - 40 * q^73 + 68 * q^74 + 28 * q^75 + 16 * q^76 - 26 * q^77 - 64 * q^78 + 19 * q^79 - 56 * q^80 + 14 * q^81 + 94 * q^82 + 7 * q^83 - 15 * q^84 + 25 * q^85 - 77 * q^86 - 120 * q^87 + 18 * q^88 - 56 * q^89 - 64 * q^90 + 20 * q^91 + 50 * q^92 - 53 * q^93 - 63 * q^94 - 77 * q^95 - 97 * q^96 - 33 * q^97 - 328 * q^98 - 182 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.45109	−	0.308439i	1.02608	−	0.218099i	0.336020	−	0.941855i	$-0.390919\pi$
$2$	1.45109	−	0.308439i	1.02608	−	0.218099i	0.690057	+	0.723755i	$0.257586\pi$
$3$	0.266086	−	1.71149i	0.153625	−	0.988129i
$3$	0.266086	−	1.71149i	0.153625	−	0.988129i
$4$	0.183441	−	0.0816732i	0.0917205	−	0.0408366i
$5$	0.0707467	+	0.0150377i	0.0316389	+	0.00672505i	0.223704	−	0.974657i	$-0.428185\pi$
$5$	0.0707467	+	0.0150377i	0.0316389	+	0.00672505i	−0.192065	+	0.981382i	$0.561518\pi$
$6$	−0.141775	−	2.56560i	−0.0578795	−	1.04740i
$7$	−0.203853	+	1.93954i	−0.0770493	+	0.733076i	0.885988	+	0.463708i	$0.153481\pi$
$7$	−0.203853	+	1.93954i	−0.0770493	+	0.733076i	−0.963037	+	0.269368i	$0.913185\pi$
$8$	−2.15937	+	1.56887i	−0.763453	+	0.554681i
$9$	−2.85840	−	0.910807i	−0.952799	−	0.303602i
$10$	0.107298			0.0339307
$11$	3.25999	−	0.610280i	0.982925	−	0.184006i
$11$	3.25999	−	0.610280i	0.982925	−	0.184006i
$12$	−0.0909718	−	0.335689i	−0.0262613	−	0.0969052i
$13$	0.742450	+	0.824574i	0.205918	+	0.228696i	0.837254	−	0.546814i	$-0.184160\pi$
$13$	0.742450	+	0.824574i	0.205918	+	0.228696i	−0.631336	+	0.775510i	$0.717493\pi$
$14$	0.302419	+	2.87732i	0.0808247	+	0.768996i
$15$	0.0445615	−	0.117081i	0.0115057	−	0.0302302i
$16$	−2.91827	+	3.24106i	−0.729567	+	0.810266i
$17$	−0.0576906	−	0.177553i	−0.0139920	−	0.0430630i	0.943817	−	0.330469i	$-0.107207\pi$
$17$	−0.0576906	−	0.177553i	−0.0139920	−	0.0430630i	−0.957809	+	0.287406i	$0.907207\pi$
$18$	−4.42872	−	0.440023i	−1.04386	−	0.103714i
$19$	−4.20255	+	3.05333i	−0.964132	+	0.700483i	−0.954107	−	0.299467i	$-0.903191\pi$
$19$	−4.20255	+	3.05333i	−0.964132	+	0.700483i	−0.0100254	+	0.999950i	$0.503191\pi$
$20$	0.0142060	−	0.00301958i	0.00317656	−	0.000675199i
$21$	3.26525	+	0.864976i	0.712537	+	0.188753i
$22$	4.54231	−	1.89108i	0.968425	−	0.403180i
$23$	3.42420	−	5.93089i	0.713995	−	1.23668i	−0.249351	−	0.968413i	$-0.580217\pi$
$23$	3.42420	−	5.93089i	0.713995	−	1.23668i	0.963346	−	0.268263i	$-0.0864495\pi$
$24$	2.11054	+	4.11320i	0.430811	+	0.839603i
$25$	−4.56295	−	2.03156i	−0.912590	−	0.406311i
$26$	1.33169	+	0.967532i	0.261166	+	0.189749i
$27$	−2.31942	+	4.64976i	−0.446372	+	0.894848i
$28$	0.121013	+	0.372440i	0.0228693	+	0.0703845i
$29$	0.337596	−	3.21201i	0.0626900	−	0.596455i	−0.917409	−	0.397946i	$-0.869723\pi$
$29$	0.337596	−	3.21201i	0.0626900	−	0.596455i	0.980099	−	0.198510i	$-0.0636101\pi$
$30$	0.0285505	−	0.183640i	0.00521259	−	0.0335279i
$31$	1.10232	+	1.22425i	0.197982	+	0.219881i	0.833958	−	0.551827i	$-0.186069\pi$
$31$	1.10232	+	1.22425i	0.197982	+	0.219881i	−0.635977	+	0.771708i	$0.719403\pi$
$32$	−0.565872	+	0.980120i	−0.100033	+	0.173262i
$33$	−0.177051	−	5.74183i	−0.0308205	−	0.999525i
$34$	−0.138479	−	0.239852i	−0.0237489	−	0.0411343i
$35$	−0.0435881	+	0.134150i	−0.00736773	+	0.0226755i
$36$	−0.598735	+	0.0663750i	−0.0997892	+	0.0110625i
$37$	−7.75416	−	5.63373i	−1.27478	−	0.926179i	−0.275395	−	0.961331i	$-0.588808\pi$
$37$	−7.75416	−	5.63373i	−1.27478	−	0.926179i	−0.999382	+	0.0351519i	$0.988808\pi$
$38$	−5.15652	+	5.72690i	−0.836499	+	0.929026i
$39$	1.60881	−	1.05129i	0.257615	−	0.168341i
$40$	−0.176361	+	0.0785208i	−0.0278851	+	0.0124152i
$41$	−0.529271	−	5.03568i	−0.0826582	−	0.786441i	−0.954812	−	0.297209i	$-0.903944\pi$
$41$	−0.529271	−	5.03568i	−0.0826582	−	0.786441i	0.872154	−	0.489231i	$-0.162723\pi$
$42$	5.00497	+	0.248028i	0.772284	+	0.0382716i
$43$	4.06266	+	7.03673i	0.619549	+	1.07309i	0.989568	+	0.144066i	$0.0460179\pi$
$43$	4.06266	+	7.03673i	0.619549	+	1.07309i	−0.370019	+	0.929024i	$0.620649\pi$
$44$	0.548173	−	0.378204i	0.0826402	−	0.0570165i
$45$	−0.188526	−	0.107420i	−0.0281038	−	0.0160133i
$46$	3.13951	−	9.66242i	0.462896	−	1.42465i
$47$	7.93189	+	3.53150i	1.15698	+	0.515123i	0.893289	−	0.449483i	$-0.148392\pi$
$47$	7.93189	+	3.53150i	1.15698	+	0.515123i	0.263696	+	0.964606i	$0.415058\pi$
$48$	4.77054	+	5.85699i	0.688568	+	0.845383i
$49$	3.12679	+	0.664620i	0.446684	+	0.0949457i
$50$	−7.24787	−	1.54058i	−1.02500	−	0.217871i
$51$	−0.319231	+	0.0514924i	−0.0447013	+	0.00721038i
$52$	0.203541	+	0.0906224i	0.0282261	+	0.0125671i
$53$	0.467571	−	1.43904i	0.0642259	−	0.197667i	−0.913794	−	0.406177i	$-0.866862\pi$
$53$	0.467571	−	1.43904i	0.0642259	−	0.197667i	0.978020	+	0.208510i	$0.0668615\pi$
$54$	−1.93152	+	7.46263i	−0.262846	+	1.01554i
$55$	0.239811	+	0.00584740i	0.0323361	+	0.000788463i
$56$	−2.60269	−	4.50800i	−0.347800	−	0.602406i
$57$	4.10751	+	8.00508i	0.544053	+	1.06030i
$58$	−0.500827	−	4.76505i	−0.0657618	−	0.625681i
$59$	−4.84750	+	2.15825i	−0.631091	+	0.280980i	−0.697248	−	0.716830i	$-0.745593\pi$
$59$	−4.84750	+	2.15825i	−0.631091	+	0.280980i	0.0661578	+	0.997809i	$0.478926\pi$
$60$	−0.00138796	−	0.0251169i	−0.000179185	−	0.00324258i
$61$	4.73508	−	5.25884i	0.606265	−	0.673325i	−0.359380	−	0.933191i	$-0.617012\pi$
$61$	4.73508	−	5.25884i	0.606265	−	0.673325i	0.965645	+	0.259866i	$0.0836784\pi$
$62$	1.97717	+	1.43649i	0.251100	+	0.182435i
$63$	2.34924	−	5.35829i	0.295976	−	0.675081i
$64$	2.17659	−	6.69887i	0.272074	−	0.837359i
$65$	0.0401262	+	0.0695006i	0.00497704	+	0.00862049i
$66$	−2.02792	−	8.27732i	−0.249620	−	1.01887i
$67$	−0.447660	+	0.775370i	−0.0546904	+	0.0947265i	−0.892074	−	0.451888i	$-0.850751\pi$
$67$	−0.447660	+	0.775370i	−0.0546904	+	0.0947265i	0.837384	+	0.546615i	$0.184084\pi$
$68$	−0.0250842	−	0.0278588i	−0.00304190	−	0.00337837i
$69$	−9.23953	−	7.43861i	−1.11231	−	0.895504i
$70$	−0.0218731	+	0.208109i	−0.00261433	+	0.0248737i
$71$	−0.476791	−	1.46741i	−0.0565847	−	0.174150i	0.918770	−	0.394794i	$-0.129184\pi$
$71$	−0.476791	−	1.46741i	−0.0565847	−	0.174150i	−0.975354	+	0.220644i	$0.929184\pi$
$72$	7.60128	−	2.51770i	0.895819	−	0.296713i
$73$	9.31301	+	6.76630i	1.09001	+	0.791935i	0.979400	−	0.201929i	$-0.0647211\pi$
$73$	9.31301	+	6.76630i	1.09001	+	0.791935i	0.110605	+	0.993864i	$0.464721\pi$
$74$	−12.9897	−	5.78337i	−1.51002	−	0.672303i
$75$	−4.69112	+	7.26887i	−0.541684	+	0.839337i
$76$	−0.521545	+	0.903343i	−0.0598253	+	0.103620i
$77$	0.519100	+	6.44728i	0.0591569	+	0.734736i
$78$	2.01027	−	2.02173i	0.227618	−	0.228916i
$79$	12.9790	−	2.75878i	1.46026	−	0.310387i	0.591772	−	0.806105i	$-0.298429\pi$
$79$	12.9790	−	2.75878i	1.46026	−	0.310387i	0.868483	+	0.495719i	$0.165095\pi$
$80$	−0.255196	+	0.185411i	−0.0285318	+	0.0207295i
$81$	7.34086	+	5.20689i	0.815651	+	0.578544i
$82$	−2.32122	−	7.14398i	−0.256336	−	0.788921i
$83$	−12.0223	+	13.3521i	−1.31962	+	1.46559i	−0.536207	+	0.844086i	$0.680143\pi$
$83$	−12.0223	+	13.3521i	−1.31962	+	1.46559i	−0.783413	+	0.621501i	$0.786523\pi$
$84$	0.669627	−	0.108012i	0.0730622	−	0.0117850i
$85$	−0.00141143	−	0.0134288i	−0.000153091	−	0.00145656i
$86$	8.06569	+	8.95785i	0.869745	+	0.965950i
$87$	−5.40749	−	1.43246i	−0.579744	−	0.153576i
$88$	−6.08208	+	6.43234i	−0.648352	+	0.685690i
$89$	−12.3990			−1.31429			−0.657145	−	0.753764i	$-0.728236\pi$
$89$	−12.3990			−1.31429			−0.657145	+	0.753764i	$0.728236\pi$
$90$	−0.306701	−	0.0977279i	−0.0323291	−	0.0103014i
$91$	−1.75064	+	1.27192i	−0.183517	+	0.133333i
$92$	0.143744	−	1.36763i	0.0149864	−	0.142586i
$93$	2.38859	−	1.56085i	0.247686	−	0.161852i
$94$	12.5992	+	2.67803i	1.29950	+	0.276218i
$95$	−0.343232	+	0.152817i	−0.0352149	+	0.0156787i
$96$	1.52689	+	1.22928i	0.155838	+	0.125463i
$97$	−10.2251	+	2.17341i	−1.03820	+	0.220676i	−0.695318	−	0.718703i	$-0.744736\pi$
$97$	−10.2251	+	2.17341i	−1.03820	+	0.220676i	−0.342881	+	0.939379i	$0.611403\pi$
$98$	4.74225			0.479040
$99$	−9.87420	−	1.22480i	−0.992395	−	0.123097i
$100$	−1.00296			−0.100296
$101$	3.38646	−	0.719815i	0.336966	−	0.0716243i	−0.0363213	−	0.999340i	$-0.511564\pi$
$101$	3.38646	−	0.719815i	0.336966	−	0.0716243i	0.373287	+	0.927716i	$0.378231\pi$
$102$	−0.447352	+	0.173184i	−0.0442944	+	0.0171477i
$103$	−16.3378	+	7.27407i	−1.60981	+	0.716735i	−0.997280	−	0.0737091i	$-0.976516\pi$
$103$	−16.3378	+	7.27407i	−1.60981	+	0.716735i	−0.612534	+	0.790444i	$0.709850\pi$
$104$	−2.89688	−	0.615750i	−0.284062	−	0.0603793i
$105$	0.217999	+	0.110296i	0.0212745	+	0.0107638i
$106$	0.234634	−	2.23239i	0.0227897	−	0.216829i
$107$	11.3281	−	8.23036i	1.09513	−	0.795659i	0.114872	−	0.993380i	$-0.463354\pi$
$107$	11.3281	−	8.23036i	1.09513	−	0.795659i	0.980258	+	0.197722i	$0.0633542\pi$
$108$	−0.0457148	+	1.04239i	−0.00439891	+	0.100304i
$109$	−5.00844			−0.479722			−0.239861	−	0.970807i	$-0.577102\pi$
$109$	−5.00844			−0.479722			−0.239861	+	0.970807i	$0.577102\pi$
$110$	0.349791	−	0.0654820i	0.0333513	−	0.00624346i
$111$	−11.7053	+	11.7721i	−1.11102	+	1.11736i
$112$	−5.69126	−	6.32078i	−0.537773	−	0.597258i
$113$	1.18013	+	11.2281i	0.111017	+	1.05626i	0.898215	+	0.439556i	$0.144864\pi$
$113$	1.18013	+	11.2281i	0.111017	+	1.05626i	−0.787198	+	0.616700i	$0.788469\pi$
$114$	8.42945	+	10.3492i	0.789491	+	0.969290i
$115$	0.331438	−	0.368099i	0.0309067	−	0.0343254i
$116$	−0.200406	−	0.616787i	−0.0186072	−	0.0572672i
$117$	−1.37119	−	3.03319i	−0.126766	−	0.280418i
$118$	−6.36848	+	4.62697i	−0.586266	+	0.425947i
$119$	0.356131	−	0.0756981i	0.0326465	−	0.00693923i
$120$	0.0874605	+	0.322733i	0.00798401	+	0.0294613i
$121$	10.2551	−	3.97902i	0.932283	−	0.361729i
$122$	5.24900	−	9.09154i	0.475222	−	0.823109i
$123$	−8.75934	−	0.434081i	−0.789803	−	0.0391397i
$124$	0.302198	+	0.134547i	0.0271382	+	0.0120827i
$125$	−0.584833	−	0.424906i	−0.0523091	−	0.0380048i
$126$	1.75625	−	8.49997i	0.156459	−	0.757237i
$127$	6.14382	+	18.9087i	0.545176	+	1.67788i	0.720570	+	0.693382i	$0.243880\pi$
$127$	6.14382	+	18.9087i	0.545176	+	1.67788i	−0.175394	+	0.984498i	$0.556120\pi$
$128$	1.32884	−	12.6431i	0.117454	−	1.11750i
$129$	13.1243	−	5.08082i	1.15553	−	0.447341i
$130$	0.0796635	+	0.0884752i	0.00698695	+	0.00775979i
$131$	4.33332	−	7.50552i	0.378604	−	0.655761i	−0.612256	−	0.790660i	$-0.709738\pi$
$131$	4.33332	−	7.50552i	0.378604	−	0.655761i	0.990859	+	0.134899i	$0.0430711\pi$
$132$	−0.501432	−	1.03883i	−0.0436441	−	0.0904183i
$133$	−5.06535	−	8.77344i	−0.439221	−	0.760753i
$134$	−0.410441	+	1.26321i	−0.0354567	+	0.109125i
$135$	−0.234013	+	0.294077i	−0.0201406	+	0.0253101i
$136$	0.403134	+	0.292894i	0.0345685	+	0.0251155i
$137$	4.90205	−	5.44428i	0.418810	−	0.465136i	−0.496411	−	0.868088i	$-0.665349\pi$
$137$	4.90205	−	5.44428i	0.418810	−	0.465136i	0.915221	+	0.402952i	$0.132016\pi$
$138$	−15.7018	−	7.94427i	−1.33662	−	0.676262i
$139$	−4.79325	+	2.13409i	−0.406558	+	0.181011i	−0.599818	−	0.800136i	$-0.704760\pi$
$139$	−4.79325	+	2.13409i	−0.406558	+	0.181011i	0.193260	+	0.981148i	$0.438094\pi$
$140$	0.00296064	+	0.0281686i	0.000250220	+	0.00238068i
$141$	8.15470	−	12.6357i	0.686750	−	1.06412i
$142$	−1.14448	−	1.98229i	−0.0960423	−	0.166350i
$143$	2.92360	+	2.23500i	0.244484	+	0.186900i
$144$	11.2935	−	6.60627i	0.941129	−	0.550522i
$145$	0.0721850	−	0.222162i	0.00599463	−	0.0184496i
$146$	15.6010	+	6.94602i	1.29115	+	0.574857i
$147$	1.96949	−	5.17463i	0.162440	−	0.426796i
$148$	−1.88256	−	0.400150i	−0.154745	−	0.0328921i
$149$	−2.11557	−	0.449679i	−0.173314	−	0.0368391i	0.120437	−	0.992721i	$-0.461570\pi$
$149$	−2.11557	−	0.449679i	−0.173314	−	0.0368391i	−0.293751	+	0.955882i	$0.594904\pi$
$150$	−4.56525	+	11.9947i	−0.372751	+	0.979365i
$151$	6.37237	+	2.83716i	0.518576	+	0.230885i	0.649298	−	0.760534i	$-0.275063\pi$
$151$	6.37237	+	2.83716i	0.518576	+	0.230885i	−0.130722	+	0.991419i	$0.541729\pi$
$152$	4.28457	−	13.1866i	0.347525	−	1.06957i
$153$	0.00318575	+	0.560063i	0.000257553	+	0.0452784i
$154$	2.74185	+	9.19548i	0.220945	+	0.740993i
$155$	0.0595754	+	0.103188i	0.00478521	+	0.00828823i
$156$	0.209259	−	0.324245i	0.0167541	−	0.0259604i
$157$	−1.84463	−	17.5505i	−0.147217	−	1.40068i	−0.779723	−	0.626125i	$-0.784640\pi$
$157$	−1.84463	−	17.5505i	−0.147217	−	1.40068i	0.632505	−	0.774556i	$-0.282027\pi$
$158$	17.9828	−	8.00648i	1.43064	−	0.636961i
$159$	−2.33848	−	1.18315i	−0.185454	−	0.0938300i
$160$	−0.0547723	+	0.0608308i	−0.00433013	+	0.00480910i
$161$	10.8051	+	7.85039i	0.851564	+	0.618697i
$162$	12.2583	+	5.29147i	0.963101	+	0.415737i
$163$	1.14520	−	3.52457i	0.0896991	−	0.276065i	−0.896137	−	0.443778i	$-0.853638\pi$
$163$	1.14520	−	3.52457i	0.0896991	−	0.276065i	0.985836	+	0.167712i	$0.0536380\pi$
$164$	−0.508370	−	0.880522i	−0.0396970	−	0.0687572i
$165$	0.0738181	−	0.408878i	0.00574673	−	0.0318311i
$166$	−13.3272	+	23.0833i	−1.03439	+	1.79161i
$167$	−1.35866	−	1.50895i	−0.105136	−	0.116766i	0.688280	−	0.725445i	$-0.258366\pi$
$167$	−1.35866	−	1.50895i	−0.105136	−	0.116766i	−0.793416	+	0.608680i	$0.791699\pi$
$168$	−8.40793	+	3.25497i	−0.648686	+	0.251126i
$169$	1.23018	−	11.7044i	0.0946292	−	0.900337i
$170$	−0.00619009	−	0.0190511i	−0.000474758	−	0.00146116i
$171$	14.7936	−	4.89993i	1.13129	−	0.374707i
$172$	1.31997	+	0.959014i	0.100647	+	0.0731241i
$173$	7.86043	+	3.49969i	0.597617	+	0.266076i	0.683172	−	0.730257i	$-0.260600\pi$
$173$	7.86043	+	3.49969i	0.597617	+	0.266076i	−0.0855552	+	0.996333i	$0.527266\pi$
$174$	−8.28859	−	0.410752i	−0.628357	−	0.0311390i
$175$	4.87045	−	8.43586i	0.368171	−	0.637691i
$176$	−7.53557	+	12.3468i	−0.568015	+	0.930676i
$177$	2.40396	+	8.87073i	0.180693	+	0.666765i
$178$	−17.9921	+	3.82433i	−1.34856	+	0.286646i
$179$	−2.03852	+	1.48107i	−0.152366	+	0.110701i	−0.661357	−	0.750072i	$-0.730019\pi$
$179$	−2.03852	+	1.48107i	−0.152366	+	0.110701i	0.508990	+	0.860772i	$0.330019\pi$
$180$	−0.0433567	−	0.00430777i	−0.00323162	−	0.000321083i
$181$	4.40514	+	13.5576i	0.327432	+	1.00773i	0.970331	+	0.241780i	$0.0777314\pi$
$181$	4.40514	+	13.5576i	0.327432	+	1.00773i	−0.642899	+	0.765951i	$0.722269\pi$
$182$	−2.14803	+	2.38563i	−0.159223	+	0.176835i
$183$	−7.74051	−	9.50334i	−0.572195	−	0.702507i
$184$	1.91070	+	18.1791i	0.140859	+	1.34018i
$185$	−0.463863	−	0.515172i	−0.0341039	−	0.0378762i
$186$	2.98464	−	3.00167i	0.218845	−	0.220093i
$187$	−0.296428	−	0.543615i	−0.0216770	−	0.0397531i
$188$	1.74346			0.127155
$189$	−8.54556	−	5.44646i	−0.621598	−	0.396172i
$190$	−0.450926	+	0.327617i	−0.0327136	+	0.0237678i
$191$	1.78748	−	17.0067i	0.129338	−	1.23057i	−0.716677	−	0.697405i	$-0.754338\pi$
$191$	1.78748	−	17.0067i	0.129338	−	1.23057i	0.846015	−	0.533160i	$-0.178996\pi$
$192$	−10.8859	−	5.50769i	−0.785621	−	0.397484i
$193$	−16.2756	−	3.45949i	−1.17154	−	0.249020i	−0.419265	−	0.907864i	$-0.637712\pi$
$193$	−16.2756	−	3.45949i	−1.17154	−	0.249020i	−0.752279	+	0.658844i	$0.771046\pi$
$194$	−14.1672	+	6.30762i	−1.01714	+	0.452861i
$195$	0.129627	−	0.0501824i	0.00928275	−	0.00359364i
$196$	0.627863	−	0.133456i	0.0448474	−	0.00953260i
$197$	−20.1670			−1.43684			−0.718421	−	0.695609i	$-0.755135\pi$
$197$	−20.1670			−1.43684			−0.718421	+	0.695609i	$0.755135\pi$
$198$	−14.7061	+	1.26829i	−1.04512	+	0.0901335i
$199$	15.9840			1.13308			0.566539	−	0.824035i	$-0.308282\pi$
$199$	15.9840			1.13308			0.566539	+	0.824035i	$0.308282\pi$
$200$	13.0404	−	2.77181i	0.922092	−	0.195997i
$201$	1.20792	+	0.972480i	0.0852002	+	0.0685935i
$202$	4.69205	−	2.08904i	0.330132	−	0.146984i
$203$	6.16099	+	1.30956i	0.432417	+	0.0919130i
$204$	−0.0543546	+	0.0355185i	−0.00380558	+	0.00248679i
$205$	0.0382807	−	0.364217i	0.00267364	−	0.0254380i
$206$	−21.4641	+	15.5946i	−1.49547	+	1.08652i
$207$	−15.1896	+	13.8340i	−1.05575	+	0.961533i
$208$	−4.83916			−0.335535
$209$	−11.8369	+	12.5186i	−0.818776	+	0.865929i
$210$	0.350356	+	0.0928103i	0.0241768	+	0.00640452i
$211$	−6.56121	−	7.28696i	−0.451692	−	0.501655i	0.473689	−	0.880692i	$-0.342922\pi$
$211$	−6.56121	−	7.28696i	−0.451692	−	0.501655i	−0.925381	+	0.379037i	$0.876255\pi$
$212$	−0.0317590	−	0.302166i	−0.00218121	−	0.0207529i
$213$	−2.63833	+	0.425566i	−0.180775	+	0.0291593i
$214$	13.8996	−	15.4370i	0.950155	−	1.05525i
$215$	0.181604	+	0.558918i	0.0123853	+	0.0381179i
$216$	−2.28642	−	13.6794i	−0.155571	−	0.930768i
$217$	−2.59918	+	1.88841i	−0.176444	+	0.128194i
$218$	−7.26771	+	1.54480i	−0.492231	+	0.104627i
$219$	14.0585	−	14.1387i	0.949986	−	0.955405i
$220$	0.0444687	−	0.0185135i	0.00299808	−	0.00124818i
$221$	0.103573	−	0.179395i	0.00696711	−	0.0120674i
$222$	−13.3545	+	20.6928i	−0.896298	+	1.38881i
$223$	15.4459	+	6.87698i	1.03434	+	0.460516i	0.852453	−	0.522804i	$-0.175114\pi$
$223$	15.4459	+	6.87698i	1.03434	+	0.460516i	0.181884	+	0.983320i	$0.441781\pi$
$224$	−1.78562	−	1.29733i	−0.119307	−	0.0866815i
$225$	11.1924	+	9.96296i	0.746157	+	0.664197i
$226$	5.17567	+	15.9291i	0.344280	+	1.05959i
$227$	−0.332814	+	3.16651i	−0.0220896	+	0.210169i	0.977910	+	0.209028i	$0.0670299\pi$
$227$	−0.332814	+	3.16651i	−0.0220896	+	0.210169i	−0.999999	+	0.00114100i	$0.999637\pi$
$228$	1.40729	+	1.13299i	0.0931998	+	0.0750338i
$229$	3.22604	+	3.58288i	0.213183	+	0.236764i	0.840247	−	0.542204i	$-0.182410\pi$
$229$	3.22604	+	3.58288i	0.213183	+	0.236764i	−0.627064	+	0.778968i	$0.715743\pi$
$230$	0.367410	−	0.636373i	0.0242263	−	0.0419612i
$231$	11.1726	+	0.827096i	0.735102	+	0.0544190i
$232$	4.31025	+	7.46557i	0.282982	+	0.490138i
$233$	−6.50281	+	20.0136i	−0.426013	+	1.31113i	0.476007	+	0.879441i	$0.342084\pi$
$233$	−6.50281	+	20.0136i	−0.426013	+	1.31113i	−0.902021	+	0.431693i	$0.857916\pi$
$234$	−2.92527	−	3.97850i	−0.191231	−	0.260083i
$235$	0.508049	+	0.369120i	0.0331415	+	0.0240787i
$236$	−0.712959	+	0.791821i	−0.0464097	+	0.0515432i
$237$	−1.26808	−	22.9476i	−0.0823709	−	1.49060i
$238$	0.493431	−	0.219690i	0.0319844	−	0.0142404i
$239$	−1.49400	−	14.2145i	−0.0966391	−	0.919460i	−0.930205	−	0.367040i	$-0.880371\pi$
$239$	−1.49400	−	14.2145i	−0.0966391	−	0.919460i	0.833566	−	0.552420i	$-0.186295\pi$
$240$	0.249424	+	0.486100i	0.0161003	+	0.0313776i
$241$	−0.0808738	−	0.140078i	−0.00520954	−	0.00902319i	0.863409	−	0.504505i	$-0.168325\pi$
$241$	−0.0808738	−	0.140078i	−0.00520954	−	0.00902319i	−0.868618	+	0.495482i	$0.834992\pi$
$242$	13.6538	−	8.93700i	0.877701	−	0.574492i
$243$	10.8648	−	11.1783i	0.696980	−	0.717090i
$244$	0.439101	−	1.35142i	0.0281106	−	0.0865155i
$245$	0.211216	+	0.0940393i	0.0134941	+	0.00600795i
$246$	−12.8445	+	2.07183i	−0.818935	+	0.132095i
$247$	−5.63788	−	1.19837i	−0.358730	−	0.0762504i
$248$	−4.30100	−	0.914205i	−0.273113	−	0.0580521i
$249$	19.6531	+	24.1289i	1.24546	+	1.52911i
$250$	−0.979705	−	0.436193i	−0.0619620	−	0.0275872i
$251$	−2.75542	+	8.48032i	−0.173921	+	0.535273i	−0.999583	−	0.0288924i	$-0.990802\pi$
$251$	−2.75542	+	8.48032i	−0.173921	+	0.535273i	0.825662	+	0.564165i	$0.190802\pi$
$252$	−0.00668250	−	1.17480i	−0.000420958	−	0.0740054i
$253$	7.54337	−	21.4244i	0.474247	−	1.34694i
$254$	14.7474	+	25.5433i	0.925337	+	1.60273i
$255$	−0.0233589	−	0.00115758i	−0.00146279	−	7.24905e-5i
$256$	−0.498838	−	4.74613i	−0.0311774	−	0.296633i
$257$	3.89143	−	1.73258i	0.242741	−	0.108075i	−0.281761	−	0.959485i	$-0.590918\pi$
$257$	3.89143	−	1.73258i	0.242741	−	0.108075i	0.524501	+	0.851410i	$0.324252\pi$
$258$	17.4774	−	11.4208i	1.08810	−	0.711027i
$259$	12.5075	−	13.8910i	0.777180	−	0.863146i
$260$	0.0130371	+	0.00947202i	0.000808528	+	0.000587430i
$261$	−3.89050	+	8.87371i	−0.240816	+	0.549269i
$262$	3.97304	−	12.2278i	0.245455	−	0.755434i
$263$	−11.6890	−	20.2459i	−0.720774	−	1.24842i	−0.960690	−	0.277623i	$-0.910453\pi$
$263$	−11.6890	−	20.2459i	−0.720774	−	1.24842i	0.239916	−	0.970794i	$-0.422880\pi$
$264$	9.39054	+	12.1210i	0.577947	+	0.745995i
$265$	0.0547189	−	0.0947759i	0.00336136	−	0.00582204i
$266$	−10.0564	−	11.1687i	−0.616594	−	0.684798i
$267$	−3.29920	+	21.2207i	−0.201908	+	1.29869i
$268$	−0.0187923	+	0.178796i	−0.00114792	+	0.0109217i
$269$	−4.69356	−	14.4453i	−0.286172	−	0.880746i	−0.986045	−	0.166479i	$-0.946760\pi$
$269$	−4.69356	−	14.4453i	−0.286172	−	0.880746i	0.699873	−	0.714267i	$-0.253240\pi$
$270$	−0.248869	+	0.498911i	−0.0151457	+	0.0303628i
$271$	−12.7047	−	9.23053i	−0.771757	−	0.560715i	0.130736	−	0.991417i	$-0.458266\pi$
$271$	−12.7047	−	9.23053i	−0.771757	−	0.560715i	−0.902494	+	0.430703i	$0.858266\pi$
$272$	0.743818	+	0.331169i	0.0451006	+	0.0200801i
$273$	1.71105	+	3.33464i	0.103557	+	0.201822i
$274$	5.43409	−	9.41212i	0.328286	−	0.568607i
$275$	−16.1150	−	3.83818i	−0.971771	−	0.231451i
$276$	−2.30244	−	0.609924i	−0.138591	−	0.0367131i
$277$	−7.31447	+	1.55474i	−0.439484	+	0.0934152i	−0.422339	−	0.906438i	$-0.638791\pi$
$277$	−7.31447	+	1.55474i	−0.439484	+	0.0934152i	−0.0171446	+	0.999853i	$0.505458\pi$
$278$	−6.29720	+	4.57519i	−0.377681	+	0.274401i
$279$	−2.03580	−	4.50338i	−0.121880	−	0.269610i
$280$	−0.116342	−	0.358064i	−0.00695277	−	0.0213984i
$281$	−8.57053	+	9.51853i	−0.511275	+	0.567828i	−0.942410	−	0.334459i	$-0.891446\pi$
$281$	−8.57053	+	9.51853i	−0.511275	+	0.567828i	0.431136	+	0.902287i	$0.358113\pi$
$282$	7.93588	−	20.8507i	0.472575	−	1.24164i
$283$	0.685781	+	6.52477i	0.0407654	+	0.387857i	0.995814	+	0.0914066i	$0.0291363\pi$
$283$	0.685781	+	6.52477i	0.0407654	+	0.387857i	−0.955048	+	0.296450i	$0.904197\pi$
$284$	−0.207311	−	0.230243i	−0.0123017	−	0.0136624i
$285$	0.170215	+	0.628100i	0.0100827	+	0.0372055i
$286$	4.93178	+	2.34144i	0.291622	+	0.138452i
$287$	9.87477			0.582889
$288$	2.51019	−	2.28617i	0.147914	−	0.134714i
$289$	13.7251	−	9.97186i	0.807358	−	0.586580i
$290$	0.0362234	−	0.344643i	0.00212711	−	0.0202381i
$291$	0.999016	+	18.0784i	0.0585633	+	1.05978i
$292$	2.26101	+	0.480593i	0.132316	+	0.0281246i
$293$	−10.7462	+	4.78450i	−0.627798	+	0.279514i	−0.695871	−	0.718167i	$-0.744982\pi$
$293$	−10.7462	+	4.78450i	−0.627798	+	0.279514i	0.0680731	+	0.997680i	$0.478315\pi$
$294$	1.26185	−	8.11632i	0.0735924	−	0.473353i
$295$	−0.375400	+	0.0797936i	−0.0218566	+	0.00464577i
$296$	25.5827			1.48697
$297$	−4.72362	+	16.5737i	−0.274092	+	0.961703i
$298$	−3.20859			−0.185869
$299$	7.43275	−	1.57988i	0.429847	−	0.0913668i
$300$	−0.266872	+	1.71655i	−0.0154079	+	0.0991049i
$301$	−14.4762	+	6.44521i	−0.834392	+	0.371495i
$302$	10.1220	+	2.15149i	0.582455	+	0.123805i
$303$	−0.330866	−	5.98743i	−0.0190078	−	0.343969i
$304$	2.36812	−	22.5312i	0.135821	−	1.29225i
$305$	0.414072	−	0.300841i	0.0237097	−	0.0172261i
$306$	0.177368	+	0.811720i	0.0101395	+	0.0464029i
$307$	−23.8127			−1.35906			−0.679530	−	0.733647i	$-0.737816\pi$
$307$	−23.8127			−1.35906			−0.679530	+	0.733647i	$0.737816\pi$
$308$	0.621794	+	1.14030i	0.0354300	+	0.0649746i
$309$	8.10223	+	29.8976i	0.460920	+	1.70081i
$310$	0.118276	+	0.131359i	0.00671765	+	0.00746070i
$311$	−2.46141	−	23.4188i	−0.139574	−	1.32796i	−0.810197	−	0.586158i	$-0.800640\pi$
$311$	−2.46141	−	23.4188i	−0.139574	−	1.32796i	0.670623	−	0.741798i	$-0.266027\pi$
$312$	−1.82467	+	4.79413i	−0.103302	+	0.271414i
$313$	−7.66215	+	8.50968i	−0.433090	+	0.480996i	−0.919699	−	0.392625i	$-0.871567\pi$
$313$	−7.66215	+	8.50968i	−0.433090	+	0.480996i	0.486608	+	0.873620i	$0.338234\pi$
$314$	−8.08998	−	24.8984i	−0.456544	−	1.40510i
$315$	0.246777	−	0.343754i	0.0139043	−	0.0193684i
$316$	2.15557	−	1.56611i	0.121260	−	0.0881007i
$317$	−14.3949	+	3.05974i	−0.808499	+	0.171852i	−0.593575	−	0.804779i	$-0.702284\pi$
$317$	−14.3949	+	3.05974i	−0.808499	+	0.171852i	−0.214925	+	0.976631i	$0.568951\pi$
$318$	−3.75828	−	0.995581i	−0.210754	−	0.0558294i
$319$	−0.859667	−	10.6772i	−0.0481321	−	0.597806i
$320$	0.254722	−	0.441192i	0.0142394	−	0.0246634i
$321$	−11.0719	−	21.5779i	−0.617975	−	1.20436i
$322$	18.1006	+	8.05891i	1.00871	+	0.449105i
$323$	0.784578	+	0.570029i	0.0436551	+	0.0317173i
$324$	1.77188	+	0.355606i	0.0984377	+	0.0197559i
$325$	−1.71259	−	5.27081i	−0.0949975	−	0.292372i
$326$	0.574678	−	5.46770i	0.0318285	−	0.302828i
$327$	−1.33268	+	8.57190i	−0.0736972	+	0.474027i
$328$	9.04324	+	10.0435i	0.499329	+	0.554561i
$329$	−8.46642	+	14.6643i	−0.466769	+	0.808468i
$330$	−0.0189972	−	0.616088i	−0.00104576	−	0.0339145i
$331$	−6.73090	−	11.6583i	−0.369964	−	0.640796i	0.619596	−	0.784921i	$-0.287297\pi$
$331$	−6.73090	−	11.6583i	−0.369964	−	0.640796i	−0.989559	+	0.144125i	$0.953963\pi$
$332$	−1.11487	+	3.43123i	−0.0611867	+	0.188313i
$333$	17.0332	+	23.1660i	0.933415	+	1.26949i
$334$	−2.43696	−	1.77055i	−0.133344	−	0.0968804i
$335$	−0.0433302	+	0.0481231i	−0.00236738	+	0.00262925i
$336$	−12.3323	+	8.05866i	−0.672783	+	0.439636i
$337$	2.67174	−	1.18953i	0.145539	−	0.0647981i	−0.332675	−	0.943042i	$-0.607951\pi$
$337$	2.67174	−	1.18953i	0.145539	−	0.0647981i	0.478214	+	0.878244i	$0.341284\pi$
$338$	−1.82498	−	17.3636i	−0.0992660	−	0.944453i
$339$	19.5309	+	0.967878i	1.06077	+	0.0525679i
$340$	−0.00135569	−	0.00234812i	−7.35226e−5	−	0.000127345i
$341$	4.34067	+	3.31831i	0.235061	+	0.179697i
$342$	19.9555	−	11.6732i	1.07907	−	0.631212i
$343$	−6.14502	+	18.9124i	−0.331800	+	1.02117i
$344$	−19.8125	−	8.82110i	−1.06822	−	0.475602i
$345$	−0.541807	−	0.665198i	−0.0291699	−	0.0358131i
$346$	12.4856	+	2.65390i	0.671232	+	0.142675i
$347$	26.3326	+	5.59716i	1.41361	+	0.300471i	0.850527	−	0.525931i	$-0.176283\pi$
$347$	26.3326	+	5.59716i	1.41361	+	0.300471i	0.563080	+	0.826402i	$0.309616\pi$
$348$	−1.10895	+	0.178875i	−0.0594459	+	0.00958870i
$349$	−1.38942	−	0.618610i	−0.0743740	−	0.0331135i	0.369213	−	0.929345i	$-0.379627\pi$
$349$	−1.38942	−	0.618610i	−0.0743740	−	0.0331135i	−0.443587	+	0.896232i	$0.646294\pi$
$350$	4.46552	−	13.7434i	0.238692	−	0.734618i
$351$	−5.55612	+	1.53969i	−0.296564	+	0.0821824i
$352$	−1.24659	+	3.54053i	−0.0664436	+	0.188711i
$353$	−0.161316	−	0.279408i	−0.00858599	−	0.0148714i	0.861700	−	0.507417i	$-0.169400\pi$
$353$	−0.161316	−	0.279408i	−0.00858599	−	0.0148714i	−0.870286	+	0.492546i	$0.836066\pi$
$354$	6.22445	+	12.1308i	0.330826	+	0.644742i
$355$	−0.0116649	−	0.110984i	−0.000619111	−	0.00589044i
$356$	−2.27448	+	1.01266i	−0.120547	+	0.0536711i
$357$	−0.0347949	−	0.629658i	−0.00184154	−	0.0333250i
$358$	−2.50126	+	2.77793i	−0.132196	+	0.146818i
$359$	8.95215	+	6.50411i	0.472476	+	0.343274i	0.798406	−	0.602120i	$-0.205677\pi$
$359$	8.95215	+	6.50411i	0.472476	+	0.343274i	−0.325929	+	0.945394i	$0.605677\pi$
$360$	0.575626	−	0.0638131i	0.0303381	−	0.00336325i
$361$	2.46729	−	7.59354i	0.129857	−	0.399660i
$362$	10.5740	+	18.3147i	0.555756	+	0.962597i
$363$	−4.08131	−	18.6103i	−0.214213	−	0.976787i
$364$	−0.217258	+	0.376302i	−0.0113874	+	0.0197236i
$365$	0.557115	+	0.618739i	0.0291607	+	0.0323863i
$366$	−14.1634	−	11.4027i	−0.740332	−	0.596031i
$367$	−1.51089	+	14.3751i	−0.0788676	+	0.750375i	0.881603	+	0.471992i	$0.156465\pi$
$367$	−1.51089	+	14.3751i	−0.0788676	+	0.750375i	−0.960470	+	0.278383i	$0.910202\pi$
$368$	9.22966	+	28.4060i	0.481129	+	1.48076i
$369$	−3.07366	+	14.8760i	−0.160008	+	0.774415i
$370$	−0.832007	−	0.604489i	−0.0432540	−	0.0314259i
$371$	2.69575	+	1.20022i	0.139956	+	0.0623125i
$372$	0.310687	−	0.481407i	0.0161084	−	0.0249598i
$373$	−4.61875	+	7.99991i	−0.239150	+	0.414219i	−0.960471	−	0.278382i	$-0.910202\pi$
$373$	−4.61875	+	7.99991i	−0.239150	+	0.414219i	0.721321	+	0.692601i	$0.243535\pi$
$374$	−0.597817	−	0.697406i	−0.0309124	−	0.0360620i
$375$	−0.882839	+	0.887875i	−0.0455896	+	0.0458497i
$376$	−22.6684	+	4.81831i	−1.16903	+	0.248486i
$377$	2.89919	−	2.10638i	0.149316	−	0.108484i
$378$	−14.0803	−	5.26753i	−0.724212	−	0.270932i
$379$	1.54865	+	4.76624i	0.0795486	+	0.244825i	0.982920	−	0.184034i	$-0.0589156\pi$
$379$	1.54865	+	4.76624i	0.0795486	+	0.244825i	−0.903371	+	0.428859i	$0.858916\pi$
$380$	−0.0504818	+	0.0560657i	−0.00258966	+	0.00287611i
$381$	33.9969	−	5.48374i	1.74172	−	0.280941i
$382$	−2.65175	−	25.2297i	−0.135675	−	1.29086i
$383$	23.3912	+	25.9786i	1.19524	+	1.32744i	0.931889	+	0.362743i	$0.118160\pi$
$383$	23.3912	+	25.9786i	1.19524	+	1.32744i	0.263347	+	0.964701i	$0.415174\pi$
$384$	−21.2850	−	5.63846i	−1.08619	−	0.287736i
$385$	−0.0602275	+	0.463930i	−0.00306948	+	0.0236441i
$386$	−24.6845			−1.25641
$387$	−5.20358	−	23.8140i	−0.264513	−	1.21054i
$388$	−1.69819	+	1.23381i	−0.0862125	+	0.0626370i
$389$	2.29083	−	21.7958i	0.116150	−	1.10509i	−0.768828	−	0.639456i	$-0.779160\pi$
$389$	2.29083	−	21.7958i	0.116150	−	1.10509i	0.884977	−	0.465634i	$-0.154174\pi$
$390$	0.172622	−	0.112801i	0.00874105	−	0.00571191i
$391$	−1.25059	−	0.265822i	−0.0632452	−	0.0134432i
$392$	−7.79461	+	3.47038i	−0.393687	+	0.175281i
$393$	−11.6926	−	9.41354i	−0.589813	−	0.474850i
$394$	−29.2642	+	6.22030i	−1.47431	+	0.313374i
$395$	0.959709			0.0482882
$396$	−1.91137	+	0.581779i	−0.0960498	+	0.0292355i
$397$	−15.3168			−0.768726			−0.384363	−	0.923182i	$-0.625579\pi$
$397$	−15.3168			−0.768726			−0.384363	+	0.923182i	$0.625579\pi$
$398$	23.1943	−	4.93010i	1.16262	−	0.247124i
$399$	−16.3635	+	6.33480i	−0.819198	+	0.317137i
$400$	19.9003	−	8.86018i	0.995015	−	0.443009i
$401$	−0.210948	−	0.0448383i	−0.0105342	−	0.00223912i	0.202642	−	0.979253i	$-0.435047\pi$
$401$	−0.210948	−	0.0448383i	−0.0105342	−	0.00223912i	−0.213176	+	0.977014i	$0.568381\pi$
$402$	2.05276	+	1.03859i	0.102382	+	0.0518001i
$403$	−0.191067	+	1.81788i	−0.00951772	+	0.0905551i
$404$	0.562427	−	0.408627i	0.0279818	−	0.0203299i
$405$	0.441042	+	0.478760i	0.0219156	+	0.0237898i
$406$	9.34407			0.463739
$407$	−28.7167	−	13.6337i	−1.42343	−	0.675798i
$408$	0.608554	−	0.612025i	0.0301279	−	0.0302998i
$409$	15.1898	+	16.8699i	0.751086	+	0.834165i	0.990609	−	0.136725i	$-0.0436578\pi$
$409$	15.1898	+	16.8699i	0.751086	+	0.834165i	−0.239523	+	0.970891i	$0.576991\pi$
$410$	−0.0567898	−	0.540319i	−0.00280465	−	0.0266844i
$411$	−8.01346	−	9.83845i	−0.395275	−	0.485295i
$412$	−2.40293	+	2.66872i	−0.118384	+	0.131479i
$413$	−3.19782	−	9.84186i	−0.157354	−	0.484286i
$414$	−17.7746	+	24.7595i	−0.873572	+	1.21686i
$415$	−1.05132	+	0.763832i	−0.0516075	+	0.0374950i
$416$	−1.22831	+	0.261086i	−0.0602230	+	0.0128008i
$417$	2.37706	+	8.77145i	0.116405	+	0.429540i
$418$	−13.3152	+	21.8166i	−0.651269	+	1.06708i
$419$	−8.54073	+	14.7930i	−0.417242	+	0.722684i	−0.995661	−	0.0930557i	$-0.970337\pi$
$419$	−8.54073	+	14.7930i	−0.417242	+	0.722684i	0.578419	+	0.815740i	$0.303670\pi$
$420$	0.0489981	+	0.00242817i	0.00239086	+	0.000118482i
$421$	−5.47900	−	2.43941i	−0.267030	−	0.118889i	0.268854	−	0.963181i	$-0.413355\pi$
$421$	−5.47900	−	2.43941i	−0.267030	−	0.118889i	−0.535884	+	0.844291i	$0.680022\pi$
$422$	−11.7685	−	8.55031i	−0.572881	−	0.416223i
$423$	−19.4560	−	17.3189i	−0.945981	−	0.842072i
$424$	1.24801	+	3.84098i	0.0606087	+	0.186534i
$425$	−0.0974704	+	0.927368i	−0.00472801	+	0.0449840i
$426$	−3.69720	+	1.43130i	−0.179130	+	0.0693467i
$427$	9.23444	+	10.2559i	0.446886	+	0.496317i
$428$	1.40584	−	2.43499i	0.0679539	−	0.117700i
$429$	4.60311	−	4.40901i	0.222240	−	0.212869i
$430$	0.435915	+	0.755028i	0.0210217	+	0.0364107i
$431$	−1.23449	+	3.79938i	−0.0594635	+	0.183010i	−0.976376	−	0.216078i	$-0.930673\pi$
$431$	−1.23449	+	3.79938i	−0.0594635	+	0.183010i	0.916912	+	0.399088i	$0.130673\pi$
$432$	−8.30151	−	21.0866i	−0.399406	−	1.01453i
$433$	21.9374	+	15.9385i	1.05425	+	0.765954i	0.973015	−	0.230741i	$-0.0741151\pi$
$433$	21.9374	+	15.9385i	1.05425	+	0.765954i	0.0812301	+	0.996695i	$0.474115\pi$
$434$	−3.18919	+	3.54195i	−0.153086	+	0.170019i
$435$	−0.361021	−	0.182658i	−0.0173097	−	0.00875779i
$436$	−0.918754	+	0.409055i	−0.0440003	+	0.0195902i
$437$	3.71860	+	35.3801i	0.177885	+	1.69246i
$438$	16.0393	−	24.8527i	0.766385	−	1.18751i
$439$	12.7238	+	22.0383i	0.607275	+	1.05183i	0.991688	+	0.128669i	$0.0410706\pi$
$439$	12.7238	+	22.0383i	0.607275	+	1.05183i	−0.384413	+	0.923161i	$0.625596\pi$
$440$	−0.527015	+	0.363607i	−0.0251244	+	0.0173343i
$441$	−8.33227	−	4.74765i	−0.396775	−	0.226079i
$442$	0.0949623	−	0.292264i	0.00451690	−	0.0139016i
$443$	9.24918	+	4.11800i	0.439442	+	0.195652i	0.614518	−	0.788903i	$-0.289351\pi$
$443$	9.24918	+	4.11800i	0.439442	+	0.195652i	−0.175076	+	0.984555i	$0.556017\pi$
$444$	−1.18577	+	3.11550i	−0.0562743	+	0.147855i
$445$	−0.877188	−	0.186452i	−0.0415827	−	0.00883867i
$446$	24.5346	+	5.21499i	1.16175	+	0.246937i
$447$	−1.33255	+	3.50113i	−0.0630272	+	0.165598i
$448$	12.5490	+	5.58717i	0.592884	+	0.263969i
$449$	5.04599	−	15.5299i	0.238135	−	0.732904i	−0.758555	−	0.651609i	$-0.774094\pi$
$449$	5.04599	−	15.5299i	0.238135	−	0.732904i	0.996690	−	0.0812949i	$-0.0259056\pi$
$450$	19.3141	+	11.0050i	0.910476	+	0.518781i
$451$	−4.79860	−	16.0933i	−0.225957	−	0.757803i
$452$	1.13352	+	1.96332i	0.0533164	+	0.0923467i
$453$	6.55137	−	10.1513i	0.307810	−	0.476951i
$454$	0.493732	+	4.69755i	0.0231720	+	0.220467i
$455$	−0.142979	+	0.0636582i	−0.00670295	+	0.00298434i
$456$	−21.4286	−	10.8418i	−1.00349	−	0.507712i
$457$	−15.7293	+	17.4691i	−0.735784	+	0.817170i	−0.988635	−	0.150335i	$-0.951965\pi$
$457$	−15.7293	+	17.4691i	−0.735784	+	0.817170i	0.252852	+	0.967505i	$0.418632\pi$
$458$	5.78639	+	4.20406i	0.270380	+	0.196443i
$459$	0.959390	+	0.143572i	0.0447805	+	0.00670139i
$460$	0.0307354	−	0.0945940i	0.00143305	−	0.00441047i
$461$	3.89658	+	6.74907i	0.181482	+	0.314336i	0.942385	−	0.334529i	$-0.108577\pi$
$461$	3.89658	+	6.74907i	0.181482	+	0.314336i	−0.760904	+	0.648865i	$0.775244\pi$
$462$	16.4675	−	2.24587i	0.766140	−	0.104487i
$463$	14.9024	−	25.8118i	0.692575	−	1.19957i	−0.278417	−	0.960460i	$-0.589810\pi$
$463$	14.9024	−	25.8118i	0.692575	−	1.19957i	0.970991	−	0.239114i	$-0.0768571\pi$
$464$	9.42513	+	10.4677i	0.437551	+	0.485949i
$465$	0.192457	−	0.0745059i	0.00892497	−	0.00345513i
$466$	−3.26320	+	31.0473i	−0.151165	+	1.43824i
$467$	−11.1849	−	34.4236i	−0.517575	−	1.59293i	−0.778547	−	0.627586i	$-0.784043\pi$
$467$	−11.1849	−	34.4236i	−0.517575	−	1.59293i	0.260972	−	0.965346i	$-0.415957\pi$
$468$	−0.499262	−	0.444421i	−0.0230784	−	0.0205434i
$469$	−1.41260	−	1.02631i	−0.0652278	−	0.0473908i
$470$	0.851077	+	0.378924i	0.0392573	+	0.0174785i
$471$	−30.5283	−	1.51287i	−1.40667	−	0.0697094i
$472$	7.08153	−	12.2656i	0.325954	−	0.564569i
$473$	17.5386	+	20.4603i	0.806426	+	0.940767i
$474$	−8.91803	−	32.9079i	−0.409619	−	1.51151i
$475$	25.3791	−	5.39449i	1.16447	−	0.247516i
$476$	0.0591466	−	0.0429725i	0.00271098	−	0.00196964i
$477$	−2.64719	+	3.68747i	−0.121206	+	0.168838i
$478$	−6.55224	−	20.1657i	−0.299693	−	0.922359i
$479$	5.00711	−	5.56096i	0.228781	−	0.254087i	−0.617815	−	0.786324i	$-0.711982\pi$
$479$	5.00711	−	5.56096i	0.228781	−	0.254087i	0.846595	+	0.532237i	$0.178648\pi$
$480$	0.0895372	+	0.109929i	0.00408680	+	0.00501753i
$481$	−1.11165	−	10.5766i	−0.0506869	−	0.482253i
$482$	−0.160561	−	0.178321i	−0.00731334	−	0.00812228i
$483$	16.3110	−	16.4040i	0.742174	−	0.746408i
$484$	1.55623	−	1.56748i	0.0707377	−	0.0712492i
$485$	−0.756073			−0.0343315
$486$	12.3181	−	19.5719i	0.558758	−	0.887800i
$487$	−6.39891	+	4.64908i	−0.289962	+	0.210670i	−0.723251	−	0.690585i	$-0.757353\pi$
$487$	−6.39891	+	4.64908i	−0.289962	+	0.210670i	0.433289	+	0.901255i	$0.357353\pi$
$488$	−1.97433	+	18.7845i	−0.0893739	+	0.850336i
$489$	−5.72754	−	2.89784i	−0.259008	−	0.131045i
$490$	0.335499	+	0.0713125i	0.0151563	+	0.00322157i
$491$	−18.8130	+	8.37608i	−0.849019	+	0.378007i	−0.784665	−	0.619920i	$-0.787165\pi$
$491$	−18.8130	+	8.37608i	−0.849019	+	0.378007i	−0.0643533	+	0.997927i	$0.520498\pi$
$492$	−1.64227	+	0.635775i	−0.0740395	+	0.0286630i
$493$	−0.589779	+	0.125361i	−0.0265623	+	0.00564600i
$494$	−8.55071			−0.384715
$495$	−0.680149	−	0.235136i	−0.0305704	−	0.0105686i
$496$	−7.18471			−0.322603
$497$	2.94330	−	0.625617i	0.132025	−	0.0280628i
$498$	35.9607	+	28.9515i	1.61144	+	1.29735i
$499$	13.2979	−	5.92062i	0.595298	−	0.265044i	−0.0868934	−	0.996218i	$-0.527694\pi$
$499$	13.2979	−	5.92062i	0.595298	−	0.265044i	0.682191	+	0.731174i	$0.261027\pi$
$500$	−0.141986	−	0.0301800i	−0.00634980	−	0.00134969i
$501$	−2.94407	+	1.92382i	−0.131531	+	0.0859501i
$502$	−1.38271	+	13.1556i	−0.0617133	+	0.587163i
$503$	25.7196	−	18.6864i	1.14678	−	0.833183i	0.158729	−	0.987322i	$-0.449260\pi$
$503$	25.7196	−	18.6864i	1.14678	−	0.833183i	0.988049	+	0.154139i	$0.0492603\pi$
$504$	3.33362	+	15.2562i	0.148491	+	0.679565i
$505$	0.250406			0.0111429
$506$	4.33800	−	33.4154i	0.192848	−	1.48550i
$507$	−19.7046	−	5.21981i	−0.875112	−	0.231820i
$508$	2.67137	+	2.96685i	0.118523	+	0.131633i
$509$	−3.66516	−	34.8717i	−0.162455	−	1.54566i	−0.707174	−	0.707040i	$-0.750030\pi$
$509$	−3.66516	−	34.8717i	−0.162455	−	1.54566i	0.544718	−	0.838619i	$-0.316637\pi$
$510$	−0.0342529	+	0.00552504i	−0.00151675	+	0.000244653i
$511$	−15.0220	+	16.6836i	−0.664532	+	0.738038i
$512$	5.66916	+	17.4479i	0.250544	+	0.771095i
$513$	−4.44981	−	26.6228i	−0.196464	−	1.17543i
$514$	5.11242	−	3.71439i	0.225499	−	0.163835i
$515$	−1.26523	+	0.268933i	−0.0557528	+	0.0118506i
$516$	1.99257	−	2.00393i	0.0877179	−	0.0882183i
$517$	28.0131	+	6.67201i	1.23202	+	0.293434i
$518$	13.8650	−	24.0150i	0.609195	−	1.05516i
$519$	8.08123	−	12.5218i	0.354727	−	0.549647i
$520$	−0.195685	−	0.0871246i	−0.00858136	−	0.00382067i
$521$	23.9643	+	17.4111i	1.04990	+	0.762794i	0.972193	−	0.234183i	$-0.0752414\pi$
$521$	23.9643	+	17.4111i	1.04990	+	0.762794i	0.0777032	+	0.996977i	$0.475241\pi$
$522$	−2.90848	+	14.0766i	−0.127301	+	0.616114i
$523$	−3.46900	−	10.6765i	−0.151689	−	0.466850i	0.846122	−	0.532990i	$-0.178932\pi$
$523$	−3.46900	−	10.6765i	−0.151689	−	0.466850i	−0.997810	+	0.0661400i	$0.978932\pi$
$524$	0.181908	−	1.73074i	0.00794667	−	0.0756075i
$525$	−13.1419	−	10.5804i	−0.573561	−	0.461766i
$526$	−23.2064	−	25.7733i	−1.01185	−	1.12377i
$527$	0.153776	−	0.266347i	0.00669857	−	0.0116023i
$528$	19.1263	+	16.1824i	0.832367	+	0.704247i
$529$	−11.9503	−	20.6985i	−0.519578	−	0.899936i
$530$	0.0501696	−	0.154406i	0.00217923	−	0.00670697i
$531$	15.8218	−	1.75399i	0.686608	−	0.0761165i
$532$	−1.64575	−	1.19570i	−0.0713522	−	0.0518404i
$533$	3.75933	−	4.17516i	0.162835	−	0.180846i
$534$	1.75787	+	31.8108i	0.0760705	+	1.37659i
$535$	0.925192	−	0.411922i	0.0399996	−	0.0178089i
$536$	−0.249794	−	2.37663i	−0.0107895	−	0.102655i
$537$	1.99242	+	3.88301i	0.0859793	+	0.167564i
$538$	−11.2663	−	19.5138i	−0.485724	−	0.841299i
$539$	10.5989	+	0.258437i	0.456528	+	0.0111317i
$540$	−0.0189093	+	0.0730583i	−0.000813727	+	0.00314393i
$541$	1.79412	−	5.52174i	0.0771354	−	0.237398i	−0.905052	−	0.425300i	$-0.860169\pi$
$541$	1.79412	−	5.52174i	0.0771354	−	0.237398i	0.982188	+	0.187902i	$0.0601686\pi$
$542$	−21.2828	−	9.47571i	−0.914174	−	0.407016i
$543$	24.3759	−	3.93186i	1.04607	−	0.168732i
$544$	0.206669	+	0.0439289i	0.00886086	+	0.00188343i
$545$	−0.354331	−	0.0753154i	−0.0151779	−	0.00322616i
$546$	3.51142	+	4.31112i	0.150275	+	0.184499i
$547$	−19.7474	−	8.79209i	−0.844336	−	0.375923i	−0.0614669	−	0.998109i	$-0.519578\pi$
$547$	−19.7474	−	8.79209i	−0.844336	−	0.375923i	−0.782869	+	0.622187i	$0.786245\pi$
$548$	0.454585	−	1.39907i	0.0194189	−	0.0597653i
$549$	−18.3245	+	10.7191i	−0.782071	+	0.457480i
$550$	−24.5682	−	0.599055i	−1.04759	−	0.0255438i
$551$	8.38858	+	14.5294i	0.357365	+	0.618975i
$552$	31.6218	+	1.56706i	1.34591	+	0.0666985i
$553$	2.70493	+	25.7357i	0.115025	+	1.09439i
$554$	−10.1344	+	4.51213i	−0.430570	+	0.191702i
$555$	−1.00514	+	0.656817i	−0.0426658	+	0.0278803i
$556$	−0.704980	+	0.782959i	−0.0298978	+	0.0332049i
$557$	5.71836	+	4.15463i	0.242295	+	0.176037i	0.702305	−	0.711876i	$-0.252154\pi$
$557$	5.71836	+	4.15463i	0.242295	+	0.176037i	−0.460010	+	0.887914i	$0.652154\pi$
$558$	−4.34315	−	5.90689i	−0.183860	−	0.250059i
$559$	−2.78598	+	8.57437i	−0.117835	+	0.362657i
$560$	−0.307588	−	0.532758i	−0.0129980	−	0.0225131i
$561$	−1.00927	+	0.362686i	−0.0426113	+	0.0153126i
$562$	−9.50073	+	16.4557i	−0.400764	+	0.694144i
$563$	−15.3191	−	17.0136i	−0.645624	−	0.717038i	0.328132	−	0.944632i	$-0.393581\pi$
$563$	−15.3191	−	17.0136i	−0.645624	−	0.717038i	−0.973756	+	0.227594i	$0.926914\pi$
$564$	0.463911	−	2.98392i	0.0195342	−	0.125646i
$565$	−0.0853552	+	0.812101i	−0.00359092	+	0.0341653i
$566$	3.00762	+	9.25651i	0.126420	+	0.389080i
$567$	−11.5954	+	13.1764i	−0.486962	+	0.553358i
$568$	3.33176	+	2.42066i	0.139797	+	0.101569i
$569$	16.7781	+	7.47011i	0.703377	+	0.313163i	0.727077	−	0.686556i	$-0.240878\pi$
$569$	16.7781	+	7.47011i	0.703377	+	0.313163i	−0.0237007	+	0.999719i	$0.507545\pi$
$570$	0.440728	+	0.858930i	0.0184601	+	0.0359766i
$571$	−4.04504	+	7.00621i	−0.169280	+	0.293201i	−0.938167	−	0.346184i	$-0.887477\pi$
$571$	−4.04504	+	7.00621i	−0.169280	+	0.293201i	0.768887	+	0.639384i	$0.220811\pi$
$572$	0.718848	+	0.171211i	0.0300565	+	0.00715870i
$573$	−28.6313	−	7.58451i	−1.19609	−	0.316848i
$574$	14.3292	−	3.04576i	0.598089	−	0.127128i
$575$	−27.6734	+	20.1059i	−1.15406	+	0.838473i
$576$	−12.3229	+	17.1656i	−0.513456	+	0.715232i
$577$	−0.856306	−	2.63544i	−0.0356485	−	0.109715i	0.931649	−	0.363360i	$-0.118370\pi$
$577$	−0.856306	−	2.63544i	−0.0356485	−	0.109715i	−0.967297	+	0.253645i	$0.918370\pi$
$578$	16.8407	−	18.7034i	0.700479	−	0.777961i
$579$	−10.2516	+	26.9350i	−0.426042	+	1.11938i
$580$	−0.00490303	−	0.0466493i	−0.000203587	−	0.00193701i
$581$	−23.4462	−	26.0396i	−0.972710	−	1.08030i
$582$	7.02576	+	25.9253i	0.291227	+	1.07464i
$583$	0.646064	−	4.97660i	0.0267572	−	0.206110i
$584$	−30.7257			−1.27144
$585$	−0.0513949	−	0.235207i	−0.00212492	−	0.00972463i
$586$	−14.1180	+	10.2573i	−0.583207	+	0.423725i
$587$	−3.79816	+	36.1371i	−0.156767	+	1.49154i	0.579571	+	0.814922i	$0.303220\pi$
$587$	−3.79816	+	36.1371i	−0.156767	+	1.49154i	−0.736338	+	0.676614i	$0.763447\pi$
$588$	−0.0613438	−	1.11009i	−0.00252978	−	0.0457794i
$589$	−8.37057	−	1.77922i	−0.344903	−	0.0733115i
$590$	−0.520128	+	0.231576i	−0.0214133	+	0.00953382i
$591$	−5.36616	+	34.5157i	−0.220734	+	1.41979i
$592$	40.8880	−	8.69101i	1.68049	−	0.357198i
$593$	7.21741			0.296384			0.148192	−	0.988959i	$-0.452655\pi$
$593$	7.21741			0.296384			0.148192	+	0.988959i	$0.452655\pi$
$594$	−1.74243	+	25.5069i	−0.0714928	+	1.04656i
$595$	0.0263335			0.00107957
$596$	−0.424809	+	0.0902960i	−0.0174009	+	0.00369867i
$597$	4.25313	−	27.3565i	0.174069	−	1.11963i
$598$	10.2983	−	4.58510i	0.421129	−	0.187499i
$599$	−15.5586	−	3.30709i	−0.635709	−	0.135124i	−0.121226	−	0.992625i	$-0.538683\pi$
$599$	−15.5586	−	3.30709i	−0.635709	−	0.135124i	−0.514483	+	0.857501i	$0.672016\pi$
$600$	−1.27408	−	23.0560i	−0.0520139	−	0.941256i
$601$	−1.11321	+	10.5915i	−0.0454090	+	0.432038i	0.948073	+	0.318052i	$0.103029\pi$
$601$	−1.11321	+	10.5915i	−0.0454090	+	0.432038i	−0.993482	+	0.113986i	$0.963638\pi$
$602$	−19.0183	+	13.8176i	−0.775128	+	0.563163i
$603$	1.98580	−	1.80858i	0.0808681	−	0.0736512i
$604$	1.40067			0.0569926
$605$	0.785351	−	0.127289i	0.0319291	−	0.00517505i
$606$	−2.32688	−	8.58626i	−0.0945228	−	0.348793i
$607$	11.3201	+	12.5722i	0.459468	+	0.510291i	0.927706	−	0.373311i	$-0.121778\pi$
$607$	11.3201	+	12.5722i	0.459468	+	0.510291i	−0.468238	+	0.883602i	$0.655111\pi$
$608$	−0.614524	−	5.84681i	−0.0249222	−	0.237119i
$609$	3.88065	−	10.1960i	0.157252	−	0.413163i
$610$	0.508065	−	0.564264i	0.0205710	−	0.0228464i
$611$	2.97704	+	9.16239i	0.120438	+	0.370671i
$612$	0.0463265	+	0.102478i	0.00187264	+	0.00414244i
$613$	15.9766	−	11.6077i	0.645290	−	0.468830i	−0.216374	−	0.976311i	$-0.569423\pi$
$613$	15.9766	−	11.6077i	0.645290	−	0.468830i	0.861663	+	0.507480i	$0.169423\pi$
$614$	−34.5544	+	7.34476i	−1.39450	+	0.296410i
$615$	−0.613167	−	0.162430i	−0.0247253	−	0.00654981i
$616$	−11.2359	−	13.1077i	−0.452708	−	0.528123i
$617$	14.2059	−	24.6053i	0.571908	−	0.990573i	−0.424462	−	0.905446i	$-0.639537\pi$
$617$	14.2059	−	24.6053i	0.571908	−	0.990573i	0.996370	−	0.0851276i	$-0.0271298\pi$
$618$	20.9786	+	40.8850i	0.843885	+	1.64464i
$619$	−30.7522	−	13.6917i	−1.23603	−	0.550317i	−0.318480	−	0.947930i	$-0.603172\pi$
$619$	−30.7522	−	13.6917i	−1.23603	−	0.550317i	−0.917554	+	0.397612i	$0.869839\pi$
$620$	0.0193562	+	0.0140631i	0.000777365	+	0.000564788i
$621$	19.6351	+	29.6779i	0.787929	+	1.19093i
$622$	−10.7950	−	33.2236i	−0.432840	−	1.33214i
$623$	2.52758	−	24.0483i	0.101265	−	0.963474i
$624$	−1.28763	+	8.28218i	−0.0515466	+	0.331552i
$625$	16.6758	+	18.5203i	0.667031	+	0.740813i
$626$	−8.49376	+	14.7116i	−0.339479	+	0.587995i
$627$	18.2758	+	23.5898i	0.729865	+	0.942085i
$628$	−1.77178	−	3.06882i	−0.0707019	−	0.122459i
$629$	−0.552945	+	1.70179i	−0.0220474	+	0.0678548i
$630$	0.252069	−	0.574935i	0.0100427	−	0.0229059i
$631$	10.5417	+	7.65896i	0.419657	+	0.304898i	0.777500	−	0.628883i	$-0.216488\pi$
$631$	10.5417	+	7.65896i	0.419657	+	0.304898i	−0.357843	+	0.933782i	$0.616488\pi$
$632$	−23.6984	+	26.3197i	−0.942670	+	1.04694i
$633$	−14.2174	+	9.29048i	−0.565091	+	0.369264i
$634$	−19.9446	+	8.87991i	−0.792102	+	0.352666i
$635$	0.150312	+	1.43012i	0.00596494	+	0.0567526i
$636$	−0.525605	−	0.0260471i	−0.0208416	−	0.00103283i
$637$	1.77346	+	3.07172i	0.0702669	+	0.121706i
$638$	−4.54071	−	15.2284i	−0.179768	−	0.602897i
$639$	0.0263291	+	4.62871i	0.00104156	+	0.183109i
$640$	0.284134	−	0.874476i	0.0112314	−	0.0345667i
$641$	3.94761	+	1.75759i	0.155921	+	0.0694207i	0.483214	−	0.875503i	$-0.339469\pi$
$641$	3.94761	+	1.75759i	0.155921	+	0.0694207i	−0.327292	+	0.944923i	$0.606136\pi$
$642$	−22.7219	−	27.8966i	−0.896760	−	1.10099i
$643$	−20.4191	−	4.34021i	−0.805249	−	0.171161i	−0.213143	−	0.977021i	$-0.568370\pi$
$643$	−20.4191	−	4.34021i	−0.805249	−	0.171161i	−0.592106	+	0.805860i	$0.701703\pi$
$644$	2.62327	+	0.557593i	0.103371	+	0.0219723i
$645$	1.00490	−	0.162092i	0.0395681	−	0.00638238i
$646$	1.31431	+	0.585170i	0.0517110	+	0.0230232i
$647$	1.77013	−	5.44789i	0.0695909	−	0.214179i	−0.910213	−	0.414141i	$-0.864082\pi$
$647$	1.77013	−	5.44789i	0.0695909	−	0.214179i	0.979804	+	0.199962i	$0.0640820\pi$
$648$	−24.0206	+	0.273277i	−0.943619	+	0.0107353i
$649$	−14.4857	+	9.99420i	−0.568613	+	0.392307i
$650$	−4.11085	−	7.12020i	−0.161241	−	0.279277i
$651$	2.54040	+	4.95095i	0.0995660	+	0.194043i
$652$	−0.0777858	−	0.740082i	−0.00304633	−	0.0289839i
$653$	−9.38126	+	4.17681i	−0.367117	+	0.163451i	−0.582000	−	0.813189i	$-0.697730\pi$
$653$	−9.38126	+	4.17681i	−0.367117	+	0.163451i	0.214883	+	0.976640i	$0.431063\pi$
$654$	0.710074	+	12.8497i	0.0277661	+	0.502462i
$655$	0.419433	−	0.465828i	0.0163886	−	0.0182014i
$656$	17.8655	+	12.9800i	0.697531	+	0.506786i
$657$	−20.4575	−	27.8231i	−0.798122	−	1.08548i
$658$	−7.76252	+	23.8906i	−0.302614	+	0.931352i
$659$	7.65543	+	13.2596i	0.298213	+	0.516520i	0.975727	−	0.218990i	$-0.0702761\pi$
$659$	7.65543	+	13.2596i	0.298213	+	0.516520i	−0.677514	+	0.735510i	$0.736943\pi$
$660$	−0.0198531	−	0.0810340i	−0.000772782	−	0.00315424i
$661$	12.8232	−	22.2105i	0.498766	−	0.863889i	−0.501233	−	0.865313i	$-0.667120\pi$
$661$	12.8232	−	22.2105i	0.498766	−	0.863889i	0.999999	+	0.00142377i	$0.000453199\pi$
$662$	−13.3630	−	14.8411i	−0.519368	−	0.576817i
$663$	−0.279473	−	0.224999i	−0.0108538	−	0.00873825i
$664$	5.01281	−	47.6937i	0.194535	−	1.85088i
$665$	−0.226424	−	0.696863i	−0.00878036	−	0.0270232i
$666$	31.8621	+	28.3622i	1.23463	+	1.09901i
$667$	−17.8941	−	13.0008i	−0.692861	−	0.503393i
$668$	−0.372474	−	0.165836i	−0.0144115	−	0.00641640i
$669$	15.8798	−	24.6057i	0.613949	−	0.951312i
$670$	−0.0480331	+	0.0831957i	−0.00185568	+	0.00321413i
$671$	12.2270	−	20.0335i	0.472017	−	0.773385i
$672$	−2.69550	+	2.71087i	−0.103981	+	0.104574i
$673$	19.4709	−	4.13867i	0.750548	−	0.159534i	0.183272	−	0.983062i	$-0.441331\pi$
$673$	19.4709	−	4.13867i	0.750548	−	0.159534i	0.567275	+	0.823528i	$0.307998\pi$
$674$	3.51004	−	2.55019i	0.135202	−	0.0982297i
$675$	20.0296	−	16.5046i	0.770941	−	0.635263i
$676$	−0.730268	−	2.24753i	−0.0280872	−	0.0864436i
$677$	−1.60354	+	1.78091i	−0.0616289	+	0.0684459i	−0.773171	−	0.634198i	$-0.781330\pi$
$677$	−1.60354	+	1.78091i	−0.0616289	+	0.0684459i	0.711542	+	0.702644i	$0.247997\pi$
$678$	28.6396	−	4.61961i	1.09990	−	0.177415i
$679$	−2.13098	−	20.2750i	−0.0817796	−	0.778081i
$680$	0.0241160	+	0.0267835i	0.000924806	+	0.00102710i
$681$	5.33089	+	1.41217i	0.204280	+	0.0541145i
$682$	7.32221	+	3.47634i	0.280382	+	0.133116i
$683$	−1.75102			−0.0670009			−0.0335005	−	0.999439i	$-0.510666\pi$
$683$	−1.75102			−0.0670009			−0.0335005	+	0.999439i	$0.510666\pi$
$684$	2.31355	−	2.10708i	0.0884609	−	0.0805664i
$685$	0.428673	−	0.311449i	0.0163788	−	0.0118999i
$686$	−3.08365	+	29.3390i	−0.117734	+	1.12017i
$687$	6.99048	−	4.56799i	0.266703	−	0.174280i
$688$	−34.6624	−	7.36772i	−1.32149	−	0.280892i
$689$	1.53374	−	0.682865i	0.0584309	−	0.0260151i
$690$	−0.991384	−	0.798149i	−0.0377413	−	0.0303850i
$691$	25.4105	−	5.40118i	0.966662	−	0.205470i	0.302575	−	0.953126i	$-0.402154\pi$
$691$	25.4105	−	5.40118i	0.966662	−	0.205470i	0.664087	+	0.747655i	$0.268820\pi$
$692$	1.72775			0.0656794
$693$	4.38843	−	18.9017i	0.166703	−	0.718016i
$694$	39.9374			1.51600
$695$	−0.371198	+	0.0789006i	−0.0140803	+	0.00299287i
$696$	13.9241	−	5.39046i	0.527793	−	0.204325i
$697$	−0.863567	+	0.384485i	−0.0327099	+	0.0145634i
$698$	−2.20698	−	0.469108i	−0.0835355	−	0.0177560i
$699$	32.5228	+	16.4548i	1.23012	+	0.622379i
$700$	0.204456	−	1.94527i	0.00772770	−	0.0735242i
$701$	−11.8682	+	8.62278i	−0.448257	+	0.325678i	−0.788907	−	0.614512i	$-0.789353\pi$
$701$	−11.8682	+	8.62278i	−0.448257	+	0.325678i	0.340650	+	0.940190i	$0.389353\pi$
$702$	−7.58754	+	3.94795i	−0.286373	+	0.149006i
$703$	49.7890			1.87783
$704$	3.00750	−	23.1666i	0.113349	−	0.873124i
$705$	0.766929	−	0.771304i	0.0288842	−	0.0290490i
$706$	−0.320265	−	0.355690i	−0.0120533	−	0.0133866i
$707$	0.705765	+	6.71491i	0.0265430	+	0.252540i
$708$	1.16549	+	1.43091i	0.0438016	+	0.0537771i
$709$	0.258911	−	0.287550i	0.00972362	−	0.0107992i	−0.738263	−	0.674513i	$-0.764354\pi$
$709$	0.258911	−	0.287550i	0.00972362	−	0.0107992i	0.747987	+	0.663713i	$0.231021\pi$
$710$	−0.0511588	−	0.157451i	−0.00191996	−	0.00590902i
$711$	−39.6119	−	3.93571i	−1.48556	−	0.147601i
$712$	26.7740	−	19.4525i	1.00340	−	0.729012i
$713$	11.0354	−	2.34565i	0.413279	−	0.0878453i
$714$	−0.244702	−	0.902959i	−0.00915773	−	0.0337924i
$715$	0.173226	+	0.202083i	0.00647828	+	0.00755749i
$716$	−0.252985	+	0.438182i	−0.00945448	+	0.0163756i
$717$	−24.7255	−	1.22531i	−0.923391	−	0.0457599i
$718$	14.9965	+	6.67687i	0.559665	+	0.249179i
$719$	−19.2508	−	13.9865i	−0.717935	−	0.521610i	0.167789	−	0.985823i	$-0.446337\pi$
$719$	−19.2508	−	13.9865i	−0.717935	−	0.521610i	−0.885724	+	0.464213i	$0.846337\pi$
$720$	0.898324	−	0.297543i	0.0334786	−	0.0110888i
$721$	−10.7778	−	33.1706i	−0.401386	−	1.23534i
$722$	1.23812	−	11.7799i	0.0460781	−	0.438403i
$723$	−0.261261	+	0.101142i	−0.00971639	+	0.00376151i
$724$	1.91538	+	2.12724i	0.0711845	+	0.0790584i
$725$	−8.06581	+	13.9704i	−0.299557	+	0.518847i
$726$	−11.6625	−	25.7464i	−0.432836	−	0.955538i
$727$	21.9528	+	38.0233i	0.814184	+	1.41021i	0.909913	+	0.414800i	$0.136148\pi$
$727$	21.9528	+	38.0233i	0.814184	+	1.41021i	−0.0957289	+	0.995407i	$0.530518\pi$
$728$	1.78481	−	5.49307i	0.0661494	−	0.203587i
$729$	−16.2406	−	21.5695i	−0.601504	−	0.798869i
$730$	0.999269	+	0.726011i	0.0369846	+	0.0268709i
$731$	1.01502	−	1.12729i	0.0375418	−	0.0416944i
$732$	−2.19610	−	1.11111i	−0.0811700	−	0.0410678i
$733$	15.0140	−	6.68468i	0.554556	−	0.246904i	−0.110271	−	0.993902i	$-0.535172\pi$
$733$	15.0140	−	6.68468i	0.554556	−	0.246904i	0.664827	+	0.746997i	$0.268505\pi$
$734$	2.24141	+	21.3256i	0.0827321	+	0.787143i
$735$	0.217149	−	0.336471i	0.00800966	−	0.0124109i
$736$	3.87532	+	6.71225i	0.142846	+	0.247417i
$737$	−0.986175	+	2.80090i	−0.0363262	+	0.103172i
$738$	0.128181	+	22.5345i	0.00471841	+	0.829507i
$739$	−1.22843	+	3.78073i	−0.0451887	+	0.139076i	−0.971105	−	0.238652i	$-0.923295\pi$
$739$	−1.22843	+	3.78073i	−0.0451887	+	0.139076i	0.925917	+	0.377728i	$0.123295\pi$
$740$	−0.127167	−	0.0566185i	−0.00467476	−	0.00208134i
$741$	−3.55116	+	9.33031i	−0.130455	+	0.342758i
$742$	4.28197	+	0.910161i	0.157196	+	0.0334131i
$743$	15.4866	+	3.29178i	0.568148	+	0.120764i	0.483024	−	0.875607i	$-0.339538\pi$
$743$	15.4866	+	3.29178i	0.568148	+	0.120764i	0.0851233	+	0.996370i	$0.472872\pi$
$744$	−2.70909	+	7.11785i	−0.0993199	+	0.260953i
$745$	−0.142908	−	0.0636266i	−0.00523573	−	0.00233110i
$746$	−4.23474	+	13.0332i	−0.155045	+	0.477179i
$747$	46.5258	−	27.2157i	1.70229	−	0.995770i
$748$	−0.0987759	−	0.0755111i	−0.00361160	−	0.00276096i
$749$	13.6538	+	23.6491i	0.498899	+	0.864118i
$750$	−1.00722	+	1.56069i	−0.0367787	+	0.0569883i
$751$	4.04300	+	38.4666i	0.147531	+	1.40367i	0.778396	+	0.627774i	$0.216034\pi$
$751$	4.04300	+	38.4666i	0.147531	+	1.40367i	−0.630864	+	0.775893i	$0.717300\pi$
$752$	−34.5932	+	15.4019i	−1.26148	+	0.561649i
$753$	13.7808	+	6.97237i	0.502200	+	0.254087i
$754$	3.55729	−	3.95078i	0.129549	−	0.143879i
$755$	0.408160	+	0.296546i	0.0148545	+	0.0107924i
$756$	−2.01244	−	0.301161i	−0.0731916	−	0.0109531i
$757$	−3.47082	+	10.6821i	−0.126149	+	0.388247i	−0.994109	−	0.108388i	$-0.965431\pi$
$757$	−3.47082	+	10.6821i	−0.126149	+	0.388247i	0.867960	+	0.496635i	$0.165431\pi$
$758$	3.71732	+	6.43859i	0.135019	+	0.233860i
$759$	−34.6604	−	18.6111i	−1.25809	−	0.675541i
$760$	0.501415	−	0.868476i	0.0181882	−	0.0315029i
$761$	−24.6913	−	27.4225i	−0.895059	−	0.994064i	0.104941	−	0.994478i	$-0.466535\pi$
$761$	−24.6913	−	27.4225i	−0.895059	−	0.994064i	−1.00000		0.000414470i	$0.999868\pi$
$762$	47.6412	−	18.4434i	1.72586	−	0.668134i
$763$	1.02099	−	9.71406i	0.0369623	−	0.351672i
$764$	−1.06110	−	3.26572i	−0.0383892	−	0.118150i
$765$	−0.00819666	+	0.0396705i	−0.000296351	+	0.00143429i
$766$	41.9556	+	30.4825i	1.51592	+	1.10138i
$767$	−5.37866	−	2.39473i	−0.194212	−	0.0864688i
$768$	−8.25569	−	0.409121i	−0.297902	−	0.0147629i
$769$	−24.4141	+	42.2864i	−0.880393	+	1.52489i	−0.0294888	+	0.999565i	$0.509388\pi$
$769$	−24.4141	+	42.2864i	−0.880393	+	1.52489i	−0.850904	+	0.525321i	$0.823945\pi$
$770$	0.0556985	+	0.691781i	0.00200723	+	0.0249301i
$771$	−1.92983	−	7.12115i	−0.0695012	−	0.256462i
$772$	−3.26816	+	0.694669i	−0.117624	+	0.0250017i
$773$	6.32496	−	4.59536i	0.227493	−	0.165283i	−0.468200	−	0.883623i	$-0.655097\pi$
$773$	6.32496	−	4.59536i	0.227493	−	0.165283i	0.695693	+	0.718339i	$0.255097\pi$
$774$	−14.8961	−	32.9514i	−0.535428	−	1.18441i
$775$	−2.54269	−	7.82558i	−0.0913360	−	0.281103i
$776$	18.6699	−	20.7351i	0.670211	−	0.744345i
$777$	−20.4463	−	25.1027i	−0.733506	−	0.900555i
$778$	−3.39847	−	32.3343i	−0.121841	−	1.15924i
$779$	17.5999	+	19.5467i	0.630582	+	0.700332i
$780$	0.0196803	−	0.0197925i	0.000704666	−	0.000708686i
$781$	−2.44987	−	4.49278i	−0.0876633	−	0.160764i
$782$	−1.89672			−0.0678264
$783$	14.1521	+	9.01973i	0.505753	+	0.322339i
$784$	−11.2789	+	8.19459i	−0.402817	+	0.292664i
$785$	0.133417	−	1.26938i	0.00476185	−	0.0453060i
$786$	−19.8705	−	10.0535i	−0.708758	−	0.358595i
$787$	−0.901534	−	0.191627i	−0.0321362	−	0.00683077i	0.191816	−	0.981431i	$-0.438562\pi$
$787$	−0.901534	−	0.191627i	−0.0321362	−	0.00683077i	−0.223952	+	0.974600i	$0.571896\pi$
$788$	−3.69946	+	1.64711i	−0.131788	+	0.0586757i
$789$	−37.7610	+	14.6184i	−1.34433	+	0.520430i
$790$	1.39263	−	0.296012i	0.0495474	−	0.0105316i
$791$	−22.0180			−0.782869
$792$	23.2436	−	12.8466i	0.825926	−	0.456484i
$793$	7.85186			0.278828
$794$	−22.2260	+	4.72428i	−0.788772	+	0.167659i
$795$	−0.147648	−	0.118869i	−0.00523654	−	0.00421586i
$796$	2.93213	−	1.30547i	0.103926	−	0.0462710i
$797$	35.8618	+	7.62267i	1.27029	+	0.270009i	0.793263	−	0.608879i	$-0.208381\pi$
$797$	35.8618	+	7.62267i	1.27029	+	0.270009i	0.477028	+	0.878888i	$0.341714\pi$
$798$	−21.7910	+	14.2395i	−0.771393	+	0.504073i
$799$	0.169435	−	1.61207i	0.00599419	−	0.0570309i
$800$	4.57321	−	3.32263i	0.161688	−	0.117473i
$801$	35.4412	+	11.2931i	1.25225	+	0.399022i
$802$	−0.319934			−0.0112973
$803$	34.4897	+	16.3745i	1.21711	+	0.577845i
$804$	0.301008	+	0.0797379i	0.0106157	+	0.00281214i
$805$	0.646376	+	0.717873i	0.0227818	+	0.0253017i
$806$	0.283450	+	2.69684i	0.00998409	+	0.0949923i
$807$	−25.9719	+	4.18930i	−0.914254	+	0.147470i
$808$	−6.18333	+	6.86729i	−0.217529	+	0.241590i
$809$	−14.1795	−	43.6399i	−0.498523	−	1.53430i	−0.811393	−	0.584501i	$-0.801290\pi$
$809$	−14.1795	−	43.6399i	−0.498523	−	1.53430i	0.312869	−	0.949796i	$-0.398710\pi$
$810$	0.787661	+	0.558690i	0.0276756	+	0.0196304i
$811$	−35.8258	+	26.0290i	−1.25801	+	0.914001i	−0.998658	−	0.0517807i	$-0.983510\pi$
$811$	−35.8258	+	26.0290i	−1.25801	+	0.914001i	−0.259356	+	0.965782i	$0.583510\pi$
$812$	1.23713	−	0.262961i	0.0434149	−	0.00922811i
$813$	−19.1785	+	19.2879i	−0.672620	+	0.676457i
$814$	−45.8757	−	10.9264i	−1.60794	−	0.382971i
$815$	0.134021	−	0.232130i	0.00469454	−	0.00813117i
$816$	0.764712	−	1.18492i	0.0267703	−	0.0414804i
$817$	−38.5590	−	17.1676i	−1.34901	−	0.600618i
$818$	27.2451	+	19.7947i	0.952602	+	0.692106i
$819$	6.16250	−	2.04114i	0.215335	−	0.0713233i
$820$	−0.0227245	−	0.0699387i	−0.000793573	−	0.00244237i
$821$	5.03265	−	47.8825i	0.175641	−	1.67111i	−0.451552	−	0.892245i	$-0.649129\pi$
$821$	5.03265	−	47.8825i	0.175641	−	1.67111i	0.627193	−	0.778864i	$-0.284204\pi$
$822$	−14.6628	−	11.8048i	−0.511425	−	0.411741i
$823$	−25.1375	−	27.9180i	−0.876237	−	0.973159i	0.123580	−	0.992335i	$-0.460563\pi$
$823$	−25.1375	−	27.9180i	−0.876237	−	0.973159i	−0.999816	+	0.0191754i	$0.993896\pi$
$824$	23.8673	−	41.3394i	0.831457	−	1.44013i
$825$	−10.8570	+	26.5594i	−0.377992	+	0.924679i
$826$	−7.67594	−	13.2951i	−0.267080	−	0.462596i
$827$	−16.6450	+	51.2279i	−0.578802	+	1.78137i	0.0440508	+	0.999029i	$0.485974\pi$
$827$	−16.6450	+	51.2279i	−0.578802	+	1.78137i	−0.622853	+	0.782339i	$0.714026\pi$
$828$	−1.65653	+	3.77831i	−0.0575683	+	0.131306i
$829$	−13.1554	−	9.55794i	−0.456905	−	0.331961i	0.335411	−	0.942072i	$-0.391125\pi$
$829$	−13.1554	−	9.55794i	−0.456905	−	0.331961i	−0.792316	+	0.610111i	$0.791125\pi$
$830$	−1.28997	+	1.43266i	−0.0447756	+	0.0497283i
$831$	0.714642	+	12.9323i	0.0247907	+	0.448618i
$832$	7.13972	−	3.17881i	0.247525	−	0.110205i
$833$	−0.0623809	−	0.593515i	−0.00216137	−	0.0205641i
$834$	6.15479	+	11.9950i	0.213123	+	0.415353i
$835$	−0.0734297	−	0.127184i	−0.00254114	−	0.00440138i
$836$	−1.14894	+	3.26318i	−0.0397370	+	0.112859i
$837$	−8.24918	+	2.28597i	−0.285133	+	0.0790148i
$838$	−7.83065	+	24.1003i	−0.270505	+	0.832529i
$839$	22.1266	+	9.85140i	0.763895	+	0.340108i	0.751429	−	0.659814i	$-0.229365\pi$
$839$	22.1266	+	9.85140i	0.763895	+	0.340108i	0.0124666	+	0.999922i	$0.496032\pi$
$840$	−0.643781	+	0.103843i	−0.0222125	+	0.00358291i
$841$	18.1632	+	3.86072i	0.626319	+	0.133128i
$842$	−8.70294	−	1.84987i	−0.299923	−	0.0637506i
$843$	14.0104	+	17.2011i	0.482543	+	0.592438i
$844$	−1.79874	−	0.800852i	−0.0619153	−	0.0275665i
$845$	0.263038	−	0.809547i	0.00904877	−	0.0278493i
$846$	−33.5742	−	19.1303i	−1.15430	−	0.657712i
$847$	5.62691	+	20.7013i	0.193343	+	0.711305i
$848$	3.29951	+	5.71492i	0.113306	+	0.196251i
$849$	11.3495	+	0.562442i	0.389516	+	0.0193030i
$850$	0.144598	+	1.37576i	0.00495968	+	0.0471882i
$851$	−59.9648	+	26.6981i	−2.05557	+	0.915198i
$852$	−0.449221	+	0.293547i	−0.0153900	+	0.0100568i
$853$	1.10267	−	1.22464i	0.0377548	−	0.0419309i	−0.723972	−	0.689830i	$-0.757685\pi$
$853$	1.10267	−	1.22464i	0.0377548	−	0.0419309i	0.761726	+	0.647899i	$0.224352\pi$
$854$	16.5633	+	12.0340i	0.566786	+	0.411794i
$855$	1.12028	−	0.124193i	0.0383128	−	0.00424730i
$856$	−11.5492	+	35.5448i	−0.394744	+	1.21490i
$857$	−23.3721	−	40.4817i	−0.798376	−	1.38283i	−0.920673	−	0.390334i	$-0.872359\pi$
$857$	−23.3721	−	40.4817i	−0.798376	−	1.38283i	0.122297	−	0.992494i	$-0.460974\pi$
$858$	5.31963	−	7.81766i	0.181609	−	0.266891i
$859$	12.7932	−	22.1585i	0.436498	−	0.756037i	−0.560918	−	0.827871i	$-0.689552\pi$
$859$	12.7932	−	22.1585i	0.436498	−	0.756037i	0.997417	+	0.0718338i	$0.0228851\pi$
$860$	0.0789621	+	0.0876963i	0.00269259	+	0.00299042i
$861$	2.62754	−	16.9006i	0.0895462	−	0.575970i
$862$	−0.619486	+	5.89402i	−0.0210998	+	0.200751i
$863$	−0.836222	−	2.57363i	−0.0284653	−	0.0876073i	0.935815	−	0.352493i	$-0.114666\pi$
$863$	−0.836222	−	2.57363i	−0.0284653	−	0.0876073i	−0.964280	+	0.264885i	$0.914666\pi$
$864$	−3.24483	−	4.90448i	−0.110391	−	0.166854i
$865$	0.503472	+	0.365794i	0.0171186	+	0.0124374i
$866$	36.7493	+	16.3618i	1.24879	+	0.555997i
$867$	−13.4147	−	26.1437i	−0.455587	−	0.887888i
$868$	−0.322563	+	0.558695i	−0.0109485	+	0.0189634i
$869$	40.6279	−	16.9144i	1.37821	−	0.573783i
$870$	−0.580214	−	0.153701i	−0.0196711	−	0.00521094i
$871$	−0.971714	+	0.206544i	−0.0329253	+	0.00699849i
$872$	10.8151	−	7.85762i	0.366245	−	0.266093i
$873$	31.2069	+	3.10061i	1.05619	+	0.104940i
$874$	16.3086	+	50.1928i	0.551648	+	1.69780i
$875$	0.943341	−	1.04769i	0.0318908	−	0.0354183i
$876$	1.42415	−	3.74182i	0.0481177	−	0.126424i
$877$	2.92890	+	27.8666i	0.0989019	+	0.940989i	0.925641	+	0.378403i	$0.123527\pi$
$877$	2.92890	+	27.8666i	0.0989019	+	0.940989i	−0.826739	+	0.562586i	$0.809807\pi$
$878$	25.2609	+	28.0551i	0.852514	+	0.946813i
$879$	5.32923	+	19.6651i	0.179750	+	0.663286i
$880$	−0.718784	+	0.760178i	−0.0242302	+	0.0256256i
$881$	30.6218			1.03167			0.515837	−	0.856687i	$-0.327481\pi$
$881$	30.6218			1.03167			0.515837	+	0.856687i	$0.327481\pi$
$882$	−13.5552	−	4.31928i	−0.456429	−	0.145438i
$883$	−21.8315	+	15.8615i	−0.734688	+	0.533782i	−0.891043	−	0.453919i	$-0.850026\pi$
$883$	−21.8315	+	15.8615i	−0.734688	+	0.533782i	0.156355	+	0.987701i	$0.450026\pi$
$884$	0.00434790	−	0.0413675i	0.000146236	−	0.00139134i
$885$	0.0366775	+	0.663725i	0.00123290	+	0.0223109i
$886$	14.6916	+	3.12279i	0.493573	+	0.104912i
$887$	34.5686	−	15.3909i	1.16070	−	0.516776i	0.266231	−	0.963909i	$-0.414222\pi$
$887$	34.5686	−	15.3909i	1.16070	−	0.516776i	0.894468	+	0.447133i	$0.147555\pi$
$888$	6.80720	−	43.7846i	0.228435	−	1.46931i
$889$	−37.9266	+	8.06155i	−1.27202	+	0.270376i
$890$	−1.33039			−0.0445947
$891$	27.1088	+	12.4945i	0.908180	+	0.418580i
$892$	3.39508			0.113676
$893$	−44.1171	+	9.37737i	−1.47632	+	0.313802i
$894$	−0.853760	+	5.49147i	−0.0285540	+	0.183662i
$895$	−0.166491	+	0.0741265i	−0.00556517	+	0.00247777i
$896$	24.2509	+	5.15468i	0.810165	+	0.172206i
$897$	−0.726199	−	13.1415i	−0.0242471	−	0.438781i
$898$	2.53215	−	24.0918i	0.0844988	−	0.803952i
$899$	4.30443	−	3.12735i	0.143561	−	0.104303i
$900$	2.86684	+	0.913498i	0.0955614	+	0.0304499i
$901$	−0.282480			−0.00941078
$902$	−11.9270	−	21.8727i	−0.397125	−	0.728282i
$903$	7.17900	+	26.4908i	0.238902	+	0.881558i
$904$	−20.1639	−	22.3943i	−0.670641	−	0.744822i
$905$	0.107774	+	1.02540i	0.00358253	+	0.0340855i
$906$	6.37558	−	16.7512i	0.211814	−	0.556521i
$907$	18.3136	−	20.3393i	0.608093	−	0.675356i	−0.357949	−	0.933741i	$-0.616524\pi$
$907$	18.3136	−	20.3393i	0.608093	−	0.675356i	0.966042	+	0.258385i	$0.0831904\pi$
$908$	0.197567	+	0.608049i	0.00655650	+	0.0201788i
$909$	−10.3355	−	1.02690i	−0.342806	−	0.0340600i
$910$	−0.187841	+	0.136474i	−0.00622685	+	0.00452407i
$911$	−18.6084	+	3.95533i	−0.616522	+	0.131046i	−0.505578	−	0.862781i	$-0.668721\pi$
$911$	−18.6084	+	3.95533i	−0.616522	+	0.131046i	−0.110944	+	0.993827i	$0.535387\pi$
$912$	−37.9318	−	10.0483i	−1.25605	−	0.332731i
$913$	−31.0441	+	50.8649i	−1.02741	+	1.68338i
$914$	−17.4364	+	30.2008i	−0.576746	+	0.998953i
$915$	−0.404707	−	0.788730i	−0.0133792	−	0.0260746i
$916$	0.884414	+	0.393766i	0.0292219	+	0.0130104i
$917$	13.6739	+	9.93465i	0.451551	+	0.328071i
$918$	1.43645	−	0.0875765i	0.0474098	−	0.00289045i
$919$	−0.367135	−	1.12992i	−0.0121107	−	0.0372728i	0.944819	−	0.327594i	$-0.106238\pi$
$919$	−0.367135	−	1.12992i	−0.0121107	−	0.0372728i	−0.956929	+	0.290321i	$0.906238\pi$
$920$	−0.138196	+	1.31485i	−0.00455618	+	0.0433492i
$921$	−6.33622	+	40.7551i	−0.208785	+	1.34293i
$922$	7.73597	+	8.59166i	0.254771	+	0.282951i
$923$	0.855997	−	1.48263i	0.0281755	−	0.0488014i
$924$	2.11706	−	0.760777i	0.0696462	−	0.0250277i
$925$	23.9366	+	41.4594i	0.787031	+	1.36318i
$926$	13.6634	−	42.0517i	0.449008	−	1.38191i
$927$	53.3253	−	5.91157i	1.75143	−	0.194161i
$928$	2.95712	+	2.14847i	0.0970722	+	0.0705271i
$929$	7.02206	−	7.79878i	0.230386	−	0.255870i	−0.616857	−	0.787075i	$-0.711594\pi$
$929$	7.02206	−	7.79878i	0.230386	−	0.255870i	0.847243	+	0.531206i	$0.178261\pi$
$930$	0.256292	−	0.167476i	0.00840414	−	0.00549176i
$931$	−15.1698	+	6.75404i	−0.497171	+	0.221355i
$932$	0.441692	+	4.20242i	0.0144681	+	0.137655i
$933$	−40.7359	−	2.01872i	−1.33363	−	0.0660900i
$934$	−26.8479	−	46.5019i	−0.878489	−	1.52159i
$935$	−0.0127966	−	0.0429166i	−0.000418494	−	0.00140352i
$936$	7.71959	+	4.39855i	0.252323	+	0.143771i
$937$	2.89184	−	8.90017i	0.0944723	−	0.290756i	−0.892643	−	0.450763i	$-0.851152\pi$
$937$	2.89184	−	8.90017i	0.0944723	−	0.290756i	0.987116	+	0.160007i	$0.0511518\pi$
$938$	−2.36637	−	1.05357i	−0.0772646	−	0.0344004i
$939$	12.5254	+	15.3780i	0.408752	+	0.501842i
$940$	0.123344	+	0.0262176i	0.00402304	+	0.000855125i
$941$	16.0772	+	3.41732i	0.524103	+	0.111402i	0.462363	−	0.886691i	$-0.347002\pi$
$941$	16.0772	+	3.41732i	0.524103	+	0.111402i	0.0617399	+	0.998092i	$0.480335\pi$
$942$	−44.7660	+	7.22081i	−1.45855	+	0.235267i
$943$	−31.6784	−	14.1041i	−1.03159	−	0.459293i
$944$	7.15128	−	22.0094i	0.232754	−	0.716345i
$945$	−0.522668	−	0.513825i	−0.0170024	−	0.0167147i
$946$	31.7609	+	24.2802i	1.03264	+	0.789418i
$947$	1.37786	+	2.38652i	0.0447744	+	0.0775515i	0.887544	−	0.460723i	$-0.152410\pi$
$947$	1.37786	+	2.38652i	0.0447744	+	0.0775515i	−0.842770	+	0.538274i	$0.819076\pi$
$948$	−2.10682	−	4.10595i	−0.0684263	−	0.133355i
$949$	1.33513	+	12.7029i	0.0433401	+	0.412353i
$950$	35.1635	−	15.6558i	1.14085	−	0.507941i
$951$	1.40642	+	25.4509i	0.0456063	+	0.825303i
$952$	−0.650259	+	0.722186i	−0.0210750	+	0.0234062i
$953$	−42.5222	−	30.8942i	−1.37743	−	1.00076i	−0.997115	−	0.0759025i	$-0.975816\pi$
$953$	−42.5222	−	30.8942i	−1.37743	−	1.00076i	−0.380313	−	0.924858i	$-0.624184\pi$
$954$	−2.70395	+	6.16735i	−0.0875437	+	0.199675i
$955$	0.382200	−	1.17629i	0.0123677	−	0.0380639i
$956$	−1.43501	−	2.48550i	−0.0464114	−	0.0803869i
$957$	−18.5026	−	1.36973i	−0.598104	−	0.0442771i
$958$	5.55056	−	9.61385i	0.179330	−	0.310609i
$959$	9.56007	+	10.6175i	0.308711	+	0.342858i
$960$	−0.687318	−	0.553350i	−0.0221831	−	0.0178593i
$961$	2.95671	−	28.1312i	0.0953776	−	0.907457i
$962$	−4.87535	−	15.0048i	−0.157188	−	0.483774i
$963$	−39.8765	+	13.2079i	−1.28500	+	0.425619i
$964$	−0.0262761	−	0.0190907i	−0.000846297	−	0.000614871i
$965$	−1.09942	−	0.489495i	−0.0353917	−	0.0157574i
$966$	18.6091	−	28.8346i	0.598737	−	0.927740i
$967$	19.5173	−	33.8050i	0.627636	−	1.08710i	−0.360389	−	0.932802i	$-0.617356\pi$
$967$	19.5173	−	33.8050i	0.627636	−	1.08710i	0.988025	−	0.154295i	$-0.0493105\pi$
$968$	−15.9020	+	24.6812i	−0.511110	+	0.793283i
$969$	1.18436	−	1.19112i	0.0380473	−	0.0382643i
$970$	−1.09713	+	0.233203i	−0.0352268	+	0.00748768i
$971$	−4.37355	+	3.17757i	−0.140354	+	0.101973i	−0.655747	−	0.754981i	$-0.727646\pi$
$971$	−4.37355	+	3.17757i	−0.140354	+	0.101973i	0.515393	+	0.856954i	$0.327646\pi$
$972$	1.08009	−	2.93793i	0.0346438	−	0.0942342i
$973$	−3.16203	−	9.73171i	−0.101370	−	0.311984i
$974$	−7.85145	+	8.71991i	−0.251577	+	0.279404i
$975$	−9.47664	+	1.52859i	−0.303495	+	0.0489542i
$976$	3.22600	+	30.6934i	0.103262	+	0.982471i
$977$	−19.4858	−	21.6412i	−0.623407	−	0.692363i	0.345885	−	0.938277i	$-0.387579\pi$
$977$	−19.4858	−	21.6412i	−0.623407	−	0.692363i	−0.969292	+	0.245914i	$0.920912\pi$
$978$	−9.20499	−	2.43843i	−0.294343	−	0.0779725i
$979$	−40.4206	+	7.56686i	−1.29185	+	0.241838i
$980$	0.0464261			0.00148303
$981$	14.3161	+	4.56172i	0.457079	+	0.145645i
$982$	−24.7159	+	17.9571i	−0.788715	+	0.573035i
$983$	1.48542	−	14.1328i	0.0473776	−	0.450767i	−0.944958	−	0.327193i	$-0.893897\pi$
$983$	1.48542	−	14.1328i	0.0473776	−	0.450767i	0.992335	−	0.123575i	$-0.0394359\pi$
$984$	19.5957	−	12.8050i	0.624688	−	0.408208i
$985$	−1.42675	−	0.303265i	−0.0454601	−	0.00966284i
$986$	−0.817157	+	0.363822i	−0.0260236	+	0.0115864i
$987$	22.8450	+	18.3922i	0.727163	+	0.585429i
$988$	−1.13209	+	0.240634i	−0.0360167	+	0.00765558i
$989$	55.6454			1.76942
$990$	−1.05948	−	0.131419i	−0.0336726	−	0.00417677i
$991$	−23.9992			−0.762358			−0.381179	−	0.924501i	$-0.624482\pi$
$991$	−23.9992			−0.762358			−0.381179	+	0.924501i	$0.624482\pi$
$992$	−1.82368	+	0.387635i	−0.0579018	+	0.0123074i
$993$	−21.7440	+	8.41777i	−0.690025	+	0.267130i
$994$	4.07803	−	1.81565i	0.129347	−	0.0575891i
$995$	1.13082	+	0.240363i	0.0358493	+	0.00762001i
$996$	5.57586	+	2.82110i	0.176678	+	0.0893899i
$997$	−5.37205	+	51.1117i	−0.170135	+	1.61872i	0.492867	+	0.870105i	$0.335949\pi$
$997$	−5.37205	+	51.1117i	−0.170135	+	1.61872i	−0.663001	+	0.748618i	$0.730718\pi$
$998$	17.4704	−	12.6930i	0.553015	−	0.401789i
$999$	44.1806	−	22.9881i	1.39781	−	0.727310i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.m.b.31.7	yes	72
3.2	odd	2		297.2.n.b.64.3		72
9.2	odd	6		297.2.n.b.262.7		72
9.4	even	3		891.2.f.f.163.3		36
9.5	odd	6		891.2.f.e.163.7		36
9.7	even	3	inner	99.2.m.b.97.3	yes	72
11.4	even	5		1089.2.e.p.364.14		36
11.5	even	5	inner	99.2.m.b.49.3	yes	72
11.7	odd	10		1089.2.e.o.364.5		36
33.5	odd	10		297.2.n.b.280.7		72
99.4	even	15		9801.2.a.cm.1.5		18
99.5	odd	30		891.2.f.e.82.7		36
99.7	odd	30		1089.2.e.o.727.5		36
99.16	even	15	inner	99.2.m.b.16.7	✓	72
99.38	odd	30		297.2.n.b.181.3		72
99.40	odd	30		9801.2.a.co.1.14		18
99.49	even	15		891.2.f.f.82.3		36
99.59	odd	30		9801.2.a.cp.1.14		18
99.70	even	15		1089.2.e.p.727.14		36
99.95	even	30		9801.2.a.cn.1.5		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.16.7	✓	72	99.16	even	15	inner
99.2.m.b.31.7	yes	72	1.1	even	1	trivial
99.2.m.b.49.3	yes	72	11.5	even	5	inner
99.2.m.b.97.3	yes	72	9.7	even	3	inner
297.2.n.b.64.3		72	3.2	odd	2
297.2.n.b.181.3		72	99.38	odd	30
297.2.n.b.262.7		72	9.2	odd	6
297.2.n.b.280.7		72	33.5	odd	10
891.2.f.e.82.7		36	99.5	odd	30
891.2.f.e.163.7		36	9.5	odd	6
891.2.f.f.82.3		36	99.49	even	15
891.2.f.f.163.3		36	9.4	even	3
1089.2.e.o.364.5		36	11.7	odd	10
1089.2.e.o.727.5		36	99.7	odd	30
1089.2.e.p.364.14		36	11.4	even	5
1089.2.e.p.727.14		36	99.70	even	15
9801.2.a.cm.1.5		18	99.4	even	15
9801.2.a.cn.1.5		18	99.95	even	30
9801.2.a.co.1.14		18	99.40	odd	30
9801.2.a.cp.1.14		18	99.59	odd	30

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.m (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.45109 - 0.308439i) q^{2} +(0.266086 - 1.71149i) q^{3} +(0.183441 - 0.0816732i) q^{4} +(0.0707467 + 0.0150377i) q^{5} +(-0.141775 - 2.56560i) q^{6} +(-0.203853 + 1.93954i) q^{7} +(-2.15937 + 1.56887i) q^{8} +(-2.85840 - 0.910807i) q^{9} +0.107298 q^{10} +(3.25999 - 0.610280i) q^{11} +(-0.0909718 - 0.335689i) q^{12} +(0.742450 + 0.824574i) q^{13} +(0.302419 + 2.87732i) q^{14} +(0.0445615 - 0.117081i) q^{15} +(-2.91827 + 3.24106i) q^{16} +(-0.0576906 - 0.177553i) q^{17} +(-4.42872 - 0.440023i) q^{18} +(-4.20255 + 3.05333i) q^{19} +(0.0142060 - 0.00301958i) q^{20} +(3.26525 + 0.864976i) q^{21} +(4.54231 - 1.89108i) q^{22} +(3.42420 - 5.93089i) q^{23} +(2.11054 + 4.11320i) q^{24} +(-4.56295 - 2.03156i) q^{25} +(1.33169 + 0.967532i) q^{26} +(-2.31942 + 4.64976i) q^{27} +(0.121013 + 0.372440i) q^{28} +(0.337596 - 3.21201i) q^{29} +(0.0285505 - 0.183640i) q^{30} +(1.10232 + 1.22425i) q^{31} +(-0.565872 + 0.980120i) q^{32} +(-0.177051 - 5.74183i) q^{33} +(-0.138479 - 0.239852i) q^{34} +(-0.0435881 + 0.134150i) q^{35} +(-0.598735 + 0.0663750i) q^{36} +(-7.75416 - 5.63373i) q^{37} +(-5.15652 + 5.72690i) q^{38} +(1.60881 - 1.05129i) q^{39} +(-0.176361 + 0.0785208i) q^{40} +(-0.529271 - 5.03568i) q^{41} +(5.00497 + 0.248028i) q^{42} +(4.06266 + 7.03673i) q^{43} +(0.548173 - 0.378204i) q^{44} +(-0.188526 - 0.107420i) q^{45} +(3.13951 - 9.66242i) q^{46} +(7.93189 + 3.53150i) q^{47} +(4.77054 + 5.85699i) q^{48} +(3.12679 + 0.664620i) q^{49} +(-7.24787 - 1.54058i) q^{50} +(-0.319231 + 0.0514924i) q^{51} +(0.203541 + 0.0906224i) q^{52} +(0.467571 - 1.43904i) q^{53} +(-1.93152 + 7.46263i) q^{54} +(0.239811 + 0.00584740i) q^{55} +(-2.60269 - 4.50800i) q^{56} +(4.10751 + 8.00508i) q^{57} +(-0.500827 - 4.76505i) q^{58} +(-4.84750 + 2.15825i) q^{59} +(-0.00138796 - 0.0251169i) q^{60} +(4.73508 - 5.25884i) q^{61} +(1.97717 + 1.43649i) q^{62} +(2.34924 - 5.35829i) q^{63} +(2.17659 - 6.69887i) q^{64} +(0.0401262 + 0.0695006i) q^{65} +(-2.02792 - 8.27732i) q^{66} +(-0.447660 + 0.775370i) q^{67} +(-0.0250842 - 0.0278588i) q^{68} +(-9.23953 - 7.43861i) q^{69} +(-0.0218731 + 0.208109i) q^{70} +(-0.476791 - 1.46741i) q^{71} +(7.60128 - 2.51770i) q^{72} +(9.31301 + 6.76630i) q^{73} +(-12.9897 - 5.78337i) q^{74} +(-4.69112 + 7.26887i) q^{75} +(-0.521545 + 0.903343i) q^{76} +(0.519100 + 6.44728i) q^{77} +(2.01027 - 2.02173i) q^{78} +(12.9790 - 2.75878i) q^{79} +(-0.255196 + 0.185411i) q^{80} +(7.34086 + 5.20689i) q^{81} +(-2.32122 - 7.14398i) q^{82} +(-12.0223 + 13.3521i) q^{83} +(0.669627 - 0.108012i) q^{84} +(-0.00141143 - 0.0134288i) q^{85} +(8.06569 + 8.95785i) q^{86} +(-5.40749 - 1.43246i) q^{87} +(-6.08208 + 6.43234i) q^{88} -12.3990 q^{89} +(-0.306701 - 0.0977279i) q^{90} +(-1.75064 + 1.27192i) q^{91} +(0.143744 - 1.36763i) q^{92} +(2.38859 - 1.56085i) q^{93} +(12.5992 + 2.67803i) q^{94} +(-0.343232 + 0.152817i) q^{95} +(1.52689 + 1.22928i) q^{96} +(-10.2251 + 2.17341i) q^{97} +4.74225 q^{98} +(-9.87420 - 1.22480i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - q^{2} - 12 q^{3} + 11 q^{4} - 8 q^{5} - 7 q^{6} - 2 q^{7} + 6 q^{8} - 22 q^{9} - 8 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 10 q^{14} - 20 q^{15} - 9 q^{16} - 20 q^{17} - 21 q^{18} + 8 q^{19}+ \cdots - 182 q^{99}+O(q^{100}) \) 72 * q - q^2 - 12 * q^3 + 11 * q^4 - 8 * q^5 - 7 * q^6 - 2 * q^7 + 6 * q^8 - 22 * q^9 - 8 * q^10 - 2 * q^11 - 16 * q^12 - 11 * q^13 - 10 * q^14 - 20 * q^15 - 9 * q^16 - 20 * q^17 - 21 * q^18 + 8 * q^19 - 45 * q^20 - 16 * q^21 - 16 * q^22 + 20 * q^23 + 36 * q^24 + 11 * q^25 - 12 * q^26 + 27 * q^27 - 54 * q^28 - 23 * q^29 - 6 * q^30 + 3 * q^31 + 18 * q^32 + 28 * q^33 + 8 * q^34 + 18 * q^35 + 75 * q^36 - 42 * q^37 - q^38 - 11 * q^39 - 25 * q^40 + 10 * q^41 + 61 * q^42 - 8 * q^43 + 38 * q^44 + 40 * q^45 - 18 * q^46 - 34 * q^47 - 50 * q^48 + q^49 + 42 * q^51 - 27 * q^52 + 4 * q^53 + 34 * q^54 + 18 * q^55 + 114 * q^56 - 21 * q^57 + q^58 - 16 * q^59 - 63 * q^60 - 3 * q^61 + 184 * q^62 - 10 * q^63 + 26 * q^64 + 84 * q^65 + 93 * q^66 + 10 * q^67 - 23 * q^68 + 42 * q^69 - 46 * q^70 - 48 * q^71 + 2 * q^72 - 40 * q^73 + 68 * q^74 + 28 * q^75 + 16 * q^76 - 26 * q^77 - 64 * q^78 + 19 * q^79 - 56 * q^80 + 14 * q^81 + 94 * q^82 + 7 * q^83 - 15 * q^84 + 25 * q^85 - 77 * q^86 - 120 * q^87 + 18 * q^88 - 56 * q^89 - 64 * q^90 + 20 * q^91 + 50 * q^92 - 53 * q^93 - 63 * q^94 - 77 * q^95 - 97 * q^96 - 33 * q^97 - 328 * q^98 - 182 * q^99

Introduction

L-functions

Modular forms

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