LMFDB - Embedded newform 144.2.u.a.83.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [144,2,Mod(11,144)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(144, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("144.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	144.u (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.14984578911$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			83.14
Character	$\chi$	$=$	144.83
Dual form			144.2.u.a.59.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.378412 - 1.36265i) q^{2} +(1.53620 + 0.800065i) q^{3} +(-1.71361 - 1.03128i) q^{4} +(1.00059 - 3.73424i) q^{5} +(1.67152 - 1.79054i) q^{6} +(-1.68236 + 2.91393i) q^{7} +(-2.05372 + 1.94479i) q^{8} +(1.71979 + 2.45811i) q^{9} +(-4.70981 - 2.77653i) q^{10} +(0.0566521 + 0.211428i) q^{11} +(-1.80734 - 2.95525i) q^{12} +(0.727551 - 2.71526i) q^{13} +(3.33403 + 3.39513i) q^{14} +(4.52473 - 4.93599i) q^{15} +(1.87291 + 3.53443i) q^{16} +4.23937i q^{17} +(4.00033 - 1.41329i) q^{18} +(-1.12365 + 1.12365i) q^{19} +(-5.56567 + 5.36714i) q^{20} +(-4.91577 + 3.13037i) q^{21} +(0.309540 + 0.00281033i) q^{22} +(3.33369 - 1.92471i) q^{23} +(-4.71088 + 1.34447i) q^{24} +(-8.61325 - 4.97286i) q^{25} +(-3.42462 - 2.01888i) q^{26} +(0.675290 + 5.15209i) q^{27} +(5.88800 - 3.25835i) q^{28} +(0.545635 + 2.03634i) q^{29} +(-5.01379 - 8.03344i) q^{30} +(-7.21206 + 4.16388i) q^{31} +(5.52491 - 1.21464i) q^{32} +(-0.0821277 + 0.370121i) q^{33} +(5.77677 + 1.60423i) q^{34} +(9.19798 + 9.19798i) q^{35} +(-0.412042 - 5.98584i) q^{36} +(-2.66564 + 2.66564i) q^{37} +(1.10593 + 1.95634i) q^{38} +(3.29004 - 3.58908i) q^{39} +(5.20739 + 9.61503i) q^{40} +(-1.70386 - 2.95117i) q^{41} +(2.40541 + 7.88302i) q^{42} +(4.68985 - 1.25664i) q^{43} +(0.120963 - 0.420730i) q^{44} +(10.9000 - 3.96257i) q^{45} +(-1.36119 - 5.27098i) q^{46} +(2.34998 - 4.07028i) q^{47} +(0.0493802 + 6.92803i) q^{48} +(-2.16067 - 3.74239i) q^{49} +(-10.0356 + 9.85502i) q^{50} +(-3.39177 + 6.51251i) q^{51} +(-4.04693 + 3.90257i) q^{52} +(-7.58271 - 7.58271i) q^{53} +(7.27601 + 1.02943i) q^{54} +0.846209 q^{55} +(-2.21189 - 9.25626i) q^{56} +(-2.62513 + 0.827151i) q^{57} +(2.98128 + 0.0270672i) q^{58} +(-5.34305 - 1.43167i) q^{59} +(-12.8440 + 3.79207i) q^{60} +(8.69958 - 2.33105i) q^{61} +(2.94477 + 11.4031i) q^{62} +(-10.0561 + 0.875933i) q^{63} +(0.435568 - 7.98813i) q^{64} +(-9.41144 - 5.43370i) q^{65} +(0.473265 + 0.251969i) q^{66} +(-5.17504 - 1.38665i) q^{67} +(4.37200 - 7.26463i) q^{68} +(6.66110 - 0.289558i) q^{69} +(16.0142 - 9.05296i) q^{70} -7.53614i q^{71} +(-8.31250 - 1.70364i) q^{72} -3.22646i q^{73} +(2.62362 + 4.64104i) q^{74} +(-9.25302 - 14.5304i) q^{75} +(3.08429 - 0.766693i) q^{76} +(-0.711397 - 0.190618i) q^{77} +(-3.64565 - 5.84131i) q^{78} +(-4.98587 - 2.87859i) q^{79} +(15.0724 - 3.45739i) q^{80} +(-3.08462 + 8.45489i) q^{81} +(-4.66616 + 1.20500i) q^{82} +(4.50604 - 1.20739i) q^{83} +(11.6520 - 0.294685i) q^{84} +(15.8308 + 4.24186i) q^{85} +(0.0623381 - 6.86613i) q^{86} +(-0.790999 + 3.56475i) q^{87} +(-0.527532 - 0.324039i) q^{88} -2.96157 q^{89} +(-1.27489 - 16.3523i) q^{90} +(6.68807 + 6.68807i) q^{91} +(-7.69756 - 0.139785i) q^{92} +(-14.4105 + 0.626426i) q^{93} +(-4.65709 - 4.74243i) q^{94} +(3.07166 + 5.32027i) q^{95} +(9.45914 + 2.55436i) q^{96} +(-7.63883 + 13.2308i) q^{97} +(-5.91718 + 1.52806i) q^{98} +(-0.422285 + 0.502870i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} - 4 q^{7} - 8 q^{10} - 6 q^{11} - 16 q^{12} - 2 q^{13} - 6 q^{14} - 2 q^{16} - 10 q^{18} - 8 q^{19} - 48 q^{20} + 2 q^{21} - 2 q^{22} - 12 q^{23} - 16 q^{27}+ \cdots + 46 q^{99}+O(q^{100}) $ 88 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 - 4 * q^7 - 8 * q^10 - 6 * q^11 - 16 * q^12 - 2 * q^13 - 6 * q^14 - 2 * q^16 - 10 * q^18 - 8 * q^19 - 48 * q^20 + 2 * q^21 - 2 * q^22 - 12 * q^23 - 16 * q^27 + 8 * q^28 - 6 * q^29 - 34 * q^30 - 6 * q^32 - 8 * q^33 + 2 * q^34 - 26 * q^36 - 8 * q^37 - 6 * q^38 - 32 * q^39 - 2 * q^40 + 48 * q^42 - 2 * q^43 + 6 * q^45 - 40 * q^46 + 42 * q^48 - 24 * q^49 + 72 * q^50 - 12 * q^51 - 2 * q^52 - 38 * q^54 - 16 * q^55 + 36 * q^56 + 16 * q^58 - 42 * q^59 + 70 * q^60 - 2 * q^61 - 44 * q^64 - 12 * q^65 + 104 * q^66 - 2 * q^67 + 96 * q^68 - 10 * q^69 - 16 * q^70 - 10 * q^72 + 78 * q^74 - 56 * q^75 - 14 * q^76 - 6 * q^77 + 12 * q^78 - 8 * q^81 - 36 * q^82 + 54 * q^83 + 158 * q^84 + 8 * q^85 + 54 * q^86 + 48 * q^87 + 22 * q^88 + 64 * q^90 + 20 * q^91 + 108 * q^92 - 34 * q^93 + 6 * q^94 - 58 * q^96 - 4 * q^97 + 46 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.378412	−	1.36265i	0.267578	−	0.963536i
$2$	0.378412	−	1.36265i	0.267578	−	0.963536i
$3$	1.53620	+	0.800065i	0.886923	+	0.461918i
$3$	1.53620	+	0.800065i	0.886923	+	0.461918i
$4$	−1.71361	−	1.03128i	−0.856804	−	0.515642i
$5$	1.00059	−	3.73424i	0.447476	−	1.67000i	−0.261839	−	0.965111i	$-0.584329\pi$
$5$	1.00059	−	3.73424i	0.447476	−	1.67000i	0.709315	−	0.704891i	$-0.249004\pi$
$6$	1.67152	−	1.79054i	0.682395	−	0.730983i
$7$	−1.68236	+	2.91393i	−0.635872	+	1.10136i	0.350457	+	0.936579i	$0.386026\pi$
$7$	−1.68236	+	2.91393i	−0.635872	+	1.10136i	−0.986330	+	0.164785i	$0.947307\pi$
$8$	−2.05372	+	1.94479i	−0.726101	+	0.687588i
$9$	1.71979	+	2.45811i	0.573264	+	0.819371i
$10$	−4.70981	−	2.77653i	−1.48937	−	0.878015i
$11$	0.0566521	+	0.211428i	0.0170812	+	0.0637480i	0.973940	−	0.226804i	$-0.0728277\pi$
$11$	0.0566521	+	0.211428i	0.0170812	+	0.0637480i	−0.956859	+	0.290552i	$0.906161\pi$
$12$	−1.80734	−	2.95525i	−0.521735	−	0.853107i
$13$	0.727551	−	2.71526i	0.201786	−	0.753076i	−0.788619	−	0.614882i	$-0.789204\pi$
$13$	0.727551	−	2.71526i	0.201786	−	0.753076i	0.990405	−	0.138194i	$-0.0441298\pi$
$14$	3.33403	+	3.39513i	0.891058	+	0.907386i
$15$	4.52473	−	4.93599i	1.16828	−	1.27447i
$16$	1.87291	+	3.53443i	0.468227	+	0.883608i
$17$			4.23937i			1.02820i	0.857731	+	0.514100i	$0.171874\pi$
$17$			4.23937i			1.02820i	−0.857731	+	0.514100i	$0.828126\pi$
$18$	4.00033	−	1.41329i	0.942886	−	0.333116i
$19$	−1.12365	+	1.12365i	−0.257782	+	0.257782i	−0.824152	−	0.566369i	$-0.808348\pi$
$19$	−1.12365	+	1.12365i	−0.257782	+	0.257782i	0.566369	+	0.824152i	$0.308348\pi$
$20$	−5.56567	+	5.36714i	−1.24452	+	1.20013i
$21$	−4.91577	+	3.13037i	−1.07271	+	0.683104i
$22$	0.309540	+	0.00281033i	0.0659941	+	0.000599165i
$23$	3.33369	−	1.92471i	0.695123	−	0.401329i	−0.110405	−	0.993887i	$-0.535215\pi$
$23$	3.33369	−	1.92471i	0.695123	−	0.401329i	0.805528	+	0.592557i	$0.201882\pi$
$24$	−4.71088	+	1.34447i	−0.961605	+	0.274438i
$25$	−8.61325	−	4.97286i	−1.72265	−	0.994572i
$26$	−3.42462	−	2.01888i	−0.671623	−	0.395935i
$27$	0.675290	+	5.15209i	0.129960	+	0.991519i
$28$	5.88800	−	3.25835i	1.11273	−	0.615771i
$29$	0.545635	+	2.03634i	0.101322	+	0.378138i	0.997902	−	0.0647434i	$-0.0206229\pi$
$29$	0.545635	+	2.03634i	0.101322	+	0.378138i	−0.896580	+	0.442882i	$0.853956\pi$
$30$	−5.01379	−	8.03344i	−0.915389	−	1.46670i
$31$	−7.21206	+	4.16388i	−1.29532	+	0.747856i	−0.979593	−	0.200993i	$-0.935583\pi$
$31$	−7.21206	+	4.16388i	−1.29532	+	0.747856i	−0.315731	+	0.948849i	$0.602250\pi$
$32$	5.52491	−	1.21464i	0.976676	−	0.214720i
$33$	−0.0821277	+	0.370121i	−0.0142966	+	0.0644297i
$34$	5.77677	+	1.60423i	0.990707	+	0.275123i
$35$	9.19798	+	9.19798i	1.55474	+	1.55474i
$36$	−0.412042	−	5.98584i	−0.0686737	−	0.997639i
$37$	−2.66564	+	2.66564i	−0.438229	+	0.438229i	−0.891416	−	0.453187i	$-0.850287\pi$
$37$	−2.66564	+	2.66564i	−0.438229	+	0.438229i	0.453187	+	0.891416i	$0.350287\pi$
$38$	1.10593	+	1.95634i	0.179406	+	0.317359i
$39$	3.29004	−	3.58908i	0.526828	−	0.574712i
$40$	5.20739	+	9.61503i	0.823361	+	1.52027i
$41$	−1.70386	−	2.95117i	−0.266098	−	0.460895i	0.701753	−	0.712420i	$-0.252401\pi$
$41$	−1.70386	−	2.95117i	−0.266098	−	0.460895i	−0.967851	+	0.251526i	$0.919068\pi$
$42$	2.40541	+	7.88302i	0.371162	+	1.21638i
$43$	4.68985	−	1.25664i	0.715195	−	0.191636i	0.117168	−	0.993112i	$-0.462618\pi$
$43$	4.68985	−	1.25664i	0.715195	−	0.191636i	0.598027	+	0.801476i	$0.295952\pi$
$44$	0.120963	−	0.420730i	0.0182359	−	0.0634274i
$45$	10.9000	−	3.96257i	1.62487	−	0.590704i
$46$	−1.36119	−	5.27098i	−0.200696	−	0.777163i
$47$	2.34998	−	4.07028i	0.342779	−	0.593711i	−0.642168	−	0.766564i	$-0.721965\pi$
$47$	2.34998	−	4.07028i	0.342779	−	0.593711i	0.984948	+	0.172852i	$0.0552984\pi$
$48$	0.0493802	+	6.92803i	0.00712741	+	0.999975i
$49$	−2.16067	−	3.74239i	−0.308667	−	0.534628i
$50$	−10.0356	+	9.85502i	−1.41925	+	1.39371i
$51$	−3.39177	+	6.51251i	−0.474943	+	0.911933i
$52$	−4.04693	+	3.90257i	−0.561209	+	0.541190i
$53$	−7.58271	−	7.58271i	−1.04157	−	1.04157i	−0.999098	−	0.0424680i	$-0.986478\pi$
$53$	−7.58271	−	7.58271i	−1.04157	−	1.04157i	−0.0424680	−	0.999098i	$-0.513522\pi$
$54$	7.27601	+	1.02943i	0.990139	+	0.140088i
$55$	0.846209			0.114103
$56$	−2.21189	−	9.25626i	−0.295576	−	1.23692i
$57$	−2.62513	+	0.827151i	−0.347707	+	0.109559i
$58$	2.98128	+	0.0270672i	0.391461	+	0.00355410i
$59$	−5.34305	−	1.43167i	−0.695605	−	0.186387i	−0.106344	−	0.994329i	$-0.533915\pi$
$59$	−5.34305	−	1.43167i	−0.695605	−	0.186387i	−0.589261	+	0.807942i	$0.700581\pi$
$60$	−12.8440	+	3.79207i	−1.65816	+	0.489555i
$61$	8.69958	−	2.33105i	1.11387	−	0.298460i	0.345468	−	0.938431i	$-0.387720\pi$
$61$	8.69958	−	2.33105i	1.11387	−	0.298460i	0.768399	+	0.639971i	$0.221054\pi$
$62$	2.94477	+	11.4031i	0.373986	+	1.44820i
$63$	−10.0561	+	0.875933i	−1.26695	+	0.110357i
$64$	0.435568	−	7.98813i	0.0544460	−	0.998517i
$65$	−9.41144	−	5.43370i	−1.16735	−	0.673967i
$66$	0.473265	+	0.251969i	0.0582549	+	0.0310153i
$67$	−5.17504	−	1.38665i	−0.632231	−	0.169406i	−0.0715493	−	0.997437i	$-0.522794\pi$
$67$	−5.17504	−	1.38665i	−0.632231	−	0.169406i	−0.560682	+	0.828031i	$0.689461\pi$
$68$	4.37200	−	7.26463i	0.530182	−	0.880965i
$69$	6.66110	−	0.289558i	0.801902	−	0.0348587i
$70$	16.0142	−	9.05296i	1.91406	−	1.08204i
$71$		−	7.53614i		−	0.894375i	−0.894440	−	0.447187i	$-0.852426\pi$
$71$		−	7.53614i		−	0.894375i	0.894440	−	0.447187i	$-0.147574\pi$
$72$	−8.31250	−	1.70364i	−0.979637	−	0.200776i
$73$		−	3.22646i		−	0.377629i	−0.982013	−	0.188814i	$-0.939536\pi$
$73$		−	3.22646i		−	0.377629i	0.982013	−	0.188814i	$-0.0604644\pi$
$74$	2.62362	+	4.64104i	0.304989	+	0.539510i
$75$	−9.25302	−	14.5304i	−1.06845	−	1.67783i
$76$	3.08429	−	0.766693i	0.353792	−	0.0879457i
$77$	−0.711397	−	0.190618i	−0.0810712	−	0.0217230i
$78$	−3.64565	−	5.84131i	−0.412788	−	0.661398i
$79$	−4.98587	−	2.87859i	−0.560954	−	0.323867i	0.192574	−	0.981282i	$-0.438316\pi$
$79$	−4.98587	−	2.87859i	−0.560954	−	0.323867i	−0.753528	+	0.657415i	$0.771650\pi$
$80$	15.0724	−	3.45739i	1.68515	−	0.386548i
$81$	−3.08462	+	8.45489i	−0.342736	+	0.939432i
$82$	−4.66616	+	1.20500i	−0.515291	+	0.133070i
$83$	4.50604	−	1.20739i	0.494602	−	0.132528i	−0.00289160	−	0.999996i	$-0.500920\pi$
$83$	4.50604	−	1.20739i	0.494602	−	0.132528i	0.497494	+	0.867468i	$0.334254\pi$
$84$	11.6520	−	0.294685i	1.27134	−	0.0321528i
$85$	15.8308	+	4.24186i	1.71710	+	0.460094i
$86$	0.0623381	−	6.86613i	0.00672209	−	0.740394i
$87$	−0.790999	+	3.56475i	−0.0848040	+	0.382182i
$88$	−0.527532	−	0.324039i	−0.0562351	−	0.0345427i
$89$	−2.96157			−0.313926			−0.156963	−	0.987605i	$-0.550170\pi$
$89$	−2.96157			−0.313926			−0.156963	+	0.987605i	$0.550170\pi$
$90$	−1.27489	−	16.3523i	−0.134385	−	1.72368i
$91$	6.68807	+	6.68807i	0.701100	+	0.701100i
$92$	−7.69756	−	0.139785i	−0.802527	−	0.0145736i
$93$	−14.4105	+	0.626426i	−1.49430	+	0.0649573i
$94$	−4.65709	−	4.74243i	−0.480342	−	0.489144i
$95$	3.07166	+	5.32027i	0.315146	+	0.545849i
$96$	9.45914	+	2.55436i	0.965419	+	0.260703i
$97$	−7.63883	+	13.2308i	−0.775606	+	1.34339i	0.158848	+	0.987303i	$0.449222\pi$
$97$	−7.63883	+	13.2308i	−0.775606	+	1.34339i	−0.934453	+	0.356085i	$0.884111\pi$
$98$	−5.91718	+	1.52806i	−0.597726	+	0.154358i
$99$	−0.422285	+	0.502870i	−0.0424412	+	0.0505403i
$100$	9.63131	+	17.4042i	0.963131	+	1.74042i
$101$	0.129684	−	0.0347486i	0.0129040	−	0.00345762i	−0.252361	−	0.967633i	$-0.581207\pi$
$101$	0.129684	−	0.0347486i	0.0129040	−	0.00345762i	0.265265	+	0.964175i	$0.414540\pi$
$102$	7.59075	+	7.08620i	0.751597	+	0.701638i
$103$	−4.09117	−	7.08611i	−0.403115	−	0.698215i	0.590985	−	0.806682i	$-0.298739\pi$
$103$	−4.09117	−	7.08611i	−0.403115	−	0.698215i	−0.994100	+	0.108467i	$0.965406\pi$
$104$	3.78642	+	6.99132i	0.371289	+	0.685555i
$105$	6.77091	+	21.4889i	0.660774	+	2.09710i
$106$	−13.2019	+	7.46316i	−1.28229	+	0.724887i
$107$	8.28837	−	8.28837i	0.801267	−	0.801267i	−0.182027	−	0.983294i	$-0.558266\pi$
$107$	8.28837	−	8.28837i	0.801267	−	0.801267i	0.983294	+	0.182027i	$0.0582658\pi$
$108$	4.15608	−	9.52507i	0.399919	−	0.916551i
$109$	6.31291	+	6.31291i	0.604667	+	0.604667i	0.941547	−	0.336881i	$-0.109372\pi$
$109$	6.31291	+	6.31291i	0.604667	+	0.604667i	−0.336881	+	0.941547i	$0.609372\pi$
$110$	0.320216	−	1.15308i	0.0305314	−	0.109942i
$111$	−6.22764	+	1.96226i	−0.591101	+	0.186250i
$112$	−13.4500	−	0.488655i	−1.27091	−	0.0461736i
$113$	14.6562	−	8.46178i	1.37874	−	0.796017i	0.386735	−	0.922191i	$-0.373603\pi$
$113$	14.6562	−	8.46178i	1.37874	−	0.796017i	0.992008	+	0.126174i	$0.0402696\pi$
$114$	0.133733	+	3.89013i	0.0125252	+	0.364344i
$115$	−3.85167	−	14.3746i	−0.359171	−	1.34044i
$116$	1.16504	−	4.05219i	0.108171	−	0.376236i
$117$	7.92564	−	2.88128i	0.732725	−	0.266374i
$118$	−3.97273	+	6.73892i	−0.365719	+	0.620368i
$119$	−12.3533	−	7.13215i	−1.13242	−	0.653803i
$120$	0.306922	+	18.9368i	0.0280181	+	1.72869i
$121$	9.48479	−	5.47604i	0.862253	−	0.497822i
$122$	0.115636	−	12.7365i	0.0104692	−	1.15311i
$123$	−0.256333	−	5.89676i	−0.0231128	−	0.531693i
$124$	16.6528	+	0.302408i	1.49546	+	0.0271571i
$125$	−13.5199	+	13.5199i	−1.20926	+	1.20926i
$126$	−2.61176	+	14.0343i	−0.232674	+	1.25028i
$127$			13.4028i			1.18931i	0.803981	+	0.594654i	$0.202711\pi$
$127$			13.4028i			1.18931i	−0.803981	+	0.594654i	$0.797289\pi$
$128$	−10.7202	−	3.61633i	−0.947539	−	0.319641i
$129$	8.20992	+	1.82174i	0.722843	+	0.160395i
$130$	−10.9656	+	10.7683i	−0.961747	+	0.944441i
$131$	0.169534	−	0.632708i	0.0148122	−	0.0552800i	−0.958124	−	0.286353i	$-0.907557\pi$
$131$	0.169534	−	0.632708i	0.0148122	−	0.0552800i	0.972936	+	0.231073i	$0.0742236\pi$
$132$	0.522434	−	0.549545i	0.0454720	−	0.0478317i
$133$	−1.38385	−	5.16461i	−0.119995	−	0.447829i
$134$	−3.84781	+	6.52702i	−0.332400	+	0.563849i
$135$	19.9148	+	2.63341i	1.71399	+	0.226648i
$136$	−8.24470	−	8.70650i	−0.706977	−	0.746577i
$137$	10.5230	−	18.2263i	0.899037	−	1.55718i	0.0703095	−	0.997525i	$-0.477601\pi$
$137$	10.5230	−	18.2263i	0.899037	−	1.55718i	0.828727	−	0.559652i	$-0.189065\pi$
$138$	2.12607	−	9.18629i	0.180983	−	0.781989i
$139$	−1.72666	+	6.44400i	−0.146454	+	0.546573i	0.853233	+	0.521530i	$0.174639\pi$
$139$	−1.72666	+	6.44400i	−0.146454	+	0.546573i	−0.999686	+	0.0250423i	$0.992028\pi$
$140$	−6.27601	−	25.2475i	−0.530420	−	2.13380i
$141$	6.86651	−	4.37261i	0.578264	−	0.368240i
$142$	−10.2691	−	2.85176i	−0.861763	−	0.239315i
$143$	0.615299			0.0514539
$144$	−5.46701	+	10.6823i	−0.455584	+	0.890193i
$145$	8.15012			0.676831
$146$	−4.39652	−	1.22093i	−0.363859	−	0.101045i
$147$	−0.325057	−	7.47772i	−0.0268103	−	0.616752i
$148$	7.31691	−	1.81884i	0.601446	−	0.149507i
$149$	−5.78161	+	21.5773i	−0.473648	+	1.76768i	0.152844	+	0.988250i	$0.451157\pi$
$149$	−5.78161	+	21.5773i	−0.473648	+	1.76768i	−0.626492	+	0.779428i	$0.715510\pi$
$150$	−23.3013	+	7.11010i	−1.90254	+	0.580537i
$151$	−9.97506	+	17.2773i	−0.811759	+	1.40601i	0.0998734	+	0.995000i	$0.468156\pi$
$151$	−9.97506	+	17.2773i	−0.811759	+	1.40601i	−0.911632	+	0.411007i	$0.865177\pi$
$152$	0.122401	−	4.49292i	0.00992807	−	0.364424i
$153$	−10.4209	+	7.29084i	−0.842476	+	0.589430i
$154$	−0.528947	+	0.897250i	−0.0426237	+	0.0723025i
$155$	8.33265	+	31.0979i	0.669295	+	2.49784i
$156$	−9.33919	+	2.75731i	−0.747734	+	0.220761i
$157$	3.85693	−	14.3943i	0.307817	−	1.14879i	−0.622677	−	0.782479i	$-0.713955\pi$
$157$	3.85693	−	14.3943i	0.307817	−	1.14879i	0.930494	−	0.366308i	$-0.119378\pi$
$158$	−5.80922	+	5.70468i	−0.462157	+	0.453840i
$159$	−5.58187	−	17.7152i	−0.442671	−	1.40491i
$160$	0.992392	−	21.8467i	0.0784555	−	1.72713i
$161$			12.9522i			1.02078i
$162$	10.3538	+	7.40268i	0.813468	+	0.581610i
$163$	−4.35766	+	4.35766i	−0.341318	+	0.341318i	−0.856863	−	0.515545i	$-0.827590\pi$
$163$	−4.35766	+	4.35766i	−0.341318	+	0.341318i	0.515545	+	0.856863i	$0.327590\pi$
$164$	−0.123745	+	6.81430i	−0.00966288	+	0.532108i
$165$	1.29994	+	0.677022i	0.101200	+	0.0527061i
$166$	0.0598948	−	6.59703i	0.00464874	−	0.512029i
$167$	−11.8952	+	6.86770i	−0.920479	+	0.531439i	−0.883788	−	0.467888i	$-0.845015\pi$
$167$	−11.8952	+	6.86770i	−0.920479	+	0.531439i	−0.0366910	+	0.999327i	$0.511682\pi$
$168$	4.00771	−	15.9891i	0.309201	−	1.23358i
$169$	4.41505	+	2.54903i	0.339619	+	0.196079i
$170$	11.7707	−	19.9667i	0.902774	−	1.53137i
$171$	−4.69449	−	0.829610i	−0.358997	−	0.0634418i
$172$	−9.33252	−	2.68317i	−0.711598	−	0.204590i
$173$	1.40497	+	5.24342i	0.106818	+	0.398650i	0.998545	−	0.0539235i	$-0.0171727\pi$
$173$	1.40497	+	5.24342i	0.106818	+	0.398650i	−0.891727	+	0.452573i	$0.850506\pi$
$174$	4.55817	+	2.42680i	0.345554	+	0.183975i
$175$	28.9812	−	16.7323i	2.19077	−	1.26484i
$176$	−0.641175	+	0.596219i	−0.0483304	+	0.0449417i
$177$	−7.06254	−	6.47410i	−0.530853	−	0.486623i
$178$	−1.12069	+	4.03557i	−0.0839995	+	0.302479i
$179$	0.380130	+	0.380130i	0.0284123	+	0.0284123i	0.721170	−	0.692758i	$-0.243605\pi$
$179$	0.380130	+	0.380130i	0.0284123	+	0.0284123i	−0.692758	+	0.721170i	$0.743605\pi$
$180$	−22.7648	−	4.45068i	−1.69679	−	0.331734i
$181$	−4.98992	+	4.98992i	−0.370898	+	0.370898i	−0.867804	−	0.496906i	$-0.834469\pi$
$181$	−4.98992	+	4.98992i	−0.370898	+	0.370898i	0.496906	+	0.867804i	$0.334469\pi$
$182$	11.6443	−	6.58263i	0.863134	−	0.487937i
$183$	15.2292	+	3.37929i	1.12578	+	0.249804i
$184$	−3.10333	+	10.4362i	−0.228780	+	0.769364i
$185$	7.28695	+	12.6214i	0.535747	+	0.927941i
$186$	−4.59951	+	19.8735i	−0.337253	+	1.45719i
$187$	−0.896324	+	0.240169i	−0.0655457	+	0.0175629i
$188$	−8.22455	+	4.55137i	−0.599837	+	0.331943i
$189$	−16.1489	−	6.69991i	−1.17466	−	0.487347i
$190$	8.41200	−	2.17233i	0.610271	−	0.157598i
$191$	−5.40555	+	9.36269i	−0.391132	+	0.677461i	−0.992599	−	0.121437i	$-0.961250\pi$
$191$	−5.40555	+	9.36269i	−0.391132	+	0.677461i	0.601467	+	0.798898i	$0.294583\pi$
$192$	7.06014	−	11.9229i	0.509522	−	0.860458i
$193$	2.60044	+	4.50410i	0.187184	+	0.324212i	0.944310	−	0.329056i	$-0.106731\pi$
$193$	2.60044	+	4.50410i	0.187184	+	0.324212i	−0.757126	+	0.653268i	$0.773397\pi$
$194$	15.1383	+	15.4157i	1.08687	+	1.10679i
$195$	−10.1105	−	15.8770i	−0.724028	−	1.13697i
$196$	−0.156922	+	8.64126i	−0.0112087	+	0.617233i
$197$	−2.94550	−	2.94550i	−0.209858	−	0.209858i	0.594349	−	0.804207i	$-0.297410\pi$
$197$	−2.94550	−	2.94550i	−0.209858	−	0.209858i	−0.804207	+	0.594349i	$0.797410\pi$
$198$	0.525436	+	0.765717i	0.0373411	+	0.0544171i
$199$	2.57285			0.182384			0.0911921	−	0.995833i	$-0.470932\pi$
$199$	2.57285			0.182384			0.0911921	+	0.995833i	$0.470932\pi$
$200$	27.3604	−	6.53809i	1.93467	−	0.462313i
$201$	−6.84046	−	6.27053i	−0.482489	−	0.442289i
$202$	0.00172377	−	0.189862i	0.000121284	−	0.0133587i
$203$	−6.85170	−	1.83591i	−0.480895	−	0.128856i
$204$	12.5284	−	7.66201i	0.877164	−	0.536448i
$205$	−12.7252	+	3.40971i	−0.888768	+	0.238145i
$206$	−11.2040	+	2.89334i	−0.780620	+	0.201589i
$207$	10.4644	+	4.88449i	0.727327	+	0.339495i
$208$	10.9595	−	2.51395i	0.759906	−	0.174311i
$209$	−0.301228	−	0.173914i	−0.0208364	−	0.0120299i
$210$	31.8439	−	1.09471i	2.19744	−	0.0755424i
$211$	17.5700	+	4.70786i	1.20957	+	0.324103i	0.806592	−	0.591108i	$-0.201309\pi$
$211$	17.5700	+	4.70786i	1.20957	+	0.324103i	0.402975	+	0.915211i	$0.367976\pi$
$212$	5.17388	+	20.8137i	0.355343	+	1.42949i
$213$	6.02940	−	11.5770i	0.413127	−	0.793242i
$214$	−8.15769	−	14.4305i	−0.557648	−	0.986451i
$215$		−	18.7704i		−	1.28013i
$216$	−11.4066	−	9.26767i	−0.776120	−	0.630585i
$217$		−	28.0206i		−	1.90216i
$218$	10.9911	−	6.21338i	0.744414	−	0.420823i
$219$	2.58138	−	4.95647i	0.174433	−	0.334927i
$220$	−1.45007	−	0.872682i	−0.0977638	−	0.0588362i
$221$	11.5110	+	3.08436i	0.774312	+	0.207476i
$222$	0.317256	+	9.22861i	0.0212928	+	0.619384i
$223$	2.82059	+	1.62847i	0.188881	+	0.109050i	0.591458	−	0.806336i	$-0.298552\pi$
$223$	2.82059	+	1.62847i	0.188881	+	0.109050i	−0.402578	+	0.915386i	$0.631886\pi$
$224$	−5.75551	+	18.1427i	−0.384556	+	1.21221i
$225$	−2.58916	−	29.7246i	−0.172610	−	1.98164i
$226$	−5.98432	−	23.1733i	−0.398071	−	1.54147i
$227$	−8.83238	+	2.36663i	−0.586226	+	0.157079i	−0.539728	−	0.841840i	$-0.681473\pi$
$227$	−8.83238	+	2.36663i	−0.586226	+	0.157079i	−0.0464979	+	0.998918i	$0.514806\pi$
$228$	5.35148	+	1.28984i	0.354410	+	0.0854218i
$229$	−5.07755	−	1.36053i	−0.335534	−	0.0899061i	0.0871183	−	0.996198i	$-0.472234\pi$
$229$	−5.07755	−	1.36053i	−0.335534	−	0.0899061i	−0.422652	+	0.906292i	$0.638901\pi$
$230$	−21.0451	−	0.191070i	−1.38767	−	0.0125988i
$231$	−0.940338	−	0.861991i	−0.0618697	−	0.0567148i
$232$	−5.08083	−	3.12093i	−0.333573	−	0.204899i
$233$	14.1506			0.927034			0.463517	−	0.886088i	$-0.346587\pi$
$233$	14.1506			0.927034			0.463517	+	0.886088i	$0.346587\pi$
$234$	−0.927004	−	11.8901i	−0.0606001	−	0.777283i
$235$	−12.8480	−	12.8480i	−0.838114	−	0.838114i
$236$	7.67944	+	7.96351i	0.499889	+	0.518380i
$237$	−5.35621	−	8.41110i	−0.347923	−	0.546360i
$238$	−14.3932	+	14.1342i	−0.932974	+	0.916185i
$239$	−7.51536	−	13.0170i	−0.486128	−	0.841999i	0.513745	−	0.857943i	$-0.328258\pi$
$239$	−7.51536	−	13.0170i	−0.486128	−	0.841999i	−0.999873	+	0.0159444i	$0.994925\pi$
$240$	25.9203	+	6.74769i	1.67315	+	0.435562i
$241$	7.18920	−	12.4521i	0.463097	−	0.802108i	−0.536016	−	0.844208i	$-0.680071\pi$
$241$	7.18920	−	12.4521i	0.463097	−	0.802108i	0.999113	+	0.0420996i	$0.0134047\pi$
$242$	−3.87275	−	14.9966i	−0.248950	−	0.964019i
$243$	−11.5030	+	10.5205i	−0.737921	+	0.674888i
$244$	−17.3116	−	4.97723i	−1.10826	−	0.318635i
$245$	−16.1369	+	4.32388i	−1.03095	+	0.276242i
$246$	−8.13220	−	1.88212i	−0.518490	−	0.119999i
$247$	2.23348	+	3.86850i	0.142113	+	0.246147i
$248$	6.71369	−	22.5774i	0.426320	−	1.43367i
$249$	7.88815	+	1.75034i	0.499891	+	0.110923i
$250$	13.3067	+	23.5389i	0.841592	+	1.48873i
$251$	−3.59758	+	3.59758i	−0.227077	+	0.227077i	−0.811471	−	0.584393i	$-0.801333\pi$
$251$	−3.59758	+	3.59758i	−0.227077	+	0.227077i	0.584393	+	0.811471i	$0.301333\pi$
$252$	18.1355	+	8.86967i	1.14243	+	0.558736i
$253$	0.595798	+	0.595798i	0.0374575	+	0.0374575i
$254$	18.2633	+	5.07179i	1.14594	+	0.318233i
$255$	20.9255	+	19.1820i	1.31041	+	1.20122i
$256$	−8.98442	+	13.2393i	−0.561526	+	0.827459i
$257$	−4.92640	+	2.84426i	−0.307300	+	0.177420i	−0.645718	−	0.763576i	$-0.723442\pi$
$257$	−4.92640	+	2.84426i	−0.307300	+	0.177420i	0.338418	+	0.940996i	$0.390108\pi$
$258$	5.58911	−	10.4978i	0.347963	−	0.653567i
$259$	−3.28294	−	12.2521i	−0.203992	−	0.761307i
$260$	10.5238	+	19.0171i	0.652661	+	1.17939i
$261$	−4.06716	+	4.84331i	−0.251751	+	0.299793i
$262$	−0.798004	−	0.470439i	−0.0493008	−	0.0290638i
$263$	18.8392	+	10.8768i	1.16167	+	0.670693i	0.951705	−	0.307015i	$-0.0993300\pi$
$263$	18.8392	+	10.8768i	1.16167	+	0.670693i	0.209970	+	0.977708i	$0.432663\pi$
$264$	−0.551140	−	0.919847i	−0.0339203	−	0.0566127i
$265$	−35.9028	+	20.7285i	−2.20549	+	1.27334i
$266$	−7.56121	−	0.0686487i	−0.463607	−	0.00420912i
$267$	−4.54955	−	2.36945i	−0.278428	−	0.145008i
$268$	7.43796	+	7.71310i	0.454346	+	0.471153i
$269$	−7.43467	+	7.43467i	−0.453300	+	0.453300i	−0.896448	−	0.443148i	$-0.853861\pi$
$269$	−7.43467	+	7.43467i	−0.453300	+	0.453300i	0.443148	+	0.896448i	$0.353861\pi$
$270$	11.1244	−	26.1403i	0.677010	−	1.59085i
$271$			11.8875i			0.722111i	0.932544	+	0.361056i	$0.117584\pi$
$271$			11.8875i			0.722111i	−0.932544	+	0.361056i	$0.882416\pi$
$272$	−14.9838	+	7.93996i	−0.908525	+	0.481431i
$273$	4.92329	+	15.6251i	0.297971	+	0.945673i
$274$	−20.8540	−	21.2361i	−1.25983	−	1.28292i
$275$	0.563445	−	2.10281i	0.0339770	−	0.126804i
$276$	−11.7131	−	6.37329i	−0.705047	−	0.383627i
$277$	2.68166	+	10.0081i	0.161126	+	0.601329i	0.998503	+	0.0547032i	$0.0174213\pi$
$277$	2.68166	+	10.0081i	0.161126	+	0.601329i	−0.837377	+	0.546626i	$0.815912\pi$
$278$	8.12750	+	4.79132i	0.487455	+	0.287364i
$279$	−22.6385	−	10.5670i	−1.35533	−	0.632631i
$280$	−36.7783	−	1.00196i	−2.19792	−	0.0598784i
$281$	−7.05630	+	12.2219i	−0.420944	+	0.729096i	−0.996032	−	0.0889955i	$-0.971634\pi$
$281$	−7.05630	+	12.2219i	−0.420944	+	0.729096i	0.575088	+	0.818091i	$0.304968\pi$
$282$	−3.35995	−	11.0113i	−0.200082	−	0.655712i
$283$	3.42843	−	12.7951i	0.203799	−	0.760588i	−0.786013	−	0.618209i	$-0.787858\pi$
$283$	3.42843	−	12.7951i	0.203799	−	0.760588i	0.989812	−	0.142378i	$-0.0454749\pi$
$284$	−7.77189	+	12.9140i	−0.461177	+	0.766304i
$285$	0.462109	+	10.6305i	0.0273730	+	0.629697i
$286$	0.232837	−	0.838435i	0.0137679	−	0.0495777i
$287$	11.4660			0.676817
$288$	12.4874	+	11.4919i	0.735829	+	0.677168i
$289$	−0.972286			−0.0571933
$290$	3.08411	−	11.1057i	0.181105	−	0.652151i
$291$	−22.3203	+	14.2136i	−1.30844	+	0.833216i
$292$	−3.32739	+	5.52889i	−0.194721	+	0.323554i
$293$	7.96005	−	29.7073i	0.465031	−	1.73552i	−0.191756	−	0.981443i	$-0.561418\pi$
$293$	7.96005	−	29.7073i	0.465031	−	1.73552i	0.656787	−	0.754077i	$-0.271915\pi$
$294$	−10.3125	−	2.38672i	−0.601437	−	0.139196i
$295$	−10.6924	+	18.5197i	−0.622533	+	1.07826i
$296$	0.290375	−	10.6586i	0.0168777	−	0.619520i
$297$	−1.05104	+	0.434652i	−0.0609875	+	0.0252210i
$298$	27.2143	+	16.0434i	1.57648	+	0.929368i
$299$	−2.80065	−	10.4522i	−0.161965	−	0.604463i
$300$	0.871054	+	34.4420i	0.0502904	+	1.98851i
$301$	−4.22825	+	15.7800i	−0.243712	+	0.909546i
$302$	19.7682	+	20.1304i	1.13753	+	1.15838i
$303$	0.227020	+	0.0503746i	0.0130420	+	0.00289395i
$304$	−6.07594	−	1.86697i	−0.348479	−	0.107078i
$305$		−	34.8187i		−	1.99371i
$306$	5.99146	+	16.9589i	0.342509	+	0.969474i
$307$	23.8109	−	23.8109i	1.35896	−	1.35896i	0.483758	−	0.875202i	$-0.339272\pi$
$307$	23.8109	−	23.8109i	1.35896	−	1.35896i	0.875202	−	0.483758i	$-0.160728\pi$
$308$	1.02247	+	1.06030i	0.0582609	+	0.0604160i
$309$	−0.615486	−	14.1588i	−0.0350138	−	0.805469i
$310$	45.5286	+	0.413357i	2.58585	+	0.0234771i
$311$	−9.20941	+	5.31706i	−0.522218	+	0.301503i	−0.737842	−	0.674974i	$-0.764155\pi$
$311$	−9.20941	+	5.31706i	−0.522218	+	0.301503i	0.215624	+	0.976477i	$0.430822\pi$
$312$	0.223171	+	13.7694i	0.0126345	+	0.779540i
$313$	16.4634	+	9.50514i	0.930565	+	0.537262i	0.886990	−	0.461788i	$-0.152792\pi$
$313$	16.4634	+	9.50514i	0.930565	+	0.537262i	0.0435750	+	0.999050i	$0.486125\pi$
$314$	−18.1548	−	10.7026i	−1.02453	−	0.603982i
$315$	−6.79104	+	38.4283i	−0.382632	+	2.16519i
$316$	5.57519	+	10.0746i	0.313629	+	0.566742i
$317$	−3.18193	−	11.8751i	−0.178715	−	0.666972i	−0.995889	−	0.0905818i	$-0.971127\pi$
$317$	−3.18193	−	11.8751i	−0.178715	−	0.666972i	0.817174	−	0.576391i	$-0.195539\pi$
$318$	−26.2518	+	0.902469i	−1.47213	+	0.0506080i
$319$	−0.399628	+	0.230725i	−0.0223749	+	0.0129181i
$320$	−29.3938	−	9.61933i	−1.64316	−	0.537737i
$321$	19.3638	−	6.10132i	1.08078	−	0.340543i
$322$	17.6493	+	4.90127i	0.983556	+	0.273137i
$323$	−4.76356	−	4.76356i	−0.265052	−	0.265052i
$324$	14.0052	−	11.3072i	0.778068	−	0.628180i
$325$	−19.7692	+	19.7692i	−1.09660	+	1.09660i
$326$	4.28896	+	7.58694i	0.237543	+	0.420202i
$327$	4.64712	+	14.7486i	0.256987	+	0.815599i
$328$	9.23866	+	2.74724i	0.510119	+	0.151691i
$329$	7.90701	+	13.6953i	0.435928	+	0.755049i
$330$	1.41446	−	1.51517i	0.0778632	−	0.0834073i
$331$	33.3960	−	8.94844i	1.83561	−	0.491851i	0.837134	−	0.546998i	$-0.184229\pi$
$331$	33.3960	−	8.94844i	1.83561	−	0.491851i	0.998478	+	0.0551468i	$0.0175627\pi$
$332$	−8.96675	−	2.57801i	−0.492114	−	0.141487i
$333$	−11.1368	−	1.96809i	−0.610293	−	0.107851i
$334$	4.85696	+	18.8078i	0.265761	+	1.02912i
$335$	−10.3561	+	17.9374i	−0.565817	+	0.980023i
$336$	−20.2709	−	11.5115i	−1.10587	−	0.628006i
$337$	−14.3693	−	24.8884i	−0.782746	−	1.35576i	−0.930336	−	0.366707i	$-0.880485\pi$
$337$	−14.3693	−	24.8884i	−0.782746	−	1.35576i	0.147591	−	0.989049i	$-0.452848\pi$
$338$	5.14413	−	5.05156i	0.279804	−	0.274769i
$339$	29.2848	−	1.27301i	1.59053	−	0.0691406i
$340$	−22.7533	−	23.5950i	−1.23397	−	1.27962i
$341$	−1.28894	−	1.28894i	−0.0698001	−	0.0698001i
$342$	−2.90692	+	6.08299i	−0.157188	+	0.328931i
$343$	−9.01293			−0.486653
$344$	−7.18775	+	11.7016i	−0.387538	+	0.630907i
$345$	5.58372	−	25.1639i	0.300617	−	1.35478i
$346$	7.67659	+	0.0696962i	0.412696	+	0.00374689i
$347$	−10.9346	−	2.92992i	−0.587002	−	0.157287i	−0.0469191	−	0.998899i	$-0.514940\pi$
$347$	−10.9346	−	2.92992i	−0.587002	−	0.157287i	−0.540082	+	0.841612i	$0.681607\pi$
$348$	5.03174	−	5.29285i	0.269729	−	0.283726i
$349$	10.8496	−	2.90715i	0.580767	−	0.155616i	0.0435372	−	0.999052i	$-0.486137\pi$
$349$	10.8496	−	2.90715i	0.580767	−	0.155616i	0.537230	+	0.843436i	$0.319471\pi$
$350$	−11.8334	−	45.8228i	−0.632520	−	2.44933i
$351$	14.4805	+	1.91482i	0.772914	+	0.102205i
$352$	0.569807	+	1.09931i	0.0303708	+	0.0585935i
$353$	1.85946	+	1.07356i	0.0989689	+	0.0571397i	0.548668	−	0.836041i	$-0.315135\pi$
$353$	1.85946	+	1.07356i	0.0989689	+	0.0571397i	−0.449699	+	0.893180i	$0.648469\pi$
$354$	−11.4945	+	7.17386i	−0.610924	+	0.381287i
$355$	−28.1417	−	7.54056i	−1.49361	−	0.400211i
$356$	5.07497	+	3.05422i	0.268973	+	0.161873i
$357$	−13.2708	−	20.8398i	−0.702366	−	1.10296i
$358$	0.661829	−	0.374137i	0.0349787	−	0.0197738i
$359$			11.0166i			0.581435i	0.956809	+	0.290718i	$0.0938941\pi$
$359$			11.0166i			0.581435i	−0.956809	+	0.290718i	$0.906106\pi$
$360$	−14.6792	+	29.3362i	−0.773661	+	1.54615i
$361$			16.4748i			0.867097i
$362$	4.91125	+	8.68775i	0.258130	+	0.456618i
$363$	18.9517	−	0.823831i	0.994705	−	0.0432399i
$364$	−4.56344	−	18.3580i	−0.239189	−	0.962222i
$365$	−12.0484	−	3.22835i	−0.630641	−	0.168980i
$366$	10.3677	−	19.4733i	0.541928	−	1.01789i
$367$	−20.1365	−	11.6258i	−1.05112	−	0.606863i	−0.128156	−	0.991754i	$-0.540906\pi$
$367$	−20.1365	−	11.6258i	−1.05112	−	0.606863i	−0.922962	+	0.384891i	$0.874239\pi$
$368$	13.0465	+	8.17791i	0.680094	+	0.426303i
$369$	4.32402	−	9.26366i	0.225099	−	0.482247i
$370$	19.9559	−	5.15345i	1.03746	−	0.267915i
$371$	34.8524	−	9.33867i	1.80945	−	0.484839i
$372$	25.3400	+	13.7879i	1.31382	+	0.714868i
$373$	9.93021	+	2.66079i	0.514167	+	0.137771i	0.506567	−	0.862201i	$-0.330914\pi$
$373$	9.93021	+	2.66079i	0.514167	+	0.137771i	0.00759967	+	0.999971i	$0.497581\pi$
$374$	−0.0119140	+	1.31225i	−0.000616061	+	0.0678551i
$375$	−31.5860	+	9.95240i	−1.63109	+	0.513940i
$376$	3.08964	+	12.9294i	0.159336	+	0.666785i
$377$	5.92615			0.305212
$378$	−15.2406	+	19.4699i	−0.783890	+	1.00142i
$379$	−6.14819	−	6.14819i	−0.315811	−	0.315811i	0.531345	−	0.847156i	$-0.321687\pi$
$379$	−6.14819	−	6.14819i	−0.315811	−	0.315811i	−0.847156	+	0.531345i	$0.821687\pi$
$380$	0.223084	−	12.2846i	0.0114440	−	0.630188i
$381$	−10.7231	+	20.5894i	−0.549363	+	1.05483i
$382$	10.7125	+	10.9088i	0.548100	+	0.558143i
$383$	−1.40170	−	2.42782i	−0.0716238	−	0.124056i	0.827989	−	0.560744i	$-0.189485\pi$
$383$	−1.40170	−	2.42782i	−0.0716238	−	0.124056i	−0.899613	+	0.436688i	$0.856151\pi$
$384$	−13.5750	−	14.1322i	−0.692746	−	0.721182i
$385$	−1.42363	+	2.46580i	−0.0725548	+	0.125669i
$386$	7.12153	−	1.83908i	0.362476	−	0.0936066i
$387$	11.1545	+	9.36701i	0.567017	+	0.476152i
$388$	26.7347	−	14.7947i	1.35725	−	0.751086i
$389$	29.1977	−	7.82350i	1.48038	−	0.396667i	0.573905	−	0.818922i	$-0.305428\pi$
$389$	29.1977	−	7.82350i	1.48038	−	0.396667i	0.906477	+	0.422255i	$0.138761\pi$
$390$	−25.4606	+	7.76899i	−1.28925	+	0.393398i
$391$	8.15956	+	14.1328i	0.412647	+	0.714725i
$392$	11.7156	+	3.48379i	0.591727	+	0.175958i
$393$	0.766644	−	0.836325i	0.0386721	−	0.0421870i
$394$	−5.12828	+	2.89906i	−0.258359	+	0.146052i
$395$	−15.7382	+	15.7382i	−0.791873	+	0.791873i
$396$	1.24223	−	0.426227i	0.0624245	−	0.0214187i
$397$	1.95789	+	1.95789i	0.0982636	+	0.0982636i	0.754530	−	0.656266i	$-0.227865\pi$
$397$	1.95789	+	1.95789i	0.0982636	+	0.0982636i	−0.656266	+	0.754530i	$0.727865\pi$
$398$	0.973596	−	3.50588i	0.0488020	−	0.175734i
$399$	2.00615	−	9.04103i	0.100433	−	0.452617i
$400$	1.44441	−	39.7567i	0.0722204	−	1.98783i
$401$	−28.7356	+	16.5905i	−1.43499	+	0.828489i	−0.997495	−	0.0707337i	$-0.977466\pi$
$401$	−28.7356	+	16.5905i	−1.43499	+	0.828489i	−0.437490	+	0.899223i	$0.644133\pi$
$402$	−11.1330	+	6.94829i	−0.555265	+	0.346549i
$403$	6.05887	+	22.6120i	0.301814	+	1.12638i
$404$	−0.258063	−	0.0741950i	−0.0128391	−	0.00369134i
$405$	28.4861	+	19.9786i	1.41549	+	0.992743i
$406$	−5.09446	+	8.64172i	−0.252834	+	0.428881i
$407$	−0.714607	−	0.412578i	−0.0354217	−	0.0204508i
$408$	−5.69970	−	19.9712i	−0.282177	−	0.988721i
$409$	−22.8959	+	13.2190i	−1.13213	+	0.653636i	−0.944470	−	0.328598i	$-0.893424\pi$
$409$	−22.8959	+	13.2190i	−1.13213	+	0.653636i	−0.187660	+	0.982234i	$0.560090\pi$
$410$	−0.169145	+	18.6302i	−0.00835349	+	0.920082i
$411$	30.7475	−	19.5801i	1.51666	−	0.965816i
$412$	−0.297127	+	16.3620i	−0.0146384	+	0.806097i
$413$	13.1607	−	13.1607i	0.647596	−	0.647596i
$414$	10.6157	−	12.4109i	0.521733	−	0.609964i
$415$		−	18.0347i		−	0.885290i
$416$	0.721592	−	15.8853i	0.0353790	−	0.778839i
$417$	−7.80811	+	8.51780i	−0.382365	+	0.417118i
$418$	−0.350971	+	0.344656i	−0.0171666	+	0.0168577i
$419$	−0.133835	+	0.499479i	−0.00653827	+	0.0244012i	−0.969118	−	0.246598i	$-0.920687\pi$
$419$	−0.133835	+	0.499479i	−0.00653827	+	0.0244012i	0.962580	+	0.270999i	$0.0873540\pi$
$420$	10.5584	−	43.8062i	0.515198	−	2.13753i
$421$	−3.44352	−	12.8514i	−0.167827	−	0.626339i	−0.997663	−	0.0683313i	$-0.978233\pi$
$421$	−3.44352	−	12.8514i	−0.167827	−	0.626339i	0.829836	−	0.558008i	$-0.188434\pi$
$422$	13.0638	−	22.1601i	0.635938	−	1.07874i
$423$	14.0467	−	1.22353i	0.682972	−	0.0594902i
$424$	30.3196	+	0.826002i	1.47245	+	0.0401142i
$425$	21.0818	−	36.5148i	1.02262	−	1.77123i
$426$	−13.4937	−	12.5968i	−0.653773	−	0.610317i
$427$	−7.84332	+	29.2717i	−0.379565	+	1.41655i
$428$	−22.7507	+	5.65536i	−1.09970	+	0.273362i
$429$	0.945220	+	0.492279i	0.0456356	+	0.0237675i
$430$	−25.5774	−	7.10295i	−1.23345	−	0.342534i
$431$	8.61129			0.414791			0.207396	−	0.978257i	$-0.433501\pi$
$431$	8.61129			0.414791			0.207396	+	0.978257i	$0.433501\pi$
$432$	−16.9449	+	12.0362i	−0.815264	+	0.579090i
$433$	6.43973			0.309474			0.154737	−	0.987956i	$-0.450547\pi$
$433$	6.43973			0.309474			0.154737	+	0.987956i	$0.450547\pi$
$434$	−38.1822	−	10.6033i	−1.83280	−	0.508976i
$435$	12.5202	+	6.52063i	0.600297	+	0.312640i
$436$	−4.30746	−	17.3282i	−0.206290	−	0.829873i
$437$	−1.58320	+	5.90859i	−0.0757348	+	0.282646i
$438$	−5.77709	−	5.39309i	−0.276040	−	0.257692i
$439$	14.4510	−	25.0298i	0.689707	−	1.19461i	−0.282225	−	0.959348i	$-0.591073\pi$
$439$	14.4510	−	25.0298i	0.689707	−	1.19461i	0.971933	−	0.235260i	$-0.0755941\pi$
$440$	−1.73788	+	1.64570i	−0.0828502	+	0.0784557i
$441$	5.48331	−	11.7473i	0.261110	−	0.559396i
$442$	8.55878	−	14.5182i	0.407100	−	0.690562i
$443$	−8.35627	−	31.1860i	−0.397018	−	1.48169i	−0.818315	−	0.574770i	$-0.805092\pi$
$443$	−8.35627	−	31.1860i	−0.397018	−	1.48169i	0.421297	−	0.906923i	$-0.361575\pi$
$444$	12.6954	+	3.05991i	0.602496	+	0.145217i
$445$	−2.96330	+	11.0592i	−0.140474	+	0.524257i
$446$	3.28637	−	3.22723i	0.155614	−	0.152814i
$447$	−26.1449	+	28.5212i	−1.23661	+	1.34901i
$448$	22.5441	+	14.7081i	1.06511	+	0.694894i
$449$			10.7097i			0.505423i	0.967542	+	0.252711i	$0.0813223\pi$
$449$			10.7097i			0.505423i	−0.967542	+	0.252711i	$0.918678\pi$
$450$	−41.4839	−	7.72005i	−1.95557	−	0.363927i
$451$	0.527433	−	0.527433i	0.0248359	−	0.0248359i
$452$	−33.8415	−	0.614550i	−1.59177	−	0.0289060i
$453$	−29.1466	+	18.5606i	−1.36943	+	0.872054i
$454$	−0.117401	+	12.9310i	−0.00550991	+	0.606880i
$455$	31.6669	−	18.2829i	1.48457	−	0.857114i
$456$	3.78266	−	6.80408i	0.177139	−	0.318630i
$457$	−13.1358	−	7.58393i	−0.614465	−	0.354761i	0.160246	−	0.987077i	$-0.448771\pi$
$457$	−13.1358	−	7.58393i	−0.614465	−	0.354761i	−0.774711	+	0.632316i	$0.782105\pi$
$458$	−3.77532	+	6.40406i	−0.176409	+	0.299242i
$459$	−21.8416	+	2.86281i	−1.01948	+	0.133624i
$460$	−8.22407	+	28.6047i	−0.383449	+	1.33370i
$461$	−3.10006	−	11.5696i	−0.144384	−	0.538849i	−0.999782	−	0.0208774i	$-0.993354\pi$
$461$	−3.10006	−	11.5696i	−0.144384	−	0.538849i	0.855398	−	0.517971i	$-0.173313\pi$
$462$	−1.53042	+	0.955160i	−0.0712018	+	0.0444381i
$463$	2.03363	−	1.17412i	0.0945107	−	0.0545658i	−0.452000	−	0.892018i	$-0.649289\pi$
$463$	2.03363	−	1.17412i	0.0945107	−	0.0545658i	0.546510	+	0.837452i	$0.315956\pi$
$464$	−6.17537	+	5.74238i	−0.286684	+	0.266583i
$465$	−12.0797	+	54.4391i	−0.560184	+	2.52455i
$466$	5.35474	−	19.2822i	0.248054	−	0.893231i
$467$	−24.1509	−	24.1509i	−1.11757	−	1.11757i	−0.992097	−	0.125473i	$-0.959955\pi$
$467$	−24.1509	−	24.1509i	−1.11757	−	1.11757i	−0.125473	−	0.992097i	$-0.540045\pi$
$468$	−16.5529	−	3.23620i	−0.765156	−	0.149593i
$469$	12.7469	−	12.7469i	0.588596	−	0.588596i
$470$	−22.3692	+	12.6455i	−1.03181	+	0.583292i
$471$	17.4413	−	19.0266i	0.803654	−	0.876700i
$472$	13.7574	−	7.45087i	0.633237	−	0.342954i
$473$	0.531379	+	0.920376i	0.0244328	+	0.0423189i
$474$	−13.4882	+	4.11576i	−0.619534	+	0.189043i
$475$	15.2660	−	4.09051i	0.700452	−	0.187685i
$476$	13.8134	+	24.9614i	0.633135	+	1.14410i
$477$	5.59846	−	31.6799i	0.256336	−	1.45052i
$478$	−20.5814	+	5.31499i	−0.941373	+	0.243102i
$479$	2.40917	−	4.17281i	0.110078	−	0.190660i	−0.805724	−	0.592292i	$-0.798223\pi$
$479$	2.40917	−	4.17281i	0.110078	−	0.190660i	0.915801	+	0.401631i	$0.131557\pi$
$480$	19.0033	−	32.7668i	0.867377	−	1.49559i
$481$	5.29851	+	9.17730i	0.241591	+	0.418449i
$482$	−14.2473	−	14.5084i	−0.648946	−	0.660837i
$483$	−10.3626	+	19.8971i	−0.471515	+	0.905351i
$484$	−21.9006	−	0.397706i	−0.995480	−	0.0180775i
$485$	41.7638	+	41.7638i	1.89640	+	1.89640i
$486$	9.98277	+	19.6556i	0.452828	+	0.891598i
$487$	37.5042			1.69948			0.849739	−	0.527204i	$-0.176760\pi$
$487$	37.5042			1.69948			0.849739	+	0.527204i	$0.176760\pi$
$488$	−13.3331	+	21.7062i	−0.603563	+	0.982593i
$489$	−10.1806	+	3.20781i	−0.460384	+	0.145062i
$490$	−0.214494	+	23.6251i	−0.00968986	+	1.06727i
$491$	−1.88310	−	0.504576i	−0.0849832	−	0.0227712i	0.216077	−	0.976376i	$-0.430674\pi$
$491$	−1.88310	−	0.504576i	−0.0849832	−	0.0227712i	−0.301060	+	0.953605i	$0.597340\pi$
$492$	−5.64198	+	10.3691i	−0.254360	+	0.467475i
$493$	−8.63279	+	2.31315i	−0.388801	+	0.104179i
$494$	6.11657	−	1.57955i	0.275198	−	0.0710675i
$495$	1.45530	+	2.08008i	0.0654111	+	0.0934925i
$496$	−28.2245	−	17.6920i	−1.26732	−	0.794392i
$497$	21.9598	+	12.6785i	0.985032	+	0.568708i
$498$	5.37006	−	10.0864i	0.240638	−	0.451983i
$499$	10.8793	+	2.91509i	0.487023	+	0.130497i	0.493971	−	0.869478i	$-0.335545\pi$
$499$	10.8793	+	2.91509i	0.487023	+	0.130497i	−0.00694794	+	0.999976i	$0.502212\pi$
$500$	37.1106	−	9.22496i	1.65964	−	0.412553i
$501$	−23.7680	+	1.03320i	−1.06187	+	0.0461598i
$502$	3.54086	+	6.26360i	0.158036	+	0.279558i
$503$		−	15.3339i		−	0.683706i	−0.939753	−	0.341853i	$-0.888945\pi$
$503$		−	15.3339i		−	0.683706i	0.939753	−	0.341853i	$-0.111055\pi$
$504$	18.9489	−	21.3559i	0.844052	−	0.951268i
$505$		−	0.519039i		−	0.0230969i
$506$	1.03732	−	0.586405i	0.0461145	−	0.0260689i
$507$	4.74299	+	7.44813i	0.210644	+	0.330783i
$508$	13.8221	−	22.9672i	0.613257	−	1.01900i
$509$	32.0866	+	8.59758i	1.42221	+	0.381081i	0.886269	−	0.463172i	$-0.153289\pi$
$509$	32.0866	+	8.59758i	1.42221	+	0.381081i	0.535945	+	0.844253i	$0.319955\pi$
$510$	34.0568	−	21.2553i	1.50806	−	0.941202i
$511$	9.40169	+	5.42807i	0.415906	+	0.240124i
$512$	14.6407	+	17.2525i	0.647035	+	0.762461i
$513$	−6.54791	−	5.03034i	−0.289097	−	0.222095i
$514$	2.01151	+	7.78924i	0.0887238	+	0.343568i
$515$	−30.5548	+	8.18713i	−1.34641	+	0.360768i
$516$	−12.1899	−	11.5885i	−0.536629	−	0.510155i
$517$	0.993703	+	0.266262i	0.0437030	+	0.0117102i
$518$	−17.9376	−	0.162856i	−0.788131	−	0.00715549i
$519$	−2.03677	+	9.17899i	−0.0894042	+	0.402913i
$520$	29.8959	−	7.14398i	1.31102	−	0.313284i
$521$	−20.5032			−0.898262			−0.449131	−	0.893466i	$-0.648266\pi$
$521$	−20.5032			−0.898262			−0.449131	+	0.893466i	$0.648266\pi$
$522$	5.06065	+	7.37487i	0.221499	+	0.322789i
$523$	−29.2406	−	29.2406i	−1.27860	−	1.27860i	−0.941451	−	0.337151i	$-0.890537\pi$
$523$	−29.2406	−	29.2406i	−1.27860	−	1.27860i	−0.337151	−	0.941451i	$-0.609463\pi$
$524$	−0.943016	+	0.909377i	−0.0411958	+	0.0397263i
$525$	57.9076	−	2.51725i	2.52730	−	0.109862i
$526$	21.9502	−	21.5552i	0.957076	−	0.939853i
$527$	−17.6523	−	30.5746i	−0.768944	−	1.33185i
$528$	−1.46198	+	0.402927i	−0.0636247	+	0.0175352i
$529$	−4.09099	+	7.08581i	−0.177869	+	0.308079i
$530$	14.6596	+	56.7668i	0.636771	+	2.46579i
$531$	−5.66974	−	15.5960i	−0.246046	−	0.676808i
$532$	−2.95479	+	10.2773i	−0.128107	+	0.445576i
$533$	−9.25281	+	2.47928i	−0.400784	+	0.107390i
$534$	−4.95032	+	5.30280i	−0.214221	+	0.229474i
$535$	−22.6575	−	39.2440i	−0.979570	−	1.69667i
$536$	13.3248	−	7.21658i	0.575545	−	0.311709i
$537$	0.279825	+	0.888083i	0.0120754	+	0.0383236i
$538$	7.31746	+	12.9442i	0.315478	+	0.558064i
$539$	0.668841	−	0.668841i	0.0288090	−	0.0288090i
$540$	−31.4104	−	25.0505i	−1.35169	−	1.07800i
$541$	20.5836	+	20.5836i	0.884956	+	0.884956i	0.994033	−	0.109077i	$-0.0347895\pi$
$541$	20.5836	+	20.5836i	0.884956	+	0.884956i	−0.109077	+	0.994033i	$0.534790\pi$
$542$	16.1984	+	4.49836i	0.695780	+	0.193221i
$543$	−11.6578	+	3.67324i	−0.500282	+	0.157634i
$544$	5.14932	+	23.4222i	0.220775	+	1.00422i
$545$	29.8905	−	17.2573i	1.28037	−	0.739221i
$546$	23.1545	−	0.795992i	0.990920	−	0.0340653i
$547$	10.2029	+	38.0779i	0.436246	+	1.62809i	0.738067	+	0.674728i	$0.235739\pi$
$547$	10.2029	+	38.0779i	0.436246	+	1.62809i	−0.301821	+	0.953365i	$0.597594\pi$
$548$	−36.8287	+	20.3806i	−1.57324	+	0.870616i
$549$	20.6914	+	17.3756i	0.883089	+	0.741574i
$550$	−2.65217	−	1.56350i	−0.113089	−	0.0666680i
$551$	−2.90122	−	1.67502i	−0.123596	−	0.0713584i
$552$	−13.1169	+	13.5491i	−0.558293	+	0.576689i
$553$	16.7761	−	9.68566i	0.713391	−	0.411876i
$554$	14.6523	+	0.133029i	0.622516	+	0.00565186i
$555$	1.09627	+	25.2189i	0.0465340	+	1.07048i
$556$	9.60441	−	9.26181i	0.407318	−	0.392788i
$557$	−1.52288	+	1.52288i	−0.0645265	+	0.0645265i	−0.738634	−	0.674107i	$-0.764529\pi$
$557$	−1.52288	+	1.52288i	−0.0645265	+	0.0645265i	0.674107	+	0.738634i	$0.264529\pi$
$558$	−22.9658	+	26.8496i	−0.972220	+	1.13664i
$559$		−	13.6484i		−	0.577266i
$560$	−15.2827	+	49.7366i	−0.645810	+	2.10176i
$561$	−1.56908	−	0.348170i	−0.0662466	−	0.0146998i
$562$	13.9839	+	14.2401i	0.589875	+	0.600684i
$563$	−1.30147	+	4.85715i	−0.0548504	+	0.204705i	−0.987913	−	0.155010i	$-0.950459\pi$
$563$	−1.30147	+	4.85715i	−0.0548504	+	0.204705i	0.933063	+	0.359714i	$0.117126\pi$
$564$	−16.2759	+	0.411626i	−0.685339	+	0.0173326i
$565$	−16.9335	−	63.1966i	−0.712397	−	2.65870i
$566$	−16.1378	−	9.51354i	−0.678322	−	0.399884i
$567$	−19.4475	−	23.2126i	−0.816719	−	0.974836i
$568$	14.6562	+	15.4771i	0.614961	+	0.649407i
$569$	−17.4710	+	30.2606i	−0.732421	+	1.26859i	0.223425	+	0.974721i	$0.428276\pi$
$569$	−17.4710	+	30.2606i	−0.732421	+	1.26859i	−0.955846	+	0.293869i	$0.905057\pi$
$570$	14.6605	+	3.39302i	0.614060	+	0.142118i
$571$	−9.16034	+	34.1869i	−0.383348	+	1.43068i	0.457406	+	0.889258i	$0.348779\pi$
$571$	−9.16034	+	34.1869i	−0.383348	+	1.43068i	−0.840754	+	0.541417i	$0.817888\pi$
$572$	−1.05438	−	0.634548i	−0.0440859	−	0.0265318i
$573$	−15.7947	+	10.0581i	−0.659835	+	0.420185i
$574$	4.33887	−	15.6241i	0.181101	−	0.652137i
$575$	−38.2852			−1.59660
$576$	20.3848	−	12.6673i	0.849367	−	0.527803i
$577$	−17.4865			−0.727972			−0.363986	−	0.931404i	$-0.618584\pi$
$577$	−17.4865			−0.727972			−0.363986	+	0.931404i	$0.618584\pi$
$578$	−0.367925	+	1.32488i	−0.0153037	+	0.0551078i
$579$	0.391218	+	8.99970i	0.0162584	+	0.374015i
$580$	−13.9661	−	8.40509i	−0.579912	−	0.349002i
$581$	−4.06253	+	15.1616i	−0.168542	+	0.629008i
$582$	10.9218	+	35.7932i	0.452725	+	1.48368i
$583$	1.17362	−	2.03278i	0.0486065	−	0.0841890i
$584$	6.27479	+	6.62626i	0.259653	+	0.274197i
$585$	−2.82909	−	32.4792i	−0.116969	−	1.34285i
$586$	−37.4684	−	22.0883i	−1.54780	−	0.912461i
$587$	3.31081	+	12.3561i	0.136652	+	0.509991i	0.999986	+	0.00535825i	$0.00170559\pi$
$587$	3.31081	+	12.3561i	0.136652	+	0.509991i	−0.863334	+	0.504633i	$0.831628\pi$
$588$	−7.15463	+	13.1491i	−0.295052	+	0.542260i
$589$	3.42507	−	12.7825i	0.141128	−	0.526696i
$590$	21.1897	+	21.5780i	0.872366	+	0.888352i
$591$	−2.16827	−	6.88145i	−0.0891907	−	0.283065i
$592$	−14.4140	−	4.42903i	−0.592414	−	0.182032i
$593$			25.7816i			1.05872i	0.848397	+	0.529361i	$0.177568\pi$
$593$			25.7816i			1.05872i	−0.848397	+	0.529361i	$0.822432\pi$
$594$	0.194550	+	1.59667i	0.00798248	+	0.0655123i
$595$	−38.9937	+	38.9937i	−1.59858	+	1.59858i
$596$	32.1597	−	31.0125i	1.31731	−	1.27032i
$597$	3.95239	+	2.05844i	0.161761	+	0.0842465i
$598$	−15.3024	−	0.138931i	−0.625761	−	0.00568132i
$599$	−27.3647	+	15.7990i	−1.11809	+	0.645531i	−0.940913	−	0.338647i	$-0.890031\pi$
$599$	−27.3647	+	15.7990i	−1.11809	+	0.645531i	−0.177180	+	0.984179i	$0.556697\pi$
$600$	47.2618	+	11.8463i	1.92946	+	0.483624i
$601$	23.3729	+	13.4944i	0.953401	+	0.550447i	0.894136	−	0.447796i	$-0.147791\pi$
$601$	23.3729	+	13.4944i	0.953401	+	0.550447i	0.0592656	+	0.998242i	$0.481124\pi$
$602$	19.9026	+	11.7330i	0.811169	+	0.478200i
$603$	−5.49146	−	15.1056i	−0.223630	−	0.615146i
$604$	34.9111	−	19.3194i	1.42051	−	0.786097i
$605$	−10.9585	−	40.8977i	−0.445527	−	1.66273i
$606$	0.154550	−	0.290286i	0.00627817	−	0.0117921i
$607$	−21.2314	+	12.2579i	−0.861755	+	0.497534i	−0.864600	−	0.502462i	$-0.832428\pi$
$607$	−21.2314	+	12.2579i	−0.861755	+	0.497534i	0.00284471	+	0.999996i	$0.499095\pi$
$608$	−4.84322	+	7.57288i	−0.196419	+	0.307121i
$609$	−9.05671	−	8.30212i	−0.366996	−	0.336419i
$610$	−47.4456	−	13.1758i	−1.92102	−	0.533474i
$611$	−9.34212	−	9.34212i	−0.377942	−	0.377942i
$612$	25.3762	−	1.74680i	1.02577	−	0.0706103i
$613$	−30.3894	+	30.3894i	−1.22742	+	1.22742i	−0.262481	+	0.964937i	$0.584541\pi$
$613$	−30.3894	+	30.3894i	−1.22742	+	1.22742i	−0.964937	+	0.262481i	$0.915459\pi$
$614$	−23.4355	−	41.4562i	−0.945780	−	1.67303i
$615$	−22.2764	−	4.94301i	−0.898272	−	0.199322i
$616$	1.83173	−	0.992042i	0.0738024	−	0.0399705i
$617$	−15.8393	−	27.4345i	−0.637668	−	1.10447i	−0.985943	−	0.167081i	$-0.946566\pi$
$617$	−15.8393	−	27.4345i	−0.637668	−	1.10447i	0.348275	−	0.937392i	$-0.386767\pi$
$618$	−19.5264	−	4.51919i	−0.785467	−	0.181788i
$619$	−20.1312	+	5.39413i	−0.809141	+	0.216809i	−0.639593	−	0.768713i	$-0.720897\pi$
$619$	−20.1312	+	5.39413i	−0.809141	+	0.216809i	−0.169547	+	0.985522i	$0.554231\pi$
$620$	17.7918	−	61.8829i	0.714537	−	2.48528i
$621$	12.1675	+	15.8757i	0.488264	+	0.637071i
$622$	3.76031	+	14.5612i	0.150775	+	0.583851i
$623$	4.98242	−	8.62981i	0.199617	−	0.345746i
$624$	18.8473	+	4.90641i	0.754495	+	0.196414i
$625$	12.0944	+	20.9481i	0.483775	+	0.837923i
$626$	19.1821	−	18.8369i	0.766670	−	0.752874i
$627$	−0.323602	−	0.508167i	−0.0129234	−	0.0202943i
$628$	−21.4538	+	20.6885i	−0.856101	+	0.825563i
$629$	−11.3007	−	11.3007i	−0.450587	−	0.450587i
$630$	49.7943	+	23.7955i	1.98385	+	0.948036i
$631$	−19.9953			−0.796002			−0.398001	−	0.917385i	$-0.630296\pi$
$631$	−19.9953			−0.796002			−0.398001	+	0.917385i	$0.630296\pi$
$632$	15.8379	−	3.78464i	0.629997	−	0.150545i
$633$	23.2243	+	21.2893i	0.923084	+	0.846174i
$634$	−17.3856	−	0.157845i	−0.690472	−	0.00626884i
$635$	50.0494	+	13.4107i	1.98615	+	0.532187i
$636$	−8.70424	+	36.1134i	−0.345146	+	1.43199i
$637$	−11.7335	+	3.14400i	−0.464900	+	0.124570i
$638$	0.163173	+	0.631861i	0.00646008	+	0.0250156i
$639$	18.5247	−	12.9606i	0.732824	−	0.512713i
$640$	−24.2307	+	36.4133i	−0.957803	+	1.43936i
$641$	12.6976	+	7.33098i	0.501526	+	0.289556i	0.729344	−	0.684148i	$-0.239826\pi$
$641$	12.6976	+	7.33098i	0.501526	+	0.289556i	−0.227818	+	0.973704i	$0.573159\pi$
$642$	−0.986454	−	28.6948i	−0.0389322	−	1.13249i
$643$	12.8777	+	3.45056i	0.507846	+	0.136077i	0.503639	−	0.863914i	$-0.331994\pi$
$643$	12.8777	+	3.45056i	0.507846	+	0.136077i	0.00420705	+	0.999991i	$0.498661\pi$
$644$	13.3574	−	22.1950i	0.526355	−	0.874606i
$645$	15.0175	−	28.8350i	0.591315	−	1.13538i
$646$	−8.29363	+	4.68846i	−0.326309	+	0.184465i
$647$			30.5078i			1.19939i	0.800231	+	0.599693i	$0.204710\pi$
$647$			30.5078i			1.19939i	−0.800231	+	0.599693i	$0.795290\pi$
$648$	−10.1080	−	23.3630i	−0.397081	−	0.917784i
$649$		−	1.21078i		−	0.0475272i
$650$	19.4575	+	34.4193i	0.763185	+	1.35003i
$651$	22.4183	−	43.0451i	0.878642	−	1.68707i
$652$	11.9613	−	2.97334i	0.468441	−	0.116445i
$653$	20.1465	+	5.39824i	0.788394	+	0.211249i	0.630482	−	0.776204i	$-0.282857\pi$
$653$	20.1465	+	5.39824i	0.788394	+	0.211249i	0.157912	+	0.987453i	$0.449524\pi$
$654$	21.8556	−	0.751341i	0.854623	−	0.0293798i
$655$	−2.19305	−	1.26616i	−0.0856896	−	0.0494729i
$656$	7.23953	−	11.5494i	0.282656	−	0.450930i
$657$	7.93100	−	5.54884i	0.309418	−	0.216481i
$658$	21.6540	−	5.59198i	0.844162	−	0.217998i
$659$	−14.5728	+	3.90477i	−0.567676	+	0.152108i	−0.531230	−	0.847227i	$-0.678270\pi$
$659$	−14.5728	+	3.90477i	−0.567676	+	0.152108i	−0.0364452	+	0.999336i	$0.511603\pi$
$660$	−1.52939	−	2.50076i	−0.0595315	−	0.0973420i
$661$	−9.11835	−	2.44325i	−0.354663	−	0.0950316i	0.0770887	−	0.997024i	$-0.475438\pi$
$661$	−9.11835	−	2.44325i	−0.354663	−	0.0950316i	−0.431751	+	0.901993i	$0.642104\pi$
$662$	0.443904	−	48.8932i	0.0172528	−	1.90029i
$663$	15.2154	+	13.9477i	0.590918	+	0.541684i
$664$	−6.90604	+	11.2430i	−0.268006	+	0.436311i
$665$	−20.6706			−0.801570
$666$	−6.89612	+	14.4308i	−0.267219	+	0.559181i
$667$	5.73833	+	5.73833i	0.222189	+	0.222189i
$668$	27.4663	+	0.498777i	1.06270	+	0.0192983i
$669$	3.03010	+	4.75830i	0.117150	+	0.183966i
$670$	20.5234	+	20.8995i	0.792888	+	0.807417i
$671$	0.985698	+	1.70728i	0.0380525	+	0.0659088i
$672$	−23.3569	+	23.2659i	−0.901012	+	0.897503i
$673$	−16.1140	+	27.9103i	−0.621149	+	1.07586i	0.368123	+	0.929777i	$0.380001\pi$
$673$	−16.1140	+	27.9103i	−0.621149	+	1.07586i	−0.989272	+	0.146085i	$0.953333\pi$
$674$	−39.3516	+	10.1622i	−1.51577	+	0.391434i
$675$	19.8042	−	47.7343i	0.762263	−	1.83729i
$676$	−4.93689	−	8.92120i	−0.189880	−	0.343123i
$677$	−15.5364	+	4.16296i	−0.597111	+	0.159996i	−0.544701	−	0.838630i	$-0.683357\pi$
$677$	−15.5364	+	4.16296i	−0.597111	+	0.159996i	−0.0524101	+	0.998626i	$0.516690\pi$
$678$	9.34706	−	40.3866i	0.358972	−	1.55104i
$679$	−25.7025	−	44.5181i	−0.986372	−	1.70845i
$680$	−40.7617	+	22.0761i	−1.56314	+	0.846579i
$681$	−15.4617	−	3.43087i	−0.592494	−	0.131471i
$682$	−2.24412	+	1.26862i	−0.0859318	+	0.0485779i
$683$	28.6734	−	28.6734i	1.09716	−	1.09716i	0.102416	−	0.994742i	$-0.467343\pi$
$683$	28.6734	−	28.6734i	1.09716	−	1.09716i	0.994742	−	0.102416i	$-0.0326571\pi$
$684$	7.18896	+	6.26298i	0.274877	+	0.239471i
$685$	−57.5322	−	57.5322i	−2.19819	−	2.19819i
$686$	−3.41060	+	12.2814i	−0.130217	+	0.468907i
$687$	−6.71160	−	6.15240i	−0.256064	−	0.234729i
$688$	13.2252	+	14.2224i	0.504205	+	0.542223i
$689$	−26.1058	+	15.0722i	−0.994552	+	0.574205i
$690$	−32.1765	−	17.1309i	−1.22494	−	0.652164i
$691$	−11.8033	−	44.0504i	−0.449017	−	1.67575i	−0.705106	−	0.709102i	$-0.749101\pi$
$691$	−11.8033	−	44.0504i	−0.449017	−	1.67575i	0.256089	−	0.966653i	$-0.417566\pi$
$692$	2.99988	−	10.4341i	0.114038	−	0.396645i
$693$	−0.754895	−	2.07652i	−0.0286761	−	0.0788804i
$694$	−8.13025	+	13.7913i	−0.308620	+	0.523511i
$695$	22.3358	+	12.8956i	0.847243	+	0.489156i
$696$	−5.30821	−	8.85935i	−0.201207	−	0.335813i
$697$	12.5111	−	7.22328i	0.473892	−	0.273601i
$698$	0.144215	−	15.8843i	0.00545861	−	0.601230i
$699$	21.7380	+	11.3214i	0.822208	+	0.428213i
$700$	−66.9181	−	1.21521i	−2.52927	−	0.0459305i
$701$	13.0178	−	13.0178i	0.491676	−	0.491676i	−0.417158	−	0.908834i	$-0.636974\pi$
$701$	13.0178	−	13.0178i	0.491676	−	0.491676i	0.908834	+	0.417158i	$0.136974\pi$
$702$	8.08883	−	19.0073i	0.305293	−	0.717383i
$703$		−	5.99049i		−	0.225935i
$704$	1.71359	−	0.360453i	0.0645835	−	0.0135851i
$705$	−9.45784	−	30.0164i	−0.356203	−	1.13048i
$706$	2.16652	−	2.12753i	0.0815380	−	0.0800708i
$707$	−0.116919	+	0.436349i	−0.00439721	+	0.0164106i
$708$	5.42580	+	18.3776i	0.203914	+	0.690671i
$709$	4.39011	+	16.3841i	0.164874	+	0.615319i	0.998056	+	0.0623199i	$0.0198499\pi$
$709$	4.39011	+	16.3841i	0.164874	+	0.615319i	−0.833182	+	0.552999i	$0.813483\pi$
$710$	−20.9243	+	35.4938i	−0.785274	+	1.33206i
$711$	−1.49876	−	17.2064i	−0.0562079	−	0.645291i
$712$	6.08224	−	5.75963i	0.227942	−	0.215851i
$713$	−16.0285	+	27.7622i	−0.600273	+	1.03970i
$714$	−33.4191	+	10.1974i	−1.25068	+	0.381629i
$715$	0.615660	−	2.29767i	0.0230244	−	0.0859282i
$716$	−0.259372	−	1.04342i	−0.00969320	−	0.0389943i
$717$	−1.13063	−	26.0094i	−0.0422242	−	0.971339i
$718$	15.0118	+	4.16883i	0.560234	+	0.155579i
$719$	43.0731			1.60635			0.803177	−	0.595740i	$-0.203141\pi$
$719$	43.0731			1.60635			0.803177	+	0.595740i	$0.203141\pi$
$720$	34.4201	+	31.1037i	1.28276	+	1.15917i
$721$	27.5313			1.02532
$722$	22.4494	+	6.23428i	0.835479	+	0.232016i
$723$	21.0065	−	13.3770i	0.781240	−	0.497495i
$724$	13.6968	−	3.40475i	0.509038	−	0.126537i
$725$	5.42673	−	20.2528i	0.201544	−	0.752171i
$726$	6.04895	−	26.1362i	0.224498	−	0.970004i
$727$	15.3101	−	26.5179i	0.567821	−	0.983495i	−0.428960	−	0.903324i	$-0.641120\pi$
$727$	15.3101	−	26.5179i	0.567821	−	0.983495i	0.996781	−	0.0801716i	$-0.0255468\pi$
$728$	−26.7424	−	0.728547i	−0.991138	−	0.0270017i
$729$	−26.0880	+	6.95830i	−0.966221	+	0.257715i
$730$	−8.95835	+	15.1960i	−0.331563	+	0.562430i
$731$	5.32737	+	19.8820i	0.197040	+	0.735363i
$732$	−22.6120	−	21.4964i	−0.835762	−	0.794531i
$733$	0.679676	−	2.53658i	0.0251044	−	0.0936909i	−0.952237	−	0.305360i	$-0.901223\pi$
$733$	0.679676	−	2.53658i	0.0251044	−	0.0936909i	0.977341	+	0.211669i	$0.0678899\pi$
$734$	−23.4618	+	23.0396i	−0.865990	+	0.850407i
$735$	−28.2489	−	6.26827i	−1.04197	−	0.231209i
$736$	16.0805	−	14.6831i	0.592736	−	0.541226i
$737$		−	1.17271i		−	0.0431972i
$738$	−10.9868	−	9.39759i	−0.404431	−	0.345930i
$739$	13.1402	−	13.1402i	0.483370	−	0.483370i	−0.422836	−	0.906206i	$-0.638965\pi$
$739$	13.1402	−	13.1402i	0.483370	−	0.483370i	0.906206	+	0.422836i	$0.138965\pi$
$740$	0.529226	−	29.1430i	0.0194547	−	1.07132i
$741$	0.336011	+	7.72970i	0.0123437	+	0.283958i
$742$	0.463262	−	51.0253i	0.0170069	−	1.87320i
$743$	−1.79055	+	1.03378i	−0.0656890	+	0.0379255i	−0.532485	−	0.846440i	$-0.678742\pi$
$743$	−1.79055	+	1.03378i	−0.0656890	+	0.0379255i	0.466796	+	0.884365i	$0.345408\pi$
$744$	28.3769	−	29.3119i	1.04035	−	1.07463i
$745$	74.7897	+	43.1798i	2.74008	+	1.58199i
$746$	7.38343	−	12.5245i	0.270327	−	0.458554i
$747$	10.7174	+	8.99989i	0.392127	+	0.329289i
$748$	1.78363	+	0.512808i	0.0652160	+	0.0187501i
$749$	10.2077	+	38.0958i	0.372982	+	1.39199i
$750$	1.60909	+	46.8066i	0.0587557	+	1.70914i
$751$	−7.86676	+	4.54188i	−0.287062	+	0.165735i	−0.636616	−	0.771181i	$-0.719666\pi$
$751$	−7.86676	+	4.54188i	−0.287062	+	0.165735i	0.349554	+	0.936916i	$0.386333\pi$
$752$	18.7874	+	0.682570i	0.685107	+	0.0248908i
$753$	−8.40489	+	2.64829i	−0.306291	+	0.0965091i
$754$	2.24253	−	8.07525i	0.0816680	−	0.294083i
$755$	54.5367	+	54.5367i	1.98479	+	1.98479i
$756$	20.7634	+	28.1351i	0.755158	+	1.02327i
$757$	18.3910	−	18.3910i	0.668433	−	0.668433i	−0.288920	−	0.957353i	$-0.593296\pi$
$757$	18.3910	−	18.3910i	0.668433	−	0.668433i	0.957353	+	0.288920i	$0.0932961\pi$
$758$	−10.7043	+	6.05125i	−0.388799	+	0.219791i
$759$	0.438586	+	1.39194i	0.0159196	+	0.0505242i
$760$	−16.6552	−	4.95263i	−0.604147	−	0.179651i
$761$	−14.1080	−	24.4358i	−0.511415	−	0.885797i	−0.999912	−	0.0132318i	$-0.995788\pi$
$761$	−14.1080	−	24.4358i	−0.511415	−	0.885797i	0.488497	−	0.872565i	$-0.337545\pi$
$762$	23.9983	+	22.4031i	0.869365	+	0.811579i
$763$	−29.0160	+	7.77481i	−1.05045	+	0.281467i
$764$	18.9186	−	10.4693i	0.684451	−	0.378767i
$765$	16.7988	+	46.2091i	0.607362	+	1.67069i
$766$	−3.83869	+	0.991310i	−0.138697	+	0.0358175i
$767$	−7.77467	+	13.4661i	−0.280727	+	0.486234i
$768$	−24.3942	+	13.1501i	−0.880248	+	0.474513i
$769$	−14.6064	−	25.2991i	−0.526722	−	0.912309i	−0.999515	−	0.0311354i	$-0.990088\pi$
$769$	−14.6064	−	25.2991i	−0.526722	−	0.912309i	0.472794	−	0.881173i	$-0.343246\pi$
$770$	2.82129	+	2.87299i	0.101672	+	0.103535i
$771$	−9.84350	+	0.427898i	−0.354505	+	0.0154104i
$772$	0.188861	−	10.4001i	0.00679726	−	0.374306i
$773$	−10.5491	−	10.5491i	−0.379425	−	0.379425i	0.491470	−	0.870895i	$-0.336460\pi$
$773$	−10.5491	−	10.5491i	−0.379425	−	0.379425i	−0.870895	+	0.491470i	$0.836460\pi$
$774$	16.9849	−	11.6551i	0.610511	−	0.418934i
$775$	82.8256			2.97518
$776$	−10.0432	−	42.0284i	−0.360529	−	1.50873i
$777$	4.75923	−	21.4482i	0.170736	−	0.769448i
$778$	0.388099	−	42.7466i	0.0139140	−	1.53254i
$779$	5.23060	+	1.40154i	0.187406	+	0.0502152i
$780$	0.951775	+	37.6337i	0.0340790	+	1.34750i
$781$	1.59335	−	0.426938i	0.0570146	−	0.0152770i
$782$	22.3456	−	5.77058i	0.799078	−	0.206356i
$783$	−10.1229	+	4.18627i	−0.361764	+	0.149605i
$784$	9.18049	−	14.6459i	0.327875	−	0.523068i
$785$	−49.8924	−	28.8054i	−1.78074	−	1.02811i
$786$	−0.849508	−	1.36114i	−0.0303010	−	0.0485503i
$787$	33.8023	+	9.05729i	1.20492	+	0.322857i	0.804767	−	0.593591i	$-0.202290\pi$
$787$	33.8023	+	9.05729i	1.20492	+	0.322857i	0.400153	+	0.916448i	$0.368957\pi$
$788$	2.00979	+	8.08507i	0.0715957	+	0.288019i
$789$	20.2385	+	31.7815i	0.720511	+	1.13145i
$790$	15.4900	+	27.4010i	0.551110	+	0.974885i
$791$			56.9431i			2.02466i
$792$	−0.110721	−	1.85401i	−0.00393431	−	0.0658795i
$793$		−	25.3175i		−	0.899052i
$794$	3.40880	−	1.92702i	0.120974	−	0.0683874i
$795$	−71.7379	+	3.11845i	−2.54428	+	0.110600i
$796$	−4.40885	−	2.65333i	−0.156268	−	0.0940449i
$797$	−27.6668	−	7.41329i	−0.980007	−	0.262592i	−0.266959	−	0.963708i	$-0.586019\pi$
$797$	−27.6668	−	7.41329i	−0.980007	−	0.262592i	−0.713048	+	0.701116i	$0.752686\pi$
$798$	−11.5606	−	6.15491i	−0.409240	−	0.217881i
$799$	17.2554	+	9.96243i	0.610453	+	0.352445i
$800$	−53.6277	−	17.0126i	−1.89602	−	0.601487i
$801$	−5.09328	−	7.27986i	−0.179962	−	0.257221i
$802$	11.7331	+	45.4344i	0.414309	+	1.60435i
$803$	0.682165	−	0.182786i	0.0240731	−	0.00645036i
$804$	5.25518	+	17.7997i	0.185336	+	0.627746i
$805$	48.3667	+	12.9598i	1.70470	+	0.456773i
$806$	33.1049	+	0.300562i	1.16607	+	0.0105868i
$807$	−17.3693	+	5.47289i	−0.611429	+	0.192655i
$808$	−0.198756	+	0.323572i	−0.00699220	+	0.0113832i
$809$	−39.9831			−1.40573			−0.702865	−	0.711323i	$-0.748096\pi$
$809$	−39.9831			−1.40573			−0.702865	+	0.711323i	$0.748096\pi$
$810$	38.0032	−	31.2564i	1.33530	−	1.09824i
$811$	−33.5121	−	33.5121i	−1.17677	−	1.17677i	−0.980563	−	0.196204i	$-0.937138\pi$
$811$	−33.5121	−	33.5121i	−1.17677	−	1.17677i	−0.196204	−	0.980563i	$-0.562862\pi$
$812$	9.84780	+	10.2121i	0.345590	+	0.358374i
$813$	−9.51073	+	18.2614i	−0.333556	+	0.640457i
$814$	−0.832614	+	0.817632i	−0.0291831	+	0.0286580i
$815$	11.9123	+	20.6328i	0.417271	+	0.722734i
$816$	−29.3705	+	0.209341i	−1.02817	+	0.00732840i
$817$	−3.85771	+	6.68176i	−0.134964	+	0.233765i
$818$	9.34868	+	36.2012i	0.326869	+	1.26575i
$819$	−4.93793	+	27.9421i	−0.172545	+	0.976377i
$820$	25.3224	+	7.28039i	0.884297	+	0.254242i
$821$	−10.8942	+	2.91908i	−0.380209	+	0.101877i	−0.443861	−	0.896096i	$-0.646392\pi$
$821$	−10.8942	+	2.91908i	−0.380209	+	0.101877i	0.0636527	+	0.997972i	$0.479725\pi$
$822$	−15.0455	−	49.3074i	−0.524773	−	1.71979i
$823$	27.4702	+	47.5798i	0.957551	+	1.65853i	0.728420	+	0.685131i	$0.240255\pi$
$823$	27.4702	+	47.5798i	0.957551	+	1.65853i	0.229131	+	0.973396i	$0.426412\pi$
$824$	22.1831	+	6.59645i	0.772786	+	0.229798i
$825$	2.54794	−	2.77953i	0.0887080	−	0.0967708i
$826$	−12.9532	−	22.9136i	−0.450700	−	0.797265i
$827$	14.2104	−	14.2104i	0.494144	−	0.494144i	−0.415465	−	0.909609i	$-0.636381\pi$
$827$	14.2104	−	14.2104i	0.494144	−	0.494144i	0.909609	+	0.415465i	$0.136381\pi$
$828$	−12.8946	−	19.1619i	−0.448119	−	0.665921i
$829$	6.15512	+	6.15512i	0.213776	+	0.213776i	0.805869	−	0.592093i	$-0.201698\pi$
$829$	6.15512	+	6.15512i	0.213776	+	0.213776i	−0.592093	+	0.805869i	$0.701698\pi$
$830$	−24.5750	−	6.82456i	−0.853009	−	0.236884i
$831$	−3.88757	+	17.5199i	−0.134858	+	0.607759i
$832$	−21.3729	−	6.99445i	−0.740973	−	0.242489i
$833$	15.8654	−	9.15989i	0.549704	−	0.317371i
$834$	8.65206	+	13.8629i	0.299596	+	0.480034i
$835$	13.7435	+	51.2913i	0.475612	+	1.77501i
$836$	0.336832	+	0.608672i	0.0116496	+	0.0210513i
$837$	−26.3229	−	34.3453i	−0.909853	−	1.18715i
$838$	0.629969	+	0.371379i	0.0217619	+	0.0128291i
$839$	−21.5384	−	12.4352i	−0.743590	−	0.429312i	0.0797833	−	0.996812i	$-0.474577\pi$
$839$	−21.5384	−	12.4352i	−0.743590	−	0.429312i	−0.823373	+	0.567500i	$0.807911\pi$
$840$	−55.6970	−	30.9642i	−1.92173	−	1.06837i
$841$	21.2658	−	12.2778i	0.733303	−	0.423373i
$842$	−18.8150	−	0.170822i	−0.648407	−	0.00588693i
$843$	−20.6181	+	13.1297i	−0.710127	+	0.452210i
$844$	−25.2529	−	26.1871i	−0.869242	−	0.901396i
$845$	13.9363	−	13.9363i	0.479424	−	0.479424i
$846$	3.64819	−	19.6036i	0.125427	−	0.673987i
$847$			36.8507i			1.26621i
$848$	12.5989	−	41.0023i	0.432646	−	1.40803i
$849$	15.5036	−	16.9128i	0.532083	−	0.580444i
$850$	−41.7791	−	42.5447i	−1.43301	−	1.45927i
$851$	−3.75585	+	14.0170i	−0.128749	+	0.480497i
$852$	−22.2712	+	13.6204i	−0.762998	+	0.466627i
$853$	−5.05023	−	18.8477i	−0.172917	−	0.645334i	−0.996897	−	0.0787157i	$-0.974918\pi$
$853$	−5.05023	−	18.8477i	−0.172917	−	0.645334i	0.823980	−	0.566618i	$-0.191749\pi$
$854$	36.9189	+	21.7644i	1.26334	+	0.744763i
$855$	−7.79521	+	16.7003i	−0.266590	+	0.571137i
$856$	−0.902871	+	33.1412i	−0.0308595	+	1.13274i
$857$	−18.6982	+	32.3862i	−0.638717	+	1.10629i	0.346998	+	0.937866i	$0.387201\pi$
$857$	−18.6982	+	32.3862i	−0.638717	+	1.10629i	−0.985715	+	0.168424i	$0.946132\pi$
$858$	1.02848	−	1.10172i	0.0351119	−	0.0376120i
$859$	−7.10549	+	26.5180i	−0.242436	+	0.904784i	0.732219	+	0.681070i	$0.238485\pi$
$859$	−7.10549	+	26.5180i	−0.242436	+	0.904784i	−0.974655	+	0.223714i	$0.928182\pi$
$860$	−19.3576	+	32.1651i	−0.660089	+	1.09682i
$861$	17.6140	+	9.17354i	0.600284	+	0.312634i
$862$	3.25862	−	11.7341i	0.110989	−	0.399667i
$863$	−10.1797			−0.346520			−0.173260	−	0.984876i	$-0.555430\pi$
$863$	−10.1797			−0.346520			−0.173260	+	0.984876i	$0.555430\pi$
$864$	9.98885	+	27.6446i	0.339828	+	0.940488i
$865$	20.9860			0.713545
$866$	2.43687	−	8.77507i	0.0828082	−	0.298189i
$867$	−1.49362	−	0.777892i	−0.0507261	−	0.0264186i
$868$	−28.8972	+	48.0164i	−0.980834	+	1.62978i
$869$	0.326156	−	1.21723i	0.0110641	−	0.0412918i
$870$	13.6231	−	14.5931i	0.461866	−	0.494752i
$871$	−7.53020	+	13.0427i	−0.255151	+	0.441935i
$872$	−25.2423	−	0.687680i	−0.854811	−	0.0232878i
$873$	−45.6601	+	3.97721i	−1.54536	+	0.134608i
$874$	7.45221	+	4.39322i	0.252075	+	0.148603i
$875$	−16.6507	−	62.1414i	−0.562897	−	2.10076i
$876$	−9.53500	+	5.83132i	−0.322158	+	0.197022i
$877$	−6.90717	+	25.7779i	−0.233239	+	0.870458i	0.745696	+	0.666286i	$0.232117\pi$
$877$	−6.90717	+	25.7779i	−0.233239	+	0.870458i	−0.978935	+	0.204172i	$0.934550\pi$
$878$	−28.6384	−	29.1631i	−0.966498	−	0.984208i
$879$	35.9960	−	39.2677i	1.21411	−	1.32447i
$880$	1.58487	+	2.99087i	0.0534261	+	0.100822i
$881$		−	30.7798i		−	1.03700i	−0.855078	−	0.518499i	$-0.826491\pi$
$881$		−	30.7798i		−	1.03700i	0.855078	−	0.518499i	$-0.173509\pi$
$882$	−13.9325	−	11.9171i	−0.469131	−	0.401271i
$883$	−19.8089	+	19.8089i	−0.666622	+	0.666622i	−0.956933	−	0.290310i	$-0.906241\pi$
$883$	−19.8089	+	19.8089i	−0.666622	+	0.666622i	0.290310	+	0.956933i	$0.406241\pi$
$884$	−16.5445	−	17.1565i	−0.556451	−	0.577034i
$885$	−31.2425	+	19.8953i	−1.05021	+	0.668774i
$886$	−45.6576	−	0.414528i	−1.53390	−	0.0139264i
$887$	21.0940	−	12.1786i	0.708266	−	0.408918i	−0.102153	−	0.994769i	$-0.532573\pi$
$887$	21.0940	−	12.1786i	0.708266	−	0.408918i	0.810419	+	0.585851i	$0.199240\pi$
$888$	8.97366	−	16.1414i	0.301136	−	0.541670i
$889$	−39.0550	−	22.5484i	−1.30986	−	0.756249i
$890$	13.9484	+	8.22287i	0.467552	+	0.275631i
$891$	−1.96235	−	0.173190i	−0.0657413	−	0.00580210i
$892$	−3.15397	−	5.69938i	−0.105603	−	0.190829i
$893$	1.93301	+	7.21410i	0.0646858	+	0.241411i
$894$	28.9708	+	46.4190i	0.968929	+	1.55248i
$895$	1.79985	−	1.03914i	0.0601624	−	0.0347348i
$896$	28.5729	−	25.1539i	0.954555	−	0.840333i
$897$	4.06006	−	18.2972i	0.135561	−	0.610927i
$898$	14.5935	+	4.05268i	0.486993	+	0.135240i
$899$	−12.4142	−	12.4142i	−0.414037	−	0.414037i
$900$	−26.2177	+	53.6065i	−0.873923	+	1.78688i
$901$	32.1460	−	32.1460i	1.07094	−	1.07094i
$902$	−0.519118	−	0.918292i	−0.0172847	−	0.0305758i
$903$	−19.1205	+	20.8583i	−0.636289	+	0.694122i
$904$	−13.6435	+	45.8815i	−0.453775	+	1.52600i
$905$	13.6407	+	23.6264i	0.453433	+	0.785369i
$906$	14.2621	+	46.7401i	0.473828	+	1.55283i
$907$	56.0698	−	15.0239i	1.86177	−	0.498859i	0.861802	−	0.507245i	$-0.169336\pi$
$907$	56.0698	−	15.0239i	1.86177	−	0.498859i	0.999965	+	0.00838605i	$0.00266939\pi$
$908$	17.5759	+	5.05321i	0.583277	+	0.167697i
$909$	0.308445	+	0.259016i	0.0102305	+	0.00859103i
$910$	−12.9300	−	50.0692i	−0.428624	−	1.65978i
$911$	11.9347	−	20.6715i	0.395414	−	0.684877i	−0.597740	−	0.801690i	$-0.703934\pi$
$911$	11.9347	−	20.6715i	0.395414	−	0.684877i	0.993154	+	0.116813i	$0.0372678\pi$
$912$	−7.84014	−	7.72917i	−0.259613	−	0.255938i
$913$	0.510553	+	0.884303i	0.0168968	+	0.0292662i
$914$	−15.3049	+	15.0295i	−0.506242	+	0.497133i
$915$	27.8572	−	53.4884i	0.920932	−	1.76827i
$916$	7.29785	+	7.56780i	0.241128	+	0.250047i
$917$	1.55845	+	1.55845i	0.0514646	+	0.0514646i
$918$	−4.36414	+	30.8457i	−0.144038	+	1.01806i
$919$	−15.7779			−0.520466			−0.260233	−	0.965546i	$-0.583799\pi$
$919$	−15.7779			−0.520466			−0.260233	+	0.965546i	$0.583799\pi$
$920$	35.8660	+	22.0309i	1.18247	+	0.726336i
$921$	55.6284	−	17.5279i	1.83302	−	0.577565i
$922$	−16.9383	−	0.153784i	−0.557834	−	0.00506461i
$923$	−20.4625	−	5.48292i	−0.673533	−	0.180473i
$924$	0.722415	+	2.44687i	0.0237657	+	0.0804961i
$925$	36.2157	−	9.70397i	1.19077	−	0.319065i
$926$	−0.830355	−	3.21541i	−0.0272872	−	0.105665i
$927$	10.3825	−	22.2432i	0.341006	−	0.730562i
$928$	5.48800	+	10.5878i	0.180152	+	0.347563i
$929$	14.3132	+	8.26371i	0.469600	+	0.271123i	0.716072	−	0.698026i	$-0.245938\pi$
$929$	14.3132	+	8.26371i	0.469600	+	0.271123i	−0.246472	+	0.969150i	$0.579271\pi$
$930$	69.6101	+	37.0608i	2.28260	+	1.21527i
$931$	6.63296	+	1.77730i	0.217387	+	0.0582485i
$932$	−24.2485	−	14.5932i	−0.794287	−	0.478017i
$933$	−18.4014	+	0.799912i	−0.602436	+	0.0261879i
$934$	−42.0481	+	23.7701i	−1.37586	+	0.777783i
$935$			3.58740i			0.117320i
$936$	−10.6736	+	21.3311i	−0.348877	+	0.697228i
$937$			5.92940i			0.193705i	0.995299	+	0.0968526i	$0.0308775\pi$
$937$			5.92940i			0.193705i	−0.995299	+	0.0968526i	$0.969122\pi$
$938$	−12.5459	−	22.1930i	−0.409638	−	0.724629i
$939$	17.6862	+	27.7735i	0.577169	+	0.906354i
$940$	8.76654	+	35.2665i	0.285933	+	1.15027i
$941$	−20.6096	−	5.52232i	−0.671853	−	0.180022i	−0.0932635	−	0.995641i	$-0.529730\pi$
$941$	−20.6096	−	5.52232i	−0.671853	−	0.180022i	−0.578589	+	0.815619i	$0.696397\pi$
$942$	−19.3265	−	30.9663i	−0.629692	−	1.00894i
$943$	−11.3603	−	6.55886i	−0.369941	−	0.213586i
$944$	−4.94692	−	21.5660i	−0.161008	−	0.701914i
$945$	−41.1775	+	53.6001i	−1.33950	+	1.74361i
$946$	1.45523	−	0.375800i	0.0473135	−	0.0122183i
$947$	−31.9863	+	8.57071i	−1.03942	+	0.278511i	−0.737871	−	0.674941i	$-0.764169\pi$
$947$	−31.9863	+	8.57071i	−1.03942	+	0.278511i	−0.301545	+	0.953452i	$0.597502\pi$
$948$	0.504219	+	19.9371i	0.0163763	+	0.647527i
$949$	−8.76066	−	2.34741i	−0.284383	−	0.0762002i
$950$	0.202917	−	22.3500i	0.00658351	−	0.725131i
$951$	4.61279	−	20.7882i	0.149580	−	0.674105i
$952$	39.2407	−	9.37703i	1.27180	−	0.303911i
$953$	−0.546564			−0.0177049			−0.00885247	−	0.999961i	$-0.502818\pi$
$953$	−0.546564			−0.0177049			−0.00885247	+	0.999961i	$0.502818\pi$
$954$	−41.0499	−	19.6168i	−1.32904	−	0.635116i
$955$	29.5538	+	29.5538i	0.956339	+	0.956339i
$956$	−0.545814	+	30.0565i	−0.0176529	+	0.972096i
$957$	−0.798502	+	0.0347109i	−0.0258119	+	0.00112205i
$958$	−4.77440	−	4.86189i	−0.154254	−	0.157080i
$959$	35.4068	+	61.3264i	1.14335	+	1.98033i
$960$	−37.4585	−	38.2941i	−1.20897	−	1.23594i
$961$	19.1758	−	33.2135i	0.618576	−	1.07140i
$962$	14.5104	−	3.74720i	0.467835	−	0.120815i
$963$	34.6280	+	6.11946i	1.11587	+	0.197197i
$964$	−25.1611	+	13.9239i	−0.810384	+	0.448457i
$965$	19.4213	−	5.20393i	0.625195	−	0.167521i
$966$	23.1914	+	21.6499i	0.746171	+	0.696573i
$967$	−7.49046	−	12.9739i	−0.240877	−	0.417211i	0.720087	−	0.693883i	$-0.244102\pi$
$967$	−7.49046	−	12.9739i	−0.240877	−	0.417211i	−0.960964	+	0.276672i	$0.910768\pi$
$968$	−8.82937	+	29.6922i	−0.283787	+	0.954344i
$969$	−3.50660	−	11.1289i	−0.112648	−	0.357512i
$970$	72.7133	−	41.1054i	2.33468	−	1.31981i
$971$	−29.4725	+	29.4725i	−0.945816	+	0.945816i	−0.998606	−	0.0527896i	$-0.983189\pi$
$971$	−29.4725	+	29.4725i	−0.945816	+	0.945816i	0.0527896	+	0.998606i	$0.483189\pi$
$972$	30.5613	−	6.16505i	0.980254	−	0.197744i
$973$	−15.8725	−	15.8725i	−0.508849	−	0.508849i
$974$	14.1920	−	51.1049i	0.454742	−	1.63751i
$975$	−46.1859	+	14.5527i	−1.47913	+	0.466059i
$976$	24.5324	+	26.3822i	0.785264	+	0.844475i
$977$	2.02199	−	1.16740i	0.0646892	−	0.0373483i	−0.467307	−	0.884095i	$-0.654776\pi$
$977$	2.02199	−	1.16740i	0.0646892	−	0.0373483i	0.531996	+	0.846747i	$0.321442\pi$
$978$	0.518634	+	15.0865i	0.0165841	+	0.482412i
$979$	−0.167779	−	0.626159i	−0.00536224	−	0.0200121i
$980$	32.1115	+	9.23231i	1.02577	+	0.294915i
$981$	−4.66094	+	26.3747i	−0.148812	+	0.842080i
$982$	−1.40015	+	2.37506i	−0.0446805	+	0.0757913i
$983$	21.5089	+	12.4182i	0.686029	+	0.396079i	0.802123	−	0.597159i	$-0.203704\pi$
$983$	21.5089	+	12.4182i	0.686029	+	0.396079i	−0.116094	+	0.993238i	$0.537037\pi$
$984$	11.9944	+	11.6118i	0.382368	+	0.370171i
$985$	−13.9464	+	8.05197i	−0.444370	+	0.256557i
$986$	−0.114748	+	12.6388i	−0.00365433	+	0.402500i
$987$	1.18955	+	27.3649i	0.0378639	+	0.871033i
$988$	0.162210	−	8.93244i	0.00516058	−	0.284179i
$989$	13.2158	−	13.2158i	0.420240	−	0.420240i
$990$	3.38511	−	1.19594i	0.107586	−	0.0380094i
$991$			7.12527i			0.226342i	0.993576	+	0.113171i	$0.0361008\pi$
$991$			7.12527i			0.226342i	−0.993576	+	0.113171i	$0.963899\pi$
$992$	−34.7884	+	31.7651i	−1.10453	+	1.00854i
$993$	58.4622	+	12.9724i	1.85524	+	0.411668i
$994$	25.5862	−	25.1257i	0.811544	−	0.796940i
$995$	2.57436	−	9.60763i	0.0816126	−	0.304582i
$996$	−11.7121	−	11.1343i	−0.371112	−	0.352804i
$997$	12.7516	+	47.5897i	0.403848	+	1.50718i	0.806170	+	0.591684i	$0.201537\pi$
$997$	12.7516	+	47.5897i	0.403848	+	1.50718i	−0.402322	+	0.915498i	$0.631797\pi$
$998$	8.08908	−	13.7215i	0.256055	−	0.434346i
$999$	−15.5337	−	11.9335i	−0.491465	−	0.377561i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.2.u.a.83.14	yes	88
3.2	odd	2		432.2.v.a.35.9		88
4.3	odd	2		576.2.y.a.47.3		88
9.4	even	3		432.2.v.a.179.16		88
9.5	odd	6	inner	144.2.u.a.131.7	yes	88
12.11	even	2		1728.2.z.a.1007.1		88
16.5	even	4		576.2.y.a.335.15		88
16.11	odd	4	inner	144.2.u.a.11.7	✓	88
36.23	even	6		576.2.y.a.239.15		88
36.31	odd	6		1728.2.z.a.1583.1		88
48.5	odd	4		1728.2.z.a.143.1		88
48.11	even	4		432.2.v.a.251.16		88
144.5	odd	12		576.2.y.a.527.3		88
144.59	even	12	inner	144.2.u.a.59.14	yes	88
144.85	even	12		1728.2.z.a.719.1		88
144.139	odd	12		432.2.v.a.395.9		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.7	✓	88	16.11	odd	4	inner
144.2.u.a.59.14	yes	88	144.59	even	12	inner
144.2.u.a.83.14	yes	88	1.1	even	1	trivial
144.2.u.a.131.7	yes	88	9.5	odd	6	inner
432.2.v.a.35.9		88	3.2	odd	2
432.2.v.a.179.16		88	9.4	even	3
432.2.v.a.251.16		88	48.11	even	4
432.2.v.a.395.9		88	144.139	odd	12
576.2.y.a.47.3		88	4.3	odd	2
576.2.y.a.239.15		88	36.23	even	6
576.2.y.a.335.15		88	16.5	even	4
576.2.y.a.527.3		88	144.5	odd	12
1728.2.z.a.143.1		88	48.5	odd	4
1728.2.z.a.719.1		88	144.85	even	12
1728.2.z.a.1007.1		88	12.11	even	2
1728.2.z.a.1583.1		88	36.31	odd	6

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	144.u (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.378412 - 1.36265i) q^{2} +(1.53620 + 0.800065i) q^{3} +(-1.71361 - 1.03128i) q^{4} +(1.00059 - 3.73424i) q^{5} +(1.67152 - 1.79054i) q^{6} +(-1.68236 + 2.91393i) q^{7} +(-2.05372 + 1.94479i) q^{8} +(1.71979 + 2.45811i) q^{9} +(-4.70981 - 2.77653i) q^{10} +(0.0566521 + 0.211428i) q^{11} +(-1.80734 - 2.95525i) q^{12} +(0.727551 - 2.71526i) q^{13} +(3.33403 + 3.39513i) q^{14} +(4.52473 - 4.93599i) q^{15} +(1.87291 + 3.53443i) q^{16} +4.23937i q^{17} +(4.00033 - 1.41329i) q^{18} +(-1.12365 + 1.12365i) q^{19} +(-5.56567 + 5.36714i) q^{20} +(-4.91577 + 3.13037i) q^{21} +(0.309540 + 0.00281033i) q^{22} +(3.33369 - 1.92471i) q^{23} +(-4.71088 + 1.34447i) q^{24} +(-8.61325 - 4.97286i) q^{25} +(-3.42462 - 2.01888i) q^{26} +(0.675290 + 5.15209i) q^{27} +(5.88800 - 3.25835i) q^{28} +(0.545635 + 2.03634i) q^{29} +(-5.01379 - 8.03344i) q^{30} +(-7.21206 + 4.16388i) q^{31} +(5.52491 - 1.21464i) q^{32} +(-0.0821277 + 0.370121i) q^{33} +(5.77677 + 1.60423i) q^{34} +(9.19798 + 9.19798i) q^{35} +(-0.412042 - 5.98584i) q^{36} +(-2.66564 + 2.66564i) q^{37} +(1.10593 + 1.95634i) q^{38} +(3.29004 - 3.58908i) q^{39} +(5.20739 + 9.61503i) q^{40} +(-1.70386 - 2.95117i) q^{41} +(2.40541 + 7.88302i) q^{42} +(4.68985 - 1.25664i) q^{43} +(0.120963 - 0.420730i) q^{44} +(10.9000 - 3.96257i) q^{45} +(-1.36119 - 5.27098i) q^{46} +(2.34998 - 4.07028i) q^{47} +(0.0493802 + 6.92803i) q^{48} +(-2.16067 - 3.74239i) q^{49} +(-10.0356 + 9.85502i) q^{50} +(-3.39177 + 6.51251i) q^{51} +(-4.04693 + 3.90257i) q^{52} +(-7.58271 - 7.58271i) q^{53} +(7.27601 + 1.02943i) q^{54} +0.846209 q^{55} +(-2.21189 - 9.25626i) q^{56} +(-2.62513 + 0.827151i) q^{57} +(2.98128 + 0.0270672i) q^{58} +(-5.34305 - 1.43167i) q^{59} +(-12.8440 + 3.79207i) q^{60} +(8.69958 - 2.33105i) q^{61} +(2.94477 + 11.4031i) q^{62} +(-10.0561 + 0.875933i) q^{63} +(0.435568 - 7.98813i) q^{64} +(-9.41144 - 5.43370i) q^{65} +(0.473265 + 0.251969i) q^{66} +(-5.17504 - 1.38665i) q^{67} +(4.37200 - 7.26463i) q^{68} +(6.66110 - 0.289558i) q^{69} +(16.0142 - 9.05296i) q^{70} -7.53614i q^{71} +(-8.31250 - 1.70364i) q^{72} -3.22646i q^{73} +(2.62362 + 4.64104i) q^{74} +(-9.25302 - 14.5304i) q^{75} +(3.08429 - 0.766693i) q^{76} +(-0.711397 - 0.190618i) q^{77} +(-3.64565 - 5.84131i) q^{78} +(-4.98587 - 2.87859i) q^{79} +(15.0724 - 3.45739i) q^{80} +(-3.08462 + 8.45489i) q^{81} +(-4.66616 + 1.20500i) q^{82} +(4.50604 - 1.20739i) q^{83} +(11.6520 - 0.294685i) q^{84} +(15.8308 + 4.24186i) q^{85} +(0.0623381 - 6.86613i) q^{86} +(-0.790999 + 3.56475i) q^{87} +(-0.527532 - 0.324039i) q^{88} -2.96157 q^{89} +(-1.27489 - 16.3523i) q^{90} +(6.68807 + 6.68807i) q^{91} +(-7.69756 - 0.139785i) q^{92} +(-14.4105 + 0.626426i) q^{93} +(-4.65709 - 4.74243i) q^{94} +(3.07166 + 5.32027i) q^{95} +(9.45914 + 2.55436i) q^{96} +(-7.63883 + 13.2308i) q^{97} +(-5.91718 + 1.52806i) q^{98} +(-0.422285 + 0.502870i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} - 4 q^{7} - 8 q^{10} - 6 q^{11} - 16 q^{12} - 2 q^{13} - 6 q^{14} - 2 q^{16} - 10 q^{18} - 8 q^{19} - 48 q^{20} + 2 q^{21} - 2 q^{22} - 12 q^{23} - 16 q^{27}+ \cdots + 46 q^{99}+O(q^{100}) \) 88 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 - 4 * q^7 - 8 * q^10 - 6 * q^11 - 16 * q^12 - 2 * q^13 - 6 * q^14 - 2 * q^16 - 10 * q^18 - 8 * q^19 - 48 * q^20 + 2 * q^21 - 2 * q^22 - 12 * q^23 - 16 * q^27 + 8 * q^28 - 6 * q^29 - 34 * q^30 - 6 * q^32 - 8 * q^33 + 2 * q^34 - 26 * q^36 - 8 * q^37 - 6 * q^38 - 32 * q^39 - 2 * q^40 + 48 * q^42 - 2 * q^43 + 6 * q^45 - 40 * q^46 + 42 * q^48 - 24 * q^49 + 72 * q^50 - 12 * q^51 - 2 * q^52 - 38 * q^54 - 16 * q^55 + 36 * q^56 + 16 * q^58 - 42 * q^59 + 70 * q^60 - 2 * q^61 - 44 * q^64 - 12 * q^65 + 104 * q^66 - 2 * q^67 + 96 * q^68 - 10 * q^69 - 16 * q^70 - 10 * q^72 + 78 * q^74 - 56 * q^75 - 14 * q^76 - 6 * q^77 + 12 * q^78 - 8 * q^81 - 36 * q^82 + 54 * q^83 + 158 * q^84 + 8 * q^85 + 54 * q^86 + 48 * q^87 + 22 * q^88 + 64 * q^90 + 20 * q^91 + 108 * q^92 - 34 * q^93 + 6 * q^94 - 58 * q^96 - 4 * q^97 + 46 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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