LMFDB - Embedded newform 207.2.m.a.4.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [207,2,Mod(4,207)] 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("207.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(207, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([22, 12])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.m (of order $33$, degree $20$, 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:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			4.12
Character	$\chi$	$=$	207.4
Dual form			207.2.m.a.52.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0256606 - 0.0360353i) q^{2} +(-1.16039 + 1.28588i) q^{3} +(0.653496 + 1.88815i) q^{4} +(0.800365 - 0.412617i) q^{5} +(0.0165606 + 0.0748116i) q^{6} +(-3.08653 + 2.42727i) q^{7} +(0.169702 + 0.0498289i) q^{8} +(-0.306974 - 2.98425i) q^{9} +(0.00566909 - 0.0394294i) q^{10} +(-1.36732 + 0.130563i) q^{11} +(-3.18625 - 1.35068i) q^{12} +(-0.321955 - 0.253188i) q^{13} +(0.00826526 + 0.173509i) q^{14} +(-0.398163 + 1.50797i) q^{15} +(-3.13499 + 2.46538i) q^{16} +(3.35687 + 3.87403i) q^{17} +(-0.115416 - 0.0655159i) q^{18} +(0.0198468 - 0.0229044i) q^{19} +(1.30212 + 1.24157i) q^{20} +(0.460406 - 6.78549i) q^{21} +(-0.0303813 + 0.0526220i) q^{22} +(3.70379 + 3.04663i) q^{23} +(-0.260994 + 0.160395i) q^{24} +(-2.42995 + 3.41239i) q^{25} +(-0.0173853 + 0.00510478i) q^{26} +(4.19360 + 3.06818i) q^{27} +(-6.60009 - 4.24162i) q^{28} +(2.00377 - 5.78951i) q^{29} +(0.0441231 + 0.0530434i) q^{30} +(0.0698557 - 0.0666073i) q^{31} +(0.0252263 + 0.529564i) q^{32} +(1.41874 - 1.90971i) q^{33} +(0.225741 - 0.0215557i) q^{34} +(-1.46882 + 3.21626i) q^{35} +(5.43412 - 2.52981i) q^{36} +(6.12138 - 3.93397i) q^{37} +(-0.000316087 - 0.00130293i) q^{38} +(0.699164 - 0.120197i) q^{39} +(0.156383 - 0.0301404i) q^{40} +(8.23813 - 4.24705i) q^{41} +(-0.232703 - 0.190711i) q^{42} +(3.69553 + 3.52369i) q^{43} +(-1.14006 - 2.49638i) q^{44} +(-1.47704 - 2.26183i) q^{45} +(0.204828 - 0.0552887i) q^{46} +(-0.422804 - 0.732318i) q^{47} +(0.467635 - 6.89203i) q^{48} +(1.98469 - 8.18099i) q^{49} +(0.0606124 + 0.175128i) q^{50} +(-8.87682 - 0.178873i) q^{51} +(0.267662 - 0.773357i) q^{52} +(0.140934 + 0.980215i) q^{53} +(0.218173 - 0.0723863i) q^{54} +(-1.04048 + 0.668676i) q^{55} +(-0.644736 + 0.258114i) q^{56} +(0.00642224 + 0.0520987i) q^{57} +(-0.157209 - 0.220769i) q^{58} +(-6.06757 - 4.77159i) q^{59} +(-3.10748 + 0.233661i) q^{60} +(2.15578 + 8.88625i) q^{61} +(-0.000607672 - 0.00422645i) q^{62} +(8.19107 + 8.46587i) q^{63} +(-6.69055 - 4.29975i) q^{64} +(-0.362151 - 0.0697989i) q^{65} +(-0.0324112 - 0.100129i) q^{66} +(5.84580 + 0.558207i) q^{67} +(-5.12106 + 8.86994i) q^{68} +(-8.21545 + 1.22734i) q^{69} +(0.0782081 + 0.135460i) q^{70} +(-3.61317 - 7.91173i) q^{71} +(0.0966080 - 0.521728i) q^{72} +(-9.12081 + 10.5260i) q^{73} +(0.0153165 - 0.321534i) q^{74} +(-1.56822 - 7.08434i) q^{75} +(0.0562168 + 0.0225058i) q^{76} +(3.90335 - 3.72183i) q^{77} +(0.0136096 - 0.0282789i) q^{78} +(0.626807 - 0.250936i) q^{79} +(-1.49188 + 3.26675i) q^{80} +(-8.81153 + 1.83217i) q^{81} +(0.0583517 - 0.405845i) q^{82} +(13.4543 + 6.93618i) q^{83} +(13.1129 - 3.56497i) q^{84} +(4.28521 + 1.71554i) q^{85} +(0.221807 - 0.0427497i) q^{86} +(5.11946 + 9.29472i) q^{87} +(-0.238541 - 0.0459751i) q^{88} +(11.8152 - 3.46926i) q^{89} +(-0.119408 - 0.00481422i) q^{90} +1.60828 q^{91} +(-3.33209 + 8.98428i) q^{92} +(0.00458885 + 0.167117i) q^{93} +(-0.0372387 - 0.00355586i) q^{94} +(0.00643393 - 0.0265210i) q^{95} +(-0.710228 - 0.582065i) q^{96} +(0.450863 - 9.46478i) q^{97} +(-0.243876 - 0.281448i) q^{98} +(0.809363 + 4.04034i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 9 q^{2} - 20 q^{3} + 11 q^{4} - 11 q^{5} - 17 q^{6} - 9 q^{7} - 50 q^{8} - 24 q^{9} - 44 q^{10} - 17 q^{11} - 30 q^{12} - 9 q^{13} - 21 q^{14} - 34 q^{15} + 11 q^{16} - 20 q^{17} + 3 q^{18} - 36 q^{19}+ \cdots - 220 q^{99}+O(q^{100}) $ 440 * q - 9 * q^2 - 20 * q^3 + 11 * q^4 - 11 * q^5 - 17 * q^6 - 9 * q^7 - 50 * q^8 - 24 * q^9 - 44 * q^10 - 17 * q^11 - 30 * q^12 - 9 * q^13 - 21 * q^14 - 34 * q^15 + 11 * q^16 - 20 * q^17 + 3 * q^18 - 36 * q^19 - 25 * q^20 + 3 * q^21 - 28 * q^22 - 5 * q^23 - 172 * q^24 + 11 * q^25 - 48 * q^26 + 31 * q^27 - 60 * q^28 + 9 * q^29 + 12 * q^30 - 3 * q^31 - 3 * q^32 - 44 * q^33 - 17 * q^34 - 56 * q^35 + 47 * q^36 - 48 * q^37 + 3 * q^38 - 64 * q^39 + 55 * q^40 - 9 * q^41 - 80 * q^42 - 9 * q^43 + 24 * q^44 - 56 * q^45 - 44 * q^46 - 12 * q^47 + 4 * q^48 - 53 * q^49 + 27 * q^50 + 14 * q^51 - 12 * q^52 - 84 * q^53 - 18 * q^54 - 68 * q^55 - 125 * q^56 + 27 * q^57 - 8 * q^58 + 81 * q^59 + 88 * q^60 + 3 * q^61 + 58 * q^62 + 43 * q^63 - 70 * q^64 - 84 * q^65 + 35 * q^66 - 3 * q^67 + 194 * q^68 + 33 * q^69 - 10 * q^70 + 86 * q^71 + 182 * q^72 - 36 * q^73 - 57 * q^74 + 55 * q^75 - 21 * q^76 + 91 * q^77 + 191 * q^78 - 9 * q^79 + 220 * q^80 - 228 * q^81 - 62 * q^82 - 68 * q^83 + 144 * q^84 + q^85 - 53 * q^86 + 160 * q^87 + 83 * q^88 - 28 * q^89 - 314 * q^90 - 108 * q^91 + q^92 + 132 * q^93 + 48 * q^94 - 3 * q^95 + 174 * q^96 - 36 * q^97 - 156 * q^98 - 220 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.0256606	−	0.0360353i	0.0181448	−	0.0254808i	−0.805404	−	0.592726i	$-0.798052\pi$
$2$	0.0256606	−	0.0360353i	0.0181448	−	0.0254808i	0.823549	+	0.567246i	$0.191991\pi$
$3$	−1.16039	+	1.28588i	−0.669954	+	0.742403i
$3$	−1.16039	+	1.28588i	−0.669954	+	0.742403i
$4$	0.653496	+	1.88815i	0.326748	+	0.944076i
$5$	0.800365	−	0.412617i	0.357934	−	0.184528i	−0.269875	−	0.962895i	$-0.586982\pi$
$5$	0.800365	−	0.412617i	0.357934	−	0.184528i	0.627809	+	0.778368i	$0.283952\pi$
$6$	0.0165606	+	0.0748116i	0.00676085	+	0.0305417i
$7$	−3.08653	+	2.42727i	−1.16660	+	0.917422i	−0.997671	−	0.0682064i	$-0.978272\pi$
$7$	−3.08653	+	2.42727i	−1.16660	+	0.917422i	−0.168926	+	0.985629i	$0.554030\pi$
$8$	0.169702	+	0.0498289i	0.0599986	+	0.0176172i
$9$	−0.306974	−	2.98425i	−0.102325	−	0.994751i
$10$	0.00566909	−	0.0394294i	0.00179272	−	0.0124687i
$11$	−1.36732	+	0.130563i	−0.412261	+	0.0393662i	−0.299126	−	0.954213i	$-0.596695\pi$
$11$	−1.36732	+	0.130563i	−0.412261	+	0.0393662i	−0.113135	+	0.993580i	$0.536089\pi$
$12$	−3.18625	−	1.35068i	−0.919791	−	0.389908i
$13$	−0.321955	−	0.253188i	−0.0892942	−	0.0702218i	0.572514	−	0.819895i	$-0.305968\pi$
$13$	−0.321955	−	0.253188i	−0.0892942	−	0.0702218i	−0.661808	+	0.749673i	$0.730211\pi$
$14$	0.00826526	+	0.173509i	0.00220898	+	0.0463723i
$15$	−0.398163	+	1.50797i	−0.102805	+	0.389357i
$16$	−3.13499	+	2.46538i	−0.783746	+	0.616345i
$17$	3.35687	+	3.87403i	0.814160	+	0.939591i	0.999068	−	0.0431653i	$-0.0137442\pi$
$17$	3.35687	+	3.87403i	0.814160	+	0.939591i	−0.184908	+	0.982756i	$0.559199\pi$
$18$	−0.115416	−	0.0655159i	−0.0272037	−	0.0154422i
$19$	0.0198468	−	0.0229044i	0.00455317	−	0.00525463i	−0.753468	−	0.657484i	$-0.771621\pi$
$19$	0.0198468	−	0.0229044i	0.00455317	−	0.00525463i	0.758022	+	0.652229i	$0.226166\pi$
$20$	1.30212	+	1.24157i	0.291163	+	0.277623i
$21$	0.460406	−	6.78549i	0.100469	−	1.48072i
$22$	−0.0303813	+	0.0526220i	−0.00647732	+	0.0112190i
$23$	3.70379	+	3.04663i	0.772293	+	0.635266i
$23$	3.70379	+	3.04663i	0.772293	+	0.635266i
$24$	−0.260994	+	0.160395i	−0.0532753	+	0.0327404i
$25$	−2.42995	+	3.41239i	−0.485991	+	0.682478i
$26$	−0.0173853	+	0.00510478i	−0.00340953	+	0.00100113i
$27$	4.19360	+	3.06818i	0.807059	+	0.590471i
$28$	−6.60009	−	4.24162i	−1.24730	−	0.801591i
$29$	2.00377	−	5.78951i	0.372091	−	1.07509i	−0.591177	−	0.806542i	$-0.701336\pi$
$29$	2.00377	−	5.78951i	0.372091	−	1.07509i	0.963268	−	0.268543i	$-0.0865423\pi$
$30$	0.0441231	+	0.0530434i	0.00805574	+	0.00968436i
$31$	0.0698557	−	0.0666073i	0.0125465	−	0.0119630i	−0.683780	−	0.729688i	$-0.739665\pi$
$31$	0.0698557	−	0.0666073i	0.0125465	−	0.0119630i	0.696326	+	0.717725i	$0.254817\pi$
$32$	0.0252263	+	0.529564i	0.00445941	+	0.0936146i
$33$	1.41874	−	1.90971i	0.246970	−	0.332438i
$34$	0.225741	−	0.0215557i	0.0387143	−	0.00369677i
$35$	−1.46882	+	3.21626i	−0.248275	+	0.543647i
$36$	5.43412	−	2.52981i	0.905686	−	0.421635i
$37$	6.12138	−	3.93397i	1.00635	−	0.646741i	0.0699030	−	0.997554i	$-0.477731\pi$
$37$	6.12138	−	3.93397i	1.00635	−	0.646741i	0.936446	+	0.350813i	$0.114095\pi$
$38$	−0.000316087	−	0.00130293i	−5.12760e−5	−	0.000211363i
$39$	0.699164	−	0.120197i	0.111956	−	0.0192470i
$40$	0.156383	−	0.0301404i	0.0247264	−	0.00476562i
$41$	8.23813	−	4.24705i	1.28658	−	0.663278i	0.327082	−	0.944996i	$-0.393935\pi$
$41$	8.23813	−	4.24705i	1.28658	−	0.663278i	0.959497	+	0.281718i	$0.0909043\pi$
$42$	−0.232703	−	0.190711i	−0.0359068	−	0.0294273i
$43$	3.69553	+	3.52369i	0.563564	+	0.537357i	0.917408	−	0.397947i	$-0.130277\pi$
$43$	3.69553	+	3.52369i	0.563564	+	0.537357i	−0.353844	+	0.935304i	$0.615126\pi$
$44$	−1.14006	−	2.49638i	−0.171870	−	0.376343i
$45$	−1.47704	−	2.26183i	−0.220185	−	0.337174i
$46$	0.204828	−	0.0552887i	0.0302002	−	0.00815187i
$47$	−0.422804	−	0.732318i	−0.0616723	−	0.106820i	0.833541	−	0.552458i	$-0.186310\pi$
$47$	−0.422804	−	0.732318i	−0.0616723	−	0.106820i	−0.895213	+	0.445638i	$0.852977\pi$
$48$	0.467635	−	6.89203i	0.0674973	−	0.994778i
$49$	1.98469	−	8.18099i	0.283527	−	1.16871i
$50$	0.0606124	+	0.175128i	0.00857189	+	0.0247669i
$51$	−8.87682	−	0.178873i	−1.24300	−	0.0250472i
$52$	0.267662	−	0.773357i	0.0371180	−	0.107245i
$53$	0.140934	+	0.980215i	0.0193587	+	0.134643i	0.997209	−	0.0746638i	$-0.0237884\pi$
$53$	0.140934	+	0.980215i	0.0193587	+	0.134643i	−0.977850	+	0.209307i	$0.932879\pi$
$54$	0.218173	−	0.0723863i	0.0296896	−	0.00985053i
$55$	−1.04048	+	0.668676i	−0.140298	+	0.0901642i
$56$	−0.644736	+	0.258114i	−0.0861565	+	0.0344919i
$57$	0.00642224	+	0.0520987i	0.000850647	+	0.00690065i
$58$	−0.157209	−	0.220769i	−0.0206425	−	0.0289884i
$59$	−6.06757	−	4.77159i	−0.789931	−	0.621208i	0.139493	−	0.990223i	$-0.455453\pi$
$59$	−6.06757	−	4.77159i	−0.789931	−	0.621208i	−0.929424	+	0.369015i	$0.879695\pi$
$60$	−3.10748	+	0.233661i	−0.401174	+	0.0301655i
$61$	2.15578	+	8.88625i	0.276019	+	1.13777i	0.925911	+	0.377741i	$0.123299\pi$
$61$	2.15578	+	8.88625i	0.276019	+	1.13777i	−0.649892	+	0.760027i	$0.725186\pi$
$62$	−0.000607672	−	0.00422645i	−7.71745e−5	−	0.000536760i
$63$	8.19107	+	8.46587i	1.03198	+	1.06660i
$64$	−6.69055	−	4.29975i	−0.836319	−	0.537469i
$65$	−0.362151	−	0.0697989i	−0.0449193	−	0.00865749i
$66$	−0.0324112	−	0.100129i	−0.00398955	−	0.0123250i
$67$	5.84580	+	0.558207i	0.714179	+	0.0681958i	0.445819	−	0.895123i	$-0.352912\pi$
$67$	5.84580	+	0.558207i	0.714179	+	0.0681958i	0.268359	+	0.963319i	$0.413518\pi$
$68$	−5.12106	+	8.86994i	−0.621020	+	1.07564i
$69$	−8.21545	+	1.22734i	−0.989024	+	0.147754i
$70$	0.0782081	+	0.135460i	0.00934765	+	0.0161906i
$71$	−3.61317	−	7.91173i	−0.428804	−	0.938950i	−0.993519	−	0.113664i	$-0.963741\pi$
$71$	−3.61317	−	7.91173i	−0.428804	−	0.938950i	0.564715	−	0.825286i	$-0.308986\pi$
$72$	0.0966080	−	0.521728i	0.0113854	−	0.0614863i
$73$	−9.12081	+	10.5260i	−1.06751	+	1.23197i	−0.0958983	+	0.995391i	$0.530572\pi$
$73$	−9.12081	+	10.5260i	−1.06751	+	1.23197i	−0.971612	+	0.236581i	$0.923973\pi$
$74$	0.0153165	−	0.321534i	0.00178051	−	0.0373776i
$75$	−1.56822	−	7.08434i	−0.181083	−	0.818030i
$76$	0.0562168	+	0.0225058i	0.00644851	+	0.00258160i
$77$	3.90335	−	3.72183i	0.444828	−	0.424142i
$78$	0.0136096	−	0.0282789i	0.00154099	−	0.00320196i
$79$	0.626807	−	0.250936i	0.0705213	−	0.0282325i	−0.336134	−	0.941814i	$-0.609119\pi$
$79$	0.626807	−	0.250936i	0.0705213	−	0.0282325i	0.406655	+	0.913582i	$0.366695\pi$
$80$	−1.49188	+	3.26675i	−0.166797	+	0.365234i
$81$	−8.81153	+	1.83217i	−0.979059	+	0.203575i
$82$	0.0583517	−	0.405845i	0.00644387	−	0.0448181i
$83$	13.4543	+	6.93618i	1.47680	+	0.761345i	0.993470	−	0.114091i	$-0.0363957\pi$
$83$	13.4543	+	6.93618i	1.47680	+	0.761345i	0.483333	+	0.875437i	$0.339426\pi$
$84$	13.1129	−	3.56497i	1.43074	−	0.388971i
$85$	4.28521	+	1.71554i	0.464796	+	0.186076i
$86$	0.221807	−	0.0427497i	0.0239180	−	0.00460982i
$87$	5.11946	+	9.29472i	0.548863	+	0.996498i
$88$	−0.238541	−	0.0459751i	−0.0254286	−	0.00490096i
$89$	11.8152	−	3.46926i	1.25241	−	0.367741i	0.412746	−	0.910846i	$-0.364570\pi$
$89$	11.8152	−	3.46926i	1.25241	−	0.367741i	0.839665	+	0.543105i	$0.182752\pi$
$90$	−0.119408	−	0.00481422i	−0.0125867	−	0.000507463i
$91$	1.60828			0.168593
$92$	−3.33209	+	8.98428i	−0.347395	+	0.936675i
$93$	0.00458885	+	0.167117i	0.000475841	+	0.0173292i
$94$	−0.0372387	−	0.00355586i	−0.00384088	−	0.000366759i
$95$	0.00643393	−	0.0265210i	0.000660107	−	0.00272100i
$96$	−0.710228	−	0.582065i	−0.0724874	−	0.0594068i
$97$	0.450863	−	9.46478i	0.0457782	−	0.961003i	−0.852813	−	0.522216i	$-0.825105\pi$
$97$	0.450863	−	9.46478i	0.0457782	−	0.961003i	0.898591	−	0.438787i	$-0.144592\pi$
$98$	−0.243876	−	0.281448i	−0.0246352	−	0.0284306i
$99$	0.809363	+	4.04034i	0.0813440	+	0.406069i
$100$	−8.03108	−	2.35814i	−0.803108	−	0.235814i
$101$	−4.92680	−	2.53994i	−0.490235	−	0.252734i	0.195340	−	0.980736i	$-0.437419\pi$
$101$	−4.92680	−	2.53994i	−0.490235	−	0.252734i	−0.685575	+	0.728002i	$0.740449\pi$
$102$	−0.234231	+	0.315289i	−0.0231923	+	0.0312183i
$103$	6.23912	+	8.76161i	0.614758	+	0.863307i	0.998182	−	0.0602651i	$-0.0191946\pi$
$103$	6.23912	+	8.76161i	0.614758	+	0.863307i	−0.383424	+	0.923572i	$0.625255\pi$
$104$	−0.0420202	−	0.0590091i	−0.00412042	−	0.00578632i
$105$	−2.43132	−	5.62084i	−0.237272	−	0.548538i
$106$	0.0389388	+	0.0200743i	0.00378207	+	0.00194979i
$107$	−18.2814	−	5.36791i	−1.76733	−	0.518936i	−0.773895	−	0.633314i	$-0.781694\pi$
$107$	−18.2814	−	5.36791i	−1.76733	−	0.518936i	−0.993437	+	0.114378i	$0.963512\pi$
$108$	−3.05268	+	9.92320i	−0.293745	+	0.954860i
$109$	6.64341	+	7.66690i	0.636323	+	0.734356i	0.978720	−	0.205199i	$-0.0657843\pi$
$109$	6.64341	+	7.66690i	0.636323	+	0.734356i	−0.342397	+	0.939555i	$0.611239\pi$
$110$	−0.00260343	+	0.0546526i	−0.000248227	+	0.00521092i
$111$	−2.04459	+	12.4363i	−0.194064	+	1.18040i
$112$	3.69207	−	15.2189i	0.348868	−	1.43805i
$113$	−18.2337	−	1.74111i	−1.71529	−	0.163790i	−0.809385	−	0.587278i	$-0.800199\pi$
$113$	−18.2337	−	1.74111i	−1.71529	−	0.163790i	−0.905902	+	0.423488i	$0.860806\pi$
$114$	0.00204219	+	0.00110546i	0.000191269	+	0.000103536i
$115$	4.22147	+	0.910171i	0.393655	+	0.0848739i
$116$	12.2409			1.13654
$117$	−0.656746	+	1.03852i	−0.0607162	+	0.0960109i
$118$	−0.327643	+	0.0962048i	−0.0301620	+	0.00885637i
$119$	−19.7644	−	3.80927i	−1.81180	−	0.349195i
$120$	−0.142709	+	0.236065i	−0.0130275	+	0.0215497i
$121$	−8.94871	+	1.72472i	−0.813519	+	0.156793i
$122$	0.375537	+	0.150342i	0.0339995	+	0.0136114i
$123$	−4.09827	+	15.5215i	−0.369529	+	1.39953i
$124$	0.171415	+	0.0883706i	0.0153935	+	0.00793591i
$125$	−1.17759	+	8.19030i	−0.105327	+	0.732563i
$126$	0.515258	−	0.0779284i	0.0459028	−	0.00694241i
$127$	8.00838	−	17.5359i	0.710629	−	1.55606i	−0.115961	−	0.993254i	$-0.536995\pi$
$127$	8.00838	−	17.5359i	0.710629	−	1.55606i	0.826589	−	0.562806i	$-0.190278\pi$
$128$	−1.31100	+	0.524846i	−0.115877	+	0.0463903i
$129$	−8.81931	+	0.663152i	−0.776497	+	0.0583873i
$130$	−0.0118083	+	0.0112591i	−0.00103565	+	0.000987492i
$131$	8.86617	+	3.54948i	0.774641	+	0.310119i	0.725092	−	0.688652i	$-0.241797\pi$
$131$	8.86617	+	3.54948i	0.774641	+	0.310119i	0.0495490	+	0.998772i	$0.484222\pi$
$132$	4.53296	+	1.43080i	0.394543	+	0.124536i
$133$	−0.00566241	+	0.118869i	−0.000490993	+	0.0103072i
$134$	0.170122	−	0.196331i	0.0146963	−	0.0169604i
$135$	4.62240	+	0.725311i	0.397832	+	0.0624248i
$136$	0.376627	+	0.824698i	0.0322955	+	0.0707173i
$137$	−3.18789	−	5.52158i	−0.272360	−	0.471741i	0.697106	−	0.716968i	$-0.254471\pi$
$137$	−3.18789	−	5.52158i	−0.272360	−	0.471741i	−0.969466	+	0.245227i	$0.921137\pi$
$138$	−0.166586	+	0.327540i	−0.0141808	+	0.0278821i
$139$	3.57352	−	6.18953i	0.303102	−	0.524989i	−0.673735	−	0.738973i	$-0.735311\pi$
$139$	3.57352	−	6.18953i	0.303102	−	0.524989i	0.976837	+	0.213985i	$0.0686443\pi$
$140$	−7.03265	−	0.671536i	−0.594367	−	0.0567552i
$141$	1.43229	+	0.306102i	0.120621	+	0.0257784i
$142$	−0.377818	−	0.0728184i	−0.0317058	−	0.00611078i
$143$	0.473271	+	0.304153i	0.0395769	+	0.0254345i
$144$	8.31968	+	8.59878i	0.693306	+	0.716565i
$145$	−0.785103	−	5.46051i	−0.0651993	−	0.453471i
$146$	0.145261	+	0.598774i	0.0120219	+	0.0495549i
$147$	8.21676	+	12.0452i	0.677707	+	0.993475i
$148$	11.4282	+	8.98726i	0.939395	+	0.738748i
$149$	−3.80454	−	5.34273i	−0.311680	−	0.437694i	0.628787	−	0.777577i	$-0.283552\pi$
$149$	−3.80454	−	5.34273i	−0.311680	−	0.437694i	−0.940467	+	0.339884i	$0.889612\pi$
$150$	−0.295528	−	0.125277i	−0.0241298	−	0.0102288i
$151$	−4.71123	+	1.88609i	−0.383395	+	0.153488i	−0.555350	−	0.831617i	$-0.687416\pi$
$151$	−4.71123	+	1.88609i	−0.383395	+	0.153488i	0.171955	+	0.985105i	$0.444991\pi$
$152$	0.00450933	−	0.00289797i	0.000365755	−	0.000235057i
$153$	10.5306	−	11.2070i	0.851350	−	0.906030i
$154$	−0.0339551	−	0.236163i	−0.00273618	−	0.0190305i
$155$	0.0284268	−	0.0821338i	0.00228329	−	0.00659714i
$156$	0.683852	+	1.24158i	0.0547520	+	0.0994059i
$157$	2.77167	+	8.00822i	0.221204	+	0.639126i	0.999931	+	0.0117630i	$0.00374436\pi$
$157$	2.77167	+	8.00822i	0.221204	+	0.639126i	−0.778727	+	0.627363i	$0.784134\pi$
$158$	0.00704171	−	0.0290263i	0.000560209	−	0.00230921i
$159$	−1.42398	−	0.956212i	−0.112929	−	0.0758325i
$160$	0.238697	+	0.413436i	0.0188707	+	0.0326850i
$161$	−18.8268	−	0.413406i	−1.48376	−	0.0325810i
$162$	−0.160086	+	0.364541i	−0.0125776	+	0.0286410i
$163$	−7.00158	−	15.3313i	−0.548406	−	1.20084i	−0.957522	−	0.288360i	$-0.906890\pi$
$163$	−7.00158	−	15.3313i	−0.548406	−	1.20084i	0.409116	−	0.912483i	$-0.365837\pi$
$164$	13.4027	+	12.7794i	1.04657	+	0.997904i
$165$	0.347529	−	2.11386i	0.0270551	−	0.164564i
$166$	0.595194	−	0.306844i	0.0461960	−	0.0238157i
$167$	−16.1888	+	3.12013i	−1.25272	+	0.241443i	−0.772110	−	0.635489i	$-0.780799\pi$
$167$	−16.1888	+	3.12013i	−1.25272	+	0.241443i	−0.480615	+	0.876932i	$0.659586\pi$
$168$	0.416245	−	1.12857i	0.0321140	−	0.0870708i
$169$	−3.02532	−	12.4705i	−0.232717	−	0.959271i
$170$	0.171781	−	0.110397i	0.0131750	−	0.00846707i
$171$	−0.0744450	−	0.0521968i	−0.00569295	−	0.00399159i
$172$	−4.23824	+	9.28045i	−0.323163	+	0.707627i
$173$	5.50554	−	0.525715i	0.418579	−	0.0399694i	0.116358	−	0.993207i	$-0.462878\pi$
$173$	5.50554	−	0.525715i	0.418579	−	0.0399694i	0.302221	+	0.953238i	$0.402272\pi$
$174$	0.466306	+	0.0540272i	0.0353506	+	0.00409579i
$175$	−0.782685	−	16.4306i	−0.0591655	−	1.24204i
$176$	3.96463	−	3.78027i	0.298845	−	0.284948i
$177$	13.1765	−	2.26524i	0.990404	−	0.170266i
$178$	0.178170	−	0.514788i	0.0133544	−	0.0385850i
$179$	1.70851	+	1.09799i	0.127700	+	0.0820679i	0.602931	−	0.797793i	$-0.293999\pi$
$179$	1.70851	+	1.09799i	0.127700	+	0.0820679i	−0.475231	+	0.879861i	$0.657636\pi$
$180$	3.30544	−	4.26698i	0.246373	−	0.318042i
$181$	8.09587	−	2.37716i	0.601761	−	0.176693i	0.0333583	−	0.999443i	$-0.489380\pi$
$181$	8.09587	−	2.37716i	0.601761	−	0.176693i	0.568403	+	0.822750i	$0.307562\pi$
$182$	0.0412694	−	0.0579548i	0.00305909	−	0.00429590i
$183$	−13.9282	−	7.53947i	−1.02960	−	0.557334i
$184$	0.476728	+	0.701573i	0.0351449	+	0.0517207i
$185$	3.27612	−	5.67440i	0.240865	−	0.417190i
$186$	0.00613985	+	0.00412296i	0.000450196	+	0.000302310i
$187$	−5.09570	−	4.85874i	−0.372635	−	0.355306i
$188$	1.10643	−	1.27688i	0.0806945	−	0.0931264i
$189$	−20.3910	+	0.708999i	−1.48322	+	0.0515721i
$190$	−0.000790594	0	0.000912395i	−5.73557e−5	0	6.61921e-5i
$191$	8.54146	−	6.71708i	0.618038	−	0.486031i	−0.259368	−	0.965779i	$-0.583514\pi$
$191$	8.54146	−	6.71708i	0.618038	−	0.486031i	0.877406	+	0.479748i	$0.159272\pi$
$192$	13.2926	−	3.61383i	0.959313	−	0.260806i
$193$	0.764177	+	16.0420i	0.0550066	+	1.15473i	0.842601	+	0.538538i	$0.181023\pi$
$193$	0.764177	+	16.0420i	0.0550066	+	1.15473i	−0.787595	+	0.616194i	$0.788674\pi$
$194$	−0.329497	−	0.259119i	−0.0236565	−	0.0186037i
$195$	0.509991	−	0.384689i	0.0365212	−	0.0275481i
$196$	16.7439	−	1.59885i	1.19600	−	0.114204i
$197$	3.45991	−	24.0642i	0.246508	−	1.71450i	−0.371585	−	0.928399i	$-0.621185\pi$
$197$	3.45991	−	24.0642i	0.246508	−	1.71450i	0.618093	−	0.786105i	$-0.287906\pi$
$198$	0.166364	+	0.0745119i	0.0118229	+	0.00529533i
$199$	−0.656555	−	0.192782i	−0.0465419	−	0.0136659i	0.258379	−	0.966044i	$-0.416812\pi$
$199$	−0.656555	−	0.192782i	−0.0465419	−	0.0136659i	−0.304921	+	0.952378i	$0.598630\pi$
$200$	−0.582402	+	0.458006i	−0.0411821	+	0.0323859i
$201$	−7.50122	+	6.86926i	−0.529095	+	0.484520i
$202$	−0.217952	+	0.112362i	−0.0153351	+	0.00790578i
$203$	7.86803	+	22.7332i	0.552227	+	1.59556i
$204$	−5.46323	−	16.8777i	−0.382503	−	1.18167i
$205$	4.84111	−	6.79838i	0.338118	−	0.474820i
$206$	0.475827			0.0331524
$207$	7.95495	−	11.9883i	0.552907	−	0.833243i
$208$	1.63353			0.113265
$209$	−0.0241464	+	0.0339088i	−0.00167024	+	0.00234552i
$210$	−0.264938	−	0.0566211i	−0.0182824	−	0.00390723i
$211$	3.62816	+	10.4829i	0.249773	+	0.721672i	0.998284	+	0.0585498i	$0.0186476\pi$
$211$	3.62816	+	10.4829i	0.249773	+	0.721672i	−0.748512	+	0.663122i	$0.769231\pi$
$212$	−1.75870	+	0.906671i	−0.120788	+	0.0622704i
$213$	14.3662	+	4.53462i	0.984358	+	0.310707i
$214$	−0.662547	+	0.521033i	−0.0452908	+	0.0356171i
$215$	4.41171	+	1.29540i	0.300876	+	0.0883452i
$216$	0.558777	+	0.729637i	0.0380199	+	0.0496455i
$217$	−0.0539375	+	0.375144i	−0.00366152	+	0.0254664i
$218$	0.446753	−	0.0426597i	0.0302579	−	0.00288928i
$219$	−2.95141	−	23.9425i	−0.199438	−	1.61789i
$220$	−1.94251	−	1.52761i	−0.130964	−	0.102991i
$221$	−0.0999011	−	2.09718i	−0.00672008	−	0.141072i
$222$	0.395681	+	0.392801i	0.0265563	+	0.0263631i
$223$	−8.70601	+	6.84648i	−0.582997	+	0.458474i	−0.865581	−	0.500768i	$-0.833051\pi$
$223$	−8.70601	+	6.84648i	−0.582997	+	0.458474i	0.282584	+	0.959243i	$0.408808\pi$
$224$	−1.36326	−	1.57328i	−0.0910865	−	0.105119i
$225$	10.9294	+	6.20408i	0.728625	+	0.413605i
$226$	−0.530631	+	0.612381i	−0.0352970	+	0.0407349i
$227$	−4.38403	−	4.18016i	−0.290978	−	0.277447i	0.530503	−	0.847683i	$-0.322003\pi$
$227$	−4.38403	−	4.18016i	−0.290978	−	0.277447i	−0.821481	+	0.570236i	$0.806852\pi$
$228$	−0.0941734	+	0.0461725i	−0.00623679	+	0.00305785i
$229$	0.900624	−	1.55993i	0.0595149	−	0.103083i	−0.834733	−	0.550655i	$-0.814378\pi$
$229$	0.900624	−	1.55993i	0.0595149	−	0.103083i	0.894248	+	0.447572i	$0.147711\pi$
$230$	0.141124	−	0.128767i	0.00930544	−	0.00849061i
$231$	0.256412	+	9.33802i	0.0168707	+	0.614397i
$232$	0.628528	−	0.882643i	0.0412649	−	0.0579484i
$233$	15.0485	−	4.41863i	0.985858	−	0.289474i	0.251218	−	0.967931i	$-0.419169\pi$
$233$	15.0485	−	4.41863i	0.985858	−	0.289474i	0.734641	+	0.678457i	$0.237351\pi$
$234$	0.0205708	+	0.0503150i	0.00134475	+	0.00328920i
$235$	−0.640564	−	0.411666i	−0.0417858	−	0.0268541i
$236$	5.04436	−	14.5747i	0.328360	−	0.948733i
$237$	−0.404670	+	1.09718i	−0.0262861	+	0.0712697i
$238$	−0.644435	+	0.614467i	−0.0417725	+	0.0398300i
$239$	−0.533514	−	11.1998i	−0.0345102	−	0.724458i	−0.948129	−	0.317886i	$-0.897027\pi$
$239$	−0.533514	−	11.1998i	−0.0345102	−	0.724458i	0.913619	−	0.406572i	$-0.133276\pi$
$240$	−2.46949	−	5.70909i	−0.159405	−	0.368520i
$241$	10.6925	−	1.02101i	0.688767	−	0.0657693i	0.255197	−	0.966889i	$-0.417860\pi$
$241$	10.6925	−	1.02101i	0.688767	−	0.0657693i	0.433570	+	0.901120i	$0.357254\pi$
$242$	−0.167479	+	0.366727i	−0.0107659	+	0.0235741i
$243$	7.86889	−	13.4566i	0.504790	−	0.863242i
$244$	−15.3698	+	9.87757i	−0.983950	+	0.632346i
$245$	−1.78714	−	7.36670i	−0.114176	−	0.470641i
$246$	0.454157	+	0.545974i	0.0289560	+	0.0348100i
$247$	−0.0121889	+	0.00234922i	−0.000775561	+	0.000149477i
$248$	0.0151736	−	0.00782252i	0.000963523	−	0.000496731i
$249$	−24.5314	+	9.25193i	−1.55461	+	0.586318i
$250$	0.264922	+	0.252603i	0.0167552	+	0.0159760i
$251$	11.6410	+	25.4902i	0.734772	+	1.60893i	0.791968	+	0.610563i	$0.209057\pi$
$251$	11.6410	+	25.4902i	0.734772	+	1.60893i	−0.0571959	+	0.998363i	$0.518216\pi$
$252$	−10.6320	+	20.9984i	−0.669754	+	1.32278i
$253$	−5.46203	−	3.68213i	−0.343395	−	0.231493i
$254$	−0.426411	−	0.738566i	−0.0267554	−	0.0463418i
$255$	−7.17851	+	3.51957i	−0.449536	+	0.220404i
$256$	3.73529	−	15.3971i	0.233455	−	0.962316i
$257$	5.93961	+	17.1614i	0.370503	+	1.07050i	0.964055	+	0.265702i	$0.0856038\pi$
$257$	5.93961	+	17.1614i	0.370503	+	1.07050i	−0.593552	+	0.804795i	$0.702275\pi$
$258$	−0.202412	+	0.334823i	−0.0126016	+	0.0208452i
$259$	−9.34498	+	27.0006i	−0.580669	+	1.67773i
$260$	−0.104873	−	0.729410i	−0.00650397	−	0.0452361i
$261$	−17.8925	−	4.20253i	−1.10752	−	0.260130i
$262$	0.355418	−	0.228413i	0.0219578	−	0.0141114i
$263$	−0.623953	+	0.249793i	−0.0384746	+	0.0154029i	−0.390820	−	0.920467i	$-0.627808\pi$
$263$	−0.623953	+	0.249793i	−0.0384746	+	0.0154029i	0.352345	+	0.935870i	$0.385384\pi$
$264$	0.335920	−	0.253386i	0.0206745	−	0.0155949i
$265$	0.517252	+	0.726379i	0.0317745	+	0.0446211i
$266$	0.00413817	+	0.00325429i	0.000253727	+	0.000199533i
$267$	−9.24925	+	19.2187i	−0.566045	+	1.17616i
$268$	2.76623	+	11.4026i	0.168974	+	0.696522i
$269$	−2.96674	−	20.6342i	−0.180886	−	1.25809i	−0.854675	−	0.519163i	$-0.826244\pi$
$269$	−2.96674	−	20.6342i	−0.180886	−	1.25809i	0.673790	−	0.738923i	$-0.264665\pi$
$270$	0.144750	−	0.147957i	0.00880922	−	0.00900440i
$271$	20.2132	+	12.9903i	1.22787	+	0.789102i	0.983557	−	0.180596i	$-0.0578026\pi$
$271$	20.2132	+	12.9903i	1.22787	+	0.789102i	0.244309	+	0.969697i	$0.421439\pi$
$272$	−20.0747	−	3.86908i	−1.21721	−	0.234597i
$273$	−1.86624	+	2.06805i	−0.112950	+	0.125164i
$274$	−0.280775	−	0.0268108i	−0.0169622	−	0.00161970i
$275$	2.87698	−	4.98308i	0.173489	−	0.300491i
$276$	−7.68616	−	14.7100i	−0.462653	−	0.885436i
$277$	2.30051	+	3.98461i	0.138224	+	0.239412i	0.926825	−	0.375495i	$-0.122527\pi$
$277$	2.30051	+	3.98461i	0.138224	+	0.239412i	−0.788600	+	0.614906i	$0.789194\pi$
$278$	−0.131343	−	0.287600i	−0.00787740	−	0.0172491i
$279$	−0.220217	−	0.188020i	−0.0131840	−	0.0112565i
$280$	−0.409523	+	0.472614i	−0.0244737	+	0.0282441i
$281$	−1.14455	+	24.0271i	−0.0682782	+	1.43334i	0.661650	+	0.749812i	$0.269856\pi$
$281$	−1.14455	+	24.0271i	−0.0682782	+	1.43334i	−0.729929	+	0.683523i	$0.760447\pi$
$282$	0.0477840	−	0.0437583i	0.00284549	−	0.00260577i
$283$	−6.97388	−	2.79192i	−0.414554	−	0.165962i	0.155003	−	0.987914i	$-0.450461\pi$
$283$	−6.97388	−	2.79192i	−0.414554	−	0.165962i	−0.569558	+	0.821951i	$0.692885\pi$
$284$	12.5774	−	11.9925i	0.746329	−	0.711624i
$285$	0.0266370	+	0.0390481i	0.00157784	+	0.00231301i
$286$	0.0231047	−	0.00924971i	0.00136621	−	0.000546947i
$287$	−15.1185	+	33.1048i	−0.892414	+	1.95411i
$288$	1.57261	−	0.237844i	0.0926669	−	0.0140151i
$289$	−1.32021	+	9.18225i	−0.0776593	+	0.540132i
$290$	−0.216917	−	0.111829i	−0.0127378	−	0.00656681i
$291$	11.6474	+	11.5626i	0.682782	+	0.677813i
$292$	−25.8351	−	10.3428i	−1.51188	−	0.605266i
$293$	20.7778	−	4.00460i	1.21385	−	0.233951i	0.458156	−	0.888872i	$-0.348510\pi$
$293$	20.7778	−	4.00460i	1.21385	−	0.233951i	0.755697	+	0.654921i	$0.227298\pi$
$294$	0.644901	+	0.0129951i	0.0376114	+	0.000757891i
$295$	−6.82511	−	1.31543i	−0.397373	−	0.0765875i
$296$	1.23483	−	0.362580i	0.0717732	−	0.0210745i
$297$	−6.13457	−	3.64764i	−0.355964	−	0.211657i
$298$	−0.290154			−0.0168082
$299$	−0.421082	−	1.91863i	−0.0243518	−	0.110957i
$300$	12.3515	−	7.59063i	0.713114	−	0.438245i
$301$	−19.9593	−	1.90588i	−1.15044	−	0.109853i
$302$	−0.0529272	+	0.218169i	−0.00304562	+	0.0125542i
$303$	8.98309	−	3.38794i	0.516065	−	0.194632i
$304$	−0.00575131	+	0.120735i	−0.000329860	+	0.00692462i
$305$	5.39203	+	6.22273i	0.308747	+	0.356313i
$306$	−0.133624	−	0.667052i	−0.00763878	−	0.0381328i
$307$	19.0090	+	5.58156i	1.08490	+	0.318556i	0.774838	−	0.632159i	$-0.217831\pi$
$307$	19.0090	+	5.58156i	1.08490	+	0.318556i	0.310065	+	0.950716i	$0.399649\pi$
$308$	9.57821	+	4.93791i	0.545769	+	0.281363i
$309$	−18.5062	−	2.14417i	−1.05278	−	0.121977i
$310$	−0.00223027	−	0.00313197i	−0.000126671	−	0.000177884i
$311$	−9.08955	−	12.7645i	−0.515421	−	0.723808i	0.472056	−	0.881569i	$-0.343512\pi$
$311$	−9.08955	−	12.7645i	−0.515421	−	0.723808i	−0.987477	+	0.157761i	$0.949573\pi$
$312$	0.124639	+	0.0144409i	0.00705627	+	0.000817553i
$313$	−27.4945	−	14.1744i	−1.55408	−	0.801184i	−0.554559	−	0.832145i	$-0.687113\pi$
$313$	−27.4945	−	14.1744i	−1.55408	−	0.801184i	−0.999521	+	0.0309610i	$0.990143\pi$
$314$	0.359701	+	0.105618i	0.0202991	+	0.00596036i
$315$	10.0490	+	3.39601i	0.566198	+	0.191344i
$316$	0.883421	+	1.01952i	0.0496963	+	0.0573526i
$317$	0.0945924	−	1.98574i	0.00531284	−	0.111530i	−0.994653	−	0.103273i	$-0.967069\pi$
$317$	0.0945924	−	1.98574i	0.00531284	−	0.111530i	0.999966	−	0.00825740i	$-0.00262844\pi$
$318$	−0.0709975	+	0.0267765i	−0.00398134	+	0.00150155i
$319$	−1.98389	+	8.17771i	−0.111077	+	0.457864i
$320$	−7.12903	−	0.680740i	−0.398525	−	0.0380545i
$321$	28.1161	−	17.2788i	1.56929	−	0.964410i
$322$	−0.498006	+	0.667822i	−0.0277528	+	0.0372163i
$323$	0.155355			0.00864421
$324$	−9.21773	−	15.4402i	−0.512096	−	0.857789i
$325$	1.64631	−	0.483401i	0.0913210	−	0.0268143i
$326$	−0.732134	−	0.141107i	−0.0405492	−	0.00781521i
$327$	−17.5677	−	0.353999i	−0.971495	−	0.0195762i
$328$	1.60965	−	0.310234i	0.0888780	−	0.0171298i
$329$	3.08253	+	1.23406i	0.169945	+	0.0680359i
$330$	−0.0672557	−	0.0667663i	−0.00370231	−	0.00367536i
$331$	−16.4776	−	8.49478i	−0.905689	−	0.466915i	−0.0585488	−	0.998285i	$-0.518647\pi$
$331$	−16.4776	−	8.49478i	−0.905689	−	0.466915i	−0.847140	+	0.531369i	$0.821678\pi$
$332$	−4.30423	+	29.9366i	−0.236225	+	1.64298i
$333$	−13.6191	−	17.0601i	−0.746320	−	0.934889i
$334$	−0.302979	+	0.663432i	−0.0165783	+	0.0363014i
$335$	4.90910	−	1.96531i	0.268213	−	0.107376i
$336$	15.2854	+	22.4075i	0.833890	+	1.22243i
$337$	−23.7444	+	22.6402i	−1.29344	+	1.23329i	−0.336949	+	0.941523i	$0.609395\pi$
$337$	−23.7444	+	22.6402i	−1.29344	+	1.23329i	−0.956489	+	0.291768i	$0.905756\pi$
$338$	−0.527010	−	0.210983i	−0.0286656	−	0.0114760i
$339$	23.3972	−	21.4260i	1.27076	−	1.16370i
$340$	−0.438833	+	9.21223i	−0.0237990	+	0.499603i
$341$	−0.0868184	+	0.100194i	−0.00470148	+	0.00542579i
$342$	−0.00379123	+	0.00134325i	−0.000205006	+	7.26345e-5i
$343$	2.31348	+	5.06582i	0.124916	+	0.273528i
$344$	0.451557	+	0.782119i	0.0243463	+	0.0421690i
$345$	−6.06894	+	4.37215i	−0.326741	+	0.235389i
$346$	0.122331	−	0.211884i	0.00657657	−	0.0113910i
$347$	25.9360	+	2.47659i	1.39232	+	0.132950i	0.764106	−	0.645091i	$-0.223180\pi$
$347$	25.9360	+	2.47659i	1.39232	+	0.132950i	0.628214	+	0.778041i	$0.283786\pi$
$348$	−14.2043	+	15.7404i	−0.761431	+	0.843772i
$349$	13.7830	+	2.65645i	0.737786	+	0.142197i	0.544281	−	0.838903i	$-0.316802\pi$
$349$	13.7830	+	2.65645i	0.737786	+	0.142197i	0.193505	+	0.981099i	$0.438015\pi$
$350$	−0.612165	−	0.393415i	−0.0327216	−	0.0210289i
$351$	−0.573325	−	2.04958i	−0.0306018	−	0.109399i
$352$	−0.103634	−	0.720788i	−0.00552369	−	0.0384181i
$353$	6.06980	+	25.0201i	0.323063	+	1.33168i	0.869396	+	0.494116i	$0.164508\pi$
$353$	6.06980	+	25.0201i	0.323063	+	1.33168i	−0.546333	+	0.837568i	$0.683977\pi$
$354$	0.256487	−	0.532945i	0.0136322	−	0.0283257i
$355$	−6.15637	−	4.84142i	−0.326746	−	0.256956i
$356$	14.2717	+	20.0418i	0.756398	+	1.06221i
$357$	27.8327	−	20.9944i	1.47306	−	1.11114i
$358$	0.0834080	−	0.0333915i	0.00440825	−	0.00176480i
$359$	9.13191	−	5.86872i	0.481964	−	0.309739i	−0.277002	−	0.960869i	$-0.589341\pi$
$359$	9.13191	−	5.86872i	0.481964	−	0.309739i	0.758966	+	0.651130i	$0.225705\pi$
$360$	−0.137952	−	0.457436i	−0.00727073	−	0.0241090i
$361$	2.70385	+	18.8057i	0.142308	+	0.989774i
$362$	0.122083	−	0.352736i	0.00641655	−	0.0185394i
$363$	8.16624	−	13.5083i	0.428616	−	0.709003i
$364$	1.05100	+	3.03668i	0.0550876	+	0.159165i
$365$	−2.95678	+	12.1880i	−0.154765	+	0.637951i
$366$	−0.629093	+	0.308439i	−0.0328832	+	0.0161224i
$367$	−10.1424	−	17.5671i	−0.529428	−	0.916996i	−0.999411	−	0.0343206i	$-0.989073\pi$
$367$	−10.1424	−	17.5671i	−0.529428	−	0.916996i	0.469983	−	0.882675i	$-0.344260\pi$
$368$	−19.1224	−	0.419897i	−0.996825	−	0.0218886i
$369$	−15.2032	−	23.2809i	−0.791445	−	1.21196i
$370$	−0.120412	−	0.263664i	−0.00625990	−	0.0137073i
$371$	−2.81424	−	2.68338i	−0.146108	−	0.139314i
$372$	−0.312543	+	0.117874i	−0.0162046	+	0.00611151i
$373$	−2.89481	+	1.49238i	−0.149888	+	0.0772725i	−0.531539	−	0.847034i	$-0.678386\pi$
$373$	−2.89481	+	1.49238i	−0.149888	+	0.0772725i	0.381651	+	0.924307i	$0.375356\pi$
$374$	−0.305845	+	0.0589468i	−0.0158149	+	0.00304807i
$375$	−9.16527	−	11.0182i	−0.473293	−	0.568978i
$376$	−0.0352599	−	0.145343i	−0.00181839	−	0.00749551i
$377$	−2.11096	+	1.35663i	−0.108720	+	0.0698701i
$378$	−0.497696	+	0.752988i	−0.0255987	+	0.0387295i
$379$	6.33566	−	13.8732i	0.325441	−	0.712616i	−0.674223	−	0.738528i	$-0.735521\pi$
$379$	6.33566	−	13.8732i	0.325441	−	0.712616i	0.999664	+	0.0259113i	$0.00824875\pi$
$380$	0.0542803	−	0.00518314i	0.00278452	−	0.000265889i
$381$	13.2562	+	30.6464i	0.679135	+	1.57006i
$382$	−0.0228728	−	0.480158i	−0.00117027	−	0.0245670i
$383$	−5.58839	+	5.32852i	−0.285553	+	0.272275i	−0.819294	−	0.573374i	$-0.805634\pi$
$383$	−5.58839	+	5.32852i	−0.285553	+	0.272275i	0.533741	+	0.845648i	$0.320786\pi$
$384$	0.846390	−	2.29482i	0.0431921	−	0.117107i
$385$	1.58841	−	4.58941i	0.0809529	−	0.233898i
$386$	0.597689	+	0.384111i	0.0304216	+	0.0195508i
$387$	9.38114	−	12.1101i	0.476870	−	0.615591i
$388$	18.1656	−	5.33390i	0.922218	−	0.270788i
$389$	14.4764	−	20.3292i	0.733981	−	1.03073i	−0.263828	−	0.964570i	$-0.584985\pi$
$389$	14.4764	−	20.3292i	0.733981	−	1.03073i	0.997809	−	0.0661620i	$-0.0210754\pi$
$390$	−0.000775689	−	0.0282490i	−3.92785e−5	−	0.00143045i
$391$	0.630384	+	24.5757i	0.0318799	+	1.24285i
$392$	0.744454	−	1.28943i	0.0376006	−	0.0651262i
$393$	−14.8524	+	7.28203i	−0.749207	+	0.367330i
$394$	−0.778378	−	0.742181i	−0.0392141	−	0.0373906i
$395$	0.398134	−	0.459471i	0.0200323	−	0.0231185i
$396$	−7.09986	+	4.16854i	−0.356781	+	0.209477i
$397$	9.92492	+	11.4540i	0.498118	+	0.574858i	0.948017	−	0.318221i	$-0.103085\pi$
$397$	9.92492	+	11.4540i	0.498118	+	0.574858i	−0.449899	+	0.893080i	$0.648540\pi$
$398$	−0.0237946	+	0.0187122i	−0.00119271	+	0.000937960i
$399$	−0.146280	−	0.145216i	−0.00732317	−	0.00726987i
$400$	−0.794974	−	16.6886i	−0.0397487	−	0.834428i
$401$	−10.3365	−	8.12873i	−0.516182	−	0.405930i	0.325798	−	0.945439i	$-0.394367\pi$
$401$	−10.3365	−	8.12873i	−0.516182	−	0.405930i	−0.841979	+	0.539510i	$0.818610\pi$
$402$	0.0550500	+	0.446578i	0.00274564	+	0.0222733i
$403$	−0.0393546	+	0.00375790i	−0.00196039	+	0.000187195i
$404$	1.57615	−	10.9624i	0.0784166	−	0.545400i
$405$	−6.29646	+	5.10220i	−0.312874	+	0.253530i
$406$	1.02110	+	0.299821i	0.0506761	+	0.0148798i
$407$	−7.85623	+	6.17821i	−0.389419	+	0.306242i
$408$	−1.49750	−	0.472677i	−0.0741372	−	0.0234010i
$409$	3.97223	−	2.04783i	0.196414	−	0.101259i	−0.357214	−	0.934023i	$-0.616273\pi$
$409$	3.97223	−	2.04783i	0.196414	−	0.101259i	0.553628	+	0.832764i	$0.313243\pi$
$410$	−0.120756	−	0.348901i	−0.00596371	−	0.0172310i
$411$	10.7993	+	2.30797i	0.532690	+	0.113844i
$412$	−12.4660	+	17.5061i	−0.614157	+	0.862463i
$413$	30.3097			1.49144
$414$	−0.227872	−	0.594286i	−0.0111993	−	0.0292075i
$415$	13.6304			0.669088
$416$	0.125958	−	0.176883i	0.00617558	−	0.00867240i
$417$	3.81229	+	11.7774i	0.186689	+	0.576742i
$418$	0.000602304		0.00174024i	2.94597e−5		8.51181e-5i
$419$	−0.689187	+	0.355301i	−0.0336690	+	0.0173576i	−0.474979	−	0.879997i	$-0.657544\pi$
$419$	−0.689187	+	0.355301i	−0.0336690	+	0.0173576i	0.441310	+	0.897355i	$0.354514\pi$
$420$	9.02415	−	8.26389i	0.440334	−	0.403237i
$421$	31.3002	−	24.6148i	1.52548	−	1.19965i	0.613305	−	0.789846i	$-0.289840\pi$
$421$	31.3002	−	24.6148i	1.52548	−	1.19965i	0.912174	−	0.409804i	$-0.134403\pi$
$422$	0.470855	+	0.138255i	0.0229209	+	0.00673017i
$423$	−2.05563	+	1.48656i	−0.0999483	+	0.0722788i
$424$	−0.0249264	+	0.173367i	−0.00121053	+	0.00841943i
$425$	−21.3767	+	2.04123i	−1.03692	+	0.0990142i
$426$	0.532053	−	0.401330i	0.0257781	−	0.0194445i
$427$	−28.2232	−	22.1950i	−1.36582	−	1.07409i
$428$	−1.81140	−	38.0260i	−0.0875575	−	1.83806i
$429$	−0.940285	+	0.255633i	−0.0453974	+	0.0123421i
$430$	0.159887	−	0.125737i	0.00771044	−	0.00606356i
$431$	−16.1943	−	18.6892i	−0.780050	−	0.900226i	0.217063	−	0.976158i	$-0.430352\pi$
$431$	−16.1943	−	18.6892i	−0.780050	−	0.900226i	−0.997113	+	0.0759320i	$0.975807\pi$
$432$	−20.7111	+	0.720130i	−0.996463	+	0.0346473i
$433$	−10.6858	+	12.3320i	−0.513525	+	0.592640i	−0.951998	−	0.306105i	$-0.900974\pi$
$433$	−10.6858	+	12.3320i	−0.513525	+	0.592640i	0.438472	+	0.898745i	$0.355520\pi$
$434$	0.0121343	+	0.0115701i	0.000582467	+	0.000555381i
$435$	7.93259	+	5.32680i	0.380339	+	0.255400i
$436$	−10.1348	+	17.5541i	−0.485371	+	0.840687i
$437$	0.143290	−	0.0243673i	0.00685447	−	0.00116565i
$438$	−0.938512	−	0.508025i	−0.0448438	−	0.0242744i
$439$	11.4675	−	16.1039i	0.547315	−	0.768596i	−0.444569	−	0.895745i	$-0.646643\pi$
$439$	11.4675	−	16.1039i	0.547315	−	0.768596i	0.991884	+	0.127149i	$0.0405826\pi$
$440$	−0.209890	+	0.0616294i	−0.0100061	+	0.00293807i
$441$	−25.0234	−	3.41146i	−1.19159	−	0.162450i
$442$	−0.0781361	−	0.0502150i	−0.00371656	−	0.00238849i
$443$	11.1196	−	32.1280i	0.528309	−	1.52645i	−0.293084	−	0.956087i	$-0.594681\pi$
$443$	11.1196	−	32.1280i	0.528309	−	1.52645i	0.821393	−	0.570363i	$-0.193197\pi$
$444$	−24.8178	+	4.26657i	−1.17780	+	0.202483i
$445$	8.02501	−	7.65183i	0.380422	−	0.362732i
$446$	0.0233134	+	0.489409i	0.00110392	+	0.0231742i
$447$	11.2849	+	1.30749i	0.533757	+	0.0618421i
$448$	31.0872	−	2.96847i	1.46873	−	0.140247i
$449$	4.42890	−	9.69794i	0.209013	−	0.457674i	−0.775871	−	0.630892i	$-0.782689\pi$
$449$	4.42890	−	9.69794i	0.209013	−	0.457674i	0.984884	+	0.173218i	$0.0554164\pi$
$450$	0.504020	−	0.234643i	0.0237597	−	0.0110612i
$451$	−10.7096	+	6.88265i	−0.504296	+	0.324091i
$452$	−8.62819	−	35.5659i	−0.405836	−	1.67288i
$453$	3.04159	−	8.24669i	0.142907	−	0.387463i
$454$	−0.263130	+	0.0507142i	−0.0123493	+	0.00238014i
$455$	1.28721	−	0.663603i	0.0603454	−	0.0311102i
$456$	−0.00150616	+	0.00916125i	−7.05322e−5	+	0.000429015i
$457$	0.888891	+	0.847556i	0.0415806	+	0.0396470i	0.710585	−	0.703612i	$-0.248431\pi$
$457$	0.888891	+	0.847556i	0.0415806	+	0.0396470i	−0.669004	+	0.743259i	$0.733279\pi$
$458$	−0.0331018	−	0.0724829i	−0.00154675	−	0.00338690i
$459$	2.19115	+	26.5456i	0.102274	+	1.23904i
$460$	1.04017	+	8.56558i	0.0484984	+	0.399372i
$461$	12.5921	+	21.8102i	0.586475	+	1.01580i	0.994690	+	0.102918i	$0.0328180\pi$
$461$	12.5921	+	21.8102i	0.586475	+	1.01580i	−0.408215	+	0.912886i	$0.633849\pi$
$462$	0.343078	+	0.230380i	0.0159614	+	0.0107182i
$463$	−2.62737	+	10.8302i	−0.122104	+	0.503321i	0.877609	+	0.479377i	$0.159137\pi$
$463$	−2.62737	+	10.8302i	−0.122104	+	0.503321i	−0.999713	+	0.0239439i	$0.992378\pi$
$464$	7.99156	+	23.0901i	0.370999	+	1.07193i
$465$	0.0726279	+	0.131861i	0.00336804	+	0.00611490i
$466$	0.226926	−	0.655661i	0.0105122	−	0.0303729i
$467$	3.76703	+	26.2002i	0.174317	+	1.21240i	0.869633	+	0.493699i	$0.164355\pi$
$467$	3.76703	+	26.2002i	0.174317	+	1.21240i	−0.695316	+	0.718704i	$0.744736\pi$
$468$	−2.39006	−	0.561370i	−0.110481	−	0.0259493i
$469$	−19.3981	+	12.4664i	−0.895723	+	0.575646i
$470$	−0.0312718	+	0.0125193i	−0.00144246	+	0.000577474i
$471$	−13.5138	−	5.72865i	−0.622685	−	0.263962i
$472$	−0.791913	−	1.11209i	−0.0364508	−	0.0511879i
$473$	−5.51303	−	4.33549i	−0.253489	−	0.199346i
$474$	0.0291532	+	0.0427368i	0.00133905	+	0.00196297i
$475$	0.0299321	+	0.123382i	0.00137338	+	0.00566114i
$476$	−5.72346	−	39.8075i	−0.262334	−	1.82457i
$477$	2.88195	−	0.721482i	0.131955	−	0.0330344i
$478$	−0.417280	−	0.268170i	−0.0190859	−	0.0122658i
$479$	−2.36879	−	0.456547i	−0.108233	−	0.0208602i	0.134847	−	0.990866i	$-0.456946\pi$
$479$	−2.36879	−	0.456547i	−0.108233	−	0.0208602i	−0.243080	+	0.970006i	$0.578158\pi$
$480$	−0.808612	−	0.172812i	−0.0369079	−	0.00788777i
$481$	−2.96684	−	0.283299i	−0.135276	−	0.0129173i
$482$	0.237585	−	0.411509i	0.0108217	−	0.0187437i
$483$	22.3781	−	23.7293i	1.01824	−	1.07972i
$484$	−9.10448	−	15.7694i	−0.413840	−	0.716792i
$485$	−3.54447	−	7.76132i	−0.160946	−	0.352423i
$486$	−0.282993	−	0.628863i	−0.0128368	−	0.0285258i
$487$	23.1731	−	26.7432i	1.05007	−	1.21185i	0.0733583	−	0.997306i	$-0.476628\pi$
$487$	23.1731	−	26.7432i	1.05007	−	1.21185i	0.976715	−	0.214543i	$-0.0688262\pi$
$488$	−0.0769524	+	1.61543i	−0.00348347	+	0.0731271i
$489$	27.8388	+	8.78718i	1.25892	+	0.397370i
$490$	−0.311320	−	0.124634i	−0.0140640	−	0.00563038i
$491$	−23.0127	+	21.9426i	−1.03855	+	0.990253i	−0.999959	−	0.00900175i	$-0.997135\pi$
$491$	−23.0127	+	21.9426i	−1.03855	+	0.990253i	−0.0385884	+	0.999255i	$0.512286\pi$
$492$	−31.9851	+	2.40506i	−1.44200	+	0.108429i
$493$	29.1551	−	11.6720i	1.31308	−	0.525678i
$494$	−0.000228120	0	0.000499513i	−1.02636e−5	0	2.24742e-5i
$495$	2.31490	+	2.89979i	0.104047	+	0.130336i
$496$	−0.0547844	+	0.381034i	−0.00245989	+	0.0171089i
$497$	30.3561	+	15.6496i	1.36166	+	0.701982i
$498$	−0.296095	+	1.12141i	−0.0132683	+	0.0502514i
$499$	6.71614	+	2.68874i	0.300656	+	0.120364i	0.517085	−	0.855934i	$-0.327017\pi$
$499$	6.71614	+	2.68874i	0.300656	+	0.120364i	−0.216430	+	0.976298i	$0.569441\pi$
$500$	−16.2341	+	3.12886i	−0.726010	+	0.139927i
$501$	14.7732	−	24.4374i	0.660019	−	1.09178i
$502$	1.21726	+	0.234608i	0.0543290	+	0.0104711i
$503$	−4.67150	+	1.37168i	−0.208292	+	0.0611600i	−0.384214	−	0.923244i	$-0.625528\pi$
$503$	−4.67150	+	1.37168i	−0.208292	+	0.0611600i	0.175922	+	0.984404i	$0.443709\pi$
$504$	0.968193	+	1.84482i	0.0431268	+	0.0821749i
$505$	−4.99127			−0.222108
$506$	−0.272846	+	0.102340i	−0.0121295	+	0.00454957i
$507$	19.5461	+	10.5805i	0.868075	+	0.469897i
$508$	38.3439	+	3.66140i	1.70124	+	0.162448i
$509$	7.33058	−	30.2171i	0.324922	−	1.33935i	−0.541779	−	0.840521i	$-0.682249\pi$
$509$	7.33058	−	30.2171i	0.324922	−	1.33935i	0.866702	−	0.498827i	$-0.166236\pi$
$510$	−0.0573764	+	0.348994i	−0.00254067	+	0.0154537i
$511$	2.60222	−	54.6274i	0.115116	−	2.41657i
$512$	−2.30852	−	2.66418i	−0.102023	−	0.117741i
$513$	0.153504	−	0.0351585i	0.00677738	−	0.00155229i
$514$	0.770830	+	0.226336i	0.0339998	+	0.00998325i
$515$	8.60876	+	4.43813i	0.379347	+	0.195567i
$516$	−7.01551	−	16.2188i	−0.308841	−	0.713994i
$517$	0.673720	+	0.946107i	0.0296302	+	0.0416098i
$518$	0.733175	+	1.02960i	0.0322139	+	0.0452380i
$519$	−5.71259	+	7.68950i	−0.250755	+	0.337532i
$520$	−0.0579796	−	0.0298906i	−0.00254258	−	0.00131079i
$521$	−4.29539	−	1.26124i	−0.188184	−	0.0552559i	0.186282	−	0.982496i	$-0.440356\pi$
$521$	−4.29539	−	1.26124i	−0.188184	−	0.0552559i	−0.374467	+	0.927240i	$0.622174\pi$
$522$	−0.610571	+	0.536921i	−0.0267240	+	0.0235004i
$523$	0.0994473	+	0.114768i	0.00434853	+	0.00501847i	0.757920	−	0.652348i	$-0.226216\pi$
$523$	0.0994473	+	0.114768i	0.00434853	+	0.00501847i	−0.753571	+	0.657366i	$0.771670\pi$
$524$	−0.907951	+	19.0602i	−0.0396640	+	0.832651i
$525$	22.0360	+	18.0595i	0.961729	+	0.788182i
$526$	−0.00700965	+	0.0288942i	−0.000305635	+	0.00125985i
$527$	0.492535	+	0.0470314i	0.0214552	+	0.00204872i
$528$	0.260438	+	9.48463i	0.0113341	+	0.412766i
$529$	4.43609	+	22.5681i	0.192874	+	0.981224i
$530$	0.0394483			0.00171352
$531$	−12.3771	+	19.5719i	−0.537118	+	0.849349i
$532$	−0.228142	+	0.0669887i	−0.00989123	+	0.00290433i
$533$	−3.72761	−	0.718438i	−0.161461	−	0.0311190i
$534$	0.455208	+	0.826462i	0.0196988	+	0.0357645i
$535$	−16.8467	+	3.24694i	−0.728347	+	0.140377i
$536$	0.964227	+	0.386018i	0.0416483	+	0.0166735i
$537$	−3.39443	+	0.922835i	−0.146481	+	0.0398233i
$538$	−0.819686	−	0.422578i	−0.0353392	−	0.0182186i
$539$	−1.64556	+	11.4451i	−0.0708793	+	0.492977i
$540$	1.65122	+	9.20177i	0.0710571	+	0.395981i
$541$	−13.3001	+	29.1233i	−0.571818	+	1.25211i	0.374006	+	0.927426i	$0.377984\pi$
$541$	−13.3001	+	29.1233i	−0.571818	+	1.25211i	−0.945824	+	0.324680i	$0.894743\pi$
$542$	0.986792	−	0.395052i	0.0423863	−	0.0169689i
$543$	−6.33765	+	13.1688i	−0.271975	+	0.565125i
$544$	−1.96687	+	1.87540i	−0.0843287	+	0.0804073i
$545$	8.48065	+	3.39514i	0.363271	+	0.145432i
$546$	0.0266341	+	0.120318i	0.00113984	+	0.00514913i
$547$	0.492983	−	10.3490i	0.0210784	−	0.442491i	−0.963518	−	0.267645i	$-0.913754\pi$
$547$	0.492983	−	10.3490i	0.0210784	−	0.442491i	0.984596	−	0.174845i	$-0.0559425\pi$
$548$	8.34232	−	9.62755i	0.356366	−	0.411269i
$549$	25.8570	−	9.16124i	1.10355	−	0.390992i
$550$	−0.105742	−	0.231542i	−0.00450884	−	0.00987297i
$551$	−0.0928370	−	0.160798i	−0.00395499	−	0.00685024i
$552$	−1.45533	−	0.201086i	−0.0619430	−	0.00855878i
$553$	−1.32557	+	2.29595i	−0.0563689	+	0.0976337i
$554$	0.202619	+	0.0193478i	0.00860846	+	0.000822008i
$555$	3.49501	+	10.7972i	0.148355	+	0.458317i
$556$	14.0220	+	2.70253i	0.594667	+	0.114613i
$557$	17.4083	+	11.1876i	0.737612	+	0.474034i	0.854723	−	0.519084i	$-0.173727\pi$
$557$	17.4083	+	11.1876i	0.737612	+	0.474034i	−0.117111	+	0.993119i	$0.537363\pi$
$558$	−0.0124263	+	0.00311086i	−0.000526046	+	0.000131693i
$559$	−0.297640	−	2.07013i	−0.0125888	−	0.0875573i
$560$	−3.32458	−	13.7041i	−0.140489	−	0.579104i
$561$	12.1608	−	0.914408i	0.513429	−	0.0386063i
$562$	0.836453	+	0.657794i	0.0352837	+	0.0277474i
$563$	2.05501	+	2.88585i	0.0866082	+	0.121624i	0.855607	−	0.517626i	$-0.173184\pi$
$563$	2.05501	+	2.88585i	0.0866082	+	0.121624i	−0.768999	+	0.639250i	$0.779245\pi$
$564$	0.358030	+	2.90442i	0.0150758	+	0.122298i
$565$	−15.3121	+	6.13003i	−0.644184	+	0.257892i
$566$	−0.279562	+	0.179663i	−0.0117509	+	0.00755182i
$567$	22.7498	−	27.0430i	0.955404	−	1.13570i
$568$	−0.218927	−	1.52267i	−0.00918599	−	0.0638899i
$569$	−8.97510	+	25.9319i	−0.376256	+	1.08712i	0.584898	+	0.811107i	$0.301135\pi$
$569$	−8.97510	+	25.9319i	−0.376256	+	1.08712i	−0.961154	+	0.276013i	$0.910987\pi$
$570$	0.00209063		4.21274e-5i	8.75669e−5		1.76452e-6i
$571$	−4.34465	−	12.5531i	−0.181818	−	0.525329i	0.816854	−	0.576844i	$-0.195716\pi$
$571$	−4.34465	−	12.5531i	−0.181818	−	0.525329i	−0.998672	+	0.0515154i	$0.983595\pi$
$572$	−0.265006	+	1.09237i	−0.0110805	+	0.0456743i
$573$	−1.27410	+	18.7777i	−0.0532263	+	0.784451i
$574$	0.804992	+	1.39429i	0.0335997	+	0.0581964i
$575$	−19.3963	+	5.23561i	−0.808883	+	0.218340i
$576$	−10.7777	+	21.2862i	−0.449072	+	0.886925i
$577$	−8.22836	−	18.0176i	−0.342551	−	0.750082i	0.657443	−	0.753504i	$-0.271638\pi$
$577$	−8.22836	−	18.0176i	−0.342551	−	0.750082i	−0.999994	+	0.00342185i	$0.998911\pi$
$578$	0.297008	+	0.283196i	0.0123539	+	0.0117794i
$579$	−21.5149	−	17.6324i	−0.894128	−	0.732779i
$580$	9.79722	−	5.05082i	0.406807	−	0.209724i
$581$	−58.3631	+	11.2486i	−2.42131	+	0.466669i
$582$	0.715542	−	0.123013i	0.0296602	−	0.00509906i
$583$	−0.320681	−	1.32186i	−0.0132812	−	0.0547460i
$584$	−2.07231	+	1.33179i	−0.0857529	+	0.0551101i
$585$	−0.0971268	+	1.10218i	−0.00401570	+	0.0455694i
$586$	0.388865	−	0.851495i	0.0160639	−	0.0351749i
$587$	−42.9330	+	4.09961i	−1.77204	+	0.169209i	−0.929351	−	0.369198i	$-0.879632\pi$
$587$	−42.9330	+	4.09961i	−1.77204	+	0.169209i	−0.842685	+	0.538407i	$0.819026\pi$
$588$	−17.3736	+	23.3860i	−0.716477	+	0.964422i
$589$	−0.000139189	−	0.00292194i	−5.73520e−6	−	0.000120397i
$590$	−0.222539	+	0.212190i	−0.00916177	+	0.00873573i
$591$	26.9288	+	32.3730i	1.10770	+	1.33165i
$592$	−9.49170	+	27.4245i	−0.390107	+	1.12714i
$593$	−29.3776	−	18.8798i	−1.20639	−	0.775301i	−0.226341	−	0.974048i	$-0.572677\pi$
$593$	−29.3776	−	18.8798i	−1.20639	−	0.775301i	−0.980051	+	0.198747i	$0.936313\pi$
$594$	−0.288861	+	0.127460i	−0.0118521	+	0.00522976i
$595$	−17.3905	+	5.10631i	−0.712941	+	0.209338i
$596$	7.60164	−	10.6750i	0.311375	−	0.437265i
$597$	1.00976	−	0.620548i	0.0413266	−	0.0253973i
$598$	−0.0799437	−	0.0340595i	−0.00326914	−	0.00139280i
$599$	−13.6406	+	23.6263i	−0.557341	+	0.965343i	0.440376	+	0.897813i	$0.354845\pi$
$599$	−13.6406	+	23.6263i	−0.557341	+	0.965343i	−0.997717	+	0.0675295i	$0.978488\pi$
$600$	0.0868749	−	1.28037i	0.00354665	−	0.0522708i
$601$	−16.5832	−	15.8120i	−0.676442	−	0.644986i	0.271867	−	0.962335i	$-0.412359\pi$
$601$	−16.5832	−	15.8120i	−0.676442	−	0.644986i	−0.948309	+	0.317349i	$0.897207\pi$
$602$	−0.580847	+	0.670333i	−0.0236736	+	0.0273208i
$603$	−0.128678	−	17.6167i	−0.00524019	−	0.717408i
$604$	−6.64000	−	7.66297i	−0.270178	−	0.311802i
$605$	−6.45059	+	5.07280i	−0.262254	+	0.206239i
$606$	0.108426	−	0.410645i	0.00440451	−	0.0166813i
$607$	−0.784354	−	16.4656i	−0.0318359	−	0.668319i	−0.957233	−	0.289319i	$-0.906571\pi$
$607$	−0.784354	−	16.4656i	−0.0318359	−	0.668319i	0.925397	−	0.379000i	$-0.123732\pi$
$608$	0.0126300	+	0.00993236i	0.000512215	+	0.000402810i
$609$	−38.3621	−	16.2621i	−1.55451	−	0.658973i
$610$	0.362601	−	0.0346242i	0.0146813	−	0.00140189i
$611$	−0.0492904	+	0.342822i	−0.00199408	+	0.0138691i
$612$	28.0422	+	12.5597i	1.13354	+	0.507696i
$613$	19.2757	+	5.65986i	0.778539	+	0.228600i	0.646774	−	0.762682i	$-0.276118\pi$
$613$	19.2757	+	5.65986i	0.778539	+	0.228600i	0.131764	+	0.991281i	$0.457936\pi$
$614$	0.688917	−	0.541770i	0.0278024	−	0.0218641i
$615$	3.12431	+	14.1139i	0.125985	+	0.569127i
$616$	0.847858	−	0.437101i	0.0341612	−	0.0176113i
$617$	−0.0275688	−	0.0796549i	−0.00110988	−	0.00320679i	0.944445	−	0.328671i	$-0.106601\pi$
$617$	−0.0275688	−	0.0796549i	−0.00110988	−	0.00320679i	−0.945554	+	0.325464i	$0.894479\pi$
$618$	−0.552146	+	0.611856i	−0.0222106	+	0.0246125i
$619$	5.51387	−	7.74314i	0.221621	−	0.311223i	−0.688764	−	0.724986i	$-0.741846\pi$
$619$	5.51387	−	7.74314i	0.221621	−	0.311223i	0.910385	+	0.413763i	$0.135786\pi$
$620$	0.173658			0.00697427
$621$	6.18461	+	24.1402i	0.248180	+	0.968714i
$622$	−0.693216			−0.0277954
$623$	−28.0471	+	39.3867i	−1.12368	+	1.57799i
$624$	−1.89554	+	2.10052i	−0.0758822	+	0.0840882i
$625$	−4.41375	−	12.7527i	−0.176550	−	0.510107i
$626$	−1.21630	+	0.627048i	−0.0486133	+	0.0250619i
$627$	−0.0155834	−	0.0703969i	−0.000622341	−	0.00281138i
$628$	−13.3095	+	10.4667i	−0.531105	+	0.417666i
$629$	35.7890	+	10.5086i	1.42700	+	0.419005i
$630$	0.380240	−	0.274975i	0.0151491	−	0.0109553i
$631$	0.764825	−	5.31947i	0.0304472	−	0.211765i	−0.968918	−	0.247381i	$-0.920430\pi$
$631$	0.764825	−	5.31947i	0.0304472	−	0.211765i	0.999366	+	0.0356158i	$0.0113393\pi$
$632$	0.118874	−	0.0113511i	0.00472855	−	0.000451522i
$633$	−17.6898	−	7.49889i	−0.703107	−	0.298054i
$634$	−0.0691294	−	0.0543640i	−0.00274548	−	0.00215907i
$635$	−0.825983	−	17.3395i	−0.0327781	−	0.688098i
$636$	0.874910	−	3.31357i	0.0346924	−	0.131391i
$637$	−2.71031	+	2.13141i	−0.107386	+	0.0844496i
$638$	0.243778	+	0.281335i	0.00965128	+	0.0111382i
$639$	−22.5015	+	13.2113i	−0.890144	+	0.522631i
$640$	−0.832721	+	0.961011i	−0.0329162	+	0.0379873i
$641$	−20.3094	−	19.3650i	−0.802173	−	0.764871i	0.173328	−	0.984864i	$-0.444548\pi$
$641$	−20.3094	−	19.3650i	−0.802173	−	0.764871i	−0.975501	+	0.219994i	$0.929396\pi$
$642$	0.0988298	−	1.45656i	0.00390050	−	0.0574858i
$643$	9.99438	−	17.3108i	0.394140	−	0.682670i	−0.598851	−	0.800860i	$-0.704376\pi$
$643$	9.99438	−	17.3108i	0.394140	−	0.682670i	0.992991	+	0.118190i	$0.0377093\pi$
$644$	−11.5227	−	35.8181i	−0.454057	−	1.41143i
$645$	−6.78504	+	4.16976i	−0.267161	+	0.164184i
$646$	0.00398652	−	0.00559828i	0.000156847	−	0.000220261i
$647$	6.95624	−	2.04254i	0.273478	−	0.0803004i	−0.142118	−	0.989850i	$-0.545391\pi$
$647$	6.95624	−	2.04254i	0.273478	−	0.0803004i	0.415596	+	0.909549i	$0.363573\pi$
$648$	−1.58663	−	0.128146i	−0.0623286	−	0.00503405i
$649$	8.91928	+	5.73207i	0.350112	+	0.225004i
$650$	0.0248259	−	0.0717297i	0.000973752	−	0.00281347i
$651$	−0.419801	−	0.504672i	−0.0164533	−	0.0197796i
$652$	24.3724	−	23.2390i	0.954496	−	0.910110i
$653$	0.776493	+	16.3006i	0.0303865	+	0.637892i	0.961771	+	0.273855i	$0.0882988\pi$
$653$	0.776493	+	16.3006i	0.0303865	+	0.637892i	−0.931385	+	0.364037i	$0.881398\pi$
$654$	−0.463554	+	0.623973i	−0.0181264	+	0.0243993i
$655$	8.56075	−	0.817452i	0.334496	−	0.0319405i
$656$	−15.3558	+	33.6246i	−0.599544	+	1.31282i
$657$	34.2120	+	23.9876i	1.33474	+	0.935846i
$658$	0.123569	−	0.0794132i	0.00481723	−	0.00309585i
$659$	2.19061	+	9.02982i	0.0853341	+	0.351752i	0.998431	−	0.0559899i	$-0.0178315\pi$
$659$	2.19061	+	9.02982i	0.0853341	+	0.351752i	−0.913097	+	0.407742i	$0.866316\pi$
$660$	4.21840	−	0.725210i	0.164201	−	0.0282288i
$661$	−10.8927	+	2.09940i	−0.423678	+	0.0816573i	−0.396634	−	0.917977i	$-0.629822\pi$
$661$	−10.8927	+	2.09940i	−0.423678	+	0.0816573i	−0.0270446	+	0.999634i	$0.508610\pi$
$662$	−0.728936	+	0.375793i	−0.0283309	+	0.0146056i
$663$	2.81265	+	2.30510i	0.109234	+	0.0895225i
$664$	1.93760	+	1.84749i	0.0751933	+	0.0716967i
$665$	0.0445152	+	0.0974748i	0.00172623	+	0.00377991i
$666$	−0.964240	+	0.0529940i	−0.0373636	+	0.00205348i
$667$	25.0600	−	15.3384i	0.970329	−	0.593904i
$668$	−16.4706	−	28.5279i	−0.637266	−	1.10378i
$669$	1.29864	−	19.1395i	0.0502085	−	0.739976i
$670$	0.0551502	−	0.227332i	0.00213064	−	0.00878260i
$671$	−4.10785	−	11.8688i	−0.158582	−	0.458192i
$672$	3.60497	+	0.0726422i	0.139065	+	0.00280223i
$673$	−9.22527	+	26.6547i	−0.355608	+	1.02746i	0.615359	+	0.788247i	$0.289011\pi$
$673$	−9.22527	+	26.6547i	−0.355608	+	1.02746i	−0.970967	+	0.239215i	$0.923110\pi$
$674$	0.206552	+	1.43660i	0.00795607	+	0.0553357i
$675$	−20.6601	+	6.85468i	−0.795207	+	0.263837i
$676$	21.5692	−	13.8617i	0.829585	−	0.533142i
$677$	29.0513	−	11.6304i	1.11653	−	0.446992i	0.261311	−	0.965255i	$-0.415845\pi$
$677$	29.0513	−	11.6304i	1.11653	−	0.446992i	0.855222	+	0.518262i	$0.173421\pi$
$678$	−0.171707	−	1.39293i	−0.00659438	−	0.0534951i
$679$	21.5820	+	30.3077i	0.828241	+	1.16310i
$680$	0.641723	+	0.504657i	0.0246090	+	0.0193527i
$681$	10.4624	−	0.786700i	0.400919	−	0.0301464i
$682$	0.00138270	+	0.00569956i	5.29462e−5	+	0.000218247i
$683$	−4.05418	−	28.1975i	−0.155129	−	1.07895i	−0.907453	−	0.420153i	$-0.861976\pi$
$683$	−4.05418	−	28.1975i	−0.155129	−	1.07895i	0.752324	−	0.658793i	$-0.228933\pi$
$684$	0.0499060	−	0.174674i	0.00190820	−	0.00667883i
$685$	−4.82977	−	3.10391i	−0.184536	−	0.118594i
$686$	0.241914	+	0.0466250i	0.00923630	+	0.00178015i
$687$	0.960799	+	2.96822i	0.0366568	+	0.113245i
$688$	−20.2727	−	1.93581i	−0.772888	−	0.0738019i
$689$	0.202805	−	0.351268i	0.00772624	−	0.0133822i
$690$	0.00181899	+	0.330888i	6.92477e−5	+	0.0125967i
$691$	0.509052	+	0.881703i	0.0193652	+	0.0335416i	0.875546	−	0.483135i	$-0.160502\pi$
$691$	0.509052	+	0.881703i	0.0193652	+	0.0335416i	−0.856180	+	0.516677i	$0.827169\pi$
$692$	4.59048	+	10.0517i	0.174504	+	0.382110i
$693$	−12.3051	−	10.5061i	−0.467433	−	0.399092i
$694$	0.754780	−	0.871062i	0.0286510	−	0.0330651i
$695$	0.306221	−	6.42838i	0.0116156	−	0.243842i
$696$	0.405634	+	1.83242i	0.0153755	+	0.0694579i
$697$	44.1075	+	17.6580i	1.67069	+	0.668844i
$698$	0.449406	−	0.428507i	0.0170103	−	0.0162192i
$699$	−11.7803	+	24.4779i	−0.445573	+	0.925838i
$700$	30.5120	−	12.2152i	1.15324	−	0.461689i
$701$	−4.75328	+	10.4082i	−0.179529	+	0.393114i	−0.977906	−	0.209044i	$-0.932965\pi$
$701$	−4.75328	+	10.4082i	−0.179529	+	0.393114i	0.798377	+	0.602158i	$0.205692\pi$
$702$	−0.0885693	−	0.0319337i	−0.00334283	−	0.00120526i
$703$	0.0313844	−	0.218283i	0.00118369	−	0.00823271i
$704$	9.70948	+	5.00559i	0.365940	+	0.188655i
$705$	1.27266	−	0.345995i	0.0479311	−	0.0130309i
$706$	1.05736	+	0.423303i	0.0397943	+	0.0159312i
$707$	21.3718	−	4.11908i	0.803771	−	0.154914i
$708$	12.8879	+	23.3988i	0.484357	+	0.879382i
$709$	27.5668	+	5.31307i	1.03529	+	0.199537i	0.678465	−	0.734633i	$-0.262646\pi$
$709$	27.5668	+	5.31307i	1.03529	+	0.199537i	0.356830	+	0.934169i	$0.383858\pi$
$710$	−0.332438	+	0.0976127i	−0.0124762	+	0.00366334i
$711$	−0.941269	−	1.79352i	−0.0353003	−	0.0672623i
$712$	2.17793			0.0816214
$713$	0.461658	−	0.0338747i	0.0172892	−	0.00126862i
$714$	−0.0423332	−	1.54169i	−0.00158428	−	0.0576963i
$715$	0.504288	+	0.0481537i	0.0188593	+	0.00180085i
$716$	−0.956674	+	3.94346i	−0.0357526	+	0.147374i
$717$	15.0207	+	12.3102i	0.560960	+	0.459733i
$718$	0.0228493	−	0.479666i	0.000852729	−	0.0179010i
$719$	−30.0700	−	34.7026i	−1.12142	−	1.29419i	−0.951129	−	0.308794i	$-0.900075\pi$
$719$	−30.0700	−	34.7026i	−1.12142	−	1.29419i	−0.170291	−	0.985394i	$-0.554471\pi$
$720$	10.2068	+	3.44933i	0.380384	+	0.128549i
$721$	−40.5240	−	11.8989i	−1.50919	−	0.443139i
$722$	0.747051	+	0.385132i	0.0278024	+	0.0143331i
$723$	−11.0947	+	14.9341i	−0.412615	+	0.555405i
$724$	9.77906	+	13.7328i	0.363436	+	0.510374i
$725$	14.8870	+	20.9059i	0.552890	+	0.776425i
$726$	−0.277226	−	0.640905i	−0.0102888	−	0.0237862i
$727$	−22.8457	−	11.7778i	−0.847302	−	0.436815i	−0.0208237	−	0.999783i	$-0.506629\pi$
$727$	−22.8457	−	11.7778i	−0.847302	−	0.436815i	−0.826478	+	0.562969i	$0.809659\pi$
$728$	0.272927	+	0.0801387i	0.0101154	+	0.00297014i
$729$	8.17258	+	25.7334i	0.302688	+	0.953090i
$730$	0.363326	+	0.419301i	0.0134473	+	0.0155190i
$731$	−1.24545	+	26.1452i	−0.0460645	+	0.967014i
$732$	5.13365	−	31.2256i	0.189745	−	1.15413i
$733$	−12.1648	+	50.1441i	−0.449318	+	1.85212i	0.0700179	+	0.997546i	$0.477694\pi$
$733$	−12.1648	+	50.1441i	−0.449318	+	1.85212i	−0.519336	+	0.854570i	$0.673821\pi$
$734$	−0.893296	−	0.0852994i	−0.0329722	−	0.00314846i
$735$	11.5465	+	6.25022i	0.425898	+	0.230543i
$736$	−1.51995	+	2.03825i	−0.0560262	+	0.0751309i
$737$	−8.06594			−0.297113
$738$	−1.22906	−	0.0495525i	−0.0452422	−	0.00182405i
$739$	−34.7538	+	10.2046i	−1.27844	+	0.375384i	−0.849327	−	0.527867i	$-0.822992\pi$
$739$	−34.7538	+	10.2046i	−1.27844	+	0.375384i	−0.429113	+	0.903251i	$0.641174\pi$
$740$	12.8551	+	2.47761i	0.472561	+	0.0910787i
$741$	0.0111231	−	0.0183995i	0.000408618	−	0.000675922i
$742$	−0.168912	+	0.0325550i	−0.00620094	+	0.00119513i
$743$	−29.7853	−	11.9242i	−1.09272	−	0.437457i	−0.245873	−	0.969302i	$-0.579075\pi$
$743$	−29.7853	−	11.9242i	−1.09272	−	0.437457i	−0.846842	+	0.531845i	$0.821499\pi$
$744$	−0.00754850	+	0.0285886i	−0.000276741	+	0.00104811i
$745$	−5.24953	−	2.70632i	−0.192328	−	0.0991519i
$746$	−0.0205043	+	0.142611i	−0.000750717	+	0.00522135i
$747$	16.5692	−	42.2803i	0.606236	−	1.54696i
$748$	5.84403	−	12.7966i	0.213679	−	0.467891i
$749$	69.4555	−	27.8058i	2.53785	−	1.01600i
$750$	−0.632231	+	0.0475394i	−0.0230858	+	0.00173589i
$751$	6.77451	−	6.45949i	0.247205	−	0.235710i	−0.556338	−	0.830956i	$-0.687794\pi$
$751$	6.77451	−	6.45949i	0.247205	−	0.235710i	0.803543	+	0.595246i	$0.202945\pi$
$752$	3.13093	+	1.25343i	0.114173	+	0.0457080i
$753$	−46.2854	−	14.6097i	−1.68673	−	0.532409i
$754$	−0.00528192	+	0.110881i	−0.000192356	+	0.00403805i
$755$	−2.99247	+	3.45350i	−0.108907	+	0.125686i
$756$	−14.6641	−	38.0379i	−0.533328	−	1.38343i
$757$	−22.1047	−	48.4026i	−0.803409	−	1.75922i	−0.633472	−	0.773766i	$-0.718371\pi$
$757$	−22.1047	−	48.4026i	−0.803409	−	1.75922i	−0.169937	−	0.985455i	$-0.554357\pi$
$758$	−0.337346	−	0.584301i	−0.0122530	−	0.0212228i
$759$	11.0729	−	2.75079i	0.401920	−	0.0998473i
$760$	0.00241336	−	0.00418006i	8.75418e−5	−	0.000151627i
$761$	19.0633	+	1.82033i	0.691045	+	0.0659868i	0.434669	−	0.900590i	$-0.356865\pi$
$761$	19.0633	+	1.82033i	0.691045	+	0.0659868i	0.256376	+	0.966577i	$0.417472\pi$
$762$	1.44451	+	0.308714i	0.0523292	+	0.0111835i
$763$	−39.1147	−	7.53874i	−1.41605	−	0.272921i
$764$	18.2647	+	11.7380i	0.660793	+	0.424666i
$765$	3.80416	−	13.3148i	0.137540	−	0.481397i
$766$	0.0486132	+	0.338112i	0.00175647	+	0.0122165i
$767$	0.745374	+	3.07247i	0.0269139	+	0.110941i
$768$	15.4644	+	22.6698i	0.558022	+	0.818025i
$769$	12.0276	+	9.45864i	0.433728	+	0.341087i	0.811032	−	0.585002i	$-0.198906\pi$
$769$	12.0276	+	9.45864i	0.433728	+	0.341087i	−0.377304	+	0.926089i	$0.623149\pi$
$770$	−0.124621	−	0.175006i	−0.00449104	−	0.00630678i
$771$	−28.9598	−	12.2763i	−1.04296	−	0.442121i
$772$	−29.7904	+	11.9263i	−1.07218	+	0.429237i
$773$	15.6826	−	10.0786i	0.564064	−	0.362502i	−0.227321	−	0.973820i	$-0.572997\pi$
$773$	15.6826	−	10.0786i	0.564064	−	0.362502i	0.791385	+	0.611318i	$0.209360\pi$
$774$	−0.195665	−	0.648804i	−0.00703303	−	0.0233208i
$775$	0.0575440	+	0.400227i	0.00206704	+	0.0143766i
$776$	0.548131	−	1.58372i	0.0196768	−	0.0568523i
$777$	−23.8756	−	43.3478i	−0.856533	−	1.55509i
$778$	−0.361097	−	1.04332i	−0.0129459	−	0.0374048i
$779$	0.0662242	−	0.272980i	0.00237273	−	0.00978052i
$780$	1.05963	+	0.711548i	0.0379408	+	0.0254775i
$781$	5.97332	+	10.3461i	0.213742	+	0.370212i
$782$	0.901769	+	0.607912i	0.0322472	+	0.0217389i
$783$	26.1663	−	18.1310i	0.935106	−	0.647949i
$784$	13.9473	+	30.5403i	0.498118	+	1.09073i
$785$	5.52268	+	5.26586i	0.197113	+	0.187947i
$786$	−0.118713	+	0.722074i	−0.00423434	+	0.0257555i
$787$	21.4258	−	11.0458i	0.763746	−	0.393739i	−0.0319069	−	0.999491i	$-0.510158\pi$
$787$	21.4258	−	11.0458i	0.763746	−	0.393739i	0.795653	+	0.605752i	$0.207128\pi$
$788$	47.6979	−	9.19302i	1.69917	−	0.327488i
$789$	0.402827	−	1.09219i	0.0143410	−	0.0388829i
$790$	−0.00634082	−	0.0261372i	−0.000225596	−	0.000929920i
$791$	60.5051	−	38.8843i	2.15131	−	1.38257i
$792$	−0.0639754	+	0.725981i	−0.00227327	+	0.0257966i
$793$	1.55583	−	3.40679i	0.0552491	−	0.120979i
$794$	0.667427	−	0.0637315i	0.0236861	−	0.00226175i
$795$	−1.53425	−	0.177761i	−0.0544143	−	0.00630455i
$796$	−0.0650543	−	1.36566i	−0.00230579	−	0.0484044i
$797$	−27.3468	+	26.0752i	−0.968675	+	0.923629i	−0.997110	−	0.0759662i	$-0.975796\pi$
$797$	−27.3468	+	26.0752i	−0.968675	+	0.923629i	0.0284357	+	0.999596i	$0.490947\pi$
$798$	−0.00898653	+	0.00154493i	−0.000318120	+	5.46898e-5i
$799$	1.41773	−	4.09625i	0.0501555	−	0.144915i
$800$	−1.86838	−	1.20073i	−0.0660572	−	0.0424524i
$801$	−13.9801	−	34.1946i	−0.493963	−	1.20821i
$802$	−0.558163	+	0.163891i	−0.0197094	+	0.00578721i
$803$	11.0967	−	15.5832i	0.391595	−	0.549918i
$804$	−17.8722	−	9.67441i	−0.630305	−	0.341190i
$805$	−15.2389	+	7.43740i	−0.537102	+	0.262134i
$806$	−0.000874445		0.00151458i	−3.08010e−5		5.33489e-5i
$807$	29.9756	+	20.1289i	1.05519	+	0.708569i
$808$	−0.709523	−	0.676529i	−0.0249609	−	0.0238002i
$809$	10.9484	−	12.6351i	0.384926	−	0.444228i	−0.529910	−	0.848054i	$-0.677774\pi$
$809$	10.9484	−	12.6351i	0.384926	−	0.444228i	0.914836	+	0.403826i	$0.132320\pi$
$810$	0.0222882	+	0.357820i	0.000783126	+	0.0125725i
$811$	−3.45561	−	3.98799i	−0.121343	−	0.140037i	0.691828	−	0.722063i	$-0.256806\pi$
$811$	−3.45561	−	3.98799i	−0.121343	−	0.140037i	−0.813170	+	0.582026i	$0.802260\pi$
$812$	−37.7820	+	29.7121i	−1.32589	+	1.04269i
$813$	−40.1592	+	10.9180i	−1.40844	+	0.382910i
$814$	0.0210378	+	0.441638i	0.000737375	+	0.0154794i
$815$	−11.9298	−	9.38169i	−0.417882	−	0.328626i
$816$	28.2697	−	21.3240i	0.989638	−	0.746489i
$817$	0.154052	−	0.0147102i	0.00538961	−	0.000514646i
$818$	0.0281359	−	0.195689i	0.000983747	−	0.00684211i
$819$	−0.493699	−	4.79951i	−0.0172513	−	0.167709i
$820$	16.0000	+	4.69803i	0.558745	+	0.164062i
$821$	1.70724	−	1.34259i	0.0595830	−	0.0468566i	−0.587923	−	0.808917i	$-0.700054\pi$
$821$	1.70724	−	1.34259i	0.0595830	−	0.0468566i	0.647506	+	0.762060i	$0.275812\pi$
$822$	0.360285	−	0.329932i	0.0125664	−	0.0115077i
$823$	9.31481	−	4.80212i	0.324694	−	0.167391i	−0.288171	−	0.957579i	$-0.593047\pi$
$823$	9.31481	−	4.80212i	0.324694	−	0.167391i	0.612865	+	0.790188i	$0.290017\pi$
$824$	0.622206	+	1.79775i	0.0216756	+	0.0626275i
$825$	3.06921	+	9.48178i	0.106856	+	0.330113i
$826$	0.777765	−	1.09222i	0.0270619	−	0.0380031i
$827$	−44.0376			−1.53134			−0.765668	−	0.643236i	$-0.777592\pi$
$827$	−44.0376			−1.53134			−0.765668	+	0.643236i	$0.777592\pi$
$828$	27.8342	+	7.18587i	0.967306	+	0.249726i
$829$	−22.3037			−0.774640			−0.387320	−	0.921945i	$-0.626599\pi$
$829$	−22.3037			−0.774640			−0.387320	+	0.921945i	$0.626599\pi$
$830$	0.349763	−	0.491174i	0.0121405	−	0.0170489i
$831$	−7.79322	−	1.66553i	−0.270344	−	0.0577765i
$832$	1.06541	+	3.07829i	0.0369364	+	0.106721i
$833$	38.3558	−	19.7738i	1.32895	−	0.685120i
$834$	0.522228	+	0.164839i	0.0180833	+	0.00570789i
$835$	−11.6695	+	9.17701i	−0.403840	+	0.317583i
$836$	−0.0798046	−	0.0234327i	−0.00276010	−	0.000810438i
$837$	0.497310	−	0.0649947i	0.0171895	−	0.00224655i
$838$	−0.00488161	+	0.0339523i	−0.000168632	+	0.00117286i
$839$	5.02179	−	0.479523i	0.173371	−	0.0165550i	−0.00800921	−	0.999968i	$-0.502549\pi$
$839$	5.02179	−	0.479523i	0.173371	−	0.0165550i	0.181381	+	0.983413i	$0.441943\pi$
$840$	−0.132518	−	1.07502i	−0.00457230	−	0.0370916i
$841$	−6.70782	−	5.27509i	−0.231304	−	0.181899i
$842$	−0.0838173	−	1.75954i	−0.00288854	−	0.0606378i
$843$	−29.5678	−	29.3526i	−1.01837	−	1.01096i
$844$	−17.4223	+	13.7010i	−0.599700	+	0.471609i
$845$	−7.56691	−	8.73268i	−0.260309	−	0.300413i
$846$	0.000819701		0.112221i	2.81819e−5		0.00385825i
$847$	23.4341	−	27.0443i	0.805204	−	0.929255i
$848$	−2.85843	−	2.72551i	−0.0981588	−	0.0935943i
$849$	11.6825	−	5.72785i	0.400943	−	0.196579i
$850$	−0.474984	+	0.822696i	−0.0162918	+	0.0282182i
$851$	34.6576	+	4.07898i	1.18805	+	0.139826i
$852$	0.826212	+	30.0890i	0.0283056	+	1.03083i
$853$	0.749240	−	1.05216i	0.0256535	−	0.0360253i	−0.801550	−	0.597928i	$-0.795991\pi$
$853$	0.749240	−	1.05216i	0.0256535	−	0.0360253i	0.827204	+	0.561902i	$0.189930\pi$
$854$	−1.52403	+	0.447495i	−0.0521511	+	0.0153130i
$855$	−0.0811205	−	0.0110592i	−0.00277426	−	0.000378217i
$856$	−2.83491	−	1.82189i	−0.0968952	−	0.0622708i
$857$	−0.922618	+	2.66573i	−0.0315160	+	0.0910596i	−0.959661	−	0.281158i	$-0.909281\pi$
$857$	−0.922618	+	2.66573i	−0.0315160	+	0.0910596i	0.928145	+	0.372218i	$0.121403\pi$
$858$	−0.0149165	+	0.0404431i	−0.000509241	+	0.00138071i
$859$	−8.89261	+	8.47909i	−0.303412	+	0.289303i	−0.826454	−	0.563004i	$-0.809646\pi$
$859$	−8.89261	+	8.47909i	−0.303412	+	0.289303i	0.523042	+	0.852307i	$0.324797\pi$
$860$	0.437131	+	9.17652i	0.0149061	+	0.312917i
$861$	−25.0254	−	57.8551i	−0.852865	−	1.97170i
$862$	−1.08902	+	0.103989i	−0.0370923	+	0.00354189i
$863$	−19.9986	+	43.7908i	−0.680759	+	1.49065i	0.181078	+	0.983469i	$0.442041\pi$
$863$	−19.9986	+	43.7908i	−0.680759	+	1.49065i	−0.861837	+	0.507186i	$0.830686\pi$
$864$	−1.51901	+	2.29818i	−0.0516777	+	0.0781857i
$865$	4.18953	−	2.69244i	0.142448	−	0.0915459i
$866$	0.170185	+	0.701513i	0.00578313	+	0.0238384i
$867$	−10.2753	−	12.3527i	−0.348968	−	0.419518i
$868$	−0.743577	+	0.143313i	−0.0252386	+	0.00486435i
$869$	−0.824280	+	0.424946i	−0.0279618	+	0.0144153i
$870$	0.395508	−	0.149164i	0.0134090	−	0.00505715i
$871$	−1.74075	−	1.65981i	−0.0589832	−	0.0562404i
$872$	0.745363	+	1.63212i	0.0252412	+	0.0552705i
$873$	−28.3837	+	1.55995i	−0.960643	+	0.0527963i
$874$	0.00279882	−	0.00578876i	9.46714e−5	−	0.000195808i
$875$	−16.2454	−	28.1379i	−0.549195	−	0.951234i
$876$	43.2784	−	21.2191i	1.46224	−	0.716926i
$877$	4.82100	−	19.8724i	0.162794	−	0.671044i	−0.830657	−	0.556784i	$-0.812035\pi$
$877$	4.82100	−	19.8724i	0.162794	−	0.671044i	0.993451	−	0.114260i	$-0.0364497\pi$
$878$	−0.286044	−	0.826471i	−0.00965353	−	0.0278920i
$879$	−18.9610	+	31.3647i	−0.639539	+	1.05790i
$880$	1.61335	−	4.66147i	0.0543860	−	0.157138i
$881$	4.24412	+	29.5185i	0.142988	+	0.994504i	0.927349	+	0.374198i	$0.122082\pi$
$881$	4.24412	+	29.5185i	0.142988	+	0.994504i	−0.784361	+	0.620305i	$0.787009\pi$
$882$	−0.765049	+	0.814186i	−0.0257605	+	0.0274151i
$883$	18.6359	−	11.9765i	0.627146	−	0.403043i	−0.188106	−	0.982149i	$-0.560235\pi$
$883$	18.6359	−	11.9765i	0.627146	−	0.403043i	0.815252	+	0.579106i	$0.196598\pi$
$884$	3.89451	−	1.55913i	0.130987	−	0.0524392i
$885$	9.61131	−	7.24986i	0.323081	−	0.243701i
$886$	−0.872407	−	1.22512i	−0.0293091	−	0.0411589i
$887$	−11.6117	−	9.13150i	−0.389881	−	0.306606i	0.403907	−	0.914800i	$-0.367652\pi$
$887$	−11.6117	−	9.13150i	−0.389881	−	0.306606i	−0.793788	+	0.608194i	$0.791894\pi$
$888$	−0.966658	+	2.00858i	−0.0324389	+	0.0674036i
$889$	17.8463	+	73.5635i	0.598546	+	2.46724i
$890$	−0.0698093	−	0.485535i	−0.00234001	−	0.0162752i
$891$	11.8089	−	3.65562i	0.395614	−	0.122468i
$892$	−18.6165	−	11.9641i	−0.623328	−	0.400588i
$893$	−0.0251646	−	0.00485008i	−0.000842102	−	0.000162302i
$894$	0.336693	−	0.373103i	0.0112607	−	0.0124784i
$895$	1.82048	+	0.173835i	0.0608521	+	0.00581067i
$896$	2.77250	−	4.80211i	0.0926227	−	0.160427i
$897$	2.95575	+	1.68491i	0.0986897	+	0.0562574i
$898$	−0.235820	−	0.408452i	−0.00786941	−	0.0136302i
$899$	−0.245649	−	0.537896i	−0.00819285	−	0.0179398i
$900$	−4.57195	+	24.6907i	−0.152398	+	0.823022i
$901$	−3.32429	+	3.83643i	−0.110748	+	0.127810i
$902$	−0.0267970	+	0.562537i	−0.000892241	+	0.0187304i
$903$	25.6114	−	23.4537i	0.852294	−	0.780490i
$904$	−3.00754	−	1.20404i	−0.100029	−	0.0400457i
$905$	5.49879	−	5.24309i	0.182786	−	0.174286i
$906$	−0.219123	−	0.321220i	−0.00727986	−	0.0106718i
$907$	−35.5593	+	14.2358i	−1.18073	+	0.472692i	−0.877197	−	0.480131i	$-0.840589\pi$
$907$	−35.5593	+	14.2358i	−1.18073	+	0.472692i	−0.303529	+	0.952822i	$0.598165\pi$
$908$	5.02784	−	11.0094i	0.166855	−	0.365361i
$909$	−6.06744	+	15.4825i	−0.201244	+	0.513523i
$910$	0.00911748	−	0.0634135i	0.000302242	−	0.00210214i
$911$	5.30477	+	2.73480i	0.175755	+	0.0906080i	0.543859	−	0.839177i	$-0.316963\pi$
$911$	5.30477	+	2.73480i	0.175755	+	0.0906080i	−0.368104	+	0.929785i	$0.619993\pi$
$912$	−0.148577	−	0.147496i	−0.00491987	−	0.00488406i
$913$	−19.3019	−	7.72732i	−0.638800	−	0.255737i
$914$	0.0533514	−	0.0102826i	0.00176471	−	0.000340120i
$915$	−14.2586	−	0.287318i	−0.471374	−	0.00949845i
$916$	3.53393	+	0.681110i	0.116764	+	0.0225045i
$917$	−35.9812	+	10.5650i	−1.18820	+	0.348888i
$918$	1.01280	+	0.602218i	0.0334275	+	0.0198762i
$919$	5.74550			0.189526			0.0947632	−	0.995500i	$-0.469791\pi$
$919$	5.74550			0.189526			0.0947632	+	0.995500i	$0.469791\pi$
$920$	0.671038	+	0.364809i	0.0221235	+	0.0120274i
$921$	−29.2352	+	17.9665i	−0.963332	+	0.592017i
$922$	1.10906	+	0.105902i	0.0365250	+	0.00348771i
$923$	−0.839880	+	3.46203i	−0.0276450	+	0.113954i
$924$	−17.4640	+	6.58651i	−0.574525	+	0.216680i
$925$	−1.45041	+	30.4479i	−0.0476893	+	1.00112i
$926$	0.322849	+	0.372587i	0.0106095	+	0.0122440i
$927$	24.2316	−	21.3087i	0.795871	−	0.699869i
$928$	3.11647	+	0.915077i	0.102303	+	0.0300389i
$929$	−24.0291	−	12.3879i	−0.788371	−	0.406433i	0.0165147	−	0.999864i	$-0.494743\pi$
$929$	−24.0291	−	12.3879i	−0.788371	−	0.406433i	−0.804885	+	0.593430i	$0.797773\pi$
$930$	0.00661533		0.000766464i	0.000216925		2.51334e-5i
$931$	−0.147991	−	0.207825i	−0.00485022	−	0.00681118i
$932$	18.1772	+	25.5263i	0.595413	+	0.836140i
$933$	26.9611	+	3.12376i	0.882666	+	0.102267i
$934$	1.04080	+	0.536569i	0.0340559	+	0.0175571i
$935$	−6.08322	−	1.78620i	−0.198943	−	0.0584148i
$936$	−0.163199	+	0.143513i	−0.00533432	+	0.00469087i
$937$	−4.54818	−	5.24888i	−0.148583	−	0.171474i	0.676579	−	0.736370i	$-0.263462\pi$
$937$	−4.54818	−	5.24888i	−0.148583	−	0.171474i	−0.825162	+	0.564896i	$0.808916\pi$
$938$	−0.0485369	+	1.01891i	−0.00158479	+	0.0332687i
$939$	50.1310	−	18.9067i	1.63596	−	0.616997i
$940$	0.358681	−	1.47850i	0.0116989	−	0.0482235i
$941$	42.8631	+	4.09293i	1.39730	+	0.133426i	0.766362	−	0.642409i	$-0.222065\pi$
$941$	42.8631	+	4.09293i	1.39730	+	0.133426i	0.630936	+	0.775835i	$0.282671\pi$
$942$	−0.553207	+	0.339974i	−0.0180245	+	0.0110770i
$943$	43.4515	+	9.36835i	1.41497	+	0.305076i
$944$	30.7855			1.00198
$945$	−16.0277	+	8.98111i	−0.521380	+	0.292156i
$946$	−0.297698	+	0.0874121i	−0.00967901	+	0.00284201i
$947$	−23.7088	−	4.56949i	−0.770431	−	0.148488i	−0.211136	−	0.977457i	$-0.567716\pi$
$947$	−23.7088	−	4.56949i	−0.770431	−	0.148488i	−0.559295	+	0.828968i	$0.688928\pi$
$948$	−2.33610	−	0.0470737i	−0.0758729	−	0.00152888i
$949$	5.60154	−	1.07961i	0.181834	−	0.0350456i
$950$	0.00521417	+	0.00208744i	0.000169170	+	6.77255e-5i
$951$	2.44366	+	2.42587i	0.0792410	+	0.0786643i
$952$	−3.16423	−	1.63128i	−0.102553	−	0.0528700i
$953$	−5.30187	+	36.8753i	−0.171745	+	1.19451i	0.703452	+	0.710742i	$0.251641\pi$
$953$	−5.30187	+	36.8753i	−0.171745	+	1.19451i	−0.875197	+	0.483767i	$0.839268\pi$
$954$	0.0479537	−	0.122366i	0.00155256	−	0.00396173i
$955$	4.06471	−	8.90047i	0.131531	−	0.288012i
$956$	20.7984	−	8.32641i	0.672667	−	0.269295i
$957$	−8.21346	−	12.0404i	−0.265503	−	0.389211i
$958$	−0.0772365	+	0.0736449i	−0.00249540	+	0.00237936i
$959$	23.2419	+	9.30465i	0.750519	+	0.300463i
$960$	9.14784	−	8.37716i	0.295245	−	0.270372i
$961$	−1.47460	+	30.9556i	−0.0475676	+	0.998567i
$962$	−0.0863398	+	0.0996415i	−0.00278371	+	0.00321257i
$963$	−10.4073	+	56.2042i	−0.335370	+	1.81116i
$964$	8.91536	+	19.5219i	0.287144	+	0.628759i
$965$	7.23084	+	12.5242i	0.232769	+	0.403168i
$966$	−0.280857	−	1.41531i	−0.00903643	−	0.0455369i
$967$	−5.67736	+	9.83348i	−0.182572	+	0.316223i	−0.942756	−	0.333485i	$-0.891775\pi$
$967$	−5.67736	+	9.83348i	−0.182572	+	0.316223i	0.760184	+	0.649708i	$0.225109\pi$
$968$	−1.60455	−	0.153216i	−0.0515722	−	0.00492455i
$969$	−0.180273	+	0.199768i	−0.00579122	+	0.00641749i
$970$	−0.370635	−	0.0714340i	−0.0119004	−	0.00229361i
$971$	36.8232	+	23.6648i	1.18171	+	0.759440i	0.975700	−	0.219109i	$-0.0703152\pi$
$971$	36.8232	+	23.6648i	1.18171	+	0.759440i	0.206012	+	0.978550i	$0.433952\pi$
$972$	30.5504	+	6.06382i	0.979906	+	0.194497i
$973$	3.99388	+	27.7780i	0.128038	+	0.890523i
$974$	−0.369062	−	1.52130i	−0.0118255	−	0.0487454i
$975$	−1.28877	+	2.67790i	−0.0412738	+	0.0857613i
$976$	−28.6663	−	22.5434i	−0.917586	−	0.721598i
$977$	−26.6513	−	37.4265i	−0.852650	−	1.19738i	−0.978688	−	0.205354i	$-0.934165\pi$
$977$	−26.6513	−	37.4265i	−0.852650	−	1.19738i	0.126037	−	0.992025i	$-0.459774\pi$
$978$	1.03101	−	0.777696i	0.0329681	−	0.0248680i
$979$	−15.7022	+	6.28620i	−0.501844	+	0.200908i
$980$	12.7416	−	8.18850i	0.407014	−	0.261572i
$981$	20.8406	−	22.1791i	0.665390	−	0.708126i
$982$	0.200187	+	1.39233i	0.00638821	+	0.0444310i
$983$	6.81975	−	19.7044i	0.217516	−	0.628472i	−0.782467	−	0.622692i	$-0.786039\pi$
$983$	6.81975	−	19.7044i	0.217516	−	0.628472i	0.999983	−	0.00577994i	$-0.00183982\pi$
$984$	−1.46890	+	2.42981i	−0.0468269	+	0.0774595i
$985$	−7.16011	−	20.6878i	−0.228140	−	0.659167i
$986$	0.327536	−	1.35012i	0.0104309	−	0.0429967i
$987$	−5.16380	+	2.53177i	−0.164366	+	0.0805871i
$988$	−0.0124011	−	0.0214793i	−0.000394531	−	0.000683347i
$989$	2.95211	+	24.3099i	0.0938717	+	0.773010i
$990$	0.163896	−	0.00900764i	0.00520897	−	0.000286282i
$991$	17.3892	+	38.0770i	0.552386	+	1.20956i	0.955659	+	0.294477i	$0.0951454\pi$
$991$	17.3892	+	38.0770i	0.552386	+	1.20956i	−0.403272	+	0.915080i	$0.632127\pi$
$992$	0.0370350	+	0.0353128i	0.00117586	+	0.00112118i
$993$	30.0437	−	11.3309i	0.953409	−	0.359575i
$994$	1.34289	−	0.692310i	0.0425940	−	0.0219587i
$995$	−0.605029	+	0.116610i	−0.0191807	+	0.00369678i
$996$	−33.5002	−	40.2729i	−1.06150	−	1.27610i
$997$	−8.54623	−	35.2281i	−0.270662	−	1.11568i	−0.931089	−	0.364793i	$-0.881140\pi$
$997$	−8.54623	−	35.2281i	−0.270662	−	1.11568i	0.660427	−	0.750891i	$-0.270375\pi$
$998$	0.269230	−	0.173023i	0.00852231	−	0.00547696i
$999$	37.7407	+	2.28397i	1.19406	+	0.0722615i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.m.a.4.12	✓	440
3.2	odd	2		621.2.q.a.280.11		440
9.2	odd	6		621.2.q.a.73.12		440
9.7	even	3	inner	207.2.m.a.142.11	yes	440
23.6	even	11	inner	207.2.m.a.121.11	yes	440
69.29	odd	22		621.2.q.a.604.12		440
207.29	odd	66		621.2.q.a.397.11		440
207.52	even	33	inner	207.2.m.a.52.12	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.m.a.4.12	✓	440	1.1	even	1	trivial
207.2.m.a.52.12	yes	440	207.52	even	33	inner
207.2.m.a.121.11	yes	440	23.6	even	11	inner
207.2.m.a.142.11	yes	440	9.7	even	3	inner
621.2.q.a.73.12		440	9.2	odd	6
621.2.q.a.280.11		440	3.2	odd	2
621.2.q.a.397.11		440	207.29	odd	66
621.2.q.a.604.12		440	69.29	odd	22

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.m (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0256606 - 0.0360353i) q^{2} +(-1.16039 + 1.28588i) q^{3} +(0.653496 + 1.88815i) q^{4} +(0.800365 - 0.412617i) q^{5} +(0.0165606 + 0.0748116i) q^{6} +(-3.08653 + 2.42727i) q^{7} +(0.169702 + 0.0498289i) q^{8} +(-0.306974 - 2.98425i) q^{9} +(0.00566909 - 0.0394294i) q^{10} +(-1.36732 + 0.130563i) q^{11} +(-3.18625 - 1.35068i) q^{12} +(-0.321955 - 0.253188i) q^{13} +(0.00826526 + 0.173509i) q^{14} +(-0.398163 + 1.50797i) q^{15} +(-3.13499 + 2.46538i) q^{16} +(3.35687 + 3.87403i) q^{17} +(-0.115416 - 0.0655159i) q^{18} +(0.0198468 - 0.0229044i) q^{19} +(1.30212 + 1.24157i) q^{20} +(0.460406 - 6.78549i) q^{21} +(-0.0303813 + 0.0526220i) q^{22} +(3.70379 + 3.04663i) q^{23} +(-0.260994 + 0.160395i) q^{24} +(-2.42995 + 3.41239i) q^{25} +(-0.0173853 + 0.00510478i) q^{26} +(4.19360 + 3.06818i) q^{27} +(-6.60009 - 4.24162i) q^{28} +(2.00377 - 5.78951i) q^{29} +(0.0441231 + 0.0530434i) q^{30} +(0.0698557 - 0.0666073i) q^{31} +(0.0252263 + 0.529564i) q^{32} +(1.41874 - 1.90971i) q^{33} +(0.225741 - 0.0215557i) q^{34} +(-1.46882 + 3.21626i) q^{35} +(5.43412 - 2.52981i) q^{36} +(6.12138 - 3.93397i) q^{37} +(-0.000316087 - 0.00130293i) q^{38} +(0.699164 - 0.120197i) q^{39} +(0.156383 - 0.0301404i) q^{40} +(8.23813 - 4.24705i) q^{41} +(-0.232703 - 0.190711i) q^{42} +(3.69553 + 3.52369i) q^{43} +(-1.14006 - 2.49638i) q^{44} +(-1.47704 - 2.26183i) q^{45} +(0.204828 - 0.0552887i) q^{46} +(-0.422804 - 0.732318i) q^{47} +(0.467635 - 6.89203i) q^{48} +(1.98469 - 8.18099i) q^{49} +(0.0606124 + 0.175128i) q^{50} +(-8.87682 - 0.178873i) q^{51} +(0.267662 - 0.773357i) q^{52} +(0.140934 + 0.980215i) q^{53} +(0.218173 - 0.0723863i) q^{54} +(-1.04048 + 0.668676i) q^{55} +(-0.644736 + 0.258114i) q^{56} +(0.00642224 + 0.0520987i) q^{57} +(-0.157209 - 0.220769i) q^{58} +(-6.06757 - 4.77159i) q^{59} +(-3.10748 + 0.233661i) q^{60} +(2.15578 + 8.88625i) q^{61} +(-0.000607672 - 0.00422645i) q^{62} +(8.19107 + 8.46587i) q^{63} +(-6.69055 - 4.29975i) q^{64} +(-0.362151 - 0.0697989i) q^{65} +(-0.0324112 - 0.100129i) q^{66} +(5.84580 + 0.558207i) q^{67} +(-5.12106 + 8.86994i) q^{68} +(-8.21545 + 1.22734i) q^{69} +(0.0782081 + 0.135460i) q^{70} +(-3.61317 - 7.91173i) q^{71} +(0.0966080 - 0.521728i) q^{72} +(-9.12081 + 10.5260i) q^{73} +(0.0153165 - 0.321534i) q^{74} +(-1.56822 - 7.08434i) q^{75} +(0.0562168 + 0.0225058i) q^{76} +(3.90335 - 3.72183i) q^{77} +(0.0136096 - 0.0282789i) q^{78} +(0.626807 - 0.250936i) q^{79} +(-1.49188 + 3.26675i) q^{80} +(-8.81153 + 1.83217i) q^{81} +(0.0583517 - 0.405845i) q^{82} +(13.4543 + 6.93618i) q^{83} +(13.1129 - 3.56497i) q^{84} +(4.28521 + 1.71554i) q^{85} +(0.221807 - 0.0427497i) q^{86} +(5.11946 + 9.29472i) q^{87} +(-0.238541 - 0.0459751i) q^{88} +(11.8152 - 3.46926i) q^{89} +(-0.119408 - 0.00481422i) q^{90} +1.60828 q^{91} +(-3.33209 + 8.98428i) q^{92} +(0.00458885 + 0.167117i) q^{93} +(-0.0372387 - 0.00355586i) q^{94} +(0.00643393 - 0.0265210i) q^{95} +(-0.710228 - 0.582065i) q^{96} +(0.450863 - 9.46478i) q^{97} +(-0.243876 - 0.281448i) q^{98} +(0.809363 + 4.04034i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 9 q^{2} - 20 q^{3} + 11 q^{4} - 11 q^{5} - 17 q^{6} - 9 q^{7} - 50 q^{8} - 24 q^{9} - 44 q^{10} - 17 q^{11} - 30 q^{12} - 9 q^{13} - 21 q^{14} - 34 q^{15} + 11 q^{16} - 20 q^{17} + 3 q^{18} - 36 q^{19}+ \cdots - 220 q^{99}+O(q^{100}) \) 440 * q - 9 * q^2 - 20 * q^3 + 11 * q^4 - 11 * q^5 - 17 * q^6 - 9 * q^7 - 50 * q^8 - 24 * q^9 - 44 * q^10 - 17 * q^11 - 30 * q^12 - 9 * q^13 - 21 * q^14 - 34 * q^15 + 11 * q^16 - 20 * q^17 + 3 * q^18 - 36 * q^19 - 25 * q^20 + 3 * q^21 - 28 * q^22 - 5 * q^23 - 172 * q^24 + 11 * q^25 - 48 * q^26 + 31 * q^27 - 60 * q^28 + 9 * q^29 + 12 * q^30 - 3 * q^31 - 3 * q^32 - 44 * q^33 - 17 * q^34 - 56 * q^35 + 47 * q^36 - 48 * q^37 + 3 * q^38 - 64 * q^39 + 55 * q^40 - 9 * q^41 - 80 * q^42 - 9 * q^43 + 24 * q^44 - 56 * q^45 - 44 * q^46 - 12 * q^47 + 4 * q^48 - 53 * q^49 + 27 * q^50 + 14 * q^51 - 12 * q^52 - 84 * q^53 - 18 * q^54 - 68 * q^55 - 125 * q^56 + 27 * q^57 - 8 * q^58 + 81 * q^59 + 88 * q^60 + 3 * q^61 + 58 * q^62 + 43 * q^63 - 70 * q^64 - 84 * q^65 + 35 * q^66 - 3 * q^67 + 194 * q^68 + 33 * q^69 - 10 * q^70 + 86 * q^71 + 182 * q^72 - 36 * q^73 - 57 * q^74 + 55 * q^75 - 21 * q^76 + 91 * q^77 + 191 * q^78 - 9 * q^79 + 220 * q^80 - 228 * q^81 - 62 * q^82 - 68 * q^83 + 144 * q^84 + q^85 - 53 * q^86 + 160 * q^87 + 83 * q^88 - 28 * q^89 - 314 * q^90 - 108 * q^91 + q^92 + 132 * q^93 + 48 * q^94 - 3 * q^95 + 174 * q^96 - 36 * q^97 - 156 * q^98 - 220 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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