LMFDB - Embedded newform 71.2.g.a.18.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [71,2,Mod(2,71)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(71, base_ring=CyclotomicField(70))

chi = DirichletCharacter(H, H._module([6]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("71.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	71.g (of order $35$, degree $24$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.566937854351$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$5$ over $\Q(\zeta_{35})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{35}]$

Embedding invariants

Embedding label			18.4
Character	$\chi$	$=$	71.18
Dual form			71.2.g.a.4.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.262709 - 0.0236442i) q^{2} +(-0.333427 + 2.46146i) q^{3} +(-1.89940 + 0.344691i) q^{4} +(0.786557 + 0.571467i) q^{5} +(-0.0293950 + 0.654532i) q^{6} +(2.26116 - 1.35098i) q^{7} +(-0.999371 + 0.275809i) q^{8} +(-3.05572 - 0.843326i) q^{9} +O(q^{10})$	\(q+(0.262709 - 0.0236442i) q^{2} +(-0.333427 + 2.46146i) q^{3} +(-1.89940 + 0.344691i) q^{4} +(0.786557 + 0.571467i) q^{5} +(-0.0293950 + 0.654532i) q^{6} +(2.26116 - 1.35098i) q^{7} +(-0.999371 + 0.275809i) q^{8} +(-3.05572 - 0.843326i) q^{9} +(0.220148 + 0.131532i) q^{10} +(2.66032 - 4.03021i) q^{11} +(-0.215130 - 4.79023i) q^{12} +(0.412875 + 0.625479i) q^{13} +(0.562085 - 0.408379i) q^{14} +(-1.66890 + 1.74554i) q^{15} +(3.35864 - 1.26052i) q^{16} +(-2.00184 + 6.16102i) q^{17} +(-0.822706 - 0.149299i) q^{18} +(-4.24805 - 4.44311i) q^{19} +(-1.69097 - 0.814327i) q^{20} +(2.57145 + 6.01621i) q^{21} +(0.603598 - 1.12167i) q^{22} +(-0.375726 - 1.64617i) q^{23} +(-0.345675 - 2.55187i) q^{24} +(-1.25299 - 3.85630i) q^{25} +(0.123255 + 0.154557i) q^{26} +(0.165921 - 0.388192i) q^{27} +(-3.82919 + 3.34546i) q^{28} +(2.51021 + 4.66476i) q^{29} +(-0.397164 + 0.498028i) q^{30} +(-3.71911 - 1.39581i) q^{31} +(2.72067 - 1.31020i) q^{32} +(9.03317 + 7.89204i) q^{33} +(-0.380228 + 1.66589i) q^{34} +(2.55057 + 0.229556i) q^{35} +(6.09473 + 0.548536i) q^{36} +(1.35600 - 5.94101i) q^{37} +(-1.22106 - 1.06680i) q^{38} +(-1.67726 + 0.807724i) q^{39} +(-0.943678 - 0.354168i) q^{40} +(-2.34812 + 2.94445i) q^{41} +(0.817793 + 1.51971i) q^{42} +(5.78873 - 5.05746i) q^{43} +(-3.66384 + 8.57197i) q^{44} +(-1.92157 - 2.40957i) q^{45} +(-0.137629 - 0.423579i) q^{46} +(0.957599 + 7.06928i) q^{47} +(1.98285 + 8.68745i) q^{48} +(-0.0293774 + 0.0545924i) q^{49} +(-0.420351 - 0.983459i) q^{50} +(-14.4976 - 6.98170i) q^{51} +(-0.999813 - 1.04572i) q^{52} +(-7.43009 - 1.34836i) q^{53} +(0.0344105 - 0.105905i) q^{54} +(4.39562 - 1.64970i) q^{55} +(-1.88713 + 1.97378i) q^{56} +(12.3530 - 8.97495i) q^{57} +(0.769750 + 1.16612i) q^{58} +(-0.302856 - 6.74361i) q^{59} +(2.56825 - 3.89073i) q^{60} +(-5.45429 - 3.25878i) q^{61} +(-1.01005 - 0.278755i) q^{62} +(-8.04880 + 2.22133i) q^{63} +(-5.47542 + 3.27141i) q^{64} +(-0.0326909 + 0.727920i) q^{65} +(2.55970 + 1.85973i) q^{66} +(8.10237 - 1.47036i) q^{67} +(1.67865 - 12.3923i) q^{68} +(4.17725 - 0.375959i) q^{69} +0.675487 q^{70} +(-0.0401258 + 8.42605i) q^{71} +3.28640 q^{72} +(-4.11920 + 0.370734i) q^{73} +(0.215762 - 1.59282i) q^{74} +(9.90991 - 1.79838i) q^{75} +(9.60026 + 6.97500i) q^{76} +(0.570672 - 12.7070i) q^{77} +(-0.421532 + 0.251854i) q^{78} +(-17.0674 + 4.71030i) q^{79} +(3.36211 + 0.927882i) q^{80} +(-7.26354 - 4.33976i) q^{81} +(-0.547254 + 0.829054i) q^{82} +(-0.158986 - 3.54010i) q^{83} +(-6.95796 - 10.5409i) q^{84} +(-5.09538 + 3.70201i) q^{85} +(1.40117 - 1.46551i) q^{86} +(-12.3191 + 4.62343i) q^{87} +(-1.54708 + 4.76141i) q^{88} +(11.5953 + 2.10424i) q^{89} +(-0.561785 - 0.587581i) q^{90} +(1.77859 + 0.856523i) q^{91} +(1.28107 + 2.99722i) q^{92} +(4.67577 - 8.68904i) q^{93} +(0.418718 + 1.83452i) q^{94} +(-0.802241 - 5.92238i) q^{95} +(2.31787 + 7.13367i) q^{96} +(10.6897 + 13.4044i) q^{97} +(-0.00642692 + 0.0150365i) q^{98} +(-11.5280 + 10.0717i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9}+O(q^{10}) $ 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9} - 8 q^{10} - 27 q^{11} + 3 q^{12} - 31 q^{13} + 2 q^{14} + 12 q^{15} + 30 q^{16} + 9 q^{17} + 27 q^{18} - 31 q^{19} + 72 q^{20} - 32 q^{21} - 24 q^{22} - 6 q^{23} - 47 q^{24} - 42 q^{25} + 77 q^{26} - 2 q^{27} - 18 q^{28} + q^{29} + 15 q^{30} + 15 q^{31} - 10 q^{32} - 24 q^{33} + 20 q^{34} + 74 q^{35} + 8 q^{36} - 22 q^{37} - 39 q^{38} + 86 q^{39} - 30 q^{40} + 39 q^{41} - 34 q^{42} + 33 q^{43} - 23 q^{44} + 121 q^{45} + 124 q^{46} + 6 q^{47} + 131 q^{48} - 22 q^{49} - 15 q^{50} + 29 q^{51} + 83 q^{52} - 30 q^{53} - 25 q^{54} + 32 q^{55} + 11 q^{56} - 10 q^{57} + 12 q^{58} - 80 q^{59} + 80 q^{60} - 12 q^{61} - 68 q^{62} - 79 q^{63} - 117 q^{64} - 89 q^{65} - 39 q^{66} - 74 q^{67} - 67 q^{68} - 95 q^{69} - 64 q^{70} - 115 q^{71} - 144 q^{72} - 14 q^{73} - 70 q^{74} - 13 q^{75} + 8 q^{76} + 47 q^{77} - 218 q^{78} - 25 q^{79} - 103 q^{80} - 28 q^{81} - 88 q^{82} - 20 q^{83} - 142 q^{84} + 22 q^{85} + 159 q^{86} - 105 q^{87} + 43 q^{88} + 33 q^{89} + 33 q^{90} + 60 q^{91} - 2 q^{92} + 63 q^{93} + 174 q^{94} + 20 q^{95} - 30 q^{96} + 121 q^{97} + 128 q^{98} - 2 q^{99}+O(q^{100}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9 - 8 * q^10 - 27 * q^11 + 3 * q^12 - 31 * q^13 + 2 * q^14 + 12 * q^15 + 30 * q^16 + 9 * q^17 + 27 * q^18 - 31 * q^19 + 72 * q^20 - 32 * q^21 - 24 * q^22 - 6 * q^23 - 47 * q^24 - 42 * q^25 + 77 * q^26 - 2 * q^27 - 18 * q^28 + q^29 + 15 * q^30 + 15 * q^31 - 10 * q^32 - 24 * q^33 + 20 * q^34 + 74 * q^35 + 8 * q^36 - 22 * q^37 - 39 * q^38 + 86 * q^39 - 30 * q^40 + 39 * q^41 - 34 * q^42 + 33 * q^43 - 23 * q^44 + 121 * q^45 + 124 * q^46 + 6 * q^47 + 131 * q^48 - 22 * q^49 - 15 * q^50 + 29 * q^51 + 83 * q^52 - 30 * q^53 - 25 * q^54 + 32 * q^55 + 11 * q^56 - 10 * q^57 + 12 * q^58 - 80 * q^59 + 80 * q^60 - 12 * q^61 - 68 * q^62 - 79 * q^63 - 117 * q^64 - 89 * q^65 - 39 * q^66 - 74 * q^67 - 67 * q^68 - 95 * q^69 - 64 * q^70 - 115 * q^71 - 144 * q^72 - 14 * q^73 - 70 * q^74 - 13 * q^75 + 8 * q^76 + 47 * q^77 - 218 * q^78 - 25 * q^79 - 103 * q^80 - 28 * q^81 - 88 * q^82 - 20 * q^83 - 142 * q^84 + 22 * q^85 + 159 * q^86 - 105 * q^87 + 43 * q^88 + 33 * q^89 + 33 * q^90 + 60 * q^91 - 2 * q^92 + 63 * q^93 + 174 * q^94 + 20 * q^95 - 30 * q^96 + 121 * q^97 + 128 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/71\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{29}{35}\right)$

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 $

$2$	0.262709	−	0.0236442i	0.185763	−	0.0167190i	0.00363303	−	0.999993i	$-0.498844\pi$
$2$	0.262709	−	0.0236442i	0.185763	−	0.0167190i	0.182130	+	0.983274i	$0.441701\pi$
$3$	−0.333427	+	2.46146i	−0.192504	+	1.42112i	0.594460	+	0.804125i	$0.297366\pi$
$3$	−0.333427	+	2.46146i	−0.192504	+	1.42112i	−0.786964	+	0.616999i	$0.788348\pi$
$4$	−1.89940	+	0.344691i	−0.949701	+	0.172345i
$5$	0.786557	+	0.571467i	0.351759	+	0.255568i	0.749607	−	0.661884i	$-0.230243\pi$
$5$	0.786557	+	0.571467i	0.351759	+	0.255568i	−0.397848	+	0.917451i	$0.630243\pi$
$6$	−0.0293950	+	0.654532i	−0.0120005	+	0.267211i
$7$	2.26116	−	1.35098i	0.854639	−	0.510623i	−0.0175195	−	0.999847i	$-0.505577\pi$
$7$	2.26116	−	1.35098i	0.854639	−	0.510623i	0.872158	+	0.489224i	$0.162720\pi$
$8$	−0.999371	+	0.275809i	−0.353331	+	0.0975132i
$9$	−3.05572	−	0.843326i	−1.01857	−	0.281109i
$10$	0.220148	+	0.131532i	0.0696168	+	0.0415941i
$11$	2.66032	−	4.03021i	0.802116	−	1.21515i	−0.171099	−	0.985254i	$-0.554732\pi$
$11$	2.66032	−	4.03021i	0.802116	−	1.21515i	0.973214	−	0.229899i	$-0.0738397\pi$
$12$	−0.215130	−	4.79023i	−0.0621025	−	1.38282i
$13$	0.412875	+	0.625479i	0.114511	+	0.173477i	0.887309	−	0.461175i	$-0.152572\pi$
$13$	0.412875	+	0.625479i	0.114511	+	0.173477i	−0.772798	+	0.634652i	$0.781143\pi$
$14$	0.562085	−	0.408379i	0.150224	−	0.109144i
$15$	−1.66890	+	1.74554i	−0.430909	+	0.450695i
$16$	3.35864	−	1.26052i	0.839660	−	0.315130i
$17$	−2.00184	+	6.16102i	−0.485517	+	1.49427i	0.345714	+	0.938340i	$0.387637\pi$
$17$	−2.00184	+	6.16102i	−0.485517	+	1.49427i	−0.831231	+	0.555928i	$0.812363\pi$
$18$	−0.822706	−	0.149299i	−0.193914	−	0.0351901i
$19$	−4.24805	−	4.44311i	−0.974570	−	1.01932i	−0.999807	−	0.0196386i	$-0.993748\pi$
$19$	−4.24805	−	4.44311i	−0.974570	−	1.01932i	0.0252374	−	0.999681i	$-0.491966\pi$
$20$	−1.69097	−	0.814327i	−0.378112	−	0.182089i
$21$	2.57145	+	6.01621i	0.561137	+	1.31285i
$22$	0.603598	−	1.12167i	0.128688	−	0.239142i
$23$	−0.375726	−	1.64617i	−0.0783444	−	0.343249i	0.920531	−	0.390670i	$-0.127757\pi$
$23$	−0.375726	−	1.64617i	−0.0783444	−	0.343249i	−0.998875	+	0.0474213i	$0.984900\pi$
$24$	−0.345675	−	2.55187i	−0.0705606	−	0.520899i
$25$	−1.25299	−	3.85630i	−0.250598	−	0.771260i
$26$	0.123255	+	0.154557i	0.0241723	+	0.0303111i
$27$	0.165921	−	0.388192i	0.0319315	−	0.0747076i
$28$	−3.82919	+	3.34546i	−0.723648	+	0.632232i
$29$	2.51021	+	4.66476i	0.466135	+	0.866224i	0.999789	+	0.0205211i	$0.00653252\pi$
$29$	2.51021	+	4.66476i	0.466135	+	0.866224i	−0.533655	+	0.845703i	$0.679182\pi$
$30$	−0.397164	+	0.498028i	−0.0725119	+	0.0909270i
$31$	−3.71911	−	1.39581i	−0.667972	−	0.250694i	−0.00572936	−	0.999984i	$-0.501824\pi$
$31$	−3.71911	−	1.39581i	−0.667972	−	0.250694i	−0.662243	+	0.749290i	$0.730395\pi$
$32$	2.72067	−	1.31020i	0.480951	−	0.231614i
$33$	9.03317	+	7.89204i	1.57247	+	1.37383i
$34$	−0.380228	+	1.66589i	−0.0652086	+	0.285698i
$35$	2.55057	+	0.229556i	0.431126	+	0.0388020i
$36$	6.09473	+	0.548536i	1.01579	+	0.0914226i
$37$	1.35600	−	5.94101i	0.222924	−	0.976696i	−0.732339	−	0.680940i	$-0.761571\pi$
$37$	1.35600	−	5.94101i	0.222924	−	0.976696i	0.955264	−	0.295756i	$-0.0955715\pi$
$38$	−1.22106	−	1.06680i	−0.198081	−	0.173059i
$39$	−1.67726	+	0.807724i	−0.268576	+	0.129339i
$40$	−0.943678	−	0.354168i	−0.149209	−	0.0559989i
$41$	−2.34812	+	2.94445i	−0.366715	+	0.459846i	−0.930616	−	0.365996i	$-0.880728\pi$
$41$	−2.34812	+	2.94445i	−0.366715	+	0.459846i	0.563901	+	0.825842i	$0.309300\pi$
$42$	0.817793	+	1.51971i	0.126188	+	0.234497i
$43$	5.78873	−	5.05746i	0.882773	−	0.771256i	−0.0916938	−	0.995787i	$-0.529228\pi$
$43$	5.78873	−	5.05746i	0.882773	−	0.771256i	0.974467	+	0.224532i	$0.0720852\pi$
$44$	−3.66384	+	8.57197i	−0.552344	+	1.29227i
$45$	−1.92157	−	2.40957i	−0.286450	−	0.359197i
$46$	−0.137629	−	0.423579i	−0.0202923	−	0.0624533i
$47$	0.957599	+	7.06928i	0.139680	+	1.03116i	0.916102	+	0.400946i	$0.131319\pi$
$47$	0.957599	+	7.06928i	0.139680	+	1.03116i	−0.776421	+	0.630214i	$0.782967\pi$
$48$	1.98285	+	8.68745i	0.286200	+	1.25392i
$49$	−0.0293774	+	0.0545924i	−0.00419677	+	0.00779891i
$50$	−0.420351	−	0.983459i	−0.0594466	−	0.139082i
$51$	−14.4976	−	6.98170i	−2.03008	−	0.977633i
$52$	−0.999813	−	1.04572i	−0.138649	−	0.145016i
$53$	−7.43009	−	1.34836i	−1.02060	−	0.185212i	−0.357636	−	0.933861i	$-0.616417\pi$
$53$	−7.43009	−	1.34836i	−1.02060	−	0.185212i	−0.662966	+	0.748649i	$0.730703\pi$
$54$	0.0344105	−	0.105905i	0.00468268	−	0.0144118i
$55$	4.39562	−	1.64970i	0.592705	−	0.222446i
$56$	−1.88713	+	1.97378i	−0.252178	+	0.263758i
$57$	12.3530	−	8.97495i	1.63619	−	1.18876i
$58$	0.769750	+	1.16612i	0.101073	+	0.153119i
$59$	−0.302856	−	6.74361i	−0.0394285	−	0.877944i	−0.917094	−	0.398670i	$-0.869472\pi$
$59$	−0.302856	−	6.74361i	−0.0394285	−	0.877944i	0.877666	−	0.479273i	$-0.159100\pi$
$60$	2.56825	−	3.89073i	0.331559	−	0.502291i
$61$	−5.45429	−	3.25878i	−0.698350	−	0.417245i	0.119379	−	0.992849i	$-0.461910\pi$
$61$	−5.45429	−	3.25878i	−0.698350	−	0.417245i	−0.817728	+	0.575604i	$0.804767\pi$
$62$	−1.01005	−	0.278755i	−0.128276	−	0.0354020i
$63$	−8.04880	+	2.22133i	−1.01405	+	0.279861i
$64$	−5.47542	+	3.27141i	−0.684427	+	0.408926i
$65$	−0.0326909	+	0.727920i	−0.00405481	+	0.0902873i
$66$	2.55970	+	1.85973i	0.315077	+	0.228917i
$67$	8.10237	−	1.47036i	0.989861	−	0.179633i	0.340608	−	0.940205i	$-0.389367\pi$
$67$	8.10237	−	1.47036i	0.989861	−	0.179633i	0.649254	+	0.760572i	$0.275081\pi$
$68$	1.67865	−	12.3923i	0.203566	−	1.50278i
$69$	4.17725	−	0.375959i	0.502881	−	0.0452601i
$70$	0.675487			0.0807361
$71$	−0.0401258	+	8.42605i	−0.00476206	+	0.999989i
$71$	−0.0401258	+	8.42605i	−0.00476206	+	0.999989i
$72$	3.28640			0.387306
$73$	−4.11920	+	0.370734i	−0.482115	+	0.0433912i	−0.328032	−	0.944667i	$-0.606385\pi$
$73$	−4.11920	+	0.370734i	−0.482115	+	0.0433912i	−0.154084	+	0.988058i	$0.549242\pi$
$74$	0.215762	−	1.59282i	0.0250818	−	0.185161i
$75$	9.90991	−	1.79838i	1.14430	−	0.207659i
$76$	9.60026	+	6.97500i	1.10123	+	0.800087i
$77$	0.570672	−	12.7070i	0.0650341	−	1.44810i
$78$	−0.421532	+	0.251854i	−0.0477292	+	0.0285168i
$79$	−17.0674	+	4.71030i	−1.92023	+	0.529950i	−0.936371	+	0.351011i	$0.885838\pi$
$79$	−17.0674	+	4.71030i	−1.92023	+	0.529950i	−0.983860	+	0.178939i	$0.942733\pi$
$80$	3.36211	+	0.927882i	0.375895	+	0.103740i
$81$	−7.26354	−	4.33976i	−0.807060	−	0.482196i
$82$	−0.547254	+	0.829054i	−0.0604341	+	0.0915537i
$83$	−0.158986	−	3.54010i	−0.0174510	−	0.388576i	−0.988643	−	0.150280i	$-0.951983\pi$
$83$	−0.158986	−	3.54010i	−0.0174510	−	0.388576i	0.971193	−	0.238296i	$-0.0765889\pi$
$84$	−6.95796	−	10.5409i	−0.759175	−	1.15010i
$85$	−5.09538	+	3.70201i	−0.552672	+	0.401539i
$86$	1.40117	−	1.46551i	0.151092	−	0.158030i
$87$	−12.3191	+	4.62343i	−1.32074	+	0.495684i
$88$	−1.54708	+	4.76141i	−0.164919	+	0.507568i
$89$	11.5953	+	2.10424i	1.22910	+	0.223049i	0.753995	−	0.656880i	$-0.228124\pi$
$89$	11.5953	+	2.10424i	1.22910	+	0.223049i	0.475106	+	0.879929i	$0.342410\pi$
$90$	−0.561785	−	0.587581i	−0.0592174	−	0.0619365i
$91$	1.77859	+	0.856523i	0.186447	+	0.0897880i
$92$	1.28107	+	2.99722i	0.133561	+	0.312482i
$93$	4.67577	−	8.68904i	0.484855	−	0.901011i
$94$	0.418718	+	1.83452i	0.0431874	+	0.189217i
$95$	−0.802241	−	5.92238i	−0.0823082	−	0.607624i
$96$	2.31787	+	7.13367i	0.236567	+	0.728077i
$97$	10.6897	+	13.4044i	1.08537	+	1.36101i	0.927617	+	0.373533i	$0.121854\pi$
$97$	10.6897	+	13.4044i	1.08537	+	1.36101i	0.157754	+	0.987479i	$0.449575\pi$
$98$	−0.00642692	+	0.0150365i	−0.000649217	+	0.00151892i
$99$	−11.5280	+	10.0717i	−1.15860	+	1.01224i
$100$	3.70916	+	6.89277i	0.370916	+	0.689277i
$101$	−2.00548	+	2.51479i	−0.199553	+	0.250231i	−0.871532	−	0.490339i	$-0.836873\pi$
$101$	−2.00548	+	2.51479i	−0.199553	+	0.250231i	0.671979	+	0.740570i	$0.265444\pi$
$102$	−3.97374	−	1.49137i	−0.393459	−	0.147668i
$103$	0.312931	−	0.150700i	0.0308340	−	0.0148489i	−0.418403	−	0.908261i	$-0.637410\pi$
$103$	0.312931	−	0.150700i	0.0308340	−	0.0148489i	0.449237	+	0.893413i	$0.351696\pi$
$104$	−0.585128	−	0.511211i	−0.0573766	−	0.0501284i
$105$	−1.41547	+	6.20159i	−0.138136	+	0.605214i
$106$	−1.98383	−	0.178548i	−0.192687	−	0.0173421i
$107$	−4.35811	−	0.392237i	−0.421314	−	0.0379190i	−0.123046	−	0.992401i	$-0.539266\pi$
$107$	−4.35811	−	0.392237i	−0.421314	−	0.0379190i	−0.298268	+	0.954482i	$0.596409\pi$
$108$	−0.181345	+	0.794524i	−0.0174499	+	0.0764531i
$109$	10.9684	+	9.58284i	1.05059	+	0.917869i	0.996740	−	0.0806800i	$-0.0257092\pi$
$109$	10.9684	+	9.58284i	1.05059	+	0.917869i	0.0538459	+	0.998549i	$0.482852\pi$
$110$	1.11576	−	0.537323i	0.106384	−	0.0512318i
$111$	14.1714	+	5.31863i	1.34509	+	0.504822i
$112$	5.89149	−	7.38770i	0.556694	−	0.698072i
$113$	5.57945	+	10.3684i	0.524871	+	0.975373i	0.995654	+	0.0931246i	$0.0296855\pi$
$113$	5.57945	+	10.3684i	0.524871	+	0.975373i	−0.470784	+	0.882249i	$0.656029\pi$
$114$	3.03303	−	2.64988i	0.284069	−	0.248184i
$115$	0.645199	−	1.50952i	0.0601651	−	0.140763i
$116$	−6.37580	−	7.99500i	−0.591978	−	0.742317i
$117$	−0.734149	−	2.25948i	−0.0678721	−	0.208889i
$118$	−0.239011	−	1.76445i	−0.0220027	−	0.162431i
$119$	3.79695	+	16.6355i	0.348066	+	1.52498i
$120$	1.18642	−	2.20474i	0.108305	−	0.201264i
$121$	−4.84201	−	11.3285i	−0.440183	−	1.02986i
$122$	−1.50994	−	0.727150i	−0.136704	−	0.0658331i
$123$	−6.46473	−	6.76157i	−0.582905	−	0.609670i
$124$	7.54521	+	1.36925i	0.677580	+	0.122963i
$125$	2.72039	−	8.37250i	0.243319	−	0.748860i
$126$	−2.06197	+	0.773871i	−0.183695	+	0.0689419i
$127$	11.5651	−	12.0961i	1.02623	−	1.07336i	0.0289582	−	0.999581i	$-0.490781\pi$
$127$	11.5651	−	12.0961i	1.02623	−	1.07336i	0.997275	−	0.0737751i	$-0.0235047\pi$
$128$	−6.24709	+	4.53878i	−0.552170	+	0.401175i
$129$	10.5186	+	15.9350i	0.926112	+	1.40300i
$130$	0.00862291	+	0.192004i	0.000756280	+	0.0168399i
$131$	7.29931	−	11.0580i	0.637744	−	0.966141i	−0.361683	−	0.932301i	$-0.617798\pi$
$131$	7.29931	−	11.0580i	0.637744	−	0.966141i	0.999427	−	0.0338398i	$-0.0107736\pi$
$132$	−19.8779	−	11.8765i	−1.73015	−	1.03372i
$133$	−15.6081	−	4.30756i	−1.35339	−	0.373513i
$134$	2.09380	−	0.577852i	0.180877	−	0.0499188i
$135$	0.352345	−	0.210516i	0.0303250	−	0.0181184i
$136$	0.301314	−	6.70927i	0.0258374	−	0.575315i
$137$	−0.189809	−	0.137904i	−0.0162165	−	0.0117820i	0.579647	−	0.814867i	$-0.303190\pi$
$137$	−0.189809	−	0.137904i	−0.0162165	−	0.0117820i	−0.595864	+	0.803085i	$0.703190\pi$
$138$	1.08851	−	0.197536i	0.0926603	−	0.0168154i
$139$	−1.48320	+	10.9494i	−0.125803	+	0.928717i	0.812514	+	0.582942i	$0.198098\pi$
$139$	−1.48320	+	10.9494i	−0.125803	+	0.928717i	−0.938317	+	0.345775i	$0.887616\pi$
$140$	−4.92369	+	0.443140i	−0.416128	+	0.0374522i
$141$	−17.7200			−1.49230
$142$	0.188686	+	2.21455i	0.0158342	+	0.185841i
$143$	3.61919			0.302652
$144$	−11.3261	+	1.01937i	−0.943841	+	0.0849472i
$145$	−0.691330	+	5.10360i	−0.0574118	+	0.423831i
$146$	−1.07338	+	0.194791i	−0.0888340	+	0.0161210i
$147$	−0.124582	−	0.0905139i	−0.0102753	−	0.00746546i
$148$	−0.527772	+	11.7518i	−0.0433826	+	0.965989i
$149$	−1.44219	+	0.861671i	−0.118149	+	0.0705908i	−0.570758	−	0.821118i	$-0.693351\pi$
$149$	−1.44219	+	0.861671i	−0.118149	+	0.0705908i	0.452609	+	0.891709i	$0.350493\pi$
$150$	2.56090	−	0.706764i	0.209097	−	0.0577070i
$151$	−5.41389	−	1.49414i	−0.440576	−	0.121591i	0.0387092	−	0.999251i	$-0.487675\pi$
$151$	−5.41389	−	1.49414i	−0.440576	−	0.121591i	−0.479285	+	0.877659i	$0.659104\pi$
$152$	5.47083	+	3.26867i	0.443743	+	0.265124i
$153$	11.3128	−	17.1382i	0.914586	−	1.38554i
$154$	−0.150527	−	3.35174i	−0.0121298	−	0.270091i
$155$	−2.12763	−	3.22323i	−0.170896	−	0.258896i
$156$	2.90737	−	2.11233i	0.232776	−	0.169122i
$157$	−1.62965	+	1.70448i	−0.130060	+	0.136032i	−0.784618	−	0.619980i	$-0.787141\pi$
$157$	−1.62965	+	1.70448i	−0.130060	+	0.136032i	0.654557	+	0.756012i	$0.272855\pi$
$158$	−4.37239	+	1.64098i	−0.347848	+	0.130550i
$159$	5.79634	−	17.8393i	0.459680	−	1.41475i
$160$	2.88870	+	0.524221i	0.228372	+	0.0414433i
$161$	−3.07352	−	3.21465i	−0.242227	−	0.253350i
$162$	−2.01081	−	0.968355i	−0.157984	−	0.0760811i
$163$	3.49896	+	8.18623i	0.274060	+	0.641195i	0.998859	−	0.0477659i	$-0.0152101\pi$
$163$	3.49896	+	8.18623i	0.274060	+	0.641195i	−0.724799	+	0.688961i	$0.758067\pi$
$164$	3.44510	−	6.40208i	0.269018	−	0.499918i
$165$	2.59506	+	11.3697i	0.202025	+	0.885130i
$166$	−0.125470	−	0.926257i	−0.00973836	−	0.0718915i
$167$	−3.82278	−	11.7653i	−0.295816	−	0.910427i	−0.982946	−	0.183893i	$-0.941130\pi$
$167$	−3.82278	−	11.7653i	−0.295816	−	0.910427i	0.687131	−	0.726534i	$-0.258870\pi$
$168$	−4.22916	−	5.30320i	−0.326287	−	0.409151i
$169$	4.88857	−	11.4374i	0.376044	−	0.879798i
$170$	−1.25107	+	1.09303i	−0.0959528	+	0.0838314i
$171$	9.23387	+	17.1594i	0.706132	+	1.31221i
$172$	−9.25187	+	11.6015i	−0.705448	+	0.884604i
$173$	−5.47682	−	2.05549i	−0.416395	−	0.156276i	0.134379	−	0.990930i	$-0.457096\pi$
$173$	−5.47682	−	2.05549i	−0.416395	−	0.156276i	−0.550774	+	0.834654i	$0.685667\pi$
$174$	−3.12702	+	1.50589i	−0.237059	+	0.114161i
$175$	−8.04300	−	7.02696i	−0.607994	−	0.531188i
$176$	3.85489	−	16.8894i	0.290574	−	1.27309i
$177$	16.7001	+	1.50304i	1.25526	+	0.112975i
$178$	3.09595	+	0.278640i	0.232051	+	0.0208850i
$179$	−1.31594	+	5.76551i	−0.0983581	+	0.430935i	−0.999999	−	0.00155100i	$-0.999506\pi$
$179$	−1.31594	+	5.76551i	−0.0983581	+	0.430935i	0.901641	+	0.432486i	$0.142363\pi$
$180$	4.48038	+	3.91439i	0.333948	+	0.291761i
$181$	−8.27364	+	3.98437i	−0.614974	+	0.296156i	−0.715321	−	0.698796i	$-0.753719\pi$
$181$	−8.27364	+	3.98437i	−0.614974	+	0.296156i	0.100346	+	0.994953i	$0.468005\pi$
$182$	0.487503	+	0.182963i	0.0361362	+	0.0135621i
$183$	9.83997	−	12.3389i	0.727392	−	0.912120i
$184$	0.829517	+	1.54150i	0.0611528	+	0.113641i
$185$	4.46166	−	3.89803i	0.328028	−	0.286589i
$186$	1.02292	−	2.39325i	0.0750043	−	0.175481i
$187$	19.5047	+	24.4581i	1.42632	+	1.78855i
$188$	−4.25558	−	13.0973i	−0.310370	−	0.955221i
$189$	−0.149265	−	1.10192i	−0.0108575	−	0.0801530i
$190$	−0.350786	−	1.53690i	−0.0254487	−	0.111498i
$191$	−8.18184	+	15.2044i	−0.592017	+	1.10015i	0.391643	+	0.920117i	$0.371907\pi$
$191$	−8.18184	+	15.2044i	−0.592017	+	1.10015i	−0.983660	+	0.180035i	$0.942379\pi$
$192$	−6.22679	−	14.5683i	−0.449380	−	1.05138i
$193$	−9.01249	−	4.34018i	−0.648733	−	0.312413i	0.0804231	−	0.996761i	$-0.474373\pi$
$193$	−9.01249	−	4.34018i	−0.648733	−	0.312413i	−0.729156	+	0.684348i	$0.760087\pi$
$194$	3.12521	+	3.26871i	0.224377	+	0.234680i
$195$	−1.78084	−	0.323176i	−0.127529	−	0.0231431i
$196$	0.0369820	−	0.113819i	0.00264157	−	0.00812993i
$197$	−13.5506	+	5.08564i	−0.965444	+	0.362337i	−0.783790	−	0.621025i	$-0.786716\pi$
$197$	−13.5506	+	5.08564i	−0.965444	+	0.362337i	−0.181653	+	0.983363i	$0.558145\pi$
$198$	−2.79036	+	2.91849i	−0.198303	+	0.207408i
$199$	−0.868670	+	0.631126i	−0.0615784	+	0.0447393i	−0.618149	−	0.786061i	$-0.712117\pi$
$199$	−0.868670	+	0.631126i	−0.0615784	+	0.0447393i	0.556570	+	0.830801i	$0.312117\pi$
$200$	2.31580	+	3.50829i	0.163752	+	0.248074i
$201$	0.917688	+	20.4339i	0.0647287	+	1.44130i
$202$	−0.467398	+	0.708078i	−0.0328860	+	0.0498202i
$203$	11.9780	+	7.15652i	0.840691	+	0.502289i
$204$	29.9434	+	8.26385i	2.09646	+	0.578585i
$205$	−3.52959	+	0.974105i	−0.246517	+	0.0680344i
$206$	0.0786467	−	0.0469892i	0.00547957	−	0.00327389i
$207$	−0.240138	+	5.34708i	−0.0166907	+	0.371648i
$208$	2.17513	+	1.58032i	0.150818	+	0.109576i
$209$	−29.2078	+	5.30044i	−2.02035	+	0.366639i
$210$	−0.225226	+	1.66268i	−0.0155421	+	0.114736i
$211$	1.38148	−	0.124336i	0.0951052	−	0.00855962i	−0.0419845	−	0.999118i	$-0.513368\pi$
$211$	1.38148	−	0.124336i	0.0951052	−	0.00855962i	0.137090	+	0.990559i	$0.456225\pi$
$212$	14.5775			1.00119
$213$	−20.7270	−	2.90825i	−1.42019	−	0.199270i
$214$	−1.15419			−0.0788987
$215$	7.44334	−	0.669912i	0.507631	−	0.0456876i
$216$	−0.0587500	+	0.433710i	−0.00399743	+	0.0295102i
$217$	−10.2952	+	1.86831i	−0.698885	+	0.126829i
$218$	3.10809	+	2.25816i	0.210506	+	0.152942i
$219$	0.460905	−	10.2628i	0.0311451	−	0.693499i
$220$	−7.78041	+	4.64858i	−0.524555	+	0.313407i
$221$	−4.68010	+	1.29163i	−0.314818	+	0.0868842i
$222$	3.84872	+	1.06218i	0.258309	+	0.0712888i
$223$	7.31667	+	4.37151i	0.489961	+	0.292738i	0.736551	−	0.676382i	$-0.236453\pi$
$223$	7.31667	+	4.37151i	0.489961	+	0.292738i	−0.246590	+	0.969120i	$0.579310\pi$
$224$	4.38181	−	6.63816i	0.292772	−	0.443531i
$225$	0.576666	+	12.8405i	0.0384444	+	0.856030i
$226$	1.71092	+	2.59194i	0.113809	+	0.172413i
$227$	1.14216	−	0.829831i	0.0758081	−	0.0550778i	−0.549236	−	0.835667i	$-0.685081\pi$
$227$	1.14216	−	0.829831i	0.0758081	−	0.0550778i	0.625044	+	0.780590i	$0.285081\pi$
$228$	−20.3697	+	21.3050i	−1.34901	+	1.41096i
$229$	−4.04212	+	1.51703i	−0.267110	+	0.100248i	−0.481337	−	0.876536i	$-0.659849\pi$
$229$	−4.04212	+	1.51703i	−0.267110	+	0.100248i	0.214226	+	0.976784i	$0.431277\pi$
$230$	0.133808	−	0.411819i	0.00882305	−	0.0271546i
$231$	31.0875	+	5.64154i	2.04541	+	0.371186i
$232$	−3.79522	−	3.96948i	−0.249168	−	0.260609i
$233$	11.0821	+	5.33684i	0.726010	+	0.349628i	0.760114	−	0.649790i	$-0.225143\pi$
$233$	11.0821	+	5.33684i	0.726010	+	0.349628i	−0.0341035	+	0.999418i	$0.510858\pi$
$234$	−0.246291	−	0.576227i	−0.0161006	−	0.0376692i
$235$	−3.28665	+	6.10763i	−0.214398	+	0.398418i
$236$	2.89971	+	12.7044i	0.188755	+	0.826989i
$237$	−5.90348	−	43.5812i	−0.383472	−	2.83091i
$238$	1.39083	+	4.28053i	0.0901539	+	0.277465i
$239$	−18.3584	−	23.0207i	−1.18750	−	1.48908i	−0.832327	−	0.554285i	$-0.812992\pi$
$239$	−18.3584	−	23.0207i	−1.18750	−	1.48908i	−0.355177	−	0.934799i	$-0.615580\pi$
$240$	−3.40496	+	7.96631i	−0.219789	+	0.514223i
$241$	10.3837	−	9.07199i	0.668875	−	0.584378i	−0.255062	−	0.966925i	$-0.582096\pi$
$241$	10.3837	−	9.07199i	0.668875	−	0.584378i	0.923936	+	0.382547i	$0.124953\pi$
$242$	−1.53989	−	2.86160i	−0.0989881	−	0.183951i
$243$	13.8937	−	17.4221i	0.891279	−	1.11763i
$244$	11.4832	+	4.30970i	0.735134	+	0.275900i
$245$	−0.0543047	+	0.0261518i	−0.00346940	+	0.00167078i
$246$	−1.85821	−	1.62347i	−0.118475	−	0.103509i
$247$	1.02516	−	4.49152i	0.0652294	−	0.285789i
$248$	4.10175	+	0.369164i	0.260461	+	0.0234419i
$249$	8.76682	+	0.789028i	0.555574	+	0.0500026i
$250$	0.516710	−	2.26386i	0.0326796	−	0.143179i
$251$	−3.32692	−	2.90664i	−0.209993	−	0.183466i	0.546516	−	0.837449i	$-0.315954\pi$
$251$	−3.32692	−	2.90664i	−0.209993	−	0.183466i	−0.756509	+	0.653983i	$0.773097\pi$
$252$	14.5222	−	6.99354i	0.914815	−	0.440552i
$253$	−7.63394	−	2.86507i	−0.479942	−	0.180125i
$254$	2.75224	−	3.45120i	0.172691	−	0.216548i
$255$	−7.41341	−	13.7764i	−0.464246	−	0.862713i
$256$	8.07273	−	7.05293i	0.504546	−	0.440808i
$257$	−7.79325	+	18.2332i	−0.486130	+	1.13736i	0.479525	+	0.877528i	$0.340809\pi$
$257$	−7.79325	+	18.2332i	−0.486130	+	1.13736i	−0.965655	+	0.259829i	$0.916334\pi$
$258$	3.14011	+	3.93757i	0.195495	+	0.245142i
$259$	−4.96007	−	15.2655i	−0.308203	−	0.948553i
$260$	−0.188814	−	1.39388i	−0.0117097	−	0.0864448i
$261$	−3.73660	−	16.3711i	−0.231290	−	1.01335i
$262$	1.65614	−	3.07762i	0.102317	−	0.190136i
$263$	6.97074	+	16.3089i	0.429834	+	1.00565i	0.984787	+	0.173765i	$0.0555934\pi$
$263$	6.97074	+	16.3089i	0.429834	+	1.00565i	−0.554953	+	0.831882i	$0.687264\pi$
$264$	−11.2042	−	5.39565i	−0.689570	−	0.332079i
$265$	−5.07365	−	5.30662i	−0.311672	−	0.325983i
$266$	−4.20224	−	0.762594i	−0.257656	−	0.0467576i
$267$	−9.04570	+	27.8398i	−0.553588	+	1.70377i
$268$	−14.8828	+	5.58562i	−0.909114	+	0.341196i
$269$	9.78775	−	10.2372i	0.596770	−	0.624172i	−0.353562	−	0.935411i	$-0.615030\pi$
$269$	9.78775	−	10.2372i	0.596770	−	0.624172i	0.950332	+	0.311239i	$0.100744\pi$
$270$	0.0875868	−	0.0636355i	0.00533036	−	0.00387274i
$271$	−1.87170	−	2.83550i	−0.113698	−	0.172245i	0.773269	−	0.634078i	$-0.218620\pi$
$271$	−1.87170	−	2.83550i	−0.113698	−	0.172245i	−0.886967	+	0.461834i	$0.847192\pi$
$272$	1.04263	+	23.2160i	0.0632189	+	1.40768i
$273$	−2.70133	+	4.09234i	−0.163492	+	0.247680i
$274$	−0.0531252	−	0.0317408i	−0.00320941	−	0.00191753i
$275$	−18.8750	−	5.20918i	−1.13821	−	0.314125i
$276$	−7.80468	+	2.15396i	−0.469787	+	0.129653i
$277$	17.1240	−	10.2311i	1.02888	−	0.614727i	0.103838	−	0.994594i	$-0.466888\pi$
$277$	17.1240	−	10.2311i	1.02888	−	0.614727i	0.925041	+	0.379867i	$0.124030\pi$
$278$	−0.130759	+	2.91158i	−0.00784241	+	0.174625i
$279$	10.1874	+	7.40161i	0.609906	+	0.443123i
$280$	−2.61228	+	0.474060i	−0.156114	+	0.0283305i
$281$	1.48909	−	10.9929i	0.0888314	−	0.655779i	−0.890715	−	0.454562i	$-0.849796\pi$
$281$	1.48909	−	10.9929i	0.0888314	−	0.655779i	0.979547	−	0.201218i	$-0.0644899\pi$
$282$	−4.65522	+	0.418977i	−0.277214	+	0.0249497i
$283$	0.793605			0.0471749			0.0235875	−	0.999722i	$-0.492491\pi$
$283$	0.793605			0.0471749			0.0235875	+	0.999722i	$0.492491\pi$
$284$	−2.82817	−	16.0183i	−0.167821	−	0.950511i
$285$	14.8452			0.879353
$286$	0.950795	−	0.0855731i	0.0562217	−	0.00506004i
$287$	−1.33159	+	9.83016i	−0.0786010	+	0.580256i
$288$	−9.41853	+	1.70921i	−0.554992	+	0.100716i
$289$	−20.1976	−	14.6744i	−1.18809	−	0.863199i
$290$	−0.0609478	+	1.35711i	−0.00357898	+	0.0796921i
$291$	−36.5586	+	21.8428i	−2.14311	+	1.28045i
$292$	7.69622	−	2.12402i	0.450387	−	0.124299i
$293$	21.8639	+	6.03404i	1.27730	+	0.352512i	0.837922	−	0.545790i	$-0.183770\pi$
$293$	21.8639	+	6.03404i	1.27730	+	0.352512i	0.439378	+	0.898302i	$0.355199\pi$
$294$	−0.0348689	−	0.0208332i	−0.00203359	−	0.00121502i
$295$	3.61554	−	5.47731i	0.210505	−	0.318901i
$296$	0.283439	+	6.31127i	0.0164746	+	0.366835i
$297$	−1.12309	−	1.70141i	−0.0651683	−	0.0987258i
$298$	−0.358504	+	0.260468i	−0.0207676	+	0.0150885i
$299$	0.874514	−	0.914670i	0.0505745	−	0.0528967i
$300$	−18.2030	+	6.83171i	−1.05095	+	0.394429i
$301$	6.25672	−	19.2562i	0.360631	−	1.10991i
$302$	−1.45760	−	0.264516i	−0.0838757	−	0.0152212i
$303$	−5.52138	−	5.77491i	−0.317195	−	0.331760i
$304$	−19.8683	−	9.56807i	−1.13953	−	0.548766i
$305$	−2.42782	−	5.68016i	−0.139016	−	0.325245i
$306$	2.56676	−	4.76984i	0.146732	−	0.272673i
$307$	2.15158	+	9.42670i	0.122797	+	0.538010i	0.998480	+	0.0551225i	$0.0175549\pi$
$307$	2.15158	+	9.42670i	0.122797	+	0.538010i	−0.875682	+	0.482888i	$0.839588\pi$
$308$	3.29605	+	24.3324i	0.187810	+	1.38647i
$309$	0.266601	+	0.820515i	0.0151664	+	0.0466775i
$310$	−0.635160	−	0.796465i	−0.0360747	−	0.0452362i
$311$	9.92442	−	23.2193i	0.562762	−	1.31665i	−0.360601	−	0.932720i	$-0.617428\pi$
$311$	9.92442	−	23.2193i	0.562762	−	1.31665i	0.923363	−	0.383927i	$-0.125429\pi$
$312$	1.45342	−	1.26982i	0.0822839	−	0.0718893i
$313$	−10.8454	−	20.1541i	−0.613017	−	1.13918i	−0.978087	−	0.208196i	$-0.933241\pi$
$313$	−10.8454	−	20.1541i	−0.613017	−	1.13918i	0.365070	−	0.930980i	$-0.381045\pi$
$314$	−0.387823	+	0.486315i	−0.0218861	+	0.0274443i
$315$	−7.60025	−	2.85242i	−0.428226	−	0.160716i
$316$	30.7942	−	14.8297i	1.73231	−	0.834237i
$317$	7.65342	+	6.68659i	0.429859	+	0.375556i	0.845503	−	0.533971i	$-0.179301\pi$
$317$	7.65342	+	6.68659i	0.429859	+	0.375556i	−0.415644	+	0.909527i	$0.636444\pi$
$318$	1.10095	−	4.82360i	0.0617384	−	0.270494i
$319$	25.4779	+	2.29305i	1.42649	+	0.128386i
$320$	−6.17623	−	0.555871i	−0.345262	−	0.0310741i
$321$	2.41859	−	10.5965i	0.134992	−	0.591440i
$322$	−0.883449	−	0.771846i	−0.0492327	−	0.0430133i
$323$	35.8780	−	17.2779i	1.99631	−	0.961371i
$324$	15.2923	+	5.73928i	0.849570	+	0.318849i
$325$	1.89471	−	2.37589i	0.105100	−	0.131791i
$326$	1.11277	+	2.06787i	0.0616304	+	0.114529i
$327$	−27.2449	+	23.8032i	−1.50665	+	1.31632i
$328$	1.53454	−	3.59024i	0.0847308	−	0.198238i
$329$	11.7158	+	14.6911i	0.645910	+	0.809946i
$330$	0.950574	+	2.92557i	0.0523274	+	0.161047i
$331$	1.48189	+	10.9397i	0.0814519	+	0.601302i	0.984967	+	0.172745i	$0.0552637\pi$
$331$	1.48189	+	10.9397i	0.0814519	+	0.601302i	−0.903515	+	0.428557i	$0.859022\pi$
$332$	1.52222	+	6.66927i	0.0835425	+	0.366024i
$333$	−9.15375	+	17.0105i	−0.501623	+	0.932171i
$334$	−1.28246	−	3.00047i	−0.0701731	−	0.164178i
$335$	7.21323	+	3.47371i	0.394101	+	0.189789i
$336$	16.2201	+	16.9649i	0.884881	+	0.925513i
$337$	−4.76067	−	0.863934i	−0.259330	−	0.0470615i	0.0473345	−	0.998879i	$-0.484927\pi$
$337$	−4.76067	−	0.863934i	−0.259330	−	0.0470615i	−0.306665	+	0.951818i	$0.599213\pi$
$338$	1.01384	−	3.12029i	0.0551458	−	0.169721i
$339$	−27.3816	+	10.2765i	−1.48717	+	0.558143i
$340$	8.40213	−	8.78794i	0.455669	−	0.476593i
$341$	−15.5194	+	11.2755i	−0.840423	+	0.610603i
$342$	2.83154	+	4.28960i	0.153112	+	0.231955i
$343$	0.834547	+	18.5826i	0.0450613	+	1.00337i
$344$	−4.39020	+	6.65086i	−0.236704	+	0.358591i
$345$	3.50049	+	2.09145i	0.188460	+	0.112600i
$346$	−1.48741	−	0.410499i	−0.0799637	−	0.0220686i
$347$	1.25141	−	0.345367i	0.0671792	−	0.0185403i	−0.232286	−	0.972648i	$-0.574620\pi$
$347$	1.25141	−	0.345367i	0.0671792	−	0.0185403i	0.299465	+	0.954107i	$0.403192\pi$
$348$	21.8052	−	13.0280i	1.16888	−	0.698375i
$349$	0.271173	−	6.03813i	0.0145155	−	0.323214i	−0.978577	−	0.205881i	$-0.933994\pi$
$349$	0.271173	−	6.03813i	0.0145155	−	0.323214i	0.993093	−	0.117333i	$-0.0374344\pi$
$350$	−2.27912	−	1.65587i	−0.121824	−	0.0885102i
$351$	0.311311	−	0.0564946i	0.0166165	−	0.00301546i
$352$	1.95744	−	14.4504i	0.104332	−	0.770210i
$353$	26.8126	−	2.41318i	1.42709	−	0.128441i	0.651009	−	0.759070i	$-0.274346\pi$
$353$	26.8126	−	2.41318i	1.42709	−	0.128441i	0.776084	+	0.630630i	$0.217203\pi$
$354$	4.42281			0.235070
$355$	−4.84677	+	6.60464i	−0.257240	+	0.350538i
$356$	−22.7495			−1.20572
$357$	−42.2137	+	3.79930i	−2.23418	+	0.201080i
$358$	−0.209388	+	1.54577i	−0.0110665	+	0.0816964i
$359$	−7.98911	+	1.44981i	−0.421649	+	0.0765180i	−0.385234	−	0.922819i	$-0.625879\pi$
$359$	−7.98911	+	1.44981i	−0.421649	+	0.0765180i	−0.0364146	+	0.999337i	$0.511594\pi$
$360$	2.58494	+	1.87807i	0.136238	+	0.0989828i
$361$	−0.842884	+	18.7683i	−0.0443623	+	0.987804i
$362$	−2.07935	+	1.24236i	−0.109288	+	0.0652967i
$363$	29.4990	−	8.14121i	1.54830	−	0.427302i
$364$	−3.67349	−	1.01382i	−0.192543	−	0.0531386i
$365$	−3.45184	−	2.06238i	−0.180678	−	0.107950i
$366$	2.29331	−	3.47421i	0.119873	−	0.181600i
$367$	0.555694	+	12.3735i	0.0290070	+	0.645890i	0.959857	+	0.280489i	$0.0904967\pi$
$367$	0.555694	+	12.3735i	0.0290070	+	0.645890i	−0.930850	+	0.365401i	$0.880932\pi$
$368$	−3.33695	−	5.05527i	−0.173951	−	0.263524i
$369$	9.65834	−	7.01720i	0.502793	−	0.365301i
$370$	1.07995	−	1.12954i	0.0561441	−	0.0587221i
$371$	−18.6223	+	6.98905i	−0.966820	+	0.362853i
$372$	−5.88614	+	18.1157i	−0.305182	+	0.939254i
$373$	−0.00162945		0.000295701i	−8.43696e−5		1.53108e-5i	0.178515	−	0.983937i	$-0.442871\pi$
$373$	−0.00162945		0.000295701i	−8.43696e−5		1.53108e-5i	−0.178599	+	0.983922i	$0.557157\pi$
$374$	5.70235	+	5.96419i	0.294862	+	0.308401i
$375$	19.7015	+	9.48776i	1.01738	+	0.489946i
$376$	−2.90677	−	6.80072i	−0.149905	−	0.350720i
$377$	−1.88130	+	3.49605i	−0.0968921	+	0.180056i
$378$	−0.0652675	−	0.285955i	−0.00335700	−	0.0147080i
$379$	0.180367	+	1.33152i	0.00926484	+	0.0683958i	0.994992	−	0.0999554i	$-0.0318700\pi$
$379$	0.180367	+	1.33152i	0.00926484	+	0.0683958i	−0.985727	+	0.168351i	$0.946156\pi$
$380$	3.56517	+	10.9725i	0.182889	+	0.562875i
$381$	25.9180	+	32.5001i	1.32782	+	1.66503i
$382$	−1.78995	+	4.18779i	−0.0915816	+	0.214266i
$383$	−24.9596	+	21.8066i	−1.27538	+	1.11426i	−0.287707	+	0.957718i	$0.592893\pi$
$383$	−24.9596	+	21.8066i	−1.27538	+	1.11426i	−0.987671	+	0.156546i	$0.949964\pi$
$384$	−9.08907	−	16.8903i	−0.463824	−	0.861930i
$385$	7.71049	−	9.66865i	0.392963	−	0.492760i
$386$	−2.47028	−	0.927113i	−0.125734	−	0.0471888i
$387$	−21.9538	+	10.5724i	−1.11598	+	0.537426i
$388$	−24.9243	−	21.7757i	−1.26534	−	1.10550i
$389$	−0.490148	+	2.14748i	−0.0248515	+	0.108882i	−0.985832	−	0.167733i	$-0.946355\pi$
$389$	−0.490148	+	2.14748i	−0.0248515	+	0.108882i	0.960981	+	0.276615i	$0.0892125\pi$
$390$	−0.475485	−	0.0427945i	−0.0240771	−	0.00216698i
$391$	10.8942	+	0.980496i	0.550944	+	0.0495858i
$392$	0.0143019	−	0.0626606i	0.000722353	−	0.00316484i
$393$	24.7850	+	21.6540i	1.25024	+	1.09230i
$394$	−3.43963	+	1.65644i	−0.173286	+	0.0834502i
$395$	−16.1163	−	6.04853i	−0.810897	−	0.304335i
$396$	18.4246	−	23.1038i	0.925872	−	1.16101i
$397$	−8.23338	−	15.3002i	−0.413222	−	0.767895i	0.585874	−	0.810402i	$-0.300751\pi$
$397$	−8.23338	−	15.3002i	−0.413222	−	0.767895i	−0.999096	+	0.0425073i	$0.986465\pi$
$398$	−0.213285	+	0.186342i	−0.0106910	+	0.00934046i
$399$	15.8071	−	36.9824i	0.791342	−	1.85144i
$400$	−9.06927	−	11.3725i	−0.453464	−	0.568625i
$401$	2.24275	+	6.90246i	0.111997	+	0.344693i	0.991309	−	0.131554i	$-0.0419968\pi$
$401$	2.24275	+	6.90246i	0.111997	+	0.344693i	−0.879312	+	0.476247i	$0.841997\pi$
$402$	0.724229	+	5.34648i	0.0361213	+	0.266658i
$403$	−0.662481	−	2.90252i	−0.0330005	−	0.144585i
$404$	2.94239	−	5.46788i	0.146389	−	0.272037i
$405$	−3.23316	−	7.56435i	−0.160657	−	0.375875i
$406$	3.31594	+	1.59687i	0.164567	+	0.0792514i
$407$	−20.3361	−	21.2699i	−1.00802	−	1.05431i
$408$	16.4141	+	2.97873i	0.812621	+	0.147469i
$409$	1.52780	−	4.70210i	0.0755450	−	0.232504i	−0.906152	−	0.422952i	$-0.860994\pi$
$409$	1.52780	−	4.70210i	0.0755450	−	0.232504i	0.981697	+	0.190448i	$0.0609940\pi$
$410$	−0.904224	+	0.339361i	−0.0446564	+	0.0167598i
$411$	0.402733	−	0.421226i	0.0198654	−	0.0207775i
$412$	−0.542437	+	0.394104i	−0.0267240	+	0.0194161i
$413$	−9.79530	−	14.8393i	−0.481995	−	0.730192i
$414$	0.0633414	+	1.41041i	0.00311306	+	0.0693176i
$415$	1.89800	−	2.87534i	0.0931690	−	0.141145i
$416$	1.94280	+	1.16077i	0.0952537	+	0.0569115i
$417$	−26.4570	−	7.30167i	−1.29560	−	0.357564i
$418$	−7.54784	+	2.08307i	−0.369177	+	0.101886i
$419$	26.0650	−	15.5731i	1.27336	−	0.760796i	0.292640	−	0.956223i	$-0.405466\pi$
$419$	26.0650	−	15.5731i	1.27336	−	0.760796i	0.980718	+	0.195426i	$0.0626091\pi$
$420$	0.550922	−	12.2672i	0.0268822	−	0.598579i
$421$	5.35490	+	3.89056i	0.260982	+	0.189615i	0.710580	−	0.703617i	$-0.248433\pi$
$421$	5.35490	+	3.89056i	0.260982	+	0.189615i	−0.449598	+	0.893231i	$0.648433\pi$
$422$	0.359988	−	0.0653282i	0.0175239	−	0.00318013i
$423$	3.03555	−	22.4093i	0.147593	−	1.08958i
$424$	7.79731	−	0.701771i	0.378671	−	0.0340810i
$425$	26.2670			1.27414
$426$	−5.51394	−	0.273948i	−0.267151	−	0.0132728i
$427$	−16.7356			−0.809892
$428$	8.41300	−	0.757184i	0.406658	−	0.0365999i
$429$	−1.20674	+	8.90849i	−0.0582618	+	0.430106i
$430$	1.93959	−	0.351984i	0.0935355	−	0.0169742i
$431$	24.9971	+	18.1614i	1.20407	+	0.874805i	0.994679	−	0.103027i	$-0.0328529\pi$
$431$	24.9971	+	18.1614i	1.20407	+	0.874805i	0.209388	+	0.977833i	$0.432853\pi$
$432$	0.0679464	−	1.51294i	0.00326907	−	0.0727915i
$433$	7.77150	−	4.64325i	0.373474	−	0.223140i	−0.313880	−	0.949463i	$-0.601629\pi$
$433$	7.77150	−	4.64325i	0.373474	−	0.223140i	0.687355	+	0.726322i	$0.258772\pi$
$434$	−2.66047	+	0.734244i	−0.127707	+	0.0352448i
$435$	−12.3318	−	3.40336i	−0.591264	−	0.163179i
$436$	−24.1366	−	14.4209i	−1.15593	−	0.690638i
$437$	−5.71799	+	8.66239i	−0.273529	+	0.414378i
$438$	−0.121573	−	2.70704i	−0.00580900	−	0.129347i
$439$	11.9237	+	18.0637i	0.569088	+	0.862132i	0.999173	−	0.0406568i	$-0.0129450\pi$
$439$	11.9237	+	18.0637i	0.569088	+	0.862132i	−0.430085	+	0.902788i	$0.641516\pi$
$440$	−3.93785	+	2.86102i	−0.187730	+	0.136394i
$441$	0.135808	−	0.142044i	0.00646706	−	0.00676402i
$442$	−1.19897	+	0.449979i	−0.0570290	+	0.0214033i
$443$	12.0809	−	37.1811i	0.573979	−	1.76653i	−0.0656490	−	0.997843i	$-0.520912\pi$
$443$	12.0809	−	37.1811i	0.573979	−	1.76653i	0.639628	−	0.768684i	$-0.279088\pi$
$444$	−28.7505	−	5.21745i	−1.36444	−	0.247609i
$445$	7.91787	+	8.28145i	0.375343	+	0.392578i
$446$	2.02552	+	0.975438i	0.0959111	+	0.0461883i
$447$	−1.64010	−	3.83721i	−0.0775741	−	0.181494i
$448$	−7.96119	+	14.7944i	−0.376131	+	0.698968i
$449$	2.79481	+	12.2449i	0.131895	+	0.577871i	0.997076	+	0.0764112i	$0.0243462\pi$
$449$	2.79481	+	12.2449i	0.131895	+	0.577871i	−0.865181	+	0.501459i	$0.832797\pi$
$450$	0.455098	+	3.35967i	0.0214535	+	0.158376i
$451$	5.62001	+	17.2966i	0.264636	+	0.814465i
$452$	−14.1715	−	17.7705i	−0.666571	−	0.835854i
$453$	5.48290	−	12.8279i	0.257609	−	0.602706i
$454$	0.280436	−	0.245010i	0.0131615	−	0.0114989i
$455$	0.909487	+	1.69011i	0.0426374	+	0.0792335i
$456$	−9.86982	+	12.3764i	−0.462197	+	0.579576i
$457$	−4.96504	−	1.86341i	−0.232255	−	0.0871667i	0.232534	−	0.972588i	$-0.425298\pi$
$457$	−4.96504	−	1.86341i	−0.232255	−	0.0871667i	−0.464789	+	0.885422i	$0.653870\pi$
$458$	−1.02603	+	0.494111i	−0.0479433	+	0.0230883i
$459$	2.05951	+	1.79934i	0.0961298	+	0.0839861i
$460$	−0.705175	+	3.08958i	−0.0328790	+	0.144052i
$461$	−30.9067	−	2.78165i	−1.43947	−	0.129554i	−0.657773	−	0.753217i	$-0.728501\pi$
$461$	−30.9067	−	2.78165i	−1.43947	−	0.129554i	−0.781694	+	0.623662i	$0.785644\pi$
$462$	8.30035	+	0.747045i	0.386167	+	0.0347557i
$463$	−0.555529	+	2.43393i	−0.0258176	+	0.113114i	−0.986195	−	0.165589i	$-0.947047\pi$
$463$	−0.555529	+	2.43393i	−0.0258176	+	0.113114i	0.960377	+	0.278703i	$0.0899046\pi$
$464$	14.3109	+	12.5031i	0.664367	+	0.580440i
$465$	8.64326	−	4.16237i	0.400822	−	0.193025i
$466$	3.03754	+	1.14001i	0.140712	+	0.0528099i
$467$	−15.5860	+	19.5443i	−0.721235	+	0.904400i	−0.998407	−	0.0564199i	$-0.982031\pi$
$467$	−15.5860	+	19.5443i	−0.721235	+	0.904400i	0.277172	+	0.960820i	$0.410603\pi$
$468$	2.17327	+	4.03860i	0.100459	+	0.186685i
$469$	16.3343	−	14.2709i	0.754249	−	0.658968i
$470$	−0.719024	+	1.68224i	−0.0331661	+	0.0775959i
$471$	−3.65214	−	4.57964i	−0.168282	−	0.211019i
$472$	2.16261	+	6.65584i	0.0995424	+	0.306360i
$473$	−4.98276	−	36.7842i	−0.229108	−	1.69134i
$474$	−2.58134	−	11.3096i	−0.118565	−	0.519467i
$475$	−11.8112	+	21.9489i	−0.541936	+	1.00709i
$476$	−12.9460	−	30.2888i	−0.593381	−	1.38828i
$477$	21.5672	+	10.3862i	0.987494	+	0.475552i
$478$	−5.36722	−	5.61367i	−0.245491	−	0.256763i
$479$	−23.4935	−	4.26344i	−1.07345	−	0.194802i	−0.387071	−	0.922050i	$-0.626513\pi$
$479$	−23.4935	−	4.26344i	−1.07345	−	0.194802i	−0.686375	+	0.727248i	$0.740799\pi$
$480$	−2.25352	+	6.93562i	−0.102859	+	0.316567i
$481$	4.27584	−	1.60475i	0.194961	−	0.0731702i
$482$	2.51340	−	2.62881i	0.114482	−	0.119739i
$483$	8.93752	−	6.49349i	0.406671	−	0.295464i
$484$	13.1017	+	19.8483i	0.595534	+	0.902195i
$485$	0.747847	+	16.6521i	0.0339580	+	0.756134i
$486$	3.23806	−	4.90545i	0.146881	−	0.222516i
$487$	−9.28559	−	5.54788i	−0.420770	−	0.251398i	0.286873	−	0.957969i	$-0.407384\pi$
$487$	−9.28559	−	5.54788i	−0.420770	−	0.251398i	−0.707643	+	0.706570i	$0.750241\pi$
$488$	6.34966	+	1.75239i	0.287436	+	0.0793272i
$489$	−21.3167	+	5.88304i	−0.963975	+	0.266040i
$490$	−0.0136480	+	0.00815430i	−0.000616554	+	0.000368374i
$491$	0.741765	−	16.5167i	0.0334754	−	0.745388i	−0.910131	−	0.414320i	$-0.864020\pi$
$491$	0.741765	−	16.5167i	0.0334754	−	0.745388i	0.943607	−	0.331068i	$-0.107409\pi$
$492$	14.6098	+	10.6146i	0.658659	+	0.478544i
$493$	−33.7647	+	6.12739i	−1.52069	+	0.275964i
$494$	0.163120	−	1.20420i	0.00733913	−	0.0541796i
$495$	−14.8230	+	1.33410i	−0.666246	+	0.0599632i
$496$	−14.2506			−0.639870
$497$	11.2927	+	19.1069i	0.506547	+	0.857061i
$498$	2.32178			0.104041
$499$	18.8559	−	1.69706i	0.844106	−	0.0759709i	0.340860	−	0.940114i	$-0.389282\pi$
$499$	18.8559	−	1.69706i	0.844106	−	0.0759709i	0.503246	+	0.864143i	$0.332139\pi$
$500$	−2.28119	+	16.8404i	−0.102018	+	0.753128i
$501$	30.2345	−	5.48674i	1.35078	−	0.245130i
$502$	−0.942738	−	0.684939i	−0.0420765	−	0.0305703i
$503$	−0.417334	+	9.29265i	−0.0186080	+	0.414339i	0.967972	+	0.251059i	$0.0807788\pi$
$503$	−0.417334	+	9.29265i	−0.0186080	+	0.414339i	−0.986580	+	0.163280i	$0.947793\pi$
$504$	7.43108	−	4.43986i	0.331006	−	0.197767i
$505$	−3.01455	+	0.831962i	−0.134146	+	0.0370218i
$506$	−2.07325	−	0.572180i	−0.0921671	−	0.0254365i
$507$	26.5226	+	15.8465i	1.17791	+	0.703770i
$508$	−17.7973	+	26.9617i	−0.789627	+	1.19623i
$509$	−0.0381662	−	0.849837i	−0.00169169	−	0.0376684i	0.997970	−	0.0636910i	$-0.0202872\pi$
$509$	−0.0381662	−	0.849837i	−0.00169169	−	0.0376684i	−0.999661	+	0.0260227i	$0.991716\pi$
$510$	−2.27330	−	3.44391i	−0.100664	−	0.152499i
$511$	−8.81332	+	6.40325i	−0.389878	+	0.283263i
$512$	12.6266	−	13.2063i	0.558020	−	0.583643i
$513$	−2.42962	+	0.911852i	−0.107270	+	0.0402593i
$514$	−1.61625	+	4.97430i	−0.0712896	+	0.219407i
$515$	0.332258	+	0.0602959i	0.0146410	+	0.00265696i
$516$	−25.4717	−	26.6413i	−1.12133	−	1.17282i
$517$	31.0382	+	14.9472i	1.36506	+	0.657377i
$518$	−1.66400	−	3.89311i	−0.0731118	−	0.171054i
$519$	6.88562	−	12.7956i	0.302245	−	0.561665i
$520$	−0.168096	−	0.736478i	−0.00737151	−	0.0322967i
$521$	3.03425	+	22.3997i	0.132933	+	0.981349i	0.927408	+	0.374052i	$0.122032\pi$
$521$	3.03425	+	22.3997i	0.132933	+	0.981349i	−0.794475	+	0.607297i	$0.792254\pi$
$522$	−1.36872	−	4.21249i	−0.0599073	−	0.184376i
$523$	0.641110	+	0.803926i	0.0280338	+	0.0351532i	0.795651	−	0.605756i	$-0.207129\pi$
$523$	0.641110	+	0.803926i	0.0280338	+	0.0351532i	−0.767617	+	0.640909i	$0.778558\pi$
$524$	−10.0527	+	23.5196i	−0.439156	+	1.02746i
$525$	19.9783	−	17.4545i	0.871926	−	0.761778i
$526$	2.21689	+	4.11967i	0.0966609	+	0.179626i
$527$	16.0446	−	20.1193i	0.698916	−	0.876413i
$528$	40.2872	+	15.1201i	1.75328	+	0.658016i
$529$	18.1536	−	8.74231i	0.789287	−	0.380100i
$530$	−1.45836	−	1.27413i	−0.0633473	−	0.0553449i
$531$	−4.76162	+	20.8620i	−0.206637	+	0.905334i
$532$	31.1308	+	2.80183i	1.34969	+	0.121475i
$533$	−2.81118	−	0.253011i	−0.121766	−	0.0109591i
$534$	−1.71814	+	7.52765i	−0.0743510	+	0.325753i
$535$	−3.20375	−	2.79903i	−0.138510	−	0.121013i
$536$	−7.69173	+	3.70414i	−0.332232	+	0.159995i
$537$	−13.7528	−	5.16152i	−0.593478	−	0.222736i
$538$	2.32928	−	2.92083i	0.100422	−	0.125926i
$539$	0.141865	+	0.263630i	0.00611057	+	0.0113553i
$540$	−0.596682	+	0.521306i	−0.0256771	+	0.0224334i
$541$	0.644843	−	1.50869i	0.0277240	−	0.0648635i	−0.905094	−	0.425212i	$-0.860199\pi$
$541$	0.644843	−	1.50869i	0.0277240	−	0.0648635i	0.932818	+	0.360349i	$0.117342\pi$
$542$	−0.558756	−	0.700658i	−0.0240006	−	0.0300958i
$543$	−7.04872	−	21.6937i	−0.302489	−	0.930967i
$544$	2.62587	+	19.3849i	0.112583	+	0.831121i
$545$	3.15103	+	13.8055i	0.134975	+	0.591365i
$546$	−0.612903	+	1.13897i	−0.0262298	+	0.0487432i
$547$	4.36275	+	10.2071i	0.186538	+	0.436426i	0.986529	−	0.163585i	$-0.0523057\pi$
$547$	4.36275	+	10.2071i	0.186538	+	0.436426i	−0.799992	+	0.600011i	$0.795163\pi$
$548$	0.408058	+	0.196510i	0.0174314	+	0.00839450i
$549$	13.9186	+	14.5577i	0.594030	+	0.621306i
$550$	−5.08181	−	0.922213i	−0.216689	−	0.0393233i
$551$	10.0625	−	30.9693i	0.428678	−	1.31934i
$552$	−4.07093	+	1.52784i	−0.173270	+	0.0650294i
$553$	−32.2286	+	33.7085i	−1.37050	+	1.43343i
$554$	4.25672	−	3.09268i	0.180851	−	0.131396i
$555$	8.10721	+	12.2819i	0.344132	+	0.521338i
$556$	−0.956969	−	21.3086i	−0.0405845	−	0.903685i
$557$	−7.40060	+	11.2114i	−0.313573	+	0.475043i	−0.956847	−	0.290593i	$-0.906147\pi$
$557$	−7.40060	+	11.2114i	−0.313573	+	0.475043i	0.643273	+	0.765637i	$0.277576\pi$
$558$	2.85134	+	1.70360i	0.120707	+	0.0721190i
$559$	5.55336	+	1.53263i	0.234882	+	0.0648234i
$560$	8.85582	−	2.44405i	0.374227	−	0.103280i
$561$	−66.7060	+	39.8550i	−2.81633	+	1.68268i
$562$	0.131278	−	2.92313i	0.00553763	−	0.123305i
$563$	0.700905	+	0.509238i	0.0295396	+	0.0214618i	0.602457	−	0.798151i	$-0.294188\pi$
$563$	0.700905	+	0.509238i	0.0295396	+	0.0214618i	−0.572917	+	0.819613i	$0.694188\pi$
$564$	33.6575	−	6.10793i	1.41724	−	0.257190i
$565$	−1.53662	+	11.3438i	−0.0646460	+	0.477236i
$566$	0.208487	−	0.0187642i	0.00876338	−	0.000788718i
$567$	−22.2870			−0.935966
$568$	−2.28388	−	8.43182i	−0.0958295	−	0.353791i
$569$	16.9428			0.710279			0.355139	−	0.934813i	$-0.384433\pi$
$569$	16.9428			0.710279			0.355139	+	0.934813i	$0.384433\pi$
$570$	3.89997	−	0.351003i	0.163352	−	0.0147019i
$571$	6.31536	−	46.6219i	0.264290	−	1.95106i	−0.0419762	−	0.999119i	$-0.513365\pi$
$571$	6.31536	−	46.6219i	0.264290	−	1.95106i	0.306266	−	0.951946i	$-0.400920\pi$
$572$	−6.87430	+	1.24750i	−0.287429	+	0.0521607i
$573$	−34.6970	−	25.2088i	−1.44949	−	1.05311i
$574$	−0.117393	+	2.61396i	−0.00489989	+	0.109104i
$575$	−5.87733	+	3.51154i	−0.245101	+	0.146441i
$576$	19.4902	−	5.37896i	0.812092	−	0.224123i
$577$	13.0143	+	3.59172i	0.541793	+	0.149525i	0.526212	−	0.850353i	$-0.323612\pi$
$577$	13.0143	+	3.59172i	0.541793	+	0.149525i	0.0155809	+	0.999879i	$0.495040\pi$
$578$	−5.65305	−	3.37754i	−0.235136	−	0.140487i
$579$	13.6882	−	20.7367i	0.568862	−	0.861789i
$580$	−0.446050	−	9.93208i	−0.0185212	−	0.412407i
$581$	−5.14210	−	7.78995i	−0.213330	−	0.323181i
$582$	−9.08783	+	6.60270i	−0.376703	+	0.273691i
$583$	−25.2006	+	26.3577i	−1.04370	+	1.09163i
$584$	4.01435	−	1.50661i	0.166115	−	0.0623441i
$585$	0.713768	−	2.19675i	0.0295107	−	0.0908245i
$586$	5.88651	+	1.06824i	0.243169	+	0.0441287i
$587$	0.222848	+	0.233081i	0.00919793	+	0.00962029i	0.727378	−	0.686237i	$-0.240739\pi$
$587$	0.222848	+	0.233081i	0.00919793	+	0.00962029i	−0.718180	+	0.695857i	$0.755025\pi$
$588$	0.267830	+	0.128980i	0.0110451	+	0.00531905i
$589$	9.59725	+	22.4539i	0.395448	+	0.925196i
$590$	0.820328	−	1.52443i	0.0337724	−	0.0627596i
$591$	−7.99995	−	35.0501i	−0.329074	−	1.44177i
$592$	−2.93445	−	21.6630i	−0.120605	−	0.890343i
$593$	−11.9704	−	36.8412i	−0.491567	−	1.51289i	−0.822240	−	0.569141i	$-0.807276\pi$
$593$	−11.9704	−	36.8412i	−0.491567	−	1.51289i	0.330673	−	0.943745i	$-0.392724\pi$
$594$	−0.335275	−	0.420421i	−0.0137565	−	0.0172501i
$595$	−6.52013	+	15.2546i	−0.267299	+	0.625378i
$596$	2.44230	−	2.13377i	0.100040	−	0.0874026i
$597$	−1.26385	−	2.34863i	−0.0517260	−	0.0961231i
$598$	0.208116	−	0.260969i	0.00851050	−	0.0106718i
$599$	−16.7681	−	6.29319i	−0.685128	−	0.257133i	−0.0155547	−	0.999879i	$-0.504951\pi$
$599$	−16.7681	−	6.29319i	−0.685128	−	0.257133i	−0.669573	+	0.742746i	$0.733523\pi$
$600$	−9.40767	+	4.53049i	−0.384066	+	0.184957i
$601$	16.6409	+	14.5387i	0.678796	+	0.593046i	0.926729	−	0.375731i	$-0.122608\pi$
$601$	16.6409	+	14.5387i	0.678796	+	0.593046i	−0.247933	+	0.968777i	$0.579751\pi$
$602$	1.18840	−	5.20672i	0.0484355	−	0.212210i
$603$	−25.9986	−	2.33991i	−1.05874	−	0.0952886i
$604$	10.7982	+	0.971852i	0.439371	+	0.0395441i
$605$	2.66532	−	11.6775i	0.108361	−	0.474759i
$606$	−1.58706	−	1.38657i	−0.0644699	−	0.0563257i
$607$	−26.9237	+	12.9658i	−1.09280	+	0.526265i	−0.891388	−	0.453242i	$-0.850267\pi$
$607$	−26.9237	+	12.9658i	−1.09280	+	0.526265i	−0.201413	+	0.979506i	$0.564553\pi$
$608$	−17.3789	−	6.52242i	−0.704808	−	0.264519i
$609$	−21.6093	+	27.0972i	−0.875652	+	1.09803i
$610$	−0.772113	−	1.43483i	−0.0312619	−	0.0580944i
$611$	−4.02632	+	3.51769i	−0.162887	+	0.142311i
$612$	−15.5802	+	36.4517i	−0.629792	+	1.47347i
$613$	7.91787	+	9.92869i	0.319800	+	0.401016i	0.915583	−	0.402129i	$-0.131730\pi$
$613$	7.91787	+	9.92869i	0.319800	+	0.401016i	−0.595783	+	0.803145i	$0.703158\pi$
$614$	0.788128	+	2.42561i	0.0318062	+	0.0978896i
$615$	−1.22086	−	9.01274i	−0.0492298	−	0.363429i
$616$	2.93439	+	12.8564i	0.118230	+	0.517999i
$617$	9.22385	−	17.1408i	0.371338	−	0.690062i	−0.624517	−	0.781011i	$-0.714704\pi$
$617$	9.22385	−	17.1408i	0.371338	−	0.690062i	0.995856	+	0.0909487i	$0.0289899\pi$
$618$	0.0894391	+	0.209253i	0.00359777	+	0.00841740i
$619$	−9.34930	−	4.50238i	−0.375780	−	0.180966i	0.236454	−	0.971643i	$-0.424015\pi$
$619$	−9.34930	−	4.50238i	−0.375780	−	0.180966i	−0.612234	+	0.790677i	$0.709729\pi$
$620$	5.15225	+	5.38883i	0.206919	+	0.216421i
$621$	−0.701369	−	0.127280i	−0.0281450	−	0.00510756i
$622$	2.05823	−	6.33458i	0.0825276	−	0.253994i
$623$	29.0617	−	10.9070i	1.16433	−	0.436981i
$624$	−4.61515	+	4.82707i	−0.184754	+	0.193237i
$625$	−9.47747	+	6.88579i	−0.379099	+	0.275431i
$626$	−3.32571	−	5.03823i	−0.132922	−	0.201368i
$627$	−3.30813	−	73.6612i	−0.132114	−	2.94175i
$628$	2.50785	−	3.79922i	0.100074	−	0.151606i
$629$	33.8882	+	20.2473i	1.35121	+	0.807311i
$630$	−2.06410	−	0.569655i	−0.0822357	−	0.0226956i
$631$	31.8210	−	8.78203i	1.26677	−	0.349607i	0.432839	−	0.901471i	$-0.357512\pi$
$631$	31.8210	−	8.78203i	1.26677	−	0.349607i	0.833934	+	0.551864i	$0.186083\pi$
$632$	15.7575	−	9.41468i	0.626800	−	0.374496i
$633$	−0.154577	+	3.44192i	−0.00614388	+	0.136804i
$634$	2.16872	+	1.57567i	0.0861309	+	0.0625778i
$635$	16.0091	−	2.90522i	0.635302	−	0.115290i
$636$	−4.86054	+	35.8819i	−0.192733	+	1.42281i
$637$	−0.0462756	+	0.00416488i	−0.00183351	+	0.000165019i
$638$	6.74749			0.267136
$639$	7.22852	−	25.7138i	0.285956	−	1.01722i
$640$	−7.50745			−0.296758
$641$	37.6914	−	3.39229i	1.48872	−	0.133987i	0.684803	−	0.728728i	$-0.259888\pi$
$641$	37.6914	−	3.39229i	1.48872	−	0.133987i	0.803917	+	0.594741i	$0.202745\pi$
$642$	0.384838	−	2.84099i	0.0151883	−	0.112125i
$643$	28.7312	−	5.21394i	1.13305	−	0.205618i	0.420534	−	0.907277i	$-0.361843\pi$
$643$	28.7312	−	5.21394i	1.13305	−	0.205618i	0.712513	+	0.701659i	$0.247557\pi$
$644$	6.94590	+	5.04649i	0.273707	+	0.198860i
$645$	−0.832850	+	18.5448i	−0.0327934	+	0.730202i
$646$	9.01696	−	5.38738i	0.354768	−	0.211964i
$647$	−19.1352	+	5.28098i	−0.752283	+	0.207617i	−0.621089	−	0.783740i	$-0.713310\pi$
$647$	−19.1352	+	5.28098i	−0.752283	+	0.207617i	−0.131194	+	0.991357i	$0.541881\pi$
$648$	8.45592	+	2.33369i	0.332180	+	0.0916758i
$649$	−27.9839	−	16.7196i	−1.09846	−	0.656301i
$650$	0.441581	−	0.668967i	0.0173202	−	0.0262390i
$651$	−1.16605	−	25.9642i	−0.0457013	−	1.01762i
$652$	−9.46765	−	14.3429i	−0.370782	−	0.561710i
$653$	−9.97198	+	7.24507i	−0.390234	+	0.283521i	−0.765551	−	0.643375i	$-0.777534\pi$
$653$	−9.97198	+	7.24507i	−0.390234	+	0.283521i	0.375318	+	0.926896i	$0.377534\pi$
$654$	−6.59469	+	6.89750i	−0.257873	+	0.269714i
$655$	12.0606	−	4.52642i	0.471247	−	0.176862i
$656$	−4.17496	+	12.8492i	−0.163005	+	0.501677i
$657$	12.8998	+	2.34096i	0.503268	+	0.0913296i
$658$	3.42520	+	3.58247i	0.133528	+	0.139659i
$659$	−40.5603	−	19.5328i	−1.58000	−	0.760890i	−0.581395	−	0.813622i	$-0.697493\pi$
$659$	−40.5603	−	19.5328i	−1.58000	−	0.760890i	−0.998609	+	0.0527319i	$0.983207\pi$
$660$	−8.84809	−	20.7011i	−0.344412	−	0.805791i
$661$	14.3649	−	26.6945i	0.558730	−	1.03829i	−0.431926	−	0.901909i	$-0.642166\pi$
$661$	14.3649	−	26.6945i	0.558730	−	1.03829i	0.990656	−	0.136386i	$-0.0435486\pi$
$662$	0.647967	+	2.83893i	0.0251840	+	0.110338i
$663$	−1.61881	−	11.9505i	−0.0628694	−	0.464121i
$664$	1.13528	+	3.49402i	0.0440573	+	0.135594i
$665$	−9.81502	−	12.3077i	−0.380610	−	0.477270i
$666$	−2.00257	+	4.68525i	−0.0775981	+	0.181550i
$667$	6.73581	−	5.88490i	0.260811	−	0.227864i
$668$	11.3164	+	21.0294i	0.437844	+	0.813651i
$669$	−13.1999	+	16.5521i	−0.510337	+	0.639942i
$670$	1.97712	+	0.742024i	0.0763826	+	0.0286669i
$671$	−27.6437	+	13.3125i	−1.06717	+	0.513924i
$672$	14.8785	+	12.9990i	0.573952	+	0.501447i
$673$	2.86187	−	12.5387i	0.110317	−	0.483330i	−0.889343	−	0.457241i	$-0.848838\pi$
$673$	2.86187	−	12.5387i	0.110317	−	0.483330i	0.999660	−	0.0260890i	$-0.00830531\pi$
$674$	−1.27110	−	0.114401i	−0.0489609	−	0.00440656i
$675$	−1.70488	−	0.153442i	−0.0656209	−	0.00590599i
$676$	−5.34300	+	23.4092i	−0.205500	+	0.900354i
$677$	−19.3934	−	16.9435i	−0.745348	−	0.651191i	0.199052	−	0.979989i	$-0.436214\pi$
$677$	−19.3934	−	16.9435i	−0.745348	−	0.651191i	−0.944400	+	0.328798i	$0.893357\pi$
$678$	−6.95043	+	3.34715i	−0.266930	+	0.128546i
$679$	42.2802	+	15.8680i	1.62256	+	0.608958i
$680$	4.07113	−	5.10503i	0.156121	−	0.195769i
$681$	1.66177	+	3.08808i	0.0636791	+	0.118336i
$682$	−3.81049	+	3.32912i	−0.145911	+	0.127479i
$683$	−10.1565	+	23.7624i	−0.388629	+	0.909242i	0.604967	+	0.796250i	$0.293186\pi$
$683$	−10.1565	+	23.7624i	−0.388629	+	0.909242i	−0.993596	+	0.112992i	$0.963957\pi$
$684$	−23.4535	−	29.4098i	−0.896768	−	1.12451i
$685$	−0.0704877	−	0.216939i	−0.00269320	−	0.00828881i
$686$	0.658615	+	4.86209i	0.0251461	+	0.185636i
$687$	−2.38636	−	10.4553i	−0.0910453	−	0.398895i
$688$	13.0672	−	24.2830i	0.498184	−	0.925780i
$689$	−2.22433	−	5.20408i	−0.0847402	−	0.198260i
$690$	0.969061	+	0.466675i	0.0368915	+	0.0177660i
$691$	−12.9111	−	13.5040i	−0.491163	−	0.513716i	0.430034	−	0.902813i	$-0.358501\pi$
$691$	−12.9111	−	13.5040i	−0.491163	−	0.513716i	−0.921197	+	0.389097i	$0.872787\pi$
$692$	11.1112	+	2.01638i	0.422384	+	0.0766514i
$693$	−12.4599	+	38.3478i	−0.473314	+	1.45671i
$694$	0.320591	−	0.120320i	0.0121695	−	0.00456727i
$695$	−7.42385	+	7.76473i	−0.281603	+	0.294533i
$696$	11.0362	−	8.01824i	0.418324	−	0.303930i
$697$	−13.4403	−	20.3612i	−0.509087	−	0.771234i
$698$	−0.0715275	−	1.59268i	−0.00270735	−	0.0602839i
$699$	−16.8315	+	25.4986i	−0.636625	+	0.964446i
$700$	17.6990	+	10.5747i	0.668960	+	0.399685i
$701$	2.11793	+	0.584513i	0.0799933	+	0.0220767i	0.305804	−	0.952094i	$-0.401075\pi$
$701$	2.11793	+	0.584513i	0.0799933	+	0.0220767i	−0.225811	+	0.974171i	$0.572503\pi$
$702$	0.0804484	−	0.0222023i	0.00303633	−	0.000837974i
$703$	−32.1569	+	19.2129i	−1.21282	+	0.724627i
$704$	−1.38188	+	30.7700i	−0.0520817	+	1.15969i
$705$	−13.9378	−	10.1264i	−0.524929	−	0.381383i
$706$	6.98687	−	1.26793i	0.262954	−	0.0477191i
$707$	−1.13728	+	8.39573i	−0.0427718	+	0.315754i
$708$	−32.2383	+	2.90150i	−1.21159	+	0.109045i
$709$	5.84657			0.219572			0.109786	−	0.993955i	$-0.464983\pi$
$709$	5.84657			0.219572			0.109786	+	0.993955i	$0.464983\pi$
$710$	−1.11713	+	1.84970i	−0.0419251	+	0.0694179i
$711$	56.1255			2.10487
$712$	−12.1684	+	1.09518i	−0.456030	+	0.0410434i
$713$	−0.900358	+	6.64671i	−0.0337187	+	0.248921i
$714$	−11.0001	+	1.99622i	−0.411668	+	0.0747067i
$715$	2.84670	+	2.06825i	0.106461	+	0.0773481i
$716$	0.512182	−	11.4046i	0.0191411	−	0.426211i
$717$	62.7856	−	37.5127i	2.34477	−	1.40094i
$718$	−2.06453	+	0.569774i	−0.0770476	+	0.0212638i
$719$	−35.0040	−	9.66050i	−1.30543	−	0.360276i	−0.456945	−	0.889495i	$-0.651056\pi$
$719$	−35.0040	−	9.66050i	−1.30543	−	0.360276i	−0.848485	+	0.529219i	$0.822485\pi$
$720$	−9.49115	−	5.67070i	−0.353714	−	0.211334i
$721$	0.503996	−	0.763521i	0.0187698	−	0.0284350i
$722$	0.222328	+	4.95053i	0.00827421	+	0.184240i
$723$	18.8681	+	28.5840i	0.701713	+	1.06305i
$724$	14.3416	−	10.4198i	0.533001	−	0.387248i
$725$	14.8434	−	15.5250i	0.551271	−	0.576585i
$726$	7.55716	−	2.83625i	0.280473	−	0.105263i
$727$	−14.3041	+	44.0236i	−0.530511	+	1.63275i	0.222641	+	0.974900i	$0.428532\pi$
$727$	−14.3041	+	44.0236i	−0.530511	+	1.63275i	−0.753153	+	0.657846i	$0.771468\pi$
$728$	−2.01371	−	0.365434i	−0.0746330	−	0.0135439i
$729$	20.7095	+	21.6605i	0.767020	+	0.802240i
$730$	−0.955594	−	0.460190i	−0.0353681	−	0.0170324i
$731$	19.5710	+	45.7887i	0.723861	+	1.69356i
$732$	−14.4370	+	26.8284i	−0.533605	+	0.991604i
$733$	6.86059	+	30.0582i	0.253402	+	1.11023i	0.928158	+	0.372185i	$0.121391\pi$
$733$	6.86059	+	30.0582i	0.253402	+	1.11023i	−0.674757	+	0.738040i	$0.735751\pi$
$734$	0.438547	+	3.23749i	0.0161871	+	0.119498i
$735$	−0.0462649	−	0.142389i	−0.00170651	−	0.00525208i
$736$	−3.17904	−	3.98639i	−0.117181	−	0.146940i
$737$	15.6290	−	36.5658i	0.575701	−	1.34692i
$738$	2.37142	−	2.07185i	0.0872931	−	0.0762657i
$739$	−8.83637	−	16.4207i	−0.325051	−	0.604046i	0.664657	−	0.747149i	$-0.268578\pi$
$739$	−8.83637	−	16.4207i	−0.325051	−	0.604046i	−0.989708	+	0.143103i	$0.954292\pi$
$740$	−7.13087	+	8.94183i	−0.262136	+	0.328708i
$741$	10.7139	+	4.02099i	0.393584	+	0.147715i
$742$	−4.72699	+	2.27640i	−0.173533	+	0.0835692i
$743$	−15.3769	−	13.4344i	−0.564124	−	0.492860i	0.327983	−	0.944683i	$-0.393631\pi$
$743$	−15.3769	−	13.4344i	−0.564124	−	0.492860i	−0.892108	+	0.451823i	$0.850774\pi$
$744$	−2.27632	+	9.97320i	−0.0834538	+	0.365635i
$745$	−1.62678	−	0.146413i	−0.0596007	−	0.00536416i
$746$	−0.000435062	0	3.91563e-5i	−1.59288e−5	0	1.43361e-6i
$747$	−2.49964	+	10.9516i	−0.0914569	+	0.400699i
$748$	−45.4777	−	39.7327i	−1.66283	−	1.45277i
$749$	−10.3843	+	5.00081i	−0.379434	+	0.182726i
$750$	5.40010	+	2.02669i	0.197184	+	0.0740043i
$751$	−32.4643	+	40.7090i	−1.18464	+	1.48549i	−0.348213	+	0.937416i	$0.613211\pi$
$751$	−32.4643	+	40.7090i	−1.18464	+	1.48549i	−0.836428	+	0.548077i	$0.815360\pi$
$752$	12.1272	+	22.5361i	0.442233	+	0.821807i
$753$	8.26387	−	7.21993i	0.301152	−	0.263109i
$754$	−0.411574	+	0.962926i	−0.0149887	+	0.0350677i
$755$	−3.40448	−	4.26908i	−0.123902	−	0.155368i
$756$	0.663337	+	2.04154i	0.0241253	+	0.0742501i
$757$	4.47287	+	33.0201i	0.162569	+	1.20013i	0.869891	+	0.493243i	$0.164189\pi$
$757$	4.47287	+	33.0201i	0.162569	+	1.20013i	−0.707322	+	0.706891i	$0.750097\pi$
$758$	0.0788670	+	0.345539i	0.00286458	+	0.0125505i
$759$	9.59761	−	17.8353i	0.348371	−	0.647382i
$760$	2.43518	+	5.69739i	0.0883333	+	0.206666i
$761$	2.18246	+	1.05102i	0.0791143	+	0.0380994i	0.473022	−	0.881050i	$-0.343163\pi$
$761$	2.18246	+	1.05102i	0.0791143	+	0.0380994i	−0.393908	+	0.919150i	$0.628877\pi$
$762$	7.57733	+	7.92526i	0.274498	+	0.287102i
$763$	37.7477	+	6.85019i	1.36656	+	0.247994i
$764$	10.2998	−	31.6995i	0.372633	−	1.14685i
$765$	18.6921	−	7.01525i	0.675813	−	0.253637i
$766$	−6.04152	+	6.31894i	−0.218289	+	0.228313i
$767$	4.09295	−	2.97370i	0.147788	−	0.107374i
$768$	14.6688	+	22.2223i	0.529316	+	0.801880i
$769$	−0.604875	−	13.4686i	−0.0218123	−	0.485690i	−0.979933	−	0.199326i	$-0.936125\pi$
$769$	−0.604875	−	13.4686i	−0.0218123	−	0.485690i	0.958121	−	0.286364i	$-0.0924466\pi$
$770$	1.79701	−	2.72235i	0.0647597	−	0.0981067i
$771$	−42.2818	−	25.2622i	−1.52274	−	0.909797i
$772$	18.6144	+	5.13724i	0.669945	+	0.184893i
$773$	16.2543	−	4.48589i	0.584626	−	0.161346i	0.0388026	−	0.999247i	$-0.487646\pi$
$773$	16.2543	−	4.48589i	0.584626	−	0.161346i	0.545823	+	0.837900i	$0.316217\pi$
$774$	−5.51749	+	3.29655i	−0.198322	+	0.118492i
$775$	−0.722645	+	16.0909i	−0.0259582	+	0.578003i
$776$	−14.3800	−	10.4477i	−0.516212	−	0.375050i
$777$	39.2293	−	7.11906i	1.40734	−	0.255395i
$778$	−0.0779909	+	0.575752i	−0.00279611	+	0.0206417i
$779$	23.0575	−	2.07521i	0.826120	−	0.0743522i
$780$	3.49394			0.125103
$781$	33.8520	+	22.5777i	1.21132	+	0.807893i
$782$	2.88519			0.103174
$783$	2.22732	−	0.200462i	0.0795978	−	0.00716394i
$784$	−0.0298534	+	0.220387i	−0.00106619	+	0.00787096i
$785$	−2.25587	+	0.409380i	−0.0805154	+	0.0146114i
$786$	7.02324	+	5.10268i	0.250511	+	0.182007i
$787$	0.928133	−	20.6665i	0.0330844	−	0.736681i	−0.912066	−	0.410044i	$-0.865513\pi$
$787$	0.928133	−	20.6665i	0.0330844	−	0.736681i	0.945150	−	0.326637i	$-0.105915\pi$
$788$	23.9852	−	14.3305i	0.854436	−	0.510502i
$789$	−42.4678	+	11.7204i	−1.51189	+	0.417256i
$790$	−4.37690	−	1.20795i	−0.155723	−	0.0429768i
$791$	26.6235	+	15.9068i	0.946623	+	0.565581i
$792$	8.74286	−	13.2449i	0.310664	−	0.470636i
$793$	−0.213638	−	4.75701i	−0.00758650	−	0.168927i
$794$	−2.52475	−	3.82483i	−0.0895999	−	0.135738i
$795$	14.7537	−	10.7192i	0.523260	−	0.380171i
$796$	1.43241	−	1.49818i	0.0507704	−	0.0531017i
$797$	34.3233	−	12.8817i	1.21579	−	0.456295i	0.340664	−	0.940185i	$-0.389348\pi$
$797$	34.3233	−	12.8817i	1.21579	−	0.456295i	0.875129	+	0.483890i	$0.160777\pi$
$798$	3.27824	−	10.0894i	0.116048	−	0.357160i
$799$	−45.4710	−	8.25176i	−1.60865	−	0.291926i
$800$	−8.46151	−	8.85004i	−0.299159	−	0.312896i
$801$	−33.6575	−	16.2086i	−1.18923	−	0.572703i
$802$	0.752394	+	1.76031i	0.0265679	+	0.0621588i
$803$	−9.46423	+	17.5875i	−0.333985	+	0.620649i
$804$	−8.78643	−	38.4959i	−0.309874	−	1.35765i
$805$	−0.580431	−	4.28492i	−0.0204575	−	0.151023i
$806$	−0.242668	−	0.746855i	−0.00854761	−	0.0263068i
$807$	21.9349	+	27.5055i	0.772146	+	0.968240i
$808$	1.31062	−	3.06634i	0.0461074	−	0.107874i
$809$	−30.5050	+	26.6514i	−1.07250	+	0.937013i	−0.998185	−	0.0602222i	$-0.980819\pi$
$809$	−30.5050	+	26.6514i	−1.07250	+	0.937013i	−0.0743125	+	0.997235i	$0.523676\pi$
$810$	−1.02823	−	1.91078i	−0.0361284	−	0.0671379i
$811$	3.81218	−	4.78032i	0.133864	−	0.167860i	−0.710382	−	0.703817i	$-0.751478\pi$
$811$	3.81218	−	4.78032i	0.133864	−	0.167860i	0.844245	+	0.535957i	$0.180049\pi$
$812$	−25.2178	−	9.46441i	−0.884972	−	0.332136i
$813$	7.60355	−	3.66168i	0.266668	−	0.128421i
$814$	−5.84540	−	5.10697i	−0.204881	−	0.178999i
$815$	−1.92603	+	8.43847i	−0.0674658	+	0.295587i
$816$	−57.4929	−	5.17446i	−2.01265	−	0.181142i
$817$	−47.0617	−	4.23563i	−1.64648	−	0.148186i
$818$	0.290190	−	1.27141i	0.0101463	−	0.0444537i
$819$	−4.71254	−	4.11723i	−0.164670	−	0.143868i
$820$	6.36835	−	3.06683i	0.222392	−	0.107098i
$821$	−35.6189	−	13.3680i	−1.24311	−	0.466546i	−0.358784	−	0.933420i	$-0.616809\pi$
$821$	−35.6189	−	13.3680i	−1.24311	−	0.466546i	−0.884324	+	0.466874i	$0.845380\pi$
$822$	0.0958421	−	0.120182i	0.00334288	−	0.00419183i
$823$	2.63327	+	4.89344i	0.0917901	+	0.170575i	0.922351	−	0.386354i	$-0.126266\pi$
$823$	2.63327	+	4.89344i	0.0917901	+	0.170575i	−0.830561	+	0.556928i	$0.811980\pi$
$824$	−0.271170	+	0.236914i	−0.00944666	+	0.00825329i
$825$	19.1156	−	44.7233i	0.665521	−	1.55706i
$826$	−2.92418	−	3.66680i	−0.101745	−	0.127584i
$827$	1.93917	+	5.96814i	0.0674314	+	0.207533i	0.979094	−	0.203406i	$-0.0652011\pi$
$827$	1.93917	+	5.96814i	0.0674314	+	0.207533i	−0.911663	+	0.410938i	$0.865201\pi$
$828$	−1.38697	−	10.2390i	−0.0482006	−	0.355831i
$829$	7.83414	+	34.3236i	0.272091	+	1.19211i	0.907540	+	0.419966i	$0.137958\pi$
$829$	7.83414	+	34.3236i	0.272091	+	1.19211i	−0.635449	+	0.772143i	$0.719185\pi$
$830$	0.430636	−	0.800255i	0.0149476	−	0.0277773i
$831$	19.4738	+	45.5613i	0.675539	+	1.58050i
$832$	−4.30686	−	2.07408i	−0.149314	−	0.0719056i
$833$	−0.277536	−	0.290280i	−0.00961605	−	0.0100576i
$834$	−7.12314	−	1.29266i	−0.246654	−	0.0447611i
$835$	3.71665	−	11.4387i	0.128620	−	0.395852i
$836$	53.6504	−	20.1353i	1.85554	−	0.696395i
$837$	−1.15892	+	1.21213i	−0.0400581	+	0.0418975i
$838$	6.47930	−	4.70749i	0.223824	−	0.162617i
$839$	−17.8214	−	26.9983i	−0.615264	−	0.932086i	−0.999959	−	0.00904194i	$-0.997122\pi$
$839$	−17.8214	−	26.9983i	−0.615264	−	0.932086i	0.384695	−	0.923044i	$-0.374307\pi$
$840$	−0.295872	−	6.58809i	−0.0102085	−	0.227311i
$841$	0.517224	−	0.783562i	0.0178353	−	0.0270194i
$842$	1.49877	+	0.895474i	0.0516511	+	0.0308601i
$843$	26.5620	+	7.33065i	0.914844	+	0.252481i
$844$	−2.58113	+	0.712347i	−0.0888463	+	0.0245200i
$845$	10.3812	−	6.20249i	0.357125	−	0.213372i
$846$	0.267615	−	5.95891i	0.00920079	−	0.204871i
$847$	−26.2531	−	19.0740i	−0.902068	−	0.655390i
$848$	−26.6546	+	4.83710i	−0.915324	+	0.166107i
$849$	−0.264610	+	1.95343i	−0.00908138	+	0.0670414i
$850$	6.90059	−	0.621064i	0.236688	−	0.0213023i
$851$	−10.2894			−0.352715
$852$	40.3714	−	1.62048i	1.38310	−	0.0555168i
$853$	−13.1768			−0.451165			−0.225583	−	0.974224i	$-0.572429\pi$
$853$	−13.1768			−0.451165			−0.225583	+	0.974224i	$0.572429\pi$
$854$	−4.39659	+	0.395700i	−0.150448	+	0.0135406i
$855$	−2.54307	+	18.7737i	−0.0869712	+	0.642047i
$856$	4.46355	−	0.810015i	0.152561	−	0.0276857i
$857$	−4.02922	−	2.92740i	−0.137635	−	0.0999980i	0.516837	−	0.856084i	$-0.327109\pi$
$857$	−4.02922	−	2.92740i	−0.137635	−	0.0999980i	−0.654473	+	0.756086i	$0.727109\pi$
$858$	−0.106386	+	2.36887i	−0.00363197	+	0.0808721i
$859$	−31.0892	+	18.5749i	−1.06075	+	0.633768i	−0.933674	−	0.358125i	$-0.883416\pi$
$859$	−31.0892	+	18.5749i	−1.06075	+	0.633768i	−0.127075	+	0.991893i	$0.540559\pi$
$860$	−13.9070	+	3.83808i	−0.474224	+	0.130877i
$861$	−23.7526	−	6.55529i	−0.809485	−	0.223404i
$862$	6.99637	+	4.18014i	0.238297	+	0.142376i
$863$	−27.9085	+	42.2795i	−0.950016	+	1.43921i	−0.0523029	+	0.998631i	$0.516656\pi$
$863$	−27.9085	+	42.2795i	−0.950016	+	1.43921i	−0.897713	+	0.440581i	$0.854772\pi$
$864$	−0.0571944	−	1.27353i	−0.00194579	−	0.0433264i
$865$	−3.13319	−	4.74658i	−0.106532	−	0.161388i
$866$	1.93186	−	1.40358i	0.0656472	−	0.0476955i
$867$	42.8548	−	44.8226i	1.45543	−	1.52226i
$868$	18.9108	−	7.09733i	0.641873	−	0.240899i
$869$	−26.4212	+	81.3160i	−0.896277	+	2.75846i
$870$	−3.32015	−	0.602518i	−0.112563	−	0.0204273i
$871$	4.26495	+	4.46079i	0.144512	+	0.151148i
$872$	−13.6046	−	6.55162i	−0.460709	−	0.221866i
$873$	−21.3603	−	49.9750i	−0.722938	−	1.69140i
$874$	−1.29735	+	2.41089i	−0.0438836	+	0.0815494i
$875$	−5.15985	−	22.6068i	−0.174435	−	0.764249i
$876$	2.66206	+	19.6521i	0.0899428	+	0.663985i
$877$	−7.66401	−	23.5874i	−0.258795	−	0.796490i	−0.993058	−	0.117624i	$-0.962472\pi$
$877$	−7.66401	−	23.5874i	−0.258795	−	0.796490i	0.734263	−	0.678865i	$-0.237528\pi$
$878$	3.55957	+	4.46356i	0.120130	+	0.150638i
$879$	−22.1426	+	51.8051i	−0.746850	+	1.74734i
$880$	12.6838	−	11.0815i	0.427572	−	0.373558i
$881$	25.8677	+	48.0702i	0.871504	+	1.61953i	0.781775	+	0.623561i	$0.214315\pi$
$881$	25.8677	+	48.0702i	0.871504	+	1.61953i	0.0897294	+	0.995966i	$0.471400\pi$
$882$	0.0323195	−	0.0405274i	0.00108826	−	0.00136463i
$883$	−25.1628	−	9.44376i	−0.846796	−	0.317808i	−0.110007	−	0.993931i	$-0.535087\pi$
$883$	−25.1628	−	9.44376i	−0.846796	−	0.317808i	−0.736789	+	0.676123i	$0.763659\pi$
$884$	8.44418	−	4.06651i	0.284009	−	0.136771i
$885$	12.2767	+	10.7258i	0.412675	+	0.360543i
$886$	2.29464	−	10.0535i	0.0770898	−	0.337752i
$887$	23.7907	+	2.14121i	0.798815	+	0.0718947i	0.481523	−	0.876433i	$-0.340084\pi$
$887$	23.7907	+	2.14121i	0.798815	+	0.0718947i	0.317292	+	0.948328i	$0.397227\pi$
$888$	−15.6294	−	1.40668i	−0.524490	−	0.0472049i
$889$	9.80886	−	42.9754i	0.328979	−	1.44135i
$890$	2.27591	+	1.98840i	0.0762885	+	0.0666513i
$891$	−36.8135	+	17.7284i	−1.23330	+	0.593925i
$892$	−15.4041	−	5.78127i	−0.515768	−	0.193571i
$893$	27.3417	−	34.2854i	0.914955	−	1.14732i
$894$	−0.521597	−	0.969290i	−0.0174448	−	0.0324179i
$895$	−4.32986	+	3.78289i	−0.144731	+	0.126448i
$896$	−7.99388	+	18.7026i	−0.267057	+	0.624810i
$897$	1.95984	+	2.45756i	0.0654370	+	0.0820555i
$898$	1.02374	+	3.15075i	0.0341627	+	0.105142i
$899$	−2.82466	−	20.8525i	−0.0942078	−	0.695470i
$900$	−5.52130	−	24.1904i	−0.184043	−	0.806347i
$901$	23.1811	−	43.0778i	0.772276	−	1.43513i
$902$	1.88539	+	4.41110i	0.0627767	+	0.146873i
$903$	45.3122	+	21.8212i	1.50790	+	0.726164i
$904$	−8.43563	−	8.82298i	−0.280565	−	0.293448i
$905$	−8.78462	−	1.59417i	−0.292011	−	0.0529921i
$906$	1.13710	−	3.49964i	0.0377777	−	0.116268i
$907$	38.3904	−	14.4081i	1.27473	−	0.478414i	0.379986	−	0.924992i	$-0.375929\pi$
$907$	38.3904	−	14.4081i	1.27473	−	0.478414i	0.894745	+	0.446578i	$0.147357\pi$
$908$	−1.88340	+	1.96988i	−0.0625027	+	0.0653727i
$909$	8.24898	−	5.99324i	0.273602	−	0.198783i
$910$	0.278892	+	0.422503i	0.00924517	+	0.0140058i
$911$	−0.153357	−	3.41476i	−0.00508095	−	0.113136i	−0.999931	−	0.0117752i	$-0.996252\pi$
$911$	−0.153357	−	3.41476i	−0.00508095	−	0.113136i	0.994850	−	0.101361i	$-0.0323197\pi$
$912$	30.1760	−	45.7148i	0.999229	−	1.51377i
$913$	−14.6903	−	8.77703i	−0.486177	−	0.290477i
$914$	−1.34842	−	0.372140i	−0.0446018	−	0.0123093i
$915$	14.7910	−	4.08205i	0.488975	−	0.134949i
$916$	7.15470	−	4.27473i	0.236398	−	0.141241i
$917$	1.56580	−	34.8651i	0.0517071	−	1.15135i
$918$	0.583597	+	0.424008i	0.0192616	+	0.0139943i
$919$	34.5915	−	6.27743i	1.14107	−	0.207073i	0.425060	−	0.905165i	$-0.360253\pi$
$919$	34.5915	−	6.27743i	1.14107	−	0.207073i	0.716008	+	0.698092i	$0.245967\pi$
$920$	−0.228455	+	1.68652i	−0.00753193	+	0.0556029i
$921$	−23.9208	+	2.15291i	−0.788219	+	0.0709410i
$922$	−8.18523			−0.269566
$923$	−5.28689	+	3.45381i	−0.174020	+	0.113684i
$924$	−60.9922			−2.00650
$925$	−24.6094	+	2.21488i	−0.809151	+	0.0728249i
$926$	−0.0883941	+	0.652551i	−0.00290481	+	0.0214442i
$927$	−1.08332	+	0.196593i	−0.0355809	+	0.00645698i
$928$	12.9412	+	9.40236i	0.424817	+	0.308648i
$929$	2.16596	−	48.2289i	0.0710630	−	1.58234i	−0.574417	−	0.818563i	$-0.694771\pi$
$929$	2.16596	−	48.2289i	0.0710630	−	1.58234i	0.645480	−	0.763777i	$-0.276657\pi$
$930$	2.17225	−	1.29786i	0.0712308	−	0.0425584i
$931$	0.367357	−	0.101384i	0.0120396	−	0.00332273i
$932$	−22.8889	−	6.31692i	−0.749749	−	0.206918i
$933$	53.8444	+	32.1705i	1.76279	+	1.05322i
$934$	−3.63248	+	5.50298i	−0.118858	+	0.180063i
$935$	1.36455	+	30.3840i	0.0446254	+	0.993662i
$936$	1.35687	+	2.05557i	0.0443507	+	0.0671885i
$937$	20.1190	−	14.6173i	0.657261	−	0.477528i	−0.208476	−	0.978027i	$-0.566850\pi$
$937$	20.1190	−	14.6173i	0.657261	−	0.477528i	0.865737	+	0.500500i	$0.166850\pi$
$938$	3.95375	−	4.13530i	0.129095	−	0.135022i
$939$	53.2246	−	19.9755i	1.73692	−	0.651877i
$940$	4.13744	−	12.7337i	0.134948	−	0.415328i
$941$	−13.6336	−	2.47413i	−0.444441	−	0.0806542i	−0.0482772	−	0.998834i	$-0.515373\pi$
$941$	−13.6336	−	2.47413i	−0.444441	−	0.0806542i	−0.396164	+	0.918180i	$0.629659\pi$
$942$	−1.06773	−	1.11676i	−0.0347886	−	0.0363861i
$943$	5.72931	+	2.75909i	0.186572	+	0.0898483i
$944$	−9.51763	−	22.2676i	−0.309773	−	0.724749i
$945$	0.512306	−	0.952024i	0.0166653	−	0.0309693i
$946$	−2.17875	−	9.54574i	−0.0708374	−	0.310359i
$947$	5.83121	+	43.0477i	0.189489	+	1.39886i	0.796725	+	0.604341i	$0.206564\pi$
$947$	5.83121	+	43.0477i	0.189489	+	1.39886i	−0.607237	+	0.794521i	$0.707722\pi$
$948$	26.2351	+	80.7434i	0.852077	+	2.62242i
$949$	−1.93260	−	2.42341i	−0.0627349	−	0.0786671i
$950$	−2.58395	+	6.04545i	−0.0838344	+	0.196140i
$951$	−19.0106	+	16.6091i	−0.616462	+	0.538586i
$952$	−8.38279	−	15.5778i	−0.271688	−	0.504880i
$953$	−27.0123	+	33.8723i	−0.875013	+	1.09723i	0.119523	+	0.992831i	$0.461864\pi$
$953$	−27.0123	+	33.8723i	−0.875013	+	1.09723i	−0.994535	+	0.104400i	$0.966708\pi$
$954$	5.91147	+	2.21861i	0.191391	+	0.0718302i
$955$	−15.1243	+	7.28347i	−0.489410	+	0.235688i
$956$	42.8049	+	37.3976i	1.38441	+	1.20952i
$957$	−14.1393	+	61.9483i	−0.457058	+	2.00250i
$958$	−6.27276	−	0.564559i	−0.202664	−	0.0182401i
$959$	−0.615495	−	0.0553955i	−0.0198754	−	0.00178881i
$960$	3.42758	−	15.0172i	0.110625	−	0.484678i
$961$	−11.4617	−	10.0138i	−0.369732	−	0.323026i
$962$	1.08536	−	0.522681i	0.0349934	−	0.0168519i
$963$	12.9864	+	4.87387i	0.418480	+	0.157058i
$964$	−16.5958	+	20.8105i	−0.534516	+	0.670262i
$965$	−4.60856	−	8.56414i	−0.148355	−	0.275689i
$966$	2.19443	−	1.91722i	0.0706048	−	0.0616855i
$967$	1.87243	−	4.38077i	0.0602133	−	0.140876i	−0.886719	−	0.462308i	$-0.847021\pi$
$967$	1.87243	−	4.38077i	0.0602133	−	0.140876i	0.946933	+	0.321432i	$0.104164\pi$
$968$	7.96346	+	9.98586i	0.255955	+	0.320958i
$969$	30.5663	+	94.0733i	0.981930	+	3.02207i
$970$	0.590193	+	4.35698i	0.0189500	+	0.139894i
$971$	−4.60682	−	20.1838i	−0.147840	−	0.647728i	−0.993483	−	0.113980i	$-0.963640\pi$
$971$	−4.60682	−	20.1838i	−0.147840	−	0.647728i	0.845643	−	0.533748i	$-0.179217\pi$
$972$	−20.3844	+	37.8806i	−0.653831	+	1.21502i
$973$	11.4387	+	26.7622i	0.366708	+	0.857956i
$974$	−2.57058	−	1.23793i	−0.0823668	−	0.0396658i
$975$	5.21641	+	5.45593i	0.167059	+	0.174730i
$976$	−22.4267	−	4.06985i	−0.717862	−	0.130273i
$977$	−7.60691	+	23.4116i	−0.243366	+	0.749005i	0.752534	+	0.658553i	$0.228831\pi$
$977$	−7.60691	+	23.4116i	−0.243366	+	0.749005i	−0.995901	+	0.0904520i	$0.971169\pi$
$978$	−5.46100	+	2.04955i	−0.174623	+	0.0655373i
$979$	39.3277	−	41.1336i	1.25692	−	1.31464i
$980$	0.0941322	−	0.0683911i	0.00300694	−	0.00218467i
$981$	−25.4350	−	38.5324i	−0.812078	−	1.23025i
$982$	−0.195656	−	4.35662i	−0.00624364	−	0.139025i
$983$	7.45522	−	11.2942i	0.237785	−	0.360228i	−0.696013	−	0.718029i	$-0.745045\pi$
$983$	7.45522	−	11.2942i	0.237785	−	0.360228i	0.933798	+	0.357800i	$0.116473\pi$
$984$	8.32556	+	4.97429i	0.265409	+	0.158575i
$985$	−13.5646	−	3.74360i	−0.432205	−	0.119281i
$986$	−8.72542	+	2.40806i	−0.277874	+	0.0766883i
$987$	−40.0679	+	23.9394i	−1.27537	+	0.762001i
$988$	−0.399006	+	8.88457i	−0.0126941	+	0.282656i
$989$	−10.5004	−	7.62898i	−0.333893	−	0.242588i
$990$	−3.86260	+	0.700959i	−0.122762	+	0.0222779i
$991$	0.0690819	−	0.509983i	0.00219446	−	0.0162002i	−0.989819	−	0.142329i	$-0.954541\pi$
$991$	0.0690819	−	0.509983i	0.00219446	−	0.0162002i	0.992014	+	0.126129i	$0.0402552\pi$
$992$	−11.9473	+	1.07527i	−0.379326	+	0.0341399i
$993$	−27.4218			−0.870205
$994$	3.41847	+	4.75255i	0.108427	+	0.150742i
$995$	−1.04393			−0.0330947
$996$	−16.9237	+	1.52316i	−0.536247	+	0.0482631i
$997$	5.14054	−	37.9490i	0.162803	−	1.20186i	−0.706549	−	0.707664i	$-0.749749\pi$
$997$	5.14054	−	37.9490i	0.162803	−	1.20186i	0.869352	−	0.494194i	$-0.164537\pi$
$998$	4.91349	−	0.891667i	0.155534	−	0.0282252i
$999$	−2.08126	−	1.51213i	−0.0658482	−	0.0478416i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	71.2.g.a.18.4	yes	120
3.2	odd	2		639.2.v.a.586.2		120
71.2	even	35		5041.2.a.s.1.29		60
71.4	even	35	inner	71.2.g.a.4.4	✓	120
71.69	odd	70		5041.2.a.t.1.29		60
213.146	odd	70		639.2.v.a.217.2		120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
71.2.g.a.4.4	✓	120	71.4	even	35	inner
71.2.g.a.18.4	yes	120	1.1	even	1	trivial
639.2.v.a.217.2		120	213.146	odd	70
639.2.v.a.586.2		120	3.2	odd	2
5041.2.a.s.1.29		60	71.2	even	35
5041.2.a.t.1.29		60	71.69	odd	70

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	71.g (of order \(35\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.262709 - 0.0236442i) q^{2} +(-0.333427 + 2.46146i) q^{3} +(-1.89940 + 0.344691i) q^{4} +(0.786557 + 0.571467i) q^{5} +(-0.0293950 + 0.654532i) q^{6} +(2.26116 - 1.35098i) q^{7} +(-0.999371 + 0.275809i) q^{8} +(-3.05572 - 0.843326i) q^{9} +O(q^{10})\)	\(q+(0.262709 - 0.0236442i) q^{2} +(-0.333427 + 2.46146i) q^{3} +(-1.89940 + 0.344691i) q^{4} +(0.786557 + 0.571467i) q^{5} +(-0.0293950 + 0.654532i) q^{6} +(2.26116 - 1.35098i) q^{7} +(-0.999371 + 0.275809i) q^{8} +(-3.05572 - 0.843326i) q^{9} +(0.220148 + 0.131532i) q^{10} +(2.66032 - 4.03021i) q^{11} +(-0.215130 - 4.79023i) q^{12} +(0.412875 + 0.625479i) q^{13} +(0.562085 - 0.408379i) q^{14} +(-1.66890 + 1.74554i) q^{15} +(3.35864 - 1.26052i) q^{16} +(-2.00184 + 6.16102i) q^{17} +(-0.822706 - 0.149299i) q^{18} +(-4.24805 - 4.44311i) q^{19} +(-1.69097 - 0.814327i) q^{20} +(2.57145 + 6.01621i) q^{21} +(0.603598 - 1.12167i) q^{22} +(-0.375726 - 1.64617i) q^{23} +(-0.345675 - 2.55187i) q^{24} +(-1.25299 - 3.85630i) q^{25} +(0.123255 + 0.154557i) q^{26} +(0.165921 - 0.388192i) q^{27} +(-3.82919 + 3.34546i) q^{28} +(2.51021 + 4.66476i) q^{29} +(-0.397164 + 0.498028i) q^{30} +(-3.71911 - 1.39581i) q^{31} +(2.72067 - 1.31020i) q^{32} +(9.03317 + 7.89204i) q^{33} +(-0.380228 + 1.66589i) q^{34} +(2.55057 + 0.229556i) q^{35} +(6.09473 + 0.548536i) q^{36} +(1.35600 - 5.94101i) q^{37} +(-1.22106 - 1.06680i) q^{38} +(-1.67726 + 0.807724i) q^{39} +(-0.943678 - 0.354168i) q^{40} +(-2.34812 + 2.94445i) q^{41} +(0.817793 + 1.51971i) q^{42} +(5.78873 - 5.05746i) q^{43} +(-3.66384 + 8.57197i) q^{44} +(-1.92157 - 2.40957i) q^{45} +(-0.137629 - 0.423579i) q^{46} +(0.957599 + 7.06928i) q^{47} +(1.98285 + 8.68745i) q^{48} +(-0.0293774 + 0.0545924i) q^{49} +(-0.420351 - 0.983459i) q^{50} +(-14.4976 - 6.98170i) q^{51} +(-0.999813 - 1.04572i) q^{52} +(-7.43009 - 1.34836i) q^{53} +(0.0344105 - 0.105905i) q^{54} +(4.39562 - 1.64970i) q^{55} +(-1.88713 + 1.97378i) q^{56} +(12.3530 - 8.97495i) q^{57} +(0.769750 + 1.16612i) q^{58} +(-0.302856 - 6.74361i) q^{59} +(2.56825 - 3.89073i) q^{60} +(-5.45429 - 3.25878i) q^{61} +(-1.01005 - 0.278755i) q^{62} +(-8.04880 + 2.22133i) q^{63} +(-5.47542 + 3.27141i) q^{64} +(-0.0326909 + 0.727920i) q^{65} +(2.55970 + 1.85973i) q^{66} +(8.10237 - 1.47036i) q^{67} +(1.67865 - 12.3923i) q^{68} +(4.17725 - 0.375959i) q^{69} +0.675487 q^{70} +(-0.0401258 + 8.42605i) q^{71} +3.28640 q^{72} +(-4.11920 + 0.370734i) q^{73} +(0.215762 - 1.59282i) q^{74} +(9.90991 - 1.79838i) q^{75} +(9.60026 + 6.97500i) q^{76} +(0.570672 - 12.7070i) q^{77} +(-0.421532 + 0.251854i) q^{78} +(-17.0674 + 4.71030i) q^{79} +(3.36211 + 0.927882i) q^{80} +(-7.26354 - 4.33976i) q^{81} +(-0.547254 + 0.829054i) q^{82} +(-0.158986 - 3.54010i) q^{83} +(-6.95796 - 10.5409i) q^{84} +(-5.09538 + 3.70201i) q^{85} +(1.40117 - 1.46551i) q^{86} +(-12.3191 + 4.62343i) q^{87} +(-1.54708 + 4.76141i) q^{88} +(11.5953 + 2.10424i) q^{89} +(-0.561785 - 0.587581i) q^{90} +(1.77859 + 0.856523i) q^{91} +(1.28107 + 2.99722i) q^{92} +(4.67577 - 8.68904i) q^{93} +(0.418718 + 1.83452i) q^{94} +(-0.802241 - 5.92238i) q^{95} +(2.31787 + 7.13367i) q^{96} +(10.6897 + 13.4044i) q^{97} +(-0.00642692 + 0.0150365i) q^{98} +(-11.5280 + 10.0717i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9}+O(q^{10}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9} - 8 q^{10} - 27 q^{11} + 3 q^{12} - 31 q^{13} + 2 q^{14} + 12 q^{15} + 30 q^{16} + 9 q^{17} + 27 q^{18} - 31 q^{19} + 72 q^{20} - 32 q^{21} - 24 q^{22} - 6 q^{23} - 47 q^{24} - 42 q^{25} + 77 q^{26} - 2 q^{27} - 18 q^{28} + q^{29} + 15 q^{30} + 15 q^{31} - 10 q^{32} - 24 q^{33} + 20 q^{34} + 74 q^{35} + 8 q^{36} - 22 q^{37} - 39 q^{38} + 86 q^{39} - 30 q^{40} + 39 q^{41} - 34 q^{42} + 33 q^{43} - 23 q^{44} + 121 q^{45} + 124 q^{46} + 6 q^{47} + 131 q^{48} - 22 q^{49} - 15 q^{50} + 29 q^{51} + 83 q^{52} - 30 q^{53} - 25 q^{54} + 32 q^{55} + 11 q^{56} - 10 q^{57} + 12 q^{58} - 80 q^{59} + 80 q^{60} - 12 q^{61} - 68 q^{62} - 79 q^{63} - 117 q^{64} - 89 q^{65} - 39 q^{66} - 74 q^{67} - 67 q^{68} - 95 q^{69} - 64 q^{70} - 115 q^{71} - 144 q^{72} - 14 q^{73} - 70 q^{74} - 13 q^{75} + 8 q^{76} + 47 q^{77} - 218 q^{78} - 25 q^{79} - 103 q^{80} - 28 q^{81} - 88 q^{82} - 20 q^{83} - 142 q^{84} + 22 q^{85} + 159 q^{86} - 105 q^{87} + 43 q^{88} + 33 q^{89} + 33 q^{90} + 60 q^{91} - 2 q^{92} + 63 q^{93} + 174 q^{94} + 20 q^{95} - 30 q^{96} + 121 q^{97} + 128 q^{98} - 2 q^{99}+O(q^{100}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9 - 8 * q^10 - 27 * q^11 + 3 * q^12 - 31 * q^13 + 2 * q^14 + 12 * q^15 + 30 * q^16 + 9 * q^17 + 27 * q^18 - 31 * q^19 + 72 * q^20 - 32 * q^21 - 24 * q^22 - 6 * q^23 - 47 * q^24 - 42 * q^25 + 77 * q^26 - 2 * q^27 - 18 * q^28 + q^29 + 15 * q^30 + 15 * q^31 - 10 * q^32 - 24 * q^33 + 20 * q^34 + 74 * q^35 + 8 * q^36 - 22 * q^37 - 39 * q^38 + 86 * q^39 - 30 * q^40 + 39 * q^41 - 34 * q^42 + 33 * q^43 - 23 * q^44 + 121 * q^45 + 124 * q^46 + 6 * q^47 + 131 * q^48 - 22 * q^49 - 15 * q^50 + 29 * q^51 + 83 * q^52 - 30 * q^53 - 25 * q^54 + 32 * q^55 + 11 * q^56 - 10 * q^57 + 12 * q^58 - 80 * q^59 + 80 * q^60 - 12 * q^61 - 68 * q^62 - 79 * q^63 - 117 * q^64 - 89 * q^65 - 39 * q^66 - 74 * q^67 - 67 * q^68 - 95 * q^69 - 64 * q^70 - 115 * q^71 - 144 * q^72 - 14 * q^73 - 70 * q^74 - 13 * q^75 + 8 * q^76 + 47 * q^77 - 218 * q^78 - 25 * q^79 - 103 * q^80 - 28 * q^81 - 88 * q^82 - 20 * q^83 - 142 * q^84 + 22 * q^85 + 159 * q^86 - 105 * q^87 + 43 * q^88 + 33 * q^89 + 33 * q^90 + 60 * q^91 - 2 * q^92 + 63 * q^93 + 174 * q^94 + 20 * q^95 - 30 * q^96 + 121 * q^97 + 128 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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