LMFDB - Embedded newform 966.2.y.b.25.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(25,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 6]))

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

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

chi := DirichletCharacter("966.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.y (of order $33$, degree $20$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			25.5
Character	$\chi$	$=$	966.25
Dual form			966.2.y.b.541.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0475819 + 0.998867i) q^{2} +(0.928368 + 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(0.149969 + 0.618179i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(-1.95013 + 1.78801i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +O(q^{10})$	\(q+(-0.0475819 + 0.998867i) q^{2} +(0.928368 + 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(0.149969 + 0.618179i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(-1.95013 + 1.78801i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +(-0.624615 + 0.120385i) q^{10} +(-0.000319367 - 0.00670434i) q^{11} +(-0.888835 - 0.458227i) q^{12} +(0.816913 + 0.942768i) q^{13} +(-1.69320 - 2.03300i) q^{14} +(-0.0905279 + 0.629635i) q^{15} +(0.981929 + 0.189251i) q^{16} +(-1.11867 - 1.57095i) q^{17} +(-0.723734 + 0.690079i) q^{18} +(-4.64119 + 6.51764i) q^{19} +(-0.0905279 - 0.629635i) q^{20} +(-2.47498 + 0.935143i) q^{21} +0.00671194 q^{22} +(-2.00868 + 4.35491i) q^{23} +(0.500000 - 0.866025i) q^{24} +(4.08452 - 2.10572i) q^{25} +(-0.980571 + 0.771129i) q^{26} +(0.415415 + 0.909632i) q^{27} +(2.11126 - 1.59454i) q^{28} +(-2.38776 + 5.22846i) q^{29} +(-0.624615 - 0.120385i) q^{30} +(-4.58806 - 3.60809i) q^{31} +(-0.235759 + 0.971812i) q^{32} +(0.00219526 - 0.00634279i) q^{33} +(1.62240 - 1.04265i) q^{34} +(-1.39777 - 0.937384i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(-5.08336 - 4.84697i) q^{37} +(-6.28942 - 4.94606i) q^{38} +(0.408005 + 1.17885i) q^{39} +(0.633229 - 0.0604661i) q^{40} +(-0.349694 - 0.102680i) q^{41} +(-0.816320 - 2.51667i) q^{42} +(0.00979684 + 0.0681385i) q^{43} +(-0.000319367 + 0.00670434i) q^{44} +(-0.318055 + 0.550887i) q^{45} +(-4.25440 - 2.21362i) q^{46} +(3.19928 + 5.54132i) q^{47} +(0.841254 + 0.540641i) q^{48} +(0.606023 - 6.97372i) q^{49} +(1.90898 + 4.18009i) q^{50} +(-0.454672 - 1.87418i) q^{51} +(-0.723599 - 1.01615i) q^{52} +(1.63913 + 4.73594i) q^{53} +(-0.928368 + 0.371662i) q^{54} +(0.00409658 - 0.00120287i) q^{55} +(1.49228 + 2.18474i) q^{56} +(-6.73110 + 4.32581i) q^{57} +(-5.10892 - 2.63383i) q^{58} +(-5.65274 + 1.08948i) q^{59} +(0.149969 - 0.618179i) q^{60} +(-4.31497 + 1.72746i) q^{61} +(3.82231 - 4.41118i) q^{62} +(-2.64525 - 0.0516991i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-0.460288 + 0.646384i) q^{65} +(0.00623115 + 0.00249458i) q^{66} +(-4.66931 + 2.40720i) q^{67} +(0.964273 + 1.67017i) q^{68} +(-3.48335 + 3.29640i) q^{69} +(1.00283 - 1.35158i) q^{70} +(8.34916 + 5.36568i) q^{71} +(0.786053 - 0.618159i) q^{72} +(11.8290 + 1.12953i) q^{73} +(5.08336 - 4.84697i) q^{74} +(4.57456 - 0.436817i) q^{75} +(5.23972 - 6.04696i) q^{76} +(0.0126102 + 0.0125033i) q^{77} +(-1.19693 + 0.351450i) q^{78} +(0.818673 - 2.36540i) q^{79} +(0.0302673 + 0.635389i) q^{80} +(0.0475819 + 0.998867i) q^{81} +(0.119202 - 0.344413i) q^{82} +(7.82284 - 2.29699i) q^{83} +(2.55266 - 0.695647i) q^{84} +(0.803362 - 0.927129i) q^{85} +(-0.0685275 + 0.00654358i) q^{86} +(-4.15994 + 3.96649i) q^{87} +(-0.00668155 - 0.000638010i) q^{88} +(-1.59386 + 1.25342i) q^{89} +(-0.535130 - 0.343907i) q^{90} +(-3.27877 - 0.377870i) q^{91} +(2.41354 - 4.14425i) q^{92} +(-2.91841 - 5.05484i) q^{93} +(-5.68728 + 2.93199i) q^{94} +(-4.72510 - 1.89165i) q^{95} +(-0.580057 + 0.814576i) q^{96} +(-8.78096 - 2.57832i) q^{97} +(6.93698 + 0.937159i) q^{98} +(0.00439538 - 0.00507254i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9	\( 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9} - 6 q^{10} + 8 q^{11} + 8 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} - 8 q^{19} + 10 q^{20} - 3 q^{21} - 28 q^{22} + 22 q^{23} + 80 q^{24} + 46 q^{25} + 2 q^{26} - 16 q^{27} - 14 q^{28} + 62 q^{29} - 6 q^{30} + 7 q^{31} - 8 q^{32} - 14 q^{33} - 4 q^{34} + 24 q^{35} - 16 q^{36} + 15 q^{37} + 19 q^{38} - 2 q^{39} + 5 q^{40} - 14 q^{41} + 10 q^{42} - 56 q^{43} + 8 q^{44} - 16 q^{45} + 66 q^{47} - 16 q^{48} + 42 q^{49} + 4 q^{50} + 9 q^{51} - 2 q^{52} + 12 q^{53} - 8 q^{54} - 14 q^{55} + 10 q^{56} - 6 q^{57} - 13 q^{58} + 62 q^{59} + 6 q^{60} + 16 q^{61} - 8 q^{62} + 2 q^{63} - 16 q^{64} + 70 q^{65} - 8 q^{66} - 14 q^{67} - 46 q^{68} + 22 q^{69} + 24 q^{70} - 108 q^{71} - 8 q^{72} + 40 q^{73} - 15 q^{74} + 2 q^{75} + 16 q^{76} + 29 q^{77} + 18 q^{78} + 22 q^{79} + 6 q^{80} + 8 q^{81} - 7 q^{82} - 18 q^{83} - 9 q^{84} + 26 q^{85} - 6 q^{86} + 2 q^{87} + 3 q^{88} + 112 q^{89} + 12 q^{90} + 18 q^{91} - 66 q^{92} - 26 q^{93} + 23 q^{95} - 8 q^{96} + 8 q^{97} + 9 q^{98} + 28 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9 - 6 * q^10 + 8 * q^11 + 8 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 - 8 * q^19 + 10 * q^20 - 3 * q^21 - 28 * q^22 + 22 * q^23 + 80 * q^24 + 46 * q^25 + 2 * q^26 - 16 * q^27 - 14 * q^28 + 62 * q^29 - 6 * q^30 + 7 * q^31 - 8 * q^32 - 14 * q^33 - 4 * q^34 + 24 * q^35 - 16 * q^36 + 15 * q^37 + 19 * q^38 - 2 * q^39 + 5 * q^40 - 14 * q^41 + 10 * q^42 - 56 * q^43 + 8 * q^44 - 16 * q^45 + 66 * q^47 - 16 * q^48 + 42 * q^49 + 4 * q^50 + 9 * q^51 - 2 * q^52 + 12 * q^53 - 8 * q^54 - 14 * q^55 + 10 * q^56 - 6 * q^57 - 13 * q^58 + 62 * q^59 + 6 * q^60 + 16 * q^61 - 8 * q^62 + 2 * q^63 - 16 * q^64 + 70 * q^65 - 8 * q^66 - 14 * q^67 - 46 * q^68 + 22 * q^69 + 24 * q^70 - 108 * q^71 - 8 * q^72 + 40 * q^73 - 15 * q^74 + 2 * q^75 + 16 * q^76 + 29 * q^77 + 18 * q^78 + 22 * q^79 + 6 * q^80 + 8 * q^81 - 7 * q^82 - 18 * q^83 - 9 * q^84 + 26 * q^85 - 6 * q^86 + 2 * q^87 + 3 * q^88 + 112 * q^89 + 12 * q^90 + 18 * q^91 - 66 * q^92 - 26 * q^93 + 23 * q^95 - 8 * q^96 + 8 * q^97 + 9 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{11}\right)$

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 $

$2$	−0.0475819	+	0.998867i	−0.0336455	+	0.706306i
$2$	−0.0475819	+	0.998867i	−0.0336455	+	0.706306i
$3$	0.928368	+	0.371662i	0.535993	+	0.214579i
$3$	0.928368	+	0.371662i	0.535993	+	0.214579i
$4$	−0.995472	−	0.0950560i	−0.497736	−	0.0475280i
$5$	0.149969	+	0.618179i	0.0670680	+	0.276458i	0.995465	−	0.0951328i	$-0.0303276\pi$
$5$	0.149969	+	0.618179i	0.0670680	+	0.276458i	−0.928397	+	0.371591i	$0.878812\pi$
$6$	−0.415415	+	0.909632i	−0.169592	+	0.371356i
$7$	−1.95013	+	1.78801i	−0.737080	+	0.675805i
$7$	−1.95013	+	1.78801i	−0.737080	+	0.675805i
$8$	0.142315	−	0.989821i	0.0503159	−	0.349955i
$9$	0.723734	+	0.690079i	0.241245	+	0.230026i
$10$	−0.624615	+	0.120385i	−0.197520	+	0.0380689i
$11$	−0.000319367	−	0.00670434i	−9.62927e−5	−	0.00202143i	0.998819	−	0.0485926i	$-0.0154736\pi$
$11$	−0.000319367	−	0.00670434i	−9.62927e−5	−	0.00202143i	−0.998915	+	0.0465712i	$0.985171\pi$
$12$	−0.888835	−	0.458227i	−0.256585	−	0.132279i
$13$	0.816913	+	0.942768i	0.226571	+	0.261477i	0.857641	−	0.514249i	$-0.171929\pi$
$13$	0.816913	+	0.942768i	0.226571	+	0.261477i	−0.631070	+	0.775726i	$0.717384\pi$
$14$	−1.69320	−	2.03300i	−0.452526	−	0.543342i
$15$	−0.0905279	+	0.629635i	−0.0233742	+	0.162571i
$16$	0.981929	+	0.189251i	0.245482	+	0.0473128i
$17$	−1.11867	−	1.57095i	−0.271317	−	0.381011i	0.656328	−	0.754476i	$-0.272109\pi$
$17$	−1.11867	−	1.57095i	−0.271317	−	0.381011i	−0.927644	+	0.373465i	$0.878170\pi$
$18$	−0.723734	+	0.690079i	−0.170586	+	0.162653i
$19$	−4.64119	+	6.51764i	−1.06476	+	1.49525i	−0.208976	+	0.977921i	$0.567013\pi$
$19$	−4.64119	+	6.51764i	−1.06476	+	1.49525i	−0.855786	+	0.517329i	$0.826926\pi$
$20$	−0.0905279	−	0.629635i	−0.0202426	−	0.140791i
$21$	−2.47498	+	0.935143i	−0.540084	+	0.204065i
$22$	0.00671194			0.00143099
$23$	−2.00868	+	4.35491i	−0.418839	+	0.908061i
$23$	−2.00868	+	4.35491i	−0.418839	+	0.908061i
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	4.08452	−	2.10572i	0.816905	−	0.421144i
$26$	−0.980571	+	0.771129i	−0.192306	+	0.151231i
$27$	0.415415	+	0.909632i	0.0799467	+	0.175059i
$28$	2.11126	−	1.59454i	0.398991	−	0.301341i
$29$	−2.38776	+	5.22846i	−0.443395	+	0.970900i	0.547567	+	0.836762i	$0.315554\pi$
$29$	−2.38776	+	5.22846i	−0.443395	+	0.970900i	−0.990963	+	0.134139i	$0.957173\pi$
$30$	−0.624615	−	0.120385i	−0.114038	−	0.0219791i
$31$	−4.58806	−	3.60809i	−0.824039	−	0.648032i	0.114416	−	0.993433i	$-0.463500\pi$
$31$	−4.58806	−	3.60809i	−0.824039	−	0.648032i	−0.938455	+	0.345401i	$0.887743\pi$
$32$	−0.235759	+	0.971812i	−0.0416767	+	0.171794i
$33$	0.00219526	−	0.00634279i	0.000382146	−	0.00110414i
$34$	1.62240	−	1.04265i	0.278239	−	0.178813i
$35$	−1.39777	−	0.937384i	−0.236266	−	0.158447i
$36$	−0.654861	−	0.755750i	−0.109143	−	0.125958i
$37$	−5.08336	−	4.84697i	−0.835699	−	0.796837i	0.145597	−	0.989344i	$-0.453490\pi$
$37$	−5.08336	−	4.84697i	−0.835699	−	0.796837i	−0.981296	+	0.192507i	$0.938338\pi$
$38$	−6.28942	−	4.94606i	−1.02028	−	0.802357i
$39$	0.408005	+	1.17885i	0.0653330	+	0.188767i
$40$	0.633229	−	0.0604661i	0.100122	−	0.00956053i
$41$	−0.349694	−	0.102680i	−0.0546131	−	0.0160359i	0.254312	−	0.967122i	$-0.418151\pi$
$41$	−0.349694	−	0.102680i	−0.0546131	−	0.0160359i	−0.308925	+	0.951086i	$0.599969\pi$
$42$	−0.816320	−	2.51667i	−0.125961	−	0.388330i
$43$	0.00979684	+	0.0681385i	0.00149400	+	0.0103910i	0.990555	−	0.137117i	$-0.0437837\pi$
$43$	0.00979684	+	0.0681385i	0.00149400	+	0.0103910i	−0.989061	+	0.147508i	$0.952875\pi$
$44$	−0.000319367		0.00670434i	−4.81464e−5		0.00101072i
$45$	−0.318055	+	0.550887i	−0.0474128	+	0.0821214i
$46$	−4.25440	−	2.21362i	−0.627277	−	0.326380i
$47$	3.19928	+	5.54132i	0.466664	+	0.808285i	0.999275	−	0.0380749i	$-0.0121225\pi$
$47$	3.19928	+	5.54132i	0.466664	+	0.808285i	−0.532611	+	0.846360i	$0.678789\pi$
$48$	0.841254	+	0.540641i	0.121424	+	0.0780348i
$49$	0.606023	−	6.97372i	0.0865747	−	0.996245i
$50$	1.90898	+	4.18009i	0.269971	+	0.591154i
$51$	−0.454672	−	1.87418i	−0.0636668	−	0.262438i
$52$	−0.723599	−	1.01615i	−0.100345	−	0.140915i
$53$	1.63913	+	4.73594i	0.225151	+	0.650532i	0.999835	+	0.0181826i	$0.00578802\pi$
$53$	1.63913	+	4.73594i	0.225151	+	0.650532i	−0.774683	+	0.632349i	$0.782091\pi$
$54$	−0.928368	+	0.371662i	−0.126335	+	0.0505769i
$55$	0.00409658	−	0.00120287i	0.000552383	−	0.000162194i
$56$	1.49228	+	2.18474i	0.199414	+	0.291948i
$57$	−6.73110	+	4.32581i	−0.891556	+	0.572968i
$58$	−5.10892	−	2.63383i	−0.670834	−	0.345839i
$59$	−5.65274	+	1.08948i	−0.735923	+	0.141838i	−0.543423	−	0.839459i	$-0.682872\pi$
$59$	−5.65274	+	1.08948i	−0.735923	+	0.141838i	−0.192501	+	0.981297i	$0.561660\pi$
$60$	0.149969	−	0.618179i	0.0193609	−	0.0798066i
$61$	−4.31497	+	1.72746i	−0.552476	+	0.221178i	−0.631066	−	0.775729i	$-0.717382\pi$
$61$	−4.31497	+	1.72746i	−0.552476	+	0.221178i	0.0785903	+	0.996907i	$0.474958\pi$
$62$	3.82231	−	4.41118i	0.485434	−	0.560220i
$63$	−2.64525	−	0.0516991i	−0.333270	−	0.00651347i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	−0.460288	+	0.646384i	−0.0570917	+	0.0801741i
$66$	0.00623115	+	0.00249458i	0.000767001	+	0.000307061i
$67$	−4.66931	+	2.40720i	−0.570447	+	0.294086i	−0.719216	−	0.694786i	$-0.755499\pi$
$67$	−4.66931	+	2.40720i	−0.570447	+	0.294086i	0.148770	+	0.988872i	$0.452469\pi$
$68$	0.964273	+	1.67017i	0.116935	+	0.202538i
$69$	−3.48335	+	3.29640i	−0.419346	+	0.396840i
$70$	1.00283	−	1.35158i	0.119861	−	0.161545i
$71$	8.34916	+	5.36568i	0.990863	+	0.636789i	0.932372	−	0.361499i	$-0.117735\pi$
$71$	8.34916	+	5.36568i	0.990863	+	0.636789i	0.0584905	+	0.998288i	$0.481371\pi$
$72$	0.786053	−	0.618159i	0.0926372	−	0.0728507i
$73$	11.8290	+	1.12953i	1.38447	+	0.132201i	0.760548	−	0.649282i	$-0.224930\pi$
$73$	11.8290	+	1.12953i	1.38447	+	0.132201i	0.623927	+	0.781483i	$0.285536\pi$
$74$	5.08336	−	4.84697i	0.590928	−	0.563449i
$75$	4.57456	−	0.436817i	0.528224	−	0.0504393i
$76$	5.23972	−	6.04696i	0.601037	−	0.693634i
$77$	0.0126102	+	0.0125033i	0.00143707	+	0.00142488i
$78$	−1.19693	+	0.351450i	−0.135526	+	0.0397939i
$79$	0.818673	−	2.36540i	0.0921079	−	0.266128i	−0.889532	−	0.456874i	$-0.848969\pi$
$79$	0.818673	−	2.36540i	0.0921079	−	0.266128i	0.981640	+	0.190745i	$0.0610904\pi$
$80$	0.0302673	+	0.635389i	0.00338399	+	0.0710387i
$81$	0.0475819	+	0.998867i	0.00528688	+	0.110985i
$82$	0.119202	−	0.344413i	0.0131637	−	0.0380340i
$83$	7.82284	−	2.29699i	0.858668	−	0.252128i	0.177380	−	0.984143i	$-0.443238\pi$
$83$	7.82284	−	2.29699i	0.858668	−	0.252128i	0.681289	+	0.732015i	$0.261420\pi$
$84$	2.55266	−	0.695647i	0.278518	−	0.0759013i
$85$	0.803362	−	0.927129i	0.0871368	−	0.100561i
$86$	−0.0685275	+	0.00654358i	−0.00738951	+	0.000705613i
$87$	−4.15994	+	3.96649i	−0.445992	+	0.425253i
$88$	−0.00668155		0.000638010i	−0.000712255		6.80121e-5i
$89$	−1.59386	+	1.25342i	−0.168949	+	0.132863i	−0.699053	−	0.715069i	$-0.746395\pi$
$89$	−1.59386	+	1.25342i	−0.168949	+	0.132863i	0.530105	+	0.847932i	$0.322153\pi$
$90$	−0.535130	−	0.343907i	−0.0564076	−	0.0362510i
$91$	−3.27877	−	0.377870i	−0.343708	−	0.0396116i
$92$	2.41354	−	4.14425i	0.251629	−	0.432068i
$93$	−2.91841	−	5.05484i	−0.302625	−	0.524163i
$94$	−5.68728	+	2.93199i	−0.586598	+	0.302412i
$95$	−4.72510	−	1.89165i	−0.484785	−	0.194079i
$96$	−0.580057	+	0.814576i	−0.0592018	+	0.0831373i
$97$	−8.78096	−	2.57832i	−0.891572	−	0.261789i	−0.196307	−	0.980543i	$-0.562895\pi$
$97$	−8.78096	−	2.57832i	−0.891572	−	0.261789i	−0.695265	+	0.718753i	$0.744713\pi$
$98$	6.93698	+	0.937159i	0.700741	+	0.0946674i
$99$	0.00439538	−	0.00507254i	0.000441753	−	0.000509810i
$100$	−4.26619	+	1.70792i	−0.426619	+	0.170792i
$101$	−0.589176	+	2.42862i	−0.0586252	+	0.241656i	−0.993583	−	0.113101i	$-0.963922\pi$
$101$	−0.589176	+	2.42862i	−0.0586252	+	0.241656i	0.934958	+	0.354758i	$0.115437\pi$
$102$	1.89370	−	0.364980i	0.187504	−	0.0361384i
$103$	3.83477	+	1.97696i	0.377851	+	0.194796i	0.636681	−	0.771127i	$-0.280307\pi$
$103$	3.83477	+	1.97696i	0.377851	+	0.194796i	−0.258830	+	0.965923i	$0.583337\pi$
$104$	1.04943	−	0.674429i	0.102905	−	0.0661332i
$105$	−0.949254	−	1.38974i	−0.0926377	−	0.135624i
$106$	−4.80857	+	1.41192i	−0.467050	+	0.137138i
$107$	5.33010	−	2.13385i	0.515280	−	0.206287i	−0.0994236	−	0.995045i	$-0.531700\pi$
$107$	5.33010	−	2.13385i	0.515280	−	0.206287i	0.614704	+	0.788758i	$0.289276\pi$
$108$	−0.327068	−	0.945001i	−0.0314721	−	0.0909327i
$109$	−1.92342	−	2.70106i	−0.184230	−	0.258715i	0.712124	−	0.702054i	$-0.247733\pi$
$109$	−1.92342	−	2.70106i	−0.184230	−	0.258715i	−0.896354	+	0.443339i	$0.853794\pi$
$110$	0.00100658	+	0.00414918i	9.59736e−5	+	0.000395609i
$111$	−2.91779	−	6.38906i	−0.276944	−	0.606423i
$112$	−2.25327	+	1.38664i	−0.212914	+	0.131025i
$113$	4.04778	+	2.60135i	0.380783	+	0.244714i	0.717004	−	0.697069i	$-0.245513\pi$
$113$	4.04778	+	2.60135i	0.380783	+	0.244714i	−0.336221	+	0.941783i	$0.609149\pi$
$114$	−4.00064	−	6.92931i	−0.374694	−	0.648989i
$115$	−2.99335	−	0.588624i	−0.279131	−	0.0548895i
$116$	2.87394	−	4.97781i	0.266839	−	0.462178i
$117$	−0.0593566	+	1.24605i	−0.00548752	+	0.115197i
$118$	−0.819273	−	5.69817i	−0.0754202	−	0.524559i
$119$	4.99042	+	1.06336i	0.457471	+	0.0974784i
$120$	0.610343	+	0.179213i	0.0557164	+	0.0163598i
$121$	10.9501	−	1.04561i	0.995468	−	0.0950557i
$122$	−1.52018	−	4.39228i	−0.137631	−	0.397659i
$123$	−0.286483	−	0.225293i	−0.0258313	−	0.0203140i
$124$	4.22431	+	4.02787i	0.379354	+	0.361714i
$125$	3.99708	+	4.61287i	0.357509	+	0.412588i
$126$	0.177506	−	2.63979i	0.0158135	−	0.235171i
$127$	−9.42270	+	6.05560i	−0.836129	+	0.537348i	−0.887220	−	0.461346i	$-0.847367\pi$
$127$	−9.42270	+	6.05560i	−0.836129	+	0.537348i	0.0510910	+	0.998694i	$0.483730\pi$
$128$	0.327068	−	0.945001i	0.0289090	−	0.0835271i
$129$	−0.0162295	+	0.0668988i	−0.00142892	+	0.00589011i
$130$	−0.623751	−	0.490523i	−0.0547066	−	0.0430217i
$131$	13.3150	+	2.56626i	1.16334	+	0.224215i	0.734142	−	0.678996i	$-0.237585\pi$
$131$	13.3150	+	2.56626i	1.16334	+	0.224215i	0.429196	+	0.903211i	$0.358797\pi$
$132$	−0.00278824	+	0.00610539i	−0.000242685	+	0.000531406i
$133$	−2.60269	−	21.0088i	−0.225682	−	1.82169i
$134$	−2.18229	−	4.77856i	−0.188521	−	0.412804i
$135$	−0.500016	+	0.393217i	−0.0430345	+	0.0338427i
$136$	−1.71416	+	0.883711i	−0.146988	+	0.0757776i
$137$	−0.415000	+	0.718801i	−0.0354559	+	0.0614114i	−0.883209	−	0.468980i	$-0.844622\pi$
$137$	−0.415000	+	0.718801i	−0.0354559	+	0.0614114i	0.847753	+	0.530391i	$0.177955\pi$
$138$	−3.12693	−	3.63625i	−0.266182	−	0.309538i
$139$	−5.76145			−0.488680			−0.244340	−	0.969690i	$-0.578571\pi$
$139$	−5.76145			−0.488680			−0.244340	+	0.969690i	$0.578571\pi$
$140$	1.30234	+	1.06601i	0.110068	+	0.0900940i
$141$	0.910611	+	6.33344i	0.0766873	+	0.533372i
$142$	−5.75687	+	8.08439i	−0.483106	+	0.678427i
$143$	0.00605974	−	0.00577795i	0.000506741	−	0.000483177i
$144$	0.580057	+	0.814576i	0.0483381	+	0.0678813i
$145$	−3.59021	−	0.691957i	−0.298151	−	0.0574639i
$146$	−1.69109	+	11.7618i	−0.139956	+	0.973415i
$147$	3.15448	−	6.24894i	0.260177	−	0.515404i
$148$	4.59960	+	5.30823i	0.378085	+	0.436334i
$149$	4.08646	+	2.10671i	0.334775	+	0.172589i	0.617415	−	0.786637i	$-0.288180\pi$
$149$	4.08646	+	2.10671i	0.334775	+	0.172589i	−0.282640	+	0.959226i	$0.591210\pi$
$150$	0.218656	+	4.59016i	0.0178532	+	0.374785i
$151$	18.4888	−	3.56341i	1.50459	−	0.289987i	0.630670	−	0.776051i	$-0.282780\pi$
$151$	18.4888	−	3.56341i	1.50459	−	0.289987i	0.873923	+	0.486064i	$0.161568\pi$
$152$	5.79079	+	5.52151i	0.469695	+	0.447854i
$153$	0.274461	−	1.90892i	0.0221888	−	0.154327i
$154$	−0.0130892	+	0.0120010i	−0.00105475	+	0.000967070i
$155$	1.54238	−	3.37734i	0.123887	−	0.271274i
$156$	−0.294100	−	1.21230i	−0.0235469	−	0.0970615i
$157$	4.08195	+	0.389779i	0.325775	+	0.0311078i	0.256663	−	0.966501i	$-0.417377\pi$
$157$	4.08195	+	0.389779i	0.325775	+	0.0311078i	0.0691128	+	0.997609i	$0.477983\pi$
$158$	2.32377	+	0.930296i	0.184869	+	0.0740104i
$159$	−0.238460	+	5.00590i	−0.0189111	+	0.396994i
$160$	−0.636110			−0.0502889
$161$	−3.86944	−	12.0842i	−0.304955	−	0.952367i
$162$	−1.00000			−0.0785674
$163$	1.01601	−	21.3287i	0.0795802	−	1.67059i	−0.507946	−	0.861389i	$-0.669595\pi$
$163$	1.01601	−	21.3287i	0.0795802	−	1.67059i	0.587526	−	0.809205i	$-0.300102\pi$
$164$	0.338351	+	0.135455i	0.0264207	+	0.0105773i
$165$	0.00425020		0.000405845i	0.000330877		3.15950e-5i
$166$	1.92217	+	7.92327i	0.149189	+	0.614965i
$167$	−6.46553	+	14.1575i	−0.500317	+	1.09554i	0.476049	+	0.879419i	$0.342069\pi$
$167$	−6.46553	+	14.1575i	−0.500317	+	1.09554i	−0.976366	+	0.216123i	$0.930659\pi$
$168$	0.573399	+	2.58287i	0.0442387	+	0.199273i
$169$	1.62863	−	11.3274i	0.125279	−	0.871335i
$170$	0.887853	+	0.846566i	0.0680952	+	0.0649287i
$171$	−7.85668	+	1.51425i	−0.600815	+	0.115798i
$172$	−0.00327550	−	0.0687613i	−0.000249755	−	0.00524300i
$173$	18.6705	+	9.62531i	1.41949	+	0.731799i	0.985588	−	0.169161i	$-0.0541057\pi$
$173$	18.6705	+	9.62531i	1.41949	+	0.731799i	0.433903	+	0.900960i	$0.357136\pi$
$174$	−3.76406	−	4.34396i	−0.285353	−	0.329315i
$175$	−4.20031	+	11.4096i	−0.317513	+	0.862485i
$176$	0.000955208	−	0.00664362i	7.20015e−5	−	0.000500782i
$177$	−5.65274	−	1.08948i	−0.424886	−	0.0818900i
$178$	−1.17617	−	1.65169i	−0.0881574	−	0.123800i
$179$	−8.04958	+	7.67526i	−0.601654	+	0.573676i	−0.928468	−	0.371413i	$-0.878873\pi$
$179$	−8.04958	+	7.67526i	−0.601654	+	0.573676i	0.326814	+	0.945089i	$0.394025\pi$
$180$	0.368980	−	0.518160i	0.0275021	−	0.0386214i
$181$	−1.47131	−	10.2332i	−0.109362	−	0.760628i	−0.968523	−	0.248923i	$-0.919923\pi$
$181$	−1.47131	−	10.2332i	−0.109362	−	0.760628i	0.859161	−	0.511705i	$-0.170986\pi$
$182$	0.533453	−	3.25708i	0.0395421	−	0.241431i
$183$	−4.64791			−0.343584
$184$	4.02471	+	2.60800i	0.296706	+	0.192264i
$185$	2.23395	−	3.86932i	0.164243	−	0.284478i
$186$	5.18798	−	2.67459i	0.380401	−	0.196110i
$187$	−0.0101749	+	0.00800163i	−0.000744062	+	0.000585137i
$188$	−2.65806	−	5.82034i	−0.193859	−	0.424492i
$189$	−2.43655	−	1.03113i	−0.177233	−	0.0750040i
$190$	2.11433	−	4.62974i	0.153390	−	0.335877i
$191$	23.1666	+	4.46500i	1.67628	+	0.323076i	0.936736	−	0.350035i	$-0.113830\pi$
$191$	23.1666	+	4.46500i	1.67628	+	0.323076i	0.739541	+	0.673111i	$0.235043\pi$
$192$	−0.786053	−	0.618159i	−0.0567285	−	0.0446118i
$193$	−2.49186	+	10.2716i	−0.179368	+	0.739365i	0.809066	+	0.587717i	$0.199973\pi$
$193$	−2.49186	+	10.2716i	−0.179368	+	0.739365i	−0.988435	+	0.151648i	$0.951542\pi$
$194$	2.99322	−	8.64834i	0.214901	−	0.620914i
$195$	−0.667554	+	0.429011i	−0.0478045	+	0.0307221i
$196$	−1.26617	+	6.88453i	−0.0904409	+	0.491752i
$197$	1.34530	+	1.55256i	0.0958486	+	0.110615i	0.801647	−	0.597797i	$-0.203957\pi$
$197$	1.34530	+	1.55256i	0.0958486	+	0.110615i	−0.705799	+	0.708412i	$0.749412\pi$
$198$	0.00485766	+	0.00463177i	0.000345219	+	0.000329165i
$199$	−5.57780	−	4.38643i	−0.395400	−	0.310946i	0.400588	−	0.916258i	$-0.368806\pi$
$199$	−5.57780	−	4.38643i	−0.395400	−	0.310946i	−0.795988	+	0.605312i	$0.793048\pi$
$200$	−1.50300	−	4.34262i	−0.106278	−	0.307070i
$201$	−5.22950	+	0.499357i	−0.368860	+	0.0352219i
$202$	−2.39783	−	0.704067i	−0.168711	−	0.0495380i
$203$	−4.69211	−	14.4655i	−0.329322	−	1.01528i
$204$	0.274461	+	1.90892i	0.0192161	+	0.133651i
$205$	0.0110312	−	0.231572i	0.000770449	−	0.0161737i
$206$	−2.15719	+	3.73636i	−0.150298	+	0.260324i
$207$	−4.45898	+	1.76565i	−0.309920	+	0.122721i
$208$	0.623731	+	1.08033i	0.0432479	+	0.0749076i
$209$	0.0451787	+	0.0290346i	0.00312508	+	0.00200837i
$210$	1.43333	−	0.882053i	0.0989091	−	0.0608674i
$211$	11.7294	+	25.6838i	0.807484	+	1.76814i	0.617861	+	0.786287i	$0.287999\pi$
$211$	11.7294	+	25.6838i	0.807484	+	1.76814i	0.189623	+	0.981857i	$0.439273\pi$
$212$	−1.18152	−	4.87031i	−0.0811474	−	0.334494i
$213$	5.75687	+	8.08439i	0.394454	+	0.553934i
$214$	1.87782	+	5.42559i	0.128365	+	0.370886i
$215$	−0.0406526	+	0.0162748i	−0.00277248	+	0.00110994i
$216$	0.959493	−	0.281733i	0.0652852	−	0.0191695i
$217$	15.3986	−	1.16726i	1.04533	−	0.0792387i
$218$	2.78952	−	1.79272i	0.188930	−	0.121418i
$219$	10.5618	+	5.44500i	0.713702	+	0.367939i
$220$	−0.00419237		0.000808014i	−0.000282650		5.44763e-5i
$221$	0.567186	−	2.33797i	0.0381530	−	0.157269i
$222$	6.52066	−	2.61048i	0.437638	−	0.175204i
$223$	−3.91749	+	4.52103i	−0.262335	+	0.302750i	−0.871602	−	0.490215i	$-0.836918\pi$
$223$	−3.91749	+	4.52103i	−0.262335	+	0.302750i	0.609267	+	0.792965i	$0.291464\pi$
$224$	−1.27785	−	2.31670i	−0.0853800	−	0.154791i
$225$	4.40922	+	1.29466i	0.293948	+	0.0863109i
$226$	−2.79100	+	3.91942i	−0.185655	+	0.260716i
$227$	−13.2303	−	5.29660i	−0.878123	−	0.351548i	−0.111592	−	0.993754i	$-0.535595\pi$
$227$	−13.2303	−	5.29660i	−0.878123	−	0.351548i	−0.766532	+	0.642207i	$0.778019\pi$
$228$	7.11181	−	3.66640i	0.470991	−	0.242813i
$229$	7.81364	+	13.5336i	0.516340	+	0.894327i	0.999820	+	0.0189719i	$0.00603930\pi$
$229$	7.81364	+	13.5336i	0.516340	+	0.894327i	−0.483480	+	0.875355i	$0.660627\pi$
$230$	0.730387	−	2.96195i	0.0481603	−	0.195305i
$231$	0.00705994	+	0.0162944i	0.000464510	+	0.00107209i
$232$	4.83543	+	3.10754i	0.317461	+	0.204020i
$233$	19.0787	−	15.0036i	1.24989	−	0.982921i	0.249994	−	0.968247i	$-0.419571\pi$
$233$	19.0787	−	15.0036i	1.24989	−	0.982921i	0.999892	−	0.0146738i	$-0.00467100\pi$
$234$	−1.24181	−	0.118579i	−0.0811798	−	0.00775173i
$235$	−2.94574	+	2.80875i	−0.192159	+	0.183223i
$236$	5.73070	−	0.547216i	0.373037	−	0.0356207i
$237$	1.63916	−	1.89169i	0.106475	−	0.122879i
$238$	−1.29961	+	4.93417i	−0.0842414	+	0.319835i
$239$	2.86541	−	0.841361i	0.185348	−	0.0544231i	−0.187741	−	0.982219i	$-0.560117\pi$
$239$	2.86541	−	0.841361i	0.185348	−	0.0544231i	0.373089	+	0.927795i	$0.378298\pi$
$240$	−0.208051	+	0.601124i	−0.0134296	+	0.0388024i
$241$	1.06696	+	22.3982i	0.0687287	+	1.44279i	0.725250	+	0.688486i	$0.241724\pi$
$241$	1.06696	+	22.3982i	0.0687287	+	1.44279i	−0.656521	+	0.754308i	$0.727973\pi$
$242$	0.523399	+	10.9875i	0.0336454	+	0.706303i
$243$	−0.327068	+	0.945001i	−0.0209814	+	0.0606218i
$244$	4.45964	−	1.30947i	0.285499	−	0.0838301i
$245$	4.40189	−	0.671208i	0.281226	−	0.0428819i
$246$	0.238669	−	0.275439i	0.0152170	−	0.0175613i
$247$	−9.93608	+	0.948781i	−0.632218	+	0.0603695i
$248$	−4.22431	+	4.02787i	−0.268244	+	0.255770i
$249$	8.11618	+	0.775001i	0.514342	+	0.0491137i
$250$	−4.79784	+	3.77306i	−0.303442	+	0.238629i
$251$	24.4580	+	15.7182i	1.54377	+	0.992123i	0.986864	+	0.161550i	$0.0516494\pi$
$251$	24.4580	+	15.7182i	1.54377	+	0.992123i	0.556910	+	0.830573i	$0.311987\pi$
$252$	2.62835	+	0.302912i	0.165571	+	0.0190816i
$253$	0.0298383	+	0.0120760i	0.00187592	+	0.000759215i
$254$	−5.60039	−	9.70016i	−0.351400	−	0.608642i
$255$	1.09039	−	0.562137i	0.0682831	−	0.0352024i
$256$	0.928368	+	0.371662i	0.0580230	+	0.0232289i
$257$	−13.4580	+	18.8991i	−0.839488	+	1.17890i	0.142470	+	0.989799i	$0.454496\pi$
$257$	−13.4580	+	18.8991i	−0.839488	+	1.17890i	−0.981958	+	0.189097i	$0.939444\pi$
$258$	−0.0660508	−	0.0193943i	−0.00411214	−	0.00120743i
$259$	18.5797	+	0.363123i	1.15448	+	0.0225634i
$260$	0.519647	−	0.599704i	0.0322271	−	0.0371921i
$261$	−5.33615	+	2.13627i	−0.330299	+	0.132232i
$262$	−3.19691	+	13.1778i	−0.197506	+	0.814129i
$263$	−14.0549	+	2.70886i	−0.866662	+	0.167035i	−0.603157	−	0.797623i	$-0.706091\pi$
$263$	−14.0549	+	2.70886i	−0.866662	+	0.167035i	−0.263505	+	0.964658i	$0.584879\pi$
$264$	−0.00596581	−	0.00307559i	−0.000367170	−	0.000189289i
$265$	−2.68184	+	1.72352i	−0.164744	+	0.105875i
$266$	21.1088	−	1.60011i	1.29426	−	0.0981089i
$267$	−1.94554	+	0.571262i	−0.119065	+	0.0349606i
$268$	4.87698	−	1.95245i	0.297909	−	0.119265i
$269$	−6.09266	−	17.6036i	−0.371476	−	1.07331i	−0.963574	−	0.267444i	$-0.913821\pi$
$269$	−6.09266	−	17.6036i	−0.371476	−	1.07331i	0.592097	−	0.805867i	$-0.298300\pi$
$270$	−0.368980	−	0.518160i	−0.0224554	−	0.0315342i
$271$	−3.68419	−	15.1865i	−0.223799	−	0.922511i	−0.967271	−	0.253745i	$-0.918338\pi$
$271$	−3.68419	−	15.1865i	−0.223799	−	0.922511i	0.743472	−	0.668767i	$-0.233177\pi$
$272$	−0.801147	−	1.75427i	−0.0485767	−	0.106368i
$273$	−2.90346	−	1.56940i	−0.175726	−	0.0949843i
$274$	−0.698241	−	0.448732i	−0.0421823	−	0.0271089i
$275$	−0.0154219	−	0.0267115i	−0.000929976	−	0.00161076i
$276$	3.78092	−	2.95036i	0.227585	−	0.177591i
$277$	9.62476	−	16.6706i	0.578296	−	1.00164i	−0.417379	−	0.908732i	$-0.637051\pi$
$277$	9.62476	−	16.6706i	0.578296	−	1.00164i	0.995675	−	0.0929053i	$-0.0296154\pi$
$278$	0.274141	−	5.75492i	0.0164419	−	0.345157i
$279$	−0.830667	−	5.77742i	−0.0497307	−	0.345885i
$280$	−1.12677	+	1.25014i	−0.0673372	+	0.0747101i
$281$	13.9320	+	4.09080i	0.831113	+	0.244037i	0.669495	−	0.742816i	$-0.266511\pi$
$281$	13.9320	+	4.09080i	0.831113	+	0.244037i	0.161618	+	0.986853i	$0.448329\pi$
$282$	−6.36960	+	0.608223i	−0.379304	+	0.0362191i
$283$	2.12926	+	6.15209i	0.126571	+	0.365704i	0.990427	−	0.138035i	$-0.0440786\pi$
$283$	2.12926	+	6.15209i	0.126571	+	0.365704i	−0.863856	+	0.503739i	$0.831957\pi$
$284$	−7.80131	−	6.13502i	−0.462923	−	0.364047i
$285$	−3.68358	−	3.51229i	−0.218196	−	0.208050i
$286$	0.00548307	+	0.00632780i	0.000324221	+	0.000374171i
$287$	0.865542	−	0.425019i	0.0510913	−	0.0250881i
$288$	−0.841254	+	0.540641i	−0.0495713	+	0.0318576i
$289$	4.34369	−	12.5503i	0.255511	−	0.738252i
$290$	0.862002	−	3.55322i	0.0506185	−	0.208652i
$291$	−7.19370	−	5.65719i	−0.421702	−	0.331630i
$292$	−11.6680	−	2.24883i	−0.682820	−	0.131603i
$293$	−9.75878	+	21.3687i	−0.570114	+	1.24837i	0.376623	+	0.926367i	$0.377085\pi$
$293$	−9.75878	+	21.3687i	−0.570114	+	1.24837i	−0.946737	+	0.322008i	$0.895642\pi$
$294$	6.09177	+	3.44824i	0.355279	+	0.201106i
$295$	−1.52122	−	3.33101i	−0.0885691	−	0.193939i
$296$	−5.52107	+	4.34182i	−0.320906	+	0.252363i
$297$	0.00596581	−	0.00307559i	0.000346171	−	0.000178464i
$298$	−2.29877	+	3.98159i	−0.133164	+	0.230647i
$299$	−5.74658	+	1.66386i	−0.332334	+	0.0962236i
$300$	−4.59536			−0.265313
$301$	−0.140938	−	0.115362i	−0.00812351	−	0.00664937i
$302$	2.67965	+	18.6374i	0.154196	+	1.07246i
$303$	−1.44960	+	2.03567i	−0.0832772	+	0.116946i
$304$	−5.79079	+	5.52151i	−0.332125	+	0.316680i
$305$	−1.71499	−	2.40836i	−0.0981999	−	0.137902i
$306$	1.89370	+	0.364980i	0.108255	+	0.0208645i
$307$	1.95038	−	13.5652i	0.111314	−	0.774206i	−0.855330	−	0.518083i	$-0.826646\pi$
$307$	1.95038	−	13.5652i	0.111314	−	0.774206i	0.966644	−	0.256123i	$-0.0824451\pi$
$308$	−0.0113646	−	0.0136454i	−0.000647560	−	0.000777517i
$309$	2.82531	+	3.26059i	0.160727	+	0.185488i
$310$	3.30012	+	1.70133i	0.187435	+	0.0966292i
$311$	0.674669	+	14.1630i	0.0382570	+	0.803113i	0.933726	+	0.357989i	$0.116537\pi$
$311$	0.674669	+	14.1630i	0.0382570	+	0.803113i	−0.895469	+	0.445124i	$0.853160\pi$
$312$	1.22492	−	0.236084i	0.0693473	−	0.0133656i
$313$	−5.19344	−	4.95194i	−0.293551	−	0.279900i	0.528964	−	0.848645i	$-0.322581\pi$
$313$	−5.19344	−	4.95194i	−0.293551	−	0.279900i	−0.822514	+	0.568745i	$0.807429\pi$
$314$	−0.583565	+	4.05878i	−0.0329325	+	0.229050i
$315$	−0.364745	−	1.64299i	−0.0205510	−	0.0925719i
$316$	−1.03981	+	2.27687i	−0.0584940	+	0.128084i
$317$	−6.11012	−	25.1863i	−0.343179	−	1.41460i	−0.838030	−	0.545624i	$-0.816293\pi$
$317$	−6.11012	−	25.1863i	−0.343179	−	1.41460i	0.494851	−	0.868978i	$-0.335223\pi$
$318$	−4.98888	−	0.476381i	−0.279763	−	0.0267141i
$319$	0.0358159	+	0.0143385i	0.00200531	+	0.000802803i
$320$	0.0302673	−	0.635389i	0.00169199	−	0.0355193i
$321$	5.74136			0.320452
$322$	12.2546	−	3.29007i	0.682923	−	0.183348i
$323$	15.4308			0.858594
$324$	0.0475819	−	0.998867i	0.00264344	−	0.0554926i
$325$	5.32191	+	2.13057i	0.295206	+	0.118183i
$326$	21.2562	+	2.02972i	1.17727	+	0.112416i
$327$	−0.781756	−	3.22244i	−0.0432312	−	0.178202i
$328$	−0.151401	+	0.331522i	−0.00835973	+	0.0183053i
$329$	−16.1470	−	5.08595i	−0.890212	−	0.280397i
$330$	−0.000607617		0.00422607i	−3.34482e−5		0.000232638i
$331$	−2.98218	−	2.84350i	−0.163915	−	0.156293i	0.603682	−	0.797225i	$-0.293700\pi$
$331$	−2.98218	−	2.84350i	−0.163915	−	0.156293i	−0.767598	+	0.640932i	$0.778548\pi$
$332$	−8.00576	+	1.54298i	−0.439373	+	0.0846822i
$333$	−0.334205	−	7.01583i	−0.0183143	−	0.384465i
$334$	−13.8339	−	7.13185i	−0.756955	−	0.390237i
$335$	−2.18833	−	2.52546i	−0.119561	−	0.137981i
$336$	−2.60723	+	0.449851i	−0.142236	+	0.0245414i
$337$	1.72725	−	12.0133i	0.0940891	−	0.654404i	−0.887132	−	0.461516i	$-0.847306\pi$
$337$	1.72725	−	12.0133i	0.0940891	−	0.654404i	0.981221	−	0.192888i	$-0.0617853\pi$
$338$	11.2370	+	2.16576i	0.611214	+	0.117802i
$339$	2.79100	+	3.91942i	0.151587	+	0.212873i
$340$	−0.887853	+	0.846566i	−0.0481506	+	0.0459115i
$341$	−0.0227246	+	0.0319122i	−0.00123060	+	0.00172814i
$342$	−1.13870	−	7.91983i	−0.0615738	−	0.428255i
$343$	11.2873	+	14.6832i	0.609455	+	0.792820i
$344$	0.0688392			0.00371156
$345$	−2.56016	−	1.65898i	−0.137834	−	0.0893162i
$346$	−10.5028	+	18.1914i	−0.564633	+	0.977973i
$347$	22.8497	−	11.7798i	1.22663	−	0.632374i	0.281659	−	0.959515i	$-0.409115\pi$
$347$	22.8497	−	11.7798i	1.22663	−	0.632374i	0.944976	+	0.327141i	$0.106085\pi$
$348$	4.51814	−	3.55311i	0.242198	−	0.190466i
$349$	4.75862	+	10.4199i	0.254723	+	0.557766i	0.993188	−	0.116527i	$-0.0371760\pi$
$349$	4.75862	+	10.4199i	0.254723	+	0.557766i	−0.738464	+	0.674292i	$0.764449\pi$
$350$	−11.1968	−	4.73844i	−0.598495	−	0.253280i
$351$	−0.518214	+	1.13473i	−0.0276602	+	0.0605674i
$352$	0.00659064	+	0.00127024i	0.000351283	+	6.77042e-5i
$353$	−16.6046	−	13.0580i	−0.883776	−	0.695009i	0.0693472	−	0.997593i	$-0.477908\pi$
$353$	−16.6046	−	13.0580i	−0.883776	−	0.695009i	−0.953123	+	0.302584i	$0.902151\pi$
$354$	1.35721	−	5.59449i	0.0721349	−	0.297344i
$355$	−2.06484	+	5.96596i	−0.109590	+	0.316640i
$356$	1.70579	−	1.09624i	0.0904065	−	0.0581008i
$357$	4.23773	+	2.84194i	0.224285	+	0.150412i
$358$	−7.28355	−	8.40567i	−0.384948	−	0.444253i
$359$	17.6463	+	16.8258i	0.931339	+	0.888030i	0.993931	−	0.110010i	$-0.0350882\pi$
$359$	17.6463	+	16.8258i	0.931339	+	0.888030i	−0.0625919	+	0.998039i	$0.519937\pi$
$360$	0.500016	+	0.393217i	0.0263532	+	0.0207244i
$361$	−14.7247	−	42.5443i	−0.774985	−	2.23917i
$362$	10.2916	−	0.982730i	0.540915	−	0.0516512i
$363$	10.5544	+	3.09905i	0.553961	+	0.162658i
$364$	3.22800	+	0.687826i	0.169193	+	0.0360519i
$365$	1.07572	+	7.48181i	0.0563058	+	0.391616i
$366$	0.221157	−	4.64265i	0.0115600	−	0.242675i
$367$	−2.75710	+	4.77545i	−0.143920	+	0.249276i	−0.928969	−	0.370157i	$-0.879304\pi$
$367$	−2.75710	+	4.77545i	−0.143920	+	0.249276i	0.785050	+	0.619433i	$0.212637\pi$
$368$	−2.79655	+	3.89606i	−0.145780	+	0.203096i
$369$	−0.182229	−	0.315629i	−0.00948645	−	0.0164310i
$370$	3.75864	+	2.41553i	0.195402	+	0.125577i
$371$	−11.6644	−	6.30493i	−0.605587	−	0.327336i
$372$	2.42471	+	5.30937i	0.125715	+	0.275278i
$373$	−1.19258	−	4.91588i	−0.0617494	−	0.254535i	0.932567	−	0.360996i	$-0.117563\pi$
$373$	−1.19258	−	4.91588i	−0.0617494	−	0.254535i	−0.994317	+	0.106461i	$0.966048\pi$
$374$	−0.00750842	−	0.0105441i	−0.000388251	−	0.000545223i
$375$	1.99633	+	5.76801i	0.103090	+	0.297859i
$376$	5.94023	−	2.37811i	0.306344	−	0.122642i
$377$	−6.87982	+	2.02010i	−0.354329	+	0.104040i
$378$	1.14590	−	2.38472i	0.0589388	−	0.122657i
$379$	4.57855	−	2.94246i	0.235184	−	0.151144i	−0.417741	−	0.908566i	$-0.637178\pi$
$379$	4.57855	−	2.94246i	0.235184	−	0.151144i	0.652925	+	0.757422i	$0.273542\pi$
$380$	4.52390	+	2.33223i	0.232071	+	0.119641i
$381$	−10.9984	+	2.11976i	−0.563463	+	0.108599i
$382$	−5.56225	+	22.9279i	−0.284590	+	1.17309i
$383$	−10.3008	+	4.12383i	−0.526348	+	0.210718i	−0.619590	−	0.784925i	$-0.712701\pi$
$383$	−10.3008	+	4.12383i	−0.526348	+	0.210718i	0.0932419	+	0.995643i	$0.470277\pi$
$384$	0.654861	−	0.755750i	0.0334182	−	0.0385667i
$385$	−0.00583814	+	0.00967049i	−0.000297539	+	0.000492854i
$386$	−10.1414	−	2.97778i	−0.516183	−	0.151565i
$387$	−0.0399307	+	0.0560748i	−0.00202979	+	0.00285044i
$388$	8.49612	+	3.40133i	0.431325	+	0.172676i
$389$	−6.55485	+	3.37926i	−0.332344	+	0.171335i	−0.616319	−	0.787496i	$-0.711377\pi$
$389$	−6.55485	+	3.37926i	−0.332344	+	0.171335i	0.283975	+	0.958832i	$0.408347\pi$
$390$	−0.396761	−	0.687211i	−0.0200908	−	0.0347983i
$391$	9.08837	−	1.71616i	0.459619	−	0.0867899i
$392$	−6.81649	−	1.59232i	−0.344285	−	0.0804242i
$393$	11.4075	+	7.33112i	0.575430	+	0.369806i
$394$	−1.61481	+	1.26990i	−0.0813530	+	0.0639767i
$395$	1.58502	+	0.151351i	0.0797508	+	0.00761528i
$396$	−0.00485766	+	0.00463177i	−0.000244106	+	0.000232755i
$397$	−12.9662	+	1.23812i	−0.650754	+	0.0621395i	−0.415212	−	0.909725i	$-0.636293\pi$
$397$	−12.9662	+	1.23812i	−0.650754	+	0.0621395i	−0.235542	+	0.971864i	$0.575687\pi$
$398$	4.64686	−	5.36276i	0.232926	−	0.268811i
$399$	5.39191	−	20.4712i	0.269933	−	1.02484i
$400$	4.40922	−	1.29466i	0.220461	−	0.0647332i
$401$	−1.81068	+	5.23161i	−0.0904209	+	0.261254i	−0.981139	−	0.193301i	$-0.938081\pi$
$401$	−1.81068	+	5.23161i	−0.0904209	+	0.261254i	0.890719	+	0.454555i	$0.150202\pi$
$402$	−0.249961	−	5.24734i	−0.0124669	−	0.261713i
$403$	−0.346454	−	7.27297i	−0.0172581	−	0.362292i
$404$	0.817363	−	2.36161i	0.0406653	−	0.117495i
$405$	−0.610343	+	0.179213i	−0.0303282	+	0.00890516i
$406$	14.6724	−	3.99850i	0.728179	−	0.198442i
$407$	−0.0308723	+	0.0356285i	−0.00153028	+	0.00176604i
$408$	−1.91981	+	0.183320i	−0.0950449	+	0.00907569i
$409$	−9.30661	+	8.87384i	−0.460182	+	0.438783i	−0.884367	−	0.466793i	$-0.845409\pi$
$409$	−9.30661	+	8.87384i	−0.460182	+	0.438783i	0.424184	+	0.905576i	$0.360561\pi$
$410$	0.230785	+	0.0220373i	0.0113977	+	0.00108835i
$411$	−0.652424	+	0.513072i	−0.0321817	+	0.0253080i
$412$	−3.62948	−	2.33253i	−0.178812	−	0.114915i
$413$	9.07558	−	12.2318i	0.446580	−	0.601887i
$414$	−1.55148	−	4.53794i	−0.0762511	−	0.223028i
$415$	2.59313	+	4.49144i	0.127292	+	0.220476i
$416$	−1.10879	+	0.571620i	−0.0543628	+	0.0280260i
$417$	−5.34875	−	2.14131i	−0.261929	−	0.104861i
$418$	−0.0311514	+	0.0437460i	−0.00152366	+	0.00213969i
$419$	−31.5227	−	9.25590i	−1.53999	−	0.452180i	−0.601896	−	0.798574i	$-0.705588\pi$
$419$	−31.5227	−	9.25590i	−1.53999	−	0.452180i	−0.938089	+	0.346394i	$0.887406\pi$
$420$	0.812853	+	1.47368i	0.0396632	+	0.0719080i
$421$	−9.19704	+	10.6139i	−0.448236	+	0.517292i	−0.934231	−	0.356670i	$-0.883912\pi$
$421$	−9.19704	+	10.6139i	−0.448236	+	0.517292i	0.485994	+	0.873962i	$0.338458\pi$
$422$	−26.2128	+	10.4940i	−1.27602	+	0.510841i
$423$	−1.50852	+	6.21820i	−0.0733467	+	0.302339i
$424$	4.92101	−	0.948447i	0.238985	−	0.0460607i
$425$	−7.87719	−	4.06097i	−0.382100	−	0.196986i
$426$	−8.34916	+	5.36568i	−0.404518	+	0.259968i
$427$	5.32605	−	11.0840i	0.257746	−	0.536392i
$428$	−5.50880	+	1.61753i	−0.266278	+	0.0781862i
$429$	0.00777312	−	0.00311189i	0.000375290	−	0.000150243i
$430$	−0.0143221	−	0.0413809i	−0.000690672	−	0.00199557i
$431$	−0.439685	−	0.617451i	−0.0211789	−	0.0297416i	0.803851	−	0.594831i	$-0.202781\pi$
$431$	−0.439685	−	0.617451i	−0.0211789	−	0.0297416i	−0.825030	+	0.565089i	$0.808842\pi$
$432$	0.235759	+	0.971812i	0.0113430	+	0.0467563i
$433$	−16.7560	−	36.6906i	−0.805243	−	1.76324i	−0.626631	−	0.779316i	$-0.715567\pi$
$433$	−16.7560	−	36.6906i	−0.805243	−	1.76324i	−0.178612	−	0.983920i	$-0.557161\pi$
$434$	0.433241	+	15.4367i	0.0207962	+	0.740986i
$435$	−3.07586	−	1.97674i	−0.147476	−	0.0947773i
$436$	1.65796	+	2.87167i	0.0794017	+	0.137528i
$437$	−19.0611	−	33.3038i	−0.911814	−	1.59314i
$438$	−5.94138	+	10.2908i	−0.283890	+	0.491712i
$439$	−1.68214	+	35.3125i	−0.0802842	+	1.68537i	0.496156	+	0.868233i	$0.334744\pi$
$439$	−1.68214	+	35.3125i	−0.0802842	+	1.68537i	−0.576440	+	0.817139i	$0.695559\pi$
$440$	−0.000607617	−	0.00422607i	−2.89670e−5	−	0.000201470i
$441$	5.25102	−	4.62891i	0.250048	−	0.220424i
$442$	2.30834	+	0.677789i	0.109796	+	0.0322391i
$443$	2.88452	−	0.275438i	0.137048	−	0.0130865i	−0.0263067	−	0.999654i	$-0.508375\pi$
$443$	2.88452	−	0.275438i	0.137048	−	0.0130865i	0.163354	+	0.986567i	$0.447769\pi$
$444$	2.29726	+	6.63749i	0.109023	+	0.315001i
$445$	−1.01387	−	0.797316i	−0.0480620	−	0.0377964i
$446$	−4.32950	−	4.12817i	−0.205008	−	0.195475i
$447$	3.01075	+	3.47459i	0.142403	+	0.164342i
$448$	2.37488	−	1.16617i	0.112202	−	0.0550964i
$449$	12.3756	−	7.95329i	0.584038	−	0.375339i	−0.215004	−	0.976613i	$-0.568976\pi$
$449$	12.3756	−	7.95329i	0.584038	−	0.375339i	0.799043	+	0.601274i	$0.205340\pi$
$450$	−1.50300	+	4.34262i	−0.0708519	+	0.204713i
$451$	−0.000576717		0.00237726i	−2.71566e−5		0.000111941i
$452$	−3.78218	−	2.97434i	−0.177899	−	0.139901i
$453$	18.4888	+	3.56341i	0.868677	+	0.167424i
$454$	5.92012	−	12.9633i	0.277845	−	0.608396i
$455$	−0.258121	−	2.08354i	−0.0121009	−	0.0976776i
$456$	3.32385	+	7.27821i	0.155653	+	0.340834i
$457$	31.4288	−	24.7158i	1.47018	−	1.15616i	0.516125	−	0.856513i	$-0.327374\pi$
$457$	31.4288	−	24.7158i	1.47018	−	1.15616i	0.954051	−	0.299645i	$-0.0968683\pi$
$458$	−13.8901	+	7.16084i	−0.649041	+	0.334604i
$459$	0.964273	−	1.67017i	0.0450084	−	0.0779569i
$460$	2.92384	+	0.870495i	0.136325	+	0.0405870i
$461$	−9.77129			−0.455095			−0.227547	−	0.973767i	$-0.573071\pi$
$461$	−9.77129			−0.455095			−0.227547	+	0.973767i	$0.573071\pi$
$462$	−0.0166119	+	0.00627662i	−0.000772855	+	0.000292015i
$463$	2.56036	+	17.8077i	0.118990	+	0.827593i	0.958672	+	0.284514i	$0.0918323\pi$
$463$	2.56036	+	17.8077i	0.118990	+	0.827593i	−0.839682	+	0.543078i	$0.817259\pi$
$464$	−3.33410	+	4.68209i	−0.154782	+	0.217360i
$465$	2.68713	−	2.56217i	0.124612	−	0.118818i
$466$	14.0788	+	19.7710i	0.652190	+	0.915873i
$467$	−9.96875	−	1.92132i	−0.461299	−	0.0889080i	−0.0466932	−	0.998909i	$-0.514868\pi$
$467$	−9.96875	−	1.92132i	−0.461299	−	0.0889080i	−0.414606	+	0.910001i	$0.636080\pi$
$468$	0.177532	−	1.23476i	0.00820643	−	0.0570770i
$469$	4.80167	−	13.0431i	0.221720	−	0.602276i
$470$	−2.66541	−	3.07605i	−0.122946	−	0.141887i
$471$	3.64469	+	1.87897i	0.167938	+	0.0865783i
$472$	0.273918	+	5.75025i	0.0126081	+	0.264677i
$473$	0.000453695	0	8.74425e-5i	2.08609e−5	0	4.02061e-6i
$474$	1.81156	+	1.72731i	0.0832075	+	0.0793382i
$475$	−5.23274	+	36.3945i	−0.240095	+	1.66989i
$476$	−4.86674	−	1.53292i	−0.223067	−	0.0702612i
$477$	−2.08188	+	4.55869i	−0.0953229	+	0.208728i
$478$	0.704066	+	2.90220i	0.0322032	+	0.132744i
$479$	−29.0746	−	2.77629i	−1.32845	−	0.126852i	−0.593426	−	0.804889i	$-0.702225\pi$
$479$	−29.0746	−	2.77629i	−1.32845	−	0.126852i	−0.735028	+	0.678037i	$0.762831\pi$
$480$	−0.590544	−	0.236418i	−0.0269545	−	0.0107910i
$481$	0.416908	−	8.75198i	0.0190094	−	0.399056i
$482$	−22.4236			−1.02137
$483$	0.898974	−	12.6567i	0.0409047	−	0.575899i
$484$	−11.0000			−0.499998
$485$	0.276997	−	5.81487i	0.0125778	−	0.264040i
$486$	−0.928368	−	0.371662i	−0.0421116	−	0.0168590i
$487$	−35.2243	−	3.36351i	−1.59617	−	0.152415i	−0.741267	−	0.671210i	$-0.765775\pi$
$487$	−35.2243	−	3.36351i	−1.59617	−	0.152415i	−0.854899	+	0.518795i	$0.826381\pi$
$488$	1.09579	+	4.51690i	0.0496040	+	0.204470i
$489$	8.87032	−	19.4233i	0.401130	−	0.878351i
$490$	0.460997	+	4.42884i	0.0208257	+	0.200075i
$491$	0.507452	−	3.52940i	0.0229010	−	0.159280i	−0.975162	−	0.221493i	$-0.928907\pi$
$491$	0.507452	−	3.52940i	0.0229010	−	0.159280i	0.998063	+	0.0622136i	$0.0198160\pi$
$492$	0.263770	+	0.251504i	0.0118917	+	0.0113387i
$493$	10.8847	−	2.09786i	0.490224	−	0.0944829i
$494$	−0.474928	−	9.96997i	−0.0213680	−	0.448570i
$495$	0.00379491	+	0.00195641i	0.000170568	+	8.79342e-5i
$496$	−3.82231	−	4.41118i	−0.171627	−	0.198068i
$497$	−25.8759	+	4.46462i	−1.16069	+	0.200266i
$498$	−1.16031	+	8.07011i	−0.0519946	+	0.361630i
$499$	1.39552	+	0.268964i	0.0624720	+	0.0120405i	0.220391	−	0.975412i	$-0.429267\pi$
$499$	1.39552	+	0.268964i	0.0624720	+	0.0120405i	−0.157919	+	0.987452i	$0.550479\pi$
$500$	−3.54050	−	4.97193i	−0.158336	−	0.222352i
$501$	−11.2642	+	10.7404i	−0.503248	+	0.479846i
$502$	−16.8641	+	23.6824i	−0.752684	+	1.05700i
$503$	−2.93385	−	20.4054i	−0.130814	−	0.909831i	−0.944497	−	0.328521i	$-0.893450\pi$
$503$	−2.93385	−	20.4054i	−0.130814	−	0.909831i	0.813683	−	0.581309i	$-0.197459\pi$
$504$	−0.427631	+	2.61096i	−0.0190482	+	0.116302i
$505$	−1.58968			−0.0707397
$506$	−0.0134821	+	0.0292299i	−0.000599354	+	0.00129943i
$507$	5.72192	−	9.91066i	0.254119	−	0.440148i
$508$	9.95565	−	5.13249i	0.441711	−	0.227718i
$509$	0.662057	−	0.520647i	0.0293451	−	0.0230773i	−0.603379	−	0.797455i	$-0.706179\pi$
$509$	0.662057	−	0.520647i	0.0293451	−	0.0230773i	0.632724	+	0.774378i	$0.281937\pi$
$510$	0.509618	+	1.11591i	0.0225662	+	0.0494132i
$511$	−25.0876	+	18.9476i	−1.10981	+	0.838192i
$512$	−0.415415	+	0.909632i	−0.0183589	+	0.0402004i
$513$	−7.85668	−	1.51425i	−0.346881	−	0.0668558i
$514$	−18.2374	−	14.3420i	−0.804416	−	0.632600i
$515$	−0.647021	+	2.66706i	−0.0285111	+	0.117524i
$516$	0.0225151	−	0.0650531i	0.000991172	−	0.00286380i
$517$	0.0361291	−	0.0232188i	0.00158896	−	0.00102116i
$518$	−1.24677	+	18.5413i	−0.0547798	+	0.814659i
$519$	13.7557	+	15.8750i	0.603809	+	0.696833i
$520$	0.574299	+	0.547593i	0.0251847	+	0.0240135i
$521$	3.42316	+	2.69201i	0.149972	+	0.117939i	0.690326	−	0.723499i	$-0.257467\pi$
$521$	3.42316	+	2.69201i	0.149972	+	0.117939i	−0.540354	+	0.841438i	$0.681710\pi$
$522$	−1.87995	−	5.43175i	−0.0822831	−	0.237741i
$523$	−38.7489	+	3.70007i	−1.69437	+	0.161793i	−0.897100	−	0.441827i	$-0.854330\pi$
$523$	−38.7489	+	3.70007i	−1.69437	+	0.161793i	−0.797272	+	0.603620i	$0.793724\pi$
$524$	−13.0108	−	3.82031i	−0.568379	−	0.166891i
$525$	−8.13995	+	9.03121i	−0.355257	+	0.394154i
$526$	−2.03703	−	14.1679i	−0.0888188	−	0.617748i
$527$	−0.535610	+	11.2438i	−0.0233316	+	0.489790i
$528$	0.00335597	−	0.00581271i	0.000146050	−	0.000252966i
$529$	−14.9304	−	17.4952i	−0.649149	−	0.760662i
$530$	−1.59396	−	2.76081i	−0.0692370	−	0.119922i
$531$	−4.84290	−	3.11234i	−0.210164	−	0.135064i
$532$	0.593898	+	21.1610i	0.0257487	+	0.917448i
$533$	−0.188867	−	0.413561i	−0.00818074	−	0.0179133i
$534$	−0.478042	−	1.97052i	−0.0206869	−	0.0852726i
$535$	2.11845	+	2.97494i	0.0915885	+	0.128618i
$536$	1.71818	+	4.96436i	0.0742141	+	0.214428i
$537$	−10.3256	+	4.13374i	−0.445582	+	0.178384i
$538$	17.8736	−	5.24815i	0.770584	−	0.226264i
$539$	−0.0469477	−	0.00183581i	−0.00202218	−	7.90737e-5i
$540$	0.535130	−	0.343907i	0.0230283	−	0.0147994i
$541$	−11.8113	−	6.08915i	−0.507808	−	0.261793i	0.185229	−	0.982695i	$-0.440697\pi$
$541$	−11.8113	−	6.08915i	−0.507808	−	0.261793i	−0.693037	+	0.720902i	$0.743728\pi$
$542$	15.3446	−	2.95742i	0.659105	−	0.127032i
$543$	2.43738	−	10.0470i	0.104598	−	0.431158i
$544$	1.79040	−	0.716768i	0.0767628	−	0.0307312i
$545$	1.38129	−	1.59409i	0.0591679	−	0.0682834i
$546$	1.70577	−	2.82550i	0.0730004	−	0.120920i
$547$	14.2338	+	4.17941i	0.608592	+	0.178699i	0.571485	−	0.820613i	$-0.306368\pi$
$547$	14.2338	+	4.17941i	0.608592	+	0.178699i	0.0371071	+	0.999311i	$0.488186\pi$
$548$	0.481447	−	0.676098i	0.0205664	−	0.0288815i
$549$	−4.31497	−	1.72746i	−0.184159	−	0.0737260i
$550$	0.0274151	−	0.0141334i	0.00116898	−	0.000602652i
$551$	−22.9952	−	39.8288i	−0.979628	−	1.69677i
$552$	2.76712	+	3.91702i	0.117776	+	0.166719i
$553$	2.63285	+	6.07664i	0.111960	+	0.258405i
$554$	16.1937	+	10.4071i	0.688006	+	0.442154i
$555$	3.51201	−	2.76187i	0.149076	−	0.117235i
$556$	5.73536	+	0.547661i	0.243234	+	0.0232260i
$557$	−19.5474	+	18.6384i	−0.828248	+	0.789733i	−0.980065	−	0.198676i	$-0.936336\pi$
$557$	−19.5474	+	18.6384i	−0.828248	+	0.789733i	0.151817	+	0.988409i	$0.451488\pi$
$558$	5.81040	−	0.554826i	0.245974	−	0.0234876i
$559$	−0.0562357	+	0.0648994i	−0.00237852	+	0.00274495i
$560$	−1.19511	−	1.18497i	−0.0505026	−	0.0500743i
$561$	−0.0124199	+	0.00364683i	−0.000524371	+	0.000153969i
$562$	−4.74908	+	13.7216i	−0.200328	+	0.578809i
$563$	−0.657969	−	13.8125i	−0.0277301	−	0.582126i	−0.969385	−	0.245546i	$-0.921033\pi$
$563$	−0.657969	−	13.8125i	−0.0277301	−	0.582126i	0.941655	−	0.336580i	$-0.109270\pi$
$564$	−0.304456	−	6.39132i	−0.0128199	−	0.269123i
$565$	−1.00106	+	2.89237i	−0.0421149	+	0.121683i
$566$	−6.24644	+	1.83412i	−0.262557	+	0.0770938i
$567$	−1.87878	−	1.86285i	−0.0789013	−	0.0782321i
$568$	6.49927	−	7.50056i	0.272703	−	0.314717i
$569$	30.5312	−	2.91538i	1.27994	−	0.122219i	0.567158	−	0.823609i	$-0.308043\pi$
$569$	30.5312	−	2.91538i	1.27994	−	0.122219i	0.712778	+	0.701390i	$0.247437\pi$
$570$	3.68358	−	3.51229i	0.154288	−	0.147114i
$571$	−44.9757	−	4.29466i	−1.88217	−	0.179726i	−0.910098	−	0.414394i	$-0.863994\pi$
$571$	−44.9757	−	4.29466i	−1.88217	−	0.179726i	−0.972076	+	0.234668i	$0.924600\pi$
$572$	−0.00658153	+	0.00517577i	−0.000275188	+	0.000216410i
$573$	19.8477	+	12.7553i	0.829148	+	0.532861i
$574$	0.383354	+	0.884785i	0.0160009	+	0.0369302i
$575$	0.965708	+	22.0174i	0.0402728	+	0.918190i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	6.12085	−	3.15552i	0.254814	−	0.131366i	−0.326087	−	0.945340i	$-0.605730\pi$
$577$	6.12085	−	3.15552i	0.254814	−	0.131366i	0.580902	+	0.813974i	$0.302700\pi$
$578$	12.3294	+	4.93594i	0.512835	+	0.205308i
$579$	−6.13093	+	8.60969i	−0.254793	+	0.357806i
$580$	3.50818	+	1.03009i	0.145669	+	0.0427724i
$581$	−11.1485	+	18.4668i	−0.462518	+	0.766131i
$582$	5.99307	−	6.91637i	0.248421	−	0.286693i
$583$	0.0312279	−	0.0125018i	0.00129333	−	0.000517770i
$584$	2.80147	−	11.5478i	0.115926	−	0.477852i
$585$	−0.779182	+	0.150175i	−0.0322152	+	0.00620898i
$586$	−20.8802	−	10.7645i	−0.862553	−	0.444677i
$587$	−25.5189	+	16.4000i	−1.05328	+	0.676900i	−0.948235	−	0.317568i	$-0.897134\pi$
$587$	−25.5189	+	16.4000i	−1.05328	+	0.676900i	−0.105041	+	0.994468i	$0.533497\pi$
$588$	−3.73420	+	5.92079i	−0.153996	+	0.244169i
$589$	44.8103	−	13.1575i	1.84638	−	0.542145i
$590$	3.39962	−	1.36100i	0.139960	−	0.0560317i
$591$	0.671905	+	1.94134i	0.0276385	+	0.0798561i
$592$	−4.07420	−	5.72141i	−0.167449	−	0.235149i
$593$	−9.05282	−	37.3162i	−0.371755	−	1.53239i	−0.783673	−	0.621173i	$-0.786656\pi$
$593$	−9.05282	−	37.3162i	−0.371755	−	1.53239i	0.411919	−	0.911221i	$-0.364859\pi$
$594$	0.00278824	+	0.00610539i	0.000114403	+	0.000250507i
$595$	0.0910573	+	3.24444i	0.00373298	+	0.133009i
$596$	−3.86770	−	2.48562i	−0.158427	−	0.101815i
$597$	−3.54798	−	6.14528i	−0.145209	−	0.251509i
$598$	−1.38854	−	5.81925i	−0.0567818	−	0.237967i
$599$	−21.2198	+	36.7538i	−0.867018	+	1.50172i	−0.00198918	+	0.999998i	$0.500633\pi$
$599$	−21.2198	+	36.7538i	−0.867018	+	1.50172i	−0.865029	+	0.501722i	$0.832700\pi$
$600$	0.218656	−	4.59016i	0.00892660	−	0.187392i
$601$	1.80162	+	12.5306i	0.0734898	+	0.511133i	0.993004	+	0.118077i	$0.0376730\pi$
$601$	1.80162	+	12.5306i	0.0734898	+	0.511133i	−0.919515	+	0.393056i	$0.871418\pi$
$602$	0.121938	−	0.135289i	0.00496981	−	0.00551396i
$603$	−5.04049	−	1.48002i	−0.205265	−	0.0602711i
$604$	−18.7438	+	1.78981i	−0.762673	+	0.0728264i
$605$	2.28855	+	6.61234i	0.0930429	+	0.268830i
$606$	−1.96439	−	1.54482i	−0.0797981	−	0.0627539i
$607$	2.85432	+	2.72159i	0.115853	+	0.110466i	0.745792	−	0.666179i	$-0.232071\pi$
$607$	2.85432	+	2.72159i	0.115853	+	0.110466i	−0.629938	+	0.776645i	$0.716920\pi$
$608$	−5.23972	−	6.04696i	−0.212499	−	0.245237i
$609$	1.02029	−	15.1732i	0.0413441	−	0.614849i
$610$	2.48724	−	1.59845i	0.100705	−	0.0647194i
$611$	−2.61065	+	7.54297i	−0.105615	+	0.305156i
$612$	−0.454672	+	1.87418i	−0.0183790	+	0.0757594i
$613$	−10.6136	−	8.34660i	−0.428678	−	0.337116i	0.380395	−	0.924824i	$-0.375788\pi$
$613$	−10.6136	−	8.34660i	−0.428678	−	0.337116i	−0.809073	+	0.587708i	$0.800030\pi$
$614$	13.4570	+	2.59363i	0.543081	+	0.104670i
$615$	0.0963077	−	0.210885i	0.00388350	−	0.00850369i
$616$	0.0141707	−	0.0107025i	0.000570952	−	0.000431215i
$617$	−17.1927	−	37.6469i	−0.692154	−	1.51561i	−0.849232	−	0.528019i	$-0.822935\pi$
$617$	−17.1927	−	37.6469i	−0.692154	−	1.51561i	0.157079	−	0.987586i	$-0.449792\pi$
$618$	−3.39133	+	2.66697i	−0.136419	+	0.107281i
$619$	2.09166	−	1.07833i	0.0840709	−	0.0433416i	−0.415678	−	0.909512i	$-0.636456\pi$
$619$	2.09166	−	1.07833i	0.0840709	−	0.0433416i	0.499749	+	0.866170i	$0.333425\pi$
$620$	−1.85643	+	3.21543i	−0.0745561	+	0.129135i
$621$	−4.79580	−	0.0180654i	−0.192449	−	0.000724941i
$622$	−14.1791			−0.568530
$623$	0.867095	−	5.29418i	0.0347394	−	0.212107i
$624$	0.177532	+	1.23476i	0.00710698	+	0.0494301i
$625$	11.0757	−	15.5537i	0.443029	−	0.622147i
$626$	5.19344	−	4.95194i	0.207572	−	0.197919i
$627$	0.0311514	+	0.0437460i	0.00124407	+	0.00174705i
$628$	−4.02642	−	0.776029i	−0.160672	−	0.0309669i
$629$	−1.92775	+	13.4078i	−0.0768646	+	0.534605i
$630$	1.65848	−	0.286155i	0.0660755	−	0.0114007i
$631$	9.60873	+	11.0891i	0.382517	+	0.441449i	0.914058	−	0.405585i	$-0.132932\pi$
$631$	9.60873	+	11.0891i	0.382517	+	0.441449i	−0.531540	+	0.847033i	$0.678387\pi$
$632$	−2.22481	−	1.14697i	−0.0884984	−	0.0456241i
$633$	1.34349	+	28.2034i	0.0533990	+	1.12098i
$634$	25.4485	−	4.90479i	1.01069	−	0.194794i
$635$	−5.15655	−	4.91676i	−0.204632	−	0.195116i
$636$	0.713222	−	4.96057i	0.0282811	−	0.196699i
$637$	7.06967	−	5.12558i	0.280110	−	0.203083i
$638$	−0.0160265	+	0.0350931i	−0.000634494	+	0.00138935i
$639$	2.33983	+	9.64490i	0.0925622	+	0.381547i
$640$	0.633229	+	0.0604661i	0.0250306	+	0.00239013i
$641$	24.8879	+	9.96362i	0.983013	+	0.393539i	0.806808	−	0.590814i	$-0.201193\pi$
$641$	24.8879	+	9.96362i	0.983013	+	0.393539i	0.176206	+	0.984353i	$0.443618\pi$
$642$	−0.273185	+	5.73486i	−0.0107818	+	0.226337i
$643$	15.5133			0.611784			0.305892	−	0.952066i	$-0.401045\pi$
$643$	15.5133			0.611784			0.305892	+	0.952066i	$0.401045\pi$
$644$	2.70324	+	12.3973i	0.106523	+	0.488521i
$645$	−0.0437893			−0.00172420
$646$	−0.734228	+	15.4133i	−0.0288878	+	0.606430i
$647$	−6.81763	−	2.72937i	−0.268028	−	0.107302i	0.233755	−	0.972295i	$-0.424898\pi$
$647$	−6.81763	−	2.72937i	−0.268028	−	0.107302i	−0.501784	+	0.864993i	$0.667323\pi$
$648$	0.995472	+	0.0950560i	0.0391058	+	0.00373415i
$649$	0.00910951	+	0.0375499i	0.000357579	+	0.00147396i
$650$	−2.38138	+	5.21450i	−0.0934055	+	0.204530i
$651$	14.7294	+	4.63944i	0.577291	+	0.181834i
$652$	−3.03884	+	21.1356i	−0.119010	+	0.827732i
$653$	−21.6766	−	20.6686i	−0.848272	−	0.808826i	0.135024	−	0.990842i	$-0.456889\pi$
$653$	−21.6766	−	20.6686i	−0.848272	−	0.808826i	−0.983295	+	0.182017i	$0.941737\pi$
$654$	3.25599	−	0.627541i	0.127319	−	0.0245388i
$655$	0.410427	+	8.61592i	0.0160367	+	0.336652i
$656$	−0.323943	−	0.167004i	−0.0126478	−	0.00652041i
$657$	7.78156	+	8.98039i	0.303587	+	0.350359i
$658$	5.84849	−	15.8867i	0.227998	−	0.619328i
$659$	0.0904608	−	0.629169i	0.00352385	−	0.0245089i	−0.987984	−	0.154558i	$-0.950605\pi$
$659$	0.0904608	−	0.629169i	0.00352385	−	0.0245089i	0.991508	+	0.130049i	$0.0415136\pi$
$660$	−0.00419237		0.000808014i	−0.000163188		3.14519e-5i
$661$	12.9489	+	18.1842i	0.503653	+	0.707282i	0.985633	−	0.168901i	$-0.0540217\pi$
$661$	12.9489	+	18.1842i	0.503653	+	0.707282i	−0.481980	+	0.876182i	$0.660082\pi$
$662$	2.98218	−	2.84350i	0.115906	−	0.110516i
$663$	1.39549	−	1.95970i	0.0541965	−	0.0761083i
$664$	−1.16031	−	8.07011i	−0.0450286	−	0.313181i
$665$	12.5969	−	4.75959i	0.488485	−	0.184569i
$666$	7.02379			0.272166
$667$	−17.9732	−	20.9008i	−0.695925	−	0.809280i
$668$	7.78201	−	13.4788i	0.301095	−	0.521512i
$669$	−5.31717	+	2.74119i	−0.205574	+	0.105981i
$670$	2.62673	−	2.06568i	0.101479	−	0.0798042i
$671$	0.0129595	+	0.0283773i	0.000500296	+	0.00109550i
$672$	−0.325285	−	2.62568i	−0.0125481	−	0.101288i
$673$	14.3491	−	31.4202i	0.553117	−	1.21116i	−0.402193	−	0.915555i	$-0.631752\pi$
$673$	14.3491	−	31.4202i	0.553117	−	1.21116i	0.955311	−	0.295604i	$-0.0955207\pi$
$674$	11.9175	+	2.29690i	0.459044	+	0.0884734i
$675$	3.61220	+	2.84067i	0.139034	+	0.109337i
$676$	−2.69799	+	11.1213i	−0.103769	+	0.427741i
$677$	−7.57555	+	21.8881i	−0.291152	+	0.841228i	0.700657	+	0.713498i	$0.252890\pi$
$677$	−7.57555	+	21.8881i	−0.291152	+	0.841228i	−0.991809	+	0.127730i	$0.959231\pi$
$678$	−4.04778	+	2.60135i	−0.155454	+	0.0999042i
$679$	21.7341	−	10.6724i	0.834078	−	0.409569i
$680$	−0.803362	−	0.927129i	−0.0308075	−	0.0355538i
$681$	−10.3140	−	9.83438i	−0.395234	−	0.376854i
$682$	−0.0307948	−	0.0242173i	−0.00117919	−	0.000927327i
$683$	−0.689554	−	1.99234i	−0.0263850	−	0.0762346i	0.931039	−	0.364919i	$-0.118903\pi$
$683$	−0.689554	−	1.99234i	−0.0263850	−	0.0762346i	−0.957424	+	0.288684i	$0.906782\pi$
$684$	7.96504	−	0.760569i	0.304551	−	0.0290811i
$685$	−0.506585	−	0.148747i	−0.0193556	−	0.00568332i
$686$	−15.2037	+	10.5758i	−0.580479	+	0.403787i
$687$	2.22399	+	15.4682i	0.0848507	+	0.590150i
$688$	−0.00327550	+	0.0687613i	−0.000124877	+	0.00262150i
$689$	−3.12587	+	5.41417i	−0.119086	+	0.206264i
$690$	1.77891	−	2.47832i	0.0677221	−	0.0943482i
$691$	11.9677	+	20.7287i	0.455273	+	0.788556i	0.998704	−	0.0508982i	$-0.0162084\pi$
$691$	11.9677	+	20.7287i	0.455273	+	0.788556i	−0.543431	+	0.839454i	$0.682875\pi$
$692$	−17.6710	−	11.3565i	−0.671751	−	0.431708i
$693$	0.000498196		0.0177511i	1.89249e−5		0.000674310i
$694$	10.6792	+	23.3843i	0.405379	+	0.887656i
$695$	−0.864037	−	3.56161i	−0.0327748	−	0.135099i
$696$	3.33410	+	4.68209i	0.126379	+	0.177474i
$697$	0.229887	+	0.664216i	0.00870760	+	0.0251590i
$698$	−10.6345	+	4.25743i	−0.402524	+	0.161146i
$699$	23.2883	−	6.83807i	0.880845	−	0.258640i
$700$	5.26584	−	10.9587i	0.199030	−	0.414199i
$701$	0.100413	−	0.0645313i	0.00379254	−	0.00243731i	−0.538743	−	0.842470i	$-0.681101\pi$
$701$	0.100413	−	0.0645313i	0.00379254	−	0.00243731i	0.542536	+	0.840033i	$0.317464\pi$
$702$	−1.10879	−	0.571620i	−0.0418485	−	0.0215744i
$703$	55.1837	−	10.6358i	2.08129	−	0.401136i
$704$	−0.00158240	+	0.00652274i	−5.96389e−5	+	0.000245835i
$705$	−3.77864	+	1.51274i	−0.142312	+	0.0569730i
$706$	13.8333	−	15.9645i	0.520624	−	0.600832i
$707$	−3.19343	−	5.78957i	−0.120101	−	0.217739i
$708$	5.52358	+	1.62187i	0.207589	+	0.0609536i
$709$	−16.7914	+	23.5802i	−0.630615	+	0.885574i	−0.999028	−	0.0440878i	$-0.985962\pi$
$709$	−16.7914	+	23.5802i	−0.630615	+	0.885574i	0.368413	+	0.929662i	$0.379901\pi$
$710$	−5.86095	−	2.34637i	−0.219958	−	0.0880577i
$711$	2.22481	−	1.14697i	0.0834371	−	0.0430148i
$712$	1.01384	+	1.75602i	0.0379951	+	0.0658095i
$713$	24.9288	−	12.7331i	0.933592	−	0.476857i
$714$	−3.04037	+	4.09771i	−0.113783	+	0.153353i
$715$	0.00448058	+	0.00287949i	0.000167564	+	0.000107687i
$716$	8.74271	−	6.87535i	0.326731	−	0.256944i
$717$	2.97286	+	0.283874i	0.111023	+	0.0106015i
$718$	−17.6463	+	16.8258i	−0.658556	+	0.627932i
$719$	47.6115	−	4.54635i	1.77561	−	0.169550i	0.844806	−	0.535072i	$-0.179716\pi$
$719$	47.6115	−	4.54635i	1.77561	−	0.169550i	0.930803	+	0.365522i	$0.119109\pi$
$720$	−0.416563	+	0.480740i	−0.0155244	+	0.0179161i
$721$	−11.0131	+	3.00128i	−0.410150	+	0.111774i
$722$	43.1967	−	12.6837i	1.60762	−	0.472038i
$723$	−7.33403	+	21.1903i	−0.272756	+	0.788076i
$724$	0.491922	+	10.3267i	0.0182821	+	0.383790i
$725$	1.25681	+	26.3837i	0.0466768	+	0.979866i
$726$	−3.59773	+	10.3950i	−0.133524	+	0.385793i
$727$	38.4192	−	11.2809i	1.42489	−	0.418385i	0.523733	−	0.851882i	$-0.324539\pi$
$727$	38.4192	−	11.2809i	1.42489	−	0.418385i	0.901155	+	0.433497i	$0.142721\pi$
$728$	−0.840642	+	3.19162i	−0.0311563	+	0.118289i
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$	−7.52452	+	0.718504i	−0.278495	+	0.0265930i
$731$	0.0960827	−	0.0916146i	0.00355375	−	0.00338849i
$732$	4.62687	+	0.441812i	0.171014	+	0.0163299i
$733$	12.0029	−	9.43917i	0.443336	−	0.348644i	−0.371402	−	0.928472i	$-0.621123\pi$
$733$	12.0029	−	9.43917i	0.443336	−	0.348644i	0.814739	+	0.579829i	$0.196880\pi$
$734$	−4.63885	−	2.98121i	−0.171223	−	0.110038i
$735$	4.33604	+	1.01289i	0.159937	+	0.0373610i
$736$	−3.75858	−	2.97877i	−0.138543	−	0.109799i
$737$	0.0176299	+	0.0305358i	0.000649404	+	0.00112480i
$738$	0.323943	−	0.167004i	0.0119245	−	0.00614751i
$739$	32.5568	+	13.0338i	1.19762	+	0.479455i	0.882824	−	0.469705i	$-0.155640\pi$
$739$	32.5568	+	13.0338i	1.19762	+	0.479455i	0.314796	+	0.949159i	$0.398064\pi$
$740$	−2.59164	+	3.63945i	−0.0952705	+	0.133789i
$741$	−9.57697	−	2.81205i	−0.351819	−	0.103303i
$742$	6.85281	−	11.3512i	0.251574	−	0.416717i
$743$	−14.3724	+	16.5866i	−0.527271	+	0.608504i	−0.955436	−	0.295197i	$-0.904615\pi$
$743$	−14.3724	+	16.5866i	−0.527271	+	0.608504i	0.428165	+	0.903701i	$0.359160\pi$
$744$	−5.41872	+	2.16933i	−0.198660	+	0.0795315i
$745$	−0.689486	+	2.84210i	−0.0252608	+	0.104127i
$746$	4.96706	−	0.957322i	0.181857	−	0.0350501i
$747$	7.24676	+	3.73597i	0.265145	+	0.136692i
$748$	0.0108894	−	0.00699821i	0.000398157	−	0.000255880i
$749$	−6.57904	+	13.6916i	−0.240393	+	0.500279i
$750$	−5.85646	+	1.71961i	−0.213848	+	0.0627914i
$751$	19.7645	−	7.91251i	0.721217	−	0.288732i	0.0181300	−	0.999836i	$-0.494229\pi$
$751$	19.7645	−	7.91251i	0.721217	−	0.288732i	0.703087	+	0.711104i	$0.251804\pi$
$752$	2.09277	+	6.04665i	0.0763154	+	0.220499i
$753$	16.8641	+	23.6824i	0.614564	+	0.863034i
$754$	−1.69045	−	6.96814i	−0.0615627	−	0.253765i
$755$	4.97556	+	10.8950i	0.181079	+	0.396508i
$756$	2.32750	+	1.25807i	0.0846503	+	0.0457557i
$757$	25.5500	+	16.4200i	0.928632	+	0.596796i	0.915150	−	0.403114i	$-0.132072\pi$
$757$	25.5500	+	16.4200i	0.928632	+	0.596796i	0.0134821	+	0.999909i	$0.495708\pi$
$758$	2.72127	+	4.71337i	0.0988408	+	0.171197i
$759$	0.0232127	+	0.0223008i	0.000842566	+	0.000809467i
$760$	−2.54484	+	4.40780i	−0.0923112	+	0.159888i
$761$	2.03948	−	42.8139i	0.0739310	−	1.55200i	−0.591969	−	0.805961i	$-0.701649\pi$
$761$	2.03948	−	42.8139i	0.0739310	−	1.55200i	0.665900	−	0.746041i	$-0.268048\pi$
$762$	−1.59404	−	11.0868i	−0.0577459	−	0.401631i
$763$	8.58046	+	1.82833i	0.310633	+	0.0661901i
$764$	−22.6373	−	6.64691i	−0.818988	−	0.240477i
$765$	1.22121	−	0.116612i	0.0441530	−	0.00421610i
$766$	−3.62903	−	10.4854i	−0.131122	−	0.378853i
$767$	−5.64492	−	4.43921i	−0.203826	−	0.160291i
$768$	0.723734	+	0.690079i	0.0261155	+	0.0249011i
$769$	−7.91656	−	9.13620i	−0.285478	−	0.329460i	0.594839	−	0.803845i	$-0.297216\pi$
$769$	−7.91656	−	9.13620i	−0.285478	−	0.329460i	−0.880317	+	0.474385i	$0.842670\pi$
$770$	−0.00938175	−	0.00629166i	−0.000338095	−	0.000226736i
$771$	−19.5181	+	12.5435i	−0.702927	+	0.451744i
$772$	3.45695	−	9.98822i	0.124419	−	0.359484i
$773$	2.66545	−	10.9871i	0.0958697	−	0.395180i	−0.903578	−	0.428425i	$-0.859069\pi$
$773$	2.66545	−	10.9871i	0.0958697	−	0.395180i	0.999447	+	0.0332443i	$0.0105839\pi$
$774$	−0.0541113	−	0.0425536i	−0.00194499	−	0.00152956i
$775$	−26.3376	−	5.07616i	−0.946076	−	0.182341i
$776$	−3.80174	+	8.32465i	−0.136475	+	0.298838i
$777$	17.1138	+	7.24247i	0.613954	+	0.259822i
$778$	−3.06354	−	6.70822i	−0.109833	−	0.240501i
$779$	2.29223	−	1.80263i	0.0821276	−	0.0645859i
$780$	0.705311	−	0.363613i	0.0252542	−	0.0130194i
$781$	0.0333069	−	0.0576892i	0.00119181	−	0.00206428i
$782$	1.28177	+	9.15974i	0.0458361	+	0.327551i
$783$	−5.74788			−0.205413
$784$	1.91486	−	6.73300i	0.0683877	−	0.240464i
$785$	0.371211	+	2.58183i	0.0132491	+	0.0921495i
$786$	−7.86561	+	11.0457i	−0.280557	+	0.393987i
$787$	−32.9281	+	31.3968i	−1.17376	+	1.11918i	−0.183060	+	0.983102i	$0.558600\pi$
$787$	−32.9281	+	31.3968i	−1.17376	+	1.11918i	−0.990699	+	0.136075i	$0.956551\pi$
$788$	−1.19163	−	1.67341i	−0.0424500	−	0.0596126i
$789$	−14.0549	−	2.70886i	−0.500367	−	0.0964379i
$790$	−0.226597	+	1.57602i	−0.00806197	+	0.0560722i
$791$	−12.5449	+	2.16451i	−0.446047	+	0.0769610i
$792$	−0.00439538	−	0.00507254i	−0.000156183	−	0.000180245i
$793$	−5.15355	−	2.65684i	−0.183008	−	0.0943472i
$794$	−0.619763	−	13.0104i	−0.0219946	−	0.461722i
$795$	−3.13030	+	0.603317i	−0.111020	+	0.0213974i
$796$	5.13558	+	4.89677i	0.182026	+	0.173561i
$797$	−6.54807	+	45.5428i	−0.231945	+	1.61321i	0.457730	+	0.889091i	$0.348663\pi$
$797$	−6.54807	+	45.5428i	−0.231945	+	1.61321i	−0.689675	+	0.724119i	$0.742247\pi$
$798$	20.1914	+	6.35987i	0.714770	+	0.225137i
$799$	5.12620	−	11.2248i	0.181352	−	0.397105i
$800$	1.08340	+	4.46583i	0.0383039	+	0.157891i
$801$	−2.01849	−	0.192743i	−0.0713199	−	0.00681022i
$802$	−5.13953	−	2.05756i	−0.181483	−	0.0726548i
$803$	0.00379496	−	0.0796660i	0.000133921	−	0.00281135i
$804$	5.25329			0.185269
$805$	6.88989	−	4.20425i	0.242837	−	0.148180i
$806$	7.28122			0.256470
$807$	0.886362	−	18.6070i	0.0312014	−	0.654998i
$808$	2.32005	+	0.928807i	0.0816190	+	0.0326753i
$809$	0.974661	+	0.0930688i	0.0342672	+	0.00327212i	0.112176	−	0.993688i	$-0.464218\pi$
$809$	0.974661	+	0.0930688i	0.0342672	+	0.00327212i	−0.0779083	+	0.996961i	$0.524824\pi$
$810$	−0.149969	−	0.618179i	−0.00526936	−	0.0217206i
$811$	−4.13949	+	9.06421i	−0.145357	+	0.318287i	−0.968281	−	0.249864i	$-0.919614\pi$
$811$	−4.13949	+	9.06421i	−0.145357	+	0.318287i	0.822924	+	0.568152i	$0.192341\pi$
$812$	3.29583	+	14.8460i	0.115661	+	0.520994i
$813$	2.22395	−	15.4679i	0.0779972	−	0.542483i
$814$	−0.0341192	−	0.0325326i	−0.00119588	−	0.00114027i
$815$	13.3373	−	2.57056i	0.467186	−	0.0900428i
$816$	−0.0917639	−	1.92636i	−0.00321238	−	0.0674362i
$817$	−0.489572	−	0.252392i	−0.0171280	−	0.00883007i
$818$	−8.42096	−	9.71831i	−0.294432	−	0.339793i
$819$	−2.11220	−	2.53609i	−0.0738061	−	0.0886181i
$820$	−0.0329936	+	0.229475i	−0.00115219	+	0.00801362i
$821$	−6.90416	−	1.33067i	−0.240957	−	0.0464406i	0.0673429	−	0.997730i	$-0.478548\pi$
$821$	−6.90416	−	1.33067i	−0.240957	−	0.0464406i	−0.308300	+	0.951289i	$0.599760\pi$
$822$	−0.481447	−	0.676098i	−0.0167924	−	0.0235816i
$823$	22.4579	−	21.4135i	0.782832	−	0.746429i	−0.189032	−	0.981971i	$-0.560535\pi$
$823$	22.4579	−	21.4135i	0.782832	−	0.746429i	0.971864	+	0.235542i	$0.0756865\pi$
$824$	2.50258	−	3.51439i	0.0871816	−	0.122429i
$825$	−0.00438953	−	0.0305299i	−0.000152824	−	0.00106291i
$826$	11.7861	+	9.64731i	0.410091	+	0.335673i
$827$	−44.9675			−1.56367			−0.781836	−	0.623484i	$-0.785717\pi$
$827$	−44.9675			−1.56367			−0.781836	+	0.623484i	$0.785717\pi$
$828$	4.60662	−	1.33380i	0.160091	−	0.0463527i
$829$	3.79816	−	6.57860i	0.131915	−	0.228484i	−0.792499	−	0.609873i	$-0.791221\pi$
$829$	3.79816	−	6.57860i	0.131915	−	0.228484i	0.924415	+	0.381388i	$0.124554\pi$
$830$	−4.60974	+	2.37648i	−0.160006	+	0.0824890i
$831$	15.1311	−	11.8993i	0.524894	−	0.412781i
$832$	−0.518214	−	1.13473i	−0.0179658	−	0.0393397i
$833$	−11.6333	+	6.84924i	−0.403069	+	0.237312i
$834$	2.39339	−	5.24080i	0.0828764	−	0.181474i
$835$	−9.72151	−	1.87367i	−0.336427	−	0.0648409i
$836$	−0.0422142	−	0.0331976i	−0.00146001	−	0.00114816i
$837$	1.37608	−	5.67230i	0.0475644	−	0.196063i
$838$	10.7453	−	31.0466i	0.371191	−	1.07249i
$839$	15.3232	−	9.84760i	0.529014	−	0.339977i	−0.248714	−	0.968577i	$-0.580008\pi$
$839$	15.3232	−	9.84760i	0.529014	−	0.339977i	0.777729	+	0.628600i	$0.216372\pi$
$840$	−1.51068	+	0.741812i	−0.0521235	+	0.0255950i
$841$	−2.64444	−	3.05184i	−0.0911874	−	0.105236i
$842$	−10.1643	−	9.69165i	−0.350285	−	0.333996i
$843$	11.4136	+	8.97577i	0.393106	+	0.309142i
$844$	−9.23488	−	26.6824i	−0.317878	−	0.918447i
$845$	7.24658	−	0.691964i	0.249290	−	0.0238043i
$846$	−6.13938	−	1.80269i	−0.211076	−	0.0619776i
$847$	−19.4847	+	21.6181i	−0.669501	+	0.742806i
$848$	0.713222	+	4.96057i	0.0244921	+	0.170347i
$849$	−0.309765	+	6.50277i	−0.0106311	+	0.223174i
$850$	4.43119	−	7.67504i	0.151988	−	0.263252i
$851$	31.3189	−	12.4015i	1.07360	−	0.425119i
$852$	−4.96233	−	8.59501i	−0.170007	−	0.294460i
$853$	3.76986	+	2.42274i	0.129078	+	0.0829532i	0.603586	−	0.797298i	$-0.293738\pi$
$853$	3.76986	+	2.42274i	0.129078	+	0.0829532i	−0.474509	+	0.880251i	$0.657374\pi$
$854$	10.8180	+	5.84742i	0.370185	+	0.200095i
$855$	−2.11433	−	4.62974i	−0.0723087	−	0.158334i
$856$	−1.35358	−	5.57952i	−0.0462643	−	0.190704i
$857$	19.6049	+	27.5312i	0.669689	+	0.940447i	0.999994	−	0.00342766i	$-0.00109106\pi$
$857$	19.6049	+	27.5312i	0.669689	+	0.940447i	−0.330305	+	0.943874i	$0.607152\pi$
$858$	0.00273850	+	0.00791238i	9.34909e−5	+	0.000270124i
$859$	19.8418	−	7.94346i	0.676993	−	0.271027i	−0.00757990	−	0.999971i	$-0.502413\pi$
$859$	19.8418	−	7.94346i	0.676993	−	0.271027i	0.684573	+	0.728944i	$0.259989\pi$
$860$	0.0420155	−	0.0123369i	0.00143272	−	0.000420684i
$861$	0.961505	−	0.0728848i	0.0327680	−	0.00248391i
$862$	0.637673	−	0.409807i	0.0217192	−	0.0139581i
$863$	33.6027	+	17.3234i	1.14385	+	0.589696i	0.922691	−	0.385541i	$-0.125985\pi$
$863$	33.6027	+	17.3234i	1.14385	+	0.589696i	0.221160	+	0.975237i	$0.429016\pi$
$864$	−0.981929	+	0.189251i	−0.0334059	+	0.00643846i
$865$	−3.15018	+	12.9852i	−0.107109	+	0.441510i
$866$	37.4463	−	14.9912i	1.27248	−	0.509423i
$867$	8.69701	−	10.0369i	0.295366	−	0.340871i
$868$	−15.4398	−	0.301758i	−0.524063	−	0.0102424i
$869$	−0.0161199	−	0.00473323i	−0.000546830	−	0.000160564i
$870$	2.12085	−	2.97832i	0.0719037	−	0.100975i
$871$	−6.08385	−	2.43561i	−0.206143	−	0.0825273i
$872$	−2.94730	+	1.51944i	−0.0998082	+	0.0514547i
$873$	−4.57584	−	7.92558i	−0.154869	−	0.268240i
$874$	34.1731	−	17.4548i	1.15592	−	0.590418i
$875$	−16.0427	−	1.84888i	−0.542342	−	0.0625037i
$876$	−9.99642	−	6.42431i	−0.337748	−	0.217057i
$877$	13.0118	−	10.2326i	0.439377	−	0.345530i	−0.373837	−	0.927494i	$-0.621958\pi$
$877$	13.0118	−	10.2326i	0.439377	−	0.345530i	0.813214	+	0.581964i	$0.197716\pi$
$878$	−35.1924	−	3.36047i	−1.18769	−	0.113410i
$879$	−17.0017	+	16.2111i	−0.573453	+	0.546786i
$880$	0.00425020		0.000405845i	0.000143274		1.36810e-5i
$881$	−23.8554	+	27.5306i	−0.803709	+	0.927530i	−0.998579	−	0.0532994i	$-0.983026\pi$
$881$	−23.8554	+	27.5306i	−0.803709	+	0.927530i	0.194869	+	0.980829i	$0.437572\pi$
$882$	4.37382	+	5.46532i	0.147274	+	0.184027i
$883$	−18.8160	+	5.52488i	−0.633209	+	0.185927i	−0.582557	−	0.812790i	$-0.697948\pi$
$883$	−18.8160	+	5.52488i	−0.633209	+	0.185927i	−0.0506513	+	0.998716i	$0.516130\pi$
$884$	−0.786856	+	2.27347i	−0.0264648	+	0.0764651i
$885$	−0.174242	−	3.65779i	−0.00585708	−	0.122955i
$886$	0.137875	+	2.89436i	0.00463201	+	0.0972380i
$887$	2.77531	−	8.01872i	0.0931857	−	0.269242i	−0.888770	−	0.458353i	$-0.848439\pi$
$887$	2.77531	−	8.01872i	0.0931857	−	0.269242i	0.981956	+	0.189111i	$0.0605606\pi$
$888$	−6.73928	+	1.97883i	−0.226155	+	0.0664052i
$889$	7.54801	−	28.6571i	0.253152	−	0.961129i
$890$	0.844654	−	0.974783i	0.0283129	−	0.0326748i
$891$	0.00668155		0.000638010i	0.000223840		2.13741e-5i
$892$	4.32950	−	4.12817i	0.144963	−	0.138222i
$893$	−50.9649	−	4.86656i	−1.70547	−	0.162853i
$894$	−3.61391	+	2.84201i	−0.120867	+	0.0950510i
$895$	−5.95187	−	3.82503i	−0.198949	−	0.127857i
$896$	1.05185	+	2.42768i	0.0351398	+	0.0811030i
$897$	−5.95334	−	0.591113i	−0.198776	−	0.0197367i
$898$	7.35542	+	12.7400i	0.245454	+	0.425138i
$899$	29.8199	−	15.3732i	0.994549	−	0.512726i
$900$	−4.26619	−	1.70792i	−0.142206	−	0.0569308i
$901$	5.60628	−	7.87292i	0.186772	−	0.262285i
$902$	−0.00234713		0.000689179i	−7.81508e−5		2.29471e-5i
$903$	−0.0879662	−	0.159480i	−0.00292733	−	0.00530716i
$904$	3.15093	−	3.63637i	0.104798	−	0.120944i
$905$	6.10530	−	2.44419i	0.202947	−	0.0812477i
$906$	−4.43911	+	18.2983i	−0.147480	+	0.607919i
$907$	−26.9266	+	5.18967i	−0.894083	+	0.172320i	−0.615542	−	0.788104i	$-0.711063\pi$
$907$	−26.9266	+	5.18967i	−0.894083	+	0.172320i	−0.278541	+	0.960424i	$0.589851\pi$
$908$	12.6669	+	6.53023i	0.420365	+	0.216713i
$909$	−2.10234	+	1.35109i	−0.0697303	+	0.0448130i
$910$	2.09346	−	0.158690i	0.0693974	−	0.00526052i
$911$	6.54714	−	1.92241i	0.216917	−	0.0636924i	−0.171469	−	0.985190i	$-0.554851\pi$
$911$	6.54714	−	1.92241i	0.216917	−	0.0636924i	0.388385	+	0.921497i	$0.373033\pi$
$912$	−7.42812	+	2.97377i	−0.245970	+	0.0984714i
$913$	−0.0178982	−	0.0517134i	−0.000592343	−	0.00171146i
$914$	23.1924	+	32.5692i	0.767137	+	1.07729i
$915$	−0.697041	−	2.87324i	−0.0230435	−	0.0949865i
$916$	−6.49181	−	14.2151i	−0.214495	−	0.469680i
$917$	−30.5545	+	18.8029i	−1.00900	+	0.620926i
$918$	1.62240	+	1.04265i	0.0535471	+	0.0344126i
$919$	3.74113	+	6.47983i	0.123409	+	0.213750i	0.921110	−	0.389303i	$-0.127284\pi$
$919$	3.74113	+	6.47983i	0.123409	+	0.213750i	−0.797701	+	0.603053i	$0.793951\pi$
$920$	−1.00863	+	2.87911i	−0.0332536	+	0.0949215i
$921$	6.85234	−	11.8686i	0.225792	−	0.391083i
$922$	0.464937	−	9.76023i	0.0153119	−	0.321436i
$923$	1.76195	+	12.2546i	0.0579952	+	0.403366i
$924$	−0.00547909	−	0.0168917i	−0.000180249	−	0.000555697i
$925$	−30.9694	−	9.09345i	−1.01827	−	0.298991i
$926$	−17.9093	+	1.71013i	−0.588537	+	0.0561985i
$927$	1.41109	+	4.07709i	0.0463464	+	0.133909i
$928$	−4.51814	−	3.55311i	−0.148315	−	0.116636i
$929$	34.8491	+	33.2285i	1.14336	+	1.09019i	0.994858	+	0.101282i	$0.0322943\pi$
$929$	34.8491	+	33.2285i	1.14336	+	1.09019i	0.148504	+	0.988912i	$0.452554\pi$
$930$	2.43141	+	2.80600i	0.0797290	+	0.0920122i
$931$	42.6395	+	36.3162i	1.39745	+	1.19022i
$932$	−20.4185	+	13.1222i	−0.668830	+	0.429831i
$933$	−4.63753	+	13.3993i	−0.151826	+	0.438672i
$934$	2.39348	−	9.86604i	0.0783169	−	0.322827i
$935$	−0.00647235	−	0.00508991i	−0.000211668	−	0.000166458i
$936$	1.22492	+	0.236084i	0.0400377	+	0.00771663i
$937$	−17.5262	+	38.3770i	−0.572556	+	1.25372i	0.372870	+	0.927884i	$0.378374\pi$
$937$	−17.5262	+	38.3770i	−0.572556	+	1.25372i	−0.945425	+	0.325839i	$0.894353\pi$
$938$	12.7999	+	5.41684i	0.417931	+	0.176866i
$939$	−2.98098	−	6.52743i	−0.0972805	−	0.213015i
$940$	3.19939	−	2.51603i	0.104353	−	0.0820637i
$941$	39.0221	−	20.1173i	1.27208	−	0.655805i	0.315962	−	0.948772i	$-0.397673\pi$
$941$	39.0221	−	20.1173i	1.27208	−	0.655805i	0.956123	+	0.292967i	$0.0946425\pi$
$942$	−2.05026	+	3.55116i	−0.0668011	+	0.115703i
$943$	1.14958	−	1.31664i	0.0374356	−	0.0428756i
$944$	−5.75677			−0.187367
$945$	0.272020	−	1.66086i	0.00884881	−	0.0540278i
$946$	6.57558e−5	0	0.000457342i	2.13791e−6	0	1.48695e-5i
$947$	22.4285	−	31.4964i	0.728828	−	1.02350i	−0.269343	−	0.963044i	$-0.586807\pi$
$947$	22.4285	−	31.4964i	0.728828	−	1.02350i	0.998171	−	0.0604515i	$-0.0192541\pi$
$948$	−1.81156	+	1.72731i	−0.0588366	+	0.0561006i
$949$	8.59835	+	12.0747i	0.279114	+	0.391961i
$950$	−36.1043	−	6.95853i	−1.17138	−	0.225765i
$951$	3.68835	−	25.6530i	0.119603	−	0.831857i
$952$	1.76275	−	4.78829i	0.0571311	−	0.155189i
$953$	24.4928	+	28.2662i	0.793400	+	0.915633i	0.998000	−	0.0632130i	$-0.0201347\pi$
$953$	24.4928	+	28.2662i	0.793400	+	0.915633i	−0.204600	+	0.978846i	$0.565589\pi$
$954$	−4.45447	−	2.29644i	−0.144219	−	0.0743499i
$955$	0.714096	+	14.9907i	0.0231076	+	0.485088i
$956$	−2.93241	+	0.565177i	−0.0948411	+	0.0182791i
$957$	0.0279213	+	0.0266229i	0.000902566	+	0.000860595i
$958$	4.15657	−	28.9096i	0.134293	−	0.934026i
$959$	−0.475921	−	2.14378i	−0.0153683	−	0.0692264i
$960$	0.264250	−	0.578626i	0.00852862	−	0.0186751i
$961$	0.723441	+	2.98206i	0.0233368	+	0.0961956i
$962$	8.72223	+	0.832872i	0.281216	+	0.0268529i
$963$	5.33010	+	2.13385i	0.171760	+	0.0687623i
$964$	1.06696	−	22.3982i	0.0343644	−	0.721397i
$965$	−6.72338			−0.216433
$966$	12.5996	+	1.50018i	0.405385	+	0.0482677i
$967$	−12.2774			−0.394813			−0.197407	−	0.980322i	$-0.563252\pi$
$967$	−12.2774			−0.394813			−0.197407	+	0.980322i	$0.563252\pi$
$968$	0.523399	−	10.9875i	0.0168227	−	0.353151i
$969$	14.3255	+	5.73506i	0.460201	+	0.184237i
$970$	5.79511	+	0.553366i	0.186070	+	0.0177675i
$971$	4.05381	+	16.7100i	0.130093	+	0.536250i	0.999138	+	0.0415170i	$0.0132191\pi$
$971$	4.05381	+	16.7100i	0.130093	+	0.536250i	−0.869045	+	0.494733i	$0.835266\pi$
$972$	0.415415	−	0.909632i	0.0133244	−	0.0291765i
$973$	11.2356	−	10.3015i	0.360196	−	0.330252i
$974$	5.03574	−	35.0244i	0.161356	−	1.12225i
$975$	4.14883	+	3.95590i	0.132869	+	0.126690i
$976$	−4.56392	+	0.879624i	−0.146088	+	0.0281561i
$977$	0.854269	+	17.9333i	0.0273305	+	0.573738i	0.970453	+	0.241291i	$0.0775710\pi$
$977$	0.854269	+	17.9333i	0.0273305	+	0.573738i	−0.943122	+	0.332446i	$0.892126\pi$
$978$	18.9792	+	9.78447i	0.606888	+	0.312873i
$979$	0.00891240	+	0.0102855i	0.000284842	+	0.000328725i
$980$	−4.44576	+	0.249743i	−0.142015	+	0.00797773i
$981$	0.471904	−	3.28216i	0.0150667	−	0.104791i
$982$	3.50126	+	0.674812i	0.111730	+	0.0215341i
$983$	−19.1731	−	26.9249i	−0.611528	−	0.858771i	0.386451	−	0.922310i	$-0.373701\pi$
$983$	−19.1731	−	26.9249i	−0.611528	−	0.858771i	−0.997979	+	0.0635385i	$0.979761\pi$
$984$	−0.263770	+	0.251504i	−0.00840869	+	0.00801767i
$985$	−0.758006	+	1.06447i	−0.0241521	+	0.0339168i
$986$	1.57757	+	10.9722i	0.0502400	+	0.349427i
$987$	−13.1001	−	10.7229i	−0.416980	−	0.341312i
$988$	9.98128			0.317547
$989$	−0.316416	−	0.0942041i	−0.0100614	−	0.00299552i
$990$	−0.00213476	+	0.00369752i	−6.78473e−5	+	0.000117515i
$991$	26.3044	−	13.5609i	0.835588	−	0.430776i	0.0133444	−	0.999911i	$-0.495752\pi$
$991$	26.3044	−	13.5609i	0.835588	−	0.430776i	0.822244	+	0.569135i	$0.192722\pi$
$992$	4.58806	−	3.60809i	0.145671	−	0.114557i
$993$	−1.71174	−	3.74818i	−0.0543203	−	0.118945i
$994$	−3.22834	−	26.0590i	−0.102397	−	0.826541i
$995$	1.87510	−	4.10590i	0.0594448	−	0.130166i
$996$	−8.00576	−	1.54298i	−0.253672	−	0.0488913i
$997$	16.7012	+	13.1340i	0.528932	+	0.415956i	0.846587	−	0.532250i	$-0.178653\pi$
$997$	16.7012	+	13.1340i	0.528932	+	0.415956i	−0.317656	+	0.948206i	$0.602896\pi$
$998$	−0.335061	+	1.38114i	−0.0106062	+	0.0437192i
$999$	2.29726	−	6.63749i	0.0726820	−	0.210001i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.b.25.5	✓	160
7.2	even	3	inner	966.2.y.b.163.5	yes	160
23.12	even	11	inner	966.2.y.b.403.5	yes	160
161.58	even	33	inner	966.2.y.b.541.5	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.b.25.5	✓	160	1.1	even	1	trivial
966.2.y.b.163.5	yes	160	7.2	even	3	inner
966.2.y.b.403.5	yes	160	23.12	even	11	inner
966.2.y.b.541.5	yes	160	161.58	even	33	inner

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0475819 + 0.998867i) q^{2} +(0.928368 + 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(0.149969 + 0.618179i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(-1.95013 + 1.78801i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +O(q^{10})\)	\(q+(-0.0475819 + 0.998867i) q^{2} +(0.928368 + 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(0.149969 + 0.618179i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(-1.95013 + 1.78801i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +(-0.624615 + 0.120385i) q^{10} +(-0.000319367 - 0.00670434i) q^{11} +(-0.888835 - 0.458227i) q^{12} +(0.816913 + 0.942768i) q^{13} +(-1.69320 - 2.03300i) q^{14} +(-0.0905279 + 0.629635i) q^{15} +(0.981929 + 0.189251i) q^{16} +(-1.11867 - 1.57095i) q^{17} +(-0.723734 + 0.690079i) q^{18} +(-4.64119 + 6.51764i) q^{19} +(-0.0905279 - 0.629635i) q^{20} +(-2.47498 + 0.935143i) q^{21} +0.00671194 q^{22} +(-2.00868 + 4.35491i) q^{23} +(0.500000 - 0.866025i) q^{24} +(4.08452 - 2.10572i) q^{25} +(-0.980571 + 0.771129i) q^{26} +(0.415415 + 0.909632i) q^{27} +(2.11126 - 1.59454i) q^{28} +(-2.38776 + 5.22846i) q^{29} +(-0.624615 - 0.120385i) q^{30} +(-4.58806 - 3.60809i) q^{31} +(-0.235759 + 0.971812i) q^{32} +(0.00219526 - 0.00634279i) q^{33} +(1.62240 - 1.04265i) q^{34} +(-1.39777 - 0.937384i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(-5.08336 - 4.84697i) q^{37} +(-6.28942 - 4.94606i) q^{38} +(0.408005 + 1.17885i) q^{39} +(0.633229 - 0.0604661i) q^{40} +(-0.349694 - 0.102680i) q^{41} +(-0.816320 - 2.51667i) q^{42} +(0.00979684 + 0.0681385i) q^{43} +(-0.000319367 + 0.00670434i) q^{44} +(-0.318055 + 0.550887i) q^{45} +(-4.25440 - 2.21362i) q^{46} +(3.19928 + 5.54132i) q^{47} +(0.841254 + 0.540641i) q^{48} +(0.606023 - 6.97372i) q^{49} +(1.90898 + 4.18009i) q^{50} +(-0.454672 - 1.87418i) q^{51} +(-0.723599 - 1.01615i) q^{52} +(1.63913 + 4.73594i) q^{53} +(-0.928368 + 0.371662i) q^{54} +(0.00409658 - 0.00120287i) q^{55} +(1.49228 + 2.18474i) q^{56} +(-6.73110 + 4.32581i) q^{57} +(-5.10892 - 2.63383i) q^{58} +(-5.65274 + 1.08948i) q^{59} +(0.149969 - 0.618179i) q^{60} +(-4.31497 + 1.72746i) q^{61} +(3.82231 - 4.41118i) q^{62} +(-2.64525 - 0.0516991i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-0.460288 + 0.646384i) q^{65} +(0.00623115 + 0.00249458i) q^{66} +(-4.66931 + 2.40720i) q^{67} +(0.964273 + 1.67017i) q^{68} +(-3.48335 + 3.29640i) q^{69} +(1.00283 - 1.35158i) q^{70} +(8.34916 + 5.36568i) q^{71} +(0.786053 - 0.618159i) q^{72} +(11.8290 + 1.12953i) q^{73} +(5.08336 - 4.84697i) q^{74} +(4.57456 - 0.436817i) q^{75} +(5.23972 - 6.04696i) q^{76} +(0.0126102 + 0.0125033i) q^{77} +(-1.19693 + 0.351450i) q^{78} +(0.818673 - 2.36540i) q^{79} +(0.0302673 + 0.635389i) q^{80} +(0.0475819 + 0.998867i) q^{81} +(0.119202 - 0.344413i) q^{82} +(7.82284 - 2.29699i) q^{83} +(2.55266 - 0.695647i) q^{84} +(0.803362 - 0.927129i) q^{85} +(-0.0685275 + 0.00654358i) q^{86} +(-4.15994 + 3.96649i) q^{87} +(-0.00668155 - 0.000638010i) q^{88} +(-1.59386 + 1.25342i) q^{89} +(-0.535130 - 0.343907i) q^{90} +(-3.27877 - 0.377870i) q^{91} +(2.41354 - 4.14425i) q^{92} +(-2.91841 - 5.05484i) q^{93} +(-5.68728 + 2.93199i) q^{94} +(-4.72510 - 1.89165i) q^{95} +(-0.580057 + 0.814576i) q^{96} +(-8.78096 - 2.57832i) q^{97} +(6.93698 + 0.937159i) q^{98} +(0.00439538 - 0.00507254i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9	\( 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9} - 6 q^{10} + 8 q^{11} + 8 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} - 8 q^{19} + 10 q^{20} - 3 q^{21} - 28 q^{22} + 22 q^{23} + 80 q^{24} + 46 q^{25} + 2 q^{26} - 16 q^{27} - 14 q^{28} + 62 q^{29} - 6 q^{30} + 7 q^{31} - 8 q^{32} - 14 q^{33} - 4 q^{34} + 24 q^{35} - 16 q^{36} + 15 q^{37} + 19 q^{38} - 2 q^{39} + 5 q^{40} - 14 q^{41} + 10 q^{42} - 56 q^{43} + 8 q^{44} - 16 q^{45} + 66 q^{47} - 16 q^{48} + 42 q^{49} + 4 q^{50} + 9 q^{51} - 2 q^{52} + 12 q^{53} - 8 q^{54} - 14 q^{55} + 10 q^{56} - 6 q^{57} - 13 q^{58} + 62 q^{59} + 6 q^{60} + 16 q^{61} - 8 q^{62} + 2 q^{63} - 16 q^{64} + 70 q^{65} - 8 q^{66} - 14 q^{67} - 46 q^{68} + 22 q^{69} + 24 q^{70} - 108 q^{71} - 8 q^{72} + 40 q^{73} - 15 q^{74} + 2 q^{75} + 16 q^{76} + 29 q^{77} + 18 q^{78} + 22 q^{79} + 6 q^{80} + 8 q^{81} - 7 q^{82} - 18 q^{83} - 9 q^{84} + 26 q^{85} - 6 q^{86} + 2 q^{87} + 3 q^{88} + 112 q^{89} + 12 q^{90} + 18 q^{91} - 66 q^{92} - 26 q^{93} + 23 q^{95} - 8 q^{96} + 8 q^{97} + 9 q^{98} + 28 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9 - 6 * q^10 + 8 * q^11 + 8 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 - 8 * q^19 + 10 * q^20 - 3 * q^21 - 28 * q^22 + 22 * q^23 + 80 * q^24 + 46 * q^25 + 2 * q^26 - 16 * q^27 - 14 * q^28 + 62 * q^29 - 6 * q^30 + 7 * q^31 - 8 * q^32 - 14 * q^33 - 4 * q^34 + 24 * q^35 - 16 * q^36 + 15 * q^37 + 19 * q^38 - 2 * q^39 + 5 * q^40 - 14 * q^41 + 10 * q^42 - 56 * q^43 + 8 * q^44 - 16 * q^45 + 66 * q^47 - 16 * q^48 + 42 * q^49 + 4 * q^50 + 9 * q^51 - 2 * q^52 + 12 * q^53 - 8 * q^54 - 14 * q^55 + 10 * q^56 - 6 * q^57 - 13 * q^58 + 62 * q^59 + 6 * q^60 + 16 * q^61 - 8 * q^62 + 2 * q^63 - 16 * q^64 + 70 * q^65 - 8 * q^66 - 14 * q^67 - 46 * q^68 + 22 * q^69 + 24 * q^70 - 108 * q^71 - 8 * q^72 + 40 * q^73 - 15 * q^74 + 2 * q^75 + 16 * q^76 + 29 * q^77 + 18 * q^78 + 22 * q^79 + 6 * q^80 + 8 * q^81 - 7 * q^82 - 18 * q^83 - 9 * q^84 + 26 * q^85 - 6 * q^86 + 2 * q^87 + 3 * q^88 + 112 * q^89 + 12 * q^90 + 18 * q^91 - 66 * q^92 - 26 * q^93 + 23 * q^95 - 8 * q^96 + 8 * q^97 + 9 * q^98 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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