LMFDB - Embedded newform 966.2.be.a.493.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(19,966)]

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, 55, 45]))

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

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

chi := DirichletCharacter("966.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.be (of order $66$, 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:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			493.9
Character	$\chi$	$=$	966.493
Dual form			966.2.be.a.145.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.327068 - 0.945001i) q^{2} +(0.458227 + 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-3.89835 + 0.372248i) q^{5} +(0.989821 - 0.142315i) q^{6} +(-2.62952 + 0.292580i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +O(q^{10})$	\(q+(0.327068 - 0.945001i) q^{2} +(0.458227 + 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-3.89835 + 0.372248i) q^{5} +(0.989821 - 0.142315i) q^{6} +(-2.62952 + 0.292580i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +(-0.923252 + 3.80570i) q^{10} +(5.29509 - 1.83265i) q^{11} +(0.189251 - 0.981929i) q^{12} +(-0.0556129 - 0.189400i) q^{13} +(-0.583544 + 2.58060i) q^{14} +(-2.11720 - 3.29442i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-1.48839 - 0.595863i) q^{17} +(0.580057 + 0.814576i) q^{18} +(7.40232 - 2.96344i) q^{19} +(3.29442 + 2.11720i) q^{20} +(-1.46497 - 2.20315i) q^{21} -5.60326i q^{22} +(4.20511 + 2.30586i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(10.1490 - 1.95605i) q^{25} +(-0.197172 - 0.00939248i) q^{26} +(-0.989821 - 0.142315i) q^{27} +(2.24781 + 1.39548i) q^{28} +(0.983186 + 6.83821i) q^{29} +(-3.80570 + 0.923252i) q^{30} +(0.478230 - 0.0227809i) q^{31} +(0.995472 + 0.0950560i) q^{32} +(4.05527 + 3.86670i) q^{33} +(-1.04990 + 1.21165i) q^{34} +(10.1419 - 2.11942i) q^{35} +(0.959493 - 0.281733i) q^{36} +(6.70237 + 4.77274i) q^{37} +(-0.379393 - 7.96445i) q^{38} +(0.142862 - 0.136219i) q^{39} +(3.07825 - 2.42076i) q^{40} +(-9.27312 - 4.23489i) q^{41} +(-2.56112 + 0.663823i) q^{42} +(5.21872 - 8.12049i) q^{43} +(-5.29509 - 1.83265i) q^{44} +(1.95804 - 3.39143i) q^{45} +(3.55440 - 3.21966i) q^{46} +(1.70922 - 0.986817i) q^{47} +(-0.755750 + 0.654861i) q^{48} +(6.82879 - 1.53869i) q^{49} +(1.47093 - 10.2305i) q^{50} +(-0.152397 - 1.59598i) q^{51} +(-0.0733647 + 0.183256i) q^{52} +(-4.70873 - 4.93838i) q^{53} +(-0.458227 + 0.888835i) q^{54} +(-19.9599 + 9.11540i) q^{55} +(2.05392 - 1.66776i) q^{56} +(6.02595 + 5.22152i) q^{57} +(6.78368 + 1.30745i) q^{58} +(5.06460 + 1.22866i) q^{59} +(-0.372248 + 3.89835i) q^{60} +(2.86847 + 1.47880i) q^{61} +(0.134886 - 0.459379i) q^{62} +(1.28694 - 2.31166i) q^{63} +(0.415415 - 0.909632i) q^{64} +(0.287302 + 0.717647i) q^{65} +(4.98038 - 2.56756i) q^{66} +(1.68414 + 8.73813i) q^{67} +(0.801619 + 1.38844i) q^{68} +(-0.122639 + 4.79426i) q^{69} +(1.31424 - 10.2773i) q^{70} +(-3.03737 - 3.50531i) q^{71} +(0.0475819 - 0.998867i) q^{72} +(-6.72569 + 8.55241i) q^{73} +(6.70237 - 4.77274i) q^{74} +(6.38913 + 8.12444i) q^{75} +(-7.65050 - 2.24639i) q^{76} +(-13.3874 + 6.36823i) q^{77} +(-0.0820013 - 0.179558i) q^{78} +(7.19257 - 7.54335i) q^{79} +(-1.28083 - 3.70071i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(-7.03492 + 7.37801i) q^{82} +(-2.88678 - 6.32117i) q^{83} +(-0.210348 + 2.63738i) q^{84} +(6.02410 + 1.76883i) q^{85} +(-5.96700 - 7.58765i) q^{86} +(-5.62752 + 4.00734i) q^{87} +(-3.46371 + 4.40446i) q^{88} +(-0.217462 + 4.56509i) q^{89} +(-2.56449 - 2.95958i) q^{90} +(0.201650 + 0.481761i) q^{91} +(-1.88005 - 4.41196i) q^{92} +(0.239386 + 0.414629i) q^{93} +(-0.373513 - 1.93797i) q^{94} +(-27.7537 + 14.3080i) q^{95} +(0.371662 + 0.928368i) q^{96} +(1.99649 - 4.37171i) q^{97} +(0.779412 - 6.95647i) q^{98} +(-1.57862 + 5.37629i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9}+O(q^{10}) $ 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9	$ 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9} - 22 q^{14} + 16 q^{16} + 66 q^{17} + 16 q^{18} + 40 q^{23} - 48 q^{25} + 12 q^{26} + 44 q^{28} - 24 q^{29} + 24 q^{31} - 16 q^{32} + 98 q^{35} + 32 q^{36} - 22 q^{37} - 66 q^{38} - 8 q^{39} - 88 q^{43} + 4 q^{46} - 144 q^{47} - 24 q^{49} + 80 q^{50} - 22 q^{51} + 12 q^{52} + 44 q^{53} + 44 q^{57} + 10 q^{58} + 12 q^{59} - 32 q^{64} + 108 q^{70} - 16 q^{71} + 16 q^{72} - 180 q^{73} - 22 q^{74} - 12 q^{75} + 18 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 36 q^{82} + 22 q^{84} + 68 q^{85} - 22 q^{86} + 48 q^{87} + 22 q^{88} + 8 q^{92} + 8 q^{93} - 12 q^{94} + 66 q^{95} - 90 q^{98}+O(q^{100}) $ 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9 - 22 * q^14 + 16 * q^16 + 66 * q^17 + 16 * q^18 + 40 * q^23 - 48 * q^25 + 12 * q^26 + 44 * q^28 - 24 * q^29 + 24 * q^31 - 16 * q^32 + 98 * q^35 + 32 * q^36 - 22 * q^37 - 66 * q^38 - 8 * q^39 - 88 * q^43 + 4 * q^46 - 144 * q^47 - 24 * q^49 + 80 * q^50 - 22 * q^51 + 12 * q^52 + 44 * q^53 + 44 * q^57 + 10 * q^58 + 12 * q^59 - 32 * q^64 + 108 * q^70 - 16 * q^71 + 16 * q^72 - 180 * q^73 - 22 * q^74 - 12 * q^75 + 18 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 36 * q^82 + 22 * q^84 + 68 * q^85 - 22 * q^86 + 48 * q^87 + 22 * q^88 + 8 * q^92 + 8 * q^93 - 12 * q^94 + 66 * q^95 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{22}\right)$

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 $

$2$	0.327068	−	0.945001i	0.231272	−	0.668216i
$2$	0.327068	−	0.945001i	0.231272	−	0.668216i
$3$	0.458227	+	0.888835i	0.264557	+	0.513169i
$3$	0.458227	+	0.888835i	0.264557	+	0.513169i
$4$	−0.786053	−	0.618159i	−0.393027	−	0.309079i
$5$	−3.89835	+	0.372248i	−1.74340	+	0.166474i	−0.917603	−	0.397498i	$-0.869879\pi$
$5$	−3.89835	+	0.372248i	−1.74340	+	0.166474i	−0.825794	+	0.563972i	$0.809273\pi$
$6$	0.989821	−	0.142315i	0.404093	−	0.0580998i
$7$	−2.62952	+	0.292580i	−0.993867	+	0.110585i
$7$	−2.62952	+	0.292580i	−0.993867	+	0.110585i
$8$	−0.841254	+	0.540641i	−0.297428	+	0.191145i
$9$	−0.580057	+	0.814576i	−0.193352	+	0.271525i
$10$	−0.923252	+	3.80570i	−0.291958	+	1.20347i
$11$	5.29509	−	1.83265i	1.59653	−	0.552564i	0.623217	−	0.782049i	$-0.285825\pi$
$11$	5.29509	−	1.83265i	1.59653	−	0.552564i	0.973312	+	0.229484i	$0.0737040\pi$
$12$	0.189251	−	0.981929i	0.0546321	−	0.283458i
$13$	−0.0556129	−	0.189400i	−0.0154242	−	0.0525301i	0.951421	−	0.307892i	$-0.0996236\pi$
$13$	−0.0556129	−	0.189400i	−0.0154242	−	0.0525301i	−0.966846	+	0.255362i	$0.917805\pi$
$14$	−0.583544	+	2.58060i	−0.155959	+	0.689693i
$15$	−2.11720	−	3.29442i	−0.546658	−	0.850616i
$16$	0.235759	+	0.971812i	0.0589397	+	0.242953i
$17$	−1.48839	−	0.595863i	−0.360989	−	0.144518i	0.184076	−	0.982912i	$-0.441071\pi$
$17$	−1.48839	−	0.595863i	−0.360989	−	0.144518i	−0.545065	+	0.838394i	$0.683495\pi$
$18$	0.580057	+	0.814576i	0.136721	+	0.191997i
$19$	7.40232	−	2.96344i	1.69821	−	0.679860i	0.698837	−	0.715281i	$-0.253701\pi$
$19$	7.40232	−	2.96344i	1.69821	−	0.679860i	0.999372	+	0.0354211i	$0.0112772\pi$
$20$	3.29442	+	2.11720i	0.736655	+	0.473419i
$21$	−1.46497	−	2.20315i	−0.319683	−	0.480766i
$22$		−	5.60326i		−	1.19462i
$23$	4.20511	+	2.30586i	0.876827	+	0.480806i
$23$	4.20511	+	2.30586i	0.876827	+	0.480806i
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	10.1490	−	1.95605i	2.02979	−	0.391210i
$26$	−0.197172	−	0.00939248i	−0.0386687	−	0.00184202i
$27$	−0.989821	−	0.142315i	−0.190491	−	0.0273885i
$28$	2.24781	+	1.39548i	0.424796	+	0.263721i
$29$	0.983186	+	6.83821i	0.182573	+	1.26982i	0.850650	+	0.525732i	$0.176208\pi$
$29$	0.983186	+	6.83821i	0.182573	+	1.26982i	−0.668077	+	0.744092i	$0.732883\pi$
$30$	−3.80570	+	0.923252i	−0.694822	+	0.168562i
$31$	0.478230	−	0.0227809i	0.0858926	−	0.00409157i	−0.00459160	−	0.999989i	$-0.501462\pi$
$31$	0.478230	−	0.0227809i	0.0858926	−	0.00409157i	0.0904842	+	0.995898i	$0.471159\pi$
$32$	0.995472	+	0.0950560i	0.175976	+	0.0168037i
$33$	4.05527	+	3.86670i	0.705932	+	0.673105i
$34$	−1.04990	+	1.21165i	−0.180056	+	0.207796i
$35$	10.1419	−	2.11942i	1.71429	−	0.358247i
$36$	0.959493	−	0.281733i	0.159915	−	0.0469554i
$37$	6.70237	+	4.77274i	1.10186	+	0.784633i	0.978195	−	0.207690i	$-0.0665946\pi$
$37$	6.70237	+	4.77274i	1.10186	+	0.784633i	0.123669	+	0.992324i	$0.460534\pi$
$38$	−0.379393	−	7.96445i	−0.0615457	−	1.29200i
$39$	0.142862	−	0.136219i	0.0228763	−	0.0218125i
$40$	3.07825	−	2.42076i	0.486714	−	0.382756i
$41$	−9.27312	−	4.23489i	−1.44822	−	0.661379i	−0.472685	−	0.881232i	$-0.656715\pi$
$41$	−9.27312	−	4.23489i	−1.44822	−	0.661379i	−0.975533	+	0.219853i	$0.929442\pi$
$42$	−2.56112	+	0.663823i	−0.395190	+	0.102430i
$43$	5.21872	−	8.12049i	0.795848	−	1.23836i	−0.171568	−	0.985172i	$-0.554883\pi$
$43$	5.21872	−	8.12049i	0.795848	−	1.23836i	0.967416	−	0.253191i	$-0.0814803\pi$
$44$	−5.29509	−	1.83265i	−0.798265	−	0.276282i
$45$	1.95804	−	3.39143i	0.291888	−	0.505565i
$46$	3.55440	−	3.21966i	0.524068	−	0.474713i
$47$	1.70922	−	0.986817i	0.249315	−	0.143942i	−0.370136	−	0.928978i	$-0.620689\pi$
$47$	1.70922	−	0.986817i	0.249315	−	0.143942i	0.619451	+	0.785036i	$0.287355\pi$
$48$	−0.755750	+	0.654861i	−0.109083	+	0.0945210i
$49$	6.82879	−	1.53869i	0.975542	−	0.219813i
$50$	1.47093	−	10.2305i	0.208021	−	1.44682i
$51$	−0.152397	−	1.59598i	−0.0213399	−	0.223482i
$52$	−0.0733647	+	0.183256i	−0.0101739	+	0.0254130i
$53$	−4.70873	−	4.93838i	−0.646794	−	0.678338i	0.315943	−	0.948778i	$-0.397679\pi$
$53$	−4.70873	−	4.93838i	−0.646794	−	0.678338i	−0.962737	+	0.270440i	$0.912831\pi$
$54$	−0.458227	+	0.888835i	−0.0623567	+	0.120955i
$55$	−19.9599	+	9.11540i	−2.69140	+	1.22912i
$56$	2.05392	−	1.66776i	0.274466	−	0.222864i
$57$	6.02595	+	5.22152i	0.798157	+	0.691607i
$58$	6.78368	+	1.30745i	0.890741	+	0.171676i
$59$	5.06460	+	1.22866i	0.659355	+	0.159958i	0.551456	−	0.834204i	$-0.314073\pi$
$59$	5.06460	+	1.22866i	0.659355	+	0.159958i	0.107899	+	0.994162i	$0.465588\pi$
$60$	−0.372248	+	3.89835i	−0.0480570	+	0.503275i
$61$	2.86847	+	1.47880i	0.367270	+	0.189341i	0.631975	−	0.774988i	$-0.282244\pi$
$61$	2.86847	+	1.47880i	0.367270	+	0.189341i	−0.264705	+	0.964329i	$0.585275\pi$
$62$	0.134886	−	0.459379i	0.0171305	−	0.0583411i
$63$	1.28694	−	2.31166i	0.162140	−	0.291242i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	0.287302	+	0.717647i	0.0356355	+	0.0890131i
$66$	4.98038	−	2.56756i	0.613042	−	0.316045i
$67$	1.68414	+	8.73813i	0.205750	+	1.06753i	0.927058	+	0.374918i	$0.122329\pi$
$67$	1.68414	+	8.73813i	0.205750	+	1.06753i	−0.721308	+	0.692615i	$0.756459\pi$
$68$	0.801619	+	1.38844i	0.0972106	+	0.168374i
$69$	−0.122639	+	4.79426i	−0.0147640	+	0.577161i
$70$	1.31424	−	10.2773i	0.157082	−	1.22837i
$71$	−3.03737	−	3.50531i	−0.360469	−	0.416004i	0.546327	−	0.837572i	$-0.316025\pi$
$71$	−3.03737	−	3.50531i	−0.360469	−	0.416004i	−0.906797	+	0.421568i	$0.861480\pi$
$72$	0.0475819	−	0.998867i	0.00560758	−	0.117718i
$73$	−6.72569	+	8.55241i	−0.787182	+	1.00098i	0.212534	+	0.977154i	$0.431828\pi$
$73$	−6.72569	+	8.55241i	−0.787182	+	1.00098i	−0.999716	+	0.0238300i	$0.992414\pi$
$74$	6.70237	−	4.77274i	0.779135	−	0.554820i
$75$	6.38913	+	8.12444i	0.737753	+	0.938129i
$76$	−7.65050	−	2.24639i	−0.877572	−	0.257678i
$77$	−13.3874	+	6.36823i	−1.52563	+	0.725727i
$78$	−0.0820013	−	0.179558i	−0.00928481	−	0.0203309i
$79$	7.19257	−	7.54335i	0.809227	−	0.848693i	−0.181664	−	0.983361i	$-0.558148\pi$
$79$	7.19257	−	7.54335i	0.809227	−	0.848693i	0.990891	+	0.134668i	$0.0429967\pi$
$80$	−1.28083	−	3.70071i	−0.143201	−	0.413751i
$81$	−0.327068	−	0.945001i	−0.0363409	−	0.105000i
$82$	−7.03492	+	7.37801i	−0.776876	+	0.814765i
$83$	−2.88678	−	6.32117i	−0.316865	−	0.693838i	0.682446	−	0.730936i	$-0.260916\pi$
$83$	−2.88678	−	6.32117i	−0.316865	−	0.693838i	−0.999312	+	0.0370974i	$0.988189\pi$
$84$	−0.210348	+	2.63738i	−0.0229508	+	0.287761i
$85$	6.02410	+	1.76883i	0.653405	+	0.191857i
$86$	−5.96700	−	7.58765i	−0.643438	−	0.818198i
$87$	−5.62752	+	4.00734i	−0.603333	+	0.429632i
$88$	−3.46371	+	4.40446i	−0.369233	+	0.469517i
$89$	−0.217462	+	4.56509i	−0.0230509	+	0.483899i	0.957596	+	0.288114i	$0.0930283\pi$
$89$	−0.217462	+	4.56509i	−0.0230509	+	0.483899i	−0.980647	+	0.195784i	$0.937275\pi$
$90$	−2.56449	−	2.95958i	−0.270321	−	0.311967i
$91$	0.201650	+	0.481761i	0.0211387	+	0.0505023i
$92$	−1.88005	−	4.41196i	−0.196009	−	0.459979i
$93$	0.239386	+	0.414629i	0.0248232	+	0.0429950i
$94$	−0.373513	−	1.93797i	−0.0385249	−	0.199886i
$95$	−27.7537	+	14.3080i	−2.84747	+	1.46797i
$96$	0.371662	+	0.928368i	0.0379326	+	0.0947512i
$97$	1.99649	−	4.37171i	0.202713	−	0.443880i	−0.780785	−	0.624800i	$-0.785180\pi$
$97$	1.99649	−	4.37171i	0.202713	−	0.443880i	0.983498	+	0.180920i	$0.0579076\pi$
$98$	0.779412	−	6.95647i	0.0787325	−	0.702710i
$99$	−1.57862	+	5.37629i	−0.158657	+	0.540338i
$100$	−9.18677	−	4.73611i	−0.918677	−	0.473611i
$101$	0.961480	−	10.0691i	0.0956708	−	1.00191i	−0.812402	−	0.583098i	$-0.801840\pi$
$101$	0.961480	−	10.0691i	0.0956708	−	1.00191i	0.908073	−	0.418812i	$-0.137553\pi$
$102$	−1.55805	−	0.377978i	−0.154269	−	0.0374254i
$103$	15.1886	+	2.92736i	1.49657	+	0.288441i	0.870829	−	0.491586i	$-0.163583\pi$
$103$	15.1886	+	2.92736i	1.49657	+	0.288441i	0.625746	+	0.780027i	$0.284795\pi$
$104$	0.149182	+	0.129267i	0.0146285	+	0.0126757i
$105$	6.53110	+	8.04331i	0.637370	+	0.784947i
$106$	−6.20685	+	2.83457i	−0.602862	+	0.275318i
$107$	−7.56077	+	14.6659i	−0.730928	+	1.41780i	0.170715	+	0.985320i	$0.445392\pi$
$107$	−7.56077	+	14.6659i	−0.730928	+	1.41780i	−0.901643	+	0.432482i	$0.857638\pi$
$108$	0.690079	+	0.723734i	0.0664029	+	0.0696413i
$109$	0.621815	−	1.55322i	0.0595591	−	0.148771i	−0.895604	−	0.444853i	$-0.853256\pi$
$109$	0.621815	−	1.55322i	0.0595591	−	0.148771i	0.955163	+	0.296082i	$0.0956801\pi$
$110$	2.08580	+	21.8435i	0.198873	+	2.08270i
$111$	−1.17097	+	8.14430i	−0.111144	+	0.773023i
$112$	−0.904267	−	2.48642i	−0.0854452	−	0.234945i
$113$	1.87919	−	1.62833i	0.176780	−	0.153181i	−0.561977	−	0.827153i	$-0.689959\pi$
$113$	1.87919	−	1.62833i	0.176780	−	0.153181i	0.738756	+	0.673973i	$0.235413\pi$
$114$	6.90523	−	3.98674i	0.646734	−	0.373392i
$115$	−17.2514	−	7.42373i	−1.60870	−	0.692267i
$116$	3.45426	−	5.98296i	0.320720	−	0.555504i
$117$	0.186539	+	0.0645619i	0.0172456	+	0.00596875i
$118$	2.81755	−	4.38420i	0.259377	−	0.403598i
$119$	4.08811	+	1.13136i	0.374756	+	0.103712i
$120$	3.56220	+	1.62680i	0.325183	+	0.148506i
$121$	16.0328	−	12.6083i	1.45753	−	1.14621i
$122$	2.33565	−	2.22704i	0.211460	−	0.201627i
$123$	−0.485067	−	10.1828i	−0.0437370	−	0.918154i
$124$	−0.389996	−	0.277715i	−0.0350227	−	0.0249396i
$125$	−20.0488	+	5.88686i	−1.79322	+	0.526537i
$126$	−1.76360	−	1.97223i	−0.157114	−	0.175701i
$127$	−1.04700	+	1.20831i	−0.0929065	+	0.107220i	−0.800299	−	0.599601i	$-0.795326\pi$
$127$	−1.04700	+	1.20831i	−0.0929065	+	0.107220i	0.707393	+	0.706821i	$0.249871\pi$
$128$	−0.723734	−	0.690079i	−0.0639697	−	0.0609949i
$129$	9.60914	+	0.917562i	0.846038	+	0.0807868i
$130$	0.772144	−	0.0367818i	0.0677215	−	0.00322597i
$131$	7.50905	−	1.82168i	0.656069	−	0.159161i	0.106113	−	0.994354i	$-0.466160\pi$
$131$	7.50905	−	1.82168i	0.656069	−	0.159161i	0.549956	+	0.835194i	$0.314644\pi$
$132$	−0.797428	−	5.54623i	−0.0694072	−	0.482737i
$133$	−18.5975	+	9.95822i	−1.61261	+	0.863487i
$134$	8.80837	+	1.26645i	0.760927	+	0.109405i
$135$	3.91165	+	0.186335i	0.336661	+	0.0160372i
$136$	1.57427	−	0.303415i	0.134992	−	0.0260176i
$137$	14.0434	+	8.10798i	1.19981	+	0.692712i	0.960513	−	0.278234i	$-0.0897492\pi$
$137$	14.0434	+	8.10798i	1.19981	+	0.692712i	0.239298	+	0.970946i	$0.423083\pi$
$138$	4.49047	+	1.68394i	0.382254	+	0.143347i
$139$		−	7.29783i		−	0.618994i	−0.950900	−	0.309497i	$-0.899839\pi$
$139$		−	7.29783i		−	0.618994i	0.950900	−	0.309497i	$-0.100161\pi$
$140$	−9.28221	−	4.60334i	−0.784490	−	0.389053i
$141$	1.66033	+	1.06703i	0.139825	+	0.0898599i
$142$	−4.30595	+	1.72384i	−0.361347	+	0.144662i
$143$	−0.641579	−	0.900971i	−0.0536515	−	0.0753430i
$144$	−0.928368	−	0.371662i	−0.0773640	−	0.0309719i
$145$	−6.37831	−	26.2918i	−0.529690	−	2.18341i
$146$	5.88228	+	9.15300i	0.486821	+	0.757508i
$147$	4.49678	+	5.36460i	0.370888	+	0.442465i
$148$	−2.31811	−	7.89476i	−0.190547	−	0.648945i
$149$	0.0319821	−	0.165939i	0.00262007	−	0.0135942i	−0.980595	−	0.196044i	$-0.937191\pi$
$149$	0.0319821	−	0.165939i	0.00262007	−	0.0135942i	0.983215	+	0.182450i	$0.0584026\pi$
$150$	9.76728	−	3.38049i	0.797495	−	0.276016i
$151$	1.89464	−	7.80982i	0.154184	−	0.635554i	−0.841295	−	0.540576i	$-0.818207\pi$
$151$	1.89464	−	7.80982i	0.154184	−	0.635554i	0.995479	−	0.0949788i	$-0.0302783\pi$
$152$	−4.62507	+	6.49500i	−0.375143	+	0.526814i
$153$	1.34873	−	0.866776i	0.109038	−	0.0700747i
$154$	1.63941	+	14.7339i	0.132107	+	1.18729i
$155$	−1.85583	+	0.266828i	−0.149064	+	0.0214321i
$156$	−0.196502	+	0.0187637i	−0.0157328	+	0.00150230i
$157$	0.798180	+	0.627696i	0.0637017	+	0.0500956i	0.649502	−	0.760360i	$-0.274977\pi$
$157$	0.798180	+	0.627696i	0.0637017	+	0.0500956i	−0.585800	+	0.810455i	$0.699220\pi$
$158$	−4.77601	−	9.26417i	−0.379959	−	0.737018i
$159$	2.23174	−	6.44819i	0.176988	−	0.511374i
$160$	−3.91609			−0.309594
$161$	−11.7321	−	4.83299i	−0.924619	−	0.380893i
$162$	−1.00000			−0.0785674
$163$	3.30045	−	9.53601i	0.258511	−	0.746918i	−0.738820	−	0.673903i	$-0.764617\pi$
$163$	3.30045	−	9.53601i	0.258511	−	0.746918i	0.997331	−	0.0730151i	$-0.0232621\pi$
$164$	4.67133	+	9.06111i	0.364769	+	0.707554i
$165$	−17.2483	−	13.5642i	−1.34278	−	1.05597i
$166$	−6.91768	+	0.660559i	−0.536916	+	0.0512693i
$167$	−15.8577	+	2.27999i	−1.22711	+	0.176431i	−0.725229	−	0.688508i	$-0.758266\pi$
$167$	−15.8577	+	2.27999i	−1.22711	+	0.176431i	−0.501876	+	0.864939i	$0.667357\pi$
$168$	2.42352	+	1.06138i	0.186979	+	0.0818872i
$169$	10.9035	−	7.00726i	0.838732	−	0.539020i
$170$	3.64184	−	5.11425i	0.279316	−	0.392245i
$171$	−1.87982	+	7.74872i	−0.143753	+	0.592559i
$172$	−9.12195	+	3.15714i	−0.695542	+	0.240730i
$173$	−0.454236	+	2.35680i	−0.0345349	+	0.179184i	−0.995100	−	0.0988697i	$-0.968477\pi$
$173$	−0.454236	+	2.35680i	−0.0345349	+	0.179184i	0.960565	+	0.278054i	$0.0896894\pi$
$174$	1.94636	+	6.62868i	0.147553	+	0.502519i
$175$	−26.1146	+	8.11287i	−1.97408	+	0.613275i
$176$	3.02935	+	4.71377i	0.228346	+	0.355313i
$177$	1.22866	+	5.06460i	0.0923516	+	0.380679i
$178$	4.24289	+	1.69860i	0.318018	+	0.127315i
$179$	−2.53012	−	3.55306i	−0.189110	−	0.265568i	0.709125	−	0.705082i	$-0.249090\pi$
$179$	−2.53012	−	3.55306i	−0.189110	−	0.265568i	−0.898236	+	0.439514i	$0.855151\pi$
$180$	−3.63557	+	1.45546i	−0.270979	+	0.108484i
$181$	16.8097	+	10.8029i	1.24945	+	0.802975i	0.986805	−	0.161916i	$-0.0517673\pi$
$181$	16.8097	+	10.8029i	1.24945	+	0.802975i	0.262650	+	0.964891i	$0.415404\pi$
$182$	0.521218	−	0.0329910i	0.0386352	−	0.00244546i
$183$			3.22723i			0.238563i
$184$	−4.78421	+	0.333640i	−0.352697	+	0.0245963i
$185$	−27.9049	−	16.1109i	−2.05161	−	1.18450i
$186$	0.470120	−	0.0906082i	0.0344709	−	0.00664372i
$187$	−8.97319	−	0.427446i	−0.656185	−	0.0312579i
$188$	−1.95355	−	0.280877i	−0.142477	−	0.0204851i
$189$	2.64440	+	0.0846180i	0.192352	+	0.00615505i
$190$	4.44376	+	30.9070i	0.322384	+	2.24223i
$191$	15.7755	−	3.82709i	1.14147	−	0.276918i	0.379919	−	0.925020i	$-0.375952\pi$
$191$	15.7755	−	3.82709i	1.14147	−	0.276918i	0.761554	+	0.648102i	$0.224437\pi$
$192$	0.998867	−	0.0475819i	0.0720870	−	0.00343393i
$193$	2.05389	+	0.196122i	0.147842	+	0.0141172i	0.168715	−	0.985665i	$-0.446038\pi$
$193$	2.05389	+	0.196122i	0.147842	+	0.0141172i	−0.0208726	+	0.999782i	$0.506644\pi$
$194$	−3.47828	−	3.31653i	−0.249726	−	0.238113i
$195$	−0.506220	+	0.584209i	−0.0362512	+	0.0418361i
$196$	−6.31895	−	3.01178i	−0.451354	−	0.215127i
$197$	−5.05352	+	1.48385i	−0.360048	+	0.105720i	−0.456753	−	0.889593i	$-0.650988\pi$
$197$	−5.05352	+	1.48385i	−0.360048	+	0.105720i	0.0967051	+	0.995313i	$0.469170\pi$
$198$	4.56428	+	3.25021i	0.324370	+	0.230983i
$199$	−0.358193	−	7.51939i	−0.0253916	−	0.533036i	−0.975351	−	0.220661i	$-0.929179\pi$
$199$	−0.358193	−	7.51939i	−0.0253916	−	0.533036i	0.949959	−	0.312375i	$-0.101124\pi$
$200$	−7.48032	+	7.13247i	−0.528939	+	0.504342i
$201$	−6.99505	+	5.50096i	−0.493392	+	0.388008i
$202$	−9.20081	−	4.20187i	−0.647367	−	0.295642i
$203$	−4.58604	−	17.6936i	−0.321877	−	1.24185i
$204$	−0.866776	+	1.34873i	−0.0606864	+	0.0944300i
$205$	37.7263	+	13.0572i	2.63492	+	0.911955i
$206$	7.73405	−	13.3958i	0.538857	−	0.933327i
$207$	−4.31751	+	2.08785i	−0.300088	+	0.145116i
$208$	0.170950	−	0.0986980i	0.0118532	−	0.00684347i
$209$	33.7650	−	29.2575i	2.33557	−	2.02379i
$210$	9.73705	−	3.54119i	0.671920	−	0.244365i
$211$	−1.55945	+	10.8462i	−0.107357	+	0.746683i	0.863035	+	0.505145i	$0.168561\pi$
$211$	−1.55945	+	10.8462i	−0.107357	+	0.746683i	−0.970391	+	0.241538i	$0.922348\pi$
$212$	0.648612	+	6.79257i	0.0445469	+	0.466516i
$213$	1.72384	−	4.30595i	0.118116	−	0.295039i
$214$	11.3864	+	11.9417i	0.778356	+	0.816316i
$215$	−17.3216	+	33.5992i	−1.18132	+	2.29145i
$216$	0.909632	−	0.415415i	0.0618926	−	0.0282654i
$217$	−1.25085	+	0.199824i	−0.0849134	+	0.0135649i
$218$	−1.26442	−	1.09562i	−0.0856372	−	0.0742050i
$219$	−10.6836	−	2.05909i	−0.721929	−	0.139140i
$220$	21.3243	+	5.17323i	1.43769	+	0.348779i
$221$	−0.0300826	+	0.315040i	−0.00202358	+	0.0211919i
$222$	7.31338	+	3.77031i	0.490842	+	0.253047i
$223$	−6.32803	+	21.5513i	−0.423756	+	1.44318i	0.420525	+	0.907281i	$0.361846\pi$
$223$	−6.32803	+	21.5513i	−0.423756	+	1.44318i	−0.844281	+	0.535900i	$0.819972\pi$
$224$	−2.64543	+	0.0413034i	−0.176755	+	0.00275970i
$225$	−4.29362	+	9.40171i	−0.286241	+	0.626781i
$226$	−0.924150	−	2.30842i	−0.0614736	−	0.153554i
$227$	10.7051	−	5.51887i	0.710524	−	0.366300i	−0.0647710	−	0.997900i	$-0.520632\pi$
$227$	10.7051	−	5.51887i	0.710524	−	0.366300i	0.775295	+	0.631600i	$0.217601\pi$
$228$	−1.50899	−	7.82939i	−0.0999353	−	0.518514i
$229$	−9.61883	−	16.6603i	−0.635630	−	1.10094i	−0.986381	−	0.164475i	$-0.947407\pi$
$229$	−9.61883	−	16.6603i	−0.635630	−	1.10094i	0.350751	−	0.936469i	$-0.385926\pi$
$230$	−12.6578	+	13.8745i	−0.834631	+	0.914858i
$231$	−11.7948	−	8.98107i	−0.776038	−	0.590911i
$232$	−4.52412	−	5.22112i	−0.297023	−	0.342783i
$233$	−0.368160	+	7.72862i	−0.0241189	+	0.506319i	0.954194	+	0.299188i	$0.0967157\pi$
$233$	−0.368160	+	7.72862i	−0.0241189	+	0.506319i	−0.978313	+	0.207131i	$0.933587\pi$
$234$	0.122022	−	0.155164i	0.00797683	−	0.0101434i
$235$	−6.29580	+	4.48322i	−0.410692	+	0.292453i
$236$	−3.22154	−	4.09652i	−0.209704	−	0.266661i
$237$	10.0006	+	2.93645i	0.649610	+	0.190743i
$238$	2.40623	−	3.49323i	0.155973	−	0.226433i
$239$	−1.18944	−	2.60451i	−0.0769385	−	0.168472i	0.867254	−	0.497866i	$-0.165883\pi$
$239$	−1.18944	−	2.60451i	−0.0769385	−	0.168472i	−0.944193	+	0.329394i	$0.893156\pi$
$240$	2.70241	−	2.83421i	0.174440	−	0.182947i
$241$	3.05949	+	8.83983i	0.197079	+	0.569423i	0.999631	−	0.0271590i	$-0.00864605\pi$
$241$	3.05949	+	8.83983i	0.197079	+	0.569423i	−0.802552	+	0.596583i	$0.796525\pi$
$242$	−6.67107	−	19.2748i	−0.428832	−	1.23903i
$243$	0.690079	−	0.723734i	0.0442686	−	0.0464276i
$244$	−1.34064	−	2.93559i	−0.0858255	−	0.187932i
$245$	−26.0483	+	8.54038i	−1.66416	+	0.545625i
$246$	−9.78142	−	2.87208i	−0.623640	−	0.183117i
$247$	−0.972941	−	1.23719i	−0.0619067	−	0.0787208i
$248$	−0.389996	+	0.277715i	−0.0247648	+	0.0176349i
$249$	4.29568	−	5.46240i	0.272228	−	0.346166i
$250$	−0.994233	+	20.8715i	−0.0628808	+	1.32003i
$251$	10.4177	+	12.0226i	0.657557	+	0.758861i	0.982376	−	0.186915i	$-0.0598489\pi$
$251$	10.4177	+	12.0226i	0.657557	+	0.758861i	−0.324819	+	0.945776i	$0.605303\pi$
$252$	−2.44058	+	1.02155i	−0.153742	+	0.0643517i
$253$	26.4923	+	4.50326i	1.66556	+	0.283118i
$254$	0.799409	+	1.38462i	0.0501594	+	0.0868786i
$255$	1.18820	+	6.16496i	0.0744079	+	0.386065i
$256$	−0.888835	+	0.458227i	−0.0555522	+	0.0286392i
$257$	2.15879	+	5.39240i	0.134662	+	0.336369i	0.980337	−	0.197328i	$-0.0632265\pi$
$257$	2.15879	+	5.39240i	0.134662	+	0.336369i	−0.845676	+	0.533697i	$0.820802\pi$
$258$	4.00994	−	8.78054i	0.249648	−	0.546653i
$259$	−19.0205	−	10.5890i	−1.18187	−	0.657971i
$260$	0.217785	−	0.741707i	0.0135064	−	0.0459987i
$261$	−6.14054	−	3.16567i	−0.380090	−	0.195950i
$262$	0.734484	−	7.69187i	0.0453766	−	0.475205i
$263$	13.2050	+	3.20349i	0.814253	+	0.197536i	0.621199	−	0.783653i	$-0.286646\pi$
$263$	13.2050	+	3.20349i	0.814253	+	0.197536i	0.193053	+	0.981188i	$0.438161\pi$
$264$	−5.50201	−	1.06042i	−0.338625	−	0.0652646i
$265$	20.1946	+	17.4987i	1.24055	+	1.07494i
$266$	3.32786	+	20.8317i	0.204044	+	1.27727i
$267$	−4.15726	+	1.89856i	−0.254420	+	0.116190i
$268$	4.07773	−	7.90970i	0.249087	−	0.483162i
$269$	3.08071	+	3.23096i	0.187834	+	0.196995i	0.810917	−	0.585161i	$-0.198969\pi$
$269$	3.08071	+	3.23096i	0.187834	+	0.196995i	−0.623083	+	0.782156i	$0.714120\pi$
$270$	1.45546	−	3.63557i	0.0885766	−	0.221254i
$271$	2.36025	+	24.7176i	0.143375	+	1.50149i	0.725406	+	0.688322i	$0.241652\pi$
$271$	2.36025	+	24.7176i	0.143375	+	1.50149i	−0.582031	+	0.813167i	$0.697742\pi$
$272$	0.228165	−	1.58692i	0.0138345	−	0.0962211i
$273$	−0.335805	+	0.399989i	−0.0203238	+	0.0242085i
$274$	12.2552	−	10.6192i	0.740364	−	0.641529i
$275$	50.1549	−	28.9569i	3.02445	−	1.74617i
$276$	3.06002	−	3.69274i	0.184191	−	0.222277i
$277$	−7.00363	+	12.1306i	−0.420808	+	0.728860i	−0.996019	−	0.0891450i	$-0.971587\pi$
$277$	−7.00363	+	12.1306i	−0.420808	+	0.728860i	0.575211	+	0.818005i	$0.304920\pi$
$278$	−6.89645	−	2.38689i	−0.413622	−	0.143156i
$279$	−0.258844	+	0.402769i	−0.0154966	+	0.0241131i
$280$	−7.38607	+	7.26609i	−0.441402	+	0.434232i
$281$	−8.68270	−	3.96525i	−0.517966	−	0.236547i	0.139239	−	0.990259i	$-0.455534\pi$
$281$	−8.68270	−	3.96525i	−0.517966	−	0.236547i	−0.657205	+	0.753712i	$0.728262\pi$
$282$	1.55138	−	1.22002i	0.0923834	−	0.0726511i
$283$	7.09913	−	6.76901i	0.421999	−	0.402376i	−0.449101	−	0.893481i	$-0.648256\pi$
$283$	7.09913	−	6.76901i	0.421999	−	0.402376i	0.871100	+	0.491105i	$0.163407\pi$
$284$	0.220694	+	4.63294i	0.0130958	+	0.274914i
$285$	−25.4350	−	18.1122i	−1.50664	−	1.07287i
$286$	−1.06126	+	0.311614i	−0.0627535	+	0.0184261i
$287$	25.6229	+	8.42262i	1.51247	+	0.497171i
$288$	−0.654861	+	0.755750i	−0.0385880	+	0.0445330i
$289$	−10.4432	−	9.95758i	−0.614307	−	0.585740i
$290$	−26.9319	−	2.57168i	−1.58149	−	0.151014i
$291$	4.80058	−	0.228680i	0.281415	−	0.0134054i
$292$	10.5735	−	2.56510i	0.618767	−	0.150111i
$293$	−2.38511	−	16.5888i	−0.139339	−	0.969126i	−0.932772	−	0.360468i	$-0.882617\pi$
$293$	−2.38511	−	16.5888i	−0.139339	−	0.969126i	0.793432	−	0.608659i	$-0.208292\pi$
$294$	6.54031	−	2.49487i	0.381438	−	0.145504i
$295$	−20.2010	−	2.90446i	−1.17615	−	0.169104i
$296$	−8.21873	−	0.391506i	−0.477704	−	0.0227559i
$297$	−5.50201	+	1.06042i	−0.319259	+	0.0615321i
$298$	−0.146352	−	0.0844963i	−0.00847794	−	0.00489474i
$299$	0.202872	−	0.924685i	0.0117324	−	0.0534759i
$300$		−	10.3357i		−	0.596734i
$301$	−11.3469	+	22.8799i	−0.654022	+	1.31878i
$302$	−6.76061	−	4.34478i	−0.389030	−	0.250014i
$303$	9.39032	−	3.75932i	0.539460	−	0.215967i
$304$	4.62507	+	6.49500i	0.265266	+	0.372514i
$305$	−11.7328	−	4.69710i	−0.671818	−	0.268955i
$306$	−0.377978	−	1.55805i	−0.0216075	−	0.0890675i
$307$	14.8185	+	23.0580i	0.845734	+	1.31599i	0.947035	+	0.321132i	$0.104063\pi$
$307$	14.8185	+	23.0580i	0.845734	+	1.31599i	−0.101301	+	0.994856i	$0.532300\pi$
$308$	14.4598	+	3.26975i	0.823921	+	0.186312i
$309$	4.35787	+	14.8415i	0.247910	+	0.844305i
$310$	−0.354830	+	1.84103i	−0.0201530	+	0.104564i
$311$	−20.2684	+	7.01496i	−1.14931	+	0.397782i	−0.834303	−	0.551306i	$-0.814130\pi$
$311$	−20.2684	+	7.01496i	−1.14931	+	0.397782i	−0.315012	+	0.949088i	$0.602008\pi$
$312$	−0.0465379	+	0.191832i	−0.00263469	+	0.0108603i
$313$	−5.71350	+	8.02349i	−0.322946	+	0.453514i	−0.943851	−	0.330372i	$-0.892826\pi$
$313$	−5.71350	+	8.02349i	−0.322946	+	0.453514i	0.620905	+	0.783886i	$0.286765\pi$
$314$	0.854232	−	0.548982i	0.0482071	−	0.0309808i
$315$	−4.15646	+	9.49073i	−0.234190	+	0.534742i
$316$	−10.3167	+	1.48332i	−0.580361	+	0.0834434i
$317$	−27.9079	+	2.66488i	−1.56746	+	0.149675i	−0.842341	−	0.538945i	$-0.818823\pi$
$317$	−27.9079	+	2.66488i	−1.56746	+	0.149675i	−0.725123	+	0.688620i	$0.758217\pi$
$318$	−5.36361	−	4.21799i	−0.300776	−	0.236533i
$319$	17.7381	+	34.4071i	0.993142	+	1.92643i
$320$	−1.28083	+	3.70071i	−0.0716004	+	0.206876i
$321$	−16.5001			−0.920945
$322$	−8.40438	+	9.50613i	−0.468358	+	0.529756i
$323$	−12.7834			−0.711286
$324$	−0.327068	+	0.945001i	−0.0181704	+	0.0525000i
$325$	−0.934889	−	1.81343i	−0.0518583	−	0.100591i
$326$	−7.93207	−	6.23785i	−0.439317	−	0.345482i
$327$	1.66549	−	0.159035i	0.0921017	−	0.00879465i
$328$	10.0906	−	1.45081i	0.557160	−	0.0801075i
$329$	−4.20571	+	3.09494i	−0.231868	+	0.170630i
$330$	−18.4595	+	11.8632i	−1.01616	+	0.653048i
$331$	−7.75010	+	10.8835i	−0.425984	+	0.598210i	−0.970666	−	0.240432i	$-0.922711\pi$
$331$	−7.75010	+	10.8835i	−0.425984	+	0.598210i	0.544682	+	0.838643i	$0.316650\pi$
$332$	−1.63832	+	6.75326i	−0.0899147	+	0.370633i
$333$	−7.77552	+	2.69113i	−0.426096	+	0.147473i
$334$	−3.03195	+	15.7312i	−0.165901	+	0.860775i
$335$	−9.81811	−	33.4374i	−0.536421	−	1.82688i
$336$	1.79566	−	1.94309i	0.0979614	−	0.106004i
$337$	−1.87007	−	2.90988i	−0.101869	−	0.158512i	0.786577	−	0.617492i	$-0.211851\pi$
$337$	−1.87007	−	2.90988i	−0.101869	−	0.158512i	−0.888446	+	0.458980i	$0.848215\pi$
$338$	−3.05568	−	12.5957i	−0.166207	−	0.685115i
$339$	2.30842	+	0.924150i	0.125376	+	0.0501929i
$340$	−3.64184	−	5.11425i	−0.197507	−	0.277359i
$341$	2.49052	−	0.997054i	0.134869	−	0.0539935i
$342$	6.70772	+	4.31079i	0.362712	+	0.233101i
$343$	−17.5063	+	6.04400i	−0.945251	+	0.326346i
$344$			9.65285i			0.520447i
$345$	−1.30656	−	18.7354i	−0.0703430	−	1.00868i
$346$	2.07861	+	1.20009i	0.111747	+	0.0645171i
$347$	−24.9595	+	4.81056i	−1.33990	+	0.258244i	−0.808309	−	0.588758i	$-0.799617\pi$
$347$	−24.9595	+	4.81056i	−1.33990	+	0.258244i	−0.531589	+	0.847003i	$0.678405\pi$
$348$	6.90070	+	0.328721i	0.369916	+	0.0176213i
$349$	−22.7224	−	3.26699i	−1.21630	−	0.174878i	−0.495866	−	0.868399i	$-0.665149\pi$
$349$	−22.7224	−	3.26699i	−1.21630	−	0.174878i	−0.720437	+	0.693521i	$0.756059\pi$
$350$	−0.874589	+	27.3318i	−0.0467487	+	1.46095i
$351$	0.0280924	+	0.195387i	0.00149946	+	0.0104290i
$352$	5.44532	−	1.32102i	0.290236	−	0.0704106i
$353$	35.1221	−	1.67307i	1.86936	−	0.0890486i	0.917898	−	0.396816i	$-0.129885\pi$
$353$	35.1221	−	1.67307i	1.86936	−	0.0890486i	0.951462	+	0.307767i	$0.0995817\pi$
$354$	5.18791	+	0.495385i	0.275734	+	0.0263294i
$355$	13.1456	+	12.5343i	0.697695	+	0.665251i
$356$	2.99289	−	3.45398i	0.158623	−	0.183060i
$357$	0.867685	+	4.15207i	0.0459227	+	0.219751i
$358$	−4.18517	+	1.22888i	−0.221193	+	0.0649481i
$359$	−7.15796	−	5.09716i	−0.377783	−	0.269018i	0.375354	−	0.926881i	$-0.377521\pi$
$359$	−7.15796	−	5.09716i	−0.377783	−	0.269018i	−0.753137	+	0.657863i	$0.771460\pi$
$360$	0.186335	+	3.91165i	0.00982071	+	0.206162i
$361$	32.2614	−	30.7612i	1.69797	−	1.61901i
$362$	15.7067	−	12.3519i	0.825525	−	0.649200i
$363$	18.5534	+	8.47304i	0.973800	+	0.444719i
$364$	0.139297	−	0.503341i	0.00730115	−	0.0263823i
$365$	23.0355	−	35.8439i	1.20573	−	1.87616i
$366$	3.04973	+	1.05552i	0.159412	+	0.0551730i
$367$	8.56404	−	14.8333i	0.447039	−	0.774294i	−0.551153	−	0.834404i	$-0.685812\pi$
$367$	8.56404	−	14.8333i	0.447039	−	0.774294i	0.998192	+	0.0601101i	$0.0191452\pi$
$368$	−1.24947	+	4.63021i	−0.0651332	+	0.241366i
$369$	8.82858	−	5.09718i	0.459597	−	0.265349i
$370$	−24.3516	+	21.1008i	−1.26598	+	1.09698i
$371$	13.8266	+	11.6079i	0.717841	+	0.602652i
$372$	0.0681364	−	0.473899i	0.00353271	−	0.0245705i
$373$	−1.41247	−	14.7920i	−0.0731347	−	0.765901i	−0.955433	−	0.295209i	$-0.904611\pi$
$373$	−1.41247	−	14.7920i	−0.0731347	−	0.765901i	0.882298	−	0.470691i	$-0.155996\pi$
$374$	−3.33878	+	8.33987i	−0.172644	+	0.431244i
$375$	−14.4193	−	15.1226i	−0.744611	−	0.780926i
$376$	−0.904372	+	1.75424i	−0.0466394	+	0.0904678i
$377$	1.24048	−	0.566508i	0.0638879	−	0.0291766i
$378$	0.944862	−	2.47128i	0.0485985	−	0.127109i
$379$	−28.0787	−	24.3303i	−1.44231	−	1.24977i	−0.917021	−	0.398839i	$-0.869413\pi$
$379$	−28.0787	−	24.3303i	−1.44231	−	1.24977i	−0.525285	−	0.850926i	$-0.676041\pi$
$380$	30.6606	+	5.90934i	1.57285	+	0.303143i
$381$	−1.55375	−	0.376935i	−0.0796010	−	0.0193110i
$382$	1.54305	−	16.1595i	0.0789493	−	0.826794i
$383$	16.6799	+	8.59907i	0.852301	+	0.439392i	0.828277	−	0.560319i	$-0.189322\pi$
$383$	16.6799	+	8.59907i	0.852301	+	0.439392i	0.0240248	+	0.999711i	$0.492352\pi$
$384$	0.281733	−	0.959493i	0.0143771	−	0.0489639i
$385$	49.8181	−	29.8090i	2.53897	−	1.51921i
$386$	0.857096	−	1.87678i	0.0436250	−	0.0955255i
$387$	3.58760	+	8.96140i	0.182368	+	0.455533i
$388$	−4.27176	+	2.20225i	−0.216866	+	0.111802i
$389$	2.67888	+	13.8993i	0.135824	+	0.704724i	0.984441	+	0.175715i	$0.0562238\pi$
$389$	2.67888	+	13.8993i	0.135824	+	0.704724i	−0.848617	+	0.529008i	$0.822564\pi$
$390$	0.386510	+	0.669455i	0.0195717	+	0.0338992i
$391$	−4.88489	−	5.93771i	−0.247040	−	0.300283i
$392$	−4.91287	+	4.98636i	−0.248137	+	0.251849i
$393$	5.06001	+	5.83957i	0.255244	+	0.294567i
$394$	−0.250607	+	5.26090i	−0.0126254	+	0.265040i
$395$	−25.2312	+	32.0841i	−1.26952	+	1.61432i
$396$	4.56428	−	3.25021i	0.229364	−	0.163329i
$397$	−10.9610	−	13.9380i	−0.550115	−	0.699528i	0.428892	−	0.903356i	$-0.358904\pi$
$397$	−10.9610	−	13.9380i	−0.550115	−	0.699528i	−0.979007	+	0.203828i	$0.934662\pi$
$398$	−7.22299	−	2.12086i	−0.362056	−	0.106309i
$399$	−17.3731	−	11.9670i	−0.869743	−	0.599101i
$400$	4.29362	+	9.40171i	0.214681	+	0.470086i
$401$	19.5293	−	20.4817i	0.975245	−	1.02281i	−0.0244884	−	0.999700i	$-0.507796\pi$
$401$	19.5293	−	20.4817i	0.975245	−	1.02281i	0.999733	−	0.0231070i	$-0.00735583\pi$
$402$	2.91056	+	8.40951i	0.145166	+	0.419428i
$403$	−0.0309104	−	0.0893099i	−0.00153976	−	0.00444884i
$404$	−6.98006	+	7.32048i	−0.347271	+	0.364207i
$405$	1.62680	+	3.56220i	0.0808364	+	0.177007i
$406$	−18.2204	−	1.45319i	−0.904263	−	0.0721207i
$407$	44.2364	+	12.9890i	2.19272	+	0.643840i
$408$	0.991056	+	1.26023i	0.0490646	+	0.0623907i
$409$	10.7552	−	7.65875i	0.531811	−	0.378701i	−0.282376	−	0.959304i	$-0.591123\pi$
$409$	10.7552	−	7.65875i	0.531811	−	0.378701i	0.814187	+	0.580603i	$0.197183\pi$
$410$	24.6781	−	31.3808i	1.21877	−	1.54979i
$411$	−0.771587	+	16.1976i	−0.0380596	+	0.798968i
$412$	−10.1295	−	11.6900i	−0.499042	−	0.575925i
$413$	−13.6770	−	1.74899i	−0.673000	−	0.0860619i
$414$	0.560904	+	4.76292i	0.0275669	+	0.234085i
$415$	13.6067	+	23.5676i	0.667928	+	1.15689i
$416$	−0.0373574	−	0.193829i	−0.00183160	−	0.00950324i
$417$	6.48657	−	3.34406i	0.317649	−	0.163759i
$418$	−16.6050	−	41.4772i	−0.812175	−	2.02871i
$419$	−15.5613	+	34.0745i	−0.760220	+	1.66465i	−0.0131412	+	0.999914i	$0.504183\pi$
$419$	−15.5613	+	34.0745i	−0.760220	+	1.66465i	−0.747079	+	0.664736i	$0.768544\pi$
$420$	−0.161748	−	10.3597i	−0.00789248	−	0.505503i
$421$	9.87379	−	33.6270i	0.481219	−	1.63888i	−0.258534	−	0.966002i	$-0.583239\pi$
$421$	9.87379	−	33.6270i	0.481219	−	1.63888i	0.739753	−	0.672879i	$-0.234942\pi$
$422$	9.73961	+	5.02112i	0.474117	+	0.244424i
$423$	−0.187606	+	1.96470i	−0.00912171	+	0.0955269i
$424$	6.63113	+	1.60869i	0.322036	+	0.0781251i
$425$	−16.2712	−	3.13601i	−0.789269	−	0.152119i
$426$	−3.50531	−	3.03737i	−0.169833	−	0.147161i
$427$	−7.97538	−	3.04928i	−0.385956	−	0.147565i
$428$	15.0090	−	6.85438i	0.725487	−	0.331319i
$429$	0.506827	−	0.983107i	0.0244698	−	0.0474649i
$430$	26.0859	+	27.3582i	1.25798	+	1.31933i
$431$	1.43738	−	3.59041i	0.0692363	−	0.172944i	−0.889714	−	0.456519i	$-0.849096\pi$
$431$	1.43738	−	3.59041i	0.0692363	−	0.172944i	0.958950	+	0.283575i	$0.0915204\pi$
$432$	−0.0950560	−	0.995472i	−0.00457339	−	0.0478947i
$433$	−0.128694	+	0.895085i	−0.00618463	+	0.0430150i	−0.992680	−	0.120774i	$-0.961462\pi$
$433$	−0.128694	+	0.895085i	−0.00618463	+	0.0430150i	0.986495	+	0.163789i	$0.0523715\pi$
$434$	−0.220280	+	1.24741i	−0.0105738	+	0.0598777i
$435$	20.4463	−	17.7169i	0.980327	−	0.849458i
$436$	−1.44892	+	0.836532i	−0.0693905	+	0.0400626i
$437$	37.9609	+	4.60713i	1.81592	+	0.220389i
$438$	−5.44010	+	9.42252i	−0.259938	+	0.450226i
$439$	16.2185	+	5.61326i	0.774065	+	0.267906i	0.685411	−	0.728156i	$-0.259622\pi$
$439$	16.2185	+	5.61326i	0.774065	+	0.267906i	0.0886533	+	0.996063i	$0.471744\pi$
$440$	11.8632	−	18.4595i	0.565556	−	0.880023i
$441$	−2.70771	+	6.45510i	−0.128938	+	0.307386i
$442$	0.287874	+	0.131468i	0.0136928	+	0.00625327i
$443$	1.83500	−	1.44306i	0.0871836	−	0.0685619i	−0.573616	−	0.819124i	$-0.694460\pi$
$443$	1.83500	−	1.44306i	0.0871836	−	0.0685619i	0.660799	+	0.750562i	$0.270217\pi$
$444$	5.95492	−	5.67801i	0.282608	−	0.269466i
$445$	−0.851601	−	17.8773i	−0.0403697	−	0.847465i
$446$	18.2963	+	13.0287i	0.866355	+	0.616928i
$447$	0.162147	−	0.0476107i	0.00766930	−	0.00225191i
$448$	−0.826203	+	2.51344i	−0.0390344	+	0.118749i
$449$	5.67684	−	6.55142i	0.267906	−	0.309180i	−0.605817	−	0.795604i	$-0.707153\pi$
$449$	5.67684	−	6.55142i	0.267906	−	0.309180i	0.873723	+	0.486424i	$0.161699\pi$
$450$	7.48032	+	7.13247i	0.352626	+	0.336228i
$451$	−56.8631	−	5.42976i	−2.67758	−	0.255678i
$452$	−2.48371	+	0.118314i	−0.116824	+	0.00556502i
$453$	7.80982	−	1.89464i	0.366937	−	0.0890181i
$454$	−1.71404	−	11.9214i	−0.0804438	−	0.559499i
$455$	−0.965438	−	1.80301i	−0.0452604	−	0.0845264i
$456$	−7.89232	−	1.13474i	−0.369592	−	0.0531393i
$457$	−30.2008	−	1.43864i	−1.41273	−	0.0672968i	−0.672725	−	0.739893i	$-0.734876\pi$
$457$	−30.2008	−	1.43864i	−1.41273	−	0.0672968i	−0.740010	+	0.672596i	$0.765179\pi$
$458$	−18.8900	+	3.64075i	−0.882673	+	0.170121i
$459$	1.38844	+	0.801619i	0.0648071	+	0.0374164i
$460$	8.97145	+	16.4995i	0.418296	+	0.769295i
$461$		−	20.4645i		−	0.953127i	−0.879140	−	0.476563i	$-0.841882\pi$
$461$		−	20.4645i		−	0.953127i	0.879140	−	0.476563i	$-0.158118\pi$
$462$	−12.3448	+	8.20863i	−0.574333	+	0.381900i
$463$	−12.6168	−	8.10832i	−0.586352	−	0.376826i	0.213572	−	0.976927i	$-0.431490\pi$
$463$	−12.6168	−	8.10832i	−0.586352	−	0.376826i	−0.799924	+	0.600102i	$0.795127\pi$
$464$	−6.41366	+	2.56764i	−0.297746	+	0.119200i
$465$	−1.08756	−	1.52726i	−0.0504342	−	0.0708250i
$466$	7.18314	+	2.87570i	0.332753	+	0.133214i
$467$	−4.61731	−	19.0328i	−0.213663	−	0.880733i	−0.973143	−	0.230202i	$-0.926061\pi$
$467$	−4.61731	−	19.0328i	−0.213663	−	0.880733i	0.759479	−	0.650531i	$-0.225454\pi$
$468$	−0.106720	−	0.166060i	−0.00493315	−	0.00767613i
$469$	−6.98508	−	22.4844i	−0.322541	−	1.03823i
$470$	2.17749	+	7.41585i	0.100440	+	0.342068i
$471$	−0.192171	+	0.997078i	−0.00885477	+	0.0459429i
$472$	−4.92488	+	1.70452i	−0.226686	+	0.0784567i
$473$	12.7516	−	52.5628i	0.586319	−	2.41684i
$474$	6.04583	−	8.49018i	0.277694	−	0.389967i
$475$	69.3292	−	44.5552i	3.18104	−	2.04433i
$476$	−2.51411	−	3.41641i	−0.115234	−	0.156591i
$477$	6.75402	−	0.971081i	0.309245	−	0.0444627i
$478$	−2.85029	+	0.272170i	−0.130369	+	0.0124488i
$479$	8.59522	+	6.75935i	0.392726	+	0.308843i	0.794923	−	0.606710i	$-0.207511\pi$
$479$	8.59522	+	6.75935i	0.392726	+	0.308843i	−0.402198	+	0.915553i	$0.631754\pi$
$480$	−1.79445	−	3.48076i	−0.0819053	−	0.158874i
$481$	0.531219	−	1.53486i	0.0242215	−	0.0699834i
$482$	9.35431			0.426077
$483$	−1.08023	−	12.6425i	−0.0491520	−	0.575254i
$484$	−20.3966			−0.927117
$485$	−6.15568	+	17.7857i	−0.279515	+	0.807606i
$486$	−0.458227	−	0.888835i	−0.0207856	−	0.0403184i
$487$	−28.9356	−	22.7552i	−1.31120	−	1.03114i	−0.996641	−	0.0818996i	$-0.973901\pi$
$487$	−28.9356	−	22.7552i	−1.31120	−	1.03114i	−0.314558	−	0.949238i	$-0.601856\pi$
$488$	−3.21261	+	0.306767i	−0.145428	+	0.0138867i
$489$	9.98830	−	1.43610i	0.451686	−	0.0649427i
$490$	−0.448894	+	27.4089i	−0.0202790	+	1.23821i
$491$	−19.2488	+	12.3705i	−0.868686	+	0.558271i	−0.897351	−	0.441318i	$-0.854511\pi$
$491$	−19.2488	+	12.3705i	−0.868686	+	0.558271i	0.0286642	+	0.999589i	$0.490875\pi$
$492$	−5.91331	+	8.30408i	−0.266593	+	0.374377i
$493$	2.61127	−	10.7638i	0.117606	−	0.484777i
$494$	−1.48737	+	0.514783i	−0.0669198	+	0.0231612i
$495$	4.15272	−	21.5463i	0.186651	−	0.968436i
$496$	0.134886	+	0.459379i	0.00605655	+	0.0206267i
$497$	9.01242	+	8.32863i	0.404262	+	0.373590i
$498$	−3.75699	−	5.84600i	−0.168355	−	0.261965i
$499$	8.84930	+	36.4773i	0.396149	+	1.63295i	0.725130	+	0.688612i	$0.241779\pi$
$499$	8.84930	+	36.4773i	0.396149	+	1.63295i	−0.328982	+	0.944336i	$0.606705\pi$
$500$	19.3984	+	7.76596i	0.867524	+	0.347304i
$501$	−9.29295	−	13.0501i	−0.415179	−	0.583037i
$502$	14.7687	−	5.91248i	0.659158	−	0.263887i
$503$	−12.0315	−	7.73216i	−0.536457	−	0.344760i	0.244195	−	0.969726i	$-0.421476\pi$
$503$	−12.0315	−	7.73216i	−0.536457	−	0.344760i	−0.780652	+	0.624966i	$0.785113\pi$
$504$	0.167131	+	2.64047i	0.00744461	+	0.117616i
$505$			39.6107i			1.76265i
$506$	12.9204	−	23.5624i	0.574380	−	1.04748i
$507$	11.2246	+	6.48052i	0.498501	+	0.287810i
$508$	1.56992	−	0.302578i	0.0696541	−	0.0134247i
$509$	20.3965	+	0.971604i	0.904058	+	0.0430656i	0.494460	−	0.869200i	$-0.335366\pi$
$509$	20.3965	+	0.971604i	0.904058	+	0.0430656i	0.409598	+	0.912266i	$0.365669\pi$
$510$	6.21451	+	0.893512i	0.275183	+	0.0395654i
$511$	15.1831	−	24.4566i	0.671660	−	1.08189i
$512$	0.142315	+	0.989821i	0.00628949	+	0.0437443i
$513$	−7.74872	+	1.87982i	−0.342114	+	0.0829960i
$514$	5.80190	−	0.276378i	0.255911	−	0.0121905i
$515$	−60.3001	−	5.75796i	−2.65714	−	0.253726i
$516$	−6.98610	−	6.66123i	−0.307546	−	0.293244i
$517$	7.24197	−	8.35768i	0.318502	−	0.367570i
$518$	−16.2276	+	14.5110i	−0.713002	+	0.637577i
$519$	−2.30295	+	0.676208i	−0.101088	+	0.0296822i
$520$	−0.629683	−	0.448395i	−0.0276134	−	0.0196634i
$521$	−0.590276	−	12.3914i	−0.0258604	−	0.542877i	−0.974209	−	0.225647i	$-0.927550\pi$
$521$	−0.590276	−	12.3914i	−0.0258604	−	0.542877i	0.948349	−	0.317230i	$-0.102753\pi$
$522$	−4.99994	+	4.76743i	−0.218841	+	0.208665i
$523$	−11.4768	+	9.02549i	−0.501847	+	0.394657i	−0.836741	−	0.547599i	$-0.815542\pi$
$523$	−11.4768	+	9.02549i	−0.501847	+	0.394657i	0.334894	+	0.942256i	$0.391300\pi$
$524$	−7.02860	−	3.20985i	−0.307046	−	0.140223i
$525$	−19.1774	−	19.4941i	−0.836971	−	0.850791i
$526$	7.34622	−	11.4309i	0.320310	−	0.498413i
$527$	−0.725369	−	0.251053i	−0.0315976	−	0.0109360i
$528$	−2.80163	+	4.85257i	−0.121925	+	0.211181i
$529$	12.3660	+	19.3928i	0.537651	+	0.843167i
$530$	23.1413	−	13.3607i	1.00519	−	0.580350i
$531$	−3.93859	+	3.41281i	−0.170920	+	0.148103i
$532$	20.7744	+	3.66855i	0.900685	+	0.159052i
$533$	−0.286384	+	1.99184i	−0.0124047	+	0.0862763i
$534$	0.434432	+	4.54957i	0.0187997	+	0.196879i
$535$	24.0152	−	59.9872i	1.03827	−	2.59347i
$536$	−6.14098	−	6.44047i	−0.265250	−	0.278186i
$537$	1.99872	−	3.87697i	0.0862510	−	0.167304i
$538$	4.06086	−	1.85453i	0.175076	−	0.0799546i
$539$	33.3392	−	20.6623i	1.43602	−	0.889988i
$540$	−2.95958	−	2.56449i	−0.127360	−	0.110358i
$541$	−7.56565	−	1.45816i	−0.325273	−	0.0626912i	0.0240010	−	0.999712i	$-0.492360\pi$
$541$	−7.56565	−	1.45816i	−0.325273	−	0.0626912i	−0.349274	+	0.937021i	$0.613572\pi$
$542$	24.1301	+	5.85391i	1.03648	+	0.251447i
$543$	−1.89938	+	19.8912i	−0.0815103	+	0.853615i
$544$	−1.42501	−	0.734646i	−0.0610970	−	0.0314977i
$545$	−1.84587	+	6.28647i	−0.0790685	+	0.269283i
$546$	0.268159	+	0.448159i	0.0114762	+	0.0191794i
$547$	−0.633061	+	1.38621i	−0.0270677	+	0.0592701i	−0.922683	−	0.385559i	$-0.874008\pi$
$547$	−0.633061	+	1.38621i	−0.0270677	+	0.0592701i	0.895615	+	0.444830i	$0.146736\pi$
$548$	−6.02686	−	15.0544i	−0.257455	−	0.643091i
$549$	−2.86847	+	1.47880i	−0.122423	+	0.0631137i
$550$	−10.9603	−	56.8673i	−0.467347	−	2.42483i
$551$	27.5425	+	47.7050i	1.17335	+	2.03230i
$552$	−2.48880	−	4.09949i	−0.105931	−	0.174486i
$553$	−16.7060	+	21.9398i	−0.710411	+	0.932976i
$554$	9.17281	+	10.5860i	0.389715	+	0.449755i
$555$	1.53317	−	32.1853i	0.0650796	−	1.36619i
$556$	−4.51122	+	5.73648i	−0.191318	+	0.243281i
$557$	−14.6090	+	10.4030i	−0.619003	+	0.440790i	−0.846057	−	0.533092i	$-0.821030\pi$
$557$	−14.6090	+	10.4030i	−0.619003	+	0.440790i	0.227054	+	0.973882i	$0.427090\pi$
$558$	0.295957	+	0.376340i	0.0125289	+	0.0159318i
$559$	−1.82825	−	0.536823i	−0.0773268	−	0.0227052i
$560$	4.45072	+	9.35635i	0.188077	+	0.395378i
$561$	−3.73183	−	8.17156i	−0.157558	−	0.345003i
$562$	−6.58700	+	6.90825i	−0.277856	+	0.291407i
$563$	−8.86250	−	25.6065i	−0.373510	−	1.07919i	−0.962555	−	0.271086i	$-0.912617\pi$
$563$	−8.86250	−	25.6065i	−0.373510	−	1.07919i	0.589046	−	0.808100i	$-0.299504\pi$
$564$	−0.645513	−	1.86509i	−0.0271810	−	0.0785343i
$565$	−6.71962	+	7.04734i	−0.282697	+	0.296484i
$566$	−4.07482	−	8.92261i	−0.171277	−	0.375045i
$567$	1.13652	+	2.38921i	0.0477294	+	0.100337i
$568$	4.45031	+	1.30673i	0.186731	+	0.0548292i
$569$	2.85435	+	3.62960i	0.119661	+	0.152161i	0.842193	−	0.539176i	$-0.181264\pi$
$569$	2.85435	+	3.62960i	0.119661	+	0.152161i	−0.722532	+	0.691337i	$0.757022\pi$
$570$	−25.4350	+	18.1122i	−1.06535	+	0.758636i
$571$	−19.8639	+	25.2590i	−0.831279	+	1.05706i	0.166200	+	0.986092i	$0.446850\pi$
$571$	−19.8639	+	25.2590i	−0.831279	+	1.05706i	−0.997479	+	0.0709652i	$0.977392\pi$
$572$	−0.0526285	+	1.10481i	−0.00220051	+	0.0461944i
$573$	10.6304	+	12.2681i	0.444091	+	0.512508i
$574$	16.3398	−	21.4589i	0.682011	−	0.895678i
$575$	47.1879	+	15.1767i	1.96787	+	0.632912i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−4.52717	−	23.4892i	−0.188469	−	0.977869i	−0.945778	−	0.324813i	$-0.894699\pi$
$577$	−4.52717	−	23.4892i	−0.188469	−	0.977869i	0.757310	−	0.653056i	$-0.226513\pi$
$578$	−12.8256	+	6.61204i	−0.533473	+	0.275025i
$579$	0.766825	+	1.91544i	0.0318681	+	0.0796028i
$580$	−11.2388	+	24.6095i	−0.466666	+	1.02186i
$581$	9.44031	+	15.7770i	0.391650	+	0.654542i
$582$	1.35401	−	4.61134i	0.0561256	−	0.191146i
$583$	−33.9835	−	17.5197i	−1.40745	−	0.725592i
$584$	1.03423	−	10.8309i	0.0427967	−	0.448187i
$585$	−0.751230	−	0.182246i	−0.0310595	−	0.00753496i
$586$	−16.4565	−	3.17173i	−0.679812	−	0.131023i
$587$	−26.1259	−	22.6382i	−1.07833	−	0.934379i	−0.0802793	−	0.996772i	$-0.525581\pi$
$587$	−26.1259	−	22.6382i	−1.07833	−	0.934379i	−0.998052	+	0.0623933i	$0.980127\pi$
$588$	−0.218530	−	6.99659i	−0.00901204	−	0.288534i
$589$	3.47250	−	1.58584i	0.143082	−	0.0653433i
$590$	−9.35181	+	18.1400i	−0.385008	+	0.746811i
$591$	−3.63455	−	3.81181i	−0.149505	−	0.156797i
$592$	−3.05806	+	7.63866i	−0.125685	+	0.313947i
$593$	4.30415	+	45.0751i	0.176750	+	1.85101i	0.454983	+	0.890500i	$0.349645\pi$
$593$	4.30415	+	45.0751i	0.176750	+	1.85101i	−0.278232	+	0.960514i	$0.589749\pi$
$594$	−0.797428	+	5.54623i	−0.0327189	+	0.227565i
$595$	−16.3580	−	2.88866i	−0.670614	−	0.118424i
$596$	−0.127716	+	0.110667i	−0.00523145	+	0.00453308i
$597$	6.51937	−	3.76396i	0.266820	−	0.154049i
$598$	−0.807475	−	0.494149i	−0.0330201	−	0.0202073i
$599$	−9.61298	+	16.6502i	−0.392776	+	0.680307i	−0.992814	−	0.119664i	$-0.961818\pi$
$599$	−9.61298	+	16.6502i	−0.392776	+	0.680307i	0.600039	+	0.799971i	$0.295152\pi$
$600$	−9.76728	−	3.38049i	−0.398747	−	0.138008i
$601$	21.3702	−	33.2527i	0.871710	−	1.35641i	−0.0618879	−	0.998083i	$-0.519712\pi$
$601$	21.3702	−	33.2527i	0.871710	−	1.35641i	0.933597	−	0.358324i	$-0.116652\pi$
$602$	17.9104	+	18.2061i	0.729972	+	0.742025i
$603$	−8.09477	−	3.69676i	−0.329644	−	0.150544i
$604$	−6.31700	+	4.96775i	−0.257035	+	0.202135i
$605$	−57.8081	+	55.1199i	−2.35023	+	2.24094i
$606$	−0.481285	−	10.1034i	−0.0195509	−	0.410423i
$607$	21.8378	+	15.5506i	0.886368	+	0.631179i	0.929876	−	0.367874i	$-0.119914\pi$
$607$	21.8378	+	15.5506i	0.886368	+	0.631179i	−0.0435083	+	0.999053i	$0.513853\pi$
$608$	7.65050	−	2.24639i	0.310269	−	0.0911031i
$609$	13.6252	−	12.1839i	0.552122	−	0.493716i
$610$	−8.27619	+	9.55123i	−0.335093	+	0.386718i
$611$	−0.281958	−	0.268846i	−0.0114068	−	0.0108764i
$612$	−1.59598	−	0.152397i	−0.0645136	−	0.00616030i
$613$	−18.1546	+	0.864808i	−0.733256	+	0.0349293i	−0.410889	−	0.911685i	$-0.634782\pi$
$613$	−18.1546	+	0.864808i	−0.733256	+	0.0349293i	−0.322367	+	0.946615i	$0.604479\pi$
$614$	26.6364	−	6.46193i	1.07496	−	0.260782i
$615$	5.68149	+	39.5157i	0.229100	+	1.59343i
$616$	7.81924	−	12.5951i	0.315046	−	0.507469i
$617$	1.86437	+	0.268055i	0.0750566	+	0.0107915i	0.179741	−	0.983714i	$-0.442474\pi$
$617$	1.86437	+	0.268055i	0.0750566	+	0.0107915i	−0.104684	+	0.994506i	$0.533383\pi$
$618$	15.4506	+	0.736002i	0.621513	+	0.0296063i
$619$	−9.94755	+	1.91723i	−0.399826	+	0.0770601i	−0.385200	−	0.922833i	$-0.625868\pi$
$619$	−9.94755	+	1.91723i	−0.399826	+	0.0770601i	−0.0146253	+	0.999893i	$0.504656\pi$
$620$	1.62372	+	0.937457i	0.0652103	+	0.0376492i
$621$	−3.83415	−	2.88084i	−0.153859	−	0.115604i
$622$			21.4480i			0.859987i
$623$	−0.763834	−	12.0676i	−0.0306024	−	0.483480i
$624$	0.166060	+	0.106720i	0.00664772	+	0.00427223i
$625$	27.9891	−	11.2052i	1.11956	−	0.448206i
$626$	5.71350	+	8.02349i	0.228357	+	0.320683i
$627$	41.4772	+	16.6050i	1.65644	+	0.663138i
$628$	−0.239396	−	0.986804i	−0.00955295	−	0.0393778i
$629$	−7.13188	−	11.0974i	−0.284367	−	0.442483i
$630$	7.60931	+	7.03197i	0.303162	+	0.280160i
$631$	−4.10205	−	13.9703i	−0.163300	−	0.556148i	−0.999964	−	0.00843261i	$-0.997316\pi$
$631$	−4.10205	−	13.9703i	−0.163300	−	0.556148i	0.836665	−	0.547716i	$-0.184502\pi$
$632$	−1.97253	+	10.2345i	−0.0784631	+	0.407105i
$633$	−10.3551	+	3.58392i	−0.411577	+	0.142448i
$634$	−6.60946	+	27.2446i	−0.262495	+	1.08202i
$635$	3.63180	−	5.10015i	0.144124	−	0.202393i
$636$	−5.74027	+	3.68905i	−0.227616	+	0.146280i
$637$	−0.671198	−	1.20780i	−0.0265938	−	0.0478549i
$638$	38.3163	−	5.50905i	1.51696	−	0.218105i
$639$	4.61719	−	0.440888i	0.182653	−	0.0174413i
$640$	3.07825	+	2.42076i	0.121679	+	0.0956891i
$641$	4.14593	+	8.04199i	0.163755	+	0.317640i	0.956408	−	0.292032i	$-0.0943315\pi$
$641$	4.14593	+	8.04199i	0.163755	+	0.317640i	−0.792654	+	0.609672i	$0.791301\pi$
$642$	−5.39665	+	15.5926i	−0.212989	+	0.615390i
$643$	−5.65319			−0.222940			−0.111470	−	0.993768i	$-0.535556\pi$
$643$	−5.65319			−0.222940			−0.111470	+	0.993768i	$0.535556\pi$
$644$	6.23450	+	11.0513i	0.245674	+	0.435482i
$645$	−37.8014			−1.48843
$646$	−4.18104	+	12.0803i	−0.164501	+	0.475293i
$647$	12.5495	+	24.3426i	0.493371	+	0.957006i	0.995727	+	0.0923454i	$0.0294364\pi$
$647$	12.5495	+	24.3426i	0.493371	+	0.957006i	−0.502356	+	0.864661i	$0.667533\pi$
$648$	0.786053	+	0.618159i	0.0308791	+	0.0242836i
$649$	29.0692	−	2.77577i	1.14107	−	0.108959i
$650$	−2.01947	+	0.290355i	−0.0792100	+	0.0113887i
$651$	−0.750784	−	1.02024i	−0.0294255	−	0.0399862i
$652$	−8.48910	+	5.45561i	−0.332459	+	0.213658i
$653$	14.1027	−	19.8045i	0.551881	−	0.775009i	−0.440561	−	0.897723i	$-0.645220\pi$
$653$	14.1027	−	19.8045i	0.551881	−	0.775009i	0.992442	+	0.122714i	$0.0391598\pi$
$654$	0.394440	−	1.62590i	0.0154238	−	0.0635778i
$655$	−28.5948	+	9.89676i	−1.11729	+	0.386699i
$656$	1.92930	−	10.0101i	0.0753263	−	0.390830i
$657$	−3.06530	−	10.4395i	−0.119589	−	0.407282i
$658$	1.54917	+	4.98665i	0.0603930	+	0.194400i
$659$	−18.1316	−	28.2134i	−0.706308	−	1.09904i	−0.990129	−	0.140159i	$-0.955238\pi$
$659$	−18.1316	−	28.2134i	−0.706308	−	1.09904i	0.283821	−	0.958877i	$-0.408398\pi$
$660$	5.17323	+	21.3243i	0.201368	+	0.830049i
$661$	−3.92024	−	1.56943i	−0.152480	−	0.0610437i	0.294167	−	0.955754i	$-0.404958\pi$
$661$	−3.92024	−	1.56943i	−0.152480	−	0.0610437i	−0.446647	+	0.894710i	$0.647382\pi$
$662$	7.75010	+	10.8835i	0.301216	+	0.422999i
$663$	−0.293803	+	0.117621i	−0.0114104	+	0.00456802i
$664$	5.84600	+	3.75699i	0.226869	+	0.145800i
$665$	68.7929	−	45.7435i	2.66767	−	1.77386i
$666$			8.22805i			0.318831i
$667$	−11.6336	+	31.0225i	−0.450454	+	1.20120i
$668$	13.8744	+	8.01038i	0.536816	+	0.309931i
$669$	−22.0552	+	4.25080i	−0.852704	+	0.164345i
$670$	−34.8096	−	1.65818i	−1.34481	−	0.0640613i
$671$	17.8989	+	2.57348i	0.690981	+	0.0993480i
$672$	−1.24892	−	2.33242i	−0.0481780	−	0.0899752i
$673$	−3.50471	−	24.3758i	−0.135097	−	0.939619i	−0.938769	−	0.344547i	$-0.888033\pi$
$673$	−3.50471	−	24.3758i	−0.135097	−	0.939619i	0.803672	−	0.595072i	$-0.202876\pi$
$674$	−3.36148	+	0.815487i	−0.129479	+	0.0314114i
$675$	−10.3240	+	0.491794i	−0.397372	+	0.0189292i
$676$	−12.9023	−	1.23202i	−0.496244	−	0.0473856i
$677$	−6.95486	−	6.63144i	−0.267297	−	0.254867i	0.544562	−	0.838720i	$-0.316696\pi$
$677$	−6.95486	−	6.63144i	−0.267297	−	0.254867i	−0.811859	+	0.583853i	$0.801544\pi$
$678$	1.62833	−	1.87919i	0.0625357	−	0.0721700i
$679$	−3.97075	+	12.0797i	−0.152383	+	0.463575i
$680$	−6.02410	+	1.76883i	−0.231014	+	0.0678317i
$681$	9.81074	+	6.98620i	0.375948	+	0.267712i
$682$	−0.127647	−	2.67965i	−0.00488787	−	0.102609i
$683$	27.5761	−	26.2938i	1.05517	−	1.00610i	0.0552006	−	0.998475i	$-0.482420\pi$
$683$	27.5761	−	26.2938i	1.05517	−	1.00610i	0.999971	−	0.00762868i	$-0.00242831\pi$
$684$	6.26758	−	4.92888i	0.239647	−	0.188460i
$685$	−57.7645	−	26.3801i	−2.20707	−	1.00793i
$686$	−0.0141559	+	18.5203i	−0.000540476	+	0.707107i
$687$	10.4007	−	16.1838i	0.396810	−	0.617449i
$688$	9.12195	+	3.15714i	0.347771	+	0.120365i
$689$	−0.673463	+	1.16647i	−0.0256569	+	0.0444390i
$690$	−18.1323	−	4.89304i	−0.690285	−	0.186275i
$691$	3.53125	−	2.03877i	0.134335	−	0.0775583i	−0.431326	−	0.902196i	$-0.641954\pi$
$691$	3.53125	−	2.03877i	0.134335	−	0.0775583i	0.565661	+	0.824638i	$0.308621\pi$
$692$	1.81393	−	1.57178i	0.0689553	−	0.0597501i
$693$	2.57803	−	14.5990i	0.0979311	−	0.554569i
$694$	−3.61748	+	25.1602i	−0.137318	+	0.955067i
$695$	2.71660	+	28.4495i	0.103046	+	1.07915i
$696$	2.56764	−	6.41366i	0.0973262	−	0.243109i
$697$	11.2786	+	11.8287i	0.427209	+	0.448044i
$698$	−10.5191	+	20.4042i	−0.398153	+	0.772309i
$699$	−7.03817	+	3.21423i	−0.266208	+	0.121573i
$700$	25.5425	+	9.76584i	0.965416	+	0.369114i
$701$	1.40617	+	1.21845i	0.0531104	+	0.0460204i	0.681012	−	0.732273i	$-0.261540\pi$
$701$	1.40617	+	1.21845i	0.0531104	+	0.0460204i	−0.627901	+	0.778293i	$0.716086\pi$
$702$	0.193829	+	0.0373574i	0.00731560	+	0.00140997i
$703$	63.7569	+	15.4672i	2.40464	+	0.583358i
$704$	0.532624	−	5.57789i	0.0200740	−	0.210225i
$705$	−6.86974	−	3.54160i	−0.258729	−	0.133384i
$706$	9.90626	−	33.7376i	0.372827	−	1.26973i
$707$	0.417778	+	26.7582i	0.0157122	+	1.00634i
$708$	2.16494	−	4.74055i	0.0813633	−	0.178161i
$709$	7.20156	+	17.9886i	0.270460	+	0.675577i	0.999965	−	0.00839879i	$-0.00267345\pi$
$709$	7.20156	+	17.9886i	0.270460	+	0.675577i	−0.729504	+	0.683976i	$0.760249\pi$
$710$	16.1444	−	8.32302i	0.605889	−	0.312358i
$711$	1.97253	+	10.2345i	0.0739757	+	0.383822i
$712$	−2.28513	−	3.95797i	−0.0856390	−	0.148331i
$713$	2.06354	+	1.00694i	0.0772802	+	0.0377101i
$714$	4.20751	+	0.538048i	0.157462	+	0.0201359i
$715$	2.83649	+	3.27348i	0.106079	+	0.122421i
$716$	−0.207545	+	4.35691i	−0.00775634	+	0.162826i
$717$	1.76995	−	2.25067i	0.0660999	−	0.0840529i
$718$	−7.15796	+	5.09716i	−0.267133	+	0.190224i
$719$	0.956741	+	1.21660i	0.0356804	+	0.0453713i	0.803566	−	0.595216i	$-0.202933\pi$
$719$	0.956741	+	1.21660i	0.0356804	+	0.0453713i	−0.767885	+	0.640587i	$0.778691\pi$
$720$	3.75746	+	1.10329i	0.140032	+	0.0411172i
$721$	−40.7952	−	3.25368i	−1.51929	−	0.121173i
$722$	−18.5177	−	40.5481i	−0.689157	−	1.50904i
$723$	−6.45521	+	6.77003i	−0.240072	+	0.251780i
$724$	−6.53538	−	18.8827i	−0.242885	−	0.701771i
$725$	23.3542	+	67.4775i	0.867353	+	2.50605i
$726$	14.0752	−	14.7617i	0.522381	−	0.547858i
$727$	−0.825116	−	1.80675i	−0.0306019	−	0.0670088i	0.893714	−	0.448638i	$-0.148091\pi$
$727$	−0.825116	−	1.80675i	−0.0306019	−	0.0670088i	−0.924316	+	0.381629i	$0.875363\pi$
$728$	−0.430098	−	0.296263i	−0.0159405	−	0.0109802i
$729$	0.959493	+	0.281733i	0.0355368	+	0.0104345i
$730$	−26.3384	−	33.4920i	−0.974827	−	1.23959i
$731$	−12.6062	+	8.97685i	−0.466258	+	0.332021i
$732$	1.99494	−	2.53677i	0.0737350	−	0.0937617i
$733$	−0.861544	+	18.0860i	−0.0318219	+	0.668023i	0.925456	+	0.378854i	$0.123682\pi$
$733$	−0.861544	+	18.0860i	−0.0318219	+	0.668023i	−0.957278	+	0.289169i	$0.906621\pi$
$734$	−11.2165	−	12.9445i	−0.414009	−	0.477791i
$735$	−19.5270	−	19.2392i	−0.720264	−	0.709649i
$736$	3.96689	+	2.69514i	0.146221	+	0.0993444i
$737$	24.9316	+	43.1828i	0.918367	+	1.59066i
$738$	−1.92930	−	10.0101i	−0.0710184	−	0.368478i
$739$	40.6199	−	20.9410i	1.49423	−	0.770328i	0.498879	−	0.866672i	$-0.333745\pi$
$739$	40.6199	−	20.9410i	1.49423	−	0.770328i	0.995348	+	0.0963440i	$0.0307149\pi$
$740$	11.9756	+	29.9137i	0.440233	+	1.09965i
$741$	0.653835	−	1.43170i	0.0240192	−	0.0525948i
$742$	15.4917	−	9.26958i	0.568719	−	0.340297i
$743$	13.5095	−	46.0091i	0.495615	−	1.68791i	−0.208663	−	0.977988i	$-0.566911\pi$
$743$	13.5095	−	46.0091i	0.495615	−	1.68791i	0.704279	−	0.709924i	$-0.251271\pi$
$744$	−0.425550	−	0.219386i	−0.0156014	−	0.00804309i
$745$	−0.0629071	+	0.658793i	−0.00230474	+	0.0241363i
$746$	−14.4404	−	3.50321i	−0.528702	−	0.128262i
$747$	6.82357	+	1.31514i	0.249661	+	0.0481183i
$748$	6.78918	+	5.88285i	0.248237	+	0.215098i
$749$	15.5903	−	40.7764i	0.569657	−	1.48994i
$750$	−19.0069	+	8.68018i	−0.694035	+	0.316955i
$751$	17.7959	−	34.5192i	0.649381	−	1.25962i	−0.302498	−	0.953150i	$-0.597820\pi$
$751$	17.7959	−	34.5192i	0.649381	−	1.25962i	0.951879	−	0.306474i	$-0.0991493\pi$
$752$	1.36196	+	1.42839i	0.0496657	+	0.0520879i
$753$	−5.91248	+	14.7687i	−0.215463	+	0.538200i
$754$	−0.129629	−	1.35754i	−0.00472082	−	0.0494387i
$755$	−4.47880	+	31.1507i	−0.163000	+	1.13369i
$756$	−2.02633	−	1.70117i	−0.0736969	−	0.0618710i
$757$	0.458500	−	0.397292i	0.0166645	−	0.0144398i	−0.646489	−	0.762924i	$-0.723763\pi$
$757$	0.458500	−	0.397292i	0.0166645	−	0.0144398i	0.663153	+	0.748484i	$0.269218\pi$
$758$	−32.1758	+	18.5767i	−1.16868	+	0.674737i
$759$	8.13681	+	25.6108i	0.295348	+	0.929613i
$760$	15.6124	−	27.0415i	0.566322	−	0.980898i
$761$	20.9246	+	7.24208i	0.758517	+	0.262525i	0.678831	−	0.734295i	$-0.262487\pi$
$761$	20.9246	+	7.24208i	0.758517	+	0.262525i	0.0796861	+	0.996820i	$0.474608\pi$
$762$	−0.864386	+	1.34501i	−0.0313134	+	0.0487246i
$763$	−1.18064	+	4.26616i	−0.0427419	+	0.154445i
$764$	−14.7661	−	6.74345i	−0.534219	−	0.243970i
$765$	−4.93517	+	3.88106i	−0.178431	+	0.140320i
$766$	13.5816	−	12.9500i	0.490722	−	0.467903i
$767$	−0.0489489	−	1.02756i	−0.00176744	−	0.0371032i
$768$	−0.814576	−	0.580057i	−0.0293935	−	0.0209310i
$769$	−43.9830	+	12.9146i	−1.58607	+	0.465712i	−0.951626	−	0.307259i	$-0.900588\pi$
$769$	−43.9830	+	12.9146i	−1.58607	+	0.465712i	−0.634442	+	0.772970i	$0.718770\pi$
$770$	−11.8756	−	56.8278i	−0.427969	−	2.04793i
$771$	−3.80374	+	4.38975i	−0.136988	+	0.158093i
$772$	−1.49323	−	1.42379i	−0.0537425	−	0.0512433i
$773$	−41.8515	−	3.99633i	−1.50529	−	0.143738i	−0.690433	−	0.723396i	$-0.742580\pi$
$773$	−41.8515	−	3.99633i	−1.50529	−	0.143738i	−0.814860	+	0.579658i	$0.803186\pi$
$774$	9.64192	−	0.459301i	0.346572	−	0.0165092i
$775$	4.80897	−	1.16664i	0.172743	−	0.0419071i
$776$	0.683968	+	4.75710i	0.0245530	+	0.170770i
$777$	0.696241	−	21.7582i	0.0249775	−	0.780573i
$778$	14.0110	+	2.01448i	0.502320	+	0.0722228i
$779$	−81.1925	−	3.86767i	−2.90902	−	0.138574i
$780$	0.759050	−	0.146295i	0.0271784	−	0.00523820i
$781$	−22.5071	−	12.9945i	−0.805369	−	0.464980i
$782$	−7.20883	+	2.67419i	−0.257787	+	0.0956289i
$783$		−	6.90853i		−	0.246891i
$784$	3.10527	+	6.27354i	0.110902	+	0.224055i
$785$	−3.34525	−	2.14986i	−0.119397	−	0.0767318i
$786$	7.17337	−	2.87178i	0.255865	−	0.102433i
$787$	29.0880	+	40.8483i	1.03687	+	1.45609i	0.883796	+	0.467872i	$0.154979\pi$
$787$	29.0880	+	40.8483i	1.03687	+	1.45609i	0.153078	+	0.988214i	$0.451081\pi$
$788$	4.88959	+	1.95750i	0.174184	+	0.0697329i
$789$	3.20349	+	13.2050i	0.114047	+	0.470109i
$790$	22.0672	+	34.3372i	0.785114	+	1.22166i
$791$	−4.46497	+	4.83155i	−0.158756	+	0.171790i
$792$	−1.57862	−	5.37629i	−0.0560939	−	0.191038i
$793$	0.120561	−	0.625529i	0.00428124	−	0.0222132i
$794$	−16.7564	+	5.79944i	−0.594662	+	0.205815i
$795$	−6.29979	+	25.9681i	−0.223430	+	0.920993i
$796$	−4.36662	+	6.13206i	−0.154771	+	0.217345i
$797$	−17.9746	+	11.5516i	−0.636695	+	0.409179i	−0.818783	−	0.574103i	$-0.805351\pi$
$797$	−17.9746	+	11.5516i	−0.636695	+	0.409179i	0.182088	+	0.983282i	$0.441714\pi$
$798$	−16.9910	+	12.5036i	−0.601476	+	0.442621i
$799$	−3.13200	+	0.450313i	−0.110802	+	0.0159309i
$800$	10.2889	−	0.982474i	0.363769	−	0.0347357i
$801$	−3.59247	−	2.82515i	−0.126934	−	0.0998219i
$802$	−12.9678	−	25.1541i	−0.457910	−	0.888221i
$803$	−19.9396	+	57.6116i	−0.703652	+	2.03307i
$804$	8.89895			0.313842
$805$	47.5350	+	14.4735i	1.67539	+	0.510123i
$806$	−0.0945077			−0.00332889
$807$	−1.46013	+	4.21876i	−0.0513989	+	0.148507i
$808$	4.63490	+	8.99046i	0.163055	+	0.316283i
$809$	28.6450	+	22.5267i	1.00711	+	0.791997i	0.978217	−	0.207586i	$-0.0665606\pi$
$809$	28.6450	+	22.5267i	1.00711	+	0.791997i	0.0288890	+	0.999583i	$0.490803\pi$
$810$	3.89835	−	0.372248i	0.136974	−	0.0130795i
$811$	−42.1757	+	6.06395i	−1.48099	+	0.212934i	−0.834931	−	0.550354i	$-0.814493\pi$
$811$	−42.1757	+	6.06395i	−1.48099	+	0.212934i	−0.646058	+	0.763288i	$0.723584\pi$
$812$	−7.33257	+	16.7430i	−0.257323	+	0.587564i
$813$	−20.8884	+	13.4241i	−0.732587	+	0.470805i
$814$	26.7429	−	37.5552i	0.937339	−	1.31631i
$815$	−9.31655	+	38.4033i	−0.326344	+	1.34521i
$816$	1.51506	−	0.524368i	0.0530377	−	0.0183565i
$817$	14.5661	−	75.5759i	0.509602	−	2.64407i
$818$	−3.71984	−	12.6686i	−0.130061	−	0.442948i
$819$	−0.509399	−	0.115189i	−0.0177999	−	0.00402504i
$820$	−21.5835	−	33.5845i	−0.753727	−	1.17282i
$821$	12.6524	+	52.1539i	0.441572	+	1.82019i	0.561593	+	0.827414i	$0.310189\pi$
$821$	12.6524	+	52.1539i	0.441572	+	1.82019i	−0.120020	+	0.992771i	$0.538296\pi$
$822$	15.0544	+	6.02686i	0.525082	+	0.210211i
$823$	20.1045	+	28.2328i	0.700797	+	0.984132i	0.999556	+	0.0298035i	$0.00948814\pi$
$823$	20.1045	+	28.2328i	0.700797	+	0.984132i	−0.298758	+	0.954329i	$0.596572\pi$
$824$	−14.3601	+	5.74891i	−0.500257	+	0.200273i
$825$	48.7202	+	31.3106i	1.69622	+	1.09009i
$826$	−6.12609	+	12.3527i	−0.213154	+	0.429806i
$827$		−	54.5629i		−	1.89734i	−0.316269	−	0.948669i	$-0.602430\pi$
$827$		−	54.5629i		−	1.89734i	0.316269	−	0.948669i	$-0.397570\pi$
$828$	4.68442	+	1.02774i	0.162795	+	0.0357165i
$829$	15.5154	+	8.95784i	0.538873	+	0.311119i	0.744622	−	0.667486i	$-0.232630\pi$
$829$	15.5154	+	8.95784i	0.538873	+	0.311119i	−0.205749	+	0.978605i	$0.565963\pi$
$830$	26.7217	−	5.15018i	0.927523	−	0.178765i
$831$	−13.9914	−	0.666493i	−0.485356	−	0.0231204i
$832$	−0.195387	−	0.0280924i	−0.00677382	−	0.000973928i
$833$	−11.0808	−	1.77884i	−0.383927	−	0.0616333i
$834$	−1.03859	−	7.22355i	−0.0359634	−	0.250131i
$835$	60.9702	−	14.7912i	2.10996	−	0.511871i
$836$	−44.6269	+	2.12584i	−1.54345	+	0.0735238i
$837$	−0.476604	−	0.0455102i	−0.0164739	−	0.00157306i
$838$	27.1108	+	25.8501i	0.936529	+	0.892978i
$839$	18.6851	−	21.5637i	0.645080	−	0.744462i	−0.335185	−	0.942152i	$-0.608799\pi$
$839$	18.6851	−	21.5637i	0.645080	−	0.744462i	0.980264	+	0.197691i	$0.0633442\pi$
$840$	−9.84285	−	3.23548i	−0.339611	−	0.111635i
$841$	−17.9691	+	5.27622i	−0.619626	+	0.181939i
$842$	−28.5482	−	20.3291i	−0.983835	−	0.700586i
$843$	−0.454183	−	9.53447i	−0.0156429	−	0.328385i
$844$	7.93048	−	7.56170i	0.272978	−	0.260284i
$845$	−39.8973	+	31.3756i	−1.37251	+	1.07935i
$846$	1.79528	+	0.819877i	0.0617230	+	0.0281880i
$847$	−38.4697	+	37.8448i	−1.32183	+	1.30036i
$848$	3.68905	−	5.74027i	0.126682	−	0.197122i
$849$	9.26954	+	3.20822i	0.318130	+	0.110106i
$850$	−8.28532	+	14.3506i	−0.284184	+	0.492221i
$851$	17.1790	+	35.5247i	0.588887	+	1.21777i
$852$	−4.01679	+	2.31910i	−0.137613	+	0.0794509i
$853$	−25.1859	+	21.8237i	−0.862349	+	0.747230i	−0.968998	−	0.247067i	$-0.920533\pi$
$853$	−25.1859	+	21.8237i	−0.862349	+	0.747230i	0.106649	+	0.994297i	$0.465988\pi$
$854$	−5.49007	+	6.53942i	−0.187866	+	0.223774i
$855$	4.44376	−	30.9070i	0.151973	−	1.05700i
$856$	−1.56843	−	16.4254i	−0.0536079	−	0.561408i
$857$	−3.80069	+	9.49366i	−0.129829	+	0.324297i	−0.979012	−	0.203801i	$-0.934670\pi$
$857$	−3.80069	+	9.49366i	−0.129829	+	0.324297i	0.849183	+	0.528098i	$0.177095\pi$
$858$	−0.763270	−	0.800495i	−0.0260576	−	0.0273284i
$859$	3.17247	−	6.15373i	0.108243	−	0.209963i	−0.828492	−	0.560000i	$-0.810801\pi$
$859$	3.17247	−	6.15373i	0.108243	−	0.209963i	0.936736	+	0.350038i	$0.113831\pi$
$860$	34.3854	−	15.7033i	1.17253	−	0.535477i
$861$	4.25479	+	26.6340i	0.145003	+	0.907686i
$862$	−2.92282	−	2.53264i	−0.0995516	−	0.0862619i
$863$	9.88621	+	1.90541i	0.336531	+	0.0648609i	0.354717	−	0.934974i	$-0.384577\pi$
$863$	9.88621	+	1.90541i	0.336531	+	0.0648609i	−0.0181866	+	0.999835i	$0.505789\pi$
$864$	−0.971812	−	0.235759i	−0.0330617	−	0.00802068i
$865$	0.893460	−	9.35674i	0.0303786	−	0.318139i
$866$	0.803764	+	0.414369i	0.0273130	+	0.0140808i
$867$	4.06530	−	13.8451i	0.138065	−	0.470205i
$868$	1.10676	+	0.616153i	0.0375658	+	0.0209136i
$869$	24.2610	−	53.1242i	0.822998	−	1.80211i
$870$	−10.0551	−	25.1164i	−0.340900	−	0.851527i
$871$	1.56134	−	0.804928i	0.0529041	−	0.0272740i
$872$	0.316630	+	1.64283i	0.0107224	+	0.0556332i
$873$	2.40301	+	4.16214i	0.0813296	+	0.140867i
$874$	16.7695	−	34.3662i	0.567238	−	1.16246i
$875$	50.9964	−	21.3455i	1.72399	−	0.721610i
$876$	7.12501	+	8.22270i	0.240732	+	0.277819i
$877$	−1.28229	+	26.9186i	−0.0432999	+	0.908977i	0.867831	+	0.496860i	$0.165514\pi$
$877$	−1.28229	+	26.9186i	−0.0432999	+	0.908977i	−0.911131	+	0.412117i	$0.864789\pi$
$878$	10.6091	−	13.4905i	0.358039	−	0.455283i
$879$	13.6518	−	9.72138i	0.460463	−	0.327894i
$880$	−13.5642	−	17.2483i	−0.457248	−	0.581439i
$881$	34.7638	+	10.2076i	1.17122	+	0.343901i	0.808783	−	0.588107i	$-0.200126\pi$
$881$	34.7638	+	10.2076i	1.17122	+	0.343901i	0.362437	+	0.932008i	$0.381945\pi$
$882$	5.21447	+	4.67004i	0.175580	+	0.157248i
$883$	8.86727	+	19.4166i	0.298407	+	0.653421i	0.998139	−	0.0609851i	$-0.0194242\pi$
$883$	8.86727	+	19.4166i	0.298407	+	0.653421i	−0.699731	+	0.714406i	$0.746697\pi$
$884$	0.218391	−	0.229042i	0.00734529	−	0.00770352i
$885$	−6.67503	−	19.2862i	−0.224379	−	0.648300i
$886$	−0.763524	−	2.20606i	−0.0256511	−	0.0741139i
$887$	−18.8432	+	19.7621i	−0.632691	+	0.663548i	−0.959554	−	0.281524i	$-0.909160\pi$
$887$	−18.8432	+	19.7621i	−0.632691	+	0.663548i	0.326863	+	0.945072i	$0.394009\pi$
$888$	−3.41806	−	7.48450i	−0.114702	−	0.251163i
$889$	2.39959	−	3.48360i	0.0804797	−	0.116836i
$890$	−17.1726	−	5.04233i	−0.575627	−	0.169019i
$891$	−3.46371	−	4.40446i	−0.116039	−	0.147555i
$892$	18.2963	−	13.0287i	0.612605	−	0.436234i
$893$	9.72780	−	12.3699i	0.325529	−	0.413943i
$894$	0.00804099	−	0.168801i	0.000268931	−	0.00564556i
$895$	11.1859	+	12.9093i	0.373905	+	0.431509i
$896$	2.10498	+	1.60283i	0.0703224	+	0.0535468i
$897$	0.914854	−	0.243395i	0.0305461	−	0.00812672i
$898$	−4.33438	−	7.50737i	−0.144640	−	0.250524i
$899$	0.625970	+	3.24784i	0.0208773	+	0.108321i
$900$	9.18677	−	4.73611i	0.306226	−	0.157870i
$901$	4.06586	+	10.1560i	0.135453	+	0.338346i
$902$	−23.7292	+	51.9597i	−0.790096	+	1.73007i
$903$	−25.5359	+	0.398695i	−0.849782	+	0.0132678i
$904$	−0.700537	+	2.38581i	−0.0232995	+	0.0793508i
$905$	−69.5515	−	35.8563i	−2.31197	−	1.19190i
$906$	0.763904	−	7.99997i	0.0253790	−	0.265781i
$907$	−34.8255	−	8.44858i	−1.15636	−	0.280531i	−0.388688	−	0.921370i	$-0.627071\pi$
$907$	−34.8255	−	8.44858i	−1.15636	−	0.280531i	−0.767675	+	0.640839i	$0.778587\pi$
$908$	−11.8263	−	2.27934i	−0.392471	−	0.0756425i
$909$	7.64431	+	6.62383i	0.253546	+	0.219699i
$910$	−2.01961	+	0.322633i	−0.0669494	+	0.0106952i
$911$	16.6134	−	7.58710i	0.550427	−	0.251372i	−0.120732	−	0.992685i	$-0.538524\pi$
$911$	16.6134	−	7.58710i	0.550427	−	0.251372i	0.671159	+	0.741313i	$0.265797\pi$
$912$	−3.65366	+	7.08711i	−0.120985	+	0.234678i
$913$	−26.8702	−	28.1807i	−0.889275	−	0.932645i
$914$	−11.2372	+	28.0693i	−0.371695	+	0.928449i
$915$	−1.20133	−	12.5809i	−0.0397146	−	0.415911i
$916$	−2.73781	+	19.0419i	−0.0904596	+	0.629161i
$917$	−19.2122	+	6.98714i	−0.634444	+	0.230736i
$918$	1.21165	−	1.04990i	0.0399903	−	0.0346518i
$919$	−4.38098	+	2.52936i	−0.144515	+	0.0834359i	−0.570514	−	0.821288i	$-0.693256\pi$
$919$	−4.38098	+	2.52936i	−0.144515	+	0.0834359i	0.425999	+	0.904724i	$0.359923\pi$
$920$	18.5264	−	3.08156i	0.610796	−	0.101596i
$921$	−13.7045	+	23.7369i	−0.451580	+	0.782159i
$922$	−19.3390	−	6.69328i	−0.636895	−	0.220432i
$923$	−0.494989	+	0.770218i	−0.0162928	+	0.0253520i
$924$	3.71957	+	14.3506i	0.122365	+	0.472101i
$925$	77.3578	+	35.3281i	2.54351	+	1.16158i
$926$	−11.7889	+	9.27091i	−0.387408	+	0.304661i
$927$	−11.1948	+	10.6742i	−0.367685	+	0.350587i
$928$	0.328721	+	6.90070i	0.0107908	+	0.226527i
$929$	−40.9869	−	29.1867i	−1.34474	−	0.957583i	−0.999820	−	0.0189500i	$-0.993968\pi$
$929$	−40.9869	−	29.1867i	−1.34474	−	0.957583i	−0.344917	−	0.938633i	$-0.612093\pi$
$930$	−1.79897	+	0.528224i	−0.0589904	+	0.0173212i
$931$	45.9891	−	31.6266i	1.50723	−	1.03652i
$932$	5.06691	−	5.84753i	0.165972	−	0.191542i
$933$	−15.5227	−	14.8008i	−0.508189	−	0.484557i
$934$	−19.4962	−	1.86166i	−0.637935	−	0.0609154i
$935$	35.1398	−	1.67391i	1.14919	−	0.0547429i
$936$	−0.191832	+	0.0465379i	−0.00627022	+	0.00152114i
$937$	5.83355	+	40.5732i	0.190574	+	1.32547i	0.830494	+	0.557028i	$0.188058\pi$
$937$	5.83355	+	40.5732i	0.190574	+	1.32547i	−0.639920	+	0.768441i	$0.721033\pi$
$938$	−23.5324	−	0.753011i	−0.768359	−	0.0245867i
$939$	−9.74964	−	1.40179i	−0.318167	−	0.0457456i
$940$	7.72017	+	0.367757i	0.251804	+	0.0119949i
$941$	0.186132	−	0.0358740i	0.00606773	−	0.00116946i	−0.186216	−	0.982509i	$-0.559623\pi$
$941$	0.186132	−	0.0358740i	0.00606773	−	0.00116946i	0.192284	+	0.981339i	$0.438410\pi$
$942$	0.879386	+	0.507714i	0.0286519	+	0.0165422i
$943$	−29.2294	−	39.1908i	−0.951842	−	1.27623i
$944$			5.21150i			0.169620i
$945$	−10.3403	+	0.654500i	−0.336370	+	0.0212909i
$946$	−45.5013	−	29.2419i	−1.47937	−	0.950736i
$947$	25.3061	−	10.1310i	0.822338	−	0.329214i	0.0779460	−	0.996958i	$-0.475164\pi$
$947$	25.3061	−	10.1310i	0.822338	−	0.329214i	0.744392	+	0.667743i	$0.232740\pi$
$948$	−6.04583	−	8.49018i	−0.196359	−	0.275748i
$949$	1.99386	+	0.798222i	0.0647235	+	0.0259114i
$950$	−19.4293	−	80.0887i	−0.630370	−	2.59842i
$951$	−15.1568	−	23.5844i	−0.491492	−	0.764777i
$952$	−4.05080	+	1.25844i	−0.131287	+	0.0407861i
$953$	14.4226	+	49.1190i	0.467195	+	1.59112i	0.769985	+	0.638062i	$0.220264\pi$
$953$	14.4226	+	49.1190i	0.467195	+	1.59112i	−0.302790	+	0.953057i	$0.597918\pi$
$954$	1.29135	−	6.70016i	0.0418090	−	0.216926i
$955$	−60.0737	+	20.7917i	−1.94394	+	0.672804i
$956$	−0.675039	+	2.78255i	−0.0218323	+	0.0899940i
$957$	−22.4542	+	31.5325i	−0.725841	+	1.01930i
$958$	9.19882	−	5.91172i	0.297200	−	0.190999i
$959$	−39.2998	−	17.2113i	−1.26906	−	0.555782i
$960$	−3.87623	+	0.557317i	−0.125105	+	0.0179873i
$961$	−30.6314	+	2.92495i	−0.988111	+	0.0943532i
$962$	−1.27670	−	1.00400i	−0.0411623	−	0.0323704i
$963$	−7.56077	−	14.6659i	−0.243643	−	0.472601i
$964$	3.05949	−	8.83983i	0.0985397	−	0.284712i
$965$	−8.07978			−0.260097
$966$	−12.3005	−	3.11415i	−0.395762	−	0.100196i
$967$	−48.2767			−1.55247			−0.776237	−	0.630441i	$-0.782874\pi$
$967$	−48.2767			−1.55247			−0.776237	+	0.630441i	$0.782874\pi$
$968$	−6.67107	+	19.2748i	−0.214416	+	0.619515i
$969$	−5.85769	−	11.3623i	−0.188176	−	0.365010i
$970$	14.7941	+	11.6342i	0.475011	+	0.373553i
$971$	−2.81137	+	0.268453i	−0.0902211	+	0.00861507i	−0.140069	−	0.990142i	$-0.544732\pi$
$971$	−2.81137	+	0.268453i	−0.0902211	+	0.00861507i	0.0498479	+	0.998757i	$0.484126\pi$
$972$	−0.989821	+	0.142315i	−0.0317485	+	0.00456475i
$973$	2.13520	+	19.1898i	0.0684514	+	0.615197i
$974$	−30.9676	+	19.9017i	−0.992267	+	0.637691i
$975$	1.18345	−	1.66192i	0.0379008	−	0.0532242i
$976$	−0.760847	+	3.13625i	−0.0243541	+	0.100389i
$977$	−24.3005	+	8.41050i	−0.777443	+	0.269076i	−0.686837	−	0.726811i	$-0.741001\pi$
$977$	−24.3005	+	8.41050i	−0.777443	+	0.269076i	−0.0906056	+	0.995887i	$0.528880\pi$
$978$	1.90974	−	9.90865i	0.0610666	−	0.316844i
$979$	7.21473	+	24.5711i	0.230584	+	0.785296i
$980$	25.7546	+	9.38879i	0.822702	+	0.299914i
$981$	0.904527	+	1.40747i	0.0288793	+	0.0449371i
$982$	5.39442	+	22.2361i	0.172143	+	0.709583i
$983$	1.91078	+	0.764962i	0.0609445	+	0.0243985i	0.401934	−	0.915668i	$-0.368338\pi$
$983$	1.91078	+	0.764962i	0.0609445	+	0.0243985i	−0.340990	+	0.940067i	$0.610762\pi$
$984$	5.91331	+	8.30408i	0.188509	+	0.264724i
$985$	19.1480	−	7.66572i	0.610108	−	0.244250i
$986$	−9.31774	−	5.98814i	−0.296737	−	0.190701i
$987$	−4.67806	−	2.32000i	−0.148904	−	0.0738463i
$988$			1.57393i			0.0500735i
$989$	40.6701	−	22.1139i	1.29323	−	0.703182i
$990$	−19.0031	−	10.9714i	−0.603958	−	0.348695i
$991$	−36.8199	+	7.09645i	−1.16962	+	0.225426i	−0.736837	−	0.676071i	$-0.763681\pi$
$991$	−36.8199	+	7.09645i	−1.16962	+	0.225426i	−0.432785	+	0.901497i	$0.642469\pi$
$992$	0.478230	+	0.0227809i	0.0151838	+	0.000723294i
$993$	−13.2249	−	1.90146i	−0.419680	−	0.0603409i
$994$	10.8182	−	5.79272i	0.343133	−	0.183734i
$995$	4.19544	+	29.1799i	0.133004	+	0.925066i
$996$	−6.75326	+	1.63832i	−0.213985	+	0.0519123i
$997$	1.80127	−	0.0858050i	0.0570467	−	0.00271747i	−0.0190392	−	0.999819i	$-0.506061\pi$
$997$	1.80127	−	0.0858050i	0.0570467	−	0.00271747i	0.0760859	+	0.997101i	$0.475758\pi$
$998$	37.3654	+	3.56796i	1.18278	+	0.112942i
$999$	−5.95492	−	5.67801i	−0.188405	−	0.179644i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.be.a.493.9	yes	320
7.5	odd	6	inner	966.2.be.a.355.9	yes	320
23.7	odd	22	inner	966.2.be.a.283.9	yes	320
161.145	even	66	inner	966.2.be.a.145.9	✓	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.be.a.145.9	✓	320	161.145	even	66	inner
966.2.be.a.283.9	yes	320	23.7	odd	22	inner
966.2.be.a.355.9	yes	320	7.5	odd	6	inner
966.2.be.a.493.9	yes	320	1.1	even	1	trivial

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.be (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.327068 - 0.945001i) q^{2} +(0.458227 + 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-3.89835 + 0.372248i) q^{5} +(0.989821 - 0.142315i) q^{6} +(-2.62952 + 0.292580i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +O(q^{10})\)	\(q+(0.327068 - 0.945001i) q^{2} +(0.458227 + 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-3.89835 + 0.372248i) q^{5} +(0.989821 - 0.142315i) q^{6} +(-2.62952 + 0.292580i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +(-0.923252 + 3.80570i) q^{10} +(5.29509 - 1.83265i) q^{11} +(0.189251 - 0.981929i) q^{12} +(-0.0556129 - 0.189400i) q^{13} +(-0.583544 + 2.58060i) q^{14} +(-2.11720 - 3.29442i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-1.48839 - 0.595863i) q^{17} +(0.580057 + 0.814576i) q^{18} +(7.40232 - 2.96344i) q^{19} +(3.29442 + 2.11720i) q^{20} +(-1.46497 - 2.20315i) q^{21} -5.60326i q^{22} +(4.20511 + 2.30586i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(10.1490 - 1.95605i) q^{25} +(-0.197172 - 0.00939248i) q^{26} +(-0.989821 - 0.142315i) q^{27} +(2.24781 + 1.39548i) q^{28} +(0.983186 + 6.83821i) q^{29} +(-3.80570 + 0.923252i) q^{30} +(0.478230 - 0.0227809i) q^{31} +(0.995472 + 0.0950560i) q^{32} +(4.05527 + 3.86670i) q^{33} +(-1.04990 + 1.21165i) q^{34} +(10.1419 - 2.11942i) q^{35} +(0.959493 - 0.281733i) q^{36} +(6.70237 + 4.77274i) q^{37} +(-0.379393 - 7.96445i) q^{38} +(0.142862 - 0.136219i) q^{39} +(3.07825 - 2.42076i) q^{40} +(-9.27312 - 4.23489i) q^{41} +(-2.56112 + 0.663823i) q^{42} +(5.21872 - 8.12049i) q^{43} +(-5.29509 - 1.83265i) q^{44} +(1.95804 - 3.39143i) q^{45} +(3.55440 - 3.21966i) q^{46} +(1.70922 - 0.986817i) q^{47} +(-0.755750 + 0.654861i) q^{48} +(6.82879 - 1.53869i) q^{49} +(1.47093 - 10.2305i) q^{50} +(-0.152397 - 1.59598i) q^{51} +(-0.0733647 + 0.183256i) q^{52} +(-4.70873 - 4.93838i) q^{53} +(-0.458227 + 0.888835i) q^{54} +(-19.9599 + 9.11540i) q^{55} +(2.05392 - 1.66776i) q^{56} +(6.02595 + 5.22152i) q^{57} +(6.78368 + 1.30745i) q^{58} +(5.06460 + 1.22866i) q^{59} +(-0.372248 + 3.89835i) q^{60} +(2.86847 + 1.47880i) q^{61} +(0.134886 - 0.459379i) q^{62} +(1.28694 - 2.31166i) q^{63} +(0.415415 - 0.909632i) q^{64} +(0.287302 + 0.717647i) q^{65} +(4.98038 - 2.56756i) q^{66} +(1.68414 + 8.73813i) q^{67} +(0.801619 + 1.38844i) q^{68} +(-0.122639 + 4.79426i) q^{69} +(1.31424 - 10.2773i) q^{70} +(-3.03737 - 3.50531i) q^{71} +(0.0475819 - 0.998867i) q^{72} +(-6.72569 + 8.55241i) q^{73} +(6.70237 - 4.77274i) q^{74} +(6.38913 + 8.12444i) q^{75} +(-7.65050 - 2.24639i) q^{76} +(-13.3874 + 6.36823i) q^{77} +(-0.0820013 - 0.179558i) q^{78} +(7.19257 - 7.54335i) q^{79} +(-1.28083 - 3.70071i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(-7.03492 + 7.37801i) q^{82} +(-2.88678 - 6.32117i) q^{83} +(-0.210348 + 2.63738i) q^{84} +(6.02410 + 1.76883i) q^{85} +(-5.96700 - 7.58765i) q^{86} +(-5.62752 + 4.00734i) q^{87} +(-3.46371 + 4.40446i) q^{88} +(-0.217462 + 4.56509i) q^{89} +(-2.56449 - 2.95958i) q^{90} +(0.201650 + 0.481761i) q^{91} +(-1.88005 - 4.41196i) q^{92} +(0.239386 + 0.414629i) q^{93} +(-0.373513 - 1.93797i) q^{94} +(-27.7537 + 14.3080i) q^{95} +(0.371662 + 0.928368i) q^{96} +(1.99649 - 4.37171i) q^{97} +(0.779412 - 6.95647i) q^{98} +(-1.57862 + 5.37629i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9}+O(q^{10}) \) 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9	\( 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9} - 22 q^{14} + 16 q^{16} + 66 q^{17} + 16 q^{18} + 40 q^{23} - 48 q^{25} + 12 q^{26} + 44 q^{28} - 24 q^{29} + 24 q^{31} - 16 q^{32} + 98 q^{35} + 32 q^{36} - 22 q^{37} - 66 q^{38} - 8 q^{39} - 88 q^{43} + 4 q^{46} - 144 q^{47} - 24 q^{49} + 80 q^{50} - 22 q^{51} + 12 q^{52} + 44 q^{53} + 44 q^{57} + 10 q^{58} + 12 q^{59} - 32 q^{64} + 108 q^{70} - 16 q^{71} + 16 q^{72} - 180 q^{73} - 22 q^{74} - 12 q^{75} + 18 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 36 q^{82} + 22 q^{84} + 68 q^{85} - 22 q^{86} + 48 q^{87} + 22 q^{88} + 8 q^{92} + 8 q^{93} - 12 q^{94} + 66 q^{95} - 90 q^{98}+O(q^{100}) \) 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9 - 22 * q^14 + 16 * q^16 + 66 * q^17 + 16 * q^18 + 40 * q^23 - 48 * q^25 + 12 * q^26 + 44 * q^28 - 24 * q^29 + 24 * q^31 - 16 * q^32 + 98 * q^35 + 32 * q^36 - 22 * q^37 - 66 * q^38 - 8 * q^39 - 88 * q^43 + 4 * q^46 - 144 * q^47 - 24 * q^49 + 80 * q^50 - 22 * q^51 + 12 * q^52 + 44 * q^53 + 44 * q^57 + 10 * q^58 + 12 * q^59 - 32 * q^64 + 108 * q^70 - 16 * q^71 + 16 * q^72 - 180 * q^73 - 22 * q^74 - 12 * q^75 + 18 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 36 * q^82 + 22 * q^84 + 68 * q^85 - 22 * q^86 + 48 * q^87 + 22 * q^88 + 8 * q^92 + 8 * q^93 - 12 * q^94 + 66 * q^95 - 90 * q^98

Introduction

L-functions

Modular forms

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