LMFDB - Embedded newform 966.2.be.b.145.13

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			145.13
Character	$\chi$	$=$	966.145
Dual form			966.2.be.b.493.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.327068 - 0.945001i) q^{2} +(0.458227 - 0.888835i) q^{3} +(-0.786053 + 0.618159i) q^{4} +(0.301743 + 0.0288129i) q^{5} +(-0.989821 - 0.142315i) q^{6} +(-0.249988 - 2.63391i) q^{7} +(0.841254 + 0.540641i) q^{8} +(-0.580057 - 0.814576i) q^{9} +O(q^{10})$	\(q+(-0.327068 - 0.945001i) q^{2} +(0.458227 - 0.888835i) q^{3} +(-0.786053 + 0.618159i) q^{4} +(0.301743 + 0.0288129i) q^{5} +(-0.989821 - 0.142315i) q^{6} +(-0.249988 - 2.63391i) q^{7} +(0.841254 + 0.540641i) q^{8} +(-0.580057 - 0.814576i) q^{9} +(-0.0714621 - 0.294571i) q^{10} +(3.73249 + 1.29183i) q^{11} +(0.189251 + 0.981929i) q^{12} +(0.539289 - 1.83665i) q^{13} +(-2.40729 + 1.09771i) q^{14} +(0.163876 - 0.254997i) q^{15} +(0.235759 - 0.971812i) q^{16} +(3.12522 - 1.25115i) q^{17} +(-0.580057 + 0.814576i) q^{18} +(7.95134 + 3.18324i) q^{19} +(-0.254997 + 0.163876i) q^{20} +(-2.45567 - 0.984732i) q^{21} -3.94973i q^{22} +(-3.17679 - 3.59277i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-4.81943 - 0.928868i) q^{25} +(-1.91202 + 0.0910808i) q^{26} +(-0.989821 + 0.142315i) q^{27} +(1.82468 + 1.91586i) q^{28} +(0.182480 - 1.26918i) q^{29} +(-0.294571 - 0.0714621i) q^{30} +(-9.93351 - 0.473191i) q^{31} +(-0.995472 + 0.0950560i) q^{32} +(2.85855 - 2.72562i) q^{33} +(-2.20450 - 2.54412i) q^{34} +(0.000458893 - 0.801967i) q^{35} +(0.959493 + 0.281733i) q^{36} +(3.33974 - 2.37822i) q^{37} +(0.407532 - 8.55516i) q^{38} +(-1.38536 - 1.32094i) q^{39} +(0.238265 + 0.187373i) q^{40} +(2.25880 - 1.03156i) q^{41} +(-0.127402 + 2.64268i) q^{42} +(2.60535 + 4.05400i) q^{43} +(-3.73249 + 1.29183i) q^{44} +(-0.151558 - 0.262505i) q^{45} +(-2.35615 + 4.17715i) q^{46} +(-9.73099 - 5.61819i) q^{47} +(-0.755750 - 0.654861i) q^{48} +(-6.87501 + 1.31689i) q^{49} +(0.698498 + 4.85816i) q^{50} +(0.319993 - 3.35111i) q^{51} +(0.711432 + 1.77707i) q^{52} +(7.27378 - 7.62852i) q^{53} +(0.458227 + 0.888835i) q^{54} +(1.08903 + 0.497344i) q^{55} +(1.21370 - 2.35094i) q^{56} +(6.47289 - 5.60879i) q^{57} +(-1.25906 + 0.242663i) q^{58} +(7.18093 - 1.74207i) q^{59} +(0.0288129 + 0.301743i) q^{60} +(-5.36778 + 2.76728i) q^{61} +(2.80177 + 9.54194i) q^{62} +(-2.00052 + 1.73145i) q^{63} +(0.415415 + 0.909632i) q^{64} +(0.215646 - 0.538657i) q^{65} +(-3.51066 - 1.80987i) q^{66} +(0.294967 - 1.53044i) q^{67} +(-1.68318 + 2.91535i) q^{68} +(-4.64907 + 1.17734i) q^{69} +(-0.758010 + 0.261864i) q^{70} +(4.04986 - 4.67379i) q^{71} +(-0.0475819 - 0.998867i) q^{72} +(0.581773 + 0.739784i) q^{73} +(-3.33974 - 2.37822i) q^{74} +(-3.03400 + 3.85804i) q^{75} +(-8.21792 + 2.41300i) q^{76} +(2.46949 - 10.1540i) q^{77} +(-0.795183 + 1.74121i) q^{78} +(-6.89580 - 7.23211i) q^{79} +(0.0991392 - 0.286444i) q^{80} +(-0.327068 + 0.945001i) q^{81} +(-1.71360 - 1.79718i) q^{82} +(4.53632 - 9.93315i) q^{83} +(2.53901 - 0.743942i) q^{84} +(0.979061 - 0.287478i) q^{85} +(2.97891 - 3.78799i) q^{86} +(-1.04447 - 0.743766i) q^{87} +(2.44156 + 3.10469i) q^{88} +(-0.299855 - 6.29474i) q^{89} +(-0.198498 + 0.229079i) q^{90} +(-4.97240 - 0.961302i) q^{91} +(4.71803 + 0.860349i) q^{92} +(-4.97239 + 8.61243i) q^{93} +(-2.12650 + 11.0333i) q^{94} +(2.30754 + 1.18962i) q^{95} +(-0.371662 + 0.928368i) q^{96} +(7.30259 + 15.9904i) q^{97} +(3.49306 + 6.06618i) q^{98} +(-1.11277 - 3.78973i) 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} + 36 q^{23} + 24 q^{25} + 12 q^{26} + 44 q^{28} + 8 q^{29} - 48 q^{31} + 16 q^{32} - 46 q^{35} + 32 q^{36} - 22 q^{37} + 66 q^{38} + 8 q^{39} + 176 q^{43} - 8 q^{46} + 120 q^{47} - 24 q^{49} - 48 q^{50} - 22 q^{51} - 12 q^{52} - 44 q^{53} + 44 q^{57} + 18 q^{58} + 12 q^{59} - 32 q^{64} - 108 q^{70} - 48 q^{71} - 16 q^{72} + 252 q^{73} + 22 q^{74} - 36 q^{75} - 42 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 12 q^{82} - 22 q^{84} - 76 q^{85} + 22 q^{86} + 24 q^{87} - 22 q^{88} + 16 q^{92} + 12 q^{94} + 26 q^{95} + 2 q^{98} + 88 q^{99}+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 + 36 * q^23 + 24 * q^25 + 12 * q^26 + 44 * q^28 + 8 * q^29 - 48 * q^31 + 16 * q^32 - 46 * q^35 + 32 * q^36 - 22 * q^37 + 66 * q^38 + 8 * q^39 + 176 * q^43 - 8 * q^46 + 120 * q^47 - 24 * q^49 - 48 * q^50 - 22 * q^51 - 12 * q^52 - 44 * q^53 + 44 * q^57 + 18 * q^58 + 12 * q^59 - 32 * q^64 - 108 * q^70 - 48 * q^71 - 16 * q^72 + 252 * q^73 + 22 * q^74 - 36 * q^75 - 42 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 12 * q^82 - 22 * q^84 - 76 * q^85 + 22 * q^86 + 24 * q^87 - 22 * q^88 + 16 * q^92 + 12 * q^94 + 26 * q^95 + 2 * q^98 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{22}\right)$

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
$5$	0.301743	+	0.0288129i	0.134943	+	0.0128855i	0.162309	−	0.986740i	$-0.448106\pi$
$5$	0.301743	+	0.0288129i	0.134943	+	0.0128855i	−0.0273658	+	0.999625i	$0.508712\pi$
$6$	−0.989821	−	0.142315i	−0.404093	−	0.0580998i
$7$	−0.249988	−	2.63391i	−0.0944864	−	0.995526i
$7$	−0.249988	−	2.63391i	−0.0944864	−	0.995526i
$8$	0.841254	+	0.540641i	0.297428	+	0.191145i
$9$	−0.580057	−	0.814576i	−0.193352	−	0.271525i
$10$	−0.0714621	−	0.294571i	−0.0225983	−	0.0931515i
$11$	3.73249	+	1.29183i	1.12539	+	0.389501i	0.825460	−	0.564461i	$-0.190916\pi$
$11$	3.73249	+	1.29183i	1.12539	+	0.389501i	0.299929	+	0.953961i	$0.403037\pi$
$12$	0.189251	+	0.981929i	0.0546321	+	0.283458i
$13$	0.539289	−	1.83665i	0.149572	−	0.509395i	−0.850285	−	0.526323i	$-0.823570\pi$
$13$	0.539289	−	1.83665i	0.149572	−	0.509395i	0.999857	+	0.0169276i	$0.00538847\pi$
$14$	−2.40729	+	1.09771i	−0.643375	+	0.293375i
$15$	0.163876	−	0.254997i	0.0423127	−	0.0658399i
$16$	0.235759	−	0.971812i	0.0589397	−	0.242953i
$17$	3.12522	−	1.25115i	0.757977	−	0.303448i	0.0397057	−	0.999211i	$-0.487358\pi$
$17$	3.12522	−	1.25115i	0.757977	−	0.303448i	0.718271	+	0.695763i	$0.244934\pi$
$18$	−0.580057	+	0.814576i	−0.136721	+	0.191997i
$19$	7.95134	+	3.18324i	1.82416	+	0.730285i	0.981393	+	0.192011i	$0.0615008\pi$
$19$	7.95134	+	3.18324i	1.82416	+	0.730285i	0.842770	+	0.538274i	$0.180923\pi$
$20$	−0.254997	+	0.163876i	−0.0570190	+	0.0366439i
$21$	−2.45567	−	0.984732i	−0.535871	−	0.214886i
$22$		−	3.94973i		−	0.842084i
$23$	−3.17679	−	3.59277i	−0.662406	−	0.749145i
$23$	−3.17679	−	3.59277i	−0.662406	−	0.749145i
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	−4.81943	−	0.928868i	−0.963885	−	0.185774i
$26$	−1.91202	+	0.0910808i	−0.374978	+	0.0178624i
$27$	−0.989821	+	0.142315i	−0.190491	+	0.0273885i
$28$	1.82468	+	1.91586i	0.344832	+	0.362064i
$29$	0.182480	−	1.26918i	0.0338857	−	0.235680i	−0.965839	−	0.259143i	$-0.916560\pi$
$29$	0.182480	−	1.26918i	0.0338857	−	0.235680i	0.999725	+	0.0234625i	$0.00746903\pi$
$30$	−0.294571	−	0.0714621i	−0.0537810	−	0.0130471i
$31$	−9.93351	−	0.473191i	−1.78411	−	0.0849877i	−0.870647	−	0.491908i	$-0.836300\pi$
$31$	−9.93351	−	0.473191i	−1.78411	−	0.0849877i	−0.913464	+	0.406920i	$0.866603\pi$
$32$	−0.995472	+	0.0950560i	−0.175976	+	0.0168037i
$33$	2.85855	−	2.72562i	0.497610	−	0.474470i
$34$	−2.20450	−	2.54412i	−0.378068	−	0.436314i
$35$	0.000458893	−	0.801967i	7.75670e−5	−	0.135557i
$36$	0.959493	+	0.281733i	0.159915	+	0.0469554i
$37$	3.33974	−	2.37822i	0.549050	−	0.390977i	−0.271598	−	0.962411i	$-0.587552\pi$
$37$	3.33974	−	2.37822i	0.549050	−	0.390977i	0.820648	+	0.571434i	$0.193613\pi$
$38$	0.407532	−	8.55516i	0.0661105	−	1.38783i
$39$	−1.38536	−	1.32094i	−0.221836	−	0.211520i
$40$	0.238265	+	0.187373i	0.0376729	+	0.0296263i
$41$	2.25880	−	1.03156i	0.352765	−	0.161102i	−0.231148	−	0.972919i	$-0.574248\pi$
$41$	2.25880	−	1.03156i	0.352765	−	0.161102i	0.583913	+	0.811816i	$0.301521\pi$
$42$	−0.127402	+	2.64268i	−0.0196586	+	0.407775i
$43$	2.60535	+	4.05400i	0.397312	+	0.618230i	0.981060	−	0.193705i	$-0.0620506\pi$
$43$	2.60535	+	4.05400i	0.397312	+	0.618230i	−0.583747	+	0.811935i	$0.698414\pi$
$44$	−3.73249	+	1.29183i	−0.562695	+	0.194750i
$45$	−0.151558	−	0.262505i	−0.0225929	−	0.0391320i
$46$	−2.35615	+	4.17715i	−0.347395	+	0.615887i
$47$	−9.73099	−	5.61819i	−1.41941	−	0.819497i	−0.423163	−	0.906054i	$-0.639080\pi$
$47$	−9.73099	−	5.61819i	−1.41941	−	0.819497i	−0.996247	+	0.0865567i	$0.972414\pi$
$48$	−0.755750	−	0.654861i	−0.109083	−	0.0945210i
$49$	−6.87501	+	1.31689i	−0.982145	+	0.188127i
$50$	0.698498	+	4.85816i	0.0987826	+	0.687048i
$51$	0.319993	−	3.35111i	0.0448079	−	0.469250i
$52$	0.711432	+	1.77707i	0.0986579	+	0.246436i
$53$	7.27378	−	7.62852i	0.999131	−	1.04786i	0.000276371	−	1.00000i	$-0.499912\pi$
$53$	7.27378	−	7.62852i	0.999131	−	1.04786i	0.998854	−	0.0478580i	$-0.0152395\pi$
$54$	0.458227	+	0.888835i	0.0623567	+	0.120955i
$55$	1.08903	+	0.497344i	0.146845	+	0.0670618i
$56$	1.21370	−	2.35094i	0.162187	−	0.314158i
$57$	6.47289	−	5.60879i	0.857355	−	0.742902i
$58$	−1.25906	+	0.242663i	−0.165322	+	0.0318633i
$59$	7.18093	−	1.74207i	0.934878	−	0.226799i	0.260744	−	0.965408i	$-0.416032\pi$
$59$	7.18093	−	1.74207i	0.934878	−	0.226799i	0.674134	+	0.738609i	$0.264517\pi$
$60$	0.0288129	+	0.301743i	0.00371973	+	0.0389548i
$61$	−5.36778	+	2.76728i	−0.687274	+	0.354314i	−0.766232	−	0.642564i	$-0.777871\pi$
$61$	−5.36778	+	2.76728i	−0.687274	+	0.354314i	0.0789585	+	0.996878i	$0.474841\pi$
$62$	2.80177	+	9.54194i	0.355825	+	1.21183i
$63$	−2.00052	+	1.73145i	−0.252041	+	0.218143i
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	0.215646	−	0.538657i	0.0267476	−	0.0668122i
$66$	−3.51066	−	1.80987i	−0.432132	−	0.222779i
$67$	0.294967	−	1.53044i	0.0360360	−	0.186972i	−0.959450	−	0.281878i	$-0.909043\pi$
$67$	0.294967	−	1.53044i	0.0360360	−	0.186972i	0.995486	+	0.0949054i	$0.0302548\pi$
$68$	−1.68318	+	2.91535i	−0.204115	+	0.353538i
$69$	−4.64907	+	1.17734i	−0.559683	+	0.141735i
$70$	−0.758010	+	0.261864i	−0.0905995	+	0.0312987i
$71$	4.04986	−	4.67379i	0.480630	−	0.554677i	−0.462707	−	0.886511i	$-0.653122\pi$
$71$	4.04986	−	4.67379i	0.480630	−	0.554677i	0.943338	+	0.331834i	$0.107667\pi$
$72$	−0.0475819	−	0.998867i	−0.00560758	−	0.117718i
$73$	0.581773	+	0.739784i	0.0680913	+	0.0865852i	0.818906	−	0.573928i	$-0.194581\pi$
$73$	0.581773	+	0.739784i	0.0680913	+	0.0865852i	−0.750814	+	0.660513i	$0.770339\pi$
$74$	−3.33974	−	2.37822i	−0.388237	−	0.276462i
$75$	−3.03400	+	3.85804i	−0.350336	+	0.445489i
$76$	−8.21792	+	2.41300i	−0.942660	+	0.276790i
$77$	2.46949	−	10.1540i	0.281424	−	1.15716i
$78$	−0.795183	+	1.74121i	−0.0900367	+	0.197153i
$79$	−6.89580	−	7.23211i	−0.775839	−	0.813676i	0.210640	−	0.977564i	$-0.432445\pi$
$79$	−6.89580	−	7.23211i	−0.775839	−	0.813676i	−0.986479	+	0.163887i	$0.947597\pi$
$80$	0.0991392	−	0.286444i	0.0110841	−	0.0320254i
$81$	−0.327068	+	0.945001i	−0.0363409	+	0.105000i
$82$	−1.71360	−	1.79718i	−0.189236	−	0.198465i
$83$	4.53632	−	9.93315i	0.497925	−	1.09030i	−0.479213	−	0.877699i	$-0.659078\pi$
$83$	4.53632	−	9.93315i	0.497925	−	1.09030i	0.977138	−	0.212606i	$-0.0681950\pi$
$84$	2.53901	−	0.743942i	0.277028	−	0.0811707i
$85$	0.979061	−	0.287478i	0.106194	−	0.0311814i
$86$	2.97891	−	3.78799i	0.321224	−	0.408470i
$87$	−1.04447	−	0.743766i	−0.111979	−	0.0797401i
$88$	2.44156	+	3.10469i	0.260271	+	0.330961i
$89$	−0.299855	−	6.29474i	−0.0317846	−	0.667241i	−0.957398	−	0.288771i	$-0.906753\pi$
$89$	−0.299855	−	6.29474i	−0.0317846	−	0.667241i	0.925614	−	0.378470i	$-0.123550\pi$
$90$	−0.198498	+	0.229079i	−0.0209235	+	0.0241471i
$91$	−4.97240	−	0.961302i	−0.521249	−	0.100772i
$92$	4.71803	+	0.860349i	0.491889	+	0.0896976i
$93$	−4.97239	+	8.61243i	−0.515612	+	0.893067i
$94$	−2.12650	+	11.0333i	−0.219331	+	1.13800i
$95$	2.30754	+	1.18962i	0.236749	+	0.122052i
$96$	−0.371662	+	0.928368i	−0.0379326	+	0.0947512i
$97$	7.30259	+	15.9904i	0.741466	+	1.62358i	0.781129	+	0.624370i	$0.214644\pi$
$97$	7.30259	+	15.9904i	0.741466	+	1.62358i	−0.0396629	+	0.999213i	$0.512628\pi$
$98$	3.49306	+	6.06618i	0.352852	+	0.612777i
$99$	−1.11277	−	3.78973i	−0.111837	−	0.380883i
$100$	4.36251	−	2.24903i	0.436251	−	0.224903i
$101$	1.55884	+	16.3249i	0.155110	+	1.62439i	0.653146	+	0.757232i	$0.273449\pi$
$101$	1.55884	+	16.3249i	0.155110	+	1.62439i	−0.498036	+	0.867157i	$0.665945\pi$
$102$	−3.27147	+	0.793649i	−0.323923	+	0.0785830i
$103$	−19.4449	+	3.74770i	−1.91596	+	0.369272i	−0.999523	−	0.0308948i	$-0.990164\pi$
$103$	−19.4449	+	3.74770i	−1.91596	+	0.369272i	−0.916442	+	0.400167i	$0.868952\pi$
$104$	1.44665	−	1.25353i	0.141855	−	0.122918i
$105$	−0.712607	−	0.367890i	−0.0695433	−	0.0359024i
$106$	−9.58798	−	4.37868i	−0.931267	−	0.425295i
$107$	2.83777	+	5.50451i	0.274338	+	0.532142i	0.985246	−	0.171143i	$-0.0547461\pi$
$107$	2.83777	+	5.50451i	0.274338	+	0.532142i	−0.710908	+	0.703285i	$0.751716\pi$
$108$	0.690079	−	0.723734i	0.0664029	−	0.0696413i
$109$	7.18823	+	17.9553i	0.688508	+	1.71981i	0.694155	+	0.719825i	$0.255778\pi$
$109$	7.18823	+	17.9553i	0.688508	+	1.71981i	−0.00564773	+	0.999984i	$0.501798\pi$
$110$	0.113803	−	1.19180i	0.0108507	−	0.113634i
$111$	−0.583487	−	4.05824i	−0.0553822	−	0.385191i
$112$	−2.61861	−	0.378028i	−0.247435	−	0.0357203i
$113$	6.43936	+	5.57973i	0.605764	+	0.524897i	0.902851	−	0.429953i	$-0.141470\pi$
$113$	6.43936	+	5.57973i	0.605764	+	0.524897i	−0.297088	+	0.954850i	$0.596015\pi$
$114$	−7.41739	−	4.28243i	−0.694702	−	0.401086i
$115$	−0.855054	−	1.17562i	−0.0797342	−	0.109628i
$116$	0.641115	+	1.11044i	0.0595260	+	0.103102i
$117$	−1.80891	+	0.626070i	−0.167234	+	0.0578802i
$118$	−3.99491	−	6.21621i	−0.367762	−	0.572248i
$119$	−4.07668	−	7.91879i	−0.373709	−	0.725914i
$120$	0.275723	−	0.125919i	0.0251700	−	0.0114947i
$121$	3.61610	+	2.84374i	0.328737	+	0.258521i
$122$	4.37071	+	4.16747i	0.395706	+	0.377305i
$123$	0.118155	−	2.48039i	0.0106537	−	0.223649i
$124$	8.10077	−	5.76853i	0.727471	−	0.518030i
$125$	−2.88165	−	0.846128i	−0.257742	−	0.0756800i
$126$	2.29053	+	1.32419i	0.204057	+	0.117968i
$127$	−0.325029	−	0.375103i	−0.0288416	−	0.0332850i	0.741145	−	0.671344i	$-0.234283\pi$
$127$	−0.325029	−	0.375103i	−0.0288416	−	0.0332850i	−0.769987	+	0.638059i	$0.779737\pi$
$128$	0.723734	−	0.690079i	0.0639697	−	0.0609949i
$129$	4.79718	−	0.458076i	0.422369	−	0.0403313i
$130$	−0.579563	−	0.0276080i	−0.0508310	−	0.00242138i
$131$	−3.67982	−	0.892715i	−0.321508	−	0.0779969i	0.0717573	−	0.997422i	$-0.477139\pi$
$131$	−3.67982	−	0.892715i	−0.321508	−	0.0779969i	−0.393265	+	0.919425i	$0.628654\pi$
$132$	−0.562105	+	3.90952i	−0.0489249	+	0.340280i
$133$	6.39664	−	21.7389i	0.554659	−	1.88500i
$134$	−1.54274	+	0.221812i	−0.133272	+	0.0191616i
$135$	−0.302772	+	0.0144228i	−0.0260584	+	0.00124132i
$136$	3.30552	+	0.637087i	0.283446	+	0.0546298i
$137$	−13.9005	+	8.02544i	−1.18760	+	0.685659i	−0.957760	−	0.287570i	$-0.907153\pi$
$137$	−13.9005	+	8.02544i	−1.18760	+	0.685659i	−0.229837	+	0.973229i	$0.573819\pi$
$138$	2.63315	+	4.00831i	0.224149	+	0.341210i
$139$		−	8.01298i		−	0.679652i	−0.940488	−	0.339826i	$-0.889632\pi$
$139$		−	8.01298i		−	0.679652i	0.940488	−	0.339826i	$-0.110368\pi$
$140$	0.495382	+	0.630672i	0.0418675	+	0.0533015i
$141$	−9.45264	+	6.07484i	−0.796056	+	0.511594i
$142$	−5.74132	−	2.29848i	−0.481801	−	0.192884i
$143$	4.38553	−	6.15862i	0.366737	−	0.515010i
$144$	−0.928368	+	0.371662i	−0.0773640	+	0.0309719i
$145$	0.0916308	−	0.377707i	0.00760952	−	0.0313669i
$146$	0.508817	−	0.791735i	0.0421100	−	0.0655245i
$147$	−1.97981	+	6.71419i	−0.163292	+	0.553777i
$148$	−1.15510	+	3.93390i	−0.0949483	+	0.323364i
$149$	1.19735	+	6.21244i	0.0980907	+	0.508943i	0.997427	+	0.0716859i	$0.0228379\pi$
$149$	1.19735	+	6.21244i	0.0980907	+	0.508943i	−0.899337	+	0.437257i	$0.855950\pi$
$150$	4.63818	+	1.60529i	0.378706	+	0.131071i
$151$	2.62598	+	10.8244i	0.213699	+	0.880880i	0.973123	+	0.230285i	$0.0739657\pi$
$151$	2.62598	+	10.8244i	0.213699	+	0.880880i	−0.759424	+	0.650596i	$0.774519\pi$
$152$	4.96811	+	6.97673i	0.402967	+	0.565887i
$153$	−2.83196	−	1.81999i	−0.228950	−	0.147138i
$154$	−10.4032	+	0.987382i	−0.838317	+	0.0795655i
$155$	−2.98373	−	0.428995i	−0.239659	−	0.0344577i
$156$	1.90552	+	0.181955i	0.152564	+	0.0145681i
$157$	15.0447	−	11.8313i	1.20069	−	0.944237i	0.201318	−	0.979526i	$-0.435478\pi$
$157$	15.0447	−	11.8313i	1.20069	−	0.944237i	0.999377	+	0.0352891i	$0.0112352\pi$
$158$	−4.57895	+	8.88193i	−0.364282	+	0.706609i
$159$	−3.44746	−	9.96078i	−0.273401	−	0.789942i
$160$	−0.303115			−0.0239634
$161$	−8.66890	+	9.26554i	−0.683205	+	0.730227i
$162$	1.00000			0.0785674
$163$	1.94138	+	5.60925i	0.152061	+	0.439350i	0.995144	−	0.0984332i	$-0.0313831\pi$
$163$	1.94138	+	5.60925i	0.152061	+	0.439350i	−0.843083	+	0.537783i	$0.819262\pi$
$164$	−1.13787	+	2.20716i	−0.0888526	+	0.172350i
$165$	0.941080	−	0.740073i	0.0732629	−	0.0576146i
$166$	−10.8705	−	1.03801i	−0.843716	−	0.0805651i
$167$	14.0825	+	2.02476i	1.08974	+	0.156680i	0.663680	−	0.748017i	$-0.268994\pi$
$167$	14.0825	+	2.02476i	1.08974	+	0.156680i	0.426056	+	0.904697i	$0.359903\pi$
$168$	−1.53345	−	2.15604i	−0.118308	−	0.166342i
$169$	7.85384	+	5.04736i	0.604142	+	0.388258i
$170$	−0.591887	−	0.831188i	−0.0453956	−	0.0637492i
$171$	−2.01924	−	8.32343i	−0.154415	−	0.636509i
$172$	−4.55396	−	1.57614i	−0.347236	−	0.120180i
$173$	−2.52808	−	13.1169i	−0.192206	−	0.997259i	−0.942006	−	0.335595i	$-0.891063\pi$
$173$	−2.52808	−	13.1169i	−0.192206	−	0.997259i	0.749800	−	0.661664i	$-0.230150\pi$
$174$	−0.361246	+	1.23029i	−0.0273860	+	0.0932680i
$175$	−1.24176	+	12.9262i	−0.0938685	+	0.977126i
$176$	2.13538	−	3.32272i	0.160961	−	0.250459i
$177$	1.74207	−	7.18093i	0.130942	−	0.539752i
$178$	−5.85046	+	2.34217i	−0.438510	+	0.175553i
$179$	6.06070	−	8.51107i	0.452998	−	0.636147i	−0.523410	−	0.852081i	$-0.675340\pi$
$179$	6.06070	−	8.51107i	0.452998	−	0.636147i	0.976408	+	0.215934i	$0.0692796\pi$
$180$	0.281402	+	0.112657i	0.0209745	+	0.00839692i
$181$	−4.40160	+	2.82874i	−0.327168	+	0.210258i	−0.693905	−	0.720066i	$-0.744111\pi$
$181$	−4.40160	+	2.82874i	−0.327168	+	0.210258i	0.366737	+	0.930325i	$0.380475\pi$
$182$	0.717881	+	5.01333i	0.0532128	+	0.371613i
$183$			6.03912i			0.446424i
$184$	−0.730086	−	4.73993i	−0.0538226	−	0.349433i
$185$	1.07627	−	0.621382i	0.0791286	−	0.0456849i
$186$	9.76506	+	1.88206i	0.716009	+	0.137999i
$187$	13.2811	−	0.632658i	0.971212	−	0.0462645i
$188$	11.1220	−	1.59910i	0.811155	−	0.116627i
$189$	0.622288	+	2.57153i	0.0452648	+	0.187051i
$190$	0.369469	−	2.56971i	0.0268041	−	0.186427i
$191$	17.3366	+	4.20581i	1.25443	+	0.304322i	0.807297	−	0.590145i	$-0.200929\pi$
$191$	17.3366	+	4.20581i	1.25443	+	0.304322i	0.447134	+	0.894467i	$0.352445\pi$
$192$	0.998867	+	0.0475819i	0.0720870	+	0.00343393i
$193$	6.90358	−	0.659212i	0.496931	−	0.0474511i	0.156418	−	0.987691i	$-0.450005\pi$
$193$	6.90358	−	0.659212i	0.496931	−	0.0474511i	0.340513	+	0.940240i	$0.389399\pi$
$194$	12.7225	−	12.1309i	0.913425	−	0.870949i
$195$	−0.379963	−	0.438501i	−0.0272097	−	0.0314017i
$196$	4.59008	−	5.28500i	0.327863	−	0.377500i
$197$	13.8271	+	4.06001i	0.985142	+	0.289264i	0.734345	−	0.678776i	$-0.237489\pi$
$197$	13.8271	+	4.06001i	0.985142	+	0.289264i	0.250797	+	0.968040i	$0.419307\pi$
$198$	−3.21735	+	2.29107i	−0.228647	+	0.162819i
$199$	0.387288	−	8.13018i	0.0274541	−	0.576333i	−0.942670	−	0.333725i	$-0.891694\pi$
$199$	0.387288	−	8.13018i	0.0274541	−	0.576333i	0.970124	−	0.242608i	$-0.0780028\pi$
$200$	−3.55217	−	3.38699i	−0.251177	−	0.239496i
$201$	−1.22514	−	0.963463i	−0.0864150	−	0.0679575i
$202$	14.9172	−	6.81246i	1.04957	−	0.479323i
$203$	−3.38852	−	0.163359i	−0.237828	−	0.0114655i
$204$	1.81999	+	2.83196i	0.127425	+	0.198277i
$205$	0.711298	−	0.246183i	0.0496792	−	0.0171941i
$206$	9.90139	+	17.1497i	0.689863	+	1.19488i
$207$	−1.08387	+	4.67175i	−0.0753340	+	0.324709i
$208$	−1.65774	−	0.957095i	−0.114943	−	0.0663626i
$209$	25.5661	+	22.1532i	1.76845	+	1.53237i
$210$	−0.114586	+	0.793739i	−0.00790719	+	0.0547732i
$211$	1.99957	+	13.9073i	0.137656	+	0.957417i	0.935191	+	0.354145i	$0.115228\pi$
$211$	1.99957	+	13.9073i	0.137656	+	0.957417i	−0.797535	+	0.603273i	$0.793863\pi$
$212$	−1.00194	+	10.4928i	−0.0688134	+	0.720647i
$213$	−2.29848	−	5.74132i	−0.157489	−	0.393389i
$214$	4.27363	−	4.48205i	0.292139	−	0.306387i
$215$	0.669338	+	1.29833i	0.0456484	+	0.0885456i
$216$	−0.909632	−	0.415415i	−0.0618926	−	0.0282654i
$217$	1.23691	+	26.2823i	0.0839668	+	1.78416i
$218$	14.6168	−	12.6655i	0.989972	−	0.857816i
$219$	0.924130	−	0.178111i	0.0624469	−	0.0120357i
$220$	−1.16347	+	0.282256i	−0.0784414	+	0.0190297i
$221$	−0.612526	−	6.41467i	−0.0412030	−	0.431497i
$222$	−3.64420	+	1.87872i	−0.244583	+	0.126091i
$223$	−2.27398	−	7.74445i	−0.152277	−	0.518607i	0.847652	−	0.530553i	$-0.178016\pi$
$223$	−2.27398	−	7.74445i	−0.152277	−	0.518607i	−0.999929	+	0.0119459i	$0.996197\pi$
$224$	0.499225	+	2.59823i	0.0333559	+	0.173601i
$225$	2.03891	+	4.46458i	0.135927	+	0.297639i
$226$	3.16675	−	7.91015i	0.210649	−	0.526175i
$227$	16.4884	+	8.50039i	1.09438	+	0.564190i	0.908289	−	0.418343i	$-0.137389\pi$
$227$	16.4884	+	8.50039i	1.09438	+	0.564190i	0.186088	+	0.982533i	$0.440419\pi$
$228$	−1.62091	+	8.41008i	−0.107347	+	0.556971i
$229$	−5.35289	+	9.27148i	−0.353729	+	0.612676i	−0.986900	−	0.161336i	$-0.948420\pi$
$229$	−5.35289	+	9.27148i	−0.353729	+	0.612676i	0.633171	+	0.774012i	$0.281753\pi$
$230$	−0.831306	+	1.19254i	−0.0548147	+	0.0786335i
$231$	−7.89366	−	6.84781i	−0.519365	−	0.450553i
$232$	0.839681	−	0.969044i	0.0551278	−	0.0636209i
$233$	−1.26772	−	26.6127i	−0.0830510	−	1.74346i	−0.529201	−	0.848497i	$-0.677508\pi$
$233$	−1.26772	−	26.6127i	−0.0830510	−	1.74346i	0.446150	−	0.894958i	$-0.352795\pi$
$234$	1.18327	+	1.50465i	0.0773530	+	0.0983623i
$235$	−2.77438	−	1.97562i	−0.180980	−	0.128876i
$236$	−4.56771	+	5.80832i	−0.297333	+	0.378089i
$237$	−9.58800	+	2.81529i	−0.622807	+	0.182873i
$238$	−6.14991	+	6.44245i	−0.398639	+	0.417602i
$239$	−7.02153	+	15.3750i	−0.454185	+	0.994526i	0.534590	+	0.845112i	$0.320466\pi$
$239$	−7.02153	+	15.3750i	−0.454185	+	0.994526i	−0.988775	+	0.149414i	$0.952261\pi$
$240$	−0.209173	−	0.219375i	−0.0135021	−	0.0141606i
$241$	0.692827	−	2.00179i	0.0446289	−	0.128947i	−0.920484	−	0.390779i	$-0.872206\pi$
$241$	0.692827	−	2.00179i	0.0446289	−	0.128947i	0.965113	+	0.261832i	$0.0843268\pi$
$242$	1.50462	−	4.34732i	0.0967207	−	0.279456i
$243$	0.690079	+	0.723734i	0.0442686	+	0.0464276i
$244$	2.50874	−	5.49337i	0.160606	−	0.351677i
$245$	−2.11243	+	0.199273i	−0.134958	+	0.0127311i
$246$	−2.38261	+	0.699598i	−0.151910	+	0.0446048i
$247$	10.1346	−	12.8872i	0.644847	−	0.819990i
$248$	−8.10077	−	5.76853i	−0.514400	−	0.366302i
$249$	−6.75027	−	8.58367i	−0.427781	−	0.543968i
$250$	0.142903	+	2.99990i	0.00903797	+	0.189730i
$251$	−0.556867	+	0.642659i	−0.0351491	+	0.0405643i	−0.773052	−	0.634343i	$-0.781271\pi$
$251$	−0.556867	+	0.642659i	−0.0351491	+	0.0405643i	0.737903	+	0.674907i	$0.235816\pi$
$252$	0.502198	−	2.59765i	0.0316355	−	0.163637i
$253$	−7.21610	−	17.5139i	−0.453672	−	1.10109i
$254$	−0.248166	+	0.429836i	−0.0155713	+	0.0269703i
$255$	0.193111	−	1.00195i	0.0120931	−	0.0627448i
$256$	−0.888835	−	0.458227i	−0.0555522	−	0.0286392i
$257$	−1.84332	+	4.60439i	−0.114983	+	0.287214i	−0.974685	−	0.223582i	$-0.928225\pi$
$257$	−1.84332	+	4.60439i	−0.114983	+	0.287214i	0.859702	+	0.510796i	$0.170649\pi$
$258$	−2.00189	−	4.38352i	−0.124632	−	0.272906i
$259$	−7.09892	−	8.20207i	−0.441105	−	0.509652i
$260$	0.163467	+	0.556717i	0.0101378	+	0.0345261i
$261$	−1.13969	+	0.587551i	−0.0705451	+	0.0363685i
$262$	0.359935	+	3.76941i	0.0222369	+	0.232875i
$263$	29.4558	−	7.14590i	1.81632	−	0.440635i	0.824241	−	0.566239i	$-0.191602\pi$
$263$	29.4558	−	7.14590i	1.81632	−	0.440635i	0.992080	+	0.125605i	$0.0400870\pi$
$264$	3.87835	−	0.747490i	0.238696	−	0.0460049i
$265$	2.41461	−	2.09227i	0.148328	−	0.128527i
$266$	−22.6354	+	1.06528i	−1.38787	+	0.0653164i
$267$	−5.73239	−	2.61789i	−0.350816	−	0.160212i
$268$	0.714192	+	1.38534i	0.0436262	+	0.0846231i
$269$	−22.5736	+	23.6745i	−1.37633	+	1.44346i	−0.634330	+	0.773062i	$0.718724\pi$
$269$	−22.5736	+	23.6745i	−1.37633	+	1.44346i	−0.742004	+	0.670395i	$0.766124\pi$
$270$	0.112657	+	0.281402i	0.00685606	+	0.0171256i
$271$	−0.388895	+	4.07269i	−0.0236237	+	0.247398i	0.975945	+	0.218018i	$0.0699593\pi$
$271$	−0.388895	+	4.07269i	−0.0236237	+	0.247398i	−0.999568	+	0.0293798i	$0.990647\pi$
$272$	−0.479083	−	3.33209i	−0.0290487	−	0.202038i
$273$	−3.13292	+	3.97915i	−0.189613	+	0.240829i
$274$	12.1304	+	10.5111i	0.732827	+	0.634998i
$275$	−16.7885	−	9.69287i	−1.01239	−	0.584502i
$276$	2.92663	−	3.79932i	0.176163	−	0.228692i
$277$	13.4391	+	23.2773i	0.807480	+	1.39860i	0.914604	+	0.404350i	$0.132502\pi$
$277$	13.4391	+	23.2773i	0.807480	+	1.39860i	−0.107124	+	0.994246i	$0.534164\pi$
$278$	−7.57227	+	2.62079i	−0.454155	+	0.157184i
$279$	5.37655	+	8.36608i	0.321886	+	0.500864i
$280$	0.433962	−	0.674410i	0.0259342	−	0.0403037i
$281$	6.27030	−	2.86355i	0.374055	−	0.170825i	−0.219512	−	0.975610i	$-0.570447\pi$
$281$	6.27030	−	2.86355i	0.374055	−	0.170825i	0.593567	+	0.804785i	$0.297719\pi$
$282$	8.83239	+	6.94587i	0.525961	+	0.413620i
$283$	−9.96805	−	9.50451i	−0.592539	−	0.564985i	0.333339	−	0.942807i	$-0.391825\pi$
$283$	−9.96805	−	9.50451i	−0.592539	−	0.564985i	−0.925878	+	0.377822i	$0.876673\pi$
$284$	−0.294261	+	6.17731i	−0.0174612	+	0.366556i
$285$	2.11475	−	1.50591i	0.125267	−	0.0892023i
$286$	−7.25427	−	2.13005i	−0.428954	−	0.125952i
$287$	−3.28171	−	5.69161i	−0.193713	−	0.335965i
$288$	0.654861	+	0.755750i	0.0385880	+	0.0445330i
$289$	−4.10186	+	3.91112i	−0.241286	+	0.230066i
$290$	−0.386903	+	0.0369448i	−0.0227197	+	0.00216947i
$291$	17.5591	+	0.836444i	1.02933	+	0.0490332i
$292$	−0.914608	−	0.221882i	−0.0535234	−	0.0129846i
$293$	−1.82380	+	12.6848i	−0.106548	+	0.741055i	0.864580	+	0.502495i	$0.167584\pi$
$293$	−1.82380	+	12.6848i	−0.106548	+	0.741055i	−0.971128	+	0.238560i	$0.923325\pi$
$294$	6.99245	−	0.325071i	0.407808	−	0.0189585i
$295$	2.21699	−	0.318755i	0.129078	−	0.0185586i
$296$	4.09533	−	0.195085i	0.238036	−	0.0113391i
$297$	−3.87835	−	0.747490i	−0.225045	−	0.0433738i
$298$	5.47915	−	3.16339i	0.317399	−	0.183250i
$299$	−8.31188	+	3.89711i	−0.480688	+	0.225376i
$300$		−	4.90812i		−	0.283371i
$301$	10.0266	−	7.87572i	0.577923	−	0.453949i
$302$	9.37023	−	6.02188i	0.539196	−	0.346520i
$303$	15.2245	+	6.09495i	0.874622	+	0.350146i
$304$	4.96811	−	6.97673i	0.284940	−	0.400143i
$305$	−1.69942	+	0.680346i	−0.0973086	+	0.0389565i
$306$	−0.793649	+	3.27147i	−0.0453699	+	0.187017i
$307$	−12.0229	+	18.7080i	−0.686182	+	1.06772i	0.307063	+	0.951689i	$0.400654\pi$
$307$	−12.0229	+	18.7080i	−0.686182	+	1.06772i	−0.993246	+	0.116031i	$0.962983\pi$
$308$	4.33564	+	9.50813i	0.247046	+	0.541776i
$309$	−5.57909	+	19.0006i	−0.317383	+	1.08091i
$310$	0.570481	+	2.95994i	0.0324011	+	0.168113i
$311$	−1.13948	−	0.394377i	−0.0646138	−	0.0223631i	0.294570	−	0.955630i	$-0.404824\pi$
$311$	−1.13948	−	0.394377i	−0.0646138	−	0.0223631i	−0.359184	+	0.933267i	$0.616945\pi$
$312$	−0.451287	−	1.86023i	−0.0255491	−	0.105315i
$313$	−19.2937	−	27.0942i	−1.09054	−	1.53145i	−0.823114	−	0.567876i	$-0.807765\pi$
$313$	−19.2937	−	27.0942i	−1.09054	−	1.53145i	−0.267430	−	0.963577i	$-0.586174\pi$
$314$	−16.1012	−	10.3476i	−0.908642	−	0.583949i
$315$	−0.653529	+	0.464813i	−0.0368222	+	0.0261892i
$316$	9.89106	+	1.42212i	0.556416	+	0.0800005i
$317$	23.3614	+	2.23074i	1.31210	+	0.125291i	0.727545	−	0.686060i	$-0.240661\pi$
$317$	23.3614	+	2.23074i	1.31210	+	0.125291i	0.584560	+	0.811351i	$0.301267\pi$
$318$	−8.28540	+	6.51571i	−0.464622	+	0.365383i
$319$	2.32067	−	4.50146i	0.129932	−	0.252034i
$320$	0.0991392	+	0.286444i	0.00554205	+	0.0160127i
$321$	6.19295			0.345657
$322$	11.5913	+	5.16165i	0.645956	+	0.287648i
$323$	28.8324			1.60428
$324$	−0.327068	−	0.945001i	−0.0181704	−	0.0525000i
$325$	−4.30507	+	8.35067i	−0.238802	+	0.463212i
$326$	4.66578	−	3.66921i	0.258414	−	0.203219i
$327$	19.2532	+	1.83846i	1.06470	+	0.101667i
$328$	2.45793	+	0.353396i	0.135716	+	0.0195130i
$329$	−12.3652	+	27.0351i	−0.681716	+	1.49049i
$330$	−1.00717	−	0.647267i	−0.0554427	−	0.0356309i
$331$	−11.0818	−	15.5622i	−0.609110	−	0.855375i	0.388711	−	0.921360i	$-0.372921\pi$
$331$	−11.0818	−	15.5622i	−0.609110	−	0.855375i	−0.997821	+	0.0659847i	$0.978981\pi$
$332$	2.57448	+	10.6121i	0.141293	+	0.582417i
$333$	−3.87448	−	1.34097i	−0.212320	−	0.0734847i
$334$	−2.69253	−	13.9702i	−0.147329	−	0.764415i
$335$	0.133101	−	0.453299i	0.00727206	−	0.0247664i
$336$	−1.53592	+	2.15429i	−0.0837913	+	0.117526i
$337$	−13.7384	+	21.3773i	−0.748376	+	1.16450i	0.233014	+	0.972473i	$0.425141\pi$
$337$	−13.7384	+	21.3773i	−0.748376	+	1.16450i	−0.981390	+	0.192023i	$0.938495\pi$
$338$	2.20102	−	9.07272i	0.119720	−	0.493491i
$339$	7.91015	−	3.16675i	0.429620	−	0.171994i
$340$	−0.591887	+	0.831188i	−0.0320996	+	0.0450775i
$341$	−36.4655	−	14.5986i	−1.97472	−	0.790557i
$342$	−7.20522	+	4.63051i	−0.389614	+	0.250389i
$343$	5.18725	+	17.7790i	0.280085	+	0.959975i
$344$			4.81900i			0.259823i
$345$	−1.43675	+	0.221300i	−0.0773518	+	0.0119144i
$346$	−11.5686	+	6.67915i	−0.621933	+	0.359073i
$347$	−10.9468	−	2.10982i	−0.587653	−	0.113261i	−0.113247	−	0.993567i	$-0.536125\pi$
$347$	−10.9468	−	2.10982i	−0.587653	−	0.113261i	−0.474406	+	0.880306i	$0.657337\pi$
$348$	1.28078	−	0.0610109i	0.0686568	−	0.00327053i
$349$	28.5332	−	4.10245i	1.52735	−	0.219599i	0.673133	−	0.739521i	$-0.264948\pi$
$349$	28.5332	−	4.10245i	1.52735	−	0.219599i	0.854214	+	0.519922i	$0.174039\pi$
$350$	12.6214	−	3.05427i	0.674641	−	0.163257i
$351$	−0.272418	+	1.89471i	−0.0145406	+	0.101132i
$352$	−3.83839	−	0.931183i	−0.204587	−	0.0496322i
$353$	−7.63635	−	0.363764i	−0.406442	−	0.0193612i	−0.156634	−	0.987657i	$-0.550064\pi$
$353$	−7.63635	−	0.363764i	−0.406442	−	0.0193612i	−0.249808	+	0.968295i	$0.580367\pi$
$354$	−7.35576	+	0.702390i	−0.390954	+	0.0373316i
$355$	1.35668	−	1.29359i	0.0720052	−	0.0686568i
$356$	4.12685	+	4.76264i	0.218723	+	0.252419i
$357$	−8.90654	−	0.00509640i	−0.471384	−	0.000269730i
$358$	−10.0252	−	2.94367i	−0.529850	−	0.155578i
$359$	−6.69926	+	4.77052i	−0.353574	+	0.251779i	−0.743018	−	0.669271i	$-0.766606\pi$
$359$	−6.69926	+	4.77052i	−0.353574	+	0.251779i	0.389445	+	0.921050i	$0.372667\pi$
$360$	0.0144228	−	0.302772i	0.000760148	−	0.0159575i
$361$	39.3399	+	37.5105i	2.07052	+	1.97424i
$362$	4.11278	+	3.23433i	0.216163	+	0.169992i
$363$	4.18461	−	1.91105i	0.219635	−	0.100304i
$364$	4.50281	−	2.31810i	0.236011	−	0.121501i
$365$	0.154230	+	0.239987i	0.00807278	+	0.0125615i
$366$	5.70697	−	1.97520i	0.298308	−	0.103245i
$367$	−15.1912	−	26.3119i	−0.792974	−	1.37347i	−0.924118	−	0.382108i	$-0.875198\pi$
$367$	−15.1912	−	26.3119i	−0.792974	−	1.37347i	0.131144	−	0.991363i	$-0.458135\pi$
$368$	−4.24045	+	2.24021i	−0.221049	+	0.116779i
$369$	−2.15051	−	1.24160i	−0.111951	−	0.0646351i
$370$	−0.939219	−	0.813838i	−0.0488277	−	0.0423094i
$371$	−21.9112	−	17.2515i	−1.13757	−	0.895652i
$372$	−1.41529	−	9.84355i	−0.0733793	−	0.510364i
$373$	−0.449886	+	4.71142i	−0.0232942	+	0.243948i	0.976324	+	0.216314i	$0.0694034\pi$
$373$	−0.449886	+	4.71142i	−0.0232942	+	0.243948i	−0.999618	+	0.0276341i	$0.991203\pi$
$374$	−4.94169	−	12.3438i	−0.255529	−	0.638280i
$375$	−2.07252	+	2.17359i	−0.107024	+	0.112244i
$376$	−5.14880	−	9.98729i	−0.265529	−	0.515055i
$377$	−2.23263	−	1.01961i	−0.114986	−	0.0525124i
$378$	2.22657	−	1.42913i	0.114522	−	0.0735064i
$379$	9.53598	−	8.26297i	0.489830	−	0.424440i	−0.374605	−	0.927184i	$-0.622222\pi$
$379$	9.53598	−	8.26297i	0.489830	−	0.424440i	0.864435	+	0.502744i	$0.167676\pi$
$380$	−2.54922	+	0.491322i	−0.130772	+	0.0252043i
$381$	−0.482341	+	0.117015i	−0.0247111	+	0.00599485i
$382$	−1.69575	−	17.7587i	−0.0867620	−	0.908613i
$383$	−20.8392	+	10.7433i	−1.06483	+	0.548959i	−0.899339	−	0.437252i	$-0.855952\pi$
$383$	−20.8392	+	10.7433i	−1.06483	+	0.548959i	−0.165493	+	0.986211i	$0.552922\pi$
$384$	−0.281733	−	0.959493i	−0.0143771	−	0.0489639i
$385$	1.03772	−	2.99274i	0.0528869	−	0.152524i
$386$	−2.88090	−	6.30829i	−0.146634	−	0.321083i
$387$	1.79104	−	4.47381i	0.0910438	−	0.227417i
$388$	−15.6249	−	8.05517i	−0.793232	−	0.408940i
$389$	−3.29355	+	17.0885i	−0.166989	+	0.866424i	0.797704	+	0.603049i	$0.206048\pi$
$389$	−3.29355	+	17.0885i	−0.166989	+	0.866424i	−0.964694	+	0.263375i	$0.915164\pi$
$390$	−0.290110	+	0.502485i	−0.0146903	+	0.0254443i
$391$	−14.4233	−	7.25356i	−0.729415	−	0.366828i
$392$	−6.49559	−	2.60907i	−0.328077	−	0.131778i
$393$	−2.47967	+	2.86169i	−0.125083	+	0.144353i
$394$	−0.685697	−	14.3945i	−0.0345449	−	0.725187i
$395$	−1.87238	−	2.38092i	−0.0942097	−	0.119797i
$396$	3.21735	+	2.29107i	0.161678	+	0.115130i
$397$	−11.4950	+	14.6171i	−0.576918	+	0.733611i	−0.983681	−	0.179923i	$-0.942415\pi$
$397$	−11.4950	+	14.6171i	−0.576918	+	0.733611i	0.406763	+	0.913534i	$0.366658\pi$
$398$	−7.80970	+	2.29313i	−0.391465	+	0.114944i
$399$	−16.3912	−	15.6469i	−0.820587	−	0.783325i
$400$	−2.03891	+	4.46458i	−0.101945	+	0.223229i
$401$	−4.55165	−	4.77363i	−0.227298	−	0.238384i	0.600202	−	0.799848i	$-0.295087\pi$
$401$	−4.55165	−	4.77363i	−0.227298	−	0.238384i	−0.827501	+	0.561464i	$0.810238\pi$
$402$	−0.509769	+	1.47288i	−0.0254249	+	0.0734606i
$403$	−6.22612	+	17.9892i	−0.310145	+	0.896106i
$404$	−11.3167	−	11.8686i	−0.563028	−	0.590486i
$405$	−0.125919	+	0.275723i	−0.00625694	+	0.0137008i
$406$	0.953903	+	3.25559i	0.0473414	+	0.161572i
$407$	15.5378	−	4.56231i	0.770181	−	0.226145i
$408$	2.08094	−	2.64614i	0.103022	−	0.131003i
$409$	−0.836731	−	0.595833i	−0.0413737	−	0.0294621i	0.559183	−	0.829044i	$-0.311115\pi$
$409$	−0.836731	−	0.595833i	−0.0413737	−	0.0294621i	−0.600557	+	0.799582i	$0.705054\pi$
$410$	−0.465286	−	0.591659i	−0.0229788	−	0.0292199i
$411$	0.763731	+	16.0327i	0.0376721	+	0.790834i
$412$	12.9681	−	14.9659i	0.638891	−	0.737319i
$413$	−6.38362	−	18.4785i	−0.314117	−	0.909266i
$414$	4.76930	−	0.503724i	0.234399	−	0.0247567i
$415$	1.65500	−	2.86655i	0.0812409	−	0.140713i
$416$	−0.362263	+	1.87960i	−0.0177614	+	0.0921548i
$417$	−7.12222	−	3.67176i	−0.348777	−	0.179807i
$418$	12.5729	−	31.4056i	0.614961	−	1.53610i
$419$	13.9851	+	30.6232i	0.683218	+	1.49604i	0.859197	+	0.511645i	$0.170964\pi$
$419$	13.9851	+	30.6232i	0.683218	+	1.49604i	−0.175979	+	0.984394i	$0.556309\pi$
$420$	0.787561	−	0.151323i	0.0384291	−	0.00738379i
$421$	5.56829	+	18.9639i	0.271382	+	0.924242i	0.976566	+	0.215218i	$0.0690461\pi$
$421$	5.56829	+	18.9639i	0.271382	+	0.924242i	−0.705184	+	0.709024i	$0.749136\pi$
$422$	12.4884	−	6.43822i	0.607926	−	0.313408i
$423$	1.06809	+	11.1855i	0.0519321	+	0.543857i
$424$	10.2434	−	2.48502i	0.497463	−	0.120683i
$425$	−16.2239	+	3.12690i	−0.786975	+	0.151677i
$426$	−4.67379	+	4.04986i	−0.226446	+	0.196217i
$427$	8.63067	+	13.4465i	0.417667	+	0.650721i
$428$	−5.63331	−	2.57264i	−0.272296	−	0.124353i
$429$	−3.46443	−	6.72006i	−0.167264	−	0.324448i
$430$	1.00801	−	1.05717i	0.0486104	−	0.0509812i
$431$	−5.06769	−	12.6585i	−0.244102	−	0.609738i	0.754831	−	0.655920i	$-0.227719\pi$
$431$	−5.06769	−	12.6585i	−0.244102	−	0.609738i	−0.998933	+	0.0461816i	$0.985295\pi$
$432$	−0.0950560	+	0.995472i	−0.00457339	+	0.0478947i
$433$	0.746406	+	5.19137i	0.0358700	+	0.249481i	0.999865	−	0.0164396i	$-0.00523313\pi$
$433$	0.746406	+	5.19137i	0.0358700	+	0.249481i	−0.963995	+	0.265921i	$0.914324\pi$
$434$	24.4322	−	9.76498i	1.17279	−	0.468734i
$435$	−0.293732	−	0.254520i	−0.0140834	−	0.0122033i
$436$	−16.7496	−	9.67038i	−0.802160	−	0.463127i
$437$	−13.8231	−	38.6798i	−0.661248	−	1.85031i
$438$	−0.470569	−	0.815049i	−0.0224846	−	0.0389445i
$439$	−6.44834	+	2.23179i	−0.307762	+	0.106518i	−0.476584	−	0.879129i	$-0.658125\pi$
$439$	−6.44834	+	2.23179i	−0.307762	+	0.106518i	0.168821	+	0.985647i	$0.446004\pi$
$440$	0.647267	+	1.00717i	0.0308572	+	0.0480148i
$441$	5.06061	+	4.83635i	0.240981	+	0.230302i
$442$	−5.86153	+	2.67687i	−0.278804	+	0.127326i
$443$	−16.7031	−	13.1355i	−0.793590	−	0.624086i	0.136824	−	0.990595i	$-0.456310\pi$
$443$	−16.7031	−	13.1355i	−0.793590	−	0.624086i	−0.930414	+	0.366509i	$0.880553\pi$
$444$	2.96729	+	2.82931i	0.140821	+	0.134273i
$445$	0.0908906	−	1.90803i	0.00430863	−	0.0904493i
$446$	−6.57477	+	4.68187i	−0.311324	+	0.221693i
$447$	6.07050	+	1.78246i	0.287125	+	0.0843074i
$448$	2.29204	−	1.32156i	0.108289	−	0.0624380i
$449$	−9.12172	−	10.5270i	−0.430480	−	0.496801i	0.498521	−	0.866878i	$-0.333877\pi$
$449$	−9.12172	−	10.5270i	−0.430480	−	0.496801i	−0.929001	+	0.370077i	$0.879331\pi$
$450$	3.55217	−	3.38699i	0.167451	−	0.159664i
$451$	9.76355	−	0.932306i	0.459748	−	0.0439006i
$452$	−8.51084	−	0.405421i	−0.400316	−	0.0190694i
$453$	10.8244	+	2.62598i	0.508577	+	0.123379i
$454$	2.64003	−	18.3618i	0.123903	−	0.861762i
$455$	−1.47269	−	0.433335i	−0.0690406	−	0.0203151i
$456$	8.47768	−	1.21891i	0.397004	−	0.0570805i
$457$	25.1149	−	1.19637i	1.17483	−	0.0559638i	0.548928	−	0.835869i	$-0.315036\pi$
$457$	25.1149	−	1.19637i	1.17483	−	0.0559638i	0.625897	+	0.779906i	$0.284733\pi$
$458$	10.5123	+	2.02608i	0.491208	+	0.0946726i
$459$	−2.91535	+	1.68318i	−0.136077	+	0.0785641i
$460$	1.39884	+	0.395544i	0.0652213	+	0.0184423i
$461$			2.86883i			0.133615i	0.997766	+	0.0668074i	$0.0212813\pi$
$461$			2.86883i			0.133615i	−0.997766	+	0.0668074i	$0.978719\pi$
$462$	−3.88942	+	9.69921i	−0.180952	+	0.451248i
$463$	25.4340	−	16.3454i	1.18202	−	0.759636i	0.206261	−	0.978497i	$-0.433870\pi$
$463$	25.4340	−	16.3454i	1.18202	−	0.759636i	0.975756	+	0.218861i	$0.0702341\pi$
$464$	−1.19038	−	0.476556i	−0.0552620	−	0.0221236i
$465$	−1.74853	+	2.45547i	−0.0810861	+	0.113870i
$466$	−24.7344	+	9.90215i	−1.14580	+	0.458708i
$467$	3.97070	−	16.3674i	0.183742	−	0.757395i	−0.803118	−	0.595819i	$-0.796827\pi$
$467$	3.97070	−	16.3674i	0.183742	−	0.757395i	0.986860	−	0.161575i	$-0.0516575\pi$
$468$	1.03489	−	1.61032i	0.0478378	−	0.0744370i
$469$	−4.10477	−	0.394329i	−0.189541	−	0.0182084i
$470$	−0.959557	+	3.26795i	−0.0442611	+	0.150739i
$471$	−3.62217	−	18.7936i	−0.166901	−	0.865965i
$472$	6.98282	+	2.41678i	0.321410	+	0.111241i
$473$	4.48738	+	18.4972i	0.206330	+	0.850503i
$474$	5.79638	+	8.13988i	0.266236	+	0.373877i
$475$	−35.3641	−	22.7271i	−1.62262	−	1.04279i
$476$	8.09956	+	3.70455i	0.371243	+	0.169798i
$477$	−10.4332	−	1.50007i	−0.477704	−	0.0686835i
$478$	16.8259	+	1.60668i	0.769599	+	0.0734878i
$479$	11.0201	−	8.66627i	0.503519	−	0.395972i	−0.333836	−	0.942631i	$-0.608343\pi$
$479$	11.0201	−	8.66627i	0.503519	−	0.395972i	0.837355	+	0.546659i	$0.184101\pi$
$480$	−0.138895	+	0.269419i	−0.00633968	+	0.0122973i
$481$	−2.56687	−	7.41649i	−0.117039	−	0.338163i
$482$	−2.11830			−0.0964858
$483$	4.26322	+	11.9509i	0.193983	+	0.543787i
$484$	−4.60033			−0.209106
$485$	1.74277	+	5.03541i	0.0791352	+	0.228646i
$486$	0.458227	−	0.888835i	0.0207856	−	0.0403184i
$487$	6.44435	−	5.06789i	0.292021	−	0.229648i	−0.461390	−	0.887197i	$-0.652649\pi$
$487$	6.44435	−	5.06789i	0.292021	−	0.229648i	0.753412	+	0.657549i	$0.228407\pi$
$488$	−6.01177	−	0.574055i	−0.272140	−	0.0259862i
$489$	5.87529	+	0.844739i	0.265690	+	0.0382004i
$490$	0.879221	+	1.93107i	0.0397191	+	0.0872368i
$491$	−24.6818	−	15.8621i	−1.11388	−	0.715845i	−0.151742	−	0.988420i	$-0.548488\pi$
$491$	−24.6818	−	15.8621i	−1.11388	−	0.715845i	−0.962134	+	0.272575i	$0.912125\pi$
$492$	1.44040	+	2.02276i	0.0649381	+	0.0911929i
$493$	−1.01764	−	4.19477i	−0.0458322	−	0.188923i
$494$	−15.4931	−	5.36220i	−0.697066	−	0.241257i
$495$	−0.226576	−	1.17559i	−0.0101838	−	0.0528387i
$496$	−2.80177	+	9.54194i	−0.125803	+	0.428446i
$497$	−13.3228	−	9.49861i	−0.597609	−	0.426071i
$498$	−5.90378	+	9.18646i	−0.264555	+	0.411655i
$499$	−4.21339	+	17.3678i	−0.188617	+	0.777491i	0.796362	+	0.604820i	$0.206755\pi$
$499$	−4.21339	+	17.3678i	−0.188617	+	0.777491i	−0.984980	+	0.172671i	$0.944760\pi$
$500$	2.78817	−	1.11621i	0.124691	−	0.0499186i
$501$	8.25264	−	11.5892i	0.368701	−	0.517768i
$502$	0.789446	+	0.316047i	0.0352347	+	0.0141059i
$503$	−18.0095	+	11.5740i	−0.803004	+	0.516060i	−0.876595	−	0.481229i	$-0.840191\pi$
$503$	−18.0095	+	11.5740i	−0.803004	+	0.516060i	0.0735906	+	0.997289i	$0.476554\pi$
$504$	−2.61904	+	0.375031i	−0.116661	+	0.0167052i
$505$			4.97083i			0.221199i
$506$	−14.1905	+	12.5474i	−0.630843	+	0.557802i
$507$	8.08511	−	4.66794i	0.359072	−	0.207310i
$508$	0.487363	+	0.0939315i	0.0216232	+	0.00416754i
$509$	3.49594	−	0.166532i	0.154955	−	0.00738141i	0.0300389	−	0.999549i	$-0.490437\pi$
$509$	3.49594	−	0.166532i	0.154955	−	0.00738141i	0.124916	+	0.992167i	$0.460134\pi$
$510$	−1.01001	+	0.145217i	−0.0447239	+	0.00643033i
$511$	1.80309	−	1.71728i	0.0797641	−	0.0759678i
$512$	−0.142315	+	0.989821i	−0.00628949	+	0.0437443i
$513$	−8.32343	−	2.01924i	−0.367488	−	0.0891517i
$514$	4.95404	+	0.235990i	0.218513	+	0.0104091i
$515$	−5.97534	+	0.570576i	−0.263305	+	0.0251426i
$516$	−3.48768	+	3.32549i	−0.153536	+	0.146397i
$517$	−29.0631	−	33.5406i	−1.27819	−	1.47511i
$518$	−5.42913	+	9.39112i	−0.238542	+	0.412622i
$519$	−12.8172	−	3.76347i	−0.562612	−	0.165198i
$520$	0.472633	−	0.336560i	0.0207263	−	0.0147592i
$521$	1.09097	−	22.9023i	0.0477963	−	1.00337i	−0.839843	−	0.542829i	$-0.817353\pi$
$521$	1.09097	−	22.9023i	0.0477963	−	1.00337i	0.887639	−	0.460539i	$-0.152344\pi$
$522$	0.927993	+	0.884839i	0.0406171	+	0.0387284i
$523$	−3.66084	−	2.87892i	−0.160078	−	0.125886i	0.534907	−	0.844911i	$-0.320347\pi$
$523$	−3.66084	−	2.87892i	−0.160078	−	0.125886i	−0.694985	+	0.719024i	$0.744589\pi$
$524$	3.44437	−	1.57299i	0.150468	−	0.0687165i
$525$	10.9202	+	7.02683i	0.476597	+	0.306676i
$526$	−16.3869	−	25.4985i	−0.714504	−	1.11179i
$527$	−31.6364	+	10.9495i	−1.37810	+	0.476966i
$528$	−1.97486	−	3.42056i	−0.0859449	−	0.148861i
$529$	−2.81602	+	22.8270i	−0.122436	+	0.992476i
$530$	−2.76694	−	1.59749i	−0.120188	−	0.0693907i
$531$	−5.58440	−	4.83891i	−0.242342	−	0.209991i
$532$	8.41001	+	21.0421i	0.364620	+	0.912290i
$533$	−0.676467	−	4.70493i	−0.0293011	−	0.203793i
$534$	−0.599031	+	6.27334i	−0.0259226	+	0.271474i
$535$	0.697676	+	1.74271i	0.0301632	+	0.0753440i
$536$	1.07556	−	1.12801i	0.0464570	−	0.0487227i
$537$	−4.78776	−	9.28697i	−0.206607	−	0.400762i
$538$	29.7555	+	13.5889i	1.28285	+	0.585858i
$539$	−27.3621	−	3.96605i	−1.17857	−	0.170830i
$540$	0.229079	−	0.198498i	0.00985800	−	0.00854200i
$541$	26.4192	−	5.09188i	1.13585	−	0.218917i	0.413540	−	0.910486i	$-0.364292\pi$
$541$	26.4192	−	5.09188i	1.13585	−	0.218917i	0.722311	+	0.691569i	$0.243080\pi$
$542$	3.97589	−	0.964540i	0.170779	−	0.0414305i
$543$	0.497351	+	5.20850i	0.0213434	+	0.223518i
$544$	−2.99214	+	1.54255i	−0.128287	+	0.0661365i
$545$	1.65165	+	5.62500i	0.0707489	+	0.240949i
$546$	4.78498	+	1.65916i	0.204778	+	0.0710057i
$547$	−0.249348	−	0.545997i	−0.0106614	−	0.0233451i	0.904226	−	0.427053i	$-0.140448\pi$
$547$	−0.249348	−	0.545997i	−0.0106614	−	0.0233451i	−0.914888	+	0.403708i	$0.867721\pi$
$548$	5.96551	−	14.9011i	0.254834	−	0.636544i
$549$	5.36778	+	2.76728i	0.229091	+	0.118105i
$550$	−3.66877	+	19.0354i	−0.156437	+	0.811672i
$551$	5.49106	−	9.51079i	0.233927	−	0.405173i
$552$	−4.54757	−	1.52304i	−0.193557	−	0.0648248i
$553$	−17.3249	+	19.9709i	−0.736730	+	0.849249i
$554$	17.6015	−	20.3133i	0.747817	−	0.863027i
$555$	−0.0591331	−	1.24136i	−0.00251006	−	0.0526927i
$556$	4.95329	+	6.29863i	0.210066	+	0.267121i
$557$	33.9748	+	24.1933i	1.43956	+	1.02510i	0.991360	+	0.131170i	$0.0418732\pi$
$557$	33.9748	+	24.1933i	1.43956	+	1.02510i	0.448197	+	0.893935i	$0.352066\pi$
$558$	6.14745	−	7.81712i	0.260242	−	0.330925i
$559$	8.85083	−	2.59884i	0.374350	−	0.109919i
$560$	−0.779253	−	0.189517i	−0.0329294	−	0.00800855i
$561$	5.52344	−	12.0946i	0.233200	−	0.510636i
$562$	−4.75687	−	4.98886i	−0.200656	−	0.210442i
$563$	6.03963	−	17.4504i	0.254540	−	0.735445i	−0.743251	−	0.669013i	$-0.766717\pi$
$563$	6.03963	−	17.4504i	0.254540	−	0.735445i	0.997791	−	0.0664324i	$-0.0211617\pi$
$564$	3.67506	−	10.6184i	0.154748	−	0.447115i
$565$	1.78226	+	1.86918i	0.0749802	+	0.0786370i
$566$	−5.72154	+	12.5284i	−0.240494	+	0.526609i
$567$	2.57081	+	0.625231i	0.107964	+	0.0262572i
$568$	5.93381	−	1.74232i	0.248977	−	0.0731062i
$569$	6.25415	−	7.95280i	0.262188	−	0.333399i	−0.637080	−	0.770798i	$-0.719858\pi$
$569$	6.25415	−	7.95280i	0.262188	−	0.333399i	0.899268	+	0.437399i	$0.144100\pi$
$570$	−2.11475	−	1.50591i	−0.0885772	−	0.0630755i
$571$	−0.717353	−	0.912188i	−0.0300203	−	0.0381739i	0.770811	−	0.637064i	$-0.219851\pi$
$571$	−0.717353	−	0.912188i	−0.0300203	−	0.0381739i	−0.800831	+	0.598890i	$0.795609\pi$
$572$	0.359744	+	7.55196i	0.0150417	+	0.315763i
$573$	11.6824	−	13.4822i	0.488038	−	0.563225i
$574$	−4.30523	+	4.96276i	−0.179697	+	0.207142i
$575$	11.9731	+	20.2659i	0.499312	+	0.845147i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	1.34407	−	6.97371i	0.0559544	−	0.290319i	−0.943163	−	0.332331i	$-0.892165\pi$
$577$	1.34407	−	6.97371i	0.0559544	−	0.290319i	0.999117	+	0.0420123i	$0.0133769\pi$
$578$	5.03760	+	2.59706i	0.209536	+	0.108024i
$579$	2.57747	−	6.43822i	0.107116	−	0.267563i
$580$	0.161456	+	0.353540i	0.00670411	+	0.0146800i
$581$	−27.2971	−	9.46511i	−1.13247	−	0.392679i
$582$	−4.95258	−	16.8669i	−0.205291	−	0.699158i
$583$	37.0041	−	19.0769i	1.53255	−	0.790086i
$584$	0.0894608	+	0.936876i	0.00370191	+	0.0387682i
$585$	−0.563864	+	0.136792i	−0.0233129	+	0.00565565i
$586$	12.5837	−	2.42530i	0.519826	−	0.100188i
$587$	−25.9863	+	22.5173i	−1.07257	+	0.929387i	−0.997699	−	0.0678063i	$-0.978400\pi$
$587$	−25.9863	+	22.5173i	−1.07257	+	0.929387i	−0.0748712	+	0.997193i	$0.523855\pi$
$588$	−2.59420	−	6.50155i	−0.106983	−	0.268119i
$589$	−77.4784	−	35.3832i	−3.19244	−	1.45794i
$590$	−1.02633	−	1.99080i	−0.0422533	−	0.0819599i
$591$	9.94464	−	10.4296i	0.409068	−	0.429018i
$592$	−1.52381	−	3.80629i	−0.0626281	−	0.156437i
$593$	−1.68828	+	17.6804i	−0.0693292	+	0.726048i	0.892254	+	0.451534i	$0.149123\pi$
$593$	−1.68828	+	17.6804i	−0.0693292	+	0.726048i	−0.961583	+	0.274514i	$0.911483\pi$
$594$	0.562105	+	3.90952i	0.0230634	+	0.160410i
$595$	−1.00195	−	2.50690i	−0.0410758	−	0.102773i
$596$	−4.78146	−	4.14316i	−0.195856	−	0.169710i
$597$	−7.04893	−	4.06970i	−0.288493	−	0.166562i
$598$	6.40132	+	6.58011i	0.261769	+	0.269081i
$599$	−8.88079	−	15.3820i	−0.362859	−	0.628490i	0.625571	−	0.780167i	$-0.284866\pi$
$599$	−8.88079	−	15.3820i	−0.362859	−	0.628490i	−0.988430	+	0.151677i	$0.951533\pi$
$600$	−4.63818	+	1.60529i	−0.189353	+	0.0655357i
$601$	−18.3578	−	28.5653i	−0.748831	−	1.16520i	−0.981278	−	0.192595i	$-0.938310\pi$
$601$	−18.3578	−	28.5653i	−0.748831	−	1.16520i	0.232447	−	0.972609i	$-0.425327\pi$
$602$	−10.7219	−	6.89925i	−0.436994	−	0.281192i
$603$	−1.41775	+	0.647466i	−0.0577354	+	0.0263669i
$604$	−8.75539	−	6.88531i	−0.356252	−	0.280159i
$605$	1.00920	+	0.962267i	0.0410297	+	0.0391217i
$606$	0.780304	−	16.3806i	0.0316977	−	0.665416i
$607$	−18.7576	+	13.3573i	−0.761349	+	0.542154i	−0.893494	−	0.449076i	$-0.851753\pi$
$607$	−18.7576	+	13.3573i	−0.761349	+	0.542154i	0.132144	+	0.991231i	$0.457814\pi$
$608$	−8.21792	−	2.41300i	−0.333281	−	0.0978601i
$609$	−1.69791	+	2.93698i	−0.0688028	+	0.119013i
$610$	1.19875	+	1.38344i	0.0485361	+	0.0560137i
$611$	−15.5665	+	14.8426i	−0.629752	+	0.600467i
$612$	3.35111	−	0.319993i	0.135461	−	0.0129349i
$613$	−5.03056	−	0.239635i	−0.203183	−	0.00967878i	−0.0542561	−	0.998527i	$-0.517279\pi$
$613$	−5.03056	−	0.239635i	−0.203183	−	0.00967878i	−0.148926	+	0.988848i	$0.547582\pi$
$614$	21.6113	+	5.24286i	0.872163	+	0.211584i
$615$	0.107120	−	0.745034i	0.00431949	−	0.0300427i
$616$	7.56714	−	7.20699i	0.304889	−	0.290378i
$617$	16.1494	−	2.32194i	0.650152	−	0.0934778i	0.190655	−	0.981657i	$-0.438939\pi$
$617$	16.1494	−	2.32194i	0.650152	−	0.0934778i	0.459497	+	0.888179i	$0.348030\pi$
$618$	19.7804	−	0.942254i	0.795682	−	0.0379030i
$619$	−30.2155	−	5.82356i	−1.21446	−	0.234069i	−0.458507	−	0.888691i	$-0.651616\pi$
$619$	−30.2155	−	5.82356i	−1.21446	−	0.234069i	−0.755956	+	0.654622i	$0.772828\pi$
$620$	2.61056	−	1.50721i	0.104842	−	0.0605308i
$621$	3.65576	+	3.10410i	0.146701	+	0.124563i
$622$			1.20579i			0.0483480i
$623$	−16.5048	+	2.36340i	−0.661252	+	0.0946876i
$624$	−1.61032	+	1.03489i	−0.0644643	+	0.0414287i
$625$	21.9376	+	8.78248i	0.877503	+	0.351299i
$626$	−19.2937	+	27.0942i	−0.771131	+	1.08290i
$627$	31.4056	−	12.5729i	1.25422	−	0.502114i
$628$	−4.51231	+	18.6000i	−0.180061	+	0.742220i
$629$	7.46191	−	11.6110i	0.297526	−	0.462960i
$630$	0.652997	+	0.465560i	0.0260160	+	0.0185484i
$631$	3.02361	−	10.2975i	0.120368	−	0.409936i	−0.877161	−	0.480197i	$-0.840565\pi$
$631$	3.02361	−	10.2975i	0.120368	−	0.409936i	0.997529	+	0.0702614i	$0.0223833\pi$
$632$	−1.89115	−	9.81219i	−0.0752257	−	0.390308i
$633$	13.2775	+	4.59540i	0.527735	+	0.182651i
$634$	−5.53270	−	22.8061i	−0.219732	−	0.905746i
$635$	−0.0872671	−	0.122550i	−0.00346309	−	0.00486323i
$636$	8.86724	+	5.69863i	0.351609	+	0.225965i
$637$	−1.28895	+	13.3372i	−0.0510701	+	0.528439i
$638$	−5.01290	−	0.720747i	−0.198463	−	0.0285346i
$639$	−6.15631	−	0.587856i	−0.243540	−	0.0232552i
$640$	0.238265	−	0.187373i	0.00941823	−	0.00740658i
$641$	−18.1831	+	35.2703i	−0.718190	+	1.39309i	0.193037	+	0.981191i	$0.438166\pi$
$641$	−18.1831	+	35.2703i	−0.718190	+	1.39309i	−0.911228	+	0.411903i	$0.864864\pi$
$642$	−2.02552	−	5.85234i	−0.0799407	−	0.230974i
$643$	−9.23450			−0.364173			−0.182087	−	0.983282i	$-0.558285\pi$
$643$	−9.23450			−0.364173			−0.182087	+	0.983282i	$0.558285\pi$
$644$	1.08664	−	12.6420i	0.0428195	−	0.498163i
$645$	1.46071			0.0575155
$646$	−9.43015	−	27.2466i	−0.371024	−	1.07200i
$647$	−1.96193	+	3.80562i	−0.0771315	+	0.149614i	−0.924248	−	0.381794i	$-0.875307\pi$
$647$	−1.96193	+	3.80562i	−0.0771315	+	0.149614i	0.847116	+	0.531408i	$0.178337\pi$
$648$	−0.786053	+	0.618159i	−0.0308791	+	0.0242836i
$649$	29.0532	+	2.77425i	1.14044	+	0.108899i
$650$	9.29944	+	1.33706i	0.364754	+	0.0524437i
$651$	23.9274	+	10.9438i	0.937790	+	0.428923i
$652$	−4.99343	−	3.20908i	−0.195558	−	0.125677i
$653$	14.7512	+	20.7152i	0.577260	+	0.810648i	0.995204	−	0.0978248i	$-0.0311885\pi$
$653$	14.7512	+	20.7152i	0.577260	+	0.810648i	−0.417944	+	0.908473i	$0.637249\pi$
$654$	−4.55976	−	18.7956i	−0.178301	−	0.734965i
$655$	−1.08464	−	0.375397i	−0.0423803	−	0.0146680i
$656$	−0.469949	−	2.43833i	−0.0183484	−	0.0952006i
$657$	0.265149	−	0.903015i	0.0103445	−	0.0352300i
$658$	29.5924	+	2.84282i	1.15363	+	0.110825i
$659$	12.6880	−	19.7429i	0.494254	−	0.769075i	−0.501096	−	0.865392i	$-0.667070\pi$
$659$	12.6880	−	19.7429i	0.494254	−	0.769075i	0.995351	+	0.0963166i	$0.0307061\pi$
$660$	−0.282256	+	1.16347i	−0.0109868	+	0.0452882i
$661$	−22.9821	+	9.20063i	−0.893899	+	0.357863i	−0.772705	−	0.634766i	$-0.781097\pi$
$661$	−22.9821	+	9.20063i	−0.893899	+	0.357863i	−0.121194	+	0.992629i	$0.538672\pi$
$662$	−11.0818	+	15.5622i	−0.430706	+	0.604842i
$663$	−5.98226	−	2.39494i	−0.232332	−	0.0930116i
$664$	9.18646	−	5.90378i	0.356504	−	0.229111i
$665$	2.55650	−	6.37525i	0.0991368	−	0.247222i
$666$			4.09997i			0.158871i
$667$	−5.13957	+	3.37630i	−0.199005	+	0.130731i
$668$	−12.3212	+	7.11365i	−0.476722	+	0.275235i
$669$	−7.92554	−	1.52752i	−0.306419	−	0.0590574i
$670$	−0.471901	+	0.0224794i	−0.0182311	+	0.000868455i
$671$	−23.6101	+	3.39461i	−0.911456	+	0.131048i
$672$	2.53815	+	0.746847i	0.0979114	+	0.0288102i
$673$	−4.82462	+	33.5560i	−0.185975	+	1.29349i	0.656325	+	0.754479i	$0.272110\pi$
$673$	−4.82462	+	33.5560i	−0.185975	+	1.29349i	−0.842300	+	0.539009i	$0.818799\pi$
$674$	24.6950	+	5.99093i	0.951214	+	0.230762i
$675$	4.90256	+	0.233538i	0.188700	+	0.00898887i
$676$	−9.29361	+	0.887432i	−0.357446	+	0.0341320i
$677$	−23.8270	+	22.7190i	−0.915747	+	0.873163i	−0.992294	−	0.123903i	$-0.960459\pi$
$677$	−23.8270	+	22.7190i	−0.915747	+	0.873163i	0.0765473	+	0.997066i	$0.475610\pi$
$678$	−5.57973	−	6.43936i	−0.214288	−	0.247302i
$679$	40.2919	−	23.2318i	1.54626	−	0.891555i
$680$	0.979061	+	0.287478i	0.0375453	+	0.0110243i
$681$	15.1109	−	10.7604i	0.579051	−	0.412340i
$682$	−1.86898	+	39.2346i	−0.0715668	+	1.50237i
$683$	14.8617	+	14.1706i	0.568667	+	0.542223i	0.918926	−	0.394430i	$-0.129058\pi$
$683$	14.8617	+	14.1706i	0.568667	+	0.542223i	−0.350259	+	0.936653i	$0.613906\pi$
$684$	6.73243	+	5.29445i	0.257421	+	0.202438i
$685$	−4.42560	+	2.02110i	−0.169093	+	0.0772224i
$686$	15.1046	−	10.7169i	0.576695	−	0.409173i
$687$	5.78798	+	9.00627i	0.220825	+	0.343611i
$688$	4.55396	−	1.57614i	0.173618	−	0.0600899i
$689$	−10.0883	−	17.4734i	−0.384332	−	0.665683i
$690$	0.679042	+	1.28535i	0.0258507	+	0.0489323i
$691$	−18.8323	−	10.8728i	−0.716414	−	0.413622i	0.0970174	−	0.995283i	$-0.469070\pi$
$691$	−18.8323	−	10.8728i	−0.716414	−	0.413622i	−0.813431	+	0.581661i	$0.802403\pi$
$692$	10.0955	+	8.74783i	0.383774	+	0.332542i
$693$	−9.70366	+	3.87832i	−0.368611	+	0.147325i
$694$	1.58656	+	11.0348i	0.0602249	+	0.418874i
$695$	0.230877	−	2.41786i	0.00875768	−	0.0917145i
$696$	−0.476556	−	1.19038i	−0.0180638	−	0.0451213i
$697$	5.76861	−	6.04994i	0.218502	−	0.229158i
$698$	−13.2091	−	25.6221i	−0.499972	−	0.969811i
$699$	−24.2352	−	11.0678i	−0.916660	−	0.418624i
$700$	−7.01433	−	10.9283i	−0.265117	−	0.413049i
$701$	−14.3776	+	12.4582i	−0.543033	+	0.470541i	−0.882655	−	0.470021i	$-0.844246\pi$
$701$	−14.3776	+	12.4582i	−0.543033	+	0.470541i	0.339622	+	0.940562i	$0.389701\pi$
$702$	1.87960	−	0.362263i	0.0709408	−	0.0136727i
$703$	34.1259	−	8.27884i	1.28708	−	0.312242i
$704$	0.375445	+	3.93184i	0.0141501	+	0.148187i
$705$	−3.02730	+	1.56068i	−0.114015	+	0.0587786i
$706$	2.15385	+	7.33533i	0.0810611	+	0.276069i
$707$	42.6087	−	8.18687i	1.60247	−	0.307899i
$708$	3.06959	+	6.72147i	0.115362	+	0.252608i
$709$	−12.6153	+	31.5115i	−0.473778	+	1.18344i	0.478468	+	0.878105i	$0.341192\pi$
$709$	−12.6153	+	31.5115i	−0.473778	+	1.18344i	−0.952245	+	0.305334i	$0.901232\pi$
$710$	−1.66617	−	0.858973i	−0.0625304	−	0.0322367i
$711$	−1.89115	+	9.81219i	−0.0709235	+	0.367986i
$712$	3.15094	−	5.45758i	0.118086	−	0.204532i
$713$	29.8566	+	37.1921i	1.11814	+	1.39285i
$714$	2.90823	+	8.41836i	0.108838	+	0.315049i
$715$	1.50075	−	1.73196i	0.0561249	−	0.0647715i
$716$	0.497158	+	10.4366i	0.0185797	+	0.390035i
$717$	10.4484	+	13.2862i	0.390202	+	0.496183i
$718$	6.69926	+	4.77052i	0.250014	+	0.178034i
$719$	−1.45733	+	1.85314i	−0.0543491	+	0.0691105i	−0.812468	−	0.583006i	$-0.801876\pi$
$719$	−1.45733	+	1.85314i	−0.0543491	+	0.0691105i	0.758119	+	0.652117i	$0.226119\pi$
$720$	−0.290837	+	0.0853974i	−0.0108388	+	0.00318257i
$721$	14.7321	+	50.2794i	0.548653	+	1.87250i
$722$	22.5806	−	49.4447i	0.840364	−	1.84014i
$723$	−1.46179	−	1.53308i	−0.0543647	−	0.0570160i
$724$	1.71128	−	4.94442i	0.0635993	−	0.183758i
$725$	−2.05835	+	5.94721i	−0.0764451	+	0.220874i
$726$	−3.17459	−	3.32942i	−0.117820	−	0.123566i
$727$	−9.20871	+	20.1643i	−0.341532	+	0.747851i	−0.999989	−	0.00476780i	$-0.998482\pi$
$727$	−9.20871	+	20.1643i	−0.341532	+	0.747851i	0.658457	+	0.752619i	$0.271210\pi$
$728$	−3.66333	−	3.49698i	−0.135772	−	0.129607i
$729$	0.959493	−	0.281733i	0.0355368	−	0.0104345i
$730$	0.176344	−	0.224240i	0.00652679	−	0.00829948i
$731$	13.2145	+	9.40997i	0.488754	+	0.348040i
$732$	−3.73313	−	4.74707i	−0.137981	−	0.175457i
$733$	−2.05122	−	43.0604i	−0.0757636	−	1.59047i	−0.642311	−	0.766444i	$-0.722024\pi$
$733$	−2.05122	−	43.0604i	−0.0757636	−	1.59047i	0.566548	−	0.824029i	$-0.308279\pi$
$734$	−19.8962	+	22.9615i	−0.734384	+	0.847524i
$735$	−0.790849	+	1.96891i	−0.0291709	+	0.0726244i
$736$	3.50392	+	3.27453i	0.129156	+	0.120701i
$737$	3.07802	−	5.33129i	0.113380	−	0.196381i
$738$	−0.469949	+	2.43833i	−0.0172991	+	0.0897560i
$739$	−11.6149	−	5.98788i	−0.427260	−	0.220268i	0.231164	−	0.972915i	$-0.425746\pi$
$739$	−11.6149	−	5.98788i	−0.427260	−	0.220268i	−0.658424	+	0.752647i	$0.728777\pi$
$740$	−0.461889	+	1.15374i	−0.0169794	+	0.0424124i
$741$	−6.81063	−	14.9132i	−0.250195	−	0.547850i
$742$	−9.13620	+	26.3485i	−0.335401	+	0.967285i
$743$	−12.7283	−	43.3486i	−0.466956	−	1.59031i	−0.770468	−	0.637478i	$-0.779977\pi$
$743$	−12.7283	−	43.3486i	−0.466956	−	1.59031i	0.303512	−	0.952828i	$-0.401841\pi$
$744$	−8.83927	+	4.55696i	−0.324063	+	0.167066i
$745$	0.182293	+	1.90906i	0.00667870	+	0.0699425i
$746$	4.59943	−	1.11581i	0.168397	−	0.0408527i
$747$	−10.7226	+	2.06662i	−0.392320	+	0.0756135i
$748$	−10.0486	+	8.70715i	−0.367413	+	0.318365i
$749$	13.7890	−	8.85052i	0.503840	−	0.323391i
$750$	2.73190	+	1.24762i	0.0997548	+	0.0455565i
$751$	−0.445981	−	0.865083i	−0.0162741	−	0.0315673i	0.880558	−	0.473938i	$-0.157168\pi$
$751$	−0.445981	−	0.865083i	−0.0162741	−	0.0315673i	−0.896832	+	0.442371i	$0.854138\pi$
$752$	−7.75399	+	8.13215i	−0.282759	+	0.296549i
$753$	0.316047	+	0.789446i	0.0115174	+	0.0287690i
$754$	−0.233308	+	2.44332i	−0.00849659	+	0.0889803i
$755$	0.480486	+	3.34186i	0.0174867	+	0.121623i
$756$	−2.07876	−	1.63668i	−0.0756039	−	0.0595256i
$757$	19.1945	+	16.6321i	0.697635	+	0.604505i	0.929753	−	0.368183i	$-0.120020\pi$
$757$	19.1945	+	16.6321i	0.697635	+	0.604505i	−0.232118	+	0.972688i	$0.574566\pi$
$758$	−10.9274	−	6.30895i	−0.396902	−	0.229151i
$759$	−18.8736	−	1.61139i	−0.685067	−	0.0584899i
$760$	1.29807	+	2.24832i	0.0470859	+	0.0815552i
$761$	8.38573	−	2.90233i	0.303983	−	0.105209i	−0.170819	−	0.985303i	$-0.554641\pi$
$761$	8.38573	−	2.90233i	0.303983	−	0.105209i	0.474801	+	0.880093i	$0.342520\pi$
$762$	0.268337	+	0.417541i	0.00972084	+	0.0151259i
$763$	45.4959	−	23.4218i	1.64706	−	0.847926i
$764$	−16.2273	+	7.41078i	−0.587085	+	0.268113i
$765$	−0.802084	−	0.630766i	−0.0289994	−	0.0228054i
$766$	16.9683	+	16.1792i	0.613090	+	0.584580i
$767$

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)

\(f(q)\)	\(=\)	\(q+(-0.327068 - 0.945001i) q^{2} +(0.458227 - 0.888835i) q^{3} +(-0.786053 + 0.618159i) q^{4} +(0.301743 + 0.0288129i) q^{5} +(-0.989821 - 0.142315i) q^{6} +(-0.249988 - 2.63391i) q^{7} +(0.841254 + 0.540641i) q^{8} +(-0.580057 - 0.814576i) q^{9} +O(q^{10})\)	\(q+(-0.327068 - 0.945001i) q^{2} +(0.458227 - 0.888835i) q^{3} +(-0.786053 + 0.618159i) q^{4} +(0.301743 + 0.0288129i) q^{5} +(-0.989821 - 0.142315i) q^{6} +(-0.249988 - 2.63391i) q^{7} +(0.841254 + 0.540641i) q^{8} +(-0.580057 - 0.814576i) q^{9} +(-0.0714621 - 0.294571i) q^{10} +(3.73249 + 1.29183i) q^{11} +(0.189251 + 0.981929i) q^{12} +(0.539289 - 1.83665i) q^{13} +(-2.40729 + 1.09771i) q^{14} +(0.163876 - 0.254997i) q^{15} +(0.235759 - 0.971812i) q^{16} +(3.12522 - 1.25115i) q^{17} +(-0.580057 + 0.814576i) q^{18} +(7.95134 + 3.18324i) q^{19} +(-0.254997 + 0.163876i) q^{20} +(-2.45567 - 0.984732i) q^{21} -3.94973i q^{22} +(-3.17679 - 3.59277i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-4.81943 - 0.928868i) q^{25} +(-1.91202 + 0.0910808i) q^{26} +(-0.989821 + 0.142315i) q^{27} +(1.82468 + 1.91586i) q^{28} +(0.182480 - 1.26918i) q^{29} +(-0.294571 - 0.0714621i) q^{30} +(-9.93351 - 0.473191i) q^{31} +(-0.995472 + 0.0950560i) q^{32} +(2.85855 - 2.72562i) q^{33} +(-2.20450 - 2.54412i) q^{34} +(0.000458893 - 0.801967i) q^{35} +(0.959493 + 0.281733i) q^{36} +(3.33974 - 2.37822i) q^{37} +(0.407532 - 8.55516i) q^{38} +(-1.38536 - 1.32094i) q^{39} +(0.238265 + 0.187373i) q^{40} +(2.25880 - 1.03156i) q^{41} +(-0.127402 + 2.64268i) q^{42} +(2.60535 + 4.05400i) q^{43} +(-3.73249 + 1.29183i) q^{44} +(-0.151558 - 0.262505i) q^{45} +(-2.35615 + 4.17715i) q^{46} +(-9.73099 - 5.61819i) q^{47} +(-0.755750 - 0.654861i) q^{48} +(-6.87501 + 1.31689i) q^{49} +(0.698498 + 4.85816i) q^{50} +(0.319993 - 3.35111i) q^{51} +(0.711432 + 1.77707i) q^{52} +(7.27378 - 7.62852i) q^{53} +(0.458227 + 0.888835i) q^{54} +(1.08903 + 0.497344i) q^{55} +(1.21370 - 2.35094i) q^{56} +(6.47289 - 5.60879i) q^{57} +(-1.25906 + 0.242663i) q^{58} +(7.18093 - 1.74207i) q^{59} +(0.0288129 + 0.301743i) q^{60} +(-5.36778 + 2.76728i) q^{61} +(2.80177 + 9.54194i) q^{62} +(-2.00052 + 1.73145i) q^{63} +(0.415415 + 0.909632i) q^{64} +(0.215646 - 0.538657i) q^{65} +(-3.51066 - 1.80987i) q^{66} +(0.294967 - 1.53044i) q^{67} +(-1.68318 + 2.91535i) q^{68} +(-4.64907 + 1.17734i) q^{69} +(-0.758010 + 0.261864i) q^{70} +(4.04986 - 4.67379i) q^{71} +(-0.0475819 - 0.998867i) q^{72} +(0.581773 + 0.739784i) q^{73} +(-3.33974 - 2.37822i) q^{74} +(-3.03400 + 3.85804i) q^{75} +(-8.21792 + 2.41300i) q^{76} +(2.46949 - 10.1540i) q^{77} +(-0.795183 + 1.74121i) q^{78} +(-6.89580 - 7.23211i) q^{79} +(0.0991392 - 0.286444i) q^{80} +(-0.327068 + 0.945001i) q^{81} +(-1.71360 - 1.79718i) q^{82} +(4.53632 - 9.93315i) q^{83} +(2.53901 - 0.743942i) q^{84} +(0.979061 - 0.287478i) q^{85} +(2.97891 - 3.78799i) q^{86} +(-1.04447 - 0.743766i) q^{87} +(2.44156 + 3.10469i) q^{88} +(-0.299855 - 6.29474i) q^{89} +(-0.198498 + 0.229079i) q^{90} +(-4.97240 - 0.961302i) q^{91} +(4.71803 + 0.860349i) q^{92} +(-4.97239 + 8.61243i) q^{93} +(-2.12650 + 11.0333i) q^{94} +(2.30754 + 1.18962i) q^{95} +(-0.371662 + 0.928368i) q^{96} +(7.30259 + 15.9904i) q^{97} +(3.49306 + 6.06618i) q^{98} +(-1.11277 - 3.78973i) 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	\( 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9} + 22 q^{14} + 16 q^{16} - 66 q^{17} - 16 q^{18} + 36 q^{23} + 24 q^{25} + 12 q^{26} + 44 q^{28} + 8 q^{29} - 48 q^{31} + 16 q^{32} - 46 q^{35} + 32 q^{36} - 22 q^{37} + 66 q^{38} + 8 q^{39} + 176 q^{43} - 8 q^{46} + 120 q^{47} - 24 q^{49} - 48 q^{50} - 22 q^{51} - 12 q^{52} - 44 q^{53} + 44 q^{57} + 18 q^{58} + 12 q^{59} - 32 q^{64} - 108 q^{70} - 48 q^{71} - 16 q^{72} + 252 q^{73} + 22 q^{74} - 36 q^{75} - 42 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 12 q^{82} - 22 q^{84} - 76 q^{85} + 22 q^{86} + 24 q^{87} - 22 q^{88} + 16 q^{92} + 12 q^{94} + 26 q^{95} + 2 q^{98} + 88 q^{99}+O(q^{100}) \) 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 + 36 * q^23 + 24 * q^25 + 12 * q^26 + 44 * q^28 + 8 * q^29 - 48 * q^31 + 16 * q^32 - 46 * q^35 + 32 * q^36 - 22 * q^37 + 66 * q^38 + 8 * q^39 + 176 * q^43 - 8 * q^46 + 120 * q^47 - 24 * q^49 - 48 * q^50 - 22 * q^51 - 12 * q^52 - 44 * q^53 + 44 * q^57 + 18 * q^58 + 12 * q^59 - 32 * q^64 - 108 * q^70 - 48 * q^71 - 16 * q^72 + 252 * q^73 + 22 * q^74 - 36 * q^75 - 42 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 12 * q^82 - 22 * q^84 - 76 * q^85 + 22 * q^86 + 24 * q^87 - 22 * q^88 + 16 * q^92 + 12 * q^94 + 26 * q^95 + 2 * q^98 + 88 * q^99

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