LMFDB - Embedded newform 966.2.be.b.493.13

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			493.13
Character	$\chi$	$=$	966.493
Dual form			966.2.be.b.145.13

$q$-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 $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

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

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
$5$	0.301743	−	0.0288129i	0.134943	−	0.0128855i	−0.0273658	−	0.999625i	$-0.508712\pi$
$5$	0.301743	−	0.0288129i	0.134943	−	0.0128855i	0.162309	+	0.986740i	$0.448106\pi$
$6$	−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	0.299929	−	0.953961i	$-0.403037\pi$
$11$	3.73249	−	1.29183i	1.12539	−	0.389501i	0.825460	+	0.564461i	$0.190916\pi$
$12$	0.189251	−	0.981929i	0.0546321	−	0.283458i
$13$	0.539289	+	1.83665i	0.149572	+	0.509395i	0.999857	−	0.0169276i	$-0.00538847\pi$
$13$	0.539289	+	1.83665i	0.149572	+	0.509395i	−0.850285	+	0.526323i	$0.823570\pi$
$14$	−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	0.718271	−	0.695763i	$-0.244934\pi$
$17$	3.12522	+	1.25115i	0.757977	+	0.303448i	0.0397057	+	0.999211i	$0.487358\pi$
$18$	−0.580057	−	0.814576i	−0.136721	−	0.191997i
$19$	7.95134	−	3.18324i	1.82416	−	0.730285i	0.842770	−	0.538274i	$-0.180923\pi$
$19$	7.95134	−	3.18324i	1.82416	−	0.730285i	0.981393	−	0.192011i	$-0.0615008\pi$
$20$	−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	0.999725	−	0.0234625i	$-0.00746903\pi$
$29$	0.182480	+	1.26918i	0.0338857	+	0.235680i	−0.965839	+	0.259143i	$0.916560\pi$
$30$	−0.294571	+	0.0714621i	−0.0537810	+	0.0130471i
$31$	−9.93351	+	0.473191i	−1.78411	+	0.0849877i	−0.913464	−	0.406920i	$-0.866603\pi$
$31$	−9.93351	+	0.473191i	−1.78411	+	0.0849877i	−0.870647	+	0.491908i	$0.836300\pi$
$32$	−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	0.820648	−	0.571434i	$-0.193613\pi$
$37$	3.33974	+	2.37822i	0.549050	+	0.390977i	−0.271598	+	0.962411i	$0.587552\pi$
$38$	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	0.583913	−	0.811816i	$-0.301521\pi$
$41$	2.25880	+	1.03156i	0.352765	+	0.161102i	−0.231148	+	0.972919i	$0.574248\pi$
$42$	−0.127402	−	2.64268i	−0.0196586	−	0.407775i
$43$	2.60535	−	4.05400i	0.397312	−	0.618230i	−0.583747	−	0.811935i	$-0.698414\pi$
$43$	2.60535	−	4.05400i	0.397312	−	0.618230i	0.981060	+	0.193705i	$0.0620506\pi$
$44$	−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	−0.996247	−	0.0865567i	$-0.972414\pi$
$47$	−9.73099	+	5.61819i	−1.41941	+	0.819497i	−0.423163	+	0.906054i	$0.639080\pi$
$48$	−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	0.998854	+	0.0478580i	$0.0152395\pi$
$53$	7.27378	+	7.62852i	0.999131	+	1.04786i	0.000276371		1.00000i	$0.499912\pi$
$54$	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	0.674134	−	0.738609i	$-0.264517\pi$
$59$	7.18093	+	1.74207i	0.934878	+	0.226799i	0.260744	+	0.965408i	$0.416032\pi$
$60$	0.0288129	−	0.301743i	0.00371973	−	0.0389548i
$61$	−5.36778	−	2.76728i	−0.687274	−	0.354314i	0.0789585	−	0.996878i	$-0.474841\pi$
$61$	−5.36778	−	2.76728i	−0.687274	−	0.354314i	−0.766232	+	0.642564i	$0.777871\pi$
$62$	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	0.995486	−	0.0949054i	$-0.0302548\pi$
$67$	0.294967	+	1.53044i	0.0360360	+	0.186972i	−0.959450	+	0.281878i	$0.909043\pi$
$68$	−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	0.943338	−	0.331834i	$-0.107667\pi$
$71$	4.04986	+	4.67379i	0.480630	+	0.554677i	−0.462707	+	0.886511i	$0.653122\pi$
$72$	−0.0475819	+	0.998867i	−0.00560758	+	0.117718i
$73$	0.581773	−	0.739784i	0.0680913	−	0.0865852i	−0.750814	−	0.660513i	$-0.770339\pi$
$73$	0.581773	−	0.739784i	0.0680913	−	0.0865852i	0.818906	+	0.573928i	$0.194581\pi$
$74$	−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	−0.986479	−	0.163887i	$-0.947597\pi$
$79$	−6.89580	+	7.23211i	−0.775839	+	0.813676i	0.210640	+	0.977564i	$0.432445\pi$
$80$	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	0.977138	+	0.212606i	$0.0681950\pi$
$83$	4.53632	+	9.93315i	0.497925	+	1.09030i	−0.479213	+	0.877699i	$0.659078\pi$
$84$	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	0.925614	+	0.378470i	$0.123550\pi$
$89$	−0.299855	+	6.29474i	−0.0317846	+	0.667241i	−0.957398	+	0.288771i	$0.906753\pi$
$90$	−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	−0.0396629	−	0.999213i	$-0.512628\pi$
$97$	7.30259	−	15.9904i	0.741466	−	1.62358i	0.781129	−	0.624370i	$-0.214644\pi$
$98$	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	−0.498036	−	0.867157i	$-0.665945\pi$
$101$	1.55884	−	16.3249i	0.155110	−	1.62439i	0.653146	−	0.757232i	$-0.273449\pi$
$102$	−3.27147	−	0.793649i	−0.323923	−	0.0785830i
$103$	−19.4449	−	3.74770i	−1.91596	−	0.369272i	−0.916442	−	0.400167i	$-0.868952\pi$
$103$	−19.4449	−	3.74770i	−1.91596	−	0.369272i	−0.999523	+	0.0308948i	$0.990164\pi$
$104$	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	−0.710908	−	0.703285i	$-0.751716\pi$
$107$	2.83777	−	5.50451i	0.274338	−	0.532142i	0.985246	+	0.171143i	$0.0547461\pi$
$108$	0.690079	+	0.723734i	0.0664029	+	0.0696413i
$109$	7.18823	−	17.9553i	0.688508	−	1.71981i	−0.00564773	−	0.999984i	$-0.501798\pi$
$109$	7.18823	−	17.9553i	0.688508	−	1.71981i	0.694155	−	0.719825i	$-0.255778\pi$
$110$	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	−0.297088	−	0.954850i	$-0.596015\pi$
$113$	6.43936	−	5.57973i	0.605764	−	0.524897i	0.902851	+	0.429953i	$0.141470\pi$
$114$	−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	−0.769987	−	0.638059i	$-0.779737\pi$
$127$	−0.325029	+	0.375103i	−0.0288416	+	0.0332850i	0.741145	+	0.671344i	$0.234283\pi$
$128$	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	−0.393265	−	0.919425i	$-0.628654\pi$
$131$	−3.67982	+	0.892715i	−0.321508	+	0.0779969i	0.0717573	+	0.997422i	$0.477139\pi$
$132$	−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	−0.229837	−	0.973229i	$-0.573819\pi$
$137$	−13.9005	−	8.02544i	−1.18760	−	0.685659i	−0.957760	+	0.287570i	$0.907153\pi$
$138$	2.63315	−	4.00831i	0.224149	−	0.341210i
$139$			8.01298i			0.679652i	0.940488	+	0.339826i	$0.110368\pi$
$139$			8.01298i			0.679652i	−0.940488	+	0.339826i	$0.889632\pi$
$140$	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	−0.899337	−	0.437257i	$-0.855950\pi$
$149$	1.19735	−	6.21244i	0.0980907	−	0.508943i	0.997427	−	0.0716859i	$-0.0228379\pi$
$150$	4.63818	−	1.60529i	0.378706	−	0.131071i
$151$	2.62598	−	10.8244i	0.213699	−	0.880880i	−0.759424	−	0.650596i	$-0.774519\pi$
$151$	2.62598	−	10.8244i	0.213699	−	0.880880i	0.973123	−	0.230285i	$-0.0739657\pi$
$152$	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	0.999377	−	0.0352891i	$-0.0112352\pi$
$157$	15.0447	+	11.8313i	1.20069	+	0.944237i	0.201318	+	0.979526i	$0.435478\pi$
$158$	−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	−0.843083	−	0.537783i	$-0.819262\pi$
$163$	1.94138	−	5.60925i	0.152061	−	0.439350i	0.995144	+	0.0984332i	$0.0313831\pi$
$164$	−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	0.426056	−	0.904697i	$-0.359903\pi$
$167$	14.0825	−	2.02476i	1.08974	−	0.156680i	0.663680	+	0.748017i	$0.268994\pi$
$168$	−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	0.749800	+	0.661664i	$0.230150\pi$
$173$	−2.52808	+	13.1169i	−0.192206	+	0.997259i	−0.942006	+	0.335595i	$0.891063\pi$
$174$	−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	0.976408	−	0.215934i	$-0.0692796\pi$
$179$	6.06070	+	8.51107i	0.452998	+	0.636147i	−0.523410	+	0.852081i	$0.675340\pi$
$180$	0.281402	−	0.112657i	0.0209745	−	0.00839692i
$181$	−4.40160	−	2.82874i	−0.327168	−	0.210258i	0.366737	−	0.930325i	$-0.380475\pi$
$181$	−4.40160	−	2.82874i	−0.327168	−	0.210258i	−0.693905	+	0.720066i	$0.744111\pi$
$182$	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	0.447134	−	0.894467i	$-0.352445\pi$
$191$	17.3366	−	4.20581i	1.25443	−	0.304322i	0.807297	+	0.590145i	$0.200929\pi$
$192$	0.998867	−	0.0475819i	0.0720870	−	0.00343393i
$193$	6.90358	+	0.659212i	0.496931	+	0.0474511i	0.340513	−	0.940240i	$-0.389399\pi$
$193$	6.90358	+	0.659212i	0.496931	+	0.0474511i	0.156418	+	0.987691i	$0.450005\pi$
$194$	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	0.250797	−	0.968040i	$-0.419307\pi$
$197$	13.8271	−	4.06001i	0.985142	−	0.289264i	0.734345	+	0.678776i	$0.237489\pi$
$198$	−3.21735	−	2.29107i	−0.228647	−	0.162819i
$199$	0.387288	+	8.13018i	0.0274541	+	0.576333i	0.970124	+	0.242608i	$0.0780028\pi$
$199$	0.387288	+	8.13018i	0.0274541	+	0.576333i	−0.942670	+	0.333725i	$0.891694\pi$
$200$	−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	−0.797535	−	0.603273i	$-0.793863\pi$
$211$	1.99957	−	13.9073i	0.137656	−	0.957417i	0.935191	−	0.354145i	$-0.115228\pi$
$212$	−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	−0.999929	−	0.0119459i	$-0.996197\pi$
$223$	−2.27398	+	7.74445i	−0.152277	+	0.518607i	0.847652	+	0.530553i	$0.178016\pi$
$224$	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	0.186088	−	0.982533i	$-0.440419\pi$
$227$	16.4884	−	8.50039i	1.09438	−	0.564190i	0.908289	+	0.418343i	$0.137389\pi$
$228$	−1.62091	−	8.41008i	−0.107347	−	0.556971i
$229$	−5.35289	−	9.27148i	−0.353729	−	0.612676i	0.633171	−	0.774012i	$-0.281753\pi$
$229$	−5.35289	−	9.27148i	−0.353729	−	0.612676i	−0.986900	+	0.161336i	$0.948420\pi$
$230$	−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	0.446150	+	0.894958i	$0.352795\pi$
$233$	−1.26772	+	26.6127i	−0.0830510	+	1.74346i	−0.529201	+	0.848497i	$0.677508\pi$
$234$	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	−0.988775	−	0.149414i	$-0.952261\pi$
$239$	−7.02153	−	15.3750i	−0.454185	−	0.994526i	0.534590	−	0.845112i	$-0.320466\pi$
$240$	−0.209173	+	0.219375i	−0.0135021	+	0.0141606i
$241$	0.692827	+	2.00179i	0.0446289	+	0.128947i	0.965113	−	0.261832i	$-0.0843268\pi$
$241$	0.692827	+	2.00179i	0.0446289	+	0.128947i	−0.920484	+	0.390779i	$0.872206\pi$
$242$	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	0.737903	−	0.674907i	$-0.235816\pi$
$251$	−0.556867	−	0.642659i	−0.0351491	−	0.0405643i	−0.773052	+	0.634343i	$0.781271\pi$
$252$	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	0.859702	−	0.510796i	$-0.170649\pi$
$257$	−1.84332	−	4.60439i	−0.114983	−	0.287214i	−0.974685	+	0.223582i	$0.928225\pi$
$258$	−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	0.992080	−	0.125605i	$-0.0400870\pi$
$263$	29.4558	+	7.14590i	1.81632	+	0.440635i	0.824241	+	0.566239i	$0.191602\pi$
$264$	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	−0.742004	−	0.670395i	$-0.766124\pi$
$269$	−22.5736	−	23.6745i	−1.37633	−	1.44346i	−0.634330	−	0.773062i	$-0.718724\pi$
$270$	0.112657	−	0.281402i	0.00685606	−	0.0171256i
$271$	−0.388895	−	4.07269i	−0.0236237	−	0.247398i	−0.999568	−	0.0293798i	$-0.990647\pi$
$271$	−0.388895	−	4.07269i	−0.0236237	−	0.247398i	0.975945	−	0.218018i	$-0.0699593\pi$
$272$	−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	−0.107124	−	0.994246i	$-0.534164\pi$
$277$	13.4391	−	23.2773i	0.807480	−	1.39860i	0.914604	−	0.404350i	$-0.132502\pi$
$278$	−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	0.593567	−	0.804785i	$-0.297719\pi$
$281$	6.27030	+	2.86355i	0.374055	+	0.170825i	−0.219512	+	0.975610i	$0.570447\pi$
$282$	8.83239	−	6.94587i	0.525961	−	0.413620i
$283$	−9.96805	+	9.50451i	−0.592539	+	0.564985i	−0.925878	−	0.377822i	$-0.876673\pi$
$283$	−9.96805	+	9.50451i	−0.592539	+	0.564985i	0.333339	+	0.942807i	$0.391825\pi$
$284$	−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	−0.971128	−	0.238560i	$-0.923325\pi$
$293$	−1.82380	−	12.6848i	−0.106548	−	0.741055i	0.864580	−	0.502495i	$-0.167584\pi$
$294$	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	−0.993246	−	0.116031i	$-0.962983\pi$
$307$	−12.0229	−	18.7080i	−0.686182	−	1.06772i	0.307063	−	0.951689i	$-0.400654\pi$
$308$	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	−0.359184	−	0.933267i	$-0.616945\pi$
$311$	−1.13948	+	0.394377i	−0.0646138	+	0.0223631i	0.294570	+	0.955630i	$0.404824\pi$
$312$	−0.451287	+	1.86023i	−0.0255491	+	0.105315i
$313$	−19.2937	+	27.0942i	−1.09054	+	1.53145i	−0.267430	+	0.963577i	$0.586174\pi$
$313$	−19.2937	+	27.0942i	−1.09054	+	1.53145i	−0.823114	+	0.567876i	$0.807765\pi$
$314$	−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	0.584560	−	0.811351i	$-0.301267\pi$
$317$	23.3614	−	2.23074i	1.31210	−	0.125291i	0.727545	+	0.686060i	$0.240661\pi$
$318$	−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	−0.997821	−	0.0659847i	$-0.978981\pi$
$331$	−11.0818	+	15.5622i	−0.609110	+	0.855375i	0.388711	+	0.921360i	$0.372921\pi$
$332$	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	−0.981390	−	0.192023i	$-0.938495\pi$
$337$	−13.7384	−	21.3773i	−0.748376	−	1.16450i	0.233014	−	0.972473i	$-0.425141\pi$
$338$	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	−0.474406	−	0.880306i	$-0.657337\pi$
$347$	−10.9468	+	2.10982i	−0.587653	+	0.113261i	−0.113247	+	0.993567i	$0.536125\pi$
$348$	1.28078	+	0.0610109i	0.0686568	+	0.00327053i
$349$	28.5332	+	4.10245i	1.52735	+	0.219599i	0.854214	−	0.519922i	$-0.174039\pi$
$349$	28.5332	+	4.10245i	1.52735	+	0.219599i	0.673133	+	0.739521i	$0.264948\pi$
$350$	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	−0.249808	−	0.968295i	$-0.580367\pi$
$353$	−7.63635	+	0.363764i	−0.406442	+	0.0193612i	−0.156634	+	0.987657i	$0.550064\pi$
$354$	−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	0.389445	−	0.921050i	$-0.372667\pi$
$359$	−6.69926	−	4.77052i	−0.353574	−	0.251779i	−0.743018	+	0.669271i	$0.766606\pi$
$360$	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	0.131144	+	0.991363i	$0.458135\pi$
$367$	−15.1912	+	26.3119i	−0.792974	+	1.37347i	−0.924118	+	0.382108i	$0.875198\pi$
$368$	−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	−0.999618	−	0.0276341i	$-0.991203\pi$
$373$	−0.449886	−	4.71142i	−0.0232942	−	0.243948i	0.976324	−	0.216314i	$-0.0694034\pi$
$374$	−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	0.864435	−	0.502744i	$-0.167676\pi$
$379$	9.53598	+	8.26297i	0.489830	+	0.424440i	−0.374605	+	0.927184i	$0.622222\pi$
$380$	−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	−0.165493	−	0.986211i	$-0.552922\pi$
$383$	−20.8392	−	10.7433i	−1.06483	−	0.548959i	−0.899339	+	0.437252i	$0.855952\pi$
$384$	−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	−0.964694	−	0.263375i	$-0.915164\pi$
$389$	−3.29355	−	17.0885i	−0.166989	−	0.866424i	0.797704	−	0.603049i	$-0.206048\pi$
$390$	−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	0.406763	−	0.913534i	$-0.366658\pi$
$397$	−11.4950	−	14.6171i	−0.576918	−	0.733611i	−0.983681	+	0.179923i	$0.942415\pi$
$398$	−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	−0.827501	−	0.561464i	$-0.810238\pi$
$401$	−4.55165	+	4.77363i	−0.227298	+	0.238384i	0.600202	+	0.799848i	$0.295087\pi$
$402$	−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	−0.600557	−	0.799582i	$-0.705054\pi$
$409$	−0.836731	+	0.595833i	−0.0413737	+	0.0294621i	0.559183	+	0.829044i	$0.311115\pi$
$410$	−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	−0.175979	−	0.984394i	$-0.556309\pi$
$419$	13.9851	−	30.6232i	0.683218	−	1.49604i	0.859197	−	0.511645i	$-0.170964\pi$
$420$	0.787561	+	0.151323i	0.0384291	+	0.00738379i
$421$	5.56829	−	18.9639i	0.271382	−	0.924242i	−0.705184	−	0.709024i	$-0.749136\pi$
$421$	5.56829	−	18.9639i	0.271382	−	0.924242i	0.976566	−	0.215218i	$-0.0690461\pi$
$422$	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	−0.998933	−	0.0461816i	$-0.985295\pi$
$431$	−5.06769	+	12.6585i	−0.244102	+	0.609738i	0.754831	+	0.655920i	$0.227719\pi$
$432$	−0.0950560	−	0.995472i	−0.00457339	−	0.0478947i
$433$	0.746406	−	5.19137i	0.0358700	−	0.249481i	−0.963995	−	0.265921i	$-0.914324\pi$
$433$	0.746406	−	5.19137i	0.0358700	−	0.249481i	0.999865	+	0.0164396i	$0.00523313\pi$
$434$	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	0.168821	−	0.985647i	$-0.446004\pi$
$439$	−6.44834	−	2.23179i	−0.307762	−	0.106518i	−0.476584	+	0.879129i	$0.658125\pi$
$440$	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	−0.930414	−	0.366509i	$-0.880553\pi$
$443$	−16.7031	+	13.1355i	−0.793590	+	0.624086i	0.136824	+	0.990595i	$0.456310\pi$
$444$	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	−0.929001	−	0.370077i	$-0.879331\pi$
$449$	−9.12172	+	10.5270i	−0.430480	+	0.496801i	0.498521	+	0.866878i	$0.333877\pi$
$450$	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	0.625897	−	0.779906i	$-0.284733\pi$
$457$	25.1149	+	1.19637i	1.17483	+	0.0559638i	0.548928	+	0.835869i	$0.315036\pi$
$458$	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	$-0.978719\pi$
$461$		−	2.86883i		−	0.133615i	0.997766	−	0.0668074i	$-0.0212813\pi$
$462$	−3.88942	−	9.69921i	−0.180952	−	0.451248i
$463$	25.4340	+	16.3454i	1.18202	+	0.759636i	0.975756	−	0.218861i	$-0.0702341\pi$
$463$	25.4340	+	16.3454i	1.18202	+	0.759636i	0.206261	+	0.978497i	$0.433870\pi$
$464$	−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	0.986860	+	0.161575i	$0.0516575\pi$
$467$	3.97070	+	16.3674i	0.183742	+	0.757395i	−0.803118	+	0.595819i	$0.796827\pi$
$468$	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	0.837355	−	0.546659i	$-0.184101\pi$
$479$	11.0201	+	8.66627i	0.503519	+	0.395972i	−0.333836	+	0.942631i	$0.608343\pi$
$480$	−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	0.753412	−	0.657549i	$-0.228407\pi$
$487$	6.44435	+	5.06789i	0.292021	+	0.229648i	−0.461390	+	0.887197i	$0.652649\pi$
$488$	−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	−0.962134	−	0.272575i	$-0.912125\pi$
$491$	−24.6818	+	15.8621i	−1.11388	+	0.715845i	−0.151742	+	0.988420i	$0.548488\pi$
$492$	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	−0.984980	−	0.172671i	$-0.944760\pi$
$499$	−4.21339	−	17.3678i	−0.188617	−	0.777491i	0.796362	−	0.604820i	$-0.206755\pi$
$500$	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	0.0735906	−	0.997289i	$-0.476554\pi$
$503$	−18.0095	−	11.5740i	−0.803004	−	0.516060i	−0.876595	+	0.481229i	$0.840191\pi$
$504$	−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	0.124916	−	0.992167i	$-0.460134\pi$
$509$	3.49594	+	0.166532i	0.154955	+	0.00738141i	0.0300389	+	0.999549i	$0.490437\pi$
$510$	−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	0.887639	+	0.460539i	$0.152344\pi$
$521$	1.09097	+	22.9023i	0.0477963	+	1.00337i	−0.839843	+	0.542829i	$0.817353\pi$
$522$	0.927993	−	0.884839i	0.0406171	−	0.0387284i
$523$	−3.66084	+	2.87892i	−0.160078	+	0.125886i	−0.694985	−	0.719024i	$-0.744589\pi$
$523$	−3.66084	+	2.87892i	−0.160078	+	0.125886i	0.534907	+	0.844911i	$0.320347\pi$
$524$	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	0.722311	−	0.691569i	$-0.243080\pi$
$541$	26.4192	+	5.09188i	1.13585	+	0.218917i	0.413540	+	0.910486i	$0.364292\pi$
$542$	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	−0.914888	−	0.403708i	$-0.867721\pi$
$547$	−0.249348	+	0.545997i	−0.0106614	+	0.0233451i	0.904226	+	0.427053i	$0.140448\pi$
$548$	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	0.448197	−	0.893935i	$-0.352066\pi$
$557$	33.9748	−	24.1933i	1.43956	−	1.02510i	0.991360	−	0.131170i	$-0.0418732\pi$
$558$	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	0.997791	+	0.0664324i	$0.0211617\pi$
$563$	6.03963	+	17.4504i	0.254540	+	0.735445i	−0.743251	+	0.669013i	$0.766717\pi$
$564$	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	0.899268	−	0.437399i	$-0.144100\pi$
$569$	6.25415	+	7.95280i	0.262188	+	0.333399i	−0.637080	+	0.770798i	$0.719858\pi$
$570$	−2.11475	+	1.50591i	−0.0885772	+	0.0630755i
$571$	−0.717353	+	0.912188i	−0.0300203	+	0.0381739i	−0.800831	−	0.598890i	$-0.795609\pi$
$571$	−0.717353	+	0.912188i	−0.0300203	+	0.0381739i	0.770811	+	0.637064i	$0.219851\pi$
$572$	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	0.999117	−	0.0420123i	$-0.0133769\pi$
$577$	1.34407	+	6.97371i	0.0559544	+	0.290319i	−0.943163	+	0.332331i	$0.892165\pi$
$578$	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	−0.0748712	−	0.997193i	$-0.523855\pi$
$587$	−25.9863	−	22.5173i	−1.07257	−	0.929387i	−0.997699	+	0.0678063i	$0.978400\pi$
$588$	−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	−0.961583	−	0.274514i	$-0.911483\pi$
$593$	−1.68828	−	17.6804i	−0.0693292	−	0.726048i	0.892254	−	0.451534i	$-0.149123\pi$
$594$	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	−0.988430	−	0.151677i	$-0.951533\pi$
$599$	−8.88079	+	15.3820i	−0.362859	+	0.628490i	0.625571	+	0.780167i	$0.284866\pi$
$600$	−4.63818	−	1.60529i	−0.189353	−	0.0655357i
$601$	−18.3578	+	28.5653i	−0.748831	+	1.16520i	0.232447	+	0.972609i	$0.425327\pi$
$601$	−18.3578	+	28.5653i	−0.748831	+	1.16520i	−0.981278	+	0.192595i	$0.938310\pi$
$602$	−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	0.132144	−	0.991231i	$-0.457814\pi$
$607$	−18.7576	−	13.3573i	−0.761349	−	0.542154i	−0.893494	+	0.449076i	$0.851753\pi$
$608$	−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	−0.148926	−	0.988848i	$-0.547582\pi$
$613$	−5.03056	+	0.239635i	−0.203183	+	0.00967878i	−0.0542561	+	0.998527i	$0.517279\pi$
$614$	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	0.459497	−	0.888179i	$-0.348030\pi$
$617$	16.1494	+	2.32194i	0.650152	+	0.0934778i	0.190655	+	0.981657i	$0.438939\pi$
$618$	19.7804	+	0.942254i	0.795682	+	0.0379030i
$619$	−30.2155	+	5.82356i	−1.21446	+	0.234069i	−0.755956	−	0.654622i	$-0.772828\pi$
$619$	−30.2155	+	5.82356i	−1.21446	+	0.234069i	−0.458507	+	0.888691i	$0.651616\pi$
$620$	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	0.997529	−	0.0702614i	$-0.0223833\pi$
$631$	3.02361	+	10.2975i	0.120368	+	0.409936i	−0.877161	+	0.480197i	$0.840565\pi$
$632$	−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	−0.911228	−	0.411903i	$-0.864864\pi$
$641$	−18.1831	−	35.2703i	−0.718190	−	1.39309i	0.193037	−	0.981191i	$-0.438166\pi$
$642$	−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	0.847116	−	0.531408i	$-0.178337\pi$
$647$	−1.96193	−	3.80562i	−0.0771315	−	0.149614i	−0.924248	+	0.381794i	$0.875307\pi$
$648$	−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	−0.417944	−	0.908473i	$-0.637249\pi$
$653$	14.7512	−	20.7152i	0.577260	−	0.810648i	0.995204	+	0.0978248i	$0.0311885\pi$
$654$	−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	0.995351	−	0.0963166i	$-0.0307061\pi$
$659$	12.6880	+	19.7429i	0.494254	+	0.769075i	−0.501096	+	0.865392i	$0.667070\pi$
$660$	−0.282256	−	1.16347i	−0.0109868	−	0.0452882i
$661$	−22.9821	−	9.20063i	−0.893899	−	0.357863i	−0.121194	−	0.992629i	$-0.538672\pi$
$661$	−22.9821	−	9.20063i	−0.893899	−	0.357863i	−0.772705	+	0.634766i	$0.781097\pi$
$662$	−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	−0.842300	−	0.539009i	$-0.818799\pi$
$673$	−4.82462	−	33.5560i	−0.185975	−	1.29349i	0.656325	−	0.754479i	$-0.272110\pi$
$674$	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	0.0765473	−	0.997066i	$-0.475610\pi$
$677$	−23.8270	−	22.7190i	−0.915747	−	0.873163i	−0.992294	+	0.123903i	$0.960459\pi$
$678$	−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	−0.350259	−	0.936653i	$-0.613906\pi$
$683$	14.8617	−	14.1706i	0.568667	−	0.542223i	0.918926	+	0.394430i	$0.129058\pi$
$684$	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	−0.813431	−	0.581661i	$-0.802403\pi$
$691$	−18.8323	+	10.8728i	−0.716414	+	0.413622i	0.0970174	+	0.995283i	$0.469070\pi$
$692$	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	0.339622	−	0.940562i	$-0.389701\pi$
$701$	−14.3776	−	12.4582i	−0.543033	−	0.470541i	−0.882655	+	0.470021i	$0.844246\pi$
$702$	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	−0.952245	−	0.305334i	$-0.901232\pi$
$709$	−12.6153	−	31.5115i	−0.473778	−	1.18344i	0.478468	−	0.878105i	$-0.341192\pi$
$710$	−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	0.758119	−	0.652117i	$-0.226119\pi$
$719$	−1.45733	−	1.85314i	−0.0543491	−	0.0691105i	−0.812468	+	0.583006i	$0.801876\pi$
$720$	−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	0.658457	−	0.752619i	$-0.271210\pi$
$727$	−9.20871	−	20.1643i	−0.341532	−	0.747851i	−0.999989	+	0.00476780i	$0.998482\pi$
$728$	−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	0.566548	+	0.824029i	$0.308279\pi$
$733$	−2.05122	+	43.0604i	−0.0757636	+	1.59047i	−0.642311	+	0.766444i	$0.722024\pi$
$734$	−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	−0.658424	−	0.752647i	$-0.728777\pi$
$739$	−11.6149	+	5.98788i	−0.427260	+	0.220268i	0.231164	+	0.972915i	$0.425746\pi$
$740$	−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	0.303512	+	0.952828i	$0.401841\pi$
$743$	−12.7283	+	43.3486i	−0.466956	+	1.59031i	−0.770468	+	0.637478i	$0.779977\pi$
$744$	−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	−0.896832	−	0.442371i	$-0.854138\pi$
$751$	−0.445981	+	0.865083i	−0.0162741	+	0.0315673i	0.880558	+	0.473938i	$0.157168\pi$
$752$	−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	−0.232118	−	0.972688i	$-0.574566\pi$
$757$	19.1945	−	16.6321i	0.697635	−	0.604505i	0.929753	+	0.368183i	$0.120020\pi$
$758$	−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	0.474801	−	0.880093i	$-0.342520\pi$
$761$	8.38573	+	2.90233i	0.303983	+	0.105209i	−0.170819	+	0.985303i	$0.554641\pi$
$762$	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
$767$	0.673016	+	14.1283i	0.0243012	+	0.510145i
$768$	−0.814576	−	0.580057i	−0.0293935	−	0.0209310i
$769$	41.3774	−	12.1495i	1.49211	−	0.438123i	0.568895	−	0.822410i	$-0.307371\pi$
$769$	41.3774	−	12.1495i	1.49211	−	0.438123i	0.923214	+	0.384287i	$0.125553\pi$
$770$	−3.16755	+	0.00181250i	−0.114151	+	6.53179e-5i
$771$	3.24789	−	3.74826i	0.116970	−	0.134990i
$772$	−5.01909	−	4.78569i	−0.180641	−	0.172241i
$773$	15.7674	+	1.50561i	0.567116	+	0.0541530i	0.374676	−	0.927156i	$-0.377754\pi$
$773$	15.7674	+	1.50561i	0.567116	+	0.0541530i	0.192440	+	0.981309i	$0.438360\pi$
$774$	−4.81355	+	0.229297i	−0.173019	+	0.00824193i
$775$	47.4343	−	11.5074i	1.70389	−	0.413359i
$776$	−2.50176	−	17.4001i	−0.0898078	−	0.624627i
$777$	−10.5432	−	2.55137i	−0.378235	−	0.0915297i
$778$	17.2259	+	2.47671i	0.617579	+	0.0887944i
$779$	21.2442	+	1.01198i	0.761152	+	0.0362581i
$780$	0.569734	−	0.109807i	0.0203998	−	0.00393173i
$781$	21.1538	+	12.2132i	0.756944	+	0.437022i
$782$	−2.13724	−	16.0024i	−0.0764275	−	0.572244i
$783$		−	1.28223i		−	0.0458231i
$784$	−0.341075	−	6.99169i	−0.0121813	−	0.249703i
$785$	4.88051	+	3.13651i	0.174193	+	0.111947i
$786$	3.51532	−	1.40732i	0.125387	−	0.0501975i
$787$	−2.55284	−	3.58497i	−0.0909990	−	0.127790i	0.766567	−	0.642165i	$-0.221964\pi$
$787$	−2.55284	−	3.58497i	−0.0909990	−	0.127790i	−0.857566	+	0.514375i	$0.828024\pi$
$788$	−13.3786	−	5.35598i	−0.476593	−	0.190799i
$789$	7.14590	+	29.4558i	0.254401	+	1.04865i
$790$	−1.63758	−	2.54812i	−0.0582625	−	0.0906582i
$791$	13.0868	+	18.3556i	0.465312	+	0.652649i
$792$	1.11277	+	3.78973i	0.0395404	+	0.134662i
$793$	2.18775	−	11.3511i	0.0776892	−	0.403090i
$794$	17.5728	−	6.08201i	0.623636	−	0.215842i
$795$	−0.753246	+	3.10492i	−0.0267149	+	0.110120i
$796$	4.72131	−	6.63016i	0.167343	−	0.235000i
$797$	29.3484	−	18.8610i	1.03957	−	0.668092i	0.0946911	−	0.995507i	$-0.469814\pi$
$797$	29.3484	−	18.8610i	1.03957	−	0.668092i	0.944881	+	0.327414i	$0.106177\pi$
$798$	−9.42530	−	20.6073i	−0.333652	−	0.729491i
$799$	−37.4406	+	5.38315i	−1.32455	+	0.190442i
$800$	4.88590	−	0.466547i	0.172743	−	0.0164949i
$801$	−4.95361	−	3.89556i	−0.175027	−	0.137643i
$802$	−3.02239	−	5.86261i	−0.106724	−	0.207016i
$803$	1.21579	−	3.51279i	0.0429042	−	0.123964i
$804$	1.55860			0.0549676
$805$	−2.88274	−	2.54603i	−0.101603	−	0.0897358i
$806$	19.0362			0.670521
$807$	10.6989	−	30.9124i	0.376619	−	1.08817i
$808$	−7.51453	−	14.5762i	−0.264360	−	0.512787i
$809$	13.0710	+	10.2791i	0.459551	+	0.361395i	0.820935	−	0.571022i	$-0.193453\pi$
$809$	13.0710	+	10.2791i	0.459551	+	0.361395i	−0.361383	+	0.932417i	$0.617695\pi$
$810$	0.301743	−	0.0288129i	0.0106022	−	0.00101238i
$811$	−2.27827	+	0.327566i	−0.0800010	+	0.0115024i	−0.182199	−	0.983262i	$-0.558322\pi$
$811$	−2.27827	+	0.327566i	−0.0800010	+	0.0115024i	0.102198	+	0.994764i	$0.467412\pi$
$812$	2.76454	+	1.96624i	0.0970164	+	0.0690014i
$813$	3.44175	−	2.21188i	0.120707	−	0.0775739i
$814$	−9.39331	+	13.1911i	−0.329235	+	0.462346i
$815$	0.424178	−	1.74849i	0.0148583	−	0.0612468i
$816$	−3.18121	+	1.10103i	−0.111365	+	0.0385437i
$817$	7.81118	−	40.5282i	0.273278	−	1.41790i
$818$	−0.289395	−	0.985589i	−0.0101185	−	0.0344603i
$819$	2.10122	−	4.60801i	0.0734226	−	0.161017i
$820$	−0.406938	−	0.633208i	−0.0142109	−	0.0221126i
$821$	5.18050	+	21.3543i	0.180801	+	0.745270i	0.987931	+	0.154896i	$0.0495044\pi$
$821$	5.18050	+	21.3543i	0.180801	+	0.745270i	−0.807130	+	0.590373i	$0.798980\pi$
$822$	14.9011	+	5.96551i	0.519736	+	0.208071i
$823$	28.6367	+	40.2146i	0.998213	+	1.40179i	0.914170	+	0.405331i	$0.132844\pi$
$823$	28.6367	+	40.2146i	0.998213	+	1.40179i	0.0840428	+	0.996462i	$0.473217\pi$
$824$	−18.3843	+	7.35995i	−0.640446	+	0.256396i
$825$	−16.3083	−	10.4807i	−0.567783	−	0.364892i
$826$	−15.3743	−	12.0762i	−0.534940	−	0.420186i
$827$		−	42.4966i		−	1.47775i	−0.673842	−	0.738875i	$-0.735357\pi$
$827$		−	42.4966i		−	1.47775i	0.673842	−	0.738875i	$-0.264643\pi$
$828$	−2.03591	+	4.34224i	−0.0707526	+	0.150903i
$829$	−10.2556	−	5.92106i	−0.356191	−	0.205647i	0.311218	−	0.950339i	$-0.399263\pi$
$829$	−10.2556	−	5.92106i	−0.356191	−	0.205647i	−0.667409	+	0.744692i	$0.732597\pi$
$830$	−3.25019	+	0.626423i	−0.112816	+	0.0217434i
$831$	26.8478	+	1.27892i	0.931341	+	0.0443652i
$832$	1.89471	+	0.272418i	0.0656871	+	0.00944438i
$833$	−19.8383	−	12.7172i	−0.687356	−	0.440626i
$834$	−1.14037	−	7.93142i	−0.0394876	−	0.274643i
$835$	4.19095	−	1.01671i	0.145034	−	0.0351848i
$836$	−33.7905	+	1.60964i	−1.16867	+	0.0556706i
$837$	9.89974	+	0.945311i	0.342185	+	0.0326747i
$838$	24.3648	+	23.2318i	0.841669	+	0.802529i
$839$	−4.78056	+	5.51707i	−0.165043	+	0.190470i	−0.832247	−	0.554405i	$-0.812946\pi$
$839$	−4.78056	+	5.51707i	−0.165043	+	0.190470i	0.667203	+	0.744876i	$0.267491\pi$
$840$	−0.400586	+	0.694753i	−0.0138215	+	0.0239713i
$841$	26.2478	−	7.70704i	0.905096	−	0.265760i
$842$	16.0997	+	11.4645i	0.554831	+	0.395093i
$843$	0.327993	+	6.88542i	0.0112967	+	0.237146i
$844$	−10.1687	+	9.69582i	−0.350020	+	0.333744i
$845$	2.22441	−	1.74929i	0.0765220	−	0.0601776i
$846$	10.2210	+	4.66776i	0.351404	+	0.160481i
$847$	6.58617	+	10.2354i	0.226304	+	0.351693i
$848$	−5.69863	+	8.86724i	−0.195692	+	0.304502i
$849$	−13.0156	−	4.50473i	−0.446693	−	0.154602i
$850$	8.26125	−	14.3089i	0.283358	−	0.490791i
$851$	−19.1541	+	4.44383i	−0.656592	+	0.152333i
$852$	5.35577	−	3.09216i	0.183486	−	0.105936i
$853$	9.47213	−	8.20765i	0.324319	−	0.281024i	−0.477449	−	0.878660i	$-0.658438\pi$
$853$	9.47213	−	8.20765i	0.324319	−	0.281024i	0.801768	+	0.597635i	$0.203893\pi$
$854$	9.88413	+	12.5539i	0.338228	+	0.429586i
$855$	−0.369469	+	2.56971i	−0.0126356	+	0.0878823i
$856$	−0.588677	−	6.16491i	−0.0201206	−	0.210712i
$857$	9.65668	−	24.1212i	0.329866	−	0.823965i	−0.667015	−	0.745044i	$-0.732428\pi$
$857$	9.65668	−	24.1212i	0.329866	−	0.823965i	0.996881	−	0.0789210i	$-0.0251475\pi$
$858$	−5.21736	−	5.47181i	−0.178118	−	0.186804i
$859$	4.21973	−	8.18514i	0.143975	−	0.279273i	−0.805811	−	0.592173i	$-0.798270\pi$
$859$	4.21973	−	8.18514i	0.143975	−	0.279273i	0.949786	+	0.312900i	$0.101300\pi$
$860$	−1.32871	+	0.606802i	−0.0453087	+	0.0206918i
$861$	−6.56267	−	0.308855i	−0.223655	−	0.0105257i
$862$	−10.3048	−	8.92916i	−0.350983	−	0.304128i
$863$	−38.3897	−	7.39902i	−1.30680	−	0.251865i	−0.512132	−	0.858907i	$-0.671144\pi$
$863$	−38.3897	−	7.39902i	−1.30680	−	0.251865i	−0.794670	+	0.607041i	$0.792356\pi$
$864$	0.971812	+	0.235759i	0.0330617	+	0.00802068i
$865$	−0.384892	+	4.03077i	−0.0130867	+	0.137050i
$866$	4.66172	+	2.40328i	0.158412	+	0.0816669i
$867$	1.59676	−	5.43806i	0.0542287	−	0.184686i
$868$	−17.2189	+	19.8947i	−0.584448	+	0.675270i
$869$	−16.3959	+	35.9020i	−0.556193	+	1.21789i
$870$	−0.144451	−	0.360822i	−0.00489736	−	0.0122330i
$871$	−2.65180	+	1.36710i	−0.0898529	+	0.0463224i
$872$	−3.66026	−	18.9912i	−0.123952	−	0.643125i
$873$	8.78951	+	15.2239i	0.297480	+	0.515250i
$874$	−32.0314	−	25.7138i	−1.08348	−	0.869781i
$875$	−1.50825	−	7.80153i	−0.0509882	−	0.263740i
$876$	−0.616314	−	0.711264i	−0.0208233	−	0.0240314i
$877$	1.80298	−	37.8492i	0.0608823	−	1.27808i	−0.737260	−	0.675609i	$-0.763881\pi$
$877$	1.80298	−	37.8492i	0.0608823	−	1.27808i	0.798143	−	0.602469i	$-0.205816\pi$
$878$	4.21809	−	5.36374i	0.142354	−	0.181017i
$879$	10.4390	−	7.43358i	0.352099	−	0.250728i
$880$	0.740073	+	0.941080i	0.0249479	+	0.0317238i
$881$	−22.1235	−	6.49605i	−0.745360	−	0.218857i	−0.113068	−	0.993587i	$-0.536068\pi$
$881$	−22.1235	−	6.49605i	−0.745360	−	0.218857i	−0.632292	+	0.774730i	$0.717886\pi$
$882$	2.91519	+	6.36409i	0.0981596	+	0.214290i
$883$	−22.6147	−	49.5193i	−0.761045	−	1.66646i	−0.745436	−	0.666578i	$-0.767759\pi$
$883$	−22.6147	−	49.5193i	−0.761045	−	1.66646i	−0.0156091	−	0.999878i	$-0.504969\pi$
$884$	4.44676	−	4.66363i	0.149561	−	0.156855i
$885$	0.732562	+	2.11660i	0.0246248	+	0.0711487i
$886$	−6.94999	−	20.0807i	−0.233490	−	0.674624i
$887$	10.6612	−	11.1812i	0.357969	−	0.375427i	−0.519982	−	0.854177i	$-0.674061\pi$
$887$	10.6612	−	11.1812i	0.357969	−	0.375427i	0.877951	+	0.478750i	$0.158910\pi$
$888$	1.70319	+	3.72947i	0.0571554	+	0.125153i
$889$	−0.906736	−	0.949868i	−0.0304109	−	0.0318576i
$890$	−1.83282	−	0.538164i	−0.0614362	−	0.0180393i
$891$	−2.44156	−	3.10469i	−0.0817953	−	0.104011i
$892$	6.57477	−	4.68187i	0.220140	−	0.156761i
$893$	−59.4904	+	75.6482i	−1.99077	+	2.53147i
$894$	−0.301040	+	6.31961i	−0.0100683	+	0.211359i
$895$	2.07400	+	2.39353i	0.0693262	+	0.0800067i
$896$	−1.99853	+	1.73374i	−0.0667663	+	0.0579203i
$897$	−0.344834	−	9.17365i	−0.0115137	−	0.306299i
$898$	−6.96462	−	12.0631i	−0.232412	−	0.402550i
$899$	−2.41323	−	12.5210i	−0.0804858	−	0.417600i
$900$	−4.36251	+	2.24903i	−0.145417	+	0.0749677i
$901$	13.1877	+	32.9414i	0.439347	+	1.09744i
$902$	−4.07437	+	8.92163i	−0.135662	+	0.297058i
$903$	−2.40577	+	12.5209i	−0.0800590	+	0.416668i
$904$	2.40050	−	8.17535i	0.0798394	−	0.271908i
$905$	−1.40965	−	0.726727i	−0.0468585	−	0.0241572i
$906$	−1.05877	+	11.0880i	−0.0351754	+	0.368373i
$907$	13.1769	+	3.19669i	0.437533	+	0.106144i	0.448474	−	0.893796i	$-0.351968\pi$
$907$	13.1769	+	3.19669i	0.437533	+	0.106144i	−0.0109414	+	0.999940i	$0.503483\pi$
$908$	−18.2154	−	3.51073i	−0.604499	−	0.116508i
$909$	12.3937	+	10.7392i	0.411072	+	0.356196i
$910$	0.0721664	−	1.53342i	0.00239229	−	0.0508324i
$911$	9.02760	−	4.12277i	0.299098	−	0.136593i	−0.260213	−	0.965551i	$-0.583793\pi$
$911$	9.02760	−	4.12277i	0.299098	−	0.136593i	0.559311	+	0.828958i	$0.311066\pi$
$912$	−3.92465	+	7.61275i	−0.129958	+	0.252083i
$913$	29.7637	+	31.2153i	0.985035	+	1.03307i
$914$	−9.34485	+	23.3423i	−0.309100	+	0.772095i
$915$	−0.174005	−	1.82226i	−0.00575241	−	0.0602420i
$916$	−1.52359	+	10.5968i	−0.0503409	+	0.350128i
$917$	−1.43143	−	9.91550i	−0.0472698	−	0.327439i
$918$	2.54412	−	2.20450i	0.0839686	−	0.0727592i
$919$	−10.1376	+	5.85295i	−0.334409	+	0.193071i	−0.657797	−	0.753195i	$-0.728511\pi$
$919$	−10.1376	+	5.85295i	−0.334409	+	0.193071i	0.323388	+	0.946266i	$0.395178\pi$
$920$	−0.0837266	+	1.45128i	−0.00276038	+	0.0478471i
$921$	11.1191	−	19.2589i	0.366387	−	0.634601i
$922$	2.71105	+	0.938303i	0.0892836	+	0.0309014i
$923$	−6.40008	+	9.95871i	−0.210661	+	0.327795i
$924$	10.4379	−	0.503203i	0.343381	−	0.0165542i
$925$	−18.3047	−	8.35947i	−0.601854	−	0.274858i
$926$	−23.7651	+	18.6891i	−0.780969	+	0.614161i
$927$	14.3319	−	13.6655i	0.470723	−	0.448833i
$928$	−0.0610109	−	1.28078i	−0.00200278	−	0.0420436i
$929$	−19.4023	−	13.8163i	−0.636568	−	0.453298i	0.215660	−	0.976469i	$-0.430810\pi$
$929$	−19.4023	−	13.8163i	−0.636568	−	0.453298i	−0.852228	+	0.523170i	$0.824749\pi$
$930$	2.89231	−	0.849258i	0.0948425	−	0.0278483i
$931$	−58.8575	+	11.4137i	−1.92898	+	0.374070i
$932$	17.4474	−	20.1353i	0.571507	−	0.659555i
$933$	−0.872675	−	0.832094i	−0.0285701	−	0.0272415i
$934$	−16.7659	−	1.60095i	−0.548598	−	0.0523848i
$935$	4.02571	−	0.191768i	0.131655	−	0.00627149i
$936$	−1.86023	+	0.451287i	−0.0608036	+	0.0147508i
$937$	6.09886	+	42.4185i	0.199241	+	1.38575i	0.806493	+	0.591243i	$0.201363\pi$
$937$	6.09886	+	42.4185i	0.199241	+	1.38575i	−0.607252	+	0.794509i	$0.707728\pi$
$938$	0.969899	−	4.00799i	0.0316683	−	0.130865i
$939$	−32.9231	−	4.73363i	−1.07441	−	0.154476i
$940$	3.40206	+	0.162060i	0.110963	+	0.00528581i
$941$	−12.7379	+	2.45503i	−0.415244	+	0.0800318i	−0.392594	−	0.919712i	$-0.628422\pi$
$941$	−12.7379	+	2.45503i	−0.415244	+	0.0800318i	−0.0226498	+	0.999743i	$0.507210\pi$
$942$	−16.5753	−	9.56975i	−0.540052	−	0.311799i
$943$	−10.8819	+	4.83830i	−0.354363	+	0.157557i
$944$			7.38922i			0.240499i
$945$	0.113678	−	0.793870i	0.00369793	−	0.0258246i
$946$	16.0122	+	10.2904i	0.520602	+	0.334570i
$947$	49.2558	−	19.7190i	1.60060	−	0.640782i	0.611931	−	0.790911i	$-0.290393\pi$
$947$	49.2558	−	19.7190i	1.60060	−	0.640782i	0.988666	+	0.150129i	$0.0479688\pi$
$948$	5.79638	+	8.13988i	0.188258	+	0.264371i
$949$	1.67247	+	0.669556i	0.0542906	+	0.0217347i
$950$	−9.91069	−	40.8524i	−0.321545	−	1.32543i
$951$	12.6876	+	19.7422i	0.411422	+	0.640185i
$952$	0.851694	+	8.86573i	0.0276036	+	0.287340i
$953$	7.08153	+	24.1175i	0.229393	+	0.781242i	0.991077	+	0.133292i	$0.0425550\pi$
$953$	7.08153	+	24.1175i	0.229393	+	0.781242i	−0.761683	+	0.647949i	$0.775627\pi$
$954$	1.99480	−	10.3500i	0.0645841	−	0.335094i
$955$	5.11001	−	1.76859i	0.165356	−	0.0572302i
$956$	−3.98490	+	16.4260i	−0.128881	+	0.531254i
$957$	−2.93767	+	4.12538i	−0.0949614	+	0.133355i
$958$	−11.7939	+	7.57951i	−0.381045	+	0.244883i
$959$	24.6133	−	34.6064i	0.794804	−	1.11750i
$960$	0.300030	−	0.0431378i	0.00968342	−	0.00139227i
$961$	67.5911	−	6.45417i	2.18036	−	0.208199i
$962$	−6.16905	−	4.85139i	−0.198898	−	0.156415i
$963$	2.83777	+	5.50451i	0.0914460	+	0.177381i
$964$	0.692827	−	2.00179i	0.0223145	−	0.0644734i
$965$	2.10210			0.0676690
$966$	9.89928	+	7.93752i	0.318504	+	0.255385i
$967$	−28.2066			−0.907063			−0.453531	−	0.891240i	$-0.649836\pi$
$967$	−28.2066			−0.907063			−0.453531	+	0.891240i	$0.649836\pi$
$968$	1.50462	−	4.34732i	0.0483603	−	0.139728i
$969$	13.2118	+	25.6272i	0.424423	+	0.823266i
$970$	4.18846	+	3.29384i	0.134483	+	0.105759i
$971$	43.0910	−	4.11469i	1.38286	−	0.132047i	0.623043	−	0.782188i	$-0.285896\pi$
$971$	43.0910	−	4.11469i	1.38286	−	0.132047i	0.759814	+	0.650141i	$0.225290\pi$
$972$	−0.989821	+	0.142315i	−0.0317485	+	0.00456475i
$973$	−21.1055	−	2.00314i	−0.676611	−	0.0642179i
$974$	−6.89690	+	4.43237i	−0.220991	+	0.142022i
$975$	5.44968	−	7.65300i	0.174529	−	0.245092i
$976$	1.42378	−	5.86888i	0.0455739	−	0.187858i
$977$	−28.1240	+	9.73381i	−0.899767	+	0.311412i	−0.737510	−	0.675336i	$-0.763998\pi$
$977$	−28.1240	+	9.73381i	−0.899767	+	0.311412i	−0.162257	+	0.986749i	$0.551877\pi$
$978$	−1.12334	+	5.82844i	−0.0359204	+	0.186373i
$979$	7.01251	+	23.8824i	0.224121	+	0.763285i
$980$	1.53730	+	1.46246i	0.0491072	+	0.0467164i
$981$	10.4564	+	16.2705i	0.333847	+	0.519476i
$982$	−6.91702	−	28.5123i	−0.220731	−	0.909865i
$983$	−26.5803	−	10.6412i	−0.847781	−	0.339400i	−0.0932325	−	0.995644i	$-0.529720\pi$
$983$	−26.5803	−	10.6412i	−0.847781	−	0.339400i	−0.754549	+	0.656244i	$0.772144\pi$
$984$	1.44040	+	2.02276i	0.0459182	+	0.0644831i
$985$	4.05525	−	1.62348i	0.129211	−	0.0517283i
$986$	−3.63122	−	2.33364i	−0.115642	−	0.0743184i
$987$	18.3637	−	23.3788i	0.584522	−	0.744156i
$988$		−	16.3948i		−	0.521587i
$989$	6.28847	+	22.2391i	0.199962	+	0.707164i
$990$	−1.03682	−	0.598611i	−0.0329524	−	0.0190251i
$991$	2.53937	−	0.489424i	0.0806659	−	0.0155471i	−0.148759	−	0.988874i	$-0.547528\pi$
$991$	2.53937	−	0.489424i	0.0806659	−	0.0155471i	0.229424	+	0.973326i	$0.426316\pi$
$992$	9.93351	+	0.473191i	0.315389	+	0.0150238i
$993$	−18.9102	−	2.71887i	−0.600097	−	0.0862809i
$994$	−4.61873	−	15.6967i	−0.146497	−	0.497870i
$995$	0.351116	+	2.44206i	0.0111311	+	0.0774186i
$996$	10.6121	−	2.57448i	0.336259	−	0.0815755i
$997$	7.17009	−	0.341553i	0.227079	−	0.0108171i	0.0662659	−	0.997802i	$-0.478891\pi$
$997$	7.17009	−	0.341553i	0.227079	−	0.0108171i	0.160813	+	0.986985i	$0.448588\pi$
$998$	17.7907	+	1.69880i	0.563154	+	0.0537747i
$999$	−2.96729	−	2.82931i	−0.0938809	−	0.0895153i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.be.b.493.13	yes	320
7.5	odd	6	inner	966.2.be.b.355.13	yes	320
23.7	odd	22	inner	966.2.be.b.283.13	yes	320
161.145	even	66	inner	966.2.be.b.145.13	✓	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.be.b.145.13	✓	320	161.145	even	66	inner
966.2.be.b.283.13	yes	320	23.7	odd	22	inner
966.2.be.b.355.13	yes	320	7.5	odd	6	inner
966.2.be.b.493.13	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)

\(f(q)\)	\(=\)	\(q+(-0.327068 + 0.945001i) q^{2} +(0.458227 + 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(0.301743 - 0.0288129i) q^{5} +(-0.989821 + 0.142315i) q^{6} +(-0.249988 + 2.63391i) q^{7} +(0.841254 - 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +O(q^{10})\)	\(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

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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