LMFDB - Embedded newform 966.2.q.e.547.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(85,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("966.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.q (of order $11$, degree $10$, 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:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 9 x^{19} + 42 x^{18} - 126 x^{17} + 277 x^{16} - 538 x^{15} + 1046 x^{14} - 1170 x^{13} + \cdots + 529 $ x^20 - 9x^19 + 42x^18 - 126x^17 + 277x^16 - 538x^15 + 1046x^14 - 1170x^13 - 619x^12 + 2218x^11 + 1660x^10 - 3225x^9 + 2719x^8 + 8761x^7 + 14705x^6 + 21691x^5 + 21163x^4 + 14656x^3 + 7846x^2 + 2622*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			547.2
Root			$-0.973019 + 2.13061i$ of defining polynomial
Character	$\chi$	$=$	966.547
Dual form			966.2.q.e.883.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959493 + 0.281733i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.0508009 - 0.353328i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(0.415415 + 0.909632i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(0.959493 + 0.281733i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.0508009 - 0.353328i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(0.415415 + 0.909632i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(0.148287 - 0.324704i) q^{10} +(4.94502 - 1.45199i) q^{11} +(-0.959493 + 0.281733i) q^{12} +(-1.93538 + 4.23789i) q^{13} +(0.142315 + 0.989821i) q^{14} +(0.233760 + 0.269773i) q^{15} +(0.415415 + 0.909632i) q^{16} +(-0.0245577 + 0.0157823i) q^{17} +(0.142315 - 0.989821i) q^{18} +(0.765226 + 0.491781i) q^{19} +(0.233760 - 0.269773i) q^{20} +(-0.959493 - 0.281733i) q^{21} +5.15379 q^{22} +(-4.16907 + 2.37041i) q^{23} -1.00000 q^{24} +(4.67520 + 1.37276i) q^{25} +(-3.05094 + 3.52097i) q^{26} +(0.841254 + 0.540641i) q^{27} +(-0.142315 + 0.989821i) q^{28} +(5.02276 - 3.22793i) q^{29} +(0.148287 + 0.324704i) q^{30} +(0.780498 + 0.900743i) q^{31} +(0.142315 + 0.989821i) q^{32} +(-2.14096 + 4.68805i) q^{33} +(-0.0280093 + 0.00822429i) q^{34} +(0.342502 - 0.100568i) q^{35} +(0.415415 - 0.909632i) q^{36} +(-0.127152 - 0.884360i) q^{37} +(0.595679 + 0.687450i) q^{38} +(-1.93538 - 4.23789i) q^{39} +(0.300295 - 0.192988i) q^{40} +(-1.29664 + 9.01835i) q^{41} +(-0.841254 - 0.540641i) q^{42} +(-3.13516 + 3.61817i) q^{43} +(4.94502 + 1.45199i) q^{44} -0.356961 q^{45} +(-4.66802 + 1.09982i) q^{46} +6.35854 q^{47} +(-0.959493 - 0.281733i) q^{48} +(-0.654861 + 0.755750i) q^{49} +(4.09907 + 2.63431i) q^{50} +(0.00415443 - 0.0288947i) q^{51} +(-3.91933 + 2.51880i) q^{52} +(1.31051 + 2.86962i) q^{53} +(0.654861 + 0.755750i) q^{54} +(-0.261817 - 1.82098i) q^{55} +(-0.415415 + 0.909632i) q^{56} +(-0.872780 + 0.256271i) q^{57} +(5.72871 - 1.68210i) q^{58} +(-3.44976 + 7.55392i) q^{59} +(0.0508009 + 0.353328i) q^{60} +(0.169051 + 0.195095i) q^{61} +(0.495114 + 1.08415i) q^{62} +(0.841254 - 0.540641i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(1.39905 + 0.899114i) q^{65} +(-3.37501 + 3.89497i) q^{66} +(-12.8021 - 3.75904i) q^{67} -0.0291918 q^{68} +(0.938729 - 4.70306i) q^{69} +0.356961 q^{70} +(6.11662 + 1.79600i) q^{71} +(0.654861 - 0.755750i) q^{72} +(-9.01716 - 5.79497i) q^{73} +(0.127152 - 0.884360i) q^{74} +(-4.09907 + 2.63431i) q^{75} +(0.377872 + 0.827425i) q^{76} +(3.37501 + 3.89497i) q^{77} +(-0.663032 - 4.61149i) q^{78} +(5.01118 - 10.9730i) q^{79} +(0.342502 - 0.100568i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-3.78488 + 8.28774i) q^{82} +(-0.239227 - 1.66386i) q^{83} +(-0.654861 - 0.755750i) q^{84} +(0.00432877 + 0.00947869i) q^{85} +(-4.02752 + 2.58833i) q^{86} +(-0.849700 + 5.90979i) q^{87} +(4.33564 + 2.78635i) q^{88} +(9.46301 - 10.9209i) q^{89} +(-0.342502 - 0.100568i) q^{90} -4.65891 q^{91} +(-4.78879 - 0.259859i) q^{92} -1.19185 q^{93} +(6.10097 + 1.79141i) q^{94} +(0.212634 - 0.245393i) q^{95} +(-0.841254 - 0.540641i) q^{96} +(0.785361 - 5.46231i) q^{97} +(-0.841254 + 0.540641i) q^{98} +(-2.14096 - 4.68805i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 10 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 10 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 10 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} - 10 q^{10} - 3 q^{11} - 2 q^{12} + 6 q^{13} + 2 q^{14} - 12 q^{15} - 2 q^{16} + 14 q^{17} + 2 q^{18} - 13 q^{19} - 12 q^{20} - 2 q^{21} - 8 q^{22} - 2 q^{23} - 20 q^{24} + 22 q^{25} - 28 q^{26} - 2 q^{27} - 2 q^{28} + 26 q^{29} - 10 q^{30} + 15 q^{31} + 2 q^{32} - 14 q^{33} - 3 q^{34} - q^{35} - 2 q^{36} - 26 q^{37} + 2 q^{38} + 6 q^{39} + q^{40} + 40 q^{41} + 2 q^{42} + 8 q^{43} - 3 q^{44} - 12 q^{45} - 20 q^{46} + 36 q^{47} - 2 q^{48} - 2 q^{49} + 11 q^{50} + 3 q^{51} - 27 q^{52} - 5 q^{53} + 2 q^{54} - 7 q^{55} + 2 q^{56} + 9 q^{57} - 15 q^{58} + 13 q^{59} + 10 q^{60} + 59 q^{61} - 4 q^{62} - 2 q^{63} - 2 q^{64} - q^{65} - 8 q^{66} - 26 q^{67} - 8 q^{68} - 35 q^{69} + 12 q^{70} + 13 q^{71} + 2 q^{72} - 34 q^{73} + 26 q^{74} - 11 q^{75} - 2 q^{76} + 8 q^{77} - 6 q^{78} - 27 q^{79} - q^{80} - 2 q^{81} - 40 q^{82} + 41 q^{83} - 2 q^{84} + 51 q^{85} + 14 q^{86} - 7 q^{87} - 8 q^{88} + 43 q^{89} + q^{90} - 16 q^{91} + 9 q^{92} + 4 q^{93} - 3 q^{94} - 26 q^{95} + 2 q^{96} - 8 q^{97} + 2 q^{98} - 14 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 10 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 - 10 * q^10 - 3 * q^11 - 2 * q^12 + 6 * q^13 + 2 * q^14 - 12 * q^15 - 2 * q^16 + 14 * q^17 + 2 * q^18 - 13 * q^19 - 12 * q^20 - 2 * q^21 - 8 * q^22 - 2 * q^23 - 20 * q^24 + 22 * q^25 - 28 * q^26 - 2 * q^27 - 2 * q^28 + 26 * q^29 - 10 * q^30 + 15 * q^31 + 2 * q^32 - 14 * q^33 - 3 * q^34 - q^35 - 2 * q^36 - 26 * q^37 + 2 * q^38 + 6 * q^39 + q^40 + 40 * q^41 + 2 * q^42 + 8 * q^43 - 3 * q^44 - 12 * q^45 - 20 * q^46 + 36 * q^47 - 2 * q^48 - 2 * q^49 + 11 * q^50 + 3 * q^51 - 27 * q^52 - 5 * q^53 + 2 * q^54 - 7 * q^55 + 2 * q^56 + 9 * q^57 - 15 * q^58 + 13 * q^59 + 10 * q^60 + 59 * q^61 - 4 * q^62 - 2 * q^63 - 2 * q^64 - q^65 - 8 * q^66 - 26 * q^67 - 8 * q^68 - 35 * q^69 + 12 * q^70 + 13 * q^71 + 2 * q^72 - 34 * q^73 + 26 * q^74 - 11 * q^75 - 2 * q^76 + 8 * q^77 - 6 * q^78 - 27 * q^79 - q^80 - 2 * q^81 - 40 * q^82 + 41 * q^83 - 2 * q^84 + 51 * q^85 + 14 * q^86 - 7 * q^87 - 8 * q^88 + 43 * q^89 + q^90 - 16 * q^91 + 9 * q^92 + 4 * q^93 - 3 * q^94 - 26 * q^95 + 2 * q^96 - 8 * q^97 + 2 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{6}{11}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.959493	+	0.281733i	0.678464	+	0.199215i
$2$	0.959493	+	0.281733i	0.678464	+	0.199215i
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$4$	0.841254	+	0.540641i	0.420627	+	0.270320i
$5$	0.0508009	−	0.353328i	0.0227189	−	0.158013i	−0.975304	−	0.220867i	$-0.929111\pi$
$5$	0.0508009	−	0.353328i	0.0227189	−	0.158013i	0.998023	+	0.0628542i	$0.0200203\pi$
$6$	−0.841254	+	0.540641i	−0.343440	+	0.220716i
$7$	0.415415	+	0.909632i	0.157012	+	0.343809i
$7$	0.415415	+	0.909632i	0.157012	+	0.343809i
$8$	0.654861	+	0.755750i	0.231528	+	0.267198i
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$	0.148287	−	0.324704i	0.0468925	−	0.102680i
$11$	4.94502	−	1.45199i	1.49098	−	0.437792i	0.568127	−	0.822941i	$-0.307668\pi$
$11$	4.94502	−	1.45199i	1.49098	−	0.437792i	0.922854	+	0.385149i	$0.125850\pi$
$12$	−0.959493	+	0.281733i	−0.276982	+	0.0813292i
$13$	−1.93538	+	4.23789i	−0.536778	+	1.17538i	0.425909	+	0.904766i	$0.359954\pi$
$13$	−1.93538	+	4.23789i	−0.536778	+	1.17538i	−0.962688	+	0.270615i	$0.912773\pi$
$14$	0.142315	+	0.989821i	0.0380352	+	0.264541i
$15$	0.233760	+	0.269773i	0.0603566	+	0.0696552i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	−0.0245577	+	0.0157823i	−0.00595612	+	0.00382777i	−0.543615	−	0.839334i	$-0.682945\pi$
$17$	−0.0245577	+	0.0157823i	−0.00595612	+	0.00382777i	0.537659	+	0.843162i	$0.319309\pi$
$18$	0.142315	−	0.989821i	0.0335439	−	0.233303i
$19$	0.765226	+	0.491781i	0.175555	+	0.112822i	0.625467	−	0.780250i	$-0.284908\pi$
$19$	0.765226	+	0.491781i	0.175555	+	0.112822i	−0.449912	+	0.893073i	$0.648545\pi$
$20$	0.233760	−	0.269773i	0.0522703	−	0.0603232i
$21$	−0.959493	−	0.281733i	−0.209379	−	0.0614791i
$22$	5.15379			1.09879
$23$	−4.16907	+	2.37041i	−0.869312	+	0.494264i
$23$	−4.16907	+	2.37041i	−0.869312	+	0.494264i
$24$	−1.00000			−0.204124
$25$	4.67520	+	1.37276i	0.935041	+	0.274553i
$26$	−3.05094	+	3.52097i	−0.598338	+	0.690519i
$27$	0.841254	+	0.540641i	0.161899	+	0.104046i
$28$	−0.142315	+	0.989821i	−0.0268950	+	0.187059i
$29$	5.02276	−	3.22793i	0.932703	−	0.599412i	0.0163859	−	0.999866i	$-0.494784\pi$
$29$	5.02276	−	3.22793i	0.932703	−	0.599412i	0.916317	+	0.400454i	$0.131148\pi$
$30$	0.148287	+	0.324704i	0.0270734	+	0.0592825i
$31$	0.780498	+	0.900743i	0.140182	+	0.161778i	0.821499	−	0.570210i	$-0.193138\pi$
$31$	0.780498	+	0.900743i	0.140182	+	0.161778i	−0.681317	+	0.731988i	$0.738593\pi$
$32$	0.142315	+	0.989821i	0.0251579	+	0.174977i
$33$	−2.14096	+	4.68805i	−0.372694	+	0.816085i
$34$	−0.0280093	+	0.00822429i	−0.00480356	+	0.00141045i
$35$	0.342502	−	0.100568i	0.0578934	−	0.0169990i
$36$	0.415415	−	0.909632i	0.0692358	−	0.151605i
$37$	−0.127152	−	0.884360i	−0.0209036	−	0.145388i	0.976697	−	0.214624i	$-0.0688528\pi$
$37$	−0.127152	−	0.884360i	−0.0209036	−	0.145388i	−0.997600	+	0.0692366i	$0.977944\pi$
$38$	0.595679	+	0.687450i	0.0966318	+	0.111519i
$39$	−1.93538	−	4.23789i	−0.309909	−	0.678606i
$40$	0.300295	−	0.192988i	0.0474808	−	0.0305141i
$41$	−1.29664	+	9.01835i	−0.202502	+	1.40843i	0.594327	+	0.804224i	$0.297419\pi$
$41$	−1.29664	+	9.01835i	−0.202502	+	1.40843i	−0.796828	+	0.604206i	$0.793490\pi$
$42$	−0.841254	−	0.540641i	−0.129808	−	0.0834227i
$43$	−3.13516	+	3.61817i	−0.478108	+	0.551766i	−0.942649	−	0.333786i	$-0.891674\pi$
$43$	−3.13516	+	3.61817i	−0.478108	+	0.551766i	0.464541	+	0.885551i	$0.346219\pi$
$44$	4.94502	+	1.45199i	0.745491	+	0.218896i
$45$	−0.356961			−0.0532127
$46$	−4.66802	+	1.09982i	−0.688262	+	0.162160i
$47$	6.35854			0.927488			0.463744	−	0.885969i	$-0.346506\pi$
$47$	6.35854			0.927488			0.463744	+	0.885969i	$0.346506\pi$
$48$	−0.959493	−	0.281733i	−0.138491	−	0.0406646i
$49$	−0.654861	+	0.755750i	−0.0935515	+	0.107964i
$50$	4.09907	+	2.63431i	0.579697	+	0.372548i
$51$	0.00415443	−	0.0288947i	0.000581736	−	0.00404607i
$52$	−3.91933	+	2.51880i	−0.543513	+	0.349294i
$53$	1.31051	+	2.86962i	0.180013	+	0.394172i	0.978031	−	0.208461i	$-0.0668454\pi$
$53$	1.31051	+	2.86962i	0.180013	+	0.394172i	−0.798018	+	0.602633i	$0.794118\pi$
$54$	0.654861	+	0.755750i	0.0891153	+	0.102844i
$55$	−0.261817	−	1.82098i	−0.0353034	−	0.245541i
$56$	−0.415415	+	0.909632i	−0.0555122	+	0.121555i
$57$	−0.872780	+	0.256271i	−0.115603	+	0.0339440i
$58$	5.72871	−	1.68210i	0.752217	−	0.220871i
$59$	−3.44976	+	7.55392i	−0.449120	+	0.983437i	0.540713	+	0.841207i	$0.318154\pi$
$59$	−3.44976	+	7.55392i	−0.449120	+	0.983437i	−0.989834	+	0.142230i	$0.954573\pi$
$60$	0.0508009	+	0.353328i	0.00655837	+	0.0456145i
$61$	0.169051	+	0.195095i	0.0216447	+	0.0249794i	0.766469	−	0.642282i	$-0.222012\pi$
$61$	0.169051	+	0.195095i	0.0216447	+	0.0249794i	−0.744824	+	0.667261i	$0.767467\pi$
$62$	0.495114	+	1.08415i	0.0628795	+	0.137687i
$63$	0.841254	−	0.540641i	0.105988	−	0.0681143i
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	1.39905	+	0.899114i	0.173531	+	0.111521i
$66$	−3.37501	+	3.89497i	−0.415436	+	0.479438i
$67$	−12.8021	−	3.75904i	−1.56403	−	0.459240i	−0.618772	−	0.785570i	$-0.712370\pi$
$67$	−12.8021	−	3.75904i	−1.56403	−	0.459240i	−0.945256	+	0.326330i	$0.894188\pi$
$68$	−0.0291918			−0.00354003
$69$	0.938729	−	4.70306i	0.113010	−	0.566182i
$70$	0.356961			0.0426651
$71$	6.11662	+	1.79600i	0.725909	+	0.213146i	0.623752	−	0.781622i	$-0.285607\pi$
$71$	6.11662	+	1.79600i	0.725909	+	0.213146i	0.102157	+	0.994768i	$0.467426\pi$
$72$	0.654861	−	0.755750i	0.0771761	−	0.0890659i
$73$	−9.01716	−	5.79497i	−1.05538	−	0.678250i	−0.106635	−	0.994298i	$-0.534008\pi$
$73$	−9.01716	−	5.79497i	−1.05538	−	0.678250i	−0.948743	+	0.316048i	$0.897644\pi$
$74$	0.127152	−	0.884360i	0.0147811	−	0.102805i
$75$	−4.09907	+	2.63431i	−0.473320	+	0.304184i
$76$	0.377872	+	0.827425i	0.0433449	+	0.0949122i
$77$	3.37501	+	3.89497i	0.384619	+	0.443873i
$78$	−0.663032	−	4.61149i	−0.0750736	−	0.522148i
$79$	5.01118	−	10.9730i	0.563802	−	1.23455i	−0.386230	−	0.922402i	$-0.626223\pi$
$79$	5.01118	−	10.9730i	0.563802	−	1.23455i	0.950032	−	0.312152i	$-0.101050\pi$
$80$	0.342502	−	0.100568i	0.0382929	−	0.0112438i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	−3.78488	+	8.28774i	−0.417970	+	0.915227i
$83$	−0.239227	−	1.66386i	−0.0262586	−	0.182632i	0.972471	−	0.233024i	$-0.0748621\pi$
$83$	−0.239227	−	1.66386i	−0.0262586	−	0.182632i	−0.998730	+	0.0503918i	$0.983953\pi$
$84$	−0.654861	−	0.755750i	−0.0714512	−	0.0824590i
$85$	0.00432877	+	0.00947869i	0.000469521	+	0.00102811i
$86$	−4.02752	+	2.58833i	−0.434299	+	0.279107i
$87$	−0.849700	+	5.90979i	−0.0910974	+	0.633596i
$88$	4.33564	+	2.78635i	0.462181	+	0.297026i
$89$	9.46301	−	10.9209i	1.00308	−	1.15761i	0.0155950	−	0.999878i	$-0.495036\pi$
$89$	9.46301	−	10.9209i	1.00308	−	1.15761i	0.987482	−	0.157734i	$-0.0504188\pi$
$90$	−0.342502	−	0.100568i	−0.0361029	−	0.0106008i
$91$	−4.65891			−0.488387
$92$	−4.78879	−	0.259859i	−0.499265	−	0.0270921i
$93$	−1.19185			−0.123589
$94$	6.10097	+	1.79141i	0.629267	+	0.184770i
$95$	0.212634	−	0.245393i	0.0218158	−	0.0251768i
$96$	−0.841254	−	0.540641i	−0.0858601	−	0.0551789i
$97$	0.785361	−	5.46231i	0.0797413	−	0.554613i	−0.910312	−	0.413922i	$-0.864159\pi$
$97$	0.785361	−	5.46231i	0.0797413	−	0.554613i	0.990054	−	0.140691i	$-0.0449324\pi$
$98$	−0.841254	+	0.540641i	−0.0849794	+	0.0546130i
$99$	−2.14096	−	4.68805i	−0.215175	−	0.471167i
$100$	3.19086	+	3.68245i	0.319086	+	0.368245i
$101$	−1.31639	−	9.15569i	−0.130986	−	0.911025i	−0.944273	−	0.329163i	$-0.893233\pi$
$101$	−1.31639	−	9.15569i	−0.130986	−	0.911025i	0.813287	−	0.581862i	$-0.197676\pi$
$102$	0.0121267	−	0.0265538i	0.00120072	−	0.00262922i
$103$	2.83142	−	0.831381i	0.278988	−	0.0819184i	−0.139245	−	0.990258i	$-0.544468\pi$
$103$	2.83142	−	0.831381i	0.278988	−	0.0819184i	0.418233	+	0.908340i	$0.362649\pi$
$104$	−4.47019	+	1.31257i	−0.438338	+	0.128708i
$105$	−0.148287	+	0.324704i	−0.0144713	+	0.0316878i
$106$	0.448961	+	3.12259i	0.0436070	+	0.303293i
$107$	−2.25888	−	2.60689i	−0.218375	−	0.252018i	0.635983	−	0.771703i	$-0.280595\pi$
$107$	−2.25888	−	2.60689i	−0.218375	−	0.252018i	−0.854358	+	0.519685i	$0.826049\pi$
$108$	0.415415	+	0.909632i	0.0399733	+	0.0875294i
$109$	14.2062	−	9.12976i	1.36071	−	0.874473i	0.362364	−	0.932037i	$-0.381970\pi$
$109$	14.2062	−	9.12976i	1.36071	−	0.874473i	0.998342	+	0.0575639i	$0.0183333\pi$
$110$	0.261817	−	1.82098i	0.0249633	−	0.173624i
$111$	0.751621	+	0.483038i	0.0713407	+	0.0458479i
$112$	−0.654861	+	0.755750i	−0.0618785	+	0.0714116i
$113$	−9.96787	−	2.92683i	−0.937698	−	0.275333i	−0.223042	−	0.974809i	$-0.571599\pi$
$113$	−9.96787	−	2.92683i	−0.937698	−	0.275333i	−0.714656	+	0.699476i	$0.753417\pi$
$114$	−0.909626			−0.0851943
$115$	0.625738	+	1.59347i	0.0583504	+	0.148592i
$116$	5.97056			0.554353
$117$	4.47019	+	1.31257i	0.413269	+	0.121347i
$118$	−5.43820	+	6.27602i	−0.500627	+	0.577755i
$119$	−0.0245577	−	0.0157823i	−0.00225120	−	0.00144676i
$120$	−0.0508009	+	0.353328i	−0.00463747	+	0.0322543i
$121$	13.0912	−	8.41321i	1.19011	−	0.764837i
$122$	0.107238	+	0.234820i	0.00970892	+	0.0212596i
$123$	−5.96649	−	6.88570i	−0.537981	−	0.620863i
$124$	0.169618	+	1.17972i	0.0152322	+	0.105942i
$125$	1.46398	−	3.20566i	0.130942	−	0.286723i
$126$	0.959493	−	0.281733i	0.0854784	−	0.0250987i
$127$	−5.97387	+	1.75409i	−0.530095	+	0.155650i	−0.535818	−	0.844334i	$-0.679997\pi$
$127$	−5.97387	+	1.75409i	−0.530095	+	0.155650i	0.00572251	+	0.999984i	$0.498178\pi$
$128$	−0.415415	+	0.909632i	−0.0367178	+	0.0804009i
$129$	−0.681336	−	4.73879i	−0.0599883	−	0.417227i
$130$	1.08907	+	1.25685i	0.0955175	+	0.110233i
$131$	2.02344	+	4.43072i	0.176789	+	0.387114i	0.977195	−	0.212344i	$-0.0681099\pi$
$131$	2.02344	+	4.43072i	0.176789	+	0.387114i	−0.800406	+	0.599459i	$0.795383\pi$
$132$	−4.33564	+	2.78635i	−0.377369	+	0.242521i
$133$	−0.129453	+	0.900368i	−0.0112250	+	0.0780718i
$134$	−11.2245	−	7.21355i	−0.969649	−	0.623156i
$135$	0.233760	−	0.269773i	0.0201189	−	0.0232184i
$136$	−0.0280093	−	0.00822429i	−0.00240178	−	0.000705227i
$137$	−0.332602			−0.0284161			−0.0142080	−	0.999899i	$-0.504523\pi$
$137$	−0.332602			−0.0284161			−0.0142080	+	0.999899i	$0.504523\pi$
$138$	2.22571	−	4.24808i	0.189465	−	0.361621i
$139$	−21.4594			−1.82016			−0.910082	−	0.414428i	$-0.863982\pi$
$139$	−21.4594			−1.82016			−0.910082	+	0.414428i	$0.863982\pi$
$140$	0.342502	+	0.100568i	0.0289467	+	0.00849952i
$141$	−4.16396	+	4.80546i	−0.350669	+	0.404693i
$142$	5.36286	+	3.44650i	0.450042	+	0.289224i
$143$	−3.41713	+	23.7667i	−0.285755	+	1.98747i
$144$	0.841254	−	0.540641i	0.0701045	−	0.0450534i
$145$	−0.885358	−	1.93866i	−0.0735250	−	0.160997i
$146$	−7.01927	−	8.10066i	−0.580919	−	0.670416i
$147$	−0.142315	−	0.989821i	−0.0117379	−	0.0816391i
$148$	0.371154	−	0.812714i	0.0305087	−	0.0668047i
$149$	21.1997	−	6.22480i	1.73675	−	0.509956i	0.748544	−	0.663085i	$-0.230753\pi$
$149$	21.1997	−	6.22480i	1.73675	−	0.509956i	0.988206	+	0.153129i	$0.0489351\pi$
$150$	−4.67520	+	1.37276i	−0.381729	+	0.112086i
$151$	1.19829	−	2.62389i	0.0975155	−	0.213529i	−0.854587	−	0.519308i	$-0.826190\pi$
$151$	1.19829	−	2.62389i	0.0975155	−	0.213529i	0.952102	+	0.305779i	$0.0989169\pi$
$152$	0.129453	+	0.900368i	0.0105001	+	0.0730295i
$153$	0.0191166	+	0.0220617i	0.00154548	+	0.00178358i
$154$	2.14096	+	4.68805i	0.172524	+	0.377774i
$155$	0.357908	−	0.230013i	0.0287479	−	0.0184751i
$156$	0.663032	−	4.61149i	0.0530851	−	0.369215i
$157$	−1.66125	−	1.06762i	−0.132582	−	0.0852054i	0.472669	−	0.881240i	$-0.343291\pi$
$157$	−1.66125	−	1.06762i	−0.132582	−	0.0852054i	−0.605251	+	0.796035i	$0.706927\pi$
$158$	7.89963	−	9.11666i	0.628461	−	0.725283i
$159$	−3.02692	−	0.888783i	−0.240050	−	0.0704850i
$160$	0.356961			0.0282203
$161$	−3.88809	−	2.80762i	−0.306425	−	0.221271i
$162$	−1.00000			−0.0785674
$163$	−6.82476	−	2.00393i	−0.534557	−	0.156960i	0.00330270	−	0.999995i	$-0.498949\pi$
$163$	−6.82476	−	2.00393i	−0.534557	−	0.156960i	−0.537859	+	0.843035i	$0.680767\pi$
$164$	−5.96649	+	6.88570i	−0.465905	+	0.537683i
$165$	1.54766	+	0.994619i	0.120485	+	0.0774310i
$166$	0.239227	−	1.66386i	0.0185676	−	0.129141i
$167$	−6.34163	+	4.07552i	−0.490730	+	0.315373i	−0.762499	−	0.646989i	$-0.776028\pi$
$167$	−6.34163	+	4.07552i	−0.490730	+	0.315373i	0.271769	+	0.962363i	$0.412391\pi$
$168$	−0.415415	−	0.909632i	−0.0320500	−	0.0701796i
$169$	−5.70086	−	6.57914i	−0.438528	−	0.506088i
$170$	0.00148297	+	0.0103143i	0.000113739	+	0.000791070i
$171$	0.377872	−	0.827425i	0.0288966	−	0.0632748i
$172$	−4.59359	+	1.34880i	−0.350258	+	0.102845i
$173$	20.1302	−	5.91077i	1.53047	−	0.449388i	0.595278	−	0.803520i	$-0.297042\pi$
$173$	20.1302	−	5.91077i	1.53047	−	0.449388i	0.935195	+	0.354132i	$0.115224\pi$
$174$	−2.48026	+	5.43102i	−0.188028	+	0.411724i
$175$	0.693440	+	4.82298i	0.0524192	+	0.364583i
$176$	3.37501	+	3.89497i	0.254401	+	0.293595i
$177$	−3.44976	−	7.55392i	−0.259300	−	0.567787i
$178$	12.1565	−	7.81248i	0.911165	−	0.585570i
$179$	−0.299295	+	2.08164i	−0.0223703	+	0.155589i	−0.997945	−	0.0640800i	$-0.979589\pi$
$179$	−0.299295	+	2.08164i	−0.0223703	+	0.155589i	0.975574	+	0.219669i	$0.0704978\pi$
$180$	−0.300295	−	0.192988i	−0.0223827	−	0.0143845i
$181$	8.03803	−	9.27638i	0.597462	−	0.689508i	−0.373803	−	0.927508i	$-0.621946\pi$
$181$	8.03803	−	9.27638i	0.597462	−	0.689508i	0.971265	+	0.238000i	$0.0764919\pi$
$182$	−4.47019	−	1.31257i	−0.331353	−	0.0972939i
$183$	−0.258148			−0.0190828
$184$	−4.52160	−	1.59849i	−0.333336	−	0.117842i
$185$	−0.318929			−0.0234481
$186$	−1.14358	−	0.335784i	−0.0838510	−	0.0246209i
$187$	−0.0985228	+	0.113701i	−0.00720470	+	0.00831467i
$188$	5.34914	+	3.43769i	0.390126	+	0.250719i
$189$	−0.142315	+	0.989821i	−0.0103519	+	0.0719989i
$190$	0.273156	−	0.175547i	0.0198168	−	0.0127355i
$191$	−6.11507	−	13.3901i	−0.442471	−	0.968877i	−0.991138	−	0.132836i	$-0.957592\pi$
$191$	−6.11507	−	13.3901i	−0.442471	−	0.968877i	0.548667	−	0.836041i	$-0.315136\pi$
$192$	−0.654861	−	0.755750i	−0.0472605	−	0.0545415i
$193$	−3.36731	−	23.4202i	−0.242384	−	1.68582i	−0.640084	−	0.768305i	$-0.721100\pi$
$193$	−3.36731	−	23.4202i	−0.242384	−	1.68582i	0.397699	−	0.917516i	$-0.369809\pi$
$194$	2.29246	−	5.01978i	0.164589	−	0.360399i
$195$	−1.59569	+	0.468536i	−0.114269	+	0.0335526i
$196$	−0.959493	+	0.281733i	−0.0685352	+	0.0201238i
$197$	2.64783	−	5.79793i	0.188650	−	0.413085i	−0.791548	−	0.611107i	$-0.790724\pi$
$197$	2.64783	−	5.79793i	0.188650	−	0.413085i	0.980198	+	0.198022i	$0.0634517\pi$
$198$	−0.733461	−	5.10133i	−0.0521248	−	0.362536i
$199$	−6.09314	−	7.03186i	−0.431931	−	0.498475i	0.497504	−	0.867462i	$-0.334250\pi$
$199$	−6.09314	−	7.03186i	−0.431931	−	0.498475i	−0.929435	+	0.368987i	$0.879705\pi$
$200$	2.02414	+	4.43225i	0.143128	+	0.313408i
$201$	11.2245	−	7.21355i	0.791715	−	0.508805i
$202$	1.31639	−	9.15569i	0.0926208	−	0.644192i
$203$	5.02276	+	3.22793i	0.352528	+	0.226556i
$204$	0.0191166	−	0.0220617i	0.00133843	−	0.00154463i
$205$	3.12057	+	0.916281i	0.217950	+	0.0639958i
$206$	2.95096			0.205603
$207$	2.93960	+	3.78929i	0.204316	+	0.263374i
$208$	−4.65891			−0.323037
$209$	4.49812	+	1.32077i	0.311142	+	0.0913595i
$210$	−0.233760	+	0.269773i	−0.0161310	+	0.0186161i
$211$	3.69923	+	2.37735i	0.254665	+	0.163663i	0.661745	−	0.749729i	$-0.269816\pi$
$211$	3.69923	+	2.37735i	0.254665	+	0.163663i	−0.407079	+	0.913393i	$0.633453\pi$
$212$	−0.448961	+	3.12259i	−0.0308348	+	0.214461i
$213$	−5.36286	+	3.44650i	−0.367457	+	0.236151i
$214$	−1.43294	−	3.13770i	−0.0979536	−	0.214488i
$215$	1.11913	+	1.29155i	0.0763242	+	0.0880828i
$216$	0.142315	+	0.989821i	0.00968330	+	0.0673488i
$217$	−0.495114	+	1.08415i	−0.0336105	+	0.0735968i
$218$	16.2029	−	4.75760i	1.09740	−	0.322225i
$219$	10.2845	−	3.01981i	0.694964	−	0.204060i
$220$	0.764241	−	1.67345i	0.0515251	−	0.112824i
$221$	−0.0193551	−	0.134618i	−0.00130197	−	0.00905537i
$222$	0.585088	+	0.675227i	0.0392685	+	0.0453183i
$223$	−10.3744	−	22.7167i	−0.694720	−	1.52123i	−0.846258	−	0.532774i	$-0.821150\pi$
$223$	−10.3744	−	22.7167i	−0.694720	−	1.52123i	0.151537	−	0.988452i	$-0.451578\pi$
$224$	−0.841254	+	0.540641i	−0.0562086	+	0.0361231i
$225$	0.693440	−	4.82298i	0.0462293	−	0.321532i
$226$	−8.73951	−	5.61654i	−0.581344	−	0.373607i
$227$	−4.50541	+	5.19953i	−0.299035	+	0.345105i	−0.885305	−	0.465011i	$-0.846050\pi$
$227$	−4.50541	+	5.19953i	−0.299035	+	0.345105i	0.586270	+	0.810116i	$0.300596\pi$
$228$	−0.872780	−	0.256271i	−0.0578013	−	0.0169720i
$229$	4.96785			0.328285			0.164142	−	0.986437i	$-0.447514\pi$
$229$	4.96785			0.328285			0.164142	+	0.986437i	$0.447514\pi$
$230$	0.151459	+	1.70521i	0.00998693	+	0.112438i
$231$	−5.15379			−0.339094
$232$	5.72871	+	1.68210i	0.376108	+	0.110435i
$233$	8.02562	−	9.26205i	0.525776	−	0.606777i	−0.429292	−	0.903166i	$-0.641237\pi$
$233$	8.02562	−	9.26205i	0.525776	−	0.606777i	0.955067	+	0.296388i	$0.0957823\pi$
$234$	3.91933	+	2.51880i	0.256214	+	0.164659i
$235$	0.323020	−	2.24665i	0.0210715	−	0.146555i
$236$	−6.98608	+	4.48968i	−0.454755	+	0.292253i
$237$	5.01118	+	10.9730i	0.325511	+	0.712770i
$238$	−0.0191166	−	0.0220617i	−0.00123914	−	0.00143005i
$239$	1.17745	+	8.18932i	0.0761627	+	0.529723i	0.991808	+	0.127736i	$0.0407711\pi$
$239$	1.17745	+	8.18932i	0.0761627	+	0.529723i	−0.915645	+	0.401987i	$0.868320\pi$
$240$	−0.148287	+	0.324704i	−0.00957190	+	0.0209595i
$241$	−28.0589	+	8.23884i	−1.80743	+	0.530710i	−0.998373	−	0.0570166i	$-0.981841\pi$
$241$	−28.0589	+	8.23884i	−1.80743	+	0.530710i	−0.809060	+	0.587727i	$0.800023\pi$
$242$	14.9312	−	4.38419i	0.959813	−	0.281827i
$243$	0.415415	−	0.909632i	0.0266489	−	0.0583529i
$244$	0.0367383	+	0.255520i	0.00235193	+	0.0163580i
$245$	0.233760	+	0.269773i	0.0149344	+	0.0172352i
$246$	−3.78488	−	8.28774i	−0.241315	−	0.528407i
$247$	−3.56512	+	2.29116i	−0.226843	+	0.145783i
$248$	−0.169618	+	1.17972i	−0.0107708	+	0.0749124i
$249$	1.41412	+	0.908801i	0.0896163	+	0.0575929i
$250$	2.30781	−	2.66336i	0.145959	−	0.168446i
$251$	19.4998	+	5.72567i	1.23082	+	0.361401i	0.831559	−	0.555437i	$-0.187449\pi$
$251$	19.4998	+	5.72567i	1.23082	+	0.361401i	0.399260	+	0.916838i	$0.369267\pi$
$252$	1.00000			0.0629941
$253$	−17.1744	+	17.7752i	−1.07974	+	1.11752i
$254$	−6.22607			−0.390658
$255$	−0.00999826	−	0.00293575i	−0.000626115	−	0.000183844i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	−17.7385	−	11.3999i	−1.10650	−	0.711103i	−0.145971	−	0.989289i	$-0.546631\pi$
$257$	−17.7385	−	11.3999i	−1.10650	−	0.711103i	−0.960527	+	0.278186i	$0.910267\pi$
$258$	0.681336	−	4.73879i	0.0424181	−	0.295024i
$259$	0.751621	−	0.483038i	0.0467035	−	0.0300145i
$260$	0.690857	+	1.51277i	0.0428451	+	0.0938177i
$261$	−3.90989	−	4.51225i	−0.242016	−	0.279301i
$262$	0.693201	+	4.82132i	0.0428261	+	0.297862i
$263$	−8.50434	+	18.6219i	−0.524400	+	1.14828i	0.443347	+	0.896350i	$0.353791\pi$
$263$	−8.50434	+	18.6219i	−0.524400	+	1.14828i	−0.967747	+	0.251925i	$0.918936\pi$
$264$	−4.94502	+	1.45199i	−0.304345	+	0.0893638i
$265$	1.08049	−	0.317261i	0.0663741	−	0.0194892i
$266$	−0.377872	+	0.827425i	−0.0231688	+	0.0507327i
$267$	2.05651	+	14.3033i	0.125856	+	0.875349i
$268$	−8.73754	−	10.0837i	−0.533730	−	0.615957i
$269$	−6.74971	−	14.7798i	−0.411537	−	0.901141i	−0.995969	−	0.0896980i	$-0.971410\pi$
$269$	−6.74971	−	14.7798i	−0.411537	−	0.901141i	0.584432	−	0.811443i	$-0.301317\pi$
$270$	0.300295	−	0.192988i	0.0182754	−	0.0117449i
$271$	−1.25484	+	8.72758i	−0.0762259	+	0.530163i	0.915553	+	0.402198i	$0.131754\pi$
$271$	−1.25484	+	8.72758i	−0.0762259	+	0.530163i	−0.991779	+	0.127965i	$0.959156\pi$
$272$	−0.0245577	−	0.0157823i	−0.00148903	−	0.000956942i
$273$	3.05094	−	3.52097i	0.184651	−	0.213099i
$274$	−0.319129	−	0.0937048i	−0.0192793	−	0.00566091i
$275$	25.1122			1.51433
$276$	3.33238	−	3.44895i	0.200585	−	0.207603i
$277$	0.914650			0.0549560			0.0274780	−	0.999622i	$-0.491252\pi$
$277$	0.914650			0.0549560			0.0274780	+	0.999622i	$0.491252\pi$
$278$	−20.5902	−	6.04582i	−1.23492	−	0.362604i
$279$	0.780498	−	0.900743i	0.0467272	−	0.0539261i
$280$	0.300295	+	0.192988i	0.0179461	+	0.0115332i
$281$	−1.97776	+	13.7556i	−0.117983	+	0.820593i	0.841788	+	0.539809i	$0.181504\pi$
$281$	−1.97776	+	13.7556i	−0.117983	+	0.820593i	−0.959771	+	0.280784i	$0.909406\pi$
$282$	−5.34914	+	3.43769i	−0.318537	+	0.204711i
$283$	2.91387	+	6.38048i	0.173212	+	0.379280i	0.976250	−	0.216647i	$-0.0695120\pi$
$283$	2.91387	+	6.38048i	0.173212	+	0.379280i	−0.803039	+	0.595927i	$0.796785\pi$
$284$	4.17464	+	4.81779i	0.247719	+	0.285883i
$285$	0.0462099	+	0.321397i	0.00273724	+	0.0190379i
$286$	−9.97455	+	21.8412i	−0.589807	+	1.29150i
$287$	−8.74202	+	2.56689i	−0.516025	+	0.151519i
$288$	0.959493	−	0.281733i	0.0565387	−	0.0166013i
$289$	−7.06170	+	15.4630i	−0.415394	+	0.909586i
$290$	−0.303310	−	2.10957i	−0.0178110	−	0.123878i
$291$	3.61383	+	4.17059i	0.211847	+	0.244484i
$292$	−4.45271	−	9.75009i	−0.260575	−	0.570581i
$293$	−8.88485	+	5.70994i	−0.519058	+	0.333579i	−0.773799	−	0.633431i	$-0.781646\pi$
$293$	−8.88485	+	5.70994i	−0.519058	+	0.333579i	0.254741	+	0.967009i	$0.418010\pi$
$294$	0.142315	−	0.989821i	0.00829997	−	0.0577276i
$295$	2.49376	+	1.60264i	0.145192	+	0.0933095i
$296$	0.585088	−	0.675227i	0.0340075	−	0.0392468i
$297$	4.94502	+	1.45199i	0.286939	+	0.0842530i
$298$	22.0947			1.27991
$299$	−1.97678	−	22.2557i	−0.114320	−	1.28708i
$300$	−4.87258			−0.281318
$301$	−4.59359	−	1.34880i	−0.264770	−	0.0777436i
$302$	1.88899	−	2.18001i	0.108699	−	0.125445i
$303$	7.78146	+	5.00084i	0.447033	+	0.287291i
$304$	−0.129453	+	0.900368i	−0.00742466	+	0.0516396i
$305$	0.0775205	−	0.0498194i	0.00443881	−	0.00285265i
$306$	0.0121267	+	0.0265538i	0.000693238	+	0.00151798i
$307$	−5.01466	−	5.78723i	−0.286202	−	0.330295i	0.594384	−	0.804182i	$-0.297396\pi$
$307$	−5.01466	−	5.78723i	−0.286202	−	0.330295i	−0.880586	+	0.473887i	$0.842851\pi$
$308$	0.733461	+	5.10133i	0.0417928	+	0.290675i
$309$	−1.22587	+	2.68429i	−0.0697374	+	0.152704i
$310$	0.408212	−	0.119862i	0.0231849	−	0.00680770i
$311$	−7.79715	+	2.28945i	−0.442136	+	0.129823i	−0.495221	−	0.868767i	$-0.664913\pi$
$311$	−7.79715	+	2.28945i	−0.442136	+	0.129823i	0.0530849	+	0.998590i	$0.483095\pi$
$312$	1.93538	−	4.23789i	0.109569	−	0.239924i
$313$	3.41370	+	23.7428i	0.192954	+	1.34202i	0.824138	+	0.566389i	$0.191660\pi$
$313$	3.41370	+	23.7428i	0.192954	+	1.34202i	−0.631185	+	0.775633i	$0.717431\pi$
$314$	−1.29317	−	1.49240i	−0.0729780	−	0.0842211i
$315$	−0.148287	−	0.324704i	−0.00835504	−	0.0182950i
$316$	10.1481	−	6.52179i	0.570875	−	0.366879i
$317$	4.81142	−	33.4642i	0.270236	−	1.87953i	−0.175661	−	0.984451i	$-0.556206\pi$
$317$	4.81142	−	33.4642i	0.270236	−	1.87953i	0.445897	−	0.895084i	$-0.352885\pi$
$318$	−2.65390	−	1.70556i	−0.148824	−	0.0956431i
$319$	20.1507	−	23.2552i	1.12822	−	1.30204i
$320$	0.342502	+	0.100568i	0.0191464	+	0.00562190i
$321$	3.44941			0.192527
$322$	−2.93960	−	3.78929i	−0.163817	−	0.211169i
$323$	−0.0265536			−0.00147748
$324$	−0.959493	−	0.281733i	−0.0533052	−	0.0156518i
$325$	−14.8659	+	17.1562i	−0.824614	+	0.951655i
$326$	−5.98374	−	3.84552i	−0.331409	−	0.212983i
$327$	−2.40326	+	16.7150i	−0.132901	+	0.924344i
$328$	−7.66473	+	4.92583i	−0.423214	+	0.271983i
$329$	2.64143	+	5.78393i	0.145627	+	0.318878i
$330$	1.20475	+	1.39036i	0.0663193	+	0.0765366i
$331$	3.44550	+	23.9640i	0.189382	+	1.31718i	0.833614	+	0.552348i	$0.186268\pi$
$331$	3.44550	+	23.9640i	0.189382	+	1.31718i	−0.644232	+	0.764830i	$0.722823\pi$
$332$	0.698300	−	1.52906i	0.0383242	−	0.0839183i
$333$	−0.857263	+	0.251715i	−0.0469777	+	0.0137939i
$334$	−7.23296	+	2.12379i	−0.395770	+	0.116209i
$335$	−1.97853	+	4.33239i	−0.108099	+	0.236704i
$336$	−0.142315	−	0.989821i	−0.00776391	−	0.0539992i
$337$	−7.21749	−	8.32943i	−0.393162	−	0.453733i	0.524314	−	0.851525i	$-0.324322\pi$
$337$	−7.21749	−	8.32943i	−0.393162	−	0.453733i	−0.917476	+	0.397792i	$0.869776\pi$
$338$	−3.61638	−	7.91876i	−0.196705	−	0.430724i
$339$	8.73951	−	5.61654i	0.474665	−	0.305049i
$340$	−0.00148297	+	0.0103143i	−8.04254e−5	+	0.000559371i
$341$	5.16745	+	3.32092i	0.279833	+	0.179838i
$342$	0.595679	−	0.687450i	0.0322106	−	0.0371730i
$343$	−0.959493	−	0.281733i	−0.0518078	−	0.0152121i
$344$	−4.78752			−0.258126
$345$	−1.61404	−	0.570599i	−0.0868968	−	0.0307200i
$346$	20.9801			1.12790
$347$	20.0025	+	5.87326i	1.07379	+	0.315293i	0.770391	−	0.637571i	$-0.220061\pi$
$347$	20.0025	+	5.87326i	1.07379	+	0.315293i	0.303398	+	0.952864i	$0.401879\pi$
$348$	−3.90989	+	4.51225i	−0.209592	+	0.241882i
$349$	−21.4853	−	13.8078i	−1.15008	−	0.739113i	−0.180427	−	0.983588i	$-0.557748\pi$
$349$	−21.4853	−	13.8078i	−1.15008	−	0.739113i	−0.969656	+	0.244475i	$0.921384\pi$
$350$	−0.693440	+	4.82298i	−0.0370659	+	0.257799i
$351$	−3.91933	+	2.51880i	−0.209198	+	0.134443i
$352$	2.14096	+	4.68805i	0.114114	+	0.249874i
$353$	7.59397	+	8.76391i	0.404186	+	0.466456i	0.920955	−	0.389669i	$-0.127411\pi$
$353$	7.59397	+	8.76391i	0.404186	+	0.466456i	−0.516768	+	0.856125i	$0.672865\pi$
$354$	−1.18183	−	8.21984i	−0.0628138	−	0.436880i
$355$	0.945308	−	2.06994i	0.0501717	−	0.109861i
$356$	13.8651	−	4.07115i	0.734847	−	0.215771i
$357$	0.0280093	−	0.00822429i	0.00148241	−	0.000435275i
$358$	−0.873637	+	1.91300i	−0.0461732	+	0.101105i
$359$	3.13650	+	21.8148i	0.165538	+	1.15134i	0.887970	+	0.459901i	$0.152115\pi$
$359$	3.13650	+	21.8148i	0.165538	+	1.15134i	−0.722432	+	0.691441i	$0.756976\pi$
$360$	−0.233760	−	0.269773i	−0.0123202	−	0.0142183i
$361$	−7.54916	−	16.5304i	−0.397324	−	0.870019i
$362$	10.3259	−	6.63605i	0.542717	−	0.348783i
$363$	−2.21464	+	15.4031i	−0.116238	+	0.808456i
$364$	−3.91933	−	2.51880i	−0.205428	−	0.132021i
$365$	−2.50561	+	2.89163i	−0.131149	+	0.151355i
$366$	−0.247691	−	0.0727286i	−0.0129470	−	0.00380159i
$367$	−8.88194			−0.463634			−0.231817	−	0.972759i	$-0.574467\pi$
$367$	−8.88194			−0.463634			−0.231817	+	0.972759i	$0.574467\pi$
$368$	−3.88809	−	2.80762i	−0.202681	−	0.146357i
$369$	9.11109			0.474304
$370$	−0.306010	−	0.0898526i	−0.0159087	−	0.00467121i
$371$	−2.06589	+	2.38417i	−0.107256	+	0.123780i
$372$	−1.00265	−	0.644365i	−0.0519850	−	0.0334088i
$373$	−0.554011	+	3.85323i	−0.0286856	+	0.199513i	−0.999125	−	0.0418338i	$-0.986680\pi$
$373$	−0.554011	+	3.85323i	−0.0286856	+	0.199513i	0.970439	+	0.241347i	$0.0775891\pi$
$374$	−0.126565	+	0.0813386i	−0.00654454	+	0.00420592i
$375$	1.46398	+	3.20566i	0.0755994	+	0.165540i
$376$	4.16396	+	4.80546i	0.214740	+	0.247823i
$377$	3.95868	+	27.5332i	0.203882	+	1.41803i
$378$	−0.415415	+	0.909632i	−0.0213666	+	0.0467864i
$379$	−2.85013	+	0.836873i	−0.146401	+	0.0429873i	−0.354112	−	0.935203i	$-0.615217\pi$
$379$	−2.85013	+	0.836873i	−0.146401	+	0.0429873i	0.207711	+	0.978190i	$0.433399\pi$
$380$	0.311549	−	0.0914790i	0.0159821	−	0.00469277i
$381$	2.58640	−	5.66343i	0.132505	−	0.290146i
$382$	−2.09493	−	14.5706i	−0.107186	−	0.745495i
$383$	−9.13099	−	10.5377i	−0.466572	−	0.538453i	0.472883	−	0.881125i	$-0.343213\pi$
$383$	−9.13099	−	10.5377i	−0.466572	−	0.538453i	−0.939455	+	0.342673i	$0.888668\pi$
$384$	−0.415415	−	0.909632i	−0.0211991	−	0.0464195i
$385$	1.54766	−	0.994619i	0.0788759	−	0.0506905i
$386$	3.36731	−	23.4202i	0.171392	−	1.19206i
$387$	4.02752	+	2.58833i	0.204730	+	0.131572i
$388$	3.61383	−	4.17059i	0.183465	−	0.211729i
$389$	34.2696	+	10.0625i	1.73754	+	0.510187i	0.988353	−	0.152176i	$-0.0486279\pi$
$389$	34.2696	+	10.0625i	1.73754	+	0.510187i	0.749184	+	0.662363i	$0.230446\pi$
$390$	−1.66305			−0.0842119
$391$	0.0649725	−	0.124009i	0.00328580	−	0.00627142i
$392$	−1.00000			−0.0505076
$393$	−4.67359	−	1.37229i	−0.235751	−	0.0692229i
$394$	4.17404	−	4.81710i	0.210285	−	0.242682i
$395$	−3.62248	−	2.32803i	−0.182267	−	0.117136i
$396$	0.733461	−	5.10133i	0.0368578	−	0.256352i
$397$	16.4955	−	10.6010i	0.827886	−	0.532050i	−0.0567195	−	0.998390i	$-0.518064\pi$
$397$	16.4955	−	10.6010i	0.827886	−	0.532050i	0.884605	+	0.466340i	$0.154428\pi$
$398$	−3.86522	−	8.46365i	−0.193746	−	0.424244i
$399$	−0.595679	−	0.687450i	−0.0298212	−	0.0344155i
$400$	0.693440	+	4.82298i	0.0346720	+	0.241149i
$401$	−8.13826	+	17.8203i	−0.406405	+	0.889904i	0.590175	+	0.807275i	$0.299059\pi$
$401$	−8.13826	+	17.8203i	−0.406405	+	0.889904i	−0.996580	+	0.0826285i	$0.973669\pi$
$402$	12.8021	−	3.75904i	0.638512	−	0.187484i
$403$	−5.32782	+	1.56439i	−0.265397	+	0.0779277i
$404$	3.84252	−	8.41395i	0.191173	−	0.418610i
$405$	0.0508009	+	0.353328i	0.00252432	+	0.0175570i
$406$	3.90989	+	4.51225i	0.194044	+	0.223939i
$407$	−1.91285	−	4.18856i	−0.0948165	−	0.207619i
$408$	0.0245577	−	0.0157823i	0.00121579	−	0.000781340i
$409$	−1.70583	+	11.8643i	−0.0843477	+	0.586651i	0.903187	+	0.429248i	$0.141221\pi$
$409$	−1.70583	+	11.8643i	−0.0843477	+	0.586651i	−0.987534	+	0.157403i	$0.949688\pi$
$410$	2.73602	+	1.75833i	0.135122	+	0.0868377i
$411$	0.217808	−	0.251364i	0.0107437	−	0.0123989i
$412$	2.83142	+	0.831381i	0.139494	+	0.0409592i
$413$	−8.30437			−0.408631
$414$	1.75296	+	4.46398i	0.0861532	+	0.219393i
$415$	−0.600041			−0.0294549
$416$	−4.47019	−	1.31257i	−0.219169	−	0.0643539i
$417$	14.0529	−	16.2179i	0.688175	−	0.794196i
$418$	3.94382	+	2.53454i	0.192898	+	0.123968i
$419$	−1.95245	+	13.5796i	−0.0953835	+	0.663407i	0.884896	+	0.465789i	$0.154230\pi$
$419$	−1.95245	+	13.5796i	−0.0953835	+	0.663407i	−0.980279	+	0.197618i	$0.936680\pi$
$420$	−0.300295	+	0.192988i	−0.0146529	+	0.00941685i
$421$	6.40347	+	14.0216i	0.312086	+	0.683373i	0.999062	−	0.0433074i	$-0.0137895\pi$
$421$	6.40347	+	14.0216i	0.312086	+	0.683373i	−0.686976	+	0.726680i	$0.741062\pi$
$422$	2.87961	+	3.32324i	0.140177	+	0.161773i
$423$	−0.904915	−	6.29382i	−0.0439985	−	0.306016i
$424$	−1.31051	+	2.86962i	−0.0636440	+	0.139361i
$425$	−0.136478	+	0.0400735i	−0.00662014	+	0.00194385i
$426$	−6.11662	+	1.79600i	−0.296351	+	0.0870166i
$427$	−0.107238	+	0.234820i	−0.00518963	+	0.0113637i
$428$	−0.490903	−	3.41430i	−0.0237287	−	0.165037i
$429$	−15.7239	−	18.1463i	−0.759157	−	0.876114i
$430$	0.709928	+	1.55453i	0.0342358	+	0.0749659i
$431$	3.25571	−	2.09232i	0.156822	−	0.100783i	−0.459876	−	0.887983i	$-0.652106\pi$
$431$	3.25571	−	2.09232i	0.156822	−	0.100783i	0.616698	+	0.787200i	$0.288470\pi$
$432$	−0.142315	+	0.989821i	−0.00684713	+	0.0476228i
$433$	31.1626	+	20.0270i	1.49758	+	0.962436i	0.995208	+	0.0977851i	$0.0311758\pi$
$433$	31.1626	+	20.0270i	1.49758	+	0.962436i	0.502373	+	0.864651i	$0.332461\pi$
$434$	−0.780498	+	0.900743i	−0.0374651	+	0.0432370i
$435$	2.04493	+	0.600446i	0.0980469	+	0.0287892i
$436$	16.8869			0.808737
$437$	−4.35601	−	0.236374i	−0.208376	−	0.0113073i
$438$	10.7187			0.512160
$439$	−3.88538	−	1.14085i	−0.185439	−	0.0544498i	0.187695	−	0.982227i	$-0.439899\pi$
$439$	−3.88538	−	1.14085i	−0.185439	−	0.0544498i	−0.373134	+	0.927778i	$0.621717\pi$
$440$	1.20475	−	1.39036i	0.0574342	−	0.0662826i
$441$	0.841254	+	0.540641i	0.0400597	+	0.0257448i
$442$	0.0193551	−	0.134618i	0.000920629	−	0.00640312i
$443$	−18.3509	+	11.7934i	−0.871877	+	0.560321i	−0.898326	−	0.439329i	$-0.855216\pi$
$443$	−18.3509	+	11.7934i	−0.871877	+	0.560321i	0.0264495	+	0.999650i	$0.491580\pi$
$444$	0.371154	+	0.812714i	0.0176142	+	0.0385697i
$445$	−3.37793	−	3.89834i	−0.160129	−	0.184799i
$446$	−3.55411	−	24.7194i	−0.168292	−	1.17050i
$447$	−9.17848	+	20.0981i	−0.434127	+	0.950606i
$448$	−0.959493	+	0.281733i	−0.0453318	+	0.0133106i
$449$	−36.3539	+	10.6745i	−1.71565	+	0.503760i	−0.984037	−	0.177963i	$-0.943049\pi$
$449$	−36.3539	+	10.6745i	−1.71565	+	0.503760i	−0.731611	+	0.681723i	$0.761231\pi$
$450$	2.02414	−	4.43225i	0.0954190	−	0.208938i
$451$	6.68262	+	46.4787i	0.314673	+	2.18860i
$452$	−6.80314	−	7.85124i	−0.319993	−	0.369291i
$453$	1.19829	+	2.62389i	0.0563006	+	0.123281i
$454$	−5.78779	+	3.71959i	−0.271634	+	0.174569i
$455$	−0.236677	+	1.64612i	−0.0110956	+	0.0771715i
$456$	−0.765226	−	0.491781i	−0.0358350	−	0.0230298i
$457$	2.83277	−	3.26919i	0.132511	−	0.152926i	−0.685616	−	0.727963i	$-0.740467\pi$
$457$	2.83277	−	3.26919i	0.132511	−	0.152926i	0.818127	+	0.575037i	$0.195012\pi$
$458$	4.76662	+	1.39960i	0.222729	+	0.0653992i
$459$	−0.0291918			−0.00136256
$460$	−0.335090	+	1.67881i	−0.0156237	+	0.0782750i
$461$	−7.37227			−0.343361			−0.171680	−	0.985153i	$-0.554920\pi$
$461$	−7.37227			−0.343361			−0.171680	+	0.985153i	$0.554920\pi$
$462$	−4.94502	−	1.45199i	−0.230063	−	0.0675527i
$463$	−17.9587	+	20.7255i	−0.834613	+	0.963195i	−0.999734	−	0.0230783i	$-0.992653\pi$
$463$	−17.9587	+	20.7255i	−0.834613	+	0.963195i	0.165120	+	0.986273i	$0.447199\pi$
$464$	5.02276	+	3.22793i	0.233176	+	0.149853i
$465$	−0.0605473	+	0.421115i	−0.00280781	+	0.0195288i
$466$	10.3099	−	6.62580i	0.477599	−	0.306934i
$467$	−10.1714	−	22.2723i	−0.470678	−	1.03064i	−0.984922	−	0.172997i	$-0.944655\pi$
$467$	−10.1714	−	22.2723i	−0.470678	−	1.03064i	0.514245	−	0.857643i	$-0.328072\pi$
$468$	3.05094	+	3.52097i	0.141030	+	0.162757i
$469$	−1.89885	−	13.2068i	−0.0876807	−	0.609833i
$470$	0.942890	−	2.06464i	0.0434923	−	0.0952348i
$471$	1.89474	−	0.556346i	0.0873050	−	0.0256351i
$472$	−7.96798	+	2.33961i	−0.366756	+	0.107689i
$473$	−10.2499	+	22.4442i	−0.471291	+	1.03198i
$474$	1.71675	+	11.9403i	0.0788531	+	0.548436i
$475$	2.90249	+	3.34965i	0.133175	+	0.153693i
$476$	−0.0121267	−	0.0265538i	−0.000555827	−	0.00121709i
$477$	2.65390	−	1.70556i	0.121514	−	0.0780923i
$478$	−1.17745	+	8.18932i	−0.0538552	+	0.374571i
$479$	−8.11715	−	5.21657i	−0.370882	−	0.238351i	0.341901	−	0.939736i	$-0.388929\pi$
$479$	−8.11715	−	5.21657i	−0.370882	−	0.238351i	−0.712783	+	0.701385i	$0.752566\pi$
$480$	−0.233760	+	0.269773i	−0.0106696	+	0.0123134i
$481$	3.99391	+	1.17272i	0.182107	+	0.0534714i
$482$	−29.2435			−1.33200
$483$	4.66802	−	1.09982i	0.212402	−	0.0500437i
$484$	15.5615			0.707343
$485$	−1.89009	−	0.554980i	−0.0858245	−	0.0252004i
$486$	0.654861	−	0.755750i	0.0297051	−	0.0342815i
$487$	−10.3465	−	6.64926i	−0.468843	−	0.301307i	0.284805	−	0.958585i	$-0.408071\pi$
$487$	−10.3465	−	6.64926i	−0.468843	−	0.301307i	−0.753648	+	0.657279i	$0.771707\pi$
$488$	−0.0367383	+	0.255520i	−0.00166306	+	0.0115669i
$489$	5.98374	−	3.84552i	0.270594	−	0.173900i
$490$	0.148287	+	0.324704i	0.00669893	+	0.0146686i
$491$	17.9014	+	20.6593i	0.807879	+	0.932342i	0.998786	−	0.0492661i	$-0.0156882\pi$
$491$	17.9014	+	20.6593i	0.807879	+	0.932342i	−0.190907	+	0.981608i	$0.561143\pi$
$492$	−1.29664	−	9.01835i	−0.0584572	−	0.406579i
$493$	−0.0724034	+	0.158541i	−0.00326088	+	0.00714034i
$494$	−4.06621	+	1.19395i	−0.182947	+	0.0537181i
$495$	−1.76518	+	0.518305i	−0.0793391	+	0.0232961i
$496$	−0.495114	+	1.08415i	−0.0222313	+	0.0486797i
$497$	0.907236	+	6.30996i	0.0406951	+	0.283040i
$498$	1.10080	+	1.27039i	0.0493281	+	0.0569276i
$499$	−17.8040	−	38.9854i	−0.797018	−	1.74523i	−0.655368	−	0.755310i	$-0.727486\pi$
$499$	−17.8040	−	38.9854i	−0.797018	−	1.74523i	−0.141650	−	0.989917i	$-0.545241\pi$
$500$	2.96469	−	1.90529i	0.132585	−	0.0852071i
$501$	1.07281	−	7.46158i	0.0479298	−	0.333359i
$502$	17.0969	+	10.9875i	0.763070	+	0.490395i
$503$	25.8862	−	29.8742i	1.15421	−	1.33203i	0.219914	−	0.975519i	$-0.429422\pi$
$503$	25.8862	−	29.8742i	1.15421	−	1.33203i	0.934293	−	0.356506i	$-0.116032\pi$
$504$	0.959493	+	0.281733i	0.0427392	+	0.0125494i
$505$	−3.30184			−0.146930
$506$	−21.4865	+	12.2166i	−0.955193	+	0.543093i
$507$	8.70546			0.386623
$508$	−5.97387	−	1.75409i	−0.265048	−	0.0778250i
$509$	24.9864	−	28.8359i	1.10750	−	1.27813i	0.150323	−	0.988637i	$-0.451969\pi$
$509$	24.9864	−	28.8359i	1.10750	−	1.27813i	0.957181	−	0.289490i	$-0.0934858\pi$
$510$	−0.00876616	−	0.00563367i	−0.000388172	−	0.000249463i
$511$	1.52543	−	10.6096i	0.0674811	−	0.469342i
$512$	−0.841254	+	0.540641i	−0.0371785	+	0.0238932i
$513$	0.377872	+	0.827425i	0.0166835	+	0.0365317i
$514$	−13.8083	−	15.9356i	−0.609057	−	0.702889i
$515$	−0.149911	−	1.04266i	−0.00660588	−	0.0459449i
$516$	1.98881	−	4.35488i	0.0875524	−	0.191713i
$517$	31.4431	−	9.23254i	1.38287	−	0.406047i
$518$	0.857263	−	0.251715i	0.0376660	−	0.0110597i
$519$	−8.71544	+	19.0842i	−0.382565	+	0.837701i
$520$	0.236677	+	1.64612i	0.0103790	+	0.0721873i
$521$	20.5320	+	23.6952i	0.899525	+	1.03811i	0.999072	+	0.0430741i	$0.0137152\pi$
$521$	20.5320	+	23.6952i	0.899525	+	1.03811i	−0.0995471	+	0.995033i	$0.531739\pi$
$522$	−2.48026	−	5.43102i	−0.108558	−	0.237709i
$523$	20.0599	−	12.8917i	0.877158	−	0.563715i	−0.0227765	−	0.999741i	$-0.507251\pi$
$523$	20.0599	−	12.8917i	0.877158	−	0.563715i	0.899934	+	0.436025i	$0.143614\pi$
$524$	−0.693201	+	4.82132i	−0.0302826	+	0.210620i
$525$	−4.09907	−	2.63431i	−0.178898	−	0.114971i
$526$	−13.4062	+	15.4716i	−0.584540	+	0.674595i
$527$	−0.0333830	−	0.00980215i	−0.00145419	−	0.000426988i
$528$	−5.15379			−0.224290
$529$	11.7623	−	19.7648i	0.511406	−	0.859339i
$530$	1.12611			0.0489150
$531$	7.96798	+	2.33961i	0.345781	+	0.101530i
$532$	−0.595679	+	0.687450i	−0.0258259	+	0.0298047i
$533$	−35.7093	−	22.9490i	−1.54674	−	0.994031i
$534$	−2.05651	+	14.3033i	−0.0889938	+	0.618965i
$535$	−1.03584	+	0.665695i	−0.0447833	+	0.0287805i
$536$	−5.54271	−	12.1368i	−0.239409	−	0.524232i
$537$	−1.37720	−	1.58938i	−0.0594307	−	0.0685867i
$538$	−2.31235	−	16.0827i	−0.0996924	−	0.693376i
$539$	−2.14096	+	4.68805i	−0.0922177	+	0.201929i
$540$	0.342502	−	0.100568i	0.0147389	−	0.00432774i
$541$	0.394743	−	0.115907i	0.0169713	−	0.00498323i	−0.273236	−	0.961947i	$-0.588094\pi$
$541$	0.394743	−	0.115907i	0.0169713	−	0.00498323i	0.290207	+	0.956964i	$0.406276\pi$
$542$	−3.66285	+	8.02052i	−0.157333	+	0.344511i
$543$	1.74683	+	12.1495i	0.0749637	+	0.521384i
$544$	−0.0191166	−	0.0220617i	−0.000819616	−	0.000945888i
$545$	−2.50411	−	5.48325i	−0.107264	−	0.234876i
$546$	3.91933	−	2.51880i	0.167732	−	0.107795i
$547$	1.09081	−	7.58674i	0.0466396	−	0.324386i	−0.953123	−	0.302584i	$-0.902151\pi$
$547$	1.09081	−	7.58674i	0.0466396	−	0.324386i	0.999762	−	0.0218015i	$-0.00694020\pi$
$548$	−0.279803	−	0.179818i	−0.0119526	−	0.00768145i
$549$	0.169051	−	0.195095i	0.00721492	−	0.00832646i
$550$	24.0950	+	7.07494i	1.02742	+	0.301676i
$551$	5.43098			0.231368
$552$	4.16907	−	2.37041i	0.177448	−	0.100891i
$553$	12.0631			0.512974
$554$	0.877601	+	0.257687i	0.0372857	+	0.0109481i
$555$	0.208854	−	0.241030i	0.00886535	−	0.0102312i
$556$	−18.0528	−	11.6018i	−0.765610	−	0.492027i
$557$	−1.84390	+	12.8246i	−0.0781286	+	0.543396i	0.912738	+	0.408546i	$0.133964\pi$
$557$	−1.84390	+	12.8246i	−0.0781286	+	0.543396i	−0.990866	+	0.134850i	$0.956945\pi$
$558$	1.00265	−	0.644365i	0.0424456	−	0.0272781i
$559$	−9.26569	−	20.2890i	−0.391897	−	0.858134i
$560$	0.233760	+	0.269773i	0.00987817	+	0.0114000i
$561$	−0.0214111	−	0.148917i	−0.000903975	−	0.00628729i
$562$	−5.77306	+	12.6412i	−0.243522	+	0.533239i
$563$	−8.02538	+	2.35646i	−0.338229	+	0.0993131i	−0.446437	−	0.894815i	$-0.647307\pi$
$563$	−8.02538	+	2.35646i	−0.338229	+	0.0993131i	0.108207	+	0.994128i	$0.465489\pi$
$564$	−6.10097	+	1.79141i	−0.256897	+	0.0754319i
$565$	−1.54051	+	3.37324i	−0.0648097	+	0.141913i
$566$	0.998247	+	6.94296i	0.0419595	+	0.291834i
$567$	−0.654861	−	0.755750i	−0.0275016	−	0.0317385i
$568$	2.64821	+	5.79877i	0.111116	+	0.243311i
$569$	3.70502	−	2.38107i	0.155323	−	0.0998198i	−0.460671	−	0.887571i	$-0.652391\pi$
$569$	3.70502	−	2.38107i	0.155323	−	0.0998198i	0.615993	+	0.787751i	$0.288755\pi$
$570$	−0.0462099	+	0.321397i	−0.00193552	+	0.0134618i
$571$	−26.1170	−	16.7844i	−1.09296	−	0.702406i	−0.135448	−	0.990784i	$-0.543247\pi$
$571$	−26.1170	−	16.7844i	−1.09296	−	0.702406i	−0.957516	+	0.288379i	$0.906884\pi$
$572$	−15.7239	+	18.1463i	−0.657449	+	0.758737i
$573$	14.1241	+	4.14721i	0.590043	+	0.173252i
$574$	−9.11109			−0.380289
$575$	−22.7453	+	5.35898i	−0.948544	+	0.223485i
$576$	1.00000			0.0416667
$577$	13.6383	+	4.00458i	0.567771	+	0.166713i	0.553005	−	0.833178i	$-0.313481\pi$
$577$	13.6383	+	4.00458i	0.567771	+	0.166713i	0.0147668	+	0.999891i	$0.495299\pi$
$578$	−11.1321	+	12.8471i	−0.463033	+	0.534369i
$579$	19.9049	+	12.7921i	0.827220	+	0.531622i
$580$	0.303310	−	2.10957i	0.0125943	−	0.0875950i
$581$	1.41412	−	0.908801i	0.0586676	−	0.0377034i
$582$	2.29246	+	5.01978i	0.0950254	+	0.208077i
$583$	10.6472	+	12.2875i	0.440961	+	0.508896i
$584$	−1.52543	−	10.6096i	−0.0631228	−	0.439029i
$585$	0.690857	−	1.51277i	0.0285634	−	0.0625451i
$586$	−10.1336	+	2.97550i	−0.418616	+	0.122917i
$587$	1.57898	−	0.463629i	0.0651713	−	0.0191360i	−0.248984	−	0.968508i	$-0.580097\pi$
$587$	1.57898	−	0.463629i	0.0651713	−	0.0191360i	0.314156	+	0.949371i	$0.398279\pi$
$588$	0.415415	−	0.909632i	0.0171314	−	0.0375126i
$589$	0.154289	+	1.07311i	0.00635738	+	0.0442166i
$590$	1.94123	+	2.24030i	0.0799192	+	0.0922316i
$591$	2.64783	+	5.79793i	0.108917	+	0.238495i
$592$	0.751621	−	0.483038i	0.0308914	−	0.0198527i
$593$	5.95144	−	41.3932i	0.244396	−	1.69981i	−0.385153	−	0.922853i	$-0.625851\pi$
$593$	5.95144	−	41.3932i	0.244396	−	1.69981i	0.629549	−	0.776961i	$-0.283240\pi$
$594$	4.33564	+	2.78635i	0.177894	+	0.114325i
$595$	−0.00682388	+	0.00787518i	−0.000279752	+	0.000322851i
$596$	21.1997	+	6.22480i	0.868375	+	0.254978i
$597$	9.30448			0.380807
$598$	4.37346	−	21.9111i	0.178844	−	0.896013i
$599$	−13.2795			−0.542587			−0.271293	−	0.962497i	$-0.587451\pi$
$599$	−13.2795			−0.542587			−0.271293	+	0.962497i	$0.587451\pi$
$600$	−4.67520	−	1.37276i	−0.190864	−	0.0560429i
$601$	−27.5446	+	31.7881i	−1.12357	+	1.29666i	−0.173424	+	0.984847i	$0.555483\pi$
$601$	−27.5446	+	31.7881i	−1.12357	+	1.29666i	−0.950142	+	0.311817i	$0.899062\pi$
$602$	−4.02752	−	2.58833i	−0.164149	−	0.105492i
$603$	−1.89885	+	13.2068i	−0.0773271	+	0.537822i
$604$	2.42665	−	1.55951i	0.0987389	−	0.0634556i
$605$	−2.30758	−	5.05289i	−0.0938164	−	0.205429i
$606$	6.05736	+	6.99056i	0.246063	+	0.283972i
$607$	4.71265	+	32.7772i	0.191280	+	1.33038i	0.828624	+	0.559805i	$0.189124\pi$
$607$	4.71265	+	32.7772i	0.191280	+	1.33038i	−0.637344	+	0.770580i	$0.719967\pi$
$608$	−0.377872	+	0.827425i	−0.0153248	+	0.0335565i
$609$	−5.72871	+	1.68210i	−0.232139	+	0.0681622i
$610$	0.0884162	−	0.0259613i	0.00357987	−	0.00105114i
$611$	−12.3062	+	26.9468i	−0.497856	+	1.09015i
$612$	0.00415443	+	0.0288947i	0.000167933	+	0.00116800i
$613$	26.2270	+	30.2676i	1.05930	+	1.22250i	0.974097	+	0.226132i	$0.0726079\pi$
$613$	26.2270	+	30.2676i	1.05930	+	1.22250i	0.0852015	+	0.996364i	$0.472847\pi$
$614$	−3.18108	−	6.96560i	−0.128378	−	0.281109i
$615$	−2.73602	+	1.75833i	−0.110327	+	0.0709027i
$616$	−0.733461	+	5.10133i	−0.0295520	+	0.205538i
$617$	3.85582	+	2.47799i	0.155230	+	0.0997601i	0.615950	−	0.787785i	$-0.288772\pi$
$617$	3.85582	+	2.47799i	0.155230	+	0.0997601i	−0.460720	+	0.887545i	$0.652409\pi$
$618$	−1.93247	+	2.23018i	−0.0777352	+	0.0897112i
$619$	3.57906	+	1.05091i	0.143855	+	0.0422395i	0.352867	−	0.935673i	$-0.385207\pi$
$619$	3.57906	+	1.05091i	0.143855	+	0.0422395i	−0.209013	+	0.977913i	$0.567025\pi$
$620$	0.425446			0.0170863
$621$	−4.78879	−	0.259859i	−0.192167	−	0.0104278i
$622$	−8.12632			−0.325836
$623$	13.8651	+	4.07115i	0.555492	+	0.163107i
$624$	3.05094	−	3.52097i	0.122135	−	0.140952i
$625$	19.4371	+	12.4915i	0.777484	+	0.499658i
$626$	−3.41370	+	23.7428i	−0.136439	+	0.948952i
$627$	−3.94382	+	2.53454i	−0.157501	+	0.101220i
$628$	−0.820333	−	1.79628i	−0.0327348	−	0.0716793i
$629$	0.0170798	+	0.0197111i	0.000681015	+	0.000785934i
$630$	−0.0508009	−	0.353328i	−0.00202396	−	0.0140769i
$631$	−6.81564	+	14.9242i	−0.271327	+	0.594122i	−0.995422	−	0.0955776i	$-0.969530\pi$
$631$	−6.81564	+	14.9242i	−0.271327	+	0.594122i	0.724095	+	0.689700i	$0.242257\pi$
$632$	11.5744	−	3.39856i	0.460406	−	0.135187i
$633$	−4.21916	+	1.23886i	−0.167697	+	0.0492401i
$634$	14.0445	−	30.7531i	0.557777	−	1.22136i
$635$	0.316290	+	2.19985i	0.0125516	+	0.0872982i
$636$	−2.06589	−	2.38417i	−0.0819179	−	0.0945383i
$637$	−1.93538	−	4.23789i	−0.0766826	−	0.167912i
$638$	25.8862	−	16.6361i	1.02485	−	0.658628i
$639$	0.907236	−	6.30996i	0.0358897	−	0.249618i
$640$	0.300295	+	0.192988i	0.0118702	+	0.00762852i
$641$	6.99835	−	8.07653i	0.276418	−	0.319004i	−0.600517	−	0.799612i	$-0.705039\pi$
$641$	6.99835	−	8.07653i	0.276418	−	0.319004i	0.876935	+	0.480608i	$0.159584\pi$
$642$	3.30969	+	0.971812i	0.130623	+	0.0383543i
$643$	43.8664			1.72992			0.864962	−	0.501837i	$-0.167342\pi$
$643$	43.8664			1.72992			0.864962	+	0.501837i	$0.167342\pi$
$644$	−1.75296	−	4.46398i	−0.0690762	−	0.175906i
$645$	−1.70896			−0.0672903
$646$	−0.0254780	−	0.00748103i	−0.00100242	−	0.000294337i
$647$	−13.8989	+	16.0401i	−0.546420	+	0.630603i	−0.960045	−	0.279845i	$-0.909717\pi$
$647$	−13.8989	+	16.0401i	−0.546420	+	0.630603i	0.413625	+	0.910447i	$0.364263\pi$
$648$	−0.841254	−	0.540641i	−0.0330476	−	0.0212384i
$649$	−6.09093	+	42.3633i	−0.239090	+	1.66291i
$650$	−19.0972	+	12.2730i	−0.749055	+	0.481388i
$651$	−0.495114	−	1.08415i	−0.0194050	−	0.0424911i
$652$	−4.65795	−	5.37556i	−0.182419	−	0.210523i
$653$	2.45482	+	17.0737i	0.0960646	+	0.668144i	0.979774	+	0.200108i	$0.0641293\pi$
$653$	2.45482	+	17.0737i	0.0960646	+	0.668144i	−0.883709	+	0.468036i	$0.844962\pi$
$654$	−7.01508	+	15.3609i	−0.274311	+	0.600658i
$655$	1.66829	−	0.489855i	0.0651856	−	0.0191402i
$656$	−8.74202	+	2.56689i	−0.341319	+	0.100220i
$657$	−4.45271	+	9.75009i	−0.173717	+	0.380387i
$658$	0.904915	+	6.29382i	0.0352772	+	0.245359i
$659$	−20.3396	−	23.4731i	−0.792317	−	0.914383i	0.205617	−	0.978633i	$-0.434080\pi$
$659$	−20.3396	−	23.4731i	−0.792317	−	0.914383i	−0.997934	+	0.0642497i	$0.979535\pi$
$660$	0.764241	+	1.67345i	0.0297480	+	0.0651391i
$661$	18.6423	−	11.9807i	0.725101	−	0.465994i	−0.125307	−	0.992118i	$-0.539992\pi$
$661$	18.6423	−	11.9807i	0.725101	−	0.465994i	0.850408	+	0.526124i	$0.176355\pi$
$662$	−3.44550	+	23.9640i	−0.133913	+	0.931386i
$663$	0.114412	+	0.0735283i	0.00444340	+	0.00285560i
$664$	1.10080	−	1.27039i	0.0427194	−	0.0493008i
$665$	0.311549	+	0.0914790i	0.0120813	+	0.00354740i
$666$	−0.893454			−0.0346206
$667$	−13.2887	+	25.3635i	−0.514542	+	0.982077i
$668$	−7.53831			−0.291666
$669$	23.9619	+	7.03586i	0.926422	+	0.272022i
$670$	−3.11896	+	3.59948i	−0.120496	+	0.139060i
$671$	1.11924	+	0.719290i	0.0432077	+	0.0277679i
$672$	0.142315	−	0.989821i	0.00548991	−	0.0381832i
$673$	−6.85614	+	4.40617i	−0.264285	+	0.169845i	−0.666072	−	0.745888i	$-0.732026\pi$
$673$	−6.85614	+	4.40617i	−0.264285	+	0.169845i	0.401787	+	0.915733i	$0.368389\pi$
$674$	−4.57846	−	10.0254i	−0.176356	−	0.386165i
$675$	3.19086	+	3.68245i	0.122816	+	0.141738i
$676$	−1.23892	−	8.61685i	−0.0476506	−	0.331417i
$677$	5.53985	−	12.1306i	0.212914	−	0.466216i	−0.772799	−	0.634651i	$-0.781144\pi$
$677$	5.53985	−	12.1306i	0.212914	−	0.466216i	0.985713	+	0.168435i	$0.0538712\pi$
$678$	9.96787	−	2.92683i	0.382814	−	0.112404i
$679$	5.29494	−	1.55473i	0.203201	−	0.0596652i
$680$	−0.00432877	+	0.00947869i	−0.000166001	+	0.000363491i
$681$	−0.979120	−	6.80993i	−0.0375200	−	0.260957i
$682$	4.02252	+	4.64224i	0.154030	+	0.177761i
$683$	6.37393	+	13.9570i	0.243892	+	0.534048i	0.991502	−	0.130089i	$-0.0415263\pi$
$683$	6.37393	+	13.9570i	0.243892	+	0.534048i	−0.747611	+	0.664137i	$0.768799\pi$
$684$	0.765226	−	0.491781i	0.0292592	−	0.0188037i
$685$	−0.0168965	+	0.117518i	−0.000645581	+	0.00449012i
$686$	−0.841254	−	0.540641i	−0.0321192	−	0.0206418i
$687$	−3.25325	+	3.75445i	−0.124119	+	0.143241i
$688$	−4.59359	−	1.34880i	−0.175129	−	0.0514226i
$689$	−14.6975			−0.559929
$690$	−1.38790	−	1.00221i	−0.0528364	−	0.0381536i
$691$	23.0053			0.875162			0.437581	−	0.899179i	$-0.355835\pi$
$691$	23.0053			0.875162			0.437581	+	0.899179i	$0.355835\pi$
$692$	20.1302	+	5.91077i	0.765237	+	0.224694i
$693$	3.37501	−	3.89497i	0.128206	−	0.147958i
$694$	17.5375	+	11.2707i	0.665716	+	0.427830i
$695$	−1.09016	+	7.58222i	−0.0413520	+	0.287610i
$696$	−5.02276	+	3.22793i	−0.190387	+	0.122354i
$697$	−0.110488	−	0.241934i	−0.00418502	−	0.00916391i
$698$	−16.7249	−	19.3016i	−0.633047	−	0.730575i
$699$	1.74413	+	12.1307i	0.0659692	+	0.458826i
$700$	−2.02414	+	4.43225i	−0.0765054	+	0.167523i
$701$	−47.4471	+	13.9317i	−1.79205	+	0.526194i	−0.996789	−	0.0800707i	$-0.974485\pi$
$701$	−47.4471	+	13.9317i	−1.79205	+	0.526194i	−0.795263	+	0.606265i	$0.792667\pi$
$702$	−4.47019	+	1.31257i	−0.168717	+	0.0495397i
$703$	0.337612	−	0.739266i	0.0127333	−	0.0278820i
$704$	0.733461	+	5.10133i	0.0276433	+	0.192264i
$705$	1.48637	+	1.71537i	0.0559800	+	0.0646044i
$706$	4.81729	+	10.5484i	0.181301	+	0.396994i
$707$	7.78146	−	5.00084i	0.292652	−	0.188076i
$708$	1.18183	−	8.21984i	0.0444161	−	0.308921i
$709$	14.9192	+	9.58797i	0.560301	+	0.360084i	0.789932	−	0.613194i	$-0.210116\pi$
$709$	14.9192	+	9.58797i	0.560301	+	0.360084i	−0.229631	+	0.973278i	$0.573752\pi$
$710$	1.49018	−	1.71977i	0.0559256	−	0.0645416i
$711$	−11.5744	−	3.39856i	−0.434075	−	0.127456i
$712$	14.4504			0.541552
$713$	−5.38908	−	1.90517i	−0.201823	−	0.0713490i
$714$	0.0291918			0.00109248
$715$	8.22383	+	2.41474i	0.307554	+	0.0903060i
$716$	−1.37720	+	1.58938i	−0.0514685	+	0.0593978i
$717$	−6.96014	−	4.47301i	−0.259931	−	0.167048i
$718$	−3.13650	+	21.8148i	−0.117053	+	0.814122i
$719$	16.9447	−	10.8897i	0.631931	−	0.406117i	−0.185093	−	0.982721i	$-0.559259\pi$
$719$	16.9447	−	10.8897i	0.631931	−	0.406117i	0.817024	+	0.576604i	$0.195622\pi$
$720$	−0.148287	−	0.324704i	−0.00552634	−	0.0121010i
$721$	1.93247	+	2.23018i	0.0719688	+	0.0830564i
$722$	−2.58623	−	17.9876i	−0.0962494	−	0.669430i
$723$	12.1482	−	26.6008i	0.451796	−	0.989294i
$724$	11.7772	−	3.45810i	0.437697	−	0.128519i
$725$	27.9136	−	8.19617i	1.03669	−	0.304398i
$726$	−6.46450	+	14.1553i	−0.239920	+	0.525352i
$727$	3.13194	+	21.7831i	0.116157	+	0.807890i	0.961724	+	0.274020i	$0.0883536\pi$
$727$	3.13194	+	21.7831i	0.116157	+	0.807890i	−0.845567	+	0.533870i	$0.820737\pi$
$728$	−3.05094	−	3.52097i	−0.113075	−	0.130496i
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$	−3.21878	+	2.06858i	−0.119132	+	0.0765617i
$731$	0.0198894	−	0.138334i	0.000735637	−	0.00511647i
$732$	−0.217168	−	0.139565i	−0.00802675	−	0.00515848i
$733$	1.69988	−	1.96177i	0.0627865	−	0.0724595i	−0.723487	−	0.690338i	$-0.757462\pi$
$733$	1.69988	−	1.96177i	0.0627865	−	0.0724595i	0.786274	+	0.617878i	$0.212007\pi$
$734$	−8.52216	−	2.50233i	−0.314559	−	0.0923628i
$735$	−0.356961			−0.0131667
$736$	−2.93960	−	3.78929i	−0.108355	−	0.139675i
$737$	−68.7649			−2.53299
$738$	8.74202	+	2.56689i	0.321798	+	0.0944885i
$739$	−0.683657	+	0.788983i	−0.0251487	+	0.0290232i	−0.768185	−	0.640228i	$-0.778840\pi$
$739$	−0.683657	+	0.788983i	−0.0251487	+	0.0290232i	0.743036	+	0.669252i	$0.233385\pi$
$740$	−0.268300	−	0.172426i	−0.00986290	−	0.00633850i
$741$	0.603112	−	4.19473i	0.0221559	−	0.154097i
$742$	−2.65390	+	1.70556i	−0.0974279	+	0.0626131i
$743$	−5.09701	−	11.1609i	−0.186991	−	0.409453i	0.792799	−	0.609484i	$-0.208623\pi$
$743$	−5.09701	−	11.1609i	−0.186991	−	0.409453i	−0.979790	+	0.200030i	$0.935896\pi$
$744$	−0.780498	−	0.900743i	−0.0286145	−	0.0330228i
$745$	−1.12243	−	7.80669i	−0.0411227	−	0.286015i
$746$	−1.61715	+	3.54107i	−0.0592081	+	0.129648i
$747$	−1.61288	+	0.473584i	−0.0590121	+	0.0173275i
$748$	−0.144354	+	0.0423862i	−0.00527811	+	0.00154979i
$749$	1.43294	−	3.13770i	0.0523584	−	0.114649i
$750$	0.501536	+	3.48826i	0.0183135	+	0.127373i
$751$	−17.9312	−	20.6937i	−0.654320	−	0.755125i	0.327519	−	0.944845i	$-0.393788\pi$
$751$	−17.9312	−	20.6937i	−0.654320	−	0.755125i	−0.981838	+	0.189720i	$0.939242\pi$
$752$	2.64143	+	5.78393i	0.0963231	+	0.210918i
$753$	−17.0969	+	10.9875i	−0.623044	+	0.400406i
$754$	−3.95868	+	27.5332i	−0.144166	+	1.00270i
$755$	−0.866220	−	0.556686i	−0.0315250	−	0.0202599i
$756$	−0.654861	+	0.755750i	−0.0238171	+	0.0274863i
$757$	37.5098	+	11.0139i	1.36332	+	0.400306i	0.879931	−	0.475102i	$-0.157589\pi$
$757$	37.5098	+	11.0139i	1.36332	+	0.400306i	0.483385	+	0.875408i	$0.339407\pi$
$758$	−2.97045			−0.107892
$759$	−2.18676	−	24.6198i	−0.0793744	−	0.893641i
$760$	0.324702			0.0117782
$761$	17.2567	+	5.06703i	0.625556	+	0.183680i	0.579121	−	0.815242i	$-0.303396\pi$
$761$	17.2567	+	5.06703i	0.625556	+	0.183680i	0.0464348	+	0.998921i	$0.485214\pi$
$762$	4.07721	−	4.70535i	0.147702	−	0.170457i
$763$	14.2062	+	9.12976i	0.514299	+	0.330520i
$764$	2.09493	−	14.5706i	0.0757919	−	0.527144i
$765$	0.00876616	−	0.00563367i	0.000316941	−	0.000203686i
$766$	−5.79230	−	12.6834i	−0.209284	−	0.458269i
$767$	−25.3361	−	29.2394i	−0.914834	−	1.05577i
$768$	−0.142315	−	0.989821i	−0.00513534	−	0.0357171i
$769$	10.7699	−	23.5827i	0.388372	−	0.850416i	−0.609946	−	0.792443i	$-0.708809\pi$
$769$	10.7699	−	23.5827i	0.388372	−	0.850416i	0.998318	−	0.0579729i	$-0.0184637\pi$
$770$	1.76518	−	0.518305i	0.0636128	−	0.0186784i
$771$	20.2317	−	5.94056i	0.728627	−	0.213944i
$772$	9.82914	−	21.5228i	0.353758	−	0.774623i
$773$	−3.36821	−	23.4264i	−0.121146	−	0.842589i	−0.956261	−	0.292514i	$-0.905508\pi$
$773$	−3.36821	−	23.4264i	−0.121146	−	0.842589i	0.835115	−	0.550075i	$-0.185401\pi$
$774$	3.13516	+	3.61817i	0.112691	+	0.130052i
$775$	2.41248	+	5.28260i	0.0866589	+	0.189757i
$776$	4.64244	−	2.98351i	0.166654	−	0.107102i
$777$	−0.127152	+	0.884360i	−0.00456154	+	0.0317262i
$778$	30.0465	+	19.3097i	1.07722	+	0.692287i
$779$	−5.42728	+	6.26341i	−0.194452	+	0.224410i
$780$	−1.59569	−	0.468536i	−0.0571347	−	0.0167763i
$781$	32.8546			1.17563
$782$	0.0972781	−	0.100681i	0.00347866	−	0.00360035i
$783$	5.97056			0.213371
$784$	−0.959493	−	0.281733i	−0.0342676	−	0.0100619i
$785$	−0.461613	+	0.532730i	−0.0164757	+	0.0190139i
$786$	−4.09766	−	2.63341i	−0.146159	−	0.0939305i
$787$	6.31826	−	43.9444i	0.225222	−	1.56645i	−0.492620	−	0.870244i	$-0.663961\pi$
$787$	6.31826	−	43.9444i	0.225222	−	1.56645i	0.717842	−	0.696206i	$-0.245130\pi$
$788$	5.36209	−	3.44601i	0.191017	−	0.122759i
$789$	−8.50434	−	18.6219i	−0.302762	−	0.662957i
$790$	−2.81986	−	3.25430i	−0.100326	−	0.115783i
$791$	−1.47846	−	10.2829i	−0.0525681	−	0.365619i
$792$	2.14096	−	4.68805i	0.0760758	−	0.166583i
$793$	−1.15397	+	0.338836i	−0.0409787	+	0.0120324i
$794$	18.8140	−	5.52428i	0.667683	−	0.196049i
$795$	−0.467802	+	1.02434i	−0.0165912	+	0.0363297i
$796$	−1.32417	−	9.20977i	−0.0469338	−	0.326432i
$797$	−32.4476	−	37.4466i	−1.14935	−	1.32643i	−0.937039	−	0.349224i	$-0.886445\pi$
$797$	−32.4476	−	37.4466i	−1.14935	−	1.32643i	−0.212315	−	0.977201i	$-0.568100\pi$
$798$	−0.377872	−	0.827425i	−0.0133765	−	0.0292905i
$799$	−0.156151	+	0.100352i	−0.00552423	+	0.00355021i
$800$	−0.693440	+	4.82298i	−0.0245168	+	0.170518i
$801$	−12.1565	−	7.81248i	−0.429527	−	0.276040i
$802$	−12.8292	+	14.8056i	−0.453014	+	0.522806i
$803$	−53.0043	−	15.5635i	−1.87048	−	0.549223i
$804$	13.3426			0.470557
$805$	−1.18953	+	1.23114i	−0.0419254	+	0.0433921i
$806$	−5.55274			−0.195587
$807$	15.5900	+	4.57762i	0.548792	+	0.161140i
$808$	6.05736	−	6.99056i	0.213097	−	0.245927i
$809$	−11.2388	−	7.22272i	−0.395134	−	0.253937i	0.327953	−	0.944694i	$-0.393641\pi$
$809$	−11.2388	−	7.22272i	−0.395134	−	0.253937i	−0.723087	+	0.690757i	$0.757278\pi$
$810$	−0.0508009	+	0.353328i	−0.00178496	+	0.0124147i
$811$	−20.2732	+	13.0288i	−0.711890	+	0.457504i	−0.845807	−	0.533489i	$-0.820881\pi$
$811$	−20.2732	+	13.0288i	−0.711890	+	0.457504i	0.133918	+	0.990992i	$0.457244\pi$
$812$	2.48026	+	5.43102i	0.0870401	+	0.190591i
$813$	−5.77412	−	6.66369i	−0.202507	−	0.233706i
$814$	−0.655313	−	4.55780i	−0.0229687	−	0.159751i
$815$	−1.05475	+	2.30958i	−0.0369463	+	0.0809010i
$816$	0.0280093	−	0.00822429i	0.000980523	−	0.000287908i
$817$	−4.17845	+	1.22691i	−0.146186	+	0.0429240i
$818$	−4.97929	+	10.9031i	−0.174097	+	0.381219i
$819$	0.663032	+	4.61149i	0.0231682	+	0.161139i
$820$	2.12981	+	2.45793i	0.0743761	+	0.0858346i
$821$	6.28476	+	13.7617i	0.219340	+	0.480287i	0.987030	−	0.160534i	$-0.0513215\pi$
$821$	6.28476	+	13.7617i	0.219340	+	0.480287i	−0.767691	+	0.640821i	$0.778594\pi$
$822$	0.279803	−	0.179818i	0.00975923	−	0.00627188i
$823$	4.67658	−	32.5263i	0.163015	−	1.13380i	−0.729894	−	0.683560i	$-0.760431\pi$
$823$	4.67658	−	32.5263i	0.163015	−	1.13380i	0.892910	−	0.450236i	$-0.148660\pi$
$824$	2.48250	+	1.59541i	0.0864821	+	0.0555787i
$825$	−16.4450	+	18.9786i	−0.572542	+	0.660749i
$826$	−7.96798	−	2.33961i	−0.277242	−	0.0814055i
$827$	34.5184			1.20032			0.600162	−	0.799879i	$-0.295103\pi$
$827$	34.5184			1.20032			0.600162	+	0.799879i	$0.295103\pi$
$828$	0.424302	+	4.77703i	0.0147455	+	0.166013i
$829$	−29.1346			−1.01189			−0.505943	−	0.862567i	$-0.668855\pi$
$829$	−29.1346			−1.01189			−0.505943	+	0.862567i	$0.668855\pi$
$830$	−0.575735	−	0.169051i	−0.0199841	−	0.00586785i
$831$	−0.598969	+	0.691247i	−0.0207780	+	0.0239791i
$832$	−3.91933	−	2.51880i	−0.135878	−	0.0873236i
$833$	0.00415443	−	0.0288947i	0.000143942	−	0.00100114i
$834$	18.0528	−	11.6018i	0.625118	−	0.401739i
$835$	1.11783	+	2.44772i	0.0386843	+	0.0847067i
$836$	3.07000	+	3.54297i	0.106178	+	0.122536i
$837$	0.169618	+	1.17972i	0.00586287	+	0.0407772i
$838$	−5.69918	+	12.4795i	−0.196875	+	0.431096i
$839$	−2.19877	+	0.645618i	−0.0759101	+	0.0222892i	−0.319467	−	0.947597i	$-0.603504\pi$
$839$	−2.19877	+	0.645618i	−0.0759101	+	0.0222892i	0.243557	+	0.969887i	$0.421686\pi$
$840$	−0.342502	+	0.100568i	−0.0118174	+	0.00346991i
$841$	2.76153	−	6.04690i	0.0952250	−	0.208514i
$842$	2.19373	+	15.2577i	0.0756009	+	0.525816i
$843$	−9.10066	−	10.5027i	−0.313444	−	0.361733i
$844$	1.82670	+	3.99991i	0.0628775	+	0.137682i
$845$	−2.61421	+	1.68005i	−0.0899314	+	0.0577954i
$846$	0.904915	−	6.29382i	0.0311116	−	0.216386i
$847$	13.0912	+	8.41321i	0.449819	+	0.289081i
$848$	−2.06589	+	2.38417i	−0.0709430	+	0.0818726i
$849$	−6.73023	−	1.97617i	−0.230981	−	0.0678221i
$850$	−0.142239			−0.00487877
$851$	2.62640	+	3.38556i	0.0900317	+	0.116056i
$852$	−6.37485			−0.218399
$853$	17.5450	+	5.15169i	0.600730	+	0.176390i	0.567937	−	0.823072i	$-0.307742\pi$
$853$	17.5450	+	5.15169i	0.600730	+	0.176390i	0.0327931	+	0.999462i	$0.489560\pi$
$854$	−0.169051	+	0.195095i	−0.00578480	+	0.00667602i
$855$	−0.273156	−	0.175547i	−0.00934175	−	0.00600358i
$856$	0.490903	−	3.41430i	0.0167787	−	0.116698i
$857$	14.9069	−	9.58009i	0.509210	−	0.327250i	−0.260681	−	0.965425i	$-0.583947\pi$
$857$	14.9069	−	9.58009i	0.509210	−	0.327250i	0.769891	+	0.638175i	$0.220311\pi$
$858$	−9.97455	−	21.8412i	−0.340526	−	0.745647i
$859$	−12.4174	−	14.3305i	−0.423678	−	0.488950i	0.503276	−	0.864126i	$-0.332128\pi$
$859$	−12.4174	−	14.3305i	−0.423678	−	0.488950i	−0.926954	+	0.375176i	$0.877582\pi$
$860$	0.243211	+	1.69157i	0.00829341	+	0.0576819i
$861$	3.78488	−	8.28774i	0.128988	−	0.282445i
$862$	3.71330	−	1.09032i	0.126476	−	0.0371366i
$863$	−44.1484	+	12.9632i	−1.50283	+	0.441271i	−0.926610	−	0.376024i	$-0.877291\pi$
$863$	−44.1484	+	12.9632i	−1.50283	+	0.441271i	−0.576220	+	0.817294i	$0.695473\pi$
$864$	−0.415415	+	0.909632i	−0.0141327	+	0.0309463i
$865$	−1.06581	−	7.41285i	−0.0362385	−	0.252045i
$866$	24.2581	+	27.9953i	0.824322	+	0.951319i
$867$	−7.06170	−	15.4630i	−0.239828	−	0.525150i
$868$	−1.00265	+	0.644365i	−0.0340322	+	0.0218712i
$869$	8.84779	−	61.5377i	0.300141	−	2.08752i
$870$	1.79293	+	1.15225i	0.0607861	+	0.0390648i
$871$	40.7074	−	46.9789i	1.37932	−	1.59182i
$872$	16.2029	+	4.75760i	0.548699	+	0.161113i
$873$	−5.51848			−0.186772
$874$	−4.11296	−	1.45403i	−0.139123	−	0.0491832i
$875$	3.52413			0.119137
$876$	10.2845	+	3.01981i	0.347482	+	0.102030i
$877$	−16.9196	+	19.5262i	−0.571333	+	0.659353i	−0.965718	−	0.259592i	$-0.916412\pi$
$877$	−16.9196	+	19.5262i	−0.571333	+	0.659353i	0.394386	+	0.918945i	$0.370957\pi$
$878$	−3.40658	−	2.18928i	−0.114966	−	0.0738845i
$879$	1.50305	−	10.4539i	0.0506966	−	0.352603i
$880$	1.54766	−	0.994619i	0.0521715	−	0.0335286i
$881$	−15.8207	−	34.6424i	−0.533011	−	1.16713i	−0.964274	−	0.264906i	$-0.914659\pi$
$881$	−15.8207	−	34.6424i	−0.533011	−	1.16713i	0.431263	−	0.902226i	$-0.358068\pi$
$882$	0.654861	+	0.755750i	0.0220503	+	0.0254474i
$883$	−1.36212	−	9.47378i	−0.0458391	−	0.318818i	−0.999820	−	0.0189520i	$-0.993967\pi$
$883$	−1.36212	−	9.47378i	−0.0458391	−	0.318818i	0.953981	−	0.299866i	$-0.0969421\pi$
$884$	0.0564973	−	0.123712i	0.00190021	−	0.00416088i
$885$	−2.84426	+	0.835151i	−0.0956089	+	0.0280733i
$886$	−20.9301	+	6.14564i	−0.703161	+	0.206467i
$887$	−17.9775	+	39.3653i	−0.603626	+	1.32176i	0.323223	+	0.946323i	$0.395234\pi$
$887$	−17.9775	+	39.3653i	−0.603626	+	1.32176i	−0.926849	+	0.375434i	$0.877494\pi$
$888$	0.127152	+	0.884360i	0.00426693	+	0.0296772i
$889$	−4.07721	−	4.70535i	−0.136745	−	0.157812i
$890$	−2.14281	−	4.69210i	−0.0718272	−	0.157280i
$891$	−4.33564	+	2.78635i	−0.145250	+	0.0933462i
$892$	3.55411	−	24.7194i	0.119000	−	0.827665i
$893$	4.86572	+	3.12701i	0.162825	+	0.104641i
$894$	−14.4690	+	16.6981i	−0.483915	+	0.558467i
$895$	0.720298	+	0.211499i	0.0240769	+	0.00706962i
$896$	−1.00000			−0.0334077
$897$	18.1143	+	13.0805i	0.604818	+	0.436744i
$898$	−37.8887			−1.26436
$899$	6.82779	+	2.00482i	0.227720	+	0.0668645i
$900$	3.19086	−	3.68245i	0.106362	−	0.122748i
$901$	−0.0774723	−	0.0497884i	−0.00258098	−	0.00165869i
$902$	−6.68262	+	46.4787i	−0.222507	+	1.54757i
$903$	4.02752	−	2.58833i	0.134028	−	0.0861342i
$904$	−4.31561	−	9.44988i	−0.143535	−	0.314298i
$905$	−2.86927	−	3.31131i	−0.0953776	−	0.110072i
$906$	0.410516	+	2.85520i	0.0136385	+	0.0948577i
$907$	−18.7900	+	41.1444i	−0.623912	+	1.36618i	0.288727	+	0.957412i	$0.406768\pi$
$907$	−18.7900	+	41.1444i	−0.623912	+	1.36618i	−0.912639	+	0.408766i	$0.865959\pi$
$908$	−6.60127	+	1.93831i	−0.219071	+	0.0643250i
$909$	−8.87516	+	2.60598i	−0.294370	+	0.0864349i
$910$	−0.690857	+	1.51277i	−0.0229017	+	0.0501477i
$911$	−0.267634	−	1.86144i	−0.00886711	−	0.0616721i	0.984907	−	0.173082i	$-0.0553725\pi$
$911$	−0.267634	−	1.86144i	−0.00886711	−	0.0616721i	−0.993775	+	0.111410i	$0.964463\pi$
$912$	−0.595679	−	0.687450i	−0.0197249	−	0.0227637i
$913$	−3.59889	−	7.88047i	−0.119106	−	0.260806i
$914$	3.63906	−	2.33868i	0.120369	−	0.0773566i
$915$	−0.0131141	+	0.0912109i	−0.000433540	+	0.00301534i
$916$	4.17922	+	2.68582i	0.138085	+	0.0887420i
$917$	−3.18976	+	3.68118i	−0.105335	+	0.121563i
$918$	−0.0280093	−	0.00822429i	−0.000924446	−	0.000271442i
$919$	30.9854			1.02211			0.511057	−	0.859547i	$-0.329254\pi$
$919$	30.9854			1.02211			0.511057	+	0.859547i	$0.329254\pi$
$920$	−0.794493	+	1.51640i	−0.0261936	+	0.0499943i
$921$	7.65760			0.252327
$922$	−7.07364	−	2.07701i	−0.232958	−	0.0684026i
$923$	−19.4493	+	22.4457i	−0.640180	+	0.738808i
$924$	−4.33564	−	2.78635i	−0.142632	−	0.0916641i
$925$	0.619557	−	4.30911i	0.0203709	−	0.141683i
$926$	−23.0703	+	14.8264i	−0.758138	+	0.487226i
$927$	−1.22587	−	2.68429i	−0.0402629	−	0.0881635i
$928$	3.90989	+	4.51225i	0.128348	+	0.148122i
$929$	−7.39452	−	51.4300i	−0.242606	−	1.68736i	−0.638939	−	0.769257i	$-0.720627\pi$
$929$	−7.39452	−	51.4300i	−0.242606	−	1.68736i	0.396333	−	0.918107i	$-0.370283\pi$
$930$	−0.176737	+	0.386999i	−0.00579542	+	0.0126902i
$931$	−0.872780	+	0.256271i	−0.0286042	+	0.00839895i
$932$	11.7590	−	3.45276i	0.385180	−	0.113099i
$933$	3.37580	−	7.39196i	0.110519	−	0.242002i
$934$	−3.48458	−	24.2358i	−0.114019	−	0.793018i
$935$	0.0351688	+	0.0405870i	0.00115014	+	0.00132734i
$936$	1.93538	+	4.23789i	0.0632599	+	0.138520i
$937$	−45.3354	+	29.1353i	−1.48104	+	0.951809i	−0.483992	+	0.875073i	$0.660814\pi$
$937$	−45.3354	+	29.1353i	−1.48104	+	0.951809i	−0.997051	+	0.0767360i	$0.975550\pi$
$938$	1.89885	−	13.2068i	0.0619996	−	0.431217i
$939$	−20.1791	−	12.9683i	−0.658520	−	0.423205i
$940$	1.48637	−	1.71537i	0.0484801	−	0.0559491i
$941$	31.5579	+	9.26625i	1.02876	+	0.302071i	0.752206	−	0.658928i	$-0.228990\pi$
$941$	31.5579	+	9.26625i	1.02876	+	0.302071i	0.276553	+	0.960999i	$0.410808\pi$
$942$	1.97473			0.0643402
$943$	−15.9714	−	40.6717i	−0.520099	−	1.32445i
$944$	−8.30437			−0.270284
$945$	0.342502	+	0.100568i	0.0111416	+	0.00327147i
$946$	−16.1580	+	18.6473i	−0.525341	+	0.606275i
$947$	34.7088	+	22.3060i	1.12788	+	0.724847i	0.965117	−	0.261818i	$-0.0843219\pi$
$947$	34.7088	+	22.3060i	1.12788	+	0.724847i	0.162767	+	0.986665i	$0.447958\pi$
$948$	−1.71675	+	11.9403i	−0.0557576	+	0.387803i
$949$	42.0101	−	26.9983i	1.36371	−	0.876401i
$950$	1.84121	+	4.03169i	0.0597368	+	0.130805i
$951$	22.1397	+	25.5506i	0.717930	+	0.828535i
$952$	−0.00415443	−	0.0288947i	−0.000134646	−	0.000936482i
$953$	14.5643	−	31.8914i	0.471784	−	1.03306i	−0.512858	−	0.858474i	$-0.671413\pi$
$953$	14.5643	−	31.8914i	0.471784	−	1.03306i	0.984641	−	0.174589i	$-0.0558596\pi$
$954$	3.02692	−	0.888783i	0.0980000	−	0.0287754i
$955$	−5.04177	+	1.48040i	−0.163148	+	0.0479045i
$956$	−3.43695	+	7.52587i	−0.111159	+	0.243404i
$957$	4.37917	+	30.4578i	0.141559	+	0.984562i
$958$	−6.31867	−	7.29213i	−0.204147	−	0.235598i
$959$	−0.138168	−	0.302545i	−0.00446167	−	0.00976970i
$960$	−0.300295	+	0.192988i	−0.00969198	+	0.00622866i
$961$	4.20960	−	29.2784i	0.135794	−	0.944465i
$962$	3.50174	+	2.25043i	0.112901	+	0.0725568i
$963$	−2.25888	+	2.60689i	−0.0727915	+	0.0840059i
$964$	−28.0589	−	8.23884i	−0.903716	−	0.265355i
$965$	−8.44607			−0.271889
$966$	4.78879	+	0.259859i	0.154077	+	0.00836082i
$967$	−2.83034			−0.0910176			−0.0455088	−	0.998964i	$-0.514491\pi$
$967$	−2.83034			−0.0910176			−0.0455088	+	0.998964i	$0.514491\pi$
$968$	14.9312	+	4.38419i	0.479907	+	0.140913i
$969$	0.0173889	−	0.0200679i	0.000558613	−	0.000644674i
$970$	−1.65717	−	1.06500i	−0.0532086	−	0.0341951i
$971$	7.17164	−	49.8799i	0.230149	−	1.60072i	−0.467308	−	0.884094i	$-0.654776\pi$
$971$	7.17164	−	49.8799i	0.230149	−	1.60072i	0.697457	−	0.716626i	$-0.254315\pi$
$972$	0.841254	−	0.540641i	0.0269832	−	0.0173411i
$973$	−8.91456	−	19.5202i	−0.285788	−	0.625788i
$974$	−8.05404	−	9.29485i	−0.258068	−	0.297826i
$975$	−3.23068	−	22.4698i	−0.103464	−	0.719611i
$976$	−0.107238	+	0.234820i	−0.00343262	+	0.00751639i
$977$	−32.2679	+	9.47470i	−1.03234	+	0.303122i	−0.753662	−	0.657262i	$-0.771714\pi$
$977$	−32.2679	+	9.47470i	−1.03234	+	0.303122i	−0.278678	+	0.960385i	$0.589896\pi$
$978$	6.82476	−	2.00393i	0.218232	−	0.0640787i
$979$	30.9378	−	67.7443i	0.988775	−	2.16512i
$980$	0.0508009	+	0.353328i	0.00162278	+	0.0112867i
$981$	−11.0586	−	12.7623i	−0.353073	−	0.407469i
$982$	11.3559	+	24.8659i	0.362380	+	0.793502i
$983$	25.9438	−	16.6731i	0.827480	−	0.531789i	−0.0569963	−	0.998374i	$-0.518152\pi$
$983$	25.9438	−	16.6731i	0.827480	−	0.531789i	0.884476	+	0.466585i	$0.154516\pi$
$984$	1.29664	−	9.01835i	0.0413355	−	0.287495i
$985$	−1.91406	−	1.23009i	−0.0609870	−	0.0391940i
$986$	−0.114137	+	0.131721i	−0.00363485	+	0.00419485i
$987$	−6.10097	−	1.79141i	−0.194196	−	0.0570211i
$988$	−4.23787			−0.134825
$989$	4.49419	−	22.5160i	0.142907	−	0.715968i
$990$	−1.83970			−0.0584696
$991$	−40.5422	−	11.9043i	−1.28786	−	0.378151i	−0.435069	−	0.900397i	$-0.643276\pi$
$991$	−40.5422	−	11.9043i	−1.28786	−	0.378151i	−0.852795	+	0.522246i	$0.825094\pi$
$992$	−0.780498	+	0.900743i	−0.0247808	+	0.0285986i
$993$	−20.3671	−	13.0891i	−0.646329	−	0.415371i
$994$	−0.907236	+	6.30996i	−0.0287758	+	0.200140i
$995$	−2.79409	+	1.79565i	−0.0885786	+	0.0569260i
$996$	0.698300	+	1.52906i	0.0221265	+	0.0484502i
$997$	16.2887	+	18.7982i	0.515868	+	0.595343i	0.952591	−	0.304252i	$-0.0984066\pi$
$997$	16.2887	+	18.7982i	0.515868	+	0.595343i	−0.436723	+	0.899596i	$0.643861\pi$
$998$	−6.09939	−	42.4222i	−0.193073	−	1.34285i
$999$	0.371154	−	0.812714i	0.0117428	−	0.0257131i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.e.547.2	✓	20
23.9	even	11	inner	966.2.q.e.883.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.e.547.2	✓	20	1.1	even	1	trivial
966.2.q.e.883.2	yes	20	23.9	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.959493 + 0.281733i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.0508009 - 0.353328i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(0.415415 + 0.909632i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.959493 + 0.281733i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.0508009 - 0.353328i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(0.415415 + 0.909632i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(0.148287 - 0.324704i) q^{10} +(4.94502 - 1.45199i) q^{11} +(-0.959493 + 0.281733i) q^{12} +(-1.93538 + 4.23789i) q^{13} +(0.142315 + 0.989821i) q^{14} +(0.233760 + 0.269773i) q^{15} +(0.415415 + 0.909632i) q^{16} +(-0.0245577 + 0.0157823i) q^{17} +(0.142315 - 0.989821i) q^{18} +(0.765226 + 0.491781i) q^{19} +(0.233760 - 0.269773i) q^{20} +(-0.959493 - 0.281733i) q^{21} +5.15379 q^{22} +(-4.16907 + 2.37041i) q^{23} -1.00000 q^{24} +(4.67520 + 1.37276i) q^{25} +(-3.05094 + 3.52097i) q^{26} +(0.841254 + 0.540641i) q^{27} +(-0.142315 + 0.989821i) q^{28} +(5.02276 - 3.22793i) q^{29} +(0.148287 + 0.324704i) q^{30} +(0.780498 + 0.900743i) q^{31} +(0.142315 + 0.989821i) q^{32} +(-2.14096 + 4.68805i) q^{33} +(-0.0280093 + 0.00822429i) q^{34} +(0.342502 - 0.100568i) q^{35} +(0.415415 - 0.909632i) q^{36} +(-0.127152 - 0.884360i) q^{37} +(0.595679 + 0.687450i) q^{38} +(-1.93538 - 4.23789i) q^{39} +(0.300295 - 0.192988i) q^{40} +(-1.29664 + 9.01835i) q^{41} +(-0.841254 - 0.540641i) q^{42} +(-3.13516 + 3.61817i) q^{43} +(4.94502 + 1.45199i) q^{44} -0.356961 q^{45} +(-4.66802 + 1.09982i) q^{46} +6.35854 q^{47} +(-0.959493 - 0.281733i) q^{48} +(-0.654861 + 0.755750i) q^{49} +(4.09907 + 2.63431i) q^{50} +(0.00415443 - 0.0288947i) q^{51} +(-3.91933 + 2.51880i) q^{52} +(1.31051 + 2.86962i) q^{53} +(0.654861 + 0.755750i) q^{54} +(-0.261817 - 1.82098i) q^{55} +(-0.415415 + 0.909632i) q^{56} +(-0.872780 + 0.256271i) q^{57} +(5.72871 - 1.68210i) q^{58} +(-3.44976 + 7.55392i) q^{59} +(0.0508009 + 0.353328i) q^{60} +(0.169051 + 0.195095i) q^{61} +(0.495114 + 1.08415i) q^{62} +(0.841254 - 0.540641i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(1.39905 + 0.899114i) q^{65} +(-3.37501 + 3.89497i) q^{66} +(-12.8021 - 3.75904i) q^{67} -0.0291918 q^{68} +(0.938729 - 4.70306i) q^{69} +0.356961 q^{70} +(6.11662 + 1.79600i) q^{71} +(0.654861 - 0.755750i) q^{72} +(-9.01716 - 5.79497i) q^{73} +(0.127152 - 0.884360i) q^{74} +(-4.09907 + 2.63431i) q^{75} +(0.377872 + 0.827425i) q^{76} +(3.37501 + 3.89497i) q^{77} +(-0.663032 - 4.61149i) q^{78} +(5.01118 - 10.9730i) q^{79} +(0.342502 - 0.100568i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-3.78488 + 8.28774i) q^{82} +(-0.239227 - 1.66386i) q^{83} +(-0.654861 - 0.755750i) q^{84} +(0.00432877 + 0.00947869i) q^{85} +(-4.02752 + 2.58833i) q^{86} +(-0.849700 + 5.90979i) q^{87} +(4.33564 + 2.78635i) q^{88} +(9.46301 - 10.9209i) q^{89} +(-0.342502 - 0.100568i) q^{90} -4.65891 q^{91} +(-4.78879 - 0.259859i) q^{92} -1.19185 q^{93} +(6.10097 + 1.79141i) q^{94} +(0.212634 - 0.245393i) q^{95} +(-0.841254 - 0.540641i) q^{96} +(0.785361 - 5.46231i) q^{97} +(-0.841254 + 0.540641i) q^{98} +(-2.14096 - 4.68805i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 10 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 10 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 10 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} - 10 q^{10} - 3 q^{11} - 2 q^{12} + 6 q^{13} + 2 q^{14} - 12 q^{15} - 2 q^{16} + 14 q^{17} + 2 q^{18} - 13 q^{19} - 12 q^{20} - 2 q^{21} - 8 q^{22} - 2 q^{23} - 20 q^{24} + 22 q^{25} - 28 q^{26} - 2 q^{27} - 2 q^{28} + 26 q^{29} - 10 q^{30} + 15 q^{31} + 2 q^{32} - 14 q^{33} - 3 q^{34} - q^{35} - 2 q^{36} - 26 q^{37} + 2 q^{38} + 6 q^{39} + q^{40} + 40 q^{41} + 2 q^{42} + 8 q^{43} - 3 q^{44} - 12 q^{45} - 20 q^{46} + 36 q^{47} - 2 q^{48} - 2 q^{49} + 11 q^{50} + 3 q^{51} - 27 q^{52} - 5 q^{53} + 2 q^{54} - 7 q^{55} + 2 q^{56} + 9 q^{57} - 15 q^{58} + 13 q^{59} + 10 q^{60} + 59 q^{61} - 4 q^{62} - 2 q^{63} - 2 q^{64} - q^{65} - 8 q^{66} - 26 q^{67} - 8 q^{68} - 35 q^{69} + 12 q^{70} + 13 q^{71} + 2 q^{72} - 34 q^{73} + 26 q^{74} - 11 q^{75} - 2 q^{76} + 8 q^{77} - 6 q^{78} - 27 q^{79} - q^{80} - 2 q^{81} - 40 q^{82} + 41 q^{83} - 2 q^{84} + 51 q^{85} + 14 q^{86} - 7 q^{87} - 8 q^{88} + 43 q^{89} + q^{90} - 16 q^{91} + 9 q^{92} + 4 q^{93} - 3 q^{94} - 26 q^{95} + 2 q^{96} - 8 q^{97} + 2 q^{98} - 14 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 10 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 - 10 * q^10 - 3 * q^11 - 2 * q^12 + 6 * q^13 + 2 * q^14 - 12 * q^15 - 2 * q^16 + 14 * q^17 + 2 * q^18 - 13 * q^19 - 12 * q^20 - 2 * q^21 - 8 * q^22 - 2 * q^23 - 20 * q^24 + 22 * q^25 - 28 * q^26 - 2 * q^27 - 2 * q^28 + 26 * q^29 - 10 * q^30 + 15 * q^31 + 2 * q^32 - 14 * q^33 - 3 * q^34 - q^35 - 2 * q^36 - 26 * q^37 + 2 * q^38 + 6 * q^39 + q^40 + 40 * q^41 + 2 * q^42 + 8 * q^43 - 3 * q^44 - 12 * q^45 - 20 * q^46 + 36 * q^47 - 2 * q^48 - 2 * q^49 + 11 * q^50 + 3 * q^51 - 27 * q^52 - 5 * q^53 + 2 * q^54 - 7 * q^55 + 2 * q^56 + 9 * q^57 - 15 * q^58 + 13 * q^59 + 10 * q^60 + 59 * q^61 - 4 * q^62 - 2 * q^63 - 2 * q^64 - q^65 - 8 * q^66 - 26 * q^67 - 8 * q^68 - 35 * q^69 + 12 * q^70 + 13 * q^71 + 2 * q^72 - 34 * q^73 + 26 * q^74 - 11 * q^75 - 2 * q^76 + 8 * q^77 - 6 * q^78 - 27 * q^79 - q^80 - 2 * q^81 - 40 * q^82 + 41 * q^83 - 2 * q^84 + 51 * q^85 + 14 * q^86 - 7 * q^87 - 8 * q^88 + 43 * q^89 + q^90 - 16 * q^91 + 9 * q^92 + 4 * q^93 - 3 * q^94 - 26 * q^95 + 2 * q^96 - 8 * q^97 + 2 * q^98 - 14 * q^99

Introduction

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