LMFDB - Embedded newform 392.2.z.a.221.54

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,2,Mod(37,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 21, 32]))

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

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

chi := DirichletCharacter("392.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.z (of order $42$, degree $12$, 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:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$54$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			221.54
Character	$\chi$	$=$	392.221
Dual form			392.2.z.a.149.54

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40664 - 0.146147i) q^{2} +(0.569538 - 0.223527i) q^{3} +(1.95728 - 0.411152i) q^{4} +(0.502846 - 3.33616i) q^{5} +(0.768468 - 0.397659i) q^{6} +(1.43535 + 2.22256i) q^{7} +(2.69311 - 0.864394i) q^{8} +(-1.92475 + 1.78590i) q^{9} +O(q^{10})$	\(q+(1.40664 - 0.146147i) q^{2} +(0.569538 - 0.223527i) q^{3} +(1.95728 - 0.411152i) q^{4} +(0.502846 - 3.33616i) q^{5} +(0.768468 - 0.397659i) q^{6} +(1.43535 + 2.22256i) q^{7} +(2.69311 - 0.864394i) q^{8} +(-1.92475 + 1.78590i) q^{9} +(0.219754 - 4.76628i) q^{10} +(-0.283012 + 0.305015i) q^{11} +(1.02284 - 0.671672i) q^{12} +(-4.40559 - 1.00555i) q^{13} +(2.34384 + 2.91658i) q^{14} +(-0.459333 - 2.01247i) q^{15} +(3.66191 - 1.60948i) q^{16} +(-0.0571472 + 0.762576i) q^{17} +(-2.44643 + 2.79342i) q^{18} +(-0.228464 + 0.131904i) q^{19} +(-0.387460 - 6.73656i) q^{20} +(1.31429 + 0.944994i) q^{21} +(-0.353520 + 0.470408i) q^{22} +(0.0580467 + 0.774579i) q^{23} +(1.34061 - 1.09429i) q^{24} +(-6.09926 - 1.88137i) q^{25} +(-6.34405 - 0.770582i) q^{26} +(-1.49341 + 3.10110i) q^{27} +(3.72319 + 3.76004i) q^{28} +(2.22644 + 4.62326i) q^{29} +(-0.940233 - 2.76369i) q^{30} +(3.35283 - 5.80727i) q^{31} +(4.91577 - 2.79914i) q^{32} +(-0.0930072 + 0.236978i) q^{33} +(0.0310624 + 1.08102i) q^{34} +(8.13659 - 3.67094i) q^{35} +(-3.03299 + 4.28688i) q^{36} +(-0.158540 + 0.232535i) q^{37} +(-0.302089 + 0.218930i) q^{38} +(-2.73392 + 0.412072i) q^{39} +(-1.52954 - 9.41930i) q^{40} +(-4.82283 + 6.04764i) q^{41} +(1.98684 + 1.13719i) q^{42} +(-6.83466 + 5.45046i) q^{43} +(-0.428528 + 0.713361i) q^{44} +(4.99022 + 7.31930i) q^{45} +(0.194853 + 1.08107i) q^{46} +(6.65193 - 2.05185i) q^{47} +(1.72583 - 1.73520i) q^{48} +(-2.87957 + 6.38029i) q^{49} +(-8.85444 - 1.75503i) q^{50} +(0.137909 + 0.447090i) q^{51} +(-9.03642 - 0.156772i) q^{52} +(4.26446 + 6.25481i) q^{53} +(-1.64748 + 4.58039i) q^{54} +(0.875268 + 1.09755i) q^{55} +(5.78671 + 4.74489i) q^{56} +(-0.100635 + 0.126192i) q^{57} +(3.80748 + 6.17788i) q^{58} +(0.176984 + 1.17421i) q^{59} +(-1.72648 - 3.75012i) q^{60} +(5.72016 - 8.38994i) q^{61} +(3.86751 - 8.65875i) q^{62} +(-6.73196 - 1.71448i) q^{63} +(6.50565 - 4.65581i) q^{64} +(-5.57000 + 14.1921i) q^{65} +(-0.0961942 + 0.346936i) q^{66} +(-11.7312 - 6.77300i) q^{67} +(0.201682 + 1.51607i) q^{68} +(0.206199 + 0.428177i) q^{69} +(10.9088 - 6.35283i) q^{70} +(-5.50564 - 2.65138i) q^{71} +(-3.63982 + 6.47337i) q^{72} +(-13.8661 - 4.27711i) q^{73} +(-0.189024 + 0.350263i) q^{74} +(-3.89430 + 0.291837i) q^{75} +(-0.392935 + 0.352106i) q^{76} +(-1.08414 - 0.191211i) q^{77} +(-3.78542 + 0.979190i) q^{78} +(-2.22959 - 3.86176i) q^{79} +(-3.52812 - 13.0260i) q^{80} +(0.431274 - 5.75495i) q^{81} +(-5.90015 + 9.21170i) q^{82} +(10.7099 - 2.44447i) q^{83} +(2.96097 + 1.30925i) q^{84} +(2.51534 + 0.574110i) q^{85} +(-8.81735 + 8.66570i) q^{86} +(2.30147 + 2.13545i) q^{87} +(-0.498530 + 1.06607i) q^{88} +(6.09822 - 5.65832i) q^{89} +(8.08914 + 9.56633i) q^{90} +(-4.08865 - 11.2350i) q^{91} +(0.432084 + 1.49220i) q^{92} +(0.611480 - 4.05690i) q^{93} +(9.05701 - 3.85837i) q^{94} +(0.325170 + 0.828519i) q^{95} +(2.17403 - 2.69302i) q^{96} +1.01801 q^{97} +(-3.11806 + 9.39562i) q^{98} -1.09251i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9}+O(q^{10}) $ 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9	$ 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25} - 12 q^{26} + 2 q^{28} - 11 q^{30} + 60 q^{31} - 13 q^{32} - 14 q^{33} - 18 q^{34} + 8 q^{36} - 46 q^{38} - 32 q^{39} + 32 q^{40} - 20 q^{41} - 36 q^{42} + 38 q^{44} - 22 q^{46} - 58 q^{47} + 28 q^{48} - 16 q^{49} - 132 q^{50} + 18 q^{52} - 37 q^{54} - 32 q^{55} + 96 q^{56} - 66 q^{57} + 100 q^{60} + 28 q^{62} - 72 q^{63} - 28 q^{64} - 36 q^{65} - 4 q^{66} - 11 q^{68} - 36 q^{70} + 60 q^{71} - 130 q^{72} - 18 q^{73} - 12 q^{74} + 11 q^{76} - 132 q^{78} - 12 q^{79} - 64 q^{80} - 58 q^{81} + 152 q^{82} - 224 q^{84} + 55 q^{86} - 8 q^{87} - 169 q^{88} - 18 q^{89} + 144 q^{90} - 54 q^{92} + 154 q^{94} - 64 q^{95} - 142 q^{96} - 96 q^{97} + 151 q^{98}+O(q^{100}) $ 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9 - 6 * q^10 - 47 * q^12 - 33 * q^14 - 8 * q^15 - 17 * q^16 - 26 * q^17 - 8 * q^18 - 22 * q^20 - 18 * q^22 - 26 * q^23 - 74 * q^24 - 72 * q^25 - 12 * q^26 + 2 * q^28 - 11 * q^30 + 60 * q^31 - 13 * q^32 - 14 * q^33 - 18 * q^34 + 8 * q^36 - 46 * q^38 - 32 * q^39 + 32 * q^40 - 20 * q^41 - 36 * q^42 + 38 * q^44 - 22 * q^46 - 58 * q^47 + 28 * q^48 - 16 * q^49 - 132 * q^50 + 18 * q^52 - 37 * q^54 - 32 * q^55 + 96 * q^56 - 66 * q^57 + 100 * q^60 + 28 * q^62 - 72 * q^63 - 28 * q^64 - 36 * q^65 - 4 * q^66 - 11 * q^68 - 36 * q^70 + 60 * q^71 - 130 * q^72 - 18 * q^73 - 12 * q^74 + 11 * q^76 - 132 * q^78 - 12 * q^79 - 64 * q^80 - 58 * q^81 + 152 * q^82 - 224 * q^84 + 55 * q^86 - 8 * q^87 - 169 * q^88 - 18 * q^89 + 144 * q^90 - 54 * q^92 + 154 * q^94 - 64 * q^95 - 142 * q^96 - 96 * q^97 + 151 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$e\left(\frac{8}{21}\right)$

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 $

$2$	1.40664	−	0.146147i	0.994646	−	0.103341i
$2$	1.40664	−	0.146147i	0.994646	−	0.103341i
$3$	0.569538	−	0.223527i	0.328823	−	0.129053i	−0.195186	−	0.980766i	$-0.562531\pi$
$3$	0.569538	−	0.223527i	0.328823	−	0.129053i	0.524009	+	0.851713i	$0.324436\pi$
$4$	1.95728	−	0.411152i	0.978641	−	0.205576i
$5$	0.502846	−	3.33616i	0.224879	−	1.49198i	−0.536627	−	0.843820i	$-0.680302\pi$
$5$	0.502846	−	3.33616i	0.224879	−	1.49198i	0.761506	−	0.648158i	$-0.224460\pi$
$6$	0.768468	−	0.397659i	0.313726	−	0.162343i
$7$	1.43535	+	2.22256i	0.542510	+	0.840050i
$7$	1.43535	+	2.22256i	0.542510	+	0.840050i
$8$	2.69311	−	0.864394i	0.952157	−	0.305610i
$9$	−1.92475	+	1.78590i	−0.641582	+	0.595301i
$10$	0.219754	−	4.76628i	0.0694924	−	1.50723i
$11$	−0.283012	+	0.305015i	−0.0853315	+	0.0919654i	−0.774274	−	0.632851i	$-0.781885\pi$
$11$	−0.283012	+	0.305015i	−0.0853315	+	0.0919654i	0.688943	+	0.724816i	$0.258075\pi$
$12$	1.02284	−	0.671672i	0.295269	−	0.193895i
$13$	−4.40559	−	1.00555i	−1.22189	−	0.278889i	−0.437536	−	0.899201i	$-0.644149\pi$
$13$	−4.40559	−	1.00555i	−1.22189	−	0.278889i	−0.784355	+	0.620312i	$0.787006\pi$
$14$	2.34384	+	2.91658i	0.626417	+	0.779488i
$15$	−0.459333	−	2.01247i	−0.118599	−	0.519618i
$16$	3.66191	−	1.60948i	0.915477	−	0.402370i
$17$	−0.0571472	+	0.762576i	−0.0138602	+	0.184952i	0.985977	+	0.166884i	$0.0533705\pi$
$17$	−0.0571472	+	0.762576i	−0.0138602	+	0.184952i	−0.999837	+	0.0180678i	$0.994249\pi$
$18$	−2.44643	+	2.79342i	−0.576628	+	0.658416i
$19$	−0.228464	+	0.131904i	−0.0524132	+	0.0302608i	−0.525978	−	0.850498i	$-0.676300\pi$
$19$	−0.228464	+	0.131904i	−0.0524132	+	0.0302608i	0.473564	+	0.880759i	$0.342967\pi$
$20$	−0.387460	−	6.73656i	−0.0866386	−	1.50634i
$21$	1.31429	+	0.944994i	0.286801	+	0.206215i
$22$	−0.353520	+	0.470408i	−0.0753708	+	0.100291i
$23$	0.0580467	+	0.774579i	0.0121036	+	0.161511i	0.999980	+	0.00627079i	$0.00199607\pi$
$23$	0.0580467	+	0.774579i	0.0121036	+	0.161511i	−0.987877	+	0.155240i	$0.950385\pi$
$24$	1.34061	−	1.09429i	0.273651	−	0.223370i
$25$	−6.09926	−	1.88137i	−1.21985	−	0.376275i
$26$	−6.34405	−	0.770582i	−1.24417	−	0.151124i
$27$	−1.49341	+	3.10110i	−0.287407	+	0.596806i
$28$	3.72319	+	3.76004i	0.703616	+	0.710580i
$29$	2.22644	+	4.62326i	0.413440	+	0.858517i	0.998858	+	0.0477853i	$0.0152163\pi$
$29$	2.22644	+	4.62326i	0.413440	+	0.858517i	−0.585417	+	0.810732i	$0.699069\pi$
$30$	−0.940233	−	2.76369i	−0.171662	−	0.504579i
$31$	3.35283	−	5.80727i	0.602185	−	1.04302i	−0.390304	−	0.920686i	$-0.627630\pi$
$31$	3.35283	−	5.80727i	0.602185	−	1.04302i	0.992490	−	0.122330i	$-0.0390366\pi$
$32$	4.91577	−	2.79914i	0.868994	−	0.494823i
$33$	−0.0930072	+	0.236978i	−0.0161905	+	0.0412526i
$34$	0.0310624	+	1.08102i	0.00532715	+	0.185394i
$35$	8.13659	−	3.67094i	1.37533	−	0.620502i
$36$	−3.03299	+	4.28688i	−0.505499	+	0.714480i
$37$	−0.158540	+	0.232535i	−0.0260637	+	0.0382285i	−0.839050	−	0.544055i	$-0.816888\pi$
$37$	−0.158540	+	0.232535i	−0.0260637	+	0.0382285i	0.812986	+	0.582284i	$0.197841\pi$
$38$	−0.302089	+	0.218930i	−0.0490054	+	0.0355152i
$39$	−2.73392	+	0.412072i	−0.437777	+	0.0659843i
$40$	−1.52954	−	9.41930i	−0.241842	−	1.48932i
$41$	−4.82283	+	6.04764i	−0.753200	+	0.944483i	−0.999696	−	0.0246612i	$-0.992149\pi$
$41$	−4.82283	+	6.04764i	−0.753200	+	0.944483i	0.246496	+	0.969144i	$0.420721\pi$
$42$	1.98684	+	1.13719i	0.306576	+	0.175472i
$43$	−6.83466	+	5.45046i	−1.04228	+	0.831187i	−0.985919	−	0.167224i	$-0.946520\pi$
$43$	−6.83466	+	5.45046i	−1.04228	+	0.831187i	−0.0563566	+	0.998411i	$0.517948\pi$
$44$	−0.428528	+	0.713361i	−0.0646030	+	0.107543i
$45$	4.99022	+	7.31930i	0.743897	+	1.09110i
$46$	0.194853	+	1.08107i	0.0287295	+	0.159395i
$47$	6.65193	−	2.05185i	0.970284	−	0.299293i	0.231200	−	0.972906i	$-0.425735\pi$
$47$	6.65193	−	2.05185i	0.970284	−	0.299293i	0.739084	+	0.673613i	$0.235259\pi$
$48$	1.72583	−	1.73520i	0.249102	−	0.250454i
$49$	−2.87957	+	6.38029i	−0.411367	+	0.911470i
$50$	−8.85444	−	1.75503i	−1.25221	−	0.248199i
$51$	0.137909	+	0.447090i	0.0193111	+	0.0626051i
$52$	−9.03642	−	0.156772i	−1.25313	−	0.0217403i
$53$	4.26446	+	6.25481i	0.585768	+	0.859164i	0.998667	−	0.0516127i	$-0.0164361\pi$
$53$	4.26446	+	6.25481i	0.585768	+	0.859164i	−0.412899	+	0.910777i	$0.635484\pi$
$54$	−1.64748	+	4.58039i	−0.224193	+	0.623312i
$55$	0.875268	+	1.09755i	0.118021	+	0.147994i
$56$	5.78671	+	4.74489i	0.773281	+	0.634063i
$57$	−0.100635	+	0.126192i	−0.0133294	+	0.0167145i
$58$	3.80748	+	6.17788i	0.499947	+	0.811195i
$59$	0.176984	+	1.17421i	0.0230413	+	0.152869i	0.997393	−	0.0721618i	$-0.0229898\pi$
$59$	0.176984	+	1.17421i	0.0230413	+	0.152869i	−0.974352	+	0.225031i	$0.927752\pi$
$60$	−1.72648	−	3.75012i	−0.222887	−	0.484138i
$61$	5.72016	−	8.38994i	0.732392	−	1.07422i	−0.261644	−	0.965165i	$-0.584264\pi$
$61$	5.72016	−	8.38994i	0.732392	−	1.07422i	0.994035	−	0.109057i	$-0.0347831\pi$
$62$	3.86751	−	8.65875i	0.491175	−	1.09966i
$63$	−6.73196	−	1.71448i	−0.848147	−	0.216004i
$64$	6.50565	−	4.65581i	0.813206	−	0.581976i
$65$	−5.57000	+	14.1921i	−0.690874	+	1.76032i
$66$	−0.0961942	+	0.346936i	−0.0118407	+	0.0427049i
$67$	−11.7312	−	6.77300i	−1.43319	−	0.827453i	−0.435828	−	0.900030i	$-0.643544\pi$
$67$	−11.7312	−	6.77300i	−1.43319	−	0.827453i	−0.997363	+	0.0725768i	$0.976878\pi$
$68$	0.201682	+	1.51607i	0.0244575	+	0.183851i
$69$	0.206199	+	0.428177i	0.0248235	+	0.0515464i
$70$	10.9088	−	6.35283i	1.30385	−	0.759309i
$71$	−5.50564	−	2.65138i	−0.653400	−	0.314661i	0.0776542	−	0.996980i	$-0.475257\pi$
$71$	−5.50564	−	2.65138i	−0.653400	−	0.314661i	−0.731054	+	0.682320i	$0.760971\pi$
$72$	−3.63982	+	6.47337i	−0.428957	+	0.762894i
$73$	−13.8661	−	4.27711i	−1.62290	−	0.500598i	−0.655786	−	0.754947i	$-0.727663\pi$
$73$	−13.8661	−	4.27711i	−1.62290	−	0.500598i	−0.967113	+	0.254349i	$0.918139\pi$
$74$	−0.189024	+	0.350263i	−0.0219736	+	0.0407173i
$75$	−3.89430	+	0.291837i	−0.449675	+	0.0336985i
$76$	−0.392935	+	0.352106i	−0.0450728	+	0.0403893i
$77$	−1.08414	−	0.191211i	−0.123549	−	0.0217905i
$78$	−3.78542	+	0.979190i	−0.428614	+	0.110871i
$79$	−2.22959	−	3.86176i	−0.250848	−	0.434482i	0.712911	−	0.701254i	$-0.247376\pi$
$79$	−2.22959	−	3.86176i	−0.250848	−	0.434482i	−0.963760	+	0.266772i	$0.914043\pi$
$80$	−3.52812	−	13.0260i	−0.394456	−	1.45636i
$81$	0.431274	−	5.75495i	0.0479194	−	0.639439i
$82$	−5.90015	+	9.21170i	−0.651563	+	1.01726i
$83$	10.7099	−	2.44447i	1.17557	−	0.268316i	0.410253	−	0.911972i	$-0.365440\pi$
$83$	10.7099	−	2.44447i	1.17557	−	0.268316i	0.765315	+	0.643656i	$0.222583\pi$
$84$	2.96097	+	1.30925i	0.323068	+	0.142851i
$85$	2.51534	+	0.574110i	0.272827	+	0.0622710i
$86$	−8.81735	+	8.66570i	−0.950799	+	0.934447i
$87$	2.30147	+	2.13545i	0.246743	+	0.228944i
$88$	−0.498530	+	1.06607i	−0.0531434	+	0.113644i
$89$	6.09822	−	5.65832i	0.646410	−	0.599780i	−0.287287	−	0.957844i	$-0.592753\pi$
$89$	6.09822	−	5.65832i	0.646410	−	0.599780i	0.933697	+	0.358064i	$0.116563\pi$
$90$	8.08914	+	9.56633i	0.852670	+	1.00838i
$91$	−4.08865	−	11.2350i	−0.428607	−	1.17775i
$92$	0.432084	+	1.49220i	0.0450478	+	0.155573i
$93$	0.611480	−	4.05690i	0.0634075	−	0.420681i
$94$	9.05701	−	3.85837i	0.934160	−	0.397961i
$95$	0.325170	+	0.828519i	0.0333617	+	0.0850043i
$96$	2.17403	−	2.69302i	0.221886	−	0.274856i
$97$	1.01801			0.103363			0.0516815	−	0.998664i	$-0.483542\pi$
$97$	1.01801			0.103363			0.0516815	+	0.998664i	$0.483542\pi$
$98$	−3.11806	+	9.39562i	−0.314972	+	0.949101i
$99$		−	1.09251i		−	0.109801i
$100$	−12.7115	−	1.17465i	−1.27115	−	0.117465i
$101$	−16.9966	+	6.67066i	−1.69122	+	0.663756i	−0.998356	−	0.0573109i	$-0.981747\pi$
$101$	−16.9966	+	6.67066i	−1.69122	+	0.663756i	−0.692866	+	0.721067i	$0.743652\pi$
$102$	0.259329	+	0.608740i	0.0256774	+	0.0602742i
$103$	6.63647	+	1.00029i	0.653911	+	0.0985612i	0.467615	−	0.883933i	$-0.345114\pi$
$103$	6.63647	+	1.00029i	0.653911	+	0.0985612i	0.186296	+	0.982494i	$0.440352\pi$
$104$	−12.7339	+	1.10012i	−1.24866	+	0.107876i
$105$	3.81354	−	3.90949i	0.372163	−	0.381527i
$106$	6.91268	+	8.17504i	0.671419	+	0.794030i
$107$	4.80241	+	5.17577i	0.464267	+	0.500361i	0.921172	−	0.389155i	$-0.127233\pi$
$107$	4.80241	+	5.17577i	0.464267	+	0.500361i	−0.456906	+	0.889515i	$0.651042\pi$
$108$	−1.64800	+	6.68374i	−0.158579	+	0.643143i
$109$	−9.63055	+	10.3793i	−0.922439	+	0.994153i	−0.999996	−	0.00283517i	$-0.999098\pi$
$109$	−9.63055	+	10.3793i	−0.922439	+	0.994153i	0.0775570	+	0.996988i	$0.475288\pi$
$110$	1.39159	+	1.41594i	0.132683	+	0.135005i
$111$	−0.0383164	+	0.167875i	−0.00363683	+	0.0159340i
$112$	8.83328	+	5.82866i	0.834666	+	0.550756i
$113$	−0.761038	−	3.33433i	−0.0715925	−	0.313667i	0.926434	−	0.376456i	$-0.122858\pi$
$113$	−0.761038	−	3.33433i	−0.0715925	−	0.313667i	−0.998027	+	0.0627893i	$0.980000\pi$
$114$	−0.123114	+	0.192214i	−0.0115307	+	0.0180025i
$115$	2.61331	+	0.195841i	0.243692	+	0.0182622i
$116$	6.25864	+	8.13361i	0.581100	+	0.755187i
$117$	10.2755	−	5.93254i	0.949966	−	0.548463i
$118$	0.420560	+	1.62583i	0.0387156	+	0.149670i
$119$	−1.77690	+	0.967547i	−0.162888	+	0.0886949i
$120$	−2.97660	−	5.02275i	−0.271725	−	0.458512i
$121$	0.809093	+	10.7966i	0.0735539	+	0.981509i
$122$	6.82006	−	12.6376i	0.617459	−	1.14416i
$123$	−1.39497	+	4.52239i	−0.125780	+	0.407770i
$124$	4.17476	−	12.7450i	0.374904	−	1.14453i
$125$	−2.02427	+	4.20345i	−0.181057	+	0.375968i
$126$	−9.72002	−	1.42781i	−0.865928	−	0.127199i
$127$	18.1782	−	8.75414i	1.61305	−	0.776804i	0.613138	−	0.789976i	$-0.289907\pi$
$127$	18.1782	−	8.75414i	1.61305	−	0.776804i	0.999913	+	0.0131716i	$0.00419278\pi$
$128$	8.47068	−	7.49984i	0.748709	−	0.662898i
$129$	−2.67427	+	4.63197i	−0.235456	+	0.407822i
$130$	−5.76086	+	20.7773i	−0.505261	+	1.82229i
$131$	7.01268	+	2.75227i	0.612701	+	0.240467i	0.651340	−	0.758786i	$-0.274207\pi$
$131$	7.01268	+	2.75227i	0.612701	+	0.240467i	−0.0386393	+	0.999253i	$0.512302\pi$
$132$	−0.0846071	+	0.502074i	−0.00736410	+	0.0436999i
$133$	−0.621088	−	0.318448i	−0.0538552	−	0.0276129i
$134$	−17.4914	−	7.81271i	−1.51103	−	0.674915i
$135$	9.59481	+	6.54163i	0.825789	+	0.563014i
$136$	0.505263	+	2.10310i	0.0433259	+	0.180339i
$137$	−0.441336	+	0.0665206i	−0.0377058	+	0.00568324i	−0.167868	−	0.985809i	$-0.553688\pi$
$137$	−0.441336	+	0.0665206i	−0.0377058	+	0.00568324i	0.130162	+	0.991493i	$0.458450\pi$
$138$	0.352625	+	0.572156i	0.0300174	+	0.0487052i
$139$	0.807236	+	0.643749i	0.0684689	+	0.0546021i	0.657126	−	0.753781i	$-0.271772\pi$
$139$	0.807236	+	0.643749i	0.0684689	+	0.0546021i	−0.588657	+	0.808383i	$0.700343\pi$
$140$	14.4163	−	10.5304i	1.21840	−	0.889985i
$141$	3.32988	−	2.65549i	0.280427	−	0.223633i
$142$	−8.13196	−	2.92491i	−0.682419	−	0.245453i
$143$	1.55354	−	1.05919i	0.129914	−	0.0885738i
$144$	−4.17387	+	9.63766i	−0.347822	+	0.803138i
$145$	16.5435	−	5.10299i	1.37386	−	0.423780i
$146$	−20.1297	−	3.98988i	−1.66594	−	0.330205i
$147$	−0.213855	+	4.27748i	−0.0176384	+	0.352800i
$148$	−0.214699	+	0.520320i	−0.0176482	+	0.0427701i
$149$	−4.36583	−	14.1537i	−0.357663	−	1.15951i	−0.938437	−	0.345449i	$-0.887727\pi$
$149$	−4.36583	−	14.1537i	−0.357663	−	1.15951i	0.580775	−	0.814064i	$-0.302750\pi$
$150$	−5.43523	+	0.979650i	−0.443785	+	0.0799881i
$151$	12.3463	−	8.41756i	1.00473	−	0.685011i	0.0551282	−	0.998479i	$-0.482443\pi$
$151$	12.3463	−	8.41756i	1.00473	−	0.685011i	0.949599	+	0.313468i	$0.101491\pi$
$152$	−0.501260	+	0.552713i	−0.0406576	+	0.0448309i
$153$	−1.25189	−	1.56982i	−0.101210	−	0.126913i
$154$	−1.55293	−	0.110523i	−0.125139	−	0.00890618i
$155$	−17.6880	−	14.1057i	−1.42074	−	1.13300i
$156$	−5.18162	+	1.93060i	−0.414862	+	0.154571i
$157$	−1.30197	−	8.63801i	−0.103909	−	0.689388i	−0.978762	−	0.205000i	$-0.934280\pi$
$157$	−1.30197	−	8.63801i	−0.103909	−	0.689388i	0.874853	−	0.484388i	$-0.160958\pi$
$158$	−3.70062	−	5.10627i	−0.294405	−	0.406233i
$159$	3.82689	+	2.60913i	0.303492	+	0.206917i
$160$	−6.86651	−	17.8074i	−0.542846	−	1.40779i
$161$	−1.63823	+	1.24080i	−0.129111	+	0.0977888i
$162$	−0.234419	−	8.15819i	−0.0184177	−	0.640968i
$163$	15.5115	+	6.08783i	1.21496	+	0.476835i	0.884302	−	0.466916i	$-0.154635\pi$
$163$	15.5115	+	6.08783i	1.21496	+	0.476835i	0.330655	+	0.943752i	$0.392730\pi$
$164$	−6.95314	+	13.8199i	−0.542949	+	1.07915i
$165$	0.743830	+	0.429451i	0.0579071	+	0.0334327i
$166$	14.7078	−	5.00372i	1.14155	−	0.388364i
$167$	−19.9633	+	9.61382i	−1.54481	+	0.743940i	−0.995772	−	0.0918589i	$-0.970719\pi$
$167$	−19.9633	+	9.61382i	−1.54481	+	0.743940i	−0.549035	+	0.835799i	$0.685005\pi$
$168$	4.35636	+	1.40891i	0.336100	+	0.108700i
$169$	6.68551	+	3.21957i	0.514270	+	0.247659i
$170$	3.62209	+	0.439959i	0.277801	+	0.0337433i
$171$	0.204168	−	0.661895i	0.0156131	−	0.0506164i
$172$	−11.1364	+	13.4782i	−0.849142	+	1.02770i
$173$	−14.5383	+	1.08950i	−1.10533	+	0.0828329i	−0.614868	−	0.788630i	$-0.710791\pi$
$173$	−14.5383	+	1.08950i	−1.10533	+	0.0828329i	−0.490461	+	0.871463i	$0.663172\pi$
$174$	3.54943	+	2.66746i	0.269081	+	0.202220i
$175$	−4.57308	−	16.2564i	−0.345692	−	1.22887i
$176$	−0.545450	+	1.57244i	−0.0411148	+	0.118527i
$177$	0.363267	+	0.629196i	0.0273048	+	0.0472933i
$178$	7.75106	−	8.85046i	0.580967	−	0.663370i
$179$	20.3882	+	1.52789i	1.52389	+	0.114200i	0.810154	−	0.586217i	$-0.199384\pi$
$179$	20.3882	+	1.52789i	1.52389	+	0.114200i	0.713734	+	0.700417i	$0.247003\pi$
$180$	12.7766	+	12.2742i	0.952312	+	0.914865i
$181$	7.78729	−	1.77740i	0.578825	−	0.132113i	0.0769220	−	0.997037i	$-0.475491\pi$
$181$	7.78729	−	1.77740i	0.578825	−	0.132113i	0.501903	+	0.864924i	$0.332634\pi$
$182$	−7.39323	−	15.2061i	−0.548023	−	1.12715i
$183$	1.38247	−	6.05700i	0.102195	−	0.447746i
$184$	0.825867	+	2.03585i	0.0608838	+	0.150085i
$185$	0.696053	+	0.645843i	0.0511748	+	0.0474833i
$186$	0.267230	−	5.79598i	0.0195943	−	0.424982i
$187$	−0.216424	−	0.233249i	−0.0158265	−	0.0170569i
$188$	12.1761	−	6.75100i	0.888032	−	0.492368i
$189$	−9.03594	+	1.13195i	−0.657268	+	0.0823372i
$190$	0.578483	+	1.11791i	0.0419676	+	0.0811015i
$191$	21.7990	+	3.28567i	1.57732	+	0.237742i	0.878566	−	0.477622i	$-0.158501\pi$
$191$	21.7990	+	3.28567i	1.57732	+	0.237742i	0.698752	+	0.715364i	$0.253739\pi$
$192$	2.66451	−	4.10585i	0.192294	−	0.296314i
$193$	−5.31068	−	13.5314i	−0.382271	−	0.974011i	−0.984452	−	0.175652i	$-0.943797\pi$
$193$	−5.31068	−	13.5314i	−0.382271	−	0.974011i	0.602181	−	0.798360i	$-0.294299\pi$
$194$	1.43197	−	0.148779i	0.102810	−	0.0106817i
$195$			9.32800i			0.667992i
$196$	−3.01286	+	13.6720i	−0.215204	+	0.976569i
$197$		−	25.0795i		−	1.78684i	−0.449224	−	0.893419i	$-0.648299\pi$
$197$		−	25.0795i		−	1.78684i	0.449224	−	0.893419i	$-0.351701\pi$
$198$	−0.159667	−	1.53677i	−0.0113470	−	0.109213i
$199$	−2.19688	−	5.59755i	−0.155732	−	0.396800i	0.831619	−	0.555347i	$-0.187414\pi$
$199$	−2.19688	−	5.59755i	−0.155732	−	0.396800i	−0.987351	+	0.158547i	$0.949319\pi$
$200$	−18.0522	+	0.205429i	−1.27648	+	0.0145260i
$201$	−8.19529	−	1.23524i	−0.578051	−	0.0871272i
$202$	−22.9332	+	11.8672i	−1.61357	+	0.834975i
$203$	−7.07976	+	11.5844i	−0.496902	+	0.813064i
$204$	0.453749	+	0.818379i	0.0317688	+	0.0572980i
$205$	17.7508	+	19.1308i	1.23977	+	1.33615i
$206$	9.48132	+	0.437147i	0.660595	+	0.0304575i
$207$	−1.49505	−	1.38720i	−0.103913	−	0.0964172i
$208$	−17.7513	+	3.40850i	−1.23083	+	0.236337i
$209$	0.0244255	−	0.107015i	0.00168955	−	0.00740239i
$210$	4.79292	−	6.05658i	0.330743	−	0.417944i
$211$	−13.6164	+	3.10786i	−0.937395	+	0.213954i	−0.663816	−	0.747896i	$-0.731064\pi$
$211$	−13.6164	+	3.10786i	−0.937395	+	0.213954i	−0.273578	+	0.961850i	$0.588207\pi$
$212$	10.9184	+	10.4891i	0.749880	+	0.720393i
$213$	−3.72833	−	0.279399i	−0.255461	−	0.0191441i
$214$	7.51170	+	6.57860i	0.513489	+	0.449704i
$215$	14.7468	+	25.5423i	1.00573	+	1.74197i
$216$	−1.34134	+	9.64247i	−0.0912666	+	0.656087i
$217$	17.7195	−	0.883566i	1.20288	−	0.0599804i
$218$	−12.0298	+	16.0074i	−0.814763	+	1.08416i
$219$	−8.85329	+	0.663462i	−0.598250	+	0.0448326i
$220$	2.16441	+	1.78835i	0.145924	+	0.120570i
$221$	1.01857	−	3.30213i	0.0685167	−	0.222126i
$222$	−0.0293631	+	0.241740i	−0.00197072	+	0.0162245i
$223$	−15.1072	−	7.27526i	−1.01166	−	0.487188i	−0.146778	−	0.989170i	$-0.546890\pi$
$223$	−15.1072	−	7.27526i	−1.01166	−	0.487188i	−0.864878	+	0.501982i	$0.832604\pi$
$224$	13.2771	+	6.90788i	0.887113	+	0.461552i
$225$	15.0995	−	7.27153i	1.00663	−	0.484769i
$226$	−1.55781	−	4.57898i	−0.103624	−	0.304589i
$227$	−5.01018	−	2.89263i	−0.332538	−	0.191991i	0.324430	−	0.945910i	$-0.394828\pi$
$227$	−5.01018	−	2.89263i	−0.332538	−	0.191991i	−0.656967	+	0.753919i	$0.728161\pi$
$228$	−0.145086	+	0.288369i	−0.00960858	+	0.0190977i
$229$	−13.5156	−	5.30448i	−0.893135	−	0.350530i	−0.126011	−	0.992029i	$-0.540218\pi$
$229$	−13.5156	−	5.30448i	−0.893135	−	0.350530i	−0.767124	+	0.641499i	$0.778313\pi$
$230$	3.70461	−	0.106449i	0.244275	−	0.00701906i
$231$	−0.660197	+	0.133432i	−0.0434378	+	0.00877916i
$232$	9.99237	+	10.5264i	0.656031	+	0.691092i
$233$	2.00745	+	1.36866i	0.131513	+	0.0896638i	0.627290	−	0.778786i	$-0.284164\pi$
$233$	2.00745	+	1.36866i	0.131513	+	0.0896638i	−0.495777	+	0.868450i	$0.665117\pi$
$234$	13.5869	−	9.84668i	0.888201	−	0.643698i
$235$	−3.50041	−	23.2237i	−0.228341	−	1.51495i
$236$	0.829186	+	2.22549i	0.0539754	+	0.144867i
$237$	−2.13304	−	1.70105i	−0.138556	−	0.110495i
$238$	−2.35806	+	1.62068i	−0.152850	+	0.105053i
$239$	−16.0553	−	20.1327i	−1.03853	−	1.30228i	−0.952024	−	0.306025i	$-0.901001\pi$
$239$	−16.0553	−	20.1327i	−1.03853	−	1.30228i	−0.0865069	−	0.996251i	$-0.527570\pi$
$240$	−4.92107	−	6.63019i	−0.317654	−	0.427977i
$241$	−2.71546	+	1.85137i	−0.174918	+	0.119257i	−0.647614	−	0.761968i	$-0.724233\pi$
$241$	−2.71546	+	1.85137i	−0.174918	+	0.119257i	0.472696	+	0.881225i	$0.343281\pi$
$242$	2.71599	+	15.0687i	0.174591	+	0.968653i
$243$	−4.08436	−	13.2412i	−0.262012	−	0.849422i
$244$	7.74643	−	18.7733i	0.495915	−	1.20184i
$245$	19.8377	+	12.8150i	1.26738	+	0.818721i
$246$	−1.30129	+	6.56526i	−0.0829675	+	0.418585i
$247$	1.13915	−	0.351382i	0.0724826	−	0.0223579i
$248$	4.00975	−	18.5378i	0.254620	−	1.17715i
$249$	5.55330	−	3.78618i	0.351926	−	0.239939i
$250$	−2.23311	+	6.20859i	−0.141234	+	0.392666i
$251$	9.97845	−	7.95755i	0.629834	−	0.502276i	−0.255757	−	0.966741i	$-0.582325\pi$
$251$	9.97845	−	7.95755i	0.629834	−	0.502276i	0.885591	+	0.464465i	$0.153753\pi$
$252$	−13.8813	−	0.587863i	−0.874437	−	0.0370319i
$253$	−0.252686	−	0.201510i	−0.0158862	−	0.0126688i
$254$	24.2908	−	14.9706i	1.52414	−	0.939340i
$255$	1.56091	−	0.235269i	0.0977480	−	0.0147331i
$256$	10.8191	−	11.7875i	0.676196	−	0.736722i
$257$	17.9196	+	12.2174i	1.11779	+	0.762097i	0.973783	−	0.227479i	$-0.0730483\pi$
$257$	17.9196	+	12.2174i	1.11779	+	0.762097i	0.144009	+	0.989576i	$0.454001\pi$
$258$	−3.08479	+	6.90636i	−0.192051	+	0.429971i
$259$	−0.744382	−	0.0185963i	−0.0462537	−	0.00115552i
$260$	−5.06694	+	30.0681i	−0.314238	+	1.86475i
$261$	−12.5420	−	4.92239i	−0.776332	−	0.304688i
$262$	10.2666	+	2.84658i	0.634271	+	0.175863i
$263$	−6.48846	+	11.2383i	−0.400096	+	0.692986i	−0.993737	−	0.111744i	$-0.964356\pi$
$263$	−6.48846	+	11.2383i	−0.400096	+	0.692986i	0.593641	+	0.804730i	$0.297690\pi$
$264$	−0.0456354	+	0.718603i	−0.00280867	+	0.0442270i
$265$	23.0114	−	11.0817i	1.41358	−	0.680745i
$266$	−0.920189	−	0.357172i	−0.0564204	−	0.0218996i
$267$	2.20838	−	4.58574i	0.135150	−	0.280643i
$268$	−25.7459	−	8.43337i	−1.57268	−	0.515150i
$269$	4.92472	−	15.9655i	0.300265	−	0.973436i	−0.672196	−	0.740373i	$-0.734649\pi$
$269$	4.92472	−	15.9655i	0.300265	−	0.973436i	0.972462	−	0.233063i	$-0.0748749\pi$
$270$	14.4525	+	7.79948i	0.879551	+	0.474661i
$271$	0.281391	+	3.75490i	0.0170933	+	0.228094i	0.999207	+	0.0398071i	$0.0126744\pi$
$271$	0.281391	+	3.75490i	0.0170933	+	0.228094i	−0.982114	+	0.188287i	$0.939707\pi$
$272$	1.01808	+	2.88446i	0.0617304	+	0.174896i
$273$	−4.83997	−	5.48484i	−0.292928	−	0.331957i
$274$	−0.611079	+	0.158070i	−0.0369166	+	0.00954938i
$275$	2.30001	−	1.32791i	0.138696	−	0.0800762i
$276$	0.579636	+	0.753284i	0.0348900	+	0.0453424i
$277$	10.6927	+	0.801308i	0.642463	+	0.0481459i	0.391978	−	0.919975i	$-0.371791\pi$
$277$	10.6927	+	0.801308i	0.642463	+	0.0481459i	0.250485	+	0.968121i	$0.419410\pi$
$278$	1.22957	+	0.787550i	0.0737449	+	0.0472341i
$279$	3.91788	+	17.1653i	0.234557	+	1.02766i
$280$	18.7396	−	16.9195i	1.11990	−	1.01113i
$281$	−1.11033	+	4.86469i	−0.0662370	+	0.290203i	−0.997188	−	0.0749410i	$-0.976123\pi$
$281$	−1.11033	+	4.86469i	−0.0662370	+	0.290203i	0.930951	+	0.365144i	$0.118980\pi$
$282$	4.29586	−	4.22198i	0.255815	−	0.251415i
$283$	3.72783	−	4.01765i	0.221597	−	0.238824i	−0.612462	−	0.790500i	$-0.709821\pi$
$283$	3.72783	−	4.01765i	0.221597	−	0.238824i	0.834059	+	0.551675i	$0.186011\pi$
$284$	−11.8662	−	2.92584i	−0.704131	−	0.173617i
$285$	0.370393	+	0.399189i	0.0219402	+	0.0236459i
$286$	2.03048	−	1.71694i	0.120065	−	0.101525i
$287$	−20.3637	−	2.03859i	−1.20203	−	0.120334i
$288$	−4.46262	+	14.1667i	−0.262962	+	0.834783i
$289$	16.2319	+	2.44656i	0.954816	+	0.143915i
$290$	22.5250	−	9.59586i	1.32271	−	0.563488i
$291$	0.579794	−	0.227552i	0.0339881	−	0.0133394i
$292$	−28.8983	−	2.67045i	−1.69115	−	0.156277i
$293$			22.0418i			1.28769i	0.765155	+	0.643846i	$0.222662\pi$
$293$			22.0418i			1.28769i	−0.765155	+	0.643846i	$0.777338\pi$
$294$	0.324322	+	6.04813i	0.0189149	+	0.352734i
$295$	4.00635			0.233259
$296$	−0.225962	+	0.763282i	−0.0131338	+	0.0443649i
$297$	−0.523227	−	1.33316i	−0.0303607	−	0.0773578i
$298$	−8.20967	−	19.2711i	−0.475573	−	1.11634i
$299$	0.523146	−	3.47085i	0.0302543	−	0.200724i
$300$	−7.50225	+	2.17236i	−0.433143	+	0.125421i
$301$	−21.9241	−	7.36716i	−1.26368	−	0.424636i
$302$	16.1366	−	13.6449i	0.928558	−	0.785173i
$303$	−8.18911	+	7.59839i	−0.470452	+	0.436516i
$304$	−0.624317	+	0.850727i	−0.0358070	+	0.0487925i
$305$	−25.1138	−	23.3022i	−1.43801	−	1.33428i
$306$	−1.99039	−	2.02522i	−0.113783	−	0.115774i
$307$	−15.0129	−	3.42660i	−0.856833	−	0.195567i	−0.228531	−	0.973537i	$-0.573392\pi$
$307$	−15.0129	−	3.42660i	−0.856833	−	0.195567i	−0.628301	+	0.777970i	$0.716250\pi$
$308$	−2.20058	+	0.0714904i	−0.125389	+	0.00407355i
$309$	4.00331	−	0.913729i	0.227740	−	0.0519802i
$310$	−26.9422	−	17.2567i	−1.53022	−	0.980113i
$311$	−1.17443	+	15.6717i	−0.0665960	+	0.888661i	0.859443	+	0.511232i	$0.170811\pi$
$311$	−1.17443	+	15.6717i	−0.0665960	+	0.888661i	−0.926039	+	0.377429i	$0.876808\pi$
$312$	−7.00654	+	3.47294i	−0.396667	+	0.196616i
$313$	−11.7738	−	20.3928i	−0.665493	−	1.15267i	−0.979151	−	0.203132i	$-0.934888\pi$
$313$	−11.7738	−	20.3928i	−0.665493	−	1.15267i	0.313659	−	0.949536i	$-0.398445\pi$
$314$	−3.09382	−	11.9603i	−0.174595	−	0.674959i
$315$	−9.10492	+	21.5968i	−0.513004	+	1.21684i
$316$	−5.95171	−	6.64186i	−0.334810	−	0.373634i
$317$	29.5686	−	2.21586i	1.66074	−	0.124455i	0.788988	−	0.614408i	$-0.210605\pi$
$317$	29.5686	−	2.21586i	1.66074	−	0.124455i	0.871749	+	0.489953i	$0.162986\pi$
$318$	5.76438	+	3.11082i	0.323250	+	0.174446i
$319$	−2.04027	−	0.629341i	−0.114233	−	0.0352363i
$320$	−12.2612	−	24.0450i	−0.685422	−	1.34416i
$321$	3.89208	+	1.87433i	0.217235	+	0.104615i
$322$	−2.12307	+	1.98478i	−0.118314	+	0.110608i
$323$	−0.0875304	−	0.181759i	−0.00487032	−	0.0101133i
$324$	−1.52204	−	11.4414i	−0.0845576	−	0.635633i
$325$	24.9791	+	14.4217i	1.38559	+	0.799970i
$326$	22.7089	+	6.29643i	1.25773	+	0.348727i
$327$	−3.16491	+	8.06407i	−0.175020	+	0.445944i
$328$	−7.76085	+	20.4558i	−0.428521	+	1.12948i
$329$	14.1082	+	11.8392i	0.777809	+	0.652717i
$330$	1.10907	+	0.495375i	0.0610520	+	0.0272695i
$331$	3.58558	−	5.25908i	0.197081	−	0.289065i	−0.714959	−	0.699167i	$-0.753554\pi$
$331$	3.58558	−	5.25908i	0.197081	−	0.289065i	0.912040	+	0.410102i	$0.134507\pi$
$332$	19.9573	−	9.18793i	1.09530	−	0.504253i
$333$	−0.110136	−	0.730707i	−0.00603544	−	0.0400425i
$334$	−26.6762	+	16.4408i	−1.45966	+	0.899599i
$335$	−28.4948	+	35.7313i	−1.55684	+	1.95221i
$336$	6.33375	+	1.34516i	0.345534	+	0.0733847i
$337$	−0.578538	−	0.725463i	−0.0315150	−	0.0395185i	0.765824	−	0.643050i	$-0.222331\pi$
$337$	−0.578538	−	0.725463i	−0.0315150	−	0.0395185i	−0.797339	+	0.603531i	$0.793760\pi$
$338$	9.87465	+	3.55172i	0.537110	+	0.193188i
$339$	−1.17875	−	1.72891i	−0.0640210	−	0.0939016i
$340$	5.15928	+	0.0895077i	0.279801	+	0.00485424i
$341$	0.822411	+	2.66619i	0.0445360	+	0.144382i
$342$	0.190457	−	0.960888i	0.0102987	−	0.0519589i
$343$	−18.3138	+	2.75790i	−0.988850	+	0.148913i
$344$	−13.6951	+	20.5865i	−0.738391	+	1.10995i
$345$	1.53215	−	0.472607i	0.0824884	−	0.0254443i
$346$	−20.2910	+	3.65726i	−1.09085	+	0.196616i
$347$	17.1168	+	25.1057i	0.918877	+	1.34774i	0.937525	+	0.347918i	$0.113111\pi$
$347$	17.1168	+	25.1057i	0.918877	+	1.34774i	−0.0186482	+	0.999826i	$0.505936\pi$
$348$	5.38261	+	3.23342i	0.288538	+	0.173330i
$349$	24.7797	−	19.7612i	1.32643	−	1.05779i	0.333050	−	0.942909i	$-0.391922\pi$
$349$	24.7797	−	19.7612i	1.32643	−	1.05779i	0.993379	−	0.114883i	$-0.0366494\pi$
$350$	−8.80851	−	22.1986i	−0.470835	−	1.18657i
$351$	9.69765	−	12.1605i	0.517622	−	0.649078i
$352$	−0.537445	+	2.29158i	−0.0286459	+	0.122141i
$353$	−29.6584	+	4.47028i	−1.57856	+	0.237929i	−0.879062	−	0.476708i	$-0.841830\pi$
$353$	−29.6584	+	4.47028i	−1.57856	+	0.237929i	−0.699495	+	0.714637i	$0.746592\pi$
$354$	0.602941	+	0.831963i	0.0320459	+	0.0442184i
$355$	−11.6139	+	17.0345i	−0.616403	+	0.904097i
$356$	9.60950	−	13.5822i	0.509303	−	0.719856i
$357$	−0.795738	+	0.948239i	−0.0421149	+	0.0501861i
$358$	28.9022	−	0.830484i	1.52753	−	0.0438924i
$359$	−0.537592	+	1.36976i	−0.0283730	+	0.0722933i	−0.944358	−	0.328919i	$-0.893316\pi$
$359$	−0.537592	+	1.36976i	−0.0283730	+	0.0722933i	0.915985	+	0.401212i	$0.131411\pi$
$360$	19.7659	+	15.3981i	1.04176	+	0.811554i
$361$	−9.46520	+	16.3942i	−0.498169	+	0.862853i
$362$	10.6942	−	3.63825i	0.562073	−	0.191222i
$363$	2.87414	+	5.96821i	0.150853	+	0.313250i
$364$	−12.6219	−	20.3090i	−0.661570	−	1.06448i
$365$	−21.2416	+	44.1087i	−1.11184	+	2.30875i
$366$	1.05943	−	8.72207i	0.0553773	−	0.455910i
$367$	−4.19138	−	1.29287i	−0.218789	−	0.0674873i	0.183423	−	0.983034i	$-0.441282\pi$
$367$	−4.19138	−	1.29287i	−0.218789	−	0.0674873i	−0.402212	+	0.915547i	$0.631758\pi$
$368$	1.45923	+	2.74301i	0.0760677	+	0.142989i
$369$	−1.51777	−	20.2533i	−0.0790122	−	1.05434i
$370$	1.07349	+	0.806744i	0.0558078	+	0.0419406i
$371$	−7.78073	+	18.4558i	−0.403956	+	0.958179i
$372$	−0.471166	−	8.19192i	−0.0244288	−	0.424731i
$373$	−21.9960	+	12.6994i	−1.13891	+	0.657550i	−0.946160	−	0.323699i	$-0.895074\pi$
$373$	−21.9960	+	12.6994i	−1.13891	+	0.657550i	−0.192749	+	0.981248i	$0.561740\pi$
$374$	−0.338519	−	0.296468i	−0.0175044	−	0.0153300i
$375$	−0.213316	+	2.84650i	−0.0110156	+	0.146993i
$376$	16.1408	−	11.2757i	0.832396	−	0.581502i
$377$	−5.15989	−	22.6070i	−0.265748	−	1.16432i
$378$	−12.5449	+	2.91282i	−0.645240	+	0.149819i
$379$	36.7888	+	8.39680i	1.88971	+	0.431315i	0.999697	−	0.0246131i	$-0.00783539\pi$
$379$	36.7888	+	8.39680i	1.88971	+	0.431315i	0.890017	+	0.455928i	$0.150693\pi$
$380$	0.977097	+	1.48795i	0.0501240	+	0.0763303i
$381$	8.39636	−	9.04912i	0.430159	−	0.463601i
$382$	31.1435	+	1.43591i	1.59344	+	0.0734674i
$383$	−19.3584	+	17.9620i	−0.989169	+	0.917814i	−0.996619	−	0.0821578i	$-0.973819\pi$
$383$	−19.3584	+	17.9620i	−0.989169	+	0.917814i	0.00745057	+	0.999972i	$0.497628\pi$
$384$	3.14796	−	6.16487i	0.160643	−	0.314600i
$385$	−1.18306	+	3.52070i	−0.0602945	+	0.179432i
$386$	−9.44780	−	18.2577i	−0.480880	−	0.929292i
$387$	3.42099	−	22.6968i	0.173899	−	1.15374i
$388$	1.99253	−	0.418556i	0.101155	−	0.0212490i
$389$	−8.02495	+	3.14956i	−0.406881	+	0.159689i	−0.559950	−	0.828526i	$-0.689180\pi$
$389$	−8.02495	+	3.14956i	−0.406881	+	0.159689i	0.153069	+	0.988216i	$0.451084\pi$
$390$	1.36326	+	13.1212i	0.0690312	+	0.664416i
$391$	−0.593992			−0.0300395
$392$	−2.23990	+	19.6719i	−0.113132	+	0.993580i
$393$	4.60919			0.232503
$394$	−3.66528	−	35.2778i	−0.184654	−	1.77727i
$395$	−14.0046	+	5.49640i	−0.704648	+	0.276554i
$396$	−0.449188	−	2.13835i	−0.0225725	−	0.107456i
$397$	−4.69705	+	31.1629i	−0.235738	+	1.56402i	0.487313	+	0.873228i	$0.337977\pi$
$397$	−4.69705	+	31.1629i	−0.235738	+	1.56402i	−0.723051	+	0.690795i	$0.757261\pi$
$398$	−3.90828	−	7.55268i	−0.195904	−	0.378582i
$399$	−0.424915	−	0.0425379i	−0.0212723	−	0.00212956i
$400$	−25.3630	+	2.92724i	−1.26815	+	0.146362i
$401$	−5.99731	+	5.56469i	−0.299491	+	0.277887i	−0.815576	−	0.578650i	$-0.803580\pi$
$401$	−5.99731	+	5.56469i	−0.299491	+	0.277887i	0.516084	+	0.856538i	$0.327389\pi$
$402$	−11.7084	−	0.539827i	−0.583960	−	0.0269241i
$403$	−20.6107	+	22.2130i	−1.02669	+	1.10651i
$404$	−30.5244	+	20.0445i	−1.51865	+	0.997254i
$405$	−18.9826	−	4.33265i	−0.943253	−	0.215291i
$406$	−8.26567	+	17.3298i	−0.410218	+	0.860061i
$407$	−0.0260579	−	0.114167i	−0.00129164	−	0.00565906i
$408$	0.757865	+	1.08485i	0.0375199	+	0.0537082i
$409$	−0.606945	+	8.09912i	−0.0300115	+	0.400476i	0.961887	+	0.273446i	$0.0881635\pi$
$409$	−0.606945	+	8.09912i	−0.0300115	+	0.400476i	−0.991899	+	0.127030i	$0.959456\pi$
$410$	27.7649	+	24.3159i	1.37121	+	1.20088i
$411$	−0.236488	+	0.136536i	−0.0116651	+	0.00673485i
$412$	13.4007	−	0.770755i	0.660206	−	0.0379724i
$413$	−2.35572	+	2.07875i	−0.115918	+	0.102289i
$414$	−2.30573	−	1.73280i	−0.113321	−	0.0851625i
$415$	−2.76971	−	36.9593i	−0.135960	−	1.81426i
$416$	−24.4715	+	7.38883i	−1.19982	+	0.362267i
$417$	0.603647	+	0.186200i	0.0295607	+	0.00911827i
$418$	0.0187180	−	0.154102i	0.000915529	−	0.00753736i
$419$	−5.27658	+	10.9569i	−0.257778	+	0.535281i	−0.989187	−	0.146657i	$-0.953149\pi$
$419$	−5.27658	+	10.9569i	−0.257778	+	0.535281i	0.731409	+	0.681939i	$0.238863\pi$
$420$	5.85678	−	9.21991i	0.285781	−	0.449886i
$421$	−8.09663	−	16.8128i	−0.394606	−	0.819407i	−0.999729	−	0.0232754i	$-0.992591\pi$
$421$	−8.09663	−	16.8128i	−0.394606	−	0.819407i	0.605123	−	0.796132i	$-0.293124\pi$
$422$	−18.6993	+	6.36165i	−0.910265	+	0.309680i
$423$	−9.13888	+	15.8290i	−0.444347	+	0.769632i
$424$	16.8913	+	13.1587i	0.820312	+	0.639043i
$425$	1.78325	−	4.54364i	0.0865001	−	0.220399i
$426$	−5.28525	+	0.151868i	−0.256071	+	0.00735802i
$427$	26.8576	+	0.670960i	1.29973	+	0.0324700i
$428$	11.5277	+	8.15592i	0.557213	+	0.394231i
$429$	0.648045	−	0.950507i	0.0312879	−	0.0458909i
$430$	24.4764	+	33.7736i	1.18036	+	1.62871i
$431$	21.9701	−	3.31146i	1.05826	−	0.159507i	0.403222	−	0.915102i	$-0.367890\pi$
$431$	21.9701	−	3.31146i	1.05826	−	0.159507i	0.655039	+	0.755595i	$0.272652\pi$
$432$	−0.477569	+	13.7595i	−0.0229770	+	0.662006i
$433$	−9.67822	+	12.1361i	−0.465105	+	0.583224i	−0.957965	−	0.286885i	$-0.907380\pi$
$433$	−9.67822	+	12.1361i	−0.465105	+	0.583224i	0.492860	+	0.870109i	$0.335952\pi$
$434$	24.7958	−	3.83250i	1.19024	−	0.183966i
$435$	8.28149	−	6.60427i	0.397067	−	0.316650i
$436$	−14.5822	+	24.2748i	−0.698363	+	1.16255i
$437$	−0.115431	−	0.169307i	−0.00552183	−	0.00809903i
$438$	−12.3564	+	2.22713i	−0.590414	+	0.106417i
$439$	−8.95504	+	2.76226i	−0.427401	+	0.131836i	−0.500990	−	0.865453i	$-0.667031\pi$
$439$	−8.95504	+	2.76226i	−0.427401	+	0.131836i	0.0735895	+	0.997289i	$0.476555\pi$
$440$	3.30591	+	2.19925i	0.157603	+	0.104845i
$441$	−5.85215	−	17.4231i	−0.278674	−	0.829670i
$442$	0.950172	−	4.79378i	0.0451951	−	0.228017i
$443$	−3.13981	−	10.1790i	−0.149177	−	0.483619i	0.849883	−	0.526971i	$-0.176672\pi$
$443$	−3.13981	−	10.1790i	−0.149177	−	0.483619i	−0.999060	+	0.0433522i	$0.986196\pi$
$444$	−0.00597379	+	0.344333i	−0.000283504	+	0.0163413i
$445$	−15.8106	−	23.1899i	−0.749495	−	1.09931i
$446$	−22.3137	−	8.02582i	−1.05659	−	0.380033i
$447$	−5.65023	−	7.08517i	−0.267247	−	0.335117i
$448$	19.6857	+	7.77650i	0.930061	+	0.367405i
$449$	6.20860	−	7.78534i	0.293002	−	0.367413i	−0.613441	−	0.789740i	$-0.710215\pi$
$449$	6.20860	−	7.78534i	0.293002	−	0.367413i	0.906443	+	0.422327i	$0.138787\pi$
$450$	20.1769	−	12.4352i	0.951147	−	0.586200i
$451$	−0.479699	−	3.18259i	−0.0225881	−	0.149862i
$452$	−2.86048	−	6.21332i	−0.134546	−	0.292250i
$453$	5.15013	−	7.55385i	0.241974	−	0.354911i
$454$	−7.47028	−	3.33667i	−0.350598	−	0.156598i
$455$	−39.5378	+	7.99094i	−1.85356	+	0.374621i
$456$	−0.161940	+	0.426836i	−0.00758355	+	0.0199884i
$457$	−11.1798	+	28.4858i	−0.522971	+	1.33251i	0.388615	+	0.921400i	$0.372954\pi$
$457$	−11.1798	+	28.4858i	−0.522971	+	1.33251i	−0.911586	+	0.411109i	$0.865142\pi$
$458$	−19.7868	−	5.48624i	−0.924577	−	0.256355i
$459$	−2.27948	−	1.31606i	−0.106397	−	0.0614283i
$460$	5.19551	−	0.691153i	0.242242	−	0.0322252i
$461$	1.40003	+	2.90720i	0.0652060	+	0.135402i	0.931025	−	0.364956i	$-0.118916\pi$
$461$	1.40003	+	2.90720i	0.0652060	+	0.135402i	−0.865819	+	0.500358i	$0.833202\pi$
$462$	−0.909160	+	0.284176i	−0.0422979	+	0.0132211i
$463$	−22.8958	−	11.0261i	−1.06406	−	0.512424i	−0.181872	−	0.983322i	$-0.558216\pi$
$463$	−22.8958	−	11.0261i	−1.06406	−	0.512424i	−0.882188	+	0.470898i	$0.843930\pi$
$464$	15.5941	+	13.3465i	0.723937	+	0.619597i
$465$	−13.2270	−	4.07999i	−0.613388	−	0.189205i
$466$	3.02379	+	1.63183i	0.140075	+	0.0755930i
$467$	35.3359	−	2.64806i	1.63515	−	0.122538i	0.774789	−	0.632220i	$-0.217856\pi$
$467$	35.3359	−	2.64806i	1.63515	−	0.122538i	0.860363	+	0.509682i	$0.170237\pi$
$468$	17.6728	−	15.8364i	0.816925	−	0.732039i
$469$	−1.78488	−	35.7949i	−0.0824181	−	1.65285i
$470$	−8.31789	−	32.1558i	−0.383675	−	1.48324i
$471$	−2.67235	−	4.62865i	−0.123135	−	0.213277i
$472$	1.49162	+	3.00929i	0.0686572	+	0.138514i
$473$	0.271823	−	3.62722i	0.0124984	−	0.166780i
$474$	−3.24903	−	2.08102i	−0.149233	−	0.0955846i
$475$	1.64162	−	0.374689i	0.0753227	−	0.0171919i
$476$	−3.08008	+	2.62434i	−0.141175	+	0.120286i
$477$	−19.3785	−	4.42301i	−0.887280	−	0.202516i
$478$	−25.5264	−	25.9731i	−1.16755	−	1.18798i
$479$	18.0167	+	16.7171i	0.823205	+	0.763823i	0.974433	−	0.224676i	$-0.0721324\pi$
$479$	18.0167	+	16.7171i	0.823205	+	0.763823i	−0.151228	+	0.988499i	$0.548323\pi$
$480$	−7.89116	−	8.60711i	−0.360181	−	0.392859i
$481$	0.932285	−	0.865034i	0.0425086	−	0.0394422i
$482$	−3.54910	+	3.00106i	−0.161657	+	0.136695i
$483$	−0.655683	+	1.07287i	−0.0298346	+	0.0488174i
$484$	6.02267	+	20.7993i	0.273758	+	0.945424i
$485$	0.511901	−	3.39624i	0.0232442	−	0.154215i
$486$	−7.68039	−	18.0287i	−0.348390	−	0.817798i
$487$	5.43984	+	13.8605i	0.246503	+	0.628079i	0.999553	−	0.0298836i	$-0.00951366\pi$
$487$	5.43984	+	13.8605i	0.246503	+	0.628079i	−0.753050	+	0.657963i	$0.771418\pi$
$488$	8.15279	−	27.5395i	0.369060	−	1.24665i
$489$	10.1952			0.461043
$490$	29.7774	+	15.1269i	1.34521	+	0.683364i
$491$			13.9223i			0.628303i	0.949373	+	0.314152i	$0.101720\pi$
$491$			13.9223i			0.628303i	−0.949373	+	0.314152i	$0.898280\pi$
$492$	−0.870965	+	9.42514i	−0.0392661	+	0.424918i
$493$	−3.65282	+	1.43363i	−0.164515	+	0.0645673i
$494$	1.55103	−	0.660752i	0.0697840	−	0.0297286i
$495$	−3.64479	−	0.549364i	−0.163821	−	0.0246921i
$496$	2.93105	−	26.6620i	0.131608	−	1.19716i
$497$	−2.00965	−	16.0423i	−0.0901450	−	0.719595i
$498$	7.25817	−	6.13739i	0.325246	−	0.275023i
$499$	−27.8200	−	29.9828i	−1.24539	−	1.34222i	−0.917620	−	0.397459i	$-0.869892\pi$
$499$	−27.8200	−	29.9828i	−1.24539	−	1.34222i	−0.327773	−	0.944756i	$-0.606298\pi$
$500$	−2.23382	+	9.05962i	−0.0998994	+	0.405159i
$501$	−9.22091	+	9.93778i	−0.411960	+	0.443987i
$502$	12.8731	−	12.6517i	0.574556	−	0.564675i
$503$	−4.12670	+	18.0803i	−0.184001	+	0.806159i	0.795700	+	0.605691i	$0.207103\pi$
$503$	−4.12670	+	18.0803i	−0.184001	+	0.806159i	−0.979700	+	0.200468i	$0.935754\pi$
$504$	−19.6119	+	1.20179i	−0.873582	+	0.0535319i
$505$	13.7078	+	60.0576i	0.609988	+	2.67253i
$506$	−0.384889	−	0.246524i	−0.0171104	−	0.0109593i
$507$	4.52731	+	0.339275i	0.201065	+	0.0150677i
$508$	31.9805	−	24.6083i	1.41891	−	1.09182i
$509$	3.15072	−	1.81907i	0.139653	−	0.0806287i	−0.428546	−	0.903520i	$-0.640974\pi$
$509$	3.15072	−	1.81907i	0.139653	−	0.0806287i	0.568199	+	0.822891i	$0.307641\pi$
$510$	2.16126	−	0.559062i	0.0957021	−	0.0247557i
$511$	−10.3964	−	36.9573i	−0.459911	−	1.63489i
$512$	13.4959	−	18.1620i	0.596442	−	0.802656i
$513$	−0.0678559	−	0.905474i	−0.00299591	−	0.0399776i
$514$	26.9919	+	14.5666i	1.19056	+	0.642503i
$515$	6.67424	−	21.6373i	0.294102	−	0.953455i
$516$	−3.32986	+	10.1656i	−0.146589	+	0.447516i
$517$	−1.25673	+	2.60964i	−0.0552711	+	0.114772i
$518$	−1.04980	+	0.0826307i	−0.0461254	+	0.00363059i
$519$	−8.03659	+	3.87022i	−0.352767	+	0.169884i
$520$	−2.73301	+	43.0356i	−0.119850	+	1.88724i
$521$	−6.44813	+	11.1685i	−0.282498	+	0.489300i	−0.971999	−	0.234984i	$-0.924496\pi$
$521$	−6.44813	+	11.1685i	−0.282498	+	0.489300i	0.689502	+	0.724284i	$0.257830\pi$
$522$	−18.3615	−	5.09106i	−0.803663	−	0.222829i
$523$	35.7821	+	14.0434i	1.56464	+	0.614077i	0.980315	−	0.197441i	$-0.0632631\pi$
$523$	35.7821	+	14.0434i	1.56464	+	0.614077i	0.584327	+	0.811518i	$0.301358\pi$
$524$	14.8574	+	2.50370i	0.649049	+	0.109375i
$525$	−6.23829	−	8.23644i	−0.272261	−	0.359467i
$526$	−7.48450	+	16.7566i	−0.326340	+	0.730622i
$527$	4.23688	+	2.88865i	0.184561	+	0.125832i
$528$	0.0408287	+	1.01749i	0.00177684	+	0.0442804i
$529$	22.1465	−	3.33805i	0.962892	−	0.145133i
$530$	30.7493	−	18.9511i	1.33566	−	0.823181i
$531$	−2.43767	−	1.94398i	−0.105786	−	0.0843616i
$532$	−1.34658	−	0.367930i	−0.0583814	−	0.0159518i
$533$	27.3286	−	21.7938i	1.18373	−	0.943996i
$534$	2.43620	−	6.77324i	0.105425	−	0.293107i
$535$	19.6821	−	13.4190i	0.850931	−	0.580155i
$536$	−37.4478	−	8.10004i	−1.61750	−	0.349868i
$537$	11.9534	−	3.68713i	0.515827	−	0.159112i
$538$	4.59400	−	23.1775i	0.198062	−	0.999254i
$539$	−1.13113	−	2.68401i	−0.0487212	−	0.115609i
$540$	21.4693	+	8.85889i	0.923894	+	0.381226i
$541$	5.04954	+	16.3702i	0.217097	+	0.703811i	0.996964	+	0.0778654i	$0.0248104\pi$
$541$	5.04954	+	16.3702i	0.217097	+	0.703811i	−0.779867	+	0.625945i	$0.784713\pi$
$542$	0.944582	+	5.24067i	0.0405733	+	0.225106i
$543$	4.03786	−	2.75296i	0.173281	−	0.118141i
$544$	1.85363	+	3.90861i	0.0794739	+	0.167580i
$545$	29.7842	+	37.3482i	1.27582	+	1.59982i
$546$	−7.60970	−	7.00785i	−0.325665	−	0.299908i
$547$	−8.77937	−	7.00132i	−0.375379	−	0.299355i	0.417568	−	0.908646i	$-0.362883\pi$
$547$	−8.77937	−	7.00132i	−0.375379	−	0.299355i	−0.792947	+	0.609291i	$0.791454\pi$
$548$	−0.836468	+	0.311656i	−0.0357321	+	0.0133133i
$549$	3.97376	+	26.3642i	0.169596	+	1.12520i
$550$	3.04123	−	2.20404i	0.129678	−	0.0939805i
$551$	−1.11849	−	0.762571i	−0.0476491	−	0.0324866i
$552$	0.925430	+	0.974889i	0.0393889	+	0.0414940i
$553$	5.38278	−	10.4984i	0.228899	−	0.446436i
$554$	15.1579	−	0.435552i	0.643999	−	0.0185048i
$555$	0.540792	+	0.212245i	0.0229553	+	0.00900931i
$556$	1.84467	+	0.928102i	0.0782313	+	0.0393603i
$557$	−26.3078	−	15.1888i	−1.11470	−	0.643570i	−0.174654	−	0.984630i	$-0.555881\pi$
$557$	−26.3078	−	15.1888i	−1.11470	−	0.643570i	−0.940042	+	0.341060i	$0.889214\pi$
$558$	8.01971	+	23.5729i	0.339501	+	0.997921i
$559$	35.5914	−	17.1399i	1.50536	−	0.724941i
$560$	23.8871	−	26.5383i	1.00942	−	1.12145i
$561$	−0.175399	−	0.0844677i	−0.00740535	−	0.00356623i
$562$	−0.850884	+	7.00515i	−0.0358924	+	0.295494i
$563$	−12.1519	+	39.3956i	−0.512143	+	1.66033i	0.217160	+	0.976136i	$0.430321\pi$
$563$	−12.1519	+	39.3956i	−0.512143	+	1.66033i	−0.729303	+	0.684191i	$0.760156\pi$
$564$	5.42571	−	6.56664i	0.228463	−	0.276505i
$565$	−11.5065	+	0.862296i	−0.484084	+	0.0362771i
$566$	4.65656	−	6.19620i	0.195730	−	0.260446i
$567$	13.4098	−	7.30181i	0.563157	−	0.306647i
$568$	−17.1191	−	2.38140i	−0.718302	−	0.0999212i
$569$	−2.11375	−	3.66112i	−0.0886128	−	0.153482i	0.818312	−	0.574774i	$-0.194910\pi$
$569$	−2.11375	−	3.66112i	−0.0886128	−	0.153482i	−0.906925	+	0.421292i	$0.861577\pi$
$570$	0.579350	+	0.507384i	0.0242663	+	0.0212520i
$571$	−10.5716	−	0.792229i	−0.442406	−	0.0331538i	−0.148335	−	0.988937i	$-0.547391\pi$
$571$	−10.5716	−	0.792229i	−0.442406	−	0.0331538i	−0.294071	+	0.955783i	$0.595010\pi$
$572$	2.60524	−	2.71187i	0.108930	−	0.113389i
$573$	13.1498	−	3.00135i	0.549339	−	0.125383i
$574$	−28.9423	+	0.108517i	−1.20803	+	0.00452940i
$575$	1.10323	−	4.83357i	0.0460079	−	0.201574i
$576$	−4.20689	+	20.5797i	−0.175287	+	0.857488i
$577$	−3.91439	−	3.63202i	−0.162958	−	0.151203i	0.594479	−	0.804111i	$-0.297358\pi$
$577$	−3.91439	−	3.63202i	−0.162958	−	0.151203i	−0.757437	+	0.652908i	$0.773549\pi$
$578$	23.1900	+	1.06920i	0.964576	+	0.0444728i
$579$	−6.04927	−	6.51956i	−0.251399	−	0.270944i
$580$	30.2822	−	16.7899i	1.25740	−	0.697162i
$581$	20.8054	+	20.2948i	0.863155	+	0.841971i
$582$	0.782306	−	0.404820i	0.0324276	−	0.0167803i
$583$	−3.11470	−	0.469466i	−0.128998	−	0.0194433i
$584$	−41.0399	+	0.467021i	−1.69824	+	0.0193255i
$585$	−14.6249	−	37.2638i	−0.604667	−	1.54067i
$586$	3.22133	+	31.0048i	0.133072	+	1.28080i
$587$			6.18058i			0.255100i	0.991832	+	0.127550i	$0.0407113\pi$
$587$			6.18058i			0.255100i	−0.991832	+	0.127550i	$0.959289\pi$
$588$	1.34012	+	8.46016i	0.0552656	+	0.348891i
$589$			1.76900i			0.0728903i
$590$	5.63550	−	0.585515i	0.232010	−	0.0241053i
$591$	−5.60594	−	14.2837i	−0.230598	−	0.587553i
$592$	−0.206297	+	1.10669i	−0.00847874	+	0.0454846i
$593$	−12.1261	−	1.82772i	−0.497960	−	0.0750553i	−0.104740	−	0.994500i	$-0.533401\pi$
$593$	−12.1261	−	1.82772i	−0.497960	−	0.0750553i	−0.393220	+	0.919444i	$0.628639\pi$
$594$	−0.930830	−	1.79881i	−0.0381924	−	0.0738061i
$595$	2.33439	+	6.41455i	0.0957006	+	0.262971i
$596$	−14.3645	−	25.9077i	−0.588392	−	1.06122i
$597$	−2.50241	−	2.69695i	−0.102417	−	0.110379i
$598$	0.228626	−	4.95869i	0.00934922	−	0.202776i
$599$	29.4874	+	27.3603i	1.20482	+	1.11791i	0.989972	+	0.141267i	$0.0451175\pi$
$599$	29.4874	+	27.3603i	1.20482	+	1.11791i	0.214852	+	0.976647i	$0.431073\pi$
$600$	−10.2355	+	4.15216i	−0.417863	+	0.169511i
$601$	4.52362	−	19.8193i	0.184522	−	0.808446i	−0.794919	−	0.606716i	$-0.792487\pi$
$601$	4.52362	−	19.8193i	0.184522	−	0.808446i	0.979441	−	0.201730i	$-0.0646563\pi$
$602$	−31.9160	−	7.15883i	−1.30080	−	0.291772i
$603$	34.6755	−	7.91445i	1.41209	−	0.322301i
$604$	20.7043	−	21.5517i	0.842445	−	0.876928i
$605$	36.4261	+	2.72976i	1.48093	+	0.110980i
$606$	−10.4087	+	11.8850i	−0.422823	+	0.482796i
$607$	−0.302288	−	0.523578i	−0.0122695	−	0.0212514i	0.859825	−	0.510588i	$-0.170572\pi$
$607$	−0.302288	−	0.523578i	−0.0122695	−	0.0212514i	−0.872095	+	0.489337i	$0.837239\pi$
$608$	−0.753859	+	1.28791i	−0.0305730	+	0.0522316i
$609$	−1.44277	+	8.18026i	−0.0584639	+	0.331481i
$610$	−38.7317	−	29.1076i	−1.56820	−	1.17853i
$611$	−31.3689	+	2.35078i	−1.26905	+	0.0951022i
$612$	−3.09575	−	2.55787i	−0.125138	−	0.103396i
$613$	2.59754	−	8.42103i	0.104914	−	0.340122i	−0.887862	−	0.460111i	$-0.847810\pi$
$613$	2.59754	−	8.42103i	0.104914	−	0.340122i	0.992775	+	0.119989i	$0.0382859\pi$
$614$	−21.6186	−	2.62591i	−0.872455	−	0.105973i
$615$	14.3860	+	6.92792i	0.580099	+	0.279361i
$616$	−3.08497	+	0.422168i	−0.124297	+	0.0170096i
$617$	20.9034	−	10.0666i	0.841540	−	0.405264i	0.0371097	−	0.999311i	$-0.488185\pi$
$617$	20.9034	−	10.0666i	0.841540	−	0.405264i	0.804430	+	0.594047i	$0.202471\pi$
$618$	5.49768	−	1.87036i	0.221149	−	0.0752369i
$619$	6.50437	+	3.75530i	0.261433	+	0.150938i	0.624988	−	0.780634i	$-0.285104\pi$
$619$	6.50437	+	3.75530i	0.261433	+	0.150938i	−0.363555	+	0.931573i	$0.618437\pi$
$620$	−40.4201	−	20.3364i	−1.62331	−	0.816731i
$621$	−2.48873	−	0.976755i	−0.0998693	−	0.0391958i
$622$	0.638364	+	22.2161i	0.0255960	+	0.890785i
$623$	21.3290	+	5.43203i	0.854529	+	0.217630i
$624$	−9.34813	+	5.90916i	−0.374225	+	0.236556i
$625$	−13.3632	−	9.11090i	−0.534530	−	0.364436i
$626$	−19.5418	−	26.9646i	−0.781048	−	1.07772i
$627$	−0.0100095	−	0.0664089i	−0.000399742	−	0.00265212i
$628$	−6.09986	−	16.3717i	−0.243411	−	0.653303i
$629$	−0.168265	−	0.134187i	−0.00670918	−	0.00535039i
$630$	−9.65106	+	31.7096i	−0.384508	+	1.26334i
$631$	14.2666	+	17.8897i	0.567943	+	0.712178i	0.980004	−	0.198978i	$-0.0637623\pi$
$631$	14.2666	+	17.8897i	0.567943	+	0.712178i	−0.412061	+	0.911156i	$0.635191\pi$
$632$	−9.34261	−	8.47289i	−0.371629	−	0.337034i
$633$	−7.06039	+	4.81369i	−0.280625	+	0.191327i
$634$	41.2686	−	7.43827i	1.63898	−	0.295412i
$635$	−20.0644	−	65.0473i	−0.796233	−	2.58132i
$636$	8.56305	+	3.53337i	0.339547	+	0.140107i
$637$	19.1019	−	25.2134i	0.756844	−	0.998991i
$638$	−2.96191	−	0.587078i	−0.117263	−	0.0232426i
$639$	15.3321	−	4.72932i	0.606528	−	0.187089i
$640$	−20.7612	−	32.0308i	−0.820660	−	1.26613i
$641$	13.6683	−	9.31887i	0.539864	−	0.368073i	−0.262478	−	0.964938i	$-0.584540\pi$
$641$	13.6683	−	9.31887i	0.539864	−	0.368073i	0.802342	+	0.596865i	$0.203587\pi$
$642$	5.74869	+	2.06769i	0.226883	+	0.0816053i
$643$	−7.76940	+	6.19589i	−0.306395	+	0.244342i	−0.764601	−	0.644504i	$-0.777064\pi$
$643$	−7.76940	+	6.19589i	−0.306395	+	0.244342i	0.458205	+	0.888846i	$0.348492\pi$
$644$	−2.69633	+	3.10216i	−0.106250	+	0.122242i
$645$	14.1083	+	11.2510i	0.555513	+	0.443006i
$646$	−0.149687	−	0.242877i	−0.00588937	−	0.00955588i
$647$	15.4923	−	2.33509i	0.609065	−	0.0918018i	0.162735	−	0.986670i	$-0.447969\pi$
$647$	15.4923	−	2.33509i	0.609065	−	0.0918018i	0.446331	+	0.894868i	$0.352730\pi$
$648$	−3.81308	−	15.8715i	−0.149792	−	0.623491i
$649$	−0.408240	−	0.278333i	−0.0160248	−	0.0109255i
$650$	37.2443	+	16.6355i	1.46084	+	0.652498i
$651$	9.89441	−	4.46401i	0.387792	−	0.174958i
$652$	32.8635	+	5.53800i	1.28703	+	0.216885i
$653$	4.83955	+	1.89939i	0.189386	+	0.0743287i	0.458139	−	0.888881i	$-0.348516\pi$
$653$	4.83955	+	1.89939i	0.189386	+	0.0743287i	−0.268753	+	0.963209i	$0.586611\pi$
$654$	−3.27336	+	11.8058i	−0.127999	+	0.461643i
$655$	12.7083	−	22.0115i	0.496556	−	0.860060i
$656$	−7.92720	+	29.9082i	−0.309505	+	1.16772i
$657$	34.3271	−	16.5311i	1.33923	−	0.644939i
$658$	21.5754	+	14.5917i	0.841097	+	0.568843i
$659$	−2.24091	+	4.65330i	−0.0872934	+	0.181267i	−0.940045	−	0.341049i	$-0.889218\pi$
$659$	−2.24091	+	4.65330i	−0.0872934	+	0.181267i	0.852752	+	0.522316i	$0.174932\pi$
$660$	1.63246	+	0.534729i	0.0635432	+	0.0208143i
$661$	−7.35316	+	23.8384i	−0.286005	+	0.927205i	0.692576	+	0.721345i	$0.256476\pi$
$661$	−7.35316	+	23.8384i	−0.286005	+	0.927205i	−0.978581	+	0.205861i	$0.934001\pi$
$662$	4.27503	−	7.92166i	0.166154	−	0.307884i
$663$	−0.158000	−	2.10837i	−0.00613623	−	0.0818822i
$664$	26.7300	−	15.8408i	1.03733	−	0.614743i
$665$	−1.37470	+	1.91192i	−0.0533088	+	0.0741411i
$666$	−0.261713	−	1.01175i	−0.0101412	−	0.0392044i
$667$	−3.45184	+	1.99292i	−0.133656	+	0.0771662i
$668$	−35.1211	+	27.0249i	−1.35888	+	1.04563i
$669$	−10.2304	−	0.766660i	−0.395529	−	0.0296408i
$670$	−34.8599	+	54.4256i	−1.34676	+	2.10264i
$671$	0.940179	+	4.11919i	0.0362952	+	0.159020i
$672$	9.10590	+	0.966506i	0.351268	+	0.0372838i
$673$	−11.0168	+	48.2677i	−0.424666	+	1.86058i	0.0792855	+	0.996852i	$0.474736\pi$
$673$	−11.0168	+	48.2677i	−0.424666	+	1.86058i	−0.503952	+	0.863732i	$0.668121\pi$
$674$	−0.919820	−	0.935916i	−0.0354301	−	0.0360501i
$675$	14.9430	−	16.1047i	0.575157	−	0.619872i
$676$	14.4092	+	3.55285i	0.554199	+	0.136648i
$677$	−3.90371	−	4.20720i	−0.150032	−	0.161696i	0.653564	−	0.756871i	$-0.273273\pi$
$677$	−3.90371	−	4.20720i	−0.150032	−	0.161696i	−0.803596	+	0.595175i	$0.797083\pi$
$678$	−1.91076	−	2.25969i	−0.0733822	−	0.0867828i
$679$	1.46119	+	2.26259i	0.0560754	+	0.0868301i
$680$	7.27034	−	0.628107i	0.278805	−	0.0240868i
$681$	−3.50007	−	0.527551i	−0.134123	−	0.0202158i
$682$	1.54649	+	3.63018i	0.0592183	+	0.139007i
$683$	5.19659	−	2.03951i	0.198842	−	0.0780397i	−0.263830	−	0.964569i	$-0.584986\pi$
$683$	5.19659	−	2.03951i	0.198842	−	0.0780397i	0.462672	+	0.886529i	$0.346891\pi$
$684$	0.127474	−	1.37946i	0.00487409	−	0.0527450i
$685$			1.50582i			0.0575343i
$686$	−25.3578	+	6.55588i	−0.968167	+	0.250305i
$687$	−8.88333			−0.338920
$688$	−16.2555	+	30.9593i	−0.619734	+	1.18031i
$689$	−12.4979	−	31.8442i	−0.476134	−	1.21317i
$690$	2.08612	−	0.888708i	0.0794173	−	0.0338325i
$691$	−1.26551	+	8.39609i	−0.0481421	+	0.319402i	0.951778	+	0.306787i	$0.0992538\pi$
$691$	−1.26551	+	8.39609i	−0.0481421	+	0.319402i	−0.999920	+	0.0126155i	$0.995984\pi$
$692$	−28.0077	+	8.10992i	−1.06469	+	0.308293i
$693$	2.42817	−	1.56813i	0.0922386	−	0.0595683i
$694$	27.7463	+	32.8132i	1.05323	+	1.24557i
$695$	2.55357	−	2.36936i	0.0968623	−	0.0898751i
$696$	8.04396	+	3.76162i	0.304906	+	0.142584i
$697$	−4.33617	−	4.02338i	−0.164244	−	0.152396i
$698$	31.9682	−	31.4184i	1.21001	−	1.18920i
$699$	1.44925	+	0.330782i	0.0548158	+	0.0125113i
$700$	−15.6347	−	29.9382i	−0.590935	−	1.13156i
$701$	13.5300	−	3.08814i	0.511022	−	0.116638i	0.0407683	−	0.999169i	$-0.487019\pi$
$701$	13.5300	−	3.08814i	0.511022	−	0.116638i	0.470254	+	0.882531i	$0.344162\pi$
$702$	11.8639	−	18.5227i	0.447774	−	0.699094i
$703$	0.00554836	−	0.0740377i	0.000209260	−	0.00279238i
$704$	−0.421087	+	3.30197i	−0.0158703	+	0.124448i
$705$	−7.18474	−	12.4443i	−0.270593	−	0.468681i
$706$	−41.0654	+	10.6226i	−1.54552	+	0.399786i
$707$	−39.2219	−	28.2012i	−1.47509	−	1.06062i
$708$	0.969711	+	1.08216i	0.0364440	+	0.0406699i
$709$	−5.21875	+	0.391091i	−0.195994	+	0.0146877i	−0.172366	−	0.985033i	$-0.555141\pi$
$709$	−5.21875	+	0.391091i	−0.195994	+	0.0146877i	−0.0236288	+	0.999721i	$0.507522\pi$
$710$	−13.8471	+	25.6588i	−0.519672	+	0.962956i
$711$	11.1881	+	3.45108i	0.419588	+	0.129426i
$712$	11.5321	−	20.5097i	0.432185	−	0.768634i
$713$	4.69281	+	2.25994i	0.175747	+	0.0846353i
$714$	−0.980736	+	1.45013i	−0.0367031	+	0.0542697i
$715$	−2.75243	−	5.71548i	−0.102935	−	0.213747i
$716$	40.5337	−	5.39216i	1.51482	−	0.201514i
$717$	−13.6443	−	7.87754i	−0.509556	−	0.294192i
$718$	−0.556013	+	2.00533i	−0.0207502	+	0.0748383i
$719$	12.9126	−	32.9008i	0.481559	−	1.22699i	−0.459326	−	0.888268i	$-0.651909\pi$
$719$	12.9126	−	32.9008i	0.481559	−	1.22699i	0.940885	−	0.338725i	$-0.109996\pi$
$720$	30.0540	+	18.7709i	1.12005	+	0.699552i
$721$	7.30242	+	16.1857i	0.271956	+	0.602788i
$722$	−10.9182	+	24.4441i	−0.406333	+	0.909715i
$723$	−1.13272	+	1.66140i	−0.0421265	+	0.0617882i
$724$	14.5111	−	6.68063i	0.539302	−	0.248284i
$725$	−4.88159	−	32.3872i	−0.181298	−	1.20283i
$726$	4.91512	+	7.97509i	0.182417	+	0.295983i
$727$	−10.6158	+	13.3118i	−0.393719	+	0.493708i	−0.938698	−	0.344742i	$-0.887966\pi$
$727$	−10.6158	+	13.3118i	−0.393719	+	0.493708i	0.544978	+	0.838450i	$0.316538\pi$
$728$	−20.7227	−	26.7229i	−0.768033	−	0.990415i
$729$	5.50869	+	6.90767i	0.204025	+	0.255840i
$730$	−23.4330	+	65.1495i	−0.867295	+	2.41129i
$731$	−3.76581	−	5.52342i	−0.139283	−	0.204291i
$732$	0.215537	−	12.4237i	0.00796646	−	0.459192i
$733$	10.8101	+	35.0454i	0.399279	+	1.29443i	0.902656	+	0.430363i	$0.141614\pi$
$733$	10.8101	+	35.0454i	0.399279	+	1.29443i	−0.503377	+	0.864067i	$0.667909\pi$
$734$	−6.08473	−	1.20605i	−0.224591	−	0.0445161i
$735$	14.1628	+	2.86436i	0.522404	+	0.105654i
$736$	2.45350	+	3.64517i	0.0904372	+	0.134363i
$737$	5.38593	−	1.66134i	0.198393	−	0.0611962i
$738$	−5.09492	−	28.2673i	−0.187546	−	1.04053i
$739$	−7.77674	−	11.4064i	−0.286072	−	0.419590i	0.656124	−	0.754653i	$-0.272195\pi$
$739$	−7.77674	−	11.4064i	−0.286072	−	0.419590i	−0.942196	+	0.335063i	$0.891242\pi$
$740$	1.62791	+	0.977913i	0.0598432	+	0.0359488i
$741$	0.570247	−	0.454757i	0.0209486	−	0.0167059i
$742$	−8.24745	+	27.0979i	−0.302773	+	0.994794i
$743$	6.90121	−	8.65384i	0.253181	−	0.317479i	−0.638957	−	0.769243i	$-0.720634\pi$
$743$	6.90121	−	8.65384i	0.253181	−	0.317479i	0.892137	+	0.451764i	$0.149205\pi$
$744$	−1.85998	−	11.4542i	−0.0681903	−	0.419933i
$745$	−49.4143	+	7.44800i	−1.81040	+	0.272874i
$746$	−29.0845	+	21.0781i	−1.06486	+	0.771725i
$747$	−16.2483	+	23.8319i	−0.594495	+	0.871964i
$748$	−0.519503	−	0.367551i	−0.0189949	−	0.0134390i
$749$	−4.61035	+	18.1027i	−0.168459	+	0.661458i
$750$	0.115948	+	4.03518i	0.00423382	+	0.147344i
$751$	19.3450	−	49.2902i	0.705909	−	1.79863i	0.112618	−	0.993638i	$-0.464076\pi$
$751$	19.3450	−	49.2902i	0.705909	−	1.79863i	0.593291	−	0.804988i	$-0.297828\pi$
$752$	21.0563	−	18.2198i	0.767846	−	0.664409i
$753$	3.90437	−	6.76258i	0.142283	−	0.246442i
$754$	−10.5621	−	31.0458i	−0.384648	−	1.13062i
$755$	−21.8741	−	45.4220i	−0.796079	−	1.65307i
$756$	−17.2205	+	5.93069i	−0.626303	+	0.215697i
$757$	−9.90831	+	20.5748i	−0.360124	+	0.747805i	−0.999783	−	0.0208544i	$-0.993361\pi$
$757$	−9.90831	+	20.5748i	−0.360124	+	0.747805i	0.639659	+	0.768659i	$0.279076\pi$
$758$	52.9758	+	6.43473i	1.92417	+	0.233720i
$759$	−0.188957	−	0.0582856i	−0.00685871	−	0.00211563i
$760$	1.59188	+	1.95022i	0.0577437	+	0.0707418i
$761$	0.489369	+	6.53018i	0.0177396	+	0.236719i	0.999025	+	0.0441576i	$0.0140604\pi$
$761$	0.489369	+	6.53018i	0.0177396	+	0.236719i	−0.981285	+	0.192561i	$0.938321\pi$
$762$	10.4882	−	13.9560i	0.379946	−	0.505572i
$763$	−36.8917	−	6.50667i	−1.33557	−	0.235557i
$764$	44.0176	−	2.53172i	1.59250	−	0.0915943i
$765$	−5.86670	+	3.38714i	−0.212111	+	0.122462i
$766$	−24.6053	+	28.0952i	−0.889025	+	1.01512i
$767$	0.401006	−	5.35105i	0.0144795	−	0.193215i
$768$	3.52707	−	9.13182i	0.127272	−	0.329516i
$769$	2.50815	+	10.9889i	0.0904462	+	0.396271i	0.999805	−	0.0197419i	$-0.00628444\pi$
$769$	2.50815	+	10.9889i	0.0904462	+	0.396271i	−0.909359	+	0.416012i	$0.863427\pi$
$770$	−1.14961	+	5.12527i	−0.0414290	+	0.184702i
$771$	12.9368	+	2.95273i	0.465907	+	0.106340i
$772$	−15.9580	−	24.3013i	−0.574340	−	0.874622i
$773$	−15.5889	+	16.8009i	−0.560694	+	0.604285i	−0.948236	−	0.317568i	$-0.897134\pi$
$773$	−15.5889	+	16.8009i	−0.560694	+	0.604285i	0.387541	+	0.921852i	$0.373324\pi$
$774$	1.49505	−	32.4262i	0.0537384	−	1.16554i
$775$	−31.3754	+	29.1121i	−1.12704	+	1.04574i
$776$	2.74160	−	0.879960i	0.0984178	−	0.0315887i
$777$	−0.428110	+	0.155798i	−0.0153584	+	0.00558923i
$778$	−10.8279	+	5.60312i	−0.388200	+	0.200882i
$779$	0.304137	−	2.01781i	0.0108968	−	0.0722957i
$780$	3.83523	+	18.2575i	0.137323	+	0.653725i
$781$	2.36688	−	0.928930i	0.0846935	−	0.0332397i
$782$	−0.835535	+	0.0868101i	−0.0298787	+	0.00310432i
$783$	−17.6622			−0.631194
$784$	−0.275749	+	27.9986i	−0.00984820	+	0.999952i
$785$	−29.4725			−1.05192
$786$	6.48349	−	0.673619i	0.231258	−	0.0240272i
$787$	−11.1610	+	4.38038i	−0.397848	+	0.156144i	−0.555826	−	0.831299i	$-0.687598\pi$
$787$	−11.1610	+	4.38038i	−0.397848	+	0.156144i	0.157978	+	0.987443i	$0.449503\pi$
$788$	−10.3115	−	49.0876i	−0.367331	−	1.74867i
$789$	−1.18335	+	7.85101i	−0.0421284	+	0.279503i
$790$	−18.8962	+	9.77820i	−0.672296	+	0.347893i
$791$	6.31840	−	6.47737i	0.224656	−	0.230309i
$792$	−0.944359	−	2.94224i	−0.0335563	−	0.104548i
$793$	−33.6372	+	31.2107i	−1.19449	+	1.10833i
$794$	−2.05271	+	44.5215i	−0.0728481	+	1.58001i
$795$	10.6288	−	11.4551i	0.376965	−	0.406272i
$796$	−6.60135	−	10.0527i	−0.233979	−	0.356310i
$797$	3.53059	+	0.805834i	0.125060	+	0.0285441i	0.284593	−	0.958649i	$-0.408142\pi$
$797$	3.53059	+	0.805834i	0.125060	+	0.0285441i	−0.159533	+	0.987193i	$0.550999\pi$
$798$	−0.603920	+	0.00226434i	−0.0213785	+	8.01568e-5i
$799$	1.18455	+	5.18986i	0.0419064	+	0.183604i
$800$	−35.2488	+	7.82429i	−1.24623	+	0.276630i
$801$	−1.63231	+	21.7817i	−0.0576748	+	0.769617i
$802$	−7.62281	+	8.70401i	−0.269171	+	0.307349i
$803$	5.22885	−	3.01888i	0.184522	−	0.106534i
$804$	−16.5484	+	0.951796i	−0.583616	+	0.0335673i
$805$	3.31573	+	6.08934i	0.116864	+	0.214621i
$806$	−25.7455	+	34.2579i	−0.906845	+	1.20668i
$807$	−0.763919	−	10.1938i	−0.0268912	−	0.358838i
$808$	−40.0075	+	32.6565i	−1.40746	+	1.14885i
$809$	−16.7322	−	5.16119i	−0.588272	−	0.181458i	−0.0136918	−	0.999906i	$-0.504358\pi$
$809$	−16.7322	−	5.16119i	−0.588272	−	0.181458i	−0.574580	+	0.818448i	$0.694835\pi$
$810$	−27.3349	−	3.32025i	−0.960451	−	0.116662i
$811$	6.45480	−	13.4035i	0.226659	−	0.470661i	−0.756363	−	0.654152i	$-0.773025\pi$
$811$	6.45480	−	13.4035i	0.226659	−	0.470661i	0.983021	+	0.183491i	$0.0587398\pi$
$812$	−9.09415	+	25.5848i	−0.319142	+	0.897849i
$813$	0.999584	+	2.07566i	0.0350569	+	0.0727965i
$814$	−0.0533393	−	0.156784i	−0.00186954	−	0.00549528i
$815$	28.1099	−	48.6878i	0.984646	−	1.70546i
$816$	1.22459	+	1.41524i	0.0428693	+	0.0495433i
$817$	0.842536	−	2.14675i	0.0294766	−	0.0751052i
$818$	0.329906	+	11.4813i	0.0115349	+	0.401433i
$819$	27.9343	+	14.3226i	0.976102	+	0.500472i
$820$	42.6089	+	30.1461i	1.48797	+	1.05275i
$821$	18.1382	−	26.6038i	0.633027	−	0.928480i	−0.366971	−	0.930232i	$-0.619605\pi$
$821$	18.1382	−	26.6038i	0.633027	−	0.928480i	0.999998	+	0.00175187i	$0.000557639\pi$
$822$	−0.312700	+	0.226620i	−0.0109067	+	0.00790427i
$823$	−27.0360	+	4.07502i	−0.942415	+	0.142046i	−0.602239	−	0.798316i	$-0.705725\pi$
$823$	−27.0360	+	4.07502i	−0.942415	+	0.142046i	−0.340176	+	0.940362i	$0.610487\pi$
$824$	18.7374	−	3.04265i	0.652747	−	0.105996i
$825$	1.01312	−	1.27041i	0.0352723	−	0.0442301i
$826$	−3.00985	+	3.26834i	−0.104726	+	0.113720i
$827$	−30.8474	+	24.6000i	−1.07267	+	0.855426i	−0.989988	−	0.141150i	$-0.954920\pi$
$827$	−30.8474	+	24.6000i	−1.07267	+	0.855426i	−0.0826817	+	0.996576i	$0.526348\pi$
$828$	−3.49658	−	2.10045i	−0.121515	−	0.0729958i
$829$	−23.3968	−	34.3168i	−0.812604	−	1.19187i	−0.978606	−	0.205745i	$-0.934038\pi$
$829$	−23.3968	−	34.3168i	−0.812604	−	1.19187i	0.166002	−	0.986125i	$-0.446914\pi$
$830$	−9.29747	−	51.5837i	−0.322720	−	1.79050i
$831$	6.26902	−	1.93374i	0.217470	−	0.0670806i
$832$	−33.3429	+	13.9699i	−1.15596	+	0.484318i
$833$	−4.70090	−	2.56050i	−0.162876	−	0.0887162i
$834$	0.876327	+	0.173696i	0.0303447	+	0.00601461i
$835$	22.0348	+	71.4351i	0.762546	+	2.47211i
$836$	0.00380810	−	0.219502i	0.000131706	−	0.00759162i
$837$	13.0017	+	19.0701i	0.449406	+	0.659158i
$838$	−5.82094	+	16.1836i	−0.201081	+	0.559055i
$839$	9.34814	+	11.7222i	0.322734	+	0.404695i	0.916559	−	0.399898i	$-0.130955\pi$
$839$	9.34814	+	11.7222i	0.322734	+	0.404695i	−0.593826	+	0.804594i	$0.702383\pi$
$840$	6.89093	−	13.8251i	0.237760	−	0.477010i
$841$	1.66375	−	2.08627i	0.0573706	−	0.0719404i
$842$	−13.8462	−	22.4663i	−0.477172	−	0.774241i
$843$	0.455013	+	3.01881i	0.0156715	+	0.103973i
$844$	−25.3734	+	11.6814i	−0.873389	+	0.402090i
$845$	14.1028	−	20.6850i	0.485151	−	0.711586i
$846$	−10.5418	+	23.6013i	−0.362434	+	0.811431i
$847$	−22.8348	+	17.2951i	−0.784612	+	0.594267i
$848$	25.6830	+	16.0410i	0.881959	+	0.550849i
$849$	1.22509	−	3.12147i	0.0420449	−	0.107129i
$850$	1.84435	−	6.65189i	0.0632607	−	0.228158i
$851$	−0.189319	−	0.109304i	−0.00648978	−	0.00374688i
$852$	−7.41226	+	0.986046i	−0.253940	+	0.0337814i
$853$	−10.8900	−	22.6133i	−0.372866	−	0.774264i	0.627123	−	0.778920i	$-0.284232\pi$
$853$	−10.8900	−	22.6133i	−0.372866	−	0.774264i	−0.999989	+	0.00465588i	$0.998518\pi$
$854$	37.8770	−	2.98135i	1.29613	−	0.102020i
$855$	−2.10553	−	1.01397i	−0.0720074	−	0.0346770i
$856$	17.4073	+	9.78772i	0.594970	+	0.334537i
$857$	43.2434	+	13.3388i	1.47717	+	0.455646i	0.925606	−	0.378488i	$-0.123556\pi$
$857$	43.2434	+	13.3388i	1.47717	+	0.455646i	0.551562	+	0.834134i	$0.314032\pi$
$858$	0.772653	−	1.43173i	0.0263779	−	0.0488785i
$859$	−6.57236	+	0.492530i	−0.224246	+	0.0168049i	−0.186379	−	0.982478i	$-0.559675\pi$
$859$	−6.57236	+	0.492530i	−0.224246	+	0.0168049i	−0.0378668	+	0.999283i	$0.512056\pi$
$860$	39.3655	+	43.9302i	1.34235	+	1.49801i
$861$	−12.0536	+	3.39078i	−0.410784	+	0.115557i
$862$	30.4201	−	7.86889i	1.03611	−	0.268015i
$863$	−16.0618	−	27.8199i	−0.546750	−	0.947000i	−0.998494	−	0.0548520i	$-0.982531\pi$
$863$	−16.0618	−	27.8199i	−0.546750	−	0.947000i	0.451744	−	0.892148i	$-0.350802\pi$
$864$	1.33914	+	19.4245i	0.0455586	+	0.660836i
$865$	−3.67579	+	49.0501i	−0.124981	+	1.66775i
$866$	−11.8401	+	18.4856i	−0.402344	+	0.628166i
$867$	9.79153	−	2.23485i	0.332538	−	0.0758996i
$868$	34.3187	−	9.01479i	1.16485	−	0.305982i
$869$	1.80890	+	0.412869i	0.0613626	+	0.0140056i
$870$	10.6839	−	10.5001i	0.362218	−	0.355988i
$871$	44.8722	+	41.6353i	1.52044	+	1.41076i
$872$	−16.9643	+	36.2770i	−0.574484	+	1.22850i
$873$	−1.95941	+	1.81806i	−0.0663159	+	0.0615322i
$874$	−0.187114	−	0.221284i	−0.00632923	−	0.00748504i
$875$	−12.2480	+	1.53432i	−0.414057	+	0.0518697i
$876$	−17.0556	+	4.93863i	−0.576255	+	0.166861i
$877$	−1.68302	+	11.1661i	−0.0568316	+	0.377053i	0.942277	+	0.334835i	$0.108681\pi$
$877$	−1.68302	+	11.1661i	−0.0568316	+	0.377053i	−0.999108	+	0.0422182i	$0.986558\pi$
$878$	−12.1928	+	5.19427i	−0.411488	+	0.175298i
$879$	4.92693	+	12.5536i	0.166181	+	0.423423i
$880$	4.97164	+	2.61040i	0.167594	+	0.0879967i
$881$	−35.5018			−1.19608			−0.598042	−	0.801465i	$-0.704054\pi$
$881$	−35.5018			−1.19608			−0.598042	+	0.801465i	$0.704054\pi$
$882$	−10.7782	−	23.6527i	−0.362921	−	0.796429i
$883$			43.9739i			1.47984i	0.672696	+	0.739919i	$0.265136\pi$
$883$			43.9739i			1.47984i	−0.672696	+	0.739919i	$0.734864\pi$
$884$	0.635956	−	6.88200i	0.0213895	−	0.231467i
$885$	2.28177	−	0.895528i	0.0767008	−	0.0301028i
$886$	−5.90421	−	13.8593i	−0.198356	−	0.465614i
$887$	0.528582	+	0.0796710i	0.0177481	+	0.00267509i	0.157910	−	0.987453i	$-0.449524\pi$
$887$	0.528582	+	0.0796710i	0.0177481	+	0.00267509i	−0.140162	+	0.990129i	$0.544762\pi$
$888$	0.0419202	+	0.485226i	0.00140675	+	0.0162831i
$889$	45.5486	+	27.8369i	1.52765	+	0.933619i
$890$	−25.6290	−	30.3092i	−0.859086	−	1.01597i
$891$	1.63329	+	1.76027i	0.0547173	+	0.0589712i
$892$	−32.5604	−	8.02837i	−1.09020	−	0.268810i
$893$	−1.24908	+	1.34619i	−0.0417988	+	0.0450484i
$894$	−8.98332	−	9.14053i	−0.300447	−	0.305705i
$895$	15.3494	−	67.2502i	0.513074	−	2.24793i
$896$	28.8272	+	8.06176i	0.963050	+	0.269324i
$897$	−0.477877	−	2.09372i	−0.0159558	−	0.0699071i
$898$	7.59547	−	11.8585i	0.253464	−	0.395725i
$899$	34.3134	+	2.57143i	1.14441	+	0.0857620i
$900$	26.5643	−	20.4406i	0.885475	−	0.681354i
$901$	−5.01347	+	2.89453i	−0.167023	+	0.0964307i
$902$	−1.13989	−	4.40666i	−0.0379542	−	0.146726i
$903$	−14.1333	+	0.704747i	−0.470328	+	0.0234525i
$904$	−4.93173	−	8.32186i	−0.164027	−	0.276781i
$905$	−2.01388	−	26.8734i	−0.0669438	−	0.893303i
$906$	6.14041	−	11.3782i	0.204002	−	0.378016i
$907$	−2.19565	+	7.11811i	−0.0729052	+	0.236353i	−0.984690	−	0.174316i	$-0.944229\pi$
$907$	−2.19565	+	7.11811i	−0.0729052	+	0.236353i	0.911785	+	0.410669i	$0.134705\pi$
$908$	−10.9957	−	3.60175i	−0.364904	−	0.119528i
$909$	20.8009	−	43.1936i	0.689923	−	1.43264i
$910$	−54.4476	+	17.0187i	−1.80492	+	0.564165i
$911$	10.5196	−	5.06596i	0.348529	−	0.167843i	−0.251426	−	0.967877i	$-0.580899\pi$
$911$	10.5196	−	5.06596i	0.348529	−	0.167843i	0.599955	+	0.800034i	$0.295185\pi$
$912$	−0.165411	+	0.624073i	−0.00547732	+	0.0206651i
$913$	−2.28544	+	3.95850i	−0.0756371	+	0.131007i
$914$	−11.5629	+	41.7032i	−0.382468	+	1.37942i
$915$	−19.5120	−	7.65788i	−0.645046	−	0.253162i
$916$	−28.6348	−	4.82540i	−0.946119	−	0.159436i
$917$	3.94852	+	19.5366i	0.130392	+	0.645155i
$918$	−3.39874	−	1.51808i	−0.112175	−	0.0501042i
$919$	−1.28331	−	0.874943i	−0.0423323	−	0.0288617i	0.541969	−	0.840398i	$-0.317679\pi$
$919$	−1.28331	−	0.874943i	−0.0423323	−	0.0288617i	−0.584301	+	0.811537i	$0.698631\pi$
$920$	7.20721	−	1.73151i	0.237615	−	0.0570862i
$921$	−9.31636	+	1.40422i	−0.306985	+	0.0462705i
$922$	2.39422	+	3.88478i	0.0788495	+	0.127938i
$923$	21.5895	+	17.2171i	0.710628	+	0.566707i
$924$	−1.23733	+	0.532605i	−0.0407052	+	0.0175214i
$925$	1.40446	−	1.12002i	0.0461784	−	0.0368260i
$926$	−33.8177	−	12.1636i	−1.11132	−	0.399719i
$927$	−14.5599	+	9.92680i	−0.478211	+	0.326039i
$928$	23.8858	+	16.4948i	0.784091	+	0.541467i
$929$	25.7680	−	7.94837i	0.845421	−	0.260778i	0.158363	−	0.987381i	$-0.449378\pi$
$929$	25.7680	−	7.94837i	0.845421	−	0.260778i	0.687057	+	0.726603i	$0.258902\pi$
$930$	−19.2019	−	3.80600i	−0.629657	−	0.124804i
$931$	−0.183706	−	1.83749i	−0.00602074	−	0.0602213i
$932$	4.49188	+	1.85348i	0.147136	+	0.0607128i
$933$	2.83417	+	9.18815i	0.0927865	+	0.300806i
$934$	49.3180	−	8.88910i	1.61373	−	0.290860i
$935$	−0.886985	+	0.604736i	−0.0290075	+	0.0197770i
$936$	22.5449	−	24.8590i	0.736902	−	0.812542i
$937$	−23.4831	−	29.4469i	−0.767159	−	0.961987i	0.232785	−	0.972528i	$-0.425216\pi$
$937$	−23.4831	−	29.4469i	−0.767159	−	0.961987i	−0.999944	+	0.0105409i	$0.996645\pi$
$938$	−7.74199	−	50.0897i	−0.252785	−	1.63549i
$939$	−11.2639	−	8.98269i	−0.367585	−	0.293139i
$940$	−16.3998	−	44.0161i	−0.534901	−	1.43565i
$941$	−2.87201	−	19.0546i	−0.0936249	−	0.621161i	−0.985602	−	0.169081i	$-0.945920\pi$
$941$	−2.87201	−	19.0546i	−0.0936249	−	0.621161i	0.891977	−	0.452080i	$-0.149318\pi$
$942$	−4.43550	−	6.12029i	−0.144516	−	0.199410i
$943$	−4.96432	−	3.38462i	−0.161661	−	0.110218i
$944$	2.53797	+	4.01500i	0.0826038	+	0.130677i
$945$	−0.767315	+	30.7145i	−0.0249608	+	0.999144i
$946$	−0.147749	−	5.14192i	−0.00480375	−	0.167178i
$947$	15.8630	+	6.22577i	0.515478	+	0.202310i	0.608797	−	0.793326i	$-0.291652\pi$
$947$	15.8630	+	6.22577i	0.515478	+	0.202310i	−0.0933188	+	0.995636i	$0.529748\pi$
$948$	−4.87436	−	2.45242i	−0.158312	−	0.0796509i
$949$	56.7873	+	32.7862i	1.84339	+	1.06428i
$950$	2.25441	−	0.766971i	0.0731428	−	0.0248838i
$951$	16.3451	−	7.87140i	0.530027	−	0.255247i
$952$	−3.94903	+	4.14165i	−0.127989	+	0.134232i
$953$	−7.26333	−	3.49783i	−0.235282	−	0.113306i	0.312528	−	0.949909i	$-0.398824\pi$
$953$	−7.26333	−	3.49783i	−0.235282	−	0.113306i	−0.547810	+	0.836603i	$0.684538\pi$
$954$	−27.9050	−	3.38949i	−0.903458	−	0.109739i
$955$	21.9230	−	71.0727i	0.709413	−	2.29986i
$956$	−39.7023	−	32.8042i	−1.28407	−	1.06096i
$957$	−1.30269	+	0.0976229i	−0.0421099	+	0.00315570i
$958$	27.7862	+	20.8819i	0.897732	+	0.674662i
$959$	−0.781315	−	0.885416i	−0.0252300	−	0.0285916i
$960$	−12.3579	−	10.9538i	−0.398851	−	0.353534i
$961$	−6.98289	−	12.0947i	−0.225255	−	0.390153i
$962$	1.18497	−	1.35304i	0.0382050	−	0.0436239i
$963$	−18.4869	−	1.38540i	−0.595731	−	0.0446438i
$964$	−4.55372	+	4.74011i	−0.146665	+	0.152669i
$965$	−47.8134	+	10.9131i	−1.53917	+	0.351305i
$966$	−0.765514	+	1.60497i	−0.0246300	+	0.0516392i
$967$	1.93633	−	8.48361i	0.0622681	−	0.272815i	−0.934204	−	0.356739i	$-0.883888\pi$
$967$	1.93633	−	8.48361i	0.0622681	−	0.272815i	0.996472	+	0.0839248i	$0.0267456\pi$
$968$	11.5115	+	28.3770i	0.369993	+	0.912072i
$969$	−0.0904799	−	0.0839531i	−0.00290663	−	0.00269696i
$970$	0.223712	−	4.85211i	0.00718295	−	0.155792i
$971$	20.5990	+	22.2004i	0.661053	+	0.712446i	0.971206	−	0.238241i	$-0.0765707\pi$
$971$	20.5990	+	22.2004i	0.661053	+	0.712446i	−0.310153	+	0.950687i	$0.600380\pi$
$972$	−13.4384	−	24.2374i	−0.431037	−	0.777416i
$973$	−0.272110	+	2.71813i	−0.00872346	+	0.0871394i
$974$	9.67758	+	18.7017i	0.310090	+	0.599242i
$975$	17.4501	+	2.63019i	0.558852	+	0.0842334i
$976$	7.44326	−	39.9297i	0.238253	−	1.27812i
$977$	4.99559	+	12.7285i	0.159823	+	0.407222i	0.988244	−	0.152883i	$-0.0488558\pi$
$977$	4.99559	+	12.7285i	0.159823	+	0.407222i	−0.828421	+	0.560105i	$0.810761\pi$
$978$	14.3410	−	1.48999i	0.458574	−	0.0476448i
$979$			3.46142i			0.110627i
$980$	44.0969	+	16.9263i	1.40862	+	0.540690i
$981$		−	37.1767i		−	1.18696i
$982$	2.03469	+	19.5836i	0.0649297	+	0.624939i
$983$	−21.3927	−	54.5078i	−0.682322	−	1.73853i	−0.674187	−	0.738561i	$-0.735506\pi$
$983$	−21.3927	−	54.5078i	−0.682322	−	1.73853i	−0.00813497	−	0.999967i	$-0.502589\pi$
$984$	0.152318	+	13.3851i	0.00485573	+	0.426701i
$985$	−83.6692	−	12.6111i	−2.66592	−	0.401823i
$986$	−4.92869	+	2.55045i	−0.156961	+	0.0812227i
$987$	10.6815	+	3.58932i	0.339997	+	0.114249i
$988$	2.08517	−	1.15612i	0.0663382	−	0.0367811i
$989$	−4.61854	−	4.97760i	−0.146861	−	0.158279i
$990$	−5.20720	−	0.240084i	−0.165496	−	0.00763036i
$991$	20.6301	+	19.1419i	0.655336	+	0.608063i	0.936108	−	0.351711i	$-0.114400\pi$
$991$	20.6301	+	19.1419i	0.655336	+	0.608063i	−0.280773	+	0.959774i	$0.590591\pi$
$992$	0.226380	−	37.9322i	0.00718756	−	1.20435i
$993$	0.866576	−	3.79672i	0.0274999	−	0.120485i
$994$	−5.17138	−	22.2720i	−0.164026	−	0.706426i
$995$	−19.7790	+	4.51443i	−0.627037	+	0.143117i
$996$	9.31269	−	9.69387i	0.295084	−	0.307162i
$997$	−10.7395	−	0.804813i	−0.340123	−	0.0254887i	−0.0964261	−	0.995340i	$-0.530741\pi$
$997$	−10.7395	−	0.804813i	−0.340123	−	0.0254887i	−0.243697	+	0.969851i	$0.578360\pi$
$998$	−43.5146	−	38.1093i	−1.37743	−	1.20633i
$999$	−0.484348	−	0.838916i	−0.0153241	−	0.0265421i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.z.a.221.54	yes	648
8.5	even	2	inner	392.2.z.a.221.47	yes	648
49.2	even	21	inner	392.2.z.a.149.47	✓	648
392.149	even	42	inner	392.2.z.a.149.54	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.z.a.149.47	✓	648	49.2	even	21	inner
392.2.z.a.149.54	yes	648	392.149	even	42	inner
392.2.z.a.221.47	yes	648	8.5	even	2	inner
392.2.z.a.221.54	yes	648	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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.z (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40664 - 0.146147i) q^{2} +(0.569538 - 0.223527i) q^{3} +(1.95728 - 0.411152i) q^{4} +(0.502846 - 3.33616i) q^{5} +(0.768468 - 0.397659i) q^{6} +(1.43535 + 2.22256i) q^{7} +(2.69311 - 0.864394i) q^{8} +(-1.92475 + 1.78590i) q^{9} +O(q^{10})\)	\(q+(1.40664 - 0.146147i) q^{2} +(0.569538 - 0.223527i) q^{3} +(1.95728 - 0.411152i) q^{4} +(0.502846 - 3.33616i) q^{5} +(0.768468 - 0.397659i) q^{6} +(1.43535 + 2.22256i) q^{7} +(2.69311 - 0.864394i) q^{8} +(-1.92475 + 1.78590i) q^{9} +(0.219754 - 4.76628i) q^{10} +(-0.283012 + 0.305015i) q^{11} +(1.02284 - 0.671672i) q^{12} +(-4.40559 - 1.00555i) q^{13} +(2.34384 + 2.91658i) q^{14} +(-0.459333 - 2.01247i) q^{15} +(3.66191 - 1.60948i) q^{16} +(-0.0571472 + 0.762576i) q^{17} +(-2.44643 + 2.79342i) q^{18} +(-0.228464 + 0.131904i) q^{19} +(-0.387460 - 6.73656i) q^{20} +(1.31429 + 0.944994i) q^{21} +(-0.353520 + 0.470408i) q^{22} +(0.0580467 + 0.774579i) q^{23} +(1.34061 - 1.09429i) q^{24} +(-6.09926 - 1.88137i) q^{25} +(-6.34405 - 0.770582i) q^{26} +(-1.49341 + 3.10110i) q^{27} +(3.72319 + 3.76004i) q^{28} +(2.22644 + 4.62326i) q^{29} +(-0.940233 - 2.76369i) q^{30} +(3.35283 - 5.80727i) q^{31} +(4.91577 - 2.79914i) q^{32} +(-0.0930072 + 0.236978i) q^{33} +(0.0310624 + 1.08102i) q^{34} +(8.13659 - 3.67094i) q^{35} +(-3.03299 + 4.28688i) q^{36} +(-0.158540 + 0.232535i) q^{37} +(-0.302089 + 0.218930i) q^{38} +(-2.73392 + 0.412072i) q^{39} +(-1.52954 - 9.41930i) q^{40} +(-4.82283 + 6.04764i) q^{41} +(1.98684 + 1.13719i) q^{42} +(-6.83466 + 5.45046i) q^{43} +(-0.428528 + 0.713361i) q^{44} +(4.99022 + 7.31930i) q^{45} +(0.194853 + 1.08107i) q^{46} +(6.65193 - 2.05185i) q^{47} +(1.72583 - 1.73520i) q^{48} +(-2.87957 + 6.38029i) q^{49} +(-8.85444 - 1.75503i) q^{50} +(0.137909 + 0.447090i) q^{51} +(-9.03642 - 0.156772i) q^{52} +(4.26446 + 6.25481i) q^{53} +(-1.64748 + 4.58039i) q^{54} +(0.875268 + 1.09755i) q^{55} +(5.78671 + 4.74489i) q^{56} +(-0.100635 + 0.126192i) q^{57} +(3.80748 + 6.17788i) q^{58} +(0.176984 + 1.17421i) q^{59} +(-1.72648 - 3.75012i) q^{60} +(5.72016 - 8.38994i) q^{61} +(3.86751 - 8.65875i) q^{62} +(-6.73196 - 1.71448i) q^{63} +(6.50565 - 4.65581i) q^{64} +(-5.57000 + 14.1921i) q^{65} +(-0.0961942 + 0.346936i) q^{66} +(-11.7312 - 6.77300i) q^{67} +(0.201682 + 1.51607i) q^{68} +(0.206199 + 0.428177i) q^{69} +(10.9088 - 6.35283i) q^{70} +(-5.50564 - 2.65138i) q^{71} +(-3.63982 + 6.47337i) q^{72} +(-13.8661 - 4.27711i) q^{73} +(-0.189024 + 0.350263i) q^{74} +(-3.89430 + 0.291837i) q^{75} +(-0.392935 + 0.352106i) q^{76} +(-1.08414 - 0.191211i) q^{77} +(-3.78542 + 0.979190i) q^{78} +(-2.22959 - 3.86176i) q^{79} +(-3.52812 - 13.0260i) q^{80} +(0.431274 - 5.75495i) q^{81} +(-5.90015 + 9.21170i) q^{82} +(10.7099 - 2.44447i) q^{83} +(2.96097 + 1.30925i) q^{84} +(2.51534 + 0.574110i) q^{85} +(-8.81735 + 8.66570i) q^{86} +(2.30147 + 2.13545i) q^{87} +(-0.498530 + 1.06607i) q^{88} +(6.09822 - 5.65832i) q^{89} +(8.08914 + 9.56633i) q^{90} +(-4.08865 - 11.2350i) q^{91} +(0.432084 + 1.49220i) q^{92} +(0.611480 - 4.05690i) q^{93} +(9.05701 - 3.85837i) q^{94} +(0.325170 + 0.828519i) q^{95} +(2.17403 - 2.69302i) q^{96} +1.01801 q^{97} +(-3.11806 + 9.39562i) q^{98} -1.09251i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9}+O(q^{10}) \) 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9	\( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25} - 12 q^{26} + 2 q^{28} - 11 q^{30} + 60 q^{31} - 13 q^{32} - 14 q^{33} - 18 q^{34} + 8 q^{36} - 46 q^{38} - 32 q^{39} + 32 q^{40} - 20 q^{41} - 36 q^{42} + 38 q^{44} - 22 q^{46} - 58 q^{47} + 28 q^{48} - 16 q^{49} - 132 q^{50} + 18 q^{52} - 37 q^{54} - 32 q^{55} + 96 q^{56} - 66 q^{57} + 100 q^{60} + 28 q^{62} - 72 q^{63} - 28 q^{64} - 36 q^{65} - 4 q^{66} - 11 q^{68} - 36 q^{70} + 60 q^{71} - 130 q^{72} - 18 q^{73} - 12 q^{74} + 11 q^{76} - 132 q^{78} - 12 q^{79} - 64 q^{80} - 58 q^{81} + 152 q^{82} - 224 q^{84} + 55 q^{86} - 8 q^{87} - 169 q^{88} - 18 q^{89} + 144 q^{90} - 54 q^{92} + 154 q^{94} - 64 q^{95} - 142 q^{96} - 96 q^{97} + 151 q^{98}+O(q^{100}) \) 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9 - 6 * q^10 - 47 * q^12 - 33 * q^14 - 8 * q^15 - 17 * q^16 - 26 * q^17 - 8 * q^18 - 22 * q^20 - 18 * q^22 - 26 * q^23 - 74 * q^24 - 72 * q^25 - 12 * q^26 + 2 * q^28 - 11 * q^30 + 60 * q^31 - 13 * q^32 - 14 * q^33 - 18 * q^34 + 8 * q^36 - 46 * q^38 - 32 * q^39 + 32 * q^40 - 20 * q^41 - 36 * q^42 + 38 * q^44 - 22 * q^46 - 58 * q^47 + 28 * q^48 - 16 * q^49 - 132 * q^50 + 18 * q^52 - 37 * q^54 - 32 * q^55 + 96 * q^56 - 66 * q^57 + 100 * q^60 + 28 * q^62 - 72 * q^63 - 28 * q^64 - 36 * q^65 - 4 * q^66 - 11 * q^68 - 36 * q^70 + 60 * q^71 - 130 * q^72 - 18 * q^73 - 12 * q^74 + 11 * q^76 - 132 * q^78 - 12 * q^79 - 64 * q^80 - 58 * q^81 + 152 * q^82 - 224 * q^84 + 55 * q^86 - 8 * q^87 - 169 * q^88 - 18 * q^89 + 144 * q^90 - 54 * q^92 + 154 * q^94 - 64 * q^95 - 142 * q^96 - 96 * q^97 + 151 * q^98

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