LMFDB - Embedded newform 169.2.h.a.12.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(12,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(26))

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

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

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

chi := DirichletCharacter("169.12");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.h (of order $26$, 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:	$1.34947179416$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			12.6
Character	$\chi$	$=$	169.12
Dual form			169.2.h.a.155.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.705316 + 0.486844i) q^{2} +(-1.15919 - 0.608391i) q^{3} +(-0.448757 + 1.18327i) q^{4} +(-0.816038 - 0.921117i) q^{5} +(1.11379 - 0.135238i) q^{6} +(0.328944 + 1.33458i) q^{7} +(-0.669753 - 2.71730i) q^{8} +(-0.730609 - 1.05847i) q^{9} +O(q^{10})$	\(q+(-0.705316 + 0.486844i) q^{2} +(-1.15919 - 0.608391i) q^{3} +(-0.448757 + 1.18327i) q^{4} +(-0.816038 - 0.921117i) q^{5} +(1.11379 - 0.135238i) q^{6} +(0.328944 + 1.33458i) q^{7} +(-0.669753 - 2.71730i) q^{8} +(-0.730609 - 1.05847i) q^{9} +(1.02401 + 0.252395i) q^{10} +(-4.34079 - 2.99623i) q^{11} +(1.24009 - 1.09862i) q^{12} +(-3.59110 - 0.322536i) q^{13} +(-0.881740 - 0.781154i) q^{14} +(0.385546 + 1.56422i) q^{15} +(-0.0992110 - 0.0878933i) q^{16} +(-1.38245 + 0.340744i) q^{17} +(1.03062 + 0.390862i) q^{18} +2.34458i q^{19} +(1.45614 - 0.552240i) q^{20} +(0.430635 - 1.74716i) q^{21} +4.52033 q^{22} +1.57912 q^{23} +(-0.876805 + 3.55734i) q^{24} +(0.420146 - 3.46021i) q^{25} +(2.68988 - 1.52082i) q^{26} +(0.676353 + 5.57027i) q^{27} +(-1.72679 - 0.209670i) q^{28} +(1.82071 + 2.63775i) q^{29} +(-1.03346 - 0.915569i) q^{30} +(-1.01979 + 0.123825i) q^{31} +(5.66919 + 0.688364i) q^{32} +(3.20893 + 6.11410i) q^{33} +(0.809177 - 0.913372i) q^{34} +(0.960870 - 1.39206i) q^{35} +(1.58032 - 0.389515i) q^{36} +(-7.12219 + 0.864790i) q^{37} +(-1.14145 - 1.65367i) q^{38} +(3.96654 + 2.55867i) q^{39} +(-1.95640 + 2.83434i) q^{40} +(4.12376 - 7.85717i) q^{41} +(0.546859 + 1.44195i) q^{42} +(-1.27272 + 10.4818i) q^{43} +(5.49332 - 3.79177i) q^{44} +(-0.378769 + 1.53673i) q^{45} +(-1.11378 + 0.768785i) q^{46} +(-2.51425 + 0.953527i) q^{47} +(0.0615311 + 0.162244i) q^{48} +(4.52530 - 2.37506i) q^{49} +(1.38825 + 2.64509i) q^{50} +(1.80983 + 0.446084i) q^{51} +(1.99318 - 4.10451i) q^{52} +(-12.6191 + 3.11032i) q^{53} +(-3.18890 - 3.59952i) q^{54} +(0.782372 + 6.44342i) q^{55} +(3.40613 - 1.78767i) q^{56} +(1.42642 - 2.71782i) q^{57} +(-2.56835 - 0.974046i) q^{58} +(-0.113453 - 0.128062i) q^{59} +(-2.02392 - 0.245748i) q^{60} +(4.08076 + 1.00582i) q^{61} +(0.658989 - 0.583813i) q^{62} +(1.17228 - 1.32323i) q^{63} +(-4.09897 + 2.15131i) q^{64} +(2.63338 + 3.57102i) q^{65} +(-5.23993 - 2.75013i) q^{66} +(1.30041 - 0.493179i) q^{67} +(0.217191 - 1.78873i) q^{68} +(-1.83050 - 0.960721i) q^{69} +1.44964i q^{70} +(0.139794 - 0.266356i) q^{71} +(-2.38685 + 2.69419i) q^{72} +(-9.71703 - 6.70718i) q^{73} +(4.60238 - 4.07735i) q^{74} +(-2.59219 + 3.75543i) q^{75} +(-2.77429 - 1.05215i) q^{76} +(2.57083 - 6.77871i) q^{77} +(-4.04334 + 0.126417i) q^{78} +(-1.34914 - 3.55738i) q^{79} +0.163109i q^{80} +(1.23667 - 3.26082i) q^{81} +(0.916666 + 7.54942i) q^{82} +(-3.48415 - 6.63849i) q^{83} +(1.87411 + 1.29361i) q^{84} +(1.44200 + 0.995340i) q^{85} +(-4.20535 - 8.01262i) q^{86} +(-0.505766 - 4.16536i) q^{87} +(-5.23439 + 13.8019i) q^{88} -13.0444i q^{89} +(-0.480995 - 1.26828i) q^{90} +(-0.750819 - 4.89869i) q^{91} +(-0.708640 + 1.86853i) q^{92} +(1.25746 + 0.476893i) q^{93} +(1.30912 - 1.89658i) q^{94} +(2.15964 - 1.91327i) q^{95} +(-6.15288 - 4.24703i) q^{96} +(9.44318 - 10.6591i) q^{97} +(-2.03548 + 3.87829i) q^{98} +6.78367i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9}+O(q^{10}) $ 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9} - 9 q^{10} - 13 q^{11} - 9 q^{12} + 52 q^{13} - 15 q^{14} + 39 q^{15} - 31 q^{16} - 11 q^{17} + 26 q^{18} - 13 q^{20} - 13 q^{21} - 6 q^{22} - 102 q^{23} - 91 q^{24} + 3 q^{25} - 13 q^{26} - 19 q^{27} - 13 q^{28} - 17 q^{29} + 23 q^{30} + 39 q^{31} - 13 q^{33} + 52 q^{34} - 21 q^{35} + 11 q^{36} - 13 q^{37} - 40 q^{38} - 65 q^{39} + 53 q^{40} - 13 q^{41} + 101 q^{42} - 3 q^{43} - 39 q^{44} - 78 q^{45} - 39 q^{46} - 39 q^{47} + 8 q^{48} + 85 q^{49} - 13 q^{50} + 62 q^{51} - 78 q^{52} + 18 q^{53} + 65 q^{54} - 103 q^{55} + 3 q^{56} + 65 q^{57} + 39 q^{58} + 91 q^{59} - 117 q^{60} - 23 q^{61} - 64 q^{62} - 78 q^{63} + 15 q^{64} - 13 q^{65} + 134 q^{66} - 65 q^{67} + 40 q^{68} - 40 q^{69} + 26 q^{71} + 156 q^{72} - 13 q^{73} - 53 q^{74} + 35 q^{75} + 221 q^{76} + 3 q^{77} - 143 q^{78} - 23 q^{79} - 43 q^{81} - 129 q^{82} + 117 q^{83} + 234 q^{84} + 26 q^{85} - 91 q^{86} + 79 q^{87} + 95 q^{88} + 17 q^{90} + 39 q^{91} - 89 q^{92} + 52 q^{93} - 61 q^{94} + 122 q^{95} - 182 q^{96} - 91 q^{97} - 13 q^{98}+O(q^{100}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9 - 9 * q^10 - 13 * q^11 - 9 * q^12 + 52 * q^13 - 15 * q^14 + 39 * q^15 - 31 * q^16 - 11 * q^17 + 26 * q^18 - 13 * q^20 - 13 * q^21 - 6 * q^22 - 102 * q^23 - 91 * q^24 + 3 * q^25 - 13 * q^26 - 19 * q^27 - 13 * q^28 - 17 * q^29 + 23 * q^30 + 39 * q^31 - 13 * q^33 + 52 * q^34 - 21 * q^35 + 11 * q^36 - 13 * q^37 - 40 * q^38 - 65 * q^39 + 53 * q^40 - 13 * q^41 + 101 * q^42 - 3 * q^43 - 39 * q^44 - 78 * q^45 - 39 * q^46 - 39 * q^47 + 8 * q^48 + 85 * q^49 - 13 * q^50 + 62 * q^51 - 78 * q^52 + 18 * q^53 + 65 * q^54 - 103 * q^55 + 3 * q^56 + 65 * q^57 + 39 * q^58 + 91 * q^59 - 117 * q^60 - 23 * q^61 - 64 * q^62 - 78 * q^63 + 15 * q^64 - 13 * q^65 + 134 * q^66 - 65 * q^67 + 40 * q^68 - 40 * q^69 + 26 * q^71 + 156 * q^72 - 13 * q^73 - 53 * q^74 + 35 * q^75 + 221 * q^76 + 3 * q^77 - 143 * q^78 - 23 * q^79 - 43 * q^81 - 129 * q^82 + 117 * q^83 + 234 * q^84 + 26 * q^85 - 91 * q^86 + 79 * q^87 + 95 * q^88 + 17 * q^90 + 39 * q^91 - 89 * q^92 + 52 * q^93 - 61 * q^94 + 122 * q^95 - 182 * q^96 - 91 * q^97 - 13 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{21}{26}\right)$

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 $

$2$	−0.705316	+	0.486844i	−0.498734	+	0.344251i	−0.790727	−	0.612169i	$-0.790297\pi$
$2$	−0.705316	+	0.486844i	−0.498734	+	0.344251i	0.291993	+	0.956420i	$0.405682\pi$
$3$	−1.15919	−	0.608391i	−0.669260	−	0.351254i	0.0956291	−	0.995417i	$-0.469514\pi$
$3$	−1.15919	−	0.608391i	−0.669260	−	0.351254i	−0.764889	+	0.644163i	$0.777206\pi$
$4$	−0.448757	+	1.18327i	−0.224378	+	0.591637i
$5$	−0.816038	−	0.921117i	−0.364943	−	0.411936i	0.537143	−	0.843491i	$-0.319503\pi$
$5$	−0.816038	−	0.921117i	−0.364943	−	0.411936i	−0.902087	+	0.431555i	$0.857965\pi$
$6$	1.11379	−	0.135238i	0.454702	−	0.0552108i
$7$	0.328944	+	1.33458i	0.124329	+	0.504422i	0.999777	+	0.0211105i	$0.00672017\pi$
$7$	0.328944	+	1.33458i	0.124329	+	0.504422i	−0.875448	+	0.483312i	$0.839434\pi$
$8$	−0.669753	−	2.71730i	−0.236793	−	0.960709i
$9$	−0.730609	−	1.05847i	−0.243536	−	0.352823i
$10$	1.02401	+	0.252395i	0.323819	+	0.0798142i
$11$	−4.34079	−	2.99623i	−1.30880	−	0.903398i	−0.309920	−	0.950763i	$-0.600302\pi$
$11$	−4.34079	−	2.99623i	−1.30880	−	0.903398i	−0.998878	+	0.0473645i	$0.984918\pi$
$12$	1.24009	−	1.09862i	0.357983	−	0.317145i
$13$	−3.59110	−	0.322536i	−0.995991	−	0.0894554i
$13$	−3.59110	−	0.322536i	−0.995991	−	0.0894554i
$14$	−0.881740	−	0.781154i	−0.235655	−	0.208772i
$15$	0.385546	+	1.56422i	0.0995475	+	0.403880i
$16$	−0.0992110	−	0.0878933i	−0.0248028	−	0.0219733i
$17$	−1.38245	+	0.340744i	−0.335294	+	0.0826426i	−0.403368	−	0.915038i	$-0.632161\pi$
$17$	−1.38245	+	0.340744i	−0.335294	+	0.0826426i	0.0680743	+	0.997680i	$0.478315\pi$
$18$	1.03062	+	0.390862i	0.242919	+	0.0921272i
$19$			2.34458i			0.537885i	0.963156	+	0.268942i	$0.0866741\pi$
$19$			2.34458i			0.537885i	−0.963156	+	0.268942i	$0.913326\pi$
$20$	1.45614	−	0.552240i	0.325602	−	0.123485i
$21$	0.430635	−	1.74716i	0.0939723	−	0.381261i
$22$	4.52033			0.963737
$23$	1.57912			0.329269			0.164634	−	0.986355i	$-0.447356\pi$
$23$	1.57912			0.329269			0.164634	+	0.986355i	$0.447356\pi$
$24$	−0.876805	+	3.55734i	−0.178977	+	0.726138i
$25$	0.420146	−	3.46021i	0.0840291	−	0.692042i
$26$	2.68988	−	1.52082i	0.527529	−	0.298256i
$27$	0.676353	+	5.57027i	0.130164	+	1.07200i
$28$	−1.72679	−	0.209670i	−0.326332	−	0.0396239i
$29$	1.82071	+	2.63775i	0.338097	+	0.489818i	0.954747	−	0.297419i	$-0.0961260\pi$
$29$	1.82071	+	2.63775i	0.338097	+	0.489818i	−0.616650	+	0.787237i	$0.711511\pi$
$30$	−1.03346	−	0.915569i	−0.188684	−	0.167159i
$31$	−1.01979	+	0.123825i	−0.183159	+	0.0222396i	−0.211602	−	0.977356i	$-0.567868\pi$
$31$	−1.01979	+	0.123825i	−0.183159	+	0.0222396i	0.0284430	+	0.999595i	$0.490945\pi$
$32$	5.66919	+	0.688364i	1.00218	+	0.121687i
$33$	3.20893	+	6.11410i	0.558603	+	1.06433i
$34$	0.809177	−	0.913372i	0.138773	−	0.156642i
$35$	0.960870	−	1.39206i	0.162417	−	0.235301i
$36$	1.58032	−	0.389515i	0.263387	−	0.0649192i
$37$	−7.12219	+	0.864790i	−1.17088	+	0.142171i	−0.682785	−	0.730619i	$-0.739231\pi$
$37$	−7.12219	+	0.864790i	−1.17088	+	0.142171i	−0.488096	+	0.872790i	$0.662308\pi$
$38$	−1.14145	−	1.65367i	−0.185167	−	0.268261i
$39$	3.96654	+	2.55867i	0.635155	+	0.409715i
$40$	−1.95640	+	2.83434i	−0.309334	+	0.448148i
$41$	4.12376	−	7.85717i	0.644024	−	1.22708i	−0.316423	−	0.948618i	$-0.602482\pi$
$41$	4.12376	−	7.85717i	0.644024	−	1.22708i	0.960446	−	0.278466i	$-0.0898260\pi$
$42$	0.546859	+	1.44195i	0.0843822	+	0.222498i
$43$	−1.27272	+	10.4818i	−0.194089	+	1.59846i	0.491768	+	0.870726i	$0.336351\pi$
$43$	−1.27272	+	10.4818i	−0.194089	+	1.59846i	−0.685856	+	0.727737i	$0.740572\pi$
$44$	5.49332	−	3.79177i	0.828150	−	0.571631i
$45$	−0.378769	+	1.53673i	−0.0564636	+	0.229082i
$46$	−1.11378	+	0.768785i	−0.164217	+	0.113351i
$47$	−2.51425	+	0.953527i	−0.366740	+	0.139086i	−0.531089	−	0.847316i	$-0.678217\pi$
$47$	−2.51425	+	0.953527i	−0.366740	+	0.139086i	0.164349	+	0.986402i	$0.447448\pi$
$48$	0.0615311	+	0.162244i	0.00888125	+	0.0234179i
$49$	4.52530	−	2.37506i	0.646472	−	0.339295i
$50$	1.38825	+	2.64509i	0.196328	+	0.374072i
$51$	1.80983	+	0.446084i	0.253427	+	0.0624642i
$52$	1.99318	−	4.10451i	0.276404	−	0.569193i
$53$	−12.6191	+	3.11032i	−1.73336	+	0.427236i	−0.974568	−	0.224093i	$-0.928058\pi$
$53$	−12.6191	+	3.11032i	−1.73336	+	0.427236i	−0.758796	+	0.651329i	$0.774212\pi$
$54$	−3.18890	−	3.59952i	−0.433954	−	0.489833i
$55$	0.782372	+	6.44342i	0.105495	+	0.868830i
$56$	3.40613	−	1.78767i	0.455163	−	0.238888i
$57$	1.42642	−	2.71782i	0.188934	−	0.359984i
$58$	−2.56835	−	0.974046i	−0.337241	−	0.127899i
$59$	−0.113453	−	0.128062i	−0.0147703	−	0.0166722i	0.741079	−	0.671418i	$-0.234314\pi$
$59$	−0.113453	−	0.128062i	−0.0147703	−	0.0166722i	−0.755849	+	0.654745i	$0.772776\pi$
$60$	−2.02392	−	0.245748i	−0.261287	−	0.0317260i
$61$	4.08076	+	1.00582i	0.522488	+	0.128782i	0.491734	−	0.870745i	$-0.336363\pi$
$61$	4.08076	+	1.00582i	0.522488	+	0.128782i	0.0307536	+	0.999527i	$0.490209\pi$
$62$	0.658989	−	0.583813i	0.0836917	−	0.0741444i
$63$	1.17228	−	1.32323i	0.147693	−	0.166711i
$64$	−4.09897	+	2.15131i	−0.512372	+	0.268913i
$65$	2.63338	+	3.57102i	0.326630	+	0.442931i
$66$	−5.23993	−	2.75013i	−0.644990	−	0.338517i
$67$	1.30041	−	0.493179i	0.158870	−	0.0602514i	−0.273888	−	0.961762i	$-0.588310\pi$
$67$	1.30041	−	0.493179i	0.158870	−	0.0602514i	0.432758	+	0.901510i	$0.357541\pi$
$68$	0.217191	−	1.78873i	0.0263383	−	0.216916i
$69$	−1.83050	−	0.960721i	−0.220366	−	0.115657i
$70$			1.44964i			0.173265i
$71$	0.139794	−	0.266356i	0.0165905	−	0.0316106i	−0.877020	−	0.480454i	$-0.840472\pi$
$71$	0.139794	−	0.266356i	0.0165905	−	0.0316106i	0.893610	+	0.448844i	$0.148164\pi$
$72$	−2.38685	+	2.69419i	−0.281293	+	0.317514i
$73$	−9.71703	−	6.70718i	−1.13729	−	0.785016i	−0.157994	−	0.987440i	$-0.550503\pi$
$73$	−9.71703	−	6.70718i	−1.13729	−	0.785016i	−0.979298	+	0.202424i	$0.935118\pi$
$74$	4.60238	−	4.07735i	0.535015	−	0.473982i
$75$	−2.59219	+	3.75543i	−0.299320	+	0.433640i
$76$	−2.77429	−	1.05215i	−0.318232	−	0.120690i
$77$	2.57083	−	6.77871i	0.292973	−	0.772506i
$78$	−4.04334	+	0.126417i	−0.457818	+	0.0143139i
$79$	−1.34914	−	3.55738i	−0.151790	−	0.400237i	0.837455	−	0.546506i	$-0.184043\pi$
$79$	−1.34914	−	3.55738i	−0.151790	−	0.400237i	−0.989245	+	0.146269i	$0.953273\pi$
$80$			0.163109i			0.0182362i
$81$	1.23667	−	3.26082i	0.137407	−	0.362313i
$82$	0.916666	+	7.54942i	0.101229	+	0.833694i
$83$	−3.48415	−	6.63849i	−0.382435	−	0.728668i	0.615810	−	0.787895i	$-0.288829\pi$
$83$	−3.48415	−	6.63849i	−0.382435	−	0.728668i	−0.998245	+	0.0592263i	$0.981137\pi$
$84$	1.87411	+	1.29361i	0.204483	+	0.141144i
$85$	1.44200	+	0.995340i	0.156407	+	0.107960i
$86$	−4.20535	−	8.01262i	−0.453474	−	0.864023i
$87$	−0.505766	−	4.16536i	−0.0542238	−	0.446573i
$88$	−5.23439	+	13.8019i	−0.557988	+	1.47129i
$89$		−	13.0444i		−	1.38271i	−0.722516	−	0.691354i	$-0.757014\pi$
$89$		−	13.0444i		−	1.38271i	0.722516	−	0.691354i	$-0.242986\pi$
$90$	−0.480995	−	1.26828i	−0.0507013	−	0.133688i
$91$	−0.750819	−	4.89869i	−0.0787072	−	0.513522i
$92$	−0.708640	+	1.86853i	−0.0738808	+	0.194808i
$93$	1.25746	+	0.476893i	0.130393	+	0.0494515i
$94$	1.30912	−	1.89658i	0.135025	−	0.195618i
$95$	2.15964	−	1.91327i	0.221574	−	0.196297i
$96$	−6.15288	−	4.24703i	−0.627976	−	0.433461i
$97$	9.44318	−	10.6591i	0.958810	−	1.08227i	−0.0377413	−	0.999288i	$-0.512016\pi$
$97$	9.44318	−	10.6591i	0.958810	−	1.08227i	0.996551	−	0.0829847i	$-0.0264453\pi$
$98$	−2.03548	+	3.87829i	−0.205615	+	0.391766i
$99$			6.78367i			0.681784i
$100$	3.90584	+	2.04994i	0.390584	+	0.204994i
$101$	0.745451	−	6.13934i	0.0741752	−	0.610887i	−0.907463	−	0.420133i	$-0.861983\pi$
$101$	0.745451	−	6.13934i	0.0741752	−	0.610887i	0.981638	−	0.190755i	$-0.0610935\pi$
$102$	−1.49368	+	0.566477i	−0.147896	+	0.0560896i
$103$	12.7157	+	6.67373i	1.25292	+	0.657582i	0.954886	−	0.296974i	$-0.0959775\pi$
$103$	12.7157	+	6.67373i	1.25292	+	0.657582i	0.298032	+	0.954556i	$0.403670\pi$
$104$	1.52872	+	9.97409i	0.149904	+	0.978040i
$105$	−1.96075	+	1.02908i	−0.191350	+	0.100428i
$106$	7.38619	−	8.33729i	0.717410	−	0.809789i
$107$	4.74075	−	4.19994i	0.458306	−	0.406023i	−0.402130	−	0.915583i	$-0.631730\pi$
$107$	4.74075	−	4.19994i	0.458306	−	0.406023i	0.860436	+	0.509559i	$0.170192\pi$
$108$	−6.89467	−	1.69938i	−0.663440	−	0.163523i
$109$	−18.6416	−	2.26350i	−1.78555	−	0.216804i	−0.840065	−	0.542485i	$-0.817483\pi$
$109$	−18.6416	−	2.26350i	−1.78555	−	0.216804i	−0.945480	+	0.325681i	$0.894407\pi$
$110$	−3.68876	−	4.16375i	−0.351710	−	0.396998i
$111$	8.78211	+	3.33062i	0.833561	+	0.316128i
$112$	0.0846655	−	0.161317i	0.00800014	−	0.0152430i
$113$	−6.74761	+	3.54142i	−0.634761	+	0.333148i	−0.751225	−	0.660047i	$-0.770537\pi$
$113$	−6.74761	+	3.54142i	−0.634761	+	0.333148i	0.116463	+	0.993195i	$0.462844\pi$
$114$	0.317078	+	2.61137i	0.0296970	+	0.244577i
$115$	−1.28862	−	1.45455i	−0.120164	−	0.135638i
$116$	−3.93824	+	0.970688i	−0.365656	+	0.0901261i
$117$	2.28229	+	4.03671i	0.210998	+	0.373194i
$118$	0.142366	+	0.0350901i	0.0131059	+	0.00323031i
$119$	−0.909498	−	1.73290i	−0.0833735	−	0.158855i
$120$	3.99223	−	2.09528i	0.364439	−	0.191272i
$121$	5.96441	+	15.7269i	0.542219	+	1.42971i
$122$	−3.36790	+	1.27728i	−0.304915	+	0.115639i
$123$	−9.56046	+	6.59911i	−0.862038	+	0.595022i
$124$	0.311118	−	1.26226i	0.0279392	−	0.113354i
$125$	−8.59393	+	5.93196i	−0.768665	+	0.530571i
$126$	−0.182620	+	1.50401i	−0.0162691	+	0.133988i
$127$	3.98296	+	10.5022i	0.353431	+	0.931921i	0.987355	+	0.158525i	$0.0506740\pi$
$127$	3.98296	+	10.5022i	0.353431	+	0.931921i	−0.633924	+	0.773395i	$0.718557\pi$
$128$	−3.46419	+	6.60046i	−0.306194	+	0.583404i
$129$	7.85237	−	11.3761i	0.691363	−	1.00161i
$130$	−3.59590	−	1.23665i	−0.315381	−	0.108462i
$131$	5.00543	+	7.25161i	0.437326	+	0.633577i	0.978234	−	0.207506i	$-0.0665345\pi$
$131$	5.00543	+	7.25161i	0.437326	+	0.633577i	−0.540908	+	0.841082i	$0.681919\pi$
$132$	−8.67469	+	1.05330i	−0.755035	+	0.0916778i
$133$	−3.12903	+	0.771236i	−0.271321	+	0.0668746i
$134$	−0.677095	+	0.980942i	−0.0584921	+	0.0847405i
$135$	4.57894	−	5.16855i	0.394092	−	0.444838i
$136$	1.85180	+	3.52832i	0.158791	+	0.302551i
$137$	−15.0864	−	1.83182i	−1.28891	−	0.156503i	−0.552774	−	0.833331i	$-0.686431\pi$
$137$	−15.0864	−	1.83182i	−1.28891	−	0.156503i	−0.736141	+	0.676829i	$0.763354\pi$
$138$	1.75880	−	0.213557i	0.149719	−	0.0181792i
$139$	−3.48418	−	3.08672i	−0.295525	−	0.261812i	0.502311	−	0.864687i	$-0.332483\pi$
$139$	−3.48418	−	3.08672i	−0.295525	−	0.261812i	−0.797836	+	0.602875i	$0.794022\pi$
$140$	1.21599	+	1.76167i	0.102770	+	0.148888i
$141$	3.49461	+	0.424322i	0.294299	+	0.0357344i
$142$	0.0310747	+	0.255923i	0.00260773	+	0.0214766i
$143$	14.6218	+	12.1598i	1.22274	+	1.01686i
$144$	−0.0205479	+	0.169227i	−0.00171233	+	0.0141023i
$145$	0.943909	−	3.82959i	0.0783874	−	0.318030i
$146$	10.1189			0.837449
$147$	−6.69066			−0.551836
$148$	2.17285	−	8.81558i	0.178607	−	0.724637i
$149$	18.7258	−	7.10175i	1.53407	−	0.581798i	0.564251	−	0.825603i	$-0.309165\pi$
$149$	18.7258	−	7.10175i	1.53407	−	0.581798i	0.969824	+	0.243806i	$0.0783959\pi$
$150$		−	3.91076i		−	0.319312i
$151$	2.84856	+	1.08031i	0.231812	+	0.0879148i	0.467776	−	0.883847i	$-0.345055\pi$
$151$	2.84856	+	1.08031i	0.231812	+	0.0879148i	−0.235964	+	0.971762i	$0.575825\pi$
$152$	6.37093	−	1.57029i	0.516751	−	0.127368i
$153$	1.37070	+	1.21433i	0.110814	+	0.0981730i
$154$	1.48693	+	6.03272i	0.119820	+	0.486131i
$155$	0.946243	+	0.838298i	0.0760040	+	0.0673337i
$156$	−4.80762	+	3.54528i	−0.384918	+	0.283850i
$157$	8.28092	−	7.33626i	0.660890	−	0.585497i	−0.264559	−	0.964369i	$-0.585226\pi$
$157$	8.28092	−	7.33626i	0.660890	−	0.585497i	0.925449	+	0.378872i	$0.123688\pi$
$158$	2.68346	+	1.85226i	0.213485	+	0.147358i
$159$	16.5202	+	4.07187i	1.31014	+	0.322920i
$160$	−3.99221	−	5.78372i	−0.315612	−	0.457243i
$161$	0.519441	+	2.10745i	0.0409377	+	0.166091i
$162$	0.715272	+	2.90197i	0.0561970	+	0.228000i
$163$	−1.05453	+	0.128043i	−0.0825973	+	0.0100291i	−0.161731	−	0.986835i	$-0.551708\pi$
$163$	−1.05453	+	0.128043i	−0.0825973	+	0.0100291i	0.0791337	+	0.996864i	$0.474785\pi$
$164$	7.44663	+	8.40550i	0.581484	+	0.656359i
$165$	3.01319	−	7.94514i	0.234577	−	0.618528i
$166$	5.68933	+	2.98599i	0.441578	+	0.231758i
$167$	−5.03142	+	3.47294i	−0.389343	+	0.268744i	−0.746615	−	0.665256i	$-0.768322\pi$
$167$	−5.03142	+	3.47294i	−0.389343	+	0.268744i	0.357272	+	0.934000i	$0.383707\pi$
$168$	−5.03596			−0.388533
$169$	12.7919	+	2.31652i	0.983995	+	0.178194i
$170$	−1.50164			−0.115171
$171$	2.48167	−	1.71297i	0.189778	−	0.130994i
$172$	−11.8317	−	6.20977i	−0.902161	−	0.473491i
$173$	−1.38930	+	3.66329i	−0.105627	+	0.278515i	−0.977401	−	0.211393i	$-0.932200\pi$
$173$	−1.38930	+	3.66329i	−0.105627	+	0.278515i	0.871775	+	0.489907i	$0.162969\pi$
$174$	2.38461	+	2.69166i	0.180777	+	0.204055i
$175$	4.75612	−	0.577498i	0.359529	−	0.0436547i
$176$	0.167306	+	0.678786i	0.0126111	+	0.0511654i
$177$	0.0536020	+	0.217472i	0.00402897	+	0.0163462i
$178$	6.35061	+	9.20045i	0.475999	+	0.689603i
$179$	−16.1617	−	3.98349i	−1.20798	−	0.297740i	−0.416614	−	0.909083i	$-0.636783\pi$
$179$	−16.1617	−	3.98349i	−1.20798	−	0.297740i	−0.791366	+	0.611343i	$0.790630\pi$
$180$	−1.64839	−	1.13780i	−0.122864	−	0.0848069i
$181$	15.0086	−	13.2964i	1.11558	−	0.988316i	0.115590	−	0.993297i	$-0.463124\pi$
$181$	15.0086	−	13.2964i	1.11558	−	0.988316i	0.999988	+	0.00498121i	$0.00158558\pi$
$182$	2.91446	+	3.08959i	0.216034	+	0.229016i
$183$	−4.11845	−	3.64863i	−0.304445	−	0.269715i
$184$	−1.05762	−	4.29093i	−0.0779687	−	0.316332i
$185$	6.60855	+	5.85467i	0.485870	+	0.430444i
$186$	−1.11908	+	0.275829i	−0.0820550	+	0.0202247i
$187$	7.02189	+	2.66305i	0.513491	+	0.194742i
$188$		−	3.40294i		−	0.248185i
$189$	−7.21147	+	2.73495i	−0.524557	+	0.198938i
$190$	−0.591761	+	2.40087i	−0.0429308	+	0.174177i
$191$	−24.0502			−1.74021			−0.870107	−	0.492864i	$-0.835950\pi$
$191$	−24.0502			−1.74021			−0.870107	+	0.492864i	$0.835950\pi$
$192$	6.06033			0.437367
$193$	−0.380703	+	1.54457i	−0.0274036	+	0.111181i	−0.983051	−	0.183333i	$-0.941311\pi$
$193$	−0.380703	+	1.54457i	−0.0274036	+	0.111181i	0.955647	+	0.294513i	$0.0951576\pi$
$194$	−1.47108	+	12.1154i	−0.105617	+	0.869837i
$195$	−0.880014	−	5.74162i	−0.0630191	−	0.411166i
$196$	0.779590	+	6.42050i	0.0556850	+	0.458607i
$197$	6.38479	+	0.775254i	0.454898	+	0.0552346i	0.344779	−	0.938684i	$-0.387954\pi$
$197$	6.38479	+	0.775254i	0.454898	+	0.0552346i	0.110119	+	0.993918i	$0.464877\pi$
$198$	−3.30259	−	4.78463i	−0.234705	−	0.340029i
$199$	−18.0565	−	15.9967i	−1.27999	−	1.13397i	−0.983882	−	0.178820i	$-0.942772\pi$
$199$	−18.0565	−	15.9967i	−1.27999	−	1.13397i	−0.296110	−	0.955154i	$-0.595690\pi$
$200$	−9.68381	+	1.17583i	−0.684749	+	0.0831436i
$201$	−1.80746	−	0.219466i	−0.127489	−	0.0154799i
$202$	2.46313	+	4.69309i	0.173305	+	0.330205i
$203$	−2.92137	+	3.29754i	−0.205040	+	0.231442i
$204$	−1.34001	+	1.94135i	−0.0938198	+	0.135921i
$205$	−10.6025	+	2.61329i	−0.740512	+	0.182520i
$206$	−12.2177	+	1.48349i	−0.851245	+	0.103360i
$207$	−1.15372	−	1.67145i	−0.0801889	−	0.116174i
$208$	0.327928	+	0.347632i	0.0227377	+	0.0241040i
$209$	7.02492	−	10.1774i	0.485924	−	0.703982i
$210$	0.881946	−	1.68041i	0.0608600	−	0.115959i
$211$	1.31360	+	3.46368i	0.0904320	+	0.238450i	0.972600	−	0.232485i	$-0.0746858\pi$
$211$	1.31360	+	3.46368i	0.0904320	+	0.238450i	−0.882168	+	0.470935i	$0.843917\pi$
$212$	1.98253	−	16.3276i	0.136161	−	1.12138i
$213$	−0.324097	+	0.223708i	−0.0222067	+	0.0153282i
$214$	−1.29901	+	5.27029i	−0.0887985	+	0.360270i
$215$	10.6936	−	7.38124i	0.729296	−	0.503397i
$216$	14.6831	−	5.56855i	0.999056	−	0.378892i
$217$	−0.500706	−	1.32025i	−0.0339901	−	0.0896246i
$218$	14.2502	−	7.47909i	0.965147	−	0.506548i
$219$	7.18331	+	13.6867i	0.485403	+	0.924859i
$220$	−7.97542	−	1.96577i	−0.537703	−	0.132532i
$221$	5.07442	−	0.777754i	0.341343	−	0.0523174i
$222$	−7.81566	+	1.92639i	−0.524552	+	0.129291i
$223$	−9.63494	−	10.8756i	−0.645203	−	0.728284i	0.331363	−	0.943503i	$-0.392492\pi$
$223$	−9.63494	−	10.8756i	−0.645203	−	0.728284i	−0.976566	+	0.215220i	$0.930953\pi$
$224$	0.946169	+	7.79240i	0.0632186	+	0.520652i
$225$	−3.96949	+	2.08335i	−0.264633	+	0.138890i
$226$	3.03507	−	5.78285i	0.201890	−	0.384670i
$227$	−13.8397	−	5.24870i	−0.918572	−	0.348368i	−0.150410	−	0.988624i	$-0.548059\pi$
$227$	−13.8397	−	5.24870i	−0.918572	−	0.348368i	−0.768162	+	0.640256i	$0.778828\pi$
$228$	2.57581	+	2.90749i	0.170587	+	0.192553i
$229$	−4.65623	−	0.565369i	−0.307692	−	0.0373606i	−0.0347658	−	0.999395i	$-0.511069\pi$
$229$	−4.65623	−	0.565369i	−0.307692	−	0.0373606i	−0.272927	+	0.962035i	$0.587992\pi$
$230$	1.61703	+	0.398561i	0.106623	+	0.0262803i
$231$	−7.10418	+	6.29376i	−0.467421	+	0.414099i
$232$	5.94812	−	6.71404i	0.390513	−	0.440799i
$233$	−22.0110	+	11.5523i	−1.44199	+	0.756814i	−0.990764	−	0.135596i	$-0.956705\pi$
$233$	−22.0110	+	11.5523i	−1.44199	+	0.756814i	−0.451225	+	0.892410i	$0.649013\pi$
$234$	−3.57499	−	1.73604i	−0.233704	−	0.113488i
$235$	2.93003	+	1.53780i	0.191134	+	0.100315i
$236$	0.202445	−	0.0767772i	0.0131780	−	0.00499777i
$237$	−0.600370	+	4.94449i	−0.0389982	+	0.321179i
$238$	1.48514	+	0.779460i	0.0962672	+	0.0505249i
$239$			15.0037i			0.970509i	0.874373	+	0.485255i	$0.161273\pi$
$239$			15.0037i			0.970509i	−0.874373	+	0.485255i	$0.838727\pi$
$240$	0.0992341	−	0.189075i	0.00640554	−	0.0122047i
$241$	−10.5874	+	11.9507i	−0.681997	+	0.769815i	−0.982960	−	0.183821i	$-0.941153\pi$
$241$	−10.5874	+	11.9507i	−0.681997	+	0.769815i	0.300963	+	0.953636i	$0.402692\pi$
$242$	−11.8633	−	8.18866i	−0.762604	−	0.526387i
$243$	9.18270	−	8.13516i	0.589070	−	0.521871i
$244$	−3.02143	+	4.37729i	−0.193427	+	0.280227i
$245$	−5.88053	−	2.23019i	−0.375693	−	0.142482i
$246$	3.53041	−	9.30891i	0.225090	−	0.593515i
$247$	0.756213	−	8.41963i	0.0481167	−	0.535728i
$248$	1.01947	+	2.68813i	0.0647367	+	0.170697i
$249$			9.81500i			0.622000i
$250$	3.17349	−	8.36781i	0.200709	−	0.529227i
$251$	−0.931171	−	7.66888i	−0.0587750	−	0.484056i	−0.992141	−	0.125128i	$-0.960066\pi$
$251$	−0.931171	−	7.66888i	−0.0587750	−	0.484056i	0.933366	−	0.358927i	$-0.116857\pi$
$252$	1.03968	+	1.98094i	0.0654934	+	0.124787i
$253$	−6.85462	−	4.73140i	−0.430946	−	0.297461i
$254$	−7.92219	−	5.46830i	−0.497083	−	0.343111i
$255$	−1.06600	−	2.03109i	−0.0667554	−	0.127192i
$256$	−1.88603	−	15.5329i	−0.117877	−	0.970805i
$257$	−0.646124	+	1.70369i	−0.0403041	+	0.106273i	−0.953657	−	0.300895i	$-0.902715\pi$
$257$	−0.646124	+	1.70369i	−0.0403041	+	0.106273i	0.913353	+	0.407168i	$0.133484\pi$
$258$			11.8466i			0.737540i
$259$	−3.49693	−	9.22064i	−0.217289	−	0.572943i
$260$	−5.40724	+	1.51349i	−0.335343	+	0.0938626i
$261$	1.46175	−	3.85433i	0.0904802	−	0.238577i
$262$	−7.06082	−	2.67781i	−0.436219	−	0.165436i
$263$	−1.19139	+	1.72602i	−0.0734640	+	0.106431i	−0.857994	−	0.513660i	$-0.828289\pi$
$263$	−1.19139	+	1.72602i	−0.0734640	+	0.106431i	0.784530	+	0.620091i	$0.212905\pi$
$264$	14.4646	−	12.8145i	0.890237	−	0.788681i
$265$	13.1626	+	9.08550i	0.808573	+	0.558118i
$266$	1.83148	−	2.06731i	0.112295	−	0.126755i
$267$	−7.93612	+	15.1210i	−0.485682	+	0.925391i
$268$			1.76005i			0.107512i
$269$	18.5421	+	9.73162i	1.13053	+	0.593348i	0.922969	−	0.384875i	$-0.125755\pi$
$269$	18.5421	+	9.73162i	1.13053	+	0.593348i	0.207561	+	0.978222i	$0.433448\pi$
$270$	−0.713317	+	5.87469i	−0.0434111	+	0.357522i
$271$	21.1300	−	8.01356i	1.28356	−	0.486789i	0.383895	−	0.923377i	$-0.374582\pi$
$271$	21.1300	−	8.01356i	1.28356	−	0.486789i	0.899662	+	0.436588i	$0.143813\pi$
$272$	0.167104	+	0.0877028i	0.0101321	+	0.00531776i
$273$	−2.10997	+	6.13531i	−0.127701	+	0.371326i
$274$	11.5325	−	6.05270i	0.696701	−	0.365657i
$275$	−12.1914	+	13.7612i	−0.735167	+	0.829832i
$276$	1.95825	−	1.73485i	0.117873	−	0.104426i
$277$	19.5112	+	4.80909i	1.17232	+	0.288950i	0.776943	−	0.629570i	$-0.216769\pi$
$277$	19.5112	+	4.80909i	1.17232	+	0.288950i	0.395373	+	0.918521i	$0.370615\pi$
$278$	3.96020	+	0.480856i	0.237517	+	0.0288398i
$279$	0.876130	+	0.988946i	0.0524525	+	0.0592067i
$280$	−4.42619	−	1.67863i	−0.264515	−	0.100317i
$281$	6.12159	−	11.6637i	0.365183	−	0.695799i	−0.631656	−	0.775249i	$-0.717624\pi$
$281$	6.12159	−	11.6637i	0.365183	−	0.695799i	0.996839	+	0.0794506i	$0.0253166\pi$
$282$	−2.67138	+	1.40205i	−0.159078	+	0.0834908i
$283$	−3.14048	−	25.8642i	−0.186682	−	1.53747i	−0.721449	−	0.692468i	$-0.756523\pi$
$283$	−3.14048	−	25.8642i	−0.186682	−	1.53747i	0.534766	−	0.845000i	$-0.320400\pi$
$284$	0.252438	+	0.284944i	0.0149795	+	0.0169083i
$285$	−3.66745	+	0.903945i	−0.217241	+	0.0535451i
$286$	−16.2329	−	1.45797i	−0.959873	−	0.0862115i
$287$	11.8425	+	2.91891i	0.699040	+	0.172298i
$288$	−3.41335	−	6.50359i	−0.201133	−	0.383228i
$289$	−13.2577	+	6.95817i	−0.779864	+	0.409304i
$290$	1.19866	+	3.16061i	0.0703878	+	0.185597i
$291$	−17.4314	+	6.61085i	−1.02185	+	0.387535i
$292$	12.2970	−	8.48802i	0.719629	−	0.496724i
$293$	0.920275	−	3.73370i	0.0537630	−	0.218125i	−0.937916	−	0.346864i	$-0.887247\pi$
$293$	0.920275	−	3.73370i	0.0537630	−	0.218125i	0.991679	+	0.128739i	$0.0410928\pi$
$294$	4.71903	−	3.25731i	0.275219	−	0.189970i
$295$	−0.0253780	+	0.209007i	−0.00147756	+	0.0121688i
$296$	7.12000	+	18.7739i	0.413842	+	1.09121i
$297$	13.7539	−	26.2059i	0.798083	−	1.52062i
$298$	−9.75014	+	14.1255i	−0.564810	+	0.818269i
$299$	−5.67076	−	0.509322i	−0.327949	−	0.0294549i
$300$	−3.28045	−	4.75255i	−0.189397	−	0.274388i
$301$	−14.4075	+	1.74938i	−0.830432	+	0.100833i
$302$	−2.53508	+	0.624840i	−0.145877	+	0.0359555i
$303$	−4.59924	+	6.66315i	−0.264219	+	0.382788i
$304$	0.206073	−	0.232609i	0.0118191	−	0.0133410i
$305$	−2.40358	−	4.57964i	−0.137629	−	0.262230i
$306$	−1.55797	−	0.189171i	−0.0890631	−	0.0108142i
$307$	−7.57460	+	0.919723i	−0.432305	+	0.0524914i	−0.333797	−	0.942645i	$-0.608330\pi$
$307$	−7.57460	+	0.919723i	−0.432305	+	0.0524914i	−0.0985081	+	0.995136i	$0.531407\pi$
$308$	6.86740	+	6.08398i	0.391306	+	0.346667i
$309$	−10.6797	−	15.4723i	−0.607548	−	0.880186i
$310$	−1.07552	−	0.130592i	−0.0610855	−	0.00741712i
$311$	0.878368	+	7.23401i	0.0498077	+	0.410203i	0.996194	+	0.0871657i	$0.0277810\pi$
$311$	0.878368	+	7.23401i	0.0498077	+	0.410203i	−0.946386	+	0.323038i	$0.895296\pi$
$312$	4.29606	−	12.4919i	0.243216	−	0.707217i
$313$	−0.352797	+	2.90555i	−0.0199413	+	0.164231i	−0.999277	−	0.0380080i	$-0.987899\pi$
$313$	−0.352797	+	2.90555i	−0.0199413	+	0.164231i	0.979336	+	0.202239i	$0.0648218\pi$
$314$	−2.26905	+	9.20590i	−0.128050	+	0.519519i
$315$	−2.17547			−0.122574
$316$	4.81480			0.270853
$317$	0.409079	−	1.65970i	0.0229762	−	0.0932180i	−0.958334	−	0.285649i	$-0.907791\pi$
$317$	0.409079	−	1.65970i	0.0229762	−	0.0932180i	0.981311	+	0.192431i	$0.0616371\pi$
$318$	−13.6343	+	5.17082i	−0.764576	+	0.289965i
$319$		−	16.9052i		−	0.946509i
$320$	5.32652	+	2.02008i	0.297762	+	0.112926i
$321$	−8.05064	+	1.98430i	−0.449343	+	0.110753i
$322$	−1.39237	−	1.23353i	−0.0775938	−	0.0687421i
$323$	−0.798903	−	3.24128i	−0.0444522	−	0.180350i
$324$	3.30348	+	2.92663i	0.183527	+	0.162590i
$325$	−2.62483	+	12.2904i	−0.145599	+	0.681751i
$326$	0.681440	−	0.603704i	0.0377415	−	0.0334360i
$327$	20.2321	+	13.9652i	1.11884	+	0.772279i
$328$	−24.1122	−	5.94311i	−1.33137	−	0.328154i
$329$	−2.09960	−	3.04180i	−0.115755	−	0.167700i
$330$	1.74279	+	7.07079i	0.0959376	+	0.389234i
$331$	4.00948	+	16.2671i	0.220381	+	0.894121i	0.972087	+	0.234622i	$0.0753853\pi$
$331$	4.00948	+	16.2671i	0.220381	+	0.894121i	−0.751706	+	0.659499i	$0.770769\pi$
$332$	9.41868	−	1.14364i	0.516917	−	0.0627651i
$333$	6.11889	+	6.90680i	0.335313	+	0.378490i
$334$	1.85796	−	4.89904i	0.101663	−	0.268064i
$335$	−1.51546	−	0.795373i	−0.0827982	−	0.0434558i
$336$	−0.196287	+	0.135487i	−0.0107083	+	0.00739143i
$337$	14.4554			0.787434			0.393717	−	0.919232i	$-0.371189\pi$
$337$	14.4554			0.787434			0.393717	+	0.919232i	$0.371189\pi$
$338$	−10.1501	+	4.59381i	−0.552095	+	0.249870i
$339$	9.97633			0.541840
$340$	−1.82487	+	1.25962i	−0.0989673	+	0.0683122i
$341$	4.79769	+	2.51802i	0.259810	+	0.136359i
$342$	−0.916410	+	2.41637i	−0.0495538	+	0.130663i
$343$	11.0386	+	12.4600i	0.596028	+	0.672776i
$344$	29.3346	−	3.56187i	1.58162	−	0.192043i
$345$	0.608822	+	2.47009i	0.0327779	+	0.132985i
$346$	−0.803555	−	3.26015i	−0.0431994	−	0.175267i
$347$	−9.66833	−	14.0070i	−0.519023	−	0.751935i	0.472575	−	0.881290i	$-0.343324\pi$
$347$	−9.66833	−	14.0070i	−0.519023	−	0.751935i	−0.991598	+	0.129356i	$0.958709\pi$
$348$	5.15573	+	1.27077i	0.276376	+	0.0681206i
$349$	−3.98649	−	2.75167i	−0.213392	−	0.147294i	0.456575	−	0.889685i	$-0.349076\pi$
$349$	−3.98649	−	2.75167i	−0.213392	−	0.147294i	−0.669966	+	0.742391i	$0.733692\pi$
$350$	−3.07342	+	2.72281i	−0.164281	+	0.145540i
$351$	−0.632236	−	20.2215i	−0.0337463	−	1.07934i
$352$	−22.5463	−	19.9743i	−1.20172	−	1.06463i
$353$	7.10467	+	28.8248i	0.378143	+	1.53419i	0.784299	+	0.620383i	$0.213023\pi$
$353$	7.10467	+	28.8248i	0.378143	+	1.53419i	−0.406155	+	0.913804i	$0.633131\pi$
$354$	−0.143681	−	0.127290i	−0.00763657	−	0.00676541i
$355$	−0.359422	+	0.0885897i	−0.0190762	+	0.00470185i
$356$	15.4352	+	5.85378i	0.818061	+	0.310250i
$357$			2.56210i			0.135601i
$358$	13.3384	−	5.05860i	0.704958	−	0.267355i
$359$	−1.81147	+	7.34940i	−0.0956055	+	0.387887i	−0.999178	−	0.0405495i	$-0.987089\pi$
$359$	−1.81147	+	7.34940i	−0.0956055	+	0.387887i	0.903572	+	0.428436i	$0.140935\pi$
$360$	4.42942			0.233451
$361$	13.5029			0.710680
$362$	−4.11249	+	16.6850i	−0.216148	+	0.876945i
$363$	2.65418	−	21.8591i	0.139308	−	1.14731i
$364$	6.13343	+	1.30989i	0.321479	+	0.0686571i
$365$	1.75137	+	14.4238i	0.0916709	+	0.754978i
$366$	4.68113	+	0.568392i	0.244686	+	0.0297103i
$367$	1.91206	+	2.77010i	0.0998087	+	0.144598i	0.869706	−	0.493569i	$-0.164308\pi$
$367$	1.91206	+	2.77010i	0.0998087	+	0.144598i	−0.769898	+	0.638167i	$0.779693\pi$
$368$	−0.156666	−	0.138794i	−0.00816678	−	0.00723513i
$369$	−11.3294	+	1.37564i	−0.589787	+	0.0716131i
$370$	−7.51143	−	0.912053i	−0.390501	−	0.0474154i
$371$	−8.30193	−	15.8180i	−0.431015	−	0.821230i
$372$	−1.12859	+	1.27391i	−0.0585147	+	0.0660494i
$373$	−2.04156	+	2.95771i	−0.105708	+	0.153144i	−0.872268	−	0.489028i	$-0.837351\pi$
$373$	−2.04156	+	2.95771i	−0.105708	+	0.153144i	0.766560	+	0.642173i	$0.221967\pi$
$374$	−6.24914	+	1.54027i	−0.323135	+	0.0796457i
$375$	13.5710	−	1.64781i	0.700801	−	0.0850927i
$376$	4.27494	+	6.19332i	0.220463	+	0.319396i
$377$	−5.68757	−	10.0597i	−0.292925	−	0.518099i
$378$	3.75487	−	5.43986i	0.193130	−	0.279796i
$379$	−2.42977	+	4.62954i	−0.124809	+	0.237804i	−0.939841	−	0.341612i	$-0.889027\pi$
$379$	−2.42977	+	4.62954i	−0.124809	+	0.237804i	0.815032	+	0.579416i	$0.196719\pi$
$380$	1.29477	+	3.41403i	0.0664204	+	0.175136i
$381$	1.77243	−	14.5973i	0.0908044	−	0.747841i
$382$	16.9630	−	11.7087i	0.867903	−	0.599070i
$383$	−6.02520	+	24.4452i	−0.307873	+	1.24909i	0.589482	+	0.807782i	$0.299332\pi$
$383$	−6.02520	+	24.4452i	−0.307873	+	1.24909i	−0.897355	+	0.441309i	$0.854514\pi$
$384$	8.03132	−	5.54362i	0.409847	−	0.282897i
$385$	−8.34188	+	3.16366i	−0.425141	+	0.161235i
$386$	−0.483450	−	1.27475i	−0.0246070	−	0.0648833i
$387$	12.0246	−	6.31097i	0.611242	−	0.320805i
$388$	8.37500	+	15.9572i	0.425176	+	0.810106i
$389$	−28.8644	−	7.11444i	−1.46348	−	0.360716i	−0.574443	−	0.818544i	$-0.694781\pi$
$389$	−28.8644	−	7.11444i	−1.46348	−	0.360716i	−0.889041	+	0.457828i	$0.848628\pi$
$390$	3.41596	+	3.62123i	0.172974	+	0.183368i
$391$	−2.18306	+	0.538075i	−0.110402	+	0.0272116i
$392$	−9.48458	−	10.7059i	−0.479044	−	0.540728i
$393$	−1.39044	−	11.4513i	−0.0701382	−	0.577640i
$394$	−4.88072	+	2.56160i	−0.245887	+	0.129052i
$395$	−2.17582	+	4.14568i	−0.109477	+	0.208592i
$396$	−8.02694	−	3.04422i	−0.403369	−	0.152978i
$397$	−0.668512	−	0.754595i	−0.0335517	−	0.0378720i	0.731495	−	0.681846i	$-0.238823\pi$
$397$	−0.668512	−	0.754595i	−0.0335517	−	0.0378720i	−0.765047	+	0.643974i	$0.777284\pi$
$398$	20.5234	+	2.49200i	1.02875	+	0.124912i
$399$	4.09635	+	1.00966i	0.205074	+	0.0505463i
$400$	−0.345812	+	0.306363i	−0.0172906	+	0.0153182i
$401$	6.86046	−	7.74386i	0.342595	−	0.386710i	−0.551808	−	0.833971i	$-0.686062\pi$
$401$	6.86046	−	7.74386i	0.342595	−	0.386710i	0.894404	+	0.447261i	$0.147600\pi$
$402$	1.38168	−	0.725161i	0.0689119	−	0.0361677i
$403$	3.70209	−	0.115748i	0.184414	−	0.00576581i
$404$	6.93000	+	3.63714i	0.344780	+	0.180955i
$405$	−4.01276	+	1.52184i	−0.199396	+	0.0756208i
$406$	0.455097	−	3.74806i	0.0225861	−	0.186013i
$407$	33.5071	+	17.5859i	1.66088	+	0.871699i
$408$		−	5.21662i		−	0.258261i
$409$	−7.89223	+	15.0374i	−0.390246	+	0.743551i	−0.998749	−	0.0500002i	$-0.984078\pi$
$409$	−7.89223	+	15.0374i	−0.390246	+	0.743551i	0.608504	+	0.793551i	$0.291770\pi$
$410$	6.20586	−	7.00497i	0.306486	−	0.345951i
$411$	16.3735	+	11.3018i	0.807646	+	0.557478i
$412$	−13.6031	+	12.0513i	−0.670177	+	0.593725i
$413$	0.133589	−	0.193537i	0.00657347	−	0.00952331i
$414$	1.62747	+	0.617218i	0.0799858	+	0.0303346i
$415$	−3.27162	+	8.62656i	−0.160598	+	0.423461i
$416$	−20.1366	−	4.30050i	−0.987277	−	0.210849i
$417$	2.16091	+	5.69784i	0.105820	+	0.279025i
$418$			10.5983i			0.518379i
$419$	0.336879	−	0.888277i	0.0164576	−	0.0433952i	−0.926536	−	0.376207i	$-0.877228\pi$
$419$	0.336879	−	0.888277i	0.0164576	−	0.0433952i	0.942993	+	0.332812i	$0.107997\pi$
$420$	−0.337785	−	2.78191i	−0.0164822	−	0.135743i
$421$	10.4205	+	19.8547i	0.507866	+	0.967657i	0.995514	+	0.0946169i	$0.0301626\pi$
$421$	10.4205	+	19.8547i	0.507866	+	0.967657i	−0.487648	+	0.873040i	$0.662145\pi$
$422$	−2.61278	−	1.80347i	−0.127188	−	0.0877915i
$423$	2.84621	+	1.96460i	0.138387	+	0.0955219i
$424$	16.9033	+	32.2066i	0.820898	+	1.56409i
$425$	0.598215	+	4.92674i	0.0290177	+	0.238982i
$426$	0.119680	−	0.315569i	0.00579850	−	0.0152894i
$427$			5.77694i			0.279566i
$428$	2.84224	+	7.49436i	0.137385	+	0.362253i
$429$	−9.55155	−	22.9913i	−0.461153	−	1.11003i
$430$	−3.94883	+	10.4122i	−0.190430	+	0.502122i
$431$	37.2776	+	14.1375i	1.79560	+	0.680981i	0.996849	+	0.0793179i	$0.0252742\pi$
$431$	37.2776	+	14.1375i	1.79560	+	0.680981i	0.798750	+	0.601663i	$0.205495\pi$
$432$	0.422488	−	0.612079i	0.0203269	−	0.0294487i
$433$	−20.5135	+	18.1734i	−0.985816	+	0.873357i	−0.991951	−	0.126624i	$-0.959586\pi$
$433$	−20.5135	+	18.1734i	−0.985816	+	0.873357i	0.00613481	+	0.999981i	$0.498047\pi$
$434$	0.995914	+	0.687430i	0.0478054	+	0.0329977i
$435$	−3.42406	+	3.86496i	−0.164171	+	0.185311i
$436$	11.0439	−	21.0424i	0.528907	−	1.00775i
$437$			3.70238i			0.177109i
$438$	−11.7298	−	6.15626i	−0.560470	−	0.294158i
$439$	3.83200	−	31.5594i	0.182892	−	1.50625i	−0.555297	−	0.831652i	$-0.687395\pi$
$439$	3.83200	−	31.5594i	0.182892	−	1.50625i	0.738188	−	0.674595i	$-0.235682\pi$
$440$	16.9847	−	6.44144i	0.809712	−	0.307083i
$441$	−5.82015	−	3.05465i	−0.277150	−	0.145460i
$442$	−3.20043	+	3.01902i	−0.152229	+	0.143600i
$443$	−0.462158	+	0.242559i	−0.0219578	+	0.0115243i	−0.475666	−	0.879626i	$-0.657793\pi$
$443$	−0.462158	+	0.242559i	−0.0219578	+	0.0115243i	0.453709	+	0.891150i	$0.350101\pi$
$444$	−7.88206	+	8.89701i	−0.374066	+	0.422233i
$445$	−12.0155	+	10.6448i	−0.569587	+	0.504610i
$446$	12.0904	+	2.98001i	0.572497	+	0.141108i
$447$	−26.0274	−	3.16030i	−1.23105	−	0.149477i
$448$	−4.21941	−	4.76273i	−0.199349	−	0.225018i
$449$	−11.6061	−	4.40161i	−0.547725	−	0.207725i	0.0651909	−	0.997873i	$-0.479234\pi$
$449$	−11.6061	−	4.40161i	−0.547725	−	0.207725i	−0.612916	+	0.790148i	$0.710004\pi$
$450$	1.78548	−	3.40194i	0.0841682	−	0.160369i
$451$	−41.4423	+	21.7506i	−1.95144	+	1.02420i
$452$	−1.16243	−	9.57350i	−0.0546763	−	0.450300i
$453$	−2.64477	−	2.98533i	−0.124262	−	0.140263i
$454$	12.3166	−	3.03578i	0.578049	−	0.142476i
$455$	−3.89957	+	4.68911i	−0.182815	+	0.219829i
$456$	−8.34048	−	2.05574i	−0.390579	−	0.0962690i
$457$	−8.28304	−	15.7820i	−0.387464	−	0.738251i	0.611115	−	0.791542i	$-0.290721\pi$
$457$	−8.28304	−	15.7820i	−0.387464	−	0.738251i	−0.998579	+	0.0532907i	$0.983029\pi$
$458$	3.55936	−	1.86810i	0.166318	−	0.0872904i
$459$	−2.83306	−	7.47017i	−0.132236	−	0.348678i
$460$	2.29941	−	0.872052i	0.107211	−	0.0406596i
$461$	−5.54616	+	3.82824i	−0.258310	+	0.178299i	−0.690181	−	0.723637i	$-0.742469\pi$
$461$	−5.54616	+	3.82824i	−0.258310	+	0.178299i	0.431871	+	0.901936i	$0.357854\pi$
$462$	1.94661	−	7.89772i	0.0905646	−	0.367435i
$463$	31.5005	−	21.7432i	1.46395	−	1.01049i	0.472314	−	0.881430i	$-0.343419\pi$
$463$	31.5005	−	21.7432i	1.46395	−	1.01049i	0.991636	−	0.129062i	$-0.0411967\pi$
$464$	0.0512063	−	0.421722i	0.00237719	−	0.0195780i
$465$	−0.586864	−	1.54743i	−0.0272152	−	0.0717605i
$466$	9.90055	−	18.8639i	0.458634	−	0.873855i
$467$	−19.8196	+	28.7136i	−0.917140	+	1.32871i	0.0271631	+	0.999631i	$0.491353\pi$
$467$	−19.8196	+	28.7136i	−0.917140	+	1.32871i	−0.944303	+	0.329076i	$0.893263\pi$
$468$	−5.80073	+	0.889074i	−0.268139	+	0.0410975i
$469$	1.08594	+	1.57326i	0.0501443	+	0.0726465i
$470$	−2.81527	+	0.341835i	−0.129859	+	0.0157677i
$471$	−14.0625	+	3.46609i	−0.647965	+	0.159709i
$472$	−0.271996	+	0.394055i	−0.0125196	+	0.0181378i
$473$	36.9306	−	41.6860i	1.69807	−	1.91673i
$474$	−1.98375	−	3.77972i	−0.0911166	−	0.173608i
$475$	8.11276	+	0.985067i	0.372239	+	0.0451980i
$476$	2.45864	−	0.298533i	0.112692	−	0.0136833i
$477$	12.5118	+	11.0845i	0.572875	+	0.507523i
$478$	−7.30447	−	10.5824i	−0.334099	−	0.484026i
$479$	−42.2209	−	5.12655i	−1.92912	−	0.234238i	−0.936063	−	0.351833i	$-0.885558\pi$
$479$	−42.2209	−	5.12655i	−1.92912	−	0.234238i	−0.993062	+	0.117595i	$0.962481\pi$
$480$	1.10898	+	9.13326i	0.0506177	+	0.416875i
$481$	25.8554	−	0.808383i	1.17890	−	0.0368591i
$482$	1.64933	−	13.5835i	0.0751251	−	0.618711i
$483$	0.680024	−	2.75897i	0.0309422	−	0.125537i
$484$	−21.2858			−0.967535
$485$	−17.5243			−0.795738
$486$	−2.51615	+	10.2084i	−0.114135	+	0.463063i
$487$	−7.23951	+	2.74558i	−0.328053	+	0.124414i	−0.513133	−	0.858309i	$-0.671515\pi$
$487$	−7.23951	+	2.74558i	−0.328053	+	0.124414i	0.185079	+	0.982724i	$0.440746\pi$
$488$		−	11.7623i		−	0.532453i
$489$	1.30030	+	0.493140i	0.0588018	+	0.0223006i
$490$	5.23339	−	1.28991i	0.236420	−	0.0582724i
$491$	−26.2828	−	23.2845i	−1.18613	−	1.05082i	−0.997635	−	0.0687406i	$-0.978102\pi$
$491$	−26.2828	−	23.2845i	−1.18613	−	1.05082i	−0.188491	−	0.982075i	$-0.560360\pi$
$492$	−3.51824	−	14.2740i	−0.158614	−	0.643524i
$493$	−3.41584	−	3.02617i	−0.153842	−	0.136292i
$494$	3.56568	+	6.30666i	0.160428	+	0.283750i
$495$	6.24855	−	5.53573i	0.280851	−	0.248813i
$496$	0.112058	+	0.0773477i	0.00503153	+	0.00347302i
$497$	0.401457	+	0.0989502i	0.0180078	+	0.00443852i
$498$	−4.77838	−	6.92267i	−0.214124	−	0.310212i
$499$	2.41408	+	9.79429i	0.108069	+	0.438453i	0.999903	−	0.0139094i	$-0.00442763\pi$
$499$	2.41408	+	9.79429i	0.108069	+	0.438453i	−0.891834	+	0.452362i	$0.850581\pi$
$500$	−3.16255	−	12.8310i	−0.141434	−	0.573819i
$501$	7.94529	−	0.964733i	0.354969	−	0.0431011i
$502$	4.39032	+	4.95565i	0.195950	+	0.221181i
$503$	2.61571	−	6.89706i	0.116629	−	0.307525i	−0.863972	−	0.503540i	$-0.832031\pi$
$503$	2.61571	−	6.89706i	0.116629	−	0.307525i	0.980601	+	0.196015i	$0.0628000\pi$
$504$	−4.38074	−	2.29919i	−0.195134	−	0.102414i
$505$	−6.26337	+	4.32329i	−0.278716	+	0.192384i
$506$	7.13813			0.317329
$507$	−13.4190	−	10.4678i	−0.595957	−	0.464891i
$508$	−14.2144			−0.630661
$509$	10.0284	−	6.92214i	0.444503	−	0.306818i	−0.324707	−	0.945815i	$-0.605266\pi$
$509$	10.0284	−	6.92214i	0.444503	−	0.306818i	0.769210	+	0.638996i	$0.220650\pi$
$510$	1.74069	+	0.913584i	0.0770790	+	0.0404542i
$511$	5.75489	−	15.1744i	0.254581	−	0.671276i
$512$	−0.993903	−	1.12188i	−0.0439247	−	0.0495808i
$513$	−13.0600	+	1.58577i	−0.576611	+	0.0700133i
$514$	−0.373710	−	1.51620i	−0.0164836	−	0.0668768i
$515$	−4.22924	−	17.1587i	−0.186362	−	0.756102i
$516$	9.93727	+	14.3966i	0.437464	+	0.633776i
$517$	13.7708	+	3.39420i	0.605639	+	0.149277i
$518$	6.95546	+	4.80100i	0.305605	+	0.210944i
$519$	3.83918	−	3.40121i	0.168521	−	0.149297i
$520$	7.93980	−	9.54737i	0.348183	−	0.418680i
$521$	6.81211	+	6.03500i	0.298444	+	0.264398i	0.799034	−	0.601286i	$-0.205345\pi$
$521$	6.81211	+	6.03500i	0.298444	+	0.264398i	−0.500590	+	0.865685i	$0.666883\pi$
$522$	0.845460	+	3.43016i	0.0370048	+	0.150134i
$523$	−24.4155	−	21.6302i	−1.06762	−	0.945825i	−0.0689576	−	0.997620i	$-0.521967\pi$
$523$	−24.4155	−	21.6302i	−1.06762	−	0.945825i	−0.998658	+	0.0517949i	$0.983506\pi$
$524$	−10.8269	+	2.66858i	−0.472974	+	0.116578i
$525$	−5.86460	−	2.22415i	−0.255952	−	0.0970698i
$526$		−	1.79741i		−	0.0783708i
$527$	1.36762	−	0.518668i	0.0595743	−	0.0225935i
$528$	0.219028	−	0.888630i	0.00953195	−	0.0386727i
$529$	−20.5064			−0.891582
$530$	−13.7070			−0.595395
$531$	−0.0526598	+	0.213649i	−0.00228524	+	0.00927159i
$532$	0.491588	−	4.04859i	0.0213131	−	0.175529i
$533$	−17.3431	+	26.8858i	−0.751211	+	1.16455i
$534$	−1.76411	−	14.5287i	−0.0763404	−	0.628720i
$535$	−7.73727	−	0.939474i	−0.334511	−	0.0406170i
$536$	−2.21106	−	3.20328i	−0.0955034	−	0.138361i
$537$	16.3110	+	14.4502i	0.703870	+	0.623574i
$538$	−17.8158	+	2.16323i	−0.768094	+	0.0932635i
$539$	−26.7596	−	3.24921i	−1.15262	−	0.139953i
$540$	4.06098	+	7.73756i	0.174757	+	0.332972i
$541$	−25.7412	+	29.0558i	−1.10670	+	1.24921i	−0.140871	+	0.990028i	$0.544990\pi$
$541$	−25.7412	+	29.0558i	−1.10670	+	1.24921i	−0.965830	+	0.259178i	$0.916548\pi$
$542$	−11.0020	+	15.9391i	−0.472575	+	0.684644i
$543$	−25.4872	+	6.28204i	−1.09376	+	0.269588i
$544$	−8.07195	+	0.980112i	−0.346082	+	0.0420219i
$545$	13.1273	+	19.0182i	0.562313	+	0.814652i
$546$	−1.49874	−	5.35456i	−0.0641403	−	0.229154i
$547$	24.1324	−	34.9619i	1.03183	−	1.49486i	0.171458	−	0.985191i	$-0.445152\pi$
$547$	24.1324	−	34.9619i	1.03183	−	1.49486i	0.860370	−	0.509670i	$-0.170232\pi$
$548$	8.93765	−	17.0293i	0.381797	−	0.727454i
$549$	−1.91681	−	5.05422i	−0.0818075	−	0.215709i
$550$	1.89920	−	15.6413i	0.0809820	−	0.666947i
$551$	−6.18443	+	4.26880i	−0.263466	+	0.181857i
$552$	−1.38458	+	5.61745i	−0.0589316	+	0.239095i
$553$	4.30381	−	2.97071i	0.183017	−	0.126327i
$554$	−16.1029	+	6.10701i	−0.684145	+	0.259462i
$555$	−4.09865	−	10.8073i	−0.173978	−	0.458743i
$556$	5.21599	−	2.73756i	0.221207	−	0.116098i
$557$	−4.57233	−	8.71184i	−0.193736	−	0.369133i	0.769139	−	0.639082i	$-0.220685\pi$
$557$	−4.57233	−	8.71184i	−0.193736	−	0.369133i	−0.962875	+	0.269949i	$0.912993\pi$
$558$	−1.09941	−	0.270981i	−0.0465418	−	0.0114715i
$559$	7.95124	−	37.2307i	0.336302	−	1.57469i
$560$	−0.217682	+	0.0536537i	−0.00919873	+	0.00226728i
$561$	−6.51954	−	7.35904i	−0.275255	−	0.310699i
$562$	1.36076	+	11.2069i	0.0574002	+	0.472733i
$563$	40.4314	−	21.2200i	1.70398	−	0.894318i	0.725434	−	0.688292i	$-0.241639\pi$
$563$	40.4314	−	21.2200i	1.70398	−	0.894318i	0.978547	−	0.206026i	$-0.0660531\pi$
$564$	−2.07032	+	3.94466i	−0.0871761	+	0.166100i
$565$	8.76836	+	3.32540i	0.368888	+	0.139901i
$566$	14.8069	+	16.7135i	0.622380	+	0.702521i
$567$	4.75860	+	0.577799i	0.199843	+	0.0242653i
$568$	−0.817395	−	0.201470i	−0.0342971	−	0.00845349i
$569$	5.24809	−	4.64940i	0.220011	−	0.194913i	−0.545917	−	0.837840i	$-0.683818\pi$
$569$	5.24809	−	4.64940i	0.220011	−	0.194913i	0.765928	+	0.642927i	$0.222280\pi$
$570$	2.14663	−	2.42304i	0.0899124	−	0.101490i
$571$	13.2488	−	6.95352i	0.554446	−	0.290996i	−0.164136	−	0.986438i	$-0.552484\pi$
$571$	13.2488	−	6.95352i	0.554446	−	0.290996i	0.718582	+	0.695442i	$0.244791\pi$
$572$	−20.9500	+	11.8448i	−0.875965	+	0.495256i
$573$	27.8788	+	14.6319i	1.16465	+	0.611258i
$574$	−9.77375	+	3.70669i	−0.407948	+	0.154714i
$575$	0.663460	−	5.46408i	0.0276682	−	0.227868i
$576$	5.27184	+	2.76687i	0.219660	+	0.115286i
$577$			40.2907i			1.67732i	0.544652	+	0.838662i	$0.316662\pi$
$577$			40.2907i			1.67732i	−0.544652	+	0.838662i	$0.683338\pi$
$578$	5.96331	−	11.3621i	0.248041	−	0.472603i
$579$	1.38101	−	1.55884i	0.0573928	−	0.0647831i
$580$	4.10787	+	2.83546i	0.170570	+	0.117736i
$581$	7.71348	−	6.83355i	0.320009	−	0.283503i
$582$	9.07617	−	13.1491i	0.376219	−	0.545048i
$583$	64.0960	+	24.3084i	2.65459	+	1.00675i
$584$	−11.7174	+	30.8962i	−0.484869	+	1.27849i
$585$	1.85585	−	5.39637i	0.0767298	−	0.223112i
$586$	1.16865	+	3.08147i	0.0482764	+	0.127294i
$587$			33.6048i			1.38702i	0.720449	+	0.693508i	$0.243936\pi$
$587$			33.6048i			1.38702i	−0.720449	+	0.693508i	$0.756064\pi$
$588$	3.00248	−	7.91688i	0.123820	−	0.326487i
$589$	−0.290317	−	2.39098i	−0.0119623	−	0.0985185i
$590$	−0.0838542	−	0.159771i	−0.00345222	−	0.00657766i
$591$	−6.92954	−	4.78311i	−0.285043	−	0.196751i
$592$	0.782609	+	0.540196i	0.0321650	+	0.0222019i
$593$	−11.3216	−	21.5715i	−0.464922	−	0.885836i	−0.999179	−	0.0405133i	$-0.987101\pi$
$593$	−11.3216	−	21.5715i	−0.464922	−	0.885836i	0.534257	−	0.845322i	$-0.320592\pi$
$594$	3.05734	+	25.1794i	0.125444	+	1.03312i
$595$	−0.854021	+	2.25187i	−0.0350115	+	0.0923176i
$596$			25.3447i			1.03816i
$597$	11.1987	+	29.5286i	0.458333	+	1.20853i
$598$	4.24764	−	2.40155i	0.173699	−	0.0982065i
$599$	−11.3243	+	29.8597i	−0.462698	+	1.22004i	0.477265	+	0.878759i	$0.341628\pi$
$599$	−11.3243	+	29.8597i	−0.462698	+	1.22004i	−0.939963	+	0.341276i	$0.889141\pi$
$600$	11.9408	+	4.52853i	0.487479	+	0.184876i
$601$	2.19752	−	3.18366i	0.0896388	−	0.129864i	−0.775599	−	0.631226i	$-0.782552\pi$
$601$	2.19752	−	3.18366i	0.0896388	−	0.129864i	0.865238	+	0.501362i	$0.167167\pi$
$602$	9.31013	−	8.24805i	0.379452	−	0.336166i
$603$	−1.47210	−	1.01612i	−0.0599486	−	0.0413795i
$604$	−2.55662	+	2.88582i	−0.104027	+	0.117423i
$605$	9.61909	−	18.3276i	0.391072	−	0.745125i
$606$		−	6.93874i		−	0.281867i
$607$	20.1689	+	10.5854i	0.818629	+	0.429650i	0.821404	−	0.570346i	$-0.193191\pi$
$607$	20.1689	+	10.5854i	0.818629	+	0.429650i	−0.00277517	+	0.999996i	$0.500883\pi$
$608$	−1.61393	+	13.2919i	−0.0654534	+	0.539058i
$609$	5.39262	−	2.04515i	0.218520	−	0.0828737i
$610$	3.92486	+	2.05992i	0.158913	+	0.0834039i
$611$	9.33644	−	2.61327i	0.377712	−	0.105722i
$612$	−2.05200	+	1.07697i	−0.0829472	+	0.0435340i
$613$	24.0162	−	27.1087i	0.970007	−	1.09491i	−0.0254480	−	0.999676i	$-0.508101\pi$
$613$	24.0162	−	27.1087i	0.970007	−	1.09491i	0.995455	−	0.0952352i	$-0.0303603\pi$
$614$	4.89473	−	4.33635i	0.197535	−	0.175001i
$615$	13.8803	+	3.42118i	0.559706	+	0.137955i
$616$	−20.1416	−	2.44563i	−0.811527	−	0.0985372i
$617$	−18.3810	−	20.7478i	−0.739990	−	0.835276i	0.251170	−	0.967943i	$-0.419185\pi$
$617$	−18.3810	−	20.7478i	−0.739990	−	0.835276i	−0.991161	+	0.132667i	$0.957646\pi$
$618$	15.0652	+	5.71346i	0.606010	+	0.229829i
$619$	14.6747	−	27.9602i	0.589824	−	1.12382i	−0.389407	−	0.921066i	$-0.627320\pi$
$619$	14.6747	−	27.9602i	0.589824	−	1.12382i	0.979231	−	0.202750i	$-0.0649878\pi$
$620$	−1.41657	+	0.743473i	−0.0568908	+	0.0298586i
$621$	1.06804	+	8.79611i	0.0428590	+	0.352976i
$622$	−4.14137	−	4.67464i	−0.166054	−	0.187436i
$623$	17.4088	−	4.29089i	0.697469	−	0.171911i
$624$	−0.168635	−	0.602481i	−0.00675078	−	0.0241185i
$625$	−4.44469	−	1.09552i	−0.177788	−	0.0438207i
$626$	−1.16572	−	2.22109i	−0.0465914	−	0.0887724i
$627$	−14.3350	+	7.52361i	−0.572486	+	0.300464i
$628$	4.96469	+	13.0908i	0.198113	+	0.522380i
$629$	9.55142	−	3.62238i	0.380840	−	0.144434i
$630$	1.53440	−	1.05912i	0.0611318	−	0.0421962i
$631$	−11.3476	+	46.0391i	−0.451742	+	1.83279i	0.0949878	+	0.995478i	$0.469719\pi$
$631$	−11.3476	+	46.0391i	−0.451742	+	1.83279i	−0.546729	+	0.837309i	$0.684127\pi$
$632$	−8.76288	+	6.04858i	−0.348568	+	0.240599i
$633$	0.584556	−	4.81425i	0.0232340	−	0.191349i
$634$	0.519485	+	1.36977i	0.0206314	+	0.0544005i
$635$	6.42351	−	12.2390i	0.254909	−	0.485689i
$636$	−12.2317	+	17.7207i	−0.485018	+	0.702670i
$637$	−17.0168	+	7.06950i	−0.674232	+	0.280104i
$638$	8.23020	+	11.9235i	0.325837	+	0.472056i
$639$	−0.384064	+	0.0466339i	−0.0151934	+	0.00184481i
$640$	8.90671	−	2.19531i	0.352069	−	0.0867771i
$641$	−13.8078	+	20.0041i	−0.545377	+	0.790115i	−0.994653	−	0.103278i	$-0.967067\pi$
$641$	−13.8078	+	20.0041i	−0.545377	+	0.790115i	0.449275	+	0.893393i	$0.351682\pi$
$642$	4.71220	−	5.31897i	0.185976	−	0.209923i
$643$	−6.57071	−	12.5195i	−0.259124	−	0.493719i	0.720787	−	0.693157i	$-0.243781\pi$
$643$	−6.57071	−	12.5195i	−0.259124	−	0.493719i	−0.979910	+	0.199438i	$0.936088\pi$
$644$	−2.72680	−	0.331093i	−0.107451	−	0.0130469i
$645$	−16.8866	+	2.05040i	−0.664908	+	0.0807345i
$646$	2.14148	+	1.89718i	0.0842553	+	0.0746437i
$647$	−11.7397	−	17.0080i	−0.461537	−	0.668652i	0.521248	−	0.853405i	$-0.325467\pi$
$647$	−11.7397	−	17.0080i	−0.461537	−	0.668652i	−0.982785	+	0.184754i	$0.940851\pi$
$648$	−9.68887	−	1.17644i	−0.380615	−	0.0462150i
$649$	0.108772	+	0.895820i	0.00426969	+	0.0351640i
$650$	−4.13220	−	9.94652i	−0.162078	−	0.390135i
$651$	−0.222816	+	1.83505i	−0.00873283	+	0.0719213i
$652$	0.321718	−	1.30526i	0.0125994	−	0.0511179i
$653$	12.6457			0.494864			0.247432	−	0.968905i	$-0.420413\pi$
$653$	12.6457			0.494864			0.247432	+	0.968905i	$0.420413\pi$
$654$	−21.0689			−0.823861
$655$	2.59496	−	10.5282i	0.101394	−	0.411370i
$656$	−1.09972	+	0.417067i	−0.0429367	+	0.0162837i
$657$			15.1855i			0.592443i
$658$	2.96176	+	1.12325i	0.115462	+	0.0437888i
$659$	−26.9401	+	6.64015i	−1.04944	+	0.258663i	−0.726078	−	0.687612i	$-0.758659\pi$
$659$	−26.9401	+	6.64015i	−1.04944	+	0.258663i	−0.323361	+	0.946276i	$0.604813\pi$
$660$	8.04909	+	7.13087i	0.313310	+	0.277569i
$661$	−1.74142	−	7.06523i	−0.0677335	−	0.274805i	0.927304	−	0.374310i	$-0.122120\pi$
$661$	−1.74142	−	7.06523i	−0.0677335	−	0.274805i	−0.995037	+	0.0995045i	$0.968274\pi$
$662$	−10.7475	−	9.52145i	−0.417713	−	0.370062i
$663$	−6.35541	−	2.18567i	−0.246824	−	0.0848842i
$664$	−15.7052	+	13.9136i	−0.609480	+	0.539952i
$665$	3.26380	+	2.25284i	0.126565	+	0.0873614i
$666$	−7.67828	−	1.89253i	−0.297527	−	0.0733339i
$667$	2.87511	+	4.16532i	0.111325	+	0.161282i
$668$	−1.85156	−	7.51206i	−0.0716389	−	0.290650i
$669$	4.55213	+	18.4687i	0.175995	+	0.714041i
$670$	1.45610	−	0.176802i	0.0562540	−	0.00683047i
$671$	−14.7001	−	16.5929i	−0.567490	−	0.640564i
$672$	3.64403	−	9.60853i	0.140572	−	0.370657i
$673$	30.3994	+	15.9548i	1.17181	+	0.615013i	0.934340	−	0.356382i	$-0.115990\pi$
$673$	30.3994	+	15.9548i	1.17181	+	0.615013i	0.237469	+	0.971395i	$0.423682\pi$
$674$	−10.1956	+	7.03752i	−0.392720	+	0.271075i
$675$	19.5585			0.752806
$676$	−8.48154	+	14.0968i	−0.326213	+	0.542185i
$677$	46.3148			1.78002			0.890011	−	0.455940i	$-0.150697\pi$
$677$	46.3148			1.78002			0.890011	+	0.455940i	$0.150697\pi$
$678$	−7.03647	+	4.85692i	−0.270234	+	0.186529i
$679$	17.3317	+	9.09639i	0.665130	+	0.349087i
$680$	1.73885	−	4.58497i	0.0666819	−	0.175826i
$681$	12.8496	+	14.5042i	0.492397	+	0.555801i
$682$	−4.60977	+	0.559728i	−0.176517	+	0.0214331i
$683$	−5.56528	−	22.5792i	−0.212949	−	0.863970i	−0.976025	−	0.217660i	$-0.930158\pi$
$683$	−5.56528	−	22.5792i	−0.212949	−	0.863970i	0.763075	−	0.646310i	$-0.223689\pi$
$684$	0.913251	+	3.70521i	0.0349190	+	0.141672i
$685$	10.6237	+	15.3911i	0.405912	+	0.588065i
$686$	−13.8518	−	3.41415i	−0.528863	−	0.130353i
$687$	5.05350	+	3.48818i	0.192803	+	0.133082i
$688$	1.04755	−	0.928049i	0.0399375	−	0.0353815i
$689$	46.3195	−	7.09936i	1.76463	−	0.270464i
$690$	−1.63196	−	1.44579i	−0.0621277	−	0.0550403i
$691$	4.25961	+	17.2819i	0.162043	+	0.657436i	0.994626	+	0.103535i	$0.0330152\pi$
$691$	4.25961	+	17.2819i	0.162043	+	0.657436i	−0.832583	+	0.553901i	$0.813139\pi$
$692$	−3.71122	−	3.28785i	−0.141079	−	0.124985i
$693$	−9.05332	+	2.23144i	−0.343907	+	0.0847655i
$694$	13.6385	+	5.17238i	0.517709	+	0.196341i
$695$			5.72822i			0.217284i
$696$	−10.9798	+	4.16408i	−0.416187	+	0.157839i
$697$	−3.02362	+	12.2673i	−0.114528	+	0.464658i
$698$	4.15137			0.157132
$699$	32.5433			1.23090
$700$	−1.45100	+	5.88695i	−0.0548428	+	0.222506i
$701$	2.20093	−	18.1263i	0.0831280	−	0.684621i	−0.890259	−	0.455454i	$-0.849477\pi$
$701$	2.20093	−	18.1263i	0.0831280	−	0.684621i	0.973387	−	0.229167i	$-0.0736000\pi$
$702$	10.2907	+	13.9548i	0.388396	+	0.526688i
$703$	−2.02757	−	16.6986i	−0.0764714	−	0.629799i
$704$	24.2386	+	2.94310i	0.913527	+	0.110922i
$705$	−2.46088	−	3.56521i	−0.0926823	−	0.134273i
$706$	−19.0442	−	16.8717i	−0.716738	−	0.634975i
$707$	8.43863	−	1.02464i	0.317367	−	0.0385354i
$708$	−0.281383	−	0.0341661i	−0.0105750	−	0.00128404i
$709$	−21.5756	−	41.1089i	−0.810289	−	1.54388i	−0.838900	−	0.544286i	$-0.816801\pi$
$709$	−21.5756	−	41.1089i	−0.810289	−	1.54388i	0.0286104	−	0.999591i	$-0.490892\pi$
$710$	0.210377	−	0.237466i	0.00789531	−	0.00891196i
$711$	−2.77969	+	4.02708i	−0.104247	+	0.151027i
$712$	−35.4456	+	8.73656i	−1.32838	+	0.327416i
$713$	−1.61036	+	0.195534i	−0.0603086	+	0.00732279i
$714$	−1.24734	−	1.80709i	−0.0466806	−	0.0676286i
$715$	−0.731341	−	23.3913i	−0.0273506	−	0.874784i
$716$	11.9662	−	17.3361i	0.447199	−	0.647879i
$717$	9.12811	−	17.3922i	0.340896	−	0.649522i
$718$	−2.30036	−	6.06555i	−0.0858487	−	0.226364i
$719$	4.74140	−	39.0489i	0.176824	−	1.45628i	−0.586335	−	0.810069i	$-0.699430\pi$
$719$	4.74140	−	39.0489i	0.176824	−	1.45628i	0.763159	−	0.646210i	$-0.223647\pi$
$720$	0.172646	−	0.119169i	0.00643414	−	0.00444117i
$721$	−4.72384	+	19.1654i	−0.175925	+	0.713756i
$722$	−9.52383	+	6.57382i	−0.354440	+	0.244652i
$723$	19.5436	−	7.41190i	0.726834	−	0.275652i
$724$	8.99813	+	23.7261i	0.334413	+	0.881774i
$725$	9.89214	−	5.19179i	0.367385	−	0.192818i
$726$	8.76996	+	16.7098i	0.325484	+	0.620158i
$727$	0.771227	+	0.190090i	0.0286032	+	0.00705006i	0.253591	−	0.967311i	$-0.418388\pi$
$727$	0.771227	+	0.190090i	0.0286032	+	0.00705006i	−0.224988	+	0.974362i	$0.572234\pi$
$728$	−12.8083	+	5.32111i	−0.474708	+	0.197213i
$729$	−25.7522	+	6.34734i	−0.953785	+	0.235087i
$730$	−8.25743	−	9.32072i	−0.305621	−	0.344975i
$731$	−1.81214	−	14.9243i	−0.0670244	−	0.551995i
$732$	6.16551	−	3.23591i	0.227884	−	0.119603i
$733$	6.22507	−	11.8609i	0.229928	−	0.438092i	−0.742970	−	0.669325i	$-0.766584\pi$
$733$	6.22507	−	11.8609i	0.229928	−	0.438092i	0.972898	+	0.231233i	$0.0742759\pi$
$734$	−2.69721	−	1.02292i	−0.0995560	−	0.0377566i
$735$	5.45983	+	6.16288i	0.201389	+	0.227321i
$736$	8.95232	+	1.08701i	0.329987	+	0.0400677i
$737$	−7.12247	−	1.75553i	−0.262359	−	0.0646658i
$738$	7.32111	−	6.48593i	0.269494	−	0.238751i
$739$	−31.4763	+	35.5294i	−1.15787	+	1.30697i	−0.213935	+	0.976848i	$0.568628\pi$
$739$	−31.4763	+	35.5294i	−1.15787	+	1.30697i	−0.943939	+	0.330121i	$0.892910\pi$
$740$	−9.89331	+	5.19241i	−0.363685	+	0.190877i
$741$	−5.99902	+	9.29989i	−0.220379	+	0.341640i
$742$	13.5564	+	7.11494i	0.497671	+	0.261198i
$743$	−21.7700	+	8.25627i	−0.798663	+	0.302893i	−0.719969	−	0.694006i	$-0.755844\pi$
$743$	−21.7700	+	8.25627i	−0.798663	+	0.302893i	−0.0786938	+	0.996899i	$0.525075\pi$
$744$	0.453669	−	3.73630i	0.0166323	−	0.136979i
$745$	−21.8225	−	11.4533i	−0.799514	−	0.419617i
$746$		−	3.08004i		−	0.112768i
$747$	−4.48109	+	8.53800i	−0.163954	+	0.312389i
$748$	−6.30224	+	7.11376i	−0.230433	+	0.260105i
$749$	7.16458	+	4.94535i	0.261788	+	0.180699i
$750$	−8.76959	+	7.76918i	−0.320220	+	0.283690i
$751$	13.3030	−	19.2727i	0.485433	−	0.703270i	−0.501364	−	0.865237i	$-0.667168\pi$
$751$	13.3030	−	19.2727i	0.485433	−	0.703270i	0.986796	+	0.161966i	$0.0517835\pi$
$752$	0.333250	+	0.126385i	0.0121524	+	0.00460878i
$753$	−3.58627	+	9.45622i	−0.130691	+	0.344604i
$754$	8.90902	+	4.32628i	0.324447	+	0.157554i
$755$	−1.32943	−	3.50543i	−0.0483831	−	0.127576i
$756$		−	9.76047i		−	0.354985i
$757$	−9.14640	+	24.1171i	−0.332432	+	0.876550i	0.659720	+	0.751511i	$0.270675\pi$
$757$	−9.14640	+	24.1171i	−0.332432	+	0.876550i	−0.992152	+	0.125039i	$0.960095\pi$
$758$	−0.540111	−	4.44821i	−0.0196177	−	0.161566i
$759$	5.06728	+	9.65489i	0.183931	+	0.350450i
$760$	−6.64534	−	4.58695i	−0.241052	−	0.166386i
$761$	−22.0358	−	15.2102i	−0.798798	−	0.551371i	0.0972849	−	0.995257i	$-0.468984\pi$
$761$	−22.0358	−	15.2102i	−0.798798	−	0.551371i	−0.896083	+	0.443886i	$0.853600\pi$
$762$	5.85648	+	11.1586i	0.212158	+	0.404233i
$763$	−3.11123	−	25.6233i	−0.112634	−	0.927624i
$764$	10.7927	−	28.4580i	0.390466	−	1.02957i
$765$		−	2.25352i		−	0.0814761i
$766$	−7.65134	−	20.1749i	−0.276454	−	0.728949i
$767$	0.366115	+

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	169.h (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.705316 + 0.486844i) q^{2} +(-1.15919 - 0.608391i) q^{3} +(-0.448757 + 1.18327i) q^{4} +(-0.816038 - 0.921117i) q^{5} +(1.11379 - 0.135238i) q^{6} +(0.328944 + 1.33458i) q^{7} +(-0.669753 - 2.71730i) q^{8} +(-0.730609 - 1.05847i) q^{9} +O(q^{10})\)	\(q+(-0.705316 + 0.486844i) q^{2} +(-1.15919 - 0.608391i) q^{3} +(-0.448757 + 1.18327i) q^{4} +(-0.816038 - 0.921117i) q^{5} +(1.11379 - 0.135238i) q^{6} +(0.328944 + 1.33458i) q^{7} +(-0.669753 - 2.71730i) q^{8} +(-0.730609 - 1.05847i) q^{9} +(1.02401 + 0.252395i) q^{10} +(-4.34079 - 2.99623i) q^{11} +(1.24009 - 1.09862i) q^{12} +(-3.59110 - 0.322536i) q^{13} +(-0.881740 - 0.781154i) q^{14} +(0.385546 + 1.56422i) q^{15} +(-0.0992110 - 0.0878933i) q^{16} +(-1.38245 + 0.340744i) q^{17} +(1.03062 + 0.390862i) q^{18} +2.34458i q^{19} +(1.45614 - 0.552240i) q^{20} +(0.430635 - 1.74716i) q^{21} +4.52033 q^{22} +1.57912 q^{23} +(-0.876805 + 3.55734i) q^{24} +(0.420146 - 3.46021i) q^{25} +(2.68988 - 1.52082i) q^{26} +(0.676353 + 5.57027i) q^{27} +(-1.72679 - 0.209670i) q^{28} +(1.82071 + 2.63775i) q^{29} +(-1.03346 - 0.915569i) q^{30} +(-1.01979 + 0.123825i) q^{31} +(5.66919 + 0.688364i) q^{32} +(3.20893 + 6.11410i) q^{33} +(0.809177 - 0.913372i) q^{34} +(0.960870 - 1.39206i) q^{35} +(1.58032 - 0.389515i) q^{36} +(-7.12219 + 0.864790i) q^{37} +(-1.14145 - 1.65367i) q^{38} +(3.96654 + 2.55867i) q^{39} +(-1.95640 + 2.83434i) q^{40} +(4.12376 - 7.85717i) q^{41} +(0.546859 + 1.44195i) q^{42} +(-1.27272 + 10.4818i) q^{43} +(5.49332 - 3.79177i) q^{44} +(-0.378769 + 1.53673i) q^{45} +(-1.11378 + 0.768785i) q^{46} +(-2.51425 + 0.953527i) q^{47} +(0.0615311 + 0.162244i) q^{48} +(4.52530 - 2.37506i) q^{49} +(1.38825 + 2.64509i) q^{50} +(1.80983 + 0.446084i) q^{51} +(1.99318 - 4.10451i) q^{52} +(-12.6191 + 3.11032i) q^{53} +(-3.18890 - 3.59952i) q^{54} +(0.782372 + 6.44342i) q^{55} +(3.40613 - 1.78767i) q^{56} +(1.42642 - 2.71782i) q^{57} +(-2.56835 - 0.974046i) q^{58} +(-0.113453 - 0.128062i) q^{59} +(-2.02392 - 0.245748i) q^{60} +(4.08076 + 1.00582i) q^{61} +(0.658989 - 0.583813i) q^{62} +(1.17228 - 1.32323i) q^{63} +(-4.09897 + 2.15131i) q^{64} +(2.63338 + 3.57102i) q^{65} +(-5.23993 - 2.75013i) q^{66} +(1.30041 - 0.493179i) q^{67} +(0.217191 - 1.78873i) q^{68} +(-1.83050 - 0.960721i) q^{69} +1.44964i q^{70} +(0.139794 - 0.266356i) q^{71} +(-2.38685 + 2.69419i) q^{72} +(-9.71703 - 6.70718i) q^{73} +(4.60238 - 4.07735i) q^{74} +(-2.59219 + 3.75543i) q^{75} +(-2.77429 - 1.05215i) q^{76} +(2.57083 - 6.77871i) q^{77} +(-4.04334 + 0.126417i) q^{78} +(-1.34914 - 3.55738i) q^{79} +0.163109i q^{80} +(1.23667 - 3.26082i) q^{81} +(0.916666 + 7.54942i) q^{82} +(-3.48415 - 6.63849i) q^{83} +(1.87411 + 1.29361i) q^{84} +(1.44200 + 0.995340i) q^{85} +(-4.20535 - 8.01262i) q^{86} +(-0.505766 - 4.16536i) q^{87} +(-5.23439 + 13.8019i) q^{88} -13.0444i q^{89} +(-0.480995 - 1.26828i) q^{90} +(-0.750819 - 4.89869i) q^{91} +(-0.708640 + 1.86853i) q^{92} +(1.25746 + 0.476893i) q^{93} +(1.30912 - 1.89658i) q^{94} +(2.15964 - 1.91327i) q^{95} +(-6.15288 - 4.24703i) q^{96} +(9.44318 - 10.6591i) q^{97} +(-2.03548 + 3.87829i) q^{98} +6.78367i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9}+O(q^{10}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9} - 9 q^{10} - 13 q^{11} - 9 q^{12} + 52 q^{13} - 15 q^{14} + 39 q^{15} - 31 q^{16} - 11 q^{17} + 26 q^{18} - 13 q^{20} - 13 q^{21} - 6 q^{22} - 102 q^{23} - 91 q^{24} + 3 q^{25} - 13 q^{26} - 19 q^{27} - 13 q^{28} - 17 q^{29} + 23 q^{30} + 39 q^{31} - 13 q^{33} + 52 q^{34} - 21 q^{35} + 11 q^{36} - 13 q^{37} - 40 q^{38} - 65 q^{39} + 53 q^{40} - 13 q^{41} + 101 q^{42} - 3 q^{43} - 39 q^{44} - 78 q^{45} - 39 q^{46} - 39 q^{47} + 8 q^{48} + 85 q^{49} - 13 q^{50} + 62 q^{51} - 78 q^{52} + 18 q^{53} + 65 q^{54} - 103 q^{55} + 3 q^{56} + 65 q^{57} + 39 q^{58} + 91 q^{59} - 117 q^{60} - 23 q^{61} - 64 q^{62} - 78 q^{63} + 15 q^{64} - 13 q^{65} + 134 q^{66} - 65 q^{67} + 40 q^{68} - 40 q^{69} + 26 q^{71} + 156 q^{72} - 13 q^{73} - 53 q^{74} + 35 q^{75} + 221 q^{76} + 3 q^{77} - 143 q^{78} - 23 q^{79} - 43 q^{81} - 129 q^{82} + 117 q^{83} + 234 q^{84} + 26 q^{85} - 91 q^{86} + 79 q^{87} + 95 q^{88} + 17 q^{90} + 39 q^{91} - 89 q^{92} + 52 q^{93} - 61 q^{94} + 122 q^{95} - 182 q^{96} - 91 q^{97} - 13 q^{98}+O(q^{100}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9 - 9 * q^10 - 13 * q^11 - 9 * q^12 + 52 * q^13 - 15 * q^14 + 39 * q^15 - 31 * q^16 - 11 * q^17 + 26 * q^18 - 13 * q^20 - 13 * q^21 - 6 * q^22 - 102 * q^23 - 91 * q^24 + 3 * q^25 - 13 * q^26 - 19 * q^27 - 13 * q^28 - 17 * q^29 + 23 * q^30 + 39 * q^31 - 13 * q^33 + 52 * q^34 - 21 * q^35 + 11 * q^36 - 13 * q^37 - 40 * q^38 - 65 * q^39 + 53 * q^40 - 13 * q^41 + 101 * q^42 - 3 * q^43 - 39 * q^44 - 78 * q^45 - 39 * q^46 - 39 * q^47 + 8 * q^48 + 85 * q^49 - 13 * q^50 + 62 * q^51 - 78 * q^52 + 18 * q^53 + 65 * q^54 - 103 * q^55 + 3 * q^56 + 65 * q^57 + 39 * q^58 + 91 * q^59 - 117 * q^60 - 23 * q^61 - 64 * q^62 - 78 * q^63 + 15 * q^64 - 13 * q^65 + 134 * q^66 - 65 * q^67 + 40 * q^68 - 40 * q^69 + 26 * q^71 + 156 * q^72 - 13 * q^73 - 53 * q^74 + 35 * q^75 + 221 * q^76 + 3 * q^77 - 143 * q^78 - 23 * q^79 - 43 * q^81 - 129 * q^82 + 117 * q^83 + 234 * q^84 + 26 * q^85 - 91 * q^86 + 79 * q^87 + 95 * q^88 + 17 * q^90 + 39 * q^91 - 89 * q^92 + 52 * q^93 - 61 * q^94 + 122 * q^95 - 182 * q^96 - 91 * q^97 - 13 * q^98

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