LMFDB - Embedded newform 8029.2.a.b.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8029,2,Mod(1,8029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8029, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8029 = 7 \cdot 31 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8029.a (trivial)

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:	yes
Analytic conductor:	$64.1118877829$
Analytic rank:	$1$
Dimension:	$64$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	8029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.97375 q^{2} +0.623779 q^{3} +1.89568 q^{4} -0.759767 q^{5} -1.23118 q^{6} +1.00000 q^{7} +0.205897 q^{8} -2.61090 q^{9} +O(q^{10})$	\(q-1.97375 q^{2} +0.623779 q^{3} +1.89568 q^{4} -0.759767 q^{5} -1.23118 q^{6} +1.00000 q^{7} +0.205897 q^{8} -2.61090 q^{9} +1.49959 q^{10} +4.38052 q^{11} +1.18249 q^{12} -1.54907 q^{13} -1.97375 q^{14} -0.473927 q^{15} -4.19775 q^{16} +1.97182 q^{17} +5.15326 q^{18} +1.01140 q^{19} -1.44028 q^{20} +0.623779 q^{21} -8.64605 q^{22} +4.19131 q^{23} +0.128434 q^{24} -4.42275 q^{25} +3.05747 q^{26} -3.49996 q^{27} +1.89568 q^{28} -0.885360 q^{29} +0.935412 q^{30} -1.00000 q^{31} +7.87351 q^{32} +2.73248 q^{33} -3.89187 q^{34} -0.759767 q^{35} -4.94944 q^{36} +1.00000 q^{37} -1.99624 q^{38} -0.966277 q^{39} -0.156433 q^{40} -0.410015 q^{41} -1.23118 q^{42} -1.69416 q^{43} +8.30408 q^{44} +1.98368 q^{45} -8.27259 q^{46} -9.81087 q^{47} -2.61847 q^{48} +1.00000 q^{49} +8.72940 q^{50} +1.22998 q^{51} -2.93654 q^{52} +8.14076 q^{53} +6.90804 q^{54} -3.32818 q^{55} +0.205897 q^{56} +0.630887 q^{57} +1.74748 q^{58} -5.02332 q^{59} -0.898414 q^{60} -13.2114 q^{61} +1.97375 q^{62} -2.61090 q^{63} -7.14483 q^{64} +1.17693 q^{65} -5.39322 q^{66} +3.27211 q^{67} +3.73794 q^{68} +2.61445 q^{69} +1.49959 q^{70} +10.8920 q^{71} -0.537575 q^{72} -4.08316 q^{73} -1.97375 q^{74} -2.75882 q^{75} +1.91728 q^{76} +4.38052 q^{77} +1.90719 q^{78} -0.168668 q^{79} +3.18932 q^{80} +5.64950 q^{81} +0.809266 q^{82} -6.81714 q^{83} +1.18249 q^{84} -1.49812 q^{85} +3.34384 q^{86} -0.552269 q^{87} +0.901935 q^{88} -7.90354 q^{89} -3.91528 q^{90} -1.54907 q^{91} +7.94539 q^{92} -0.623779 q^{93} +19.3642 q^{94} -0.768425 q^{95} +4.91133 q^{96} -3.42019 q^{97} -1.97375 q^{98} -11.4371 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 5 q^{2} - 18 q^{3} + 57 q^{4} - 26 q^{5} - 13 q^{6} + 64 q^{7} - 15 q^{8} + 56 q^{9}+O(q^{10}) $ 64 * q - 5 * q^2 - 18 * q^3 + 57 * q^4 - 26 * q^5 - 13 * q^6 + 64 * q^7 - 15 * q^8 + 56 * q^9	\( 64 q - 5 q^{2} - 18 q^{3} + 57 q^{4} - 26 q^{5} - 13 q^{6} + 64 q^{7} - 15 q^{8} + 56 q^{9} - 14 q^{10} - 37 q^{11} - 27 q^{12} - 18 q^{13} - 5 q^{14} + 6 q^{15} + 39 q^{16} - 27 q^{17} - 32 q^{18} - 27 q^{19} - 55 q^{20} - 18 q^{21} + 2 q^{22} - 10 q^{23} - 39 q^{24} + 58 q^{25} - 47 q^{26} - 66 q^{27} + 57 q^{28} + 4 q^{29} + 14 q^{30} - 64 q^{31} - 30 q^{32} - 44 q^{33} - 4 q^{34} - 26 q^{35} + 32 q^{36} + 64 q^{37} - 75 q^{38} + 2 q^{39} - 5 q^{40} - 85 q^{41} - 13 q^{42} + 16 q^{43} - 66 q^{44} - 77 q^{45} - 100 q^{47} - 15 q^{48} + 64 q^{49} - 10 q^{50} - 55 q^{51} - 21 q^{52} - 23 q^{53} - 25 q^{54} - 19 q^{55} - 15 q^{56} + 7 q^{57} - 40 q^{58} - 125 q^{59} + 67 q^{60} - 17 q^{61} + 5 q^{62} + 56 q^{63} + 19 q^{64} - 38 q^{65} - 11 q^{66} - 33 q^{67} - 47 q^{68} - 52 q^{69} - 14 q^{70} - 129 q^{71} - 42 q^{72} - 37 q^{73} - 5 q^{74} - 108 q^{75} - 33 q^{76} - 37 q^{77} + 13 q^{78} - 14 q^{79} - 90 q^{80} + 56 q^{81} - 40 q^{82} - 114 q^{83} - 27 q^{84} + 3 q^{85} - 26 q^{86} + 7 q^{87} - 11 q^{88} - 72 q^{89} - 21 q^{90} - 18 q^{91} + 6 q^{92} + 18 q^{93} + q^{94} - 80 q^{95} - 26 q^{96} + q^{97} - 5 q^{98} - 82 q^{99}+O(q^{100}) \) 64 * q - 5 * q^2 - 18 * q^3 + 57 * q^4 - 26 * q^5 - 13 * q^6 + 64 * q^7 - 15 * q^8 + 56 * q^9 - 14 * q^10 - 37 * q^11 - 27 * q^12 - 18 * q^13 - 5 * q^14 + 6 * q^15 + 39 * q^16 - 27 * q^17 - 32 * q^18 - 27 * q^19 - 55 * q^20 - 18 * q^21 + 2 * q^22 - 10 * q^23 - 39 * q^24 + 58 * q^25 - 47 * q^26 - 66 * q^27 + 57 * q^28 + 4 * q^29 + 14 * q^30 - 64 * q^31 - 30 * q^32 - 44 * q^33 - 4 * q^34 - 26 * q^35 + 32 * q^36 + 64 * q^37 - 75 * q^38 + 2 * q^39 - 5 * q^40 - 85 * q^41 - 13 * q^42 + 16 * q^43 - 66 * q^44 - 77 * q^45 - 100 * q^47 - 15 * q^48 + 64 * q^49 - 10 * q^50 - 55 * q^51 - 21 * q^52 - 23 * q^53 - 25 * q^54 - 19 * q^55 - 15 * q^56 + 7 * q^57 - 40 * q^58 - 125 * q^59 + 67 * q^60 - 17 * q^61 + 5 * q^62 + 56 * q^63 + 19 * q^64 - 38 * q^65 - 11 * q^66 - 33 * q^67 - 47 * q^68 - 52 * q^69 - 14 * q^70 - 129 * q^71 - 42 * q^72 - 37 * q^73 - 5 * q^74 - 108 * q^75 - 33 * q^76 - 37 * q^77 + 13 * q^78 - 14 * q^79 - 90 * q^80 + 56 * q^81 - 40 * q^82 - 114 * q^83 - 27 * q^84 + 3 * q^85 - 26 * q^86 + 7 * q^87 - 11 * q^88 - 72 * q^89 - 21 * q^90 - 18 * q^91 + 6 * q^92 + 18 * q^93 + q^94 - 80 * q^95 - 26 * q^96 + q^97 - 5 * q^98 - 82 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−1.97375	−1.39565	−0.697825	−	0.716268i	$-0.745849\pi$
$2$	−1.97375	−1.39565	−0.697825	+	0.716268i	$0.745849\pi$
$3$	0.623779	0.360139	0.180069	−	0.983654i	$-0.442368\pi$
$3$	0.623779	0.360139	0.180069	+	0.983654i	$0.442368\pi$
$4$	1.89568	0.947841
$5$	−0.759767	−0.339778	−0.169889	−	0.985463i	$-0.554341\pi$
$5$	−0.759767	−0.339778	−0.169889	+	0.985463i	$0.554341\pi$
$6$	−1.23118	−0.502628
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0.205897	0.0727954
$9$	−2.61090	−0.870300
$10$	1.49959	0.474212
$11$	4.38052	1.32078	0.660388	−	0.750924i	$-0.270392\pi$
$11$	4.38052	1.32078	0.660388	+	0.750924i	$0.270392\pi$
$12$	1.18249	0.341354
$13$	−1.54907	−0.429635	−0.214817	−	0.976654i	$-0.568916\pi$
$13$	−1.54907	−0.429635	−0.214817	+	0.976654i	$0.568916\pi$
$14$	−1.97375	−0.527506
$15$	−0.473927	−0.122367
$16$	−4.19775	−1.04944
$17$	1.97182	0.478236	0.239118	−	0.970991i	$-0.423142\pi$
$17$	1.97182	0.478236	0.239118	+	0.970991i	$0.423142\pi$
$18$	5.15326	1.21464
$19$	1.01140	0.232030	0.116015	−	0.993247i	$-0.462988\pi$
$19$	1.01140	0.232030	0.116015	+	0.993247i	$0.462988\pi$
$20$	−1.44028	−0.322056
$21$	0.623779	0.136120
$22$	−8.64605	−1.84334
$23$	4.19131	0.873948	0.436974	−	0.899474i	$-0.356050\pi$
$23$	4.19131	0.873948	0.436974	+	0.899474i	$0.356050\pi$
$24$	0.128434	0.0262165
$25$	−4.42275	−0.884551
$26$	3.05747	0.599620
$27$	−3.49996	−0.673568
$28$	1.89568	0.358250
$29$	−0.885360	−0.164407	−0.0822036	−	0.996616i	$-0.526196\pi$
$29$	−0.885360	−0.164407	−0.0822036	+	0.996616i	$0.526196\pi$
$30$	0.935412	0.170782
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	7.87351	1.39185
$33$	2.73248	0.475663
$34$	−3.89187	−0.667450
$35$	−0.759767	−0.128424
$36$	−4.94944	−0.824906
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−1.99624	−0.323833
$39$	−0.966277	−0.154728
$40$	−0.156433	−0.0247343
$41$	−0.410015	−0.0640335	−0.0320168	−	0.999487i	$-0.510193\pi$
$41$	−0.410015	−0.0640335	−0.0320168	+	0.999487i	$0.510193\pi$
$42$	−1.23118	−0.189976
$43$	−1.69416	−0.258357	−0.129178	−	0.991621i	$-0.541234\pi$
$43$	−1.69416	−0.258357	−0.129178	+	0.991621i	$0.541234\pi$
$44$	8.30408	1.25189
$45$	1.98368	0.295709
$46$	−8.27259	−1.21973
$47$	−9.81087	−1.43106	−0.715531	−	0.698581i	$-0.753815\pi$
$47$	−9.81087	−1.43106	−0.715531	+	0.698581i	$0.753815\pi$
$48$	−2.61847	−0.377943
$49$	1.00000	0.142857
$50$	8.72940	1.23452
$51$	1.22998	0.172231
$52$	−2.93654	−0.407225
$53$	8.14076	1.11822	0.559109	−	0.829094i	$-0.311143\pi$
$53$	8.14076	1.11822	0.559109	+	0.829094i	$0.311143\pi$
$54$	6.90804	0.940065
$55$	−3.32818	−0.448771
$56$	0.205897	0.0275141
$57$	0.630887	0.0835630
$58$	1.74748	0.229455
$59$	−5.02332	−0.653981	−0.326990	−	0.945028i	$-0.606034\pi$
$59$	−5.02332	−0.653981	−0.326990	+	0.945028i	$0.606034\pi$
$60$	−0.898414	−0.115985
$61$	−13.2114	−1.69155	−0.845775	−	0.533540i	$-0.820861\pi$
$61$	−13.2114	−1.69155	−0.845775	+	0.533540i	$0.820861\pi$
$62$	1.97375	0.250666
$63$	−2.61090	−0.328943
$64$	−7.14483	−0.893104
$65$	1.17693	0.145981
$66$	−5.39322	−0.663859
$67$	3.27211	0.399752	0.199876	−	0.979821i	$-0.435946\pi$
$67$	3.27211	0.399752	0.199876	+	0.979821i	$0.435946\pi$
$68$	3.73794	0.453292
$69$	2.61445	0.314743
$70$	1.49959	0.179235
$71$	10.8920	1.29264	0.646322	−	0.763065i	$-0.276306\pi$
$71$	10.8920	1.29264	0.646322	+	0.763065i	$0.276306\pi$
$72$	−0.537575	−0.0633539
$73$	−4.08316	−0.477898	−0.238949	−	0.971032i	$-0.576803\pi$
$73$	−4.08316	−0.477898	−0.238949	+	0.971032i	$0.576803\pi$
$74$	−1.97375	−0.229444
$75$	−2.75882	−0.318561
$76$	1.91728	0.219928
$77$	4.38052	0.499207
$78$	1.90719	0.215946
$79$	−0.168668	−0.0189766	−0.00948830	−	0.999955i	$-0.503020\pi$
$79$	−0.168668	−0.0189766	−0.00948830	+	0.999955i	$0.503020\pi$
$80$	3.18932	0.356576
$81$	5.64950	0.627722
$82$	0.809266	0.0893685
$83$	−6.81714	−0.748278	−0.374139	−	0.927373i	$-0.622062\pi$
$83$	−6.81714	−0.748278	−0.374139	+	0.927373i	$0.622062\pi$
$84$	1.18249	0.129020
$85$	−1.49812	−0.162494
$86$	3.34384	0.360576
$87$	−0.552269	−0.0592094
$88$	0.901935	0.0961465
$89$	−7.90354	−0.837774	−0.418887	−	0.908038i	$-0.637580\pi$
$89$	−7.90354	−0.837774	−0.418887	+	0.908038i	$0.637580\pi$
$90$	−3.91528	−0.412707
$91$	−1.54907	−0.162387
$92$	7.94539	0.828364
$93$	−0.623779	−0.0646828
$94$	19.3642	1.99726
$95$	−0.768425	−0.0788388
$96$	4.91133	0.501261
$97$	−3.42019	−0.347268	−0.173634	−	0.984810i	$-0.555551\pi$
$97$	−3.42019	−0.347268	−0.173634	+	0.984810i	$0.555551\pi$
$98$	−1.97375	−0.199379
$99$	−11.4371	−1.14947
$100$	−8.38414	−0.838414
$101$	−10.6518	−1.05990	−0.529948	−	0.848030i	$-0.677789\pi$
$101$	−10.6518	−1.05990	−0.529948	+	0.848030i	$0.677789\pi$
$102$	−2.42767	−0.240375
$103$	−9.23345	−0.909799	−0.454899	−	0.890543i	$-0.650325\pi$
$103$	−9.23345	−0.909799	−0.454899	+	0.890543i	$0.650325\pi$
$104$	−0.318948	−0.0312754
$105$	−0.473927	−0.0462505
$106$	−16.0678	−1.56064
$107$	3.03755	0.293651	0.146826	−	0.989162i	$-0.453094\pi$
$107$	3.03755	0.293651	0.146826	+	0.989162i	$0.453094\pi$
$108$	−6.63481	−0.638435
$109$	19.4197	1.86007	0.930037	−	0.367465i	$-0.119774\pi$
$109$	19.4197	1.86007	0.930037	+	0.367465i	$0.119774\pi$
$110$	6.56898	0.626328
$111$	0.623779	0.0592064
$112$	−4.19775	−0.396650
$113$	−16.5598	−1.55781	−0.778906	−	0.627141i	$-0.784225\pi$
$113$	−16.5598	−1.55781	−0.778906	+	0.627141i	$0.784225\pi$
$114$	−1.24521	−0.116625
$115$	−3.18442	−0.296949
$116$	−1.67836	−0.155832
$117$	4.04447	0.373911
$118$	9.91477	0.912728
$119$	1.97182	0.180756
$120$	−0.0975799	−0.00890778
$121$	8.18897	0.744452
$122$	26.0760	2.36081
$123$	−0.255758	−0.0230610
$124$	−1.89568	−0.170237
$125$	7.15910	0.640329
$126$	5.15326	0.459089
$127$	3.39170	0.300965	0.150482	−	0.988613i	$-0.451917\pi$
$127$	3.39170	0.300965	0.150482	+	0.988613i	$0.451917\pi$
$128$	−1.64493	−0.145393
$129$	−1.05678	−0.0930443
$130$	−2.32297	−0.203738
$131$	14.6523	1.28017	0.640087	−	0.768302i	$-0.278898\pi$
$131$	14.6523	1.28017	0.640087	+	0.768302i	$0.278898\pi$
$132$	5.17991	0.450853
$133$	1.01140	0.0876991
$134$	−6.45833	−0.557914
$135$	2.65915	0.228864
$136$	0.405990	0.0348134
$137$	3.98421	0.340394	0.170197	−	0.985410i	$-0.445560\pi$
$137$	3.98421	0.340394	0.170197	+	0.985410i	$0.445560\pi$
$138$	−5.16026	−0.439271
$139$	−13.6483	−1.15763	−0.578815	−	0.815459i	$-0.696485\pi$
$139$	−13.6483	−1.15763	−0.578815	+	0.815459i	$0.696485\pi$
$140$	−1.44028	−0.121726
$141$	−6.11981	−0.515381
$142$	−21.4981	−1.80408
$143$	−6.78573	−0.567452
$144$	10.9599	0.913326
$145$	0.672668	0.0558620
$146$	8.05914	0.666979
$147$	0.623779	0.0514484
$148$	1.89568	0.155824
$149$	−1.78728	−0.146420	−0.0732098	−	0.997317i	$-0.523324\pi$
$149$	−1.78728	−0.146420	−0.0732098	+	0.997317i	$0.523324\pi$
$150$	5.44522	0.444600
$151$	21.5987	1.75768	0.878841	−	0.477115i	$-0.158318\pi$
$151$	21.5987	1.75768	0.878841	+	0.477115i	$0.158318\pi$
$152$	0.208243	0.0168907
$153$	−5.14822	−0.416209
$154$	−8.64605	−0.696718
$155$	0.759767	0.0610260
$156$	−1.83175	−0.146658
$157$	−10.7081	−0.854603	−0.427302	−	0.904109i	$-0.640536\pi$
$157$	−10.7081	−0.854603	−0.427302	+	0.904109i	$0.640536\pi$
$158$	0.332907	0.0264847
$159$	5.07803	0.402714
$160$	−5.98204	−0.472922
$161$	4.19131	0.330321
$162$	−11.1507	−0.876081
$163$	9.82558	0.769599	0.384799	−	0.923000i	$-0.374271\pi$
$163$	9.82558	0.769599	0.384799	+	0.923000i	$0.374271\pi$
$164$	−0.777258	−0.0606936
$165$	−2.07605	−0.161620
$166$	13.4553	1.04434
$167$	−1.79927	−0.139232	−0.0696158	−	0.997574i	$-0.522177\pi$
$167$	−1.79927	−0.139232	−0.0696158	+	0.997574i	$0.522177\pi$
$168$	0.128434	0.00990889
$169$	−10.6004	−0.815414
$170$	2.95692	0.226785
$171$	−2.64065	−0.201936
$172$	−3.21159	−0.244881
$173$	−13.7594	−1.04611	−0.523055	−	0.852299i	$-0.675208\pi$
$173$	−13.7594	−1.04611	−0.523055	+	0.852299i	$0.675208\pi$
$174$	1.09004	0.0826357
$175$	−4.42275	−0.334329
$176$	−18.3883	−1.38607
$177$	−3.13344	−0.235524
$178$	15.5996	1.16924
$179$	7.60404	0.568352	0.284176	−	0.958772i	$-0.408280\pi$
$179$	7.60404	0.568352	0.284176	+	0.958772i	$0.408280\pi$
$180$	3.76042	0.280285
$181$	4.17161	0.310074	0.155037	−	0.987909i	$-0.450450\pi$
$181$	4.17161	0.310074	0.155037	+	0.987909i	$0.450450\pi$
$182$	3.05747	0.226635
$183$	−8.24100	−0.609193
$184$	0.862976	0.0636195
$185$	−0.759767	−0.0558592
$186$	1.23118	0.0902746
$187$	8.63759	0.631643
$188$	−18.5983	−1.35642
$189$	−3.49996	−0.254585
$190$	1.51668	0.110031
$191$	−15.7703	−1.14110	−0.570550	−	0.821263i	$-0.693270\pi$
$191$	−15.7703	−1.14110	−0.570550	+	0.821263i	$0.693270\pi$
$192$	−4.45679	−0.321641
$193$	−9.42206	−0.678214	−0.339107	−	0.940748i	$-0.610125\pi$
$193$	−9.42206	−0.678214	−0.339107	+	0.940748i	$0.610125\pi$
$194$	6.75060	0.484665
$195$	0.734145	0.0525732
$196$	1.89568	0.135406
$197$	−13.3117	−0.948419	−0.474209	−	0.880412i	$-0.657266\pi$
$197$	−13.3117	−0.948419	−0.474209	+	0.880412i	$0.657266\pi$
$198$	22.5740	1.60426
$199$	−15.6084	−1.10645	−0.553224	−	0.833032i	$-0.686603\pi$
$199$	−15.6084	−1.10645	−0.553224	+	0.833032i	$0.686603\pi$
$200$	−0.910630	−0.0643913
$201$	2.04107	0.143966
$202$	21.0240	1.47925
$203$	−0.885360	−0.0621401
$204$	2.33165	0.163248
$205$	0.311516	0.0217572
$206$	18.2245	1.26976
$207$	−10.9431	−0.760597
$208$	6.50261	0.450875
$209$	4.43044	0.306460
$210$	0.935412	0.0645495
$211$	2.59000	0.178303	0.0891516	−	0.996018i	$-0.471584\pi$
$211$	2.59000	0.178303	0.0891516	+	0.996018i	$0.471584\pi$
$212$	15.4323	1.05989
$213$	6.79421	0.465531
$214$	−5.99536	−0.409834
$215$	1.28717	0.0877840
$216$	−0.720630	−0.0490326
$217$	−1.00000	−0.0678844
$218$	−38.3297	−2.59601
$219$	−2.54699	−0.172110
$220$	−6.30917	−0.425364
$221$	−3.05448	−0.205467
$222$	−1.23118	−0.0826315
$223$	−1.68145	−0.112598	−0.0562992	−	0.998414i	$-0.517930\pi$
$223$	−1.68145	−0.112598	−0.0562992	+	0.998414i	$0.517930\pi$
$224$	7.87351	0.526071
$225$	11.5474	0.769825
$226$	32.6848	2.17416
$227$	23.9003	1.58632	0.793161	−	0.609012i	$-0.208434\pi$
$227$	23.9003	1.58632	0.793161	+	0.609012i	$0.208434\pi$
$228$	1.19596	0.0792045
$229$	15.0057	0.991603	0.495802	−	0.868436i	$-0.334874\pi$
$229$	15.0057	0.991603	0.495802	+	0.868436i	$0.334874\pi$
$230$	6.28524	0.414437
$231$	2.73248	0.179784
$232$	−0.182293	−0.0119681
$233$	6.65469	0.435963	0.217982	−	0.975953i	$-0.430053\pi$
$233$	6.65469	0.435963	0.217982	+	0.975953i	$0.430053\pi$
$234$	−7.98276	−0.521849
$235$	7.45398	0.486244
$236$	−9.52262	−0.619870
$237$	−0.105211	−0.00683421
$238$	−3.89187	−0.252272
$239$	−21.5147	−1.39167	−0.695835	−	0.718201i	$-0.744966\pi$
$239$	−21.5147	−1.39167	−0.695835	+	0.718201i	$0.744966\pi$
$240$	1.98943	0.128417
$241$	2.35820	0.151905	0.0759524	−	0.997111i	$-0.475800\pi$
$241$	2.35820	0.151905	0.0759524	+	0.997111i	$0.475800\pi$
$242$	−16.1630	−1.03899
$243$	14.0239	0.899635
$244$	−25.0447	−1.60332
$245$	−0.759767	−0.0485397
$246$	0.504803	0.0321850
$247$	−1.56672	−0.0996882
$248$	−0.205897	−0.0130744
$249$	−4.25239	−0.269484
$250$	−14.1303	−0.893676
$251$	6.66214	0.420510	0.210255	−	0.977647i	$-0.432571\pi$
$251$	6.66214	0.420510	0.210255	+	0.977647i	$0.432571\pi$
$252$	−4.94944	−0.311785
$253$	18.3601	1.15429
$254$	−6.69437	−0.420042
$255$	−0.934496	−0.0585204
$256$	17.5363	1.09602
$257$	22.4161	1.39827	0.699137	−	0.714987i	$-0.253568\pi$
$257$	22.4161	1.39827	0.699137	+	0.714987i	$0.253568\pi$
$258$	2.08582	0.129857
$259$	1.00000	0.0621370
$260$	2.23109	0.138366
$261$	2.31159	0.143084
$262$	−28.9199	−1.78668
$263$	20.1261	1.24103	0.620515	−	0.784195i	$-0.286924\pi$
$263$	20.1261	1.24103	0.620515	+	0.784195i	$0.286924\pi$
$264$	0.562608	0.0346261
$265$	−6.18508	−0.379946
$266$	−1.99624	−0.122397
$267$	−4.93006	−0.301715
$268$	6.20289	0.378902
$269$	−6.24245	−0.380609	−0.190304	−	0.981725i	$-0.560947\pi$
$269$	−6.24245	−0.380609	−0.190304	+	0.981725i	$0.560947\pi$
$270$	−5.24850	−0.319414
$271$	11.5828	0.703608	0.351804	−	0.936074i	$-0.385568\pi$
$271$	11.5828	0.703608	0.351804	+	0.936074i	$0.385568\pi$
$272$	−8.27720	−0.501879
$273$	−0.966277	−0.0584817
$274$	−7.86382	−0.475071
$275$	−19.3740	−1.16829
$276$	4.95617	0.298326
$277$	12.9375	0.777341	0.388671	−	0.921377i	$-0.372934\pi$
$277$	12.9375	0.777341	0.388671	+	0.921377i	$0.372934\pi$
$278$	26.9382	1.61565
$279$	2.61090	0.156311
$280$	−0.156433	−0.00934869
$281$	−13.0817	−0.780387	−0.390193	−	0.920733i	$-0.627592\pi$
$281$	−13.0817	−0.780387	−0.390193	+	0.920733i	$0.627592\pi$
$282$	12.0790	0.719292
$283$	−23.2815	−1.38394	−0.691971	−	0.721926i	$-0.743257\pi$
$283$	−23.2815	−1.38394	−0.691971	+	0.721926i	$0.743257\pi$
$284$	20.6478	1.22522
$285$	−0.479327	−0.0283929
$286$	13.3933	0.791964
$287$	−0.410015	−0.0242024
$288$	−20.5570	−1.21133
$289$	−13.1119	−0.771291
$290$	−1.32768	−0.0779639
$291$	−2.13344	−0.125065
$292$	−7.74038	−0.452972
$293$	−32.3891	−1.89219	−0.946097	−	0.323884i	$-0.895011\pi$
$293$	−32.3891	−1.89219	−0.946097	+	0.323884i	$0.895011\pi$
$294$	−1.23118	−0.0718040
$295$	3.81655	0.222208
$296$	0.205897	0.0119675
$297$	−15.3316	−0.889633
$298$	3.52764	0.204351
$299$	−6.49263	−0.375479
$300$	−5.22985	−0.301945
$301$	−1.69416	−0.0976496
$302$	−42.6305	−2.45311
$303$	−6.64438	−0.381710
$304$	−4.24559	−0.243501
$305$	10.0376	0.574752
$306$	10.1613	0.580882
$307$	28.6745	1.63654	0.818269	−	0.574835i	$-0.194934\pi$
$307$	28.6745	1.63654	0.818269	+	0.574835i	$0.194934\pi$
$308$	8.30408	0.473169
$309$	−5.75963	−0.327654
$310$	−1.49959	−0.0851710
$311$	−8.10682	−0.459696	−0.229848	−	0.973227i	$-0.573823\pi$
$311$	−8.10682	−0.459696	−0.229848	+	0.973227i	$0.573823\pi$
$312$	−0.198953	−0.0112635
$313$	7.57081	0.427928	0.213964	−	0.976842i	$-0.431363\pi$
$313$	7.57081	0.427928	0.213964	+	0.976842i	$0.431363\pi$
$314$	21.1352	1.19273
$315$	1.98368	0.111768
$316$	−0.319740	−0.0179868
$317$	−25.0246	−1.40552	−0.702762	−	0.711425i	$-0.748050\pi$
$317$	−25.0246	−1.40552	−0.702762	+	0.711425i	$0.748050\pi$
$318$	−10.0228	−0.562048
$319$	−3.87834	−0.217145
$320$	5.42841	0.303457
$321$	1.89476	0.105755
$322$	−8.27259	−0.461013
$323$	1.99429	0.110965
$324$	10.7097	0.594981
$325$	6.85115	0.380034
$326$	−19.3932	−1.07409
$327$	12.1136	0.669885
$328$	−0.0844206	−0.00466135
$329$	−9.81087	−0.540891
$330$	4.09759	0.225565
$331$	19.9246	1.09515	0.547577	−	0.836755i	$-0.315550\pi$
$331$	19.9246	1.09515	0.547577	+	0.836755i	$0.315550\pi$
$332$	−12.9231	−0.709249
$333$	−2.61090	−0.143076
$334$	3.55130	0.194319
$335$	−2.48604	−0.135827
$336$	−2.61847	−0.142849
$337$	−28.4059	−1.54737	−0.773683	−	0.633572i	$-0.781588\pi$
$337$	−28.4059	−1.54737	−0.773683	+	0.633572i	$0.781588\pi$
$338$	20.9225	1.13803
$339$	−10.3296	−0.561029
$340$	−2.83996	−0.154019
$341$	−4.38052	−0.237219
$342$	5.21198	0.281832
$343$	1.00000	0.0539949
$344$	−0.348821	−0.0188072
$345$	−1.98637	−0.106943
$346$	27.1576	1.46000
$347$	−10.4715	−0.562141	−0.281071	−	0.959687i	$-0.590689\pi$
$347$	−10.4715	−0.562141	−0.281071	+	0.959687i	$0.590689\pi$
$348$	−1.04693	−0.0561211
$349$	−10.0484	−0.537881	−0.268940	−	0.963157i	$-0.586673\pi$
$349$	−10.0484	−0.537881	−0.268940	+	0.963157i	$0.586673\pi$
$350$	8.72940	0.466606
$351$	5.42168	0.289388
$352$	34.4901	1.83833
$353$	−13.2326	−0.704301	−0.352150	−	0.935943i	$-0.614549\pi$
$353$	−13.2326	−0.704301	−0.352150	+	0.935943i	$0.614549\pi$
$354$	6.18462	0.328709
$355$	−8.27540	−0.439213
$356$	−14.9826	−0.794076
$357$	1.22998	0.0650973
$358$	−15.0085	−0.793222
$359$	8.66190	0.457158	0.228579	−	0.973525i	$-0.426592\pi$
$359$	8.66190	0.457158	0.228579	+	0.973525i	$0.426592\pi$
$360$	0.408432	0.0215263
$361$	−17.9771	−0.946162
$362$	−8.23371	−0.432754
$363$	5.10810	0.268106
$364$	−2.93654	−0.153917
$365$	3.10225	0.162379
$366$	16.2657	0.850220
$367$	1.03548	0.0540514	0.0270257	−	0.999635i	$-0.491396\pi$
$367$	1.03548	0.0540514	0.0270257	+	0.999635i	$0.491396\pi$
$368$	−17.5941	−0.917155
$369$	1.07051	0.0557284
$370$	1.49959	0.0779599
$371$	8.14076	0.422647
$372$	−1.18249	−0.0613091
$373$	15.8470	0.820526	0.410263	−	0.911967i	$-0.365437\pi$
$373$	15.8470	0.820526	0.410263	+	0.911967i	$0.365437\pi$
$374$	−17.0484	−0.881553
$375$	4.46569	0.230607
$376$	−2.02002	−0.104175
$377$	1.37149	0.0706351
$378$	6.90804	0.355311
$379$	−7.35541	−0.377822	−0.188911	−	0.981994i	$-0.560496\pi$
$379$	−7.35541	−0.377822	−0.188911	+	0.981994i	$0.560496\pi$
$380$	−1.45669	−0.0747266
$381$	2.11567	0.108389
$382$	31.1267	1.59258
$383$	−11.2947	−0.577132	−0.288566	−	0.957460i	$-0.593179\pi$
$383$	−11.2947	−0.577132	−0.288566	+	0.957460i	$0.593179\pi$
$384$	−1.02607	−0.0523616
$385$	−3.32818	−0.169620
$386$	18.5968	0.946551
$387$	4.42328	0.224848
$388$	−6.48360	−0.329155
$389$	−36.5807	−1.85472	−0.927358	−	0.374175i	$-0.877926\pi$
$389$	−36.5807	−1.85472	−0.927358	+	0.374175i	$0.877926\pi$
$390$	−1.44902	−0.0733739
$391$	8.26449	0.417953
$392$	0.205897	0.0103993
$393$	9.13977	0.461040
$394$	26.2739	1.32366
$395$	0.128148	0.00644783
$396$	−21.6811	−1.08952
$397$	−26.0998	−1.30991	−0.654956	−	0.755667i	$-0.727313\pi$
$397$	−26.0998	−1.30991	−0.654956	+	0.755667i	$0.727313\pi$
$398$	30.8070	1.54422
$399$	0.630887	0.0315839
$400$	18.5656	0.928281
$401$	28.9229	1.44434	0.722171	−	0.691715i	$-0.243144\pi$
$401$	28.9229	1.44434	0.722171	+	0.691715i	$0.243144\pi$
$402$	−4.02857	−0.200927
$403$	1.54907	0.0771647
$404$	−20.1925	−1.00461
$405$	−4.29231	−0.213286
$406$	1.74748	0.0867259
$407$	4.38052	0.217134
$408$	0.253248	0.0125377
$409$	2.72151	0.134570	0.0672851	−	0.997734i	$-0.478566\pi$
$409$	2.72151	0.134570	0.0672851	+	0.997734i	$0.478566\pi$
$410$	−0.614854	−0.0303655
$411$	2.48526	0.122589
$412$	−17.5037	−0.862345
$413$	−5.02332	−0.247181
$414$	21.5989	1.06153
$415$	5.17944	0.254249
$416$	−12.1966	−0.597989
$417$	−8.51349	−0.416908
$418$	−8.74457	−0.427711
$419$	2.11042	0.103101	0.0515503	−	0.998670i	$-0.483584\pi$
$419$	2.11042	0.103101	0.0515503	+	0.998670i	$0.483584\pi$
$420$	−0.898414	−0.0438381
$421$	4.00644	0.195262	0.0976311	−	0.995223i	$-0.468873\pi$
$421$	4.00644	0.195262	0.0976311	+	0.995223i	$0.468873\pi$
$422$	−5.11201	−0.248849
$423$	25.6152	1.24545
$424$	1.67615	0.0814012
$425$	−8.72086	−0.423024
$426$	−13.4101	−0.649719
$427$	−13.2114	−0.639346
$428$	5.75823	0.278335
$429$	−4.23280	−0.204361
$430$	−2.54054	−0.122516
$431$	−32.8801	−1.58378	−0.791889	−	0.610665i	$-0.790902\pi$
$431$	−32.8801	−1.58378	−0.791889	+	0.610665i	$0.790902\pi$
$432$	14.6920	0.706868
$433$	−3.66438	−0.176099	−0.0880495	−	0.996116i	$-0.528063\pi$
$433$	−3.66438	−0.176099	−0.0880495	+	0.996116i	$0.528063\pi$
$434$	1.97375	0.0947430
$435$	0.419596	0.0201181
$436$	36.8137	1.76306
$437$	4.23907	0.202782
$438$	5.02712	0.240205
$439$	13.5613	0.647247	0.323623	−	0.946186i	$-0.395099\pi$
$439$	13.5613	0.647247	0.323623	+	0.946186i	$0.395099\pi$
$440$	−0.685260	−0.0326685
$441$	−2.61090	−0.124329
$442$	6.02878	0.286760
$443$	−8.42078	−0.400083	−0.200042	−	0.979787i	$-0.564108\pi$
$443$	−8.42078	−0.400083	−0.200042	+	0.979787i	$0.564108\pi$
$444$	1.18249	0.0561183
$445$	6.00485	0.284657
$446$	3.31876	0.157148
$447$	−1.11487	−0.0527314
$448$	−7.14483	−0.337562
$449$	2.04013	0.0962799	0.0481400	−	0.998841i	$-0.484671\pi$
$449$	2.04013	0.0962799	0.0481400	+	0.998841i	$0.484671\pi$
$450$	−22.7916	−1.07441
$451$	−1.79608	−0.0845740
$452$	−31.3921	−1.47656
$453$	13.4728	0.633009
$454$	−47.1733	−2.21395
$455$	1.17693	0.0551755
$456$	0.129897	0.00608301
$457$	−16.5168	−0.772624	−0.386312	−	0.922368i	$-0.626251\pi$
$457$	−16.5168	−0.772624	−0.386312	+	0.922368i	$0.626251\pi$
$458$	−29.6174	−1.38393
$459$	−6.90128	−0.322124
$460$	−6.03665	−0.281460
$461$	21.0321	0.979564	0.489782	−	0.871845i	$-0.337076\pi$
$461$	21.0321	0.979564	0.489782	+	0.871845i	$0.337076\pi$
$462$	−5.39322	−0.250915
$463$	15.0658	0.700169	0.350084	−	0.936718i	$-0.386153\pi$
$463$	15.0658	0.700169	0.350084	+	0.936718i	$0.386153\pi$
$464$	3.71652	0.172535
$465$	0.473927	0.0219778
$466$	−13.1347	−0.608452
$467$	−14.0890	−0.651959	−0.325980	−	0.945377i	$-0.605694\pi$
$467$	−14.0890	−0.651959	−0.325980	+	0.945377i	$0.605694\pi$
$468$	7.66703	0.354408
$469$	3.27211	0.151092
$470$	−14.7123	−0.678627
$471$	−6.67951	−0.307776
$472$	−1.03428	−0.0476068
$473$	−7.42130	−0.341232
$474$	0.207661	0.00953817
$475$	−4.47315	−0.205242
$476$	3.73794	0.171328
$477$	−21.2547	−0.973186
$478$	42.4646	1.94229
$479$	−23.4894	−1.07326	−0.536628	−	0.843819i	$-0.680302\pi$
$479$	−23.4894	−1.07326	−0.536628	+	0.843819i	$0.680302\pi$
$480$	−3.73147	−0.170317
$481$	−1.54907	−0.0706315
$482$	−4.65448	−0.212006
$483$	2.61445	0.118962
$484$	15.5237	0.705622
$485$	2.59855	0.117994
$486$	−27.6797	−1.25558
$487$	33.8519	1.53398	0.766988	−	0.641661i	$-0.221754\pi$
$487$	33.8519	1.53398	0.766988	+	0.641661i	$0.221754\pi$
$488$	−2.72019	−0.123137
$489$	6.12899	0.277162
$490$	1.49959	0.0677445
$491$	16.9397	0.764477	0.382238	−	0.924064i	$-0.375153\pi$
$491$	16.9397	0.764477	0.382238	+	0.924064i	$0.375153\pi$
$492$	−0.484837	−0.0218581
$493$	−1.74577	−0.0786254
$494$	3.09232	0.139130
$495$	8.68954	0.390566
$496$	4.19775	0.188485
$497$	10.8920	0.488574
$498$	8.39314	0.376106
$499$	21.0113	0.940594	0.470297	−	0.882508i	$-0.344147\pi$
$499$	21.0113	0.940594	0.470297	+	0.882508i	$0.344147\pi$
$500$	13.5714	0.606931
$501$	−1.12235	−0.0501427
$502$	−13.1494	−0.586885
$503$	4.58914	0.204620	0.102310	−	0.994753i	$-0.467377\pi$
$503$	4.58914	0.204620	0.102310	+	0.994753i	$0.467377\pi$
$504$	−0.537575	−0.0239455
$505$	8.09291	0.360130
$506$	−36.2383	−1.61099
$507$	−6.61229	−0.293662
$508$	6.42959	0.285267
$509$	1.45303	0.0644045	0.0322023	−	0.999481i	$-0.489748\pi$
$509$	1.45303	0.0644045	0.0322023	+	0.999481i	$0.489748\pi$
$510$	1.84446	0.0816741
$511$	−4.08316	−0.180629
$512$	−31.3225	−1.38427
$513$	−3.53984	−0.156288
$514$	−44.2436	−1.95150
$515$	7.01527	0.309130
$516$	−2.00332	−0.0881912
$517$	−42.9767	−1.89011
$518$	−1.97375	−0.0867215
$519$	−8.58283	−0.376745
$520$	0.242326	0.0106267
$521$	−20.6596	−0.905115	−0.452558	−	0.891735i	$-0.649488\pi$
$521$	−20.6596	−0.905115	−0.452558	+	0.891735i	$0.649488\pi$
$522$	−4.56249	−0.199695
$523$	13.8172	0.604186	0.302093	−	0.953278i	$-0.402315\pi$
$523$	13.8172	0.604186	0.302093	+	0.953278i	$0.402315\pi$
$524$	27.7760	1.21340
$525$	−2.75882	−0.120405
$526$	−39.7239	−1.73204
$527$	−1.97182	−0.0858937
$528$	−11.4703	−0.499179
$529$	−5.43293	−0.236214
$530$	12.2078	0.530273
$531$	13.1154	0.569159
$532$	1.91728	0.0831248
$533$	0.635141	0.0275110
$534$	9.73070	0.421088
$535$	−2.30783	−0.0997763
$536$	0.673717	0.0291001
$537$	4.74324	0.204686
$538$	12.3210	0.531197
$539$	4.38052	0.188682
$540$	5.04091	0.216926
$541$	−1.24476	−0.0535166	−0.0267583	−	0.999642i	$-0.508518\pi$
$541$	−1.24476	−0.0535166	−0.0267583	+	0.999642i	$0.508518\pi$
$542$	−22.8616	−0.981991
$543$	2.60216	0.111670
$544$	15.5251	0.665634
$545$	−14.7545	−0.632013
$546$	1.90719	0.0816201
$547$	−0.726469	−0.0310616	−0.0155308	−	0.999879i	$-0.504944\pi$
$547$	−0.726469	−0.0310616	−0.0155308	+	0.999879i	$0.504944\pi$
$548$	7.55279	0.322639
$549$	34.4937	1.47216
$550$	38.2393	1.63053
$551$	−0.895450	−0.0381474
$552$	0.538306	0.0229118
$553$	−0.168668	−0.00717248
$554$	−25.5354	−1.08490
$555$	−0.473927	−0.0201171
$556$	−25.8728	−1.09725
$557$	−36.8619	−1.56189	−0.780943	−	0.624602i	$-0.785261\pi$
$557$	−36.8619	−1.56189	−0.780943	+	0.624602i	$0.785261\pi$
$558$	−5.15326	−0.218155
$559$	2.62437	0.110999
$560$	3.18932	0.134773
$561$	5.38794	0.227479
$562$	25.8199	1.08915
$563$	−14.7990	−0.623703	−0.311852	−	0.950131i	$-0.600949\pi$
$563$	−14.7990	−0.623703	−0.311852	+	0.950131i	$0.600949\pi$
$564$	−11.6012	−0.488499
$565$	12.5816	0.529311
$566$	45.9518	1.93150
$567$	5.64950	0.237257
$568$	2.24263	0.0940986
$569$	−27.4013	−1.14872	−0.574361	−	0.818602i	$-0.694749\pi$
$569$	−27.4013	−1.14872	−0.574361	+	0.818602i	$0.694749\pi$
$570$	0.946071	0.0396266
$571$	33.1047	1.38539	0.692695	−	0.721231i	$-0.256423\pi$
$571$	33.1047	1.38539	0.692695	+	0.721231i	$0.256423\pi$
$572$	−12.8636	−0.537854
$573$	−9.83719	−0.410955
$574$	0.809266	0.0337781
$575$	−18.5371	−0.773052
$576$	18.6544	0.777268
$577$	43.5277	1.81208	0.906040	−	0.423191i	$-0.139090\pi$
$577$	43.5277	1.81208	0.906040	+	0.423191i	$0.139090\pi$
$578$	25.8797	1.07645
$579$	−5.87728	−0.244251
$580$	1.27516	0.0529483
$581$	−6.81714	−0.282823
$582$	4.21088	0.174547
$583$	35.6608	1.47692
$584$	−0.840710	−0.0347888
$585$	−3.07285	−0.127047
$586$	63.9280	2.64084
$587$	38.8457	1.60333	0.801667	−	0.597772i	$-0.203947\pi$
$587$	38.8457	1.60333	0.801667	+	0.597772i	$0.203947\pi$
$588$	1.18249	0.0487649
$589$	−1.01140	−0.0416738
$590$	−7.53292	−0.310125
$591$	−8.30355	−0.341562
$592$	−4.19775	−0.172527
$593$	−4.20248	−0.172575	−0.0862876	−	0.996270i	$-0.527500\pi$
$593$	−4.20248	−0.172575	−0.0862876	+	0.996270i	$0.527500\pi$
$594$	30.2608	1.24162
$595$	−1.49812	−0.0614170
$596$	−3.38811	−0.138783
$597$	−9.73617	−0.398475
$598$	12.8148	0.524037
$599$	6.82439	0.278837	0.139419	−	0.990234i	$-0.455477\pi$
$599$	6.82439	0.278837	0.139419	+	0.990234i	$0.455477\pi$
$600$	−0.568032	−0.0231898
$601$	−28.3014	−1.15444	−0.577218	−	0.816590i	$-0.695862\pi$
$601$	−28.3014	−1.15444	−0.577218	+	0.816590i	$0.695862\pi$
$602$	3.34384	0.136285
$603$	−8.54316	−0.347904
$604$	40.9444	1.66600
$605$	−6.22171	−0.252949
$606$	13.1143	0.532734
$607$	44.3485	1.80005	0.900025	−	0.435838i	$-0.143548\pi$
$607$	44.3485	1.80005	0.900025	+	0.435838i	$0.143548\pi$
$608$	7.96324	0.322952
$609$	−0.552269	−0.0223791
$610$	−19.8117	−0.802153
$611$	15.1977	0.614834
$612$	−9.75938	−0.394500
$613$	−44.5723	−1.80026	−0.900130	−	0.435622i	$-0.856529\pi$
$613$	−44.5723	−1.80026	−0.900130	+	0.435622i	$0.856529\pi$
$614$	−56.5962	−2.28404
$615$	0.194317	0.00783561
$616$	0.901935	0.0363400
$617$	17.9280	0.721756	0.360878	−	0.932613i	$-0.382477\pi$
$617$	17.9280	0.721756	0.360878	+	0.932613i	$0.382477\pi$
$618$	11.3681	0.457290
$619$	−32.2387	−1.29578	−0.647891	−	0.761733i	$-0.724349\pi$
$619$	−32.2387	−1.29578	−0.647891	+	0.761733i	$0.724349\pi$
$620$	1.44028	0.0578429
$621$	−14.6694	−0.588663
$622$	16.0008	0.641575
$623$	−7.90354	−0.316649
$624$	4.05619	0.162378
$625$	16.6745	0.666981
$626$	−14.9429	−0.597238
$627$	2.76361	0.110368
$628$	−20.2993	−0.810028
$629$	1.97182	0.0786215
$630$	−3.91528	−0.155988
$631$	41.4566	1.65036	0.825181	−	0.564869i	$-0.191073\pi$
$631$	41.4566	1.65036	0.825181	+	0.564869i	$0.191073\pi$
$632$	−0.0347281	−0.00138141
$633$	1.61559	0.0642139
$634$	49.3924	1.96162
$635$	−2.57690	−0.102261
$636$	9.62633	0.381709
$637$	−1.54907	−0.0613764
$638$	7.65487	0.303059
$639$	−28.4380	−1.12499
$640$	1.24977	0.0494013
$641$	4.28034	0.169063	0.0845316	−	0.996421i	$-0.473061\pi$
$641$	4.28034	0.169063	0.0845316	+	0.996421i	$0.473061\pi$
$642$	−3.73978	−0.147597
$643$	−39.7910	−1.56920	−0.784602	−	0.620000i	$-0.787133\pi$
$643$	−39.7910	−1.56920	−0.784602	+	0.620000i	$0.787133\pi$
$644$	7.94539	0.313092
$645$	0.802907	0.0316144
$646$	−3.93622	−0.154869
$647$	−13.5242	−0.531691	−0.265846	−	0.964016i	$-0.585651\pi$
$647$	−13.5242	−0.531691	−0.265846	+	0.964016i	$0.585651\pi$
$648$	1.16321	0.0456953
$649$	−22.0048	−0.863762
$650$	−13.5225	−0.530394
$651$	−0.623779	−0.0244478
$652$	18.6262	0.729457
$653$	−4.24042	−0.165940	−0.0829702	−	0.996552i	$-0.526441\pi$
$653$	−4.24042	−0.165940	−0.0829702	+	0.996552i	$0.526441\pi$
$654$	−23.9092	−0.934926
$655$	−11.1323	−0.434975
$656$	1.72114	0.0671992
$657$	10.6607	0.415915
$658$	19.3642	0.754894
$659$	−1.04656	−0.0407683	−0.0203842	−	0.999792i	$-0.506489\pi$
$659$	−1.04656	−0.0407683	−0.0203842	+	0.999792i	$0.506489\pi$
$660$	−3.93552	−0.153190
$661$	−18.6118	−0.723913	−0.361957	−	0.932195i	$-0.617891\pi$
$661$	−18.6118	−0.723913	−0.361957	+	0.932195i	$0.617891\pi$
$662$	−39.3261	−1.52845
$663$	−1.90532	−0.0739965
$664$	−1.40363	−0.0544713
$665$	−0.768425	−0.0297983
$666$	5.15326	0.199685
$667$	−3.71082	−0.143683
$668$	−3.41084	−0.131969
$669$	−1.04885	−0.0405510
$670$	4.90682	0.189567
$671$	−57.8729	−2.23416
$672$	4.91133	0.189459
$673$	−38.9143	−1.50004	−0.750018	−	0.661418i	$-0.769955\pi$
$673$	−38.9143	−1.50004	−0.750018	+	0.661418i	$0.769955\pi$
$674$	56.0661	2.15958
$675$	15.4795	0.595805
$676$	−20.0950	−0.772883
$677$	−36.9357	−1.41955	−0.709777	−	0.704427i	$-0.751204\pi$
$677$	−36.9357	−1.41955	−0.709777	+	0.704427i	$0.751204\pi$
$678$	20.3881	0.783000
$679$	−3.42019	−0.131255
$680$	−0.308458	−0.0118288
$681$	14.9085	0.571296
$682$	8.64605	0.331074
$683$	10.5050	0.401964	0.200982	−	0.979595i	$-0.435587\pi$
$683$	10.5050	0.401964	0.200982	+	0.979595i	$0.435587\pi$
$684$	−5.00584	−0.191403
$685$	−3.02707	−0.115658
$686$	−1.97375	−0.0753581
$687$	9.36022	0.357115
$688$	7.11166	0.271129
$689$	−12.6106	−0.480426
$690$	3.92060	0.149255
$691$	−13.6543	−0.519434	−0.259717	−	0.965685i	$-0.583629\pi$
$691$	−13.6543	−0.519434	−0.259717	+	0.965685i	$0.583629\pi$
$692$	−26.0835	−0.991546
$693$	−11.4371	−0.434460
$694$	20.6682	0.784553
$695$	10.3695	0.393338
$696$	−0.113710	−0.00431018
$697$	−0.808474	−0.0306231
$698$	19.8331	0.750693
$699$	4.15105	0.157007
$700$	−8.38414	−0.316891
$701$	−36.0800	−1.36272	−0.681362	−	0.731947i	$-0.738612\pi$
$701$	−36.0800	−1.36272	−0.681362	+	0.731947i	$0.738612\pi$
$702$	−10.7010	−0.403885
$703$	1.01140	0.0381455
$704$	−31.2981	−1.17959
$705$	4.64963	0.175115
$706$	26.1178	0.982958
$707$	−10.6518	−0.400603
$708$	−5.94001	−0.223239
$709$	−43.0286	−1.61597	−0.807987	−	0.589200i	$-0.799443\pi$
$709$	−43.0286	−1.61597	−0.807987	+	0.589200i	$0.799443\pi$
$710$	16.3336	0.612987
$711$	0.440374	0.0165153
$712$	−1.62731	−0.0609861
$713$	−4.19131	−0.156966
$714$	−2.42767	−0.0908531
$715$	5.15558	0.192808
$716$	14.4148	0.538708
$717$	−13.4204	−0.501195
$718$	−17.0964	−0.638032
$719$	1.39941	0.0521890	0.0260945	−	0.999659i	$-0.491693\pi$
$719$	1.39941	0.0521890	0.0260945	+	0.999659i	$0.491693\pi$
$720$	−8.32698	−0.310328
$721$	−9.23345	−0.343872
$722$	35.4822	1.32051
$723$	1.47099	0.0547068
$724$	7.90805	0.293900
$725$	3.91573	0.145427
$726$	−10.0821	−0.374182
$727$	−0.653193	−0.0242256	−0.0121128	−	0.999927i	$-0.503856\pi$
$727$	−0.653193	−0.0242256	−0.0121128	+	0.999927i	$0.503856\pi$
$728$	−0.318948	−0.0118210
$729$	−8.20068	−0.303729
$730$	−6.12307	−0.226625
$731$	−3.34057	−0.123555
$732$	−15.6223	−0.577418
$733$	21.9930	0.812331	0.406165	−	0.913800i	$-0.366866\pi$
$733$	21.9930	0.812331	0.406165	+	0.913800i	$0.366866\pi$
$734$	−2.04377	−0.0754369
$735$	−0.473927	−0.0174810
$736$	33.0003	1.21641
$737$	14.3336	0.527983
$738$	−2.11291	−0.0777774
$739$	−39.0282	−1.43568	−0.717838	−	0.696210i	$-0.754868\pi$
$739$	−39.0282	−1.43568	−0.717838	+	0.696210i	$0.754868\pi$
$740$	−1.44028	−0.0529457
$741$	−0.977288	−0.0359016
$742$	−16.0678	−0.589868
$743$	−31.0061	−1.13750	−0.568751	−	0.822510i	$-0.692573\pi$
$743$	−31.0061	−1.13750	−0.568751	+	0.822510i	$0.692573\pi$
$744$	−0.128434	−0.00470862
$745$	1.35792	0.0497502
$746$	−31.2780	−1.14517
$747$	17.7989	0.651227
$748$	16.3741	0.598697
$749$	3.03755	0.110990
$750$	−8.81416	−0.321847
$751$	−31.3512	−1.14402	−0.572011	−	0.820246i	$-0.693836\pi$
$751$	−31.3512	−1.14402	−0.572011	+	0.820246i	$0.693836\pi$
$752$	41.1836	1.50181
$753$	4.15570	0.151442
$754$	−2.70697	−0.0985819
$755$	−16.4100	−0.597222
$756$	−6.63481	−0.241306
$757$	−34.5625	−1.25620	−0.628098	−	0.778134i	$-0.716166\pi$
$757$	−34.5625	−1.25620	−0.628098	+	0.778134i	$0.716166\pi$
$758$	14.5177	0.527308
$759$	11.4527	0.415705
$760$	−0.158216	−0.00573910
$761$	−7.90008	−0.286378	−0.143189	−	0.989695i	$-0.545736\pi$
$761$	−7.90008	−0.286378	−0.143189	+	0.989695i	$0.545736\pi$
$762$	−4.17580	−0.151273
$763$	19.4197	0.703042
$764$	−29.8955	−1.08158
$765$	3.91145	0.141419
$766$	22.2929	0.805475
$767$	7.78147	0.280973
$768$	10.9388	0.394720
$769$	−25.1394	−0.906549	−0.453275	−	0.891371i	$-0.649744\pi$
$769$	−25.1394	−0.906549	−0.453275	+	0.891371i	$0.649744\pi$
$770$	6.56898	0.236730
$771$	13.9827	0.503573
$772$	−17.8612	−0.642840
$773$	49.3044	1.77336	0.886678	−	0.462387i	$-0.153007\pi$
$773$	49.3044	1.77336	0.886678	+	0.462387i	$0.153007\pi$
$774$	−8.73044	−0.313809
$775$	4.42275	0.158870
$776$	−0.704206	−0.0252795
$777$	0.623779	0.0223779
$778$	72.2011	2.58854
$779$	−0.414687	−0.0148577
$780$	1.39171	0.0498311
$781$	47.7127	1.70730
$782$	−16.3120	−0.583317
$783$	3.09873	0.110739
$784$	−4.19775	−0.149920
$785$	8.13570	0.290376
$786$	−18.0396	−0.643451
$787$	−34.4114	−1.22663	−0.613317	−	0.789837i	$-0.710165\pi$
$787$	−34.4114	−1.22663	−0.613317	+	0.789837i	$0.710165\pi$
$788$	−25.2347	−0.898950
$789$	12.5542	0.446943
$790$	−0.252932	−0.00899892
$791$	−16.5598	−0.588798
$792$	−2.35486	−0.0836763
$793$	20.4654	0.726748
$794$	51.5145	1.82818
$795$	−3.85812	−0.136833
$796$	−29.5885	−1.04874
$797$	28.2114	0.999300	0.499650	−	0.866227i	$-0.333462\pi$
$797$	28.2114	0.999300	0.499650	+	0.866227i	$0.333462\pi$
$798$	−1.24521	−0.0440800
$799$	−19.3452	−0.684385
$800$	−34.8226	−1.23117
$801$	20.6354	0.729114
$802$	−57.0866	−2.01580
$803$	−17.8864	−0.631197
$804$	3.86923	0.136457
$805$	−3.18442	−0.112236
$806$	−3.05747	−0.107695
$807$	−3.89391	−0.137072
$808$	−2.19318	−0.0771556
$809$	25.0123	0.879387	0.439694	−	0.898148i	$-0.355087\pi$
$809$	25.0123	0.879387	0.439694	+	0.898148i	$0.355087\pi$
$810$	8.47193	0.297673
$811$	3.01982	0.106040	0.0530200	−	0.998593i	$-0.483115\pi$
$811$	3.01982	0.106040	0.0530200	+	0.998593i	$0.483115\pi$
$812$	−1.67836	−0.0588990
$813$	7.22513	0.253397
$814$	−8.64605	−0.303044
$815$	−7.46515	−0.261493
$816$	−5.16314	−0.180746
$817$	−1.71346	−0.0599465
$818$	−5.37158	−0.187813
$819$	4.04447	0.141325
$820$	0.590535	0.0206224
$821$	−55.8390	−1.94880	−0.974398	−	0.224831i	$-0.927817\pi$
$821$	−55.8390	−1.94880	−0.974398	+	0.224831i	$0.927817\pi$
$822$	−4.90528	−0.171091
$823$	−14.9611	−0.521512	−0.260756	−	0.965405i	$-0.583972\pi$
$823$	−14.9611	−0.521512	−0.260756	+	0.965405i	$0.583972\pi$
$824$	−1.90114	−0.0662292
$825$	−12.0851	−0.420748
$826$	9.91477	0.344979
$827$	−0.0453555	−0.00157717	−0.000788583	−	1.00000i	$-0.500251\pi$
$827$	−0.0453555	−0.00157717	−0.000788583		1.00000i	$0.500251\pi$
$828$	−20.7446	−0.720925
$829$	37.3663	1.29778	0.648892	−	0.760880i	$-0.275233\pi$
$829$	37.3663	1.29778	0.648892	+	0.760880i	$0.275233\pi$
$830$	−10.2229	−0.354842
$831$	8.07016	0.279951
$832$	11.0678	0.383708
$833$	1.97182	0.0683194
$834$	16.8035	0.581857
$835$	1.36703	0.0473079
$836$	8.39871	0.290475
$837$	3.49996	0.120976
$838$	−4.16543	−0.143892
$839$	10.3244	0.356437	0.178218	−	0.983991i	$-0.442967\pi$
$839$	10.3244	0.356437	0.178218	+	0.983991i	$0.442967\pi$
$840$	−0.0975799	−0.00336683
$841$	−28.2161	−0.972970
$842$	−7.90771	−0.272518
$843$	−8.16007	−0.281048
$844$	4.90982	0.169003
$845$	8.05382	0.277060
$846$	−50.5580	−1.73822
$847$	8.18897	0.281376
$848$	−34.1729	−1.17350
$849$	−14.5225	−0.498411
$850$	17.2128	0.590394
$851$	4.19131	0.143676
$852$	12.8797	0.441250
$853$	48.2909	1.65345	0.826725	−	0.562606i	$-0.190201\pi$
$853$	48.2909	1.65345	0.826725	+	0.562606i	$0.190201\pi$
$854$	26.0760	0.892303
$855$	2.00628	0.0686134
$856$	0.625421	0.0213765
$857$	−41.8386	−1.42918	−0.714590	−	0.699544i	$-0.753387\pi$
$857$	−41.8386	−1.42918	−0.714590	+	0.699544i	$0.753387\pi$
$858$	8.35447	0.285217
$859$	−51.7397	−1.76533	−0.882667	−	0.469999i	$-0.844254\pi$
$859$	−51.7397	−1.76533	−0.882667	+	0.469999i	$0.844254\pi$
$860$	2.44006	0.0832053
$861$	−0.255758	−0.00871622
$862$	64.8970	2.21040
$863$	24.7956	0.844051	0.422026	−	0.906584i	$-0.361319\pi$
$863$	24.7956	0.844051	0.422026	+	0.906584i	$0.361319\pi$
$864$	−27.5570	−0.937508
$865$	10.4540	0.355445
$866$	7.23257	0.245773
$867$	−8.17895	−0.277772
$868$	−1.89568	−0.0643437
$869$	−0.738852	−0.0250638
$870$	−0.828176	−0.0280778
$871$	−5.06873	−0.171747
$872$	3.99846	0.135405
$873$	8.92978	0.302227
$874$	−8.36686	−0.283013
$875$	7.15910	0.242022
$876$	−4.82829	−0.163133
$877$	16.4652	0.555991	0.277996	−	0.960582i	$-0.410330\pi$
$877$	16.4652	0.555991	0.277996	+	0.960582i	$0.410330\pi$
$878$	−26.7666	−0.903330
$879$	−20.2037	−0.681452
$880$	13.9709	0.470958
$881$	−34.3400	−1.15694	−0.578471	−	0.815703i	$-0.696351\pi$
$881$	−34.3400	−1.15694	−0.578471	+	0.815703i	$0.696351\pi$
$882$	5.15326	0.173519
$883$	−35.2189	−1.18521	−0.592606	−	0.805492i	$-0.701901\pi$
$883$	−35.2189	−1.18521	−0.592606	+	0.805492i	$0.701901\pi$
$884$	−5.79033	−0.194750
$885$	2.38068	0.0800258
$886$	16.6205	0.558377
$887$	−38.4878	−1.29229	−0.646147	−	0.763213i	$-0.723621\pi$
$887$	−38.4878	−1.29229	−0.646147	+	0.763213i	$0.723621\pi$
$888$	0.128434	0.00430996
$889$	3.39170	0.113754
$890$	−11.8521	−0.397282
$891$	24.7478	0.829081
$892$	−3.18750	−0.106725
$893$	−9.92267	−0.332049
$894$	2.20047	0.0735946
$895$	−5.77730	−0.193114
$896$	−1.64493	−0.0549533
$897$	−4.04996	−0.135224
$898$	−4.02671	−0.134373
$899$	0.885360	0.0295284
$900$	21.8901	0.729671
$901$	16.0521	0.534772
$902$	3.54501	0.118036
$903$	−1.05678	−0.0351674
$904$	−3.40960	−0.113402
$905$	−3.16945	−0.105356
$906$	−26.5920	−0.883460
$907$	0.975426	0.0323885	0.0161942	−	0.999869i	$-0.494845\pi$
$907$	0.975426	0.0323885	0.0161942	+	0.999869i	$0.494845\pi$
$908$	45.3075	1.50358
$909$	27.8109	0.922428
$910$	−2.32297	−0.0770057
$911$	−28.2351	−0.935470	−0.467735	−	0.883869i	$-0.654930\pi$
$911$	−28.2351	−0.935470	−0.467735	+	0.883869i	$0.654930\pi$
$912$	−2.64831	−0.0876942
$913$	−29.8626	−0.988309
$914$	32.6000	1.07831
$915$	6.26125	0.206990
$916$	28.4460	0.939882
$917$	14.6523	0.483860
$918$	13.6214	0.449573
$919$	15.9351	0.525649	0.262825	−	0.964844i	$-0.415346\pi$
$919$	15.9351	0.525649	0.262825	+	0.964844i	$0.415346\pi$
$920$	−0.655661	−0.0216165
$921$	17.8865	0.589381
$922$	−41.5121	−1.36713
$923$	−16.8725	−0.555365
$924$	5.17991	0.170406
$925$	−4.42275	−0.145419
$926$	−29.7362	−0.977191
$927$	24.1076	0.791798
$928$	−6.97090	−0.228831
$929$	−42.0855	−1.38078	−0.690391	−	0.723437i	$-0.742561\pi$
$929$	−42.0855	−1.38078	−0.690391	+	0.723437i	$0.742561\pi$
$930$	−0.935412	−0.0306734
$931$	1.01140	0.0331472
$932$	12.6152	0.413224
$933$	−5.05686	−0.165554
$934$	27.8081	0.909907
$935$	−6.56255	−0.214618
$936$	0.832742	0.0272190
$937$	−36.9298	−1.20644	−0.603221	−	0.797574i	$-0.706116\pi$
$937$	−36.9298	−1.20644	−0.603221	+	0.797574i	$0.706116\pi$
$938$	−6.45833	−0.210872
$939$	4.72251	0.154113
$940$	14.1304	0.460882
$941$	−50.8336	−1.65713	−0.828564	−	0.559895i	$-0.810842\pi$
$941$	−50.8336	−1.65713	−0.828564	+	0.559895i	$0.810842\pi$
$942$	13.1837	0.429548
$943$	−1.71850	−0.0559620
$944$	21.0867	0.686312
$945$	2.65915	0.0865023
$946$	14.6478	0.476240
$947$	53.5775	1.74104	0.870518	−	0.492136i	$-0.163784\pi$
$947$	53.5775	1.74104	0.870518	+	0.492136i	$0.163784\pi$
$948$	−0.199447	−0.00647774
$949$	6.32511	0.205322
$950$	8.82888	0.286447
$951$	−15.6098	−0.506184
$952$	0.405990	0.0131582
$953$	−55.2547	−1.78988	−0.894938	−	0.446191i	$-0.852780\pi$
$953$	−55.2547	−1.78988	−0.894938	+	0.446191i	$0.852780\pi$
$954$	41.9514	1.35823
$955$	11.9818	0.387721
$956$	−40.7851	−1.31908
$957$	−2.41923	−0.0782025
$958$	46.3621	1.49789
$959$	3.98421	0.128657
$960$	3.38613	0.109287
$961$	1.00000	0.0322581
$962$	3.05747	0.0985769
$963$	−7.93074	−0.255565
$964$	4.47039	0.143982
$965$	7.15857	0.230443
$966$	−5.16026	−0.166029
$967$	0.0950029	0.00305509	0.00152754	−	0.999999i	$-0.499514\pi$
$967$	0.0950029	0.00305509	0.00152754	+	0.999999i	$0.499514\pi$
$968$	1.68608	0.0541927
$969$	1.24399	0.0399628
$970$	−5.12889	−0.164679
$971$	10.8151	0.347072	0.173536	−	0.984828i	$-0.444481\pi$
$971$	10.8151	0.347072	0.173536	+	0.984828i	$0.444481\pi$
$972$	26.5849	0.852711
$973$	−13.6483	−0.437543
$974$	−66.8152	−2.14090
$975$	4.27360	0.136865
$976$	55.4583	1.77518
$977$	−15.2991	−0.489463	−0.244732	−	0.969591i	$-0.578700\pi$
$977$	−15.2991	−0.489463	−0.244732	+	0.969591i	$0.578700\pi$
$978$	−12.0971	−0.386822
$979$	−34.6216	−1.10651
$980$	−1.44028	−0.0460080
$981$	−50.7030	−1.61882
$982$	−33.4346	−1.06694
$983$	−13.0016	−0.414686	−0.207343	−	0.978268i	$-0.566482\pi$
$983$	−13.0016	−0.414686	−0.207343	+	0.978268i	$0.566482\pi$
$984$	−0.0526598	−0.00167873
$985$	10.1138	0.322252
$986$	3.44571	0.109734
$987$	−6.11981	−0.194796
$988$	−2.97001	−0.0944886
$989$	−7.10074	−0.225790
$990$	−17.1510	−0.545093
$991$	26.6675	0.847120	0.423560	−	0.905868i	$-0.360780\pi$
$991$	26.6675	0.847120	0.423560	+	0.905868i	$0.360780\pi$
$992$	−7.87351	−0.249984
$993$	12.4285	0.394408
$994$	−21.4981	−0.681878
$995$	11.8587	0.375947
$996$	−8.06118	−0.255428
$997$	−12.3804	−0.392092	−0.196046	−	0.980595i	$-0.562810\pi$
$997$	−12.3804	−0.392092	−0.196046	+	0.980595i	$0.562810\pi$
$998$	−41.4710	−1.31274
$999$	−3.49996	−0.110734

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8029.2.a.b.1.12	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8029.2.a.b.1.12	✓	64	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:	\( N \)	\(=\)	\( 8029 = 7 \cdot 31 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8029.a (trivial)

\(f(q)\)	\(=\)	\(q-1.97375 q^{2} +0.623779 q^{3} +1.89568 q^{4} -0.759767 q^{5} -1.23118 q^{6} +1.00000 q^{7} +0.205897 q^{8} -2.61090 q^{9} +O(q^{10})\)	\(q-1.97375 q^{2} +0.623779 q^{3} +1.89568 q^{4} -0.759767 q^{5} -1.23118 q^{6} +1.00000 q^{7} +0.205897 q^{8} -2.61090 q^{9} +1.49959 q^{10} +4.38052 q^{11} +1.18249 q^{12} -1.54907 q^{13} -1.97375 q^{14} -0.473927 q^{15} -4.19775 q^{16} +1.97182 q^{17} +5.15326 q^{18} +1.01140 q^{19} -1.44028 q^{20} +0.623779 q^{21} -8.64605 q^{22} +4.19131 q^{23} +0.128434 q^{24} -4.42275 q^{25} +3.05747 q^{26} -3.49996 q^{27} +1.89568 q^{28} -0.885360 q^{29} +0.935412 q^{30} -1.00000 q^{31} +7.87351 q^{32} +2.73248 q^{33} -3.89187 q^{34} -0.759767 q^{35} -4.94944 q^{36} +1.00000 q^{37} -1.99624 q^{38} -0.966277 q^{39} -0.156433 q^{40} -0.410015 q^{41} -1.23118 q^{42} -1.69416 q^{43} +8.30408 q^{44} +1.98368 q^{45} -8.27259 q^{46} -9.81087 q^{47} -2.61847 q^{48} +1.00000 q^{49} +8.72940 q^{50} +1.22998 q^{51} -2.93654 q^{52} +8.14076 q^{53} +6.90804 q^{54} -3.32818 q^{55} +0.205897 q^{56} +0.630887 q^{57} +1.74748 q^{58} -5.02332 q^{59} -0.898414 q^{60} -13.2114 q^{61} +1.97375 q^{62} -2.61090 q^{63} -7.14483 q^{64} +1.17693 q^{65} -5.39322 q^{66} +3.27211 q^{67} +3.73794 q^{68} +2.61445 q^{69} +1.49959 q^{70} +10.8920 q^{71} -0.537575 q^{72} -4.08316 q^{73} -1.97375 q^{74} -2.75882 q^{75} +1.91728 q^{76} +4.38052 q^{77} +1.90719 q^{78} -0.168668 q^{79} +3.18932 q^{80} +5.64950 q^{81} +0.809266 q^{82} -6.81714 q^{83} +1.18249 q^{84} -1.49812 q^{85} +3.34384 q^{86} -0.552269 q^{87} +0.901935 q^{88} -7.90354 q^{89} -3.91528 q^{90} -1.54907 q^{91} +7.94539 q^{92} -0.623779 q^{93} +19.3642 q^{94} -0.768425 q^{95} +4.91133 q^{96} -3.42019 q^{97} -1.97375 q^{98} -11.4371 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 5 q^{2} - 18 q^{3} + 57 q^{4} - 26 q^{5} - 13 q^{6} + 64 q^{7} - 15 q^{8} + 56 q^{9}+O(q^{10}) \) 64 * q - 5 * q^2 - 18 * q^3 + 57 * q^4 - 26 * q^5 - 13 * q^6 + 64 * q^7 - 15 * q^8 + 56 * q^9	\( 64 q - 5 q^{2} - 18 q^{3} + 57 q^{4} - 26 q^{5} - 13 q^{6} + 64 q^{7} - 15 q^{8} + 56 q^{9} - 14 q^{10} - 37 q^{11} - 27 q^{12} - 18 q^{13} - 5 q^{14} + 6 q^{15} + 39 q^{16} - 27 q^{17} - 32 q^{18} - 27 q^{19} - 55 q^{20} - 18 q^{21} + 2 q^{22} - 10 q^{23} - 39 q^{24} + 58 q^{25} - 47 q^{26} - 66 q^{27} + 57 q^{28} + 4 q^{29} + 14 q^{30} - 64 q^{31} - 30 q^{32} - 44 q^{33} - 4 q^{34} - 26 q^{35} + 32 q^{36} + 64 q^{37} - 75 q^{38} + 2 q^{39} - 5 q^{40} - 85 q^{41} - 13 q^{42} + 16 q^{43} - 66 q^{44} - 77 q^{45} - 100 q^{47} - 15 q^{48} + 64 q^{49} - 10 q^{50} - 55 q^{51} - 21 q^{52} - 23 q^{53} - 25 q^{54} - 19 q^{55} - 15 q^{56} + 7 q^{57} - 40 q^{58} - 125 q^{59} + 67 q^{60} - 17 q^{61} + 5 q^{62} + 56 q^{63} + 19 q^{64} - 38 q^{65} - 11 q^{66} - 33 q^{67} - 47 q^{68} - 52 q^{69} - 14 q^{70} - 129 q^{71} - 42 q^{72} - 37 q^{73} - 5 q^{74} - 108 q^{75} - 33 q^{76} - 37 q^{77} + 13 q^{78} - 14 q^{79} - 90 q^{80} + 56 q^{81} - 40 q^{82} - 114 q^{83} - 27 q^{84} + 3 q^{85} - 26 q^{86} + 7 q^{87} - 11 q^{88} - 72 q^{89} - 21 q^{90} - 18 q^{91} + 6 q^{92} + 18 q^{93} + q^{94} - 80 q^{95} - 26 q^{96} + q^{97} - 5 q^{98} - 82 q^{99}+O(q^{100}) \) 64 * q - 5 * q^2 - 18 * q^3 + 57 * q^4 - 26 * q^5 - 13 * q^6 + 64 * q^7 - 15 * q^8 + 56 * q^9 - 14 * q^10 - 37 * q^11 - 27 * q^12 - 18 * q^13 - 5 * q^14 + 6 * q^15 + 39 * q^16 - 27 * q^17 - 32 * q^18 - 27 * q^19 - 55 * q^20 - 18 * q^21 + 2 * q^22 - 10 * q^23 - 39 * q^24 + 58 * q^25 - 47 * q^26 - 66 * q^27 + 57 * q^28 + 4 * q^29 + 14 * q^30 - 64 * q^31 - 30 * q^32 - 44 * q^33 - 4 * q^34 - 26 * q^35 + 32 * q^36 + 64 * q^37 - 75 * q^38 + 2 * q^39 - 5 * q^40 - 85 * q^41 - 13 * q^42 + 16 * q^43 - 66 * q^44 - 77 * q^45 - 100 * q^47 - 15 * q^48 + 64 * q^49 - 10 * q^50 - 55 * q^51 - 21 * q^52 - 23 * q^53 - 25 * q^54 - 19 * q^55 - 15 * q^56 + 7 * q^57 - 40 * q^58 - 125 * q^59 + 67 * q^60 - 17 * q^61 + 5 * q^62 + 56 * q^63 + 19 * q^64 - 38 * q^65 - 11 * q^66 - 33 * q^67 - 47 * q^68 - 52 * q^69 - 14 * q^70 - 129 * q^71 - 42 * q^72 - 37 * q^73 - 5 * q^74 - 108 * q^75 - 33 * q^76 - 37 * q^77 + 13 * q^78 - 14 * q^79 - 90 * q^80 + 56 * q^81 - 40 * q^82 - 114 * q^83 - 27 * q^84 + 3 * q^85 - 26 * q^86 + 7 * q^87 - 11 * q^88 - 72 * q^89 - 21 * q^90 - 18 * q^91 + 6 * q^92 + 18 * q^93 + q^94 - 80 * q^95 - 26 * q^96 + q^97 - 5 * q^98 - 82 * q^99

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