LMFDB - Embedded newform 4011.2.a.l.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, 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("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.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:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.386952 q^{2} -1.00000 q^{3} -1.85027 q^{4} +3.15570 q^{5} +0.386952 q^{6} +1.00000 q^{7} +1.48987 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.386952 q^{2} -1.00000 q^{3} -1.85027 q^{4} +3.15570 q^{5} +0.386952 q^{6} +1.00000 q^{7} +1.48987 q^{8} +1.00000 q^{9} -1.22110 q^{10} -2.06858 q^{11} +1.85027 q^{12} +6.13443 q^{13} -0.386952 q^{14} -3.15570 q^{15} +3.12403 q^{16} -6.05517 q^{17} -0.386952 q^{18} +6.43652 q^{19} -5.83889 q^{20} -1.00000 q^{21} +0.800441 q^{22} +4.78003 q^{23} -1.48987 q^{24} +4.95842 q^{25} -2.37373 q^{26} -1.00000 q^{27} -1.85027 q^{28} -2.93407 q^{29} +1.22110 q^{30} +8.36068 q^{31} -4.18859 q^{32} +2.06858 q^{33} +2.34306 q^{34} +3.15570 q^{35} -1.85027 q^{36} +7.85727 q^{37} -2.49062 q^{38} -6.13443 q^{39} +4.70158 q^{40} -4.18096 q^{41} +0.386952 q^{42} -4.79732 q^{43} +3.82743 q^{44} +3.15570 q^{45} -1.84964 q^{46} -3.66296 q^{47} -3.12403 q^{48} +1.00000 q^{49} -1.91867 q^{50} +6.05517 q^{51} -11.3503 q^{52} +1.57999 q^{53} +0.386952 q^{54} -6.52781 q^{55} +1.48987 q^{56} -6.43652 q^{57} +1.13534 q^{58} -7.54407 q^{59} +5.83889 q^{60} +9.43972 q^{61} -3.23518 q^{62} +1.00000 q^{63} -4.62728 q^{64} +19.3584 q^{65} -0.800441 q^{66} -5.85099 q^{67} +11.2037 q^{68} -4.78003 q^{69} -1.22110 q^{70} +12.5639 q^{71} +1.48987 q^{72} +11.7898 q^{73} -3.04039 q^{74} -4.95842 q^{75} -11.9093 q^{76} -2.06858 q^{77} +2.37373 q^{78} -6.35325 q^{79} +9.85849 q^{80} +1.00000 q^{81} +1.61783 q^{82} -0.231947 q^{83} +1.85027 q^{84} -19.1083 q^{85} +1.85633 q^{86} +2.93407 q^{87} -3.08191 q^{88} -1.20390 q^{89} -1.22110 q^{90} +6.13443 q^{91} -8.84434 q^{92} -8.36068 q^{93} +1.41739 q^{94} +20.3117 q^{95} +4.18859 q^{96} -6.99944 q^{97} -0.386952 q^{98} -2.06858 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9}+O(q^{10}) $ 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9	\( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9} + 4 q^{10} - 8 q^{11} - 34 q^{12} + 26 q^{13} - 6 q^{14} - 8 q^{15} + 62 q^{16} + 9 q^{17} - 6 q^{18} + 25 q^{19} + 20 q^{20} - 28 q^{21} + 3 q^{22} - 30 q^{23} + 15 q^{24} + 42 q^{25} + 25 q^{26} - 28 q^{27} + 34 q^{28} - 5 q^{29} - 4 q^{30} + 18 q^{31} - 26 q^{32} + 8 q^{33} + 30 q^{34} + 8 q^{35} + 34 q^{36} + 36 q^{37} - 2 q^{38} - 26 q^{39} + 28 q^{40} + 21 q^{41} + 6 q^{42} + 8 q^{43} - 20 q^{44} + 8 q^{45} + 24 q^{46} + 6 q^{47} - 62 q^{48} + 28 q^{49} - 48 q^{50} - 9 q^{51} + 54 q^{52} - 12 q^{53} + 6 q^{54} + 15 q^{55} - 15 q^{56} - 25 q^{57} + 19 q^{58} + 33 q^{59} - 20 q^{60} + 48 q^{61} + 28 q^{63} + 75 q^{64} + 21 q^{65} - 3 q^{66} + 27 q^{67} + 19 q^{68} + 30 q^{69} + 4 q^{70} - 45 q^{71} - 15 q^{72} + 61 q^{73} - 31 q^{74} - 42 q^{75} + 63 q^{76} - 8 q^{77} - 25 q^{78} + 35 q^{79} + 84 q^{80} + 28 q^{81} + 11 q^{82} + 43 q^{83} - 34 q^{84} + 43 q^{85} - q^{86} + 5 q^{87} - 27 q^{88} + 25 q^{89} + 4 q^{90} + 26 q^{91} - 102 q^{92} - 18 q^{93} + 55 q^{94} - 43 q^{95} + 26 q^{96} + 40 q^{97} - 6 q^{98} - 8 q^{99}+O(q^{100}) \) 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9 + 4 * q^10 - 8 * q^11 - 34 * q^12 + 26 * q^13 - 6 * q^14 - 8 * q^15 + 62 * q^16 + 9 * q^17 - 6 * q^18 + 25 * q^19 + 20 * q^20 - 28 * q^21 + 3 * q^22 - 30 * q^23 + 15 * q^24 + 42 * q^25 + 25 * q^26 - 28 * q^27 + 34 * q^28 - 5 * q^29 - 4 * q^30 + 18 * q^31 - 26 * q^32 + 8 * q^33 + 30 * q^34 + 8 * q^35 + 34 * q^36 + 36 * q^37 - 2 * q^38 - 26 * q^39 + 28 * q^40 + 21 * q^41 + 6 * q^42 + 8 * q^43 - 20 * q^44 + 8 * q^45 + 24 * q^46 + 6 * q^47 - 62 * q^48 + 28 * q^49 - 48 * q^50 - 9 * q^51 + 54 * q^52 - 12 * q^53 + 6 * q^54 + 15 * q^55 - 15 * q^56 - 25 * q^57 + 19 * q^58 + 33 * q^59 - 20 * q^60 + 48 * q^61 + 28 * q^63 + 75 * q^64 + 21 * q^65 - 3 * q^66 + 27 * q^67 + 19 * q^68 + 30 * q^69 + 4 * q^70 - 45 * q^71 - 15 * q^72 + 61 * q^73 - 31 * q^74 - 42 * q^75 + 63 * q^76 - 8 * q^77 - 25 * q^78 + 35 * q^79 + 84 * q^80 + 28 * q^81 + 11 * q^82 + 43 * q^83 - 34 * q^84 + 43 * q^85 - q^86 + 5 * q^87 - 27 * q^88 + 25 * q^89 + 4 * q^90 + 26 * q^91 - 102 * q^92 - 18 * q^93 + 55 * q^94 - 43 * q^95 + 26 * q^96 + 40 * q^97 - 6 * q^98 - 8 * 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 $

$2$	−0.386952	−0.273616	−0.136808	−	0.990598i	$-0.543684\pi$
$2$	−0.386952	−0.273616	−0.136808	+	0.990598i	$0.543684\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.85027	−0.925134
$5$	3.15570	1.41127	0.705635	−	0.708575i	$-0.250662\pi$
$5$	3.15570	1.41127	0.705635	+	0.708575i	$0.250662\pi$
$6$	0.386952	0.157972
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.48987	0.526748
$9$	1.00000	0.333333
$10$	−1.22110	−0.386147
$11$	−2.06858	−0.623700	−0.311850	−	0.950131i	$-0.600949\pi$
$11$	−2.06858	−0.623700	−0.311850	+	0.950131i	$0.600949\pi$
$12$	1.85027	0.534126
$13$	6.13443	1.70138	0.850692	−	0.525664i	$-0.176183\pi$
$13$	6.13443	1.70138	0.850692	+	0.525664i	$0.176183\pi$
$14$	−0.386952	−0.103417
$15$	−3.15570	−0.814797
$16$	3.12403	0.781007
$17$	−6.05517	−1.46859	−0.734297	−	0.678828i	$-0.762488\pi$
$17$	−6.05517	−1.46859	−0.734297	+	0.678828i	$0.762488\pi$
$18$	−0.386952	−0.0912055
$19$	6.43652	1.47664	0.738319	−	0.674451i	$-0.235620\pi$
$19$	6.43652	1.47664	0.738319	+	0.674451i	$0.235620\pi$
$20$	−5.83889	−1.30561
$21$	−1.00000	−0.218218
$22$	0.800441	0.170655
$23$	4.78003	0.996706	0.498353	−	0.866974i	$-0.333938\pi$
$23$	4.78003	0.996706	0.498353	+	0.866974i	$0.333938\pi$
$24$	−1.48987	−0.304118
$25$	4.95842	0.991685
$26$	−2.37373	−0.465527
$27$	−1.00000	−0.192450
$28$	−1.85027	−0.349668
$29$	−2.93407	−0.544843	−0.272422	−	0.962178i	$-0.587825\pi$
$29$	−2.93407	−0.544843	−0.272422	+	0.962178i	$0.587825\pi$
$30$	1.22110	0.222942
$31$	8.36068	1.50162	0.750811	−	0.660517i	$-0.229663\pi$
$31$	8.36068	1.50162	0.750811	+	0.660517i	$0.229663\pi$
$32$	−4.18859	−0.740445
$33$	2.06858	0.360093
$34$	2.34306	0.401832
$35$	3.15570	0.533410
$36$	−1.85027	−0.308378
$37$	7.85727	1.29173	0.645864	−	0.763453i	$-0.276497\pi$
$37$	7.85727	1.29173	0.645864	+	0.763453i	$0.276497\pi$
$38$	−2.49062	−0.404032
$39$	−6.13443	−0.982295
$40$	4.70158	0.743384
$41$	−4.18096	−0.652957	−0.326478	−	0.945205i	$-0.605862\pi$
$41$	−4.18096	−0.652957	−0.326478	+	0.945205i	$0.605862\pi$
$42$	0.386952	0.0597080
$43$	−4.79732	−0.731584	−0.365792	−	0.930697i	$-0.619202\pi$
$43$	−4.79732	−0.731584	−0.365792	+	0.930697i	$0.619202\pi$
$44$	3.82743	0.577006
$45$	3.15570	0.470424
$46$	−1.84964	−0.272715
$47$	−3.66296	−0.534298	−0.267149	−	0.963655i	$-0.586082\pi$
$47$	−3.66296	−0.534298	−0.267149	+	0.963655i	$0.586082\pi$
$48$	−3.12403	−0.450915
$49$	1.00000	0.142857
$50$	−1.91867	−0.271341
$51$	6.05517	0.847894
$52$	−11.3503	−1.57401
$53$	1.57999	0.217028	0.108514	−	0.994095i	$-0.465391\pi$
$53$	1.57999	0.217028	0.108514	+	0.994095i	$0.465391\pi$
$54$	0.386952	0.0526575
$55$	−6.52781	−0.880210
$56$	1.48987	0.199092
$57$	−6.43652	−0.852538
$58$	1.13534	0.149078
$59$	−7.54407	−0.982154	−0.491077	−	0.871116i	$-0.663397\pi$
$59$	−7.54407	−0.982154	−0.491077	+	0.871116i	$0.663397\pi$
$60$	5.83889	0.753797
$61$	9.43972	1.20863	0.604316	−	0.796744i	$-0.293446\pi$
$61$	9.43972	1.20863	0.604316	+	0.796744i	$0.293446\pi$
$62$	−3.23518	−0.410869
$63$	1.00000	0.125988
$64$	−4.62728	−0.578409
$65$	19.3584	2.40111
$66$	−0.800441	−0.0985275
$67$	−5.85099	−0.714813	−0.357406	−	0.933949i	$-0.616339\pi$
$67$	−5.85099	−0.714813	−0.357406	+	0.933949i	$0.616339\pi$
$68$	11.2037	1.35865
$69$	−4.78003	−0.575448
$70$	−1.22110	−0.145950
$71$	12.5639	1.49107	0.745533	−	0.666469i	$-0.232195\pi$
$71$	12.5639	1.49107	0.745533	+	0.666469i	$0.232195\pi$
$72$	1.48987	0.175583
$73$	11.7898	1.37989	0.689947	−	0.723859i	$-0.257634\pi$
$73$	11.7898	1.37989	0.689947	+	0.723859i	$0.257634\pi$
$74$	−3.04039	−0.353438
$75$	−4.95842	−0.572549
$76$	−11.9093	−1.36609
$77$	−2.06858	−0.235736
$78$	2.37373	0.268772
$79$	−6.35325	−0.714796	−0.357398	−	0.933952i	$-0.616336\pi$
$79$	−6.35325	−0.714796	−0.357398	+	0.933952i	$0.616336\pi$
$80$	9.85849	1.10221
$81$	1.00000	0.111111
$82$	1.61783	0.178660
$83$	−0.231947	−0.0254594	−0.0127297	−	0.999919i	$-0.504052\pi$
$83$	−0.231947	−0.0254594	−0.0127297	+	0.999919i	$0.504052\pi$
$84$	1.85027	0.201881
$85$	−19.1083	−2.07258
$86$	1.85633	0.200173
$87$	2.93407	0.314565
$88$	−3.08191	−0.328533
$89$	−1.20390	−0.127613	−0.0638063	−	0.997962i	$-0.520324\pi$
$89$	−1.20390	−0.127613	−0.0638063	+	0.997962i	$0.520324\pi$
$90$	−1.22110	−0.128716
$91$	6.13443	0.643063
$92$	−8.84434	−0.922086
$93$	−8.36068	−0.866962
$94$	1.41739	0.146193
$95$	20.3117	2.08394
$96$	4.18859	0.427496
$97$	−6.99944	−0.710685	−0.355342	−	0.934736i	$-0.615636\pi$
$97$	−6.99944	−0.710685	−0.355342	+	0.934736i	$0.615636\pi$
$98$	−0.386952	−0.0390881
$99$	−2.06858	−0.207900
$100$	−9.17441	−0.917441
$101$	9.84027	0.979144	0.489572	−	0.871963i	$-0.337153\pi$
$101$	9.84027	0.979144	0.489572	+	0.871963i	$0.337153\pi$
$102$	−2.34306	−0.231998
$103$	−13.9598	−1.37550	−0.687752	−	0.725946i	$-0.741402\pi$
$103$	−13.9598	−1.37550	−0.687752	+	0.725946i	$0.741402\pi$
$104$	9.13950	0.896201
$105$	−3.15570	−0.307965
$106$	−0.611380	−0.0593825
$107$	−15.5389	−1.50221	−0.751103	−	0.660185i	$-0.770478\pi$
$107$	−15.5389	−1.50221	−0.751103	+	0.660185i	$0.770478\pi$
$108$	1.85027	0.178042
$109$	−3.37003	−0.322790	−0.161395	−	0.986890i	$-0.551599\pi$
$109$	−3.37003	−0.322790	−0.161395	+	0.986890i	$0.551599\pi$
$110$	2.52595	0.240840
$111$	−7.85727	−0.745779
$112$	3.12403	0.295193
$113$	11.0637	1.04079	0.520393	−	0.853927i	$-0.325786\pi$
$113$	11.0637	1.04079	0.520393	+	0.853927i	$0.325786\pi$
$114$	2.49062	0.233268
$115$	15.0843	1.40662
$116$	5.42882	0.504053
$117$	6.13443	0.567128
$118$	2.91919	0.268733
$119$	−6.05517	−0.555077
$120$	−4.70158	−0.429193
$121$	−6.72098	−0.610998
$122$	−3.65272	−0.330702
$123$	4.18096	0.376985
$124$	−15.4695	−1.38920
$125$	−0.131201	−0.0117350
$126$	−0.386952	−0.0344724
$127$	10.4289	0.925412	0.462706	−	0.886512i	$-0.346878\pi$
$127$	10.4289	0.925412	0.462706	+	0.886512i	$0.346878\pi$
$128$	10.1677	0.898707
$129$	4.79732	0.422380
$130$	−7.49077	−0.656984
$131$	−19.1883	−1.67649	−0.838244	−	0.545295i	$-0.816417\pi$
$131$	−19.1883	−1.67649	−0.838244	+	0.545295i	$0.816417\pi$
$132$	−3.82743	−0.333135
$133$	6.43652	0.558117
$134$	2.26405	0.195584
$135$	−3.15570	−0.271599
$136$	−9.02141	−0.773580
$137$	−8.15969	−0.697129	−0.348565	−	0.937285i	$-0.613331\pi$
$137$	−8.15969	−0.697129	−0.348565	+	0.937285i	$0.613331\pi$
$138$	1.84964	0.157452
$139$	−5.85146	−0.496315	−0.248157	−	0.968720i	$-0.579825\pi$
$139$	−5.85146	−0.496315	−0.248157	+	0.968720i	$0.579825\pi$
$140$	−5.83889	−0.493476
$141$	3.66296	0.308477
$142$	−4.86164	−0.407980
$143$	−12.6896	−1.06115
$144$	3.12403	0.260336
$145$	−9.25904	−0.768921
$146$	−4.56210	−0.377562
$147$	−1.00000	−0.0824786
$148$	−14.5381	−1.19502
$149$	−3.77742	−0.309458	−0.154729	−	0.987957i	$-0.549450\pi$
$149$	−3.77742	−0.309458	−0.154729	+	0.987957i	$0.549450\pi$
$150$	1.91867	0.156659
$151$	16.1661	1.31558	0.657790	−	0.753202i	$-0.271492\pi$
$151$	16.1661	1.31558	0.657790	+	0.753202i	$0.271492\pi$
$152$	9.58957	0.777817
$153$	−6.05517	−0.489532
$154$	0.800441	0.0645014
$155$	26.3838	2.11920
$156$	11.3503	0.908754
$157$	−1.54814	−0.123555	−0.0617775	−	0.998090i	$-0.519677\pi$
$157$	−1.54814	−0.123555	−0.0617775	+	0.998090i	$0.519677\pi$
$158$	2.45840	0.195580
$159$	−1.57999	−0.125301
$160$	−13.2179	−1.04497
$161$	4.78003	0.376719
$162$	−0.386952	−0.0304018
$163$	24.5816	1.92538	0.962691	−	0.270604i	$-0.0872235\pi$
$163$	24.5816	1.92538	0.962691	+	0.270604i	$0.0872235\pi$
$164$	7.73590	0.604073
$165$	6.52781	0.508189
$166$	0.0897522	0.00696612
$167$	−24.1743	−1.87066	−0.935330	−	0.353777i	$-0.884897\pi$
$167$	−24.1743	−1.87066	−0.935330	+	0.353777i	$0.884897\pi$
$168$	−1.48987	−0.114946
$169$	24.6312	1.89471
$170$	7.39399	0.567093
$171$	6.43652	0.492213
$172$	8.87633	0.676814
$173$	10.7845	0.819928	0.409964	−	0.912102i	$-0.365541\pi$
$173$	10.7845	0.819928	0.409964	+	0.912102i	$0.365541\pi$
$174$	−1.13534	−0.0860702
$175$	4.95842	0.374822
$176$	−6.46230	−0.487114
$177$	7.54407	0.567047
$178$	0.465850	0.0349169
$179$	18.8918	1.41204	0.706019	−	0.708193i	$-0.250489\pi$
$179$	18.8918	1.41204	0.706019	+	0.708193i	$0.250489\pi$
$180$	−5.83889	−0.435205
$181$	16.7549	1.24538	0.622692	−	0.782467i	$-0.286039\pi$
$181$	16.7549	1.24538	0.622692	+	0.782467i	$0.286039\pi$
$182$	−2.37373	−0.175953
$183$	−9.43972	−0.697804
$184$	7.12162	0.525013
$185$	24.7952	1.82298
$186$	3.23518	0.237215
$187$	12.5256	0.915963
$188$	6.77747	0.494298
$189$	−1.00000	−0.0727393
$190$	−7.85965	−0.570199
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	4.62728	0.333945
$193$	−20.9667	−1.50922	−0.754609	−	0.656175i	$-0.772173\pi$
$193$	−20.9667	−1.50922	−0.754609	+	0.656175i	$0.772173\pi$
$194$	2.70845	0.194455
$195$	−19.3584	−1.38628
$196$	−1.85027	−0.132162
$197$	25.1068	1.78878	0.894392	−	0.447284i	$-0.147609\pi$
$197$	25.1068	1.78878	0.894392	+	0.447284i	$0.147609\pi$
$198$	0.800441	0.0568849
$199$	−22.6090	−1.60271	−0.801356	−	0.598188i	$-0.795888\pi$
$199$	−22.6090	−1.60271	−0.801356	+	0.598188i	$0.795888\pi$
$200$	7.38740	0.522368
$201$	5.85099	0.412697
$202$	−3.80771	−0.267910
$203$	−2.93407	−0.205931
$204$	−11.2037	−0.784415
$205$	−13.1939	−0.921499
$206$	5.40179	0.376360
$207$	4.78003	0.332235
$208$	19.1641	1.32879
$209$	−13.3144	−0.920980
$210$	1.22110	0.0842641
$211$	−1.41013	−0.0970775	−0.0485387	−	0.998821i	$-0.515456\pi$
$211$	−1.41013	−0.0970775	−0.0485387	+	0.998821i	$0.515456\pi$
$212$	−2.92341	−0.200780
$213$	−12.5639	−0.860867
$214$	6.01283	0.411028
$215$	−15.1389	−1.03246
$216$	−1.48987	−0.101373
$217$	8.36068	0.567560
$218$	1.30404	0.0883207
$219$	−11.7898	−0.796683
$220$	12.0782	0.814312
$221$	−37.1450	−2.49864
$222$	3.04039	0.204057
$223$	11.3200	0.758041	0.379021	−	0.925388i	$-0.376261\pi$
$223$	11.3200	0.758041	0.379021	+	0.925388i	$0.376261\pi$
$224$	−4.18859	−0.279862
$225$	4.95842	0.330562
$226$	−4.28112	−0.284776
$227$	17.2900	1.14758	0.573788	−	0.819004i	$-0.305473\pi$
$227$	17.2900	1.14758	0.573788	+	0.819004i	$0.305473\pi$
$228$	11.9093	0.788712
$229$	29.8730	1.97406	0.987031	−	0.160527i	$-0.0513195\pi$
$229$	29.8730	1.97406	0.987031	+	0.160527i	$0.0513195\pi$
$230$	−5.83691	−0.384875
$231$	2.06858	0.136103
$232$	−4.37138	−0.286995
$233$	0.101892	0.00667517	0.00333759	−	0.999994i	$-0.498938\pi$
$233$	0.101892	0.00667517	0.00333759	+	0.999994i	$0.498938\pi$
$234$	−2.37373	−0.155176
$235$	−11.5592	−0.754040
$236$	13.9586	0.908624
$237$	6.35325	0.412688
$238$	2.34306	0.151878
$239$	13.7344	0.888402	0.444201	−	0.895927i	$-0.353488\pi$
$239$	13.7344	0.888402	0.444201	+	0.895927i	$0.353488\pi$
$240$	−9.85849	−0.636363
$241$	−19.7975	−1.27527	−0.637634	−	0.770339i	$-0.720087\pi$
$241$	−19.7975	−1.27527	−0.637634	+	0.770339i	$0.720087\pi$
$242$	2.60070	0.167179
$243$	−1.00000	−0.0641500
$244$	−17.4660	−1.11815
$245$	3.15570	0.201610
$246$	−1.61783	−0.103149
$247$	39.4844	2.51233
$248$	12.4563	0.790977
$249$	0.231947	0.0146990
$250$	0.0507685	0.00321088
$251$	−1.78331	−0.112561	−0.0562807	−	0.998415i	$-0.517924\pi$
$251$	−1.78331	−0.112561	−0.0562807	+	0.998415i	$0.517924\pi$
$252$	−1.85027	−0.116556
$253$	−9.88788	−0.621645
$254$	−4.03547	−0.253208
$255$	19.1083	1.19661
$256$	5.32014	0.332508
$257$	19.0840	1.19043	0.595213	−	0.803568i	$-0.297068\pi$
$257$	19.0840	1.19043	0.595213	+	0.803568i	$0.297068\pi$
$258$	−1.85633	−0.115570
$259$	7.85727	0.488227
$260$	−35.8182	−2.22135
$261$	−2.93407	−0.181614
$262$	7.42494	0.458715
$263$	9.22283	0.568704	0.284352	−	0.958720i	$-0.408222\pi$
$263$	9.22283	0.568704	0.284352	+	0.958720i	$0.408222\pi$
$264$	3.08191	0.189679
$265$	4.98597	0.306286
$266$	−2.49062	−0.152710
$267$	1.20390	0.0736772
$268$	10.8259	0.661297
$269$	−17.9524	−1.09457	−0.547287	−	0.836945i	$-0.684340\pi$
$269$	−17.9524	−1.09457	−0.547287	+	0.836945i	$0.684340\pi$
$270$	1.22110	0.0743140
$271$	26.2970	1.59743	0.798713	−	0.601712i	$-0.205514\pi$
$271$	26.2970	1.59743	0.798713	+	0.601712i	$0.205514\pi$
$272$	−18.9165	−1.14698
$273$	−6.13443	−0.371273
$274$	3.15741	0.190746
$275$	−10.2569	−0.618514
$276$	8.84434	0.532367
$277$	17.7769	1.06811	0.534055	−	0.845450i	$-0.320667\pi$
$277$	17.7769	1.06811	0.534055	+	0.845450i	$0.320667\pi$
$278$	2.26423	0.135800
$279$	8.36068	0.500541
$280$	4.70158	0.280973
$281$	18.3289	1.09341	0.546706	−	0.837325i	$-0.315881\pi$
$281$	18.3289	1.09341	0.546706	+	0.837325i	$0.315881\pi$
$282$	−1.41739	−0.0844044
$283$	−16.8949	−1.00430	−0.502150	−	0.864780i	$-0.667458\pi$
$283$	−16.8949	−1.00430	−0.502150	+	0.864780i	$0.667458\pi$
$284$	−23.2467	−1.37944
$285$	−20.3117	−1.20316
$286$	4.91025	0.290349
$287$	−4.18096	−0.246795
$288$	−4.18859	−0.246815
$289$	19.6651	1.15677
$290$	3.58280	0.210389
$291$	6.99944	0.410314
$292$	−21.8143	−1.27659
$293$	16.7316	0.977469	0.488734	−	0.872433i	$-0.337459\pi$
$293$	16.7316	0.977469	0.488734	+	0.872433i	$0.337459\pi$
$294$	0.386952	0.0225675
$295$	−23.8068	−1.38609
$296$	11.7063	0.680415
$297$	2.06858	0.120031
$298$	1.46168	0.0846729
$299$	29.3228	1.69578
$300$	9.17441	0.529685
$301$	−4.79732	−0.276513
$302$	−6.25551	−0.359964
$303$	−9.84027	−0.565309
$304$	20.1079	1.15327
$305$	29.7889	1.70571
$306$	2.34306	0.133944
$307$	−4.53417	−0.258779	−0.129389	−	0.991594i	$-0.541302\pi$
$307$	−4.53417	−0.258779	−0.129389	+	0.991594i	$0.541302\pi$
$308$	3.82743	0.218088
$309$	13.9598	0.794148
$310$	−10.2093	−0.579847
$311$	4.21363	0.238933	0.119467	−	0.992838i	$-0.461882\pi$
$311$	4.21363	0.238933	0.119467	+	0.992838i	$0.461882\pi$
$312$	−9.13950	−0.517422
$313$	23.7052	1.33990	0.669949	−	0.742407i	$-0.266316\pi$
$313$	23.7052	1.33990	0.669949	+	0.742407i	$0.266316\pi$
$314$	0.599055	0.0338066
$315$	3.15570	0.177803
$316$	11.7552	0.661282
$317$	15.5194	0.871657	0.435828	−	0.900030i	$-0.356455\pi$
$317$	15.5194	0.871657	0.435828	+	0.900030i	$0.356455\pi$
$318$	0.611380	0.0342845
$319$	6.06936	0.339819
$320$	−14.6023	−0.816292
$321$	15.5389	0.867299
$322$	−1.84964	−0.103077
$323$	−38.9742	−2.16858
$324$	−1.85027	−0.102793
$325$	30.4171	1.68724
$326$	−9.51191	−0.526816
$327$	3.37003	0.186363
$328$	−6.22909	−0.343944
$329$	−3.66296	−0.201946
$330$	−2.52595	−0.139049
$331$	−12.1437	−0.667477	−0.333738	−	0.942666i	$-0.608310\pi$
$331$	−12.1437	−0.667477	−0.333738	+	0.942666i	$0.608310\pi$
$332$	0.429163	0.0235534
$333$	7.85727	0.430576
$334$	9.35427	0.511843
$335$	−18.4640	−1.00879
$336$	−3.12403	−0.170430
$337$	9.48922	0.516911	0.258455	−	0.966023i	$-0.416786\pi$
$337$	9.48922	0.516911	0.258455	+	0.966023i	$0.416786\pi$
$338$	−9.53110	−0.518424
$339$	−11.0637	−0.600898
$340$	35.3555	1.91742
$341$	−17.2947	−0.936562
$342$	−2.49062	−0.134677
$343$	1.00000	0.0539949
$344$	−7.14738	−0.385361
$345$	−15.0843	−0.812113
$346$	−4.17307	−0.224346
$347$	−3.24342	−0.174116	−0.0870580	−	0.996203i	$-0.527747\pi$
$347$	−3.24342	−0.174116	−0.0870580	+	0.996203i	$0.527747\pi$
$348$	−5.42882	−0.291015
$349$	−12.7928	−0.684783	−0.342391	−	0.939557i	$-0.611237\pi$
$349$	−12.7928	−0.684783	−0.342391	+	0.939557i	$0.611237\pi$
$350$	−1.91867	−0.102557
$351$	−6.13443	−0.327432
$352$	8.66442	0.461815
$353$	21.6780	1.15380	0.576901	−	0.816814i	$-0.304262\pi$
$353$	21.6780	1.15380	0.576901	+	0.816814i	$0.304262\pi$
$354$	−2.91919	−0.155153
$355$	39.6480	2.10430
$356$	2.22753	0.118059
$357$	6.05517	0.320474
$358$	−7.31021	−0.386357
$359$	13.0510	0.688805	0.344402	−	0.938822i	$-0.388082\pi$
$359$	13.0510	0.688805	0.344402	+	0.938822i	$0.388082\pi$
$360$	4.70158	0.247795
$361$	22.4288	1.18046
$362$	−6.48335	−0.340757
$363$	6.72098	0.352760
$364$	−11.3503	−0.594919
$365$	37.2051	1.94741
$366$	3.65272	0.190931
$367$	8.12931	0.424347	0.212173	−	0.977232i	$-0.431946\pi$
$367$	8.12931	0.424347	0.212173	+	0.977232i	$0.431946\pi$
$368$	14.9330	0.778434
$369$	−4.18096	−0.217652
$370$	−9.59454	−0.498796
$371$	1.57999	0.0820290
$372$	15.4695	0.802056
$373$	−19.6114	−1.01544	−0.507721	−	0.861522i	$-0.669512\pi$
$373$	−19.6114	−1.01544	−0.507721	+	0.861522i	$0.669512\pi$
$374$	−4.84681	−0.250622
$375$	0.131201	0.00677519
$376$	−5.45734	−0.281441
$377$	−17.9988	−0.926988
$378$	0.386952	0.0199027
$379$	22.0289	1.13155	0.565774	−	0.824561i	$-0.308578\pi$
$379$	22.0289	1.13155	0.565774	+	0.824561i	$0.308578\pi$
$380$	−37.5821	−1.92792
$381$	−10.4289	−0.534287
$382$	0.386952	0.0197982
$383$	−34.4124	−1.75839	−0.879195	−	0.476462i	$-0.841919\pi$
$383$	−34.4124	−1.75839	−0.879195	+	0.476462i	$0.841919\pi$
$384$	−10.1677	−0.518869
$385$	−6.52781	−0.332688
$386$	8.11312	0.412947
$387$	−4.79732	−0.243861
$388$	12.9508	0.657479
$389$	−22.0991	−1.12047	−0.560233	−	0.828335i	$-0.689289\pi$
$389$	−22.0991	−1.12047	−0.560233	+	0.828335i	$0.689289\pi$
$390$	7.49077	0.379310
$391$	−28.9439	−1.46376
$392$	1.48987	0.0752497
$393$	19.1883	0.967921
$394$	−9.71512	−0.489441
$395$	−20.0489	−1.00877
$396$	3.82743	0.192335
$397$	−2.37588	−0.119242	−0.0596209	−	0.998221i	$-0.518989\pi$
$397$	−2.37588	−0.119242	−0.0596209	+	0.998221i	$0.518989\pi$
$398$	8.74861	0.438528
$399$	−6.43652	−0.322229
$400$	15.4903	0.774513
$401$	7.06672	0.352895	0.176448	−	0.984310i	$-0.443539\pi$
$401$	7.06672	0.352895	0.176448	+	0.984310i	$0.443539\pi$
$402$	−2.26405	−0.112921
$403$	51.2880	2.55484
$404$	−18.2071	−0.905839
$405$	3.15570	0.156808
$406$	1.13534	0.0563462
$407$	−16.2534	−0.805651
$408$	9.02141	0.446626
$409$	−32.9763	−1.63057	−0.815287	−	0.579056i	$-0.803421\pi$
$409$	−32.9763	−1.63057	−0.815287	+	0.579056i	$0.803421\pi$
$410$	5.10539	0.252137
$411$	8.15969	0.402488
$412$	25.8294	1.27253
$413$	−7.54407	−0.371219
$414$	−1.84964	−0.0909050
$415$	−0.731953	−0.0359302
$416$	−25.6946	−1.25978
$417$	5.85146	0.286547
$418$	5.15205	0.251995
$419$	20.9496	1.02346	0.511728	−	0.859148i	$-0.329006\pi$
$419$	20.9496	1.02346	0.511728	+	0.859148i	$0.329006\pi$
$420$	5.83889	0.284908
$421$	−6.02730	−0.293753	−0.146876	−	0.989155i	$-0.546922\pi$
$421$	−6.02730	−0.293753	−0.146876	+	0.989155i	$0.546922\pi$
$422$	0.545653	0.0265620
$423$	−3.66296	−0.178099
$424$	2.35398	0.114319
$425$	−30.0241	−1.45638
$426$	4.86164	0.235547
$427$	9.43972	0.456820
$428$	28.7512	1.38974
$429$	12.6896	0.612657
$430$	5.85802	0.282499
$431$	1.36422	0.0657122	0.0328561	−	0.999460i	$-0.489540\pi$
$431$	1.36422	0.0657122	0.0328561	+	0.999460i	$0.489540\pi$
$432$	−3.12403	−0.150305
$433$	−0.309039	−0.0148515	−0.00742573	−	0.999972i	$-0.502364\pi$
$433$	−0.309039	−0.0148515	−0.00742573	+	0.999972i	$0.502364\pi$
$434$	−3.23518	−0.155294
$435$	9.25904	0.443937
$436$	6.23546	0.298624
$437$	30.7668	1.47177
$438$	4.56210	0.217985
$439$	15.1837	0.724679	0.362339	−	0.932046i	$-0.381978\pi$
$439$	15.1837	0.724679	0.362339	+	0.932046i	$0.381978\pi$
$440$	−9.72558	−0.463649
$441$	1.00000	0.0476190
$442$	14.3733	0.683670
$443$	−31.0413	−1.47482	−0.737409	−	0.675447i	$-0.763951\pi$
$443$	−31.0413	−1.47482	−0.737409	+	0.675447i	$0.763951\pi$
$444$	14.5381	0.689946
$445$	−3.79913	−0.180096
$446$	−4.38028	−0.207412
$447$	3.77742	0.178666
$448$	−4.62728	−0.218618
$449$	9.85211	0.464950	0.232475	−	0.972602i	$-0.425318\pi$
$449$	9.85211	0.464950	0.232475	+	0.972602i	$0.425318\pi$
$450$	−1.91867	−0.0904471
$451$	8.64866	0.407249
$452$	−20.4708	−0.962866
$453$	−16.1661	−0.759550
$454$	−6.69039	−0.313995
$455$	19.3584	0.907536
$456$	−9.58957	−0.449073
$457$	18.1164	0.847452	0.423726	−	0.905791i	$-0.360722\pi$
$457$	18.1164	0.847452	0.423726	+	0.905791i	$0.360722\pi$
$458$	−11.5594	−0.540136
$459$	6.05517	0.282631
$460$	−27.9101	−1.30131
$461$	11.9606	0.557062	0.278531	−	0.960427i	$-0.410152\pi$
$461$	11.9606	0.557062	0.278531	+	0.960427i	$0.410152\pi$
$462$	−0.800441	−0.0372399
$463$	17.5439	0.815336	0.407668	−	0.913130i	$-0.366342\pi$
$463$	17.5439	0.815336	0.407668	+	0.913130i	$0.366342\pi$
$464$	−9.16612	−0.425526
$465$	−26.3838	−1.22352
$466$	−0.0394274	−0.00182644
$467$	3.96610	0.183529	0.0917646	−	0.995781i	$-0.470749\pi$
$467$	3.96610	0.183529	0.0917646	+	0.995781i	$0.470749\pi$
$468$	−11.3503	−0.524670
$469$	−5.85099	−0.270174
$470$	4.47286	0.206318
$471$	1.54814	0.0713345
$472$	−11.2397	−0.517348
$473$	9.92363	0.456289
$474$	−2.45840	−0.112918
$475$	31.9150	1.46436
$476$	11.2037	0.513520
$477$	1.57999	0.0723428
$478$	−5.31454	−0.243081
$479$	−14.7686	−0.674795	−0.337398	−	0.941362i	$-0.609547\pi$
$479$	−14.7686	−0.674795	−0.337398	+	0.941362i	$0.609547\pi$
$480$	13.2179	0.603312
$481$	48.1999	2.19773
$482$	7.66068	0.348934
$483$	−4.78003	−0.217499
$484$	12.4356	0.565255
$485$	−22.0881	−1.00297
$486$	0.386952	0.0175525
$487$	−2.57089	−0.116498	−0.0582491	−	0.998302i	$-0.518552\pi$
$487$	−2.57089	−0.116498	−0.0582491	+	0.998302i	$0.518552\pi$
$488$	14.0640	0.636645
$489$	−24.5816	−1.11162
$490$	−1.22110	−0.0551638
$491$	−31.0978	−1.40342	−0.701711	−	0.712462i	$-0.747580\pi$
$491$	−31.0978	−1.40342	−0.701711	+	0.712462i	$0.747580\pi$
$492$	−7.73590	−0.348762
$493$	17.7663	0.800154
$494$	−15.2786	−0.687415
$495$	−6.52781	−0.293403
$496$	26.1190	1.17278
$497$	12.5639	0.563570
$498$	−0.0897522	−0.00402189
$499$	−30.0376	−1.34467	−0.672334	−	0.740248i	$-0.734708\pi$
$499$	−30.0376	−1.34467	−0.672334	+	0.740248i	$0.734708\pi$
$500$	0.242757	0.0108564
$501$	24.1743	1.08003
$502$	0.690054	0.0307986
$503$	−29.1893	−1.30149	−0.650743	−	0.759298i	$-0.725542\pi$
$503$	−29.1893	−1.30149	−0.650743	+	0.759298i	$0.725542\pi$
$504$	1.48987	0.0663640
$505$	31.0529	1.38184
$506$	3.82613	0.170092
$507$	−24.6312	−1.09391
$508$	−19.2962	−0.856130
$509$	13.4654	0.596844	0.298422	−	0.954434i	$-0.403540\pi$
$509$	13.4654	0.596844	0.298422	+	0.954434i	$0.403540\pi$
$510$	−7.39399	−0.327411
$511$	11.7898	0.521551
$512$	−22.3941	−0.989687
$513$	−6.43652	−0.284179
$514$	−7.38459	−0.325720
$515$	−44.0530	−1.94121
$516$	−8.87633	−0.390758
$517$	7.57713	0.333242
$518$	−3.04039	−0.133587
$519$	−10.7845	−0.473386
$520$	28.8415	1.26478
$521$	39.6647	1.73774	0.868872	−	0.495037i	$-0.164845\pi$
$521$	39.6647	1.73774	0.868872	+	0.495037i	$0.164845\pi$
$522$	1.13534	0.0496927
$523$	19.8076	0.866126	0.433063	−	0.901364i	$-0.357433\pi$
$523$	19.8076	0.866126	0.433063	+	0.901364i	$0.357433\pi$
$524$	35.5035	1.55098
$525$	−4.95842	−0.216403
$526$	−3.56879	−0.155607
$527$	−50.6254	−2.20528
$528$	6.46230	0.281236
$529$	−0.151291	−0.00657789
$530$	−1.92933	−0.0838048
$531$	−7.54407	−0.327385
$532$	−11.9093	−0.516333
$533$	−25.6478	−1.11093
$534$	−0.465850	−0.0201593
$535$	−49.0362	−2.12002
$536$	−8.71721	−0.376526
$537$	−18.8918	−0.815241
$538$	6.94670	0.299494
$539$	−2.06858	−0.0891000
$540$	5.83889	0.251266
$541$	−10.6163	−0.456432	−0.228216	−	0.973611i	$-0.573289\pi$
$541$	−10.6163	−0.456432	−0.228216	+	0.973611i	$0.573289\pi$
$542$	−10.1757	−0.437082
$543$	−16.7549	−0.719023
$544$	25.3626	1.08741
$545$	−10.6348	−0.455544
$546$	2.37373	0.101586
$547$	−27.0344	−1.15591	−0.577955	−	0.816069i	$-0.696149\pi$
$547$	−27.0344	−1.15591	−0.577955	+	0.816069i	$0.696149\pi$
$548$	15.0976	0.644938
$549$	9.43972	0.402878
$550$	3.96893	0.169236
$551$	−18.8852	−0.804536
$552$	−7.12162	−0.303116
$553$	−6.35325	−0.270168
$554$	−6.87881	−0.292253
$555$	−24.7952	−1.05250
$556$	10.8268	0.459157
$557$	−10.8634	−0.460296	−0.230148	−	0.973156i	$-0.573921\pi$
$557$	−10.8634	−0.460296	−0.230148	+	0.973156i	$0.573921\pi$
$558$	−3.23518	−0.136956
$559$	−29.4288	−1.24471
$560$	9.85849	0.416597
$561$	−12.5256	−0.528831
$562$	−7.09242	−0.299176
$563$	3.69015	0.155521	0.0777606	−	0.996972i	$-0.475223\pi$
$563$	3.69015	0.155521	0.0777606	+	0.996972i	$0.475223\pi$
$564$	−6.77747	−0.285383
$565$	34.9137	1.46883
$566$	6.53753	0.274793
$567$	1.00000	0.0419961
$568$	18.7186	0.785416
$569$	−11.4633	−0.480568	−0.240284	−	0.970703i	$-0.577241\pi$
$569$	−11.4633	−0.480568	−0.240284	+	0.970703i	$0.577241\pi$
$570$	7.85965	0.329205
$571$	−37.0683	−1.55126	−0.775631	−	0.631187i	$-0.782568\pi$
$571$	−37.0683	−1.55126	−0.775631	+	0.631187i	$0.782568\pi$
$572$	23.4791	0.981710
$573$	1.00000	0.0417756
$574$	1.61783	0.0675270
$575$	23.7014	0.988418
$576$	−4.62728	−0.192803
$577$	13.6382	0.567764	0.283882	−	0.958859i	$-0.408378\pi$
$577$	13.6382	0.567764	0.283882	+	0.958859i	$0.408378\pi$
$578$	−7.60945	−0.316511
$579$	20.9667	0.871348
$580$	17.1317	0.711355
$581$	−0.231947	−0.00962276
$582$	−2.70845	−0.112269
$583$	−3.26833	−0.135361
$584$	17.5653	0.726857
$585$	19.3584	0.800371
$586$	−6.47431	−0.267451
$587$	−25.2660	−1.04284	−0.521419	−	0.853301i	$-0.674597\pi$
$587$	−25.2660	−1.04284	−0.521419	+	0.853301i	$0.674597\pi$
$588$	1.85027	0.0763038
$589$	53.8137	2.21735
$590$	9.21209	0.379256
$591$	−25.1068	−1.03275
$592$	24.5463	1.00885
$593$	19.3797	0.795829	0.397915	−	0.917422i	$-0.369734\pi$
$593$	19.3797	0.795829	0.397915	+	0.917422i	$0.369734\pi$
$594$	−0.800441	−0.0328425
$595$	−19.1083	−0.783363
$596$	6.98924	0.286290
$597$	22.6090	0.925326
$598$	−11.3465	−0.463993
$599$	22.2568	0.909390	0.454695	−	0.890647i	$-0.349748\pi$
$599$	22.2568	0.909390	0.454695	+	0.890647i	$0.349748\pi$
$600$	−7.38740	−0.301589
$601$	5.50165	0.224417	0.112209	−	0.993685i	$-0.464208\pi$
$601$	5.50165	0.224417	0.112209	+	0.993685i	$0.464208\pi$
$602$	1.85633	0.0756584
$603$	−5.85099	−0.238271
$604$	−29.9116	−1.21709
$605$	−21.2094	−0.862284
$606$	3.80771	0.154678
$607$	−16.6070	−0.674057	−0.337028	−	0.941494i	$-0.609422\pi$
$607$	−16.6070	−0.674057	−0.337028	+	0.941494i	$0.609422\pi$
$608$	−26.9599	−1.09337
$609$	2.93407	0.118895
$610$	−11.5269	−0.466710
$611$	−22.4702	−0.909047
$612$	11.2037	0.452882
$613$	6.30961	0.254843	0.127421	−	0.991849i	$-0.459330\pi$
$613$	6.30961	0.254843	0.127421	+	0.991849i	$0.459330\pi$
$614$	1.75451	0.0708062
$615$	13.1939	0.532028
$616$	−3.08191	−0.124174
$617$	2.94121	0.118408	0.0592042	−	0.998246i	$-0.481144\pi$
$617$	2.94121	0.118408	0.0592042	+	0.998246i	$0.481144\pi$
$618$	−5.40179	−0.217292
$619$	−15.1164	−0.607581	−0.303791	−	0.952739i	$-0.598252\pi$
$619$	−15.1164	−0.607581	−0.303791	+	0.952739i	$0.598252\pi$
$620$	−48.8171	−1.96054
$621$	−4.78003	−0.191816
$622$	−1.63047	−0.0653760
$623$	−1.20390	−0.0482331
$624$	−19.1641	−0.767179
$625$	−25.2062	−1.00825
$626$	−9.17277	−0.366618
$627$	13.3144	0.531728
$628$	2.86447	0.114305
$629$	−47.5771	−1.89702
$630$	−1.22110	−0.0486499
$631$	−37.0265	−1.47400	−0.737000	−	0.675892i	$-0.763758\pi$
$631$	−37.0265	−1.47400	−0.737000	+	0.675892i	$0.763758\pi$
$632$	−9.46551	−0.376518
$633$	1.41013	0.0560477
$634$	−6.00527	−0.238500
$635$	32.9103	1.30601
$636$	2.92341	0.115921
$637$	6.13443	0.243055
$638$	−2.34855	−0.0929800
$639$	12.5639	0.497022
$640$	32.0862	1.26832
$641$	18.8670	0.745200	0.372600	−	0.927992i	$-0.378466\pi$
$641$	18.8670	0.745200	0.372600	+	0.927992i	$0.378466\pi$
$642$	−6.01283	−0.237307
$643$	−12.1625	−0.479641	−0.239820	−	0.970817i	$-0.577089\pi$
$643$	−12.1625	−0.479641	−0.239820	+	0.970817i	$0.577089\pi$
$644$	−8.84434	−0.348516
$645$	15.1389	0.596093
$646$	15.0812	0.593360
$647$	−12.9716	−0.509965	−0.254983	−	0.966946i	$-0.582070\pi$
$647$	−12.9716	−0.509965	−0.254983	+	0.966946i	$0.582070\pi$
$648$	1.48987	0.0585276
$649$	15.6055	0.612570
$650$	−11.7700	−0.461656
$651$	−8.36068	−0.327681
$652$	−45.4826	−1.78124
$653$	4.09097	0.160092	0.0800459	−	0.996791i	$-0.474493\pi$
$653$	4.09097	0.160092	0.0800459	+	0.996791i	$0.474493\pi$
$654$	−1.30404	−0.0509920
$655$	−60.5524	−2.36598
$656$	−13.0615	−0.509964
$657$	11.7898	0.459965
$658$	1.41739	0.0552557
$659$	−5.67058	−0.220894	−0.110447	−	0.993882i	$-0.535228\pi$
$659$	−5.67058	−0.220894	−0.110447	+	0.993882i	$0.535228\pi$
$660$	−12.0782	−0.470143
$661$	11.0409	0.429441	0.214720	−	0.976676i	$-0.431116\pi$
$661$	11.0409	0.429441	0.214720	+	0.976676i	$0.431116\pi$
$662$	4.69902	0.182633
$663$	37.1450	1.44259
$664$	−0.345570	−0.0134107
$665$	20.3117	0.787654
$666$	−3.04039	−0.117813
$667$	−14.0250	−0.543048
$668$	44.7288	1.73061
$669$	−11.3200	−0.437655
$670$	7.14467	0.276023
$671$	−19.5268	−0.753824
$672$	4.18859	0.161578
$673$	31.5964	1.21795	0.608976	−	0.793188i	$-0.291580\pi$
$673$	31.5964	1.21795	0.608976	+	0.793188i	$0.291580\pi$
$674$	−3.67187	−0.141435
$675$	−4.95842	−0.190850
$676$	−45.5744	−1.75286
$677$	−48.4960	−1.86385	−0.931927	−	0.362647i	$-0.881873\pi$
$677$	−48.4960	−1.86385	−0.931927	+	0.362647i	$0.881873\pi$
$678$	4.28112	0.164415
$679$	−6.99944	−0.268614
$680$	−28.4688	−1.09173
$681$	−17.2900	−0.662553
$682$	6.69223	0.256259
$683$	−8.31980	−0.318348	−0.159174	−	0.987251i	$-0.550883\pi$
$683$	−8.31980	−0.318348	−0.159174	+	0.987251i	$0.550883\pi$
$684$	−11.9093	−0.455363
$685$	−25.7495	−0.983838
$686$	−0.386952	−0.0147739
$687$	−29.8730	−1.13973
$688$	−14.9870	−0.571373
$689$	9.69234	0.369249
$690$	5.83691	0.222207
$691$	−36.1828	−1.37646	−0.688229	−	0.725493i	$-0.741612\pi$
$691$	−36.1828	−1.37646	−0.688229	+	0.725493i	$0.741612\pi$
$692$	−19.9542	−0.758544
$693$	−2.06858	−0.0785788
$694$	1.25505	0.0476410
$695$	−18.4654	−0.700434
$696$	4.37138	0.165697
$697$	25.3165	0.958929
$698$	4.95020	0.187368
$699$	−0.101892	−0.00385391
$700$	−9.17441	−0.346760
$701$	−19.4361	−0.734091	−0.367046	−	0.930203i	$-0.619631\pi$
$701$	−19.4361	−0.734091	−0.367046	+	0.930203i	$0.619631\pi$
$702$	2.37373	0.0895907
$703$	50.5735	1.90741
$704$	9.57189	0.360754
$705$	11.5592	0.435345
$706$	−8.38833	−0.315699
$707$	9.84027	0.370082
$708$	−13.9586	−0.524594
$709$	20.9700	0.787545	0.393772	−	0.919208i	$-0.371170\pi$
$709$	20.9700	0.787545	0.393772	+	0.919208i	$0.371170\pi$
$710$	−15.3419	−0.575770
$711$	−6.35325	−0.238265
$712$	−1.79365	−0.0672197
$713$	39.9643	1.49668
$714$	−2.34306	−0.0876868
$715$	−40.0444	−1.49758
$716$	−34.9549	−1.30632
$717$	−13.7344	−0.512919
$718$	−5.05010	−0.188468
$719$	−1.83112	−0.0682894	−0.0341447	−	0.999417i	$-0.510871\pi$
$719$	−1.83112	−0.0682894	−0.0341447	+	0.999417i	$0.510871\pi$
$720$	9.85849	0.367404
$721$	−13.9598	−0.519892
$722$	−8.67885	−0.322994
$723$	19.7975	0.736277
$724$	−31.0011	−1.15215
$725$	−14.5484	−0.540313
$726$	−2.60070	−0.0965209
$727$	15.2374	0.565122	0.282561	−	0.959249i	$-0.408816\pi$
$727$	15.2374	0.565122	0.282561	+	0.959249i	$0.408816\pi$
$728$	9.13950	0.338732
$729$	1.00000	0.0370370
$730$	−14.3966	−0.532842
$731$	29.0486	1.07440
$732$	17.4660	0.645563
$733$	−42.8892	−1.58415	−0.792074	−	0.610425i	$-0.790999\pi$
$733$	−42.8892	−1.58415	−0.792074	+	0.610425i	$0.790999\pi$
$734$	−3.14565	−0.116108
$735$	−3.15570	−0.116400
$736$	−20.0216	−0.738005
$737$	12.1032	0.445829
$738$	1.61783	0.0595532
$739$	−45.7769	−1.68393	−0.841966	−	0.539531i	$-0.818602\pi$
$739$	−45.7769	−1.68393	−0.841966	+	0.539531i	$0.818602\pi$
$740$	−45.8777	−1.68650
$741$	−39.4844	−1.45049
$742$	−0.611380	−0.0224445
$743$	34.4482	1.26378	0.631892	−	0.775057i	$-0.282279\pi$
$743$	34.4482	1.26378	0.631892	+	0.775057i	$0.282279\pi$
$744$	−12.4563	−0.456671
$745$	−11.9204	−0.436729
$746$	7.58868	0.277841
$747$	−0.231947	−0.00848648
$748$	−23.1757	−0.847388
$749$	−15.5389	−0.567781
$750$	−0.0507685	−0.00185380
$751$	9.93299	0.362460	0.181230	−	0.983441i	$-0.441992\pi$
$751$	9.93299	0.362460	0.181230	+	0.983441i	$0.441992\pi$
$752$	−11.4432	−0.417291
$753$	1.78331	0.0649873
$754$	6.96469	0.253639
$755$	51.0153	1.85664
$756$	1.85027	0.0672936
$757$	33.1463	1.20472	0.602362	−	0.798223i	$-0.294227\pi$
$757$	33.1463	1.20472	0.602362	+	0.798223i	$0.294227\pi$
$758$	−8.52412	−0.309610
$759$	9.88788	0.358907
$760$	30.2618	1.09771
$761$	41.8088	1.51557	0.757784	−	0.652505i	$-0.226282\pi$
$761$	41.8088	1.51557	0.757784	+	0.652505i	$0.226282\pi$
$762$	4.03547	0.146190
$763$	−3.37003	−0.122003
$764$	1.85027	0.0669404
$765$	−19.1083	−0.690862
$766$	13.3159	0.481124
$767$	−46.2786	−1.67102
$768$	−5.32014	−0.191974
$769$	−37.9220	−1.36750	−0.683750	−	0.729716i	$-0.739652\pi$
$769$	−37.9220	−1.36750	−0.683750	+	0.729716i	$0.739652\pi$
$770$	2.52595	0.0910289
$771$	−19.0840	−0.687293
$772$	38.7941	1.39623
$773$	−22.5108	−0.809657	−0.404828	−	0.914393i	$-0.632669\pi$
$773$	−22.5108	−0.809657	−0.404828	+	0.914393i	$0.632669\pi$
$774$	1.85633	0.0667245
$775$	41.4558	1.48914
$776$	−10.4282	−0.374352
$777$	−7.85727	−0.281878
$778$	8.55128	0.306578
$779$	−26.9109	−0.964181
$780$	35.8182	1.28250
$781$	−25.9895	−0.929978
$782$	11.1999	0.400508
$783$	2.93407	0.104855
$784$	3.12403	0.111572
$785$	−4.88546	−0.174369
$786$	−7.42494	−0.264839
$787$	−24.4882	−0.872908	−0.436454	−	0.899726i	$-0.643766\pi$
$787$	−24.4882	−0.872908	−0.436454	+	0.899726i	$0.643766\pi$
$788$	−46.4543	−1.65487
$789$	−9.22283	−0.328341
$790$	7.75797	0.276016
$791$	11.0637	0.393380
$792$	−3.08191	−0.109511
$793$	57.9073	2.05635
$794$	0.919350	0.0326265
$795$	−4.98597	−0.176834
$796$	41.8328	1.48272
$797$	−19.1457	−0.678174	−0.339087	−	0.940755i	$-0.610118\pi$
$797$	−19.1457	−0.678174	−0.339087	+	0.940755i	$0.610118\pi$
$798$	2.49062	0.0881671
$799$	22.1799	0.784668
$800$	−20.7688	−0.734288
$801$	−1.20390	−0.0425376
$802$	−2.73448	−0.0965579
$803$	−24.3882	−0.860641
$804$	−10.8259	−0.381800
$805$	15.0843	0.531653
$806$	−19.8460	−0.699046
$807$	17.9524	0.631953
$808$	14.6607	0.515762
$809$	−45.6877	−1.60629	−0.803146	−	0.595782i	$-0.796842\pi$
$809$	−45.6877	−1.60629	−0.803146	+	0.595782i	$0.796842\pi$
$810$	−1.22110	−0.0429052
$811$	23.9611	0.841387	0.420694	−	0.907203i	$-0.361787\pi$
$811$	23.9611	0.841387	0.420694	+	0.907203i	$0.361787\pi$
$812$	5.42882	0.190514
$813$	−26.2970	−0.922274
$814$	6.28928	0.220439
$815$	77.5722	2.71723
$816$	18.9165	0.662211
$817$	−30.8780	−1.08029
$818$	12.7603	0.446152
$819$	6.13443	0.214354
$820$	24.4122	0.852510
$821$	6.47678	0.226041	0.113021	−	0.993593i	$-0.463947\pi$
$821$	6.47678	0.226041	0.113021	+	0.993593i	$0.463947\pi$
$822$	−3.15741	−0.110127
$823$	−50.1860	−1.74937	−0.874687	−	0.484688i	$-0.838933\pi$
$823$	−50.1860	−1.74937	−0.874687	+	0.484688i	$0.838933\pi$
$824$	−20.7983	−0.724544
$825$	10.2569	0.357099
$826$	2.91919	0.101572
$827$	11.7342	0.408040	0.204020	−	0.978967i	$-0.434599\pi$
$827$	11.7342	0.408040	0.204020	+	0.978967i	$0.434599\pi$
$828$	−8.84434	−0.307362
$829$	−5.72075	−0.198690	−0.0993449	−	0.995053i	$-0.531675\pi$
$829$	−5.72075	−0.198690	−0.0993449	+	0.995053i	$0.531675\pi$
$830$	0.283231	0.00983108
$831$	−17.7769	−0.616674
$832$	−28.3857	−0.984097
$833$	−6.05517	−0.209799
$834$	−2.26423	−0.0784040
$835$	−76.2866	−2.64001
$836$	24.6353	0.852030
$837$	−8.36068	−0.288987
$838$	−8.10649	−0.280034
$839$	47.7670	1.64910	0.824550	−	0.565789i	$-0.191428\pi$
$839$	47.7670	1.64910	0.824550	+	0.565789i	$0.191428\pi$
$840$	−4.70158	−0.162220
$841$	−20.3912	−0.703146
$842$	2.33228	0.0803756
$843$	−18.3289	−0.631282
$844$	2.60912	0.0898097
$845$	77.7287	2.67395
$846$	1.41739	0.0487309
$847$	−6.72098	−0.230936
$848$	4.93593	0.169501
$849$	16.8949	0.579833
$850$	11.6179	0.398490
$851$	37.5580	1.28747
$852$	23.2467	0.796418
$853$	10.0603	0.344458	0.172229	−	0.985057i	$-0.444903\pi$
$853$	10.0603	0.344458	0.172229	+	0.985057i	$0.444903\pi$
$854$	−3.65272	−0.124993
$855$	20.3117	0.694646
$856$	−23.1510	−0.791285
$857$	43.2642	1.47788	0.738939	−	0.673772i	$-0.235327\pi$
$857$	43.2642	1.47788	0.738939	+	0.673772i	$0.235327\pi$
$858$	−4.91025	−0.167633
$859$	38.4528	1.31199	0.655996	−	0.754764i	$-0.272249\pi$
$859$	38.4528	1.31199	0.655996	+	0.754764i	$0.272249\pi$
$860$	28.0110	0.955167
$861$	4.18096	0.142487
$862$	−0.527888	−0.0179799
$863$	30.6663	1.04389	0.521947	−	0.852978i	$-0.325206\pi$
$863$	30.6663	1.04389	0.521947	+	0.852978i	$0.325206\pi$
$864$	4.18859	0.142499
$865$	34.0325	1.15714
$866$	0.119583	0.00406360
$867$	−19.6651	−0.667862
$868$	−15.4695	−0.525069
$869$	13.1422	0.445818
$870$	−3.58280	−0.121468
$871$	−35.8925	−1.21617
$872$	−5.02090	−0.170029
$873$	−6.99944	−0.236895
$874$	−11.9053	−0.402701
$875$	−0.131201	−0.00443540
$876$	21.8143	0.737038
$877$	−30.7471	−1.03826	−0.519128	−	0.854696i	$-0.673743\pi$
$877$	−30.7471	−1.03826	−0.519128	+	0.854696i	$0.673743\pi$
$878$	−5.87536	−0.198284
$879$	−16.7316	−0.564342
$880$	−20.3931	−0.687450
$881$	0.377134	0.0127060	0.00635298	−	0.999980i	$-0.497978\pi$
$881$	0.377134	0.0127060	0.00635298	+	0.999980i	$0.497978\pi$
$882$	−0.386952	−0.0130294
$883$	6.66939	0.224443	0.112221	−	0.993683i	$-0.464203\pi$
$883$	6.66939	0.224443	0.112221	+	0.993683i	$0.464203\pi$
$884$	68.7282	2.31158
$885$	23.8068	0.800257
$886$	12.0115	0.403534
$887$	−40.0097	−1.34339	−0.671696	−	0.740826i	$-0.734434\pi$
$887$	−40.0097	−1.34339	−0.671696	+	0.740826i	$0.734434\pi$
$888$	−11.7063	−0.392838
$889$	10.4289	0.349773
$890$	1.47008	0.0492772
$891$	−2.06858	−0.0693000
$892$	−20.9450	−0.701290
$893$	−23.5767	−0.788965
$894$	−1.46168	−0.0488859
$895$	59.6167	1.99277
$896$	10.1677	0.339679
$897$	−29.3228	−0.979059
$898$	−3.81229	−0.127218
$899$	−24.5308	−0.818149
$900$	−9.17441	−0.305814
$901$	−9.56711	−0.318727
$902$	−3.34661	−0.111430
$903$	4.79732	0.159645
$904$	16.4835	0.548232
$905$	52.8735	1.75757
$906$	6.25551	0.207825
$907$	16.2651	0.540074	0.270037	−	0.962850i	$-0.412964\pi$
$907$	16.2651	0.540074	0.270037	+	0.962850i	$0.412964\pi$
$908$	−31.9911	−1.06166
$909$	9.84027	0.326381
$910$	−7.49077	−0.248317
$911$	−53.7100	−1.77949	−0.889746	−	0.456455i	$-0.849119\pi$
$911$	−53.7100	−1.77949	−0.889746	+	0.456455i	$0.849119\pi$
$912$	−20.1079	−0.665838
$913$	0.479800	0.0158791
$914$	−7.01019	−0.231877
$915$	−29.7889	−0.984791
$916$	−55.2730	−1.82627
$917$	−19.1883	−0.633653
$918$	−2.34306	−0.0773325
$919$	30.5056	1.00629	0.503144	−	0.864203i	$-0.332177\pi$
$919$	30.5056	1.00629	0.503144	+	0.864203i	$0.332177\pi$
$920$	22.4737	0.740935
$921$	4.53417	0.149406
$922$	−4.62819	−0.152421
$923$	77.0726	2.53688
$924$	−3.82743	−0.125913
$925$	38.9597	1.28099
$926$	−6.78866	−0.223089
$927$	−13.9598	−0.458501
$928$	12.2896	0.403426
$929$	8.94080	0.293338	0.146669	−	0.989186i	$-0.453145\pi$
$929$	8.94080	0.293338	0.146669	+	0.989186i	$0.453145\pi$
$930$	10.2093	0.334775
$931$	6.43652	0.210948
$932$	−0.188528	−0.00617543
$933$	−4.21363	−0.137948
$934$	−1.53469	−0.0502166
$935$	39.5270	1.29267
$936$	9.13950	0.298734
$937$	−21.9057	−0.715629	−0.357815	−	0.933793i	$-0.616478\pi$
$937$	−21.9057	−0.715629	−0.357815	+	0.933793i	$0.616478\pi$
$938$	2.26405	0.0739240
$939$	−23.7052	−0.773590
$940$	21.3876	0.697588
$941$	52.3104	1.70527	0.852636	−	0.522506i	$-0.175003\pi$
$941$	52.3104	1.70527	0.852636	+	0.522506i	$0.175003\pi$
$942$	−0.599055	−0.0195183
$943$	−19.9851	−0.650806
$944$	−23.5679	−0.767069
$945$	−3.15570	−0.102655
$946$	−3.83997	−0.124848
$947$	−36.0157	−1.17035	−0.585177	−	0.810906i	$-0.698975\pi$
$947$	−36.0157	−1.17035	−0.585177	+	0.810906i	$0.698975\pi$
$948$	−11.7552	−0.381791
$949$	72.3239	2.34773
$950$	−12.3496	−0.400673
$951$	−15.5194	−0.503251
$952$	−9.02141	−0.292386
$953$	42.7581	1.38507	0.692536	−	0.721383i	$-0.256493\pi$
$953$	42.7581	1.38507	0.692536	+	0.721383i	$0.256493\pi$
$954$	−0.611380	−0.0197942
$955$	−3.15570	−0.102116
$956$	−25.4122	−0.821891
$957$	−6.06936	−0.196194
$958$	5.71475	0.184635
$959$	−8.15969	−0.263490
$960$	14.6023	0.471287
$961$	38.9010	1.25487
$962$	−18.6510	−0.601334
$963$	−15.5389	−0.500735
$964$	36.6307	1.17979
$965$	−66.1646	−2.12992
$966$	1.84964	0.0595113
$967$	25.7292	0.827397	0.413698	−	0.910414i	$-0.364237\pi$
$967$	25.7292	0.827397	0.413698	+	0.910414i	$0.364237\pi$
$968$	−10.0134	−0.321842
$969$	38.9742	1.25203
$970$	8.54703	0.274429
$971$	3.35399	0.107635	0.0538173	−	0.998551i	$-0.482861\pi$
$971$	3.35399	0.107635	0.0538173	+	0.998551i	$0.482861\pi$
$972$	1.85027	0.0593474
$973$	−5.85146	−0.187589
$974$	0.994812	0.0318758
$975$	−30.4171	−0.974127
$976$	29.4900	0.943951
$977$	−27.4464	−0.878087	−0.439044	−	0.898466i	$-0.644683\pi$
$977$	−27.4464	−0.878087	−0.439044	+	0.898466i	$0.644683\pi$
$978$	9.51191	0.304157
$979$	2.49035	0.0795920
$980$	−5.83889	−0.186516
$981$	−3.37003	−0.107597
$982$	12.0333	0.383999
$983$	−10.4785	−0.334214	−0.167107	−	0.985939i	$-0.553442\pi$
$983$	−10.4785	−0.334214	−0.167107	+	0.985939i	$0.553442\pi$
$984$	6.22909	0.198576
$985$	79.2294	2.52446
$986$	−6.87470	−0.218935
$987$	3.66296	0.116593
$988$	−73.0567	−2.32424
$989$	−22.9313	−0.729174
$990$	2.52595	0.0802799
$991$	16.9460	0.538309	0.269154	−	0.963097i	$-0.413256\pi$
$991$	16.9460	0.538309	0.269154	+	0.963097i	$0.413256\pi$
$992$	−35.0194	−1.11187
$993$	12.1437	0.385368
$994$	−4.86164	−0.154202
$995$	−71.3472	−2.26186
$996$	−0.429163	−0.0135986
$997$	8.82763	0.279574	0.139787	−	0.990182i	$-0.455358\pi$
$997$	8.82763	0.279574	0.139787	+	0.990182i	$0.455358\pi$
$998$	11.6231	0.367923
$999$	−7.85727	−0.248593

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.l.1.14	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.l.1.14	✓	28	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q-0.386952 q^{2} -1.00000 q^{3} -1.85027 q^{4} +3.15570 q^{5} +0.386952 q^{6} +1.00000 q^{7} +1.48987 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.386952 q^{2} -1.00000 q^{3} -1.85027 q^{4} +3.15570 q^{5} +0.386952 q^{6} +1.00000 q^{7} +1.48987 q^{8} +1.00000 q^{9} -1.22110 q^{10} -2.06858 q^{11} +1.85027 q^{12} +6.13443 q^{13} -0.386952 q^{14} -3.15570 q^{15} +3.12403 q^{16} -6.05517 q^{17} -0.386952 q^{18} +6.43652 q^{19} -5.83889 q^{20} -1.00000 q^{21} +0.800441 q^{22} +4.78003 q^{23} -1.48987 q^{24} +4.95842 q^{25} -2.37373 q^{26} -1.00000 q^{27} -1.85027 q^{28} -2.93407 q^{29} +1.22110 q^{30} +8.36068 q^{31} -4.18859 q^{32} +2.06858 q^{33} +2.34306 q^{34} +3.15570 q^{35} -1.85027 q^{36} +7.85727 q^{37} -2.49062 q^{38} -6.13443 q^{39} +4.70158 q^{40} -4.18096 q^{41} +0.386952 q^{42} -4.79732 q^{43} +3.82743 q^{44} +3.15570 q^{45} -1.84964 q^{46} -3.66296 q^{47} -3.12403 q^{48} +1.00000 q^{49} -1.91867 q^{50} +6.05517 q^{51} -11.3503 q^{52} +1.57999 q^{53} +0.386952 q^{54} -6.52781 q^{55} +1.48987 q^{56} -6.43652 q^{57} +1.13534 q^{58} -7.54407 q^{59} +5.83889 q^{60} +9.43972 q^{61} -3.23518 q^{62} +1.00000 q^{63} -4.62728 q^{64} +19.3584 q^{65} -0.800441 q^{66} -5.85099 q^{67} +11.2037 q^{68} -4.78003 q^{69} -1.22110 q^{70} +12.5639 q^{71} +1.48987 q^{72} +11.7898 q^{73} -3.04039 q^{74} -4.95842 q^{75} -11.9093 q^{76} -2.06858 q^{77} +2.37373 q^{78} -6.35325 q^{79} +9.85849 q^{80} +1.00000 q^{81} +1.61783 q^{82} -0.231947 q^{83} +1.85027 q^{84} -19.1083 q^{85} +1.85633 q^{86} +2.93407 q^{87} -3.08191 q^{88} -1.20390 q^{89} -1.22110 q^{90} +6.13443 q^{91} -8.84434 q^{92} -8.36068 q^{93} +1.41739 q^{94} +20.3117 q^{95} +4.18859 q^{96} -6.99944 q^{97} -0.386952 q^{98} -2.06858 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9}+O(q^{10}) \) 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9	\( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9} + 4 q^{10} - 8 q^{11} - 34 q^{12} + 26 q^{13} - 6 q^{14} - 8 q^{15} + 62 q^{16} + 9 q^{17} - 6 q^{18} + 25 q^{19} + 20 q^{20} - 28 q^{21} + 3 q^{22} - 30 q^{23} + 15 q^{24} + 42 q^{25} + 25 q^{26} - 28 q^{27} + 34 q^{28} - 5 q^{29} - 4 q^{30} + 18 q^{31} - 26 q^{32} + 8 q^{33} + 30 q^{34} + 8 q^{35} + 34 q^{36} + 36 q^{37} - 2 q^{38} - 26 q^{39} + 28 q^{40} + 21 q^{41} + 6 q^{42} + 8 q^{43} - 20 q^{44} + 8 q^{45} + 24 q^{46} + 6 q^{47} - 62 q^{48} + 28 q^{49} - 48 q^{50} - 9 q^{51} + 54 q^{52} - 12 q^{53} + 6 q^{54} + 15 q^{55} - 15 q^{56} - 25 q^{57} + 19 q^{58} + 33 q^{59} - 20 q^{60} + 48 q^{61} + 28 q^{63} + 75 q^{64} + 21 q^{65} - 3 q^{66} + 27 q^{67} + 19 q^{68} + 30 q^{69} + 4 q^{70} - 45 q^{71} - 15 q^{72} + 61 q^{73} - 31 q^{74} - 42 q^{75} + 63 q^{76} - 8 q^{77} - 25 q^{78} + 35 q^{79} + 84 q^{80} + 28 q^{81} + 11 q^{82} + 43 q^{83} - 34 q^{84} + 43 q^{85} - q^{86} + 5 q^{87} - 27 q^{88} + 25 q^{89} + 4 q^{90} + 26 q^{91} - 102 q^{92} - 18 q^{93} + 55 q^{94} - 43 q^{95} + 26 q^{96} + 40 q^{97} - 6 q^{98} - 8 q^{99}+O(q^{100}) \) 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9 + 4 * q^10 - 8 * q^11 - 34 * q^12 + 26 * q^13 - 6 * q^14 - 8 * q^15 + 62 * q^16 + 9 * q^17 - 6 * q^18 + 25 * q^19 + 20 * q^20 - 28 * q^21 + 3 * q^22 - 30 * q^23 + 15 * q^24 + 42 * q^25 + 25 * q^26 - 28 * q^27 + 34 * q^28 - 5 * q^29 - 4 * q^30 + 18 * q^31 - 26 * q^32 + 8 * q^33 + 30 * q^34 + 8 * q^35 + 34 * q^36 + 36 * q^37 - 2 * q^38 - 26 * q^39 + 28 * q^40 + 21 * q^41 + 6 * q^42 + 8 * q^43 - 20 * q^44 + 8 * q^45 + 24 * q^46 + 6 * q^47 - 62 * q^48 + 28 * q^49 - 48 * q^50 - 9 * q^51 + 54 * q^52 - 12 * q^53 + 6 * q^54 + 15 * q^55 - 15 * q^56 - 25 * q^57 + 19 * q^58 + 33 * q^59 - 20 * q^60 + 48 * q^61 + 28 * q^63 + 75 * q^64 + 21 * q^65 - 3 * q^66 + 27 * q^67 + 19 * q^68 + 30 * q^69 + 4 * q^70 - 45 * q^71 - 15 * q^72 + 61 * q^73 - 31 * q^74 - 42 * q^75 + 63 * q^76 - 8 * q^77 - 25 * q^78 + 35 * q^79 + 84 * q^80 + 28 * q^81 + 11 * q^82 + 43 * q^83 - 34 * q^84 + 43 * q^85 - q^86 + 5 * q^87 - 27 * q^88 + 25 * q^89 + 4 * q^90 + 26 * q^91 - 102 * q^92 - 18 * q^93 + 55 * q^94 - 43 * q^95 + 26 * q^96 + 40 * q^97 - 6 * q^98 - 8 * q^99

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