LMFDB - Embedded newform 8041.2.a.d.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.79824 q^{2} -0.403049 q^{3} +1.23368 q^{4} -0.0361831 q^{5} +0.724781 q^{6} +4.76370 q^{7} +1.37802 q^{8} -2.83755 q^{9} +O(q^{10})$	\(q-1.79824 q^{2} -0.403049 q^{3} +1.23368 q^{4} -0.0361831 q^{5} +0.724781 q^{6} +4.76370 q^{7} +1.37802 q^{8} -2.83755 q^{9} +0.0650661 q^{10} +1.00000 q^{11} -0.497236 q^{12} +2.74171 q^{13} -8.56629 q^{14} +0.0145836 q^{15} -4.94539 q^{16} -1.00000 q^{17} +5.10261 q^{18} +3.93141 q^{19} -0.0446386 q^{20} -1.92000 q^{21} -1.79824 q^{22} -7.09132 q^{23} -0.555411 q^{24} -4.99869 q^{25} -4.93027 q^{26} +2.35282 q^{27} +5.87690 q^{28} -1.95348 q^{29} -0.0262248 q^{30} +6.08772 q^{31} +6.13698 q^{32} -0.403049 q^{33} +1.79824 q^{34} -0.172365 q^{35} -3.50064 q^{36} +1.78540 q^{37} -7.06964 q^{38} -1.10504 q^{39} -0.0498611 q^{40} -5.94180 q^{41} +3.45264 q^{42} +1.00000 q^{43} +1.23368 q^{44} +0.102671 q^{45} +12.7519 q^{46} +11.5817 q^{47} +1.99324 q^{48} +15.6928 q^{49} +8.98887 q^{50} +0.403049 q^{51} +3.38241 q^{52} -1.40054 q^{53} -4.23095 q^{54} -0.0361831 q^{55} +6.56448 q^{56} -1.58455 q^{57} +3.51283 q^{58} -13.0268 q^{59} +0.0179915 q^{60} +1.01174 q^{61} -10.9472 q^{62} -13.5172 q^{63} -1.14501 q^{64} -0.0992036 q^{65} +0.724781 q^{66} -12.2567 q^{67} -1.23368 q^{68} +2.85815 q^{69} +0.309955 q^{70} -15.9271 q^{71} -3.91021 q^{72} -16.3137 q^{73} -3.21059 q^{74} +2.01472 q^{75} +4.85012 q^{76} +4.76370 q^{77} +1.98714 q^{78} -12.0857 q^{79} +0.178940 q^{80} +7.56435 q^{81} +10.6848 q^{82} -3.46417 q^{83} -2.36868 q^{84} +0.0361831 q^{85} -1.79824 q^{86} +0.787348 q^{87} +1.37802 q^{88} -7.17858 q^{89} -0.184628 q^{90} +13.0607 q^{91} -8.74845 q^{92} -2.45365 q^{93} -20.8268 q^{94} -0.142251 q^{95} -2.47351 q^{96} +8.00484 q^{97} -28.2195 q^{98} -2.83755 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9}+O(q^{10}) $ 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9} - 7 q^{10} + 62 q^{11} - 17 q^{12} - 31 q^{14} - 20 q^{15} + 27 q^{16} - 62 q^{17} + 3 q^{18} - 29 q^{20} - 18 q^{21} - 7 q^{22} - 50 q^{23} - 31 q^{24} + 35 q^{25} - 32 q^{26} - 14 q^{27} - 13 q^{28} - 26 q^{29} - 10 q^{30} - 58 q^{31} - 5 q^{32} - 8 q^{33} + 7 q^{34} - 32 q^{35} - 29 q^{36} - 41 q^{37} - 10 q^{38} - 53 q^{39} - 31 q^{40} - 55 q^{41} - 7 q^{42} + 62 q^{43} + 49 q^{44} - 34 q^{45} - 39 q^{46} - 31 q^{47} - 30 q^{48} + 35 q^{49} - 40 q^{50} + 8 q^{51} + 13 q^{52} - 74 q^{53} + 48 q^{54} - 13 q^{55} - 75 q^{56} - 43 q^{57} - 46 q^{58} - 65 q^{59} - 8 q^{60} - 14 q^{61} - 29 q^{62} - 23 q^{63} - 15 q^{64} - 9 q^{65} - 2 q^{66} - q^{67} - 49 q^{68} - 59 q^{69} - 31 q^{70} - 141 q^{71} + 9 q^{72} - 4 q^{73} - 94 q^{74} - 43 q^{75} + 34 q^{76} - 11 q^{77} - 11 q^{78} - 63 q^{79} - 41 q^{80} - 30 q^{81} + 38 q^{82} - 44 q^{83} - 16 q^{84} + 13 q^{85} - 7 q^{86} - 8 q^{87} - 9 q^{88} - 58 q^{89} - 55 q^{90} - 78 q^{91} - 104 q^{92} - 5 q^{94} - 99 q^{95} - 148 q^{96} - 26 q^{97} + 16 q^{98} + 40 q^{99}+O(q^{100}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9 - 7 * q^10 + 62 * q^11 - 17 * q^12 - 31 * q^14 - 20 * q^15 + 27 * q^16 - 62 * q^17 + 3 * q^18 - 29 * q^20 - 18 * q^21 - 7 * q^22 - 50 * q^23 - 31 * q^24 + 35 * q^25 - 32 * q^26 - 14 * q^27 - 13 * q^28 - 26 * q^29 - 10 * q^30 - 58 * q^31 - 5 * q^32 - 8 * q^33 + 7 * q^34 - 32 * q^35 - 29 * q^36 - 41 * q^37 - 10 * q^38 - 53 * q^39 - 31 * q^40 - 55 * q^41 - 7 * q^42 + 62 * q^43 + 49 * q^44 - 34 * q^45 - 39 * q^46 - 31 * q^47 - 30 * q^48 + 35 * q^49 - 40 * q^50 + 8 * q^51 + 13 * q^52 - 74 * q^53 + 48 * q^54 - 13 * q^55 - 75 * q^56 - 43 * q^57 - 46 * q^58 - 65 * q^59 - 8 * q^60 - 14 * q^61 - 29 * q^62 - 23 * q^63 - 15 * q^64 - 9 * q^65 - 2 * q^66 - q^67 - 49 * q^68 - 59 * q^69 - 31 * q^70 - 141 * q^71 + 9 * q^72 - 4 * q^73 - 94 * q^74 - 43 * q^75 + 34 * q^76 - 11 * q^77 - 11 * q^78 - 63 * q^79 - 41 * q^80 - 30 * q^81 + 38 * q^82 - 44 * q^83 - 16 * q^84 + 13 * q^85 - 7 * q^86 - 8 * q^87 - 9 * q^88 - 58 * q^89 - 55 * q^90 - 78 * q^91 - 104 * q^92 - 5 * q^94 - 99 * q^95 - 148 * q^96 - 26 * q^97 + 16 * q^98 + 40 * 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 $

$2$	−1.79824	−1.27155	−0.635776	−	0.771874i	$-0.719320\pi$
$2$	−1.79824	−1.27155	−0.635776	+	0.771874i	$0.719320\pi$
$3$	−0.403049	−0.232701	−0.116350	−	0.993208i	$-0.537120\pi$
$3$	−0.403049	−0.232701	−0.116350	+	0.993208i	$0.537120\pi$
$4$	1.23368	0.616842
$5$	−0.0361831	−0.0161816	−0.00809079	−	0.999967i	$-0.502575\pi$
$5$	−0.0361831	−0.0161816	−0.00809079	+	0.999967i	$0.502575\pi$
$6$	0.724781	0.295891
$7$	4.76370	1.80051	0.900254	−	0.435365i	$-0.143381\pi$
$7$	4.76370	1.80051	0.900254	+	0.435365i	$0.143381\pi$
$8$	1.37802	0.487204
$9$	−2.83755	−0.945850
$10$	0.0650661	0.0205757
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.497236	−0.143540
$13$	2.74171	0.760413	0.380207	−	0.924902i	$-0.375853\pi$
$13$	2.74171	0.760413	0.380207	+	0.924902i	$0.375853\pi$
$14$	−8.56629	−2.28944
$15$	0.0145836	0.00376546
$16$	−4.94539	−1.23635
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	5.10261	1.20270
$19$	3.93141	0.901927	0.450964	−	0.892542i	$-0.351080\pi$
$19$	3.93141	0.901927	0.450964	+	0.892542i	$0.351080\pi$
$20$	−0.0446386	−0.00998148
$21$	−1.92000	−0.418979
$22$	−1.79824	−0.383387
$23$	−7.09132	−1.47864	−0.739321	−	0.673353i	$-0.764853\pi$
$23$	−7.09132	−1.47864	−0.739321	+	0.673353i	$0.764853\pi$
$24$	−0.555411	−0.113373
$25$	−4.99869	−0.999738
$26$	−4.93027	−0.966905
$27$	2.35282	0.452801
$28$	5.87690	1.11063
$29$	−1.95348	−0.362752	−0.181376	−	0.983414i	$-0.558055\pi$
$29$	−1.95348	−0.362752	−0.181376	+	0.983414i	$0.558055\pi$
$30$	−0.0262248	−0.00478798
$31$	6.08772	1.09339	0.546693	−	0.837333i	$-0.315886\pi$
$31$	6.08772	1.09339	0.546693	+	0.837333i	$0.315886\pi$
$32$	6.13698	1.08488
$33$	−0.403049	−0.0701619
$34$	1.79824	0.308396
$35$	−0.172365	−0.0291351
$36$	−3.50064	−0.583441
$37$	1.78540	0.293518	0.146759	−	0.989172i	$-0.453116\pi$
$37$	1.78540	0.293518	0.146759	+	0.989172i	$0.453116\pi$
$38$	−7.06964	−1.14685
$39$	−1.10504	−0.176949
$40$	−0.0498611	−0.00788374
$41$	−5.94180	−0.927954	−0.463977	−	0.885847i	$-0.653578\pi$
$41$	−5.94180	−0.927954	−0.463977	+	0.885847i	$0.653578\pi$
$42$	3.45264	0.532754
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	1.23368	0.185985
$45$	0.102671	0.0153054
$46$	12.7519	1.88017
$47$	11.5817	1.68937	0.844684	−	0.535265i	$-0.179788\pi$
$47$	11.5817	1.68937	0.844684	+	0.535265i	$0.179788\pi$
$48$	1.99324	0.287699
$49$	15.6928	2.24183
$50$	8.98887	1.27122
$51$	0.403049	0.0564382
$52$	3.38241	0.469055
$53$	−1.40054	−0.192380	−0.0961898	−	0.995363i	$-0.530666\pi$
$53$	−1.40054	−0.192380	−0.0961898	+	0.995363i	$0.530666\pi$
$54$	−4.23095	−0.575759
$55$	−0.0361831	−0.00487893
$56$	6.56448	0.877215
$57$	−1.58455	−0.209879
$58$	3.51283	0.461257
$59$	−13.0268	−1.69595	−0.847974	−	0.530039i	$-0.822177\pi$
$59$	−13.0268	−1.69595	−0.847974	+	0.530039i	$0.822177\pi$
$60$	0.0179915	0.00232270
$61$	1.01174	0.129540	0.0647699	−	0.997900i	$-0.479369\pi$
$61$	1.01174	0.129540	0.0647699	+	0.997900i	$0.479369\pi$
$62$	−10.9472	−1.39030
$63$	−13.5172	−1.70301
$64$	−1.14501	−0.143126
$65$	−0.0992036	−0.0123047
$66$	0.724781	0.0892144
$67$	−12.2567	−1.49740	−0.748699	−	0.662910i	$-0.769321\pi$
$67$	−12.2567	−1.49740	−0.748699	+	0.662910i	$0.769321\pi$
$68$	−1.23368	−0.149606
$69$	2.85815	0.344081
$70$	0.309955	0.0370467
$71$	−15.9271	−1.89020	−0.945098	−	0.326786i	$-0.894034\pi$
$71$	−15.9271	−1.89020	−0.945098	+	0.326786i	$0.894034\pi$
$72$	−3.91021	−0.460823
$73$	−16.3137	−1.90937	−0.954687	−	0.297611i	$-0.903810\pi$
$73$	−16.3137	−1.90937	−0.954687	+	0.297611i	$0.903810\pi$
$74$	−3.21059	−0.373223
$75$	2.01472	0.232640
$76$	4.85012	0.556347
$77$	4.76370	0.542874
$78$	1.98714	0.224999
$79$	−12.0857	−1.35975	−0.679875	−	0.733328i	$-0.737966\pi$
$79$	−12.0857	−1.35975	−0.679875	+	0.733328i	$0.737966\pi$
$80$	0.178940	0.0200061
$81$	7.56435	0.840483
$82$	10.6848	1.17994
$83$	−3.46417	−0.380242	−0.190121	−	0.981761i	$-0.560888\pi$
$83$	−3.46417	−0.380242	−0.190121	+	0.981761i	$0.560888\pi$
$84$	−2.36868	−0.258444
$85$	0.0361831	0.00392461
$86$	−1.79824	−0.193910
$87$	0.787348	0.0844126
$88$	1.37802	0.146898
$89$	−7.17858	−0.760928	−0.380464	−	0.924796i	$-0.624236\pi$
$89$	−7.17858	−0.760928	−0.380464	+	0.924796i	$0.624236\pi$
$90$	−0.184628	−0.0194615
$91$	13.0607	1.36913
$92$	−8.74845	−0.912089
$93$	−2.45365	−0.254432
$94$	−20.8268	−2.14812
$95$	−0.142251	−0.0145946
$96$	−2.47351	−0.252451
$97$	8.00484	0.812768	0.406384	−	0.913702i	$-0.366790\pi$
$97$	8.00484	0.812768	0.406384	+	0.913702i	$0.366790\pi$
$98$	−28.2195	−2.85060
$99$	−2.83755	−0.285185
$100$	−6.16681	−0.616681
$101$	−15.3582	−1.52820	−0.764098	−	0.645101i	$-0.776815\pi$
$101$	−15.3582	−1.52820	−0.764098	+	0.645101i	$0.776815\pi$
$102$	−0.724781	−0.0717640
$103$	5.66472	0.558161	0.279081	−	0.960268i	$-0.409970\pi$
$103$	5.66472	0.558161	0.279081	+	0.960268i	$0.409970\pi$
$104$	3.77814	0.370477
$105$	0.0694717	0.00677974
$106$	2.51852	0.244620
$107$	1.97084	0.190528	0.0952642	−	0.995452i	$-0.469630\pi$
$107$	1.97084	0.190528	0.0952642	+	0.995452i	$0.469630\pi$
$108$	2.90264	0.279307
$109$	−10.9295	−1.04685	−0.523426	−	0.852071i	$-0.675346\pi$
$109$	−10.9295	−1.04685	−0.523426	+	0.852071i	$0.675346\pi$
$110$	0.0650661	0.00620381
$111$	−0.719604	−0.0683018
$112$	−23.5583	−2.22605
$113$	−18.7540	−1.76423	−0.882113	−	0.471037i	$-0.843880\pi$
$113$	−18.7540	−1.76423	−0.882113	+	0.471037i	$0.843880\pi$
$114$	2.84941	0.266872
$115$	0.256586	0.0239268
$116$	−2.40998	−0.223761
$117$	−7.77974	−0.719237
$118$	23.4254	2.15648
$119$	−4.76370	−0.436687
$120$	0.0200965	0.00183455
$121$	1.00000	0.0909091
$122$	−1.81935	−0.164716
$123$	2.39484	0.215935
$124$	7.51033	0.674447
$125$	0.361784	0.0323589
$126$	24.3073	2.16547
$127$	−7.99473	−0.709417	−0.354709	−	0.934977i	$-0.615420\pi$
$127$	−7.99473	−0.709417	−0.354709	+	0.934977i	$0.615420\pi$
$128$	−10.2149	−0.902883
$129$	−0.403049	−0.0354865
$130$	0.178392	0.0156460
$131$	20.0223	1.74936	0.874680	−	0.484700i	$-0.161071\pi$
$131$	20.0223	1.74936	0.874680	+	0.484700i	$0.161071\pi$
$132$	−0.497236	−0.0432788
$133$	18.7280	1.62393
$134$	22.0406	1.90402
$135$	−0.0851324	−0.00732703
$136$	−1.37802	−0.118164
$137$	−2.93951	−0.251139	−0.125570	−	0.992085i	$-0.540076\pi$
$137$	−2.93951	−0.251139	−0.125570	+	0.992085i	$0.540076\pi$
$138$	−5.13965	−0.437516
$139$	−0.393257	−0.0333556	−0.0166778	−	0.999861i	$-0.505309\pi$
$139$	−0.393257	−0.0333556	−0.0166778	+	0.999861i	$0.505309\pi$
$140$	−0.212644	−0.0179717
$141$	−4.66801	−0.393117
$142$	28.6408	2.40348
$143$	2.74171	0.229273
$144$	14.0328	1.16940
$145$	0.0706829	0.00586990
$146$	29.3360	2.42787
$147$	−6.32497	−0.521675
$148$	2.20262	0.181054
$149$	−0.0350565	−0.00287194	−0.00143597	−	0.999999i	$-0.500457\pi$
$149$	−0.0350565	−0.00287194	−0.00143597	+	0.999999i	$0.500457\pi$
$150$	−3.62296	−0.295813
$151$	15.7250	1.27968	0.639839	−	0.768509i	$-0.279001\pi$
$151$	15.7250	1.27968	0.639839	+	0.768509i	$0.279001\pi$
$152$	5.41757	0.439423
$153$	2.83755	0.229402
$154$	−8.56629	−0.690291
$155$	−0.220273	−0.0176927
$156$	−1.36328	−0.109149
$157$	8.22483	0.656413	0.328206	−	0.944606i	$-0.393556\pi$
$157$	8.22483	0.656413	0.328206	+	0.944606i	$0.393556\pi$
$158$	21.7331	1.72899
$159$	0.564488	0.0447668
$160$	−0.222055	−0.0175550
$161$	−33.7809	−2.66231
$162$	−13.6026	−1.06872
$163$	−3.87987	−0.303895	−0.151947	−	0.988389i	$-0.548554\pi$
$163$	−3.87987	−0.303895	−0.151947	+	0.988389i	$0.548554\pi$
$164$	−7.33031	−0.572401
$165$	0.0145836	0.00113533
$166$	6.22943	0.483497
$167$	4.27098	0.330498	0.165249	−	0.986252i	$-0.447157\pi$
$167$	4.27098	0.330498	0.165249	+	0.986252i	$0.447157\pi$
$168$	−2.64581	−0.204129
$169$	−5.48303	−0.421771
$170$	−0.0650661	−0.00499034
$171$	−11.1556	−0.853088
$172$	1.23368	0.0940676
$173$	−20.6434	−1.56949	−0.784743	−	0.619822i	$-0.787205\pi$
$173$	−20.6434	−1.56949	−0.784743	+	0.619822i	$0.787205\pi$
$174$	−1.41584	−0.107335
$175$	−23.8122	−1.80004
$176$	−4.94539	−0.372773
$177$	5.25045	0.394648
$178$	12.9088	0.967559
$179$	23.2947	1.74113	0.870563	−	0.492057i	$-0.163755\pi$
$179$	23.2947	1.74113	0.870563	+	0.492057i	$0.163755\pi$
$180$	0.126664	0.00944099
$181$	−7.38709	−0.549078	−0.274539	−	0.961576i	$-0.588525\pi$
$181$	−7.38709	−0.549078	−0.274539	+	0.961576i	$0.588525\pi$
$182$	−23.4863	−1.74092
$183$	−0.407780	−0.0301440
$184$	−9.77199	−0.720401
$185$	−0.0646013	−0.00474958
$186$	4.41226	0.323523
$187$	−1.00000	−0.0731272
$188$	14.2882	1.04207
$189$	11.2081	0.815271
$190$	0.255801	0.0185578
$191$	14.2581	1.03168	0.515841	−	0.856685i	$-0.327480\pi$
$191$	14.2581	1.03168	0.515841	+	0.856685i	$0.327480\pi$
$192$	0.461496	0.0333056
$193$	4.68333	0.337114	0.168557	−	0.985692i	$-0.446089\pi$
$193$	4.68333	0.337114	0.168557	+	0.985692i	$0.446089\pi$
$194$	−14.3947	−1.03348
$195$	0.0399839	0.00286331
$196$	19.3600	1.38285
$197$	21.1557	1.50728	0.753642	−	0.657286i	$-0.228296\pi$
$197$	21.1557	1.50728	0.753642	+	0.657286i	$0.228296\pi$
$198$	5.10261	0.362627
$199$	10.4885	0.743507	0.371754	−	0.928331i	$-0.378757\pi$
$199$	10.4885	0.743507	0.371754	+	0.928331i	$0.378757\pi$
$200$	−6.88831	−0.487077
$201$	4.94007	0.348446
$202$	27.6178	1.94318
$203$	−9.30578	−0.653137
$204$	0.497236	0.0348135
$205$	0.214993	0.0150158
$206$	−10.1866	−0.709731
$207$	20.1220	1.39857
$208$	−13.5588	−0.940136
$209$	3.93141	0.271941
$210$	−0.124927	−0.00862079
$211$	−22.1538	−1.52513	−0.762564	−	0.646913i	$-0.776060\pi$
$211$	−22.1538	−1.52513	−0.762564	+	0.646913i	$0.776060\pi$
$212$	−1.72783	−0.118668
$213$	6.41940	0.439850
$214$	−3.54406	−0.242267
$215$	−0.0361831	−0.00246767
$216$	3.24224	0.220606
$217$	29.0000	1.96865
$218$	19.6539	1.33113
$219$	6.57523	0.444313
$220$	−0.0446386	−0.00300953
$221$	−2.74171	−0.184427
$222$	1.29402	0.0868492
$223$	15.8319	1.06018	0.530091	−	0.847941i	$-0.322158\pi$
$223$	15.8319	1.06018	0.530091	+	0.847941i	$0.322158\pi$
$224$	29.2347	1.95333
$225$	14.1840	0.945603
$226$	33.7243	2.24330
$227$	−29.2431	−1.94093	−0.970467	−	0.241235i	$-0.922447\pi$
$227$	−29.2431	−1.94093	−0.970467	+	0.241235i	$0.922447\pi$
$228$	−1.95484	−0.129462
$229$	−26.0544	−1.72172	−0.860862	−	0.508838i	$-0.830075\pi$
$229$	−26.0544	−1.72172	−0.860862	+	0.508838i	$0.830075\pi$
$230$	−0.461404	−0.0304241
$231$	−1.92000	−0.126327
$232$	−2.69194	−0.176734
$233$	−13.7571	−0.901259	−0.450630	−	0.892711i	$-0.648801\pi$
$233$	−13.7571	−0.901259	−0.450630	+	0.892711i	$0.648801\pi$
$234$	13.9899	0.914547
$235$	−0.419063	−0.0273367
$236$	−16.0710	−1.04613
$237$	4.87114	0.316415
$238$	8.56629	0.555270
$239$	−13.1989	−0.853767	−0.426883	−	0.904307i	$-0.640388\pi$
$239$	−13.1989	−0.853767	−0.426883	+	0.904307i	$0.640388\pi$
$240$	−0.0721215	−0.00465542
$241$	−3.95354	−0.254670	−0.127335	−	0.991860i	$-0.540642\pi$
$241$	−3.95354	−0.254670	−0.127335	+	0.991860i	$0.540642\pi$
$242$	−1.79824	−0.115596
$243$	−10.1073	−0.648382
$244$	1.24817	0.0799056
$245$	−0.567814	−0.0362763
$246$	−4.30651	−0.274573
$247$	10.7788	0.685838
$248$	8.38901	0.532703
$249$	1.39623	0.0884826
$250$	−0.650576	−0.0411460
$251$	8.26332	0.521576	0.260788	−	0.965396i	$-0.416018\pi$
$251$	8.26332	0.521576	0.260788	+	0.965396i	$0.416018\pi$
$252$	−16.6760	−1.05049
$253$	−7.09132	−0.445827
$254$	14.3765	0.902060
$255$	−0.0145836	−0.000913259 0
$256$	20.6590	1.29119
$257$	−20.1753	−1.25850	−0.629250	−	0.777203i	$-0.716638\pi$
$257$	−20.1753	−1.25850	−0.629250	+	0.777203i	$0.716638\pi$
$258$	0.724781	0.0451229
$259$	8.50510	0.528481
$260$	−0.122386	−0.00759005
$261$	5.54309	0.343109
$262$	−36.0051	−2.22440
$263$	3.11864	0.192303	0.0961517	−	0.995367i	$-0.469347\pi$
$263$	3.11864	0.192303	0.0961517	+	0.995367i	$0.469347\pi$
$264$	−0.555411	−0.0341832
$265$	0.0506760	0.00311300
$266$	−33.6776	−2.06491
$267$	2.89332	0.177068
$268$	−15.1209	−0.923659
$269$	7.29431	0.444742	0.222371	−	0.974962i	$-0.428620\pi$
$269$	7.29431	0.444742	0.222371	+	0.974962i	$0.428620\pi$
$270$	0.153089	0.00931669
$271$	22.8641	1.38890	0.694448	−	0.719543i	$-0.255649\pi$
$271$	22.8641	1.38890	0.694448	+	0.719543i	$0.255649\pi$
$272$	4.94539	0.299858
$273$	−5.26409	−0.318597
$274$	5.28596	0.319336
$275$	−4.99869	−0.301432
$276$	3.52606	0.212244
$277$	−14.5712	−0.875496	−0.437748	−	0.899098i	$-0.644224\pi$
$277$	−14.5712	−0.875496	−0.437748	+	0.899098i	$0.644224\pi$
$278$	0.707173	0.0424134
$279$	−17.2742	−1.03418
$280$	−0.237523	−0.0141947
$281$	26.6462	1.58958	0.794791	−	0.606883i	$-0.207581\pi$
$281$	26.6462	1.58958	0.794791	+	0.606883i	$0.207581\pi$
$282$	8.39422	0.499869
$283$	−5.50953	−0.327508	−0.163754	−	0.986501i	$-0.552360\pi$
$283$	−5.50953	−0.327508	−0.163754	+	0.986501i	$0.552360\pi$
$284$	−19.6490	−1.16595
$285$	0.0573340	0.00339617
$286$	−4.93027	−0.291533
$287$	−28.3049	−1.67079
$288$	−17.4140	−1.02613
$289$	1.00000	0.0588235
$290$	−0.127105	−0.00746387
$291$	−3.22634	−0.189132
$292$	−20.1260	−1.17778
$293$	0.128919	0.00753150	0.00376575	−	0.999993i	$-0.498801\pi$
$293$	0.128919	0.00753150	0.00376575	+	0.999993i	$0.498801\pi$
$294$	11.3738	0.663336
$295$	0.471351	0.0274431
$296$	2.46032	0.143003
$297$	2.35282	0.136525
$298$	0.0630402	0.00365182
$299$	−19.4423	−1.12438
$300$	2.48553	0.143502
$301$	4.76370	0.274575
$302$	−28.2773	−1.62718
$303$	6.19010	0.355612
$304$	−19.4424	−1.11510
$305$	−0.0366078	−0.00209616
$306$	−5.10261	−0.291697
$307$	15.3782	0.877679	0.438839	−	0.898566i	$-0.355390\pi$
$307$	15.3782	0.877679	0.438839	+	0.898566i	$0.355390\pi$
$308$	5.87690	0.334867
$309$	−2.28316	−0.129884
$310$	0.396104	0.0224972
$311$	25.6499	1.45447	0.727236	−	0.686387i	$-0.240804\pi$
$311$	25.6499	1.45447	0.727236	+	0.686387i	$0.240804\pi$
$312$	−1.52278	−0.0862102
$313$	−20.5059	−1.15906	−0.579531	−	0.814950i	$-0.696764\pi$
$313$	−20.5059	−1.15906	−0.579531	+	0.814950i	$0.696764\pi$
$314$	−14.7903	−0.834662
$315$	0.489095	0.0275574
$316$	−14.9100	−0.838752
$317$	−19.5585	−1.09851	−0.549257	−	0.835653i	$-0.685089\pi$
$317$	−19.5585	−1.09851	−0.549257	+	0.835653i	$0.685089\pi$
$318$	−1.01509	−0.0569233
$319$	−1.95348	−0.109374
$320$	0.0414301	0.00231601
$321$	−0.794346	−0.0443361
$322$	60.7463	3.38526
$323$	−3.93141	−0.218749
$324$	9.33203	0.518446
$325$	−13.7050	−0.760214
$326$	6.97695	0.386418
$327$	4.40511	0.243603
$328$	−8.18794	−0.452103
$329$	55.1718	3.04172
$330$	−0.0262248	−0.00144363
$331$	13.0498	0.717280	0.358640	−	0.933476i	$-0.383241\pi$
$331$	13.0498	0.717280	0.358640	+	0.933476i	$0.383241\pi$
$332$	−4.27370	−0.234550
$333$	−5.06616	−0.277624
$334$	−7.68027	−0.420246
$335$	0.443487	0.0242303
$336$	9.49517	0.518004
$337$	−1.62422	−0.0884768	−0.0442384	−	0.999021i	$-0.514086\pi$
$337$	−1.62422	−0.0884768	−0.0442384	+	0.999021i	$0.514086\pi$
$338$	9.85983	0.536304
$339$	7.55878	0.410537
$340$	0.0446386	0.00242087
$341$	6.08772	0.329668
$342$	20.0605	1.08475
$343$	41.4098	2.23592
$344$	1.37802	0.0742980
$345$	−0.103417	−0.00556777
$346$	37.1218	1.99568
$347$	−15.6992	−0.842778	−0.421389	−	0.906880i	$-0.638457\pi$
$347$	−15.6992	−0.842778	−0.421389	+	0.906880i	$0.638457\pi$
$348$	0.971339	0.0520692
$349$	−5.33553	−0.285604	−0.142802	−	0.989751i	$-0.545611\pi$
$349$	−5.33553	−0.285604	−0.142802	+	0.989751i	$0.545611\pi$
$350$	42.8202	2.28884
$351$	6.45075	0.344316
$352$	6.13698	0.327102
$353$	9.13246	0.486072	0.243036	−	0.970017i	$-0.421857\pi$
$353$	9.13246	0.486072	0.243036	+	0.970017i	$0.421857\pi$
$354$	−9.44159	−0.501815
$355$	0.576291	0.0305864
$356$	−8.85611	−0.469373
$357$	1.92000	0.101617
$358$	−41.8895	−2.21393
$359$	26.6908	1.40869	0.704344	−	0.709859i	$-0.251241\pi$
$359$	26.6908	1.40869	0.704344	+	0.709859i	$0.251241\pi$
$360$	0.141483	0.00745683
$361$	−3.54402	−0.186527
$362$	13.2838	0.698181
$363$	−0.403049	−0.0211546
$364$	16.1128	0.844538
$365$	0.590280	0.0308967
$366$	0.733289	0.0383296
$367$	21.4360	1.11895	0.559475	−	0.828847i	$-0.311003\pi$
$367$	21.4360	1.11895	0.559475	+	0.828847i	$0.311003\pi$
$368$	35.0693	1.82812
$369$	16.8602	0.877706
$370$	0.116169	0.00603934
$371$	−6.67177	−0.346381
$372$	−3.02703	−0.156944
$373$	1.10907	0.0574254	0.0287127	−	0.999588i	$-0.490859\pi$
$373$	1.10907	0.0574254	0.0287127	+	0.999588i	$0.490859\pi$
$374$	1.79824	0.0929850
$375$	−0.145817	−0.00752994
$376$	15.9599	0.823068
$377$	−5.35587	−0.275841
$378$	−20.1549	−1.03666
$379$	38.3469	1.96975	0.984875	−	0.173269i	$-0.0554329\pi$
$379$	38.3469	1.96975	0.984875	+	0.173269i	$0.0554329\pi$
$380$	−0.175492	−0.00900257
$381$	3.22227	0.165082
$382$	−25.6396	−1.31184
$383$	5.95778	0.304428	0.152214	−	0.988348i	$-0.451360\pi$
$383$	5.95778	0.304428	0.152214	+	0.988348i	$0.451360\pi$
$384$	4.11713	0.210101
$385$	−0.172365	−0.00878455
$386$	−8.42178	−0.428657
$387$	−2.83755	−0.144241
$388$	9.87545	0.501350
$389$	23.5932	1.19622	0.598111	−	0.801413i	$-0.295918\pi$
$389$	23.5932	1.19622	0.598111	+	0.801413i	$0.295918\pi$
$390$	−0.0719009	−0.00364084
$391$	7.09132	0.358623
$392$	21.6250	1.09223
$393$	−8.06999	−0.407077
$394$	−38.0432	−1.91659
$395$	0.437299	0.0220029
$396$	−3.50064	−0.175914
$397$	−15.6933	−0.787623	−0.393811	−	0.919191i	$-0.628844\pi$
$397$	−15.6933	−0.787623	−0.393811	+	0.919191i	$0.628844\pi$
$398$	−18.8608	−0.945407
$399$	−7.54832	−0.377889
$400$	24.7205	1.23602
$401$	−12.0632	−0.602409	−0.301204	−	0.953560i	$-0.597389\pi$
$401$	−12.0632	−0.602409	−0.301204	+	0.953560i	$0.597389\pi$
$402$	−8.88345	−0.443066
$403$	16.6908	0.831426
$404$	−18.9471	−0.942656
$405$	−0.273702	−0.0136003
$406$	16.7341	0.830498
$407$	1.78540	0.0884990
$408$	0.555411	0.0274969
$409$	−10.1253	−0.500665	−0.250332	−	0.968160i	$-0.580540\pi$
$409$	−10.1253	−0.500665	−0.250332	+	0.968160i	$0.580540\pi$
$410$	−0.386610	−0.0190933
$411$	1.18477	0.0584402
$412$	6.98848	0.344298
$413$	−62.0558	−3.05357
$414$	−36.1842	−1.77836
$415$	0.125344	0.00615292
$416$	16.8258	0.824954
$417$	0.158502	0.00776188
$418$	−7.06964	−0.345787
$419$	−14.3527	−0.701177	−0.350589	−	0.936530i	$-0.614018\pi$
$419$	−14.3527	−0.701177	−0.350589	+	0.936530i	$0.614018\pi$
$420$	0.0857062	0.00418203
$421$	−2.68856	−0.131032	−0.0655162	−	0.997852i	$-0.520869\pi$
$421$	−2.68856	−0.131032	−0.0655162	+	0.997852i	$0.520869\pi$
$422$	39.8379	1.93928
$423$	−32.8638	−1.59789
$424$	−1.92998	−0.0937281
$425$	4.99869	0.242472
$426$	−11.5437	−0.559292
$427$	4.81961	0.233237
$428$	2.43140	0.117526
$429$	−1.10504	−0.0533520
$430$	0.0650661	0.00313777
$431$	−25.6652	−1.23625	−0.618125	−	0.786079i	$-0.712108\pi$
$431$	−25.6652	−1.23625	−0.618125	+	0.786079i	$0.712108\pi$
$432$	−11.6356	−0.559819
$433$	−13.4429	−0.646025	−0.323013	−	0.946395i	$-0.604696\pi$
$433$	−13.4429	−0.646025	−0.323013	+	0.946395i	$0.604696\pi$
$434$	−52.1492	−2.50324
$435$	−0.0284887	−0.00136593
$436$	−13.4835	−0.645743
$437$	−27.8789	−1.33363
$438$	−11.8239	−0.564966
$439$	37.3473	1.78249	0.891244	−	0.453523i	$-0.149833\pi$
$439$	37.3473	1.78249	0.891244	+	0.453523i	$0.149833\pi$
$440$	−0.0498611	−0.00237704
$441$	−44.5291	−2.12043
$442$	4.93027	0.234509
$443$	30.4152	1.44507	0.722534	−	0.691335i	$-0.242977\pi$
$443$	30.4152	1.44507	0.722534	+	0.691335i	$0.242977\pi$
$444$	−0.887764	−0.0421314
$445$	0.259743	0.0123130
$446$	−28.4696	−1.34808
$447$	0.0141295	0.000668302 0
$448$	−5.45449	−0.257700
$449$	−30.9849	−1.46227	−0.731133	−	0.682235i	$-0.761008\pi$
$449$	−30.9849	−1.46227	−0.731133	+	0.682235i	$0.761008\pi$
$450$	−25.5064	−1.20238
$451$	−5.94180	−0.279789
$452$	−23.1365	−1.08825
$453$	−6.33793	−0.297782
$454$	52.5863	2.46800
$455$	−0.472576	−0.0221547
$456$	−2.18355	−0.102254
$457$	9.18618	0.429711	0.214856	−	0.976646i	$-0.431072\pi$
$457$	9.18618	0.429711	0.214856	+	0.976646i	$0.431072\pi$
$458$	46.8522	2.18926
$459$	−2.35282	−0.109820
$460$	0.316546	0.0147590
$461$	−14.5831	−0.679203	−0.339601	−	0.940569i	$-0.610292\pi$
$461$	−14.5831	−0.679203	−0.339601	+	0.940569i	$0.610292\pi$
$462$	3.45264	0.160631
$463$	7.13042	0.331379	0.165689	−	0.986178i	$-0.447015\pi$
$463$	7.13042	0.331379	0.165689	+	0.986178i	$0.447015\pi$
$464$	9.66071	0.448487
$465$	0.0887807	0.00411711
$466$	24.7387	1.14600
$467$	−39.1584	−1.81204	−0.906018	−	0.423239i	$-0.860893\pi$
$467$	−39.1584	−1.81204	−0.906018	+	0.423239i	$0.860893\pi$
$468$	−9.59775	−0.443656
$469$	−58.3874	−2.69608
$470$	0.753578	0.0347600
$471$	−3.31501	−0.152748
$472$	−17.9512	−0.826273
$473$	1.00000	0.0459800
$474$	−8.75951	−0.402338
$475$	−19.6519	−0.901691
$476$	−5.87690	−0.269367
$477$	3.97412	0.181962
$478$	23.7349	1.08561
$479$	−27.6677	−1.26417	−0.632084	−	0.774900i	$-0.717800\pi$
$479$	−27.6677	−1.26417	−0.632084	+	0.774900i	$0.717800\pi$
$480$	0.0894991	0.00408506
$481$	4.89505	0.223195
$482$	7.10944	0.323826
$483$	13.6154	0.619520
$484$	1.23368	0.0560766
$485$	−0.289640	−0.0131519
$486$	18.1753	0.824450
$487$	−1.27108	−0.0575981	−0.0287991	−	0.999585i	$-0.509168\pi$
$487$	−1.27108	−0.0575981	−0.0287991	+	0.999585i	$0.509168\pi$
$488$	1.39420	0.0631124
$489$	1.56378	0.0707165
$490$	1.02107	0.0461272
$491$	11.7156	0.528716	0.264358	−	0.964425i	$-0.414840\pi$
$491$	11.7156	0.528716	0.264358	+	0.964425i	$0.414840\pi$
$492$	2.95448	0.133198
$493$	1.95348	0.0879802
$494$	−19.3829	−0.872078
$495$	0.102671	0.00461474
$496$	−30.1062	−1.35181
$497$	−75.8718	−3.40331
$498$	−2.51077	−0.112510
$499$	21.6309	0.968332	0.484166	−	0.874976i	$-0.339123\pi$
$499$	21.6309	0.968332	0.484166	+	0.874976i	$0.339123\pi$
$500$	0.446327	0.0199604
$501$	−1.72142	−0.0769072
$502$	−14.8595	−0.663211
$503$	8.69334	0.387617	0.193808	−	0.981039i	$-0.437916\pi$
$503$	8.69334	0.387617	0.193808	+	0.981039i	$0.437916\pi$
$504$	−18.6270	−0.829715
$505$	0.555706	0.0247286
$506$	12.7519	0.566892
$507$	2.20993	0.0981464
$508$	−9.86297	−0.437599
$509$	15.0203	0.665761	0.332881	−	0.942969i	$-0.391979\pi$
$509$	15.0203	0.665761	0.332881	+	0.942969i	$0.391979\pi$
$510$	0.0262248	0.00116126
$511$	−77.7135	−3.43784
$512$	−16.7201	−0.738929
$513$	9.24990	0.408393
$514$	36.2801	1.60025
$515$	−0.204967	−0.00903193
$516$	−0.497236	−0.0218896
$517$	11.5817	0.509364
$518$	−15.2943	−0.671991
$519$	8.32029	0.365220
$520$	−0.136705	−0.00599490
$521$	−0.838214	−0.0367228	−0.0183614	−	0.999831i	$-0.505845\pi$
$521$	−0.838214	−0.0367228	−0.0183614	+	0.999831i	$0.505845\pi$
$522$	−9.96784	−0.436281
$523$	−26.8815	−1.17545	−0.587723	−	0.809062i	$-0.699975\pi$
$523$	−26.8815	−1.17545	−0.587723	+	0.809062i	$0.699975\pi$
$524$	24.7013	1.07908
$525$	9.59751	0.418870
$526$	−5.60807	−0.244524
$527$	−6.08772	−0.265185
$528$	1.99324	0.0867445
$529$	27.2868	1.18638
$530$	−0.0911279	−0.00395834
$531$	36.9643	1.60411
$532$	23.1045	1.00171
$533$	−16.2907	−0.705629
$534$	−5.20290	−0.225152
$535$	−0.0713111	−0.00308305
$536$	−16.8901	−0.729539
$537$	−9.38890	−0.405161
$538$	−13.1170	−0.565512
$539$	15.6928	0.675937
$540$	−0.105027	−0.00451962
$541$	−1.31304	−0.0564519	−0.0282260	−	0.999602i	$-0.508986\pi$
$541$	−1.31304	−0.0564519	−0.0282260	+	0.999602i	$0.508986\pi$
$542$	−41.1153	−1.76605
$543$	2.97736	0.127771
$544$	−6.13698	−0.263121
$545$	0.395462	0.0169397
$546$	9.46613	0.405113
$547$	2.41412	0.103220	0.0516101	−	0.998667i	$-0.483565\pi$
$547$	2.41412	0.103220	0.0516101	+	0.998667i	$0.483565\pi$
$548$	−3.62643	−0.154913
$549$	−2.87086	−0.122525
$550$	8.98887	0.383287
$551$	−7.67992	−0.327176
$552$	3.93859	0.167638
$553$	−57.5727	−2.44824
$554$	26.2025	1.11324
$555$	0.0260375	0.00110523
$556$	−0.485155	−0.0205752
$557$	−34.5290	−1.46304	−0.731520	−	0.681820i	$-0.761189\pi$
$557$	−34.5290	−1.46304	−0.731520	+	0.681820i	$0.761189\pi$
$558$	31.0633	1.31501
$559$	2.74171	0.115962
$560$	0.852414	0.0360211
$561$	0.403049	0.0170168
$562$	−47.9165	−2.02123
$563$	7.36112	0.310234	0.155117	−	0.987896i	$-0.450424\pi$
$563$	7.36112	0.310234	0.155117	+	0.987896i	$0.450424\pi$
$564$	−5.75885	−0.242491
$565$	0.678577	0.0285480
$566$	9.90749	0.416443
$567$	36.0343	1.51330
$568$	−21.9479	−0.920912
$569$	40.8783	1.71371	0.856854	−	0.515560i	$-0.172416\pi$
$569$	40.8783	1.71371	0.856854	+	0.515560i	$0.172416\pi$
$570$	−0.103101	−0.00431841
$571$	−39.1338	−1.63770	−0.818849	−	0.574008i	$-0.805388\pi$
$571$	−39.1338	−1.63770	−0.818849	+	0.574008i	$0.805388\pi$
$572$	3.38241	0.141426
$573$	−5.74672	−0.240073
$574$	50.8992	2.12449
$575$	35.4473	1.47825
$576$	3.24903	0.135376
$577$	−24.9166	−1.03729	−0.518646	−	0.854989i	$-0.673564\pi$
$577$	−24.9166	−1.03729	−0.518646	+	0.854989i	$0.673564\pi$
$578$	−1.79824	−0.0747971
$579$	−1.88761	−0.0784465
$580$	0.0872004	0.00362080
$581$	−16.5023	−0.684629
$582$	5.80176	0.240491
$583$	−1.40054	−0.0580046
$584$	−22.4806	−0.930256
$585$	0.281495	0.0116384
$586$	−0.231827	−0.00957669
$587$	−32.5473	−1.34337	−0.671685	−	0.740837i	$-0.734429\pi$
$587$	−32.5473	−1.34337	−0.671685	+	0.740837i	$0.734429\pi$
$588$	−7.80302	−0.321791
$589$	23.9333	0.986155
$590$	−0.847604	−0.0348953
$591$	−8.52680	−0.350746
$592$	−8.82950	−0.362890
$593$	−7.73867	−0.317789	−0.158894	−	0.987296i	$-0.550793\pi$
$593$	−7.73867	−0.317789	−0.158894	+	0.987296i	$0.550793\pi$
$594$	−4.23095	−0.173598
$595$	0.172365	0.00706629
$596$	−0.0432487	−0.00177153
$597$	−4.22737	−0.173015
$598$	34.9621	1.42971
$599$	−0.217898	−0.00890308	−0.00445154	−	0.999990i	$-0.501417\pi$
$599$	−0.217898	−0.00890308	−0.00445154	+	0.999990i	$0.501417\pi$
$600$	2.77633	0.113343
$601$	−9.13597	−0.372664	−0.186332	−	0.982487i	$-0.559660\pi$
$601$	−9.13597	−0.372664	−0.186332	+	0.982487i	$0.559660\pi$
$602$	−8.56629	−0.349136
$603$	34.7791	1.41631
$604$	19.3996	0.789360
$605$	−0.0361831	−0.00147105
$606$	−11.1313	−0.452179
$607$	32.9898	1.33902	0.669508	−	0.742805i	$-0.266505\pi$
$607$	32.9898	1.33902	0.669508	+	0.742805i	$0.266505\pi$
$608$	24.1270	0.978478
$609$	3.75069	0.151985
$610$	0.0658298	0.00266537
$611$	31.7537	1.28462
$612$	3.50064	0.141505
$613$	−20.0688	−0.810569	−0.405285	−	0.914191i	$-0.632828\pi$
$613$	−20.0688	−0.810569	−0.405285	+	0.914191i	$0.632828\pi$
$614$	−27.6537	−1.11601
$615$	−0.0866527	−0.00349418
$616$	6.56448	0.264490
$617$	37.0858	1.49302	0.746509	−	0.665376i	$-0.231729\pi$
$617$	37.0858	1.49302	0.746509	+	0.665376i	$0.231729\pi$
$618$	4.10568	0.165155
$619$	6.74313	0.271029	0.135515	−	0.990775i	$-0.456731\pi$
$619$	6.74313	0.271029	0.135515	+	0.990775i	$0.456731\pi$
$620$	−0.271747	−0.0109136
$621$	−16.6846	−0.669530
$622$	−46.1248	−1.84944
$623$	−34.1966	−1.37006
$624$	5.46488	0.218770
$625$	24.9804	0.999215
$626$	36.8746	1.47381
$627$	−1.58455	−0.0632809
$628$	10.1468	0.404903
$629$	−1.78540	−0.0711885
$630$	−0.879513	−0.0350406
$631$	−27.7261	−1.10376	−0.551879	−	0.833925i	$-0.686089\pi$
$631$	−27.7261	−1.10376	−0.551879	+	0.833925i	$0.686089\pi$
$632$	−16.6544	−0.662476
$633$	8.92905	0.354898
$634$	35.1710	1.39682
$635$	0.289274	0.0114795
$636$	0.696401	0.0276141
$637$	43.0251	1.70472
$638$	3.51283	0.139074
$639$	45.1939	1.78784
$640$	0.369609	0.0146101
$641$	6.38270	0.252101	0.126051	−	0.992024i	$-0.459770\pi$
$641$	6.38270	0.252101	0.126051	+	0.992024i	$0.459770\pi$
$642$	1.42843	0.0563756
$643$	−12.3363	−0.486498	−0.243249	−	0.969964i	$-0.578213\pi$
$643$	−12.3363	−0.486498	−0.243249	+	0.969964i	$0.578213\pi$
$644$	−41.6750	−1.64222
$645$	0.0145836	0.000574228 0
$646$	7.06964	0.278151
$647$	−8.76692	−0.344663	−0.172332	−	0.985039i	$-0.555130\pi$
$647$	−8.76692	−0.344663	−0.172332	+	0.985039i	$0.555130\pi$
$648$	10.4238	0.409487
$649$	−13.0268	−0.511347
$650$	24.6449	0.966652
$651$	−11.6884	−0.458106
$652$	−4.78654	−0.187455
$653$	−14.7110	−0.575685	−0.287843	−	0.957678i	$-0.592938\pi$
$653$	−14.7110	−0.575685	−0.287843	+	0.957678i	$0.592938\pi$
$654$	−7.92147	−0.309754
$655$	−0.724471	−0.0283074
$656$	29.3845	1.14727
$657$	46.2910	1.80598
$658$	−99.2125	−3.86771
$659$	1.29512	0.0504507	0.0252254	−	0.999682i	$-0.491970\pi$
$659$	1.29512	0.0504507	0.0252254	+	0.999682i	$0.491970\pi$
$660$	0.0179915	0.000700320 0
$661$	−43.1303	−1.67757	−0.838787	−	0.544460i	$-0.816735\pi$
$661$	−43.1303	−1.67757	−0.838787	+	0.544460i	$0.816735\pi$
$662$	−23.4667	−0.912059
$663$	1.10504	0.0429164
$664$	−4.77370	−0.185256
$665$	−0.677639	−0.0262777
$666$	9.11020	0.353013
$667$	13.8527	0.536380
$668$	5.26904	0.203865
$669$	−6.38104	−0.246705
$670$	−0.797498	−0.0308100
$671$	1.01174	0.0390577
$672$	−11.7830	−0.454540
$673$	−42.6546	−1.64422	−0.822108	−	0.569332i	$-0.807202\pi$
$673$	−42.6546	−1.64422	−0.822108	+	0.569332i	$0.807202\pi$
$674$	2.92074	0.112503
$675$	−11.7610	−0.452682
$676$	−6.76433	−0.260166
$677$	27.8600	1.07075	0.535373	−	0.844616i	$-0.320171\pi$
$677$	27.8600	1.07075	0.535373	+	0.844616i	$0.320171\pi$
$678$	−13.5925	−0.522018
$679$	38.1326	1.46340
$680$	0.0498611	0.00191209
$681$	11.7864	0.451656
$682$	−10.9472	−0.419190
$683$	15.2212	0.582423	0.291212	−	0.956659i	$-0.405942\pi$
$683$	15.2212	0.582423	0.291212	+	0.956659i	$0.405942\pi$
$684$	−13.7625	−0.526221
$685$	0.106361	0.00406383
$686$	−74.4650	−2.84309
$687$	10.5012	0.400646
$688$	−4.94539	−0.188541
$689$	−3.83989	−0.146288
$690$	0.185969	0.00707970
$691$	18.0240	0.685664	0.342832	−	0.939397i	$-0.388614\pi$
$691$	18.0240	0.685664	0.342832	+	0.939397i	$0.388614\pi$
$692$	−25.4674	−0.968125
$693$	−13.5172	−0.513477
$694$	28.2310	1.07164
$695$	0.0142293	0.000539747 0
$696$	1.08498	0.0411262
$697$	5.94180	0.225062
$698$	9.59459	0.363161
$699$	5.54480	0.209724
$700$	−29.3768	−1.11034
$701$	24.2155	0.914608	0.457304	−	0.889310i	$-0.348815\pi$
$701$	24.2155	0.914608	0.457304	+	0.889310i	$0.348815\pi$
$702$	−11.6000	−0.437815
$703$	7.01914	0.264732
$704$	−1.14501	−0.0431543
$705$	0.168903	0.00636126
$706$	−16.4224	−0.618065
$707$	−73.1617	−2.75153
$708$	6.47740	0.243436
$709$	−14.7819	−0.555144	−0.277572	−	0.960705i	$-0.589530\pi$
$709$	−14.7819	−0.555144	−0.277572	+	0.960705i	$0.589530\pi$
$710$	−1.03631	−0.0388921
$711$	34.2939	1.28612
$712$	−9.89225	−0.370728
$713$	−43.1699	−1.61673
$714$	−3.45264	−0.129212
$715$	−0.0992036	−0.00371000
$716$	28.7383	1.07400
$717$	5.31981	0.198672
$718$	−47.9966	−1.79122
$719$	5.59896	0.208806	0.104403	−	0.994535i	$-0.466707\pi$
$719$	5.59896	0.208806	0.104403	+	0.994535i	$0.466707\pi$
$720$	−0.507750	−0.0189227
$721$	26.9850	1.00497
$722$	6.37301	0.237179
$723$	1.59347	0.0592619
$724$	−9.11335	−0.338695
$725$	9.76483	0.362657
$726$	0.724781	0.0268992
$727$	−0.224881	−0.00834036	−0.00417018	−	0.999991i	$-0.501327\pi$
$727$	−0.224881	−0.00834036	−0.00417018	+	0.999991i	$0.501327\pi$
$728$	17.9979	0.667046
$729$	−18.6193	−0.689605
$730$	−1.06147	−0.0392867
$731$	−1.00000	−0.0369863
$732$	−0.503072	−0.0185941
$733$	31.8506	1.17643	0.588214	−	0.808705i	$-0.299831\pi$
$733$	31.8506	1.17643	0.588214	+	0.808705i	$0.299831\pi$
$734$	−38.5472	−1.42280
$735$	0.228857	0.00844152
$736$	−43.5193	−1.60414
$737$	−12.2567	−0.451483
$738$	−30.3187	−1.11605
$739$	−10.3124	−0.379347	−0.189674	−	0.981847i	$-0.560743\pi$
$739$	−10.3124	−0.379347	−0.189674	+	0.981847i	$0.560743\pi$
$740$	−0.0796976	−0.00292974
$741$	−4.34438	−0.159595
$742$	11.9975	0.440441
$743$	−38.4434	−1.41035	−0.705176	−	0.709033i	$-0.749132\pi$
$743$	−38.4434	−1.41035	−0.705176	+	0.709033i	$0.749132\pi$
$744$	−3.38118	−0.123960
$745$	0.00126845	4.64725e−5 0
$746$	−1.99438	−0.0730193
$747$	9.82976	0.359652
$748$	−1.23368	−0.0451080
$749$	9.38849	0.343048
$750$	0.262214	0.00957470
$751$	−6.40997	−0.233903	−0.116952	−	0.993138i	$-0.537312\pi$
$751$	−6.40997	−0.233903	−0.116952	+	0.993138i	$0.537312\pi$
$752$	−57.2762	−2.08865
$753$	−3.33053	−0.121371
$754$	9.63117	0.350746
$755$	−0.568978	−0.0207072
$756$	13.8273	0.502894
$757$	−14.3339	−0.520974	−0.260487	−	0.965477i	$-0.583883\pi$
$757$	−14.3339	−0.520974	−0.260487	+	0.965477i	$0.583883\pi$
$758$	−68.9572	−2.50464
$759$	2.85815	0.103744
$760$	−0.196024	−0.00711056
$761$	40.2819	1.46022	0.730110	−	0.683330i	$-0.239469\pi$
$761$	40.2819	1.46022	0.730110	+	0.683330i	$0.239469\pi$
$762$	−5.79443	−0.209910
$763$	−52.0646	−1.88487
$764$	17.5900	0.636385
$765$	−0.102671	−0.00371209
$766$	−10.7136	−0.387096
$767$	−35.7158	−1.28962
$768$	−8.32660	−0.300460
$769$	33.5133	1.20852	0.604259	−	0.796788i	$-0.293469\pi$
$769$	33.5133	1.20852	0.604259	+	0.796788i	$0.293469\pi$
$770$	0.309955	0.0111700
$771$	8.13163	0.292854
$772$	5.77775	0.207946
$773$	−4.76185	−0.171272	−0.0856359	−	0.996326i	$-0.527292\pi$
$773$	−4.76185	−0.171272	−0.0856359	+	0.996326i	$0.527292\pi$
$774$	5.10261	0.183410
$775$	−30.4306	−1.09310
$776$	11.0308	0.395984
$777$	−3.42797	−0.122978
$778$	−42.4263	−1.52106
$779$	−23.3597	−0.836947
$780$	0.0493276	0.00176621
$781$	−15.9271	−0.569916
$782$	−12.7519	−0.456008
$783$	−4.59618	−0.164254
$784$	−77.6070	−2.77168
$785$	−0.297600	−0.0106218
$786$	14.5118	0.517620
$787$	37.2428	1.32756	0.663781	−	0.747927i	$-0.268951\pi$
$787$	37.2428	1.32756	0.663781	+	0.747927i	$0.268951\pi$
$788$	26.0995	0.929756
$789$	−1.25696	−0.0447491
$790$	−0.786371	−0.0279778
$791$	−89.3383	−3.17650
$792$	−3.91021	−0.138943
$793$	2.77389	0.0985038
$794$	28.2203	1.00150
$795$	−0.0204249	−0.000724398 0
$796$	12.9395	0.458627
$797$	22.7645	0.806359	0.403180	−	0.915121i	$-0.367905\pi$
$797$	22.7645	0.806359	0.403180	+	0.915121i	$0.367905\pi$
$798$	13.5737	0.480505
$799$	−11.5817	−0.409732
$800$	−30.6769	−1.08459
$801$	20.3696	0.719724
$802$	21.6926	0.765994
$803$	−16.3137	−0.575698
$804$	6.09449	0.214936
$805$	1.22230	0.0430803
$806$	−30.0141	−1.05720
$807$	−2.93997	−0.103492
$808$	−21.1639	−0.744543
$809$	−33.2111	−1.16764	−0.583820	−	0.811883i	$-0.698443\pi$
$809$	−33.2111	−1.16764	−0.583820	+	0.811883i	$0.698443\pi$
$810$	0.492183	0.0172935
$811$	−24.6297	−0.864867	−0.432433	−	0.901666i	$-0.642345\pi$
$811$	−24.6297	−0.864867	−0.432433	+	0.901666i	$0.642345\pi$
$812$	−11.4804	−0.402883
$813$	−9.21536	−0.323197
$814$	−3.21059	−0.112531
$815$	0.140386	0.00491750
$816$	−1.99324	−0.0697772
$817$	3.93141	0.137543
$818$	18.2078	0.636621
$819$	−37.0603	−1.29499
$820$	0.265234	0.00926236
$821$	−40.4106	−1.41034	−0.705170	−	0.709038i	$-0.749129\pi$
$821$	−40.4106	−1.41034	−0.705170	+	0.709038i	$0.749129\pi$
$822$	−2.13050	−0.0743098
$823$	−8.47409	−0.295388	−0.147694	−	0.989033i	$-0.547185\pi$
$823$	−8.47409	−0.295388	−0.147694	+	0.989033i	$0.547185\pi$
$824$	7.80611	0.271939
$825$	2.01472	0.0701435
$826$	111.592	3.88277
$827$	7.64184	0.265733	0.132866	−	0.991134i	$-0.457582\pi$
$827$	7.64184	0.265733	0.132866	+	0.991134i	$0.457582\pi$
$828$	24.8242	0.862700
$829$	−23.1895	−0.805406	−0.402703	−	0.915331i	$-0.631929\pi$
$829$	−23.1895	−0.805406	−0.402703	+	0.915331i	$0.631929\pi$
$830$	−0.225400	−0.00782375
$831$	5.87289	0.203728
$832$	−3.13929	−0.108835
$833$	−15.6928	−0.543723
$834$	−0.285025	−0.00986962
$835$	−0.154537	−0.00534798
$836$	4.85012	0.167745
$837$	14.3233	0.495086
$838$	25.8097	0.891583
$839$	9.03146	0.311801	0.155900	−	0.987773i	$-0.450172\pi$
$839$	9.03146	0.311801	0.155900	+	0.987773i	$0.450172\pi$
$840$	0.0957335	0.00330312
$841$	−25.1839	−0.868411
$842$	4.83469	0.166614
$843$	−10.7397	−0.369897
$844$	−27.3308	−0.940763
$845$	0.198393	0.00682492
$846$	59.0971	2.03180
$847$	4.76370	0.163683
$848$	6.92624	0.237848
$849$	2.22061	0.0762113
$850$	−8.98887	−0.308316
$851$	−12.6608	−0.434008
$852$	7.91951	0.271318
$853$	43.5239	1.49023	0.745114	−	0.666937i	$-0.232395\pi$
$853$	43.5239	1.49023	0.745114	+	0.666937i	$0.232395\pi$
$854$	−8.66684	−0.296573
$855$	0.403643	0.0138043
$856$	2.71586	0.0928263
$857$	−35.3453	−1.20737	−0.603687	−	0.797222i	$-0.706302\pi$
$857$	−35.3453	−1.20737	−0.603687	+	0.797222i	$0.706302\pi$
$858$	1.98714	0.0678398
$859$	−17.1561	−0.585358	−0.292679	−	0.956211i	$-0.594547\pi$
$859$	−17.1561	−0.585358	−0.292679	+	0.956211i	$0.594547\pi$
$860$	−0.0446386	−0.00152216
$861$	11.4083	0.388793
$862$	46.1524	1.57196
$863$	23.9933	0.816742	0.408371	−	0.912816i	$-0.366097\pi$
$863$	23.9933	0.816742	0.408371	+	0.912816i	$0.366097\pi$
$864$	14.4392	0.491232
$865$	0.746941	0.0253967
$866$	24.1737	0.821454
$867$	−0.403049	−0.0136883
$868$	35.7769	1.21435
$869$	−12.0857	−0.409980
$870$	0.0512296	0.00173685
$871$	−33.6044	−1.13864
$872$	−15.0610	−0.510031
$873$	−22.7141	−0.768757
$874$	50.1330	1.69578
$875$	1.72343	0.0582625
$876$	8.11176	0.274071
$877$	57.5069	1.94187	0.970935	−	0.239343i	$-0.0769319\pi$
$877$	57.5069	1.94187	0.970935	+	0.239343i	$0.0769319\pi$
$878$	−67.1596	−2.26653
$879$	−0.0519605	−0.00175258
$880$	0.178940	0.00603205
$881$	9.91852	0.334163	0.167082	−	0.985943i	$-0.446566\pi$
$881$	9.91852	0.334163	0.167082	+	0.985943i	$0.446566\pi$
$882$	80.0743	2.69624
$883$	−23.8902	−0.803971	−0.401985	−	0.915646i	$-0.631680\pi$
$883$	−23.8902	−0.803971	−0.401985	+	0.915646i	$0.631680\pi$
$884$	−3.38241	−0.113763
$885$	−0.189978	−0.00638602
$886$	−54.6939	−1.83748
$887$	−28.2554	−0.948724	−0.474362	−	0.880330i	$-0.657321\pi$
$887$	−28.2554	−0.948724	−0.474362	+	0.880330i	$0.657321\pi$
$888$	−0.991630	−0.0332769
$889$	−38.0844	−1.27731
$890$	−0.467082	−0.0156566
$891$	7.56435	0.253415
$892$	19.5316	0.653966
$893$	45.5325	1.52369
$894$	−0.0254083	−0.000849780 0
$895$	−0.842874	−0.0281742
$896$	−48.6609	−1.62565
$897$	7.83622	0.261644
$898$	55.7184	1.85935
$899$	−11.8922	−0.396628
$900$	17.4986	0.583288
$901$	1.40054	0.0466589
$902$	10.6848	0.355766
$903$	−1.92000	−0.0638937
$904$	−25.8434	−0.859539
$905$	0.267288	0.00888495
$906$	11.3972	0.378645
$907$	20.8865	0.693525	0.346763	−	0.937953i	$-0.387281\pi$
$907$	20.8865	0.693525	0.346763	+	0.937953i	$0.387281\pi$
$908$	−36.0768	−1.19725
$909$	43.5796	1.44544
$910$	0.849807	0.0281708
$911$	28.3126	0.938038	0.469019	−	0.883188i	$-0.344608\pi$
$911$	28.3126	0.938038	0.469019	+	0.883188i	$0.344608\pi$
$912$	7.83623	0.259483
$913$	−3.46417	−0.114647
$914$	−16.5190	−0.546400
$915$	0.0147548	0.000487777 0
$916$	−32.1429	−1.06203
$917$	95.3804	3.14974
$918$	4.23095	0.139642
$919$	−29.8926	−0.986067	−0.493033	−	0.870010i	$-0.664112\pi$
$919$	−29.8926	−0.986067	−0.493033	+	0.870010i	$0.664112\pi$
$920$	0.353581	0.0116572
$921$	−6.19816	−0.204236
$922$	26.2240	0.863641
$923$	−43.6674	−1.43733
$924$	−2.36868	−0.0779239
$925$	−8.92466	−0.293441
$926$	−12.8222	−0.421365
$927$	−16.0739	−0.527937
$928$	−11.9885	−0.393540
$929$	−59.5982	−1.95535	−0.977677	−	0.210111i	$-0.932617\pi$
$929$	−59.5982	−1.95535	−0.977677	+	0.210111i	$0.932617\pi$
$930$	−0.159649	−0.00523511
$931$	61.6948	2.02197
$932$	−16.9720	−0.555935
$933$	−10.3382	−0.338457
$934$	70.4164	2.30410
$935$	0.0361831	0.00118331
$936$	−10.7207	−0.350416
$937$	−33.6581	−1.09956	−0.549781	−	0.835309i	$-0.685289\pi$
$937$	−33.6581	−1.09956	−0.549781	+	0.835309i	$0.685289\pi$
$938$	104.995	3.42820
$939$	8.26489	0.269715
$940$	−0.516992	−0.0168624
$941$	−42.1271	−1.37331	−0.686653	−	0.726985i	$-0.740921\pi$
$941$	−42.1271	−1.37331	−0.686653	+	0.726985i	$0.740921\pi$
$942$	5.96120	0.194226
$943$	42.1352	1.37211
$944$	64.4227	2.09678
$945$	−0.405545	−0.0131924
$946$	−1.79824	−0.0584660
$947$	35.0584	1.13924	0.569622	−	0.821907i	$-0.307089\pi$
$947$	35.0584	1.13924	0.569622	+	0.821907i	$0.307089\pi$
$948$	6.00946	0.195178
$949$	−44.7274	−1.45191
$950$	35.3389	1.14655
$951$	7.88304	0.255625
$952$	−6.56448	−0.212756
$953$	25.6682	0.831475	0.415738	−	0.909485i	$-0.363523\pi$
$953$	25.6682	0.831475	0.415738	+	0.909485i	$0.363523\pi$
$954$	−7.14643	−0.231374
$955$	−0.515903	−0.0166942
$956$	−16.2833	−0.526639
$957$	0.787348	0.0254513
$958$	49.7532	1.60745
$959$	−14.0029	−0.452178
$960$	−0.0166984	−0.000538937 0
$961$	6.06032	0.195494
$962$	−8.80249	−0.283804
$963$	−5.59236	−0.180211
$964$	−4.87743	−0.157091
$965$	−0.169457	−0.00545503
$966$	−24.4837	−0.787752
$967$	0.732707	0.0235623	0.0117811	−	0.999931i	$-0.496250\pi$
$967$	0.732707	0.0235623	0.0117811	+	0.999931i	$0.496250\pi$
$968$	1.37802	0.0442913
$969$	1.58455	0.0509031
$970$	0.520843	0.0167233
$971$	−10.9859	−0.352553	−0.176277	−	0.984341i	$-0.556405\pi$
$971$	−10.9859	−0.352553	−0.176277	+	0.984341i	$0.556405\pi$
$972$	−12.4692	−0.399949
$973$	−1.87336	−0.0600571
$974$	2.28571	0.0732390
$975$	5.52377	0.176902
$976$	−5.00344	−0.160156
$977$	−29.0452	−0.929237	−0.464618	−	0.885511i	$-0.653809\pi$
$977$	−29.0452	−0.929237	−0.464618	+	0.885511i	$0.653809\pi$
$978$	−2.81206	−0.0899196
$979$	−7.17858	−0.229428
$980$	−0.700504	−0.0223768
$981$	31.0129	0.990166
$982$	−21.0674	−0.672289
$983$	9.70765	0.309626	0.154813	−	0.987944i	$-0.450523\pi$
$983$	9.70765	0.309626	0.154813	+	0.987944i	$0.450523\pi$
$984$	3.30014	0.105205
$985$	−0.765480	−0.0243902
$986$	−3.51283	−0.111871
$987$	−22.2370	−0.707810
$988$	13.2976	0.423054
$989$	−7.09132	−0.225491
$990$	−0.184628	−0.00586787
$991$	−33.5721	−1.06645	−0.533226	−	0.845973i	$-0.679020\pi$
$991$	−33.5721	−1.06645	−0.533226	+	0.845973i	$0.679020\pi$
$992$	37.3602	1.18619
$993$	−5.25970	−0.166912
$994$	136.436	4.32749
$995$	−0.379505	−0.0120311
$996$	1.72251	0.0545798
$997$	4.58491	0.145206	0.0726028	−	0.997361i	$-0.476869\pi$
$997$	4.58491	0.145206	0.0726028	+	0.997361i	$0.476869\pi$
$998$	−38.8977	−1.23128
$999$	4.20072	0.132905

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.d.1.15	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.d.1.15	✓	62	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-1.79824 q^{2} -0.403049 q^{3} +1.23368 q^{4} -0.0361831 q^{5} +0.724781 q^{6} +4.76370 q^{7} +1.37802 q^{8} -2.83755 q^{9} +O(q^{10})\)	\(q-1.79824 q^{2} -0.403049 q^{3} +1.23368 q^{4} -0.0361831 q^{5} +0.724781 q^{6} +4.76370 q^{7} +1.37802 q^{8} -2.83755 q^{9} +0.0650661 q^{10} +1.00000 q^{11} -0.497236 q^{12} +2.74171 q^{13} -8.56629 q^{14} +0.0145836 q^{15} -4.94539 q^{16} -1.00000 q^{17} +5.10261 q^{18} +3.93141 q^{19} -0.0446386 q^{20} -1.92000 q^{21} -1.79824 q^{22} -7.09132 q^{23} -0.555411 q^{24} -4.99869 q^{25} -4.93027 q^{26} +2.35282 q^{27} +5.87690 q^{28} -1.95348 q^{29} -0.0262248 q^{30} +6.08772 q^{31} +6.13698 q^{32} -0.403049 q^{33} +1.79824 q^{34} -0.172365 q^{35} -3.50064 q^{36} +1.78540 q^{37} -7.06964 q^{38} -1.10504 q^{39} -0.0498611 q^{40} -5.94180 q^{41} +3.45264 q^{42} +1.00000 q^{43} +1.23368 q^{44} +0.102671 q^{45} +12.7519 q^{46} +11.5817 q^{47} +1.99324 q^{48} +15.6928 q^{49} +8.98887 q^{50} +0.403049 q^{51} +3.38241 q^{52} -1.40054 q^{53} -4.23095 q^{54} -0.0361831 q^{55} +6.56448 q^{56} -1.58455 q^{57} +3.51283 q^{58} -13.0268 q^{59} +0.0179915 q^{60} +1.01174 q^{61} -10.9472 q^{62} -13.5172 q^{63} -1.14501 q^{64} -0.0992036 q^{65} +0.724781 q^{66} -12.2567 q^{67} -1.23368 q^{68} +2.85815 q^{69} +0.309955 q^{70} -15.9271 q^{71} -3.91021 q^{72} -16.3137 q^{73} -3.21059 q^{74} +2.01472 q^{75} +4.85012 q^{76} +4.76370 q^{77} +1.98714 q^{78} -12.0857 q^{79} +0.178940 q^{80} +7.56435 q^{81} +10.6848 q^{82} -3.46417 q^{83} -2.36868 q^{84} +0.0361831 q^{85} -1.79824 q^{86} +0.787348 q^{87} +1.37802 q^{88} -7.17858 q^{89} -0.184628 q^{90} +13.0607 q^{91} -8.74845 q^{92} -2.45365 q^{93} -20.8268 q^{94} -0.142251 q^{95} -2.47351 q^{96} +8.00484 q^{97} -28.2195 q^{98} -2.83755 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9}+O(q^{10}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9} - 7 q^{10} + 62 q^{11} - 17 q^{12} - 31 q^{14} - 20 q^{15} + 27 q^{16} - 62 q^{17} + 3 q^{18} - 29 q^{20} - 18 q^{21} - 7 q^{22} - 50 q^{23} - 31 q^{24} + 35 q^{25} - 32 q^{26} - 14 q^{27} - 13 q^{28} - 26 q^{29} - 10 q^{30} - 58 q^{31} - 5 q^{32} - 8 q^{33} + 7 q^{34} - 32 q^{35} - 29 q^{36} - 41 q^{37} - 10 q^{38} - 53 q^{39} - 31 q^{40} - 55 q^{41} - 7 q^{42} + 62 q^{43} + 49 q^{44} - 34 q^{45} - 39 q^{46} - 31 q^{47} - 30 q^{48} + 35 q^{49} - 40 q^{50} + 8 q^{51} + 13 q^{52} - 74 q^{53} + 48 q^{54} - 13 q^{55} - 75 q^{56} - 43 q^{57} - 46 q^{58} - 65 q^{59} - 8 q^{60} - 14 q^{61} - 29 q^{62} - 23 q^{63} - 15 q^{64} - 9 q^{65} - 2 q^{66} - q^{67} - 49 q^{68} - 59 q^{69} - 31 q^{70} - 141 q^{71} + 9 q^{72} - 4 q^{73} - 94 q^{74} - 43 q^{75} + 34 q^{76} - 11 q^{77} - 11 q^{78} - 63 q^{79} - 41 q^{80} - 30 q^{81} + 38 q^{82} - 44 q^{83} - 16 q^{84} + 13 q^{85} - 7 q^{86} - 8 q^{87} - 9 q^{88} - 58 q^{89} - 55 q^{90} - 78 q^{91} - 104 q^{92} - 5 q^{94} - 99 q^{95} - 148 q^{96} - 26 q^{97} + 16 q^{98} + 40 q^{99}+O(q^{100}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9 - 7 * q^10 + 62 * q^11 - 17 * q^12 - 31 * q^14 - 20 * q^15 + 27 * q^16 - 62 * q^17 + 3 * q^18 - 29 * q^20 - 18 * q^21 - 7 * q^22 - 50 * q^23 - 31 * q^24 + 35 * q^25 - 32 * q^26 - 14 * q^27 - 13 * q^28 - 26 * q^29 - 10 * q^30 - 58 * q^31 - 5 * q^32 - 8 * q^33 + 7 * q^34 - 32 * q^35 - 29 * q^36 - 41 * q^37 - 10 * q^38 - 53 * q^39 - 31 * q^40 - 55 * q^41 - 7 * q^42 + 62 * q^43 + 49 * q^44 - 34 * q^45 - 39 * q^46 - 31 * q^47 - 30 * q^48 + 35 * q^49 - 40 * q^50 + 8 * q^51 + 13 * q^52 - 74 * q^53 + 48 * q^54 - 13 * q^55 - 75 * q^56 - 43 * q^57 - 46 * q^58 - 65 * q^59 - 8 * q^60 - 14 * q^61 - 29 * q^62 - 23 * q^63 - 15 * q^64 - 9 * q^65 - 2 * q^66 - q^67 - 49 * q^68 - 59 * q^69 - 31 * q^70 - 141 * q^71 + 9 * q^72 - 4 * q^73 - 94 * q^74 - 43 * q^75 + 34 * q^76 - 11 * q^77 - 11 * q^78 - 63 * q^79 - 41 * q^80 - 30 * q^81 + 38 * q^82 - 44 * q^83 - 16 * q^84 + 13 * q^85 - 7 * q^86 - 8 * q^87 - 9 * q^88 - 58 * q^89 - 55 * q^90 - 78 * q^91 - 104 * q^92 - 5 * q^94 - 99 * q^95 - 148 * q^96 - 26 * q^97 + 16 * q^98 + 40 * q^99

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