LMFDB - Embedded newform 4033.2.a.d.1.68

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.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:	$32.2036671352$
Analytic rank:	$1$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.68
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.97722 q^{2} -0.844659 q^{3} +1.90938 q^{4} +0.614325 q^{5} -1.67007 q^{6} +1.36766 q^{7} -0.179172 q^{8} -2.28655 q^{9} +O(q^{10})$	\(q+1.97722 q^{2} -0.844659 q^{3} +1.90938 q^{4} +0.614325 q^{5} -1.67007 q^{6} +1.36766 q^{7} -0.179172 q^{8} -2.28655 q^{9} +1.21465 q^{10} -2.63598 q^{11} -1.61278 q^{12} +4.87808 q^{13} +2.70415 q^{14} -0.518895 q^{15} -4.17302 q^{16} -7.57566 q^{17} -4.52100 q^{18} +3.99555 q^{19} +1.17298 q^{20} -1.15520 q^{21} -5.21191 q^{22} +2.88047 q^{23} +0.151339 q^{24} -4.62260 q^{25} +9.64502 q^{26} +4.46533 q^{27} +2.61138 q^{28} -7.60523 q^{29} -1.02597 q^{30} -1.29815 q^{31} -7.89263 q^{32} +2.22651 q^{33} -14.9787 q^{34} +0.840186 q^{35} -4.36590 q^{36} -1.00000 q^{37} +7.90006 q^{38} -4.12032 q^{39} -0.110070 q^{40} +3.56060 q^{41} -2.28409 q^{42} +0.705969 q^{43} -5.03310 q^{44} -1.40469 q^{45} +5.69531 q^{46} +4.33906 q^{47} +3.52478 q^{48} -5.12951 q^{49} -9.13989 q^{50} +6.39885 q^{51} +9.31412 q^{52} -7.77401 q^{53} +8.82893 q^{54} -1.61935 q^{55} -0.245045 q^{56} -3.37488 q^{57} -15.0372 q^{58} -6.16758 q^{59} -0.990769 q^{60} -12.5683 q^{61} -2.56673 q^{62} -3.12722 q^{63} -7.25938 q^{64} +2.99673 q^{65} +4.40228 q^{66} -0.139780 q^{67} -14.4648 q^{68} -2.43301 q^{69} +1.66123 q^{70} -10.7372 q^{71} +0.409685 q^{72} +1.91378 q^{73} -1.97722 q^{74} +3.90452 q^{75} +7.62903 q^{76} -3.60512 q^{77} -8.14675 q^{78} -13.8909 q^{79} -2.56359 q^{80} +3.08797 q^{81} +7.04007 q^{82} +12.3001 q^{83} -2.20573 q^{84} -4.65392 q^{85} +1.39585 q^{86} +6.42382 q^{87} +0.472293 q^{88} -2.29695 q^{89} -2.77737 q^{90} +6.67155 q^{91} +5.49992 q^{92} +1.09650 q^{93} +8.57926 q^{94} +2.45457 q^{95} +6.66658 q^{96} -2.63289 q^{97} -10.1422 q^{98} +6.02731 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) $ 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + 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 $

$2$	1.97722	1.39810	0.699051	−	0.715072i	$-0.253606\pi$
$2$	1.97722	1.39810	0.699051	+	0.715072i	$0.253606\pi$
$3$	−0.844659	−0.487664	−0.243832	−	0.969817i	$-0.578405\pi$
$3$	−0.844659	−0.487664	−0.243832	+	0.969817i	$0.578405\pi$
$4$	1.90938	0.954691
$5$	0.614325	0.274735	0.137367	−	0.990520i	$-0.456136\pi$
$5$	0.614325	0.274735	0.137367	+	0.990520i	$0.456136\pi$
$6$	−1.67007	−0.681804
$7$	1.36766	0.516926	0.258463	−	0.966021i	$-0.416784\pi$
$7$	1.36766	0.516926	0.258463	+	0.966021i	$0.416784\pi$
$8$	−0.179172	−0.0633467
$9$	−2.28655	−0.762184
$10$	1.21465	0.384107
$11$	−2.63598	−0.794779	−0.397389	−	0.917650i	$-0.630084\pi$
$11$	−2.63598	−0.794779	−0.397389	+	0.917650i	$0.630084\pi$
$12$	−1.61278	−0.465568
$13$	4.87808	1.35294	0.676468	−	0.736472i	$-0.263510\pi$
$13$	4.87808	1.35294	0.676468	+	0.736472i	$0.263510\pi$
$14$	2.70415	0.722716
$15$	−0.518895	−0.133978
$16$	−4.17302	−1.04326
$17$	−7.57566	−1.83737	−0.918683	−	0.394995i	$-0.870746\pi$
$17$	−7.57566	−1.83737	−0.918683	+	0.394995i	$0.870746\pi$
$18$	−4.52100	−1.06561
$19$	3.99555	0.916641	0.458321	−	0.888787i	$-0.348451\pi$
$19$	3.99555	0.916641	0.458321	+	0.888787i	$0.348451\pi$
$20$	1.17298	0.262287
$21$	−1.15520	−0.252086
$22$	−5.21191	−1.11118
$23$	2.88047	0.600619	0.300310	−	0.953842i	$-0.402910\pi$
$23$	2.88047	0.600619	0.300310	+	0.953842i	$0.402910\pi$
$24$	0.151339	0.0308919
$25$	−4.62260	−0.924521
$26$	9.64502	1.89154
$27$	4.46533	0.859354
$28$	2.61138	0.493505
$29$	−7.60523	−1.41226	−0.706128	−	0.708085i	$-0.749560\pi$
$29$	−7.60523	−1.41226	−0.706128	+	0.708085i	$0.749560\pi$
$30$	−1.02597	−0.187315
$31$	−1.29815	−0.233155	−0.116577	−	0.993182i	$-0.537192\pi$
$31$	−1.29815	−0.233155	−0.116577	+	0.993182i	$0.537192\pi$
$32$	−7.89263	−1.39523
$33$	2.22651	0.387585
$34$	−14.9787	−2.56883
$35$	0.840186	0.142017
$36$	−4.36590	−0.727650
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	7.90006	1.28156
$39$	−4.12032	−0.659779
$40$	−0.110070	−0.0174035
$41$	3.56060	0.556072	0.278036	−	0.960571i	$-0.410317\pi$
$41$	3.56060	0.556072	0.278036	+	0.960571i	$0.410317\pi$
$42$	−2.28409	−0.352442
$43$	0.705969	0.107659	0.0538296	−	0.998550i	$-0.482857\pi$
$43$	0.705969	0.107659	0.0538296	+	0.998550i	$0.482857\pi$
$44$	−5.03310	−0.758768
$45$	−1.40469	−0.209398
$46$	5.69531	0.839728
$47$	4.33906	0.632917	0.316459	−	0.948606i	$-0.397506\pi$
$47$	4.33906	0.632917	0.316459	+	0.948606i	$0.397506\pi$
$48$	3.52478	0.508759
$49$	−5.12951	−0.732788
$50$	−9.13989	−1.29258
$51$	6.39885	0.896018
$52$	9.31412	1.29164
$53$	−7.77401	−1.06784	−0.533921	−	0.845534i	$-0.679282\pi$
$53$	−7.77401	−1.06784	−0.533921	+	0.845534i	$0.679282\pi$
$54$	8.82893	1.20146
$55$	−1.61935	−0.218353
$56$	−0.245045	−0.0327456
$57$	−3.37488	−0.447013
$58$	−15.0372	−1.97448
$59$	−6.16758	−0.802950	−0.401475	−	0.915870i	$-0.631502\pi$
$59$	−6.16758	−0.802950	−0.401475	+	0.915870i	$0.631502\pi$
$60$	−0.990769	−0.127908
$61$	−12.5683	−1.60921	−0.804603	−	0.593813i	$-0.797622\pi$
$61$	−12.5683	−1.60921	−0.804603	+	0.593813i	$0.797622\pi$
$62$	−2.56673	−0.325974
$63$	−3.12722	−0.393993
$64$	−7.25938	−0.907422
$65$	2.99673	0.371698
$66$	4.40228	0.541884
$67$	−0.139780	−0.0170769	−0.00853843	−	0.999964i	$-0.502718\pi$
$67$	−0.139780	−0.0170769	−0.00853843	+	0.999964i	$0.502718\pi$
$68$	−14.4648	−1.75412
$69$	−2.43301	−0.292901
$70$	1.66123	0.198555
$71$	−10.7372	−1.27428	−0.637138	−	0.770750i	$-0.719882\pi$
$71$	−10.7372	−1.27428	−0.637138	+	0.770750i	$0.719882\pi$
$72$	0.409685	0.0482818
$73$	1.91378	0.223991	0.111995	−	0.993709i	$-0.464276\pi$
$73$	1.91378	0.223991	0.111995	+	0.993709i	$0.464276\pi$
$74$	−1.97722	−0.229847
$75$	3.90452	0.450856
$76$	7.62903	0.875109
$77$	−3.60512	−0.410842
$78$	−8.14675	−0.922438
$79$	−13.8909	−1.56285	−0.781425	−	0.624000i	$-0.785507\pi$
$79$	−13.8909	−1.56285	−0.781425	+	0.624000i	$0.785507\pi$
$80$	−2.56359	−0.286619
$81$	3.08797	0.343108
$82$	7.04007	0.777446
$83$	12.3001	1.35011	0.675056	−	0.737766i	$-0.264119\pi$
$83$	12.3001	1.35011	0.675056	+	0.737766i	$0.264119\pi$
$84$	−2.20573	−0.240664
$85$	−4.65392	−0.504788
$86$	1.39585	0.150519
$87$	6.42382	0.688706
$88$	0.472293	0.0503466
$89$	−2.29695	−0.243477	−0.121738	−	0.992562i	$-0.538847\pi$
$89$	−2.29695	−0.243477	−0.121738	+	0.992562i	$0.538847\pi$
$90$	−2.77737	−0.292760
$91$	6.67155	0.699368
$92$	5.49992	0.573406
$93$	1.09650	0.113701
$94$	8.57926	0.884883
$95$	2.45457	0.251833
$96$	6.66658	0.680405
$97$	−2.63289	−0.267329	−0.133665	−	0.991027i	$-0.542674\pi$
$97$	−2.63289	−0.267329	−0.133665	+	0.991027i	$0.542674\pi$
$98$	−10.1422	−1.02451
$99$	6.02731	0.605767
$100$	−8.82632	−0.882632
$101$	3.99977	0.397992	0.198996	−	0.980000i	$-0.436232\pi$
$101$	3.99977	0.397992	0.198996	+	0.980000i	$0.436232\pi$
$102$	12.6519	1.25272
$103$	6.72618	0.662751	0.331375	−	0.943499i	$-0.392487\pi$
$103$	6.72618	0.662751	0.331375	+	0.943499i	$0.392487\pi$
$104$	−0.874014	−0.0857041
$105$	−0.709671	−0.0692568
$106$	−15.3709	−1.49295
$107$	−8.33461	−0.805737	−0.402869	−	0.915258i	$-0.631987\pi$
$107$	−8.33461	−0.805737	−0.402869	+	0.915258i	$0.631987\pi$
$108$	8.52603	0.820417
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−3.20180	−0.305280
$111$	0.844659	0.0801715
$112$	−5.70727	−0.539286
$113$	5.53501	0.520690	0.260345	−	0.965516i	$-0.416164\pi$
$113$	5.53501	0.520690	0.260345	+	0.965516i	$0.416164\pi$
$114$	−6.67286	−0.624970
$115$	1.76954	0.165011
$116$	−14.5213	−1.34827
$117$	−11.1540	−1.03119
$118$	−12.1946	−1.12261
$119$	−10.3609	−0.949783
$120$	0.0929713	0.00848708
$121$	−4.05160	−0.368327
$122$	−24.8502	−2.24983
$123$	−3.00749	−0.271176
$124$	−2.47867	−0.222591
$125$	−5.91141	−0.528732
$126$	−6.18319	−0.550842
$127$	4.89305	0.434188	0.217094	−	0.976151i	$-0.430342\pi$
$127$	4.89305	0.434188	0.217094	+	0.976151i	$0.430342\pi$
$128$	1.43190	0.126563
$129$	−0.596303	−0.0525015
$130$	5.92518	0.519673
$131$	12.6143	1.10212	0.551060	−	0.834466i	$-0.314223\pi$
$131$	12.6143	1.10212	0.551060	+	0.834466i	$0.314223\pi$
$132$	4.25125	0.370024
$133$	5.46454	0.473836
$134$	−0.276375	−0.0238752
$135$	2.74317	0.236094
$136$	1.35734	0.116391
$137$	10.5449	0.900908	0.450454	−	0.892800i	$-0.351262\pi$
$137$	10.5449	0.900908	0.450454	+	0.892800i	$0.351262\pi$
$138$	−4.81059	−0.409505
$139$	6.88657	0.584112	0.292056	−	0.956401i	$-0.405661\pi$
$139$	6.88657	0.584112	0.292056	+	0.956401i	$0.405661\pi$
$140$	1.60424	0.135583
$141$	−3.66503	−0.308651
$142$	−21.2298	−1.78157
$143$	−12.8585	−1.07528
$144$	9.54183	0.795153
$145$	−4.67208	−0.387995
$146$	3.78395	0.313162
$147$	4.33269	0.357354
$148$	−1.90938	−0.156950
$149$	−15.4273	−1.26385	−0.631926	−	0.775029i	$-0.717735\pi$
$149$	−15.4273	−1.26385	−0.631926	+	0.775029i	$0.717735\pi$
$150$	7.72009	0.630342
$151$	−3.82152	−0.310991	−0.155495	−	0.987837i	$-0.549697\pi$
$151$	−3.82152	−0.310991	−0.155495	+	0.987837i	$0.549697\pi$
$152$	−0.715889	−0.0580662
$153$	17.3221	1.40041
$154$	−7.12810	−0.574399
$155$	−0.797487	−0.0640557
$156$	−7.86726	−0.629885
$157$	−22.6141	−1.80480	−0.902399	−	0.430901i	$-0.858196\pi$
$157$	−22.6141	−1.80480	−0.902399	+	0.430901i	$0.858196\pi$
$158$	−27.4653	−2.18502
$159$	6.56639	0.520749
$160$	−4.84864	−0.383319
$161$	3.93950	0.310476
$162$	6.10558	0.479700
$163$	2.70258	0.211682	0.105841	−	0.994383i	$-0.466246\pi$
$163$	2.70258	0.211682	0.105841	+	0.994383i	$0.466246\pi$
$164$	6.79854	0.530877
$165$	1.36780	0.106483
$166$	24.3200	1.88760
$167$	13.8911	1.07492	0.537461	−	0.843288i	$-0.319383\pi$
$167$	13.8911	1.07492	0.537461	+	0.843288i	$0.319383\pi$
$168$	0.206980	0.0159688
$169$	10.7957	0.830437
$170$	−9.20180	−0.705746
$171$	−9.13602	−0.698649
$172$	1.34796	0.102781
$173$	10.4477	0.794326	0.397163	−	0.917748i	$-0.369995\pi$
$173$	10.4477	0.794326	0.397163	+	0.917748i	$0.369995\pi$
$174$	12.7013	0.962882
$175$	−6.32214	−0.477909
$176$	11.0000	0.829158
$177$	5.20950	0.391570
$178$	−4.54157	−0.340405
$179$	−15.2361	−1.13880	−0.569400	−	0.822061i	$-0.692824\pi$
$179$	−15.2361	−1.13880	−0.569400	+	0.822061i	$0.692824\pi$
$180$	−2.68208	−0.199911
$181$	23.5119	1.74763	0.873813	−	0.486262i	$-0.161640\pi$
$181$	23.5119	1.74763	0.873813	+	0.486262i	$0.161640\pi$
$182$	13.1911	0.977788
$183$	10.6159	0.784752
$184$	−0.516098	−0.0380473
$185$	−0.614325	−0.0451661
$186$	2.16801	0.158966
$187$	19.9693	1.46030
$188$	8.28493	0.604240
$189$	6.10705	0.444222
$190$	4.85321	0.352089
$191$	−21.6380	−1.56567	−0.782835	−	0.622229i	$-0.786227\pi$
$191$	−21.6380	−1.56567	−0.782835	+	0.622229i	$0.786227\pi$
$192$	6.13170	0.442517
$193$	13.0907	0.942290	0.471145	−	0.882056i	$-0.343841\pi$
$193$	13.0907	0.942290	0.471145	+	0.882056i	$0.343841\pi$
$194$	−5.20579	−0.373754
$195$	−2.53121	−0.181264
$196$	−9.79420	−0.699586
$197$	−19.6322	−1.39873	−0.699367	−	0.714762i	$-0.746535\pi$
$197$	−19.6322	−1.39873	−0.699367	+	0.714762i	$0.746535\pi$
$198$	11.9173	0.846925
$199$	−13.8508	−0.981855	−0.490927	−	0.871201i	$-0.663342\pi$
$199$	−13.8508	−0.981855	−0.490927	+	0.871201i	$0.663342\pi$
$200$	0.828239	0.0585654
$201$	0.118067	0.00832777
$202$	7.90841	0.556433
$203$	−10.4013	−0.730031
$204$	12.2178	0.855420
$205$	2.18736	0.152772
$206$	13.2991	0.926593
$207$	−6.58634	−0.457782
$208$	−20.3564	−1.41146
$209$	−10.5322	−0.728527
$210$	−1.40317	−0.0968281
$211$	−23.3036	−1.60429	−0.802144	−	0.597131i	$-0.796307\pi$
$211$	−23.3036	−1.60429	−0.802144	+	0.597131i	$0.796307\pi$
$212$	−14.8436	−1.01946
$213$	9.06930	0.621418
$214$	−16.4793	−1.12650
$215$	0.433694	0.0295777
$216$	−0.800061	−0.0544372
$217$	−1.77543	−0.120524
$218$	−1.97722	−0.133914
$219$	−1.61649	−0.109232
$220$	−3.09196	−0.208460
$221$	−36.9547	−2.48584
$222$	1.67007	0.112088
$223$	12.6935	0.850019	0.425009	−	0.905189i	$-0.360271\pi$
$223$	12.6935	0.850019	0.425009	+	0.905189i	$0.360271\pi$
$224$	−10.7944	−0.721232
$225$	10.5698	0.704655
$226$	10.9439	0.727978
$227$	0.524762	0.0348297	0.0174148	−	0.999848i	$-0.494456\pi$
$227$	0.524762	0.0348297	0.0174148	+	0.999848i	$0.494456\pi$
$228$	−6.44393	−0.426759
$229$	18.8504	1.24567	0.622834	−	0.782354i	$-0.285981\pi$
$229$	18.8504	1.24567	0.622834	+	0.782354i	$0.285981\pi$
$230$	3.49877	0.230702
$231$	3.04510	0.200353
$232$	1.36264	0.0894617
$233$	11.5693	0.757932	0.378966	−	0.925411i	$-0.376280\pi$
$233$	11.5693	0.757932	0.378966	+	0.925411i	$0.376280\pi$
$234$	−22.0538	−1.44170
$235$	2.66560	0.173884
$236$	−11.7763	−0.766569
$237$	11.7331	0.762145
$238$	−20.4857	−1.32789
$239$	−1.00425	−0.0649593	−0.0324797	−	0.999472i	$-0.510340\pi$
$239$	−1.00425	−0.0649593	−0.0324797	+	0.999472i	$0.510340\pi$
$240$	2.16536	0.139774
$241$	−15.1149	−0.973636	−0.486818	−	0.873503i	$-0.661842\pi$
$241$	−15.1149	−0.973636	−0.486818	+	0.873503i	$0.661842\pi$
$242$	−8.01088	−0.514959
$243$	−16.0043	−1.02668
$244$	−23.9977	−1.53629
$245$	−3.15119	−0.201322
$246$	−5.94646	−0.379132
$247$	19.4906	1.24016
$248$	0.232592	0.0147696
$249$	−10.3894	−0.658401
$250$	−11.6881	−0.739222
$251$	−13.5726	−0.856697	−0.428349	−	0.903614i	$-0.640904\pi$
$251$	−13.5726	−0.856697	−0.428349	+	0.903614i	$0.640904\pi$
$252$	−5.97106	−0.376141
$253$	−7.59287	−0.477359
$254$	9.67461	0.607039
$255$	3.93097	0.246167
$256$	17.3499	1.08437
$257$	−0.604706	−0.0377205	−0.0188603	−	0.999822i	$-0.506004\pi$
$257$	−0.604706	−0.0377205	−0.0188603	+	0.999822i	$0.506004\pi$
$258$	−1.17902	−0.0734025
$259$	−1.36766	−0.0849821
$260$	5.72190	0.354857
$261$	17.3897	1.07640
$262$	24.9413	1.54088
$263$	−29.1636	−1.79830	−0.899152	−	0.437636i	$-0.855816\pi$
$263$	−29.1636	−1.79830	−0.899152	+	0.437636i	$0.855816\pi$
$264$	−0.398927	−0.0245522
$265$	−4.77577	−0.293373
$266$	10.8046	0.662471
$267$	1.94014	0.118735
$268$	−0.266894	−0.0163031
$269$	6.62883	0.404167	0.202084	−	0.979368i	$-0.435229\pi$
$269$	6.62883	0.404167	0.202084	+	0.979368i	$0.435229\pi$
$270$	5.42383	0.330084
$271$	16.0290	0.973693	0.486846	−	0.873488i	$-0.338147\pi$
$271$	16.0290	0.973693	0.486846	+	0.873488i	$0.338147\pi$
$272$	31.6134	1.91684
$273$	−5.63518	−0.341057
$274$	20.8495	1.25956
$275$	12.1851	0.734789
$276$	−4.64555	−0.279629
$277$	−4.96847	−0.298527	−0.149263	−	0.988797i	$-0.547690\pi$
$277$	−4.96847	−0.298527	−0.149263	+	0.988797i	$0.547690\pi$
$278$	13.6162	0.816648
$279$	2.96829	0.177707
$280$	−0.150538	−0.00899634
$281$	−26.6508	−1.58985	−0.794927	−	0.606705i	$-0.792491\pi$
$281$	−26.6508	−1.58985	−0.794927	+	0.606705i	$0.792491\pi$
$282$	−7.24655	−0.431526
$283$	−2.66611	−0.158484	−0.0792418	−	0.996855i	$-0.525250\pi$
$283$	−2.66611	−0.158484	−0.0792418	+	0.996855i	$0.525250\pi$
$284$	−20.5015	−1.21654
$285$	−2.07327	−0.122810
$286$	−25.4241	−1.50336
$287$	4.86968	0.287448
$288$	18.0469	1.06342
$289$	40.3906	2.37592
$290$	−9.23772	−0.542457
$291$	2.22389	0.130367
$292$	3.65413	0.213842
$293$	−15.4102	−0.900276	−0.450138	−	0.892959i	$-0.648625\pi$
$293$	−15.4102	−0.900276	−0.450138	+	0.892959i	$0.648625\pi$
$294$	8.56666	0.499618
$295$	−3.78890	−0.220598
$296$	0.179172	0.0104141
$297$	−11.7705	−0.682996
$298$	−30.5030	−1.76699
$299$	14.0512	0.812600
$300$	7.45523	0.430428
$301$	0.965523	0.0556518
$302$	−7.55597	−0.434797
$303$	−3.37844	−0.194086
$304$	−16.6735	−0.956292
$305$	−7.72102	−0.442104
$306$	34.2496	1.95792
$307$	33.2685	1.89873	0.949366	−	0.314173i	$-0.101727\pi$
$307$	33.2685	1.89873	0.949366	+	0.314173i	$0.101727\pi$
$308$	−6.88355	−0.392227
$309$	−5.68133	−0.323200
$310$	−1.57680	−0.0895564
$311$	25.6595	1.45502	0.727508	−	0.686100i	$-0.240679\pi$
$311$	25.6595	1.45502	0.727508	+	0.686100i	$0.240679\pi$
$312$	0.738244	0.0417948
$313$	26.6015	1.50360	0.751802	−	0.659389i	$-0.229185\pi$
$313$	26.6015	1.50360	0.751802	+	0.659389i	$0.229185\pi$
$314$	−44.7129	−2.52329
$315$	−1.92113	−0.108243
$316$	−26.5230	−1.49204
$317$	9.63243	0.541011	0.270506	−	0.962718i	$-0.412809\pi$
$317$	9.63243	0.541011	0.270506	+	0.962718i	$0.412809\pi$
$318$	12.9832	0.728060
$319$	20.0472	1.12243
$320$	−4.45962	−0.249300
$321$	7.03990	0.392929
$322$	7.78923	0.434077
$323$	−30.2689	−1.68421
$324$	5.89611	0.327562
$325$	−22.5494	−1.25082
$326$	5.34358	0.295954
$327$	0.844659	0.0467097
$328$	−0.637958	−0.0352253
$329$	5.93435	0.327171
$330$	2.70443	0.148874
$331$	−13.6059	−0.747846	−0.373923	−	0.927460i	$-0.621988\pi$
$331$	−13.6059	−0.747846	−0.373923	+	0.927460i	$0.621988\pi$
$332$	23.4856	1.28894
$333$	2.28655	0.125302
$334$	27.4656	1.50285
$335$	−0.0858705	−0.00469160
$336$	4.82070	0.262991
$337$	13.6237	0.742130	0.371065	−	0.928607i	$-0.378993\pi$
$337$	13.6237	0.742130	0.371065	+	0.928607i	$0.378993\pi$
$338$	21.3454	1.16104
$339$	−4.67519	−0.253922
$340$	−8.88610	−0.481917
$341$	3.42190	0.185306
$342$	−18.0639	−0.976783
$343$	−16.5890	−0.895723
$344$	−0.126490	−0.00681986
$345$	−1.49466	−0.0804699
$346$	20.6574	1.11055
$347$	23.3582	1.25393	0.626966	−	0.779047i	$-0.284296\pi$
$347$	23.3582	1.25393	0.626966	+	0.779047i	$0.284296\pi$
$348$	12.2655	0.657502
$349$	27.8488	1.49071	0.745357	−	0.666665i	$-0.232279\pi$
$349$	27.8488	1.49071	0.745357	+	0.666665i	$0.232279\pi$
$350$	−12.5002	−0.668166
$351$	21.7823	1.16265
$352$	20.8048	1.10890
$353$	10.7822	0.573877	0.286939	−	0.957949i	$-0.407362\pi$
$353$	10.7822	0.573877	0.286939	+	0.957949i	$0.407362\pi$
$354$	10.3003	0.547455
$355$	−6.59615	−0.350087
$356$	−4.38576	−0.232445
$357$	8.75143	0.463175
$358$	−30.1251	−1.59216
$359$	29.7902	1.57227	0.786134	−	0.618056i	$-0.212080\pi$
$359$	29.7902	1.57227	0.786134	+	0.618056i	$0.212080\pi$
$360$	0.251680	0.0132647
$361$	−3.03560	−0.159768
$362$	46.4881	2.44336
$363$	3.42222	0.179620
$364$	12.7385	0.667680
$365$	1.17568	0.0615380
$366$	20.9900	1.09716
$367$	9.50922	0.496377	0.248189	−	0.968712i	$-0.420165\pi$
$367$	9.50922	0.496377	0.248189	+	0.968712i	$0.420165\pi$
$368$	−12.0203	−0.626600
$369$	−8.14149	−0.423829
$370$	−1.21465	−0.0631468
$371$	−10.6322	−0.551996
$372$	2.09363	0.108550
$373$	27.4998	1.42389	0.711944	−	0.702236i	$-0.247815\pi$
$373$	27.4998	1.42389	0.711944	+	0.702236i	$0.247815\pi$
$374$	39.4836	2.04165
$375$	4.99312	0.257844
$376$	−0.777437	−0.0400932
$377$	−37.0989	−1.91069
$378$	12.0749	0.621068
$379$	18.8466	0.968086	0.484043	−	0.875044i	$-0.339168\pi$
$379$	18.8466	0.968086	0.484043	+	0.875044i	$0.339168\pi$
$380$	4.68670	0.240423
$381$	−4.13296	−0.211738
$382$	−42.7830	−2.18897
$383$	−23.3183	−1.19151	−0.595754	−	0.803167i	$-0.703147\pi$
$383$	−23.3183	−1.19151	−0.595754	+	0.803167i	$0.703147\pi$
$384$	−1.20947	−0.0617204
$385$	−2.21472	−0.112872
$386$	25.8832	1.31742
$387$	−1.61423	−0.0820561
$388$	−5.02719	−0.255217
$389$	−5.99151	−0.303781	−0.151891	−	0.988397i	$-0.548536\pi$
$389$	−5.99151	−0.303781	−0.151891	+	0.988397i	$0.548536\pi$
$390$	−5.00476	−0.253426
$391$	−21.8214	−1.10356
$392$	0.919063	0.0464197
$393$	−10.6548	−0.537464
$394$	−38.8171	−1.95557
$395$	−8.53353	−0.429369
$396$	11.5084	0.578321
$397$	21.3616	1.07211	0.536054	−	0.844184i	$-0.319914\pi$
$397$	21.3616	1.07211	0.536054	+	0.844184i	$0.319914\pi$
$398$	−27.3859	−1.37273
$399$	−4.61567	−0.231073
$400$	19.2902	0.964512
$401$	−16.9527	−0.846578	−0.423289	−	0.905995i	$-0.639124\pi$
$401$	−16.9527	−0.846578	−0.423289	+	0.905995i	$0.639124\pi$
$402$	0.233443	0.0116431
$403$	−6.33249	−0.315444
$404$	7.63709	0.379959
$405$	1.89702	0.0942636
$406$	−20.5657	−1.02066
$407$	2.63598	0.130661
$408$	−1.14649	−0.0567598
$409$	29.7384	1.47047	0.735234	−	0.677814i	$-0.237072\pi$
$409$	29.7384	1.47047	0.735234	+	0.677814i	$0.237072\pi$
$410$	4.32489	0.213591
$411$	−8.90681	−0.439341
$412$	12.8429	0.632722
$413$	−8.43513	−0.415066
$414$	−13.0226	−0.640027
$415$	7.55627	0.370923
$416$	−38.5009	−1.88766
$417$	−5.81681	−0.284850
$418$	−20.8244	−1.01856
$419$	−30.1939	−1.47507	−0.737535	−	0.675309i	$-0.764010\pi$
$419$	−30.1939	−1.47507	−0.737535	+	0.675309i	$0.764010\pi$
$420$	−1.35503	−0.0661188
$421$	0.316198	0.0154105	0.00770527	−	0.999970i	$-0.497547\pi$
$421$	0.316198	0.0154105	0.00770527	+	0.999970i	$0.497547\pi$
$422$	−46.0763	−2.24296
$423$	−9.92149	−0.482399
$424$	1.39288	0.0676443
$425$	35.0193	1.69868
$426$	17.9320	0.868806
$427$	−17.1891	−0.831840
$428$	−15.9140	−0.769230
$429$	10.8611	0.524378
$430$	0.857507	0.0413527
$431$	17.3643	0.836410	0.418205	−	0.908353i	$-0.362659\pi$
$431$	17.3643	0.836410	0.418205	+	0.908353i	$0.362659\pi$
$432$	−18.6339	−0.896526
$433$	18.6070	0.894198	0.447099	−	0.894485i	$-0.352457\pi$
$433$	18.6070	0.894198	0.447099	+	0.894485i	$0.352457\pi$
$434$	−3.51040	−0.168505
$435$	3.94632	0.189211
$436$	−1.90938	−0.0914428
$437$	11.5091	0.550553
$438$	−3.19615	−0.152718
$439$	−12.8933	−0.615366	−0.307683	−	0.951489i	$-0.599554\pi$
$439$	−12.8933	−0.615366	−0.307683	+	0.951489i	$0.599554\pi$
$440$	0.290142	0.0138320
$441$	11.7289	0.558519
$442$	−73.0674	−3.47546
$443$	−39.0619	−1.85588	−0.927942	−	0.372724i	$-0.878424\pi$
$443$	−39.0619	−1.85588	−0.927942	+	0.372724i	$0.878424\pi$
$444$	1.61278	0.0765390
$445$	−1.41108	−0.0668914
$446$	25.0978	1.18841
$447$	13.0308	0.616335
$448$	−9.92834	−0.469070
$449$	31.3696	1.48042	0.740211	−	0.672374i	$-0.234726\pi$
$449$	31.3696	1.48042	0.740211	+	0.672374i	$0.234726\pi$
$450$	20.8988	0.985180
$451$	−9.38567	−0.441954
$452$	10.5684	0.497098
$453$	3.22788	0.151659
$454$	1.03757	0.0486955
$455$	4.09850	0.192141
$456$	0.604682	0.0283168
$457$	−1.36468	−0.0638370	−0.0319185	−	0.999490i	$-0.510162\pi$
$457$	−1.36468	−0.0638370	−0.0319185	+	0.999490i	$0.510162\pi$
$458$	37.2712	1.74157
$459$	−33.8278	−1.57895
$460$	3.37874	0.157534
$461$	−23.7309	−1.10526	−0.552629	−	0.833427i	$-0.686375\pi$
$461$	−23.7309	−1.10526	−0.552629	+	0.833427i	$0.686375\pi$
$462$	6.02082	0.280114
$463$	−8.14141	−0.378363	−0.189182	−	0.981942i	$-0.560584\pi$
$463$	−8.14141	−0.378363	−0.189182	+	0.981942i	$0.560584\pi$
$464$	31.7368	1.47334
$465$	0.673605	0.0312377
$466$	22.8751	1.05967
$467$	41.2670	1.90961	0.954804	−	0.297237i	$-0.0960653\pi$
$467$	41.2670	1.90961	0.954804	+	0.297237i	$0.0960653\pi$
$468$	−21.2972	−0.984464
$469$	−0.191171	−0.00882747
$470$	5.27046	0.243108
$471$	19.1012	0.880135
$472$	1.10505	0.0508642
$473$	−1.86092	−0.0855652
$474$	23.1988	1.06556
$475$	−18.4698	−0.847454
$476$	−19.7829	−0.906749
$477$	17.7757	0.813892
$478$	−1.98561	−0.0908198
$479$	−32.1366	−1.46836	−0.734180	−	0.678955i	$-0.762433\pi$
$479$	−32.1366	−1.46836	−0.734180	+	0.678955i	$0.762433\pi$
$480$	4.09545	0.186931
$481$	−4.87808	−0.222421
$482$	−29.8854	−1.36124
$483$	−3.32753	−0.151408
$484$	−7.73605	−0.351639
$485$	−1.61745	−0.0734446
$486$	−31.6439	−1.43540
$487$	−12.1022	−0.548403	−0.274201	−	0.961672i	$-0.588413\pi$
$487$	−12.1022	−0.548403	−0.274201	+	0.961672i	$0.588413\pi$
$488$	2.25188	0.101938
$489$	−2.28276	−0.103230
$490$	−6.23058	−0.281469
$491$	−30.7004	−1.38549	−0.692744	−	0.721183i	$-0.743598\pi$
$491$	−30.7004	−1.38549	−0.692744	+	0.721183i	$0.743598\pi$
$492$	−5.74245	−0.258890
$493$	57.6146	2.59483
$494$	38.5371	1.73387
$495$	3.70273	0.166425
$496$	5.41722	0.243240
$497$	−14.6849	−0.658706
$498$	−20.5421	−0.920513
$499$	19.8952	0.890630	0.445315	−	0.895374i	$-0.353092\pi$
$499$	19.8952	0.890630	0.445315	+	0.895374i	$0.353092\pi$
$500$	−11.2871	−0.504776
$501$	−11.7332	−0.524201
$502$	−26.8360	−1.19775
$503$	12.9014	0.575244	0.287622	−	0.957744i	$-0.407135\pi$
$503$	12.9014	0.575244	0.287622	+	0.957744i	$0.407135\pi$
$504$	0.560309	0.0249581
$505$	2.45716	0.109342
$506$	−15.0127	−0.667397
$507$	−9.11867	−0.404975
$508$	9.34270	0.414515
$509$	−9.57963	−0.424610	−0.212305	−	0.977203i	$-0.568097\pi$
$509$	−9.57963	−0.424610	−0.212305	+	0.977203i	$0.568097\pi$
$510$	7.77238	0.344167
$511$	2.61739	0.115787
$512$	31.4408	1.38950
$513$	17.8415	0.787719
$514$	−1.19563	−0.0527372
$515$	4.13206	0.182081
$516$	−1.13857	−0.0501227
$517$	−11.4377	−0.503029
$518$	−2.70415	−0.118814
$519$	−8.82477	−0.387364
$520$	−0.536929	−0.0235459
$521$	−42.8130	−1.87567	−0.937835	−	0.347081i	$-0.887173\pi$
$521$	−42.8130	−1.87567	−0.937835	+	0.347081i	$0.887173\pi$
$522$	34.3833	1.50491
$523$	−32.1467	−1.40568	−0.702838	−	0.711350i	$-0.748084\pi$
$523$	−32.1467	−1.40568	−0.702838	+	0.711350i	$0.748084\pi$
$524$	24.0856	1.05218
$525$	5.34005	0.233059
$526$	−57.6627	−2.51421
$527$	9.83435	0.428391
$528$	−9.29126	−0.404350
$529$	−14.7029	−0.639256
$530$	−9.44273	−0.410166
$531$	14.1025	0.611995
$532$	10.4339	0.452367
$533$	17.3689	0.752330
$534$	3.83608	0.166003
$535$	−5.12016	−0.221364
$536$	0.0250446	0.00108176
$537$	12.8693	0.555352
$538$	13.1066	0.565067
$539$	13.5213	0.582404
$540$	5.23775	0.225397
$541$	−14.2474	−0.612545	−0.306273	−	0.951944i	$-0.599082\pi$
$541$	−14.2474	−0.612545	−0.306273	+	0.951944i	$0.599082\pi$
$542$	31.6928	1.36132
$543$	−19.8595	−0.852255
$544$	59.7918	2.56355
$545$	−0.614325	−0.0263148
$546$	−11.1420	−0.476832
$547$	−24.4814	−1.04675	−0.523375	−	0.852103i	$-0.675327\pi$
$547$	−24.4814	−1.04675	−0.523375	+	0.852103i	$0.675327\pi$
$548$	20.1342	0.860089
$549$	28.7381	1.22651
$550$	24.0926	1.02731
$551$	−30.3870	−1.29453
$552$	0.435927	0.0185543
$553$	−18.9980	−0.807877
$554$	−9.82374	−0.417371
$555$	0.518895	0.0220259
$556$	13.1491	0.557646
$557$	37.4969	1.58879	0.794396	−	0.607400i	$-0.207787\pi$
$557$	37.4969	1.58879	0.794396	+	0.607400i	$0.207787\pi$
$558$	5.86895	0.248452
$559$	3.44377	0.145656
$560$	−3.50612	−0.148161
$561$	−16.8672	−0.712136
$562$	−52.6944	−2.22278
$563$	−8.86803	−0.373743	−0.186872	−	0.982384i	$-0.559835\pi$
$563$	−8.86803	−0.373743	−0.186872	+	0.982384i	$0.559835\pi$
$564$	−6.99794	−0.294666
$565$	3.40030	0.143051
$566$	−5.27147	−0.221576
$567$	4.22329	0.177361
$568$	1.92381	0.0807211
$569$	−19.5351	−0.818953	−0.409476	−	0.912321i	$-0.634289\pi$
$569$	−19.5351	−0.818953	−0.409476	+	0.912321i	$0.634289\pi$
$570$	−4.09930	−0.171701
$571$	41.7209	1.74596	0.872982	−	0.487752i	$-0.162183\pi$
$571$	41.7209	1.74596	0.872982	+	0.487752i	$0.162183\pi$
$572$	−24.5519	−1.02656
$573$	18.2767	0.763521
$574$	9.62840	0.401882
$575$	−13.3153	−0.555285
$576$	16.5989	0.691622
$577$	13.0856	0.544760	0.272380	−	0.962190i	$-0.412189\pi$
$577$	13.0856	0.544760	0.272380	+	0.962190i	$0.412189\pi$
$578$	79.8609	3.32177
$579$	−11.0572	−0.459521
$580$	−8.92079	−0.370416
$581$	16.8223	0.697908
$582$	4.39711	0.182266
$583$	20.4922	0.848698
$584$	−0.342894	−0.0141891
$585$	−6.85217	−0.283303
$586$	−30.4694	−1.25868
$587$	−30.6343	−1.26441	−0.632206	−	0.774800i	$-0.717850\pi$
$587$	−30.6343	−1.26441	−0.632206	+	0.774800i	$0.717850\pi$
$588$	8.27276	0.341163
$589$	−5.18683	−0.213719
$590$	−7.49147	−0.308419
$591$	16.5825	0.682113
$592$	4.17302	0.171510
$593$	8.30041	0.340857	0.170428	−	0.985370i	$-0.445485\pi$
$593$	8.30041	0.340857	0.170428	+	0.985370i	$0.445485\pi$
$594$	−23.2729	−0.954898
$595$	−6.36496	−0.260938
$596$	−29.4565	−1.20659
$597$	11.6992	0.478815
$598$	27.7822	1.13610
$599$	26.5007	1.08279	0.541394	−	0.840769i	$-0.317897\pi$
$599$	26.5007	1.08279	0.541394	+	0.840769i	$0.317897\pi$
$600$	−0.699580	−0.0285602
$601$	−13.8654	−0.565582	−0.282791	−	0.959182i	$-0.591260\pi$
$601$	−13.8654	−0.565582	−0.282791	+	0.959182i	$0.591260\pi$
$602$	1.90905	0.0778070
$603$	0.319614	0.0130157
$604$	−7.29674	−0.296900
$605$	−2.48900	−0.101192
$606$	−6.67991	−0.271353
$607$	2.94292	0.119449	0.0597246	−	0.998215i	$-0.480978\pi$
$607$	2.94292	0.119449	0.0597246	+	0.998215i	$0.480978\pi$
$608$	−31.5354	−1.27893
$609$	8.78559	0.356010
$610$	−15.2661	−0.618107
$611$	21.1663	0.856297
$612$	33.0746	1.33696
$613$	−4.91720	−0.198604	−0.0993019	−	0.995057i	$-0.531661\pi$
$613$	−4.91720	−0.198604	−0.0993019	+	0.995057i	$0.531661\pi$
$614$	65.7789	2.65462
$615$	−1.84758	−0.0745015
$616$	0.645935	0.0260255
$617$	32.2975	1.30025	0.650124	−	0.759828i	$-0.274717\pi$
$617$	32.2975	1.30025	0.650124	+	0.759828i	$0.274717\pi$
$618$	−11.2332	−0.451866
$619$	3.76428	0.151299	0.0756496	−	0.997134i	$-0.475897\pi$
$619$	3.76428	0.151299	0.0756496	+	0.997134i	$0.475897\pi$
$620$	−1.52271	−0.0611534
$621$	12.8623	0.516145
$622$	50.7343	2.03426
$623$	−3.14145	−0.125859
$624$	17.1942	0.688318
$625$	19.4815	0.779260
$626$	52.5968	2.10219
$627$	8.89611	0.355276
$628$	−43.1789	−1.72302
$629$	7.57566	0.302061
$630$	−3.79849	−0.151335
$631$	14.7105	0.585618	0.292809	−	0.956171i	$-0.405410\pi$
$631$	14.7105	0.585618	0.292809	+	0.956171i	$0.405410\pi$
$632$	2.48886	0.0990014
$633$	19.6836	0.782353
$634$	19.0454	0.756389
$635$	3.00592	0.119286
$636$	12.5377	0.497154
$637$	−25.0222	−0.991415
$638$	39.6377	1.56927
$639$	24.5512	0.971232
$640$	0.879653	0.0347713
$641$	29.3084	1.15761	0.578806	−	0.815465i	$-0.303519\pi$
$641$	29.3084	1.15761	0.578806	+	0.815465i	$0.303519\pi$
$642$	13.9194	0.549355
$643$	38.6280	1.52334	0.761670	−	0.647965i	$-0.224380\pi$
$643$	38.6280	1.52334	0.761670	+	0.647965i	$0.224380\pi$
$644$	7.52200	0.296408
$645$	−0.366324	−0.0144240
$646$	−59.8481	−2.35469
$647$	−47.1484	−1.85360	−0.926798	−	0.375559i	$-0.877451\pi$
$647$	−47.1484	−1.85360	−0.926798	+	0.375559i	$0.877451\pi$
$648$	−0.553276	−0.0217347
$649$	16.2576	0.638167
$650$	−44.5851	−1.74877
$651$	1.49963	0.0587751
$652$	5.16026	0.202091
$653$	29.3785	1.14967	0.574835	−	0.818269i	$-0.305066\pi$
$653$	29.3785	1.14967	0.574835	+	0.818269i	$0.305066\pi$
$654$	1.67007	0.0653050
$655$	7.74931	0.302791
$656$	−14.8585	−0.580125
$657$	−4.37595	−0.170722
$658$	11.7335	0.457419
$659$	−33.2185	−1.29401	−0.647005	−	0.762485i	$-0.723979\pi$
$659$	−33.2185	−1.29401	−0.647005	+	0.762485i	$0.723979\pi$
$660$	2.61165	0.101658
$661$	−26.8289	−1.04352	−0.521761	−	0.853092i	$-0.674725\pi$
$661$	−26.8289	−1.04352	−0.521761	+	0.853092i	$0.674725\pi$
$662$	−26.9017	−1.04557
$663$	31.2141	1.21226
$664$	−2.20383	−0.0855252
$665$	3.35701	0.130179
$666$	4.52100	0.175185
$667$	−21.9066	−0.848228
$668$	26.5233	1.02622
$669$	−10.7217	−0.414524
$670$	−0.169784	−0.00655934
$671$	33.1298	1.27896
$672$	9.11760	0.351719
$673$	−36.9022	−1.42247	−0.711237	−	0.702953i	$-0.751865\pi$
$673$	−36.9022	−1.42247	−0.711237	+	0.702953i	$0.751865\pi$
$674$	26.9370	1.03757
$675$	−20.6415	−0.794491
$676$	20.6131	0.792811
$677$	36.7750	1.41338	0.706689	−	0.707525i	$-0.250188\pi$
$677$	36.7750	1.41338	0.706689	+	0.707525i	$0.250188\pi$
$678$	−9.24387	−0.355009
$679$	−3.60089	−0.138189
$680$	0.833850	0.0319767
$681$	−0.443245	−0.0169852
$682$	6.76584	0.259077
$683$	−43.0319	−1.64657	−0.823284	−	0.567629i	$-0.807861\pi$
$683$	−43.0319	−1.64657	−0.823284	+	0.567629i	$0.807861\pi$
$684$	−17.4442	−0.666994
$685$	6.47797	0.247511
$686$	−32.8001	−1.25231
$687$	−15.9221	−0.607467
$688$	−2.94602	−0.112316
$689$	−37.9223	−1.44472
$690$	−2.95527	−0.112505
$691$	−31.8018	−1.20980	−0.604898	−	0.796303i	$-0.706786\pi$
$691$	−31.8018	−1.20980	−0.604898	+	0.796303i	$0.706786\pi$
$692$	19.9487	0.758336
$693$	8.24329	0.313137
$694$	46.1841	1.75313
$695$	4.23060	0.160476
$696$	−1.15097	−0.0436273
$697$	−26.9739	−1.02171
$698$	55.0632	2.08417
$699$	−9.77214	−0.369616
$700$	−12.0714	−0.456255
$701$	−14.7074	−0.555492	−0.277746	−	0.960654i	$-0.589587\pi$
$701$	−14.7074	−0.555492	−0.277746	+	0.960654i	$0.589587\pi$
$702$	43.0682	1.62551
$703$	−3.99555	−0.150695
$704$	19.1356	0.721200
$705$	−2.25152	−0.0847971
$706$	21.3187	0.802339
$707$	5.47031	0.205732
$708$	9.94692	0.373828
$709$	−35.8182	−1.34518	−0.672590	−	0.740015i	$-0.734818\pi$
$709$	−35.8182	−1.34518	−0.672590	+	0.740015i	$0.734818\pi$
$710$	−13.0420	−0.489458
$711$	31.7623	1.19118
$712$	0.411549	0.0154234
$713$	−3.73929	−0.140037
$714$	17.3035	0.647566
$715$	−7.89932	−0.295418
$716$	−29.0915	−1.08720
$717$	0.848246	0.0316783
$718$	58.9017	2.19819
$719$	26.4644	0.986957	0.493479	−	0.869758i	$-0.335725\pi$
$719$	26.4644	0.986957	0.493479	+	0.869758i	$0.335725\pi$
$720$	5.86179	0.218456
$721$	9.19912	0.342593
$722$	−6.00203	−0.223373
$723$	12.7669	0.474807
$724$	44.8932	1.66844
$725$	35.1560	1.30566
$726$	6.76646	0.251127
$727$	−32.0684	−1.18935	−0.594676	−	0.803966i	$-0.702720\pi$
$727$	−32.0684	−1.18935	−0.594676	+	0.803966i	$0.702720\pi$
$728$	−1.19535	−0.0443027
$729$	4.25425	0.157565
$730$	2.32458	0.0860364
$731$	−5.34818	−0.197809
$732$	20.2699	0.749196
$733$	−11.2067	−0.413930	−0.206965	−	0.978348i	$-0.566359\pi$
$733$	−11.2067	−0.413930	−0.206965	+	0.978348i	$0.566359\pi$
$734$	18.8018	0.693986
$735$	2.66168	0.0981775
$736$	−22.7345	−0.838004
$737$	0.368458	0.0135723
$738$	−16.0975	−0.592556
$739$	26.7846	0.985286	0.492643	−	0.870231i	$-0.336031\pi$
$739$	26.7846	0.985286	0.492643	+	0.870231i	$0.336031\pi$
$740$	−1.17298	−0.0431197
$741$	−16.4629	−0.604780
$742$	−21.0221	−0.771746
$743$	8.47336	0.310857	0.155429	−	0.987847i	$-0.450324\pi$
$743$	8.47336	0.310857	0.155429	+	0.987847i	$0.450324\pi$
$744$	−0.196461	−0.00720260
$745$	−9.47736	−0.347224
$746$	54.3731	1.99074
$747$	−28.1248	−1.02903
$748$	38.1290	1.39413
$749$	−11.3989	−0.416507
$750$	9.87248	0.360492
$751$	9.62853	0.351350	0.175675	−	0.984448i	$-0.443789\pi$
$751$	9.62853	0.351350	0.175675	+	0.984448i	$0.443789\pi$
$752$	−18.1070	−0.660295
$753$	11.4642	0.417780
$754$	−73.3526	−2.67134
$755$	−2.34766	−0.0854400
$756$	11.6607	0.424095
$757$	12.8991	0.468825	0.234412	−	0.972137i	$-0.424683\pi$
$757$	12.8991	0.468825	0.234412	+	0.972137i	$0.424683\pi$
$758$	37.2638	1.35348
$759$	6.41338	0.232791
$760$	−0.439788	−0.0159528
$761$	11.9093	0.431712	0.215856	−	0.976425i	$-0.430746\pi$
$761$	11.9093	0.431712	0.215856	+	0.976425i	$0.430746\pi$
$762$	−8.17175	−0.296031
$763$	−1.36766	−0.0495125
$764$	−41.3152	−1.49473
$765$	10.6414	0.384741
$766$	−46.1052	−1.66585
$767$	−30.0859	−1.08634
$768$	−14.6548	−0.528809
$769$	41.2287	1.48675	0.743373	−	0.668877i	$-0.233225\pi$
$769$	41.2287	1.48675	0.743373	+	0.668877i	$0.233225\pi$
$770$	−4.37897	−0.157807
$771$	0.510770	0.0183949
$772$	24.9952	0.899596
$773$	15.2584	0.548806	0.274403	−	0.961615i	$-0.411520\pi$
$773$	15.2584	0.548806	0.274403	+	0.961615i	$0.411520\pi$
$774$	−3.19169	−0.114723
$775$	6.00084	0.215557
$776$	0.471739	0.0169344
$777$	1.15520	0.0414427
$778$	−11.8465	−0.424718
$779$	14.2265	0.509719
$780$	−4.83305	−0.173051
$781$	28.3032	1.01277
$782$	−43.1457	−1.54289
$783$	−33.9599	−1.21363
$784$	21.4056	0.764485
$785$	−13.8924	−0.495840
$786$	−21.0669	−0.751430
$787$	−11.3788	−0.405610	−0.202805	−	0.979219i	$-0.565006\pi$
$787$	−11.3788	−0.405610	−0.202805	+	0.979219i	$0.565006\pi$
$788$	−37.4853	−1.33536
$789$	24.6333	0.876969
$790$	−16.8726	−0.600301
$791$	7.57000	0.269158
$792$	−1.07992	−0.0383734
$793$	−61.3092	−2.17715
$794$	42.2365	1.49892
$795$	4.03390	0.143068
$796$	−26.4464	−0.937368
$797$	−3.51128	−0.124376	−0.0621880	−	0.998064i	$-0.519808\pi$
$797$	−3.51128	−0.124376	−0.0621880	+	0.998064i	$0.519808\pi$
$798$	−9.12618	−0.323063
$799$	−32.8712	−1.16290
$800$	36.4845	1.28992
$801$	5.25210	0.185574
$802$	−33.5192	−1.18360
$803$	−5.04468	−0.178023
$804$	0.225434	0.00795045
$805$	2.42013	0.0852984
$806$	−12.5207	−0.441023
$807$	−5.59910	−0.197098
$808$	−0.716645	−0.0252115
$809$	20.6324	0.725396	0.362698	−	0.931907i	$-0.381856\pi$
$809$	20.6324	0.725396	0.362698	+	0.931907i	$0.381856\pi$
$810$	3.75081	0.131790
$811$	1.40042	0.0491753	0.0245876	−	0.999698i	$-0.492173\pi$
$811$	1.40042	0.0491753	0.0245876	+	0.999698i	$0.492173\pi$
$812$	−19.8601	−0.696954
$813$	−13.5390	−0.474835
$814$	5.21191	0.182677
$815$	1.66026	0.0581565
$816$	−26.7025	−0.934776
$817$	2.82073	0.0986849
$818$	58.7991	2.05586
$819$	−15.2548	−0.533047
$820$	4.17651	0.145850
$821$	−45.8252	−1.59931	−0.799655	−	0.600460i	$-0.794984\pi$
$821$	−45.8252	−1.59931	−0.799655	+	0.600460i	$0.794984\pi$
$822$	−17.6107	−0.614243
$823$	28.8121	1.00433	0.502163	−	0.864773i	$-0.332538\pi$
$823$	28.8121	1.00433	0.502163	+	0.864773i	$0.332538\pi$
$824$	−1.20514	−0.0419831
$825$	−10.2923	−0.358330
$826$	−16.6781	−0.580304
$827$	−28.5376	−0.992349	−0.496174	−	0.868223i	$-0.665262\pi$
$827$	−28.5376	−0.992349	−0.496174	+	0.868223i	$0.665262\pi$
$828$	−12.5758	−0.437041
$829$	−33.7211	−1.17118	−0.585592	−	0.810606i	$-0.699138\pi$
$829$	−33.7211	−1.17118	−0.585592	+	0.810606i	$0.699138\pi$
$830$	14.9404	0.518588
$831$	4.19666	0.145581
$832$	−35.4118	−1.22768
$833$	38.8594	1.34640
$834$	−11.5011	−0.398250
$835$	8.53363	0.295318
$836$	−20.1100	−0.695518
$837$	−5.79668	−0.200362
$838$	−59.6999	−2.06230
$839$	27.3746	0.945075	0.472537	−	0.881311i	$-0.343338\pi$
$839$	27.3746	0.945075	0.472537	+	0.881311i	$0.343338\pi$
$840$	0.127153	0.00438719
$841$	28.8395	0.994465
$842$	0.625192	0.0215455
$843$	22.5109	0.775315
$844$	−44.4955	−1.53160
$845$	6.63206	0.228150
$846$	−19.6169	−0.674444
$847$	−5.54120	−0.190398
$848$	32.4411	1.11403
$849$	2.25195	0.0772867
$850$	69.2406	2.37493
$851$	−2.88047	−0.0987412
$852$	17.3168	0.593262
$853$	53.2490	1.82321	0.911605	−	0.411067i	$-0.134844\pi$
$853$	53.2490	1.82321	0.911605	+	0.411067i	$0.134844\pi$
$854$	−33.9866	−1.16300
$855$	−5.61249	−0.191943
$856$	1.49333	0.0510408
$857$	−35.9158	−1.22686	−0.613431	−	0.789749i	$-0.710211\pi$
$857$	−35.9158	−1.22686	−0.613431	+	0.789749i	$0.710211\pi$
$858$	21.4747	0.733134
$859$	−6.46786	−0.220681	−0.110340	−	0.993894i	$-0.535194\pi$
$859$	−6.46786	−0.220681	−0.110340	+	0.993894i	$0.535194\pi$
$860$	0.828088	0.0282376
$861$	−4.11322	−0.140178
$862$	34.3330	1.16939
$863$	48.6565	1.65629	0.828143	−	0.560517i	$-0.189397\pi$
$863$	48.6565	1.65629	0.828143	+	0.560517i	$0.189397\pi$
$864$	−35.2432	−1.19900
$865$	6.41830	0.218229
$866$	36.7901	1.25018
$867$	−34.1163	−1.15865
$868$	−3.38997	−0.115063
$869$	36.6162	1.24212
$870$	7.80272	0.264537
$871$	−0.681859	−0.0231039
$872$	0.179172	0.00606751
$873$	6.02023	0.203754
$874$	22.7559	0.769729
$875$	−8.08478	−0.273316
$876$	−3.08649	−0.104283
$877$	−11.2955	−0.381424	−0.190712	−	0.981646i	$-0.561080\pi$
$877$	−11.2955	−0.381424	−0.190712	+	0.981646i	$0.561080\pi$
$878$	−25.4929	−0.860345
$879$	13.0164	0.439032
$880$	6.75759	0.227798
$881$	−6.96989	−0.234821	−0.117411	−	0.993083i	$-0.537459\pi$
$881$	−6.96989	−0.234821	−0.117411	+	0.993083i	$0.537459\pi$
$882$	23.1906	0.780867
$883$	40.8259	1.37390	0.686951	−	0.726704i	$-0.258949\pi$
$883$	40.8259	1.37390	0.686951	+	0.726704i	$0.258949\pi$
$884$	−70.5606	−2.37321
$885$	3.20033	0.107578
$886$	−77.2337	−2.59472
$887$	−19.3940	−0.651187	−0.325594	−	0.945510i	$-0.605564\pi$
$887$	−19.3940	−0.651187	−0.325594	+	0.945510i	$0.605564\pi$
$888$	−0.151339	−0.00507860
$889$	6.69201	0.224443
$890$	−2.79000	−0.0935211
$891$	−8.13983	−0.272695
$892$	24.2367	0.811505
$893$	17.3369	0.580158
$894$	25.7647	0.861699
$895$	−9.35992	−0.312868
$896$	1.95835	0.0654239
$897$	−11.8684	−0.396276
$898$	62.0244	2.06978
$899$	9.87274	0.329274
$900$	20.1818	0.672728
$901$	58.8932	1.96202
$902$	−18.5575	−0.617897
$903$	−0.815538	−0.0271394
$904$	−0.991716	−0.0329840
$905$	14.4440	0.480133
$906$	6.38222	0.212035
$907$	19.9551	0.662599	0.331300	−	0.943526i	$-0.392513\pi$
$907$	19.9551	0.662599	0.331300	+	0.943526i	$0.392513\pi$
$908$	1.00197	0.0332516
$909$	−9.14568	−0.303343
$910$	8.10362	0.268632
$911$	−44.6129	−1.47809	−0.739045	−	0.673656i	$-0.764723\pi$
$911$	−44.6129	−1.47809	−0.739045	+	0.673656i	$0.764723\pi$
$912$	14.0834	0.466349
$913$	−32.4229	−1.07304
$914$	−2.69826	−0.0892507
$915$	6.52163	0.215598
$916$	35.9925	1.18923
$917$	17.2521	0.569715
$918$	−66.8849	−2.20753
$919$	51.1995	1.68891	0.844457	−	0.535623i	$-0.179923\pi$
$919$	51.1995	1.68891	0.844457	+	0.535623i	$0.179923\pi$
$920$	−0.317052	−0.0104529
$921$	−28.1005	−0.925943
$922$	−46.9211	−1.54526
$923$	−52.3771	−1.72401
$924$	5.81425	0.191275
$925$	4.62260	0.151990
$926$	−16.0973	−0.528991
$927$	−15.3798	−0.505138
$928$	60.0252	1.97042
$929$	1.55058	0.0508727	0.0254364	−	0.999676i	$-0.491902\pi$
$929$	1.55058	0.0508727	0.0254364	+	0.999676i	$0.491902\pi$
$930$	1.33186	0.0436735
$931$	−20.4952	−0.671703
$932$	22.0903	0.723591
$933$	−21.6735	−0.709559
$934$	81.5937	2.66983
$935$	12.2676	0.401195
$936$	1.99848	0.0653223
$937$	−3.88918	−0.127054	−0.0635270	−	0.997980i	$-0.520235\pi$
$937$	−3.88918	−0.127054	−0.0635270	+	0.997980i	$0.520235\pi$
$938$	−0.377987	−0.0123417
$939$	−22.4692	−0.733253
$940$	5.08964	0.166006
$941$	−42.9524	−1.40021	−0.700104	−	0.714040i	$-0.746863\pi$
$941$	−42.9524	−1.40021	−0.700104	+	0.714040i	$0.746863\pi$
$942$	37.7671	1.23052
$943$	10.2562	0.333988
$944$	25.7374	0.837683
$945$	3.75171	0.122043
$946$	−3.67944	−0.119629
$947$	35.5186	1.15420	0.577100	−	0.816674i	$-0.304184\pi$
$947$	35.5186	1.15420	0.577100	+	0.816674i	$0.304184\pi$
$948$	22.4029	0.727613
$949$	9.33556	0.303045
$950$	−36.5189	−1.18483
$951$	−8.13612	−0.263832
$952$	1.85638	0.0601656
$953$	28.4921	0.922951	0.461476	−	0.887153i	$-0.347320\pi$
$953$	28.4921	0.922951	0.461476	+	0.887153i	$0.347320\pi$
$954$	35.1463	1.13790
$955$	−13.2928	−0.430144
$956$	−1.91749	−0.0620161
$957$	−16.9331	−0.547369
$958$	−63.5411	−2.05292
$959$	14.4218	0.465703
$960$	3.76686	0.121575
$961$	−29.3148	−0.945639
$962$	−9.64502	−0.310968
$963$	19.0575	0.614120
$964$	−28.8601	−0.929521
$965$	8.04195	0.258880
$966$	−6.57925	−0.211684
$967$	40.9049	1.31541	0.657706	−	0.753275i	$-0.271527\pi$
$967$	40.9049	1.31541	0.657706	+	0.753275i	$0.271527\pi$
$968$	0.725931	0.0233323
$969$	25.5669	0.821327
$970$	−3.19805	−0.102683
$971$	−5.68275	−0.182368	−0.0911840	−	0.995834i	$-0.529065\pi$
$971$	−5.68275	−0.182368	−0.0911840	+	0.995834i	$0.529065\pi$
$972$	−30.5583	−0.980157
$973$	9.41848	0.301942
$974$	−23.9286	−0.766723
$975$	19.0466	0.609979
$976$	52.4478	1.67881
$977$	43.6482	1.39643	0.698215	−	0.715888i	$-0.253978\pi$
$977$	43.6482	1.39643	0.698215	+	0.715888i	$0.253978\pi$
$978$	−4.51351	−0.144326
$979$	6.05473	0.193510
$980$	−6.01682	−0.192200
$981$	2.28655	0.0730040
$982$	−60.7013	−1.93705
$983$	−50.9660	−1.62556	−0.812781	−	0.582570i	$-0.802047\pi$
$983$	−50.9660	−1.62556	−0.812781	+	0.582570i	$0.802047\pi$
$984$	0.538857	0.0171781
$985$	−12.0605	−0.384281
$986$	113.916	3.62784
$987$	−5.01250	−0.159550
$988$	37.2150	1.18397
$989$	2.03352	0.0646622
$990$	7.32109	0.232680
$991$	−57.4663	−1.82548	−0.912738	−	0.408544i	$-0.866036\pi$
$991$	−57.4663	−1.82548	−0.912738	+	0.408544i	$0.866036\pi$
$992$	10.2458	0.325305
$993$	11.4923	0.364698
$994$	−29.0351	−0.920938
$995$	−8.50887	−0.269749
$996$	−19.8373	−0.628570
$997$	−33.2477	−1.05297	−0.526483	−	0.850186i	$-0.676490\pi$
$997$	−33.2477	−1.05297	−0.526483	+	0.850186i	$0.676490\pi$
$998$	39.3370	1.24519
$999$	−4.46533	−0.141277

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.68	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.68	✓	79	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q+1.97722 q^{2} -0.844659 q^{3} +1.90938 q^{4} +0.614325 q^{5} -1.67007 q^{6} +1.36766 q^{7} -0.179172 q^{8} -2.28655 q^{9} +O(q^{10})\)	\(q+1.97722 q^{2} -0.844659 q^{3} +1.90938 q^{4} +0.614325 q^{5} -1.67007 q^{6} +1.36766 q^{7} -0.179172 q^{8} -2.28655 q^{9} +1.21465 q^{10} -2.63598 q^{11} -1.61278 q^{12} +4.87808 q^{13} +2.70415 q^{14} -0.518895 q^{15} -4.17302 q^{16} -7.57566 q^{17} -4.52100 q^{18} +3.99555 q^{19} +1.17298 q^{20} -1.15520 q^{21} -5.21191 q^{22} +2.88047 q^{23} +0.151339 q^{24} -4.62260 q^{25} +9.64502 q^{26} +4.46533 q^{27} +2.61138 q^{28} -7.60523 q^{29} -1.02597 q^{30} -1.29815 q^{31} -7.89263 q^{32} +2.22651 q^{33} -14.9787 q^{34} +0.840186 q^{35} -4.36590 q^{36} -1.00000 q^{37} +7.90006 q^{38} -4.12032 q^{39} -0.110070 q^{40} +3.56060 q^{41} -2.28409 q^{42} +0.705969 q^{43} -5.03310 q^{44} -1.40469 q^{45} +5.69531 q^{46} +4.33906 q^{47} +3.52478 q^{48} -5.12951 q^{49} -9.13989 q^{50} +6.39885 q^{51} +9.31412 q^{52} -7.77401 q^{53} +8.82893 q^{54} -1.61935 q^{55} -0.245045 q^{56} -3.37488 q^{57} -15.0372 q^{58} -6.16758 q^{59} -0.990769 q^{60} -12.5683 q^{61} -2.56673 q^{62} -3.12722 q^{63} -7.25938 q^{64} +2.99673 q^{65} +4.40228 q^{66} -0.139780 q^{67} -14.4648 q^{68} -2.43301 q^{69} +1.66123 q^{70} -10.7372 q^{71} +0.409685 q^{72} +1.91378 q^{73} -1.97722 q^{74} +3.90452 q^{75} +7.62903 q^{76} -3.60512 q^{77} -8.14675 q^{78} -13.8909 q^{79} -2.56359 q^{80} +3.08797 q^{81} +7.04007 q^{82} +12.3001 q^{83} -2.20573 q^{84} -4.65392 q^{85} +1.39585 q^{86} +6.42382 q^{87} +0.472293 q^{88} -2.29695 q^{89} -2.77737 q^{90} +6.67155 q^{91} +5.49992 q^{92} +1.09650 q^{93} +8.57926 q^{94} +2.45457 q^{95} +6.66658 q^{96} -2.63289 q^{97} -10.1422 q^{98} +6.02731 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

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