LMFDB - Embedded newform 8026.2.a.d.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8026,2,Mod(1,8026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.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:	$64.0879326623$
Analytic rank:	$0$
Dimension:	$96$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.26664 q^{3} +1.00000 q^{4} -3.59818 q^{5} -2.26664 q^{6} +5.23582 q^{7} +1.00000 q^{8} +2.13767 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.26664 q^{3} +1.00000 q^{4} -3.59818 q^{5} -2.26664 q^{6} +5.23582 q^{7} +1.00000 q^{8} +2.13767 q^{9} -3.59818 q^{10} +2.01309 q^{11} -2.26664 q^{12} +3.00587 q^{13} +5.23582 q^{14} +8.15578 q^{15} +1.00000 q^{16} +1.11072 q^{17} +2.13767 q^{18} -3.44867 q^{19} -3.59818 q^{20} -11.8677 q^{21} +2.01309 q^{22} +4.31456 q^{23} -2.26664 q^{24} +7.94687 q^{25} +3.00587 q^{26} +1.95460 q^{27} +5.23582 q^{28} +9.02644 q^{29} +8.15578 q^{30} +9.20790 q^{31} +1.00000 q^{32} -4.56296 q^{33} +1.11072 q^{34} -18.8394 q^{35} +2.13767 q^{36} -10.8879 q^{37} -3.44867 q^{38} -6.81322 q^{39} -3.59818 q^{40} +4.11618 q^{41} -11.8677 q^{42} -4.89092 q^{43} +2.01309 q^{44} -7.69170 q^{45} +4.31456 q^{46} +0.960680 q^{47} -2.26664 q^{48} +20.4138 q^{49} +7.94687 q^{50} -2.51761 q^{51} +3.00587 q^{52} -12.3649 q^{53} +1.95460 q^{54} -7.24346 q^{55} +5.23582 q^{56} +7.81690 q^{57} +9.02644 q^{58} +14.2673 q^{59} +8.15578 q^{60} +5.73358 q^{61} +9.20790 q^{62} +11.1924 q^{63} +1.00000 q^{64} -10.8156 q^{65} -4.56296 q^{66} -13.5762 q^{67} +1.11072 q^{68} -9.77957 q^{69} -18.8394 q^{70} +12.2038 q^{71} +2.13767 q^{72} +2.37312 q^{73} -10.8879 q^{74} -18.0127 q^{75} -3.44867 q^{76} +10.5402 q^{77} -6.81322 q^{78} -2.88134 q^{79} -3.59818 q^{80} -10.8434 q^{81} +4.11618 q^{82} +1.09009 q^{83} -11.8677 q^{84} -3.99658 q^{85} -4.89092 q^{86} -20.4597 q^{87} +2.01309 q^{88} -6.25753 q^{89} -7.69170 q^{90} +15.7382 q^{91} +4.31456 q^{92} -20.8710 q^{93} +0.960680 q^{94} +12.4089 q^{95} -2.26664 q^{96} -12.8858 q^{97} +20.4138 q^{98} +4.30332 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9}+O(q^{10}) $ 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9} + 39 q^{10} + 36 q^{11} + 8 q^{12} + 63 q^{13} + 19 q^{14} + 17 q^{15} + 96 q^{16} + 56 q^{17} + 130 q^{18} + 17 q^{19} + 39 q^{20} + 51 q^{21} + 36 q^{22} + 47 q^{23} + 8 q^{24} + 147 q^{25} + 63 q^{26} + 17 q^{27} + 19 q^{28} + 60 q^{29} + 17 q^{30} + 63 q^{31} + 96 q^{32} + 55 q^{33} + 56 q^{34} + 45 q^{35} + 130 q^{36} + 46 q^{37} + 17 q^{38} + 22 q^{39} + 39 q^{40} + 101 q^{41} + 51 q^{42} - 3 q^{43} + 36 q^{44} + 106 q^{45} + 47 q^{46} + 99 q^{47} + 8 q^{48} + 175 q^{49} + 147 q^{50} - q^{51} + 63 q^{52} + 75 q^{53} + 17 q^{54} + 80 q^{55} + 19 q^{56} + 35 q^{57} + 60 q^{58} + 129 q^{59} + 17 q^{60} + 75 q^{61} + 63 q^{62} + 20 q^{63} + 96 q^{64} + 55 q^{65} + 55 q^{66} + 2 q^{67} + 56 q^{68} + 57 q^{69} + 45 q^{70} + 87 q^{71} + 130 q^{72} + 120 q^{73} + 46 q^{74} - 15 q^{75} + 17 q^{76} + 95 q^{77} + 22 q^{78} + 21 q^{79} + 39 q^{80} + 180 q^{81} + 101 q^{82} + 69 q^{83} + 51 q^{84} + 59 q^{85} - 3 q^{86} + 63 q^{87} + 36 q^{88} + 144 q^{89} + 106 q^{90} - 5 q^{91} + 47 q^{92} + 59 q^{93} + 99 q^{94} + 23 q^{95} + 8 q^{96} + 99 q^{97} + 175 q^{98} + 42 q^{99}+O(q^{100}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9 + 39 * q^10 + 36 * q^11 + 8 * q^12 + 63 * q^13 + 19 * q^14 + 17 * q^15 + 96 * q^16 + 56 * q^17 + 130 * q^18 + 17 * q^19 + 39 * q^20 + 51 * q^21 + 36 * q^22 + 47 * q^23 + 8 * q^24 + 147 * q^25 + 63 * q^26 + 17 * q^27 + 19 * q^28 + 60 * q^29 + 17 * q^30 + 63 * q^31 + 96 * q^32 + 55 * q^33 + 56 * q^34 + 45 * q^35 + 130 * q^36 + 46 * q^37 + 17 * q^38 + 22 * q^39 + 39 * q^40 + 101 * q^41 + 51 * q^42 - 3 * q^43 + 36 * q^44 + 106 * q^45 + 47 * q^46 + 99 * q^47 + 8 * q^48 + 175 * q^49 + 147 * q^50 - q^51 + 63 * q^52 + 75 * q^53 + 17 * q^54 + 80 * q^55 + 19 * q^56 + 35 * q^57 + 60 * q^58 + 129 * q^59 + 17 * q^60 + 75 * q^61 + 63 * q^62 + 20 * q^63 + 96 * q^64 + 55 * q^65 + 55 * q^66 + 2 * q^67 + 56 * q^68 + 57 * q^69 + 45 * q^70 + 87 * q^71 + 130 * q^72 + 120 * q^73 + 46 * q^74 - 15 * q^75 + 17 * q^76 + 95 * q^77 + 22 * q^78 + 21 * q^79 + 39 * q^80 + 180 * q^81 + 101 * q^82 + 69 * q^83 + 51 * q^84 + 59 * q^85 - 3 * q^86 + 63 * q^87 + 36 * q^88 + 144 * q^89 + 106 * q^90 - 5 * q^91 + 47 * q^92 + 59 * q^93 + 99 * q^94 + 23 * q^95 + 8 * q^96 + 99 * q^97 + 175 * q^98 + 42 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.26664	−1.30865	−0.654323	−	0.756215i	$-0.727046\pi$
$3$	−2.26664	−1.30865	−0.654323	+	0.756215i	$0.727046\pi$
$4$	1.00000	0.500000
$5$	−3.59818	−1.60915	−0.804577	−	0.593849i	$-0.797608\pi$
$5$	−3.59818	−1.60915	−0.804577	+	0.593849i	$0.797608\pi$
$6$	−2.26664	−0.925353
$7$	5.23582	1.97895	0.989477	−	0.144692i	$-0.0462191\pi$
$7$	5.23582	1.97895	0.989477	+	0.144692i	$0.0462191\pi$
$8$	1.00000	0.353553
$9$	2.13767	0.712555
$10$	−3.59818	−1.13784
$11$	2.01309	0.606970	0.303485	−	0.952836i	$-0.401850\pi$
$11$	2.01309	0.606970	0.303485	+	0.952836i	$0.401850\pi$
$12$	−2.26664	−0.654323
$13$	3.00587	0.833677	0.416839	−	0.908981i	$-0.363138\pi$
$13$	3.00587	0.833677	0.416839	+	0.908981i	$0.363138\pi$
$14$	5.23582	1.39933
$15$	8.15578	2.10581
$16$	1.00000	0.250000
$17$	1.11072	0.269390	0.134695	−	0.990887i	$-0.456995\pi$
$17$	1.11072	0.269390	0.134695	+	0.990887i	$0.456995\pi$
$18$	2.13767	0.503853
$19$	−3.44867	−0.791180	−0.395590	−	0.918427i	$-0.629460\pi$
$19$	−3.44867	−0.791180	−0.395590	+	0.918427i	$0.629460\pi$
$20$	−3.59818	−0.804577
$21$	−11.8677	−2.58975
$22$	2.01309	0.429193
$23$	4.31456	0.899649	0.449824	−	0.893117i	$-0.351487\pi$
$23$	4.31456	0.899649	0.449824	+	0.893117i	$0.351487\pi$
$24$	−2.26664	−0.462676
$25$	7.94687	1.58937
$26$	3.00587	0.589499
$27$	1.95460	0.376164
$28$	5.23582	0.989477
$29$	9.02644	1.67617	0.838084	−	0.545541i	$-0.183676\pi$
$29$	9.02644	1.67617	0.838084	+	0.545541i	$0.183676\pi$
$30$	8.15578	1.48903
$31$	9.20790	1.65379	0.826894	−	0.562358i	$-0.190106\pi$
$31$	9.20790	1.65379	0.826894	+	0.562358i	$0.190106\pi$
$32$	1.00000	0.176777
$33$	−4.56296	−0.794309
$34$	1.11072	0.190488
$35$	−18.8394	−3.18444
$36$	2.13767	0.356278
$37$	−10.8879	−1.78996	−0.894982	−	0.446103i	$-0.852812\pi$
$37$	−10.8879	−1.78996	−0.894982	+	0.446103i	$0.852812\pi$
$38$	−3.44867	−0.559448
$39$	−6.81322	−1.09099
$40$	−3.59818	−0.568922
$41$	4.11618	0.642840	0.321420	−	0.946937i	$-0.395840\pi$
$41$	4.11618	0.642840	0.321420	+	0.946937i	$0.395840\pi$
$42$	−11.8677	−1.83123
$43$	−4.89092	−0.745858	−0.372929	−	0.927860i	$-0.621647\pi$
$43$	−4.89092	−0.745858	−0.372929	+	0.927860i	$0.621647\pi$
$44$	2.01309	0.303485
$45$	−7.69170	−1.14661
$46$	4.31456	0.636148
$47$	0.960680	0.140130	0.0700648	−	0.997542i	$-0.477679\pi$
$47$	0.960680	0.140130	0.0700648	+	0.997542i	$0.477679\pi$
$48$	−2.26664	−0.327162
$49$	20.4138	2.91626
$50$	7.94687	1.12386
$51$	−2.51761	−0.352536
$52$	3.00587	0.416839
$53$	−12.3649	−1.69845	−0.849227	−	0.528028i	$-0.822931\pi$
$53$	−12.3649	−1.69845	−0.849227	+	0.528028i	$0.822931\pi$
$54$	1.95460	0.265988
$55$	−7.24346	−0.976708
$56$	5.23582	0.699666
$57$	7.81690	1.03537
$58$	9.02644	1.18523
$59$	14.2673	1.85745	0.928725	−	0.370770i	$-0.120906\pi$
$59$	14.2673	1.85745	0.928725	+	0.370770i	$0.120906\pi$
$60$	8.15578	1.05291
$61$	5.73358	0.734110	0.367055	−	0.930199i	$-0.380366\pi$
$61$	5.73358	0.734110	0.367055	+	0.930199i	$0.380366\pi$
$62$	9.20790	1.16940
$63$	11.1924	1.41011
$64$	1.00000	0.125000
$65$	−10.8156	−1.34151
$66$	−4.56296	−0.561662
$67$	−13.5762	−1.65860	−0.829299	−	0.558806i	$-0.811260\pi$
$67$	−13.5762	−1.65860	−0.829299	+	0.558806i	$0.811260\pi$
$68$	1.11072	0.134695
$69$	−9.77957	−1.17732
$70$	−18.8394	−2.25174
$71$	12.2038	1.44832	0.724161	−	0.689631i	$-0.242227\pi$
$71$	12.2038	1.44832	0.724161	+	0.689631i	$0.242227\pi$
$72$	2.13767	0.251926
$73$	2.37312	0.277753	0.138877	−	0.990310i	$-0.455651\pi$
$73$	2.37312	0.277753	0.138877	+	0.990310i	$0.455651\pi$
$74$	−10.8879	−1.26570
$75$	−18.0127	−2.07993
$76$	−3.44867	−0.395590
$77$	10.5402	1.20117
$78$	−6.81322	−0.771445
$79$	−2.88134	−0.324176	−0.162088	−	0.986776i	$-0.551823\pi$
$79$	−2.88134	−0.324176	−0.162088	+	0.986776i	$0.551823\pi$
$80$	−3.59818	−0.402288
$81$	−10.8434	−1.20482
$82$	4.11618	0.454557
$83$	1.09009	0.119653	0.0598265	−	0.998209i	$-0.480945\pi$
$83$	1.09009	0.119653	0.0598265	+	0.998209i	$0.480945\pi$
$84$	−11.8677	−1.29488
$85$	−3.99658	−0.433490
$86$	−4.89092	−0.527401
$87$	−20.4597	−2.19351
$88$	2.01309	0.214596
$89$	−6.25753	−0.663297	−0.331649	−	0.943403i	$-0.607605\pi$
$89$	−6.25753	−0.663297	−0.331649	+	0.943403i	$0.607605\pi$
$90$	−7.69170	−0.810776
$91$	15.7382	1.64981
$92$	4.31456	0.449824
$93$	−20.8710	−2.16422
$94$	0.960680	0.0990866
$95$	12.4089	1.27313
$96$	−2.26664	−0.231338
$97$	−12.8858	−1.30836	−0.654178	−	0.756340i	$-0.726985\pi$
$97$	−12.8858	−1.30836	−0.654178	+	0.756340i	$0.726985\pi$
$98$	20.4138	2.06211
$99$	4.30332	0.432500
$100$	7.94687	0.794687
$101$	−2.64431	−0.263118	−0.131559	−	0.991308i	$-0.541998\pi$
$101$	−2.64431	−0.263118	−0.131559	+	0.991308i	$0.541998\pi$
$102$	−2.51761	−0.249281
$103$	9.44133	0.930282	0.465141	−	0.885237i	$-0.346004\pi$
$103$	9.44133	0.930282	0.465141	+	0.885237i	$0.346004\pi$
$104$	3.00587	0.294749
$105$	42.7022	4.16731
$106$	−12.3649	−1.20099
$107$	−10.6893	−1.03337	−0.516686	−	0.856175i	$-0.672835\pi$
$107$	−10.6893	−1.03337	−0.516686	+	0.856175i	$0.672835\pi$
$108$	1.95460	0.188082
$109$	−12.0737	−1.15645	−0.578224	−	0.815878i	$-0.696254\pi$
$109$	−12.0737	−1.15645	−0.578224	+	0.815878i	$0.696254\pi$
$110$	−7.24346	−0.690637
$111$	24.6790	2.34243
$112$	5.23582	0.494738
$113$	−3.49343	−0.328634	−0.164317	−	0.986408i	$-0.552542\pi$
$113$	−3.49343	−0.328634	−0.164317	+	0.986408i	$0.552542\pi$
$114$	7.81690	0.732120
$115$	−15.5246	−1.44767
$116$	9.02644	0.838084
$117$	6.42554	0.594041
$118$	14.2673	1.31342
$119$	5.81555	0.533110
$120$	8.15578	0.744517
$121$	−6.94746	−0.631587
$122$	5.73358	0.519094
$123$	−9.32992	−0.841250
$124$	9.20790	0.826894
$125$	−10.6034	−0.948394
$126$	11.1924	0.997101
$127$	−17.1778	−1.52429	−0.762143	−	0.647408i	$-0.775853\pi$
$127$	−17.1778	−1.52429	−0.762143	+	0.647408i	$0.775853\pi$
$128$	1.00000	0.0883883
$129$	11.0860	0.976064
$130$	−10.8156	−0.948594
$131$	4.09751	0.358001	0.179001	−	0.983849i	$-0.442714\pi$
$131$	4.09751	0.358001	0.179001	+	0.983849i	$0.442714\pi$
$132$	−4.56296	−0.397155
$133$	−18.0566	−1.56571
$134$	−13.5762	−1.17281
$135$	−7.03301	−0.605305
$136$	1.11072	0.0952438
$137$	8.10123	0.692135	0.346068	−	0.938210i	$-0.387517\pi$
$137$	8.10123	0.692135	0.346068	+	0.938210i	$0.387517\pi$
$138$	−9.77957	−0.832493
$139$	−4.94676	−0.419578	−0.209789	−	0.977747i	$-0.567278\pi$
$139$	−4.94676	−0.419578	−0.209789	+	0.977747i	$0.567278\pi$
$140$	−18.8394	−1.59222
$141$	−2.17752	−0.183380
$142$	12.2038	1.02412
$143$	6.05109	0.506017
$144$	2.13767	0.178139
$145$	−32.4787	−2.69721
$146$	2.37312	0.196401
$147$	−46.2708	−3.81635
$148$	−10.8879	−0.894982
$149$	4.08858	0.334950	0.167475	−	0.985876i	$-0.446439\pi$
$149$	4.08858	0.334950	0.167475	+	0.985876i	$0.446439\pi$
$150$	−18.0127	−1.47073
$151$	12.7626	1.03861	0.519303	−	0.854590i	$-0.326192\pi$
$151$	12.7626	1.03861	0.519303	+	0.854590i	$0.326192\pi$
$152$	−3.44867	−0.279724
$153$	2.37435	0.191955
$154$	10.5402	0.849353
$155$	−33.1317	−2.66120
$156$	−6.81322	−0.545494
$157$	−3.87868	−0.309552	−0.154776	−	0.987950i	$-0.549466\pi$
$157$	−3.87868	−0.309552	−0.154776	+	0.987950i	$0.549466\pi$
$158$	−2.88134	−0.229227
$159$	28.0269	2.22267
$160$	−3.59818	−0.284461
$161$	22.5903	1.78036
$162$	−10.8434	−0.851937
$163$	1.31142	0.102718	0.0513591	−	0.998680i	$-0.483645\pi$
$163$	1.31142	0.102718	0.0513591	+	0.998680i	$0.483645\pi$
$164$	4.11618	0.321420
$165$	16.4183	1.27817
$166$	1.09009	0.0846074
$167$	22.7943	1.76387	0.881937	−	0.471368i	$-0.156240\pi$
$167$	22.7943	1.76387	0.881937	+	0.471368i	$0.156240\pi$
$168$	−11.8677	−0.915615
$169$	−3.96477	−0.304982
$170$	−3.99658	−0.306524
$171$	−7.37211	−0.563759
$172$	−4.89092	−0.372929
$173$	−16.2635	−1.23649	−0.618245	−	0.785985i	$-0.712156\pi$
$173$	−16.2635	−1.23649	−0.618245	+	0.785985i	$0.712156\pi$
$174$	−20.4597	−1.55105
$175$	41.6084	3.14530
$176$	2.01309	0.151743
$177$	−32.3389	−2.43074
$178$	−6.25753	−0.469022
$179$	24.9980	1.86844	0.934220	−	0.356697i	$-0.116097\pi$
$179$	24.9980	1.86844	0.934220	+	0.356697i	$0.116097\pi$
$180$	−7.69170	−0.573305
$181$	−1.34845	−0.100229	−0.0501147	−	0.998743i	$-0.515959\pi$
$181$	−1.34845	−0.100229	−0.0501147	+	0.998743i	$0.515959\pi$
$182$	15.7382	1.16659
$183$	−12.9960	−0.960690
$184$	4.31456	0.318074
$185$	39.1767	2.88033
$186$	−20.8710	−1.53034
$187$	2.23599	0.163512
$188$	0.960680	0.0700648
$189$	10.2340	0.744411
$190$	12.4089	0.900238
$191$	0.653993	0.0473213	0.0236606	−	0.999720i	$-0.492468\pi$
$191$	0.653993	0.0473213	0.0236606	+	0.999720i	$0.492468\pi$
$192$	−2.26664	−0.163581
$193$	21.8581	1.57338	0.786692	−	0.617346i	$-0.211792\pi$
$193$	21.8581	1.57338	0.786692	+	0.617346i	$0.211792\pi$
$194$	−12.8858	−0.925148
$195$	24.5152	1.75557
$196$	20.4138	1.45813
$197$	12.2454	0.872452	0.436226	−	0.899837i	$-0.356315\pi$
$197$	12.2454	0.872452	0.436226	+	0.899837i	$0.356315\pi$
$198$	4.30332	0.305824
$199$	−5.28835	−0.374881	−0.187441	−	0.982276i	$-0.560019\pi$
$199$	−5.28835	−0.374881	−0.187441	+	0.982276i	$0.560019\pi$
$200$	7.94687	0.561929
$201$	30.7724	2.17052
$202$	−2.64431	−0.186053
$203$	47.2608	3.31706
$204$	−2.51761	−0.176268
$205$	−14.8108	−1.03443
$206$	9.44133	0.657809
$207$	9.22309	0.641049
$208$	3.00587	0.208419
$209$	−6.94250	−0.480223
$210$	42.7022	2.94673
$211$	20.3441	1.40054	0.700272	−	0.713876i	$-0.253062\pi$
$211$	20.3441	1.40054	0.700272	+	0.713876i	$0.253062\pi$
$212$	−12.3649	−0.849227
$213$	−27.6616	−1.89534
$214$	−10.6893	−0.730704
$215$	17.5984	1.20020
$216$	1.95460	0.132994
$217$	48.2109	3.27277
$218$	−12.0737	−0.817732
$219$	−5.37902	−0.363481
$220$	−7.24346	−0.488354
$221$	3.33869	0.224584
$222$	24.6790	1.65635
$223$	−24.7192	−1.65532	−0.827662	−	0.561228i	$-0.810329\pi$
$223$	−24.7192	−1.65532	−0.827662	+	0.561228i	$0.810329\pi$
$224$	5.23582	0.349833
$225$	16.9878	1.13252
$226$	−3.49343	−0.232379
$227$	16.0602	1.06595	0.532975	−	0.846131i	$-0.321074\pi$
$227$	16.0602	1.06595	0.532975	+	0.846131i	$0.321074\pi$
$228$	7.81690	0.517687
$229$	9.09248	0.600848	0.300424	−	0.953806i	$-0.402872\pi$
$229$	9.09248	0.600848	0.300424	+	0.953806i	$0.402872\pi$
$230$	−15.5246	−1.02366
$231$	−23.8908	−1.57190
$232$	9.02644	0.592615
$233$	9.69171	0.634925	0.317463	−	0.948271i	$-0.397169\pi$
$233$	9.69171	0.634925	0.317463	+	0.948271i	$0.397169\pi$
$234$	6.42554	0.420050
$235$	−3.45670	−0.225490
$236$	14.2673	0.928725
$237$	6.53097	0.424232
$238$	5.81555	0.376966
$239$	2.24615	0.145292	0.0726458	−	0.997358i	$-0.476856\pi$
$239$	2.24615	0.145292	0.0726458	+	0.997358i	$0.476856\pi$
$240$	8.15578	0.526453
$241$	2.60541	0.167829	0.0839145	−	0.996473i	$-0.473258\pi$
$241$	2.60541	0.167829	0.0839145	+	0.996473i	$0.473258\pi$
$242$	−6.94746	−0.446599
$243$	18.7143	1.20052
$244$	5.73358	0.367055
$245$	−73.4525	−4.69271
$246$	−9.32992	−0.594854
$247$	−10.3662	−0.659588
$248$	9.20790	0.584702
$249$	−2.47084	−0.156583
$250$	−10.6034	−0.670616
$251$	4.10121	0.258866	0.129433	−	0.991588i	$-0.458684\pi$
$251$	4.10121	0.258866	0.129433	+	0.991588i	$0.458684\pi$
$252$	11.1924	0.705057
$253$	8.68562	0.546060
$254$	−17.1778	−1.07783
$255$	9.05881	0.567285
$256$	1.00000	0.0625000
$257$	1.44047	0.0898542	0.0449271	−	0.998990i	$-0.485694\pi$
$257$	1.44047	0.0898542	0.0449271	+	0.998990i	$0.485694\pi$
$258$	11.0860	0.690182
$259$	−57.0072	−3.54225
$260$	−10.8156	−0.670757
$261$	19.2955	1.19436
$262$	4.09751	0.253145
$263$	−3.19434	−0.196971	−0.0984857	−	0.995138i	$-0.531400\pi$
$263$	−3.19434	−0.196971	−0.0984857	+	0.995138i	$0.531400\pi$
$264$	−4.56296	−0.280831
$265$	44.4912	2.73307
$266$	−18.0566	−1.10712
$267$	14.1836	0.868021
$268$	−13.5762	−0.829299
$269$	19.0631	1.16230	0.581148	−	0.813798i	$-0.302604\pi$
$269$	19.0631	1.16230	0.581148	+	0.813798i	$0.302604\pi$
$270$	−7.03301	−0.428015
$271$	−12.9338	−0.785671	−0.392836	−	0.919609i	$-0.628506\pi$
$271$	−12.9338	−0.785671	−0.392836	+	0.919609i	$0.628506\pi$
$272$	1.11072	0.0673475
$273$	−35.6728	−2.15902
$274$	8.10123	0.489413
$275$	15.9978	0.964703
$276$	−9.77957	−0.588661
$277$	−7.46420	−0.448480	−0.224240	−	0.974534i	$-0.571990\pi$
$277$	−7.46420	−0.448480	−0.224240	+	0.974534i	$0.571990\pi$
$278$	−4.94676	−0.296687
$279$	19.6834	1.17841
$280$	−18.8394	−1.12587
$281$	−23.0207	−1.37330	−0.686649	−	0.726990i	$-0.740919\pi$
$281$	−23.0207	−1.37330	−0.686649	+	0.726990i	$0.740919\pi$
$282$	−2.17752	−0.129669
$283$	−1.63195	−0.0970094	−0.0485047	−	0.998823i	$-0.515446\pi$
$283$	−1.63195	−0.0970094	−0.0485047	+	0.998823i	$0.515446\pi$
$284$	12.2038	0.724161
$285$	−28.1266	−1.66608
$286$	6.05109	0.357808
$287$	21.5516	1.27215
$288$	2.13767	0.125963
$289$	−15.7663	−0.927429
$290$	−32.4787	−1.90722
$291$	29.2075	1.71218
$292$	2.37312	0.138877
$293$	−18.9296	−1.10588	−0.552939	−	0.833222i	$-0.686494\pi$
$293$	−18.9296	−1.10588	−0.552939	+	0.833222i	$0.686494\pi$
$294$	−46.2708	−2.69857
$295$	−51.3364	−2.98892
$296$	−10.8879	−0.632848
$297$	3.93480	0.228320
$298$	4.08858	0.236845
$299$	12.9690	0.750017
$300$	−18.0127	−1.03996
$301$	−25.6080	−1.47602
$302$	12.7626	0.734405
$303$	5.99369	0.344329
$304$	−3.44867	−0.197795
$305$	−20.6304	−1.18130
$306$	2.37435	0.135733
$307$	11.1296	0.635200	0.317600	−	0.948225i	$-0.397123\pi$
$307$	11.1296	0.635200	0.317600	+	0.948225i	$0.397123\pi$
$308$	10.5402	0.600583
$309$	−21.4001	−1.21741
$310$	−33.1317	−1.88175
$311$	2.25033	0.127604	0.0638022	−	0.997963i	$-0.479677\pi$
$311$	2.25033	0.127604	0.0638022	+	0.997963i	$0.479677\pi$
$312$	−6.81322	−0.385723
$313$	−7.44998	−0.421098	−0.210549	−	0.977583i	$-0.567525\pi$
$313$	−7.44998	−0.421098	−0.210549	+	0.977583i	$0.567525\pi$
$314$	−3.87868	−0.218887
$315$	−40.2723	−2.26909
$316$	−2.88134	−0.162088
$317$	19.3957	1.08937	0.544685	−	0.838640i	$-0.316649\pi$
$317$	19.3957	1.08937	0.544685	+	0.838640i	$0.316649\pi$
$318$	28.0269	1.57167
$319$	18.1711	1.01738
$320$	−3.59818	−0.201144
$321$	24.2288	1.35232
$322$	22.5903	1.25891
$323$	−3.83052	−0.213136
$324$	−10.8434	−0.602410
$325$	23.8872	1.32503
$326$	1.31142	0.0726327
$327$	27.3667	1.51338
$328$	4.11618	0.227278
$329$	5.02995	0.277310
$330$	16.4183	0.903800
$331$	11.2162	0.616501	0.308250	−	0.951305i	$-0.400257\pi$
$331$	11.2162	0.616501	0.308250	+	0.951305i	$0.400257\pi$
$332$	1.09009	0.0598265
$333$	−23.2747	−1.27545
$334$	22.7943	1.24725
$335$	48.8496	2.66894
$336$	−11.8677	−0.647438
$337$	−25.8274	−1.40691	−0.703455	−	0.710740i	$-0.748360\pi$
$337$	−25.8274	−1.40691	−0.703455	+	0.710740i	$0.748360\pi$
$338$	−3.96477	−0.215655
$339$	7.91835	0.430066
$340$	−3.99658	−0.216745
$341$	18.5364	1.00380
$342$	−7.37211	−0.398638
$343$	70.2322	3.79218
$344$	−4.89092	−0.263701
$345$	35.1886	1.89449
$346$	−16.2635	−0.874331
$347$	24.1631	1.29715	0.648573	−	0.761153i	$-0.275366\pi$
$347$	24.1631	1.29715	0.648573	+	0.761153i	$0.275366\pi$
$348$	−20.4597	−1.09676
$349$	21.4173	1.14644	0.573222	−	0.819400i	$-0.305693\pi$
$349$	21.4173	1.14644	0.573222	+	0.819400i	$0.305693\pi$
$350$	41.6084	2.22406
$351$	5.87528	0.313599
$352$	2.01309	0.107298
$353$	−9.47410	−0.504256	−0.252128	−	0.967694i	$-0.581130\pi$
$353$	−9.47410	−0.504256	−0.252128	+	0.967694i	$0.581130\pi$
$354$	−32.3389	−1.71880
$355$	−43.9113	−2.33057
$356$	−6.25753	−0.331649
$357$	−13.1818	−0.697653
$358$	24.9980	1.32119
$359$	10.6299	0.561025	0.280512	−	0.959850i	$-0.409496\pi$
$359$	10.6299	0.561025	0.280512	+	0.959850i	$0.409496\pi$
$360$	−7.69170	−0.405388
$361$	−7.10666	−0.374035
$362$	−1.34845	−0.0708729
$363$	15.7474	0.826524
$364$	15.7382	0.824904
$365$	−8.53892	−0.446947
$366$	−12.9960	−0.679311
$367$	28.8875	1.50792	0.753958	−	0.656923i	$-0.228142\pi$
$367$	28.8875	1.50792	0.753958	+	0.656923i	$0.228142\pi$
$368$	4.31456	0.224912
$369$	8.79902	0.458059
$370$	39.1767	2.03670
$371$	−64.7405	−3.36116
$372$	−20.8710	−1.08211
$373$	20.1587	1.04378	0.521888	−	0.853014i	$-0.325228\pi$
$373$	20.1587	1.04378	0.521888	+	0.853014i	$0.325228\pi$
$374$	2.23599	0.115620
$375$	24.0340	1.24111
$376$	0.960680	0.0495433
$377$	27.1323	1.39738
$378$	10.2340	0.526378
$379$	23.7210	1.21847	0.609234	−	0.792991i	$-0.291477\pi$
$379$	23.7210	1.21847	0.609234	+	0.792991i	$0.291477\pi$
$380$	12.4089	0.636565
$381$	38.9360	1.99475
$382$	0.653993	0.0334612
$383$	−6.38988	−0.326507	−0.163254	−	0.986584i	$-0.552199\pi$
$383$	−6.38988	−0.326507	−0.163254	+	0.986584i	$0.552199\pi$
$384$	−2.26664	−0.115669
$385$	−37.9255	−1.93286
$386$	21.8581	1.11255
$387$	−10.4551	−0.531465
$388$	−12.8858	−0.654178
$389$	−4.80209	−0.243476	−0.121738	−	0.992562i	$-0.538847\pi$
$389$	−4.80209	−0.243476	−0.121738	+	0.992562i	$0.538847\pi$
$390$	24.5152	1.24137
$391$	4.79229	0.242356
$392$	20.4138	1.03105
$393$	−9.28759	−0.468497
$394$	12.2454	0.616917
$395$	10.3676	0.521649
$396$	4.30332	0.216250
$397$	−3.61028	−0.181195	−0.0905973	−	0.995888i	$-0.528878\pi$
$397$	−3.61028	−0.181195	−0.0905973	+	0.995888i	$0.528878\pi$
$398$	−5.28835	−0.265081
$399$	40.9279	2.04896
$400$	7.94687	0.397344
$401$	−1.30873	−0.0653549	−0.0326774	−	0.999466i	$-0.510403\pi$
$401$	−1.30873	−0.0653549	−0.0326774	+	0.999466i	$0.510403\pi$
$402$	30.7724	1.53479
$403$	27.6777	1.37873
$404$	−2.64431	−0.131559
$405$	39.0164	1.93874
$406$	47.2608	2.34551
$407$	−21.9184	−1.08645
$408$	−2.51761	−0.124640
$409$	−5.04775	−0.249595	−0.124798	−	0.992182i	$-0.539828\pi$
$409$	−5.04775	−0.249595	−0.124798	+	0.992182i	$0.539828\pi$
$410$	−14.8108	−0.731451
$411$	−18.3626	−0.905760
$412$	9.44133	0.465141
$413$	74.7012	3.67581
$414$	9.22309	0.453290
$415$	−3.92234	−0.192540
$416$	3.00587	0.147375
$417$	11.2125	0.549080
$418$	−6.94250	−0.339569
$419$	20.1341	0.983613	0.491806	−	0.870705i	$-0.336337\pi$
$419$	20.1341	0.983613	0.491806	+	0.870705i	$0.336337\pi$
$420$	42.7022	2.08365
$421$	−9.36474	−0.456409	−0.228205	−	0.973613i	$-0.573286\pi$
$421$	−9.36474	−0.456409	−0.228205	+	0.973613i	$0.573286\pi$
$422$	20.3441	0.990334
$423$	2.05361	0.0998500
$424$	−12.3649	−0.600494
$425$	8.82678	0.428162
$426$	−27.6616	−1.34021
$427$	30.0200	1.45277
$428$	−10.6893	−0.516686
$429$	−13.7156	−0.662198
$430$	17.5984	0.848670
$431$	−21.1098	−1.01682	−0.508411	−	0.861114i	$-0.669767\pi$
$431$	−21.1098	−1.01682	−0.508411	+	0.861114i	$0.669767\pi$
$432$	1.95460	0.0940409
$433$	24.7569	1.18974	0.594871	−	0.803821i	$-0.297203\pi$
$433$	24.7569	1.18974	0.594871	+	0.803821i	$0.297203\pi$
$434$	48.2109	2.31420
$435$	73.6176	3.52970
$436$	−12.0737	−0.578224
$437$	−14.8795	−0.711784
$438$	−5.37902	−0.257020
$439$	−9.84039	−0.469656	−0.234828	−	0.972037i	$-0.575453\pi$
$439$	−9.84039	−0.469656	−0.234828	+	0.972037i	$0.575453\pi$
$440$	−7.24346	−0.345319
$441$	43.6379	2.07799
$442$	3.33869	0.158805
$443$	−28.1068	−1.33539	−0.667697	−	0.744433i	$-0.732720\pi$
$443$	−28.1068	−1.33539	−0.667697	+	0.744433i	$0.732720\pi$
$444$	24.6790	1.17121
$445$	22.5157	1.06735
$446$	−24.7192	−1.17049
$447$	−9.26736	−0.438331
$448$	5.23582	0.247369
$449$	−29.8059	−1.40663	−0.703314	−	0.710879i	$-0.748297\pi$
$449$	−29.8059	−1.40663	−0.703314	+	0.710879i	$0.748297\pi$
$450$	16.9878	0.800810
$451$	8.28626	0.390185
$452$	−3.49343	−0.164317
$453$	−28.9283	−1.35917
$454$	16.0602	0.753741
$455$	−56.6287	−2.65480
$456$	7.81690	0.366060
$457$	21.1693	0.990256	0.495128	−	0.868820i	$-0.335121\pi$
$457$	21.1693	0.990256	0.495128	+	0.868820i	$0.335121\pi$
$458$	9.09248	0.424864
$459$	2.17102	0.101335
$460$	−15.5246	−0.723837
$461$	6.26710	0.291888	0.145944	−	0.989293i	$-0.453378\pi$
$461$	6.26710	0.291888	0.145944	+	0.989293i	$0.453378\pi$
$462$	−23.8908	−1.11150
$463$	−9.66077	−0.448974	−0.224487	−	0.974477i	$-0.572071\pi$
$463$	−9.66077	−0.448974	−0.224487	+	0.974477i	$0.572071\pi$
$464$	9.02644	0.419042
$465$	75.0976	3.48257
$466$	9.69171	0.448960
$467$	−7.81856	−0.361800	−0.180900	−	0.983502i	$-0.557901\pi$
$467$	−7.81856	−0.361800	−0.180900	+	0.983502i	$0.557901\pi$
$468$	6.42554	0.297020
$469$	−71.0825	−3.28229
$470$	−3.45670	−0.159446
$471$	8.79158	0.405094
$472$	14.2673	0.656708
$473$	−9.84587	−0.452714
$474$	6.53097	0.299977
$475$	−27.4062	−1.25748
$476$	5.81555	0.266555
$477$	−26.4321	−1.21024
$478$	2.24615	0.102737
$479$	42.0733	1.92238	0.961190	−	0.275887i	$-0.0889715\pi$
$479$	42.0733	1.92238	0.961190	+	0.275887i	$0.0889715\pi$
$480$	8.15578	0.372259
$481$	−32.7276	−1.49225
$482$	2.60541	0.118673
$483$	−51.2041	−2.32987
$484$	−6.94746	−0.315794
$485$	46.3654	2.10535
$486$	18.7143	0.848896
$487$	21.5059	0.974526	0.487263	−	0.873255i	$-0.337995\pi$
$487$	21.5059	0.974526	0.487263	+	0.873255i	$0.337995\pi$
$488$	5.73358	0.259547
$489$	−2.97252	−0.134422
$490$	−73.4525	−3.31824
$491$	−4.72223	−0.213111	−0.106556	−	0.994307i	$-0.533982\pi$
$491$	−4.72223	−0.213111	−0.106556	+	0.994307i	$0.533982\pi$
$492$	−9.32992	−0.420625
$493$	10.0259	0.451543
$494$	−10.3662	−0.466399
$495$	−15.4841	−0.695958
$496$	9.20790	0.413447
$497$	63.8968	2.86616
$498$	−2.47084	−0.110721
$499$	−9.53738	−0.426952	−0.213476	−	0.976948i	$-0.568478\pi$
$499$	−9.53738	−0.426952	−0.213476	+	0.976948i	$0.568478\pi$
$500$	−10.6034	−0.474197
$501$	−51.6664	−2.30829
$502$	4.10121	0.183046
$503$	32.9334	1.46843	0.734214	−	0.678918i	$-0.237551\pi$
$503$	32.9334	1.46843	0.734214	+	0.678918i	$0.237551\pi$
$504$	11.1924	0.498550
$505$	9.51468	0.423398
$506$	8.68562	0.386123
$507$	8.98671	0.399114
$508$	−17.1778	−0.762143
$509$	−26.5228	−1.17560	−0.587801	−	0.809005i	$-0.700006\pi$
$509$	−26.5228	−1.17560	−0.587801	+	0.809005i	$0.700006\pi$
$510$	9.05881	0.401131
$511$	12.4252	0.549660
$512$	1.00000	0.0441942
$513$	−6.74079	−0.297613
$514$	1.44047	0.0635365
$515$	−33.9716	−1.49697
$516$	11.0860	0.488032
$517$	1.93394	0.0850545
$518$	−57.0072	−2.50475
$519$	36.8635	1.61813
$520$	−10.8156	−0.474297
$521$	16.3609	0.716786	0.358393	−	0.933571i	$-0.383325\pi$
$521$	16.3609	0.716786	0.358393	+	0.933571i	$0.383325\pi$
$522$	19.2955	0.844542
$523$	5.89310	0.257687	0.128844	−	0.991665i	$-0.458873\pi$
$523$	5.89310	0.257687	0.128844	+	0.991665i	$0.458873\pi$
$524$	4.09751	0.179001
$525$	−94.3113	−4.11608
$526$	−3.19434	−0.139280
$527$	10.2274	0.445514
$528$	−4.56296	−0.198577
$529$	−4.38453	−0.190632
$530$	44.4912	1.93257
$531$	30.4988	1.32353
$532$	−18.0566	−0.782854
$533$	12.3727	0.535921
$534$	14.1836	0.613784
$535$	38.4619	1.66285
$536$	−13.5762	−0.586403
$537$	−56.6616	−2.44513
$538$	19.0631	0.821867
$539$	41.0949	1.77008
$540$	−7.03301	−0.302653
$541$	18.9385	0.814231	0.407116	−	0.913377i	$-0.366535\pi$
$541$	18.9385	0.814231	0.407116	+	0.913377i	$0.366535\pi$
$542$	−12.9338	−0.555553
$543$	3.05645	0.131165
$544$	1.11072	0.0476219
$545$	43.4432	1.86090
$546$	−35.6728	−1.52665
$547$	5.01626	0.214480	0.107240	−	0.994233i	$-0.465799\pi$
$547$	5.01626	0.214480	0.107240	+	0.994233i	$0.465799\pi$
$548$	8.10123	0.346068
$549$	12.2565	0.523094
$550$	15.9978	0.682148
$551$	−31.1292	−1.32615
$552$	−9.77957	−0.416246
$553$	−15.0862	−0.641530
$554$	−7.46420	−0.317123
$555$	−88.7995	−3.76933
$556$	−4.94676	−0.209789
$557$	11.4194	0.483857	0.241928	−	0.970294i	$-0.422220\pi$
$557$	11.4194	0.483857	0.241928	+	0.970294i	$0.422220\pi$
$558$	19.6834	0.833265
$559$	−14.7014	−0.621805
$560$	−18.8394	−0.796110
$561$	−5.06819	−0.213979
$562$	−23.0207	−0.971068
$563$	36.1319	1.52278	0.761389	−	0.648296i	$-0.224518\pi$
$563$	36.1319	1.52278	0.761389	+	0.648296i	$0.224518\pi$
$564$	−2.17752	−0.0916900
$565$	12.5700	0.528822
$566$	−1.63195	−0.0685960
$567$	−56.7740	−2.38428
$568$	12.2038	0.512059
$569$	28.6210	1.19986	0.599928	−	0.800054i	$-0.295196\pi$
$569$	28.6210	1.19986	0.599928	+	0.800054i	$0.295196\pi$
$570$	−28.1266	−1.17809
$571$	17.9226	0.750038	0.375019	−	0.927017i	$-0.377636\pi$
$571$	17.9226	0.750038	0.375019	+	0.927017i	$0.377636\pi$
$572$	6.05109	0.253009
$573$	−1.48237	−0.0619268
$574$	21.5516	0.899546
$575$	34.2873	1.42988
$576$	2.13767	0.0890694
$577$	−16.3859	−0.682152	−0.341076	−	0.940036i	$-0.610791\pi$
$577$	−16.3859	−0.682152	−0.341076	+	0.940036i	$0.610791\pi$
$578$	−15.7663	−0.655791
$579$	−49.5446	−2.05900
$580$	−32.4787	−1.34861
$581$	5.70751	0.236788
$582$	29.2075	1.21069
$583$	−24.8917	−1.03091
$584$	2.37312	0.0982006
$585$	−23.1202	−0.955903
$586$	−18.9296	−0.781973
$587$	−6.87411	−0.283725	−0.141862	−	0.989886i	$-0.545309\pi$
$587$	−6.87411	−0.283725	−0.141862	+	0.989886i	$0.545309\pi$
$588$	−46.2708	−1.90817
$589$	−31.7550	−1.30844
$590$	−51.3364	−2.11349
$591$	−27.7560	−1.14173
$592$	−10.8879	−0.447491
$593$	−19.8432	−0.814863	−0.407432	−	0.913236i	$-0.633576\pi$
$593$	−19.8432	−0.814863	−0.407432	+	0.913236i	$0.633576\pi$
$594$	3.93480	0.161447
$595$	−20.9254	−0.857856
$596$	4.08858	0.167475
$597$	11.9868	0.490587
$598$	12.9690	0.530342
$599$	−19.6236	−0.801797	−0.400898	−	0.916123i	$-0.631302\pi$
$599$	−19.6236	−0.801797	−0.400898	+	0.916123i	$0.631302\pi$
$600$	−18.0127	−0.735366
$601$	31.8204	1.29798	0.648990	−	0.760797i	$-0.275192\pi$
$601$	31.8204	1.29798	0.648990	+	0.760797i	$0.275192\pi$
$602$	−25.6080	−1.04370
$603$	−29.0214	−1.18184
$604$	12.7626	0.519303
$605$	24.9982	1.01632
$606$	5.99369	0.243477
$607$	25.0076	1.01503	0.507513	−	0.861644i	$-0.330565\pi$
$607$	25.0076	1.01503	0.507513	+	0.861644i	$0.330565\pi$
$608$	−3.44867	−0.139862
$609$	−107.123	−4.34086
$610$	−20.6304	−0.835302
$611$	2.88768	0.116823
$612$	2.37435	0.0959776
$613$	−29.9021	−1.20773	−0.603866	−	0.797086i	$-0.706374\pi$
$613$	−29.9021	−1.20773	−0.603866	+	0.797086i	$0.706374\pi$
$614$	11.1296	0.449154
$615$	33.5707	1.35370
$616$	10.5402	0.424676
$617$	−44.0032	−1.77150	−0.885751	−	0.464162i	$-0.846356\pi$
$617$	−44.0032	−1.77150	−0.885751	+	0.464162i	$0.846356\pi$
$618$	−21.4001	−0.860839
$619$	23.0899	0.928062	0.464031	−	0.885819i	$-0.346403\pi$
$619$	23.0899	0.928062	0.464031	+	0.885819i	$0.346403\pi$
$620$	−33.1317	−1.33060
$621$	8.43327	0.338415
$622$	2.25033	0.0902299
$623$	−32.7633	−1.31263
$624$	−6.81322	−0.272747
$625$	−1.58157	−0.0632628
$626$	−7.44998	−0.297761
$627$	15.7362	0.628441
$628$	−3.87868	−0.154776
$629$	−12.0935	−0.482198
$630$	−40.2723	−1.60449
$631$	−18.4891	−0.736041	−0.368020	−	0.929818i	$-0.619964\pi$
$631$	−18.4891	−0.736041	−0.368020	+	0.929818i	$0.619964\pi$
$632$	−2.88134	−0.114614
$633$	−46.1127	−1.83282
$634$	19.3957	0.770301
$635$	61.8089	2.45281
$636$	28.0269	1.11134
$637$	61.3611	2.43122
$638$	18.1711	0.719399
$639$	26.0876	1.03201
$640$	−3.59818	−0.142230
$641$	24.2973	0.959684	0.479842	−	0.877355i	$-0.340694\pi$
$641$	24.2973	0.959684	0.479842	+	0.877355i	$0.340694\pi$
$642$	24.2288	0.956234
$643$	−33.7021	−1.32908	−0.664541	−	0.747252i	$-0.731373\pi$
$643$	−33.7021	−1.32908	−0.664541	+	0.747252i	$0.731373\pi$
$644$	22.5903	0.890182
$645$	−39.8892	−1.57064
$646$	−3.83052	−0.150710
$647$	−22.7905	−0.895987	−0.447993	−	0.894037i	$-0.647861\pi$
$647$	−22.7905	−0.895987	−0.447993	+	0.894037i	$0.647861\pi$
$648$	−10.8434	−0.425968
$649$	28.7215	1.12742
$650$	23.8872	0.936935
$651$	−109.277	−4.28290
$652$	1.31142	0.0513591
$653$	−44.8259	−1.75417	−0.877087	−	0.480331i	$-0.840517\pi$
$653$	−44.8259	−1.75417	−0.877087	+	0.480331i	$0.840517\pi$
$654$	27.3667	1.07012
$655$	−14.7436	−0.576079
$656$	4.11618	0.160710
$657$	5.07294	0.197914
$658$	5.02995	0.196088
$659$	21.3565	0.831932	0.415966	−	0.909380i	$-0.363443\pi$
$659$	21.3565	0.831932	0.415966	+	0.909380i	$0.363443\pi$
$660$	16.4183	0.639083
$661$	47.5760	1.85049	0.925246	−	0.379367i	$-0.123858\pi$
$661$	47.5760	1.85049	0.925246	+	0.379367i	$0.123858\pi$
$662$	11.2162	0.435932
$663$	−7.56761	−0.293901
$664$	1.09009	0.0423037
$665$	64.9709	2.51946
$666$	−23.2747	−0.901878
$667$	38.9452	1.50796
$668$	22.7943	0.881937
$669$	56.0297	2.16623
$670$	48.8496	1.88722
$671$	11.5422	0.445583
$672$	−11.8677	−0.457807
$673$	8.23132	0.317294	0.158647	−	0.987335i	$-0.449287\pi$
$673$	8.23132	0.317294	0.158647	+	0.987335i	$0.449287\pi$
$674$	−25.8274	−0.994836
$675$	15.5330	0.597865
$676$	−3.96477	−0.152491
$677$	−20.7326	−0.796820	−0.398410	−	0.917208i	$-0.630438\pi$
$677$	−20.7326	−0.796820	−0.398410	+	0.917208i	$0.630438\pi$
$678$	7.91835	0.304102
$679$	−67.4678	−2.58918
$680$	−3.99658	−0.153262
$681$	−36.4026	−1.39495
$682$	18.5364	0.709794
$683$	−24.6173	−0.941953	−0.470976	−	0.882146i	$-0.656098\pi$
$683$	−24.6173	−0.941953	−0.470976	+	0.882146i	$0.656098\pi$
$684$	−7.37211	−0.281880
$685$	−29.1497	−1.11375
$686$	70.2322	2.68148
$687$	−20.6094	−0.786297
$688$	−4.89092	−0.186465
$689$	−37.1673	−1.41596
$690$	35.1886	1.33961
$691$	−48.8600	−1.85872	−0.929361	−	0.369172i	$-0.879641\pi$
$691$	−48.8600	−1.85872	−0.929361	+	0.369172i	$0.879641\pi$
$692$	−16.2635	−0.618245
$693$	22.5314	0.855897
$694$	24.1631	0.917220
$695$	17.7993	0.675166
$696$	−20.4597	−0.775523
$697$	4.57194	0.173175
$698$	21.4173	0.810658
$699$	−21.9676	−0.830892
$700$	41.6084	1.57265
$701$	16.6301	0.628112	0.314056	−	0.949405i	$-0.398312\pi$
$701$	16.6301	0.628112	0.314056	+	0.949405i	$0.398312\pi$
$702$	5.87528	0.221748
$703$	37.5489	1.41618
$704$	2.01309	0.0758713
$705$	7.83509	0.295087
$706$	−9.47410	−0.356563
$707$	−13.8451	−0.520699
$708$	−32.3389	−1.21537
$709$	9.62712	0.361554	0.180777	−	0.983524i	$-0.442139\pi$
$709$	9.62712	0.361554	0.180777	+	0.983524i	$0.442139\pi$
$710$	−43.9113	−1.64796
$711$	−6.15934	−0.230993
$712$	−6.25753	−0.234511
$713$	39.7281	1.48783
$714$	−13.1818	−0.493315
$715$	−21.7729	−0.814260
$716$	24.9980	0.934220
$717$	−5.09122	−0.190135
$718$	10.6299	0.396705
$719$	−29.8043	−1.11151	−0.555756	−	0.831345i	$-0.687571\pi$
$719$	−29.8043	−1.11151	−0.555756	+	0.831345i	$0.687571\pi$
$720$	−7.69170	−0.286653
$721$	49.4331	1.84098
$722$	−7.10666	−0.264483
$723$	−5.90552	−0.219629
$724$	−1.34845	−0.0501147
$725$	71.7320	2.66406
$726$	15.7474	0.584441
$727$	−34.9891	−1.29767	−0.648837	−	0.760927i	$-0.724744\pi$
$727$	−34.9891	−1.29767	−0.648837	+	0.760927i	$0.724744\pi$
$728$	15.7382	0.583295
$729$	−9.88836	−0.366236
$730$	−8.53892	−0.316040
$731$	−5.43246	−0.200927
$732$	−12.9960	−0.480345
$733$	−26.5555	−0.980848	−0.490424	−	0.871484i	$-0.663158\pi$
$733$	−26.5555	−0.980848	−0.490424	+	0.871484i	$0.663158\pi$
$734$	28.8875	1.06626
$735$	166.490	6.14109
$736$	4.31456	0.159037
$737$	−27.3302	−1.00672
$738$	8.79902	0.323897
$739$	−41.0612	−1.51046	−0.755231	−	0.655459i	$-0.772475\pi$
$739$	−41.0612	−1.51046	−0.755231	+	0.655459i	$0.772475\pi$
$740$	39.1767	1.44016
$741$	23.4966	0.863168
$742$	−64.7405	−2.37670
$743$	−28.7074	−1.05317	−0.526586	−	0.850122i	$-0.676528\pi$
$743$	−28.7074	−1.05317	−0.526586	+	0.850122i	$0.676528\pi$
$744$	−20.8710	−0.765169
$745$	−14.7114	−0.538986
$746$	20.1587	0.738062
$747$	2.33025	0.0852593
$748$	2.23599	0.0817559
$749$	−55.9672	−2.04500
$750$	24.0340	0.877599
$751$	−33.3626	−1.21742	−0.608709	−	0.793393i	$-0.708312\pi$
$751$	−33.3626	−1.21742	−0.608709	+	0.793393i	$0.708312\pi$
$752$	0.960680	0.0350324
$753$	−9.29599	−0.338765
$754$	27.1323	0.988099
$755$	−45.9221	−1.67128
$756$	10.2340	0.372205
$757$	23.6921	0.861104	0.430552	−	0.902566i	$-0.358319\pi$
$757$	23.6921	0.861104	0.430552	+	0.902566i	$0.358319\pi$
$758$	23.7210	0.861587
$759$	−19.6872	−0.714600
$760$	12.4089	0.450119
$761$	35.0157	1.26932	0.634660	−	0.772792i	$-0.281140\pi$
$761$	35.0157	1.26932	0.634660	+	0.772792i	$0.281140\pi$
$762$	38.9360	1.41050
$763$	−63.2155	−2.28856
$764$	0.653993	0.0236606
$765$	−8.54335	−0.308885
$766$	−6.38988	−0.230876
$767$	42.8857	1.54851
$768$	−2.26664	−0.0817904
$769$	2.67614	0.0965039	0.0482519	−	0.998835i	$-0.484635\pi$
$769$	2.67614	0.0965039	0.0482519	+	0.998835i	$0.484635\pi$
$770$	−37.9255	−1.36674
$771$	−3.26503	−0.117587
$772$	21.8581	0.786692
$773$	−16.6333	−0.598259	−0.299130	−	0.954212i	$-0.596696\pi$
$773$	−16.6333	−0.598259	−0.299130	+	0.954212i	$0.596696\pi$
$774$	−10.4551	−0.375802
$775$	73.1740	2.62849
$776$	−12.8858	−0.462574
$777$	129.215	4.63556
$778$	−4.80209	−0.172163
$779$	−14.1954	−0.508602
$780$	24.5152	0.877784
$781$	24.5673	0.879088
$782$	4.79229	0.171372
$783$	17.6431	0.630514
$784$	20.4138	0.729064
$785$	13.9562	0.498117
$786$	−9.28759	−0.331277
$787$	−17.9095	−0.638406	−0.319203	−	0.947686i	$-0.603415\pi$
$787$	−17.9095	−0.638406	−0.319203	+	0.947686i	$0.603415\pi$
$788$	12.2454	0.436226
$789$	7.24042	0.257766
$790$	10.3676	0.368862
$791$	−18.2909	−0.650351
$792$	4.30332	0.152912
$793$	17.2344	0.612011
$794$	−3.61028	−0.128124
$795$	−100.846	−3.57662
$796$	−5.28835	−0.187441
$797$	−4.82893	−0.171049	−0.0855247	−	0.996336i	$-0.527257\pi$
$797$	−4.82893	−0.171049	−0.0855247	+	0.996336i	$0.527257\pi$
$798$	40.9279	1.44883
$799$	1.06705	0.0377495
$800$	7.94687	0.280964
$801$	−13.3765	−0.472636
$802$	−1.30873	−0.0462129
$803$	4.77732	0.168588
$804$	30.7724	1.08526
$805$	−81.2838	−2.86488
$806$	27.6777	0.974906
$807$	−43.2092	−1.52103
$808$	−2.64431	−0.0930263
$809$	2.36886	0.0832846	0.0416423	−	0.999133i	$-0.486741\pi$
$809$	2.36886	0.0832846	0.0416423	+	0.999133i	$0.486741\pi$
$810$	39.0164	1.37090
$811$	55.4206	1.94608	0.973040	−	0.230638i	$-0.0740812\pi$
$811$	55.4206	1.94608	0.973040	+	0.230638i	$0.0740812\pi$
$812$	47.2608	1.65853
$813$	29.3162	1.02817
$814$	−21.9184	−0.768239
$815$	−4.71871	−0.165289
$816$	−2.51761	−0.0881341
$817$	16.8672	0.590108
$818$	−5.04775	−0.176491
$819$	33.6429	1.17558
$820$	−14.8108	−0.517214
$821$	3.82800	0.133598	0.0667991	−	0.997766i	$-0.478721\pi$
$821$	3.82800	0.133598	0.0667991	+	0.997766i	$0.478721\pi$
$822$	−18.3626	−0.640469
$823$	11.2441	0.391946	0.195973	−	0.980609i	$-0.437214\pi$
$823$	11.2441	0.391946	0.195973	+	0.980609i	$0.437214\pi$
$824$	9.44133	0.328904
$825$	−36.2613	−1.26246
$826$	74.7012	2.59919
$827$	−22.0204	−0.765723	−0.382861	−	0.923806i	$-0.625061\pi$
$827$	−22.0204	−0.765723	−0.382861	+	0.923806i	$0.625061\pi$
$828$	9.22309	0.320525
$829$	−55.8105	−1.93838	−0.969189	−	0.246319i	$-0.920779\pi$
$829$	−55.8105	−1.93838	−0.969189	+	0.246319i	$0.920779\pi$
$830$	−3.92234	−0.136146
$831$	16.9187	0.586902
$832$	3.00587	0.104210
$833$	22.6741	0.785611
$834$	11.2125	0.388258
$835$	−82.0178	−2.83834
$836$	−6.94250	−0.240111
$837$	17.9978	0.622095
$838$	20.1341	0.695519
$839$	−44.5041	−1.53645	−0.768225	−	0.640180i	$-0.778860\pi$
$839$	−44.5041	−1.53645	−0.768225	+	0.640180i	$0.778860\pi$
$840$	42.7022	1.47336
$841$	52.4767	1.80954
$842$	−9.36474	−0.322730
$843$	52.1796	1.79716
$844$	20.3441	0.700272
$845$	14.2659	0.490763
$846$	2.05361	0.0706046
$847$	−36.3756	−1.24988
$848$	−12.3649	−0.424613
$849$	3.69905	0.126951
$850$	8.82678	0.302756
$851$	−46.9766	−1.61034
$852$	−27.6616	−0.947671
$853$	10.2257	0.350120	0.175060	−	0.984558i	$-0.443988\pi$
$853$	10.2257	0.350120	0.175060	+	0.984558i	$0.443988\pi$
$854$	30.0200	1.02726
$855$	26.5261	0.907175
$856$	−10.6893	−0.365352
$857$	31.5597	1.07806	0.539030	−	0.842287i	$-0.318791\pi$
$857$	31.5597	1.07806	0.539030	+	0.842287i	$0.318791\pi$
$858$	−13.7156	−0.468244
$859$	16.5991	0.566353	0.283176	−	0.959068i	$-0.408612\pi$
$859$	16.5991	0.566353	0.283176	+	0.959068i	$0.408612\pi$
$860$	17.5984	0.600100
$861$	−48.8497	−1.66479
$862$	−21.1098	−0.719002
$863$	−25.7572	−0.876785	−0.438393	−	0.898784i	$-0.644452\pi$
$863$	−25.7572	−0.876785	−0.438393	+	0.898784i	$0.644452\pi$
$864$	1.95460	0.0664970
$865$	58.5189	1.98970
$866$	24.7569	0.841275
$867$	35.7365	1.21368
$868$	48.2109	1.63638
$869$	−5.80041	−0.196765
$870$	73.6176	2.49587
$871$	−40.8082	−1.38273
$872$	−12.0737	−0.408866
$873$	−27.5456	−0.932276
$874$	−14.8795	−0.503307
$875$	−55.5173	−1.87683
$876$	−5.37902	−0.181740
$877$	−52.6052	−1.77635	−0.888176	−	0.459503i	$-0.848027\pi$
$877$	−52.6052	−1.77635	−0.888176	+	0.459503i	$0.848027\pi$
$878$	−9.84039	−0.332097
$879$	42.9065	1.44720
$880$	−7.24346	−0.244177
$881$	21.7504	0.732789	0.366395	−	0.930460i	$-0.380592\pi$
$881$	21.7504	0.732789	0.366395	+	0.930460i	$0.380592\pi$
$882$	43.6379	1.46936
$883$	−30.9957	−1.04309	−0.521544	−	0.853225i	$-0.674644\pi$
$883$	−30.9957	−1.04309	−0.521544	+	0.853225i	$0.674644\pi$
$884$	3.33869	0.112292
$885$	116.361	3.91144
$886$	−28.1068	−0.944266
$887$	25.2466	0.847698	0.423849	−	0.905733i	$-0.360679\pi$
$887$	25.2466	0.847698	0.423849	+	0.905733i	$0.360679\pi$
$888$	24.6790	0.828174
$889$	−89.9401	−3.01649
$890$	22.5157	0.754728
$891$	−21.8287	−0.731290
$892$	−24.7192	−0.827662
$893$	−3.31307	−0.110868
$894$	−9.26736	−0.309947
$895$	−89.9473	−3.00661
$896$	5.23582	0.174916
$897$	−29.3961	−0.981507
$898$	−29.8059	−0.994637
$899$	83.1146	2.77203
$900$	16.9878	0.566258
$901$	−13.7340	−0.457546
$902$	8.28626	0.275902
$903$	58.0441	1.93159
$904$	−3.49343	−0.116190
$905$	4.85196	0.161285
$906$	−28.9283	−0.961077
$907$	26.1826	0.869380	0.434690	−	0.900580i	$-0.356858\pi$
$907$	26.1826	0.869380	0.434690	+	0.900580i	$0.356858\pi$
$908$	16.0602	0.532975
$909$	−5.65264	−0.187486
$910$	−56.6287	−1.87722
$911$	20.2159	0.669783	0.334892	−	0.942257i	$-0.391300\pi$
$911$	20.2159	0.669783	0.334892	+	0.942257i	$0.391300\pi$
$912$	7.81690	0.258844
$913$	2.19445	0.0726258
$914$	21.1693	0.700217
$915$	46.7618	1.54590
$916$	9.09248	0.300424
$917$	21.4538	0.708467
$918$	2.17102	0.0716545
$919$	−29.3418	−0.967898	−0.483949	−	0.875096i	$-0.660798\pi$
$919$	−29.3418	−0.967898	−0.483949	+	0.875096i	$0.660798\pi$
$920$	−15.5246	−0.511830
$921$	−25.2268	−0.831252
$922$	6.26710	0.206396
$923$	36.6829	1.20743
$924$	−23.8908	−0.785951
$925$	−86.5249	−2.84492
$926$	−9.66077	−0.317473
$927$	20.1824	0.662877
$928$	9.02644	0.296307
$929$	58.8199	1.92982	0.964909	−	0.262584i	$-0.0845746\pi$
$929$	58.8199	1.92982	0.964909	+	0.262584i	$0.0845746\pi$
$930$	75.0976	2.46255
$931$	−70.4005	−2.30728
$932$	9.69171	0.317463
$933$	−5.10069	−0.166989
$934$	−7.81856	−0.255831
$935$	−8.04548	−0.263115
$936$	6.42554	0.210025
$937$	43.8177	1.43146	0.715730	−	0.698377i	$-0.246094\pi$
$937$	43.8177	1.43146	0.715730	+	0.698377i	$0.246094\pi$
$938$	−71.0825	−2.32093
$939$	16.8864	0.551068
$940$	−3.45670	−0.112745
$941$	25.3858	0.827553	0.413777	−	0.910378i	$-0.364209\pi$
$941$	25.3858	0.827553	0.413777	+	0.910378i	$0.364209\pi$
$942$	8.79158	0.286445
$943$	17.7595	0.578330
$944$	14.2673	0.464362
$945$	−36.8236	−1.19787
$946$	−9.84587	−0.320117
$947$	29.6199	0.962519	0.481259	−	0.876578i	$-0.340180\pi$
$947$	29.6199	0.962519	0.481259	+	0.876578i	$0.340180\pi$
$948$	6.53097	0.212116
$949$	7.13329	0.231556
$950$	−27.4062	−0.889173
$951$	−43.9631	−1.42560
$952$	5.81555	0.188483
$953$	11.2622	0.364820	0.182410	−	0.983223i	$-0.441610\pi$
$953$	11.2622	0.364820	0.182410	+	0.983223i	$0.441610\pi$
$954$	−26.4321	−0.855770
$955$	−2.35318	−0.0761472
$956$	2.24615	0.0726458
$957$	−41.1873	−1.33140
$958$	42.0733	1.35933
$959$	42.4166	1.36970
$960$	8.15578	0.263227
$961$	53.7855	1.73501
$962$	−32.7276	−1.05518
$963$	−22.8501	−0.736335
$964$	2.60541	0.0839145
$965$	−78.6495	−2.53182
$966$	−51.2041	−1.64746
$967$	11.4504	0.368220	0.184110	−	0.982906i	$-0.441060\pi$
$967$	11.4504	0.368220	0.184110	+	0.982906i	$0.441060\pi$
$968$	−6.94746	−0.223300
$969$	8.68242	0.278919
$970$	46.3654	1.48870
$971$	−18.4831	−0.593152	−0.296576	−	0.955009i	$-0.595845\pi$
$971$	−18.4831	−0.593152	−0.296576	+	0.955009i	$0.595845\pi$
$972$	18.7143	0.600260
$973$	−25.9003	−0.830326
$974$	21.5059	0.689094
$975$	−54.1438	−1.73399
$976$	5.73358	0.183528
$977$	55.0127	1.76001	0.880006	−	0.474963i	$-0.157539\pi$
$977$	55.0127	1.76001	0.880006	+	0.474963i	$0.157539\pi$
$978$	−2.97252	−0.0950506
$979$	−12.5970	−0.402602
$980$	−73.4525	−2.34635
$981$	−25.8095	−0.824033
$982$	−4.72223	−0.150693
$983$	−50.9210	−1.62413	−0.812064	−	0.583568i	$-0.801656\pi$
$983$	−50.9210	−1.62413	−0.812064	+	0.583568i	$0.801656\pi$
$984$	−9.32992	−0.297427
$985$	−44.0613	−1.40391
$986$	10.0259	0.319289
$987$	−11.4011	−0.362901
$988$	−10.3662	−0.329794
$989$	−21.1022	−0.671011
$990$	−15.4841	−0.492117
$991$	−16.3435	−0.519167	−0.259584	−	0.965721i	$-0.583585\pi$
$991$	−16.3435	−0.519167	−0.259584	+	0.965721i	$0.583585\pi$
$992$	9.20790	0.292351
$993$	−25.4232	−0.806781
$994$	63.8968	2.02668
$995$	19.0284	0.603241
$996$	−2.47084	−0.0782917
$997$	−0.699527	−0.0221543	−0.0110771	−	0.999939i	$-0.503526\pi$
$997$	−0.699527	−0.0221543	−0.0110771	+	0.999939i	$0.503526\pi$
$998$	−9.53738	−0.301901
$999$	−21.2816	−0.673319

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.d.1.19	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.d.1.19	✓	96	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:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.26664 q^{3} +1.00000 q^{4} -3.59818 q^{5} -2.26664 q^{6} +5.23582 q^{7} +1.00000 q^{8} +2.13767 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.26664 q^{3} +1.00000 q^{4} -3.59818 q^{5} -2.26664 q^{6} +5.23582 q^{7} +1.00000 q^{8} +2.13767 q^{9} -3.59818 q^{10} +2.01309 q^{11} -2.26664 q^{12} +3.00587 q^{13} +5.23582 q^{14} +8.15578 q^{15} +1.00000 q^{16} +1.11072 q^{17} +2.13767 q^{18} -3.44867 q^{19} -3.59818 q^{20} -11.8677 q^{21} +2.01309 q^{22} +4.31456 q^{23} -2.26664 q^{24} +7.94687 q^{25} +3.00587 q^{26} +1.95460 q^{27} +5.23582 q^{28} +9.02644 q^{29} +8.15578 q^{30} +9.20790 q^{31} +1.00000 q^{32} -4.56296 q^{33} +1.11072 q^{34} -18.8394 q^{35} +2.13767 q^{36} -10.8879 q^{37} -3.44867 q^{38} -6.81322 q^{39} -3.59818 q^{40} +4.11618 q^{41} -11.8677 q^{42} -4.89092 q^{43} +2.01309 q^{44} -7.69170 q^{45} +4.31456 q^{46} +0.960680 q^{47} -2.26664 q^{48} +20.4138 q^{49} +7.94687 q^{50} -2.51761 q^{51} +3.00587 q^{52} -12.3649 q^{53} +1.95460 q^{54} -7.24346 q^{55} +5.23582 q^{56} +7.81690 q^{57} +9.02644 q^{58} +14.2673 q^{59} +8.15578 q^{60} +5.73358 q^{61} +9.20790 q^{62} +11.1924 q^{63} +1.00000 q^{64} -10.8156 q^{65} -4.56296 q^{66} -13.5762 q^{67} +1.11072 q^{68} -9.77957 q^{69} -18.8394 q^{70} +12.2038 q^{71} +2.13767 q^{72} +2.37312 q^{73} -10.8879 q^{74} -18.0127 q^{75} -3.44867 q^{76} +10.5402 q^{77} -6.81322 q^{78} -2.88134 q^{79} -3.59818 q^{80} -10.8434 q^{81} +4.11618 q^{82} +1.09009 q^{83} -11.8677 q^{84} -3.99658 q^{85} -4.89092 q^{86} -20.4597 q^{87} +2.01309 q^{88} -6.25753 q^{89} -7.69170 q^{90} +15.7382 q^{91} +4.31456 q^{92} -20.8710 q^{93} +0.960680 q^{94} +12.4089 q^{95} -2.26664 q^{96} -12.8858 q^{97} +20.4138 q^{98} +4.30332 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9}+O(q^{10}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9} + 39 q^{10} + 36 q^{11} + 8 q^{12} + 63 q^{13} + 19 q^{14} + 17 q^{15} + 96 q^{16} + 56 q^{17} + 130 q^{18} + 17 q^{19} + 39 q^{20} + 51 q^{21} + 36 q^{22} + 47 q^{23} + 8 q^{24} + 147 q^{25} + 63 q^{26} + 17 q^{27} + 19 q^{28} + 60 q^{29} + 17 q^{30} + 63 q^{31} + 96 q^{32} + 55 q^{33} + 56 q^{34} + 45 q^{35} + 130 q^{36} + 46 q^{37} + 17 q^{38} + 22 q^{39} + 39 q^{40} + 101 q^{41} + 51 q^{42} - 3 q^{43} + 36 q^{44} + 106 q^{45} + 47 q^{46} + 99 q^{47} + 8 q^{48} + 175 q^{49} + 147 q^{50} - q^{51} + 63 q^{52} + 75 q^{53} + 17 q^{54} + 80 q^{55} + 19 q^{56} + 35 q^{57} + 60 q^{58} + 129 q^{59} + 17 q^{60} + 75 q^{61} + 63 q^{62} + 20 q^{63} + 96 q^{64} + 55 q^{65} + 55 q^{66} + 2 q^{67} + 56 q^{68} + 57 q^{69} + 45 q^{70} + 87 q^{71} + 130 q^{72} + 120 q^{73} + 46 q^{74} - 15 q^{75} + 17 q^{76} + 95 q^{77} + 22 q^{78} + 21 q^{79} + 39 q^{80} + 180 q^{81} + 101 q^{82} + 69 q^{83} + 51 q^{84} + 59 q^{85} - 3 q^{86} + 63 q^{87} + 36 q^{88} + 144 q^{89} + 106 q^{90} - 5 q^{91} + 47 q^{92} + 59 q^{93} + 99 q^{94} + 23 q^{95} + 8 q^{96} + 99 q^{97} + 175 q^{98} + 42 q^{99}+O(q^{100}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9 + 39 * q^10 + 36 * q^11 + 8 * q^12 + 63 * q^13 + 19 * q^14 + 17 * q^15 + 96 * q^16 + 56 * q^17 + 130 * q^18 + 17 * q^19 + 39 * q^20 + 51 * q^21 + 36 * q^22 + 47 * q^23 + 8 * q^24 + 147 * q^25 + 63 * q^26 + 17 * q^27 + 19 * q^28 + 60 * q^29 + 17 * q^30 + 63 * q^31 + 96 * q^32 + 55 * q^33 + 56 * q^34 + 45 * q^35 + 130 * q^36 + 46 * q^37 + 17 * q^38 + 22 * q^39 + 39 * q^40 + 101 * q^41 + 51 * q^42 - 3 * q^43 + 36 * q^44 + 106 * q^45 + 47 * q^46 + 99 * q^47 + 8 * q^48 + 175 * q^49 + 147 * q^50 - q^51 + 63 * q^52 + 75 * q^53 + 17 * q^54 + 80 * q^55 + 19 * q^56 + 35 * q^57 + 60 * q^58 + 129 * q^59 + 17 * q^60 + 75 * q^61 + 63 * q^62 + 20 * q^63 + 96 * q^64 + 55 * q^65 + 55 * q^66 + 2 * q^67 + 56 * q^68 + 57 * q^69 + 45 * q^70 + 87 * q^71 + 130 * q^72 + 120 * q^73 + 46 * q^74 - 15 * q^75 + 17 * q^76 + 95 * q^77 + 22 * q^78 + 21 * q^79 + 39 * q^80 + 180 * q^81 + 101 * q^82 + 69 * q^83 + 51 * q^84 + 59 * q^85 - 3 * q^86 + 63 * q^87 + 36 * q^88 + 144 * q^89 + 106 * q^90 - 5 * q^91 + 47 * q^92 + 59 * q^93 + 99 * q^94 + 23 * q^95 + 8 * q^96 + 99 * q^97 + 175 * q^98 + 42 * q^99

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