LMFDB - Embedded newform 8041.2.a.e.1.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$66$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.26
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.567481 q^{2} -2.99162 q^{3} -1.67797 q^{4} -1.94972 q^{5} +1.69769 q^{6} -4.52835 q^{7} +2.08718 q^{8} +5.94982 q^{9} +O(q^{10})$	\(q-0.567481 q^{2} -2.99162 q^{3} -1.67797 q^{4} -1.94972 q^{5} +1.69769 q^{6} -4.52835 q^{7} +2.08718 q^{8} +5.94982 q^{9} +1.10643 q^{10} -1.00000 q^{11} +5.01984 q^{12} -4.51065 q^{13} +2.56975 q^{14} +5.83284 q^{15} +2.17150 q^{16} -1.00000 q^{17} -3.37641 q^{18} +1.75796 q^{19} +3.27157 q^{20} +13.5471 q^{21} +0.567481 q^{22} +5.22945 q^{23} -6.24405 q^{24} -1.19858 q^{25} +2.55971 q^{26} -8.82474 q^{27} +7.59842 q^{28} -0.647842 q^{29} -3.31003 q^{30} +6.82939 q^{31} -5.40664 q^{32} +2.99162 q^{33} +0.567481 q^{34} +8.82903 q^{35} -9.98359 q^{36} -2.20875 q^{37} -0.997609 q^{38} +13.4942 q^{39} -4.06941 q^{40} +1.04663 q^{41} -7.68774 q^{42} +1.00000 q^{43} +1.67797 q^{44} -11.6005 q^{45} -2.96761 q^{46} -11.7925 q^{47} -6.49631 q^{48} +13.5060 q^{49} +0.680172 q^{50} +2.99162 q^{51} +7.56872 q^{52} +10.2123 q^{53} +5.00787 q^{54} +1.94972 q^{55} -9.45147 q^{56} -5.25916 q^{57} +0.367638 q^{58} -8.84733 q^{59} -9.78730 q^{60} -9.15436 q^{61} -3.87555 q^{62} -26.9429 q^{63} -1.27483 q^{64} +8.79453 q^{65} -1.69769 q^{66} -13.9159 q^{67} +1.67797 q^{68} -15.6445 q^{69} -5.01031 q^{70} +15.8525 q^{71} +12.4183 q^{72} -5.72531 q^{73} +1.25343 q^{74} +3.58570 q^{75} -2.94980 q^{76} +4.52835 q^{77} -7.65769 q^{78} -9.59456 q^{79} -4.23382 q^{80} +8.55087 q^{81} -0.593944 q^{82} -8.30780 q^{83} -22.7316 q^{84} +1.94972 q^{85} -0.567481 q^{86} +1.93810 q^{87} -2.08718 q^{88} +4.82690 q^{89} +6.58306 q^{90} +20.4258 q^{91} -8.77483 q^{92} -20.4310 q^{93} +6.69203 q^{94} -3.42754 q^{95} +16.1746 q^{96} +5.60304 q^{97} -7.66439 q^{98} -5.94982 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) $ 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9} + 13 q^{10} - 66 q^{11} + 9 q^{12} - 12 q^{13} + 25 q^{14} + 13 q^{15} + 47 q^{16} - 66 q^{17} + 37 q^{18} + 19 q^{20} + 26 q^{21} - 7 q^{22} + 47 q^{23} + 15 q^{24} + 52 q^{25} + 16 q^{26} + 9 q^{27} + 3 q^{28} + 57 q^{29} + 2 q^{30} + 31 q^{31} + 39 q^{32} - 3 q^{33} - 7 q^{34} + 36 q^{35} + 39 q^{36} - 14 q^{37} + 18 q^{38} + 71 q^{39} + 29 q^{40} + 62 q^{41} - 3 q^{42} + 66 q^{43} - 61 q^{44} - 2 q^{45} + 19 q^{46} + 32 q^{47} + 26 q^{48} + 42 q^{49} + 10 q^{50} - 3 q^{51} - 7 q^{52} + 33 q^{53} + 100 q^{54} - 4 q^{55} + 61 q^{56} + 35 q^{57} - 16 q^{58} + 59 q^{59} + 50 q^{60} + 26 q^{61} + 29 q^{62} + 62 q^{63} + 29 q^{64} + 55 q^{65} - 10 q^{66} + 5 q^{67} - 61 q^{68} - 36 q^{69} - 35 q^{70} + 128 q^{71} + 87 q^{72} + 23 q^{73} + 64 q^{74} - 11 q^{75} + 74 q^{76} - 14 q^{77} + 45 q^{78} + 39 q^{79} + 95 q^{80} + 54 q^{81} - 6 q^{82} + 48 q^{83} + 38 q^{84} - 4 q^{85} + 7 q^{86} + 14 q^{87} - 21 q^{88} + 28 q^{89} + 135 q^{90} - 18 q^{91} + 108 q^{92} - 9 q^{93} + 37 q^{94} + 149 q^{95} + 104 q^{96} + 19 q^{97} + 30 q^{98} - 65 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9 + 13 * q^10 - 66 * q^11 + 9 * q^12 - 12 * q^13 + 25 * q^14 + 13 * q^15 + 47 * q^16 - 66 * q^17 + 37 * q^18 + 19 * q^20 + 26 * q^21 - 7 * q^22 + 47 * q^23 + 15 * q^24 + 52 * q^25 + 16 * q^26 + 9 * q^27 + 3 * q^28 + 57 * q^29 + 2 * q^30 + 31 * q^31 + 39 * q^32 - 3 * q^33 - 7 * q^34 + 36 * q^35 + 39 * q^36 - 14 * q^37 + 18 * q^38 + 71 * q^39 + 29 * q^40 + 62 * q^41 - 3 * q^42 + 66 * q^43 - 61 * q^44 - 2 * q^45 + 19 * q^46 + 32 * q^47 + 26 * q^48 + 42 * q^49 + 10 * q^50 - 3 * q^51 - 7 * q^52 + 33 * q^53 + 100 * q^54 - 4 * q^55 + 61 * q^56 + 35 * q^57 - 16 * q^58 + 59 * q^59 + 50 * q^60 + 26 * q^61 + 29 * q^62 + 62 * q^63 + 29 * q^64 + 55 * q^65 - 10 * q^66 + 5 * q^67 - 61 * q^68 - 36 * q^69 - 35 * q^70 + 128 * q^71 + 87 * q^72 + 23 * q^73 + 64 * q^74 - 11 * q^75 + 74 * q^76 - 14 * q^77 + 45 * q^78 + 39 * q^79 + 95 * q^80 + 54 * q^81 - 6 * q^82 + 48 * q^83 + 38 * q^84 - 4 * q^85 + 7 * q^86 + 14 * q^87 - 21 * q^88 + 28 * q^89 + 135 * q^90 - 18 * q^91 + 108 * q^92 - 9 * q^93 + 37 * q^94 + 149 * q^95 + 104 * q^96 + 19 * q^97 + 30 * q^98 - 65 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.567481	−0.401270	−0.200635	−	0.979666i	$-0.564300\pi$
$2$	−0.567481	−0.401270	−0.200635	+	0.979666i	$0.564300\pi$
$3$	−2.99162	−1.72722	−0.863608	−	0.504165i	$-0.831800\pi$
$3$	−2.99162	−1.72722	−0.863608	+	0.504165i	$0.831800\pi$
$4$	−1.67797	−0.838983
$5$	−1.94972	−0.871943	−0.435971	−	0.899961i	$-0.643595\pi$
$5$	−1.94972	−0.871943	−0.435971	+	0.899961i	$0.643595\pi$
$6$	1.69769	0.693079
$7$	−4.52835	−1.71156	−0.855778	−	0.517343i	$-0.826921\pi$
$7$	−4.52835	−1.71156	−0.855778	+	0.517343i	$0.826921\pi$
$8$	2.08718	0.737928
$9$	5.94982	1.98327
$10$	1.10643	0.349884
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	5.01984	1.44910
$13$	−4.51065	−1.25103	−0.625515	−	0.780212i	$-0.715111\pi$
$13$	−4.51065	−1.25103	−0.625515	+	0.780212i	$0.715111\pi$
$14$	2.56975	0.686796
$15$	5.83284	1.50603
$16$	2.17150	0.542874
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−3.37641	−0.795827
$19$	1.75796	0.403304	0.201652	−	0.979457i	$-0.435369\pi$
$19$	1.75796	0.403304	0.201652	+	0.979457i	$0.435369\pi$
$20$	3.27157	0.731545
$21$	13.5471	2.95623
$22$	0.567481	0.120987
$23$	5.22945	1.09042	0.545208	−	0.838301i	$-0.316451\pi$
$23$	5.22945	1.09042	0.545208	+	0.838301i	$0.316451\pi$
$24$	−6.24405	−1.27456
$25$	−1.19858	−0.239716
$26$	2.55971	0.502001
$27$	−8.82474	−1.69832
$28$	7.59842	1.43597
$29$	−0.647842	−0.120301	−0.0601506	−	0.998189i	$-0.519158\pi$
$29$	−0.647842	−0.120301	−0.0601506	+	0.998189i	$0.519158\pi$
$30$	−3.31003	−0.604325
$31$	6.82939	1.22659	0.613297	−	0.789852i	$-0.289843\pi$
$31$	6.82939	1.22659	0.613297	+	0.789852i	$0.289843\pi$
$32$	−5.40664	−0.955767
$33$	2.99162	0.520775
$34$	0.567481	0.0973222
$35$	8.82903	1.49238
$36$	−9.98359	−1.66393
$37$	−2.20875	−0.363117	−0.181558	−	0.983380i	$-0.558114\pi$
$37$	−2.20875	−0.363117	−0.181558	+	0.983380i	$0.558114\pi$
$38$	−0.997609	−0.161834
$39$	13.4942	2.16080
$40$	−4.06941	−0.643431
$41$	1.04663	0.163456	0.0817282	−	0.996655i	$-0.473956\pi$
$41$	1.04663	0.163456	0.0817282	+	0.996655i	$0.473956\pi$
$42$	−7.68774	−1.18624
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	1.67797	0.252963
$45$	−11.6005	−1.72930
$46$	−2.96761	−0.437551
$47$	−11.7925	−1.72012	−0.860058	−	0.510196i	$-0.829573\pi$
$47$	−11.7925	−1.72012	−0.860058	+	0.510196i	$0.829573\pi$
$48$	−6.49631	−0.937661
$49$	13.5060	1.92943
$50$	0.680172	0.0961908
$51$	2.99162	0.418911
$52$	7.56872	1.04959
$53$	10.2123	1.40276	0.701381	−	0.712787i	$-0.252567\pi$
$53$	10.2123	1.40276	0.701381	+	0.712787i	$0.252567\pi$
$54$	5.00787	0.681485
$55$	1.94972	0.262901
$56$	−9.45147	−1.26301
$57$	−5.25916	−0.696593
$58$	0.367638	0.0482732
$59$	−8.84733	−1.15182	−0.575912	−	0.817512i	$-0.695353\pi$
$59$	−8.84733	−1.15182	−0.575912	+	0.817512i	$0.695353\pi$
$60$	−9.78730	−1.26354
$61$	−9.15436	−1.17210	−0.586048	−	0.810276i	$-0.699317\pi$
$61$	−9.15436	−1.17210	−0.586048	+	0.810276i	$0.699317\pi$
$62$	−3.87555	−0.492195
$63$	−26.9429	−3.39448
$64$	−1.27483	−0.159354
$65$	8.79453	1.09083
$66$	−1.69769	−0.208971
$67$	−13.9159	−1.70010	−0.850048	−	0.526705i	$-0.823427\pi$
$67$	−13.9159	−1.70010	−0.850048	+	0.526705i	$0.823427\pi$
$68$	1.67797	0.203483
$69$	−15.6445	−1.88338
$70$	−5.01031	−0.598847
$71$	15.8525	1.88135	0.940676	−	0.339307i	$-0.110193\pi$
$71$	15.8525	1.88135	0.940676	+	0.339307i	$0.110193\pi$
$72$	12.4183	1.46351
$73$	−5.72531	−0.670097	−0.335049	−	0.942201i	$-0.608753\pi$
$73$	−5.72531	−0.670097	−0.335049	+	0.942201i	$0.608753\pi$
$74$	1.25343	0.145708
$75$	3.58570	0.414041
$76$	−2.94980	−0.338365
$77$	4.52835	0.516054
$78$	−7.65769	−0.867063
$79$	−9.59456	−1.07947	−0.539736	−	0.841834i	$-0.681476\pi$
$79$	−9.59456	−1.07947	−0.539736	+	0.841834i	$0.681476\pi$
$80$	−4.23382	−0.473355
$81$	8.55087	0.950096
$82$	−0.593944	−0.0655901
$83$	−8.30780	−0.911899	−0.455950	−	0.890006i	$-0.650700\pi$
$83$	−8.30780	−0.911899	−0.455950	+	0.890006i	$0.650700\pi$
$84$	−22.7316	−2.48022
$85$	1.94972	0.211477
$86$	−0.567481	−0.0611931
$87$	1.93810	0.207786
$88$	−2.08718	−0.222494
$89$	4.82690	0.511650	0.255825	−	0.966723i	$-0.417653\pi$
$89$	4.82690	0.511650	0.255825	+	0.966723i	$0.417653\pi$
$90$	6.58306	0.693915
$91$	20.4258	2.14121
$92$	−8.77483	−0.914840
$93$	−20.4310	−2.11859
$94$	6.69203	0.690231
$95$	−3.42754	−0.351658
$96$	16.1746	1.65082
$97$	5.60304	0.568903	0.284451	−	0.958690i	$-0.408189\pi$
$97$	5.60304	0.568903	0.284451	+	0.958690i	$0.408189\pi$
$98$	−7.66439	−0.774220
$99$	−5.94982	−0.597979
$100$	2.01118	0.201118
$101$	−16.7712	−1.66880	−0.834400	−	0.551160i	$-0.814185\pi$
$101$	−16.7712	−1.66880	−0.834400	+	0.551160i	$0.814185\pi$
$102$	−1.69769	−0.168096
$103$	7.99415	0.787687	0.393844	−	0.919177i	$-0.371145\pi$
$103$	7.99415	0.787687	0.393844	+	0.919177i	$0.371145\pi$
$104$	−9.41453	−0.923171
$105$	−26.4132	−2.57766
$106$	−5.79526	−0.562886
$107$	−11.1186	−1.07487	−0.537436	−	0.843305i	$-0.680607\pi$
$107$	−11.1186	−1.07487	−0.537436	+	0.843305i	$0.680607\pi$
$108$	14.8076	1.42486
$109$	7.20403	0.690021	0.345011	−	0.938599i	$-0.387875\pi$
$109$	7.20403	0.690021	0.345011	+	0.938599i	$0.387875\pi$
$110$	−1.10643	−0.105494
$111$	6.60776	0.627181
$112$	−9.83331	−0.929160
$113$	−13.0813	−1.23059	−0.615295	−	0.788297i	$-0.710963\pi$
$113$	−13.0813	−1.23059	−0.615295	+	0.788297i	$0.710963\pi$
$114$	2.98447	0.279521
$115$	−10.1960	−0.950780
$116$	1.08706	0.100931
$117$	−26.8376	−2.48113
$118$	5.02069	0.462192
$119$	4.52835	0.415113
$120$	12.1742	1.11134
$121$	1.00000	0.0909091
$122$	5.19493	0.470327
$123$	−3.13113	−0.282324
$124$	−11.4595	−1.02909
$125$	12.0855	1.08096
$126$	15.2896	1.36210
$127$	8.74163	0.775694	0.387847	−	0.921724i	$-0.373219\pi$
$127$	8.74163	0.775694	0.387847	+	0.921724i	$0.373219\pi$
$128$	11.5367	1.01971
$129$	−2.99162	−0.263398
$130$	−4.99073	−0.437716
$131$	7.74566	0.676741	0.338371	−	0.941013i	$-0.390124\pi$
$131$	7.74566	0.676741	0.338371	+	0.941013i	$0.390124\pi$
$132$	−5.01984	−0.436921
$133$	−7.96067	−0.690277
$134$	7.89700	0.682197
$135$	17.2058	1.48084
$136$	−2.08718	−0.178974
$137$	−17.7477	−1.51629	−0.758145	−	0.652085i	$-0.773894\pi$
$137$	−17.7477	−1.51629	−0.758145	+	0.652085i	$0.773894\pi$
$138$	8.87798	0.755744
$139$	14.5957	1.23799	0.618997	−	0.785394i	$-0.287539\pi$
$139$	14.5957	1.23799	0.618997	+	0.785394i	$0.287539\pi$
$140$	−14.8148	−1.25208
$141$	35.2788	2.97101
$142$	−8.99602	−0.754929
$143$	4.51065	0.377200
$144$	12.9200	1.07667
$145$	1.26311	0.104896
$146$	3.24901	0.268890
$147$	−40.4048	−3.33253
$148$	3.70621	0.304649
$149$	−21.5648	−1.76666	−0.883330	−	0.468753i	$-0.844704\pi$
$149$	−21.5648	−1.76666	−0.883330	+	0.468753i	$0.844704\pi$
$150$	−2.03482	−0.166142
$151$	−12.1242	−0.986652	−0.493326	−	0.869845i	$-0.664219\pi$
$151$	−12.1242	−0.986652	−0.493326	+	0.869845i	$0.664219\pi$
$152$	3.66917	0.297609
$153$	−5.94982	−0.481014
$154$	−2.56975	−0.207077
$155$	−13.3154	−1.06952
$156$	−22.6428	−1.81287
$157$	−23.1185	−1.84506	−0.922530	−	0.385924i	$-0.873883\pi$
$157$	−23.1185	−1.84506	−0.922530	+	0.385924i	$0.873883\pi$
$158$	5.44473	0.433160
$159$	−30.5512	−2.42287
$160$	10.5414	0.833374
$161$	−23.6808	−1.86631
$162$	−4.85245	−0.381245
$163$	−3.95680	−0.309921	−0.154960	−	0.987921i	$-0.549525\pi$
$163$	−3.95680	−0.309921	−0.154960	+	0.987921i	$0.549525\pi$
$164$	−1.75621	−0.137137
$165$	−5.83284	−0.454086
$166$	4.71452	0.365918
$167$	−11.8414	−0.916312	−0.458156	−	0.888872i	$-0.651490\pi$
$167$	−11.8414	−0.916312	−0.458156	+	0.888872i	$0.651490\pi$
$168$	28.2752	2.18148
$169$	7.34601	0.565078
$170$	−1.10643	−0.0848594
$171$	10.4595	0.799861
$172$	−1.67797	−0.127944
$173$	12.4690	0.948002	0.474001	−	0.880524i	$-0.342809\pi$
$173$	12.4690	0.948002	0.474001	+	0.880524i	$0.342809\pi$
$174$	−1.09983	−0.0833782
$175$	5.42760	0.410288
$176$	−2.17150	−0.163683
$177$	26.4679	1.98945
$178$	−2.73917	−0.205310
$179$	−19.5216	−1.45911	−0.729556	−	0.683921i	$-0.760273\pi$
$179$	−19.5216	−1.45911	−0.729556	+	0.683921i	$0.760273\pi$
$180$	19.4652	1.45085
$181$	−17.3538	−1.28990	−0.644950	−	0.764225i	$-0.723122\pi$
$181$	−17.3538	−1.28990	−0.644950	+	0.764225i	$0.723122\pi$
$182$	−11.5913	−0.859203
$183$	27.3864	2.02446
$184$	10.9148	0.804648
$185$	4.30646	0.316617
$186$	11.5942	0.850127
$187$	1.00000	0.0731272
$188$	19.7874	1.44315
$189$	39.9616	2.90678
$190$	1.94506	0.141110
$191$	−3.78013	−0.273520	−0.136760	−	0.990604i	$-0.543669\pi$
$191$	−3.78013	−0.273520	−0.136760	+	0.990604i	$0.543669\pi$
$192$	3.81382	0.275239
$193$	4.99919	0.359850	0.179925	−	0.983680i	$-0.442415\pi$
$193$	4.99919	0.359850	0.179925	+	0.983680i	$0.442415\pi$
$194$	−3.17962	−0.228283
$195$	−26.3099	−1.88409
$196$	−22.6626	−1.61876
$197$	−5.02350	−0.357909	−0.178955	−	0.983857i	$-0.557272\pi$
$197$	−5.02350	−0.357909	−0.178955	+	0.983857i	$0.557272\pi$
$198$	3.37641	0.239951
$199$	−12.7590	−0.904461	−0.452230	−	0.891901i	$-0.649372\pi$
$199$	−12.7590	−0.904461	−0.452230	+	0.891901i	$0.649372\pi$
$200$	−2.50165	−0.176893
$201$	41.6311	2.93643
$202$	9.51735	0.669639
$203$	2.93366	0.205902
$204$	−5.01984	−0.351459
$205$	−2.04064	−0.142525
$206$	−4.53653	−0.316075
$207$	31.1143	2.16259
$208$	−9.79488	−0.679153
$209$	−1.75796	−0.121601
$210$	14.9890	1.03434
$211$	−11.1116	−0.764952	−0.382476	−	0.923965i	$-0.624928\pi$
$211$	−11.1116	−0.764952	−0.382476	+	0.923965i	$0.624928\pi$
$212$	−17.1358	−1.17689
$213$	−47.4249	−3.24950
$214$	6.30957	0.431314
$215$	−1.94972	−0.132970
$216$	−18.4188	−1.25324
$217$	−30.9259	−2.09939
$218$	−4.08815	−0.276885
$219$	17.1280	1.15740
$220$	−3.27157	−0.220569
$221$	4.51065	0.303419
$222$	−3.74978	−0.251669
$223$	−13.7999	−0.924107	−0.462053	−	0.886852i	$-0.652887\pi$
$223$	−13.7999	−0.924107	−0.462053	+	0.886852i	$0.652887\pi$
$224$	24.4832	1.63585
$225$	−7.13134	−0.475422
$226$	7.42342	0.493798
$227$	−13.1208	−0.870861	−0.435430	−	0.900222i	$-0.643404\pi$
$227$	−13.1208	−0.870861	−0.435430	+	0.900222i	$0.643404\pi$
$228$	8.82469	0.584429
$229$	−17.8861	−1.18195	−0.590974	−	0.806690i	$-0.701257\pi$
$229$	−17.8861	−1.18195	−0.590974	+	0.806690i	$0.701257\pi$
$230$	5.78602	0.381519
$231$	−13.5471	−0.891336
$232$	−1.35216	−0.0887736
$233$	4.54041	0.297452	0.148726	−	0.988878i	$-0.452483\pi$
$233$	4.54041	0.297452	0.148726	+	0.988878i	$0.452483\pi$
$234$	15.2298	0.995604
$235$	22.9922	1.49984
$236$	14.8455	0.966360
$237$	28.7033	1.86448
$238$	−2.56975	−0.166572
$239$	19.8217	1.28216	0.641081	−	0.767473i	$-0.278486\pi$
$239$	19.8217	1.28216	0.641081	+	0.767473i	$0.278486\pi$
$240$	12.6660	0.817587
$241$	6.60963	0.425764	0.212882	−	0.977078i	$-0.431715\pi$
$241$	6.60963	0.425764	0.212882	+	0.977078i	$0.431715\pi$
$242$	−0.567481	−0.0364791
$243$	0.893249	0.0573020
$244$	15.3607	0.983368
$245$	−26.3329	−1.68235
$246$	1.77686	0.113288
$247$	−7.92955	−0.504545
$248$	14.2541	0.905138
$249$	24.8538	1.57505
$250$	−6.85830	−0.433757
$251$	−22.5611	−1.42404	−0.712021	−	0.702158i	$-0.752220\pi$
$251$	−22.5611	−1.42404	−0.712021	+	0.702158i	$0.752220\pi$
$252$	45.2092	2.84791
$253$	−5.22945	−0.328773
$254$	−4.96071	−0.311263
$255$	−5.83284	−0.365267
$256$	−3.99720	−0.249825
$257$	−4.76111	−0.296990	−0.148495	−	0.988913i	$-0.547443\pi$
$257$	−4.76111	−0.296990	−0.148495	+	0.988913i	$0.547443\pi$
$258$	1.69769	0.105694
$259$	10.0020	0.621495
$260$	−14.7569	−0.915185
$261$	−3.85454	−0.238590
$262$	−4.39551	−0.271556
$263$	−6.07495	−0.374598	−0.187299	−	0.982303i	$-0.559973\pi$
$263$	−6.07495	−0.374598	−0.187299	+	0.982303i	$0.559973\pi$
$264$	6.24405	0.384294
$265$	−19.9111	−1.22313
$266$	4.51753	0.276987
$267$	−14.4403	−0.883730
$268$	23.3504	1.42635
$269$	1.15386	0.0703523	0.0351761	−	0.999381i	$-0.488801\pi$
$269$	1.15386	0.0703523	0.0351761	+	0.999381i	$0.488801\pi$
$270$	−9.76397	−0.594216
$271$	18.5163	1.12479	0.562394	−	0.826869i	$-0.309880\pi$
$271$	18.5163	1.12479	0.562394	+	0.826869i	$0.309880\pi$
$272$	−2.17150	−0.131666
$273$	−61.1064	−3.69833
$274$	10.0715	0.608442
$275$	1.19858	0.0722771
$276$	26.2510	1.58012
$277$	32.2726	1.93907	0.969536	−	0.244947i	$-0.0787706\pi$
$277$	32.2726	1.93907	0.969536	+	0.244947i	$0.0787706\pi$
$278$	−8.28280	−0.496769
$279$	40.6336	2.43267
$280$	18.4277	1.10127
$281$	30.6457	1.82817	0.914085	−	0.405524i	$-0.132911\pi$
$281$	30.6457	1.82817	0.914085	+	0.405524i	$0.132911\pi$
$282$	−20.0201	−1.19218
$283$	7.86802	0.467705	0.233853	−	0.972272i	$-0.424867\pi$
$283$	7.86802	0.467705	0.233853	+	0.972272i	$0.424867\pi$
$284$	−26.6000	−1.57842
$285$	10.2539	0.607389
$286$	−2.55971	−0.151359
$287$	−4.73952	−0.279765
$288$	−32.1685	−1.89555
$289$	1.00000	0.0588235
$290$	−0.716792	−0.0420915
$291$	−16.7622	−0.982617
$292$	9.60688	0.562200
$293$	−23.5581	−1.37628	−0.688139	−	0.725579i	$-0.741572\pi$
$293$	−23.5581	−1.37628	−0.688139	+	0.725579i	$0.741572\pi$
$294$	22.9290	1.33725
$295$	17.2498	1.00432
$296$	−4.61006	−0.267954
$297$	8.82474	0.512063
$298$	12.2376	0.708907
$299$	−23.5882	−1.36414
$300$	−6.01669	−0.347374
$301$	−4.52835	−0.261010
$302$	6.88024	0.395914
$303$	50.1732	2.88238
$304$	3.81741	0.218943
$305$	17.8485	1.02200
$306$	3.37641	0.193016
$307$	9.22784	0.526660	0.263330	−	0.964706i	$-0.415179\pi$
$307$	9.22784	0.526660	0.263330	+	0.964706i	$0.415179\pi$
$308$	−7.59842	−0.432960
$309$	−23.9155	−1.36051
$310$	7.55625	0.429166
$311$	−21.5917	−1.22436	−0.612178	−	0.790720i	$-0.709706\pi$
$311$	−21.5917	−1.22436	−0.612178	+	0.790720i	$0.709706\pi$
$312$	28.1647	1.59451
$313$	−13.4951	−0.762790	−0.381395	−	0.924412i	$-0.624556\pi$
$313$	−13.4951	−0.762790	−0.381395	+	0.924412i	$0.624556\pi$
$314$	13.1193	0.740367
$315$	52.5311	2.95979
$316$	16.0993	0.905659
$317$	−32.7300	−1.83830	−0.919151	−	0.393905i	$-0.871124\pi$
$317$	−32.7300	−1.83830	−0.919151	+	0.393905i	$0.871124\pi$
$318$	17.3373	0.972225
$319$	0.647842	0.0362722
$320$	2.48557	0.138948
$321$	33.2626	1.85653
$322$	13.4384	0.748893
$323$	−1.75796	−0.0978156
$324$	−14.3481	−0.797114
$325$	5.40638	0.299892
$326$	2.24541	0.124362
$327$	−21.5518	−1.19181
$328$	2.18450	0.120619
$329$	53.4007	2.94408
$330$	3.31003	0.182211
$331$	15.1389	0.832107	0.416054	−	0.909340i	$-0.363413\pi$
$331$	15.1389	0.832107	0.416054	+	0.909340i	$0.363413\pi$
$332$	13.9402	0.765068
$333$	−13.1417	−0.720159
$334$	6.71975	0.367688
$335$	27.1321	1.48239
$336$	29.4176	1.60486
$337$	−13.0762	−0.712304	−0.356152	−	0.934428i	$-0.615911\pi$
$337$	−13.0762	−0.712304	−0.356152	+	0.934428i	$0.615911\pi$
$338$	−4.16872	−0.226748
$339$	39.1345	2.12549
$340$	−3.27157	−0.177426
$341$	−6.82939	−0.369832
$342$	−5.93559	−0.320960
$343$	−29.4614	−1.59077
$344$	2.08718	0.112533
$345$	30.5025	1.64220
$346$	−7.07593	−0.380405
$347$	3.93218	0.211090	0.105545	−	0.994415i	$-0.466341\pi$
$347$	3.93218	0.211090	0.105545	+	0.994415i	$0.466341\pi$
$348$	−3.25206	−0.174329
$349$	0.131549	0.00704166	0.00352083	−	0.999994i	$-0.498879\pi$
$349$	0.131549	0.00704166	0.00352083	+	0.999994i	$0.498879\pi$
$350$	−3.08006	−0.164636
$351$	39.8054	2.12465
$352$	5.40664	0.288175
$353$	−28.5036	−1.51709	−0.758546	−	0.651619i	$-0.774090\pi$
$353$	−28.5036	−1.51709	−0.758546	+	0.651619i	$0.774090\pi$
$354$	−15.0200	−0.798305
$355$	−30.9081	−1.64043
$356$	−8.09936	−0.429265
$357$	−13.5471	−0.716990
$358$	11.0781	0.585497
$359$	27.8345	1.46905	0.734526	−	0.678581i	$-0.237405\pi$
$359$	27.8345	1.46905	0.734526	+	0.678581i	$0.237405\pi$
$360$	−24.2123	−1.27610
$361$	−15.9096	−0.837346
$362$	9.84797	0.517598
$363$	−2.99162	−0.157020
$364$	−34.2739	−1.79644
$365$	11.1628	0.584286
$366$	−15.5413	−0.812355
$367$	17.2828	0.902155	0.451078	−	0.892485i	$-0.351040\pi$
$367$	17.2828	0.902155	0.451078	+	0.892485i	$0.351040\pi$
$368$	11.3557	0.591959
$369$	6.22727	0.324179
$370$	−2.44383	−0.127049
$371$	−46.2447	−2.40091
$372$	34.2824	1.77746
$373$	−28.1896	−1.45960	−0.729800	−	0.683661i	$-0.760387\pi$
$373$	−28.1896	−1.45960	−0.729800	+	0.683661i	$0.760387\pi$
$374$	−0.567481	−0.0293437
$375$	−36.1553	−1.86705
$376$	−24.6131	−1.26932
$377$	2.92219	0.150500
$378$	−22.6774	−1.16640
$379$	16.2646	0.835455	0.417727	−	0.908572i	$-0.362827\pi$
$379$	16.2646	0.835455	0.417727	+	0.908572i	$0.362827\pi$
$380$	5.75129	0.295035
$381$	−26.1517	−1.33979
$382$	2.14515	0.109755
$383$	−21.9408	−1.12113	−0.560563	−	0.828112i	$-0.689415\pi$
$383$	−21.9408	−1.12113	−0.560563	+	0.828112i	$0.689415\pi$
$384$	−34.5135	−1.76126
$385$	−8.82903	−0.449969
$386$	−2.83695	−0.144397
$387$	5.94982	0.302446
$388$	−9.40171	−0.477299
$389$	−23.4369	−1.18830	−0.594148	−	0.804356i	$-0.702511\pi$
$389$	−23.4369	−1.18830	−0.594148	+	0.804356i	$0.702511\pi$
$390$	14.9304	0.756029
$391$	−5.22945	−0.264465
$392$	28.1894	1.42378
$393$	−23.1721	−1.16888
$394$	2.85074	0.143618
$395$	18.7067	0.941238
$396$	9.98359	0.501694
$397$	1.72452	0.0865509	0.0432755	−	0.999063i	$-0.486221\pi$
$397$	1.72452	0.0865509	0.0432755	+	0.999063i	$0.486221\pi$
$398$	7.24048	0.362933
$399$	23.8153	1.19226
$400$	−2.60272	−0.130136
$401$	12.0827	0.603382	0.301691	−	0.953406i	$-0.402449\pi$
$401$	12.0827	0.603382	0.301691	+	0.953406i	$0.402449\pi$
$402$	−23.6249	−1.17830
$403$	−30.8050	−1.53451
$404$	28.1415	1.40009
$405$	−16.6718	−0.828429
$406$	−1.66479	−0.0826224
$407$	2.20875	0.109484
$408$	6.24405	0.309126
$409$	−37.1657	−1.83772	−0.918862	−	0.394578i	$-0.870891\pi$
$409$	−37.1657	−1.83772	−0.918862	+	0.394578i	$0.870891\pi$
$410$	1.15803	0.0571908
$411$	53.0945	2.61896
$412$	−13.4139	−0.660856
$413$	40.0638	1.97141
$414$	−17.6568	−0.867782
$415$	16.1979	0.795124
$416$	24.3875	1.19569
$417$	−43.6649	−2.13828
$418$	0.997609	0.0487947
$419$	20.4069	0.996944	0.498472	−	0.866906i	$-0.333895\pi$
$419$	20.4069	0.996944	0.498472	+	0.866906i	$0.333895\pi$
$420$	44.3204	2.16261
$421$	0.489418	0.0238528	0.0119264	−	0.999929i	$-0.496204\pi$
$421$	0.489418	0.0238528	0.0119264	+	0.999929i	$0.496204\pi$
$422$	6.30560	0.306952
$423$	−70.1634	−3.41146
$424$	21.3148	1.03514
$425$	1.19858	0.0581397
$426$	26.9127	1.30393
$427$	41.4542	2.00611
$428$	18.6566	0.901799
$429$	−13.4942	−0.651505
$430$	1.10643	0.0533568
$431$	−5.44539	−0.262295	−0.131148	−	0.991363i	$-0.541866\pi$
$431$	−5.44539	−0.262295	−0.131148	+	0.991363i	$0.541866\pi$
$432$	−19.1629	−0.921976
$433$	2.67968	0.128777	0.0643886	−	0.997925i	$-0.479490\pi$
$433$	2.67968	0.128777	0.0643886	+	0.997925i	$0.479490\pi$
$434$	17.5499	0.842420
$435$	−3.77876	−0.181178
$436$	−12.0881	−0.578916
$437$	9.19317	0.439769
$438$	−9.71981	−0.464430
$439$	37.2233	1.77657	0.888285	−	0.459293i	$-0.151897\pi$
$439$	37.2233	1.77657	0.888285	+	0.459293i	$0.151897\pi$
$440$	4.06941	0.194002
$441$	80.3581	3.82658
$442$	−2.55971	−0.121753
$443$	34.9246	1.65932	0.829658	−	0.558272i	$-0.188535\pi$
$443$	34.9246	1.65932	0.829658	+	0.558272i	$0.188535\pi$
$444$	−11.0876	−0.526194
$445$	−9.41111	−0.446129
$446$	7.83116	0.370816
$447$	64.5138	3.05140
$448$	5.77289	0.272744
$449$	−19.6803	−0.928773	−0.464386	−	0.885633i	$-0.653725\pi$
$449$	−19.6803	−0.928773	−0.464386	+	0.885633i	$0.653725\pi$
$450$	4.04690	0.190773
$451$	−1.04663	−0.0492840
$452$	21.9500	1.03244
$453$	36.2710	1.70416
$454$	7.44583	0.349450
$455$	−39.8247	−1.86701
$456$	−10.9768	−0.514035
$457$	4.70539	0.220109	0.110055	−	0.993926i	$-0.464897\pi$
$457$	4.70539	0.220109	0.110055	+	0.993926i	$0.464897\pi$
$458$	10.1500	0.474280
$459$	8.82474	0.411904
$460$	17.1085	0.797688
$461$	37.6262	1.75243	0.876214	−	0.481922i	$-0.160061\pi$
$461$	37.6262	1.75243	0.876214	+	0.481922i	$0.160061\pi$
$462$	7.68774	0.357666
$463$	9.12471	0.424061	0.212031	−	0.977263i	$-0.431992\pi$
$463$	9.12471	0.424061	0.212031	+	0.977263i	$0.431992\pi$
$464$	−1.40679	−0.0653085
$465$	39.8347	1.84729
$466$	−2.57660	−0.119359
$467$	−18.2600	−0.844970	−0.422485	−	0.906370i	$-0.638842\pi$
$467$	−18.2600	−0.844970	−0.422485	+	0.906370i	$0.638842\pi$
$468$	45.0325	2.08163
$469$	63.0161	2.90981
$470$	−13.0476	−0.601841
$471$	69.1620	3.18682
$472$	−18.4659	−0.849963
$473$	−1.00000	−0.0459800
$474$	−16.2886	−0.748160
$475$	−2.10706	−0.0966785
$476$	−7.59842	−0.348273
$477$	60.7611	2.78206
$478$	−11.2485	−0.514493
$479$	−19.5311	−0.892401	−0.446200	−	0.894933i	$-0.647223\pi$
$479$	−19.5311	−0.892401	−0.446200	+	0.894933i	$0.647223\pi$
$480$	−31.5360	−1.43942
$481$	9.96292	0.454270
$482$	−3.75084	−0.170846
$483$	70.8440	3.22352
$484$	−1.67797	−0.0762711
$485$	−10.9244	−0.496050
$486$	−0.506902	−0.0229935
$487$	−6.94343	−0.314637	−0.157318	−	0.987548i	$-0.550285\pi$
$487$	−6.94343	−0.314637	−0.157318	+	0.987548i	$0.550285\pi$
$488$	−19.1068	−0.864923
$489$	11.8373	0.535300
$490$	14.9434	0.675076
$491$	8.42583	0.380252	0.190126	−	0.981760i	$-0.439110\pi$
$491$	8.42583	0.380252	0.190126	+	0.981760i	$0.439110\pi$
$492$	5.25393	0.236865
$493$	0.647842	0.0291773
$494$	4.49987	0.202459
$495$	11.6005	0.521403
$496$	14.8300	0.665887
$497$	−71.7859	−3.22004
$498$	−14.1041	−0.632018
$499$	−12.2473	−0.548263	−0.274131	−	0.961692i	$-0.588390\pi$
$499$	−12.2473	−0.548263	−0.274131	+	0.961692i	$0.588390\pi$
$500$	−20.2791	−0.906908
$501$	35.4249	1.58267
$502$	12.8030	0.571425
$503$	−27.1186	−1.20916	−0.604579	−	0.796545i	$-0.706659\pi$
$503$	−27.1186	−1.20916	−0.604579	+	0.796545i	$0.706659\pi$
$504$	−56.2345	−2.50488
$505$	32.6992	1.45510
$506$	2.96761	0.131926
$507$	−21.9765	−0.976010
$508$	−14.6682	−0.650794
$509$	−1.34139	−0.0594561	−0.0297281	−	0.999558i	$-0.509464\pi$
$509$	−1.34139	−0.0594561	−0.0297281	+	0.999558i	$0.509464\pi$
$510$	3.31003	0.146570
$511$	25.9262	1.14691
$512$	−20.8051	−0.919464
$513$	−15.5136	−0.684940
$514$	2.70184	0.119173
$515$	−15.5864	−0.686818
$516$	5.01984	0.220986
$517$	11.7925	0.518635
$518$	−5.67595	−0.249387
$519$	−37.3026	−1.63740
$520$	18.3557	0.804952
$521$	−22.0907	−0.967812	−0.483906	−	0.875120i	$-0.660782\pi$
$521$	−22.0907	−0.967812	−0.483906	+	0.875120i	$0.660782\pi$
$522$	2.18738	0.0957389
$523$	3.23864	0.141616	0.0708079	−	0.997490i	$-0.477442\pi$
$523$	3.23864	0.141616	0.0708079	+	0.997490i	$0.477442\pi$
$524$	−12.9969	−0.567774
$525$	−16.2373	−0.708655
$526$	3.44742	0.150315
$527$	−6.82939	−0.297493
$528$	6.49631	0.282715
$529$	4.34713	0.189006
$530$	11.2992	0.490804
$531$	−52.6400	−2.28438
$532$	13.3577	0.579131
$533$	−4.72100	−0.204489
$534$	8.19457	0.354614
$535$	21.6781	0.937227
$536$	−29.0449	−1.25455
$537$	58.4012	2.52020
$538$	−0.654795	−0.0282302
$539$	−13.5060	−0.581744
$540$	−28.8707	−1.24240
$541$	19.1720	0.824271	0.412135	−	0.911123i	$-0.364783\pi$
$541$	19.1720	0.824271	0.412135	+	0.911123i	$0.364783\pi$
$542$	−10.5077	−0.451343
$543$	51.9161	2.22793
$544$	5.40664	0.231808
$545$	−14.0459	−0.601659
$546$	34.6767	1.48403
$547$	−3.84604	−0.164445	−0.0822224	−	0.996614i	$-0.526202\pi$
$547$	−3.84604	−0.164445	−0.0822224	+	0.996614i	$0.526202\pi$
$548$	29.7801	1.27214
$549$	−54.4668	−2.32459
$550$	−0.680172	−0.0290026
$551$	−1.13888	−0.0485179
$552$	−32.6529	−1.38980
$553$	43.4476	1.84758
$554$	−18.3141	−0.778091
$555$	−12.8833	−0.546866
$556$	−24.4911	−1.03865
$557$	29.8978	1.26681	0.633405	−	0.773821i	$-0.281657\pi$
$557$	29.8978	1.26681	0.633405	+	0.773821i	$0.281657\pi$
$558$	−23.0588	−0.976157
$559$	−4.51065	−0.190780
$560$	19.1722	0.810175
$561$	−2.99162	−0.126306
$562$	−17.3909	−0.733589
$563$	23.7919	1.00271	0.501355	−	0.865242i	$-0.332835\pi$
$563$	23.7919	1.00271	0.501355	+	0.865242i	$0.332835\pi$
$564$	−59.1966	−2.49263
$565$	25.5050	1.07300
$566$	−4.46495	−0.187676
$567$	−38.7213	−1.62614
$568$	33.0870	1.38830
$569$	−39.7711	−1.66729	−0.833646	−	0.552299i	$-0.813751\pi$
$569$	−39.7711	−1.66729	−0.833646	+	0.552299i	$0.813751\pi$
$570$	−5.81889	−0.243727
$571$	7.69801	0.322152	0.161076	−	0.986942i	$-0.448504\pi$
$571$	7.69801	0.322152	0.161076	+	0.986942i	$0.448504\pi$
$572$	−7.56872	−0.316464
$573$	11.3087	0.472428
$574$	2.68959	0.112261
$575$	−6.26792	−0.261390
$576$	−7.58502	−0.316043
$577$	15.7890	0.657306	0.328653	−	0.944451i	$-0.393405\pi$
$577$	15.7890	0.657306	0.328653	+	0.944451i	$0.393405\pi$
$578$	−0.567481	−0.0236041
$579$	−14.9557	−0.621538
$580$	−2.11946	−0.0880057
$581$	37.6206	1.56077
$582$	9.51223	0.394294
$583$	−10.2123	−0.422949
$584$	−11.9497	−0.494484
$585$	52.3258	2.16341
$586$	13.3688	0.552258
$587$	−6.42453	−0.265169	−0.132584	−	0.991172i	$-0.542328\pi$
$587$	−6.42453	−0.265169	−0.132584	+	0.991172i	$0.542328\pi$
$588$	67.7979	2.79594
$589$	12.0058	0.494690
$590$	−9.78896	−0.403005
$591$	15.0284	0.618187
$592$	−4.79630	−0.197127
$593$	−11.2319	−0.461241	−0.230620	−	0.973044i	$-0.574076\pi$
$593$	−11.2319	−0.461241	−0.230620	+	0.973044i	$0.574076\pi$
$594$	−5.00787	−0.205476
$595$	−8.82903	−0.361955
$596$	36.1850	1.48220
$597$	38.1701	1.56220
$598$	13.3859	0.547389
$599$	33.8329	1.38238	0.691188	−	0.722675i	$-0.257088\pi$
$599$	33.8329	1.38238	0.691188	+	0.722675i	$0.257088\pi$
$600$	7.48399	0.305533
$601$	−20.5875	−0.839783	−0.419892	−	0.907574i	$-0.637932\pi$
$601$	−20.5875	−0.839783	−0.419892	+	0.907574i	$0.637932\pi$
$602$	2.56975	0.104735
$603$	−82.7970	−3.37175
$604$	20.3440	0.827784
$605$	−1.94972	−0.0792675
$606$	−28.4723	−1.15661
$607$	8.23220	0.334135	0.167067	−	0.985945i	$-0.446570\pi$
$607$	8.23220	0.334135	0.167067	+	0.985945i	$0.446570\pi$
$608$	−9.50465	−0.385465
$609$	−8.77640	−0.355638
$610$	−10.1287	−0.410098
$611$	53.1920	2.15192
$612$	9.98359	0.403563
$613$	30.9536	1.25021	0.625103	−	0.780542i	$-0.285057\pi$
$613$	30.9536	1.25021	0.625103	+	0.780542i	$0.285057\pi$
$614$	−5.23662	−0.211333
$615$	6.10484	0.246171
$616$	9.45147	0.380811
$617$	8.52288	0.343118	0.171559	−	0.985174i	$-0.445120\pi$
$617$	8.52288	0.343118	0.171559	+	0.985174i	$0.445120\pi$
$618$	13.5716	0.545930
$619$	0.689926	0.0277305	0.0138652	−	0.999904i	$-0.495586\pi$
$619$	0.689926	0.0277305	0.0138652	+	0.999904i	$0.495586\pi$
$620$	22.3428	0.897309
$621$	−46.1485	−1.85188
$622$	12.2529	0.491297
$623$	−21.8579	−0.875718
$624$	29.3026	1.17304
$625$	−17.5705	−0.702820
$626$	7.65823	0.306085
$627$	5.25916	0.210031
$628$	38.7921	1.54797
$629$	2.20875	0.0880687
$630$	−29.8104	−1.18768
$631$	−37.9470	−1.51065	−0.755324	−	0.655352i	$-0.772520\pi$
$631$	−37.9470	−1.51065	−0.755324	+	0.655352i	$0.772520\pi$
$632$	−20.0255	−0.796573
$633$	33.2416	1.32124
$634$	18.5737	0.737655
$635$	−17.0438	−0.676361
$636$	51.2639	2.03275
$637$	−60.9208	−2.41377
$638$	−0.367638	−0.0145549
$639$	94.3197	3.73123
$640$	−22.4934	−0.889129
$641$	−43.3522	−1.71231	−0.856155	−	0.516719i	$-0.827153\pi$
$641$	−43.3522	−1.71231	−0.856155	+	0.516719i	$0.827153\pi$
$642$	−18.8759	−0.744971
$643$	14.6766	0.578789	0.289394	−	0.957210i	$-0.406546\pi$
$643$	14.6766	0.578789	0.289394	+	0.957210i	$0.406546\pi$
$644$	39.7355	1.56580
$645$	5.83284	0.229668
$646$	0.997609	0.0392504
$647$	−2.60816	−0.102537	−0.0512687	−	0.998685i	$-0.516326\pi$
$647$	−2.60816	−0.102537	−0.0512687	+	0.998685i	$0.516326\pi$
$648$	17.8472	0.701103
$649$	8.84733	0.347288
$650$	−3.06802	−0.120338
$651$	92.5186	3.62609
$652$	6.63938	0.260018
$653$	−33.1682	−1.29797	−0.648987	−	0.760800i	$-0.724807\pi$
$653$	−33.1682	−1.29797	−0.648987	+	0.760800i	$0.724807\pi$
$654$	12.2302	0.478239
$655$	−15.1019	−0.590080
$656$	2.27276	0.0887363
$657$	−34.0646	−1.32899
$658$	−30.3039	−1.18137
$659$	25.1223	0.978625	0.489312	−	0.872109i	$-0.337248\pi$
$659$	25.1223	0.978625	0.489312	+	0.872109i	$0.337248\pi$
$660$	9.78730	0.380970
$661$	−42.9235	−1.66953	−0.834765	−	0.550606i	$-0.814397\pi$
$661$	−42.9235	−1.66953	−0.834765	+	0.550606i	$0.814397\pi$
$662$	−8.59102	−0.333899
$663$	−13.4942	−0.524071
$664$	−17.3398	−0.672916
$665$	15.5211	0.601882
$666$	7.45765	0.288978
$667$	−3.38786	−0.131178
$668$	19.8694	0.768770
$669$	41.2840	1.59613
$670$	−15.3970	−0.594837
$671$	9.15436	0.353400
$672$	−73.2444	−2.82546
$673$	30.8394	1.18877	0.594386	−	0.804180i	$-0.297395\pi$
$673$	30.8394	1.18877	0.594386	+	0.804180i	$0.297395\pi$
$674$	7.42047	0.285826
$675$	10.5772	0.407115
$676$	−12.3263	−0.474090
$677$	−9.04392	−0.347586	−0.173793	−	0.984782i	$-0.555602\pi$
$677$	−9.04392	−0.347586	−0.173793	+	0.984782i	$0.555602\pi$
$678$	−22.2081	−0.852896
$679$	−25.3725	−0.973709
$680$	4.06941	0.156055
$681$	39.2526	1.50416
$682$	3.87555	0.148402
$683$	−7.46942	−0.285810	−0.142905	−	0.989736i	$-0.545644\pi$
$683$	−7.46942	−0.285810	−0.142905	+	0.989736i	$0.545644\pi$
$684$	−17.5508	−0.671070
$685$	34.6032	1.32212
$686$	16.7188	0.638326
$687$	53.5086	2.04148
$688$	2.17150	0.0827876
$689$	−46.0640	−1.75490
$690$	−17.3096	−0.658965
$691$	−44.0782	−1.67682	−0.838408	−	0.545044i	$-0.816513\pi$
$691$	−44.0782	−1.67682	−0.838408	+	0.545044i	$0.816513\pi$
$692$	−20.9226	−0.795357
$693$	26.9429	1.02348
$694$	−2.23144	−0.0847042
$695$	−28.4576	−1.07946
$696$	4.04515	0.153331
$697$	−1.04663	−0.0396440
$698$	−0.0746517	−0.00282561
$699$	−13.5832	−0.513764
$700$	−9.10732	−0.344224
$701$	15.2255	0.575061	0.287530	−	0.957772i	$-0.407166\pi$
$701$	15.2255	0.575061	0.287530	+	0.957772i	$0.407166\pi$
$702$	−22.5888	−0.852559
$703$	−3.88290	−0.146446
$704$	1.27483	0.0480471
$705$	−68.7839	−2.59055
$706$	16.1752	0.608763
$707$	75.9460	2.85624
$708$	−44.4122	−1.66911
$709$	−39.9260	−1.49945	−0.749726	−	0.661749i	$-0.769815\pi$
$709$	−39.9260	−1.49945	−0.749726	+	0.661749i	$0.769815\pi$
$710$	17.5397	0.658255
$711$	−57.0859	−2.14089
$712$	10.0746	0.377561
$713$	35.7139	1.33750
$714$	7.68774	0.287706
$715$	−8.79453	−0.328897
$716$	32.7565	1.22417
$717$	−59.2992	−2.21457
$718$	−15.7956	−0.589486
$719$	−15.6534	−0.583774	−0.291887	−	0.956453i	$-0.594283\pi$
$719$	−15.6534	−0.583774	−0.291887	+	0.956453i	$0.594283\pi$
$720$	−25.1904	−0.938793
$721$	−36.2004	−1.34817
$722$	9.02838	0.336002
$723$	−19.7735	−0.735385
$724$	29.1191	1.08220
$725$	0.776491	0.0288381
$726$	1.69769	0.0630072
$727$	−1.27817	−0.0474045	−0.0237023	−	0.999719i	$-0.507545\pi$
$727$	−1.27817	−0.0474045	−0.0237023	+	0.999719i	$0.507545\pi$
$728$	42.6323	1.58006
$729$	−28.3249	−1.04907
$730$	−6.33466	−0.234456
$731$	−1.00000	−0.0369863
$732$	−45.9535	−1.69849
$733$	24.2402	0.895331	0.447665	−	0.894201i	$-0.352256\pi$
$733$	24.2402	0.895331	0.447665	+	0.894201i	$0.352256\pi$
$734$	−9.80767	−0.362008
$735$	78.7782	2.90578
$736$	−28.2737	−1.04218
$737$	13.9159	0.512598
$738$	−3.53386	−0.130083
$739$	32.0623	1.17943	0.589715	−	0.807612i	$-0.299240\pi$
$739$	32.0623	1.17943	0.589715	+	0.807612i	$0.299240\pi$
$740$	−7.22608	−0.265636
$741$	23.7222	0.871459
$742$	26.2430	0.963411
$743$	−29.0500	−1.06574	−0.532871	−	0.846196i	$-0.678887\pi$
$743$	−29.0500	−1.06574	−0.532871	+	0.846196i	$0.678887\pi$
$744$	−42.6430	−1.56337
$745$	42.0454	1.54043
$746$	15.9970	0.585693
$747$	−49.4299	−1.80854
$748$	−1.67797	−0.0613525
$749$	50.3488	1.83970
$750$	20.5175	0.749192
$751$	−2.92987	−0.106913	−0.0534563	−	0.998570i	$-0.517024\pi$
$751$	−2.92987	−0.106913	−0.0534563	+	0.998570i	$0.517024\pi$
$752$	−25.6074	−0.933807
$753$	67.4943	2.45963
$754$	−1.65829	−0.0603913
$755$	23.6388	0.860304
$756$	−67.0541	−2.43873
$757$	−36.9734	−1.34382	−0.671911	−	0.740632i	$-0.734526\pi$
$757$	−36.9734	−1.34382	−0.671911	+	0.740632i	$0.734526\pi$
$758$	−9.22984	−0.335243
$759$	15.6445	0.567861
$760$	−7.15387	−0.259498
$761$	−33.8688	−1.22774	−0.613871	−	0.789407i	$-0.710388\pi$
$761$	−33.8688	−1.22774	−0.613871	+	0.789407i	$0.710388\pi$
$762$	14.8406	0.537618
$763$	−32.6224	−1.18101
$764$	6.34292	0.229479
$765$	11.6005	0.419417
$766$	12.4510	0.449874
$767$	39.9072	1.44097
$768$	11.9581	0.431502
$769$	−20.7867	−0.749588	−0.374794	−	0.927108i	$-0.622287\pi$
$769$	−20.7867	−0.749588	−0.374794	+	0.927108i	$0.622287\pi$
$770$	5.01031	0.180559
$771$	14.2435	0.512966
$772$	−8.38847	−0.301908
$773$	−22.5885	−0.812453	−0.406226	−	0.913772i	$-0.633156\pi$
$773$	−22.5885	−0.812453	−0.406226	+	0.913772i	$0.633156\pi$
$774$	−3.37641	−0.121362
$775$	−8.18557	−0.294034
$776$	11.6945	0.419809
$777$	−29.9223	−1.07346
$778$	13.3000	0.476827
$779$	1.83994	0.0659226
$780$	44.1471	1.58072
$781$	−15.8525	−0.567249
$782$	2.96761	0.106122
$783$	5.71704	0.204310
$784$	29.3282	1.04744
$785$	45.0748	1.60879
$786$	13.1497	0.469035
$787$	−20.2975	−0.723528	−0.361764	−	0.932270i	$-0.617825\pi$
$787$	−20.2975	−0.723528	−0.361764	+	0.932270i	$0.617825\pi$
$788$	8.42926	0.300280
$789$	18.1740	0.647011
$790$	−10.6157	−0.377690
$791$	59.2370	2.10622
$792$	−12.4183	−0.441265
$793$	41.2922	1.46633
$794$	−0.978630	−0.0347303
$795$	59.5665	2.11260
$796$	21.4091	0.758827
$797$	−23.8470	−0.844706	−0.422353	−	0.906432i	$-0.638796\pi$
$797$	−23.8470	−0.844706	−0.422353	+	0.906432i	$0.638796\pi$
$798$	−13.5147	−0.478417
$799$	11.7925	0.417190
$800$	6.48029	0.229113
$801$	28.7191	1.01474
$802$	−6.85671	−0.242119
$803$	5.72531	0.202042
$804$	−69.8556	−2.46362
$805$	46.1710	1.62731
$806$	17.4813	0.615751
$807$	−3.45192	−0.121513
$808$	−35.0045	−1.23145
$809$	−29.3388	−1.03150	−0.515748	−	0.856740i	$-0.672486\pi$
$809$	−29.3388	−1.03150	−0.515748	+	0.856740i	$0.672486\pi$
$810$	9.46094	0.332424
$811$	−4.48456	−0.157474	−0.0787372	−	0.996895i	$-0.525089\pi$
$811$	−4.48456	−0.157474	−0.0787372	+	0.996895i	$0.525089\pi$
$812$	−4.92257	−0.172748
$813$	−55.3940	−1.94275
$814$	−1.25343	−0.0439325
$815$	7.71467	0.270233
$816$	6.49631	0.227416
$817$	1.75796	0.0615033
$818$	21.0908	0.737423
$819$	121.530	4.24660
$820$	3.42413	0.119576
$821$	0.991077	0.0345888	0.0172944	−	0.999850i	$-0.494495\pi$
$821$	0.991077	0.0345888	0.0172944	+	0.999850i	$0.494495\pi$
$822$	−30.1301	−1.05091
$823$	20.8204	0.725752	0.362876	−	0.931837i	$-0.381795\pi$
$823$	20.8204	0.725752	0.362876	+	0.931837i	$0.381795\pi$
$824$	16.6852	0.581257
$825$	−3.58570	−0.124838
$826$	−22.7355	−0.791068
$827$	−5.02135	−0.174609	−0.0873047	−	0.996182i	$-0.527825\pi$
$827$	−5.02135	−0.174609	−0.0873047	+	0.996182i	$0.527825\pi$
$828$	−52.2086	−1.81438
$829$	−40.1804	−1.39552	−0.697761	−	0.716331i	$-0.745820\pi$
$829$	−40.1804	−1.39552	−0.697761	+	0.716331i	$0.745820\pi$
$830$	−9.19200	−0.319059
$831$	−96.5475	−3.34920
$832$	5.75033	0.199357
$833$	−13.5060	−0.467955
$834$	24.7790	0.858027
$835$	23.0874	0.798971
$836$	2.94980	0.102021
$837$	−60.2676	−2.08315
$838$	−11.5805	−0.400043
$839$	27.4759	0.948573	0.474286	−	0.880371i	$-0.342706\pi$
$839$	27.4759	0.948573	0.474286	+	0.880371i	$0.342706\pi$
$840$	−55.1289	−1.90213
$841$	−28.5803	−0.985528
$842$	−0.277735	−0.00957139
$843$	−91.6804	−3.15764
$844$	18.6448	0.641781
$845$	−14.3227	−0.492715
$846$	39.8164	1.36892
$847$	−4.52835	−0.155596
$848$	22.1759	0.761524
$849$	−23.5382	−0.807828
$850$	−0.680172	−0.0233297
$851$	−11.5506	−0.395948
$852$	79.5773	2.72627
$853$	−30.9736	−1.06052	−0.530258	−	0.847836i	$-0.677905\pi$
$853$	−30.9736	−1.06052	−0.530258	+	0.847836i	$0.677905\pi$
$854$	−23.5245	−0.804991
$855$	−20.3932	−0.697433
$856$	−23.2064	−0.793178
$857$	−51.3239	−1.75319	−0.876596	−	0.481227i	$-0.840191\pi$
$857$	−51.3239	−1.75319	−0.876596	+	0.481227i	$0.840191\pi$
$858$	7.65769	0.261429
$859$	−37.7584	−1.28830	−0.644150	−	0.764899i	$-0.722789\pi$
$859$	−37.7584	−1.28830	−0.644150	+	0.764899i	$0.722789\pi$
$860$	3.27157	0.111560
$861$	14.1789	0.483214
$862$	3.09015	0.105251
$863$	−11.8772	−0.404304	−0.202152	−	0.979354i	$-0.564793\pi$
$863$	−11.8772	−0.404304	−0.202152	+	0.979354i	$0.564793\pi$
$864$	47.7122	1.62320
$865$	−24.3111	−0.826603
$866$	−1.52067	−0.0516744
$867$	−2.99162	−0.101601
$868$	51.8926	1.76135
$869$	9.59456	0.325473
$870$	2.14437	0.0727010
$871$	62.7698	2.12687
$872$	15.0361	0.509186
$873$	33.3371	1.12829
$874$	−5.21695	−0.176466
$875$	−54.7275	−1.85013
$876$	−28.7402	−0.971040
$877$	6.22858	0.210324	0.105162	−	0.994455i	$-0.466464\pi$
$877$	6.22858	0.210324	0.105162	+	0.994455i	$0.466464\pi$
$878$	−21.1235	−0.712884
$879$	70.4769	2.37713
$880$	4.23382	0.142722
$881$	38.9507	1.31228	0.656141	−	0.754639i	$-0.272188\pi$
$881$	38.9507	1.31228	0.656141	+	0.754639i	$0.272188\pi$
$882$	−45.6017	−1.53549
$883$	−7.05296	−0.237351	−0.118676	−	0.992933i	$-0.537865\pi$
$883$	−7.05296	−0.237351	−0.118676	+	0.992933i	$0.537865\pi$
$884$	−7.56872	−0.254564
$885$	−51.6050	−1.73468
$886$	−19.8190	−0.665833
$887$	7.96785	0.267534	0.133767	−	0.991013i	$-0.457293\pi$
$887$	7.96785	0.267534	0.133767	+	0.991013i	$0.457293\pi$
$888$	13.7916	0.462814
$889$	−39.5852	−1.32764
$890$	5.34063	0.179018
$891$	−8.55087	−0.286465
$892$	23.1557	0.775309
$893$	−20.7308	−0.693730
$894$	−36.6104	−1.22443
$895$	38.0617	1.27226
$896$	−52.2423	−1.74529
$897$	70.5671	2.35617
$898$	11.1682	0.372688
$899$	−4.42436	−0.147561
$900$	11.9661	0.398871
$901$	−10.2123	−0.340220
$902$	0.593944	0.0197762
$903$	13.5471	0.450820
$904$	−27.3031	−0.908087
$905$	33.8352	1.12472
$906$	−20.5831	−0.683828
$907$	−38.1760	−1.26761	−0.633806	−	0.773492i	$-0.718508\pi$
$907$	−38.1760	−1.26761	−0.633806	+	0.773492i	$0.718508\pi$
$908$	22.0163	0.730637
$909$	−99.7857	−3.30968
$910$	22.5998	0.749175
$911$	−3.21038	−0.106365	−0.0531823	−	0.998585i	$-0.516936\pi$
$911$	−3.21038	−0.106365	−0.0531823	+	0.998585i	$0.516936\pi$
$912$	−11.4203	−0.378162
$913$	8.30780	0.274948
$914$	−2.67022	−0.0883231
$915$	−53.3959	−1.76521
$916$	30.0123	0.991635
$917$	−35.0751	−1.15828
$918$	−5.00787	−0.165284
$919$	−16.2505	−0.536055	−0.268027	−	0.963411i	$-0.586372\pi$
$919$	−16.2505	−0.536055	−0.268027	+	0.963411i	$0.586372\pi$
$920$	−21.2808	−0.701607
$921$	−27.6062	−0.909656
$922$	−21.3522	−0.703197
$923$	−71.5054	−2.35363
$924$	22.7316	0.747815
$925$	2.64737	0.0870450
$926$	−5.17810	−0.170163
$927$	47.5637	1.56220
$928$	3.50264	0.114980
$929$	43.8292	1.43799	0.718995	−	0.695015i	$-0.244602\pi$
$929$	43.8292	1.43799	0.718995	+	0.695015i	$0.244602\pi$
$930$	−22.6054	−0.741262
$931$	23.7430	0.778145
$932$	−7.61865	−0.249557
$933$	64.5944	2.11473
$934$	10.3622	0.339061
$935$	−1.94972	−0.0637628
$936$	−56.0147	−1.83090
$937$	10.3549	0.338279	0.169139	−	0.985592i	$-0.445901\pi$
$937$	10.3549	0.338279	0.169139	+	0.985592i	$0.445901\pi$
$938$	−35.7604	−1.16762
$939$	40.3724	1.31750
$940$	−38.5800	−1.25834
$941$	−14.9199	−0.486375	−0.243187	−	0.969979i	$-0.578193\pi$
$941$	−14.9199	−0.486375	−0.243187	+	0.969979i	$0.578193\pi$
$942$	−39.2481	−1.27877
$943$	5.47331	0.178235
$944$	−19.2120	−0.625296
$945$	−77.9140	−2.53454
$946$	0.567481	0.0184504
$947$	27.7849	0.902887	0.451444	−	0.892300i	$-0.350909\pi$
$947$	27.7849	0.902887	0.451444	+	0.892300i	$0.350909\pi$
$948$	−48.1632	−1.56427
$949$	25.8249	0.838312
$950$	1.19572	0.0387941
$951$	97.9160	3.17514
$952$	9.45147	0.306324
$953$	−24.0083	−0.777706	−0.388853	−	0.921300i	$-0.627129\pi$
$953$	−24.0083	−0.777706	−0.388853	+	0.921300i	$0.627129\pi$
$954$	−34.4808	−1.11636
$955$	7.37020	0.238494
$956$	−33.2602	−1.07571
$957$	−1.93810	−0.0626499
$958$	11.0836	0.358093
$959$	80.3680	2.59522
$960$	−7.43589	−0.239992
$961$	15.6405	0.504534
$962$	−5.65377	−0.182285
$963$	−66.1534	−2.13176
$964$	−11.0907	−0.357208
$965$	−9.74704	−0.313768
$966$	−40.2026	−1.29350
$967$	−3.54521	−0.114006	−0.0570031	−	0.998374i	$-0.518154\pi$
$967$	−3.54521	−0.114006	−0.0570031	+	0.998374i	$0.518154\pi$
$968$	2.08718	0.0670844
$969$	5.25916	0.168949
$970$	6.19938	0.199050
$971$	−13.4349	−0.431146	−0.215573	−	0.976488i	$-0.569162\pi$
$971$	−13.4349	−0.431146	−0.215573	+	0.976488i	$0.569162\pi$
$972$	−1.49884	−0.0480754
$973$	−66.0946	−2.11890
$974$	3.94026	0.126254
$975$	−16.1739	−0.517978
$976$	−19.8787	−0.636301
$977$	44.9743	1.43885	0.719427	−	0.694568i	$-0.244404\pi$
$977$	44.9743	1.43885	0.719427	+	0.694568i	$0.244404\pi$
$978$	−6.71742	−0.214799
$979$	−4.82690	−0.154268
$980$	44.1857	1.41146
$981$	42.8627	1.36850
$982$	−4.78150	−0.152584
$983$	0.0285685	0.000911192 0	0.000455596	−	1.00000i	$-0.499855\pi$
$983$	0.0285685	0.000911192 0	0.000455596		1.00000i	$0.499855\pi$
$984$	−6.53522	−0.208335
$985$	9.79443	0.312076
$986$	−0.367638	−0.0117080
$987$	−159.755	−5.08505
$988$	13.3055	0.423305
$989$	5.22945	0.166287
$990$	−6.58306	−0.209223
$991$	−31.1636	−0.989944	−0.494972	−	0.868909i	$-0.664822\pi$
$991$	−31.1636	−0.989944	−0.494972	+	0.868909i	$0.664822\pi$
$992$	−36.9240	−1.17234
$993$	−45.2898	−1.43723
$994$	40.7372	1.29210
$995$	24.8765	0.788638
$996$	−41.7038	−1.32144
$997$	−36.4982	−1.15591	−0.577955	−	0.816069i	$-0.696149\pi$
$997$	−36.4982	−1.15591	−0.577955	+	0.816069i	$0.696149\pi$
$998$	6.95009	0.220001
$999$	19.4917	0.616689

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.e.1.26	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.e.1.26	✓	66	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-0.567481 q^{2} -2.99162 q^{3} -1.67797 q^{4} -1.94972 q^{5} +1.69769 q^{6} -4.52835 q^{7} +2.08718 q^{8} +5.94982 q^{9} +O(q^{10})\)	\(q-0.567481 q^{2} -2.99162 q^{3} -1.67797 q^{4} -1.94972 q^{5} +1.69769 q^{6} -4.52835 q^{7} +2.08718 q^{8} +5.94982 q^{9} +1.10643 q^{10} -1.00000 q^{11} +5.01984 q^{12} -4.51065 q^{13} +2.56975 q^{14} +5.83284 q^{15} +2.17150 q^{16} -1.00000 q^{17} -3.37641 q^{18} +1.75796 q^{19} +3.27157 q^{20} +13.5471 q^{21} +0.567481 q^{22} +5.22945 q^{23} -6.24405 q^{24} -1.19858 q^{25} +2.55971 q^{26} -8.82474 q^{27} +7.59842 q^{28} -0.647842 q^{29} -3.31003 q^{30} +6.82939 q^{31} -5.40664 q^{32} +2.99162 q^{33} +0.567481 q^{34} +8.82903 q^{35} -9.98359 q^{36} -2.20875 q^{37} -0.997609 q^{38} +13.4942 q^{39} -4.06941 q^{40} +1.04663 q^{41} -7.68774 q^{42} +1.00000 q^{43} +1.67797 q^{44} -11.6005 q^{45} -2.96761 q^{46} -11.7925 q^{47} -6.49631 q^{48} +13.5060 q^{49} +0.680172 q^{50} +2.99162 q^{51} +7.56872 q^{52} +10.2123 q^{53} +5.00787 q^{54} +1.94972 q^{55} -9.45147 q^{56} -5.25916 q^{57} +0.367638 q^{58} -8.84733 q^{59} -9.78730 q^{60} -9.15436 q^{61} -3.87555 q^{62} -26.9429 q^{63} -1.27483 q^{64} +8.79453 q^{65} -1.69769 q^{66} -13.9159 q^{67} +1.67797 q^{68} -15.6445 q^{69} -5.01031 q^{70} +15.8525 q^{71} +12.4183 q^{72} -5.72531 q^{73} +1.25343 q^{74} +3.58570 q^{75} -2.94980 q^{76} +4.52835 q^{77} -7.65769 q^{78} -9.59456 q^{79} -4.23382 q^{80} +8.55087 q^{81} -0.593944 q^{82} -8.30780 q^{83} -22.7316 q^{84} +1.94972 q^{85} -0.567481 q^{86} +1.93810 q^{87} -2.08718 q^{88} +4.82690 q^{89} +6.58306 q^{90} +20.4258 q^{91} -8.77483 q^{92} -20.4310 q^{93} +6.69203 q^{94} -3.42754 q^{95} +16.1746 q^{96} +5.60304 q^{97} -7.66439 q^{98} -5.94982 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9} + 13 q^{10} - 66 q^{11} + 9 q^{12} - 12 q^{13} + 25 q^{14} + 13 q^{15} + 47 q^{16} - 66 q^{17} + 37 q^{18} + 19 q^{20} + 26 q^{21} - 7 q^{22} + 47 q^{23} + 15 q^{24} + 52 q^{25} + 16 q^{26} + 9 q^{27} + 3 q^{28} + 57 q^{29} + 2 q^{30} + 31 q^{31} + 39 q^{32} - 3 q^{33} - 7 q^{34} + 36 q^{35} + 39 q^{36} - 14 q^{37} + 18 q^{38} + 71 q^{39} + 29 q^{40} + 62 q^{41} - 3 q^{42} + 66 q^{43} - 61 q^{44} - 2 q^{45} + 19 q^{46} + 32 q^{47} + 26 q^{48} + 42 q^{49} + 10 q^{50} - 3 q^{51} - 7 q^{52} + 33 q^{53} + 100 q^{54} - 4 q^{55} + 61 q^{56} + 35 q^{57} - 16 q^{58} + 59 q^{59} + 50 q^{60} + 26 q^{61} + 29 q^{62} + 62 q^{63} + 29 q^{64} + 55 q^{65} - 10 q^{66} + 5 q^{67} - 61 q^{68} - 36 q^{69} - 35 q^{70} + 128 q^{71} + 87 q^{72} + 23 q^{73} + 64 q^{74} - 11 q^{75} + 74 q^{76} - 14 q^{77} + 45 q^{78} + 39 q^{79} + 95 q^{80} + 54 q^{81} - 6 q^{82} + 48 q^{83} + 38 q^{84} - 4 q^{85} + 7 q^{86} + 14 q^{87} - 21 q^{88} + 28 q^{89} + 135 q^{90} - 18 q^{91} + 108 q^{92} - 9 q^{93} + 37 q^{94} + 149 q^{95} + 104 q^{96} + 19 q^{97} + 30 q^{98} - 65 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9 + 13 * q^10 - 66 * q^11 + 9 * q^12 - 12 * q^13 + 25 * q^14 + 13 * q^15 + 47 * q^16 - 66 * q^17 + 37 * q^18 + 19 * q^20 + 26 * q^21 - 7 * q^22 + 47 * q^23 + 15 * q^24 + 52 * q^25 + 16 * q^26 + 9 * q^27 + 3 * q^28 + 57 * q^29 + 2 * q^30 + 31 * q^31 + 39 * q^32 - 3 * q^33 - 7 * q^34 + 36 * q^35 + 39 * q^36 - 14 * q^37 + 18 * q^38 + 71 * q^39 + 29 * q^40 + 62 * q^41 - 3 * q^42 + 66 * q^43 - 61 * q^44 - 2 * q^45 + 19 * q^46 + 32 * q^47 + 26 * q^48 + 42 * q^49 + 10 * q^50 - 3 * q^51 - 7 * q^52 + 33 * q^53 + 100 * q^54 - 4 * q^55 + 61 * q^56 + 35 * q^57 - 16 * q^58 + 59 * q^59 + 50 * q^60 + 26 * q^61 + 29 * q^62 + 62 * q^63 + 29 * q^64 + 55 * q^65 - 10 * q^66 + 5 * q^67 - 61 * q^68 - 36 * q^69 - 35 * q^70 + 128 * q^71 + 87 * q^72 + 23 * q^73 + 64 * q^74 - 11 * q^75 + 74 * q^76 - 14 * q^77 + 45 * q^78 + 39 * q^79 + 95 * q^80 + 54 * q^81 - 6 * q^82 + 48 * q^83 + 38 * q^84 - 4 * q^85 + 7 * q^86 + 14 * q^87 - 21 * q^88 + 28 * q^89 + 135 * q^90 - 18 * q^91 + 108 * q^92 - 9 * q^93 + 37 * q^94 + 149 * q^95 + 104 * q^96 + 19 * q^97 + 30 * q^98 - 65 * q^99

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