LMFDB - Embedded newform 8041.2.a.d.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.34818 q^{2} -2.19319 q^{3} -0.182400 q^{4} -0.782983 q^{5} +2.95682 q^{6} -4.69818 q^{7} +2.94228 q^{8} +1.81007 q^{9} +O(q^{10})$	\(q-1.34818 q^{2} -2.19319 q^{3} -0.182400 q^{4} -0.782983 q^{5} +2.95682 q^{6} -4.69818 q^{7} +2.94228 q^{8} +1.81007 q^{9} +1.05561 q^{10} +1.00000 q^{11} +0.400037 q^{12} +6.86395 q^{13} +6.33401 q^{14} +1.71723 q^{15} -3.60193 q^{16} -1.00000 q^{17} -2.44031 q^{18} +0.927929 q^{19} +0.142816 q^{20} +10.3040 q^{21} -1.34818 q^{22} -9.01514 q^{23} -6.45296 q^{24} -4.38694 q^{25} -9.25386 q^{26} +2.60974 q^{27} +0.856946 q^{28} +6.25934 q^{29} -2.31514 q^{30} -1.66386 q^{31} -1.02849 q^{32} -2.19319 q^{33} +1.34818 q^{34} +3.67859 q^{35} -0.330156 q^{36} -5.93563 q^{37} -1.25102 q^{38} -15.0539 q^{39} -2.30375 q^{40} -5.54604 q^{41} -13.8917 q^{42} +1.00000 q^{43} -0.182400 q^{44} -1.41725 q^{45} +12.1541 q^{46} -1.07693 q^{47} +7.89971 q^{48} +15.0729 q^{49} +5.91440 q^{50} +2.19319 q^{51} -1.25198 q^{52} -1.01410 q^{53} -3.51841 q^{54} -0.782983 q^{55} -13.8233 q^{56} -2.03512 q^{57} -8.43874 q^{58} -6.92875 q^{59} -0.313222 q^{60} -9.86359 q^{61} +2.24319 q^{62} -8.50402 q^{63} +8.59045 q^{64} -5.37435 q^{65} +2.95682 q^{66} +6.59360 q^{67} +0.182400 q^{68} +19.7719 q^{69} -4.95942 q^{70} -4.29550 q^{71} +5.32572 q^{72} +3.59186 q^{73} +8.00233 q^{74} +9.62137 q^{75} -0.169254 q^{76} -4.69818 q^{77} +20.2955 q^{78} -7.57183 q^{79} +2.82025 q^{80} -11.1539 q^{81} +7.47708 q^{82} +15.4706 q^{83} -1.87944 q^{84} +0.782983 q^{85} -1.34818 q^{86} -13.7279 q^{87} +2.94228 q^{88} +4.90723 q^{89} +1.91072 q^{90} -32.2480 q^{91} +1.64436 q^{92} +3.64916 q^{93} +1.45190 q^{94} -0.726553 q^{95} +2.25566 q^{96} +13.7807 q^{97} -20.3210 q^{98} +1.81007 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9}+O(q^{10}) $ 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9} - 7 q^{10} + 62 q^{11} - 17 q^{12} - 31 q^{14} - 20 q^{15} + 27 q^{16} - 62 q^{17} + 3 q^{18} - 29 q^{20} - 18 q^{21} - 7 q^{22} - 50 q^{23} - 31 q^{24} + 35 q^{25} - 32 q^{26} - 14 q^{27} - 13 q^{28} - 26 q^{29} - 10 q^{30} - 58 q^{31} - 5 q^{32} - 8 q^{33} + 7 q^{34} - 32 q^{35} - 29 q^{36} - 41 q^{37} - 10 q^{38} - 53 q^{39} - 31 q^{40} - 55 q^{41} - 7 q^{42} + 62 q^{43} + 49 q^{44} - 34 q^{45} - 39 q^{46} - 31 q^{47} - 30 q^{48} + 35 q^{49} - 40 q^{50} + 8 q^{51} + 13 q^{52} - 74 q^{53} + 48 q^{54} - 13 q^{55} - 75 q^{56} - 43 q^{57} - 46 q^{58} - 65 q^{59} - 8 q^{60} - 14 q^{61} - 29 q^{62} - 23 q^{63} - 15 q^{64} - 9 q^{65} - 2 q^{66} - q^{67} - 49 q^{68} - 59 q^{69} - 31 q^{70} - 141 q^{71} + 9 q^{72} - 4 q^{73} - 94 q^{74} - 43 q^{75} + 34 q^{76} - 11 q^{77} - 11 q^{78} - 63 q^{79} - 41 q^{80} - 30 q^{81} + 38 q^{82} - 44 q^{83} - 16 q^{84} + 13 q^{85} - 7 q^{86} - 8 q^{87} - 9 q^{88} - 58 q^{89} - 55 q^{90} - 78 q^{91} - 104 q^{92} - 5 q^{94} - 99 q^{95} - 148 q^{96} - 26 q^{97} + 16 q^{98} + 40 q^{99}+O(q^{100}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9 - 7 * q^10 + 62 * q^11 - 17 * q^12 - 31 * q^14 - 20 * q^15 + 27 * q^16 - 62 * q^17 + 3 * q^18 - 29 * q^20 - 18 * q^21 - 7 * q^22 - 50 * q^23 - 31 * q^24 + 35 * q^25 - 32 * q^26 - 14 * q^27 - 13 * q^28 - 26 * q^29 - 10 * q^30 - 58 * q^31 - 5 * q^32 - 8 * q^33 + 7 * q^34 - 32 * q^35 - 29 * q^36 - 41 * q^37 - 10 * q^38 - 53 * q^39 - 31 * q^40 - 55 * q^41 - 7 * q^42 + 62 * q^43 + 49 * q^44 - 34 * q^45 - 39 * q^46 - 31 * q^47 - 30 * q^48 + 35 * q^49 - 40 * q^50 + 8 * q^51 + 13 * q^52 - 74 * q^53 + 48 * q^54 - 13 * q^55 - 75 * q^56 - 43 * q^57 - 46 * q^58 - 65 * q^59 - 8 * q^60 - 14 * q^61 - 29 * q^62 - 23 * q^63 - 15 * q^64 - 9 * q^65 - 2 * q^66 - q^67 - 49 * q^68 - 59 * q^69 - 31 * q^70 - 141 * q^71 + 9 * q^72 - 4 * q^73 - 94 * q^74 - 43 * q^75 + 34 * q^76 - 11 * q^77 - 11 * q^78 - 63 * q^79 - 41 * q^80 - 30 * q^81 + 38 * q^82 - 44 * q^83 - 16 * q^84 + 13 * q^85 - 7 * q^86 - 8 * q^87 - 9 * q^88 - 58 * q^89 - 55 * q^90 - 78 * q^91 - 104 * q^92 - 5 * q^94 - 99 * q^95 - 148 * q^96 - 26 * q^97 + 16 * q^98 + 40 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.34818	−0.953310	−0.476655	−	0.879090i	$-0.658151\pi$
$2$	−1.34818	−0.953310	−0.476655	+	0.879090i	$0.658151\pi$
$3$	−2.19319	−1.26624	−0.633119	−	0.774055i	$-0.718225\pi$
$3$	−2.19319	−1.26624	−0.633119	+	0.774055i	$0.718225\pi$
$4$	−0.182400	−0.0911998
$5$	−0.782983	−0.350161	−0.175080	−	0.984554i	$-0.556019\pi$
$5$	−0.782983	−0.350161	−0.175080	+	0.984554i	$0.556019\pi$
$6$	2.95682	1.20712
$7$	−4.69818	−1.77574	−0.887872	−	0.460090i	$-0.847817\pi$
$7$	−4.69818	−1.77574	−0.887872	+	0.460090i	$0.847817\pi$
$8$	2.94228	1.04025
$9$	1.81007	0.603356
$10$	1.05561	0.333812
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.400037	0.115481
$13$	6.86395	1.90372	0.951858	−	0.306539i	$-0.0991709\pi$
$13$	6.86395	1.90372	0.951858	+	0.306539i	$0.0991709\pi$
$14$	6.33401	1.69284
$15$	1.71723	0.443386
$16$	−3.60193	−0.900483
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.44031	−0.575186
$19$	0.927929	0.212882	0.106441	−	0.994319i	$-0.466055\pi$
$19$	0.927929	0.212882	0.106441	+	0.994319i	$0.466055\pi$
$20$	0.142816	0.0319346
$21$	10.3040	2.24851
$22$	−1.34818	−0.287434
$23$	−9.01514	−1.87979	−0.939893	−	0.341470i	$-0.889075\pi$
$23$	−9.01514	−1.87979	−0.939893	+	0.341470i	$0.889075\pi$
$24$	−6.45296	−1.31721
$25$	−4.38694	−0.877388
$26$	−9.25386	−1.81483
$27$	2.60974	0.502245
$28$	0.856946	0.161948
$29$	6.25934	1.16233	0.581165	−	0.813786i	$-0.302597\pi$
$29$	6.25934	1.16233	0.581165	+	0.813786i	$0.302597\pi$
$30$	−2.31514	−0.422685
$31$	−1.66386	−0.298838	−0.149419	−	0.988774i	$-0.547740\pi$
$31$	−1.66386	−0.298838	−0.149419	+	0.988774i	$0.547740\pi$
$32$	−1.02849	−0.181813
$33$	−2.19319	−0.381785
$34$	1.34818	0.231212
$35$	3.67859	0.621796
$36$	−0.330156	−0.0550260
$37$	−5.93563	−0.975812	−0.487906	−	0.872896i	$-0.662239\pi$
$37$	−5.93563	−0.975812	−0.487906	+	0.872896i	$0.662239\pi$
$38$	−1.25102	−0.202942
$39$	−15.0539	−2.41056
$40$	−2.30375	−0.364255
$41$	−5.54604	−0.866146	−0.433073	−	0.901359i	$-0.642571\pi$
$41$	−5.54604	−0.866146	−0.433073	+	0.901359i	$0.642571\pi$
$42$	−13.8917	−2.14353
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−0.182400	−0.0274978
$45$	−1.41725	−0.211272
$46$	12.1541	1.79202
$47$	−1.07693	−0.157086	−0.0785430	−	0.996911i	$-0.525027\pi$
$47$	−1.07693	−0.157086	−0.0785430	+	0.996911i	$0.525027\pi$
$48$	7.89971	1.14022
$49$	15.0729	2.15327
$50$	5.91440	0.836422
$51$	2.19319	0.307108
$52$	−1.25198	−0.173619
$53$	−1.01410	−0.139297	−0.0696485	−	0.997572i	$-0.522188\pi$
$53$	−1.01410	−0.139297	−0.0696485	+	0.997572i	$0.522188\pi$
$54$	−3.51841	−0.478795
$55$	−0.782983	−0.105577
$56$	−13.8233	−1.84722
$57$	−2.03512	−0.269559
$58$	−8.43874	−1.10806
$59$	−6.92875	−0.902047	−0.451023	−	0.892512i	$-0.648941\pi$
$59$	−6.92875	−0.902047	−0.451023	+	0.892512i	$0.648941\pi$
$60$	−0.313222	−0.0404368
$61$	−9.86359	−1.26290	−0.631451	−	0.775415i	$-0.717540\pi$
$61$	−9.86359	−1.26290	−0.631451	+	0.775415i	$0.717540\pi$
$62$	2.24319	0.284885
$63$	−8.50402	−1.07141
$64$	8.59045	1.07381
$65$	−5.37435	−0.666606
$66$	2.95682	0.363959
$67$	6.59360	0.805536	0.402768	−	0.915302i	$-0.368048\pi$
$67$	6.59360	0.805536	0.402768	+	0.915302i	$0.368048\pi$
$68$	0.182400	0.0221192
$69$	19.7719	2.38025
$70$	−4.95942	−0.592764
$71$	−4.29550	−0.509782	−0.254891	−	0.966970i	$-0.582040\pi$
$71$	−4.29550	−0.509782	−0.254891	+	0.966970i	$0.582040\pi$
$72$	5.32572	0.627642
$73$	3.59186	0.420396	0.210198	−	0.977659i	$-0.432589\pi$
$73$	3.59186	0.420396	0.210198	+	0.977659i	$0.432589\pi$
$74$	8.00233	0.930251
$75$	9.62137	1.11098
$76$	−0.169254	−0.0194148
$77$	−4.69818	−0.535407
$78$	20.2955	2.29801
$79$	−7.57183	−0.851897	−0.425949	−	0.904747i	$-0.640060\pi$
$79$	−7.57183	−0.851897	−0.425949	+	0.904747i	$0.640060\pi$
$80$	2.82025	0.315314
$81$	−11.1539	−1.23932
$82$	7.47708	0.825706
$83$	15.4706	1.69812	0.849062	−	0.528293i	$-0.177168\pi$
$83$	15.4706	1.69812	0.849062	+	0.528293i	$0.177168\pi$
$84$	−1.87944	−0.205064
$85$	0.782983	0.0849264
$86$	−1.34818	−0.145378
$87$	−13.7279	−1.47179
$88$	2.94228	0.313648
$89$	4.90723	0.520166	0.260083	−	0.965586i	$-0.416250\pi$
$89$	4.90723	0.520166	0.260083	+	0.965586i	$0.416250\pi$
$90$	1.91072	0.201407
$91$	−32.2480	−3.38051
$92$	1.64436	0.171436
$93$	3.64916	0.378400
$94$	1.45190	0.149752
$95$	−0.726553	−0.0745428
$96$	2.25566	0.230218
$97$	13.7807	1.39922	0.699609	−	0.714526i	$-0.253357\pi$
$97$	13.7807	1.39922	0.699609	+	0.714526i	$0.253357\pi$
$98$	−20.3210	−2.05273
$99$	1.81007	0.181919
$100$	0.800176	0.0800176
$101$	−2.44825	−0.243610	−0.121805	−	0.992554i	$-0.538868\pi$
$101$	−2.44825	−0.243610	−0.121805	+	0.992554i	$0.538868\pi$
$102$	−2.95682	−0.292769
$103$	14.0119	1.38064	0.690319	−	0.723506i	$-0.257470\pi$
$103$	14.0119	1.38064	0.690319	+	0.723506i	$0.257470\pi$
$104$	20.1956	1.98034
$105$	−8.06784	−0.787341
$106$	1.36719	0.132793
$107$	−12.8109	−1.23847	−0.619237	−	0.785204i	$-0.712558\pi$
$107$	−12.8109	−1.23847	−0.619237	+	0.785204i	$0.712558\pi$
$108$	−0.476016	−0.0458047
$109$	7.92788	0.759353	0.379677	−	0.925119i	$-0.376035\pi$
$109$	7.92788	0.759353	0.379677	+	0.925119i	$0.376035\pi$
$110$	1.05561	0.100648
$111$	13.0180	1.23561
$112$	16.9225	1.59903
$113$	17.6112	1.65673	0.828363	−	0.560191i	$-0.189272\pi$
$113$	17.6112	1.65673	0.828363	+	0.560191i	$0.189272\pi$
$114$	2.74372	0.256973
$115$	7.05870	0.658227
$116$	−1.14170	−0.106004
$117$	12.4242	1.14862
$118$	9.34123	0.859930
$119$	4.69818	0.430681
$120$	5.05256	0.461233
$121$	1.00000	0.0909091
$122$	13.2979	1.20394
$123$	12.1635	1.09675
$124$	0.303488	0.0272540
$125$	7.34981	0.657387
$126$	11.4650	1.02138
$127$	−4.53301	−0.402239	−0.201120	−	0.979567i	$-0.564458\pi$
$127$	−4.53301	−0.402239	−0.201120	+	0.979567i	$0.564458\pi$
$128$	−9.52454	−0.841858
$129$	−2.19319	−0.193099
$130$	7.24562	0.635483
$131$	14.6156	1.27697	0.638484	−	0.769635i	$-0.279562\pi$
$131$	14.6156	1.27697	0.638484	+	0.769635i	$0.279562\pi$
$132$	0.400037	0.0348187
$133$	−4.35958	−0.378023
$134$	−8.88938	−0.767926
$135$	−2.04338	−0.175866
$136$	−2.94228	−0.252298
$137$	8.33539	0.712141	0.356070	−	0.934459i	$-0.384116\pi$
$137$	8.33539	0.712141	0.356070	+	0.934459i	$0.384116\pi$
$138$	−26.6561	−2.26912
$139$	−5.02921	−0.426572	−0.213286	−	0.976990i	$-0.568417\pi$
$139$	−5.02921	−0.426572	−0.213286	+	0.976990i	$0.568417\pi$
$140$	−0.670974	−0.0567077
$141$	2.36190	0.198908
$142$	5.79112	0.485980
$143$	6.86395	0.573992
$144$	−6.51974	−0.543312
$145$	−4.90096	−0.407002
$146$	−4.84249	−0.400768
$147$	−33.0576	−2.72655
$148$	1.08266	0.0889939
$149$	1.46007	0.119613	0.0598066	−	0.998210i	$-0.480952\pi$
$149$	1.46007	0.119613	0.0598066	+	0.998210i	$0.480952\pi$
$150$	−12.9714	−1.05911
$151$	−13.2219	−1.07599	−0.537994	−	0.842949i	$-0.680818\pi$
$151$	−13.2219	−1.07599	−0.537994	+	0.842949i	$0.680818\pi$
$152$	2.73022	0.221450
$153$	−1.81007	−0.146335
$154$	6.33401	0.510409
$155$	1.30277	0.104641
$156$	2.74583	0.219842
$157$	0.827495	0.0660413	0.0330206	−	0.999455i	$-0.489487\pi$
$157$	0.827495	0.0660413	0.0330206	+	0.999455i	$0.489487\pi$
$158$	10.2082	0.812122
$159$	2.22410	0.176383
$160$	0.805288	0.0636636
$161$	42.3547	3.33802
$162$	15.0375	1.18145
$163$	24.1015	1.88778	0.943888	−	0.330264i	$-0.107138\pi$
$163$	24.1015	1.88778	0.943888	+	0.330264i	$0.107138\pi$
$164$	1.01160	0.0789924
$165$	1.71723	0.133686
$166$	−20.8573	−1.61884
$167$	−21.6668	−1.67663	−0.838313	−	0.545190i	$-0.816458\pi$
$167$	−21.6668	−1.67663	−0.838313	+	0.545190i	$0.816458\pi$
$168$	30.3172	2.33902
$169$	34.1138	2.62414
$170$	−1.05561	−0.0809612
$171$	1.67962	0.128443
$172$	−0.182400	−0.0139078
$173$	−9.78952	−0.744284	−0.372142	−	0.928176i	$-0.621377\pi$
$173$	−9.78952	−0.744284	−0.372142	+	0.928176i	$0.621377\pi$
$174$	18.5077	1.40307
$175$	20.6106	1.55802
$176$	−3.60193	−0.271506
$177$	15.1960	1.14220
$178$	−6.61586	−0.495879
$179$	−1.38671	−0.103647	−0.0518237	−	0.998656i	$-0.516503\pi$
$179$	−1.38671	−0.103647	−0.0518237	+	0.998656i	$0.516503\pi$
$180$	0.258506	0.0192679
$181$	−7.28237	−0.541294	−0.270647	−	0.962679i	$-0.587238\pi$
$181$	−7.28237	−0.541294	−0.270647	+	0.962679i	$0.587238\pi$
$182$	43.4763	3.22268
$183$	21.6327	1.59913
$184$	−26.5250	−1.95545
$185$	4.64750	0.341691
$186$	−4.91974	−0.360733
$187$	−1.00000	−0.0731272
$188$	0.196431	0.0143262
$189$	−12.2610	−0.891859
$190$	0.979527	0.0710624
$191$	22.5533	1.63190	0.815948	−	0.578125i	$-0.196215\pi$
$191$	22.5533	1.63190	0.815948	+	0.578125i	$0.196215\pi$
$192$	−18.8405	−1.35969
$193$	20.3664	1.46600	0.733002	−	0.680226i	$-0.238119\pi$
$193$	20.3664	1.46600	0.733002	+	0.680226i	$0.238119\pi$
$194$	−18.5789	−1.33389
$195$	11.7870	0.844082
$196$	−2.74929	−0.196378
$197$	−9.18613	−0.654485	−0.327242	−	0.944940i	$-0.606119\pi$
$197$	−9.18613	−0.654485	−0.327242	+	0.944940i	$0.606119\pi$
$198$	−2.44031	−0.173425
$199$	−0.000612087 0	−4.33897e−5 0	−2.16948e−5	−	1.00000i	$-0.500007\pi$
$199$	−0.000612087 0	−4.33897e−5 0	−2.16948e−5		1.00000i	$0.500007\pi$
$200$	−12.9076	−0.912704
$201$	−14.4610	−1.02000
$202$	3.30070	0.232236
$203$	−29.4075	−2.06400
$204$	−0.400037	−0.0280082
$205$	4.34245	0.303290
$206$	−18.8907	−1.31618
$207$	−16.3180	−1.13418
$208$	−24.7235	−1.71426
$209$	0.927929	0.0641862
$210$	10.8769	0.750580
$211$	−13.8182	−0.951281	−0.475640	−	0.879640i	$-0.657784\pi$
$211$	−13.8182	−0.951281	−0.475640	+	0.879640i	$0.657784\pi$
$212$	0.184971	0.0127039
$213$	9.42083	0.645504
$214$	17.2714	1.18065
$215$	−0.782983	−0.0533990
$216$	7.67858	0.522461
$217$	7.81711	0.530660
$218$	−10.6882	−0.723899
$219$	−7.87763	−0.532321
$220$	0.142816	0.00962864
$221$	−6.86395	−0.461719
$222$	−17.5506	−1.17792
$223$	−17.5468	−1.17502	−0.587509	−	0.809218i	$-0.699891\pi$
$223$	−17.5468	−1.17502	−0.587509	+	0.809218i	$0.699891\pi$
$224$	4.83201	0.322853
$225$	−7.94066	−0.529377
$226$	−23.7432	−1.57937
$227$	−5.92753	−0.393424	−0.196712	−	0.980461i	$-0.563026\pi$
$227$	−5.92753	−0.393424	−0.196712	+	0.980461i	$0.563026\pi$
$228$	0.371206	0.0245837
$229$	−13.2033	−0.872498	−0.436249	−	0.899826i	$-0.643693\pi$
$229$	−13.2033	−0.872498	−0.436249	+	0.899826i	$0.643693\pi$
$230$	−9.51642	−0.627494
$231$	10.3040	0.677952
$232$	18.4167	1.20912
$233$	11.2322	0.735847	0.367924	−	0.929856i	$-0.380069\pi$
$233$	11.2322	0.735847	0.367924	+	0.929856i	$0.380069\pi$
$234$	−16.7501	−1.09499
$235$	0.843216	0.0550053
$236$	1.26380	0.0822665
$237$	16.6064	1.07870
$238$	−6.33401	−0.410573
$239$	19.1595	1.23933	0.619663	−	0.784868i	$-0.287269\pi$
$239$	19.1595	1.23933	0.619663	+	0.784868i	$0.287269\pi$
$240$	−6.18534	−0.399262
$241$	−7.54184	−0.485812	−0.242906	−	0.970050i	$-0.578101\pi$
$241$	−7.54184	−0.485812	−0.242906	+	0.970050i	$0.578101\pi$
$242$	−1.34818	−0.0866646
$243$	16.6333	1.06702
$244$	1.79911	0.115177
$245$	−11.8018	−0.753990
$246$	−16.3986	−1.04554
$247$	6.36926	0.405266
$248$	−4.89554	−0.310867
$249$	−33.9300	−2.15023
$250$	−9.90890	−0.626694
$251$	27.7075	1.74888	0.874442	−	0.485130i	$-0.161228\pi$
$251$	27.7075	1.74888	0.874442	+	0.485130i	$0.161228\pi$
$252$	1.55113	0.0977121
$253$	−9.01514	−0.566777
$254$	6.11133	0.383459
$255$	−1.71723	−0.107537
$256$	−4.34007	−0.271255
$257$	26.4189	1.64796	0.823982	−	0.566616i	$-0.191748\pi$
$257$	26.4189	1.64796	0.823982	+	0.566616i	$0.191748\pi$
$258$	2.95682	0.184084
$259$	27.8867	1.73279
$260$	0.980280	0.0607944
$261$	11.3298	0.701299
$262$	−19.7045	−1.21735
$263$	5.32352	0.328262	0.164131	−	0.986439i	$-0.447518\pi$
$263$	5.32352	0.328262	0.164131	+	0.986439i	$0.447518\pi$
$264$	−6.45296	−0.397152
$265$	0.794021	0.0487763
$266$	5.87751	0.360373
$267$	−10.7625	−0.658653
$268$	−1.20267	−0.0734648
$269$	−10.3230	−0.629406	−0.314703	−	0.949190i	$-0.601905\pi$
$269$	−10.3230	−0.629406	−0.314703	+	0.949190i	$0.601905\pi$
$270$	2.75486	0.167655
$271$	−8.80537	−0.534888	−0.267444	−	0.963573i	$-0.586179\pi$
$271$	−8.80537	−0.534888	−0.267444	+	0.963573i	$0.586179\pi$
$272$	3.60193	0.218399
$273$	70.7260	4.28053
$274$	−11.2376	−0.678891
$275$	−4.38694	−0.264542
$276$	−3.60638	−0.217079
$277$	6.09497	0.366212	0.183106	−	0.983093i	$-0.441385\pi$
$277$	6.09497	0.366212	0.183106	+	0.983093i	$0.441385\pi$
$278$	6.78030	0.406655
$279$	−3.01170	−0.180306
$280$	10.8234	0.646824
$281$	−14.9108	−0.889504	−0.444752	−	0.895654i	$-0.646708\pi$
$281$	−14.9108	−0.889504	−0.444752	+	0.895654i	$0.646708\pi$
$282$	−3.18428	−0.189621
$283$	−6.36979	−0.378645	−0.189322	−	0.981915i	$-0.560629\pi$
$283$	−6.36979	−0.378645	−0.189322	+	0.981915i	$0.560629\pi$
$284$	0.783497	0.0464920
$285$	1.59347	0.0943888
$286$	−9.25386	−0.547192
$287$	26.0563	1.53805
$288$	−1.86163	−0.109698
$289$	1.00000	0.0588235
$290$	6.60739	0.387999
$291$	−30.2237	−1.77174
$292$	−0.655155	−0.0383400
$293$	6.24883	0.365061	0.182530	−	0.983200i	$-0.441571\pi$
$293$	6.24883	0.365061	0.182530	+	0.983200i	$0.441571\pi$
$294$	44.5678	2.59925
$295$	5.42509	0.315861
$296$	−17.4643	−1.01509
$297$	2.60974	0.151433
$298$	−1.96844	−0.114028
$299$	−61.8794	−3.57858
$300$	−1.75494	−0.101321
$301$	−4.69818	−0.270798
$302$	17.8256	1.02575
$303$	5.36948	0.308468
$304$	−3.34234	−0.191696
$305$	7.72302	0.442219
$306$	2.44031	0.139503
$307$	−12.8361	−0.732595	−0.366298	−	0.930498i	$-0.619375\pi$
$307$	−12.8361	−0.732595	−0.366298	+	0.930498i	$0.619375\pi$
$308$	0.856946	0.0488290
$309$	−30.7308	−1.74821
$310$	−1.75638	−0.0997557
$311$	−15.9333	−0.903496	−0.451748	−	0.892146i	$-0.649199\pi$
$311$	−15.9333	−0.903496	−0.451748	+	0.892146i	$0.649199\pi$
$312$	−44.2928	−2.50759
$313$	−17.5376	−0.991281	−0.495641	−	0.868528i	$-0.665067\pi$
$313$	−17.5376	−0.991281	−0.495641	+	0.868528i	$0.665067\pi$
$314$	−1.11562	−0.0629578
$315$	6.65851	0.375164
$316$	1.38110	0.0776929
$317$	26.4002	1.48279	0.741393	−	0.671071i	$-0.234166\pi$
$317$	26.4002	1.48279	0.741393	+	0.671071i	$0.234166\pi$
$318$	−2.99850	−0.168148
$319$	6.25934	0.350456
$320$	−6.72618	−0.376005
$321$	28.0966	1.56820
$322$	−57.1019	−3.18217
$323$	−0.927929	−0.0516314
$324$	2.03446	0.113026
$325$	−30.1117	−1.67030
$326$	−32.4933	−1.79964
$327$	−17.3873	−0.961521
$328$	−16.3180	−0.901010
$329$	5.05960	0.278945
$330$	−2.31514	−0.127444
$331$	9.47545	0.520818	0.260409	−	0.965498i	$-0.416143\pi$
$331$	9.47545	0.520818	0.260409	+	0.965498i	$0.416143\pi$
$332$	−2.82184	−0.154869
$333$	−10.7439	−0.588762
$334$	29.2108	1.59834
$335$	−5.16267	−0.282067
$336$	−37.1142	−2.02475
$337$	8.08933	0.440654	0.220327	−	0.975426i	$-0.429288\pi$
$337$	8.08933	0.440654	0.220327	+	0.975426i	$0.429288\pi$
$338$	−45.9916	−2.50162
$339$	−38.6247	−2.09781
$340$	−0.142816	−0.00774528
$341$	−1.66386	−0.0901031
$342$	−2.26443	−0.122446
$343$	−37.9278	−2.04791
$344$	2.94228	0.158637
$345$	−15.4810	−0.833471
$346$	13.1981	0.709533
$347$	22.1780	1.19058	0.595288	−	0.803512i	$-0.297038\pi$
$347$	22.1780	1.19058	0.595288	+	0.803512i	$0.297038\pi$
$348$	2.50397	0.134227
$349$	27.0726	1.44917	0.724583	−	0.689188i	$-0.242033\pi$
$349$	27.0726	1.44917	0.724583	+	0.689188i	$0.242033\pi$
$350$	−27.7869	−1.48527
$351$	17.9131	0.956132
$352$	−1.02849	−0.0548185
$353$	−20.8960	−1.11218	−0.556091	−	0.831121i	$-0.687699\pi$
$353$	−20.8960	−1.11218	−0.556091	+	0.831121i	$0.687699\pi$
$354$	−20.4871	−1.08888
$355$	3.36330	0.178505
$356$	−0.895078	−0.0474390
$357$	−10.3040	−0.545345
$358$	1.86954	0.0988081
$359$	−15.2500	−0.804866	−0.402433	−	0.915450i	$-0.631835\pi$
$359$	−15.2500	−0.804866	−0.402433	+	0.915450i	$0.631835\pi$
$360$	−4.16995	−0.219776
$361$	−18.1389	−0.954681
$362$	9.81797	0.516021
$363$	−2.19319	−0.115112
$364$	5.88203	0.308302
$365$	−2.81237	−0.147206
$366$	−29.1648	−1.52447
$367$	−12.3531	−0.644829	−0.322414	−	0.946599i	$-0.604494\pi$
$367$	−12.3531	−0.644829	−0.322414	+	0.946599i	$0.604494\pi$
$368$	32.4719	1.69271
$369$	−10.0387	−0.522594
$370$	−6.26568	−0.325737
$371$	4.76441	0.247356
$372$	−0.665605	−0.0345100
$373$	15.0832	0.780981	0.390490	−	0.920607i	$-0.372306\pi$
$373$	15.0832	0.780981	0.390490	+	0.920607i	$0.372306\pi$
$374$	1.34818	0.0697129
$375$	−16.1195	−0.832408
$376$	−3.16862	−0.163409
$377$	42.9638	2.21275
$378$	16.5301	0.850218
$379$	20.8664	1.07183	0.535917	−	0.844271i	$-0.319966\pi$
$379$	20.8664	1.07183	0.535917	+	0.844271i	$0.319966\pi$
$380$	0.132523	0.00679829
$381$	9.94173	0.509330
$382$	−30.4059	−1.55570
$383$	11.7823	0.602046	0.301023	−	0.953617i	$-0.402672\pi$
$383$	11.7823	0.602046	0.301023	+	0.953617i	$0.402672\pi$
$384$	20.8891	1.06599
$385$	3.67859	0.187478
$386$	−27.4576	−1.39756
$387$	1.81007	0.0920110
$388$	−2.51360	−0.127608
$389$	−37.7859	−1.91582	−0.957911	−	0.287066i	$-0.907320\pi$
$389$	−37.7859	−1.91582	−0.957911	+	0.287066i	$0.907320\pi$
$390$	−15.8910	−0.804672
$391$	9.01514	0.455915
$392$	44.3486	2.23994
$393$	−32.0547	−1.61694
$394$	12.3846	0.623927
$395$	5.92861	0.298301
$396$	−0.330156	−0.0165910
$397$	7.64960	0.383922	0.191961	−	0.981403i	$-0.438515\pi$
$397$	7.64960	0.383922	0.191961	+	0.981403i	$0.438515\pi$
$398$	0.000825205 0	4.13638e−5 0
$399$	9.56137	0.478667
$400$	15.8014	0.790072
$401$	4.97671	0.248525	0.124263	−	0.992249i	$-0.460343\pi$
$401$	4.97671	0.248525	0.124263	+	0.992249i	$0.460343\pi$
$402$	19.4961	0.972376
$403$	−11.4207	−0.568903
$404$	0.446561	0.0222172
$405$	8.73328	0.433960
$406$	39.6467	1.96763
$407$	−5.93563	−0.294218
$408$	6.45296	0.319469
$409$	17.3107	0.855960	0.427980	−	0.903788i	$-0.359225\pi$
$409$	17.3107	0.855960	0.427980	+	0.903788i	$0.359225\pi$
$410$	−5.85443	−0.289130
$411$	−18.2811	−0.901739
$412$	−2.55577	−0.125914
$413$	32.5525	1.60180
$414$	21.9997	1.08123
$415$	−12.1132	−0.594616
$416$	−7.05948	−0.346119
$417$	11.0300	0.540141
$418$	−1.25102	−0.0611894
$419$	−20.5566	−1.00426	−0.502129	−	0.864793i	$-0.667450\pi$
$419$	−20.5566	−1.00426	−0.502129	+	0.864793i	$0.667450\pi$
$420$	1.47157	0.0718053
$421$	−15.5609	−0.758391	−0.379196	−	0.925316i	$-0.623799\pi$
$421$	−15.5609	−0.758391	−0.379196	+	0.925316i	$0.623799\pi$
$422$	18.6294	0.906866
$423$	−1.94931	−0.0947788
$424$	−2.98375	−0.144904
$425$	4.38694	0.212798
$426$	−12.7010	−0.615366
$427$	46.3409	2.24259
$428$	2.33670	0.112949
$429$	−15.0539	−0.726810
$430$	1.05561	0.0509058
$431$	8.64870	0.416593	0.208297	−	0.978066i	$-0.433208\pi$
$431$	8.64870	0.416593	0.208297	+	0.978066i	$0.433208\pi$
$432$	−9.40011	−0.452263
$433$	12.1594	0.584341	0.292171	−	0.956366i	$-0.405622\pi$
$433$	12.1594	0.584341	0.292171	+	0.956366i	$0.405622\pi$
$434$	−10.5389	−0.505884
$435$	10.7487	0.515361
$436$	−1.44604	−0.0692529
$437$	−8.36541	−0.400172
$438$	10.6205	0.507467
$439$	−15.0304	−0.717362	−0.358681	−	0.933460i	$-0.616773\pi$
$439$	−15.0304	−0.717362	−0.358681	+	0.933460i	$0.616773\pi$
$440$	−2.30375	−0.109827
$441$	27.2829	1.29919
$442$	9.25386	0.440161
$443$	−4.89849	−0.232734	−0.116367	−	0.993206i	$-0.537125\pi$
$443$	−4.89849	−0.232734	−0.116367	+	0.993206i	$0.537125\pi$
$444$	−2.37447	−0.112687
$445$	−3.84228	−0.182142
$446$	23.6563	1.12016
$447$	−3.20220	−0.151459
$448$	−40.3595	−1.90681
$449$	32.3264	1.52558	0.762789	−	0.646647i	$-0.223829\pi$
$449$	32.3264	1.52558	0.762789	+	0.646647i	$0.223829\pi$
$450$	10.7055	0.504661
$451$	−5.54604	−0.261153
$452$	−3.21228	−0.151093
$453$	28.9982	1.36245
$454$	7.99140	0.375055
$455$	25.2497	1.18372
$456$	−5.98789	−0.280409
$457$	13.5112	0.632025	0.316013	−	0.948755i	$-0.397656\pi$
$457$	13.5112	0.632025	0.316013	+	0.948755i	$0.397656\pi$
$458$	17.8005	0.831761
$459$	−2.60974	−0.121812
$460$	−1.28750	−0.0600302
$461$	21.9586	1.02271	0.511357	−	0.859369i	$-0.329143\pi$
$461$	21.9586	1.02271	0.511357	+	0.859369i	$0.329143\pi$
$462$	−13.8917	−0.646299
$463$	4.52919	0.210490	0.105245	−	0.994446i	$-0.466437\pi$
$463$	4.52919	0.210490	0.105245	+	0.994446i	$0.466437\pi$
$464$	−22.5457	−1.04666
$465$	−2.85723	−0.132501
$466$	−15.1431	−0.701491
$467$	−24.3421	−1.12642	−0.563210	−	0.826314i	$-0.690434\pi$
$467$	−24.3421	−1.12642	−0.563210	+	0.826314i	$0.690434\pi$
$468$	−2.26617	−0.104754
$469$	−30.9779	−1.43043
$470$	−1.13681	−0.0524371
$471$	−1.81485	−0.0836239
$472$	−20.3863	−0.938356
$473$	1.00000	0.0459800
$474$	−22.3885	−1.02834
$475$	−4.07077	−0.186780
$476$	−0.856946	−0.0392781
$477$	−1.83559	−0.0840457
$478$	−25.8306	−1.18146
$479$	25.6609	1.17248	0.586239	−	0.810138i	$-0.300608\pi$
$479$	25.6609	1.17248	0.586239	+	0.810138i	$0.300608\pi$
$480$	−1.76615	−0.0806132
$481$	−40.7419	−1.85767
$482$	10.1678	0.463130
$483$	−92.8918	−4.22672
$484$	−0.182400	−0.00829089
$485$	−10.7901	−0.489951
$486$	−22.4247	−1.01721
$487$	−24.0652	−1.09050	−0.545249	−	0.838274i	$-0.683565\pi$
$487$	−24.0652	−1.09050	−0.545249	+	0.838274i	$0.683565\pi$
$488$	−29.0214	−1.31374
$489$	−52.8591	−2.39037
$490$	15.9110	0.718786
$491$	−32.5339	−1.46823	−0.734117	−	0.679023i	$-0.762404\pi$
$491$	−32.5339	−1.46823	−0.734117	+	0.679023i	$0.762404\pi$
$492$	−2.21862	−0.100023
$493$	−6.25934	−0.281907
$494$	−8.58693	−0.386344
$495$	−1.41725	−0.0637008
$496$	5.99311	0.269099
$497$	20.1810	0.905242
$498$	45.7439	2.04983
$499$	6.62601	0.296621	0.148310	−	0.988941i	$-0.452617\pi$
$499$	6.62601	0.296621	0.148310	+	0.988941i	$0.452617\pi$
$500$	−1.34060	−0.0599536
$501$	47.5193	2.12300
$502$	−37.3549	−1.66723
$503$	−31.4416	−1.40191	−0.700956	−	0.713205i	$-0.747243\pi$
$503$	−31.4416	−1.40191	−0.700956	+	0.713205i	$0.747243\pi$
$504$	−25.0212	−1.11453
$505$	1.91694	0.0853028
$506$	12.1541	0.540314
$507$	−74.8179	−3.32278
$508$	0.826819	0.0366842
$509$	−2.40194	−0.106464	−0.0532321	−	0.998582i	$-0.516952\pi$
$509$	−2.40194	−0.106464	−0.0532321	+	0.998582i	$0.516952\pi$
$510$	2.31514	0.102516
$511$	−16.8752	−0.746516
$512$	24.9003	1.10045
$513$	2.42166	0.106919
$514$	−35.6175	−1.57102
$515$	−10.9711	−0.483445
$516$	0.400037	0.0176106
$517$	−1.07693	−0.0473632
$518$	−37.5964	−1.65189
$519$	21.4703	0.942440
$520$	−15.8128	−0.693439
$521$	8.45867	0.370581	0.185290	−	0.982684i	$-0.440677\pi$
$521$	8.45867	0.370581	0.185290	+	0.982684i	$0.440677\pi$
$522$	−15.2747	−0.668556
$523$	3.24883	0.142061	0.0710307	−	0.997474i	$-0.477371\pi$
$523$	3.24883	0.142061	0.0710307	+	0.997474i	$0.477371\pi$
$524$	−2.66588	−0.116459
$525$	−45.2029	−1.97282
$526$	−7.17709	−0.312936
$527$	1.66386	0.0724789
$528$	7.89971	0.343791
$529$	58.2727	2.53359
$530$	−1.07049	−0.0464989
$531$	−12.5415	−0.544255
$532$	0.795185	0.0344757
$533$	−38.0677	−1.64890
$534$	14.5098	0.627901
$535$	10.0307	0.433665
$536$	19.4002	0.837961
$537$	3.04131	0.131242
$538$	13.9173	0.600019
$539$	15.0729	0.649235
$540$	0.372712	0.0160390
$541$	26.1379	1.12376	0.561878	−	0.827220i	$-0.310079\pi$
$541$	26.1379	1.12376	0.561878	+	0.827220i	$0.310079\pi$
$542$	11.8713	0.509915
$543$	15.9716	0.685406
$544$	1.02849	0.0440960
$545$	−6.20740	−0.265896
$546$	−95.3516	−4.08067
$547$	36.5764	1.56390	0.781948	−	0.623344i	$-0.214226\pi$
$547$	36.5764	1.56390	0.781948	+	0.623344i	$0.214226\pi$
$548$	−1.52037	−0.0649471
$549$	−17.8538	−0.761980
$550$	5.91440	0.252191
$551$	5.80823	0.247439
$552$	58.1743	2.47606
$553$	35.5738	1.51275
$554$	−8.21715	−0.349113
$555$	−10.1928	−0.432662
$556$	0.917326	0.0389033
$557$	37.2917	1.58010	0.790050	−	0.613042i	$-0.210054\pi$
$557$	37.2917	1.58010	0.790050	+	0.613042i	$0.210054\pi$
$558$	4.06033	0.171887
$559$	6.86395	0.290314
$560$	−13.2500	−0.559916
$561$	2.19319	0.0925964
$562$	20.1025	0.847973
$563$	9.60760	0.404912	0.202456	−	0.979291i	$-0.435108\pi$
$563$	9.60760	0.404912	0.202456	+	0.979291i	$0.435108\pi$
$564$	−0.430810	−0.0181404
$565$	−13.7893	−0.580120
$566$	8.58765	0.360966
$567$	52.4028	2.20071
$568$	−12.6385	−0.530301
$569$	−12.3599	−0.518153	−0.259076	−	0.965857i	$-0.583418\pi$
$569$	−12.3599	−0.518153	−0.259076	+	0.965857i	$0.583418\pi$
$570$	−2.14829	−0.0899818
$571$	42.0168	1.75835	0.879174	−	0.476501i	$-0.158095\pi$
$571$	42.0168	1.75835	0.879174	+	0.476501i	$0.158095\pi$
$572$	−1.25198	−0.0523480
$573$	−49.4635	−2.06637
$574$	−35.1287	−1.46624
$575$	39.5488	1.64930
$576$	15.5493	0.647888
$577$	−12.3826	−0.515494	−0.257747	−	0.966212i	$-0.582980\pi$
$577$	−12.3826	−0.515494	−0.257747	+	0.966212i	$0.582980\pi$
$578$	−1.34818	−0.0560771
$579$	−44.6673	−1.85631
$580$	0.893933	0.0371185
$581$	−72.6838	−3.01543
$582$	40.7471	1.68902
$583$	−1.01410	−0.0419996
$584$	10.5683	0.437318
$585$	−9.72795	−0.402201
$586$	−8.42458	−0.348016
$587$	−28.8497	−1.19075	−0.595376	−	0.803447i	$-0.702997\pi$
$587$	−28.8497	−1.19075	−0.595376	+	0.803447i	$0.702997\pi$
$588$	6.02970	0.248661
$589$	−1.54395	−0.0636172
$590$	−7.31403	−0.301114
$591$	20.1469	0.828733
$592$	21.3797	0.878702
$593$	−22.1796	−0.910806	−0.455403	−	0.890285i	$-0.650505\pi$
$593$	−22.1796	−0.910806	−0.455403	+	0.890285i	$0.650505\pi$
$594$	−3.51841	−0.144362
$595$	−3.67859	−0.150808
$596$	−0.266315	−0.0109087
$597$	0.00134242	5.49416e−5 0
$598$	83.4248	3.41150
$599$	−33.8914	−1.38476	−0.692382	−	0.721531i	$-0.743439\pi$
$599$	−33.8914	−1.38476	−0.692382	+	0.721531i	$0.743439\pi$
$600$	28.3087	1.15570
$601$	25.0577	1.02213	0.511063	−	0.859543i	$-0.329252\pi$
$601$	25.0577	1.02213	0.511063	+	0.859543i	$0.329252\pi$
$602$	6.33401	0.258155
$603$	11.9349	0.486025
$604$	2.41168	0.0981298
$605$	−0.782983	−0.0318328
$606$	−7.23905	−0.294066
$607$	39.3548	1.59736	0.798680	−	0.601755i	$-0.205532\pi$
$607$	39.3548	1.59736	0.798680	+	0.601755i	$0.205532\pi$
$608$	−0.954363	−0.0387045
$609$	64.4961	2.61352
$610$	−10.4121	−0.421572
$611$	−7.39197	−0.299047
$612$	0.330156	0.0133458
$613$	26.1424	1.05588	0.527940	−	0.849282i	$-0.322965\pi$
$613$	26.1424	1.05588	0.527940	+	0.849282i	$0.322965\pi$
$614$	17.3054	0.698391
$615$	−9.52381	−0.384037
$616$	−13.8233	−0.556958
$617$	44.0654	1.77401	0.887003	−	0.461764i	$-0.152783\pi$
$617$	44.0654	1.77401	0.887003	+	0.461764i	$0.152783\pi$
$618$	41.4308	1.66659
$619$	−30.7010	−1.23398	−0.616989	−	0.786971i	$-0.711648\pi$
$619$	−30.7010	−1.23398	−0.616989	+	0.786971i	$0.711648\pi$
$620$	−0.237626	−0.00954327
$621$	−23.5272	−0.944113
$622$	21.4811	0.861312
$623$	−23.0551	−0.923682
$624$	54.2232	2.17066
$625$	16.1799	0.647196
$626$	23.6439	0.944998
$627$	−2.03512	−0.0812750
$628$	−0.150935	−0.00602295
$629$	5.93563	0.236669
$630$	−8.97689	−0.357648
$631$	−20.0677	−0.798884	−0.399442	−	0.916758i	$-0.630796\pi$
$631$	−20.0677	−0.798884	−0.399442	+	0.916758i	$0.630796\pi$
$632$	−22.2784	−0.886188
$633$	30.3058	1.20455
$634$	−35.5924	−1.41355
$635$	3.54927	0.140848
$636$	−0.405676	−0.0160861
$637$	103.459	4.09921
$638$	−8.43874	−0.334093
$639$	−7.77514	−0.307580
$640$	7.45755	0.294786
$641$	37.8950	1.49676	0.748382	−	0.663268i	$-0.230831\pi$
$641$	37.8950	1.49676	0.748382	+	0.663268i	$0.230831\pi$
$642$	−37.8794	−1.49498
$643$	−34.6463	−1.36632	−0.683159	−	0.730269i	$-0.739395\pi$
$643$	−34.6463	−1.36632	−0.683159	+	0.730269i	$0.739395\pi$
$644$	−7.72548	−0.304427
$645$	1.71723	0.0676158
$646$	1.25102	0.0492207
$647$	−32.7091	−1.28593	−0.642963	−	0.765897i	$-0.722295\pi$
$647$	−32.7091	−1.28593	−0.642963	+	0.765897i	$0.722295\pi$
$648$	−32.8177	−1.28920
$649$	−6.92875	−0.271977
$650$	40.5961	1.59231
$651$	−17.1444	−0.671942
$652$	−4.39611	−0.172165
$653$	−21.0151	−0.822383	−0.411191	−	0.911549i	$-0.634887\pi$
$653$	−21.0151	−0.822383	−0.411191	+	0.911549i	$0.634887\pi$
$654$	23.4413	0.916628
$655$	−11.4437	−0.447144
$656$	19.9765	0.779949
$657$	6.50152	0.253648
$658$	−6.82127	−0.265921
$659$	−44.3756	−1.72863	−0.864314	−	0.502952i	$-0.832247\pi$
$659$	−44.3756	−1.72863	−0.864314	+	0.502952i	$0.832247\pi$
$660$	−0.313222	−0.0121921
$661$	−13.7274	−0.533933	−0.266967	−	0.963706i	$-0.586021\pi$
$661$	−13.7274	−0.533933	−0.266967	+	0.963706i	$0.586021\pi$
$662$	−12.7746	−0.496501
$663$	15.0539	0.584646
$664$	45.5189	1.76648
$665$	3.41347	0.132369
$666$	14.4848	0.561273
$667$	−56.4288	−2.18493
$668$	3.95201	0.152908
$669$	38.4833	1.48785
$670$	6.96024	0.268897
$671$	−9.86359	−0.380780
$672$	−10.5975	−0.408808
$673$	5.97009	0.230130	0.115065	−	0.993358i	$-0.463292\pi$
$673$	5.97009	0.230130	0.115065	+	0.993358i	$0.463292\pi$
$674$	−10.9059	−0.420080
$675$	−11.4488	−0.440664
$676$	−6.22234	−0.239321
$677$	−6.34402	−0.243821	−0.121910	−	0.992541i	$-0.538902\pi$
$677$	−6.34402	−0.243821	−0.121910	+	0.992541i	$0.538902\pi$
$678$	52.0733	1.99986
$679$	−64.7442	−2.48465
$680$	2.30375	0.0883449
$681$	13.0002	0.498168
$682$	2.24319	0.0858962
$683$	35.1259	1.34405	0.672027	−	0.740527i	$-0.265424\pi$
$683$	35.1259	1.34405	0.672027	+	0.740527i	$0.265424\pi$
$684$	−0.306361	−0.0117140
$685$	−6.52647	−0.249364
$686$	51.1337	1.95229
$687$	28.9573	1.10479
$688$	−3.60193	−0.137322
$689$	−6.96071	−0.265182
$690$	20.8713	0.794557
$691$	−6.54255	−0.248890	−0.124445	−	0.992226i	$-0.539715\pi$
$691$	−6.54255	−0.248890	−0.124445	+	0.992226i	$0.539715\pi$
$692$	1.78561	0.0678785
$693$	−8.50402	−0.323041
$694$	−29.9000	−1.13499
$695$	3.93778	0.149369
$696$	−40.3913	−1.53103
$697$	5.54604	0.210071
$698$	−36.4989	−1.38150
$699$	−24.6344	−0.931757
$700$	−3.75937	−0.142091
$701$	−46.2988	−1.74868	−0.874341	−	0.485313i	$-0.838706\pi$
$701$	−46.2988	−1.74868	−0.874341	+	0.485313i	$0.838706\pi$
$702$	−24.1502	−0.911491
$703$	−5.50785	−0.207732
$704$	8.59045	0.323765
$705$	−1.84933	−0.0696498
$706$	28.1717	1.06025
$707$	11.5023	0.432590
$708$	−2.77175	−0.104169
$709$	−40.3672	−1.51602	−0.758011	−	0.652242i	$-0.773829\pi$
$709$	−40.3672	−1.51602	−0.758011	+	0.652242i	$0.773829\pi$
$710$	−4.53435	−0.170171
$711$	−13.7055	−0.513998
$712$	14.4384	0.541103
$713$	14.9999	0.561752
$714$	13.8917	0.519882
$715$	−5.37435	−0.200989
$716$	0.252935	0.00945263
$717$	−42.0204	−1.56928
$718$	20.5598	0.767287
$719$	17.3304	0.646314	0.323157	−	0.946345i	$-0.395256\pi$
$719$	17.3304	0.646314	0.323157	+	0.946345i	$0.395256\pi$
$720$	5.10485	0.190246
$721$	−65.8306	−2.45166
$722$	24.4546	0.910107
$723$	16.5407	0.615154
$724$	1.32830	0.0493659
$725$	−27.4593	−1.01981
$726$	2.95682	0.109738
$727$	32.1834	1.19362	0.596809	−	0.802384i	$-0.296435\pi$
$727$	32.1834	1.19362	0.596809	+	0.802384i	$0.296435\pi$
$728$	−94.8827	−3.51659
$729$	−3.01829	−0.111788
$730$	3.79159	0.140333
$731$	−1.00000	−0.0369863
$732$	−3.94579	−0.145841
$733$	16.9543	0.626220	0.313110	−	0.949717i	$-0.398629\pi$
$733$	16.9543	0.626220	0.313110	+	0.949717i	$0.398629\pi$
$734$	16.6543	0.614722
$735$	25.8836	0.954730
$736$	9.27195	0.341769
$737$	6.59360	0.242878
$738$	13.5340	0.498195
$739$	−2.77724	−0.102163	−0.0510813	−	0.998694i	$-0.516267\pi$
$739$	−2.77724	−0.102163	−0.0510813	+	0.998694i	$0.516267\pi$
$740$	−0.847702	−0.0311622
$741$	−13.9690	−0.513163
$742$	−6.42330	−0.235807
$743$	−5.90254	−0.216543	−0.108272	−	0.994121i	$-0.534532\pi$
$743$	−5.90254	−0.216543	−0.108272	+	0.994121i	$0.534532\pi$
$744$	10.7368	0.393631
$745$	−1.14321	−0.0418838
$746$	−20.3350	−0.744517
$747$	28.0029	1.02457
$748$	0.182400	0.00666919
$749$	60.1877	2.19921
$750$	21.7321	0.793543
$751$	25.2535	0.921512	0.460756	−	0.887527i	$-0.347578\pi$
$751$	25.2535	0.921512	0.460756	+	0.887527i	$0.347578\pi$
$752$	3.87902	0.141453
$753$	−60.7678	−2.21450
$754$	−57.9231	−2.10943
$755$	10.3526	0.376768
$756$	2.23641	0.0813374
$757$	22.8865	0.831825	0.415913	−	0.909405i	$-0.363462\pi$
$757$	22.8865	0.831825	0.415913	+	0.909405i	$0.363462\pi$
$758$	−28.1317	−1.02179
$759$	19.7719	0.717674
$760$	−2.13772	−0.0775432
$761$	16.7293	0.606435	0.303217	−	0.952921i	$-0.401939\pi$
$761$	16.7293	0.606435	0.303217	+	0.952921i	$0.401939\pi$
$762$	−13.4033	−0.485550
$763$	−37.2466	−1.34842
$764$	−4.11371	−0.148829
$765$	1.41725	0.0512409
$766$	−15.8847	−0.573936
$767$	−47.5586	−1.71724
$768$	9.51859	0.343473
$769$	−52.3432	−1.88754	−0.943772	−	0.330596i	$-0.892750\pi$
$769$	−52.3432	−1.88754	−0.943772	+	0.330596i	$0.892750\pi$
$770$	−4.95942	−0.178725
$771$	−57.9415	−2.08671
$772$	−3.71482	−0.133699
$773$	−24.8424	−0.893520	−0.446760	−	0.894654i	$-0.647422\pi$
$773$	−24.8424	−0.893520	−0.446760	+	0.894654i	$0.647422\pi$
$774$	−2.44031	−0.0877150
$775$	7.29925	0.262197
$776$	40.5466	1.45554
$777$	−61.1607	−2.19413
$778$	50.9424	1.82637
$779$	−5.14633	−0.184387
$780$	−2.14994	−0.0769801
$781$	−4.29550	−0.153705
$782$	−12.1541	−0.434628
$783$	16.3353	0.583775
$784$	−54.2915	−1.93898
$785$	−0.647914	−0.0231250
$786$	43.2156	1.54145
$787$	14.7154	0.524548	0.262274	−	0.964993i	$-0.415528\pi$
$787$	14.7154	0.524548	0.262274	+	0.964993i	$0.415528\pi$
$788$	1.67555	0.0596889
$789$	−11.6755	−0.415658
$790$	−7.99286	−0.284373
$791$	−82.7408	−2.94192
$792$	5.32572	0.189241
$793$	−67.7031	−2.40421
$794$	−10.3131	−0.365997
$795$	−1.74144	−0.0617624
$796$	0.000111644 0	3.95713e−6 0
$797$	−11.6472	−0.412566	−0.206283	−	0.978492i	$-0.566137\pi$
$797$	−11.6472	−0.412566	−0.206283	+	0.978492i	$0.566137\pi$
$798$	−12.8905	−0.456318
$799$	1.07693	0.0380989
$800$	4.51191	0.159520
$801$	8.88243	0.313845
$802$	−6.70953	−0.236922
$803$	3.59186	0.126754
$804$	2.63768	0.0930238
$805$	−33.1630	−1.16884
$806$	15.3971	0.542341
$807$	22.6403	0.796977
$808$	−7.20344	−0.253416
$809$	−9.79189	−0.344264	−0.172132	−	0.985074i	$-0.555066\pi$
$809$	−9.79189	−0.344264	−0.172132	+	0.985074i	$0.555066\pi$
$810$	−11.7741	−0.413699
$811$	−35.9076	−1.26089	−0.630444	−	0.776235i	$-0.717127\pi$
$811$	−35.9076	−1.26089	−0.630444	+	0.776235i	$0.717127\pi$
$812$	5.36392	0.188237
$813$	19.3118	0.677296
$814$	8.00233	0.280481
$815$	−18.8711	−0.661025
$816$	−7.89971	−0.276545
$817$	0.927929	0.0324641
$818$	−23.3380	−0.815995
$819$	−58.3712	−2.03965
$820$	−0.792062	−0.0276600
$821$	−21.2470	−0.741527	−0.370763	−	0.928727i	$-0.620904\pi$
$821$	−21.2470	−0.741527	−0.370763	+	0.928727i	$0.620904\pi$
$822$	24.6463	0.859637
$823$	−23.2367	−0.809979	−0.404990	−	0.914321i	$-0.632725\pi$
$823$	−23.2367	−0.809979	−0.404990	+	0.914321i	$0.632725\pi$
$824$	41.2270	1.43621
$825$	9.62137	0.334973
$826$	−43.8868	−1.52702
$827$	−48.7745	−1.69605	−0.848027	−	0.529953i	$-0.822210\pi$
$827$	−48.7745	−1.69605	−0.848027	+	0.529953i	$0.822210\pi$
$828$	2.97640	0.103437
$829$	−25.6120	−0.889543	−0.444772	−	0.895644i	$-0.646715\pi$
$829$	−25.6120	−0.889543	−0.444772	+	0.895644i	$0.646715\pi$
$830$	16.3309	0.566853
$831$	−13.3674	−0.463711
$832$	58.9644	2.04422
$833$	−15.0729	−0.522244
$834$	−14.8705	−0.514922
$835$	16.9647	0.587088
$836$	−0.169254	−0.00585377
$837$	−4.34225	−0.150090
$838$	27.7141	0.957369
$839$	2.55676	0.0882692	0.0441346	−	0.999026i	$-0.485947\pi$
$839$	2.55676	0.0882692	0.0441346	+	0.999026i	$0.485947\pi$
$840$	−23.7378	−0.819033
$841$	10.1794	0.351012
$842$	20.9789	0.722982
$843$	32.7022	1.12632
$844$	2.52043	0.0867566
$845$	−26.7105	−0.918869
$846$	2.62803	0.0903536
$847$	−4.69818	−0.161431
$848$	3.65271	0.125435
$849$	13.9701	0.479454
$850$	−5.91440	−0.202862
$851$	53.5105	1.83432
$852$	−1.71836	−0.0588699
$853$	−12.1988	−0.417678	−0.208839	−	0.977950i	$-0.566968\pi$
$853$	−12.1988	−0.417678	−0.208839	+	0.977950i	$0.566968\pi$
$854$	−62.4760	−2.13789
$855$	−1.31511	−0.0449758
$856$	−37.6931	−1.28832
$857$	0.110082	0.00376033	0.00188017	−	0.999998i	$-0.499402\pi$
$857$	0.110082	0.00376033	0.00188017	+	0.999998i	$0.499402\pi$
$858$	20.2955	0.692875
$859$	27.3925	0.934620	0.467310	−	0.884094i	$-0.345223\pi$
$859$	27.3925	0.934620	0.467310	+	0.884094i	$0.345223\pi$
$860$	0.142816	0.00486998
$861$	−57.1463	−1.94754
$862$	−11.6600	−0.397143
$863$	−42.4190	−1.44396	−0.721980	−	0.691914i	$-0.756768\pi$
$863$	−42.4190	−1.44396	−0.721980	+	0.691914i	$0.756768\pi$
$864$	−2.68409	−0.0913144
$865$	7.66503	0.260619
$866$	−16.3930	−0.557058
$867$	−2.19319	−0.0744845
$868$	−1.42584	−0.0483961
$869$	−7.57183	−0.256857
$870$	−14.4912	−0.491299
$871$	45.2581	1.53351
$872$	23.3260	0.789919
$873$	24.9440	0.844227
$874$	11.2781	0.381488
$875$	−34.5307	−1.16735
$876$	1.43688	0.0485476
$877$	−33.9040	−1.14486	−0.572428	−	0.819955i	$-0.693999\pi$
$877$	−33.9040	−1.14486	−0.572428	+	0.819955i	$0.693999\pi$
$878$	20.2638	0.683869
$879$	−13.7049	−0.462253
$880$	2.82025	0.0950706
$881$	−23.2770	−0.784222	−0.392111	−	0.919918i	$-0.628255\pi$
$881$	−23.2770	−0.784222	−0.392111	+	0.919918i	$0.628255\pi$
$882$	−36.7824	−1.23853
$883$	−44.9962	−1.51424	−0.757121	−	0.653275i	$-0.773395\pi$
$883$	−44.9962	−1.51424	−0.757121	+	0.653275i	$0.773395\pi$
$884$	1.25198	0.0421087
$885$	−11.8982	−0.399955
$886$	6.60406	0.221868
$887$	−32.7291	−1.09894	−0.549468	−	0.835515i	$-0.685169\pi$
$887$	−32.7291	−1.09894	−0.549468	+	0.835515i	$0.685169\pi$
$888$	38.3024	1.28534
$889$	21.2969	0.714274
$890$	5.18010	0.173637
$891$	−11.1539	−0.373668
$892$	3.20052	0.107161
$893$	−0.999312	−0.0334407
$894$	4.31715	0.144387
$895$	1.08577	0.0362932
$896$	44.7480	1.49492
$897$	135.713	4.53133
$898$	−43.5820	−1.45435
$899$	−10.4147	−0.347349
$900$	1.44837	0.0482791
$901$	1.01410	0.0337845
$902$	7.47708	0.248960
$903$	10.3040	0.342895
$904$	51.8171	1.72341
$905$	5.70197	0.189540
$906$	−39.0949	−1.29884
$907$	22.4336	0.744897	0.372448	−	0.928053i	$-0.378518\pi$
$907$	22.4336	0.744897	0.372448	+	0.928053i	$0.378518\pi$
$908$	1.08118	0.0358802
$909$	−4.43151	−0.146984
$910$	−34.0412	−1.12845
$911$	−45.6834	−1.51356	−0.756780	−	0.653670i	$-0.773229\pi$
$911$	−45.6834	−1.51356	−0.756780	+	0.653670i	$0.773229\pi$
$912$	7.33037	0.242733
$913$	15.4706	0.512004
$914$	−18.2155	−0.602516
$915$	−16.9380	−0.559954
$916$	2.40828	0.0795717
$917$	−68.6666	−2.26757
$918$	3.51841	0.116125
$919$	−29.6752	−0.978893	−0.489447	−	0.872033i	$-0.662801\pi$
$919$	−29.6752	−0.978893	−0.489447	+	0.872033i	$0.662801\pi$
$920$	20.7686	0.684722
$921$	28.1520	0.927640
$922$	−29.6042	−0.974963
$923$	−29.4841	−0.970480
$924$	−1.87944	−0.0618291
$925$	26.0393	0.856165
$926$	−6.10619	−0.200662
$927$	25.3626	0.833016
$928$	−6.43765	−0.211326
$929$	14.6203	0.479675	0.239838	−	0.970813i	$-0.422906\pi$
$929$	14.6203	0.479675	0.239838	+	0.970813i	$0.422906\pi$
$930$	3.85207	0.126314
$931$	13.9866	0.458391
$932$	−2.04875	−0.0671092
$933$	34.9448	1.14404
$934$	32.8177	1.07383
$935$	0.782983	0.0256063
$936$	36.5555	1.19485
$937$	19.9189	0.650721	0.325360	−	0.945590i	$-0.394514\pi$
$937$	19.9189	0.650721	0.325360	+	0.945590i	$0.394514\pi$
$938$	41.7639	1.36364
$939$	38.4631	1.25520
$940$	−0.153802	−0.00501648
$941$	−58.8102	−1.91716	−0.958579	−	0.284828i	$-0.908064\pi$
$941$	−58.8102	−1.91716	−0.958579	+	0.284828i	$0.908064\pi$
$942$	2.44675	0.0797195
$943$	49.9983	1.62817
$944$	24.9569	0.812278
$945$	9.60018	0.312294
$946$	−1.34818	−0.0438332
$947$	−26.0337	−0.845981	−0.422991	−	0.906134i	$-0.639020\pi$
$947$	−26.0337	−0.845981	−0.422991	+	0.906134i	$0.639020\pi$
$948$	−3.02901	−0.0983776
$949$	24.6544	0.800315
$950$	5.48815	0.178059
$951$	−57.9007	−1.87756
$952$	13.8233	0.448017
$953$	22.7408	0.736647	0.368323	−	0.929698i	$-0.379932\pi$
$953$	22.7408	0.736647	0.368323	+	0.929698i	$0.379932\pi$
$954$	2.47471	0.0801216
$955$	−17.6588	−0.571426
$956$	−3.49469	−0.113026
$957$	−13.7279	−0.443760
$958$	−34.5957	−1.11773
$959$	−39.1612	−1.26458
$960$	14.7518	0.476111
$961$	−28.2316	−0.910696
$962$	54.9275	1.77093
$963$	−23.1886	−0.747241
$964$	1.37563	0.0443060
$965$	−15.9465	−0.513337
$966$	125.235	4.02938
$967$	55.5308	1.78575	0.892875	−	0.450304i	$-0.148685\pi$
$967$	55.5308	1.78575	0.892875	+	0.450304i	$0.148685\pi$
$968$	2.94228	0.0945683
$969$	2.03512	0.0653776
$970$	14.5470	0.467075
$971$	−33.3818	−1.07127	−0.535636	−	0.844449i	$-0.679928\pi$
$971$	−33.3818	−1.07127	−0.535636	+	0.844449i	$0.679928\pi$
$972$	−3.03390	−0.0973125
$973$	23.6281	0.757483
$974$	32.4443	1.03958
$975$	66.0406	2.11499
$976$	35.5280	1.13722
$977$	−53.0149	−1.69610	−0.848049	−	0.529918i	$-0.822223\pi$
$977$	−53.0149	−1.69610	−0.848049	+	0.529918i	$0.822223\pi$
$978$	71.2639	2.27877
$979$	4.90723	0.156836
$980$	2.15265	0.0687637
$981$	14.3500	0.458161
$982$	43.8617	1.39968
$983$	−0.364824	−0.0116361	−0.00581803	−	0.999983i	$-0.501852\pi$
$983$	−0.364824	−0.0116361	−0.00581803	+	0.999983i	$0.501852\pi$
$984$	35.7884	1.14089
$985$	7.19258	0.229175
$986$	8.43874	0.268744
$987$	−11.0966	−0.353210
$988$	−1.16175	−0.0369602
$989$	−9.01514	−0.286665
$990$	1.91072	0.0607266
$991$	9.59430	0.304773	0.152386	−	0.988321i	$-0.451304\pi$
$991$	9.59430	0.304773	0.152386	+	0.988321i	$0.451304\pi$
$992$	1.71126	0.0543325
$993$	−20.7814	−0.659478
$994$	−27.2077	−0.862976
$995$	0.000479253 0	1.51934e−5 0
$996$	6.18882	0.196100
$997$	−9.08243	−0.287644	−0.143822	−	0.989604i	$-0.545939\pi$
$997$	−9.08243	−0.287644	−0.143822	+	0.989604i	$0.545939\pi$
$998$	−8.93308	−0.282772
$999$	−15.4905	−0.490097

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.d.1.19	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.d.1.19	✓	62	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.34818 q^{2} -2.19319 q^{3} -0.182400 q^{4} -0.782983 q^{5} +2.95682 q^{6} -4.69818 q^{7} +2.94228 q^{8} +1.81007 q^{9} +O(q^{10})\)	\(q-1.34818 q^{2} -2.19319 q^{3} -0.182400 q^{4} -0.782983 q^{5} +2.95682 q^{6} -4.69818 q^{7} +2.94228 q^{8} +1.81007 q^{9} +1.05561 q^{10} +1.00000 q^{11} +0.400037 q^{12} +6.86395 q^{13} +6.33401 q^{14} +1.71723 q^{15} -3.60193 q^{16} -1.00000 q^{17} -2.44031 q^{18} +0.927929 q^{19} +0.142816 q^{20} +10.3040 q^{21} -1.34818 q^{22} -9.01514 q^{23} -6.45296 q^{24} -4.38694 q^{25} -9.25386 q^{26} +2.60974 q^{27} +0.856946 q^{28} +6.25934 q^{29} -2.31514 q^{30} -1.66386 q^{31} -1.02849 q^{32} -2.19319 q^{33} +1.34818 q^{34} +3.67859 q^{35} -0.330156 q^{36} -5.93563 q^{37} -1.25102 q^{38} -15.0539 q^{39} -2.30375 q^{40} -5.54604 q^{41} -13.8917 q^{42} +1.00000 q^{43} -0.182400 q^{44} -1.41725 q^{45} +12.1541 q^{46} -1.07693 q^{47} +7.89971 q^{48} +15.0729 q^{49} +5.91440 q^{50} +2.19319 q^{51} -1.25198 q^{52} -1.01410 q^{53} -3.51841 q^{54} -0.782983 q^{55} -13.8233 q^{56} -2.03512 q^{57} -8.43874 q^{58} -6.92875 q^{59} -0.313222 q^{60} -9.86359 q^{61} +2.24319 q^{62} -8.50402 q^{63} +8.59045 q^{64} -5.37435 q^{65} +2.95682 q^{66} +6.59360 q^{67} +0.182400 q^{68} +19.7719 q^{69} -4.95942 q^{70} -4.29550 q^{71} +5.32572 q^{72} +3.59186 q^{73} +8.00233 q^{74} +9.62137 q^{75} -0.169254 q^{76} -4.69818 q^{77} +20.2955 q^{78} -7.57183 q^{79} +2.82025 q^{80} -11.1539 q^{81} +7.47708 q^{82} +15.4706 q^{83} -1.87944 q^{84} +0.782983 q^{85} -1.34818 q^{86} -13.7279 q^{87} +2.94228 q^{88} +4.90723 q^{89} +1.91072 q^{90} -32.2480 q^{91} +1.64436 q^{92} +3.64916 q^{93} +1.45190 q^{94} -0.726553 q^{95} +2.25566 q^{96} +13.7807 q^{97} -20.3210 q^{98} +1.81007 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9}+O(q^{10}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9} - 7 q^{10} + 62 q^{11} - 17 q^{12} - 31 q^{14} - 20 q^{15} + 27 q^{16} - 62 q^{17} + 3 q^{18} - 29 q^{20} - 18 q^{21} - 7 q^{22} - 50 q^{23} - 31 q^{24} + 35 q^{25} - 32 q^{26} - 14 q^{27} - 13 q^{28} - 26 q^{29} - 10 q^{30} - 58 q^{31} - 5 q^{32} - 8 q^{33} + 7 q^{34} - 32 q^{35} - 29 q^{36} - 41 q^{37} - 10 q^{38} - 53 q^{39} - 31 q^{40} - 55 q^{41} - 7 q^{42} + 62 q^{43} + 49 q^{44} - 34 q^{45} - 39 q^{46} - 31 q^{47} - 30 q^{48} + 35 q^{49} - 40 q^{50} + 8 q^{51} + 13 q^{52} - 74 q^{53} + 48 q^{54} - 13 q^{55} - 75 q^{56} - 43 q^{57} - 46 q^{58} - 65 q^{59} - 8 q^{60} - 14 q^{61} - 29 q^{62} - 23 q^{63} - 15 q^{64} - 9 q^{65} - 2 q^{66} - q^{67} - 49 q^{68} - 59 q^{69} - 31 q^{70} - 141 q^{71} + 9 q^{72} - 4 q^{73} - 94 q^{74} - 43 q^{75} + 34 q^{76} - 11 q^{77} - 11 q^{78} - 63 q^{79} - 41 q^{80} - 30 q^{81} + 38 q^{82} - 44 q^{83} - 16 q^{84} + 13 q^{85} - 7 q^{86} - 8 q^{87} - 9 q^{88} - 58 q^{89} - 55 q^{90} - 78 q^{91} - 104 q^{92} - 5 q^{94} - 99 q^{95} - 148 q^{96} - 26 q^{97} + 16 q^{98} + 40 q^{99}+O(q^{100}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9 - 7 * q^10 + 62 * q^11 - 17 * q^12 - 31 * q^14 - 20 * q^15 + 27 * q^16 - 62 * q^17 + 3 * q^18 - 29 * q^20 - 18 * q^21 - 7 * q^22 - 50 * q^23 - 31 * q^24 + 35 * q^25 - 32 * q^26 - 14 * q^27 - 13 * q^28 - 26 * q^29 - 10 * q^30 - 58 * q^31 - 5 * q^32 - 8 * q^33 + 7 * q^34 - 32 * q^35 - 29 * q^36 - 41 * q^37 - 10 * q^38 - 53 * q^39 - 31 * q^40 - 55 * q^41 - 7 * q^42 + 62 * q^43 + 49 * q^44 - 34 * q^45 - 39 * q^46 - 31 * q^47 - 30 * q^48 + 35 * q^49 - 40 * q^50 + 8 * q^51 + 13 * q^52 - 74 * q^53 + 48 * q^54 - 13 * q^55 - 75 * q^56 - 43 * q^57 - 46 * q^58 - 65 * q^59 - 8 * q^60 - 14 * q^61 - 29 * q^62 - 23 * q^63 - 15 * q^64 - 9 * q^65 - 2 * q^66 - q^67 - 49 * q^68 - 59 * q^69 - 31 * q^70 - 141 * q^71 + 9 * q^72 - 4 * q^73 - 94 * q^74 - 43 * q^75 + 34 * q^76 - 11 * q^77 - 11 * q^78 - 63 * q^79 - 41 * q^80 - 30 * q^81 + 38 * q^82 - 44 * q^83 - 16 * q^84 + 13 * q^85 - 7 * q^86 - 8 * q^87 - 9 * q^88 - 58 * q^89 - 55 * q^90 - 78 * q^91 - 104 * q^92 - 5 * q^94 - 99 * q^95 - 148 * q^96 - 26 * q^97 + 16 * q^98 + 40 * q^99

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