LMFDB - Embedded newform 8041.2.a.e.1.6

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			1.6
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)

$f(q)$	$=$	$q-2.41404 q^{2} +0.194701 q^{3} +3.82757 q^{4} -3.15933 q^{5} -0.470017 q^{6} -0.226574 q^{7} -4.41183 q^{8} -2.96209 q^{9} +O(q^{10})$	\(q-2.41404 q^{2} +0.194701 q^{3} +3.82757 q^{4} -3.15933 q^{5} -0.470017 q^{6} -0.226574 q^{7} -4.41183 q^{8} -2.96209 q^{9} +7.62675 q^{10} -1.00000 q^{11} +0.745235 q^{12} -0.669053 q^{13} +0.546958 q^{14} -0.615127 q^{15} +2.99518 q^{16} -1.00000 q^{17} +7.15060 q^{18} -1.62047 q^{19} -12.0926 q^{20} -0.0441143 q^{21} +2.41404 q^{22} +7.84192 q^{23} -0.858991 q^{24} +4.98139 q^{25} +1.61512 q^{26} -1.16083 q^{27} -0.867229 q^{28} -9.64954 q^{29} +1.48494 q^{30} -10.8616 q^{31} +1.59319 q^{32} -0.194701 q^{33} +2.41404 q^{34} +0.715823 q^{35} -11.3376 q^{36} -1.35806 q^{37} +3.91188 q^{38} -0.130266 q^{39} +13.9385 q^{40} +4.70667 q^{41} +0.106494 q^{42} +1.00000 q^{43} -3.82757 q^{44} +9.35823 q^{45} -18.9307 q^{46} +2.81293 q^{47} +0.583166 q^{48} -6.94866 q^{49} -12.0253 q^{50} -0.194701 q^{51} -2.56085 q^{52} +1.04925 q^{53} +2.80228 q^{54} +3.15933 q^{55} +0.999607 q^{56} -0.315508 q^{57} +23.2943 q^{58} +1.77223 q^{59} -2.35444 q^{60} -6.97773 q^{61} +26.2204 q^{62} +0.671133 q^{63} -9.83638 q^{64} +2.11376 q^{65} +0.470017 q^{66} -12.1196 q^{67} -3.82757 q^{68} +1.52683 q^{69} -1.72802 q^{70} -1.59379 q^{71} +13.0683 q^{72} -10.5744 q^{73} +3.27841 q^{74} +0.969883 q^{75} -6.20247 q^{76} +0.226574 q^{77} +0.314466 q^{78} -0.657039 q^{79} -9.46277 q^{80} +8.66026 q^{81} -11.3621 q^{82} -0.411610 q^{83} -0.168851 q^{84} +3.15933 q^{85} -2.41404 q^{86} -1.87878 q^{87} +4.41183 q^{88} -2.10791 q^{89} -22.5911 q^{90} +0.151590 q^{91} +30.0156 q^{92} -2.11478 q^{93} -6.79052 q^{94} +5.11961 q^{95} +0.310197 q^{96} -2.00517 q^{97} +16.7743 q^{98} +2.96209 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.41404	−1.70698	−0.853491	−	0.521108i	$-0.825519\pi$
$2$	−2.41404	−1.70698	−0.853491	+	0.521108i	$0.825519\pi$
$3$	0.194701	0.112411	0.0562055	−	0.998419i	$-0.482100\pi$
$3$	0.194701	0.112411	0.0562055	+	0.998419i	$0.482100\pi$
$4$	3.82757	1.91379
$5$	−3.15933	−1.41290	−0.706448	−	0.707765i	$-0.749704\pi$
$5$	−3.15933	−1.41290	−0.706448	+	0.707765i	$0.749704\pi$
$6$	−0.470017	−0.191883
$7$	−0.226574	−0.0856369	−0.0428185	−	0.999083i	$-0.513634\pi$
$7$	−0.226574	−0.0856369	−0.0428185	+	0.999083i	$0.513634\pi$
$8$	−4.41183	−1.55982
$9$	−2.96209	−0.987364
$10$	7.62675	2.41179
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.745235	0.215131
$13$	−0.669053	−0.185562	−0.0927809	−	0.995687i	$-0.529576\pi$
$13$	−0.669053	−0.185562	−0.0927809	+	0.995687i	$0.529576\pi$
$14$	0.546958	0.146181
$15$	−0.615127	−0.158825
$16$	2.99518	0.748795
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	7.15060	1.68541
$19$	−1.62047	−0.371761	−0.185881	−	0.982572i	$-0.559514\pi$
$19$	−1.62047	−0.371761	−0.185881	+	0.982572i	$0.559514\pi$
$20$	−12.0926	−2.70398
$21$	−0.0441143	−0.00962653
$22$	2.41404	0.514674
$23$	7.84192	1.63515	0.817577	−	0.575819i	$-0.195317\pi$
$23$	7.84192	1.63515	0.817577	+	0.575819i	$0.195317\pi$
$24$	−0.858991	−0.175341
$25$	4.98139	0.996277
$26$	1.61512	0.316751
$27$	−1.16083	−0.223401
$28$	−0.867229	−0.163891
$29$	−9.64954	−1.79187	−0.895937	−	0.444181i	$-0.853495\pi$
$29$	−9.64954	−1.79187	−0.895937	+	0.444181i	$0.853495\pi$
$30$	1.48494	0.271112
$31$	−10.8616	−1.95081	−0.975404	−	0.220424i	$-0.929256\pi$
$31$	−10.8616	−1.95081	−0.975404	+	0.220424i	$0.929256\pi$
$32$	1.59319	0.281639
$33$	−0.194701	−0.0338932
$34$	2.41404	0.414004
$35$	0.715823	0.120996
$36$	−11.3376	−1.88960
$37$	−1.35806	−0.223264	−0.111632	−	0.993750i	$-0.535608\pi$
$37$	−1.35806	−0.223264	−0.111632	+	0.993750i	$0.535608\pi$
$38$	3.91188	0.634590
$39$	−0.130266	−0.0208592
$40$	13.9385	2.20386
$41$	4.70667	0.735058	0.367529	−	0.930012i	$-0.380204\pi$
$41$	4.70667	0.735058	0.367529	+	0.930012i	$0.380204\pi$
$42$	0.106494	0.0164323
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−3.82757	−0.577029
$45$	9.35823	1.39504
$46$	−18.9307	−2.79118
$47$	2.81293	0.410308	0.205154	−	0.978730i	$-0.434230\pi$
$47$	2.81293	0.410308	0.205154	+	0.978730i	$0.434230\pi$
$48$	0.583166	0.0841728
$49$	−6.94866	−0.992666
$50$	−12.0253	−1.70063
$51$	−0.194701	−0.0272637
$52$	−2.56085	−0.355126
$53$	1.04925	0.144125	0.0720626	−	0.997400i	$-0.477042\pi$
$53$	1.04925	0.144125	0.0720626	+	0.997400i	$0.477042\pi$
$54$	2.80228	0.381342
$55$	3.15933	0.426004
$56$	0.999607	0.133578
$57$	−0.315508	−0.0417901
$58$	23.2943	3.05870
$59$	1.77223	0.230725	0.115362	−	0.993323i	$-0.463197\pi$
$59$	1.77223	0.230725	0.115362	+	0.993323i	$0.463197\pi$
$60$	−2.35444	−0.303957
$61$	−6.97773	−0.893407	−0.446704	−	0.894682i	$-0.647402\pi$
$61$	−6.97773	−0.893407	−0.446704	+	0.894682i	$0.647402\pi$
$62$	26.2204	3.32999
$63$	0.671133	0.0845548
$64$	−9.83638	−1.22955
$65$	2.11376	0.262180
$66$	0.470017	0.0578550
$67$	−12.1196	−1.48064	−0.740321	−	0.672254i	$-0.765326\pi$
$67$	−12.1196	−1.48064	−0.740321	+	0.672254i	$0.765326\pi$
$68$	−3.82757	−0.464162
$69$	1.52683	0.183809
$70$	−1.72802	−0.206538
$71$	−1.59379	−0.189149	−0.0945743	−	0.995518i	$-0.530149\pi$
$71$	−1.59379	−0.189149	−0.0945743	+	0.995518i	$0.530149\pi$
$72$	13.0683	1.54011
$73$	−10.5744	−1.23764	−0.618820	−	0.785533i	$-0.712389\pi$
$73$	−10.5744	−1.23764	−0.618820	+	0.785533i	$0.712389\pi$
$74$	3.27841	0.381107
$75$	0.969883	0.111992
$76$	−6.20247	−0.711472
$77$	0.226574	0.0258205
$78$	0.314466	0.0356062
$79$	−0.657039	−0.0739227	−0.0369613	−	0.999317i	$-0.511768\pi$
$79$	−0.657039	−0.0739227	−0.0369613	+	0.999317i	$0.511768\pi$
$80$	−9.46277	−1.05797
$81$	8.66026	0.962251
$82$	−11.3621	−1.25473
$83$	−0.411610	−0.0451801	−0.0225900	−	0.999745i	$-0.507191\pi$
$83$	−0.411610	−0.0451801	−0.0225900	+	0.999745i	$0.507191\pi$
$84$	−0.168851	−0.0184231
$85$	3.15933	0.342678
$86$	−2.41404	−0.260312
$87$	−1.87878	−0.201426
$88$	4.41183	0.470303
$89$	−2.10791	−0.223438	−0.111719	−	0.993740i	$-0.535636\pi$
$89$	−2.10791	−0.223438	−0.111719	+	0.993740i	$0.535636\pi$
$90$	−22.5911	−2.38131
$91$	0.151590	0.0158909
$92$	30.0156	3.12934
$93$	−2.11478	−0.219292
$94$	−6.79052	−0.700389
$95$	5.11961	0.525260
$96$	0.310197	0.0316593
$97$	−2.00517	−0.203594	−0.101797	−	0.994805i	$-0.532459\pi$
$97$	−2.00517	−0.203594	−0.101797	+	0.994805i	$0.532459\pi$
$98$	16.7743	1.69446
$99$	2.96209	0.297701
$100$	19.0666	1.90666
$101$	−7.10045	−0.706521	−0.353260	−	0.935525i	$-0.614927\pi$
$101$	−7.10045	−0.706521	−0.353260	+	0.935525i	$0.614927\pi$
$102$	0.470017	0.0465386
$103$	−16.2508	−1.60124	−0.800618	−	0.599176i	$-0.795495\pi$
$103$	−16.2508	−1.60124	−0.800618	+	0.599176i	$0.795495\pi$
$104$	2.95175	0.289443
$105$	0.139372	0.0136013
$106$	−2.53292	−0.246019
$107$	14.0292	1.35626	0.678128	−	0.734944i	$-0.262791\pi$
$107$	14.0292	1.35626	0.678128	+	0.734944i	$0.262791\pi$
$108$	−4.44316	−0.427543
$109$	−0.799273	−0.0765564	−0.0382782	−	0.999267i	$-0.512187\pi$
$109$	−0.799273	−0.0765564	−0.0382782	+	0.999267i	$0.512187\pi$
$110$	−7.62675	−0.727182
$111$	−0.264417	−0.0250973
$112$	−0.678630	−0.0641245
$113$	−15.3997	−1.44869	−0.724343	−	0.689440i	$-0.757857\pi$
$113$	−15.3997	−1.44869	−0.724343	+	0.689440i	$0.757857\pi$
$114$	0.761648	0.0713349
$115$	−24.7753	−2.31030
$116$	−36.9343	−3.42927
$117$	1.98179	0.183217
$118$	−4.27823	−0.393843
$119$	0.226574	0.0207700
$120$	2.71384	0.247738
$121$	1.00000	0.0909091
$122$	16.8445	1.52503
$123$	0.916395	0.0826286
$124$	−41.5737	−3.73343
$125$	0.0588080	0.00525995
$126$	−1.62014	−0.144333
$127$	−21.0349	−1.86655	−0.933273	−	0.359169i	$-0.883060\pi$
$127$	−21.0349	−1.86655	−0.933273	+	0.359169i	$0.883060\pi$
$128$	20.5590	1.81718
$129$	0.194701	0.0171425
$130$	−5.10269	−0.447536
$131$	−13.8951	−1.21402	−0.607011	−	0.794693i	$-0.707632\pi$
$131$	−13.8951	−1.21402	−0.607011	+	0.794693i	$0.707632\pi$
$132$	−0.745235	−0.0648643
$133$	0.367156	0.0318365
$134$	29.2571	2.52743
$135$	3.66744	0.315643
$136$	4.41183	0.378312
$137$	3.95965	0.338295	0.169148	−	0.985591i	$-0.445899\pi$
$137$	3.95965	0.338295	0.169148	+	0.985591i	$0.445899\pi$
$138$	−3.68583	−0.313759
$139$	−2.37748	−0.201655	−0.100828	−	0.994904i	$-0.532149\pi$
$139$	−2.37748	−0.201655	−0.100828	+	0.994904i	$0.532149\pi$
$140$	2.73986	0.231561
$141$	0.547682	0.0461231
$142$	3.84748	0.322873
$143$	0.669053	0.0559490
$144$	−8.87200	−0.739333
$145$	30.4861	2.53173
$146$	25.5270	2.11263
$147$	−1.35292	−0.111587
$148$	−5.19808	−0.427280
$149$	−18.9407	−1.55169	−0.775843	−	0.630926i	$-0.782675\pi$
$149$	−18.9407	−1.55169	−0.775843	+	0.630926i	$0.782675\pi$
$150$	−2.34133	−0.191169
$151$	−7.34606	−0.597814	−0.298907	−	0.954282i	$-0.596622\pi$
$151$	−7.34606	−0.597814	−0.298907	+	0.954282i	$0.596622\pi$
$152$	7.14924	0.579880
$153$	2.96209	0.239471
$154$	−0.546958	−0.0440751
$155$	34.3155	2.75629
$156$	−0.498601	−0.0399200
$157$	13.5939	1.08491	0.542455	−	0.840085i	$-0.317495\pi$
$157$	13.5939	1.08491	0.542455	+	0.840085i	$0.317495\pi$
$158$	1.58612	0.126185
$159$	0.204290	0.0162013
$160$	−5.03342	−0.397927
$161$	−1.77678	−0.140030
$162$	−20.9062	−1.64255
$163$	6.65627	0.521360	0.260680	−	0.965425i	$-0.416053\pi$
$163$	6.65627	0.521360	0.260680	+	0.965425i	$0.416053\pi$
$164$	18.0151	1.40674
$165$	0.615127	0.0478876
$166$	0.993642	0.0771216
$167$	20.1168	1.55668	0.778342	−	0.627840i	$-0.216061\pi$
$167$	20.1168	1.55668	0.778342	+	0.627840i	$0.216061\pi$
$168$	0.194625	0.0150156
$169$	−12.5524	−0.965567
$170$	−7.62675	−0.584945
$171$	4.79998	0.367064
$172$	3.82757	0.291850
$173$	−3.82318	−0.290671	−0.145336	−	0.989382i	$-0.546426\pi$
$173$	−3.82318	−0.290671	−0.145336	+	0.989382i	$0.546426\pi$
$174$	4.53544	0.343831
$175$	−1.12865	−0.0853181
$176$	−2.99518	−0.225770
$177$	0.345056	0.0259360
$178$	5.08857	0.381404
$179$	−16.1904	−1.21012	−0.605062	−	0.796178i	$-0.706852\pi$
$179$	−16.1904	−1.21012	−0.605062	+	0.796178i	$0.706852\pi$
$180$	35.8193	2.66982
$181$	14.3318	1.06528	0.532638	−	0.846343i	$-0.321201\pi$
$181$	14.3318	1.06528	0.532638	+	0.846343i	$0.321201\pi$
$182$	−0.365944	−0.0271255
$183$	−1.35857	−0.100429
$184$	−34.5973	−2.55054
$185$	4.29057	0.315449
$186$	5.10515	0.374328
$187$	1.00000	0.0731272
$188$	10.7667	0.785243
$189$	0.263013	0.0191314
$190$	−12.3589	−0.896610
$191$	1.60710	0.116285	0.0581427	−	0.998308i	$-0.481482\pi$
$191$	1.60710	0.116285	0.0581427	+	0.998308i	$0.481482\pi$
$192$	−1.91516	−0.138215
$193$	−8.83957	−0.636286	−0.318143	−	0.948043i	$-0.603059\pi$
$193$	−8.83957	−0.636286	−0.318143	+	0.948043i	$0.603059\pi$
$194$	4.84055	0.347532
$195$	0.411552	0.0294719
$196$	−26.5965	−1.89975
$197$	−21.5634	−1.53633	−0.768165	−	0.640252i	$-0.778830\pi$
$197$	−21.5634	−1.53633	−0.768165	+	0.640252i	$0.778830\pi$
$198$	−7.15060	−0.508171
$199$	−13.5743	−0.962260	−0.481130	−	0.876649i	$-0.659774\pi$
$199$	−13.5743	−0.962260	−0.481130	+	0.876649i	$0.659774\pi$
$200$	−21.9770	−1.55401
$201$	−2.35970	−0.166440
$202$	17.1407	1.20602
$203$	2.18633	0.153451
$204$	−0.745235	−0.0521769
$205$	−14.8699	−1.03856
$206$	39.2299	2.73328
$207$	−23.2285	−1.61449
$208$	−2.00393	−0.138948
$209$	1.62047	0.112090
$210$	−0.336449	−0.0232172
$211$	−15.6273	−1.07583	−0.537914	−	0.843000i	$-0.680787\pi$
$211$	−15.6273	−1.07583	−0.537914	+	0.843000i	$0.680787\pi$
$212$	4.01607	0.275825
$213$	−0.310314	−0.0212624
$214$	−33.8671	−2.31510
$215$	−3.15933	−0.215465
$216$	5.12138	0.348466
$217$	2.46096	0.167061
$218$	1.92947	0.130680
$219$	−2.05885	−0.139124
$220$	12.0926	0.815282
$221$	0.669053	0.0450053
$222$	0.638311	0.0428407
$223$	2.72271	0.182326	0.0911630	−	0.995836i	$-0.470942\pi$
$223$	2.72271	0.182326	0.0911630	+	0.995836i	$0.470942\pi$
$224$	−0.360976	−0.0241187
$225$	−14.7553	−0.983688
$226$	37.1756	2.47288
$227$	2.98403	0.198057	0.0990286	−	0.995085i	$-0.468426\pi$
$227$	2.98403	0.198057	0.0990286	+	0.995085i	$0.468426\pi$
$228$	−1.20763	−0.0799773
$229$	15.5251	1.02593	0.512963	−	0.858411i	$-0.328548\pi$
$229$	15.5251	1.02593	0.512963	+	0.858411i	$0.328548\pi$
$230$	59.8084	3.94365
$231$	0.0441143	0.00290251
$232$	42.5722	2.79500
$233$	4.06488	0.266299	0.133149	−	0.991096i	$-0.457491\pi$
$233$	4.06488	0.266299	0.133149	+	0.991096i	$0.457491\pi$
$234$	−4.78413	−0.312748
$235$	−8.88699	−0.579723
$236$	6.78334	0.441558
$237$	−0.127926	−0.00830972
$238$	−0.546958	−0.0354540
$239$	6.60924	0.427516	0.213758	−	0.976887i	$-0.431430\pi$
$239$	6.60924	0.427516	0.213758	+	0.976887i	$0.431430\pi$
$240$	−1.84242	−0.118927
$241$	−9.20068	−0.592668	−0.296334	−	0.955084i	$-0.595764\pi$
$241$	−9.20068	−0.592668	−0.296334	+	0.955084i	$0.595764\pi$
$242$	−2.41404	−0.155180
$243$	5.16865	0.331569
$244$	−26.7078	−1.70979
$245$	21.9531	1.40254
$246$	−2.21221	−0.141045
$247$	1.08418	0.0689847
$248$	47.9197	3.04291
$249$	−0.0801411	−0.00507874
$250$	−0.141965	−0.00897864
$251$	2.23555	0.141107	0.0705533	−	0.997508i	$-0.477524\pi$
$251$	2.23555	0.141107	0.0705533	+	0.997508i	$0.477524\pi$
$252$	2.56881	0.161820
$253$	−7.84192	−0.493018
$254$	50.7790	3.18616
$255$	0.615127	0.0385207
$256$	−29.9574	−1.87234
$257$	−13.8039	−0.861066	−0.430533	−	0.902575i	$-0.641674\pi$
$257$	−13.8039	−0.861066	−0.430533	+	0.902575i	$0.641674\pi$
$258$	−0.470017	−0.0292620
$259$	0.307701	0.0191196
$260$	8.09057	0.501756
$261$	28.5828	1.76923
$262$	33.5433	2.07231
$263$	−9.91415	−0.611333	−0.305666	−	0.952139i	$-0.598879\pi$
$263$	−9.91415	−0.611333	−0.305666	+	0.952139i	$0.598879\pi$
$264$	0.858991	0.0528672
$265$	−3.31492	−0.203634
$266$	−0.886329	−0.0543443
$267$	−0.410413	−0.0251169
$268$	−46.3886	−2.83363
$269$	0.0195002	0.00118895	0.000594473	−	1.00000i	$-0.499811\pi$
$269$	0.0195002	0.00118895	0.000594473		1.00000i	$0.499811\pi$
$270$	−8.85334	−0.538797
$271$	24.9627	1.51638	0.758188	−	0.652036i	$-0.226085\pi$
$271$	24.9627	1.51638	0.758188	+	0.652036i	$0.226085\pi$
$272$	−2.99518	−0.181609
$273$	0.0295148	0.00178632
$274$	−9.55873	−0.577464
$275$	−4.98139	−0.300389
$276$	5.84407	0.351772
$277$	30.8145	1.85146	0.925732	−	0.378181i	$-0.123450\pi$
$277$	30.8145	1.85146	0.925732	+	0.378181i	$0.123450\pi$
$278$	5.73932	0.344222
$279$	32.1732	1.92616
$280$	−3.15809	−0.188732
$281$	28.5146	1.70104	0.850519	−	0.525944i	$-0.176288\pi$
$281$	28.5146	1.70104	0.850519	+	0.525944i	$0.176288\pi$
$282$	−1.32212	−0.0787314
$283$	−17.1171	−1.01750	−0.508752	−	0.860913i	$-0.669893\pi$
$283$	−17.1171	−1.01750	−0.508752	+	0.860913i	$0.669893\pi$
$284$	−6.10037	−0.361990
$285$	0.996795	0.0590450
$286$	−1.61512	−0.0955039
$287$	−1.06641	−0.0629481
$288$	−4.71918	−0.278080
$289$	1.00000	0.0588235
$290$	−73.5946	−4.32162
$291$	−0.390410	−0.0228862
$292$	−40.4743	−2.36858
$293$	3.72351	0.217530	0.108765	−	0.994068i	$-0.465310\pi$
$293$	3.72351	0.217530	0.108765	+	0.994068i	$0.465310\pi$
$294$	3.26599	0.190476
$295$	−5.59906	−0.325990
$296$	5.99154	0.348251
$297$	1.16083	0.0673581
$298$	45.7236	2.64870
$299$	−5.24666	−0.303422
$300$	3.71230	0.214330
$301$	−0.226574	−0.0130595
$302$	17.7337	1.02046
$303$	−1.38247	−0.0794207
$304$	−4.85360	−0.278373
$305$	22.0450	1.26229
$306$	−7.15060	−0.408772
$307$	−16.2501	−0.927442	−0.463721	−	0.885981i	$-0.653486\pi$
$307$	−16.2501	−0.927442	−0.463721	+	0.885981i	$0.653486\pi$
$308$	0.867229	0.0494149
$309$	−3.16405	−0.179996
$310$	−82.8390	−4.70494
$311$	−3.70071	−0.209848	−0.104924	−	0.994480i	$-0.533460\pi$
$311$	−3.70071	−0.209848	−0.104924	+	0.994480i	$0.533460\pi$
$312$	0.574710	0.0325365
$313$	−22.0628	−1.24707	−0.623533	−	0.781797i	$-0.714303\pi$
$313$	−22.0628	−1.24707	−0.623533	+	0.781797i	$0.714303\pi$
$314$	−32.8162	−1.85192
$315$	−2.12033	−0.119467
$316$	−2.51487	−0.141472
$317$	−17.2699	−0.969976	−0.484988	−	0.874521i	$-0.661176\pi$
$317$	−17.2699	−0.969976	−0.484988	+	0.874521i	$0.661176\pi$
$318$	−0.493164	−0.0276553
$319$	9.64954	0.540270
$320$	31.0764	1.73722
$321$	2.73151	0.152458
$322$	4.28920	0.239028
$323$	1.62047	0.0901654
$324$	33.1478	1.84154
$325$	−3.33281	−0.184871
$326$	−16.0685	−0.889951
$327$	−0.155620	−0.00860578
$328$	−20.7650	−1.14656
$329$	−0.637337	−0.0351375
$330$	−1.48494	−0.0817432
$331$	−3.13367	−0.172242	−0.0861211	−	0.996285i	$-0.527447\pi$
$331$	−3.13367	−0.172242	−0.0861211	+	0.996285i	$0.527447\pi$
$332$	−1.57547	−0.0864651
$333$	4.02270	0.220443
$334$	−48.5627	−2.65723
$335$	38.2898	2.09199
$336$	−0.132130	−0.00720829
$337$	24.6129	1.34075	0.670376	−	0.742022i	$-0.266133\pi$
$337$	24.6129	1.34075	0.670376	+	0.742022i	$0.266133\pi$
$338$	30.3019	1.64821
$339$	−2.99835	−0.162848
$340$	12.0926	0.655812
$341$	10.8616	0.588191
$342$	−11.5873	−0.626571
$343$	3.16040	0.170646
$344$	−4.41183	−0.237870
$345$	−4.82378	−0.259703
$346$	9.22930	0.496170
$347$	14.9355	0.801782	0.400891	−	0.916126i	$-0.368701\pi$
$347$	14.9355	0.801782	0.400891	+	0.916126i	$0.368701\pi$
$348$	−7.19117	−0.385487
$349$	16.1541	0.864710	0.432355	−	0.901703i	$-0.357683\pi$
$349$	16.1541	0.864710	0.432355	+	0.901703i	$0.357683\pi$
$350$	2.72461	0.145636
$351$	0.776655	0.0414548
$352$	−1.59319	−0.0849174
$353$	10.2485	0.545475	0.272737	−	0.962089i	$-0.412071\pi$
$353$	10.2485	0.545475	0.272737	+	0.962089i	$0.412071\pi$
$354$	−0.832977	−0.0442722
$355$	5.03533	0.267247
$356$	−8.06818	−0.427612
$357$	0.0441143	0.00233478
$358$	39.0841	2.06566
$359$	−12.2982	−0.649073	−0.324537	−	0.945873i	$-0.605208\pi$
$359$	−12.2982	−0.649073	−0.324537	+	0.945873i	$0.605208\pi$
$360$	−41.2870	−2.17601
$361$	−16.3741	−0.861793
$362$	−34.5975	−1.81841
$363$	0.194701	0.0102192
$364$	0.580222	0.0304119
$365$	33.4081	1.74866
$366$	3.27965	0.171430
$367$	19.4654	1.01609	0.508043	−	0.861331i	$-0.330369\pi$
$367$	19.4654	1.01609	0.508043	+	0.861331i	$0.330369\pi$
$368$	23.4880	1.22440
$369$	−13.9416	−0.725770
$370$	−10.3576	−0.538465
$371$	−0.237732	−0.0123424
$372$	−8.09447	−0.419679
$373$	3.37169	0.174580	0.0872898	−	0.996183i	$-0.472179\pi$
$373$	3.37169	0.174580	0.0872898	+	0.996183i	$0.472179\pi$
$374$	−2.41404	−0.124827
$375$	0.0114500	0.000591276 0
$376$	−12.4102	−0.640006
$377$	6.45605	0.332503
$378$	−0.634924	−0.0326570
$379$	−4.17334	−0.214370	−0.107185	−	0.994239i	$-0.534184\pi$
$379$	−4.17334	−0.214370	−0.107185	+	0.994239i	$0.534184\pi$
$380$	19.5957	1.00524
$381$	−4.09553	−0.209820
$382$	−3.87959	−0.198497
$383$	−16.1396	−0.824697	−0.412348	−	0.911026i	$-0.635291\pi$
$383$	−16.1396	−0.824697	−0.412348	+	0.911026i	$0.635291\pi$
$384$	4.00287	0.204271
$385$	−0.715823	−0.0364817
$386$	21.3391	1.08613
$387$	−2.96209	−0.150572
$388$	−7.67494	−0.389636
$389$	−28.0028	−1.41980	−0.709899	−	0.704303i	$-0.751259\pi$
$389$	−28.0028	−1.41980	−0.709899	+	0.704303i	$0.751259\pi$
$390$	−0.993502	−0.0503079
$391$	−7.84192	−0.396583
$392$	30.6563	1.54838
$393$	−2.70540	−0.136469
$394$	52.0549	2.62249
$395$	2.07581	0.104445
$396$	11.3376	0.569737
$397$	6.32495	0.317440	0.158720	−	0.987324i	$-0.449263\pi$
$397$	6.32495	0.317440	0.158720	+	0.987324i	$0.449263\pi$
$398$	32.7690	1.64256
$399$	0.0714859	0.00357877
$400$	14.9201	0.746007
$401$	−12.5648	−0.627458	−0.313729	−	0.949513i	$-0.601578\pi$
$401$	−12.5648	−0.627458	−0.313729	+	0.949513i	$0.601578\pi$
$402$	5.69640	0.284111
$403$	7.26701	0.361995
$404$	−27.1775	−1.35213
$405$	−27.3606	−1.35956
$406$	−5.27789	−0.261937
$407$	1.35806	0.0673166
$408$	0.858991	0.0425264
$409$	−29.5188	−1.45961	−0.729804	−	0.683656i	$-0.760389\pi$
$409$	−29.5188	−1.45961	−0.729804	+	0.683656i	$0.760389\pi$
$410$	35.8966	1.77281
$411$	0.770949	0.0380281
$412$	−62.2010	−3.06442
$413$	−0.401541	−0.0197585
$414$	56.0744	2.75591
$415$	1.30041	0.0638348
$416$	−1.06593	−0.0522615
$417$	−0.462899	−0.0226683
$418$	−3.91188	−0.191336
$419$	−28.5044	−1.39253	−0.696266	−	0.717784i	$-0.745157\pi$
$419$	−28.5044	−1.39253	−0.696266	+	0.717784i	$0.745157\pi$
$420$	0.533456	0.0260300
$421$	4.72342	0.230206	0.115103	−	0.993354i	$-0.463280\pi$
$421$	4.72342	0.230206	0.115103	+	0.993354i	$0.463280\pi$
$422$	37.7249	1.83642
$423$	−8.33216	−0.405123
$424$	−4.62911	−0.224809
$425$	−4.98139	−0.241633
$426$	0.749110	0.0362945
$427$	1.58097	0.0765086
$428$	53.6979	2.59559
$429$	0.130266	0.00628928
$430$	7.62675	0.367794
$431$	23.6944	1.14132	0.570659	−	0.821187i	$-0.306688\pi$
$431$	23.6944	1.14132	0.570659	+	0.821187i	$0.306688\pi$
$432$	−3.47689	−0.167282
$433$	25.7574	1.23782	0.618912	−	0.785461i	$-0.287574\pi$
$433$	25.7574	1.23782	0.618912	+	0.785461i	$0.287574\pi$
$434$	−5.94086	−0.285170
$435$	5.93569	0.284595
$436$	−3.05928	−0.146513
$437$	−12.7076	−0.607887
$438$	4.97014	0.237483
$439$	25.6612	1.22474	0.612371	−	0.790571i	$-0.290216\pi$
$439$	25.6612	1.22474	0.612371	+	0.790571i	$0.290216\pi$
$440$	−13.9385	−0.664490
$441$	20.5826	0.980123
$442$	−1.61512	−0.0768233
$443$	−26.5962	−1.26362	−0.631812	−	0.775122i	$-0.717688\pi$
$443$	−26.5962	−1.26362	−0.631812	+	0.775122i	$0.717688\pi$
$444$	−1.01207	−0.0480309
$445$	6.65958	0.315695
$446$	−6.57272	−0.311227
$447$	−3.68779	−0.174426
$448$	2.22867	0.105295
$449$	21.9378	1.03531	0.517654	−	0.855590i	$-0.326806\pi$
$449$	21.9378	1.03531	0.517654	+	0.855590i	$0.326806\pi$
$450$	35.6199	1.67914
$451$	−4.70667	−0.221628
$452$	−58.9437	−2.77248
$453$	−1.43029	−0.0672008
$454$	−7.20356	−0.338080
$455$	−0.478923	−0.0224523
$456$	1.39197	0.0651849
$457$	8.41008	0.393407	0.196704	−	0.980463i	$-0.436976\pi$
$457$	8.41008	0.393407	0.196704	+	0.980463i	$0.436976\pi$
$458$	−37.4781	−1.75124
$459$	1.16083	0.0541828
$460$	−94.8291	−4.42143
$461$	0.634041	0.0295302	0.0147651	−	0.999891i	$-0.495300\pi$
$461$	0.634041	0.0295302	0.0147651	+	0.999891i	$0.495300\pi$
$462$	−0.106494	−0.00495453
$463$	3.23013	0.150117	0.0750584	−	0.997179i	$-0.476086\pi$
$463$	3.23013	0.150117	0.0750584	+	0.997179i	$0.476086\pi$
$464$	−28.9021	−1.34175
$465$	6.68129	0.309837
$466$	−9.81276	−0.454567
$467$	−5.81931	−0.269286	−0.134643	−	0.990894i	$-0.542989\pi$
$467$	−5.81931	−0.269286	−0.134643	+	0.990894i	$0.542989\pi$
$468$	7.58547	0.350638
$469$	2.74598	0.126798
$470$	21.4535	0.989577
$471$	2.64675	0.121956
$472$	−7.81878	−0.359889
$473$	−1.00000	−0.0459800
$474$	0.308819	0.0141845
$475$	−8.07219	−0.370377
$476$	0.867229	0.0397494
$477$	−3.10797	−0.142304
$478$	−15.9550	−0.729763
$479$	15.4044	0.703843	0.351922	−	0.936030i	$-0.385528\pi$
$479$	15.4044	0.703843	0.351922	+	0.936030i	$0.385528\pi$
$480$	−0.980015	−0.0447314
$481$	0.908614	0.0414292
$482$	22.2108	1.01167
$483$	−0.345941	−0.0157409
$484$	3.82757	0.173981
$485$	6.33500	0.287657
$486$	−12.4773	−0.565982
$487$	−23.8810	−1.08215	−0.541077	−	0.840973i	$-0.681983\pi$
$487$	−23.8810	−1.08215	−0.541077	+	0.840973i	$0.681983\pi$
$488$	30.7846	1.39355
$489$	1.29599	0.0586065
$490$	−52.9957	−2.39410
$491$	−4.68218	−0.211304	−0.105652	−	0.994403i	$-0.533693\pi$
$491$	−4.68218	−0.211304	−0.105652	+	0.994403i	$0.533693\pi$
$492$	3.50757	0.158134
$493$	9.64954	0.434593
$494$	−2.61725	−0.117756
$495$	−9.35823	−0.420621
$496$	−32.5326	−1.46076
$497$	0.361112	0.0161981
$498$	0.193464	0.00866931
$499$	25.7094	1.15091	0.575455	−	0.817833i	$-0.304825\pi$
$499$	25.7094	1.15091	0.575455	+	0.817833i	$0.304825\pi$
$500$	0.225092	0.0100664
$501$	3.91677	0.174988
$502$	−5.39670	−0.240866
$503$	−29.1603	−1.30019	−0.650097	−	0.759852i	$-0.725272\pi$
$503$	−29.1603	−1.30019	−0.650097	+	0.759852i	$0.725272\pi$
$504$	−2.96093	−0.131890
$505$	22.4327	0.998241
$506$	18.9307	0.841572
$507$	−2.44396	−0.108540
$508$	−80.5126	−3.57217
$509$	−16.3317	−0.723889	−0.361945	−	0.932200i	$-0.617887\pi$
$509$	−16.3317	−0.723889	−0.361945	+	0.932200i	$0.617887\pi$
$510$	−1.48494	−0.0657542
$511$	2.39588	0.105988
$512$	31.2004	1.37887
$513$	1.88109	0.0830520
$514$	33.3232	1.46982
$515$	51.3416	2.26238
$516$	0.745235	0.0328071
$517$	−2.81293	−0.123713
$518$	−0.742802	−0.0326369
$519$	−0.744379	−0.0326746
$520$	−9.32556	−0.408953
$521$	3.93115	0.172227	0.0861134	−	0.996285i	$-0.472555\pi$
$521$	3.93115	0.172227	0.0861134	+	0.996285i	$0.472555\pi$
$522$	−69.0000	−3.02005
$523$	−5.08080	−0.222168	−0.111084	−	0.993811i	$-0.535432\pi$
$523$	−5.08080	−0.222168	−0.111084	+	0.993811i	$0.535432\pi$
$524$	−53.1846	−2.32338
$525$	−0.219750	−0.00959069
$526$	23.9331	1.04353
$527$	10.8616	0.473140
$528$	−0.583166	−0.0253790
$529$	38.4958	1.67373
$530$	8.00235	0.347600
$531$	−5.24950	−0.227809
$532$	1.40532	0.0609283
$533$	−3.14901	−0.136399
$534$	0.990752	0.0428740
$535$	−44.3230	−1.91625
$536$	53.4695	2.30953
$537$	−3.15229	−0.136031
$538$	−0.0470741	−0.00202951
$539$	6.94866	0.299300
$540$	14.0374	0.604074
$541$	−14.7941	−0.636048	−0.318024	−	0.948083i	$-0.603019\pi$
$541$	−14.7941	−0.636048	−0.318024	+	0.948083i	$0.603019\pi$
$542$	−60.2609	−2.58843
$543$	2.79043	0.119749
$544$	−1.59319	−0.0683075
$545$	2.52517	0.108166
$546$	−0.0712498	−0.00304921
$547$	−20.1011	−0.859463	−0.429732	−	0.902957i	$-0.641392\pi$
$547$	−20.1011	−0.859463	−0.429732	+	0.902957i	$0.641392\pi$
$548$	15.1558	0.647425
$549$	20.6687	0.882118
$550$	12.0253	0.512758
$551$	15.6368	0.666150
$552$	−6.73614	−0.286709
$553$	0.148868	0.00633051
$554$	−74.3873	−3.16042
$555$	0.835380	0.0354599
$556$	−9.09998	−0.385925
$557$	−8.17410	−0.346348	−0.173174	−	0.984891i	$-0.555402\pi$
$557$	−8.17410	−0.346348	−0.173174	+	0.984891i	$0.555402\pi$
$558$	−77.6672	−3.28792
$559$	−0.669053	−0.0282979
$560$	2.14402	0.0906013
$561$	0.194701	0.00822030
$562$	−68.8353	−2.90364
$563$	−10.9407	−0.461096	−0.230548	−	0.973061i	$-0.574052\pi$
$563$	−10.9407	−0.461096	−0.230548	+	0.973061i	$0.574052\pi$
$564$	2.09629	0.0882699
$565$	48.6529	2.04684
$566$	41.3212	1.73686
$567$	−1.96219	−0.0824042
$568$	7.03155	0.295037
$569$	40.5191	1.69865	0.849324	−	0.527872i	$-0.177010\pi$
$569$	40.5191	1.69865	0.849324	+	0.527872i	$0.177010\pi$
$570$	−2.40630	−0.100789
$571$	−9.71716	−0.406650	−0.203325	−	0.979111i	$-0.565175\pi$
$571$	−9.71716	−0.406650	−0.203325	+	0.979111i	$0.565175\pi$
$572$	2.56085	0.107074
$573$	0.312904	0.0130718
$574$	2.57435	0.107451
$575$	39.0636	1.62907
$576$	29.1363	1.21401
$577$	−16.2420	−0.676163	−0.338082	−	0.941117i	$-0.609778\pi$
$577$	−16.2420	−0.676163	−0.338082	+	0.941117i	$0.609778\pi$
$578$	−2.41404	−0.100411
$579$	−1.72108	−0.0715256
$580$	116.688	4.84520
$581$	0.0932601	0.00386908
$582$	0.942463	0.0390664
$583$	−1.04925	−0.0434554
$584$	46.6525	1.93049
$585$	−6.26115	−0.258867
$586$	−8.98869	−0.371319
$587$	8.02381	0.331178	0.165589	−	0.986195i	$-0.447047\pi$
$587$	8.02381	0.331178	0.165589	+	0.986195i	$0.447047\pi$
$588$	−5.17838	−0.213553
$589$	17.6010	0.725235
$590$	13.5163	0.556459
$591$	−4.19843	−0.172700
$592$	−4.06764	−0.167179
$593$	−29.3047	−1.20340	−0.601700	−	0.798722i	$-0.705510\pi$
$593$	−29.3047	−1.20340	−0.601700	+	0.798722i	$0.705510\pi$
$594$	−2.80228	−0.114979
$595$	−0.715823	−0.0293459
$596$	−72.4971	−2.96960
$597$	−2.64295	−0.108169
$598$	12.6656	0.517936
$599$	−19.7088	−0.805279	−0.402640	−	0.915359i	$-0.631907\pi$
$599$	−19.7088	−0.805279	−0.402640	+	0.915359i	$0.631907\pi$
$600$	−4.27896	−0.174688
$601$	15.9549	0.650813	0.325406	−	0.945574i	$-0.394499\pi$
$601$	15.9549	0.650813	0.325406	+	0.945574i	$0.394499\pi$
$602$	0.546958	0.0222923
$603$	35.8993	1.46193
$604$	−28.1176	−1.14409
$605$	−3.15933	−0.128445
$606$	3.33733	0.135570
$607$	14.6156	0.593228	0.296614	−	0.954998i	$-0.404143\pi$
$607$	14.6156	0.593228	0.296614	+	0.954998i	$0.404143\pi$
$608$	−2.58172	−0.104703
$609$	0.425683	0.0172495
$610$	−53.2174	−2.15471
$611$	−1.88200	−0.0761375
$612$	11.3376	0.458296
$613$	20.8850	0.843536	0.421768	−	0.906704i	$-0.361410\pi$
$613$	20.8850	0.843536	0.421768	+	0.906704i	$0.361410\pi$
$614$	39.2283	1.58313
$615$	−2.89520	−0.116746
$616$	−0.999607	−0.0402753
$617$	15.3052	0.616165	0.308082	−	0.951360i	$-0.400313\pi$
$617$	15.3052	0.616165	0.308082	+	0.951360i	$0.400313\pi$
$618$	7.63813	0.307251
$619$	−6.83812	−0.274847	−0.137424	−	0.990512i	$-0.543882\pi$
$619$	−6.83812	−0.274847	−0.137424	+	0.990512i	$0.543882\pi$
$620$	131.345	5.27495
$621$	−9.10313	−0.365296
$622$	8.93366	0.358207
$623$	0.477597	0.0191345
$624$	−0.390169	−0.0156192
$625$	−25.0927	−1.00371
$626$	53.2605	2.12872
$627$	0.315508	0.0126002
$628$	52.0316	2.07629
$629$	1.35806	0.0541494
$630$	5.11856	0.203928
$631$	26.8134	1.06742	0.533712	−	0.845666i	$-0.320797\pi$
$631$	26.8134	1.06742	0.533712	+	0.845666i	$0.320797\pi$
$632$	2.89875	0.115306
$633$	−3.04266	−0.120935
$634$	41.6902	1.65573
$635$	66.4562	2.63724
$636$	0.781936	0.0310058
$637$	4.64902	0.184201
$638$	−23.2943	−0.922232
$639$	4.72096	0.186758
$640$	−64.9528	−2.56748
$641$	−15.1876	−0.599874	−0.299937	−	0.953959i	$-0.596966\pi$
$641$	−15.1876	−0.599874	−0.299937	+	0.953959i	$0.596966\pi$
$642$	−6.59397	−0.260243
$643$	−3.31080	−0.130565	−0.0652827	−	0.997867i	$-0.520795\pi$
$643$	−3.31080	−0.130565	−0.0652827	+	0.997867i	$0.520795\pi$
$644$	−6.80074	−0.267987
$645$	−0.615127	−0.0242206
$646$	−3.91188	−0.153911
$647$	−20.1824	−0.793451	−0.396726	−	0.917937i	$-0.629854\pi$
$647$	−20.1824	−0.793451	−0.396726	+	0.917937i	$0.629854\pi$
$648$	−38.2076	−1.50094
$649$	−1.77223	−0.0695661
$650$	8.04552	0.315571
$651$	0.479153	0.0187795
$652$	25.4774	0.997771
$653$	0.581390	0.0227516	0.0113758	−	0.999935i	$-0.496379\pi$
$653$	0.581390	0.0227516	0.0113758	+	0.999935i	$0.496379\pi$
$654$	0.375671	0.0146899
$655$	43.8993	1.71529
$656$	14.0973	0.550408
$657$	31.3223	1.22200
$658$	1.53856	0.0599791
$659$	41.1985	1.60487	0.802433	−	0.596742i	$-0.203539\pi$
$659$	41.1985	1.60487	0.802433	+	0.596742i	$0.203539\pi$
$660$	2.35444	0.0916466
$661$	26.8740	1.04528	0.522638	−	0.852555i	$-0.324948\pi$
$661$	26.8740	1.04528	0.522638	+	0.852555i	$0.324948\pi$
$662$	7.56480	0.294014
$663$	0.130266	0.00505909
$664$	1.81596	0.0704727
$665$	−1.15997	−0.0449817
$666$	−9.71095	−0.376292
$667$	−75.6710	−2.92999
$668$	76.9986	2.97916
$669$	0.530116	0.0204954
$670$	−92.4329	−3.57100
$671$	6.97773	0.269372
$672$	−0.0702825	−0.00271121
$673$	31.4499	1.21231	0.606153	−	0.795348i	$-0.292712\pi$
$673$	31.4499	1.21231	0.606153	+	0.795348i	$0.292712\pi$
$674$	−59.4165	−2.28864
$675$	−5.78253	−0.222570
$676$	−48.0451	−1.84789
$677$	−1.77022	−0.0680349	−0.0340174	−	0.999421i	$-0.510830\pi$
$677$	−1.77022	−0.0680349	−0.0340174	+	0.999421i	$0.510830\pi$
$678$	7.23814	0.277979
$679$	0.454319	0.0174352
$680$	−13.9385	−0.534515
$681$	0.580996	0.0222638
$682$	−26.2204	−1.00403
$683$	−24.6723	−0.944058	−0.472029	−	0.881583i	$-0.656478\pi$
$683$	−24.6723	−0.944058	−0.472029	+	0.881583i	$0.656478\pi$
$684$	18.3723	0.702482
$685$	−12.5098	−0.477976
$686$	−7.62933	−0.291289
$687$	3.02276	0.115325
$688$	2.99518	0.114190
$689$	−0.702002	−0.0267441
$690$	11.6448	0.443309
$691$	−6.42427	−0.244391	−0.122195	−	0.992506i	$-0.538993\pi$
$691$	−6.42427	−0.244391	−0.122195	+	0.992506i	$0.538993\pi$
$692$	−14.6335	−0.556283
$693$	−0.671133	−0.0254942
$694$	−36.0550	−1.36863
$695$	7.51125	0.284918
$696$	8.28886	0.314189
$697$	−4.70667	−0.178278
$698$	−38.9966	−1.47604
$699$	0.791437	0.0299349
$700$	−4.32000	−0.163281
$701$	28.5094	1.07679	0.538393	−	0.842694i	$-0.319032\pi$
$701$	28.5094	1.07679	0.538393	+	0.842694i	$0.319032\pi$
$702$	−1.87487	−0.0707626
$703$	2.20070	0.0830009
$704$	9.83638	0.370723
$705$	−1.73031	−0.0651672
$706$	−24.7404	−0.931115
$707$	1.60878	0.0605043
$708$	1.32073	0.0496359
$709$	−30.2742	−1.13697	−0.568486	−	0.822693i	$-0.692471\pi$
$709$	−30.2742	−1.13697	−0.568486	+	0.822693i	$0.692471\pi$
$710$	−12.1555	−0.456186
$711$	1.94621	0.0729886
$712$	9.29974	0.348522
$713$	−85.1762	−3.18987
$714$	−0.106494	−0.00398542
$715$	−2.11376	−0.0790501
$716$	−61.9698	−2.31592
$717$	1.28683	0.0480575
$718$	29.6883	1.10796
$719$	−2.72959	−0.101797	−0.0508983	−	0.998704i	$-0.516208\pi$
$719$	−2.72959	−0.101797	−0.0508983	+	0.998704i	$0.516208\pi$
$720$	28.0296	1.04460
$721$	3.68200	0.137125
$722$	39.5276	1.47107
$723$	−1.79139	−0.0666223
$724$	54.8561	2.03871
$725$	−48.0681	−1.78520
$726$	−0.470017	−0.0174440
$727$	−12.7728	−0.473717	−0.236859	−	0.971544i	$-0.576118\pi$
$727$	−12.7728	−0.473717	−0.236859	+	0.971544i	$0.576118\pi$
$728$	−0.668789	−0.0247870
$729$	−24.9744	−0.924979
$730$	−80.6483	−2.98493
$731$	−1.00000	−0.0369863
$732$	−5.20005	−0.192199
$733$	−35.6365	−1.31627	−0.658133	−	0.752902i	$-0.728654\pi$
$733$	−35.6365	−1.31627	−0.658133	+	0.752902i	$0.728654\pi$
$734$	−46.9903	−1.73444
$735$	4.27431	0.157660
$736$	12.4937	0.460524
$737$	12.1196	0.446430
$738$	33.6555	1.23888
$739$	−27.5743	−1.01434	−0.507168	−	0.861847i	$-0.669308\pi$
$739$	−27.5743	−1.01434	−0.507168	+	0.861847i	$0.669308\pi$
$740$	16.4225	0.603702
$741$	0.211091	0.00775464
$742$	0.573894	0.0210683
$743$	29.5661	1.08467	0.542337	−	0.840161i	$-0.317540\pi$
$743$	29.5661	1.08467	0.542337	+	0.840161i	$0.317540\pi$
$744$	9.33005	0.342056
$745$	59.8401	2.19237
$746$	−8.13939	−0.298004
$747$	1.21923	0.0446092
$748$	3.82757	0.139950
$749$	−3.17866	−0.116146
$750$	−0.0276408	−0.00100930
$751$	16.2067	0.591389	0.295695	−	0.955282i	$-0.404449\pi$
$751$	16.2067	0.591389	0.295695	+	0.955282i	$0.404449\pi$
$752$	8.42524	0.307237
$753$	0.435265	0.0158619
$754$	−15.5851	−0.567577
$755$	23.2086	0.844649
$756$	1.00670	0.0366135
$757$	−12.1662	−0.442187	−0.221093	−	0.975253i	$-0.570963\pi$
$757$	−12.1662	−0.442187	−0.221093	+	0.975253i	$0.570963\pi$
$758$	10.0746	0.365926
$759$	−1.52683	−0.0554206
$760$	−22.5868	−0.819311
$761$	22.9676	0.832575	0.416288	−	0.909233i	$-0.363331\pi$
$761$	22.9676	0.832575	0.416288	+	0.909233i	$0.363331\pi$
$762$	9.88675	0.358159
$763$	0.181094	0.00655606
$764$	6.15128	0.222546
$765$	−9.35823	−0.338348
$766$	38.9617	1.40774
$767$	−1.18571	−0.0428137
$768$	−5.83276	−0.210472
$769$	18.5500	0.668930	0.334465	−	0.942408i	$-0.391444\pi$
$769$	18.5500	0.668930	0.334465	+	0.942408i	$0.391444\pi$
$770$	1.72802	0.0622736
$771$	−2.68765	−0.0967933
$772$	−33.8341	−1.21772
$773$	−32.1830	−1.15754	−0.578772	−	0.815490i	$-0.696468\pi$
$773$	−32.1830	−1.15754	−0.578772	+	0.815490i	$0.696468\pi$
$774$	7.15060	0.257023
$775$	−54.1060	−1.94355
$776$	8.84647	0.317570
$777$	0.0599099	0.00214926
$778$	67.5998	2.42357
$779$	−7.62702	−0.273266
$780$	1.57525	0.0564029
$781$	1.59379	0.0570304
$782$	18.9307	0.676960
$783$	11.2015	0.400307
$784$	−20.8125	−0.743304
$785$	−42.9476	−1.53287
$786$	6.53094	0.232951
$787$	−13.8683	−0.494352	−0.247176	−	0.968971i	$-0.579503\pi$
$787$	−13.8683	−0.494352	−0.247176	+	0.968971i	$0.579503\pi$
$788$	−82.5356	−2.94021
$789$	−1.93030	−0.0687205
$790$	−5.01107	−0.178286
$791$	3.48918	0.124061
$792$	−13.0683	−0.464360
$793$	4.66847	0.165782
$794$	−15.2687	−0.541865
$795$	−0.645420	−0.0228907
$796$	−51.9568	−1.84156
$797$	24.6805	0.874230	0.437115	−	0.899406i	$-0.356000\pi$
$797$	24.6805	0.874230	0.437115	+	0.899406i	$0.356000\pi$
$798$	−0.172570	−0.00610890
$799$	−2.81293	−0.0995144
$800$	7.93630	0.280591
$801$	6.24382	0.220614
$802$	30.3320	1.07106
$803$	10.5744	0.373163
$804$	−9.03192	−0.318531
$805$	5.61343	0.197847
$806$	−17.5428	−0.617920
$807$	0.00379671	0.000133651 0
$808$	31.3260	1.10204
$809$	32.8598	1.15529	0.577645	−	0.816288i	$-0.303972\pi$
$809$	32.8598	1.15529	0.577645	+	0.816288i	$0.303972\pi$
$810$	66.0496	2.32075
$811$	40.5112	1.42254	0.711271	−	0.702918i	$-0.248120\pi$
$811$	40.5112	1.42254	0.711271	+	0.702918i	$0.248120\pi$
$812$	8.36836	0.293672
$813$	4.86027	0.170457
$814$	−3.27841	−0.114908
$815$	−21.0294	−0.736627
$816$	−0.583166	−0.0204149
$817$	−1.62047	−0.0566931
$818$	71.2594	2.49153
$819$	−0.449023	−0.0156901
$820$	−56.9158	−1.98759
$821$	−5.14201	−0.179457	−0.0897287	−	0.995966i	$-0.528600\pi$
$821$	−5.14201	−0.179457	−0.0897287	+	0.995966i	$0.528600\pi$
$822$	−1.86110	−0.0649133
$823$	9.78679	0.341146	0.170573	−	0.985345i	$-0.445438\pi$
$823$	9.78679	0.341146	0.170573	+	0.985345i	$0.445438\pi$
$824$	71.6957	2.49764
$825$	−0.969883	−0.0337670
$826$	0.969335	0.0337275
$827$	24.2210	0.842247	0.421124	−	0.907003i	$-0.361636\pi$
$827$	24.2210	0.842247	0.421124	+	0.907003i	$0.361636\pi$
$828$	−88.9088	−3.08979
$829$	12.7081	0.441370	0.220685	−	0.975345i	$-0.429171\pi$
$829$	12.7081	0.441370	0.220685	+	0.975345i	$0.429171\pi$
$830$	−3.13925	−0.108965
$831$	5.99963	0.208125
$832$	6.58106	0.228157
$833$	6.94866	0.240757
$834$	1.11746	0.0386943
$835$	−63.5557	−2.19943
$836$	6.20247	0.214517
$837$	12.6085	0.435813
$838$	68.8108	2.37703
$839$	14.7377	0.508801	0.254401	−	0.967099i	$-0.418122\pi$
$839$	14.7377	0.508801	0.254401	+	0.967099i	$0.418122\pi$
$840$	−0.614885	−0.0212155
$841$	64.1136	2.21081
$842$	−11.4025	−0.392957
$843$	5.55184	0.191215
$844$	−59.8147	−2.05891
$845$	39.6571	1.36425
$846$	20.1141	0.691538
$847$	−0.226574	−0.00778517
$848$	3.14269	0.107920
$849$	−3.33272	−0.114379
$850$	12.0253	0.412463
$851$	−10.6498	−0.365071
$852$	−1.18775	−0.0406917
$853$	44.5484	1.52531	0.762654	−	0.646807i	$-0.223896\pi$
$853$	44.5484	1.52531	0.762654	+	0.646807i	$0.223896\pi$
$854$	−3.81653	−0.130599
$855$	−15.1647	−0.518623
$856$	−61.8946	−2.11551
$857$	47.5295	1.62358	0.811789	−	0.583951i	$-0.198494\pi$
$857$	47.5295	1.62358	0.811789	+	0.583951i	$0.198494\pi$
$858$	−0.314466	−0.0107357
$859$	−39.8119	−1.35837	−0.679183	−	0.733969i	$-0.737666\pi$
$859$	−39.8119	−1.35837	−0.679183	+	0.733969i	$0.737666\pi$
$860$	−12.0926	−0.412354
$861$	−0.207631	−0.00707606
$862$	−57.1991	−1.94821
$863$	49.9738	1.70113	0.850565	−	0.525871i	$-0.176260\pi$
$863$	49.9738	1.70113	0.850565	+	0.525871i	$0.176260\pi$
$864$	−1.84942	−0.0629186
$865$	12.0787	0.410688
$866$	−62.1794	−2.11294
$867$	0.194701	0.00661241
$868$	9.41953	0.319720
$869$	0.657039	0.0222885
$870$	−14.3290	−0.485798
$871$	8.10863	0.274750
$872$	3.52626	0.119414
$873$	5.93950	0.201021
$874$	30.6766	1.03765
$875$	−0.0133244	−0.000450446 0
$876$	−7.88041	−0.266254
$877$	−18.5635	−0.626845	−0.313423	−	0.949614i	$-0.601476\pi$
$877$	−18.5635	−0.626845	−0.313423	+	0.949614i	$0.601476\pi$
$878$	−61.9471	−2.09061
$879$	0.724973	0.0244527
$880$	9.46277	0.318990
$881$	−15.6737	−0.528061	−0.264030	−	0.964514i	$-0.585052\pi$
$881$	−15.6737	−0.528061	−0.264030	+	0.964514i	$0.585052\pi$
$882$	−49.6871	−1.67305
$883$	−52.2160	−1.75721	−0.878605	−	0.477549i	$-0.841525\pi$
$883$	−52.2160	−1.75721	−0.878605	+	0.477549i	$0.841525\pi$
$884$	2.56085	0.0861307
$885$	−1.09015	−0.0366448
$886$	64.2042	2.15698
$887$	−19.3303	−0.649049	−0.324525	−	0.945877i	$-0.605204\pi$
$887$	−19.3303	−0.649049	−0.324525	+	0.945877i	$0.605204\pi$
$888$	1.16656	0.0391473
$889$	4.76596	0.159845
$890$	−16.0765	−0.538885
$891$	−8.66026	−0.290130
$892$	10.4214	0.348933
$893$	−4.55827	−0.152537
$894$	8.90246	0.297743
$895$	51.1508	1.70978
$896$	−4.65814	−0.155617
$897$	−1.02153	−0.0341080
$898$	−52.9586	−1.76725
$899$	104.810	3.49560
$900$	−56.4771	−1.88257
$901$	−1.04925	−0.0349555
$902$	11.3621	0.378316
$903$	−0.0441143	−0.00146803
$904$	67.9411	2.25969
$905$	−45.2790	−1.50512
$906$	3.45277	0.114711
$907$	53.7016	1.78313	0.891566	−	0.452890i	$-0.149607\pi$
$907$	53.7016	1.78313	0.891566	+	0.452890i	$0.149607\pi$
$908$	11.4216	0.379039
$909$	21.0322	0.697593
$910$	1.15614	0.0383256
$911$	27.7625	0.919811	0.459906	−	0.887968i	$-0.347883\pi$
$911$	27.7625	0.919811	0.459906	+	0.887968i	$0.347883\pi$
$912$	−0.945003	−0.0312922
$913$	0.411610	0.0136223
$914$	−20.3023	−0.671539
$915$	4.29219	0.141895
$916$	59.4234	1.96341
$917$	3.14827	0.103965
$918$	−2.80228	−0.0924891
$919$	−13.6903	−0.451601	−0.225801	−	0.974174i	$-0.572500\pi$
$919$	−13.6903	−0.451601	−0.225801	+	0.974174i	$0.572500\pi$
$920$	109.304	3.60366
$921$	−3.16392	−0.104255
$922$	−1.53060	−0.0504076
$923$	1.06633	0.0350987
$924$	0.168851	0.00555478
$925$	−6.76503	−0.222433
$926$	−7.79765	−0.256247
$927$	48.1362	1.58100
$928$	−15.3736	−0.504662
$929$	7.20465	0.236377	0.118188	−	0.992991i	$-0.462291\pi$
$929$	7.20465	0.236377	0.118188	+	0.992991i	$0.462291\pi$
$930$	−16.1289	−0.528887
$931$	11.2601	0.369035
$932$	15.5586	0.509639
$933$	−0.720535	−0.0235892
$934$	14.0480	0.459666
$935$	−3.15933	−0.103321
$936$	−8.74335	−0.285785
$937$	0.801168	0.0261730	0.0130865	−	0.999914i	$-0.495834\pi$
$937$	0.801168	0.0261730	0.0130865	+	0.999914i	$0.495834\pi$
$938$	−6.62890	−0.216441
$939$	−4.29567	−0.140184
$940$	−34.0156	−1.10947
$941$	36.8445	1.20110	0.600549	−	0.799588i	$-0.294949\pi$
$941$	36.8445	1.20110	0.600549	+	0.799588i	$0.294949\pi$
$942$	−6.38935	−0.208176
$943$	36.9093	1.20193
$944$	5.30814	0.172765
$945$	−0.830947	−0.0270307
$946$	2.41404	0.0784871
$947$	28.9977	0.942297	0.471149	−	0.882054i	$-0.343840\pi$
$947$	28.9977	0.942297	0.471149	+	0.882054i	$0.343840\pi$
$948$	−0.489648	−0.0159030
$949$	7.07483	0.229659
$950$	19.4866	0.632227
$951$	−3.36248	−0.109036
$952$	−0.999607	−0.0323974
$953$	32.0222	1.03730	0.518650	−	0.854986i	$-0.326435\pi$
$953$	32.0222	1.03730	0.518650	+	0.854986i	$0.326435\pi$
$954$	7.50275	0.242910
$955$	−5.07735	−0.164299
$956$	25.2974	0.818175
$957$	1.87878	0.0607323
$958$	−37.1867	−1.20145
$959$	−0.897153	−0.0289706
$960$	6.05062	0.195283
$961$	86.9752	2.80565
$962$	−2.19343	−0.0707190
$963$	−41.5558	−1.33912
$964$	−35.2163	−1.13424
$965$	27.9272	0.899007
$966$	0.835114	0.0268694
$967$	21.5695	0.693629	0.346815	−	0.937934i	$-0.387263\pi$
$967$	21.5695	0.693629	0.346815	+	0.937934i	$0.387263\pi$
$968$	−4.41183	−0.141802
$969$	0.315508	0.0101356
$970$	−15.2929	−0.491026
$971$	1.78242	0.0572005	0.0286003	−	0.999591i	$-0.490895\pi$
$971$	1.78242	0.0572005	0.0286003	+	0.999591i	$0.490895\pi$
$972$	19.7834	0.634553
$973$	0.538675	0.0172691
$974$	57.6497	1.84722
$975$	−0.648903	−0.0207815
$976$	−20.8996	−0.668979
$977$	27.5465	0.881291	0.440645	−	0.897681i	$-0.354750\pi$
$977$	27.5465	0.881291	0.440645	+	0.897681i	$0.354750\pi$
$978$	−3.12856	−0.100040
$979$	2.10791	0.0673690
$980$	84.0273	2.68415
$981$	2.36752	0.0755891
$982$	11.3030	0.360692
$983$	−39.3584	−1.25534	−0.627669	−	0.778480i	$-0.715991\pi$
$983$	−39.3584	−1.25534	−0.627669	+	0.778480i	$0.715991\pi$
$984$	−4.04298	−0.128886
$985$	68.1260	2.17067
$986$	−23.2943	−0.741843
$987$	−0.124090	−0.00394984
$988$	4.14978	0.132022
$989$	7.84192	0.249359
$990$	22.5911	0.717993
$991$	−21.0381	−0.668298	−0.334149	−	0.942520i	$-0.608449\pi$
$991$	−21.0381	−0.668298	−0.334149	+	0.942520i	$0.608449\pi$
$992$	−17.3047	−0.549424
$993$	−0.610131	−0.0193619
$994$	−0.871738	−0.0276499
$995$	42.8859	1.35957
$996$	−0.306746	−0.00971962
$997$	17.9799	0.569429	0.284715	−	0.958612i	$-0.408101\pi$
$997$	17.9799	0.569429	0.284715	+	0.958612i	$0.408101\pi$
$998$	−62.0634	−1.96458
$999$	1.57648	0.0498775

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.e.1.6	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.e.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-2.41404 q^{2} +0.194701 q^{3} +3.82757 q^{4} -3.15933 q^{5} -0.470017 q^{6} -0.226574 q^{7} -4.41183 q^{8} -2.96209 q^{9} +O(q^{10})\)	\(q-2.41404 q^{2} +0.194701 q^{3} +3.82757 q^{4} -3.15933 q^{5} -0.470017 q^{6} -0.226574 q^{7} -4.41183 q^{8} -2.96209 q^{9} +7.62675 q^{10} -1.00000 q^{11} +0.745235 q^{12} -0.669053 q^{13} +0.546958 q^{14} -0.615127 q^{15} +2.99518 q^{16} -1.00000 q^{17} +7.15060 q^{18} -1.62047 q^{19} -12.0926 q^{20} -0.0441143 q^{21} +2.41404 q^{22} +7.84192 q^{23} -0.858991 q^{24} +4.98139 q^{25} +1.61512 q^{26} -1.16083 q^{27} -0.867229 q^{28} -9.64954 q^{29} +1.48494 q^{30} -10.8616 q^{31} +1.59319 q^{32} -0.194701 q^{33} +2.41404 q^{34} +0.715823 q^{35} -11.3376 q^{36} -1.35806 q^{37} +3.91188 q^{38} -0.130266 q^{39} +13.9385 q^{40} +4.70667 q^{41} +0.106494 q^{42} +1.00000 q^{43} -3.82757 q^{44} +9.35823 q^{45} -18.9307 q^{46} +2.81293 q^{47} +0.583166 q^{48} -6.94866 q^{49} -12.0253 q^{50} -0.194701 q^{51} -2.56085 q^{52} +1.04925 q^{53} +2.80228 q^{54} +3.15933 q^{55} +0.999607 q^{56} -0.315508 q^{57} +23.2943 q^{58} +1.77223 q^{59} -2.35444 q^{60} -6.97773 q^{61} +26.2204 q^{62} +0.671133 q^{63} -9.83638 q^{64} +2.11376 q^{65} +0.470017 q^{66} -12.1196 q^{67} -3.82757 q^{68} +1.52683 q^{69} -1.72802 q^{70} -1.59379 q^{71} +13.0683 q^{72} -10.5744 q^{73} +3.27841 q^{74} +0.969883 q^{75} -6.20247 q^{76} +0.226574 q^{77} +0.314466 q^{78} -0.657039 q^{79} -9.46277 q^{80} +8.66026 q^{81} -11.3621 q^{82} -0.411610 q^{83} -0.168851 q^{84} +3.15933 q^{85} -2.41404 q^{86} -1.87878 q^{87} +4.41183 q^{88} -2.10791 q^{89} -22.5911 q^{90} +0.151590 q^{91} +30.0156 q^{92} -2.11478 q^{93} -6.79052 q^{94} +5.11961 q^{95} +0.310197 q^{96} -2.00517 q^{97} +16.7743 q^{98} +2.96209 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) \) 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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