LMFDB - Embedded newform 8041.2.a.j.1.35

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:	$82$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.35
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.425983 q^{2} -1.37205 q^{3} -1.81854 q^{4} -0.119265 q^{5} +0.584473 q^{6} -3.28017 q^{7} +1.62663 q^{8} -1.11747 q^{9} +O(q^{10})$	\(q-0.425983 q^{2} -1.37205 q^{3} -1.81854 q^{4} -0.119265 q^{5} +0.584473 q^{6} -3.28017 q^{7} +1.62663 q^{8} -1.11747 q^{9} +0.0508049 q^{10} +1.00000 q^{11} +2.49513 q^{12} +3.12921 q^{13} +1.39730 q^{14} +0.163638 q^{15} +2.94416 q^{16} +1.00000 q^{17} +0.476022 q^{18} +3.73883 q^{19} +0.216888 q^{20} +4.50058 q^{21} -0.425983 q^{22} +9.46245 q^{23} -2.23183 q^{24} -4.98578 q^{25} -1.33299 q^{26} +5.64939 q^{27} +5.96512 q^{28} +2.21793 q^{29} -0.0697071 q^{30} -5.91352 q^{31} -4.50743 q^{32} -1.37205 q^{33} -0.425983 q^{34} +0.391210 q^{35} +2.03215 q^{36} +3.11760 q^{37} -1.59268 q^{38} -4.29345 q^{39} -0.194001 q^{40} +6.38610 q^{41} -1.91717 q^{42} +1.00000 q^{43} -1.81854 q^{44} +0.133275 q^{45} -4.03085 q^{46} +2.43780 q^{47} -4.03954 q^{48} +3.75954 q^{49} +2.12386 q^{50} -1.37205 q^{51} -5.69059 q^{52} -4.97695 q^{53} -2.40655 q^{54} -0.119265 q^{55} -5.33564 q^{56} -5.12988 q^{57} -0.944800 q^{58} -11.8542 q^{59} -0.297582 q^{60} +5.56770 q^{61} +2.51906 q^{62} +3.66548 q^{63} -3.96822 q^{64} -0.373205 q^{65} +0.584473 q^{66} -11.3013 q^{67} -1.81854 q^{68} -12.9830 q^{69} -0.166649 q^{70} -12.8284 q^{71} -1.81771 q^{72} +12.8767 q^{73} -1.32804 q^{74} +6.84076 q^{75} -6.79921 q^{76} -3.28017 q^{77} +1.82894 q^{78} -3.70184 q^{79} -0.351135 q^{80} -4.39887 q^{81} -2.72037 q^{82} +12.8218 q^{83} -8.18447 q^{84} -0.119265 q^{85} -0.425983 q^{86} -3.04312 q^{87} +1.62663 q^{88} -13.6768 q^{89} -0.0567728 q^{90} -10.2644 q^{91} -17.2078 q^{92} +8.11368 q^{93} -1.03846 q^{94} -0.445912 q^{95} +6.18444 q^{96} +8.97487 q^{97} -1.60150 q^{98} -1.11747 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) $ 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9} + q^{10} + 82 q^{11} + 3 q^{12} + 26 q^{13} + 17 q^{14} + 66 q^{15} + 122 q^{16} + 82 q^{17} + 18 q^{18} + 12 q^{19} + 9 q^{20} + 22 q^{21} + 8 q^{22} + 50 q^{23} + 15 q^{24} + 117 q^{25} + 36 q^{26} + 30 q^{27} + 11 q^{28} + 33 q^{29} - 26 q^{30} + 40 q^{31} + 58 q^{32} + 6 q^{33} + 8 q^{34} + 16 q^{35} + 160 q^{36} + 31 q^{37} + 18 q^{38} + 41 q^{39} - 29 q^{40} + 42 q^{41} - 51 q^{42} + 82 q^{43} + 98 q^{44} - 2 q^{45} - 19 q^{46} + 84 q^{47} - 46 q^{48} + 136 q^{49} + 59 q^{50} + 6 q^{51} + 45 q^{52} + 83 q^{53} + 24 q^{54} + 11 q^{55} + 21 q^{56} + 23 q^{57} + 14 q^{58} + 96 q^{59} + 184 q^{60} - 6 q^{61} - 23 q^{62} + 8 q^{63} + 148 q^{64} + 5 q^{65} + 10 q^{66} + 78 q^{67} + 98 q^{68} + 61 q^{69} - 3 q^{70} + 155 q^{71} + 50 q^{72} - 23 q^{73} + 10 q^{74} - 19 q^{75} + 44 q^{76} + 8 q^{77} - 27 q^{78} + 31 q^{79} + 19 q^{80} + 150 q^{81} - 12 q^{82} + 54 q^{83} + 8 q^{84} + 11 q^{85} + 8 q^{86} + 20 q^{87} + 30 q^{88} + 25 q^{89} - 81 q^{90} - 14 q^{91} + 60 q^{92} + 36 q^{93} + 19 q^{94} + 111 q^{95} - 6 q^{96} + 2 q^{97} - 5 q^{98} + 108 q^{99}+O(q^{100}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9 + q^10 + 82 * q^11 + 3 * q^12 + 26 * q^13 + 17 * q^14 + 66 * q^15 + 122 * q^16 + 82 * q^17 + 18 * q^18 + 12 * q^19 + 9 * q^20 + 22 * q^21 + 8 * q^22 + 50 * q^23 + 15 * q^24 + 117 * q^25 + 36 * q^26 + 30 * q^27 + 11 * q^28 + 33 * q^29 - 26 * q^30 + 40 * q^31 + 58 * q^32 + 6 * q^33 + 8 * q^34 + 16 * q^35 + 160 * q^36 + 31 * q^37 + 18 * q^38 + 41 * q^39 - 29 * q^40 + 42 * q^41 - 51 * q^42 + 82 * q^43 + 98 * q^44 - 2 * q^45 - 19 * q^46 + 84 * q^47 - 46 * q^48 + 136 * q^49 + 59 * q^50 + 6 * q^51 + 45 * q^52 + 83 * q^53 + 24 * q^54 + 11 * q^55 + 21 * q^56 + 23 * q^57 + 14 * q^58 + 96 * q^59 + 184 * q^60 - 6 * q^61 - 23 * q^62 + 8 * q^63 + 148 * q^64 + 5 * q^65 + 10 * q^66 + 78 * q^67 + 98 * q^68 + 61 * q^69 - 3 * q^70 + 155 * q^71 + 50 * q^72 - 23 * q^73 + 10 * q^74 - 19 * q^75 + 44 * q^76 + 8 * q^77 - 27 * q^78 + 31 * q^79 + 19 * q^80 + 150 * q^81 - 12 * q^82 + 54 * q^83 + 8 * q^84 + 11 * q^85 + 8 * q^86 + 20 * q^87 + 30 * q^88 + 25 * q^89 - 81 * q^90 - 14 * q^91 + 60 * q^92 + 36 * q^93 + 19 * q^94 + 111 * q^95 - 6 * q^96 + 2 * q^97 - 5 * q^98 + 108 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.425983	−0.301216	−0.150608	−	0.988594i	$-0.548123\pi$
$2$	−0.425983	−0.301216	−0.150608	+	0.988594i	$0.548123\pi$
$3$	−1.37205	−0.792156	−0.396078	−	0.918217i	$-0.629629\pi$
$3$	−1.37205	−0.792156	−0.396078	+	0.918217i	$0.629629\pi$
$4$	−1.81854	−0.909269
$5$	−0.119265	−0.0533369	−0.0266685	−	0.999644i	$-0.508490\pi$
$5$	−0.119265	−0.0533369	−0.0266685	+	0.999644i	$0.508490\pi$
$6$	0.584473	0.238610
$7$	−3.28017	−1.23979	−0.619895	−	0.784685i	$-0.712825\pi$
$7$	−3.28017	−1.23979	−0.619895	+	0.784685i	$0.712825\pi$
$8$	1.62663	0.575102
$9$	−1.11747	−0.372489
$10$	0.0508049	0.0160659
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.49513	0.720283
$13$	3.12921	0.867887	0.433943	−	0.900940i	$-0.357122\pi$
$13$	3.12921	0.867887	0.433943	+	0.900940i	$0.357122\pi$
$14$	1.39730	0.373444
$15$	0.163638	0.0422512
$16$	2.94416	0.736039
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	0.476022	0.112199
$19$	3.73883	0.857747	0.428874	−	0.903365i	$-0.358911\pi$
$19$	3.73883	0.857747	0.428874	+	0.903365i	$0.358911\pi$
$20$	0.216888	0.0484976
$21$	4.50058	0.982107
$22$	−0.425983	−0.0908200
$23$	9.46245	1.97306	0.986529	−	0.163587i	$-0.0523065\pi$
$23$	9.46245	1.97306	0.986529	+	0.163587i	$0.0523065\pi$
$24$	−2.23183	−0.455571
$25$	−4.98578	−0.997155
$26$	−1.33299	−0.261421
$27$	5.64939	1.08723
$28$	5.96512	1.12730
$29$	2.21793	0.411859	0.205929	−	0.978567i	$-0.433978\pi$
$29$	2.21793	0.411859	0.205929	+	0.978567i	$0.433978\pi$
$30$	−0.0697071	−0.0127267
$31$	−5.91352	−1.06210	−0.531050	−	0.847340i	$-0.678202\pi$
$31$	−5.91352	−1.06210	−0.531050	+	0.847340i	$0.678202\pi$
$32$	−4.50743	−0.796809
$33$	−1.37205	−0.238844
$34$	−0.425983	−0.0730556
$35$	0.391210	0.0661266
$36$	2.03215	0.338692
$37$	3.11760	0.512530	0.256265	−	0.966607i	$-0.417508\pi$
$37$	3.11760	0.512530	0.256265	+	0.966607i	$0.417508\pi$
$38$	−1.59268	−0.258367
$39$	−4.29345	−0.687502
$40$	−0.194001	−0.0306742
$41$	6.38610	0.997341	0.498671	−	0.866792i	$-0.333822\pi$
$41$	6.38610	0.997341	0.498671	+	0.866792i	$0.333822\pi$
$42$	−1.91717	−0.295826
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.81854	−0.274155
$45$	0.133275	0.0198674
$46$	−4.03085	−0.594316
$47$	2.43780	0.355590	0.177795	−	0.984068i	$-0.443104\pi$
$47$	2.43780	0.355590	0.177795	+	0.984068i	$0.443104\pi$
$48$	−4.03954	−0.583058
$49$	3.75954	0.537077
$50$	2.12386	0.300359
$51$	−1.37205	−0.192126
$52$	−5.69059	−0.789143
$53$	−4.97695	−0.683636	−0.341818	−	0.939766i	$-0.611043\pi$
$53$	−4.97695	−0.683636	−0.341818	+	0.939766i	$0.611043\pi$
$54$	−2.40655	−0.327489
$55$	−0.119265	−0.0160817
$56$	−5.33564	−0.713005
$57$	−5.12988	−0.679470
$58$	−0.944800	−0.124058
$59$	−11.8542	−1.54328	−0.771642	−	0.636057i	$-0.780564\pi$
$59$	−11.8542	−1.54328	−0.771642	+	0.636057i	$0.780564\pi$
$60$	−0.297582	−0.0384177
$61$	5.56770	0.712871	0.356436	−	0.934320i	$-0.383992\pi$
$61$	5.56770	0.712871	0.356436	+	0.934320i	$0.383992\pi$
$62$	2.51906	0.319921
$63$	3.66548	0.461807
$64$	−3.96822	−0.496028
$65$	−0.373205	−0.0462904
$66$	0.584473	0.0719436
$67$	−11.3013	−1.38068	−0.690338	−	0.723487i	$-0.742538\pi$
$67$	−11.3013	−1.38068	−0.690338	+	0.723487i	$0.742538\pi$
$68$	−1.81854	−0.220530
$69$	−12.9830	−1.56297
$70$	−0.166649	−0.0199184
$71$	−12.8284	−1.52245	−0.761224	−	0.648489i	$-0.775401\pi$
$71$	−12.8284	−1.52245	−0.761224	+	0.648489i	$0.775401\pi$
$72$	−1.81771	−0.214219
$73$	12.8767	1.50710	0.753549	−	0.657392i	$-0.228340\pi$
$73$	12.8767	1.50710	0.753549	+	0.657392i	$0.228340\pi$
$74$	−1.32804	−0.154382
$75$	6.84076	0.789903
$76$	−6.79921	−0.779923
$77$	−3.28017	−0.373810
$78$	1.82894	0.207086
$79$	−3.70184	−0.416490	−0.208245	−	0.978077i	$-0.566775\pi$
$79$	−3.70184	−0.416490	−0.208245	+	0.978077i	$0.566775\pi$
$80$	−0.351135	−0.0392581
$81$	−4.39887	−0.488764
$82$	−2.72037	−0.300415
$83$	12.8218	1.40737	0.703687	−	0.710510i	$-0.251536\pi$
$83$	12.8218	1.40737	0.703687	+	0.710510i	$0.251536\pi$
$84$	−8.18447	−0.892999
$85$	−0.119265	−0.0129361
$86$	−0.425983	−0.0459350
$87$	−3.04312	−0.326256
$88$	1.62663	0.173400
$89$	−13.6768	−1.44974	−0.724868	−	0.688888i	$-0.758099\pi$
$89$	−13.6768	−1.44974	−0.724868	+	0.688888i	$0.758099\pi$
$90$	−0.0567728	−0.00598438
$91$	−10.2644	−1.07600
$92$	−17.2078	−1.79404
$93$	8.11368	0.841349
$94$	−1.03846	−0.107109
$95$	−0.445912	−0.0457496
$96$	6.18444	0.631197
$97$	8.97487	0.911260	0.455630	−	0.890169i	$-0.349414\pi$
$97$	8.97487	0.911260	0.455630	+	0.890169i	$0.349414\pi$
$98$	−1.60150	−0.161776
$99$	−1.11747	−0.112310
$100$	9.06682	0.906682
$101$	−9.90489	−0.985574	−0.492787	−	0.870150i	$-0.664022\pi$
$101$	−9.90489	−0.985574	−0.492787	+	0.870150i	$0.664022\pi$
$102$	0.584473	0.0578714
$103$	11.1943	1.10301	0.551503	−	0.834173i	$-0.314055\pi$
$103$	11.1943	1.10301	0.551503	+	0.834173i	$0.314055\pi$
$104$	5.09008	0.499123
$105$	−0.536762	−0.0523826
$106$	2.12010	0.205922
$107$	15.9242	1.53945	0.769726	−	0.638374i	$-0.220393\pi$
$107$	15.9242	1.53945	0.769726	+	0.638374i	$0.220393\pi$
$108$	−10.2736	−0.988580
$109$	−19.4655	−1.86446	−0.932230	−	0.361866i	$-0.882140\pi$
$109$	−19.4655	−1.86446	−0.932230	+	0.361866i	$0.882140\pi$
$110$	0.0508049	0.00484406
$111$	−4.27751	−0.406003
$112$	−9.65735	−0.912533
$113$	−6.65167	−0.625737	−0.312868	−	0.949796i	$-0.601290\pi$
$113$	−6.65167	−0.625737	−0.312868	+	0.949796i	$0.601290\pi$
$114$	2.18525	0.204667
$115$	−1.12854	−0.105237
$116$	−4.03339	−0.374490
$117$	−3.49679	−0.323278
$118$	5.04969	0.464861
$119$	−3.28017	−0.300693
$120$	0.266179	0.0242987
$121$	1.00000	0.0909091
$122$	−2.37175	−0.214728
$123$	−8.76208	−0.790050
$124$	10.7540	0.965735
$125$	1.19095	0.106522
$126$	−1.56143	−0.139104
$127$	−7.07945	−0.628200	−0.314100	−	0.949390i	$-0.601703\pi$
$127$	−7.07945	−0.628200	−0.314100	+	0.949390i	$0.601703\pi$
$128$	10.7053	0.946220
$129$	−1.37205	−0.120803
$130$	0.158979	0.0139434
$131$	9.17733	0.801827	0.400914	−	0.916116i	$-0.368693\pi$
$131$	9.17733	0.801827	0.400914	+	0.916116i	$0.368693\pi$
$132$	2.49513	0.217174
$133$	−12.2640	−1.06343
$134$	4.81417	0.415881
$135$	−0.673775	−0.0579893
$136$	1.62663	0.139483
$137$	−4.04482	−0.345572	−0.172786	−	0.984959i	$-0.555277\pi$
$137$	−4.04482	−0.345572	−0.172786	+	0.984959i	$0.555277\pi$
$138$	5.53054	0.470791
$139$	10.0622	0.853465	0.426733	−	0.904378i	$-0.359665\pi$
$139$	10.0622	0.853465	0.426733	+	0.904378i	$0.359665\pi$
$140$	−0.711430	−0.0601268
$141$	−3.34480	−0.281683
$142$	5.46467	0.458585
$143$	3.12921	0.261678
$144$	−3.29000	−0.274166
$145$	−0.264521	−0.0219673
$146$	−5.48524	−0.453962
$147$	−5.15829	−0.425449
$148$	−5.66947	−0.466027
$149$	−4.39221	−0.359824	−0.179912	−	0.983683i	$-0.557581\pi$
$149$	−4.39221	−0.359824	−0.179912	+	0.983683i	$0.557581\pi$
$150$	−2.91405	−0.237931
$151$	−0.907792	−0.0738751	−0.0369375	−	0.999318i	$-0.511760\pi$
$151$	−0.907792	−0.0738751	−0.0369375	+	0.999318i	$0.511760\pi$
$152$	6.08171	0.493292
$153$	−1.11747	−0.0903418
$154$	1.39730	0.112598
$155$	0.705277	0.0566492
$156$	7.80780	0.625124
$157$	16.6209	1.32649	0.663244	−	0.748403i	$-0.269179\pi$
$157$	16.6209	1.32649	0.663244	+	0.748403i	$0.269179\pi$
$158$	1.57692	0.125453
$159$	6.82864	0.541547
$160$	0.537579	0.0424993
$161$	−31.0385	−2.44618
$162$	1.87385	0.147223
$163$	−0.888073	−0.0695592	−0.0347796	−	0.999395i	$-0.511073\pi$
$163$	−0.888073	−0.0695592	−0.0347796	+	0.999395i	$0.511073\pi$
$164$	−11.6134	−0.906851
$165$	0.163638	0.0127392
$166$	−5.46187	−0.423923
$167$	4.96465	0.384176	0.192088	−	0.981378i	$-0.438474\pi$
$167$	4.96465	0.384176	0.192088	+	0.981378i	$0.438474\pi$
$168$	7.32079	0.564811
$169$	−3.20804	−0.246773
$170$	0.0508049	0.00389656
$171$	−4.17802	−0.319501
$172$	−1.81854	−0.138662
$173$	15.0578	1.14482	0.572412	−	0.819966i	$-0.306008\pi$
$173$	15.0578	1.14482	0.572412	+	0.819966i	$0.306008\pi$
$174$	1.29632	0.0982736
$175$	16.3542	1.23626
$176$	2.94416	0.221924
$177$	16.2646	1.22252
$178$	5.82608	0.436683
$179$	−10.9742	−0.820249	−0.410125	−	0.912029i	$-0.634515\pi$
$179$	−10.9742	−0.820249	−0.410125	+	0.912029i	$0.634515\pi$
$180$	−0.242365	−0.0180648
$181$	16.7170	1.24256	0.621282	−	0.783587i	$-0.286612\pi$
$181$	16.7170	1.24256	0.621282	+	0.783587i	$0.286612\pi$
$182$	4.37244	0.324107
$183$	−7.63919	−0.564705
$184$	15.3919	1.13471
$185$	−0.371820	−0.0273368
$186$	−3.45629	−0.253428
$187$	1.00000	0.0731272
$188$	−4.43324	−0.323327
$189$	−18.5310	−1.34793
$190$	0.189951	0.0137805
$191$	25.0635	1.81353	0.906765	−	0.421635i	$-0.138544\pi$
$191$	25.0635	1.81353	0.906765	+	0.421635i	$0.138544\pi$
$192$	5.44462	0.392932
$193$	−11.7381	−0.844929	−0.422465	−	0.906379i	$-0.638835\pi$
$193$	−11.7381	−0.844929	−0.422465	+	0.906379i	$0.638835\pi$
$194$	−3.82315	−0.274486
$195$	0.512058	0.0366693
$196$	−6.83687	−0.488348
$197$	−25.7606	−1.83537	−0.917683	−	0.397313i	$-0.869943\pi$
$197$	−25.7606	−1.83537	−0.917683	+	0.397313i	$0.869943\pi$
$198$	0.476022	0.0338294
$199$	−20.0071	−1.41827	−0.709133	−	0.705075i	$-0.750913\pi$
$199$	−20.0071	−1.41827	−0.709133	+	0.705075i	$0.750913\pi$
$200$	−8.11003	−0.573466
$201$	15.5060	1.09371
$202$	4.21932	0.296870
$203$	−7.27519	−0.510618
$204$	2.49513	0.174694
$205$	−0.761638	−0.0531951
$206$	−4.76858	−0.332243
$207$	−10.5740	−0.734942
$208$	9.21289	0.638799
$209$	3.73883	0.258620
$210$	0.228652	0.0157785
$211$	0.458426	0.0315594	0.0157797	−	0.999875i	$-0.494977\pi$
$211$	0.458426	0.0315594	0.0157797	+	0.999875i	$0.494977\pi$
$212$	9.05077	0.621609
$213$	17.6012	1.20602
$214$	−6.78346	−0.463707
$215$	−0.119265	−0.00813381
$216$	9.18949	0.625265
$217$	19.3974	1.31678
$218$	8.29200	0.561605
$219$	−17.6675	−1.19386
$220$	0.216888	0.0146226
$221$	3.12921	0.210493
$222$	1.82215	0.122295
$223$	−5.87700	−0.393553	−0.196777	−	0.980448i	$-0.563047\pi$
$223$	−5.87700	−0.393553	−0.196777	+	0.980448i	$0.563047\pi$
$224$	14.7852	0.987875
$225$	5.57143	0.371429
$226$	2.83350	0.188482
$227$	0.388739	0.0258015	0.0129008	−	0.999917i	$-0.495893\pi$
$227$	0.388739	0.0258015	0.0129008	+	0.999917i	$0.495893\pi$
$228$	9.32889	0.617821
$229$	15.1614	1.00189	0.500947	−	0.865478i	$-0.332985\pi$
$229$	15.1614	1.00189	0.500947	+	0.865478i	$0.332985\pi$
$230$	0.480739	0.0316990
$231$	4.50058	0.296116
$232$	3.60776	0.236861
$233$	10.1087	0.662244	0.331122	−	0.943588i	$-0.392573\pi$
$233$	10.1087	0.662244	0.331122	+	0.943588i	$0.392573\pi$
$234$	1.48957	0.0973764
$235$	−0.290745	−0.0189661
$236$	21.5573	1.40326
$237$	5.07913	0.329925
$238$	1.39730	0.0905735
$239$	7.94961	0.514218	0.257109	−	0.966382i	$-0.417230\pi$
$239$	7.94961	0.514218	0.257109	+	0.966382i	$0.417230\pi$
$240$	0.481776	0.0310985
$241$	12.3615	0.796275	0.398138	−	0.917326i	$-0.369657\pi$
$241$	12.3615	0.796275	0.398138	+	0.917326i	$0.369657\pi$
$242$	−0.425983	−0.0273833
$243$	−10.9127	−0.700048
$244$	−10.1251	−0.648192
$245$	−0.448382	−0.0286461
$246$	3.73250	0.237975
$247$	11.6996	0.744427
$248$	−9.61914	−0.610816
$249$	−17.5922	−1.11486
$250$	−0.507327	−0.0320862
$251$	−1.34441	−0.0848585	−0.0424293	−	0.999099i	$-0.513510\pi$
$251$	−1.34441	−0.0848585	−0.0424293	+	0.999099i	$0.513510\pi$
$252$	−6.66582	−0.419907
$253$	9.46245	0.594899
$254$	3.01573	0.189224
$255$	0.163638	0.0102474
$256$	3.37618	0.211011
$257$	−29.9179	−1.86623	−0.933115	−	0.359579i	$-0.882920\pi$
$257$	−29.9179	−1.86623	−0.933115	+	0.359579i	$0.882920\pi$
$258$	0.584473	0.0363877
$259$	−10.2263	−0.635429
$260$	0.678688	0.0420905
$261$	−2.47846	−0.153413
$262$	−3.90939	−0.241523
$263$	10.3248	0.636652	0.318326	−	0.947981i	$-0.396879\pi$
$263$	10.3248	0.636652	0.318326	+	0.947981i	$0.396879\pi$
$264$	−2.23183	−0.137360
$265$	0.593576	0.0364631
$266$	5.22427	0.320321
$267$	18.7653	1.14842
$268$	20.5519	1.25541
$269$	18.7972	1.14608	0.573041	−	0.819527i	$-0.305763\pi$
$269$	18.7972	1.14608	0.573041	+	0.819527i	$0.305763\pi$
$270$	0.287017	0.0174673
$271$	−5.00229	−0.303868	−0.151934	−	0.988391i	$-0.548550\pi$
$271$	−5.00229	−0.303868	−0.151934	+	0.988391i	$0.548550\pi$
$272$	2.94416	0.178516
$273$	14.0833	0.852357
$274$	1.72303	0.104092
$275$	−4.98578	−0.300654
$276$	23.6101	1.42116
$277$	1.56172	0.0938346	0.0469173	−	0.998899i	$-0.485060\pi$
$277$	1.56172	0.0938346	0.0469173	+	0.998899i	$0.485060\pi$
$278$	−4.28633	−0.257077
$279$	6.60816	0.395620
$280$	0.636356	0.0380295
$281$	14.2225	0.848441	0.424220	−	0.905559i	$-0.360548\pi$
$281$	14.2225	0.848441	0.424220	+	0.905559i	$0.360548\pi$
$282$	1.42483	0.0848473
$283$	15.8148	0.940093	0.470046	−	0.882642i	$-0.344237\pi$
$283$	15.8148	0.940093	0.470046	+	0.882642i	$0.344237\pi$
$284$	23.3289	1.38431
$285$	0.611816	0.0362408
$286$	−1.33299	−0.0788215
$287$	−20.9475	−1.23649
$288$	5.03690	0.296802
$289$	1.00000	0.0588235
$290$	0.112682	0.00661690
$291$	−12.3140	−0.721860
$292$	−23.4167	−1.37036
$293$	−12.3978	−0.724289	−0.362144	−	0.932122i	$-0.617955\pi$
$293$	−12.3978	−0.724289	−0.362144	+	0.932122i	$0.617955\pi$
$294$	2.19735	0.128152
$295$	1.41379	0.0823140
$296$	5.07119	0.294757
$297$	5.64939	0.327811
$298$	1.87101	0.108385
$299$	29.6100	1.71239
$300$	−12.4402	−0.718234
$301$	−3.28017	−0.189066
$302$	0.386704	0.0222523
$303$	13.5901	0.780728
$304$	11.0077	0.631336
$305$	−0.664032	−0.0380224
$306$	0.476022	0.0272124
$307$	29.0163	1.65605	0.828023	−	0.560694i	$-0.189466\pi$
$307$	29.0163	1.65605	0.828023	+	0.560694i	$0.189466\pi$
$308$	5.96512	0.339894
$309$	−15.3592	−0.873753
$310$	−0.300436	−0.0170636
$311$	−0.585418	−0.0331960	−0.0165980	−	0.999862i	$-0.505284\pi$
$311$	−0.585418	−0.0331960	−0.0165980	+	0.999862i	$0.505284\pi$
$312$	−6.98387	−0.395384
$313$	−10.0006	−0.565267	−0.282633	−	0.959228i	$-0.591208\pi$
$313$	−10.0006	−0.565267	−0.282633	+	0.959228i	$0.591208\pi$
$314$	−7.08021	−0.399559
$315$	−0.437164	−0.0246314
$316$	6.73194	0.378701
$317$	−20.7214	−1.16383	−0.581915	−	0.813249i	$-0.697696\pi$
$317$	−20.7214	−1.16383	−0.581915	+	0.813249i	$0.697696\pi$
$318$	−2.90889	−0.163122
$319$	2.21793	0.124180
$320$	0.473270	0.0264566
$321$	−21.8489	−1.21949
$322$	13.2219	0.736827
$323$	3.73883	0.208034
$324$	7.99952	0.444418
$325$	−15.6015	−0.865418
$326$	0.378304	0.0209523
$327$	26.7078	1.47694
$328$	10.3878	0.573573
$329$	−7.99641	−0.440857
$330$	−0.0697071	−0.00383725
$331$	23.7864	1.30742	0.653709	−	0.756746i	$-0.273212\pi$
$331$	23.7864	1.30742	0.653709	+	0.756746i	$0.273212\pi$
$332$	−23.3169	−1.27968
$333$	−3.48381	−0.190911
$334$	−2.11486	−0.115720
$335$	1.34785	0.0736410
$336$	13.2504	0.722869
$337$	−10.2107	−0.556214	−0.278107	−	0.960550i	$-0.589707\pi$
$337$	−10.2107	−0.556214	−0.278107	+	0.960550i	$0.589707\pi$
$338$	1.36657	0.0743318
$339$	9.12646	0.495681
$340$	0.216888	0.0117624
$341$	−5.91352	−0.320235
$342$	1.77977	0.0962388
$343$	10.6293	0.573927
$344$	1.62663	0.0877022
$345$	1.54842	0.0833640
$346$	−6.41438	−0.344839
$347$	−19.3696	−1.03982	−0.519908	−	0.854222i	$-0.674034\pi$
$347$	−19.3696	−1.03982	−0.519908	+	0.854222i	$0.674034\pi$
$348$	5.53403	0.296655
$349$	13.6910	0.732863	0.366432	−	0.930445i	$-0.380579\pi$
$349$	13.6910	0.732863	0.366432	+	0.930445i	$0.380579\pi$
$350$	−6.96662	−0.372382
$351$	17.6781	0.943588
$352$	−4.50743	−0.240247
$353$	−19.8337	−1.05564	−0.527822	−	0.849355i	$-0.676991\pi$
$353$	−19.8337	−1.05564	−0.527822	+	0.849355i	$0.676991\pi$
$354$	−6.92845	−0.368243
$355$	1.52998	0.0812027
$356$	24.8718	1.31820
$357$	4.50058	0.238196
$358$	4.67482	0.247072
$359$	7.13627	0.376638	0.188319	−	0.982108i	$-0.439696\pi$
$359$	7.13627	0.376638	0.188319	+	0.982108i	$0.439696\pi$
$360$	0.216789	0.0114258
$361$	−5.02113	−0.264270
$362$	−7.12116	−0.374280
$363$	−1.37205	−0.0720142
$364$	18.6661	0.978370
$365$	−1.53573	−0.0803840
$366$	3.25417	0.170098
$367$	−22.6870	−1.18425	−0.592126	−	0.805846i	$-0.701711\pi$
$367$	−22.6870	−1.18425	−0.592126	+	0.805846i	$0.701711\pi$
$368$	27.8589	1.45225
$369$	−7.13625	−0.371498
$370$	0.158389	0.00823427
$371$	16.3252	0.847565
$372$	−14.7550	−0.765013
$373$	−15.6127	−0.808393	−0.404197	−	0.914672i	$-0.632449\pi$
$373$	−15.6127	−0.808393	−0.404197	+	0.914672i	$0.632449\pi$
$374$	−0.425983	−0.0220271
$375$	−1.63405	−0.0843822
$376$	3.96541	0.204500
$377$	6.94036	0.357447
$378$	7.89389	0.406018
$379$	16.2641	0.835429	0.417715	−	0.908578i	$-0.362831\pi$
$379$	16.2641	0.835429	0.417715	+	0.908578i	$0.362831\pi$
$380$	0.810908	0.0415987
$381$	9.71340	0.497632
$382$	−10.6766	−0.546264
$383$	18.1651	0.928193	0.464096	−	0.885785i	$-0.346379\pi$
$383$	18.1651	0.928193	0.464096	+	0.885785i	$0.346379\pi$
$384$	−14.6882	−0.749554
$385$	0.391210	0.0199379
$386$	5.00025	0.254506
$387$	−1.11747	−0.0568040
$388$	−16.3211	−0.828580
$389$	7.69324	0.390063	0.195031	−	0.980797i	$-0.437519\pi$
$389$	7.69324	0.390063	0.195031	+	0.980797i	$0.437519\pi$
$390$	−0.218128	−0.0110454
$391$	9.46245	0.478537
$392$	6.11539	0.308874
$393$	−12.5918	−0.635173
$394$	10.9736	0.552841
$395$	0.441500	0.0222143
$396$	2.03215	0.102120
$397$	4.82410	0.242115	0.121057	−	0.992646i	$-0.461372\pi$
$397$	4.82410	0.242115	0.121057	+	0.992646i	$0.461372\pi$
$398$	8.52269	0.427204
$399$	16.8269	0.842399
$400$	−14.6789	−0.733945
$401$	−23.1130	−1.15421	−0.577103	−	0.816671i	$-0.695817\pi$
$401$	−23.1130	−1.15421	−0.577103	+	0.816671i	$0.695817\pi$
$402$	−6.60531	−0.329443
$403$	−18.5047	−0.921783
$404$	18.0124	0.896152
$405$	0.524632	0.0260692
$406$	3.09911	0.153806
$407$	3.11760	0.154533
$408$	−2.23183	−0.110492
$409$	18.4776	0.913661	0.456830	−	0.889554i	$-0.348985\pi$
$409$	18.4776	0.913661	0.456830	+	0.889554i	$0.348985\pi$
$410$	0.324445	0.0160232
$411$	5.54971	0.273747
$412$	−20.3572	−1.00293
$413$	38.8838	1.91335
$414$	4.50434	0.221376
$415$	−1.52919	−0.0750650
$416$	−14.1047	−0.691540
$417$	−13.8059	−0.676078
$418$	−1.59268	−0.0779006
$419$	−25.3888	−1.24032	−0.620162	−	0.784474i	$-0.712933\pi$
$419$	−25.3888	−1.24032	−0.620162	+	0.784474i	$0.712933\pi$
$420$	0.976121	0.0476298
$421$	24.6261	1.20020	0.600102	−	0.799923i	$-0.295127\pi$
$421$	24.6261	1.20020	0.600102	+	0.799923i	$0.295127\pi$
$422$	−0.195282	−0.00950618
$423$	−2.72416	−0.132453
$424$	−8.09567	−0.393161
$425$	−4.98578	−0.241846
$426$	−7.49783	−0.363271
$427$	−18.2630	−0.883810
$428$	−28.9588	−1.39978
$429$	−4.29345	−0.207290
$430$	0.0508049	0.00245003
$431$	−17.1039	−0.823867	−0.411934	−	0.911214i	$-0.635146\pi$
$431$	−17.1039	−0.823867	−0.411934	+	0.911214i	$0.635146\pi$
$432$	16.6327	0.800241
$433$	−3.13581	−0.150697	−0.0753487	−	0.997157i	$-0.524007\pi$
$433$	−3.13581	−0.150697	−0.0753487	+	0.997157i	$0.524007\pi$
$434$	−8.26297	−0.396635
$435$	0.362938	0.0174015
$436$	35.3988	1.69530
$437$	35.3785	1.69238
$438$	7.52605	0.359609
$439$	−13.4389	−0.641405	−0.320702	−	0.947180i	$-0.603919\pi$
$439$	−13.4389	−0.641405	−0.320702	+	0.947180i	$0.603919\pi$
$440$	−0.194001	−0.00924861
$441$	−4.20116	−0.200055
$442$	−1.33299	−0.0634040
$443$	−39.8926	−1.89536	−0.947678	−	0.319227i	$-0.896577\pi$
$443$	−39.8926	−1.89536	−0.947678	+	0.319227i	$0.896577\pi$
$444$	7.77882	0.369166
$445$	1.63116	0.0773245
$446$	2.50351	0.118544
$447$	6.02636	0.285037
$448$	13.0165	0.614970
$449$	1.07330	0.0506523	0.0253262	−	0.999679i	$-0.491938\pi$
$449$	1.07330	0.0506523	0.0253262	+	0.999679i	$0.491938\pi$
$450$	−2.37334	−0.111880
$451$	6.38610	0.300710
$452$	12.0963	0.568963
$453$	1.24554	0.0585206
$454$	−0.165596	−0.00777183
$455$	1.22418	0.0573904
$456$	−8.34444	−0.390764
$457$	−28.1193	−1.31536	−0.657682	−	0.753296i	$-0.728463\pi$
$457$	−28.1193	−1.31536	−0.657682	+	0.753296i	$0.728463\pi$
$458$	−6.45851	−0.301787
$459$	5.64939	0.263691
$460$	2.05229	0.0956886
$461$	8.74242	0.407175	0.203588	−	0.979057i	$-0.434740\pi$
$461$	8.74242	0.407175	0.203588	+	0.979057i	$0.434740\pi$
$462$	−1.91717	−0.0891949
$463$	27.1284	1.26076	0.630382	−	0.776285i	$-0.282898\pi$
$463$	27.1284	1.26076	0.630382	+	0.776285i	$0.282898\pi$
$464$	6.52993	0.303144
$465$	−0.967678	−0.0448750
$466$	−4.30614	−0.199478
$467$	24.4886	1.13320	0.566599	−	0.823993i	$-0.308259\pi$
$467$	24.4886	1.13320	0.566599	+	0.823993i	$0.308259\pi$
$468$	6.35904	0.293947
$469$	37.0703	1.71175
$470$	0.123852	0.00571288
$471$	−22.8047	−1.05079
$472$	−19.2824	−0.887545
$473$	1.00000	0.0459800
$474$	−2.16362	−0.0993786
$475$	−18.6410	−0.855307
$476$	5.96512	0.273411
$477$	5.56157	0.254647
$478$	−3.38640	−0.154890
$479$	0.638962	0.0291949	0.0145975	−	0.999893i	$-0.495353\pi$
$479$	0.638962	0.0291949	0.0145975	+	0.999893i	$0.495353\pi$
$480$	−0.737588	−0.0336661
$481$	9.75561	0.444818
$482$	−5.26580	−0.239851
$483$	42.5865	1.93775
$484$	−1.81854	−0.0826608
$485$	−1.07039	−0.0486038
$486$	4.64862	0.210866
$487$	15.2621	0.691591	0.345795	−	0.938310i	$-0.387609\pi$
$487$	15.2621	0.691591	0.345795	+	0.938310i	$0.387609\pi$
$488$	9.05662	0.409974
$489$	1.21848	0.0551018
$490$	0.191003	0.00862864
$491$	14.6975	0.663288	0.331644	−	0.943405i	$-0.392397\pi$
$491$	14.6975	0.663288	0.331644	+	0.943405i	$0.392397\pi$
$492$	15.9342	0.718368
$493$	2.21793	0.0998904
$494$	−4.98383	−0.224233
$495$	0.133275	0.00599025
$496$	−17.4103	−0.781748
$497$	42.0793	1.88751
$498$	7.49398	0.335813
$499$	−13.2845	−0.594695	−0.297348	−	0.954769i	$-0.596102\pi$
$499$	−13.2845	−0.594695	−0.297348	+	0.954769i	$0.596102\pi$
$500$	−2.16580	−0.0968573
$501$	−6.81177	−0.304327
$502$	0.572697	0.0255607
$503$	2.99917	0.133726	0.0668632	−	0.997762i	$-0.478701\pi$
$503$	2.99917	0.133726	0.0668632	+	0.997762i	$0.478701\pi$
$504$	5.96240	0.265586
$505$	1.18131	0.0525675
$506$	−4.03085	−0.179193
$507$	4.40161	0.195482
$508$	12.8743	0.571203
$509$	−14.2479	−0.631527	−0.315764	−	0.948838i	$-0.602261\pi$
$509$	−14.2479	−0.631527	−0.315764	+	0.948838i	$0.602261\pi$
$510$	−0.0697071	−0.00308668
$511$	−42.2376	−1.86848
$512$	−22.8487	−1.00978
$513$	21.1221	0.932564
$514$	12.7445	0.562138
$515$	−1.33509	−0.0588310
$516$	2.49513	0.109842
$517$	2.43780	0.107214
$518$	4.35622	0.191401
$519$	−20.6601	−0.906879
$520$	−0.607069	−0.0266217
$521$	4.55221	0.199436	0.0997180	−	0.995016i	$-0.468206\pi$
$521$	4.55221	0.199436	0.0997180	+	0.995016i	$0.468206\pi$
$522$	1.05578	0.0462103
$523$	10.0059	0.437529	0.218765	−	0.975778i	$-0.429797\pi$
$523$	10.0059	0.437529	0.218765	+	0.975778i	$0.429797\pi$
$524$	−16.6893	−0.729077
$525$	−22.4389	−0.979313
$526$	−4.39818	−0.191770
$527$	−5.91352	−0.257597
$528$	−4.03954	−0.175799
$529$	66.5380	2.89296
$530$	−0.252853	−0.0109833
$531$	13.2466	0.574856
$532$	22.3026	0.966940
$533$	19.9834	0.865579
$534$	−7.99370	−0.345921
$535$	−1.89920	−0.0821097
$536$	−18.3831	−0.794029
$537$	15.0572	0.649766
$538$	−8.00728	−0.345218
$539$	3.75954	0.161935
$540$	1.22528	0.0527279
$541$	22.1605	0.952755	0.476378	−	0.879241i	$-0.341950\pi$
$541$	22.1605	0.952755	0.476378	+	0.879241i	$0.341950\pi$
$542$	2.13089	0.0915298
$543$	−22.9366	−0.984305
$544$	−4.50743	−0.193254
$545$	2.32156	0.0994446
$546$	−5.99923	−0.256743
$547$	−16.4587	−0.703723	−0.351861	−	0.936052i	$-0.614451\pi$
$547$	−16.4587	−0.703723	−0.351861	+	0.936052i	$0.614451\pi$
$548$	7.35566	0.314218
$549$	−6.22172	−0.265537
$550$	2.12386	0.0905616
$551$	8.29246	0.353271
$552$	−21.1186	−0.898867
$553$	12.1427	0.516359
$554$	−0.665267	−0.0282645
$555$	0.510158	0.0216550
$556$	−18.2985	−0.776029
$557$	37.7307	1.59870	0.799351	−	0.600865i	$-0.205177\pi$
$557$	37.7307	1.59870	0.799351	+	0.600865i	$0.205177\pi$
$558$	−2.81497	−0.119167
$559$	3.12921	0.132351
$560$	1.15178	0.0486718
$561$	−1.37205	−0.0579282
$562$	−6.05853	−0.255564
$563$	−33.6386	−1.41770	−0.708848	−	0.705361i	$-0.750785\pi$
$563$	−33.6386	−1.41770	−0.708848	+	0.705361i	$0.750785\pi$
$564$	6.08264	0.256125
$565$	0.793312	0.0333749
$566$	−6.73685	−0.283171
$567$	14.4291	0.605964
$568$	−20.8671	−0.875563
$569$	10.2579	0.430033	0.215017	−	0.976610i	$-0.431019\pi$
$569$	10.2579	0.430033	0.215017	+	0.976610i	$0.431019\pi$
$570$	−0.260623	−0.0109163
$571$	−7.01740	−0.293669	−0.146834	−	0.989161i	$-0.546908\pi$
$571$	−7.01740	−0.293669	−0.146834	+	0.989161i	$0.546908\pi$
$572$	−5.69059	−0.237935
$573$	−34.3885	−1.43660
$574$	8.92329	0.372451
$575$	−47.1777	−1.96744
$576$	4.43435	0.184765
$577$	3.46823	0.144384	0.0721921	−	0.997391i	$-0.477001\pi$
$577$	3.46823	0.144384	0.0721921	+	0.997391i	$0.477001\pi$
$578$	−0.425983	−0.0177186
$579$	16.1054	0.669316
$580$	0.481042	0.0199742
$581$	−42.0577	−1.74485
$582$	5.24556	0.217436
$583$	−4.97695	−0.206124
$584$	20.9456	0.866735
$585$	0.417044	0.0172427
$586$	5.28127	0.218167
$587$	18.1620	0.749626	0.374813	−	0.927100i	$-0.377707\pi$
$587$	18.1620	0.749626	0.374813	+	0.927100i	$0.377707\pi$
$588$	9.38055	0.386848
$589$	−22.1097	−0.911014
$590$	−0.602251	−0.0247943
$591$	35.3449	1.45390
$592$	9.17869	0.377242
$593$	46.3182	1.90206	0.951029	−	0.309100i	$-0.100028\pi$
$593$	46.3182	1.90206	0.951029	+	0.309100i	$0.100028\pi$
$594$	−2.40655	−0.0987418
$595$	0.391210	0.0160380
$596$	7.98741	0.327177
$597$	27.4508	1.12349
$598$	−12.6134	−0.515799
$599$	14.1866	0.579647	0.289824	−	0.957080i	$-0.406403\pi$
$599$	14.1866	0.579647	0.289824	+	0.957080i	$0.406403\pi$
$600$	11.1274	0.454275
$601$	−16.9197	−0.690170	−0.345085	−	0.938571i	$-0.612150\pi$
$601$	−16.9197	−0.690170	−0.345085	+	0.938571i	$0.612150\pi$
$602$	1.39730	0.0569497
$603$	12.6288	0.514286
$604$	1.65085	0.0671723
$605$	−0.119265	−0.00484881
$606$	−5.78914	−0.235168
$607$	−7.16033	−0.290629	−0.145314	−	0.989386i	$-0.546419\pi$
$607$	−7.16033	−0.290629	−0.145314	+	0.989386i	$0.546419\pi$
$608$	−16.8525	−0.683460
$609$	9.98196	0.404489
$610$	0.282867	0.0114529
$611$	7.62839	0.308612
$612$	2.03215	0.0821450
$613$	43.4461	1.75477	0.877385	−	0.479787i	$-0.159286\pi$
$613$	43.4461	1.75477	0.877385	+	0.479787i	$0.159286\pi$
$614$	−12.3605	−0.498827
$615$	1.04501	0.0421389
$616$	−5.33564	−0.214979
$617$	−16.8600	−0.678759	−0.339380	−	0.940650i	$-0.610217\pi$
$617$	−16.8600	−0.678759	−0.339380	+	0.940650i	$0.610217\pi$
$618$	6.54275	0.263188
$619$	−0.971564	−0.0390504	−0.0195252	−	0.999809i	$-0.506215\pi$
$619$	−0.971564	−0.0390504	−0.0195252	+	0.999809i	$0.506215\pi$
$620$	−1.28257	−0.0515094
$621$	53.4571	2.14516
$622$	0.249378	0.00999916
$623$	44.8622	1.79737
$624$	−12.6406	−0.506028
$625$	24.7868	0.991474
$626$	4.26009	0.170267
$627$	−5.12988	−0.204868
$628$	−30.2257	−1.20614
$629$	3.11760	0.124307
$630$	0.186225	0.00741937
$631$	−48.7860	−1.94214	−0.971071	−	0.238791i	$-0.923249\pi$
$631$	−48.7860	−1.94214	−0.971071	+	0.238791i	$0.923249\pi$
$632$	−6.02154	−0.239524
$633$	−0.628986	−0.0250000
$634$	8.82698	0.350564
$635$	0.844331	0.0335063
$636$	−12.4181	−0.492412
$637$	11.7644	0.466122
$638$	−0.944800	−0.0374050
$639$	14.3353	0.567095
$640$	−1.27676	−0.0504685
$641$	−34.8559	−1.37672	−0.688362	−	0.725368i	$-0.741670\pi$
$641$	−34.8559	−1.37672	−0.688362	+	0.725368i	$0.741670\pi$
$642$	9.30727	0.367329
$643$	−5.71522	−0.225386	−0.112693	−	0.993630i	$-0.535948\pi$
$643$	−5.71522	−0.225386	−0.112693	+	0.993630i	$0.535948\pi$
$644$	56.4447	2.22423
$645$	0.163638	0.00644325
$646$	−1.59268	−0.0626632
$647$	41.9941	1.65096	0.825480	−	0.564432i	$-0.190905\pi$
$647$	41.9941	1.65096	0.825480	+	0.564432i	$0.190905\pi$
$648$	−7.15535	−0.281089
$649$	−11.8542	−0.465317
$650$	6.64600	0.260678
$651$	−26.6143	−1.04310
$652$	1.61499	0.0632481
$653$	1.88310	0.0736914	0.0368457	−	0.999321i	$-0.488269\pi$
$653$	1.88310	0.0736914	0.0368457	+	0.999321i	$0.488269\pi$
$654$	−11.3771	−0.444879
$655$	−1.09454	−0.0427670
$656$	18.8017	0.734082
$657$	−14.3892	−0.561377
$658$	3.40634	0.132793
$659$	27.1239	1.05660	0.528299	−	0.849058i	$-0.322830\pi$
$659$	27.1239	1.05660	0.528299	+	0.849058i	$0.322830\pi$
$660$	−0.297582	−0.0115834
$661$	42.4689	1.65185	0.825924	−	0.563782i	$-0.190654\pi$
$661$	42.4689	1.65185	0.825924	+	0.563782i	$0.190654\pi$
$662$	−10.1326	−0.393815
$663$	−4.29345	−0.166744
$664$	20.8564	0.809383
$665$	1.46267	0.0567199
$666$	1.48404	0.0575056
$667$	20.9870	0.812621
$668$	−9.02840	−0.349319
$669$	8.06357	0.311756
$670$	−0.574163	−0.0221818
$671$	5.56770	0.214939
$672$	−20.2860	−0.782551
$673$	−13.0689	−0.503771	−0.251885	−	0.967757i	$-0.581051\pi$
$673$	−13.0689	−0.503771	−0.251885	+	0.967757i	$0.581051\pi$
$674$	4.34960	0.167540
$675$	−28.1666	−1.08413
$676$	5.83395	0.224383
$677$	−42.1870	−1.62138	−0.810689	−	0.585477i	$-0.800907\pi$
$677$	−42.1870	−1.62138	−0.810689	+	0.585477i	$0.800907\pi$
$678$	−3.88772	−0.149307
$679$	−29.4391	−1.12977
$680$	−0.194001	−0.00743958
$681$	−0.533371	−0.0204388
$682$	2.51906	0.0964599
$683$	33.9494	1.29904	0.649519	−	0.760345i	$-0.274970\pi$
$683$	33.9494	1.29904	0.649519	+	0.760345i	$0.274970\pi$
$684$	7.59789	0.290512
$685$	0.482406	0.0184318
$686$	−4.52789	−0.172876
$687$	−20.8023	−0.793657
$688$	2.94416	0.112245
$689$	−15.5739	−0.593319
$690$	−0.659601	−0.0251106
$691$	−47.3172	−1.80003	−0.900016	−	0.435857i	$-0.856445\pi$
$691$	−47.3172	−1.80003	−0.900016	+	0.435857i	$0.856445\pi$
$692$	−27.3832	−1.04095
$693$	3.66548	0.139240
$694$	8.25114	0.313209
$695$	−1.20007	−0.0455212
$696$	−4.95004	−0.187631
$697$	6.38610	0.241891
$698$	−5.83214	−0.220750
$699$	−13.8697	−0.524600
$700$	−29.7408	−1.12409
$701$	45.8801	1.73287	0.866434	−	0.499292i	$-0.166407\pi$
$701$	45.8801	1.73287	0.866434	+	0.499292i	$0.166407\pi$
$702$	−7.53059	−0.284224
$703$	11.6562	0.439621
$704$	−3.96822	−0.149558
$705$	0.398917	0.0150241
$706$	8.44884	0.317976
$707$	32.4898	1.22190
$708$	−29.5778	−1.11160
$709$	−4.33343	−0.162745	−0.0813726	−	0.996684i	$-0.525930\pi$
$709$	−4.33343	−0.162745	−0.0813726	+	0.996684i	$0.525930\pi$
$710$	−0.651745	−0.0244595
$711$	4.13668	0.155138
$712$	−22.2471	−0.833746
$713$	−55.9564	−2.09559
$714$	−1.91717	−0.0717483
$715$	−0.373205	−0.0139571
$716$	19.9570	0.745827
$717$	−10.9073	−0.407341
$718$	−3.03993	−0.113449
$719$	0.548723	0.0204639	0.0102320	−	0.999948i	$-0.496743\pi$
$719$	0.548723	0.0204639	0.0102320	+	0.999948i	$0.496743\pi$
$720$	0.392381	0.0146232
$721$	−36.7192	−1.36749
$722$	2.13892	0.0796023
$723$	−16.9607	−0.630774
$724$	−30.4005	−1.12983
$725$	−11.0581	−0.410687
$726$	0.584473	0.0216918
$727$	−31.2998	−1.16085	−0.580423	−	0.814315i	$-0.697113\pi$
$727$	−31.2998	−1.16085	−0.580423	+	0.814315i	$0.697113\pi$
$728$	−16.6963	−0.618808
$729$	28.1694	1.04331
$730$	0.654197	0.0242129
$731$	1.00000	0.0369863
$732$	13.8922	0.513469
$733$	2.81880	0.104115	0.0520574	−	0.998644i	$-0.483422\pi$
$733$	2.81880	0.104115	0.0520574	+	0.998644i	$0.483422\pi$
$734$	9.66428	0.356715
$735$	0.615204	0.0226921
$736$	−42.6513	−1.57215
$737$	−11.3013	−0.416289
$738$	3.03992	0.111901
$739$	30.7493	1.13113	0.565565	−	0.824703i	$-0.308658\pi$
$739$	30.7493	1.13113	0.565565	+	0.824703i	$0.308658\pi$
$740$	0.676169	0.0248565
$741$	−16.0525	−0.589703
$742$	−6.95429	−0.255300
$743$	−20.1148	−0.737940	−0.368970	−	0.929441i	$-0.620289\pi$
$743$	−20.1148	−0.737940	−0.368970	+	0.929441i	$0.620289\pi$
$744$	13.1980	0.483862
$745$	0.523837	0.0191919
$746$	6.65074	0.243501
$747$	−14.3279	−0.524231
$748$	−1.81854	−0.0664923
$749$	−52.2342	−1.90860
$750$	0.696080	0.0254172
$751$	36.0267	1.31463	0.657316	−	0.753615i	$-0.271692\pi$
$751$	36.0267	1.31463	0.657316	+	0.753615i	$0.271692\pi$
$752$	7.17727	0.261728
$753$	1.84461	0.0672212
$754$	−2.95648	−0.107669
$755$	0.108268	0.00394027
$756$	33.6993	1.22563
$757$	−18.6739	−0.678714	−0.339357	−	0.940658i	$-0.610209\pi$
$757$	−18.6739	−0.678714	−0.339357	+	0.940658i	$0.610209\pi$
$758$	−6.92822	−0.251644
$759$	−12.9830	−0.471253
$760$	−0.725336	−0.0263107
$761$	−14.7221	−0.533677	−0.266838	−	0.963741i	$-0.585979\pi$
$761$	−14.7221	−0.533677	−0.266838	+	0.963741i	$0.585979\pi$
$762$	−4.13775	−0.149895
$763$	63.8503	2.31154
$764$	−45.5789	−1.64899
$765$	0.133275	0.00481855
$766$	−7.73803	−0.279586
$767$	−37.0942	−1.33940
$768$	−4.63231	−0.167154
$769$	38.3288	1.38217	0.691085	−	0.722773i	$-0.257133\pi$
$769$	38.3288	1.38217	0.691085	+	0.722773i	$0.257133\pi$
$770$	−0.166649	−0.00600561
$771$	41.0490	1.47834
$772$	21.3462	0.768268
$773$	−37.8801	−1.36245	−0.681227	−	0.732072i	$-0.738553\pi$
$773$	−37.8801	−1.36245	−0.681227	+	0.732072i	$0.738553\pi$
$774$	0.476022	0.0171103
$775$	29.4835	1.05908
$776$	14.5988	0.524067
$777$	14.0310	0.503359
$778$	−3.27719	−0.117493
$779$	23.8766	0.855466
$780$	−0.931197	−0.0333422
$781$	−12.8284	−0.459035
$782$	−4.03085	−0.144143
$783$	12.5299	0.447783
$784$	11.0687	0.395310
$785$	−1.98229	−0.0707509
$786$	5.36390	0.191324
$787$	30.7990	1.09786	0.548932	−	0.835867i	$-0.315035\pi$
$787$	30.7990	1.09786	0.548932	+	0.835867i	$0.315035\pi$
$788$	46.8466	1.66884
$789$	−14.1661	−0.504328
$790$	−0.188072	−0.00669129
$791$	21.8186	0.775782
$792$	−1.81771	−0.0645894
$793$	17.4225	0.618692
$794$	−2.05499	−0.0729288
$795$	−0.814418	−0.0288844
$796$	36.3837	1.28959
$797$	25.6249	0.907681	0.453841	−	0.891083i	$-0.350054\pi$
$797$	25.6249	0.907681	0.453841	+	0.891083i	$0.350054\pi$
$798$	−7.16798	−0.253744
$799$	2.43780	0.0862432
$800$	22.4730	0.794542
$801$	15.2833	0.540010
$802$	9.84574	0.347665
$803$	12.8767	0.454407
$804$	−28.1983	−0.994477
$805$	3.70181	0.130472
$806$	7.88268	0.277656
$807$	−25.7907	−0.907876
$808$	−16.1116	−0.566805
$809$	2.55233	0.0897350	0.0448675	−	0.998993i	$-0.485713\pi$
$809$	2.55233	0.0897350	0.0448675	+	0.998993i	$0.485713\pi$
$810$	−0.223484	−0.00785244
$811$	43.2744	1.51957	0.759786	−	0.650174i	$-0.225304\pi$
$811$	43.2744	1.51957	0.759786	+	0.650174i	$0.225304\pi$
$812$	13.2302	0.464289
$813$	6.86342	0.240711
$814$	−1.32804	−0.0465479
$815$	0.105916	0.00371008
$816$	−4.03954	−0.141412
$817$	3.73883	0.130805
$818$	−7.87117	−0.275209
$819$	11.4701	0.400797
$820$	1.38507	0.0483687
$821$	−45.0053	−1.57070	−0.785348	−	0.619055i	$-0.787516\pi$
$821$	−45.0053	−1.57070	−0.785348	+	0.619055i	$0.787516\pi$
$822$	−2.36409	−0.0824570
$823$	−8.94084	−0.311658	−0.155829	−	0.987784i	$-0.549805\pi$
$823$	−8.94084	−0.311658	−0.155829	+	0.987784i	$0.549805\pi$
$824$	18.2090	0.634341
$825$	6.84076	0.238165
$826$	−16.5638	−0.576330
$827$	55.5066	1.93015	0.965077	−	0.261965i	$-0.0843706\pi$
$827$	55.5066	1.93015	0.965077	+	0.261965i	$0.0843706\pi$
$828$	19.2292	0.668260
$829$	−50.3406	−1.74840	−0.874201	−	0.485563i	$-0.838615\pi$
$829$	−50.3406	−1.74840	−0.874201	+	0.485563i	$0.838615\pi$
$830$	0.651410	0.0226108
$831$	−2.14276	−0.0743317
$832$	−12.4174	−0.430496
$833$	3.75954	0.130260
$834$	5.88108	0.203645
$835$	−0.592109	−0.0204908
$836$	−6.79921	−0.235156
$837$	−33.4078	−1.15474
$838$	10.8152	0.373605
$839$	50.6305	1.74796	0.873979	−	0.485964i	$-0.161531\pi$
$839$	50.6305	1.74796	0.873979	+	0.485964i	$0.161531\pi$
$840$	−0.873115	−0.0301253
$841$	−24.0808	−0.830372
$842$	−10.4903	−0.361520
$843$	−19.5140	−0.672098
$844$	−0.833666	−0.0286960
$845$	0.382607	0.0131621
$846$	1.16045	0.0398970
$847$	−3.28017	−0.112708
$848$	−14.6529	−0.503183
$849$	−21.6988	−0.744700
$850$	2.12386	0.0728477
$851$	29.5001	1.01125
$852$	−32.0085	−1.09659
$853$	−1.82526	−0.0624956	−0.0312478	−	0.999512i	$-0.509948\pi$
$853$	−1.82526	−0.0624956	−0.0312478	+	0.999512i	$0.509948\pi$
$854$	7.77975	0.266218
$855$	0.498292	0.0170412
$856$	25.9029	0.885342
$857$	32.9022	1.12392	0.561959	−	0.827165i	$-0.310048\pi$
$857$	32.9022	1.12392	0.561959	+	0.827165i	$0.310048\pi$
$858$	1.82894	0.0624389
$859$	22.7703	0.776912	0.388456	−	0.921467i	$-0.373008\pi$
$859$	22.7703	0.776912	0.388456	+	0.921467i	$0.373008\pi$
$860$	0.216888	0.00739582
$861$	28.7411	0.979495
$862$	7.28599	0.248162
$863$	−16.1573	−0.550002	−0.275001	−	0.961444i	$-0.588678\pi$
$863$	−16.1573	−0.550002	−0.275001	+	0.961444i	$0.588678\pi$
$864$	−25.4642	−0.866311
$865$	−1.79587	−0.0610614
$866$	1.33580	0.0453924
$867$	−1.37205	−0.0465974
$868$	−35.2749	−1.19731
$869$	−3.70184	−0.125576
$870$	−0.154605	−0.00524161
$871$	−35.3642	−1.19827
$872$	−31.6633	−1.07225
$873$	−10.0291	−0.339434
$874$	−15.0707	−0.509773
$875$	−3.90654	−0.132065
$876$	32.1290	1.08554
$877$	38.3769	1.29590	0.647948	−	0.761685i	$-0.275627\pi$
$877$	38.3769	1.29590	0.647948	+	0.761685i	$0.275627\pi$
$878$	5.72476	0.193201
$879$	17.0105	0.573750
$880$	−0.351135	−0.0118368
$881$	−28.2455	−0.951616	−0.475808	−	0.879549i	$-0.657844\pi$
$881$	−28.2455	−0.951616	−0.475808	+	0.879549i	$0.657844\pi$
$882$	1.78962	0.0602598
$883$	32.8440	1.10529	0.552645	−	0.833417i	$-0.313619\pi$
$883$	32.8440	1.10529	0.552645	+	0.833417i	$0.313619\pi$
$884$	−5.69059	−0.191395
$885$	−1.93980	−0.0652056
$886$	16.9936	0.570911
$887$	−39.0680	−1.31178	−0.655888	−	0.754858i	$-0.727706\pi$
$887$	−39.0680	−1.31178	−0.655888	+	0.754858i	$0.727706\pi$
$888$	−6.95795	−0.233493
$889$	23.2218	0.778835
$890$	−0.694848	−0.0232914
$891$	−4.39887	−0.147368
$892$	10.6876	0.357846
$893$	9.11453	0.305006
$894$	−2.56713	−0.0858576
$895$	1.30884	0.0437496
$896$	−35.1151	−1.17311
$897$	−40.6265	−1.35648
$898$	−0.457209	−0.0152573
$899$	−13.1158	−0.437435
$900$	−10.1319	−0.337729
$901$	−4.97695	−0.165806
$902$	−2.72037	−0.0905785
$903$	4.50058	0.149770
$904$	−10.8198	−0.359862
$905$	−1.99375	−0.0662746
$906$	−0.530580	−0.0176273
$907$	50.2514	1.66857	0.834285	−	0.551333i	$-0.185881\pi$
$907$	50.2514	1.66857	0.834285	+	0.551333i	$0.185881\pi$
$908$	−0.706937	−0.0234605
$909$	11.0684	0.367115
$910$	−0.521480	−0.0172869
$911$	50.4766	1.67237	0.836183	−	0.548451i	$-0.184782\pi$
$911$	50.4766	1.67237	0.836183	+	0.548451i	$0.184782\pi$
$912$	−15.1032	−0.500116
$913$	12.8218	0.424339
$914$	11.9783	0.396208
$915$	0.911089	0.0301197
$916$	−27.5716	−0.910992
$917$	−30.1033	−0.994097
$918$	−2.40655	−0.0794279
$919$	51.3563	1.69409	0.847044	−	0.531522i	$-0.178380\pi$
$919$	51.3563	1.69409	0.847044	+	0.531522i	$0.178380\pi$
$920$	−1.83572	−0.0605219
$921$	−39.8119	−1.31185
$922$	−3.72413	−0.122648
$923$	−40.1427	−1.32131
$924$	−8.18447	−0.269249
$925$	−15.5436	−0.511072
$926$	−11.5563	−0.379762
$927$	−12.5092	−0.410857
$928$	−9.99715	−0.328173
$929$	−45.3572	−1.48812	−0.744061	−	0.668112i	$-0.767103\pi$
$929$	−45.3572	−1.48812	−0.744061	+	0.668112i	$0.767103\pi$
$930$	0.412215	0.0135171
$931$	14.0563	0.460676
$932$	−18.3831	−0.602158
$933$	0.803225	0.0262964
$934$	−10.4317	−0.341337
$935$	−0.119265	−0.00390038
$936$	−5.68799	−0.185918
$937$	29.9548	0.978580	0.489290	−	0.872121i	$-0.337256\pi$
$937$	29.9548	0.978580	0.489290	+	0.872121i	$0.337256\pi$
$938$	−15.7913	−0.515605
$939$	13.7214	0.447780
$940$	0.528730	0.0172453
$941$	49.4012	1.61043	0.805217	−	0.592981i	$-0.202049\pi$
$941$	49.4012	1.61043	0.805217	+	0.592981i	$0.202049\pi$
$942$	9.71443	0.316513
$943$	60.4282	1.96781
$944$	−34.9006	−1.13592
$945$	2.21010	0.0718945
$946$	−0.425983	−0.0138499
$947$	−14.7129	−0.478104	−0.239052	−	0.971007i	$-0.576837\pi$
$947$	−14.7129	−0.478104	−0.239052	+	0.971007i	$0.576837\pi$
$948$	−9.23659	−0.299990
$949$	40.2937	1.30799
$950$	7.94075	0.257632
$951$	28.4309	0.921935
$952$	−5.33564	−0.172929
$953$	−9.93747	−0.321906	−0.160953	−	0.986962i	$-0.551457\pi$
$953$	−9.93747	−0.321906	−0.160953	+	0.986962i	$0.551457\pi$
$954$	−2.36914	−0.0767036
$955$	−2.98920	−0.0967282
$956$	−14.4567	−0.467562
$957$	−3.04312	−0.0983700
$958$	−0.272187	−0.00879397
$959$	13.2677	0.428437
$960$	−0.649353	−0.0209578
$961$	3.96978	0.128057
$962$	−4.15573	−0.133986
$963$	−17.7948	−0.573429
$964$	−22.4799	−0.724028
$965$	1.39995	0.0450660
$966$	−18.1411	−0.583682
$967$	42.3053	1.36045	0.680224	−	0.733005i	$-0.261883\pi$
$967$	42.3053	1.36045	0.680224	+	0.733005i	$0.261883\pi$
$968$	1.62663	0.0522820
$969$	−5.12988	−0.164796
$970$	0.455968	0.0146402
$971$	36.4827	1.17078	0.585392	−	0.810750i	$-0.300940\pi$
$971$	36.4827	1.17078	0.585392	+	0.810750i	$0.300940\pi$
$972$	19.8451	0.636532
$973$	−33.0058	−1.05812
$974$	−6.50139	−0.208318
$975$	21.4062	0.685546
$976$	16.3922	0.524701
$977$	−10.0069	−0.320149	−0.160075	−	0.987105i	$-0.551174\pi$
$977$	−10.0069	−0.320149	−0.160075	+	0.987105i	$0.551174\pi$
$978$	−0.519054	−0.0165975
$979$	−13.6768	−0.437112
$980$	0.815399	0.0260470
$981$	21.7521	0.694490
$982$	−6.26088	−0.199793
$983$	40.8315	1.30232	0.651161	−	0.758939i	$-0.274282\pi$
$983$	40.8315	1.30232	0.651161	+	0.758939i	$0.274282\pi$
$984$	−14.2527	−0.454359
$985$	3.07234	0.0978928
$986$	−0.944800	−0.0300886
$987$	10.9715	0.349227
$988$	−21.2762	−0.676885
$989$	9.46245	0.300888
$990$	−0.0567728	−0.00180436
$991$	−18.9463	−0.601849	−0.300924	−	0.953648i	$-0.597295\pi$
$991$	−18.9463	−0.601849	−0.300924	+	0.953648i	$0.597295\pi$
$992$	26.6548	0.846291
$993$	−32.6362	−1.03568
$994$	−17.9251	−0.568549
$995$	2.38615	0.0756460
$996$	31.9921	1.01371
$997$	−39.3401	−1.24591	−0.622957	−	0.782256i	$-0.714069\pi$
$997$	−39.3401	−1.24591	−0.622957	+	0.782256i	$0.714069\pi$
$998$	5.65897	0.179132
$999$	17.6125	0.557235

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.j.1.35	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.j.1.35	✓	82	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.425983 q^{2} -1.37205 q^{3} -1.81854 q^{4} -0.119265 q^{5} +0.584473 q^{6} -3.28017 q^{7} +1.62663 q^{8} -1.11747 q^{9} +O(q^{10})\)	\(q-0.425983 q^{2} -1.37205 q^{3} -1.81854 q^{4} -0.119265 q^{5} +0.584473 q^{6} -3.28017 q^{7} +1.62663 q^{8} -1.11747 q^{9} +0.0508049 q^{10} +1.00000 q^{11} +2.49513 q^{12} +3.12921 q^{13} +1.39730 q^{14} +0.163638 q^{15} +2.94416 q^{16} +1.00000 q^{17} +0.476022 q^{18} +3.73883 q^{19} +0.216888 q^{20} +4.50058 q^{21} -0.425983 q^{22} +9.46245 q^{23} -2.23183 q^{24} -4.98578 q^{25} -1.33299 q^{26} +5.64939 q^{27} +5.96512 q^{28} +2.21793 q^{29} -0.0697071 q^{30} -5.91352 q^{31} -4.50743 q^{32} -1.37205 q^{33} -0.425983 q^{34} +0.391210 q^{35} +2.03215 q^{36} +3.11760 q^{37} -1.59268 q^{38} -4.29345 q^{39} -0.194001 q^{40} +6.38610 q^{41} -1.91717 q^{42} +1.00000 q^{43} -1.81854 q^{44} +0.133275 q^{45} -4.03085 q^{46} +2.43780 q^{47} -4.03954 q^{48} +3.75954 q^{49} +2.12386 q^{50} -1.37205 q^{51} -5.69059 q^{52} -4.97695 q^{53} -2.40655 q^{54} -0.119265 q^{55} -5.33564 q^{56} -5.12988 q^{57} -0.944800 q^{58} -11.8542 q^{59} -0.297582 q^{60} +5.56770 q^{61} +2.51906 q^{62} +3.66548 q^{63} -3.96822 q^{64} -0.373205 q^{65} +0.584473 q^{66} -11.3013 q^{67} -1.81854 q^{68} -12.9830 q^{69} -0.166649 q^{70} -12.8284 q^{71} -1.81771 q^{72} +12.8767 q^{73} -1.32804 q^{74} +6.84076 q^{75} -6.79921 q^{76} -3.28017 q^{77} +1.82894 q^{78} -3.70184 q^{79} -0.351135 q^{80} -4.39887 q^{81} -2.72037 q^{82} +12.8218 q^{83} -8.18447 q^{84} -0.119265 q^{85} -0.425983 q^{86} -3.04312 q^{87} +1.62663 q^{88} -13.6768 q^{89} -0.0567728 q^{90} -10.2644 q^{91} -17.2078 q^{92} +8.11368 q^{93} -1.03846 q^{94} -0.445912 q^{95} +6.18444 q^{96} +8.97487 q^{97} -1.60150 q^{98} -1.11747 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9} + q^{10} + 82 q^{11} + 3 q^{12} + 26 q^{13} + 17 q^{14} + 66 q^{15} + 122 q^{16} + 82 q^{17} + 18 q^{18} + 12 q^{19} + 9 q^{20} + 22 q^{21} + 8 q^{22} + 50 q^{23} + 15 q^{24} + 117 q^{25} + 36 q^{26} + 30 q^{27} + 11 q^{28} + 33 q^{29} - 26 q^{30} + 40 q^{31} + 58 q^{32} + 6 q^{33} + 8 q^{34} + 16 q^{35} + 160 q^{36} + 31 q^{37} + 18 q^{38} + 41 q^{39} - 29 q^{40} + 42 q^{41} - 51 q^{42} + 82 q^{43} + 98 q^{44} - 2 q^{45} - 19 q^{46} + 84 q^{47} - 46 q^{48} + 136 q^{49} + 59 q^{50} + 6 q^{51} + 45 q^{52} + 83 q^{53} + 24 q^{54} + 11 q^{55} + 21 q^{56} + 23 q^{57} + 14 q^{58} + 96 q^{59} + 184 q^{60} - 6 q^{61} - 23 q^{62} + 8 q^{63} + 148 q^{64} + 5 q^{65} + 10 q^{66} + 78 q^{67} + 98 q^{68} + 61 q^{69} - 3 q^{70} + 155 q^{71} + 50 q^{72} - 23 q^{73} + 10 q^{74} - 19 q^{75} + 44 q^{76} + 8 q^{77} - 27 q^{78} + 31 q^{79} + 19 q^{80} + 150 q^{81} - 12 q^{82} + 54 q^{83} + 8 q^{84} + 11 q^{85} + 8 q^{86} + 20 q^{87} + 30 q^{88} + 25 q^{89} - 81 q^{90} - 14 q^{91} + 60 q^{92} + 36 q^{93} + 19 q^{94} + 111 q^{95} - 6 q^{96} + 2 q^{97} - 5 q^{98} + 108 q^{99}+O(q^{100}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9 + q^10 + 82 * q^11 + 3 * q^12 + 26 * q^13 + 17 * q^14 + 66 * q^15 + 122 * q^16 + 82 * q^17 + 18 * q^18 + 12 * q^19 + 9 * q^20 + 22 * q^21 + 8 * q^22 + 50 * q^23 + 15 * q^24 + 117 * q^25 + 36 * q^26 + 30 * q^27 + 11 * q^28 + 33 * q^29 - 26 * q^30 + 40 * q^31 + 58 * q^32 + 6 * q^33 + 8 * q^34 + 16 * q^35 + 160 * q^36 + 31 * q^37 + 18 * q^38 + 41 * q^39 - 29 * q^40 + 42 * q^41 - 51 * q^42 + 82 * q^43 + 98 * q^44 - 2 * q^45 - 19 * q^46 + 84 * q^47 - 46 * q^48 + 136 * q^49 + 59 * q^50 + 6 * q^51 + 45 * q^52 + 83 * q^53 + 24 * q^54 + 11 * q^55 + 21 * q^56 + 23 * q^57 + 14 * q^58 + 96 * q^59 + 184 * q^60 - 6 * q^61 - 23 * q^62 + 8 * q^63 + 148 * q^64 + 5 * q^65 + 10 * q^66 + 78 * q^67 + 98 * q^68 + 61 * q^69 - 3 * q^70 + 155 * q^71 + 50 * q^72 - 23 * q^73 + 10 * q^74 - 19 * q^75 + 44 * q^76 + 8 * q^77 - 27 * q^78 + 31 * q^79 + 19 * q^80 + 150 * q^81 - 12 * q^82 + 54 * q^83 + 8 * q^84 + 11 * q^85 + 8 * q^86 + 20 * q^87 + 30 * q^88 + 25 * q^89 - 81 * q^90 - 14 * q^91 + 60 * q^92 + 36 * q^93 + 19 * q^94 + 111 * q^95 - 6 * q^96 + 2 * q^97 - 5 * q^98 + 108 * q^99

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